From 4be6b6551c7fbd569ec9392f8b4e582faef6750a Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 15 Jan 2024 21:47:55 -0300 Subject: [PATCH 01/27] Fixing wrong macros. --- .../perturbations/nc_hipert_itwo_fluids.c | 40 ++++++++++++++++--- numcosmo/perturbations/nc_hipert_two_fluids.c | 3 -- 2 files changed, 34 insertions(+), 9 deletions(-) diff --git a/numcosmo/perturbations/nc_hipert_itwo_fluids.c b/numcosmo/perturbations/nc_hipert_itwo_fluids.c index 975734c56..7815f3b31 100644 --- a/numcosmo/perturbations/nc_hipert_itwo_fluids.c +++ b/numcosmo/perturbations/nc_hipert_itwo_fluids.c @@ -13,12 +13,12 @@ * under the terms of the GNU General Public License as published by the * Free Software Foundation, either version 3 of the License, or * (at your option) any later version. - * + * * numcosmo is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * See the GNU General Public License for more details. - * + * * You should have received a copy of the GNU General Public License along * with this program. If not, see . */ @@ -57,13 +57,14 @@ nc_hipert_itwo_fluids_default_init (NcHIPertITwoFluidsInterface *iface) * @tf_eom: a #NcHIPertITwoFluidsEOM. * * Duplicates @tf_eom. - * + * * Returns: (transfer full): a copy of @tf_eom. */ NcHIPertITwoFluidsEOM * nc_hipert_itwo_fluids_eom_dup (NcHIPertITwoFluidsEOM *tf_eom) { NcHIPertITwoFluidsEOM *tf_eom_dup = g_new (NcHIPertITwoFluidsEOM, 1); + *tf_eom_dup = *tf_eom; return tf_eom_dup; @@ -74,7 +75,7 @@ nc_hipert_itwo_fluids_eom_dup (NcHIPertITwoFluidsEOM *tf_eom) * @tf_eom: a #NcHIPertITwoFluidsEOM. * * Frees @tf_eom. - * + * */ void nc_hipert_itwo_fluids_eom_free (NcHIPertITwoFluidsEOM *tf_eom) @@ -87,13 +88,14 @@ nc_hipert_itwo_fluids_eom_free (NcHIPertITwoFluidsEOM *tf_eom) * @tf_tv: a #NcHIPertITwoFluidsTV * * Duplicates @tf_tv. - * + * * Returns: (transfer full): a copy of @tf_tv. */ NcHIPertITwoFluidsTV * nc_hipert_itwo_fluids_tv_dup (NcHIPertITwoFluidsTV *tf_tv) { NcHIPertITwoFluidsTV *tf_tv_dup = g_new (NcHIPertITwoFluidsTV, 1); + *tf_tv_dup = *tf_tv; return tf_tv_dup; @@ -104,10 +106,36 @@ nc_hipert_itwo_fluids_tv_dup (NcHIPertITwoFluidsTV *tf_tv) * @tf_tv: a #NcHIPertITwoFluidsTV. * * Frees @tf_tv. - * + * */ void nc_hipert_itwo_fluids_tv_free (NcHIPertITwoFluidsTV *tf_tv) { g_free (tf_tv); } + +/** + * nc_hipert_itwo_fluids_eom_eval: + * @itf: a #NcHIPertITwoFluids + * @alpha: time in log of scale factor + * + * Computes the coefficients of the differential equation for the + * perturbations of the two fluids system. + * + * + * Returns: (transfer none): a #NcHIPertITwoFluidsEOM. + */ + + +/** + * nc_hipert_itwo_fluids_tv_eval: + * @itf: a #NcHIPertITwoFluids + * @alpha: time in log of scale factor + * + * Computes the transformation matrix between the perturbations of the + * two fluids system and the variables used in the differential + * equation. + * + * Returns: (transfer none): a #NcHIPertITwoFluidsTV. + */ + diff --git a/numcosmo/perturbations/nc_hipert_two_fluids.c b/numcosmo/perturbations/nc_hipert_two_fluids.c index 47bfb8ada..5429d0ab3 100644 --- a/numcosmo/perturbations/nc_hipert_two_fluids.c +++ b/numcosmo/perturbations/nc_hipert_two_fluids.c @@ -1378,7 +1378,6 @@ nc_hipert_two_fluids_set_init_cond (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gd flag = ARKodeSetLinear (self->arkode, 1); NCM_CVODE_CHECK (&flag, "ARKodeSetLinear", 1, ); -#endif /* HAVE_SUNDIALS_ARKODE */ if (useQP) { @@ -1391,8 +1390,6 @@ nc_hipert_two_fluids_set_init_cond (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gd NCM_CVODE_CHECK (&flag, "ARKodeSetJacFn", 1, ); } -#ifdef HAVE_SUNDIALS_ARKODE - switch (main_mode) { case 1: From 57c89a5546952337524261563a4b98c1c5aac64c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Luiz=20Dem=C3=A9trio?= Date: Wed, 24 Jan 2024 10:31:21 -0400 Subject: [PATCH 02/27] New notebook where we compute perturbations for the two fluid model. (draft) --- .../two_fluids_perturbations.ipynb | 1562 +++++++++++++++++ 1 file changed, 1562 insertions(+) create mode 100644 notebooks/primordial_perturbations/two_fluids_perturbations.ipynb diff --git a/notebooks/primordial_perturbations/two_fluids_perturbations.ipynb b/notebooks/primordial_perturbations/two_fluids_perturbations.ipynb new file mode 100644 index 000000000..97f3df095 --- /dev/null +++ b/notebooks/primordial_perturbations/two_fluids_perturbations.ipynb @@ -0,0 +1,1562 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "152b1c34", + "metadata": { + "id": "152b1c34" + }, + "source": [ + "# Two Fluid Quantum Cosmological Model" + ] + }, + { + "cell_type": "code", + "source": [ + "# Importing the relevant libraries\n", + "\n", + "import sys\n", + "import math\n", + "import numpy as np # imports the Numpy Library\n", + "\n", + "from tqdm import tqdm\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from numcosmo_py import Nc, Ncm # imports the NumCosmo library\n", + "from numcosmo_py.plotting.tools import set_rc_params_article # imports Numcosmo plotting tools\n", + "\n", + "Ncm.cfg_init() # starts the NumCosmo library" + ], + "metadata": { + "id": "Xna_qd5unXpw" + }, + "id": "Xna_qd5unXpw", + "execution_count": 5, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "# Introduction" + ], + "metadata": { + "id": "SSYdpVinZzn1" + }, + "id": "SSYdpVinZzn1" + }, + { + "cell_type": "markdown", + "source": [ + "In this notebook we shall analyze the predictions a two fluid quantum cosmological model where gravity is coupled though matter using the Wheeler-De Witt equation.\n", + "\n", + "A single fluid with equation of state $p(\\rho) = w\\rho$ was considered in $\\tt \\text{arXiv:0610205}$ , using the framework of Bohmian mechanics. At background level, it lead to a non-singular scale factor. At perturbative level, the primordial spectrum of adiabatic perturbations was found to be approximately scale invariant, with\n", + "\n", + "$${\\cal P}_{\\zeta}(k \\gg 1) \\approx A_{s}k^{n_{s} - 1}\\, , $$\n", + "$$ n_{s} = 1 + \\frac{12w}{1 + 3w}\\, ,$$\n", + "\n", + "for which the explicit value for dust $w \\approx 0$ and radiation $w=1/3$ are given by" + ], + "metadata": { + "id": "eMicLj9IZ8gC" + }, + "id": "eMicLj9IZ8gC" + }, + { + "cell_type": "code", + "source": [ + "def nsw(w): # defines a function that calculates the single fluid spectral index ns\n", + " return 1 + 12*w/(1+3*w)\n", + "\n", + "print(r'w=0 => '+str(nsw(0))) # dust w=0 spectral index\n", + "print(r'w=1/3 => '+str(nsw(1/3))) # radiation w = 1/3 spectral index" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "jgV564_mbm_v", + "outputId": "c8412475-fc2d-4b02-b6d9-34070311921d" + }, + "id": "jgV564_mbm_v", + "execution_count": 1, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "w=0 => 1.0\n", + "w=1/3 => 3.0\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "The above results mean that ordinary matter cannot describe the approximately flat red spectrum with $n_{s}$. Therefore, a natural extension of said model is to consider the two fluid coupled to geometry.\n", + "\n", + "Said model was analyzed at background level with great detail in $\\tt \\text{arXiv:0505109}$ , where it was found that the obtained scale factor is also non-singular. However, the perturbative analysis has not yet been performed due to theoretical difficulties.\n", + "\n", + "Reference $\\tt \\text{arXiv:1510.06628}$ analyzes the cosmological perturbations formalism for $N$ fluid models. In the 2 fluid case, the obtained Hamiltonian that describes perturbations is given explicitly by\n", + "\n", + "\\begin{align}\n", + " \\delta {\\cal H}^{(2,s)} & = \\frac{1}{2m_{z}}P_{\\zeta}^{2} + \\frac{1}{2m_{S}}P_{Q}^{2} + \\left({ \\frac{ \\bar{c}_{n} }{ \\bar{c}_{S}\\bar{c}_{m} } }^{2}\\frac{1}{m_{z}m_{S}}\\frac{1}{NH}\\right)P_{\\zeta}P_{Q} \\\\\n", + " %\n", + " & \\, \\, + \\frac{1}{2}m_{z}\\nu_{\\zeta}^{2} z^{2} + \\frac{1}{2}m_{S}\\nu_{S}^{2}Q^{2} \\, ,\n", + "\\end{align}\n", + "\n", + "where $\\zeta$ and $Q$ denote adiabatic and entropy perturbations, respectively. We also introduced\n", + "\n", + "\\begin{align*}\n", + " m_{z} \\equiv \\frac{ a^{3}({ \\bar{\\rho} + \\bar{p} }) }{N\\bar{c}_{S}^{2}\\bar{H}^{2} }\\, , \\hspace{2.4cm} & \\hspace{-0.1cm} m_{S} \\equiv \\frac{ 1 }{ N a^{3}\\bar{c}_{m}^2\\bar{\\omega} } \\, , \\\\\n", + " %\n", + " \\nu_{z}^{2} \\equiv \\bar{c}_{S}^{2}F^{2}_{k} \\, , \\hspace{3.15cm} & \\hspace{0.05cm} \\nu_{S}^{2} \\equiv {c}_{m}^{2}F^{2}_{k} \\, , \\\\\n", + " %\n", + " \\bar{c}_{S}^{2} \\equiv \\bar{c}_{1}^{2}\\cos^{2}\\phi+\\bar{c}_{2}^{2}\\sin^{2}\\phi \\, , \\hspace{1cm} & \\bar{c}_{m}^{2} \\equiv \\bar{c}_{2}^{2}\\cos^{2}\\phi+\\bar{c}_{1}^{2}\\sin^{2}\\phi\n", + " \\, .\n", + "\\end{align*}\n", + "\n", + "where $\\bar{\\omega} \\equiv (\\rho_1 + p_1)(\\rho_2 + p_2)/(\\rho + p)$ and $\\bar{c}_{n}^{2} \\equiv \\bar{c}_{1}^{2} - \\bar{c}_{2}^{2}$. Here, for later convenience, we have also introduced the angular variable $\\phi$ and the functions $F_{k}(t)$ by\n", + "\n", + "\\begin{equation}\n", + " \\cos^{2}\\phi \\equiv \\frac{ \\rho_1 + p_1 }{ \\rho + p }\\, ,\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " \\sin^{2}\\phi \\equiv \\frac{ \\rho_2 + p_2 }{ \\rho + p }\\, ,\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " \\hspace{0.8cm} F^{2}_{k} \\equiv \\left({\\frac{ Nk }{ a }}\\right)^{2}\\, ,\n", + "\\end{equation}\n", + "\n", + "the angular variable $\\phi$ is also associated to the dominant fluid, with $\\phi=0$ denoting domination by the fluid $1$ and $\\phi=\\pi/2$ denoting domination by the fluid $2$.\n", + "\n", + "\n", + "By direct inspection of the perturbative Hamiltonian, one sees that the equations of motion for perturbations are coupled. While at classical level this could be solved by numerical methods, at quantum level this demands the use of special quantization techniques to define the associated vacuum state and extract predictions, as proposed by $\\tt \\text{arXiv:1510.06628}$.\n", + "\n", + "Therefore in this notebook, we analyze explicitly the background and perturbative quantities, with our final aim to calculate the modes $\\zeta_{k}, Q_{k}$ and their associated power spectrum." + ], + "metadata": { + "id": "9VIf518scRQW" + }, + "id": "9VIf518scRQW" + }, + { + "cell_type": "markdown", + "source": [ + "# Background Quantities" + ], + "metadata": { + "id": "1et0L5cgdOyP" + }, + "id": "1et0L5cgdOyP" + }, + { + "cell_type": "markdown", + "source": [ + "In this section we study the quantities $m_{S}, m_{Q}, \\phi, c^{2}_{S}, c^{2}_{m}$ that occur in the perturbative Hamiltonian. We also study the evolution of the eigenvalues $\\nu_{1}, \\nu_{2}$ that diagonalize the Hamiltonian tensor. Finally, we study the behavior of the coupling matrices $\\gamma_{ij}, \\tau_{ij}$, which define the dynamics of the relevant perturbative quantities.\n", + "\n", + "To do so, we start by defining our cosmological parameters." + ], + "metadata": { + "id": "cmnX2kzJmRde" + }, + "id": "cmnX2kzJmRde" + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "1515a28b", + "metadata": { + "id": "1515a28b", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "632cccd1-efb5-44fc-a6a2-aad64d411884" + }, + "outputs": [ + { + "output_type": "error", + "ename": "NameError", + "evalue": "name 'Nc' is not defined", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[2], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m cosmo \u001b[38;5;241m=\u001b[39m Nc\u001b[38;5;241m.\u001b[39mHICosmoQGRW() \u001b[38;5;66;03m# defines a cosmological model, which is represented by a NumCosmo object. Then, the relevant cosmological parameters are added to this object\u001b[39;00m\n\u001b[1;32m 3\u001b[0m \u001b[38;5;66;03m# these lines set the relevant cosmological parameters\u001b[39;00m\n\u001b[1;32m 4\u001b[0m cosmo\u001b[38;5;241m.\u001b[39mprops\u001b[38;5;241m.\u001b[39mw \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1.0e-2\u001b[39m \u001b[38;5;66;03m# dust/dark matter equation of state\u001b[39;00m\n", + "\u001b[0;31mNameError\u001b[0m: name 'Nc' is not defined" + ] + } + ], + "source": [ + "cosmo = Nc.HICosmoQGRW() # defines a cosmological model, which is represented by a NumCosmo object. Then, the relevant cosmological parameters are added to this object\n", + "\n", + "# these lines set the relevant cosmological parameters\n", + "cosmo.props.w = 1.0e-2 # dust/dark matter equation of state\n", + "cosmo.props.Omegar = 2.0 * (1.0e-8) # radiation abundance today\n", + "cosmo.props.Omegaw = 2.0 * (1.0 - 1.0e-8) # dust/dark matter abundance today\n", + "cosmo.props.xb = 1.0e30 # inverse scale factor x=1/a at the time of the bounce" + ] + }, + { + "cell_type": "markdown", + "source": [ + "To study the behavior of said quantities, we shall vary our cosmological parameters. However, before we dwell into such analysis, let's perform a consistency check by considering the dust only $\\Omega_{r} = 0$ and radiation only $\\Omega_{w} = 0$ cases. The complete model shall present regimes of domination by each fluid, and we shall also check if we indeed recover the $n_{s}$ values for the single fluid case." + ], + "metadata": { + "id": "-aSx2PR7oHee" + }, + "id": "-aSx2PR7oHee" + }, + { + "cell_type": "markdown", + "source": [ + "## Consistency Check" + ], + "metadata": { + "id": "KiOdkZDMoq87" + }, + "id": "KiOdkZDMoq87" + }, + { + "cell_type": "markdown", + "source": [ + "## Evolution of ...." + ], + "metadata": { + "id": "iiIp6-GfovaW" + }, + "id": "iiIp6-GfovaW" + }, + { + "cell_type": "code", + "source": [ + "k = 1.0\n", + "min_alpha_c = -120.0\n", + "max_alpha_c = -1.0\n", + "min_alpha_scale = 1.0e-12\n", + "np_plot = 100\n", + "\n", + "# Time arrays for the contraction and bounce phases\n", + "\n", + "alpha_c = np.linspace(min_alpha_c, max_alpha_c, np_plot)\n", + "alpha_b_e = np.geomspace(min_alpha_scale, 2.0, np_plot)\n", + "alpha_b = np.concatenate((np.flip(-alpha_b_e), alpha_b_e))" + ], + "metadata": { + "id": "Bysmnq-koGoW" + }, + "id": "Bysmnq-koGoW", + "execution_count": 4, + "outputs": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9b5ebdeb", + "metadata": { + "id": "9b5ebdeb", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "b640709a-e502-41aa-8661-37d8c7d1e068" + }, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "execution_count": 4 + } + ], + "source": [ + "cosmo.eom_eval(-120,-1)\n", + "#m_s_c = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_c])\n", + "#print(m_s_c)\n", + "#m_zeta_c = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_c])" + ] + }, + { + "cell_type": "code", + "source": [ + "cosmo.eom_eval(-120,1).nu1\n", + "#cosmo.props.m_s" + ], + "metadata": { + "id": "WuQyCqQSWpGW" + }, + "id": "WuQyCqQSWpGW", + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "533290e5-dc2a-467a-8319-11811d78cc2b", + "metadata": { + "id": "533290e5-dc2a-467a-8319-11811d78cc2b" + }, + "outputs": [], + "source": [ + "# Computing background observables in the contraction phase\n", + "\n", + "m_s_c = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_c])\n", + "m_zeta_c = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_c])\n", + "mnu2_s_c = np.array([cosmo.eom_eval(alpha, k).mnu2_s for alpha in alpha_c])\n", + "mnu2_zeta_c = np.array([cosmo.eom_eval(alpha, k).mnu2_zeta for alpha in alpha_c])\n", + "nu1_c = np.array([cosmo.eom_eval(alpha, k).nu1 for alpha in alpha_c])\n", + "nu2_c = np.array([cosmo.eom_eval(alpha, k).nu2 for alpha in alpha_c])\n", + "nu_s_c = np.sqrt(mnu2_s_c / m_s_c)\n", + "nu_zeta_c = np.sqrt(mnu2_zeta_c / m_zeta_c)\n", + "y_c = np.array([cosmo.eom_eval(alpha, k).y for alpha in alpha_c])\n", + "gamma11_c = np.array([cosmo.eom_eval(alpha, k).gammabar11 for alpha in alpha_c])\n", + "gamma22_c = np.array([cosmo.eom_eval(alpha, k).gammabar22 for alpha in alpha_c])\n", + "gamma12_c = np.array([cosmo.eom_eval(alpha, k).gammabar12 for alpha in alpha_c])\n", + "tau_c = np.array([cosmo.eom_eval(alpha, k).taubar for alpha in alpha_c])\n", + "\n", + "# Computing background observables in the bounce phase\n", + "\n", + "m_s_b = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_b])\n", + "m_zeta_b = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_b])\n", + "mnu2_s_b = np.array([cosmo.eom_eval(alpha, k).mnu2_s for alpha in alpha_b])\n", + "mnu2_zeta_b = np.array([cosmo.eom_eval(alpha, k).mnu2_zeta for alpha in alpha_b])\n", + "nu1_b = np.array([cosmo.eom_eval(alpha, k).nu1 for alpha in alpha_b])\n", + "nu2_b = np.array([cosmo.eom_eval(alpha, k).nu2 for alpha in alpha_b])\n", + "nu_s_b = np.sqrt(mnu2_s_b / m_s_b)\n", + "nu_zeta_b = np.sqrt(mnu2_zeta_b / m_zeta_b)\n", + "y_b = np.array([cosmo.eom_eval(alpha, k).y for alpha in alpha_b])\n", + "gamma11_b = np.array([cosmo.eom_eval(alpha, k).gammabar11 for alpha in alpha_b])\n", + "gamma22_b = np.array([cosmo.eom_eval(alpha, k).gammabar22 for alpha in alpha_b])\n", + "gamma12_b = np.array([cosmo.eom_eval(alpha, k).gammabar12 for alpha in alpha_b])\n", + "tau_b = np.array([cosmo.eom_eval(alpha, k).taubar for alpha in alpha_b])\n", + "\n", + "cos2_phi_c = (nu1_c**2 * nu_zeta_c**2 - nu2_c**2 * nu_s_c**2) / (nu1_c**4 - nu2_c**4)\n", + "sin2_phi_c = (nu1_c**2 * nu_s_c**2 - nu2_c**2 * nu_zeta_c**2) / (nu1_c**4 - nu2_c**4)\n", + "\n", + "cos2_phi_b = (nu1_b**2 * nu_zeta_b**2 - nu2_b**2 * nu_s_b**2) / (nu1_b**4 - nu2_b**4)\n", + "sin2_phi_b = (nu1_b**2 * nu_s_b**2 - nu2_b**2 * nu_zeta_b**2) / (nu1_b**4 - nu2_b**4)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a4daed56-57bc-4993-b8ab-3468d8f83d5f", + "metadata": { + "id": "a4daed56-57bc-4993-b8ab-3468d8f83d5f" + }, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(2,2,2)\n", + "ax3= fig.add_subplot(2,2,4)\n", + "\n", + "ax1.plot(alpha_c, m_s_c, c='r', label=r'$m_s$')\n", + "ax1.plot(alpha_c, m_zeta_c, c='b', label=r'$m_\\zeta$')\n", + "ax1.set_yscale('log')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax2.plot(alpha_b, m_s_b, c='r', label=r'$m_s$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('log')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax3.plot(alpha_b, m_zeta_b, c='b', label=r'$m_\\zeta$')\n", + "ax3.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax3.set_yscale('log')\n", + "ax3.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax1.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8470dc58-92f9-46ab-8ec6-982e346cda0d", + "metadata": { + "id": "8470dc58-92f9-46ab-8ec6-982e346cda0d" + }, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_c, mnu2_s_c / m_s_c, c='r', label=r'$\\nu_s^2$')\n", + "ax1.plot(alpha_c, mnu2_zeta_c / m_zeta_c, c='b', label=r'$\\nu_\\zeta^2$')\n", + "ax1.set_yscale('log')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_b, mnu2_s_b / m_s_b, c='r', label=r'$\\nu_s^2$')\n", + "ax2.plot(alpha_b, mnu2_zeta_b / m_zeta_b, c='b', label=r'$\\nu_\\zeta^2$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('log')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0fcea250-ab16-4d75-b437-254e07cb70cb", + "metadata": { + "id": "0fcea250-ab16-4d75-b437-254e07cb70cb" + }, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_c, y_c * np.sqrt(m_s_c * m_zeta_c), c='k', label=r'$\\nu_s^2$')\n", + "ax1.set_yscale('symlog', linthresh=1.0e-10)\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax2.plot(alpha_b, y_b * np.sqrt(m_s_b * m_zeta_b), c='k', label=r'$\\nu_s^2$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('symlog')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax1.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f09ef1fb-3287-4c23-953e-a9325f45a419", + "metadata": { + "id": "f09ef1fb-3287-4c23-953e-a9325f45a419" + }, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=1)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,1,1)\n", + "\n", + "ax1.plot(alpha_c, cos2_phi_c, label=r'$\\cos^2(\\phi)$')\n", + "ax1.plot(alpha_c, sin2_phi_c, label=r'$\\sin^2(\\phi)$')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "af2c3d95-97ec-4f81-b226-dfec9ae4a6f4", + "metadata": { + "id": "af2c3d95-97ec-4f81-b226-dfec9ae4a6f4" + }, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_c, nu1_c, label=r'$\\nu_1$')\n", + "ax1.plot(alpha_c, gamma11_c, label=r'$\\gamma_{11}$')\n", + "ax1.plot(alpha_c, gamma12_c, label=r'$\\gamma_{12}$')\n", + "ax1.plot(alpha_c, tau_c, label=r'$\\tau_{12}$')\n", + "\n", + "ax1.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_c, nu2_c, label=r'$\\nu_2$')\n", + "ax2.plot(alpha_c, gamma22_c, label=r'$\\gamma_{22}$')\n", + "ax2.plot(alpha_c, gamma12_c, label=r'$\\gamma_{12}$')\n", + "ax2.plot(alpha_c, tau_c, label=r'$\\tau_{12}$')\n", + "\n", + "ax2.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "60453966-409d-44d7-969a-ee67005bb392", + "metadata": { + "id": "60453966-409d-44d7-969a-ee67005bb392" + }, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_b, nu1_b, label=r'$\\nu_1$')\n", + "ax1.plot(alpha_b, gamma11_b, label=r'$\\gamma_{11}$')\n", + "ax1.plot(alpha_b, gamma12_b, label=r'$\\gamma_{12}$')\n", + "ax1.plot(alpha_b, tau_b, label=r'$\\tau_{12}$')\n", + "ax1.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax1.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_b, nu2_b, label=r'$\\nu_2$')\n", + "ax2.plot(alpha_b, gamma22_b, label=r'$\\gamma_{22}$')\n", + "ax2.plot(alpha_b, gamma12_b, label=r'$\\gamma_{12}$')\n", + "ax2.plot(alpha_b, tau_b, label=r'$\\tau_{12}$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Perturbative Quantities" + ], + "metadata": { + "id": "WqocAbPmfI5P" + }, + "id": "WqocAbPmfI5P" + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ab63ada8-c087-4d13-ac4a-80429306b37a", + "metadata": { + "id": "ab63ada8-c087-4d13-ac4a-80429306b37a" + }, + "outputs": [], + "source": [ + "def get_zeta(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.ZETA_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.ZETA_I)\n", + "\n", + "def get_S(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.S_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.S_I)\n", + "\n", + "def get_Pzeta(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.PZETA_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.PZETA_I)\n", + "\n", + "def get_PS(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.PS_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.PS_I)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b73ca8cc-9168-4ecf-bed5-c14f56b1e753", + "metadata": { + "id": "b73ca8cc-9168-4ecf-bed5-c14f56b1e753" + }, + "outputs": [], + "source": [ + "def integrate_system(k):\n", + " # Defining relative tolerance for integration\n", + " prec = 1.0e-10\n", + " # Ratio potential frequency to define cross time\n", + " cross_size = 1.0e-9\n", + "\n", + " # New perturbations object\n", + " pert1 = Nc.HIPertTwoFluids.new()\n", + " pert2 = Nc.HIPertTwoFluids.new()\n", + " # Setting reltol\n", + " pert1.props.reltol = prec\n", + " pert2.props.reltol = prec\n", + " # Setting k\n", + " pert1.set_mode_k(k)\n", + " pert2.set_mode_k(k)\n", + "\n", + " # Choose an initial condition\n", + " alpha_try = -cosmo.abs_alpha(1.0e-14 * k**2)\n", + "\n", + " # New vector to store initial conditions\n", + " # 8 dimensional (Q_1, Q_2, P_1, P_2), real and imaginary parts\n", + " ci1 = Ncm.Vector.new(8)\n", + " ci2 = Ncm.Vector.new(8)\n", + "\n", + " alphai1 = pert1.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE1MAIN, alpha_try, cross_size)\n", + " alphai2 = pert2.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE2MAIN, alpha_try, cross_size)\n", + "\n", + " # Compute initial conditions at alpha_try store at ci and use normalization factor\n", + " # pi/4\n", + " pert1.get_init_cond_zetaS(cosmo, alphai1, 1, 0.25 * math.pi, ci1)\n", + " pert2.get_init_cond_zetaS(cosmo, alphai2, 2, 0.25 * math.pi, ci2)\n", + "\n", + " # Use the previously computed initial conditions to start the system at alpha_try\n", + " pert1.set_init_cond(cosmo, alphai1, 30, False, ci1)\n", + " pert2.set_init_cond(cosmo, alphai2, 30, False, ci2)\n", + " # print(f\"Setting initial conditions for zeta1 and S1 at {alphai1}\")\n", + " # print(f\"Setting initial conditions for zeta2 and S2 at {alphai2}\")\n", + "\n", + " if alphai2 > alphai1:\n", + " pert1.evolve(cosmo, alphai2)\n", + " ci1, _ = pert1.peek_state(cosmo)\n", + " else:\n", + " pert2.evolve(cosmo, alphai1)\n", + " ci2, _ = pert2.peek_state(cosmo)\n", + "\n", + " alphai = max(alphai1, alphai2)\n", + "\n", + " # Create a array of times to integrate the system over\n", + " alpha_evol = np.linspace(alphai, -1.0e-1, 1000)\n", + "\n", + " # Integrate the system by stepping through alpha_evol using .evolve\n", + " zeta1_a = [get_zeta(ci1)]\n", + " S1_a = [get_S(ci1)]\n", + " Pzeta1_a = [get_Pzeta(ci1)]\n", + " PS1_a = [get_PS(ci1)]\n", + "\n", + " zeta2_a = [get_zeta(ci2)]\n", + " S2_a = [get_S(ci2)]\n", + " Pzeta2_a = [get_Pzeta(ci2)]\n", + " PS2_a = [get_PS(ci2)]\n", + "\n", + " for alpha in tqdm(alpha_evol[1:], desc=\"Time evolution\", position=1, leave=False):\n", + " pert1.evolve(cosmo, alpha)\n", + " pert2.evolve(cosmo, alpha)\n", + " v1, _alphac1 = pert1.peek_state(cosmo)\n", + " v2, _alphac2 = pert2.peek_state(cosmo)\n", + "\n", + " zeta1_a.append(get_zeta(v1))\n", + " S1_a.append(get_S(v1))\n", + " Pzeta1_a.append(get_Pzeta(v1))\n", + " PS1_a.append(get_PS(v1))\n", + "\n", + " zeta2_a.append(get_zeta(v2))\n", + " S2_a.append(get_S(v2))\n", + " Pzeta2_a.append(get_Pzeta(v2))\n", + " PS2_a.append(get_PS(v2))\n", + "\n", + " zeta1 = np.array(zeta1_a)\n", + " S1 = np.array(S1_a)\n", + " Pzeta1 = np.array(Pzeta1_a)\n", + " PS1 = np.array(PS1_a)\n", + "\n", + " zeta2 = np.array(zeta2_a)\n", + " S2 = np.array(S2_a)\n", + " Pzeta2 = np.array(Pzeta2_a)\n", + " PS2 = np.array(PS2_a)\n", + "\n", + " return (alpha_evol, zeta1, S1, Pzeta1, PS1, zeta2, S2, Pzeta2, PS2)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "13668ef8-43cd-4a07-a777-ea5bbdf1dd96", + "metadata": { + "id": "13668ef8-43cd-4a07-a777-ea5bbdf1dd96" + }, + "outputs": [], + "source": [ + "alpha_evol, zeta1, S1, Pzeta1, PS1, zeta2, S2, Pzeta2, PS2 = integrate_system(1.0)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3d343fd0-19b8-4b76-aeff-28a443f081bd", + "metadata": { + "id": "3d343fd0-19b8-4b76-aeff-28a443f081bd" + }, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(2,1,1)\n", + "ax2= fig.add_subplot(2,1,2)\n", + "\n", + "ax1.plot(alpha_evol, np.real(zeta1), label=r'$\\mathrm{Re}(\\zeta_1)$')\n", + "ax1.plot(alpha_evol, np.imag(zeta1), label=r'$\\mathrm{Im}(\\zeta_1)$')\n", + "ax1.plot(alpha_evol, np.real(zeta2), label=r'$\\mathrm{Re}(\\zeta_2)$')\n", + "ax1.plot(alpha_evol, np.imag(zeta2), label=r'$\\mathrm{Im}(\\zeta_2)$')\n", + "ax1.set_yscale('symlog')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_evol, np.real(S1), label=r'$\\mathrm{Re}(S_1)$')\n", + "ax2.plot(alpha_evol, np.imag(S1), label=r'$\\mathrm{Im}(S_1)$')\n", + "ax2.plot(alpha_evol, np.real(S2), label=r'$\\mathrm{Re}(S_2)$')\n", + "ax2.plot(alpha_evol, np.imag(S2), label=r'$\\mathrm{Im}(S_2)$')\n", + "ax2.set_yscale('symlog')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "ax2.legend()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0048f301-a4f1-48a4-9de3-c2a3ef103f59", + "metadata": { + "id": "0048f301-a4f1-48a4-9de3-c2a3ef103f59" + }, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(2,1,1)\n", + "ax2= fig.add_subplot(2,1,2)\n", + "\n", + "ax1.plot(alpha_evol, np.abs(zeta1)**2, label=r'$|\\zeta_1|^2$')\n", + "ax1.plot(alpha_evol, np.abs(zeta2)**2, label=r'$|\\zeta_2|^2$')\n", + "ax1.set_yscale('log')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_evol, np.abs(S1)**2, label=r'$|S_1|^2$')\n", + "ax2.plot(alpha_evol, np.abs(S2)**2, label=r'$|S_2|^2$')\n", + "ax2.set_yscale('log')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d8694a1e-6562-434c-b5da-9d60cdb3de4f", + "metadata": { + "id": "d8694a1e-6562-434c-b5da-9d60cdb3de4f" + }, + "outputs": [], + "source": [ + "k_a = np.geomspace(1.0e-3, 1.0e3, 100)\n", + "\n", + "PI_zeta1 = []\n", + "PI_zeta2 = []\n", + "PI_S1 = []\n", + "PI_S2 = []\n", + "\n", + "for k in tqdm(k_a, desc= \"Mode evolution\", position=0):\n", + " alpha_evol, zeta1, S1, Pzeta1, PS1, zeta2, S2, Pzeta2, PS2 = integrate_system(k)\n", + " PI_zeta1.append(np.abs(zeta1[-1])**2)\n", + " PI_zeta2.append(np.abs(zeta2[-1])**2)\n", + " PI_S1.append(np.abs(S1[-1])**2)\n", + " PI_S2.append(np.abs(S2[-1])**2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b69e8502-f742-440f-b997-9b3de0dc2dd8", + "metadata": { + "id": "b69e8502-f742-440f-b997-9b3de0dc2dd8" + }, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(2,1,1)\n", + "ax2= fig.add_subplot(2,1,2)\n", + "\n", + "ax1.plot(k_a, k_a**3 * PI_zeta1, label=r'$\\Pi_{\\zeta_1}$')\n", + "ax1.plot(k_a, k_a**3 * PI_zeta2, label=r'$\\Pi_{\\zeta_2}$')\n", + "ax1.set_xscale('log')\n", + "ax1.set_yscale('log')\n", + "ax1.set_xlabel(r'$k$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(k_a, k_a**3 * PI_S1, label=r'$\\Pi_{S_1}$')\n", + "ax2.plot(k_a, k_a**3 * PI_S2, label=r'$\\Pi_{S_2}$')\n", + "ax2.set_xscale('log')\n", + "ax2.set_yscale('log')\n", + "ax2.set_xlabel(r'$k$')\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "818e4ad0-510c-4d31-a2bf-83bde5f04c58", + "metadata": { + "id": "818e4ad0-510c-4d31-a2bf-83bde5f04c58" + }, + "outputs": [], + "source": [ + "#print(np.polyfit(np.log(k_a),np.log(k_a**3 * PI_zeta2),1)[0])\n", + "\n", + "print(1.0 + 12.0 * cosmo.props.w / (1.0 + 3.0 *cosmo.props.w))\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Parte do Eduado" + ], + "metadata": { + "id": "fuB-VSqxNTu3" + }, + "id": "fuB-VSqxNTu3" + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6b2523f8", + "metadata": { + "id": "6b2523f8" + }, + "outputs": [], + "source": [ + "def test_two_fluids_wkb_mode(mode: int = Nc.HIPertTwoFluidsCross.MODE1SUB, case_f: int = 1, nullr = 1.0, nulli = 1.0) -> None:\n", + " \"\"\"Compute WKB approximation for the two-fluids model.\"\"\"\n", + "\n", + " #\n", + " # New homogeneous and isotropic cosmological model NcHICosmoQGRW\n", + " #\n", + " cosmo = Nc.HICosmoQGRW()\n", + "\n", + " w = 0.00001\n", + " prec = 1.0e-6\n", + " mode_k = 1000\n", + "\n", + " cosmo.props.w = w\n", + " cosmo.props.Omegar = 2.0 * (1.0e-8)\n", + " cosmo.props.Omegaw = 2.0 * (1.0 - 1.0e-8)\n", + " cosmo.props.xb = 1.0e30\n", + "\n", + " pert = Nc.HIPertTwoFluids.new()\n", + "\n", + " pert.props.reltol = prec\n", + " pert.set_mode_k(mode_k)\n", + "\n", + " cross_size = 1.0e-5\n", + " alpha_try = -cosmo.abs_alpha(1.0e-12 * mode_k**2)\n", + " # Chuta tempo incial e depois calcula ele aqui embaixo, dependendo de qual modo é o main\n", + "\n", + " # Pra descobrir se o alpha1 da outra funcao faz sentido, coloca auqi o caso que vc quiser e imprime o tempo calcualdo (ex: mode1main, da um alpha 1.0e-9. Por isso ele deve ter colocado na 2 funçao)\n", + " if mode == Nc.HIPertTwoFluidsCross.MODE1MAIN:\n", + " alphai = pert.get_cross_time(\n", + " cosmo, Nc.HIPertTwoFluidsCross.MODE1MAIN, alpha_try, cross_size\n", + " )\n", + " elif mode == Nc.HIPertTwoFluidsCross.MODE1SUB:\n", + " alphai = pert.get_cross_time(\n", + " cosmo, Nc.HIPertTwoFluidsCross.MODE1SUB, alpha_try, cross_size\n", + " )\n", + " elif mode == Nc.HIPertTwoFluidsCross.MODE2MAIN:\n", + " alphai = pert.get_cross_time(\n", + " cosmo, Nc.HIPertTwoFluidsCross.MODE2MAIN, alpha_try, cross_size\n", + " )\n", + " elif mode == Nc.HIPertTwoFluidsCross.MODE2SUB:\n", + " alphai = pert.get_cross_time(\n", + " cosmo, Nc.HIPertTwoFluidsCross.MODE2SUB, alpha_try, cross_size\n", + " )\n", + " else:\n", + " raise ValueError(\"Invalid mode\")\n", + "\n", + " alphaf = +cosmo.abs_alpha(1.0e20)\n", + "\n", + " print(f\"Mode k = mode_k: {mode_k}\")\n", + "\n", + " pert.set_stiff_solver(True)\n", + "\n", + " alpha_a = []\n", + " gammabar11_a = []\n", + " gammabar22_a = []\n", + " gammabar12_a = []\n", + " taubar12_a = []\n", + " nu1_a = []\n", + " nu2_a = []\n", + "\n", + " for alpha in np.linspace(alphai, alphaf, 10000):\n", + " eom = pert.eom(cosmo, alpha)\n", + " alpha_a.append(alpha)\n", + "\n", + " gammabar11_a.append(math.fabs(eom.gammabar11))\n", + " gammabar22_a.append(math.fabs(eom.gammabar22))\n", + " gammabar12_a.append(math.fabs(eom.gammabar12))\n", + " taubar12_a.append(math.fabs(eom.taubar))\n", + " nu1_a.append(eom.nu1)\n", + " nu2_a.append(eom.nu2)\n", + "\n", + " print(\n", + " f\"# Calculating mode 1, initial time {alphai}, redshift_alpha {cosmo.x_alpha(alphai):8.2e}]: \"\n", + " )\n", + "\n", + " ci = Ncm.Vector.new(8)\n", + "\n", + " pert.get_init_cond_zetaS(cosmo, alphai, case_f, 0.25 * math.pi, ci)\n", + " pert.set_init_cond(cosmo, alphai, 3, False, ci)\n", + "\n", + " Ps_zeta1 = []\n", + " Ps_S1 = []\n", + " Ps_Pzeta1 = []\n", + " Ps_PS1 = []\n", + "\n", + " Ps_zeta1.append(\n", + " math.hypot(\n", + " nullr * ci.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " nulli * ci.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_S1.append(\n", + " math.hypot(\n", + " nullr *ci.get(Nc.HIPertITwoFluidsVars.S_R),\n", + " nulli *ci.get(Nc.HIPertITwoFluidsVars.S_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_Pzeta1.append(\n", + " math.hypot(\n", + " nullr *ci.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " nulli *ci.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_PS1.append(\n", + " math.hypot(\n", + " nullr * ci.get(Nc.HIPertITwoFluidsVars.PS_R),\n", + " nulli * ci.get(Nc.HIPertITwoFluidsVars.PS_I),\n", + " )\n", + " ** 2\n", + " )\n", + "\n", + " for alpha in tqdm(alpha_a[1:]):\n", + " # for alpha in alpha_a[1:]:\n", + " pert.evolve(cosmo, alpha)\n", + " v, _alphac = pert.peek_state(cosmo)\n", + " Ps_zeta1.append(\n", + " math.hypot(\n", + " nullr * v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " nulli * v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_S1.append(\n", + " math.hypot(\n", + " nullr * v.get(Nc.HIPertITwoFluidsVars.S_R),\n", + " nulli * v.get(Nc.HIPertITwoFluidsVars.S_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_Pzeta1.append(\n", + " math.hypot(\n", + " nullr * v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " nulli * v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_PS1.append(\n", + " math.hypot(\n", + " nullr * v.get(Nc.HIPertITwoFluidsVars.PS_R),\n", + " nulli * v.get(Nc.HIPertITwoFluidsVars.PS_I),\n", + " )\n", + " ** 2\n", + " )\n", + " plt.plot(alpha_a, Ps_zeta1, label=r\"$P_\\zeta$\")\n", + " plt.plot(alpha_a, Ps_S1, label=r\"$P_Q$\")\n", + " plt.plot(alpha_a, Ps_Pzeta1, label=r\"$P_{P_\\zeta}$\")\n", + " plt.plot(alpha_a, Ps_PS1, label=r\"$P_{P_Q}$\")\n", + " plt.xlabel(r\"$\\alpha$\")\n", + " plt.ylabel(r\"Mode\")\n", + " plt.grid()\n", + " plt.legend(loc=\"upper left\")\n", + " # plt.xscale('log')\n", + " plt.yscale(\"log\")\n", + "\n", + " Delta_zeta1 = (\n", + " mode_k**3 * Ps_zeta1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_S1 = mode_k**3 * Ps_S1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " Delta_Pzeta1 = (\n", + " mode_k**3 * Ps_Pzeta1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_PS1 = (\n", + " mode_k**3 * Ps_PS1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " print(\n", + " f\"# Final values k = {mode_k: 20.15g} Ps_zeta{case_f} = {Delta_zeta1: 21.15e} \"\n", + " f\"Ps_Pzeta{case_f} = {Delta_Pzeta1: 21.15e} Ps_S{case_f} = {Delta_S1: 21.15e} \"\n", + " f\"Ps_PS{case_f} = {Delta_PS1: 21.15e}\"\n", + " )\n", + "\n", + "\n", + "\n", + " #plt.savefig('mode_I_p_R')\n", + " #plt.clf()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a81352e0", + "metadata": { + "id": "a81352e0" + }, + "outputs": [], + "source": [ + "def test_two_fluids_wkb_spec() -> None:\n", + " \"\"\"Compute WKB approximation for the two-fluids model spectrum.\"\"\"\n", + "\n", + " #\n", + " # New homogeneous and isotropic cosmological model NcHICosmoQGRW\n", + " #\n", + " cosmo = Nc.HICosmoQGRW() # P1 = Cosmologia\n", + "\n", + " w = 1.0e-5 #P2 eq de estado da materia escura\n", + " prec = 1.0e-7\n", + "\n", + " #P3 densidade de radiação e materia escura e energia escura (1 - resto)\n", + " cosmo.props.w = w\n", + " cosmo.props.Omegar = (1.0e-8) * 1.0\n", + " cosmo.props.Omegaw = (1.0 - 1.0e-8) * 1.0\n", + " cosmo.props.xb = 1.0e30 # P4 x do bounce\n", + "\n", + " pert = Nc.HIPertTwoFluids.new()\n", + "\n", + " pert.props.reltol = prec\n", + " # pert.set_stiff_solver (True)\n", + "\n", + " # k = 1 => lambda = 5 Gpc\n", + " # k = 10^5 => lambda = 50 kpc\n", + " lnki = math.log(1.0e0)# P5 intervalo de momento de interesse\n", + " lnkf = math.log(1.0e5)\n", + " lnk_a = np.linspace(lnki, lnkf, 20)\n", + "\n", + " ci = Ncm.Vector.new(8)\n", + "\n", + " k_a = []\n", + " Ps_zeta1 = []\n", + " Ps_S1 = []\n", + " Ps_zeta2 = []\n", + " Ps_S2 = []\n", + " Ps_Pzeta1 = []\n", + " Ps_PS1 = []\n", + "\n", + " out_file = open(\"twofluids_spectrum_{w}.dat\", \"w\", encoding=\"utf-8\")\n", + "#alpha is related to the time variable. The log-redshift time\n", + " start_alpha1 = 1.0e-10 # P5 tempo inicial dependente do redshift.\n", + " start_alpha2 = 1.0e-14\n", + "\n", + " for lnk in tqdm(lnk_a):\n", + " k = math.exp(lnk)\n", + " pert.set_mode_k(k)\n", + " k_a.append(k)\n", + "\n", + " alphaf = cosmo.abs_alpha(1.0e20)\n", + "\n", + " # print (\"# Evolving mode %e from %f to %f\" % (k, alphai, alphaf))\n", + " #S is our variable Q.\n", + " alphai = -cosmo.abs_alpha(start_alpha1 * k**2)\n", + "\n", + " #### Ate aqui só coloca todos os parametros, define o tempo inicial, e converte o alpha1 em algum tipo de numero absoluto nessa funçao de cima.\n", + "\n", + " ##### Agora embaixo, calcula as cond iniciais, seta as condicioes iniciais e evolui no tempo.\n", + "\n", + " pert.get_init_cond_zetaS(cosmo, alphai, 1, 0.25 * math.pi, ci)\n", + "#This function does the following: Calls get_init_cond_zetaS, which calls cond_QP.\n", + "#IN cond_QP:\n", + " #Starts interface that have the equations of motion and the decomposition TV.\n", + " #Defines which case: 1 or 2, defining which momentum we assume as non-zero\n", + " #Computes all the init cond\n", + " #I believe that R and I represents each solutioon 1 and 2.\n", + "#Then we call to_zetaS, which changes from QP to zeta Q\n", + " pert.set_init_cond(cosmo, alphai, 1, False, ci)\n", + "\n", + " print(f\"# Mode 1 k {k: 21.15e}, state module {pert.get_state_mod():f}\")\n", + "\n", + " pert.evolve(cosmo, alphaf)#Evolve the system untill alphaF\n", + "\n", + "\n", + "\n", + " v, _alphac = pert.peek_state(cosmo)#Get the current time and values of the numerical solution for the modes. V é o vetor com os modos, n sei a ordem\n", + "#I believe that Delta represents the spectrum here.\n", + "\n", + "\n", + "##Aqui terminou de calcular os modos pro momento do loop. Ai agora calcula o espectro\n", + " Delta_zeta1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_S1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_Pzeta1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_PS1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + "\n", + " Ps_zeta1.append(Delta_zeta1)\n", + " Ps_S1.append(Delta_S1)\n", + " Ps_Pzeta1.append(Delta_Pzeta1)\n", + " Ps_PS1.append(Delta_PS1)\n", + "\n", + "\n", + " #### Aqui acabou o espectro pro modo 1. Ai faz de novo pro modo 2. ####3\n", + "\n", + " alphai = -cosmo.abs_alpha(start_alpha2 * k**2)\n", + " pert.get_init_cond_zetaS(cosmo, alphai, 2, 0.25 * math.pi, ci)\n", + " pert.set_init_cond(cosmo, alphai, 0, False, ci)\n", + "\n", + " pert.evolve(cosmo, alphaf)\n", + " v, _alphac = pert.peek_state(cosmo)\n", + " print(_alphac)\n", + " Delta_zeta2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_S2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_Pzeta2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_PS2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + "\n", + " Ps_zeta2.append(Delta_zeta2)\n", + " Ps_S2.append(Delta_S2)\n", + " Ps_zeta2.append(Delta_Pzeta2)\n", + " Ps_S2.append(Delta_PS2)\n", + "\n", + " out_file.write(\n", + " f\"{k: 20.15e} {Delta_zeta1: 20.15e} {Delta_zeta2: 20.15e} {Delta_S1: 20.15e} \"\n", + " f\"{Delta_S2: 20.15e} {Delta_Pzeta1: 20.15e} {Delta_Pzeta2: 20.15e} \"\n", + " f\"{Delta_PS1: 20.15e} {Delta_PS2: 20.15e}\\n\"\n", + " )\n", + " out_file.flush()\n", + "\n", + " out_file.close()\n", + "\n", + "###Plot\n", + "\n", + " plt.plot(k_a, Ps_zeta1, label=r\"$P_\\zeta$\")\n", + " plt.plot(k_a, Ps_S1, label=r\"$P_Q$\")\n", + " #plt.plot(k_a, Ps_zeta2, label=r\"$P^2_\\zeta$\")\n", + " # plt.plot(k_a, Ps_S2, label=r\"$P^2_Q$\")\n", + " plt.xlabel(r\"$k $\")\n", + " plt.ylabel(r\"$Spectrum$\")\n", + " plt.grid()\n", + " plt.legend(loc=\"upper left\")\n", + " #plt.xscale(\"log\")\n", + " #plt.yscale(\"log\")\n", + "\n", + "\n", + " plt.savefig('spec')\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1e644bda", + "metadata": { + "id": "1e644bda" + }, + "outputs": [], + "source": [ + "def test_two_fluids_wkb_spec_log() -> None:\n", + " \"\"\"Compute WKB approximation for the two-fluids model spectrum.\"\"\"\n", + "\n", + " #\n", + " # New homogeneous and isotropic cosmological model NcHICosmoQGRW\n", + " #\n", + " cosmo = Nc.HICosmoQGRW() # P1 = Cosmologia\n", + "\n", + " w = 0.00001 #P2 eq de estado da materia escura\n", + " prec = 1.0e-7\n", + "\n", + " #P3 densidade de radiação e materia escura e energia escura (1 - resto)\n", + " cosmo.props.w = w\n", + " cosmo.props.Omegar = (1.0e-8) * 1.0\n", + " cosmo.props.Omegaw = (1.0 - 1.0e-8) * 1.0\n", + " cosmo.props.xb = 1.0e30 # P4 x do bounce\n", + "\n", + " pert = Nc.HIPertTwoFluids.new()\n", + "\n", + " pert.props.reltol = prec\n", + " # pert.set_stiff_solver (True)\n", + "\n", + " lnki = math.log(1.0e-5)# P5 intervalo de momento de interesse\n", + " lnkf = math.log(1.0e5)\n", + " lnk_a = np.linspace(lnki, lnkf, 50)\n", + "\n", + " ci = Ncm.Vector.new(8)\n", + "\n", + " k_a = []\n", + " Ps_zeta1 = []\n", + " Ps_S1 = []\n", + " Ps_zeta2 = []\n", + " Ps_S2 = []\n", + " Ps_Pzeta1 = []\n", + " Ps_PS1 = []\n", + "\n", + " out_file = open(\"twofluids_spectrum_{w}.dat\", \"w\", encoding=\"utf-8\")\n", + "#alpha is related to the time variable. The log-redshift time\n", + " start_alpha1 = 1.0e-10 # P5 tempo inicial dependente do redshift.\n", + " start_alpha2 = 1.0e-14\n", + "\n", + " for lnk in tqdm(lnk_a):\n", + " k = math.exp(lnk)\n", + " pert.set_mode_k(k)\n", + " k_a.append(k)\n", + "\n", + " alphaf = cosmo.abs_alpha(1.0e20)\n", + "\n", + " # print (\"# Evolving mode %e from %f to %f\" % (k, alphai, alphaf))\n", + " #S is our variable Q.\n", + " alphai = -cosmo.abs_alpha(start_alpha1 * k**2)\n", + "\n", + " #### Ate aqui só coloca todos os parametros, define o tempo inicial, e converte o alpha1 em algum tipo de numero absoluto nessa funçao de cima.\n", + "\n", + " ##### Agora embaixo, calcula as cond iniciais, seta as condicioes iniciais e evolui no tempo.\n", + "\n", + " pert.get_init_cond_zetaS(cosmo, alphai, 1, 0.25 * math.pi, ci)\n", + "#This function does the following: Calls get_init_cond_zetaS, which calls cond_QP.\n", + "#IN cond_QP:\n", + " #Starts interface that have the equations of motion and the decomposition TV.\n", + " #Defines which case: 1 or 2, defining which momentum we assume as non-zero\n", + " #Computes all the init cond\n", + " #I believe that R and I represents each solutioon 1 and 2.\n", + "#Then we call to_zetaS, which changes from QP to zeta Q\n", + " pert.set_init_cond(cosmo, alphai, 1, False, ci)\n", + "\n", + " print(f\"# Mode 1 k {k: 21.15e}, state module {pert.get_state_mod():f}\")\n", + "\n", + " pert.evolve(cosmo, alphaf)#Evolve the system untill alphaF\n", + "\n", + "\n", + "\n", + " v, _alphac = pert.peek_state(cosmo)#Get the current time and values of the numerical solution for the modes. V é o vetor com os modos, n sei a ordem\n", + "#I believe that Delta represents the spectrum here.\n", + "\n", + "\n", + "##Aqui terminou de calcular os modos pro momento do loop. Ai agora calcula o espectro\n", + " Delta_zeta1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_S1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_Pzeta1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_PS1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + "\n", + " Ps_zeta1.append(Delta_zeta1)\n", + " Ps_S1.append(Delta_S1)\n", + " Ps_Pzeta1.append(Delta_Pzeta1)\n", + " Ps_PS1.append(Delta_PS1)\n", + "\n", + "\n", + " #### Aqui acabou o espectro pro modo 1. Ai faz de novo pro modo 2. ####3\n", + "\n", + " alphai = -cosmo.abs_alpha(start_alpha2 * k**2)\n", + " pert.get_init_cond_zetaS(cosmo, alphai, 2, 0.25 * math.pi, ci)\n", + " pert.set_init_cond(cosmo, alphai, 0, False, ci)\n", + "\n", + " pert.evolve(cosmo, alphaf)\n", + " v, _alphac = pert.peek_state(cosmo)\n", + " print(_alphac)\n", + " Delta_zeta2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_S2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_Pzeta2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_PS2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + "\n", + " Ps_zeta2.append(Delta_zeta2)\n", + " Ps_S2.append(Delta_S2)\n", + " Ps_zeta2.append(Delta_Pzeta2)\n", + " Ps_S2.append(Delta_PS2)\n", + "\n", + " out_file.write(\n", + " f\"{k: 20.15e} {Delta_zeta1: 20.15e} {Delta_zeta2: 20.15e} {Delta_S1: 20.15e} \"\n", + " f\"{Delta_S2: 20.15e} {Delta_Pzeta1: 20.15e} {Delta_Pzeta2: 20.15e} \"\n", + " f\"{Delta_PS1: 20.15e} {Delta_PS2: 20.15e}\\n\"\n", + " )\n", + " out_file.flush()\n", + "\n", + " out_file.close()\n", + "\n", + "###Plot\n", + "\n", + " plt.plot(np.log(k_a), np.log(Ps_zeta1), label=r\"$P_\\zeta$\")\n", + " plt.plot(np.log(k_a), np.log(Ps_S1), label=r\"$P_Q$\")\n", + " #plt.plot(k_a, Ps_zeta2, label=r\"$P^2_\\zeta$\")\n", + " # plt.plot(k_a, Ps_S2, label=r\"$P^2_Q$\")\n", + " plt.xlabel(r\"$k $\")\n", + " plt.ylabel(r\"$Spectrum$\")\n", + " plt.grid()\n", + " plt.legend(loc=\"upper left\")\n", + " #plt.xscale(\"log\")\n", + " #plt.yscale(\"log\")\n", + "\n", + "\n", + " #plt.savefig('spec')\n", + " plt.show()\n", + " return np.log(Ps_zeta1), k_a" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "17f092b6", + "metadata": { + "id": "17f092b6" + }, + "outputs": [], + "source": [ + "#test_two_fluids_wkb_mode(Nc.HIPertTwoFluidsCross.MODE1MAIN, 1, 0.0, 1.0)\n", + "test_two_fluids_wkb_mode(Nc.HIPertTwoFluidsCross.MODE1MAIN, 1, 1.0, 0.0)\n", + "#test_two_fluids_wkb_mode(Nc.HIPertTwoFluidsCross.MODE1MAIN, 1, 1.0, 1.0)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "98260fc2", + "metadata": { + "id": "98260fc2" + }, + "outputs": [], + "source": [ + "test_two_fluids_wkb_spec()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "84556565", + "metadata": { + "id": "84556565" + }, + "outputs": [], + "source": [ + "test_two_fluids_wkb_spec_log()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f3f21975", + "metadata": { + "id": "f3f21975" + }, + "outputs": [], + "source": [ + "z1 = [-172.29336504, -171.47725159, -170.67740675, -169.40963547,\n", + " -168.3753366 , -167.40418261, -166.617099 , -165.69081201,\n", + " -164.60277739, -163.8977755 , -162.91261604, -161.89532066,\n", + " -160.95146111, -159.82933117, -158.99936059, -158.1648807 ,\n", + " -157.3978438 , -156.18665031, -155.4043561 , -154.44173584,\n", + " -153.5056154 , -152.43139744, -151.48454113, -150.74967245,\n", + " -149.71138271, -148.85570926, -147.97343268, -146.87265029,\n", + " -145.89153898, -145.029969 , -143.98543597, -143.28854835,\n", + " -142.18761254, -141.23608627, -140.32638846, -139.48824811,\n", + " -138.47120016, -137.4639825 , -136.53337746, -135.66450856,\n", + " -134.71280034, -133.5931724 , -132.540295 , -131.19474152,\n", + " -129.90695834, -128.57067396, -127.17615592, -125.87341712,\n", + " -124.6418451 , -123.48007829]\n", + "\n", + "lnki = math.log(1.0e-5)# P5 intervalo de momento de interesse\n", + "lnkf = math.log(1.0e5)\n", + "lnk_a = np.linspace(lnki, lnkf, 50)\n", + "result=np.polyfit(lnk_a[:30], z1[:30], 1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5618578b", + "metadata": { + "id": "5618578b" + }, + "outputs": [], + "source": [ + "print(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "07fa8d3b", + "metadata": { + "id": "07fa8d3b" + }, + "outputs": [], + "source": [ + "ns = result[0] + 1\n", + "print(ns)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "36e209f8", + "metadata": { + "id": "36e209f8" + }, + "outputs": [], + "source": [ + "12*1/3/(1+3*1/3) + 1" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "720f771b-3dc7-42b4-9342-ae3c1b16a651", + "metadata": { + "id": "720f771b-3dc7-42b4-9342-ae3c1b16a651" + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.4" + }, + "colab": { + "provenance": [], + "collapsed_sections": [ + "iiIp6-GfovaW", + "WqocAbPmfI5P", + "fuB-VSqxNTu3" + ] + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file From 34a4f0b351a9926092689a128606e04d448858cf Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Thu, 8 Feb 2024 17:36:22 -0300 Subject: [PATCH 03/27] Updates on two fluids code and notebook. --- meson.build | 6 + .../primordial_perturbations/two_fluids.ipynb | 6363 +++++++++++++++++ .../two_fluids_perturbations.ipynb | 2773 ++++--- numcosmo/perturbations/nc_hipert_two_fluids.c | 261 +- numcosmo/perturbations/nc_hipert_two_fluids.h | 20 +- 5 files changed, 7873 insertions(+), 1550 deletions(-) create mode 100644 notebooks/primordial_perturbations/two_fluids.ipynb diff --git a/meson.build b/meson.build index 79e59a431..8f01b4ca7 100644 --- a/meson.build +++ b/meson.build @@ -533,6 +533,12 @@ endif numcosmo_conf.set('HAVE_LIBCUBA', 1) numcosmo_conf.set('HAVE_LIBCUBA_4_0', 1) +####################################################################################### +# Using internal sundials: +####################################################################################### + +numcosmo_conf.set('HAVE_SUNDIALS_ARKODE', 1) + ####################################################################################### # Checking for NLopt (optional): ####################################################################################### diff --git a/notebooks/primordial_perturbations/two_fluids.ipynb b/notebooks/primordial_perturbations/two_fluids.ipynb new file mode 100644 index 000000000..368401e75 --- /dev/null +++ b/notebooks/primordial_perturbations/two_fluids.ipynb @@ -0,0 +1,6363 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "34003942", + "metadata": {}, + "outputs": [], + "source": [ + "import sys\n", + "import math\n", + "import numpy as np\n", + "\n", + "from tqdm import tqdm\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from numcosmo_py import Nc, Ncm\n", + "from numcosmo_py.plotting.tools import set_rc_params_article" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "b31c9f4d", + "metadata": {}, + "outputs": [], + "source": [ + "Ncm.cfg_init()" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "533290e5-dc2a-467a-8319-11811d78cc2b", + "metadata": {}, + "outputs": [], + "source": [ + "cosmo = Nc.HICosmoQGRW()\n", + "cosmo.props.w = 1.0e-5\n", + "cosmo.props.Omegar = 1.0 * (1.0e-5)\n", + "cosmo.props.Omegaw = 1.0 * (1.0 - 1.0e-5)\n", + "cosmo.props.xb = 1.0e30\n", + "\n", + "k = 1.0\n", + "min_alpha_c = -120.0\n", + "max_alpha_c = -1.0\n", + "min_alpha_scale = 1.0e-12\n", + "np_plot = 1000\n", + "\n", + "# Time arrays for the contraction and bounce phases\n", + "\n", + "alpha_c = np.linspace(min_alpha_c, max_alpha_c, np_plot)\n", + "alpha_b_e = np.geomspace(min_alpha_scale, 2.0, np_plot)\n", + "alpha_b = np.concatenate((np.flip(-alpha_b_e), alpha_b_e))\n", + "\n", + "# Computing background observables in the contraction phase\n", + "\n", + "m_s_c = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_c])\n", + "m_zeta_c = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_c])\n", + "mnu2_s_c = np.array([cosmo.eom_eval(alpha, k).mnu2_s for alpha in alpha_c])\n", + "mnu2_zeta_c = np.array([cosmo.eom_eval(alpha, k).mnu2_zeta for alpha in alpha_c])\n", + "nu1_c = np.array([cosmo.eom_eval(alpha, k).nu1 for alpha in alpha_c])\n", + "nu2_c = np.array([cosmo.eom_eval(alpha, k).nu2 for alpha in alpha_c])\n", + "nu_s_c = np.sqrt(mnu2_s_c / m_s_c)\n", + "nu_zeta_c = np.sqrt(mnu2_zeta_c / m_zeta_c)\n", + "y_c = np.array([cosmo.eom_eval(alpha, k).y for alpha in alpha_c])\n", + "gamma11_c = np.array([cosmo.eom_eval(alpha, k).gammabar11 for alpha in alpha_c])\n", + "gamma22_c = np.array([cosmo.eom_eval(alpha, k).gammabar22 for alpha in alpha_c])\n", + "gamma12_c = np.array([cosmo.eom_eval(alpha, k).gammabar12 for alpha in alpha_c])\n", + "tau_c = np.array([cosmo.eom_eval(alpha, k).taubar for alpha in alpha_c])\n", + "\n", + "# Computing background observables in the bounce phase\n", + "\n", + "m_s_b = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_b])\n", + "m_zeta_b = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_b])\n", + "mnu2_s_b = np.array([cosmo.eom_eval(alpha, k).mnu2_s for alpha in alpha_b])\n", + "mnu2_zeta_b = np.array([cosmo.eom_eval(alpha, k).mnu2_zeta for alpha in alpha_b])\n", + "nu1_b = np.array([cosmo.eom_eval(alpha, k).nu1 for alpha in alpha_b])\n", + "nu2_b = np.array([cosmo.eom_eval(alpha, k).nu2 for alpha in alpha_b])\n", + "nu_s_b = np.sqrt(mnu2_s_b / m_s_b)\n", + "nu_zeta_b = np.sqrt(mnu2_zeta_b / m_zeta_b)\n", + "y_b = np.array([cosmo.eom_eval(alpha, k).y for alpha in alpha_b])\n", + "gamma11_b = np.array([cosmo.eom_eval(alpha, k).gammabar11 for alpha in alpha_b])\n", + "gamma22_b = np.array([cosmo.eom_eval(alpha, k).gammabar22 for alpha in alpha_b])\n", + "gamma12_b = np.array([cosmo.eom_eval(alpha, k).gammabar12 for alpha in alpha_b])\n", + "tau_b = np.array([cosmo.eom_eval(alpha, k).taubar for alpha in alpha_b])\n", + "\n", + "cos2_phi_c = (nu1_c**2 * nu_zeta_c**2 - nu2_c**2 * nu_s_c**2) / (nu1_c**4 - nu2_c**4)\n", + "sin2_phi_c = (nu1_c**2 * nu_s_c**2 - nu2_c**2 * nu_zeta_c**2) / (nu1_c**4 - nu2_c**4)\n", + "\n", + "cos2_phi_b = (nu1_b**2 * nu_zeta_b**2 - nu2_b**2 * nu_s_b**2) / (nu1_b**4 - nu2_b**4)\n", + "sin2_phi_b = (nu1_b**2 * nu_s_b**2 - nu2_b**2 * nu_zeta_b**2) / (nu1_b**4 - nu2_b**4)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a4daed56-57bc-4993-b8ab-3468d8f83d5f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(2,2,2)\n", + "ax3= fig.add_subplot(2,2,4)\n", + "\n", + "ax1.plot(alpha_c, m_s_c, c='r', label=r'$m_s$')\n", + "ax1.plot(alpha_c, m_zeta_c, c='b', label=r'$m_\\zeta$')\n", + "ax1.set_yscale('log')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax2.plot(alpha_b, m_s_b, c='r', label=r'$m_s$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('log')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax3.plot(alpha_b, m_zeta_b, c='b', label=r'$m_\\zeta$')\n", + "ax3.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax3.set_yscale('log')\n", + "ax3.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax1.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "8470dc58-92f9-46ab-8ec6-982e346cda0d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_c, mnu2_s_c / m_s_c, c='r', label=r'$\\nu_s^2$')\n", + "ax1.plot(alpha_c, mnu2_zeta_c / m_zeta_c, c='b', label=r'$\\nu_\\zeta^2$')\n", + "ax1.set_yscale('log')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_b, mnu2_s_b / m_s_b, c='r', label=r'$\\nu_s^2$')\n", + "ax2.plot(alpha_b, mnu2_zeta_b / m_zeta_b, c='b', label=r'$\\nu_\\zeta^2$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('log')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "0fcea250-ab16-4d75-b437-254e07cb70cb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_c, y_c * np.sqrt(m_s_c * m_zeta_c), c='k', label=r'$\\nu_s^2$')\n", + "ax1.set_yscale('symlog', linthresh=1.0e-10)\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax2.plot(alpha_b, y_b * np.sqrt(m_s_b * m_zeta_b), c='k', label=r'$\\nu_s^2$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('symlog')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax1.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "f09ef1fb-3287-4c23-953e-a9325f45a419", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=1)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,1,1)\n", + "\n", + "ax1.plot(alpha_c, cos2_phi_c, label=r'$\\cos^2(\\phi)$')\n", + "ax1.plot(alpha_c, sin2_phi_c, label=r'$\\sin^2(\\phi)$')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "af2c3d95-97ec-4f81-b226-dfec9ae4a6f4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_c, nu1_c, label=r'$\\nu_1$')\n", + "ax1.plot(alpha_c, gamma11_c, label=r'$\\gamma_{11}$')\n", + "ax1.plot(alpha_c, gamma12_c, label=r'$\\gamma_{12}$')\n", + "ax1.plot(alpha_c, tau_c, label=r'$\\tau_{12}$')\n", + "\n", + "ax1.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_c, nu2_c, label=r'$\\nu_2$')\n", + "ax2.plot(alpha_c, gamma22_c, label=r'$\\gamma_{22}$')\n", + "ax2.plot(alpha_c, gamma12_c, label=r'$\\gamma_{12}$')\n", + "ax2.plot(alpha_c, tau_c, label=r'$\\tau_{12}$')\n", + "\n", + "ax2.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "60453966-409d-44d7-969a-ee67005bb392", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_b, nu1_b, label=r'$\\nu_1$')\n", + "ax1.plot(alpha_b, gamma11_b, label=r'$\\gamma_{11}$')\n", + "ax1.plot(alpha_b, gamma12_b, label=r'$\\gamma_{12}$')\n", + "ax1.plot(alpha_b, tau_b, label=r'$\\tau_{12}$')\n", + "ax1.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax1.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_b, nu2_b, label=r'$\\nu_2$')\n", + "ax2.plot(alpha_b, gamma22_b, label=r'$\\gamma_{22}$')\n", + "ax2.plot(alpha_b, gamma12_b, label=r'$\\gamma_{12}$')\n", + "ax2.plot(alpha_b, tau_b, label=r'$\\tau_{12}$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "ab63ada8-c087-4d13-ac4a-80429306b37a", + "metadata": {}, + "outputs": [], + "source": [ + "def get_zeta(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.ZETA_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.ZETA_I)\n", + "\n", + "def get_S(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.S_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.S_I)\n", + "\n", + "def get_Pzeta(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.PZETA_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.PZETA_I)\n", + "\n", + "def get_PS(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.PS_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.PS_I)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "09c12f7e-052d-4d30-b3aa-e8555e9c2497", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1min 36s, sys: 109 ms, total: 1min 36s\n", + "Wall time: 1min 37s\n" + ] + } + ], + "source": [ + "%%time\n", + "\n", + "def spec_params(Omegars = 1.0e-5, w = 1.0e-3, E0 = 1.0):\n", + " cosmo.props.w = w\n", + " cosmo.props.Omegar = E0 * Omegars\n", + " cosmo.props.Omegaw = E0 * (1.0 - Omegars)\n", + " \n", + " pert = Nc.HIPertTwoFluids.new()\n", + " pert.props.reltol = 1.0e-9\n", + " \n", + " spec1 = pert.compute_zeta_spectrum(cosmo, 1, -cosmo.abs_alpha(1.0e-14), -1.0, 1.0e-3, 1.0e14, 100)\n", + " spec2 = pert.compute_zeta_spectrum(cosmo, 2, -cosmo.abs_alpha(1.0e-14), -1.0, 1.0e-3, 1.0e14, 100)\n", + "\n", + " return spec1, spec2\n", + "\n", + "specs1 = []\n", + "specs2 = []\n", + "for Omegars in np.geomspace(1.0e-2, 1.0e-8, 10):\n", + "#for E0 in np.geomspace(1.0e-1, 1.0e1, 10):\n", + " \n", + " spec1, spec2 = spec_params(Omegars, 1.0e-5, 1.0)\n", + " specs1.append(spec1)\n", + " specs2.append(spec2)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "476f9a4d-2dd3-4dbe-87fd-012d513dd66d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "134.57836099164655 3.000000006559785\n", + "141.52141095439333 2.0000300099855415\n", + "134.57836114168347 3.000000000960305\n", + "142.2968566197709 2.0000299868417066\n", + "134.57836097984554 3.00000000632813\n", + "143.06610105865937 2.00002997116096\n", + "134.57836014857665 3.0000000340371296\n", + "143.83401935805443 2.000029878833156\n", + "134.57835645181956 3.000000157285378\n", + "144.6016525115409 2.0000297711644537\n", + "134.57834224436107 3.000000630514608\n", + "145.36922825485252 2.00002952780053\n", + "134.57831375726963 3.000001575271915\n", + "146.13680167873076 2.000028915218776\n", + "134.57831642529098 3.000001467599617\n", + "146.9043920037454 2.000027652723656\n", + "134.5783181026893 3.000001390309717\n", + "147.67202561358476 2.0000249393415572\n", + "134.57832747686788 3.000001051688091\n", + "148.43975348446267 2.0000191058865715\n" + ] + }, + { + "data": { + 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,1,1)\n", + "\n", + "for spec1, spec2, Omegar in zip(specs1, specs2, np.geomspace(1.0e-2, 1.0e-8, 10)):\n", + "\n", + " lnk_a1 = np.array(spec1.peek_xv().dup_array())\n", + " lnPk_a1 = np.array(spec1.peek_yv().dup_array())\n", + " \n", + " lnk_a2 = np.array(spec2.peek_xv().dup_array())\n", + " lnPk_a2 = np.array(spec2.peek_yv().dup_array())\n", + " \n", + " b1, a1 = np.polyfit(lnk_a1[-20:], lnPk_a1[-20:], 1)\n", + " print(a1, b1 + 1)\n", + " \n", + " b2, a2 = np.polyfit(lnk_a2[-20:], lnPk_a2[-20:], 1)\n", + " print(a2, b2 + 1)\n", + " \n", + " #ax1.plot(np.exp(lnk_a1), np.exp(lnPk_a1), label=r'$k^3|\\zeta_1|^2$')\n", + " #ax1.plot(np.exp(lnk_a1), np.exp(a1 + b1 * lnk_a1), label=r'Poly: $k^3|\\zeta_1|^2$')\n", + " \n", + " #ax1.plot(np.exp(lnk_a2), np.exp(lnPk_a2), label=r'$k^3|\\zeta_2|^2$')\n", + " #ax1.plot(np.exp(lnk_a2), np.exp(a2 + b2 * lnk_a2), label=r'Poly: $k^3|\\zeta_2|^2$')\n", + " \n", + " ax1.plot(np.exp(lnk_a2)*Omegar**(1/2), (np.exp(lnPk_a2) + np.exp([spec1.eval(lnk) for lnk in lnk_a2]))*Omegar, label=r'$k^3|\\zeta|^2$')\n", + " #ax1.plot(np.exp(lnk_a2)*E0**(-1/2), (np.exp(lnPk_a2) + np.exp([spec1.eval(lnk) for lnk in lnk_a2]))*E0**(-1), label=r'$k^3|\\zeta|^2$')\n", + " #ax1.plot(np.exp(lnk_a2), (np.exp(lnPk_a2) + np.exp([spec1.eval(lnk) for lnk in lnk_a2])), label=r'$k^3|\\zeta|^2$')\n", + "\n", + "ax1.set_xscale('log')\n", + "ax1.set_yscale('log')\n", + "ax1.set_xlabel(r'$k$')\n", + "ax1.legend()\n", + "\n", + "pass\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "id": "1a554573-e2b6-4657-9faa-cf2a3d158a0d", + "metadata": {}, + "outputs": [], + "source": [ + "from pysr import PySRRegressor\n", + "\n", + "model = PySRRegressor(\n", + " niterations=300, # < Increase me for better results\n", + " binary_operators=[\"+\", \"-\", \"*\", \"/\"],\n", + " unary_operators=[\n", + " \"tanh\", \n", + " ],\n", + " # ^ Define operator for SymPy as well\n", + " loss=\"loss(prediction, target) = (prediction - target)^2\",\n", + " # ^ Custom loss function (julia syntax)\n", + " populations = 60,\n", + ")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "id": "b6db60c6-74da-4d92-8b95-28ad8cf777a2", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/sandro/.local/lib/python3.11/site-packages/pysr/sr.py:1281: UserWarning: Note: it looks like you are running in Jupyter. The progress bar will be turned off.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Expressions evaluated per second: 5.940e+05\n", + "Head worker occupation: 11.2%\n", + "Progress: 1186 / 18000 total iterations (6.589%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39161 * x₀) - -184.54)\n", + "7 2.219e+01 1.490e-07 y = (184.54 + (-0.19581 * (x₀ + x₀)))\n", + "9 2.212e+01 1.662e-03 y = (((785.47 / (-2005.8 - x₀)) * x₀) - -184.54)\n", + "10 8.285e+00 9.819e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", + "12 8.184e+00 6.158e-03 y = (179.54 + (tanh(((2.3223 / 0.182) - x₀) * 0.68639) / 0.167...\n", + " 4))\n", + "13 8.178e+00 7.094e-04 y = (179.54 + (tanh(((2.3223 / 0.182) - x₀) * 0.68639) / tanh(...\n", + " 0.1674)))\n", + "14 8.065e+00 1.398e-02 y = ((179.54 + (tanh((2.1379 / 0.1674) - x₀) / 0.1674)) - (-0....\n", + " 030648 * x₀))\n", + "15 8.065e+00 1.907e-06 y = ((179.54 + (tanh((2.1379 / 0.1674) - x₀) / 0.1674)) - (tan...\n", + " h(-0.030648) * x₀))\n", + "16 7.925e+00 1.742e-02 y = (((179.54 + (tanh((2.1379 / 0.1674) - x₀) / 0.1674)) - (-0...\n", + " .030648 * x₀)) - 0.32827)\n", + "18 7.536e+00 2.518e-02 y = ((179.56 + (0.1674 * x₀)) + ((tanh(((2.5389 / 0.182) + -1....\n", + " 4805) - x₀) - 0.28773) / 0.15))\n", + "19 7.437e+00 1.326e-02 y = ((179.56 + (0.1674 * x₀)) + ((tanh(((2.5389 / 0.182) + -1....\n", + " 4805) - x₀) - 0.28773) / tanh(0.15)))\n", + "20 7.237e+00 2.720e-02 y = ((179.56 + ((0.182 * 0.69808) * x₀)) + ((tanh(((2.5389 / 0...\n", + " .182) + -1.332) - x₀) - 0.28773) / 0.15))\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.450e+05\n", + "Head worker occupation: 9.4%\n", + "Progress: 2234 / 18000 total iterations (12.411%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39161 * x₀) - -184.54)\n", + "7 2.219e+01 3.278e-07 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 1.673e+01 2.825e-01 y = ((x₀ * tanh(-17.291 / x₀)) - -189.25)\n", + "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", + "12 8.172e+00 6.875e-03 y = (179.58 + (tanh(((2.654 / 0.20935) - x₀) / 1.495) / 0.1650...\n", + " 5))\n", + "14 7.874e+00 1.856e-02 y = ((178.94 + (tanh((2.1667 / 0.17141) - x₀) / 0.12876)) + (0...\n", + " .12876 * x₀))\n", + "15 7.869e+00 6.215e-04 y = (178.94 + ((tanh((2.1667 / 0.17141) - x₀) / 0.12876) + (ta...\n", + " nh(0.12876) * x₀)))\n", + "16 6.322e+00 2.190e-01 y = (178.94 + (((tanh((2.1888 / 0.17141) - x₀) + -0.22259) / 0...\n", + " .12876) + (0.19232 * x₀)))\n", + "17 6.305e+00 2.673e-03 y = (178.94 + (((tanh((2.1888 / 0.17141) - x₀) + -0.22259) / t...\n", + " anh(0.12876)) + (0.19232 * x₀)))\n", + "18 5.812e+00 8.138e-02 y = (178.94 + (((tanh(((2.1667 / 0.17141) - x₀) / 1.9154) + -0...\n", + " .22259) / 0.12876) + (0.19232 * x₀)))\n", + "19 5.778e+00 5.904e-03 y = (178.94 + (((tanh(((2.1667 / 0.17141) - x₀) / 1.9154) + -0...\n", + " .22259) / tanh(0.12876)) + (0.19232 * x₀)))\n", + "20 5.747e+00 5.301e-03 y = (178.94 + (((tanh(((2.1667 / 0.17141) - x₀) / 1.9154) + -0...\n", + " .22259) / tanh(tanh(0.12876))) + (0.19232 * x₀)))\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.280e+05\n", + "Head worker occupation: 9.2%\n", + "Progress: 3322 / 18000 total iterations (18.456%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39161 * x₀) - -184.54)\n", + "7 2.219e+01 3.278e-07 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 1.673e+01 2.825e-01 y = ((x₀ * tanh(-17.291 / x₀)) - -189.25)\n", + "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", + "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", + " 503))\n", + "14 7.729e+00 2.786e-02 y = ((tanh((((-17.291 / 0.47296) + x₀) * 1.839) / x₀) * x₀) - ...\n", + " -189.25)\n", + "16 6.315e+00 1.011e-01 y = (178.94 + (((tanh((2.1888 / 0.17141) - x₀) + -0.228) / 0.1...\n", + " 2876) + (0.19232 * x₀)))\n", + "17 4.538e+00 3.304e-01 y = (178.94 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17141) ...\n", + " + (0.19232 * x₀)) / 0.17141))\n", + "18 4.437e+00 2.258e-02 y = (178.94 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17141) ...\n", + " + (0.19232 * x₀)) / tanh(0.17141)))\n", + "19 3.530e+00 2.287e-01 y = (178.94 + ((tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17141)...\n", + " + (0.19232 * x₀)) / 0.17141) * 1.2226))\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.470e+05\n", + "Head worker occupation: 10.1%\n", + "Progress: 4630 / 18000 total iterations (25.722%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = (184.54 + (-0.39161 * x₀))\n", + "6 2.219e+01 -0.000e+00 y = (184.54 + (tanh(-0.41372) * x₀))\n", + "7 2.219e+01 4.172e-07 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 1.673e+01 2.825e-01 y = ((x₀ * tanh(-17.291 / x₀)) - -189.25)\n", + "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", + "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", + " 503))\n", + "14 7.464e+00 4.531e-02 y = ((tanh((((-17.291 / 0.47296) + x₀) / 0.58405) / x₀) * x₀) ...\n", + " - -189.25)\n", + "16 6.313e+00 8.375e-02 y = (178.94 + (((tanh((2.1888 / 0.17141) - x₀) / 0.12876) + (0...\n", + " .19232 * x₀)) - 1.7868))\n", + "17 3.418e+00 6.136e-01 y = (178.84 + (tanh((tanh((2.1699 / 0.17585) - x₀) / 0.17704) ...\n", + " + (0.1873 * x₀)) / 0.14429))\n", + "18 3.335e+00 2.440e-02 y = (178.84 + (tanh((tanh((2.1699 / tanh(0.17585)) - x₀) / 0.1...\n", + " 7704) + (0.1873 * x₀)) / 0.14429))\n", + "19 2.429e+00 3.170e-01 y = ((178.94 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.19605)...\n", + " + (0.17757 * x₀)) / 0.1319)) + -1.2866)\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.380e+05\n", + "Head worker occupation: 10.0%\n", + "Progress: 5759 / 18000 total iterations (31.994%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = (184.54 + (-0.39161 * x₀))\n", + "6 2.219e+01 4.172e-07 y = (184.54 + (tanh(-0.41372) * x₀))\n", + "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 1.673e+01 2.825e-01 y = ((x₀ * tanh(-17.291 / x₀)) - -189.25)\n", + "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", + "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", + " 503))\n", + "14 7.155e+00 6.646e-02 y = ((tanh((((-17.294 / 0.48751) + x₀) / 0.50115) / x₀) * x₀) ...\n", + " - -189.79)\n", + "16 6.312e+00 6.264e-02 y = (178.94 + (((tanh((2.3223 / 0.182) - x₀) / 0.12876) + (0.1...\n", + " 9232 * x₀)) - 1.7868))\n", + "17 3.350e+00 6.335e-01 y = (178.84 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17704) ...\n", + " + (0.1873 * x₀)) / 0.14429))\n", + "18 3.324e+00 7.797e-03 y = (178.84 + (tanh((tanh((2.3223 / 0.1873) - x₀) / tanh(0.182...\n", + " )) + (0.1873 * x₀)) / 0.14429))\n", + "19 2.418e+00 3.181e-01 y = ((178.94 + -1.2737) + (tanh((tanh((2.1888 / 0.17141) - x₀)...\n", + " / 0.1969) + (0.17757 * x₀)) / 0.1319))\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.570e+05\n", + "Head worker occupation: 9.9%\n", + "Progress: 7012 / 18000 total iterations (38.956%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = (184.54 + (-0.39161 * x₀))\n", + "6 2.219e+01 4.172e-07 y = (184.54 + (tanh(-0.41372) * x₀))\n", + "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 1.673e+01 2.825e-01 y = ((tanh(-17.292 / x₀) * x₀) - -189.25)\n", + "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", + "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", + " 503))\n", + "14 7.155e+00 6.646e-02 y = ((tanh((((-17.294 / 0.48751) + x₀) / 0.50115) / x₀) * x₀) ...\n", + " - -189.79)\n", + "16 6.312e+00 6.264e-02 y = (178.94 + (((tanh((2.3223 / 0.182) - x₀) / 0.12876) + (0.1...\n", + " 9232 * x₀)) - 1.7868))\n", + "17 3.350e+00 6.335e-01 y = (178.84 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17704) ...\n", + " + (0.1873 * x₀)) / 0.14429))\n", + "18 3.324e+00 7.797e-03 y = (178.84 + (tanh((tanh((2.3223 / 0.1873) - x₀) / tanh(0.182...\n", + " )) + (0.1873 * x₀)) / 0.14429))\n", + "19 2.418e+00 3.184e-01 y = (178.94 + ((tanh((tanh((2.1888 / 0.17141) - x₀) / 0.1969) ...\n", + " + (0.17757 * x₀)) / 0.1319) - 1.285))\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.710e+05\n", + "Head worker occupation: 10.8%\n", + "Progress: 8207 / 18000 total iterations (45.594%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39155 * x₀) + 184.54)\n", + "6 2.219e+01 1.192e-07 y = (184.54 + (tanh(-0.41372) * x₀))\n", + "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 1.673e+01 2.825e-01 y = ((tanh(-17.292 / x₀) * x₀) - -189.25)\n", + "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", + "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", + " 503))\n", + "14 7.155e+00 6.646e-02 y = ((tanh((((-17.294 / 0.48751) + x₀) / 0.50115) / x₀) * x₀) ...\n", + " - -189.79)\n", + "16 6.312e+00 6.264e-02 y = (178.94 + (((tanh((2.3223 / 0.182) - x₀) / 0.12876) + (0.1...\n", + " 9232 * x₀)) - 1.7868))\n", + "17 3.350e+00 6.335e-01 y = (178.84 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17704) ...\n", + " + (0.1873 * x₀)) / 0.14429))\n", + "18 3.324e+00 7.797e-03 y = (178.84 + (tanh((tanh((2.3223 / 0.1873) - x₀) / tanh(0.182...\n", + " )) + (0.1873 * x₀)) / 0.14429))\n", + "19 2.417e+00 3.187e-01 y = (178.94 + ((tanh((tanh((2.1888 / 0.17141) - x₀) / 0.1969) ...\n", + " + (0.17757 * x₀)) / 0.1319) - 1.3127))\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.600e+05\n", + "Head worker occupation: 11.4%\n", + "Progress: 9399 / 18000 total iterations (52.217%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", + "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 1.673e+01 2.825e-01 y = ((tanh(-17.292 / x₀) * x₀) - -189.25)\n", + "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", + "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", + " 503))\n", + "14 7.155e+00 6.646e-02 y = ((tanh((((-17.294 / 0.48751) + x₀) / 0.50115) / x₀) * x₀) ...\n", + " - -189.79)\n", + "16 6.312e+00 6.264e-02 y = (178.94 + (((tanh((2.3223 / 0.182) - x₀) / 0.12876) + (0.1...\n", + " 9232 * x₀)) - 1.7868))\n", + "17 3.332e+00 6.389e-01 y = (178.84 + (tanh((tanh((2.3223 / 0.182) - x₀) / 0.18279) + ...\n", + " (0.18279 * x₀)) / 0.14429))\n", + "18 3.324e+00 2.539e-03 y = (178.84 + (tanh((tanh((2.3223 / 0.182) - x₀) / 0.18279) + ...\n", + " (0.18279 * x₀)) / tanh(0.14429)))\n", + "19 2.417e+00 3.186e-01 y = (178.94 + ((tanh((tanh((2.1888 / 0.17141) - x₀) / 0.1969) ...\n", + " + (0.17757 * x₀)) / 0.1319) - 1.3127))\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.620e+05\n", + "Head worker occupation: 10.8%\n", + "Progress: 10588 / 18000 total iterations (58.822%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", + "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 8.285e+00 9.852e-01 y = (179.55 + (tanh(12.762 - x₀) / 0.16742))\n", + "10 8.172e+00 6.878e-03 y = (179.58 + (tanh((12.672 - x₀) / 1.4917) / 0.16504))\n", + "14 7.155e+00 3.323e-02 y = ((tanh((((-17.294 / 0.48751) + x₀) / 0.50115) / x₀) * x₀) ...\n", + " - -189.79)\n", + "16 3.943e+00 2.979e-01 y = (178.94 + (tanh((tanh(12.672 - x₀) / 0.1969) + (tanh(0.177...\n", + " 57) * x₀)) / 0.1319))\n", + "17 2.512e+00 4.510e-01 y = (178.94 + ((tanh((tanh(12.672 - x₀) / 0.1969) + (0.17757 *...\n", + " x₀)) / 0.1319) - 1.3127))\n", + "19 2.417e+00 1.924e-02 y = (178.94 + ((tanh((tanh((2.1888 / 0.17141) - x₀) / 0.1969) ...\n", + " + (0.17757 * x₀)) / 0.1319) - 1.3127))\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.530e+05\n", + "Head worker occupation: 11.5%\n", + "Progress: 11751 / 18000 total iterations (65.283%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", + "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", + "10 8.172e+00 6.878e-03 y = (179.58 + (tanh((12.672 - x₀) / 1.4917) / 0.16504))\n", + "12 7.346e+00 5.326e-02 y = ((178.94 + (tanh(12.672 - x₀) / 0.14744)) - (-0.086907 * x...\n", + " ₀))\n", + "13 7.340e+00 8.773e-04 y = ((178.94 + (tanh(12.672 - x₀) / tanh(0.14744))) - (-0.0869...\n", + " 07 * x₀))\n", + "14 6.035e+00 1.958e-01 y = ((176.37 + (tanh(12.765 - x₀) / 0.11286)) - (0.27904 * (1....\n", + " 2977 - x₀)))\n", + "15 3.682e+00 4.942e-01 y = (178.94 + (tanh((tanh(12.377 - x₀) / 0.17757) + (0.18953 *...\n", + " x₀)) / 0.1319))\n", + "17 2.417e+00 2.104e-01 y = (178.94 + ((tanh((tanh(12.762 - x₀) / 0.19774) + (0.17757 ...\n", + " * x₀)) / 0.1319) - 1.3155))\n", + "19 1.677e+00 1.826e-01 y = (178.94 + ((tanh((tanh((12.377 - x₀) * 0.3928) / 0.19774) ...\n", + " + (0.17757 * x₀)) / 0.1319) - 1.7223))\n", + "20 1.655e+00 1.361e-02 y = (178.94 + ((tanh((tanh((12.377 - x₀) * 0.3928) / 0.19774) ...\n", + " + (0.17757 * x₀)) / tanh(0.1319)) - 1.7223))\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.560e+05\n", + "Head worker occupation: 11.7%\n", + "Progress: 12940 / 18000 total iterations (71.889%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", + "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", + "10 8.172e+00 6.878e-03 y = (179.58 + (tanh((12.672 - x₀) / 1.4917) / 0.16504))\n", + "12 7.345e+00 5.336e-02 y = ((178.94 + (x₀ / 12.672)) + (tanh(12.672 - x₀) / 0.14744))\n", + "13 7.340e+00 6.743e-04 y = ((178.94 + (tanh(12.672 - x₀) / tanh(0.14744))) - (-0.0869...\n", + " 07 * x₀))\n", + "14 6.035e+00 1.958e-01 y = ((176.37 + (tanh(12.765 - x₀) / 0.11286)) - (0.27904 * (1....\n", + " 2977 - x₀)))\n", + "15 3.525e+00 5.378e-01 y = (178.94 + (tanh((tanh(12.377 - x₀) / 0.18816) + (0.17757 *...\n", + " x₀)) / 0.14744))\n", + "16 3.505e+00 5.538e-03 y = (178.94 + (tanh((tanh(12.377 - x₀) / 0.18816) + (0.17757 *...\n", + " x₀)) / tanh(0.14744)))\n", + "17 2.405e+00 3.765e-01 y = (178.94 + ((tanh((tanh(12.785 - x₀) / 0.19774) + (0.17757 ...\n", + " * x₀)) / 0.1319) - 1.3155))\n", + "19 1.649e+00 1.889e-01 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", + " + (0.17757 * x₀)) / 0.1319)) - 1.5548)\n", + "20 1.630e+00 1.115e-02 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", + " + (0.17757 * x₀)) / tanh(0.1319))) - 1.5548)\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.420e+05\n", + "Head worker occupation: 11.6%\n", + "Progress: 14054 / 18000 total iterations (78.078%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", + "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", + "10 8.172e+00 6.878e-03 y = (179.58 + (tanh((12.674 - x₀) / 1.4857) / 0.16488))\n", + "12 7.342e+00 5.352e-02 y = (178.94 + ((tanh(12.672 - x₀) / 0.14744) + (x₀ * 0.084886)...\n", + " ))\n", + "13 7.338e+00 6.113e-04 y = (178.94 + ((tanh(12.672 - x₀) / tanh(0.14744)) + (x₀ * 0.0...\n", + " 84886)))\n", + "14 6.035e+00 1.955e-01 y = ((176.37 + (tanh(12.765 - x₀) / 0.11286)) - (0.27904 * (1....\n", + " 3155 - x₀)))\n", + "15 3.525e+00 5.378e-01 y = (178.94 + (tanh((tanh(12.377 - x₀) / 0.18816) + (0.17757 *...\n", + " x₀)) / 0.14744))\n", + "16 3.505e+00 5.538e-03 y = (178.94 + (tanh((tanh(12.377 - x₀) / 0.18816) + (0.17757 *...\n", + " x₀)) / tanh(0.14744)))\n", + "17 2.404e+00 3.770e-01 y = ((178.94 + -1.3794) + (tanh((tanh(12.785 - x₀) / 0.19774) ...\n", + " + (0.17757 * x₀)) / 0.1319))\n", + "18 2.404e+00 2.361e-04 y = ((178.94 + -1.3794) + (tanh((tanh(12.785 - x₀) / 0.19774) ...\n", + " + (0.17757 * x₀)) / tanh(0.13234)))\n", + "19 1.649e+00 3.770e-01 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", + " + (0.17757 * x₀)) / 0.1319)) - 1.5548)\n", + "20 1.630e+00 1.115e-02 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", + " + (0.17757 * x₀)) / tanh(0.1319))) - 1.5548)\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.390e+05\n", + "Head worker occupation: 11.6%\n", + "Progress: 15222 / 18000 total iterations (84.567%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", + "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", + "10 8.172e+00 6.879e-03 y = (179.58 + (tanh((12.673 - x₀) * 0.67247) / 0.16498))\n", + "12 6.102e+00 1.460e-01 y = ((176.37 + (tanh(12.765 - x₀) / 0.11286)) + (x₀ * 0.25852)...\n", + " )\n", + "14 5.293e+00 7.119e-02 y = ((176.37 + (tanh((12.765 - x₀) * 0.40616) / 0.11286)) + (x...\n", + " ₀ * 0.27904))\n", + "15 3.227e+00 4.947e-01 y = (178.62 + (tanh((tanh(12.785 - x₀) / 0.17757) + (0.18874 *...\n", + " x₀)) / 0.1319))\n", + "17 2.404e+00 1.472e-01 y = ((178.94 + -1.3794) + (tanh((tanh(12.785 - x₀) / 0.19774) ...\n", + " + (0.17757 * x₀)) / 0.1319))\n", + "18 2.404e+00 2.361e-04 y = ((178.94 + -1.3794) + (tanh((tanh(12.785 - x₀) / 0.19774) ...\n", + " + (0.17757 * x₀)) / tanh(0.13234)))\n", + "19 1.607e+00 4.025e-01 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", + " + (0.17757 * x₀)) / 0.12996)) - 1.5548)\n", + "20 1.596e+00 6.797e-03 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", + " + (0.17757 * x₀)) / tanh(0.12996))) - 1.5548)\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.390e+05\n", + "Head worker occupation: 12.2%\n", + "Progress: 16401 / 18000 total iterations (91.117%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", + "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", + "10 8.172e+00 6.879e-03 y = (179.58 + (tanh((12.673 - x₀) * 0.67247) / 0.16498))\n", + "12 4.428e+00 3.064e-01 y = (175.18 + (tanh(14.175 - x₀) * (11.229 - (0.40177 * x₀))))\n", + "14 4.195e+00 2.693e-02 y = (175.18 + ((tanh(14.175 - x₀) - 0.056134) * (11" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "[ Info: Started!\n" + ] + }, + { + "data": { + "text/html": [ + "
PySRRegressor.equations_ = [\n",
+       "\t    pick         score                                           equation  \\\n",
+       "\t0         0.000000e+00                                           179.5845   \n",
+       "\t1         3.209774e-02                             (180.22537 - tanh(x0))   \n",
+       "\t2         5.457020e-01                  ((-0.39166483 * x0) - -184.54474)   \n",
+       "\t3         4.506454e-08             ((0.60839283 * x0) - (x0 - 184.54402))   \n",
+       "\t4         9.851865e-01     (179.55518 + (tanh(12.761697 - x0) * 5.97393))   \n",
+       "\t5         6.878725e-03  (179.58165 + (tanh((12.67312 - x0) * 0.6724680...   \n",
+       "\t6         5.337357e-02  (171.31406 + (tanh(tanh(15.395343 - x0)) * (21...   \n",
+       "\t7         5.594758e-01  (175.17535 + (tanh(14.175411 - x0) * (11.22903...   \n",
+       "\t8         3.709056e-02  (169.95616 + (tanh(15.848622 - x0) * (20.68860...   \n",
+       "\t9         4.994208e-01  (172.24475 + (tanh(15.065756 - x0) * (17.05391...   \n",
+       "\t10        8.544651e-02  (173.39519 + (tanh(14.70492 - x0) * (15.266392...   \n",
+       "\t11  >>>>  8.171071e-01  (172.24475 + (tanh(15.010006 - x0) * (15.01000...   \n",
+       "\t12        1.408766e-02  (172.24475 + (tanh(15.065757 - x0) * (15.06575...   \n",
+       "\t13        1.660253e-01  (172.24475 + (tanh(15.065757 - x0) * (15.06575...   \n",
+       "\t14        1.504349e-01  (172.24477 + (tanh((15.149901 - x0) * 0.365321...   \n",
+       "\t\n",
+       "\t         loss  complexity  \n",
+       "\t0   42.167710           1  \n",
+       "\t1   38.296616           4  \n",
+       "\t2   22.190395           5  \n",
+       "\t3   22.190393           7  \n",
+       "\t4    8.285218           8  \n",
+       "\t5    8.172015          10  \n",
+       "\t6    7.747281          11  \n",
+       "\t7    4.427638          12  \n",
+       "\t8    4.266422          13  \n",
+       "\t9    2.589215          14  \n",
+       "\t10   2.377164          15  \n",
+       "\t11   1.050012          16  \n",
+       "\t12   1.035323          17  \n",
+       "\t13   0.876944          18  \n",
+       "\t14   0.754465          19  \n",
+       "]
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "PySRRegressor.equations_ = [\n", + "\t pick score equation \\\n", + "\t0 0.000000e+00 179.5845 \n", + "\t1 3.209774e-02 (180.22537 - tanh(x0)) \n", + "\t2 5.457020e-01 ((-0.39166483 * x0) - -184.54474) \n", + "\t3 4.506454e-08 ((0.60839283 * x0) - (x0 - 184.54402)) \n", + "\t4 9.851865e-01 (179.55518 + (tanh(12.761697 - x0) * 5.97393)) \n", + "\t5 6.878725e-03 (179.58165 + (tanh((12.67312 - x0) * 0.6724680... \n", + "\t6 5.337357e-02 (171.31406 + (tanh(tanh(15.395343 - x0)) * (21... \n", + "\t7 5.594758e-01 (175.17535 + (tanh(14.175411 - x0) * (11.22903... \n", + "\t8 3.709056e-02 (169.95616 + (tanh(15.848622 - x0) * (20.68860... \n", + "\t9 4.994208e-01 (172.24475 + (tanh(15.065756 - x0) * (17.05391... \n", + "\t10 8.544651e-02 (173.39519 + (tanh(14.70492 - x0) * (15.266392... \n", + "\t11 >>>> 8.171071e-01 (172.24475 + (tanh(15.010006 - x0) * (15.01000... \n", + "\t12 1.408766e-02 (172.24475 + (tanh(15.065757 - x0) * (15.06575... \n", + "\t13 1.660253e-01 (172.24475 + (tanh(15.065757 - x0) * (15.06575... \n", + "\t14 1.504349e-01 (172.24477 + (tanh((15.149901 - x0) * 0.365321... \n", + "\t\n", + "\t loss complexity \n", + "\t0 42.167710 1 \n", + "\t1 38.296616 4 \n", + "\t2 22.190395 5 \n", + "\t3 22.190393 7 \n", + "\t4 8.285218 8 \n", + "\t5 8.172015 10 \n", + "\t6 7.747281 11 \n", + "\t7 4.427638 12 \n", + "\t8 4.266422 13 \n", + "\t9 2.589215 14 \n", + "\t10 2.377164 15 \n", + "\t11 1.050012 16 \n", + "\t12 1.035323 17 \n", + "\t13 0.876944 18 \n", + "\t14 0.754465 19 \n", + "]" + ] + }, + "execution_count": 84, + "metadata": {}, + "output_type": "execute_result" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + ".229 - (0.4...\n", + " 0177 * x₀))))\n", + "15 2.377e+00 5.680e-01 y = (173.4 + (tanh(14.702 - x₀) * (15.274 - (tanh(tanh(tanh(x₀...\n", + " ))) * x₀))))\n", + "17 2.352e+00 5.418e-03 y = (173.4 + (tanh(14.702 - x₀) * (15.274 - (tanh(tanh(tanh(x₀...\n", + " + x₀))) * x₀))))\n", + "19 1.607e+00 1.903e-01 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", + " + (0.17757 * x₀)) / 0.12996)) - 1.5548)\n", + "20 1.596e+00 6.797e-03 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", + " + (0.17757 * x₀)) / tanh(0.12996))) - 1.5548)\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n", + "\n", + "Expressions evaluated per second: 5.250e+05\n", + "Head worker occupation: 12.6%\n", + "Progress: 17491 / 18000 total iterations (97.172%)\n", + "====================================================================================================\n", + "Hall of Fame:\n", + "---------------------------------------------------------------------------------------------------\n", + "Complexity Loss Score Equation\n", + "1 4.217e+01 1.594e+01 y = 179.58\n", + "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", + "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", + "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", + "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", + "10 8.172e+00 6.879e-03 y = (179.58 + (tanh((12.673 - x₀) * 0.67247) / 0.16498))\n", + "11 7.747e+00 5.337e-02 y = (171.31 + (tanh(tanh(15.395 - x₀)) * (21.191 - x₀)))\n", + "12 4.428e+00 5.595e-01 y = (175.18 + (tanh(14.175 - x₀) * (11.229 - (0.40177 * x₀))))\n", + "13 4.266e+00 3.709e-02 y = (169.96 + (tanh(15.849 - x₀) * (20.689 - (tanh(x₀) * x₀)))...\n", + " )\n", + "14 2.589e+00 4.994e-01 y = (172.24 + (tanh(15.066 - x₀) * (17.054 - (tanh(tanh(x₀)) *...\n", + " x₀))))\n", + "15 2.377e+00 8.545e-02 y = (173.4 + (tanh(14.705 - x₀) * (15.266 - (tanh(tanh(tanh(x₀...\n", + " ))) * x₀))))\n", + "16 1.774e+00 2.926e-01 y = (172.24 + (tanh(15.15 - x₀) * (15.15 - (tanh(tanh(x₀ / 15....\n", + " 15)) * x₀))))\n", + "17 1.529e+00 1.488e-01 y = (172.24 + (tanh(15.01 - x₀) * (15.15 - (tanh(x₀ / (15.15 +...\n", + " 15.15)) * x₀))))\n", + "18 1.073e+00 3.538e-01 y = (172.24 + (tanh(15.15 - x₀) * (15.15 - (tanh(tanh(x₀ / (15...\n", + " .15 / 0.752))) * x₀))))\n", + "19 9.611e-01 1.105e-01 y = (172.24 + (tanh((15.01 - x₀) * 0.6549) * (15.15 - (tanh(x₀...\n", + " / (15.15 + 15.15)) * x₀))))\n", + "20 8.244e-01 1.534e-01 y = (172.24 + (tanh((15.15 - x₀) * 0.56801) * (15.15 - (tanh(t...\n", + " anh((0.73638 * x₀) / 15.15)) * x₀))))\n", + "---------------------------------------------------------------------------------------------------\n", + "====================================================================================================\n", + "Press 'q' and then to stop execution early.\n" + ] + } + ], + "source": [ + "model.fit(lnk_a2.reshape(-1,1), lnPk_a2)" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "id": "96633b71-f2b6-4a05-9abd-a54310418289", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
PySRRegressor.equations_ = [\n",
+       "\t    pick         score                                           equation  \\\n",
+       "\t0         0.000000e+00                                           179.5845   \n",
+       "\t1         3.209774e-02                             (180.22537 - tanh(x0))   \n",
+       "\t2         5.457020e-01                  ((-0.39166483 * x0) - -184.54474)   \n",
+       "\t3         4.506454e-08             ((0.60839283 * x0) - (x0 - 184.54402))   \n",
+       "\t4         9.851865e-01     (179.55518 + (tanh(12.761697 - x0) * 5.97393))   \n",
+       "\t5         6.878725e-03  (179.58165 + (tanh((12.67312 - x0) * 0.6724680...   \n",
+       "\t6         5.337357e-02  (171.31406 + (tanh(tanh(15.395343 - x0)) * (21...   \n",
+       "\t7         5.594758e-01  (175.17535 + (tanh(14.175411 - x0) * (11.22903...   \n",
+       "\t8         3.709056e-02  (169.95616 + (tanh(15.848622 - x0) * (20.68860...   \n",
+       "\t9         4.994208e-01  (172.24475 + (tanh(15.065756 - x0) * (17.05391...   \n",
+       "\t10        8.544651e-02  (173.39519 + (tanh(14.70492 - x0) * (15.266392...   \n",
+       "\t11  >>>>  8.171071e-01  (172.24475 + (tanh(15.010006 - x0) * (15.01000...   \n",
+       "\t12        1.408766e-02  (172.24475 + (tanh(15.065757 - x0) * (15.06575...   \n",
+       "\t13        1.660253e-01  (172.24475 + (tanh(15.065757 - x0) * (15.06575...   \n",
+       "\t14        1.504349e-01  (172.24477 + (tanh((15.149901 - x0) * 0.365321...   \n",
+       "\t\n",
+       "\t         loss  complexity  \n",
+       "\t0   42.167710           1  \n",
+       "\t1   38.296616           4  \n",
+       "\t2   22.190395           5  \n",
+       "\t3   22.190393           7  \n",
+       "\t4    8.285218           8  \n",
+       "\t5    8.172015          10  \n",
+       "\t6    7.747281          11  \n",
+       "\t7    4.427638          12  \n",
+       "\t8    4.266422          13  \n",
+       "\t9    2.589215          14  \n",
+       "\t10   2.377164          15  \n",
+       "\t11   1.050012          16  \n",
+       "\t12   1.035323          17  \n",
+       "\t13   0.876944          18  \n",
+       "\t14   0.754465          19  \n",
+       "]
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "PySRRegressor.equations_ = [\n", + "\t pick score equation \\\n", + "\t0 0.000000e+00 179.5845 \n", + "\t1 3.209774e-02 (180.22537 - tanh(x0)) \n", + "\t2 5.457020e-01 ((-0.39166483 * x0) - -184.54474) \n", + "\t3 4.506454e-08 ((0.60839283 * x0) - (x0 - 184.54402)) \n", + "\t4 9.851865e-01 (179.55518 + (tanh(12.761697 - x0) * 5.97393)) \n", + "\t5 6.878725e-03 (179.58165 + (tanh((12.67312 - x0) * 0.6724680... \n", + "\t6 5.337357e-02 (171.31406 + (tanh(tanh(15.395343 - x0)) * (21... \n", + "\t7 5.594758e-01 (175.17535 + (tanh(14.175411 - x0) * (11.22903... \n", + "\t8 3.709056e-02 (169.95616 + (tanh(15.848622 - x0) * (20.68860... \n", + "\t9 4.994208e-01 (172.24475 + (tanh(15.065756 - x0) * (17.05391... \n", + "\t10 8.544651e-02 (173.39519 + (tanh(14.70492 - x0) * (15.266392... \n", + "\t11 >>>> 8.171071e-01 (172.24475 + (tanh(15.010006 - x0) * (15.01000... \n", + "\t12 1.408766e-02 (172.24475 + (tanh(15.065757 - x0) * (15.06575... \n", + "\t13 1.660253e-01 (172.24475 + (tanh(15.065757 - x0) * (15.06575... \n", + "\t14 1.504349e-01 (172.24477 + (tanh((15.149901 - x0) * 0.365321... \n", + "\t\n", + "\t loss complexity \n", + "\t0 42.167710 1 \n", + "\t1 38.296616 4 \n", + "\t2 22.190395 5 \n", + "\t3 22.190393 7 \n", + "\t4 8.285218 8 \n", + "\t5 8.172015 10 \n", + "\t6 7.747281 11 \n", + "\t7 4.427638 12 \n", + "\t8 4.266422 13 \n", + "\t9 2.589215 14 \n", + "\t10 2.377164 15 \n", + "\t11 1.050012 16 \n", + "\t12 1.035323 17 \n", + "\t13 0.876944 18 \n", + "\t14 0.754465 19 \n", + "]" + ] + }, + "execution_count": 86, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "id": "c215ccee-6c88-4d55-b3bd-d00071c1507f", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/sandro/.local/lib/python3.11/site-packages/pysr/sr.py:1121: FutureWarning: PySRRegressor.equations is now deprecated. Please use PySRRegressor.equations_ instead.\n", + " warnings.warn(\n" + ] + }, + { + "data": { + "text/plain": [ + "'(172.24475 + (tanh(15.010006 - x0) * (15.010006 - (tanh(tanh(0.051303983 * x0)) * x0))))'" + ] + }, + "execution_count": 87, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.equations.iloc[11]['equation']" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "b73ca8cc-9168-4ecf-bed5-c14f56b1e753", + "metadata": {}, + "outputs": [], + "source": [ + "def integrate_system(k):\n", + " # Defining relative tolerance for integration\n", + " prec = 1.0e-10\n", + " # Ratio potential frequency to define cross time\n", + " cross_size = 1.0e-9\n", + " \n", + " # New perturbations object\n", + " pert1 = Nc.HIPertTwoFluids.new()\n", + " pert2 = Nc.HIPertTwoFluids.new()\n", + " # Setting reltol\n", + " pert1.props.reltol = prec\n", + " pert2.props.reltol = prec\n", + " # Setting k\n", + " pert1.set_mode_k(k)\n", + " pert2.set_mode_k(k)\n", + " \n", + " # Choose an initial condition\n", + " alpha_try = -cosmo.abs_alpha(1.0e-14 * k**2)\n", + " \n", + " # New vector to store initial conditions \n", + " # 8 dimensional (Q_1, Q_2, P_1, P_2), real and imaginary parts\n", + " ci1 = Ncm.Vector.new(8)\n", + " ci2 = Ncm.Vector.new(8)\n", + " \n", + " alphai1 = pert1.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE1MAIN, alpha_try, cross_size)\n", + " alphai2 = pert2.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE2MAIN, alpha_try, cross_size)\n", + " \n", + " # Compute initial conditions at alpha_try store at ci and use normalization factor\n", + " # pi/4\n", + " pert1.get_init_cond_zetaS(cosmo, alphai1, 1, 0.25 * math.pi, ci1)\n", + " pert2.get_init_cond_zetaS(cosmo, alphai2, 2, 0.25 * math.pi, ci2)\n", + " \n", + " # Use the previously computed initial conditions to start the system at alpha_try\n", + " pert1.set_init_cond(cosmo, alphai1, 30, False, ci1)\n", + " pert2.set_init_cond(cosmo, alphai2, 30, False, ci2)\n", + " # print(f\"Setting initial conditions for zeta1 and S1 at {alphai1}\")\n", + " # print(f\"Setting initial conditions for zeta2 and S2 at {alphai2}\")\n", + " \n", + " if alphai2 > alphai1:\n", + " pert1.evolve(cosmo, alphai2)\n", + " ci1, _ = pert1.peek_state(cosmo)\n", + " else:\n", + " pert2.evolve(cosmo, alphai1)\n", + " ci2, _ = pert2.peek_state(cosmo)\n", + " \n", + " alphai = max(alphai1, alphai2)\n", + " \n", + " # Create a array of times to integrate the system over\n", + " alpha_evol = np.linspace(alphai, -1.0e-1, 1000)\n", + " \n", + " # Integrate the system by stepping through alpha_evol using .evolve\n", + " zeta1_a = [get_zeta(ci1)]\n", + " S1_a = [get_S(ci1)]\n", + " Pzeta1_a = [get_Pzeta(ci1)]\n", + " PS1_a = [get_PS(ci1)]\n", + " \n", + " zeta2_a = [get_zeta(ci2)]\n", + " S2_a = [get_S(ci2)]\n", + " Pzeta2_a = [get_Pzeta(ci2)]\n", + " PS2_a = [get_PS(ci2)]\n", + " \n", + " for alpha in tqdm(alpha_evol[1:], desc=\"Time evolution\", position=1, leave=False):\n", + " pert1.evolve(cosmo, alpha)\n", + " pert2.evolve(cosmo, alpha)\n", + " v1, _alphac1 = pert1.peek_state(cosmo)\n", + " v2, _alphac2 = pert2.peek_state(cosmo)\n", + " \n", + " zeta1_a.append(get_zeta(v1))\n", + " S1_a.append(get_S(v1))\n", + " Pzeta1_a.append(get_Pzeta(v1))\n", + " PS1_a.append(get_PS(v1))\n", + " \n", + " zeta2_a.append(get_zeta(v2))\n", + " S2_a.append(get_S(v2))\n", + " Pzeta2_a.append(get_Pzeta(v2))\n", + " PS2_a.append(get_PS(v2))\n", + " \n", + " zeta1 = np.array(zeta1_a)\n", + " S1 = np.array(S1_a)\n", + " Pzeta1 = np.array(Pzeta1_a)\n", + " PS1 = np.array(PS1_a)\n", + " \n", + " zeta2 = np.array(zeta2_a)\n", + " S2 = np.array(S2_a)\n", + " Pzeta2 = np.array(Pzeta2_a)\n", + " PS2 = np.array(PS2_a)\n", + "\n", + " return (alpha_evol, zeta1, S1, Pzeta1, PS1, zeta2, S2, Pzeta2, PS2)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "13668ef8-43cd-4a07-a777-ea5bbdf1dd96", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "Time evolution: 0%| | 0/999 [00:00" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(2,1,1)\n", + "ax2= fig.add_subplot(2,1,2)\n", + "\n", + "ax1.plot(alpha_evol, np.real(zeta1), label=r'$\\mathrm{Re}(\\zeta_1)$')\n", + "ax1.plot(alpha_evol, np.imag(zeta1), label=r'$\\mathrm{Im}(\\zeta_1)$')\n", + "ax1.plot(alpha_evol, np.real(zeta2), label=r'$\\mathrm{Re}(\\zeta_2)$')\n", + "ax1.plot(alpha_evol, np.imag(zeta2), label=r'$\\mathrm{Im}(\\zeta_2)$')\n", + "ax1.set_yscale('symlog')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_evol, np.real(S1), label=r'$\\mathrm{Re}(S_1)$')\n", + "ax2.plot(alpha_evol, np.imag(S1), label=r'$\\mathrm{Im}(S_1)$')\n", + "ax2.plot(alpha_evol, np.real(S2), label=r'$\\mathrm{Re}(S_2)$')\n", + "ax2.plot(alpha_evol, np.imag(S2), label=r'$\\mathrm{Im}(S_2)$')\n", + "ax2.set_yscale('symlog')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "ax2.legend()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "0048f301-a4f1-48a4-9de3-c2a3ef103f59", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(2,1,1)\n", + "ax2= fig.add_subplot(2,1,2)\n", + "\n", + "ax1.plot(alpha_evol, np.abs(zeta1)**2, label=r'$|\\zeta_1|^2$')\n", + "ax1.plot(alpha_evol, np.abs(zeta2)**2, label=r'$|\\zeta_2|^2$')\n", + "ax1.set_yscale('log')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_evol, np.abs(S1)**2, label=r'$|S_1|^2$')\n", + "ax2.plot(alpha_evol, np.abs(S2)**2, label=r'$|S_2|^2$')\n", + "ax2.set_yscale('log')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "d8694a1e-6562-434c-b5da-9d60cdb3de4f", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Mode evolution: 0%| | 0/100 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(2,1,1)\n", + "ax2= fig.add_subplot(2,1,2)\n", + "\n", + "ax1.plot(k_a, k_a**3 * PI_zeta1, label=r'$\\Pi_{\\zeta_1}$')\n", + "ax1.plot(k_a, k_a**3 * PI_zeta2, label=r'$\\Pi_{\\zeta_2}$')\n", + "ax1.set_xscale('log')\n", + "ax1.set_yscale('log')\n", + "ax1.set_xlabel(r'$k$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(k_a, k_a**3 * PI_S1, label=r'$\\Pi_{S_1}$')\n", + "ax2.plot(k_a, k_a**3 * PI_S2, label=r'$\\Pi_{S_2}$')\n", + "ax2.set_xscale('log')\n", + "ax2.set_yscale('log')\n", + "ax2.set_xlabel(r'$k$')\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "818e4ad0-510c-4d31-a2bf-83bde5f04c58", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-0.00017585144466178716\n", + "1.000011999964\n" + ] + } + ], + "source": [ + "print(np.polyfit(np.log(k_a),np.log(k_a**3 * PI_zeta2),1)[0])\n", + "\n", + "print(1.0 + 12.0 * cosmo.props.w / (1.0 + 3.0 *cosmo.props.w))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "6b2523f8", + "metadata": {}, + "outputs": [], + "source": [ + "def test_two_fluids_wkb_mode(mode: int = Nc.HIPertTwoFluidsCross.MODE1SUB, case_f: int = 1, nullr = 1.0, nulli = 1.0) -> None:\n", + " \"\"\"Compute WKB approximation for the two-fluids model.\"\"\"\n", + "\n", + " #\n", + " # New homogeneous and isotropic cosmological model NcHICosmoQGRW\n", + " #\n", + " cosmo = Nc.HICosmoQGRW()\n", + "\n", + " w = 0.00001\n", + " prec = 1.0e-6\n", + " mode_k = 1000\n", + "\n", + " cosmo.props.w = w\n", + " cosmo.props.Omegar = 2.0 * (1.0e-8)\n", + " cosmo.props.Omegaw = 2.0 * (1.0 - 1.0e-8)\n", + " cosmo.props.xb = 1.0e30\n", + " \n", + " pert = Nc.HIPertTwoFluids.new()\n", + "\n", + " pert.props.reltol = prec\n", + " pert.set_mode_k(mode_k)\n", + "\n", + " cross_size = 1.0e-5\n", + " alpha_try = -cosmo.abs_alpha(1.0e-12 * mode_k**2)\n", + " # Chuta tempo incial e depois calcula ele aqui embaixo, dependendo de qual modo é o main\n", + " \n", + " # Pra descobrir se o alpha1 da outra funcao faz sentido, coloca auqi o caso que vc quiser e imprime o tempo calcualdo (ex: mode1main, da um alpha 1.0e-9. Por isso ele deve ter colocado na 2 funçao)\n", + " if mode == Nc.HIPertTwoFluidsCross.MODE1MAIN:\n", + " alphai = pert.get_cross_time(\n", + " cosmo, Nc.HIPertTwoFluidsCross.MODE1MAIN, alpha_try, cross_size\n", + " )\n", + " elif mode == Nc.HIPertTwoFluidsCross.MODE1SUB:\n", + " alphai = pert.get_cross_time(\n", + " cosmo, Nc.HIPertTwoFluidsCross.MODE1SUB, alpha_try, cross_size\n", + " )\n", + " elif mode == Nc.HIPertTwoFluidsCross.MODE2MAIN:\n", + " alphai = pert.get_cross_time(\n", + " cosmo, Nc.HIPertTwoFluidsCross.MODE2MAIN, alpha_try, cross_size\n", + " )\n", + " elif mode == Nc.HIPertTwoFluidsCross.MODE2SUB:\n", + " alphai = pert.get_cross_time(\n", + " cosmo, Nc.HIPertTwoFluidsCross.MODE2SUB, alpha_try, cross_size\n", + " )\n", + " else:\n", + " raise ValueError(\"Invalid mode\")\n", + "\n", + " alphaf = +cosmo.abs_alpha(1.0e20)\n", + "\n", + " print(f\"Mode k = mode_k: {mode_k}\")\n", + "\n", + " pert.set_stiff_solver(True)\n", + "\n", + " alpha_a = []\n", + " gammabar11_a = []\n", + " gammabar22_a = []\n", + " gammabar12_a = []\n", + " taubar12_a = []\n", + " nu1_a = []\n", + " nu2_a = []\n", + "\n", + " for alpha in np.linspace(alphai, alphaf, 10000):\n", + " eom = pert.eom(cosmo, alpha)\n", + " alpha_a.append(alpha)\n", + "\n", + " gammabar11_a.append(math.fabs(eom.gammabar11))\n", + " gammabar22_a.append(math.fabs(eom.gammabar22))\n", + " gammabar12_a.append(math.fabs(eom.gammabar12))\n", + " taubar12_a.append(math.fabs(eom.taubar))\n", + " nu1_a.append(eom.nu1)\n", + " nu2_a.append(eom.nu2)\n", + "\n", + " print(\n", + " f\"# Calculating mode 1, initial time {alphai}, redshift_alpha {cosmo.x_alpha(alphai):8.2e}]: \"\n", + " )\n", + "\n", + " ci = Ncm.Vector.new(8)\n", + "\n", + " pert.get_init_cond_zetaS(cosmo, alphai, case_f, 0.25 * math.pi, ci)\n", + " pert.set_init_cond(cosmo, alphai, 3, False, ci)\n", + "\n", + " Ps_zeta1 = []\n", + " Ps_S1 = []\n", + " Ps_Pzeta1 = []\n", + " Ps_PS1 = []\n", + "\n", + " Ps_zeta1.append(\n", + " math.hypot(\n", + " nullr * ci.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " nulli * ci.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_S1.append(\n", + " math.hypot(\n", + " nullr *ci.get(Nc.HIPertITwoFluidsVars.S_R),\n", + " nulli *ci.get(Nc.HIPertITwoFluidsVars.S_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_Pzeta1.append(\n", + " math.hypot(\n", + " nullr *ci.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " nulli *ci.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_PS1.append(\n", + " math.hypot(\n", + " nullr * ci.get(Nc.HIPertITwoFluidsVars.PS_R),\n", + " nulli * ci.get(Nc.HIPertITwoFluidsVars.PS_I),\n", + " )\n", + " ** 2\n", + " )\n", + "\n", + " for alpha in tqdm(alpha_a[1:]):\n", + " # for alpha in alpha_a[1:]:\n", + " pert.evolve(cosmo, alpha)\n", + " v, _alphac = pert.peek_state(cosmo)\n", + " Ps_zeta1.append(\n", + " math.hypot(\n", + " nullr * v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " nulli * v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_S1.append(\n", + " math.hypot(\n", + " nullr * v.get(Nc.HIPertITwoFluidsVars.S_R),\n", + " nulli * v.get(Nc.HIPertITwoFluidsVars.S_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_Pzeta1.append(\n", + " math.hypot(\n", + " nullr * v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " nulli * v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " )\n", + " Ps_PS1.append(\n", + " math.hypot(\n", + " nullr * v.get(Nc.HIPertITwoFluidsVars.PS_R),\n", + " nulli * v.get(Nc.HIPertITwoFluidsVars.PS_I),\n", + " )\n", + " ** 2\n", + " ) \n", + " plt.plot(alpha_a, Ps_zeta1, label=r\"$P_\\zeta$\")\n", + " plt.plot(alpha_a, Ps_S1, label=r\"$P_Q$\")\n", + " plt.plot(alpha_a, Ps_Pzeta1, label=r\"$P_{P_\\zeta}$\")\n", + " plt.plot(alpha_a, Ps_PS1, label=r\"$P_{P_Q}$\")\n", + " plt.xlabel(r\"$\\alpha$\")\n", + " plt.ylabel(r\"Mode\")\n", + " plt.grid()\n", + " plt.legend(loc=\"upper left\")\n", + " # plt.xscale('log')\n", + " plt.yscale(\"log\")\n", + "\n", + " Delta_zeta1 = (\n", + " mode_k**3 * Ps_zeta1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_S1 = mode_k**3 * Ps_S1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " Delta_Pzeta1 = (\n", + " mode_k**3 * Ps_Pzeta1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_PS1 = (\n", + " mode_k**3 * Ps_PS1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " print(\n", + " f\"# Final values k = {mode_k: 20.15g} Ps_zeta{case_f} = {Delta_zeta1: 21.15e} \"\n", + " f\"Ps_Pzeta{case_f} = {Delta_Pzeta1: 21.15e} Ps_S{case_f} = {Delta_S1: 21.15e} \"\n", + " f\"Ps_PS{case_f} = {Delta_PS1: 21.15e}\"\n", + " )\n", + "\n", + "\n", + " \n", + " #plt.savefig('mode_I_p_R')\n", + " #plt.clf()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "a81352e0", + "metadata": {}, + "outputs": [], + "source": [ + "def test_two_fluids_wkb_spec() -> None:\n", + " \"\"\"Compute WKB approximation for the two-fluids model spectrum.\"\"\"\n", + "\n", + " #\n", + " # New homogeneous and isotropic cosmological model NcHICosmoQGRW\n", + " #\n", + " cosmo = Nc.HICosmoQGRW() # P1 = Cosmologia \n", + "\n", + " w = 1.0e-5 #P2 eq de estado da materia escura\n", + " prec = 1.0e-7\n", + "\n", + " #P3 densidade de radiação e materia escura e energia escura (1 - resto)\n", + " cosmo.props.w = w\n", + " cosmo.props.Omegar = (1.0e-8) * 1.0\n", + " cosmo.props.Omegaw = (1.0 - 1.0e-8) * 1.0\n", + " cosmo.props.xb = 1.0e30 # P4 x do bounce\n", + "\n", + " pert = Nc.HIPertTwoFluids.new()\n", + "\n", + " pert.props.reltol = prec\n", + " # pert.set_stiff_solver (True)\n", + "\n", + " # k = 1 => lambda = 5 Gpc\n", + " # k = 10^5 => lambda = 50 kpc\n", + " lnki = math.log(1.0e0)# P5 intervalo de momento de interesse\n", + " lnkf = math.log(1.0e5)\n", + " lnk_a = np.linspace(lnki, lnkf, 20)\n", + "\n", + " ci = Ncm.Vector.new(8)\n", + "\n", + " k_a = []\n", + " Ps_zeta1 = []\n", + " Ps_S1 = []\n", + " Ps_zeta2 = []\n", + " Ps_S2 = []\n", + " Ps_Pzeta1 = []\n", + " Ps_PS1 = []\n", + "\n", + " out_file = open(\"twofluids_spectrum_{w}.dat\", \"w\", encoding=\"utf-8\")\n", + "#alpha is related to the time variable. The log-redshift time\n", + " start_alpha1 = 1.0e-10 # P5 tempo inicial dependente do redshift.\n", + " start_alpha2 = 1.0e-14\n", + "\n", + " for lnk in tqdm(lnk_a):\n", + " k = math.exp(lnk)\n", + " pert.set_mode_k(k)\n", + " k_a.append(k)\n", + "\n", + " alphaf = cosmo.abs_alpha(1.0e20)\n", + "\n", + " # print (\"# Evolving mode %e from %f to %f\" % (k, alphai, alphaf))\n", + " #S is our variable Q.\n", + " alphai = -cosmo.abs_alpha(start_alpha1 * k**2)\n", + " \n", + " #### Ate aqui só coloca todos os parametros, define o tempo inicial, e converte o alpha1 em algum tipo de numero absoluto nessa funçao de cima.\n", + " \n", + " ##### Agora embaixo, calcula as cond iniciais, seta as condicioes iniciais e evolui no tempo. \n", + " \n", + " pert.get_init_cond_zetaS(cosmo, alphai, 1, 0.25 * math.pi, ci)\n", + "#This function does the following: Calls get_init_cond_zetaS, which calls cond_QP.\n", + "#IN cond_QP:\n", + " #Starts interface that have the equations of motion and the decomposition TV.\n", + " #Defines which case: 1 or 2, defining which momentum we assume as non-zero\n", + " #Computes all the init cond\n", + " #I believe that R and I represents each solutioon 1 and 2.\n", + "#Then we call to_zetaS, which changes from QP to zeta Q\n", + " pert.set_init_cond(cosmo, alphai, 1, False, ci)\n", + "\n", + " print(f\"# Mode 1 k {k: 21.15e}, state module {pert.get_state_mod():f}\")\n", + "\n", + " pert.evolve(cosmo, alphaf)#Evolve the system untill alphaF\n", + " \n", + " \n", + " \n", + " v, _alphac = pert.peek_state(cosmo)#Get the current time and values of the numerical solution for the modes. V é o vetor com os modos, n sei a ordem\n", + "#I believe that Delta represents the spectrum here.\n", + "\n", + "\n", + "##Aqui terminou de calcular os modos pro momento do loop. Ai agora calcula o espectro\n", + " Delta_zeta1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_S1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_Pzeta1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_PS1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + "\n", + " Ps_zeta1.append(Delta_zeta1)\n", + " Ps_S1.append(Delta_S1)\n", + " Ps_Pzeta1.append(Delta_Pzeta1)\n", + " Ps_PS1.append(Delta_PS1)\n", + "\n", + " \n", + " #### Aqui acabou o espectro pro modo 1. Ai faz de novo pro modo 2. ####3\n", + " \n", + " alphai = -cosmo.abs_alpha(start_alpha2 * k**2)\n", + " pert.get_init_cond_zetaS(cosmo, alphai, 2, 0.25 * math.pi, ci)\n", + " pert.set_init_cond(cosmo, alphai, 0, False, ci)\n", + "\n", + " pert.evolve(cosmo, alphaf)\n", + " v, _alphac = pert.peek_state(cosmo)\n", + " print(_alphac)\n", + " Delta_zeta2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_S2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_Pzeta2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_PS2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + "\n", + " Ps_zeta2.append(Delta_zeta2)\n", + " Ps_S2.append(Delta_S2)\n", + " Ps_zeta2.append(Delta_Pzeta2)\n", + " Ps_S2.append(Delta_PS2)\n", + "\n", + " out_file.write(\n", + " f\"{k: 20.15e} {Delta_zeta1: 20.15e} {Delta_zeta2: 20.15e} {Delta_S1: 20.15e} \"\n", + " f\"{Delta_S2: 20.15e} {Delta_Pzeta1: 20.15e} {Delta_Pzeta2: 20.15e} \"\n", + " f\"{Delta_PS1: 20.15e} {Delta_PS2: 20.15e}\\n\"\n", + " )\n", + " out_file.flush()\n", + "\n", + " out_file.close()\n", + " \n", + "###Plot\n", + "\n", + " plt.plot(k_a, Ps_zeta1, label=r\"$P_\\zeta$\")\n", + " plt.plot(k_a, Ps_S1, label=r\"$P_Q$\")\n", + " #plt.plot(k_a, Ps_zeta2, label=r\"$P^2_\\zeta$\")\n", + " # plt.plot(k_a, Ps_S2, label=r\"$P^2_Q$\")\n", + " plt.xlabel(r\"$k $\")\n", + " plt.ylabel(r\"$Spectrum$\")\n", + " plt.grid()\n", + " plt.legend(loc=\"upper left\")\n", + " #plt.xscale(\"log\")\n", + " #plt.yscale(\"log\")\n", + "\n", + "\n", + " plt.savefig('spec')\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "1e644bda", + "metadata": {}, + "outputs": [], + "source": [ + "def test_two_fluids_wkb_spec_log() -> None:\n", + " \"\"\"Compute WKB approximation for the two-fluids model spectrum.\"\"\"\n", + "\n", + " #\n", + " # New homogeneous and isotropic cosmological model NcHICosmoQGRW\n", + " #\n", + " cosmo = Nc.HICosmoQGRW() # P1 = Cosmologia \n", + "\n", + " w = 0.00001 #P2 eq de estado da materia escura\n", + " prec = 1.0e-7\n", + "\n", + " #P3 densidade de radiação e materia escura e energia escura (1 - resto)\n", + " cosmo.props.w = w\n", + " cosmo.props.Omegar = (1.0e-8) * 1.0\n", + " cosmo.props.Omegaw = (1.0 - 1.0e-8) * 1.0\n", + " cosmo.props.xb = 1.0e30 # P4 x do bounce\n", + "\n", + " pert = Nc.HIPertTwoFluids.new()\n", + "\n", + " pert.props.reltol = prec\n", + " # pert.set_stiff_solver (True)\n", + "\n", + " lnki = math.log(1.0e-5)# P5 intervalo de momento de interesse\n", + " lnkf = math.log(1.0e5)\n", + " lnk_a = np.linspace(lnki, lnkf, 50)\n", + "\n", + " ci = Ncm.Vector.new(8)\n", + "\n", + " k_a = []\n", + " Ps_zeta1 = []\n", + " Ps_S1 = []\n", + " Ps_zeta2 = []\n", + " Ps_S2 = []\n", + " Ps_Pzeta1 = []\n", + " Ps_PS1 = []\n", + "\n", + " out_file = open(\"twofluids_spectrum_{w}.dat\", \"w\", encoding=\"utf-8\")\n", + "#alpha is related to the time variable. The log-redshift time\n", + " start_alpha1 = 1.0e-10 # P5 tempo inicial dependente do redshift.\n", + " start_alpha2 = 1.0e-14\n", + "\n", + " for lnk in tqdm(lnk_a):\n", + " k = math.exp(lnk)\n", + " pert.set_mode_k(k)\n", + " k_a.append(k)\n", + "\n", + " alphaf = cosmo.abs_alpha(1.0e20)\n", + "\n", + " # print (\"# Evolving mode %e from %f to %f\" % (k, alphai, alphaf))\n", + " #S is our variable Q.\n", + " alphai = -cosmo.abs_alpha(start_alpha1 * k**2)\n", + " \n", + " #### Ate aqui só coloca todos os parametros, define o tempo inicial, e converte o alpha1 em algum tipo de numero absoluto nessa funçao de cima.\n", + " \n", + " ##### Agora embaixo, calcula as cond iniciais, seta as condicioes iniciais e evolui no tempo. \n", + " \n", + " pert.get_init_cond_zetaS(cosmo, alphai, 1, 0.25 * math.pi, ci)\n", + "#This function does the following: Calls get_init_cond_zetaS, which calls cond_QP.\n", + "#IN cond_QP:\n", + " #Starts interface that have the equations of motion and the decomposition TV.\n", + " #Defines which case: 1 or 2, defining which momentum we assume as non-zero\n", + " #Computes all the init cond\n", + " #I believe that R and I represents each solutioon 1 and 2.\n", + "#Then we call to_zetaS, which changes from QP to zeta Q\n", + " pert.set_init_cond(cosmo, alphai, 1, False, ci)\n", + "\n", + " print(f\"# Mode 1 k {k: 21.15e}, state module {pert.get_state_mod():f}\")\n", + "\n", + " pert.evolve(cosmo, alphaf)#Evolve the system untill alphaF\n", + " \n", + " \n", + " \n", + " v, _alphac = pert.peek_state(cosmo)#Get the current time and values of the numerical solution for the modes. V é o vetor com os modos, n sei a ordem\n", + "#I believe that Delta represents the spectrum here.\n", + "\n", + "\n", + "##Aqui terminou de calcular os modos pro momento do loop. Ai agora calcula o espectro\n", + " Delta_zeta1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_S1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_Pzeta1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_PS1 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + "\n", + " Ps_zeta1.append(Delta_zeta1)\n", + " Ps_S1.append(Delta_S1)\n", + " Ps_Pzeta1.append(Delta_Pzeta1)\n", + " Ps_PS1.append(Delta_PS1)\n", + "\n", + " \n", + " #### Aqui acabou o espectro pro modo 1. Ai faz de novo pro modo 2. ####3\n", + " \n", + " alphai = -cosmo.abs_alpha(start_alpha2 * k**2)\n", + " pert.get_init_cond_zetaS(cosmo, alphai, 2, 0.25 * math.pi, ci)\n", + " pert.set_init_cond(cosmo, alphai, 0, False, ci)\n", + "\n", + " pert.evolve(cosmo, alphaf)\n", + " v, _alphac = pert.peek_state(cosmo)\n", + " print(_alphac)\n", + " Delta_zeta2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_S2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_Pzeta2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", + " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + " Delta_PS2 = (\n", + " k**3\n", + " * math.hypot(\n", + " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", + " )\n", + " ** 2\n", + " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", + " )\n", + "\n", + " Ps_zeta2.append(Delta_zeta2)\n", + " Ps_S2.append(Delta_S2)\n", + " Ps_zeta2.append(Delta_Pzeta2)\n", + " Ps_S2.append(Delta_PS2)\n", + "\n", + " out_file.write(\n", + " f\"{k: 20.15e} {Delta_zeta1: 20.15e} {Delta_zeta2: 20.15e} {Delta_S1: 20.15e} \"\n", + " f\"{Delta_S2: 20.15e} {Delta_Pzeta1: 20.15e} {Delta_Pzeta2: 20.15e} \"\n", + " f\"{Delta_PS1: 20.15e} {Delta_PS2: 20.15e}\\n\"\n", + " )\n", + " out_file.flush()\n", + "\n", + " out_file.close()\n", + " \n", + "###Plot\n", + "\n", + " plt.plot(np.log(k_a), np.log(Ps_zeta1), label=r\"$P_\\zeta$\")\n", + " plt.plot(np.log(k_a), np.log(Ps_S1), label=r\"$P_Q$\")\n", + " #plt.plot(k_a, Ps_zeta2, label=r\"$P^2_\\zeta$\")\n", + " # plt.plot(k_a, Ps_S2, label=r\"$P^2_Q$\")\n", + " plt.xlabel(r\"$k $\")\n", + " plt.ylabel(r\"$Spectrum$\")\n", + " plt.grid()\n", + " plt.legend(loc=\"upper left\")\n", + " #plt.xscale(\"log\")\n", + " #plt.yscale(\"log\")\n", + "\n", + "\n", + " #plt.savefig('spec')\n", + " plt.show()\n", + " return np.log(Ps_zeta1), k_a" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "17f092b6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mode k = mode_k: 1000\n", + "# Calculating mode 1, initial time -63.10759538973279, redshift_alpha 3.91e+02]: \n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 9999/9999 [00:00<00:00, 215664.91it/s]" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "# Final values k = 1000 Ps_zeta1 = 5.115284221544647e-55 Ps_Pzeta1 = 6.634574990849296e-122 Ps_S1 = 6.566648912425620e-123 Ps_PS1 = 4.819512169162375e-100\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#test_two_fluids_wkb_mode(Nc.HIPertTwoFluidsCross.MODE1MAIN, 1, 0.0, 1.0)\n", + "test_two_fluids_wkb_mode(Nc.HIPertTwoFluidsCross.MODE1MAIN, 1, 1.0, 0.0)\n", + "#test_two_fluids_wkb_mode(Nc.HIPertTwoFluidsCross.MODE1MAIN, 1, 1.0, 1.0)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "98260fc2", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0%| | 0/20 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "test_two_fluids_wkb_spec()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "84556565", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0%| | 0/50 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "(array([-172.29336504, -171.47725159, -170.67740675, 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-146.87265029,\n", + " -145.89153898, -145.029969 , -143.98543597, -143.28854835,\n", + " -142.18761254, -141.23608627, -140.32638846, -139.48824811,\n", + " -138.47120016, -137.4639825 , -136.53337746, -135.66450856,\n", + " -134.71280034, -133.5931724 , -132.540295 , -131.19474152,\n", + " -129.90695834, -128.57067396, -127.17615592, -125.87341712,\n", + " -124.6418451 , -123.48007829]\n", + "\n", + "lnki = math.log(1.0e-5)# P5 intervalo de momento de interesse\n", + "lnkf = math.log(1.0e5)\n", + "lnk_a = np.linspace(lnki, lnkf, 50)\n", + "result=np.polyfit(lnk_a[:30], z1[:30], 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "5618578b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 2.00007129 -149.23919541]\n" + ] + } + ], + "source": [ + "print(result)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "07fa8d3b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.0000712909085103\n" + ] + } + ], + "source": [ + "ns = result[0] + 1\n", + "print(ns)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "36e209f8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.0" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "12*1/3/(1+3*1/3) + 1" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "720f771b-3dc7-42b4-9342-ae3c1b16a651", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/primordial_perturbations/two_fluids_perturbations.ipynb b/notebooks/primordial_perturbations/two_fluids_perturbations.ipynb index 97f3df095..7fdd965b7 100644 --- a/notebooks/primordial_perturbations/two_fluids_perturbations.ipynb +++ b/notebooks/primordial_perturbations/two_fluids_perturbations.ipynb @@ -1,1562 +1,1335 @@ { - "cells": [ - { - "cell_type": "markdown", - "id": "152b1c34", - "metadata": { - "id": "152b1c34" - }, - "source": [ - "# Two Fluid Quantum Cosmological Model" - ] - }, - { - "cell_type": "code", - "source": [ - "# Importing the relevant libraries\n", - "\n", - "import sys\n", - "import math\n", - "import numpy as np # imports the Numpy Library\n", - "\n", - "from tqdm import tqdm\n", - "\n", - "import matplotlib.pyplot as plt\n", - "\n", - "from numcosmo_py import Nc, Ncm # imports the NumCosmo library\n", - "from numcosmo_py.plotting.tools import set_rc_params_article # imports Numcosmo plotting tools\n", - "\n", - "Ncm.cfg_init() # starts the NumCosmo library" - ], - "metadata": { - "id": "Xna_qd5unXpw" - }, - "id": "Xna_qd5unXpw", - "execution_count": 5, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "# Introduction" - ], - "metadata": { - "id": "SSYdpVinZzn1" - }, - "id": "SSYdpVinZzn1" - }, - { - "cell_type": "markdown", - "source": [ - "In this notebook we shall analyze the predictions a two fluid quantum cosmological model where gravity is coupled though matter using the Wheeler-De Witt equation.\n", - "\n", - "A single fluid with equation of state $p(\\rho) = w\\rho$ was considered in $\\tt \\text{arXiv:0610205}$ , using the framework of Bohmian mechanics. At background level, it lead to a non-singular scale factor. At perturbative level, the primordial spectrum of adiabatic perturbations was found to be approximately scale invariant, with\n", - "\n", - "$${\\cal P}_{\\zeta}(k \\gg 1) \\approx A_{s}k^{n_{s} - 1}\\, , $$\n", - "$$ n_{s} = 1 + \\frac{12w}{1 + 3w}\\, ,$$\n", - "\n", - "for which the explicit value for dust $w \\approx 0$ and radiation $w=1/3$ are given by" - ], - "metadata": { - "id": "eMicLj9IZ8gC" - }, - "id": "eMicLj9IZ8gC" - }, - { - "cell_type": "code", - "source": [ - "def nsw(w): # defines a function that calculates the single fluid spectral index ns\n", - " return 1 + 12*w/(1+3*w)\n", - "\n", - "print(r'w=0 => '+str(nsw(0))) # dust w=0 spectral index\n", - "print(r'w=1/3 => '+str(nsw(1/3))) # radiation w = 1/3 spectral index" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "jgV564_mbm_v", - "outputId": "c8412475-fc2d-4b02-b6d9-34070311921d" - }, - "id": "jgV564_mbm_v", - "execution_count": 1, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "w=0 => 1.0\n", - "w=1/3 => 3.0\n" - ] - } - ] - }, - { - "cell_type": "markdown", - "source": [ - "The above results mean that ordinary matter cannot describe the approximately flat red spectrum with $n_{s}$. Therefore, a natural extension of said model is to consider the two fluid coupled to geometry.\n", - "\n", - "Said model was analyzed at background level with great detail in $\\tt \\text{arXiv:0505109}$ , where it was found that the obtained scale factor is also non-singular. However, the perturbative analysis has not yet been performed due to theoretical difficulties.\n", - "\n", - "Reference $\\tt \\text{arXiv:1510.06628}$ analyzes the cosmological perturbations formalism for $N$ fluid models. In the 2 fluid case, the obtained Hamiltonian that describes perturbations is given explicitly by\n", - "\n", - "\\begin{align}\n", - " \\delta {\\cal H}^{(2,s)} & = \\frac{1}{2m_{z}}P_{\\zeta}^{2} + \\frac{1}{2m_{S}}P_{Q}^{2} + \\left({ \\frac{ \\bar{c}_{n} }{ \\bar{c}_{S}\\bar{c}_{m} } }^{2}\\frac{1}{m_{z}m_{S}}\\frac{1}{NH}\\right)P_{\\zeta}P_{Q} \\\\\n", - " %\n", - " & \\, \\, + \\frac{1}{2}m_{z}\\nu_{\\zeta}^{2} z^{2} + \\frac{1}{2}m_{S}\\nu_{S}^{2}Q^{2} \\, ,\n", - "\\end{align}\n", - "\n", - "where $\\zeta$ and $Q$ denote adiabatic and entropy perturbations, respectively. We also introduced\n", - "\n", - "\\begin{align*}\n", - " m_{z} \\equiv \\frac{ a^{3}({ \\bar{\\rho} + \\bar{p} }) }{N\\bar{c}_{S}^{2}\\bar{H}^{2} }\\, , \\hspace{2.4cm} & \\hspace{-0.1cm} m_{S} \\equiv \\frac{ 1 }{ N a^{3}\\bar{c}_{m}^2\\bar{\\omega} } \\, , \\\\\n", - " %\n", - " \\nu_{z}^{2} \\equiv \\bar{c}_{S}^{2}F^{2}_{k} \\, , \\hspace{3.15cm} & \\hspace{0.05cm} \\nu_{S}^{2} \\equiv {c}_{m}^{2}F^{2}_{k} \\, , \\\\\n", - " %\n", - " \\bar{c}_{S}^{2} \\equiv \\bar{c}_{1}^{2}\\cos^{2}\\phi+\\bar{c}_{2}^{2}\\sin^{2}\\phi \\, , \\hspace{1cm} & \\bar{c}_{m}^{2} \\equiv \\bar{c}_{2}^{2}\\cos^{2}\\phi+\\bar{c}_{1}^{2}\\sin^{2}\\phi\n", - " \\, .\n", - "\\end{align*}\n", - "\n", - "where $\\bar{\\omega} \\equiv (\\rho_1 + p_1)(\\rho_2 + p_2)/(\\rho + p)$ and $\\bar{c}_{n}^{2} \\equiv \\bar{c}_{1}^{2} - \\bar{c}_{2}^{2}$. Here, for later convenience, we have also introduced the angular variable $\\phi$ and the functions $F_{k}(t)$ by\n", - "\n", - "\\begin{equation}\n", - " \\cos^{2}\\phi \\equiv \\frac{ \\rho_1 + p_1 }{ \\rho + p }\\, ,\n", - "\\end{equation}\n", - "\n", - "\\begin{equation}\n", - " \\sin^{2}\\phi \\equiv \\frac{ \\rho_2 + p_2 }{ \\rho + p }\\, ,\n", - "\\end{equation}\n", - "\n", - "\\begin{equation}\n", - " \\hspace{0.8cm} F^{2}_{k} \\equiv \\left({\\frac{ Nk }{ a }}\\right)^{2}\\, ,\n", - "\\end{equation}\n", - "\n", - "the angular variable $\\phi$ is also associated to the dominant fluid, with $\\phi=0$ denoting domination by the fluid $1$ and $\\phi=\\pi/2$ denoting domination by the fluid $2$.\n", - "\n", - "\n", - "By direct inspection of the perturbative Hamiltonian, one sees that the equations of motion for perturbations are coupled. While at classical level this could be solved by numerical methods, at quantum level this demands the use of special quantization techniques to define the associated vacuum state and extract predictions, as proposed by $\\tt \\text{arXiv:1510.06628}$.\n", - "\n", - "Therefore in this notebook, we analyze explicitly the background and perturbative quantities, with our final aim to calculate the modes $\\zeta_{k}, Q_{k}$ and their associated power spectrum." - ], - "metadata": { - "id": "9VIf518scRQW" - }, - "id": "9VIf518scRQW" - }, - { - "cell_type": "markdown", - "source": [ - "# Background Quantities" - ], - "metadata": { - "id": "1et0L5cgdOyP" - }, - "id": "1et0L5cgdOyP" - }, - { - "cell_type": "markdown", - "source": [ - "In this section we study the quantities $m_{S}, m_{Q}, \\phi, c^{2}_{S}, c^{2}_{m}$ that occur in the perturbative Hamiltonian. We also study the evolution of the eigenvalues $\\nu_{1}, \\nu_{2}$ that diagonalize the Hamiltonian tensor. Finally, we study the behavior of the coupling matrices $\\gamma_{ij}, \\tau_{ij}$, which define the dynamics of the relevant perturbative quantities.\n", - "\n", - "To do so, we start by defining our cosmological parameters." - ], - "metadata": { - "id": "cmnX2kzJmRde" - }, - "id": "cmnX2kzJmRde" - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "1515a28b", - "metadata": { - "id": "1515a28b", - "colab": { - "base_uri": "https://localhost:8080/" - }, - "outputId": "632cccd1-efb5-44fc-a6a2-aad64d411884" - }, - "outputs": [ - { - "output_type": "error", - "ename": "NameError", - "evalue": "name 'Nc' is not defined", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[2], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m cosmo \u001b[38;5;241m=\u001b[39m Nc\u001b[38;5;241m.\u001b[39mHICosmoQGRW() \u001b[38;5;66;03m# defines a cosmological model, which is represented by a NumCosmo object. Then, the relevant cosmological parameters are added to this object\u001b[39;00m\n\u001b[1;32m 3\u001b[0m \u001b[38;5;66;03m# these lines set the relevant cosmological parameters\u001b[39;00m\n\u001b[1;32m 4\u001b[0m cosmo\u001b[38;5;241m.\u001b[39mprops\u001b[38;5;241m.\u001b[39mw \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1.0e-2\u001b[39m \u001b[38;5;66;03m# dust/dark matter equation of state\u001b[39;00m\n", - "\u001b[0;31mNameError\u001b[0m: name 'Nc' is not defined" - ] - } - ], - "source": [ - "cosmo = Nc.HICosmoQGRW() # defines a cosmological model, which is represented by a NumCosmo object. Then, the relevant cosmological parameters are added to this object\n", - "\n", - "# these lines set the relevant cosmological parameters\n", - "cosmo.props.w = 1.0e-2 # dust/dark matter equation of state\n", - "cosmo.props.Omegar = 2.0 * (1.0e-8) # radiation abundance today\n", - "cosmo.props.Omegaw = 2.0 * (1.0 - 1.0e-8) # dust/dark matter abundance today\n", - "cosmo.props.xb = 1.0e30 # inverse scale factor x=1/a at the time of the bounce" - ] - }, - { - "cell_type": "markdown", - "source": [ - "To study the behavior of said quantities, we shall vary our cosmological parameters. However, before we dwell into such analysis, let's perform a consistency check by considering the dust only $\\Omega_{r} = 0$ and radiation only $\\Omega_{w} = 0$ cases. The complete model shall present regimes of domination by each fluid, and we shall also check if we indeed recover the $n_{s}$ values for the single fluid case." - ], - "metadata": { - "id": "-aSx2PR7oHee" - }, - "id": "-aSx2PR7oHee" - }, - { - "cell_type": "markdown", - "source": [ - "## Consistency Check" - ], - "metadata": { - "id": "KiOdkZDMoq87" - }, - "id": "KiOdkZDMoq87" + "cells": [ + { + "cell_type": "markdown", + "id": "152b1c34", + "metadata": { + "id": "152b1c34" + }, + "source": [ + "# Two Fluid Quantum Cosmological Model" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "Xna_qd5unXpw", + "metadata": { + "id": "Xna_qd5unXpw" + }, + "outputs": [], + "source": [ + "# Importing the relevant libraries\n", + "\n", + "import sys\n", + "import math\n", + "import numpy as np # imports the Numpy Library\n", + "\n", + "from tqdm import tqdm\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from numcosmo_py import Nc, Ncm # imports the NumCosmo library\n", + "from numcosmo_py.plotting.tools import set_rc_params_article # imports Numcosmo plotting tools\n", + "\n", + "Ncm.cfg_init() # starts the NumCosmo library" + ] + }, + { + "cell_type": "markdown", + "id": "SSYdpVinZzn1", + "metadata": { + "id": "SSYdpVinZzn1" + }, + "source": [ + "# Introduction" + ] + }, + { + "cell_type": "markdown", + "id": "eMicLj9IZ8gC", + "metadata": { + "id": "eMicLj9IZ8gC" + }, + "source": [ + "In this notebook we shall analyze the predictions a two fluid quantum cosmological model where gravity is coupled though matter using the Wheeler-De Witt equation.\n", + "\n", + "A single fluid with equation of state $p(\\rho) = w\\rho$ was considered in $\\tt \\text{arXiv:0610205}$ , using the framework of Bohmian mechanics. At background level, it lead to a non-singular scale factor. At perturbative level, the primordial spectrum of adiabatic perturbations was found to be approximately scale invariant, with\n", + "\n", + "$${\\cal P}_{\\zeta}(k \\gg 1) \\approx A_{s}k^{n_{s} - 1}\\, , $$\n", + "$$ n_{s} = 1 + \\frac{12w}{1 + 3w}\\, ,$$\n", + "\n", + "for which the explicit value for dust $w \\approx 0$ and radiation $w=1/3$ are given by" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "jgV564_mbm_v", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" }, + "id": "jgV564_mbm_v", + "outputId": "c8412475-fc2d-4b02-b6d9-34070311921d" + }, + "outputs": [ { - "cell_type": "markdown", - "source": [ - "## Evolution of ...." - ], - "metadata": { - "id": "iiIp6-GfovaW" - }, - "id": "iiIp6-GfovaW" + "name": "stdout", + "output_type": "stream", + "text": [ + "w=0 => 1.0\n", + "w=1/3 => 3.0\n" + ] + } + ], + "source": [ + "def nsw(w): # defines a function that calculates the single fluid spectral index ns\n", + " return 1 + 12*w/(1+3*w)\n", + "\n", + "print(r'w=0 => '+str(nsw(0))) # dust w=0 spectral index\n", + "print(r'w=1/3 => '+str(nsw(1/3))) # radiation w = 1/3 spectral index" + ] + }, + { + "cell_type": "markdown", + "id": "9VIf518scRQW", + "metadata": { + "id": "9VIf518scRQW" + }, + "source": [ + "The above results mean that ordinary matter cannot describe the approximately flat red spectrum with $n_{s}$. Therefore, a natural extension of said model is to consider the two fluid coupled to geometry.\n", + "\n", + "Said model was analyzed at background level with great detail in $\\tt \\text{arXiv:0505109}$ , where it was found that the obtained scale factor is also non-singular. However, the perturbative analysis has not yet been performed due to theoretical difficulties.\n", + "\n", + "Reference $\\tt \\text{arXiv:1510.06628}$ analyzes the cosmological perturbations formalism for $N$ fluid models. In the 2 fluid case, the obtained Hamiltonian that describes perturbations is given explicitly by\n", + "\n", + "\\begin{align}\n", + " \\delta {\\cal H}^{(2,s)} & = \\frac{1}{2m_{z}}P_{\\zeta}^{2} + \\frac{1}{2m_{S}}P_{Q}^{2} + \\left({ \\frac{ \\bar{c}_{n} }{ \\bar{c}_{S}\\bar{c}_{m} } }^{2}\\frac{1}{m_{z}m_{S}}\\frac{1}{NH}\\right)P_{\\zeta}P_{Q} \\\\\n", + " %\n", + " & \\, \\, + \\frac{1}{2}m_{z}\\nu_{\\zeta}^{2} z^{2} + \\frac{1}{2}m_{S}\\nu_{S}^{2}Q^{2} \\, ,\n", + "\\end{align}\n", + "\n", + "where $\\zeta$ and $Q$ denote adiabatic and entropy perturbations, respectively. We also introduced\n", + "\n", + "\\begin{align*}\n", + " m_{z} \\equiv \\frac{ a^{3}({ \\bar{\\rho} + \\bar{p} }) }{N\\bar{c}_{S}^{2}\\bar{H}^{2} }\\, , \\hspace{2.4cm} & \\hspace{-0.1cm} m_{S} \\equiv \\frac{ 1 }{ N a^{3}\\bar{c}_{m}^2\\bar{\\omega} } \\, , \\\\\n", + " %\n", + " \\nu_{z}^{2} \\equiv \\bar{c}_{S}^{2}F^{2}_{k} \\, , \\hspace{3.15cm} & \\hspace{0.05cm} \\nu_{S}^{2} \\equiv {c}_{m}^{2}F^{2}_{k} \\, , \\\\\n", + " %\n", + " \\bar{c}_{S}^{2} \\equiv \\bar{c}_{1}^{2}\\cos^{2}\\phi+\\bar{c}_{2}^{2}\\sin^{2}\\phi \\, , \\hspace{1cm} & \\bar{c}_{m}^{2} \\equiv \\bar{c}_{2}^{2}\\cos^{2}\\phi+\\bar{c}_{1}^{2}\\sin^{2}\\phi\n", + " \\, .\n", + "\\end{align*}\n", + "\n", + "where $\\bar{\\omega} \\equiv (\\rho_1 + p_1)(\\rho_2 + p_2)/(\\rho + p)$ and $\\bar{c}_{n}^{2} \\equiv \\bar{c}_{1}^{2} - \\bar{c}_{2}^{2}$. Here, for later convenience, we have also introduced the angular variable $\\phi$ and the functions $F_{k}(t)$ by\n", + "\n", + "\\begin{equation}\n", + " \\cos^{2}\\phi \\equiv \\frac{ \\rho_1 + p_1 }{ \\rho + p }\\, ,\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " \\sin^{2}\\phi \\equiv \\frac{ \\rho_2 + p_2 }{ \\rho + p }\\, ,\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " \\hspace{0.8cm} F^{2}_{k} \\equiv \\left({\\frac{ Nk }{ a }}\\right)^{2}\\, ,\n", + "\\end{equation}\n", + "\n", + "the angular variable $\\phi$ is also associated to the dominant fluid, with $\\phi=0$ denoting domination by the fluid $1$ and $\\phi=\\pi/2$ denoting domination by the fluid $2$.\n", + "\n", + "\n", + "By direct inspection of the perturbative Hamiltonian, one sees that the equations of motion for perturbations are coupled. While at classical level this could be solved by numerical methods, at quantum level this demands the use of special quantization techniques to define the associated vacuum state and extract predictions, as proposed by $\\tt \\text{arXiv:1510.06628}$.\n", + "\n", + "Therefore in this notebook, we analyze explicitly the background and perturbative quantities, with our final aim to calculate the modes $\\zeta_{k}, Q_{k}$ and their associated power spectrum." + ] + }, + { + "cell_type": "markdown", + "id": "1et0L5cgdOyP", + "metadata": { + "id": "1et0L5cgdOyP" + }, + "source": [ + "# Background Quantities" + ] + }, + { + "cell_type": "markdown", + "id": "cmnX2kzJmRde", + "metadata": { + "id": "cmnX2kzJmRde" + }, + "source": [ + "In this section we study the quantities $m_{S}, m_{Q}, \\phi, c^{2}_{S}, c^{2}_{m}$ that occur in the perturbative Hamiltonian. We also study the evolution of the eigenvalues $\\nu_{1}, \\nu_{2}$ that diagonalize the Hamiltonian tensor. Finally, we study the behavior of the coupling matrices $\\gamma_{ij}, \\tau_{ij}$, which define the dynamics of the relevant perturbative quantities.\n", + "\n", + "To do so, we start by defining our cosmological parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "1515a28b", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" }, - { - "cell_type": "code", - "source": [ - "k = 1.0\n", - "min_alpha_c = -120.0\n", - "max_alpha_c = -1.0\n", - "min_alpha_scale = 1.0e-12\n", - "np_plot = 100\n", - "\n", - "# Time arrays for the contraction and bounce phases\n", - "\n", - "alpha_c = np.linspace(min_alpha_c, max_alpha_c, np_plot)\n", - "alpha_b_e = np.geomspace(min_alpha_scale, 2.0, np_plot)\n", - "alpha_b = np.concatenate((np.flip(-alpha_b_e), alpha_b_e))" - ], - "metadata": { - "id": "Bysmnq-koGoW" - }, - "id": "Bysmnq-koGoW", - "execution_count": 4, - "outputs": [] + "id": "1515a28b", + "outputId": "632cccd1-efb5-44fc-a6a2-aad64d411884" + }, + "outputs": [], + "source": [ + "cosmo = Nc.HICosmoQGRW() # defines a cosmological model, which is represented by a NumCosmo object. Then, the relevant cosmological parameters are added to this object\n", + "\n", + "# these lines set the relevant cosmological parameters\n", + "cosmo.props.w = 1.0e-5 # dust/dark matter equation of state\n", + "cosmo.props.Omegar = 2.0 * (1.0e-8) # radiation abundance today\n", + "cosmo.props.Omegaw = 2.0 * (1.0 - 1.0e-8) # dust/dark matter abundance today\n", + "cosmo.props.xb = 1.0e30 # inverse scale factor x=1/a at the time of the bounce" + ] + }, + { + "cell_type": "markdown", + "id": "-aSx2PR7oHee", + "metadata": { + "id": "-aSx2PR7oHee" + }, + "source": [ + "To study the behavior of said quantities, we shall vary our cosmological parameters. However, before we dwell into such analysis, let's perform a consistency check by considering the dust only $\\Omega_{r} = 0$ and radiation only $\\Omega_{w} = 0$ cases. The complete model shall present regimes of domination by each fluid, and we shall also check if we indeed recover the $n_{s}$ values for the single fluid case." + ] + }, + { + "cell_type": "markdown", + "id": "KiOdkZDMoq87", + "metadata": { + "id": "KiOdkZDMoq87" + }, + "source": [ + "## Consistency Check" + ] + }, + { + "cell_type": "markdown", + "id": "iiIp6-GfovaW", + "metadata": { + "id": "iiIp6-GfovaW" + }, + "source": [ + "## Evolution of ...." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "Bysmnq-koGoW", + "metadata": { + "id": "Bysmnq-koGoW" + }, + "outputs": [], + "source": [ + "k = 1.0\n", + "min_alpha_c = -120.0\n", + "max_alpha_c = -1.0\n", + "min_alpha_scale = 1.0e-12\n", + "np_plot = 100\n", + "\n", + "# Time arrays for the contraction and bounce phases\n", + "\n", + "alpha_c = np.linspace(min_alpha_c, max_alpha_c, np_plot)\n", + "alpha_b_e = np.geomspace(min_alpha_scale, 2.0, np_plot)\n", + "alpha_b = np.concatenate((np.flip(-alpha_b_e), alpha_b_e))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "9b5ebdeb", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" }, + "id": "9b5ebdeb", + "outputId": "b640709a-e502-41aa-8661-37d8c7d1e068" + }, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "9b5ebdeb", - "metadata": { - "id": "9b5ebdeb", - "colab": { - "base_uri": "https://localhost:8080/" - }, - "outputId": "b640709a-e502-41aa-8661-37d8c7d1e068" - }, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "" - ] - }, - "metadata": {}, - "execution_count": 4 - } - ], - "source": [ - "cosmo.eom_eval(-120,-1)\n", - "#m_s_c = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_c])\n", - "#print(m_s_c)\n", - "#m_zeta_c = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_c])" + "data": { + "text/plain": [ + "" ] - }, - { - "cell_type": "code", - "source": [ - "cosmo.eom_eval(-120,1).nu1\n", - "#cosmo.props.m_s" - ], - "metadata": { - "id": "WuQyCqQSWpGW" - }, - "id": "WuQyCqQSWpGW", - "execution_count": null, - "outputs": [] - }, + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cosmo.eom_eval(-120,-1)\n", + "#m_s_c = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_c])\n", + "#print(m_s_c)\n", + "#m_zeta_c = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_c])" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "WuQyCqQSWpGW", + "metadata": { + "id": "WuQyCqQSWpGW" + }, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "533290e5-dc2a-467a-8319-11811d78cc2b", - "metadata": { - "id": "533290e5-dc2a-467a-8319-11811d78cc2b" - }, - "outputs": [], - "source": [ - "# Computing background observables in the contraction phase\n", - "\n", - "m_s_c = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_c])\n", - "m_zeta_c = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_c])\n", - "mnu2_s_c = np.array([cosmo.eom_eval(alpha, k).mnu2_s for alpha in alpha_c])\n", - "mnu2_zeta_c = np.array([cosmo.eom_eval(alpha, k).mnu2_zeta for alpha in alpha_c])\n", - "nu1_c = np.array([cosmo.eom_eval(alpha, k).nu1 for alpha in alpha_c])\n", - "nu2_c = np.array([cosmo.eom_eval(alpha, k).nu2 for alpha in alpha_c])\n", - "nu_s_c = np.sqrt(mnu2_s_c / m_s_c)\n", - "nu_zeta_c = np.sqrt(mnu2_zeta_c / m_zeta_c)\n", - "y_c = np.array([cosmo.eom_eval(alpha, k).y for alpha in alpha_c])\n", - "gamma11_c = np.array([cosmo.eom_eval(alpha, k).gammabar11 for alpha in alpha_c])\n", - "gamma22_c = np.array([cosmo.eom_eval(alpha, k).gammabar22 for alpha in alpha_c])\n", - "gamma12_c = np.array([cosmo.eom_eval(alpha, k).gammabar12 for alpha in alpha_c])\n", - "tau_c = np.array([cosmo.eom_eval(alpha, k).taubar for alpha in alpha_c])\n", - "\n", - "# Computing background observables in the bounce phase\n", - "\n", - "m_s_b = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_b])\n", - "m_zeta_b = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_b])\n", - "mnu2_s_b = np.array([cosmo.eom_eval(alpha, k).mnu2_s for alpha in alpha_b])\n", - "mnu2_zeta_b = np.array([cosmo.eom_eval(alpha, k).mnu2_zeta for alpha in alpha_b])\n", - "nu1_b = np.array([cosmo.eom_eval(alpha, k).nu1 for alpha in alpha_b])\n", - "nu2_b = np.array([cosmo.eom_eval(alpha, k).nu2 for alpha in alpha_b])\n", - "nu_s_b = np.sqrt(mnu2_s_b / m_s_b)\n", - "nu_zeta_b = np.sqrt(mnu2_zeta_b / m_zeta_b)\n", - "y_b = np.array([cosmo.eom_eval(alpha, k).y for alpha in alpha_b])\n", - "gamma11_b = np.array([cosmo.eom_eval(alpha, k).gammabar11 for alpha in alpha_b])\n", - "gamma22_b = np.array([cosmo.eom_eval(alpha, k).gammabar22 for alpha in alpha_b])\n", - "gamma12_b = np.array([cosmo.eom_eval(alpha, k).gammabar12 for alpha in alpha_b])\n", - "tau_b = np.array([cosmo.eom_eval(alpha, k).taubar for alpha in alpha_b])\n", - "\n", - "cos2_phi_c = (nu1_c**2 * nu_zeta_c**2 - nu2_c**2 * nu_s_c**2) / (nu1_c**4 - nu2_c**4)\n", - "sin2_phi_c = (nu1_c**2 * nu_s_c**2 - nu2_c**2 * nu_zeta_c**2) / (nu1_c**4 - nu2_c**4)\n", - "\n", - "cos2_phi_b = (nu1_b**2 * nu_zeta_b**2 - nu2_b**2 * nu_s_b**2) / (nu1_b**4 - nu2_b**4)\n", - "sin2_phi_b = (nu1_b**2 * nu_s_b**2 - nu2_b**2 * nu_zeta_b**2) / (nu1_b**4 - nu2_b**4)\n", - "\n" + "data": { + "text/plain": [ + "46657882087.38496" ] - }, + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cosmo.eom_eval(-120,1).nu1\n", + "#cosmo.props.m_s" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "533290e5-dc2a-467a-8319-11811d78cc2b", + "metadata": { + "id": "533290e5-dc2a-467a-8319-11811d78cc2b" + }, + "outputs": [], + "source": [ + "# Computing background observables in the contraction phase\n", + "\n", + "m_s_c = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_c])\n", + "m_zeta_c = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_c])\n", + "mnu2_s_c = np.array([cosmo.eom_eval(alpha, k).mnu2_s for alpha in alpha_c])\n", + "mnu2_zeta_c = np.array([cosmo.eom_eval(alpha, k).mnu2_zeta for alpha in alpha_c])\n", + "nu1_c = np.array([cosmo.eom_eval(alpha, k).nu1 for alpha in alpha_c])\n", + "nu2_c = np.array([cosmo.eom_eval(alpha, k).nu2 for alpha in alpha_c])\n", + "nu_s_c = np.sqrt(mnu2_s_c / m_s_c)\n", + "nu_zeta_c = np.sqrt(mnu2_zeta_c / m_zeta_c)\n", + "y_c = np.array([cosmo.eom_eval(alpha, k).y for alpha in alpha_c])\n", + "gamma11_c = np.array([cosmo.eom_eval(alpha, k).gammabar11 for alpha in alpha_c])\n", + "gamma22_c = np.array([cosmo.eom_eval(alpha, k).gammabar22 for alpha in alpha_c])\n", + "gamma12_c = np.array([cosmo.eom_eval(alpha, k).gammabar12 for alpha in alpha_c])\n", + "tau_c = np.array([cosmo.eom_eval(alpha, k).taubar for alpha in alpha_c])\n", + "\n", + "# Computing background observables in the bounce phase\n", + "\n", + "m_s_b = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_b])\n", + "m_zeta_b = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_b])\n", + "mnu2_s_b = np.array([cosmo.eom_eval(alpha, k).mnu2_s for alpha in alpha_b])\n", + "mnu2_zeta_b = np.array([cosmo.eom_eval(alpha, k).mnu2_zeta for alpha in alpha_b])\n", + "nu1_b = np.array([cosmo.eom_eval(alpha, k).nu1 for alpha in alpha_b])\n", + "nu2_b = np.array([cosmo.eom_eval(alpha, k).nu2 for alpha in alpha_b])\n", + "nu_s_b = np.sqrt(mnu2_s_b / m_s_b)\n", + "nu_zeta_b = np.sqrt(mnu2_zeta_b / m_zeta_b)\n", + "y_b = np.array([cosmo.eom_eval(alpha, k).y for alpha in alpha_b])\n", + "gamma11_b = np.array([cosmo.eom_eval(alpha, k).gammabar11 for alpha in alpha_b])\n", + "gamma22_b = np.array([cosmo.eom_eval(alpha, k).gammabar22 for alpha in alpha_b])\n", + "gamma12_b = np.array([cosmo.eom_eval(alpha, k).gammabar12 for alpha in alpha_b])\n", + "tau_b = np.array([cosmo.eom_eval(alpha, k).taubar for alpha in alpha_b])\n", + "\n", + "cos2_phi_c = (nu1_c**2 * nu_zeta_c**2 - nu2_c**2 * nu_s_c**2) / (nu1_c**4 - nu2_c**4)\n", + "sin2_phi_c = (nu1_c**2 * nu_s_c**2 - nu2_c**2 * nu_zeta_c**2) / (nu1_c**4 - nu2_c**4)\n", + "\n", + "cos2_phi_b = (nu1_b**2 * nu_zeta_b**2 - nu2_b**2 * nu_s_b**2) / (nu1_b**4 - nu2_b**4)\n", + "sin2_phi_b = (nu1_b**2 * nu_s_b**2 - nu2_b**2 * nu_zeta_b**2) / (nu1_b**4 - nu2_b**4)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "a4daed56-57bc-4993-b8ab-3468d8f83d5f", + "metadata": { + "id": "a4daed56-57bc-4993-b8ab-3468d8f83d5f" + }, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "a4daed56-57bc-4993-b8ab-3468d8f83d5f", - "metadata": { - "id": "a4daed56-57bc-4993-b8ab-3468d8f83d5f" - }, - "outputs": [], - "source": [ - "set_rc_params_article(ncol=2)\n", - "fig = plt.figure()\n", - "\n", - "ax1= fig.add_subplot(1,2,1)\n", - "ax2= fig.add_subplot(2,2,2)\n", - "ax3= fig.add_subplot(2,2,4)\n", - "\n", - "ax1.plot(alpha_c, m_s_c, c='r', label=r'$m_s$')\n", - "ax1.plot(alpha_c, m_zeta_c, c='b', label=r'$m_\\zeta$')\n", - "ax1.set_yscale('log')\n", - "ax1.set_xlabel(r'$\\alpha$')\n", - "\n", - "ax2.plot(alpha_b, m_s_b, c='r', label=r'$m_s$')\n", - "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", - "ax2.set_yscale('log')\n", - "ax2.set_xlabel(r'$\\alpha$')\n", - "\n", - "ax3.plot(alpha_b, m_zeta_b, c='b', label=r'$m_\\zeta$')\n", - "ax3.set_xscale('symlog', linthresh=min_alpha_scale)\n", - "ax3.set_yscale('log')\n", - "ax3.set_xlabel(r'$\\alpha$')\n", - "\n", - "ax1.legend()\n", - "\n", - "pass" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(2,2,2)\n", + "ax3= fig.add_subplot(2,2,4)\n", + "\n", + "ax1.plot(alpha_c, m_s_c, c='r', label=r'$m_s$')\n", + "ax1.plot(alpha_c, m_zeta_c, c='b', label=r'$m_\\zeta$')\n", + "ax1.set_yscale('log')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax2.plot(alpha_b, m_s_b, c='r', label=r'$m_s$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('log')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax3.plot(alpha_b, m_zeta_b, c='b', label=r'$m_\\zeta$')\n", + "ax3.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax3.set_yscale('log')\n", + "ax3.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax1.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "8470dc58-92f9-46ab-8ec6-982e346cda0d", + "metadata": { + "id": "8470dc58-92f9-46ab-8ec6-982e346cda0d" + }, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "8470dc58-92f9-46ab-8ec6-982e346cda0d", - "metadata": { - "id": "8470dc58-92f9-46ab-8ec6-982e346cda0d" - }, - "outputs": [], - "source": [ - "set_rc_params_article(ncol=2)\n", - "fig = plt.figure()\n", - "\n", - "ax1= fig.add_subplot(1,2,1)\n", - "ax2= fig.add_subplot(1,2,2)\n", - "\n", - "ax1.plot(alpha_c, mnu2_s_c / m_s_c, c='r', label=r'$\\nu_s^2$')\n", - "ax1.plot(alpha_c, mnu2_zeta_c / m_zeta_c, c='b', label=r'$\\nu_\\zeta^2$')\n", - "ax1.set_yscale('log')\n", - "ax1.set_xlabel(r'$\\alpha$')\n", - "ax1.legend()\n", - "\n", - "ax2.plot(alpha_b, mnu2_s_b / m_s_b, c='r', label=r'$\\nu_s^2$')\n", - "ax2.plot(alpha_b, mnu2_zeta_b / m_zeta_b, c='b', label=r'$\\nu_\\zeta^2$')\n", - "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", - "ax2.set_yscale('log')\n", - "ax2.set_xlabel(r'$\\alpha$')\n", - "\n", - "pass" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_c, mnu2_s_c / m_s_c, c='r', label=r'$\\nu_s^2$')\n", + "ax1.plot(alpha_c, mnu2_zeta_c / m_zeta_c, c='b', label=r'$\\nu_\\zeta^2$')\n", + "ax1.set_yscale('log')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_b, mnu2_s_b / m_s_b, c='r', label=r'$\\nu_s^2$')\n", + "ax2.plot(alpha_b, mnu2_zeta_b / m_zeta_b, c='b', label=r'$\\nu_\\zeta^2$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('log')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "0fcea250-ab16-4d75-b437-254e07cb70cb", + "metadata": { + "id": "0fcea250-ab16-4d75-b437-254e07cb70cb" + }, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "0fcea250-ab16-4d75-b437-254e07cb70cb", - "metadata": { - "id": "0fcea250-ab16-4d75-b437-254e07cb70cb" - }, - "outputs": [], - "source": [ - "set_rc_params_article(ncol=2)\n", - "fig = plt.figure()\n", - "\n", - "ax1= fig.add_subplot(1,2,1)\n", - "ax2= fig.add_subplot(1,2,2)\n", - "\n", - "ax1.plot(alpha_c, y_c * np.sqrt(m_s_c * m_zeta_c), c='k', label=r'$\\nu_s^2$')\n", - "ax1.set_yscale('symlog', linthresh=1.0e-10)\n", - "ax1.set_xlabel(r'$\\alpha$')\n", - "\n", - "ax2.plot(alpha_b, y_b * np.sqrt(m_s_b * m_zeta_b), c='k', label=r'$\\nu_s^2$')\n", - "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", - "ax2.set_yscale('symlog')\n", - "ax2.set_xlabel(r'$\\alpha$')\n", - "\n", - "ax1.legend()\n", - "\n", - "pass" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_c, y_c * np.sqrt(m_s_c * m_zeta_c), c='k', label=r'$\\nu_s^2$')\n", + "ax1.set_yscale('symlog', linthresh=1.0e-10)\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax2.plot(alpha_b, y_b * np.sqrt(m_s_b * m_zeta_b), c='k', label=r'$\\nu_s^2$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('symlog')\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax1.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "f09ef1fb-3287-4c23-953e-a9325f45a419", + "metadata": { + "id": "f09ef1fb-3287-4c23-953e-a9325f45a419" + }, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "f09ef1fb-3287-4c23-953e-a9325f45a419", - "metadata": { - "id": "f09ef1fb-3287-4c23-953e-a9325f45a419" - }, - "outputs": [], - "source": [ - "set_rc_params_article(ncol=1)\n", - "fig = plt.figure()\n", - "\n", - "ax1= fig.add_subplot(1,1,1)\n", - "\n", - "ax1.plot(alpha_c, cos2_phi_c, label=r'$\\cos^2(\\phi)$')\n", - "ax1.plot(alpha_c, sin2_phi_c, label=r'$\\sin^2(\\phi)$')\n", - "ax1.set_xlabel(r'$\\alpha$')\n", - "ax1.legend()\n", - "pass" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=1)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,1,1)\n", + "\n", + "ax1.plot(alpha_c, cos2_phi_c, label=r'$\\cos^2(\\phi)$')\n", + "ax1.plot(alpha_c, sin2_phi_c, label=r'$\\sin^2(\\phi)$')\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "af2c3d95-97ec-4f81-b226-dfec9ae4a6f4", + "metadata": { + "id": "af2c3d95-97ec-4f81-b226-dfec9ae4a6f4" + }, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "af2c3d95-97ec-4f81-b226-dfec9ae4a6f4", - "metadata": { - "id": "af2c3d95-97ec-4f81-b226-dfec9ae4a6f4" - }, - "outputs": [], - "source": [ - "set_rc_params_article(ncol=2)\n", - "fig = plt.figure()\n", - "\n", - "ax1= fig.add_subplot(1,2,1)\n", - "ax2= fig.add_subplot(1,2,2)\n", - "\n", - "ax1.plot(alpha_c, nu1_c, label=r'$\\nu_1$')\n", - "ax1.plot(alpha_c, gamma11_c, label=r'$\\gamma_{11}$')\n", - "ax1.plot(alpha_c, gamma12_c, label=r'$\\gamma_{12}$')\n", - "ax1.plot(alpha_c, tau_c, label=r'$\\tau_{12}$')\n", - "\n", - "ax1.set_yscale('symlog', linthresh=1.0e-6)\n", - "ax1.set_xlabel(r'$\\alpha$')\n", - "ax1.legend()\n", - "\n", - "ax2.plot(alpha_c, nu2_c, label=r'$\\nu_2$')\n", - "ax2.plot(alpha_c, gamma22_c, label=r'$\\gamma_{22}$')\n", - "ax2.plot(alpha_c, gamma12_c, label=r'$\\gamma_{12}$')\n", - "ax2.plot(alpha_c, tau_c, label=r'$\\tau_{12}$')\n", - "\n", - "ax2.set_yscale('symlog', linthresh=1.0e-6)\n", - "ax2.set_xlabel(r'$\\alpha$')\n", - "ax2.legend()\n", - "\n", - "pass" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_c, nu1_c, label=r'$\\nu_1$')\n", + "ax1.plot(alpha_c, gamma11_c, label=r'$\\gamma_{11}$')\n", + "ax1.plot(alpha_c, gamma12_c, label=r'$\\gamma_{12}$')\n", + "ax1.plot(alpha_c, tau_c, label=r'$\\tau_{12}$')\n", + "\n", + "ax1.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_c, nu2_c, label=r'$\\nu_2$')\n", + "ax2.plot(alpha_c, gamma22_c, label=r'$\\gamma_{22}$')\n", + "ax2.plot(alpha_c, gamma12_c, label=r'$\\gamma_{12}$')\n", + "ax2.plot(alpha_c, tau_c, label=r'$\\tau_{12}$')\n", + "\n", + "ax2.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "60453966-409d-44d7-969a-ee67005bb392", + "metadata": { + "id": "60453966-409d-44d7-969a-ee67005bb392" + }, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "60453966-409d-44d7-969a-ee67005bb392", - "metadata": { - "id": "60453966-409d-44d7-969a-ee67005bb392" - }, - "outputs": [], - "source": [ - "set_rc_params_article(ncol=2)\n", - "fig = plt.figure()\n", - "\n", - "ax1= fig.add_subplot(1,2,1)\n", - "ax2= fig.add_subplot(1,2,2)\n", - "\n", - "ax1.plot(alpha_b, nu1_b, label=r'$\\nu_1$')\n", - "ax1.plot(alpha_b, gamma11_b, label=r'$\\gamma_{11}$')\n", - "ax1.plot(alpha_b, gamma12_b, label=r'$\\gamma_{12}$')\n", - "ax1.plot(alpha_b, tau_b, label=r'$\\tau_{12}$')\n", - "ax1.set_xscale('symlog', linthresh=min_alpha_scale)\n", - "ax1.set_yscale('symlog', linthresh=1.0e-6)\n", - "ax1.set_xlabel(r'$\\alpha$')\n", - "\n", - "ax1.legend()\n", - "\n", - "ax2.plot(alpha_b, nu2_b, label=r'$\\nu_2$')\n", - "ax2.plot(alpha_b, gamma22_b, label=r'$\\gamma_{22}$')\n", - "ax2.plot(alpha_b, gamma12_b, label=r'$\\gamma_{12}$')\n", - "ax2.plot(alpha_b, tau_b, label=r'$\\tau_{12}$')\n", - "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", - "ax2.set_yscale('symlog', linthresh=1.0e-6)\n", - "ax2.set_xlabel(r'$\\alpha$')\n", - "ax2.legend()\n", - "\n", - "pass" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, - { - "cell_type": "markdown", - "source": [ - "# Perturbative Quantities" - ], - "metadata": { - "id": "WqocAbPmfI5P" - }, - "id": "WqocAbPmfI5P" - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(alpha_b, nu1_b, label=r'$\\nu_1$')\n", + "ax1.plot(alpha_b, gamma11_b, label=r'$\\gamma_{11}$')\n", + "ax1.plot(alpha_b, gamma12_b, label=r'$\\gamma_{12}$')\n", + "ax1.plot(alpha_b, tau_b, label=r'$\\tau_{12}$')\n", + "ax1.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax1.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax1.set_xlabel(r'$\\alpha$')\n", + "\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_b, nu2_b, label=r'$\\nu_2$')\n", + "ax2.plot(alpha_b, gamma22_b, label=r'$\\gamma_{22}$')\n", + "ax2.plot(alpha_b, gamma12_b, label=r'$\\gamma_{12}$')\n", + "ax2.plot(alpha_b, tau_b, label=r'$\\tau_{12}$')\n", + "ax2.set_xscale('symlog', linthresh=min_alpha_scale)\n", + "ax2.set_yscale('symlog', linthresh=1.0e-6)\n", + "ax2.set_xlabel(r'$\\alpha$')\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "markdown", + "id": "WqocAbPmfI5P", + "metadata": { + "id": "WqocAbPmfI5P" + }, + "source": [ + "# Perturbative Quantities" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "ab63ada8-c087-4d13-ac4a-80429306b37a", + "metadata": { + "id": "ab63ada8-c087-4d13-ac4a-80429306b37a" + }, + "outputs": [], + "source": [ + "def get_zeta(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.ZETA_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.ZETA_I)\n", + "\n", + "def get_S(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.S_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.S_I)\n", + "\n", + "def get_Pzeta(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.PZETA_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.PZETA_I)\n", + "\n", + "def get_PS(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.PS_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.PS_I)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "70436600-32f4-4325-9b1f-049325be6471", + "metadata": {}, + "outputs": [], + "source": [ + "def integrate_mode1(k, max_time=-1.0):\n", + " # Defining relative tolerance for integration\n", + " prec = 1.0e-7\n", + " # Ratio potential frequency to define cross time\n", + " cross_size = 1.0e-13\n", + "\n", + " pert = Nc.HIPertTwoFluids.new()\n", + " pert.set_stiff_solver(True)\n", + " pert.props.reltol = prec\n", + " pert.set_mode_k(k)\n", + " alpha_try = -cosmo.abs_alpha(1.0e-14 * k**2)\n", + " ci = Ncm.Vector.new(8)\n", + " alphai = pert.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE1MAIN, alpha_try, cross_size)\n", + " pert.get_init_cond_zetaS(cosmo, alphai, 1, 0.25 * math.pi, ci)\n", + " pert.set_init_cond(cosmo, alphai, 1, False, ci)\n", + "\n", + " res = pert.evolve_array(cosmo, max_time)\n", + " res_a = np.array(res.dup_array()).reshape(-1,9)\n", + "\n", + " return res_a\n", + "\n", + "def integrate_mode2(k, max_time=-1.0):\n", + " # Defining relative tolerance for integration\n", + " prec = 1.0e-7\n", + " # Ratio potential frequency to define cross time\n", + " cross_size = 1.0e-5\n", + "\n", + " pert = Nc.HIPertTwoFluids.new()\n", + " pert.set_stiff_solver(True)\n", + " pert.props.reltol = prec\n", + " pert.set_mode_k(k)\n", + " alpha_try = -cosmo.abs_alpha(1.0e-14 * k**2)\n", + " ci = Ncm.Vector.new(8)\n", + " alphai = pert.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE2MAIN, alpha_try, cross_size)\n", + " pert.get_init_cond_zetaS(cosmo, alphai, 2, 0.25 * math.pi, ci)\n", + " pert.set_init_cond(cosmo, alphai, 2, False, ci)\n", + "\n", + " res = pert.evolve_array(cosmo, max_time)\n", + " res_a = np.array(res.dup_array()).reshape(-1,9)\n", + "\n", + " return res_a\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "13668ef8-43cd-4a07-a777-ea5bbdf1dd96", + "metadata": { + "id": "13668ef8-43cd-4a07-a777-ea5bbdf1dd96" + }, + "outputs": [], + "source": [ + "res1_a = integrate_mode1(1.0e8, -1.0)\n", + "res2_a = integrate_mode2(1.0e8, -1.0)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "e8992080-d34e-47e8-ae91-556e2e0c2a40", + "metadata": {}, + "outputs": [], + "source": [ + "def integrate_mode1_qp(k, max_time=-1.):\n", + " # Defining relative tolerance for integration\n", + " prec = 1.0e-11\n", + " # Ratio potential frequency to define cross time\n", + " cross_size = 1.0e-13\n", + "\n", + " pert = Nc.HIPertTwoFluids.new()\n", + " pert.set_stiff_solver(True)\n", + " pert.props.reltol = prec\n", + " pert.set_mode_k(k)\n", + " alpha_try = -cosmo.abs_alpha(1.0e-14 * k**2)\n", + " ci = Ncm.Vector.new(8)\n", + " alphai = pert.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE1MAIN, alpha_try, cross_size)\n", + " alphaf = pert.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE1MAIN, alpha_try, 1.0)\n", + " pert.get_init_cond_QP(cosmo, alphai, 1, 0.25 * math.pi, ci)\n", + " pert.set_init_cond(cosmo, alphai, 1, True, ci)\n", + "\n", + " res = pert.evolve_array(cosmo, min(alphaf, max_time))\n", + " res_a = np.array(res.dup_array()).reshape(-1,9)\n", + " for row in res_a:\n", + " alpha = row[0]\n", + " ci.set_array(row[1:])\n", + " pert.to_zeta_s(cosmo, alpha, ci)\n", + " row[1:] = np.array(ci.dup_array())\n", + " #print(f\"A {max_time} {alphaf} {res_a[-1,0]}\")\n", + "\n", + " if max_time > alphaf:\n", + " pert.set_init_cond(cosmo, alphaf, 1, False, ci)\n", + " res_c = pert.evolve_array(cosmo, max_time)\n", + " res_c_a = np.array(res_c.dup_array()).reshape(-1,9)\n", + " res_a = np.concatenate((res_a, res_c_a))\n", + "\n", + " return res_a, alphaf\n", + "\n", + "\n", + "def integrate_mode2_qp(k, max_time=-1.0):\n", + " # Defining relative tolerance for integration\n", + " prec = 1.0e-11\n", + " # Ratio potential frequency to define cross time\n", + " cross_size = 1.0e-5\n", + "\n", + " pert = Nc.HIPertTwoFluids.new()\n", + " pert.set_stiff_solver(True)\n", + " pert.props.reltol = prec\n", + " pert.set_mode_k(k)\n", + " alpha_try = -cosmo.abs_alpha(1.0e-14 * k**2)\n", + " ci = Ncm.Vector.new(8)\n", + " alphai = pert.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE2MAIN, alpha_try, cross_size)\n", + " alphaf = pert.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE2MAIN, alpha_try, 1.0)\n", + " pert.get_init_cond_QP(cosmo, alphai, 2, 0.25 * math.pi, ci)\n", + " pert.set_init_cond(cosmo, alphai, 2, True, ci)\n", + "\n", + " res = pert.evolve_array(cosmo, min(alphaf, max_time))\n", + " res_a = np.array(res.dup_array()).reshape(-1,9)\n", + " for row in res_a:\n", + " alpha = row[0]\n", + " ci.set_array(row[1:])\n", + " pert.to_zeta_s(cosmo, alpha, ci)\n", + " row[1:] = np.array(ci.dup_array())\n", + " #print(f\"B {max_time} {alphaf} {res_a[-1,0]}\")\n", + "\n", + " if max_time > alphaf:\n", + " pert.set_init_cond(cosmo, alphaf, 2, False, ci)\n", + " res_c = pert.evolve_array(cosmo, max_time)\n", + " res_c_a = np.array(res_c.dup_array()).reshape(-1,9)\n", + " res_a = np.concatenate((res_a, res_c_a))\n", + "\n", + " return res_a, alphaf\n" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "194fd91b-c10e-4895-b54e-2437dfe5b5b5", + "metadata": {}, + "outputs": [], + "source": [ + "res1_qp, alpha1_f = integrate_mode1_qp(1.0e1)\n", + "res2_qp, alpha2_f = integrate_mode2_qp(1.0e1)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "543d7fe5-0e28-436c-a7cd-b4498e08e7ab", + "metadata": {}, + "outputs": [], + "source": [ + "zr_index = Nc.HIPertITwoFluidsVars.ZETA_R+1\n", + "zi_index = Nc.HIPertITwoFluidsVars.ZETA_I+1\n", + "\n", + "sr_index = Nc.HIPertITwoFluidsVars.S_R+1\n", + "si_index = Nc.HIPertITwoFluidsVars.S_I+1" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2aa32a26-3337-4fcd-9a31-87b09cbe63aa", + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "ab63ada8-c087-4d13-ac4a-80429306b37a", - "metadata": { - "id": "ab63ada8-c087-4d13-ac4a-80429306b37a" - }, - "outputs": [], - "source": [ - "def get_zeta(v):\n", - " return v.get(Nc.HIPertITwoFluidsVars.ZETA_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.ZETA_I)\n", - "\n", - "def get_S(v):\n", - " return v.get(Nc.HIPertITwoFluidsVars.S_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.S_I)\n", - "\n", - "def get_Pzeta(v):\n", - " return v.get(Nc.HIPertITwoFluidsVars.PZETA_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.PZETA_I)\n", - "\n", - "def get_PS(v):\n", - " return v.get(Nc.HIPertITwoFluidsVars.PS_R) + 1.0j * v.get(Nc.HIPertITwoFluidsVars.PS_I)\n" - ] - }, + "name": "stderr", + "output_type": "stream", + "text": [ + " 1%|██ | 1/100 [00:03<05:17, 3.21s/it]" + ] + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1 = fig.add_subplot(2,1,1)\n", + "ax2 = fig.add_subplot(2,1,2)\n", + "\n", + "k_a = np.geomspace(1.0e-1, 1.0e4, 100)\n", + "Pk1 = []\n", + "Pk2 = []\n", + "for k in tqdm(k_a):\n", + " res1_qp, alpha1_f = integrate_mode1_qp(k, -50.0)\n", + " res2_qp, alpha2_f = integrate_mode2_qp(k, -35.0)\n", + " Pkt1 = k**3*np.hypot(res1_qp[:,zr_index], res1_qp[:,zi_index])**2\n", + " Pkt2 = k**3*np.hypot(res2_qp[:,zr_index], res2_qp[:,zi_index])**2\n", + " ax1.plot(res1_qp[:,0], Pkt1, label=\"Mode1\")\n", + " ax1.set_yscale('log')\n", + " \n", + " ax2.plot(res2_qp[:,0], Pkt2, label=\"Mode2\")\n", + " ax2.set_yscale('log')\n", + "\n", + " Pk1.append(Pkt1[-1])\n", + " Pk2.append(Pkt2[-1])\n", + "\n", + "#plt.legend()\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "9ffc96e2-346c-4c7a-9a7a-eb1a09cb00af", + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "b73ca8cc-9168-4ecf-bed5-c14f56b1e753", - "metadata": { - "id": "b73ca8cc-9168-4ecf-bed5-c14f56b1e753" - }, - "outputs": [], - "source": [ - "def integrate_system(k):\n", - " # Defining relative tolerance for integration\n", - " prec = 1.0e-10\n", - " # Ratio potential frequency to define cross time\n", - " cross_size = 1.0e-9\n", - "\n", - " # New perturbations object\n", - " pert1 = Nc.HIPertTwoFluids.new()\n", - " pert2 = Nc.HIPertTwoFluids.new()\n", - " # Setting reltol\n", - " pert1.props.reltol = prec\n", - " pert2.props.reltol = prec\n", - " # Setting k\n", - " pert1.set_mode_k(k)\n", - " pert2.set_mode_k(k)\n", - "\n", - " # Choose an initial condition\n", - " alpha_try = -cosmo.abs_alpha(1.0e-14 * k**2)\n", - "\n", - " # New vector to store initial conditions\n", - " # 8 dimensional (Q_1, Q_2, P_1, P_2), real and imaginary parts\n", - " ci1 = Ncm.Vector.new(8)\n", - " ci2 = Ncm.Vector.new(8)\n", - "\n", - " alphai1 = pert1.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE1MAIN, alpha_try, cross_size)\n", - " alphai2 = pert2.get_cross_time(cosmo, Nc.HIPertTwoFluidsCross.MODE2MAIN, alpha_try, cross_size)\n", - "\n", - " # Compute initial conditions at alpha_try store at ci and use normalization factor\n", - " # pi/4\n", - " pert1.get_init_cond_zetaS(cosmo, alphai1, 1, 0.25 * math.pi, ci1)\n", - " pert2.get_init_cond_zetaS(cosmo, alphai2, 2, 0.25 * math.pi, ci2)\n", - "\n", - " # Use the previously computed initial conditions to start the system at alpha_try\n", - " pert1.set_init_cond(cosmo, alphai1, 30, False, ci1)\n", - " pert2.set_init_cond(cosmo, alphai2, 30, False, ci2)\n", - " # print(f\"Setting initial conditions for zeta1 and S1 at {alphai1}\")\n", - " # print(f\"Setting initial conditions for zeta2 and S2 at {alphai2}\")\n", - "\n", - " if alphai2 > alphai1:\n", - " pert1.evolve(cosmo, alphai2)\n", - " ci1, _ = pert1.peek_state(cosmo)\n", - " else:\n", - " pert2.evolve(cosmo, alphai1)\n", - " ci2, _ = pert2.peek_state(cosmo)\n", - "\n", - " alphai = max(alphai1, alphai2)\n", - "\n", - " # Create a array of times to integrate the system over\n", - " alpha_evol = np.linspace(alphai, -1.0e-1, 1000)\n", - "\n", - " # Integrate the system by stepping through alpha_evol using .evolve\n", - " zeta1_a = [get_zeta(ci1)]\n", - " S1_a = [get_S(ci1)]\n", - " Pzeta1_a = [get_Pzeta(ci1)]\n", - " PS1_a = [get_PS(ci1)]\n", - "\n", - " zeta2_a = [get_zeta(ci2)]\n", - " S2_a = [get_S(ci2)]\n", - " Pzeta2_a = [get_Pzeta(ci2)]\n", - " PS2_a = [get_PS(ci2)]\n", - "\n", - " for alpha in tqdm(alpha_evol[1:], desc=\"Time evolution\", position=1, leave=False):\n", - " pert1.evolve(cosmo, alpha)\n", - " pert2.evolve(cosmo, alpha)\n", - " v1, _alphac1 = pert1.peek_state(cosmo)\n", - " v2, _alphac2 = pert2.peek_state(cosmo)\n", - "\n", - " zeta1_a.append(get_zeta(v1))\n", - " S1_a.append(get_S(v1))\n", - " Pzeta1_a.append(get_Pzeta(v1))\n", - " PS1_a.append(get_PS(v1))\n", - "\n", - " zeta2_a.append(get_zeta(v2))\n", - " S2_a.append(get_S(v2))\n", - " Pzeta2_a.append(get_Pzeta(v2))\n", - " PS2_a.append(get_PS(v2))\n", - "\n", - " zeta1 = np.array(zeta1_a)\n", - " S1 = np.array(S1_a)\n", - " Pzeta1 = np.array(Pzeta1_a)\n", - " PS1 = np.array(PS1_a)\n", - "\n", - " zeta2 = np.array(zeta2_a)\n", - " S2 = np.array(S2_a)\n", - " Pzeta2 = np.array(Pzeta2_a)\n", - " PS2 = np.array(PS2_a)\n", - "\n", - " return (alpha_evol, zeta1, S1, Pzeta1, PS1, zeta2, S2, Pzeta2, PS2)\n" - ] + "ename": "NameError", + "evalue": "name 'k_a' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[20], line 4\u001b[0m\n\u001b[1;32m 1\u001b[0m set_rc_params_article(ncol\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m2\u001b[39m)\n\u001b[1;32m 2\u001b[0m fig \u001b[38;5;241m=\u001b[39m plt\u001b[38;5;241m.\u001b[39mfigure()\n\u001b[0;32m----> 4\u001b[0m b, a \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mpolyfit(np\u001b[38;5;241m.\u001b[39mlog(\u001b[43mk_a\u001b[49m), np\u001b[38;5;241m.\u001b[39mlog(Pk2), \u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m 6\u001b[0m ax1 \u001b[38;5;241m=\u001b[39m fig\u001b[38;5;241m.\u001b[39madd_subplot(\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m 7\u001b[0m ax1\u001b[38;5;241m.\u001b[39mplot(k_a, Pk2)\n", + "\u001b[0;31mNameError\u001b[0m: name 'k_a' is not defined" + ] }, { - "cell_type": "code", - "execution_count": null, - "id": "13668ef8-43cd-4a07-a777-ea5bbdf1dd96", - "metadata": { - "id": "13668ef8-43cd-4a07-a777-ea5bbdf1dd96" - }, - "outputs": [], - "source": [ - "alpha_evol, zeta1, S1, Pzeta1, PS1, zeta2, S2, Pzeta2, PS2 = integrate_system(1.0)" + "data": { + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "b, a = np.polyfit(np.log(k_a), np.log(Pk2), 1)\n", + "\n", + "ax1 = fig.add_subplot(2,1,1)\n", + "ax1.plot(k_a, Pk2)\n", + "ax1.plot(k_a, np.exp(a+b*np.log(k_a)))\n", + "ax1.set_xscale('log')\n", + "ax1.set_yscale('log')\n", + "\n", + "plt.show()\n", + "b+1" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "id": "63ab0826-e401-424e-a6fb-0ef10443823c", + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "3d343fd0-19b8-4b76-aeff-28a443f081bd", - "metadata": { - "id": "3d343fd0-19b8-4b76-aeff-28a443f081bd" - }, - "outputs": [], - "source": [ - "set_rc_params_article(ncol=2)\n", - "fig = plt.figure()\n", - "\n", - "ax1= fig.add_subplot(2,1,1)\n", - "ax2= fig.add_subplot(2,1,2)\n", - "\n", - "ax1.plot(alpha_evol, np.real(zeta1), label=r'$\\mathrm{Re}(\\zeta_1)$')\n", - "ax1.plot(alpha_evol, np.imag(zeta1), label=r'$\\mathrm{Im}(\\zeta_1)$')\n", - "ax1.plot(alpha_evol, np.real(zeta2), label=r'$\\mathrm{Re}(\\zeta_2)$')\n", - "ax1.plot(alpha_evol, np.imag(zeta2), label=r'$\\mathrm{Im}(\\zeta_2)$')\n", - "ax1.set_yscale('symlog')\n", - "ax1.set_xlabel(r'$\\alpha$')\n", - "ax1.legend()\n", - "\n", - "ax2.plot(alpha_evol, np.real(S1), label=r'$\\mathrm{Re}(S_1)$')\n", - "ax2.plot(alpha_evol, np.imag(S1), label=r'$\\mathrm{Im}(S_1)$')\n", - "ax2.plot(alpha_evol, np.real(S2), label=r'$\\mathrm{Re}(S_2)$')\n", - "ax2.plot(alpha_evol, np.imag(S2), label=r'$\\mathrm{Im}(S_2)$')\n", - "ax2.set_yscale('symlog')\n", - "ax2.set_xlabel(r'$\\alpha$')\n", - "ax2.legend()\n" + "data": { + "text/plain": [ + "array([-8.13964193e-03, 1.06259987e+02])" ] - }, + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "d2940da2-4e1a-4e49-8a06-30a5db9a4cd5", + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "0048f301-a4f1-48a4-9de3-c2a3ef103f59", - "metadata": { - "id": "0048f301-a4f1-48a4-9de3-c2a3ef103f59" - }, - "outputs": [], - "source": [ - "set_rc_params_article(ncol=2)\n", - "fig = plt.figure()\n", - "\n", - "ax1= fig.add_subplot(2,1,1)\n", - "ax2= fig.add_subplot(2,1,2)\n", - "\n", - "ax1.plot(alpha_evol, np.abs(zeta1)**2, label=r'$|\\zeta_1|^2$')\n", - "ax1.plot(alpha_evol, np.abs(zeta2)**2, label=r'$|\\zeta_2|^2$')\n", - "ax1.set_yscale('log')\n", - "ax1.set_xlabel(r'$\\alpha$')\n", - "ax1.legend()\n", - "\n", - "ax2.plot(alpha_evol, np.abs(S1)**2, label=r'$|S_1|^2$')\n", - "ax2.plot(alpha_evol, np.abs(S2)**2, label=r'$|S_2|^2$')\n", - "ax2.set_yscale('log')\n", - "ax2.set_xlabel(r'$\\alpha$')\n", - "ax2.legend()\n", - "\n", - "pass" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1 = fig.add_subplot(2,1,1)\n", + "ax2 = fig.add_subplot(2,1,2)\n", + "\n", + "ax1.plot(res1_qp[:,0], np.hypot(res1_qp[:,sr_index], res1_qp[:,si_index]), label=\"Mode1\")\n", + "ax1.set_yscale('log')\n", + "\n", + "ax2.plot(res2_qp[:,0], np.hypot(res2_qp[:,sr_index], res2_qp[:,si_index]), label=\"Mode2\")\n", + "ax2.set_yscale('log')\n", + "\n", + "plt.legend()\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "b2d4b0fd-2cba-4881-a5a0-e391eb0a237d", + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "d8694a1e-6562-434c-b5da-9d60cdb3de4f", - "metadata": { - "id": "d8694a1e-6562-434c-b5da-9d60cdb3de4f" - }, - "outputs": [], - "source": [ - "k_a = np.geomspace(1.0e-3, 1.0e3, 100)\n", - "\n", - "PI_zeta1 = []\n", - "PI_zeta2 = []\n", - "PI_S1 = []\n", - "PI_S2 = []\n", - "\n", - "for k in tqdm(k_a, desc= \"Mode evolution\", position=0):\n", - " alpha_evol, zeta1, S1, Pzeta1, PS1, zeta2, S2, Pzeta2, PS2 = integrate_system(k)\n", - " PI_zeta1.append(np.abs(zeta1[-1])**2)\n", - " PI_zeta2.append(np.abs(zeta2[-1])**2)\n", - " PI_S1.append(np.abs(S1[-1])**2)\n", - " PI_S2.append(np.abs(S2[-1])**2)" - ] - }, + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of time steps: Mode1 (207222, 9) Mode2 (153237, 9)\n" + ] + } + ], + "source": [ + "print(f\"Number of time steps: Mode1 {res1_a.shape} Mode2 {res2_a.shape}\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "7373590b-1669-45d8-97e7-e5c9614f6365", + "metadata": {}, + "outputs": [], + "source": [ + "zr_index = Nc.HIPertITwoFluidsVars.ZETA_R+1\n", + "zi_index = Nc.HIPertITwoFluidsVars.ZETA_I+1\n", + "\n", + "sr_index = Nc.HIPertITwoFluidsVars.S_R+1\n", + "si_index = Nc.HIPertITwoFluidsVars.S_I+1" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "e4ee0de8-36b0-4da0-b494-f7047f88284f", + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "b69e8502-f742-440f-b997-9b3de0dc2dd8", - "metadata": { - "id": "b69e8502-f742-440f-b997-9b3de0dc2dd8" - }, - "outputs": [], - "source": [ - "set_rc_params_article(ncol=2)\n", - "fig = plt.figure()\n", - "\n", - "ax1= fig.add_subplot(2,1,1)\n", - "ax2= fig.add_subplot(2,1,2)\n", - "\n", - "ax1.plot(k_a, k_a**3 * PI_zeta1, label=r'$\\Pi_{\\zeta_1}$')\n", - "ax1.plot(k_a, k_a**3 * PI_zeta2, label=r'$\\Pi_{\\zeta_2}$')\n", - "ax1.set_xscale('log')\n", - "ax1.set_yscale('log')\n", - "ax1.set_xlabel(r'$k$')\n", - "ax1.legend()\n", - "\n", - "ax2.plot(k_a, k_a**3 * PI_S1, label=r'$\\Pi_{S_1}$')\n", - "ax2.plot(k_a, k_a**3 * PI_S2, label=r'$\\Pi_{S_2}$')\n", - "ax2.set_xscale('log')\n", - "ax2.set_yscale('log')\n", - "ax2.set_xlabel(r'$k$')\n", - "ax2.legend()\n", - "\n", - "pass" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(2,2,1)\n", + "ax2= fig.add_subplot(2,2,2)\n", + "ax3= fig.add_subplot(2,2,3)\n", + "ax4= fig.add_subplot(2,2,4)\n", + "\n", + "ax1.plot(res1_a[:,0], np.abs(res1_a[:,zr_index]))\n", + "ax1.plot(res1_a[:,0], np.abs(res1_a[:,zi_index]))\n", + "ax1.plot(res1_a[:,0], np.hypot(res1_a[:,zr_index], res1_a[:,zi_index]))\n", + "ax1.plot(res1_qp[:,0], np.hypot(res1_qp[:,zr_index], res1_qp[:,zi_index]))\n", + "ax1.set_yscale('log')\n", + "\n", + "ax2.plot(res2_a[:,0], np.abs(res2_a[:,zr_index]))\n", + "ax2.plot(res2_a[:,0], np.abs(res2_a[:,zi_index]))\n", + "ax2.plot(res2_a[:,0], np.hypot(res2_a[:,zr_index], res2_a[:,zi_index]))\n", + "ax2.set_yscale('log')\n", + "\n", + "ax3.plot(res1_a[:,0], np.abs(res1_a[:,sr_index]))\n", + "ax3.plot(res1_a[:,0], np.abs(res1_a[:,si_index]))\n", + "ax3.plot(res1_a[:,0], np.hypot(res1_a[:,sr_index], res1_a[:,si_index]))\n", + "ax3.set_yscale('log')\n", + "\n", + "ax4.plot(res2_a[:,0], np.abs(res2_a[:,sr_index]))\n", + "ax4.plot(res2_a[:,0], np.abs(res2_a[:,si_index]))\n", + "ax4.plot(res2_a[:,0], np.hypot(res2_a[:,sr_index], res2_a[:,si_index]))\n", + "ax4.set_yscale('log')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "daefdce6-1bda-4847-83bc-b0ad02c33522", + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "818e4ad0-510c-4d31-a2bf-83bde5f04c58", - "metadata": { - "id": "818e4ad0-510c-4d31-a2bf-83bde5f04c58" - }, - "outputs": [], - "source": [ - "#print(np.polyfit(np.log(k_a),np.log(k_a**3 * PI_zeta2),1)[0])\n", - "\n", - "print(1.0 + 12.0 * cosmo.props.w / (1.0 + 3.0 *cosmo.props.w))\n" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, - { - "cell_type": "markdown", - "source": [ - "# Parte do Eduado" - ], - "metadata": { - "id": "fuB-VSqxNTu3" - }, - "id": "fuB-VSqxNTu3" - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,1,1)\n", + "\n", + "ax1.plot(res1_a[:,0], np.hypot(res1_a[:,zr_index], res1_a[:,zi_index]), label=\"Mode1\")\n", + "ax1.plot(res2_a[:,0], np.hypot(res2_a[:,zr_index], res2_a[:,zi_index]), label=\"Mode2\")\n", + "ax1.set_yscale('log')\n", + "\n", + "plt.legend()\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "378c8f1f-8f53-4de8-b63c-5a20ddb89421", + "metadata": {}, + "outputs": [], + "source": [ + "pert_tmp = Nc.HIPertTwoFluids.new()\n", + "pert_tmp.set_mode_k(1.0e0)\n", + "ci1 = Ncm.Vector.new(8)\n", + "\n", + "zeta1_wkb = []\n", + "for t in res1_a[:,0]:\n", + " pert_tmp.get_init_cond_zetaS(cosmo, t, 1, 0.25 * math.pi, ci1)\n", + " zeta1_wkb.append(np.hypot(ci1.get(Nc.HIPertITwoFluidsVars.ZETA_R), ci1.get(Nc.HIPertITwoFluidsVars.ZETA_I)))\n", + "\n", + "zeta2_wkb = []\n", + "for t in res2_a[:,0]:\n", + " pert_tmp.get_init_cond_zetaS(cosmo, t, 2, 0.25 * math.pi, ci1)\n", + " zeta2_wkb.append(np.hypot(ci1.get(Nc.HIPertITwoFluidsVars.ZETA_R), ci1.get(Nc.HIPertITwoFluidsVars.ZETA_I)))\n", + "\n", + "s1_wkb = []\n", + "for t in res1_a[:,0]:\n", + " pert_tmp.get_init_cond_zetaS(cosmo, t, 1, 0.25 * math.pi, ci1)\n", + " s1_wkb.append(np.hypot(ci1.get(Nc.HIPertITwoFluidsVars.S_R), ci1.get(Nc.HIPertITwoFluidsVars.S_I)))\n", + "\n", + "s2_wkb = []\n", + "for t in res2_a[:,0]:\n", + " pert_tmp.get_init_cond_zetaS(cosmo, t, 2, 0.25 * math.pi, ci1)\n", + " s2_wkb.append(np.hypot(ci1.get(Nc.HIPertITwoFluidsVars.S_R), ci1.get(Nc.HIPertITwoFluidsVars.S_I)))\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "14f3527d-fd7f-493e-8d64-1bf8e1b3cf8f", + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "6b2523f8", - "metadata": { - "id": "6b2523f8" - }, - "outputs": [], - "source": [ - "def test_two_fluids_wkb_mode(mode: int = Nc.HIPertTwoFluidsCross.MODE1SUB, case_f: int = 1, nullr = 1.0, nulli = 1.0) -> None:\n", - " \"\"\"Compute WKB approximation for the two-fluids model.\"\"\"\n", - "\n", - " #\n", - " # New homogeneous and isotropic cosmological model NcHICosmoQGRW\n", - " #\n", - " cosmo = Nc.HICosmoQGRW()\n", - "\n", - " w = 0.00001\n", - " prec = 1.0e-6\n", - " mode_k = 1000\n", - "\n", - " cosmo.props.w = w\n", - " cosmo.props.Omegar = 2.0 * (1.0e-8)\n", - " cosmo.props.Omegaw = 2.0 * (1.0 - 1.0e-8)\n", - " cosmo.props.xb = 1.0e30\n", - "\n", - " pert = Nc.HIPertTwoFluids.new()\n", - "\n", - " pert.props.reltol = prec\n", - " pert.set_mode_k(mode_k)\n", - "\n", - " cross_size = 1.0e-5\n", - " alpha_try = -cosmo.abs_alpha(1.0e-12 * mode_k**2)\n", - " # Chuta tempo incial e depois calcula ele aqui embaixo, dependendo de qual modo é o main\n", - "\n", - " # Pra descobrir se o alpha1 da outra funcao faz sentido, coloca auqi o caso que vc quiser e imprime o tempo calcualdo (ex: mode1main, da um alpha 1.0e-9. Por isso ele deve ter colocado na 2 funçao)\n", - " if mode == Nc.HIPertTwoFluidsCross.MODE1MAIN:\n", - " alphai = pert.get_cross_time(\n", - " cosmo, Nc.HIPertTwoFluidsCross.MODE1MAIN, alpha_try, cross_size\n", - " )\n", - " elif mode == Nc.HIPertTwoFluidsCross.MODE1SUB:\n", - " alphai = pert.get_cross_time(\n", - " cosmo, Nc.HIPertTwoFluidsCross.MODE1SUB, alpha_try, cross_size\n", - " )\n", - " elif mode == Nc.HIPertTwoFluidsCross.MODE2MAIN:\n", - " alphai = pert.get_cross_time(\n", - " cosmo, Nc.HIPertTwoFluidsCross.MODE2MAIN, alpha_try, cross_size\n", - " )\n", - " elif mode == Nc.HIPertTwoFluidsCross.MODE2SUB:\n", - " alphai = pert.get_cross_time(\n", - " cosmo, Nc.HIPertTwoFluidsCross.MODE2SUB, alpha_try, cross_size\n", - " )\n", - " else:\n", - " raise ValueError(\"Invalid mode\")\n", - "\n", - " alphaf = +cosmo.abs_alpha(1.0e20)\n", - "\n", - " print(f\"Mode k = mode_k: {mode_k}\")\n", - "\n", - " pert.set_stiff_solver(True)\n", - "\n", - " alpha_a = []\n", - " gammabar11_a = []\n", - " gammabar22_a = []\n", - " gammabar12_a = []\n", - " taubar12_a = []\n", - " nu1_a = []\n", - " nu2_a = []\n", - "\n", - " for alpha in np.linspace(alphai, alphaf, 10000):\n", - " eom = pert.eom(cosmo, alpha)\n", - " alpha_a.append(alpha)\n", - "\n", - " gammabar11_a.append(math.fabs(eom.gammabar11))\n", - " gammabar22_a.append(math.fabs(eom.gammabar22))\n", - " gammabar12_a.append(math.fabs(eom.gammabar12))\n", - " taubar12_a.append(math.fabs(eom.taubar))\n", - " nu1_a.append(eom.nu1)\n", - " nu2_a.append(eom.nu2)\n", - "\n", - " print(\n", - " f\"# Calculating mode 1, initial time {alphai}, redshift_alpha {cosmo.x_alpha(alphai):8.2e}]: \"\n", - " )\n", - "\n", - " ci = Ncm.Vector.new(8)\n", - "\n", - " pert.get_init_cond_zetaS(cosmo, alphai, case_f, 0.25 * math.pi, ci)\n", - " pert.set_init_cond(cosmo, alphai, 3, False, ci)\n", - "\n", - " Ps_zeta1 = []\n", - " Ps_S1 = []\n", - " Ps_Pzeta1 = []\n", - " Ps_PS1 = []\n", - "\n", - " Ps_zeta1.append(\n", - " math.hypot(\n", - " nullr * ci.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", - " nulli * ci.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", - " )\n", - " ** 2\n", - " )\n", - " Ps_S1.append(\n", - " math.hypot(\n", - " nullr *ci.get(Nc.HIPertITwoFluidsVars.S_R),\n", - " nulli *ci.get(Nc.HIPertITwoFluidsVars.S_I),\n", - " )\n", - " ** 2\n", - " )\n", - " Ps_Pzeta1.append(\n", - " math.hypot(\n", - " nullr *ci.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", - " nulli *ci.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", - " )\n", - " ** 2\n", - " )\n", - " Ps_PS1.append(\n", - " math.hypot(\n", - " nullr * ci.get(Nc.HIPertITwoFluidsVars.PS_R),\n", - " nulli * ci.get(Nc.HIPertITwoFluidsVars.PS_I),\n", - " )\n", - " ** 2\n", - " )\n", - "\n", - " for alpha in tqdm(alpha_a[1:]):\n", - " # for alpha in alpha_a[1:]:\n", - " pert.evolve(cosmo, alpha)\n", - " v, _alphac = pert.peek_state(cosmo)\n", - " Ps_zeta1.append(\n", - " math.hypot(\n", - " nullr * v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", - " nulli * v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", - " )\n", - " ** 2\n", - " )\n", - " Ps_S1.append(\n", - " math.hypot(\n", - " nullr * v.get(Nc.HIPertITwoFluidsVars.S_R),\n", - " nulli * v.get(Nc.HIPertITwoFluidsVars.S_I),\n", - " )\n", - " ** 2\n", - " )\n", - " Ps_Pzeta1.append(\n", - " math.hypot(\n", - " nullr * v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", - " nulli * v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", - " )\n", - " ** 2\n", - " )\n", - " Ps_PS1.append(\n", - " math.hypot(\n", - " nullr * v.get(Nc.HIPertITwoFluidsVars.PS_R),\n", - " nulli * v.get(Nc.HIPertITwoFluidsVars.PS_I),\n", - " )\n", - " ** 2\n", - " )\n", - " plt.plot(alpha_a, Ps_zeta1, label=r\"$P_\\zeta$\")\n", - " plt.plot(alpha_a, Ps_S1, label=r\"$P_Q$\")\n", - " plt.plot(alpha_a, Ps_Pzeta1, label=r\"$P_{P_\\zeta}$\")\n", - " plt.plot(alpha_a, Ps_PS1, label=r\"$P_{P_Q}$\")\n", - " plt.xlabel(r\"$\\alpha$\")\n", - " plt.ylabel(r\"Mode\")\n", - " plt.grid()\n", - " plt.legend(loc=\"upper left\")\n", - " # plt.xscale('log')\n", - " plt.yscale(\"log\")\n", - "\n", - " Delta_zeta1 = (\n", - " mode_k**3 * Ps_zeta1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_S1 = mode_k**3 * Ps_S1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " Delta_Pzeta1 = (\n", - " mode_k**3 * Ps_Pzeta1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_PS1 = (\n", - " mode_k**3 * Ps_PS1.pop() / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " print(\n", - " f\"# Final values k = {mode_k: 20.15g} Ps_zeta{case_f} = {Delta_zeta1: 21.15e} \"\n", - " f\"Ps_Pzeta{case_f} = {Delta_Pzeta1: 21.15e} Ps_S{case_f} = {Delta_S1: 21.15e} \"\n", - " f\"Ps_PS{case_f} = {Delta_PS1: 21.15e}\"\n", - " )\n", - "\n", - "\n", - "\n", - " #plt.savefig('mode_I_p_R')\n", - " #plt.clf()\n", - " plt.show()" + "data": { + "text/plain": [ + "" ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" }, { - "cell_type": "code", - "execution_count": null, - "id": "a81352e0", - "metadata": { - "id": "a81352e0" - }, - "outputs": [], - "source": [ - "def test_two_fluids_wkb_spec() -> None:\n", - " \"\"\"Compute WKB approximation for the two-fluids model spectrum.\"\"\"\n", - "\n", - " #\n", - " # New homogeneous and isotropic cosmological model NcHICosmoQGRW\n", - " #\n", - " cosmo = Nc.HICosmoQGRW() # P1 = Cosmologia\n", - "\n", - " w = 1.0e-5 #P2 eq de estado da materia escura\n", - " prec = 1.0e-7\n", - "\n", - " #P3 densidade de radiação e materia escura e energia escura (1 - resto)\n", - " cosmo.props.w = w\n", - " cosmo.props.Omegar = (1.0e-8) * 1.0\n", - " cosmo.props.Omegaw = (1.0 - 1.0e-8) * 1.0\n", - " cosmo.props.xb = 1.0e30 # P4 x do bounce\n", - "\n", - " pert = Nc.HIPertTwoFluids.new()\n", - "\n", - " pert.props.reltol = prec\n", - " # pert.set_stiff_solver (True)\n", - "\n", - " # k = 1 => lambda = 5 Gpc\n", - " # k = 10^5 => lambda = 50 kpc\n", - " lnki = math.log(1.0e0)# P5 intervalo de momento de interesse\n", - " lnkf = math.log(1.0e5)\n", - " lnk_a = np.linspace(lnki, lnkf, 20)\n", - "\n", - " ci = Ncm.Vector.new(8)\n", - "\n", - " k_a = []\n", - " Ps_zeta1 = []\n", - " Ps_S1 = []\n", - " Ps_zeta2 = []\n", - " Ps_S2 = []\n", - " Ps_Pzeta1 = []\n", - " Ps_PS1 = []\n", - "\n", - " out_file = open(\"twofluids_spectrum_{w}.dat\", \"w\", encoding=\"utf-8\")\n", - "#alpha is related to the time variable. The log-redshift time\n", - " start_alpha1 = 1.0e-10 # P5 tempo inicial dependente do redshift.\n", - " start_alpha2 = 1.0e-14\n", - "\n", - " for lnk in tqdm(lnk_a):\n", - " k = math.exp(lnk)\n", - " pert.set_mode_k(k)\n", - " k_a.append(k)\n", - "\n", - " alphaf = cosmo.abs_alpha(1.0e20)\n", - "\n", - " # print (\"# Evolving mode %e from %f to %f\" % (k, alphai, alphaf))\n", - " #S is our variable Q.\n", - " alphai = -cosmo.abs_alpha(start_alpha1 * k**2)\n", - "\n", - " #### Ate aqui só coloca todos os parametros, define o tempo inicial, e converte o alpha1 em algum tipo de numero absoluto nessa funçao de cima.\n", - "\n", - " ##### Agora embaixo, calcula as cond iniciais, seta as condicioes iniciais e evolui no tempo.\n", - "\n", - " pert.get_init_cond_zetaS(cosmo, alphai, 1, 0.25 * math.pi, ci)\n", - "#This function does the following: Calls get_init_cond_zetaS, which calls cond_QP.\n", - "#IN cond_QP:\n", - " #Starts interface that have the equations of motion and the decomposition TV.\n", - " #Defines which case: 1 or 2, defining which momentum we assume as non-zero\n", - " #Computes all the init cond\n", - " #I believe that R and I represents each solutioon 1 and 2.\n", - "#Then we call to_zetaS, which changes from QP to zeta Q\n", - " pert.set_init_cond(cosmo, alphai, 1, False, ci)\n", - "\n", - " print(f\"# Mode 1 k {k: 21.15e}, state module {pert.get_state_mod():f}\")\n", - "\n", - " pert.evolve(cosmo, alphaf)#Evolve the system untill alphaF\n", - "\n", - "\n", - "\n", - " v, _alphac = pert.peek_state(cosmo)#Get the current time and values of the numerical solution for the modes. V é o vetor com os modos, n sei a ordem\n", - "#I believe that Delta represents the spectrum here.\n", - "\n", - "\n", - "##Aqui terminou de calcular os modos pro momento do loop. Ai agora calcula o espectro\n", - " Delta_zeta1 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", - " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_S1 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_Pzeta1 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", - " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_PS1 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - "\n", - " Ps_zeta1.append(Delta_zeta1)\n", - " Ps_S1.append(Delta_S1)\n", - " Ps_Pzeta1.append(Delta_Pzeta1)\n", - " Ps_PS1.append(Delta_PS1)\n", - "\n", - "\n", - " #### Aqui acabou o espectro pro modo 1. Ai faz de novo pro modo 2. ####3\n", - "\n", - " alphai = -cosmo.abs_alpha(start_alpha2 * k**2)\n", - " pert.get_init_cond_zetaS(cosmo, alphai, 2, 0.25 * math.pi, ci)\n", - " pert.set_init_cond(cosmo, alphai, 0, False, ci)\n", - "\n", - " pert.evolve(cosmo, alphaf)\n", - " v, _alphac = pert.peek_state(cosmo)\n", - " print(_alphac)\n", - " Delta_zeta2 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", - " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_S2 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_Pzeta2 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", - " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_PS2 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - "\n", - " Ps_zeta2.append(Delta_zeta2)\n", - " Ps_S2.append(Delta_S2)\n", - " Ps_zeta2.append(Delta_Pzeta2)\n", - " Ps_S2.append(Delta_PS2)\n", - "\n", - " out_file.write(\n", - " f\"{k: 20.15e} {Delta_zeta1: 20.15e} {Delta_zeta2: 20.15e} {Delta_S1: 20.15e} \"\n", - " f\"{Delta_S2: 20.15e} {Delta_Pzeta1: 20.15e} {Delta_Pzeta2: 20.15e} \"\n", - " f\"{Delta_PS1: 20.15e} {Delta_PS2: 20.15e}\\n\"\n", - " )\n", - " out_file.flush()\n", - "\n", - " out_file.close()\n", - "\n", - "###Plot\n", - "\n", - " plt.plot(k_a, Ps_zeta1, label=r\"$P_\\zeta$\")\n", - " plt.plot(k_a, Ps_S1, label=r\"$P_Q$\")\n", - " #plt.plot(k_a, Ps_zeta2, label=r\"$P^2_\\zeta$\")\n", - " # plt.plot(k_a, Ps_S2, label=r\"$P^2_Q$\")\n", - " plt.xlabel(r\"$k $\")\n", - " plt.ylabel(r\"$Spectrum$\")\n", - " plt.grid()\n", - " plt.legend(loc=\"upper left\")\n", - " #plt.xscale(\"log\")\n", - " #plt.yscale(\"log\")\n", - "\n", - "\n", - " plt.savefig('spec')\n", - " plt.show()" + "data": { + "image/png": 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8ccD1TSNuok9MH5UT+Y/ahlrGfjC23Y+z9Oqlh+36nDBhArm5ue4PsWazmeTk5Fa1Fh1JcnIyycnJQOPSHQaDAYvF0qJlPERg+2bLN6wvW090SDQ3H6vuZI4H0+LCKDU11f0ppInZbG726UCn02E2mzEajZhMpgPWvdHr9e61bFrKbrdjt9vd2xUVFa16vRCiuVdXvkpxTTG9ont55UVJtF16ejrjxo1zF0Y5OTlkZWU16+7KzMx0b2dkZLgXjm1a/8xoNGKxWA54vl6vd69638Rms2G1WqUoEkfkcDl48Y8XAbj+mOvRhevUDXQQbZowoLCwsFkLkl6vdxdOrS2ADmXOnDnMnj3bI/sSItAV2gr5v7//D4DpY6cTHixrQ3lSRHAES69e2iHHOZLk5GQKCgoO2pJjMpmw2WzuxVVTUlJITk5mxYoVQOO1HWDBggXu51ssFvLz87HZbGRmZjYbCjFx4sQ2LSArAsenmz5lW+U29OF6rh1+rdpxDsrjMyn9u5XoUMxmMxaLpdmKyAeTlZXFlClT3NsVFRX06SNN/0K0lqIoPLb0MRqUBs7ocwan9T5N7Uh+R6PReM3dfRkZGeTk5JCUlERGRkazn+Xl5TUboJ2YmIjZbKawsLDZ43q93v18i8VCWloaQLPWooyMDDIyMmQYhTiiuoY6Xv2zcemPiSMmqr70x6G0qTBKSEho1rXWNAC7JYxGo/tTyeGEhYURFhZ2tBGFEPt8tfkrlu9eTnhQONOOn6Z2HNHOEhMTWbFiBStWrGDJkiXNfpaUlEROTo77Q6nJZCInJwedTkdeXp67W63pg25SUhJWq9XdKtR03W8qiqQLTbTER+s+ori2mB5RPRg/ZLzacQ6pTYWR0WgkMzPTvW2xWORTgxBeqLK+knnL5wEw8biJ9IrupXIi0REyMjIoLCw84E6x9PR0CgsLSUhIABrHDzVdu/Py8khISMBoNLo/6DY9PykpCb1eT2JiIgkJCSxYsKDZuKWFCxdKkSQOqrK+ktdXNy5UfdvI2wgNClU50aFpFEVRWvJEs9lMTk4ONpuNjIyMZp80oPGTxdEMrm6tiooKYmNjKS8vJyYmpl2PJYS/eGLZE7y/9n36x/Tn44s/VuWi5Ou/u4fKX1dXx+bNmxkwYADh4TJmy9fI+9cxXvzjRXJW5jAgdgD/vfi/Hb4mWmuuPy1OZjQaD9oa1N6FkBCibdZZ1/Hhug8ByBqb5dWf1IQQ/qe0tpR317wLwOTRk71iodjDkSVBhPBjLsXFo78/iktxcU7/czip50lqRxJCBJg3V79JbUMtx8Qfg7Gv9w+3kcJICD/22abP+GvvX0QGR3J/8v1qxxFCBJiS2hIWrG+c9mHy6Mk+Mcu+FEZC+KlyeznP5D8DwKRRk+gW1U3lREKIQPPm6jepc9ZxXJfjfKbFWgojIfzUcwXPUWYvY6BuIFcPu1rtOEKIALN/a9GkkZN8orUIpDASwi+tLlmNaUPjHaMzxs4gRBuiciIhRKB5Y9Ub2J12RnYZ6TOtRSCFkRB+x+ly8sjvj6CgcJHhIpK7J6sdSXSghISEZrNXN5k7dy4ajaZVC8kmJSUd9vmZmZmkpKSQkJDQbD6j1khJSXFP+9JEo9FQUFDg3rbZbCQlJQEQFxfXbA23goKCZjnj4uJISUkhLS2NpKQk0tLSPLp4rmiZvTV7WbihcUJQX2otAimMhPA7pg0m1pSuoVNIJ6YkTznyC4Tf+feC3wDz588/YKLHtjCbzcTHx5OXl8fChQtJSUk5qgIkLS2N+fPnu7dNJhNGo7FZobVgwQImTJhwwGsLCgrc67Ttf245OTksXLiQ/Px8UlJSmDhxYqtzibZ5c/Wb2J12RnUZxYk9T1Q7TqtIYSSEHymtLeW5P54D4I7Rd9A5orPKiQKLoii4amra/etI8/JOmDCB3Nxc97bZbCY5Odm99pknJCcnu5cOSUxMdC9W21rjx49vVgTl5eWRnZ3drFhauHDhAXPm7V8UHW4pKpvN5tHzFke2f2vRbaNu86nWImiHRWSFEOp5Jv8ZKusrGaYfxoQhB37CFu1Lqa1lfWJSux9nSEE+mshDL1abnp7OuHHjmDp1KtDYgpKVldWsAMnMzHRvZ2RkuIuctLQ0CgoKMBqNzQqdpufr9XpycnKaFSM2mw2r1XpUy4HodDoMBgMFBQUkJiZisVhITEzEZrNhs9nQ6XRYLJZmx2sqisaPH3/QoigtLQ29Xs+KFSvIysoiJyen1bnE0Xtj9Rv/tBb18K3WIpAWIyH8RsGeAj4r/AyAGSfMIEgbpHIioabk5GQKCgqw2WzuYqOJyWTCZrORn59Pfn4+CxcupKCgwN3KVFhY2KyYMJlMWCwW93Ozs7ObHaup5eZoTZgwgfnz57uLI2hcVaFpLbZ/txZlZmaSn5+P2Ww+6NimhQsXkpeXR35+PoWFhc3W9BTtq7immIXr940tGuVbY4uaSIuREH6gwdXAo0sfBeCKQVcwsstIlRMFJk1EBEMK8jvkOEeSkZFBTk4OSUlJZGRkNPtZXl5eswHaiYmJmM1mCgsLmz3e1AWVl5eHxWIhLS0NoFkrTUZGBhkZGYdcQDwjIwOr1QpAdnb2QVt4jEYjEydOJD4+3j2WKCUlxd0y9e/B5E3dZwsXLiQtLY3CwsKDHttgMJCTk0NcXBxZWVkeHWMlDu7N1W9S76pndNfRnNDjBLXjHBUpjITwAx+s/YCNZRuJDYvlrsS71I4TsDQazWG7uDpSYmIiK1asYMWKFSxZsqTZz5KSksjJyWm2GHhOTg46nY68vDx3t1pTQZOUlITVanW3CjUNsm4qig7XhdaSbqymLrS8vDx395/RaCQjIwOLxXJAC1VTgZOYmEhqaqq7CDyYprvbpChqfyW1Je5pQm4b6Xtji5pIYSSEjyuuKeblv14G4J7Ee4gLj1M5kfAWGRkZFBYWHlAUpKenU1hYSEJCAtDYNdXU4pOXl0dCQgJGo9HdutP0/KSkJPR6PYmJiSQkJLi7uposXLjwqMYZQeMg7KZCrElL9pWdnU1SUhImk8ld6GVkZLjHJun1evLz278VT8C7a97F7rRzXOfjfLa1CECjHOn2Bi9TUVFBbGws5eXlxMTEqB1HCNVN/WEqX2/5muO6HMf/nfd/aDXeOXTQ1393D5W/rq6OzZs3M2DAAMLDw1VMKI6GvH+eUW4v52zT2dQ01PDCWS9wRp8z1I7UTGuuP955BRVCtMjvu37n6y1fo9VomTl2ptcWRUII//bBug+oaahhcNxgTu99utpx2kSuokL4KIfTweNLHwdgwpAJDIsfpnIiIUQgqnHU8P7a9wGYOGKiz44taiKFkRA+6p0177C5fDPx4fHcMfoOVTJU/fwLtatWqXJsIYR3WLB+AeX2cvrF9COl34HL0fgaGXwthA/aVbWL3JWNc87cm3wvMaEdP2anduVKdkyeDBoN/d/7P8KHD+/wDN7Ex4Zrin3kfWsbu9POO2veAeDmY2/2i/nTpDASwgdlL8+mtqGWpG5JXGi4sMOPb9+8me0Zt6LU1hJ18smEDRzY4Rm8RUhICBqNhr1799KlSxef70YIJIqisHfvXjQaDSEhIWrH8UmfbvyUktoSukd1V+Va1B6kMBLCx/y04yeWbFtCkCaIGWNndPgfYkdxMdtvmYizrIzwY4+l13PPoQkN7dAM3iQoKIjevXuzY8cOtmzZonYc0UoajYbevXsTFOT7LR0dzeFy8ObqNwG48ZgbCQnyj+JSCiMhfEhdQ517wPV/hv2HQXGDOvT4zspKtk9Mx7FzJyH9+tIn51WCoqM6NIM3io6OZtCgQTgcDrWjiFYKCQmRougofWX5iqLqIvThei4fdLnacTxGCiMhfMibq99kR9UOukZ05bZRt3XosV12Ozsm3Y59/XqCOnem7+uvExwf36EZvFlQUJD8gRUBw+ly8vqq1wG4bvh1hAf7zxxQcleaED5ie8V23lj1BgD3H38/USEd11KjOJ0U3T+VmuXL0UZF0fe1XEL79Omw4wshvMv3279nS8UWOoV2YsKQCWrH8ShpMRLCByiKwuPLHqfeVc8JPU7gnH7ndOix9zz2GJWLF6MJCaH3Sy8RPsy350wym83uVefT09NlHS0hWkFRFN78u3Fs0ZVDriQ6NFrlRJ4lhZEQPuDbbd/y886fCdYGM33s9A4dcF366quUffAhaDT0nDeXqBPGdtixm9hsNnJzG6cnaFpkFBoXP4XGxU4NBsMhV3jfX9NipdnZ2dhsNimKhGilP4r/YOXelYRqQ7l62NVqx/E46UoTwsvVOGp4YvkTQOOdHwNiB3TYscsWLmTvc88D0G3GDGLOPbfDjr0/s9lMaWlps8eaCpzU1FTS09MPWIH9cPuy2WyYTCbmzJnTHnGF8GtvrX4LgIsSLqJzRGeV03ietBgJ4eVyV+ayu3o3PaN6MvG4iR123Mpvv2X3rIcAiM/IQP+fazrs2P+WmpqK1WrFZrO5HzObzc1ae3Q6HWazGaPRiMlkOmCldr1e7159PSEhwb3P3Nxc0tPTDzim3W7Hbre7tysqKjx7UkL4IIvNwvc7vkeDhuuPuV7tOO1CCiMhvJil3OKeVXba8dOICI7okOPWFBSw854p4HIRe8XldLn7rg45bmsUFhYSv99dcXq93l04NRVAB5OcnIzZbHa/5t8FVJM5c+Ywe/ZszwUWwg80XY/O7HNmh7ZedyTpShPCSymKwuO/P06Dq4HTe5/OmX3P7JDj2jduZPutt6HY7USfcQY9Zs/2mdmcD1Xk7C8xMRFoHJ+0fPnyg7YWAWRlZVFeXu7+2r59u0ezCuFr9tbs5YvCLwC48dgbVU7TfqTFSAgvtWjLIpbuXkpYUBjTjp/WIcd07NrFtonpuCoqiBg1il7PPI0m2DsvEwkJCc261poGYLdE0wDuw7UshYWFERYW1qaMQviT99e+j8PlYHTX0YzqOkrtOO1GWoyE8EJV9VXMWz4PgFtG3ELvTr3b/ZhOm41tt0ykYfduQhMS6P3Ky2gjOqbr7mgYjUaWL1/u3rZYLC26K00I0XrVjmoWrF8ANN4E4s+886OgEAHu5b9eZm/tXvp26tshTdau2lq23zaJ+sJCgrt1o+/rrxEcF9fux20ps9lMXl4eNpsNg8FAamoqBoOBCRMmuAdaZ2VlqR1TCL9l2mCi0lHJgNgBnN7ndLXjtCspjITwMhvKNvDB2g8AmD52OmFB7dudozQ0sHPKvdT+8QfamBj6vv4aIT16tOsxW8toNB60NehwXWFCCM9wuBz835r/A+D64dej1fh3Z5N/n50QPsaluHj090dxKk5S+qVwcq+T2/V4iqKw66GHqPruOzRhYfR55WXCBnXswrRCCO+2aPMi9tTsoXNEZy5MuFDtOO1OCiMhvMjnhZ/zR/EfRARHMHXM1CO/oI32Pv885aaPQaul19NPEZmU1O7HFEL4DkVReOvvxgkdrxl2Tbu3YHsDKYyE8BLl9nKeyX8GgFtH3kr3qO7tejzr++9T+sqrAHR/aBadxo1r1+MJIXzPL0W/sLFsI5HBkaQNTlM7ToeQwkgIL/FcwXNY66wYYg1cO+zadj1WxaJF7Hn0MQA6T76DuPHj2/V4Qgjf9M7fjRM6XjH4CmLDYlVO0zGkMBLCC6zcuxLThsYFUWeeMJOQoJB2O1b170spun8qKAq6KyfQedKkdjuWEMJ3bSjbwO+7fker0fKfYf9RO06HkcJICJU1uBp45PdHUFC4OOFixnQf027Hqlu3jh133IHicNApJYXuDzzgM7NaCyE61ntr3gPA2NdIz+ieKqfpOFIYCaGyj9Z9xDrrOmJCY5iSNKXdjlO/YwfbJk7EVVVF5Jgx9HxyHpqgoHY7nhDCd5XWlvKl5UsArh3evl373kYKIyFUVFxTzIt/vgjA3Ul3Ex8Rf4RXHJ0Gq5XtN9+Cc28JYYMH0/ulF9HKchdCiENYsH4B9a56jut8nF8v/3EwUhgJoaK5y+dS7ajmuC7HccWgK9rlGK7qarZn3Er91q2E9OxJn9deIygmpl2OJYTwfXannY/WfwTAf4YHztiiJlIYCaGSX3f+yjdbvkGr0fLACQ+0y2yyisPBjrvupm7VKoJ0Ovq8/joh3bp6/DhCCP/xleUrrHVWukV2w9jPe9cfVBQFxeXy+H6lMBJCBXannceWNt4uf/XQqxmqH+rxYyguF0UzZlD9889oIiLok/MqYYYBHj+OEMJ/KIrC/61tXP7j6mFXE6Jtvztk28KxZw87bpuE9Z13Pb5vKYyEUMEbq95gW+U2ukZ05Y7Rd7TLMYqffIqKz7+AoCB6P/csESNHtstxhBD+Y+nupWws20hEcES7de+3haIo2EwmLBdcSNX331Py8ss4q6o9egxZRFaIDra1Yiuvr3odgKnHTyUqJMrjxyh9622sb74JQI9HHyX6tNM8fgwhhP9pWiz2koRLvG5CR0dREbtmPkD1r78CED5iBD0ff4ygaM9eQ1UrjHJzczEYDOTl5ZGdna1WDCE6lKIoPPb7YzhcDk7ueTJn9zvb48co/+ILivf9TnW97150l13q8WMIIfzP5vLN/LjjRzRovGrQtaIolP/3E/bMmYOrqgpNWBhd7rwT/fXXoQn2fBnT4j3abDZyc3MBmDr1n8UtTabG2XqtVisGgwGj8cgDtWw2GwBGo5GcnBwsFgsGg6E1uYXwSYu2LOK3Xb8Rqg1l+tjpHp9csernXyjKmg6A/vrr0N98s0f3L4TwX++vfR+A03ufTr+YfiqnaeQoLmb3g7Oo+v57ACJGjqTHE3MIG9B+4yVbXBiZzWZKS0uJj/9nnhWLxUJeXh45OTkApKSktKgw0ul0pKenu1uNpCgSgaCyvpK5y+cCcMtxt9A3pq9H91+7ajU77rwTGhqIueACumZmyqzWQogWKbeX83nh54D3TOhY8dVX7J79MM7ycjQhIXS56070N97Y7hPTtrgwSk1NxWq1ult7oLFY0ul07m2dTofZbMZoNGIymbBarc32odfrSU1NdW+np6eTkZFx2BYju92O3W53b1dUVLQ0shBe5cU/XqSktoR+Mf24+VjPtuTUb9nC9owMlJoaok46kZ5zHkejlXsrhBAtY9pgorahliFxQ9p1WaKWaCgrY/fsh6lctAiAsOHD6PnEE4QPHtwhx29T51xhYWGzFiS9Xu8unPYvgP7NZDKh0+kwGo0kJCRgMpmadc/tb86cOcyePbstMYVQ3ZrSNe4J02aMnUFoUKjH9t2wdy/bbpmI02olfPhwej3/AppQz+1fCOHfHC4HH677EGhsLVKzpbnqxx8pmj4DZ0kJBAfTOSODzrdmoAnpuGkDPP6R8t+tRAdjNBqx2WyYTCYKCwsPWRQBZGVlUV5e7v7avn27J+MK0e6cLieP/PYILsXFef3P48SeJ3pu31VVbMvIwLFjByF9+9InN8fjd2gIIfzbkm1L2FOzh/jweM4bcJ4qGVz19ex+/HG2p2fgLCkhdGAC/T/6iC6T7+jQogja2GKUkJDQrGutaQD2keh0OneL0uFalgDCwsIIkzWdhA8zbTCxunQ10SHR3D/mfo/tV6mvZ+edd2Jfs5ag+Hj6vv4awZ07e2z/QojA8OHaxtaitCFpHm3Nbil7YSE7770P+7p1AMT95z90vf8+1dZzbFOLkdFoZPny5e5ti8XSosHXQgSKktoSnit4DoDJoyfTJbKLR/aruFwUzZxJ9a+/oYmMpM+rrxLa17ODuYUQ/m9t6VoKigsI1gSTNjitQ4+tKApl8xew+YpU7OvWERQXR+9XX6H7zBmqLnLdqrvS8vLysNlsGAwGUlNTMRgMTJgwwT3QOisrqz2zCuFznlrxFJWOSobHD2fCkAke2+/eZ55pPqv1iGM9tm8hROD4YN0HAKT0S6FrZMeto+isqmLXjJlUfvMNAFEnn0yPOY8T0lX9tRxbXBgZjcaDtgYdqStMCG9St2YNJbmv0fXuuwjt379dj7Vs1zL+Z/kfGjQ8eMKDBGk9c4up9f/eo/S1xpmzezzyCNGnnuqR/QohAktZXRlfWb4CGtdF6yh1Gzawc/Kd1G/dCiEhdL3nHvQ3XO81d9LKkiAioGy+IhUUhXqLBcPnn7Xbceqd9Tzy+yMAjB8ynmM6H+OR/VZ8s5g9jz8OQJe770Z3+WUe2a8QIvB8vPFj6l31DI8fzsguHbOWYvnnn7Nr1kMotbUE9+hB72ef8bp1HKUwEoFFUYDGeX/a0xur3mBLxRY6R3TmzsQ7PbLPmhUrKLr/flAUdFddSXxGukf2K4QIPA2uBuavnw/A1UOvbvdb9F319eyZMwfbh43TlkSdfDI9n5xHcFxcux73aEhhJAJTO6yv08RSbuG1Va8BkHl8JjGhMW3ep33jRrZPuh2lvp5o4zi6z5wps1oLIY7a99u/Z3f1buLC4jh3wLnteqwGq5Udk++kNj8fNBo633YbnW+f1O4zWB8tKYxEQGqPhQeh8S6LR357BIfLwam9TuWcfue0eZ+O3bvZNjEdV0UFEaNH0+vJJ732giKE8A1Ng65TB6cSFtR+d4DVbdjAjtsm4di5E210NL2eepLo009vt+N5ghRGIiC1V2Hx6aZPWbFnBRHBEcw4YUabW3WcFRVsn5hOw+7dhA4YQO+XX0IbHu6htEKIQLTeup7lu5cTpAli/JDx7Xacyu++o+je+3DV1DROQPvKy4QlJLTb8TzFO4aAC9HB2qPFyFpn5an8pwCYNHISvaJ7tWl/rvp6dtwxGfvGjQR16Uyf117zyv54IYRvaVr+46y+Z9E9qnu7HMP67rvsmHQ7rpoaIo8/nv7zP/KJogikxUgEqnYojOYtn0e5vZwhcUO4Zvg1bdqX4nKxa9o0apYtQxsVRd/cXEJ7t63QEkKIcns5X1q+BBoHXXuaoijsfeZZSnNzAdCNH0/3mTN8av1GKYxEQPJ0i9GvRb+65yyadeIsQrRtW9uneO48Kr76GkJC6P3iC4QPG+ahpEKIQPbJxk+oc9YxJG4ISd2SPLpvpaGBXQ89RLnpYwC63HMP8ekTfe5GESmMREDy5BijuoY6Hv39UQCuGnoVI7qMaNP+St96G+vbbwPQ8/HHiDrRc4vOCiECl9Pl5KP1jbfLXz3Ms7fou+rq2HnvfVQtWQJaLd1nP0RcWscuMeIpUhiJgKQJ8dx//dyVuWyv3E7XyK5MHj25Tfsq//JLirOzAeh6/33EXnSRJyIKIQQ/7viRnVU7iQ2L5fwB53tsv67qarbfNomaZcvQhIbS6+mn6OTD66ZKYSQChuJ0/rMR5Jn/+hvLNvLW6rcAmH78dKJDo496XzUrVrBrWuN6g3HXXov+pps8klEIIQDeX/c+AJcPupzwYM/c3eqqrmZbRga1K/LRRkfT++WXiDr+eI/sWy1SGImA4aqtc3/viTFGLsXFw789TIPSwJl9zmRcv3FHvS+7ZTM7br8DxeGgU4qRbtMyfa5fXgjhvQpthSzdtRStRsuVQ670yD6dVdVsz8igNj8fbadO9H3jdSKOO84j+1aTFEYiYCh1tf9sBLV9pgrTBhN/7v2TyOBIpo+dftT7abBa2Z6RgbO8nPCRx9Fz7lyZwFEI4VFNt+if0fsMekb3bPP+XDU1zYuiN98gYkTbxld6C5nHSAQMV+1+hZGjoU37Kqkt4dn8ZwGYPHryUc8F4qqra5wVdvt2Qnr3ps/LL6ONiGhTNiGE2F9lfSWfF34ONA66bitXfb17iQ9/K4pACiMRQPYvjBSHo037enzp41Q6KhkeP5yrhl51VPtQXC6KpmZS+9dfaGNj6ZObQ3B8fJtyCSHEv3266VNqG2oZqBvI8d3bNv5HcTopmppJ9S+/oImIoO9ruX5VFIEURiKAKB4qjMxbzeRtzSNIE8Tsk2YTpD26bq/iJ5+icvFiNCEh9HnxBcIMhqPOJIQQB+NSXHy0rvEW/auGXtWmsYuKorD7odlULlrknmMtYtQoDyX1HlIYiYCx/+Droy2Myu3lPLb0MQBuOvYmhuqHHtV+rB98gPXNNwHo8fjjRI4Zc1T7EUKIw/m96He2VW4jOiSaCw0XtmlfJS+8iG3hQtBq6fXkk0SffLKHUnoXKYxEwHDVtb3F6KkVT1FSW0L/mP5kjMw4qn1Ufvcdex5tLK663H03sRe17WIlhBCHMn/9fAAuTriYyJDIo96P7dNPKXn5ZQC6PzSLmHPO9kg+bySFkQgY+3elNRuI3UK/Ff3GJ5s+QYOGh09+mLCgsFbvo/bvv9k55V5wuYhNvYL4jPRW70MIIVpid/Vuvt/xPQAThkw46v1UL13GrgceBCA+PZ248eM9Ec9rSWEkAsb+XWmuqioUl6vFr61x1DD7t9kAXDn0SkZ3Hd3q4zv2FLNj0u0otbVEnXQSPWbNkrmKhBDtZuGGhbgUF8d3Px6D7ujGMNotm9kxeTI4HHQ671y63H2Xh1N6HymMRMBw1dT8s6EouGpa3mr0wh8vsLNqJz2ienBXYusvDK66OnbccQcNe/YQmpBAr+eeRRPStoVmhRDiUBxOBx9vaFzMdfyQo2vhcVZWsmPSJFwVFUSMGkXPOXPQaP2/bPD/MxRiH2dFebNtV1Vli173196/eH9t41T6D574IFEhUa06rqIo7Jo+g7pVqwiKjaXPKy8T1KlTq/YhhBCtsWT7EkrrSukc0Zmz+p7V6tcrLhdFmdOo37KF4O7d6f3Si2jDPbOMiLeTwkgEDFf5vwqjyiMXRvXOemb9MgsFhYsTLuaUXqe0+rglr7xCxVdfQXAwvZ5/ntC+fVu9DyGEaI356xoHXacOTiVE2/rW6ZJXX6Xq22/RhIbS+4XnA2qONSmMRMBw2poXRs7KqiO+5vVVr1NYXog+XM/UMVNbfcyKbxZT8vwLAHR/8AGixvr24opCCO+3qWwTK/asIEgTxBWDrmj166t++IGSF14EoPusB/1uAscjkcJIBIyGMmuz7SN1pa23rue1Va8BMGPsDGLDYlt1vNq//6YoMxOAuOuu9fs7OYQQ3qHpFv0z+5zZ6uWK6rdtY+f9U0FR0E2YgO6K1hdWvk4KIxEwGor3Ntt2/qtrbX8Op4MZP8+gwdXAuL7jSOmX0rpjlZQ03oFWV0fUKafQbWrrW5uEEKK1ahw1fGH5Amj9oGtXfT07776ncbD1yJF0m3H0i2P7MimMRMBo2LMHgLDBgxu3/1Uo7S9nZQ7ry9YTFxbHAyc80Krb6hWHg51339N4B5rBQK9nnkYTHNy28EII0QL/s/yPakc1/WP6M7bH2Fa9du9TT1O3Zg1BsbH0evYZtKGh7ZTSu0lhJAKCq74eZ1kZAOHHHgtAQ3HxQZ/7d+nfvL7qdQBmnDCD+IjWDTosfvIpalasQBsVRe8XX5A70IQQHUJRFHc32vgh49FqWv4nvvL777G+8w4APeY8TkiPHu2S0RdIYSQCQlPrkCY0lLBBgxof23tgi1G9s56ZP8/EqTg5t/+5nNP/nFYdp/zLL5tdXGRhWCFER/lz759sKNtAeFA4Fydc3OLXOfbsYVdWY7dZ3LXX0ums1t/e70+kfV8EhIbduwAI7taN4K5dGh87SIvRy3++zCbbJvTheqaPbV3/et2GDeya+QAA8RMnEnO2/64l5OtMJhM6nY6CggKmyvgv4Sc+WvcRAOcNOK/FN4s0zVfkLCsjbPgwut5/X3tG9AlSGImAUL9lCwChffsS0rUrcGCL0V97/+Ktv98CYNaJs4gLj2vx/p1V1eycfOe+5T5ODIhp8zuSzWYjNzcXoFkhYzKZALBarRgMBoxG4xH3ZbFYsFgsTJ06FZvNhsViwSAte8LHldaWsnjrYgAmDG35umhl771Hze+/o4mIoNdTTwXsuKL9SVeaCAj2zZsBCB0wgOB9hZFjv8KorqGOmT/PxKW4uNBwYatnit3zyMPUb91KcI8e9HzqKTRBQZ4LLzCbzZSWljZ7zGKxkJeXR2pqKunp6WRnZ7doXwaDgeXLl5OSkiJFkfAbn2z6hAZXAyM6j+CY+GNa9Bp7YSHFTz0NQLfMqYQNGNCeEX2GtBiJgFC/eQsAof37E9ylsStNqanBWVVNUHQUL/zxAlsqttAlogvTjp/Wqn2Xf/YZ5Z99DlotvZ56kuC4lrc0iZZJTU3FarVis9ncj5nNZnQ6nXtbp9NhNpsxGo2YTCas1ubzVun1elJTU7HZbIwZM4bExEQyMjIwGo0kJiZ20JkI4XlOl5OF6xcCMGFIy1qLFIeDosxpKHY7Uaecgm5Cy1uZ/J0URiIg2NetAyBsYALayEi00dG4qqpo2LObgior/7fm/wB46KSHWjWRY/3Wreye/TAAnW+fRKT8ge0whYWFxO+3TIFer3cXTqmpqYd83YIFC0hNTcVgMJCXl4fJZDpoYWS327Hb7e7tiooKz4UXwoN+3vkzRdVFxIbFtviGkZKcXOpWr0YbG0uPxx5t1ZQk/k660oTfa7BacRQVARB+TGMTc0jfPgDYNq0h66csFBSuGHQFp/U+rcX7Verr2XnvfbhqaohMTqbzrbd6PrxolX+3Eh3M+PHjMZlMmM1mCgoKSE9PP+jz5syZQ2xsrPurT58+no4rhEd8tL5x0PWlCZcSHnzkhV5rV62m5NVXgcalikK6dWvXfL5GWoyE36tbtQpoHF/UNKdQWP/+2NesZdGPb7Fn8B76durb6rXQSl57zf2Jq+e8uTKuqIMlJCQ061prGoB9JDqdrkV3omVlZTFlyhT3dkVFhRRHwutsr9zOLzt/AVo207Wrvp6irGnQ0ECn884l9oIL2juiz5EWI+H3alc2FkbhI451Pxbav3GQYUXhOoI0QTxx6hNEhkS2eJ916zdQ8moOAN0feCCgJ0NTi9FoZPny5e5ti8XSorvSWiosLIyYmJhmX0J4m4UbFqKgcHLPk+kb0/eIzy/NyaV+UyFB8fF0f/DBDkjoe6TFSPi9mqVLAYgcPdr9WHWPxnFEPUsVbh15KyO6tHz1aKWhgV3Tp4PDQfS4ccRccL5nA4sDmM1m8vLysNlsGAwG9xihCRMmuAdaZ2VlqR1TiA5ld9r5ZOMnQMsGXds3bqRk37QX3WfOkBtFDkEKI+HXnFVV1Pz5JwBRp5zS+JjLySvWz7gB6GsL4ZIRt7Rqn9Z33qHu77/RxsTQfdaDMmixAxiNxoO2Bh1ukLUQ/m7xlsXY7DZ6RPU44vhIxemkaObMxg90Z51Fp3PP7aCUvke60oRfq1m6FBoaCOnXl9B940PeWP0G37EegOhKB5rq2hbvz1FcTMlLLwPQLTPTPVmkEEJ0tKZB16mDUwnSHn6MY9n771P310q00dHyge4IpDASfq1ycR4A0ac2fppaXbKaV/58hdpwDQ3xjWNG7Js2tXh/e596GldNDeEjjyP2sks9nlcIIVpibelaVu5dSbA2mMsHXX7Y59bv2EnxM88C0PW+e+UutCOQwkj4LVddHZVmMwAx559HZX0l9/9wPw1KA+f0P4eYIY2DsVtaGNX+9Rfln30GQPcZM9Bo5dcHRQF7pdophAg489fPByClbwqdIzof8nmKorB71iyU2loik5PRjT/ynWuBTq7swm9V/fAjrupqgnv2IHzkSGb/NpsdVTvoGdWTB054gPBBAwGob2FhVPz0MwDEXnopEccd1265fcq6L+G5UfDXfLWTCBEwKuor+GrzV8CR10Wr+Pxzqn/5BU1oKN0feVg+0LWADL4Wfsu2YAEAsRdcgGnTx3yz5RuCNcHMPX0usWGxuAY2Fkb2jUcujKqXLWscrxQSQpe77mzX3D6jvhoWTYOaEti7Tu00QgSMLwq/oLahloG6gSR2PfRs+87ycvZkzwWg86RJshZaC0lhJPySvbCQ6l9+AY0G6zljyF52DwB3Jd7FyC4jAQhrKoxa0GLUNOBad8XlMmdRk5+egvLtENsHTrtP7TRCBARFUdzdaBOGTDjsIOriZ5/FabUSmpBA/E03dlREn6dam1pSUhIpKSlkZmaqFUH4Met77wEQccZp3L9xHvWuek7tdSrXHXOd+zlhgwYB0FBcjLO8/JD7ql250t1a1PkQy0cEnJKN8Mvzjd+fOwdCo9TNI0SAWL57OZvLNxMZHMmFhgsP+bzaVauwfdRYQHV/8EE0oaEdFdHntbjFyGazkbtvYqj9p9M3mUzAP9Pxt3Tm2aysLJmDRLSLhpISyj9tHCT9eZKLLRVb6BrRlcdOeQyt5p/PAkHR0QT36EHDrl3YN20iMinpoPsre/99AGLPP5+Qnj3b/wS8naLAV/eDywEDU2DooS/OQgjParpF/6KEi4gOjT7ocxSns3Fxa0Uh5qKLiBp7fEdG9HktbjEym82UlpY2e8xisZCXl0dqairp6elkZ2e3+MAWiwWz2SwtRsLjSnJzUWprqRvUm9eCf0Wr0ZJ9WjZx4QfO8hp2hHFGDVYrFV99DUDcNVe3X2hfsuZTsHwHQWFw/lyQ+VCE6BDFNcV8u+1b4PDrotkWLGhcxzE6mm5T7++oeH6jxS1GqampWK3WZos2ms1mdDqde1un02E2mzEaje5p+ven1+vdrURNrU4WiwWTySStR8IjHLt2Yfuw8RPV88eXgkbDpJGTSO6efNDnhw0cSPVPPx1ynFH5Z5+jOByEH3OM3IkGYK+CRdMbvz/lbtAfedFWIYRnfLzhY5yKk8SuiQyOG3zQ5zSUlrrnLOpy990Ed+nSgQn9Q5sGXxcWFhIfH+/e1uv17sLpcIWOed/cMkajEZvNhl6vP+Rz7XY7drvdvV1RUdGWyMLP7X3pJRSHg8IB4azoU88JPU7klsMs+dE0zuhQhVHFV423xMZefpnnw/qiH7Khsgh0/eCUe9ROI0TAcLgcmDY0Dl053LpoxfOexFVRQdjwYcRddWVHxfMrHh98/e9WooNpKoiaCqTDFVFz5swhNjbW/dVn37IOQvxb7cqVlH/8XwDeOsVB9+geZJ+Wfdip8sMGHfrOtPpt26hbtQq0WmJkXSEoXge/N96dx3lzISRC3TxCBJAftv9AcW0x+nA9xn4HH8tbs3w55Z9+ChoNPWbNQhN0+GVCxMG1qTBKSEhott00ALslUlNTMRqNzQZyH0xWVhbl5eXur+3btx91XuG/FKeT3Q8/AorCD8dq2Nw3lKdPfxp9+KFbIwHC9v1/dZaU0FBW1uxnleYlAESdMJbg/VpGA5KiwFf3gasBhpwPQ/4pFPdW2g/zQiGEJzQNur5i0BWEBh14h5nicLD74YcB0I0fT8TIkR2az5+0qTAyGo0sX77cvW2xWFp8V1pLhYWFERMT0+xLiH+zLTRRt3o1NWHw3plaph0/jRFdRhzxddqoKEJ69QIOnAG7+tdfAYg67fCrVgeE1R/Dlp8gOLzx9vx9vly5i9Pnfcenf+xUMZwQ/s1SbmHprqVoNVpSBx+8h6Xsw4+wb9xEUFwcXe+5u2MD+pkWjzEym83k5eVhs9kwGAykpqZiMBiYMGGCe6B1VlZWe2YV4qAcRUXsntc4u+v8U7WcMfJS0gantfj1YQMH4ti5k7qNG4kcMwYAl91OzYoVAESddJLnQ/uSugr4Zkbj96feB3H9AbDsrSLz45XU1DtZt1vWSxOivSxcvxCA03qdRs/oA6cMabBa2fvii0DjgOug/W6KEq3X4sLIaDQetDVI7iYTalIUhZ0zZkB1Det6wZaUYbx7wszDzgb7b2GDB1H1ww/NWoxq//gDpa6O4C5d3AO0A9b3T0DV7sY70E6aDEBtvZNJ7xdQZW/g+AF67jv74HfICCHapsZRw2ebGudlO9S6aHufe9494FqXekVHxvNLsiSI8Gm2jz6i9rffsQfDu5fF8vxZzxAeHN6qfRxsLqPaP/4AIHLs2FYVWX5nz9+w9NXG78+bByGN/7YPfLaadbsr6RwdxotXjSY4SBamFKI9LNqyiEpHJb2je3NSzwNbr+vWrnWvC9l9+nQZcO0BcjUTPqt+2zZ2Zj8BwAdnaLnn0rn06dT6uxZDD7JmWu3ffwMQfuwxHkjqoxQFvrwXFCcMuwgGNbYYL1i+HVP+DrQaeP6qUXSNaV0hKoRoGUVR+Ghd46DrCUMmNJu5v+nnex57vHGG6/PPIzL54PO1idaRwkj4JFd9PRvuuJWgunr+7gsDb7mT03of3SDpMIMBNBqcZWU07JvdvW51Y2EUcUwAF0Z/fQTbfoOQSDinccD1mqIKHvhsNQBTUgZzUkJnNRMK4ddWlaxirXUtodpQLh146QE/r1y0iJoVK9CEh9P1fpnh2lOkMBI+afOc2QRt2ExFBKyaNI6JI49+cVdtRAQh++bHsm8qpMFqpWH3btBoCBs23FORfUutDfIeaPz+tPtB14eKOgeT3s/H3uDijCFdmHTGQFUjCuHv5q9vXAT23AHnogvXNfuZq7aWPXPnARA/8RZCevTo6Hh+Swoj4XNKFn1J/YeNEzl+flU/pl04r83jgEJ7N96y37B7F/VbtgAQ0qMHQdEBumr8d49B9V6IHwQn3oGiKEz7eCVbSmvoGRvOM+NHodUG8NgrIdqZrc7Gos2LgIPPdF36+hs07NpFcM8exN90U0fH82sy+Fr4FPuOHeyYPo0wYPFJkUy+/W0igts+A3Nw124AOPYUoygKACF9+7Z5vz5p11+w/PXG7y94EoJDee+3LXy1ajchQRpeuiaRuKgDJ5gTQnjOp5s+pd5VzzD9MEZ0bj4nm6OoiNLXG39Hu02dijZCZqH3JCmMhM9w2e38mfEfYmoa2NhTw2mPvEr3qO4e2Xdw98bCqGH3bpS6OgBCA3H5GZdr34BrFxxzORjO4O+ich75ci0AmecOZXTfOJVDCuHfXIrL3Y125dArD2gR3zNvHordTuSYMXQ65xw1Ivo1KYyET1AUhYL7Mogp3ENlOGgfvo/RvcZ4bP8h3ZpajPbgrGycrDCkbwAWRn++DzuWQ2g0nPMY1fYGJn/wB/UNLsYN7crNpwxQO6EQfu/Xol/ZUbWDTiGdOLd/83Uaq5cto/LrRaDV0m3G9MCeTqSdSGEkfML6154hKm8pLg2suvNsbj7Fs33qwV27AtBQshcNjRea0D4B1pVWYwXzrMbvz5gGMT15cMFfWEqq6R4Tzry0kXIRFqIDNLUWXTLwEiJDIt2PK04nex5vvENUNz6N8KFDVcnn76QwEl6v6Kc8Gp59jSDgp0v6c8sNT3n8GE1T6DttNpS6xkVRQ3odOPW+X1vyMNSUQpdhMPZW/luwg48LGucreu7KUehlXJEQ7a6oqogfd/wIwPgh45v9zLbQhH3dOrQxMXS56y414gUEuStNeLXK7RaK7p5CkAv+GBnNlQ99SLDW8/V8UGwsAE5bOU6rFYDg+HiPH8dr7cyH/Lcbv7/gSSxWOzM/bZyv6K5xgxlrCKB/CyHaSdlH89l6w404q6oO+RzTBhMuxcXYHmMZEPtP17WzvJy9zz4LQJfJkwmOk7F+7UUKI+G1Gmpr+OOmq4iqbmBb9yBOeeGDA+by8JSmFiNXeTmKw9H4mF7fLsfyOi5n44BrFDhuAnW9TuSOD/6gpt7JiYZ47jhL5isSwhN2P/QQNb//jvXNtw7683pnPR9v/BiAK4dc2exne198CafNRujABOKuPPiaacIzpDASXklRFH64bTxdtldQGQFdn32Kvl3bbzHXphajJtrISLThAbLURcE7UPQHhMVAyiPM+Wota3ZVEB8VyrNXjiJI5isSwqOabvD4N/NWM9Y6K10junJGnzPcj9s3bqTsgw+AfeuhhYR0RMyAJYWR8Eo/zp5Ez98LadBC5YO3MnpU+96SqgkJQRv1z2SOAdNaVF0C5tmN3585g2+2Kbzz21YAnhw/km6yDpoQnrdvrrR/axp0nTo41T1kQFEU9sx5ApxOoo3jiDrpwIVkhWdJYSS8zop3n6brR98DsGniOMZd1jGDDJu60wCC4gOkMDI/BHU26DaCosHXMNW0EoD00wycOaSrqtGE8FsHKYw2lG2goLiAIE0QVwy+wv141XffUf3rr2hCQug2dWpHpgxYUhgJr7Lxhy8IzX4NgNXnDOTSu1/osGNrY2Lc3wd1ijnMM/3E9mXwx/8B4DxvHvcsXE15rYORfXTcd/YQlcMJEVgWrF8AwFl9z6JrZOOHEld9PXueyAZAf+ONhAbqbPwdTAoj4TX2bFyJ7Z5phDhhw4g4Ln5yYYfOm6ON/Ge+EL+fYt/lhC+nNH4/6hpyt3Rl6WYrkaFBPDdhFKHBcmkQot38q8Wo2lHNF4VfAM0HXVvfeQfHtm0Ed+lCfPrRL5QtWkeufsIrVFv3suHm64iucbGjZyin5n5MWEjHjm9pVhhF+nlhtPwN2L0KwmNZc8y9PJ23HoCHLj6G/p0DdOFcITpM88Lof4X/o6ahhgGxAxjTvXFGf0dxMaWvvApAl3unBO6C1iqQwkiozllv57ebL6dzsR1rJw0Dc99EH9ejw3PsXxhpwv24MKoqhm8fBaD+9Jnc8fl2HE6F847tTlpSb5XDCeH/lP1ajBRF4aP1HwEwYcgEdyv53meexVVTQ/jI44i9+GJVcgYqKYyEqhRFwXz3lfRaW0JdCIQ/PZsBA5NUydKsxcifb9XPexDs5dBjJA/vOh7L3sYlP+ZcPkKW/BCinShO534b/xRGBcUFbLJtIiI4gosSLgKgduVKyj/5BNh3e75W/lR3JPnXFqoyPzGZvt+uwwVYp11P0qlpqmXRRvxTDGki/LQw2vor/PUhoGHp8Jm8t2wnGg08PX4kukhZ8kOI9tI0cWzjxj/fzl/XeIv++QPOJyY0BsXlYvdjjwEQe8klRIwc2ZExBVIYCRX98k42vd9ZAsDW605n3DXTVM2jCfmnMND6Y1easwG+vA+A2hHXcNv3ja1DE081cNLAzmomE8LvNS+MGiujktoS8rblAXDl0MZB1xX/+x91f61EGxlJl3undHhOIYWRUMmfiz+g09y3AdiUMoRzp72sbiBAE7pfYeSPg6+X5ULx3ygRcdxrvRRrdT3De8Rw79mD1U4mhN87WGH0343/pcHVwMguIxmqH4qrupriJxsXyY6/9VZCuspcYmqQwkh0uMI/vqdh6qOEOKFwVBfOe3oBWi/oQ9+/MNL42xijil3w3eMA/Nr/Dr4qrCcsWMvzV40iLDhI5XBC+L/9CyPF4aDB1cDCDQuBxkHXAHtffpmG4mJC+vRBf/11quQUUhiJDrZn6zr23HoHUXUK2/tHcebrnxEc4h1jW5q1GPnbPEZ5D0B9JbVdR3HTqmEAzLxgGAO7dlI5mBCBQamvb/b9jzt+ZHf1buLC4ji7/9nUrd+A9e13AOg2YzrasDC1ogY8KYxEh6kqK+bvG64irtxJcecQEt9eSFR0nNqx3Py2xWjzj7BqIQoaptlvwN4AZw7pwn9O6Kd2MiECxv4tRq56u3tdtMsGXUaoJoTds2eD00mnFCOdzjhDpZQCIFjtACIw1NfV8MsNl9B3Vx0VURr6vfY6nbsPUDtWM5rQf1as9pvB106He8D1yu6X89mWrugiQ8i+4ji5NV+IDrR/YVRTWsyvRWvRoCFtcBrln3xCbUEBmshIuk2frmJKAdJiJDqAy+XCPOly+q63YQ+ByGcfp/+w49WOdYBmXWnhftKM/fvLULKehvB4bth2LgCPXnosXWP8qEVMCB+wf1da5c4tAJza+1S614VRPHceAF1uv52QHh0/ua1oTgoj0e6+eeBGBvy6FacGambdzohTL1U70kFp9yuMCPKDxtTynfB94wKUT/MfylxRXHhcDy48rqfKwYQIPPu3GIWWVqJRFCYMHs+uBx7EWV5O2NCh6K+7VsWEookURqJdffvidPp/vAyAXZMu4qTUO1ROdGiakH+60jRaP+hm+mY6OKrZHj2CV2xj6NIpjEcuOVbtVEIEJKX+n8IoxAnDXN055oftVH3/PZqQEHrOzW52DRLq8YOPxcJbLfv4Fbq+1DitveWyJC6YPFflREeg3e+2dS+YPqBNNi2BNZ+iaLRkWK9GQUv2FSOIi/KOOwCFCDSKo77Z9l15oRSvfAKALlOmED5Y5hPzFlIYiXax5ufPCX3oeYIUKDyxL+c/9q7akY5s/1YijQ8XRg12+HoqAKag81jj6seE5D6cNbSbysGECFzNJngE4v7YDEDMxRehv+F6NSKJQ5DCSHjc9nXLqbwrixgHbBmi4+xXPvGKCRyPpNlCjb7clfbrC1C6icpgPQ9XXUYvXQQzLxymdiohAlpTV5qlG0Tou9Brpx3d5ZfT9d4pcoeol5HCSHiUddcWNt9yM12qXezqEcZJb/2X0PDII7/QG+zXleazq1nbtsGPTwLwQM2VVBJJTtpxdAqXsQtCqKm62gZAVYSG3rkvMKSLLA7rrXz06i+8UVV5KfnXX0GXEgfW2CCGvfU+sXofuvV0/1YiXy2MFmVBQy0FmuF86jqZG0/uz0kJskCsEGorKGq8CSU8PJrjOh+nchpxOD569Rfept5ew083XUzvbTVUh2vo9uqL9Oh/jNqxWqVZK5EvNm1vWAzr/oeTIKbVXY+hczRTzxmqdiohAp5LcZG/YykA3XW9pevMy0lXmmgzl8vF4tsuI+FvK/ZgCHnqIQaOPkPtWK2334Brn+tKc9S5B1y/0XAum+jDx+NHEhEqC8QKobbfin6jsqYMgO66PiqnEUfiY1d/4Y2+zryahF+34dRA7YOTGDluvNqRjoomaP/B1z72q/HLc1C2mWL0PNdwORNPNTC6r/esQ6cmk8lEUlJSs8dyc3Mxm83k5uaqlEoEko/Wf0SIs/H7kDCZdd7b+djVX3ibxdl3YvjiLwCK77yCE8dPVjlRG2h9tMXIuhl+fhqAh+uvoVvnztyT4rtzothsNubOncvcuc3nvTKZTJhMJndR01Kpqano9Xr3dtNrjUYjer0ek8nkmeBCHERRVRE/7viR4H2FETKJo9fzoau/8DY/vvUYfd7KA2DrVadw1m2PqpyojTQ+2mK0aBo01PGL8xi+VE5gbupxhIf4bhea2WymtLS02WMWi4W8vDxSU1NJT08nOzv7qPdfUFCAwWAAQKfTsXz58jblFeJwTBtMuBQX/SJ6Af9aekh4JRljJI7Kss9fI27eewAUpgzl/AdyVE7UdhpfvCtt3VewYREOgnmw4QauP3EAyf31R36dF0tNTcVqtWKz2dyPmc1mdDqde1un02E2mzEajZhMJqxWa7N96PV6UlNTD3mM/fd9KHa7Hbvd7t6uqKho8TkIAVDvrOfjjR8DcGzsEGC7LPvhA6QwEq329y+fEzzzaYJdYEnqwXnPLvSJCRyPaP+uNF+4a6S+Br7OBOD1hvOojxvI1HOHqByqfRQWFhIfH+/e1uv17uLmcAXQwSQmJmKxWIDGAmnMmDEHfd6cOXOYPXv20QUWAsjbmoe1zkrXiK70De+JDaQw8gF+8NdMdKQtq3+j6s5pRNTD1sGxGF//nCB/WIkemrcS+UKh9/PTUL6NnUo8zzdcRvblxxEZ6ifvRQv8u5XoUMxmMxaLxT2WyGg0YrPZ3I8fqrDKysqivLzc/bV9+3aPZReB4YN1HwCQOiQVTUPT6GspjLxd4FxFRZsVb1/PjonpxFcrFPUK56S3PyUsIlrtWB6j8aXCqLQQ5Zfn0ACPOK7lsrGDOWmg/07kmJCQ0Kz7y2q1uscJHYnRaKSwsLDZY1OnTnX/7FDCwsIICwtrfVghgL9L/mbl3pUEa4NJG5yGo/55QMYY+QIvv/oLb1Fh3c3q668kvqyBEn0wI97+iBh9d7VjeZavTPCoKPDV/Wic9fzgPI6V0aeSdZ5/T+RoNBqbDZK2WCyHLWqEUFtTa9G5/c+lc0Rn9yKy0pXm/aTFSByRvbaKX6+/lH5FdVREaejzWi5d+/jhWBZfmeBx7RdQuAS7EsyshuuZkzrSr9ZCM5vN5OXlYbPZMBgMpKamYjAYmDBhgnugdVZWltoxhTik0tpSvt78NQBXD70aAFdtLQCa8AjVcomWUaUwstlsZGZmkp2d3exOE+F9nM4GzLdcjGFjObWhEP38E/Q/5kS1Y7ULn7grrb4aZdE0NECO80LGJI7h9MFd1E7lUUaj8aCtQa0dZC2EWkwbTDhcDkZ0HsGILiMAcFVWAhDUyX+GH/irFhdGNpvNPUtsU/884B7Q2NTn35LmbYvFwooVKxg3bhzQeCFsy7wkon24XC4W3ZWKIX8XDVpwPnovx5x8sdqxOoa3dqX9OA9NxU62u7qwMHw8/7tguNqJhBD7cbgcLFi/AICrhl7lftxZVQWAtlMnVXKJlmtxYdQ06dr+t8w2TbqWk9M4h01KSkqLCiOdTkd+fj7QWFjJJ0HvtPiRDAzm9QCU3X8tp118i8qJOo4myAsnSNy7AdevL6IFZjdcx4NXJhMb6T9daEL4gyXbllBcW4w+XM85/c/BVVeHff16HLuKANBGS4uRt2txYeTJSdea7ibJzc1l/HjfXFfL33370gz6ffgzANtvSuHsG6ernKiDeVtXmqLg+uo+tC4HZudowo69kJTh3dROJYT4lw/XfghA2uA0XBsKKbxtEg27d7t/HiQtRl6vTWOM2jrpWl5eHunp6Yd9jsw+2/F+W/AC3V78LwCWi0ZywdTnVU7UQfbrPvO6CR7//i/azT9Qp4TwVNBNvHORdKEJ4W3WWddRUFxAsCaYK6JOYdu1N+IsL2/2nNAWTjMh1OPxj8UtnXTNZrM1W9jxUObMmUNsbKz7q0+fPm2NKA7jryULiHz4ZbQKFJ7Ul/OyP1A7kjq8qcXIXknD140tdi83XMINF5xB106yQrcQ3uaDtftu0e95FnXTHsFZXk74sccy8Ltv0aWl0n3Wg2hlbiyv16arf0JCQrPt1ky6ptPp3GOTDkdmn+04m/74Dse9DxHaAFuO0XP2K5/4x1IfR8OLzlv5/gmCq3ezxdWNP/pex/hk+XAghLex1dn4avNXAFz9vYu6NWsI0uno/cLzhPToQY9HHiHuqquOsBfhDdp09e+ISdfCwsKIiYlp9iU8r6hwJcUZk4mqU9jRN5JT3/yc0LBItWOpxmu60vasQfn9FQAeVW7g4SuSvSebEMJt/vr52J12Uir6EvzxNwD0zH6CkB49VE4mWqtVd6XJpGv+qax4GxtuvJZuFU6Ku4SQ9O5/iY6NP/IL/Y3Gy+YxUhQcX0whRHHyjTOZ0WeNZ0DnKLVTCSH+xe608+G6DwluULj+i2pQFGIvuYTo009XO5o4Ci0ujGTSNf9UU1nGiuuuoHdxPbZOWga+9S767v3UjqU+byiMVi4gZMdv1CqhvB93G2+cJoM2hfBGX1m+orSulBtWRBK6bQ9Bej1dp2WqHUscJS+4+gu1OOrr+P6mi+m9pYrqcA3xrzxHr4Gj1I7lHdTurqorp37fgOsXnZdyT+o4QoLk11UIb6MoCu/8/Q699yqc+1M1AN1nziA4Lk7lZOJoyZU2QLlcLhZPupwBq0qoD4KguTMYnBzYi3IG7XchU3scj8P8KKF1JRS6elCXPInRfeUiK4Q3+nnnz1jKNjHpa9A2uIg+4ww6nXee2rFEG8gisgFq0fTrMPy8GZcGqmZO5OSzr1E7kupCunWj1zNPo41SeRzP7lUErXgdgOfDJvLYeSPUzSOEOKR3/n6HcwoUBu50oY2KovtDs1T/YCXaRgqjAJT31D0M+LRxSZZdky7GeNUUlRN5jxi1P+m5XFR/chdRuPifcyyXXPkfosPk11QIb7S2dC2F63/n6e9dAHS9715CundXOZVoK+lKCzA/vfsEPV9bBMDmtLEYJ8vivd7E+ecHRO3Jp1oJ4/eB93LWUFn2Qwhv9drKXG5Z5CLcARFJSegmTFA7kvAAKYwCSP6XbxOb/Q5aoPCsQZw7+021I4n91ZZR//VMAHI0adx1+Rnq5hFCHNKmsk3UfrWYRIsCIcH0eORhNN5wN6toM3kXA8Ta375Ck5VNiBMso7tx7nOmwJ3V2ktVfvUQEY4yNrp60fe8e+nSSZYOEMJbvfPrC9xgbuxC63L77YTJGmh+Q/4yBoBta5dTPvl+IuphW0Inznrjc4JDQtWOJfaj7PyDqFXvAPBB5zu54vgBKicSQhzK5vLN9H0jj5haIKEf8TffrHYk4UFSGPm5vTs3seWWm4itcrGrRxhj3/2UiEhZVsWruFyUm+5Ei8IXrpO45spr5K4WIbzYl+8/zClrFFwa6P/EPDQhIWpHEh4khZEfq7LtZeX14+lS2kCpLojhb3+ALr6n2rHEv9Qtfxtd2UoqlQh2jJnJwK6d1I4khDiEdZblJL7xOwCa8RcRMUKm0/A3Uhj5qfraGn6+4WJ67qilMlJDz9depXu/4WrHEv9WY8W1eBYAb4dexY3nnqByICHEoSiKwsasKcRVQ1mPaIZmPax2JNEOpDDyQ05nA3kZF9NvnQ17CEQ88xiGEaeoHUschPXz6UQ6K1jr6sNxV0wlPCRI7UhCiEMoeOdpBv5VQoMWemZnow0PVzuSaAdSGPkZl8vFoikTMCzbSYMW7A/fxYjTL1M7ljgI57bl6NZ9BMCivvdx+tAeKicSQhxKzRYL2mcapzjZcEUi/Y8/S+VEor1IYeRnFj8+CcM3awAouedKxl52q8qJxEG5nNhMk9Gi8JlyGteMv1LtREKIQ3DV1bHm1hsIt7vY2DeYs6Y9r3Yk0Y6kMPIj3+c+RL/3fgBg63VncubEWSonEodS+ctrxFespUKJxH7mQ3SNkSZ5IbyRoihYHphG1Ja9lEeC9uH7iIuKVzuWaEdSGPmJ3z9+mc7PzAfAct6xnDv9ZZUTiUOq2kvQd48A8GH0dVxxWqLKgYQQh2L98EMcX3yDSwNf3zCMC8Zep3Yk0c6kMPIDq77/mPCHXiBIgcITenPukx+qHUkcxu7/ZhLpqmK1qz8nX5lJkFbmLBLCG1X9+CN7Hn0UANOZodx0wzMyx1gAkMLIxxX+9SN19zxAmAO2DIvj7Fc/IyhIVmP3VnbLL3S3fAzAsmHTObaPXuVEQoiDqVu7lm133YXGpfDdCA2jpzxMv5h+ascSHUAKIx+2a8vf7E6fRHStws4+kZz69ueEhkeqHUscirOBctOdAHyuHcf4y69QOZAQ4mDsmzax+aab0NTWsbK/hp2TLuKihIvVjiU6iDQt+ChbyU7W3XAN3cud7I0PYdQ7C4iO7ax2LHEYe797ka41m7ApUURd8AjRYfLrJ4S3sW/axObrroMyG5Zu8M3E43j51NnShRZApMXIB9VWl7PsusvovttOebSW/m+8QeeeCWrHEoehVOwi6pdsAD7vPJGzEmUWciG8Te3ff7P5+utQrGVs7gZv3tKHuee/SHiw3DUaSKQw8jENjnq+u/kS+lgqqQkD3UtP0XfoGLVjiSPYNv9+IpUaVikGzrzqPvn0KYSXqfrpJzb/5z8opfuKool9eenyd+kcIS3xgUYKIx/icrlYdMflDPhzD44g0DyRxdCx56odSxxB5brv6LfzC1yKhg3Js+nTWRaJFcJbKIpC2UcfsS3jVveYordvS+Cly96le1R3teMJFcggBx/yzQM3kvBDIS6gPOtGTj1P5tPwek4H1Z/cQyfg67BzuPj8C9VOJITYx1Vby45ZD1D9+ZdogB+O1bDqllN546wn6RQqH2AClRRGPsL87P30/3gZAEUZ55Pyn6kqJxItse3rp+lr34xViaZX6hxCgqSRVghvYLdspnDybWgKt+LSwIena4m/5WaeS7yTYK38aQxk8u77gF/ef4oer/4PgM2XJ3P+PU+pnEi0RL11B51XPAPAd31u54rBBpUTCSEUl4uid97A+sxzBNc7sUXCO1fGc+O1TzG2x1i14wkvIIWRlytY9H9EP/46WqDwNAPnP/qO2pFEC2376B4GUstfDGbcVVPUjiNEwKsvKmLlPRlE/bWJYGBlfw3rbk8h++yHiQ2LVTue8BJSGHmx9csXo2Q+TqgTLMd14ZwXP0arla4YX1CycjEDixfjVDTsPf1xRkbJ7b5CqEVxuVj/fy9T+8yrRNU5sQfD1xd0Zdyd2UzodYLa8YSXkcLIS+3YUEDZpHuItcP2AdGc+ebnhITKH1ef0FCP44t7AVgcdRHnnmlUOZAQgatszV+smXYn+g3FhAObemmpzLyR+8bdRUhQiNrxhBeSwsgLle7ajOWmG+hS6WJ39zDGvPtfIqN1ascSLVT4RTYJjm2UKDEMnDBH5iwSQgXO6mqWz7mf6P9+h94FdSHw50VDOGfqi/TU9VY7nvBiUhh5maryUv64PpVeJQ6ssUEMeev/iOvSR+1YooXqSrbS868XAPg14W4u7icXYCE62qb/fUTpY08QW2YHYNXwSHrPfJAbEy9ROZnwBVIYeZF6ew0/3Xgx/bfVUBWhoVvOS/QcMELtWKIVtn14N4Ox86dmGOPG36l2HCECSuX2zeRPv51uyzcTA5TEaNiVcQGX3PAoYUFhascTPkIKIy/hcjrJu/UyDGus2IMh9OnZDBx1utqxRCvszv+SwaXf0qBoqTQ+QVS4jF8QoiO46utZ9uJDhL/9Kd3qFRq08Ne4vpz2wAuc2nWw2vGEj5HCyEt8PfVqDL9tw6mB2odu58Qz09SOJFpBcdTB1/cBkNfpUs49WYpaITrC1l8Xs+2BGXTeWQWApW8onWbczzWnXSPj+8RRkcLICyx+4g4MX64EoPjOKzgr9Q6VE4nW2vjJ4wxuKGKPEsewq2XAtRDtrdZawm8PTqKbeRWdgcoI2HrtGZx/+zyiwqLVjid8mBRGKvvhjUfo8/YSALZccyrn3faoyolEa1XvsdB3zSsArBhyLxf0lIUnhWgviqJQ8H/P4HruTXpUOwFYNbYrSQ8/y/H9RqucTvgDKYxUtOyzXPRPfQBA4dnDOH/GqyonEkdj54d3Mph68rXHMi71NrXjCOG3dq3JZ23WXfRYXwpAUZcguC+dtIsnSyut8BgpjFTy90+fETLzGYJdYBnTk/OeWSCzWvugHUs/YbDtJxxKEA3nzCU8VH6lhPA0R001P825m87//ZkeTrAHw6bLRpMy7QVio+LVjif8jFzFVbB51S9U35VFJwdsHRKLMfczgoLkrfA1Sn0NIYunAfCt7grOGXuyyomE8D+r//d/2OY8SY/SegA2Do0h4ZE5pI44S+Vkwl/JX+MOtmfbOnamZxBfo1DUK5yT3v6MsAgZKOiL1pkeZphzN7sVPcde/bjacYTwK9btm1g+43b6LttGPGDtpKFy0njOv24mwfJBUrQj+d/VgSpKd/P39VfRo8xJiT6YEe/MJyaum9qxxFGo3Lkew4bXAfjrmKmc062LyomE8A+uhgZ+emEGnd7+gr52BZcG1hsHcsqsl+jaua/a8UQAkMKog9TVVPLb9ZfQd1cdFVEa+rz+Gl17y8RjPklR2PXRnQzGwYqgUZx5WbraiYTwCxt+/ZodD86kx44aALb3CSf+welcfqrM6yY6jhRGHaDBUc+SWy7GsKmC2lDo9OJc+g8/Qe1Y4iht/WUhgyt/p14JQnvBPEJDgtSOJIRPq7Lu4aeHJtF38Rp6ANVhsOe6FFImzyU0NFzteCLAyG1Q7czlcrHo7vEYCnbToAXn4/cz/MQL1Y4ljpKzroqIb6cD8H3nq0hMPF7lROJITCYTSUlJBzxmMpnIzMxUKZWAxuvjL/83j9XnnEX/xWvQAhvG9KD75wu54N7npSgSqpAWo3a2ePZEEpasxwVYp17L6RfepHYk0QZrF87iWNdeipTOjLr6YbXj+CWbzUZubi4AU6dOdT9uMpkAsFqtGAwGjEZji/aXmppKTk5Os/3odDqMRiMWi4Xc3FzS06U7tKNtW7uMNdPvod9aKwDFnYMJuf8OLrkkQ+VkItBJYdSOvn0xi37zfwVgx81nc84N01VOJNqibNvfDCl8C4C1o6YzLl7mT2kPZrOZ0tJS4vf797VYLOTl5bkLnJSUlBYXRv+Wmprq/r6wsJCMDPlD3JHstVV8O+dOen78G/2cUB8E2y4bw7jpLxAZGat2PCHUK4wyMzMZM2YMFoul2adCf/Hb/Ofo9tKnAFguHsUF9z+nbiDRNopC8fw7icPJsuBkTr/oBrUT+a3U1FSsVis2m839mNlsRqfTubd1Oh1msxmj0YjJZMJqtTbbh16vb1YAHYzZbCYpKYnExERPxheHsfzLN6l54ln673UAsGWIjsGPzeOiY09ROZkQ/2hxYeTJ5m2TyURCQgKpqank5ua6L3D+4q8l84l85FW0Cmw6pT8XPPG+2pFEG2364T2GVK/AroQQcclTBAfLgOuOVFhY2KwFSa/XuwunIxVAB1NQUIDNZiM9PZ2CgoKDFkd2ux273e7erqioaH1wAcCe7etZNvN2Bi7dSTRQHq2l7varOef6LJnxX3idFv+PbGre3l9T83Zqairp6elkZ2e3aF///jRYUFDQ0hheb2P+Ehz3zia0ATYfG885L/9XfvF9XENtBbE/zALgp27/YcSIUeoGEgAHtBIditlsxmKxuD/EWSwW0tLSyMnJISkp6ZD7mTNnDrGxse6vPn36eCx7oGhocPDNs1PYftFlDFy6ExdgMQ5h2DdmzrhxhlwbhVdqcYuRJ5u309PTyczMxGw2k5+fT0JCQptPxBsUbfqLvbfdSVydwvb+UZz+1ueEhkaoHUu00ZoPZ3KcUsoOupJ49Wy14wSkhISEZteephbqljAajRQWFrq3DQZDs+1DycrKYsqUKe7tiooKKY5aYdVvX7Br1iz6bqsFoKhXBN1nz+KCUy5ROZkQh9emMUZtad7OyspCp9NRUFBw2Of6SnN22Z5tbLjpOrpVuNjTNZTkdz4mqpNe7ViijfZa/mLY1vdAA4XJszhdJ4ND1WA0GpvdWm+xWNq9+z0sLIywsLB2PYY/KrMW8cPsSQxcvJ4+CtSGQtn153H6nU8QHBKqdjwhjsjjg69b0rzdNF7JYDC4vw5lzpw5zJ7t3Z/SqyutrLjucnoX11MWo2XQm++i79ZP7ViirRSFsoV30kXjZFnoCZx6/jVqJwoIZrOZvLw8bDYbBoOB1NRUDAYDEyZMcLdEZ2VlqR1T/IvL5eK79+YQ/uIHDKlwAbAluRdJj71EYr8hKqcTouXaVBgdbfO2Tqdr8Z1o3t6c7bDX8uONl9B/azXV4Ro6v/I8vQaOVDuW8IB15rcYWvsndUoIuiueQqvVqB0pIBiNxoO2Bh3NIGvRMTau+YV1M+9j4BobAKX6EKIy7+a8S2TeNuF72lQYdUTztjc3Z7tcLhZPuhzD6hLqgyHoyQcYnDRO7VjCA+zVZXT+tXECx1973sBZQ45VOZEQ3qe6ppy8uZPpb1rOwAZo0MLuy07ktBnPERbZSe14QhyVFhdG0rx9oEXT/oPhly24NFD1QAYnG69SO5LwkLUfTGeUUsY2upN8zUNqxxHC6/z0ZS712S8wpLgBgJ2D4xj6+DOMOHasysmEaJsWF0bSvN1c3ry7GfD5HwDsuv0SjBPuVjeQ8JjdG/I5dsdHoIEdJz5M3+hotSMJ4TV27ljH0gduZ9hvRQBURmlRbr+OcTdORaOR7mbh+2RJkKPw4ztz6PnGNwBsnnAi59/xhMqJhMcoChUf30l3jYul4adw4tnj1U4khFeob7Cz+OUsur61iGG1CgDbzxrGSY+8THR8d5XTCeE5Uhi10or/vUlc9rtogcJxgzl/1utqRxIetPrrHI61r6ZGCaNb2tPyCVgI4K+lX1D00EMkbK4BoLhHBD0ems3Zp1+kcjIhPE8Ko1ZY++v/0E6fR7ALLIndOffZhTJzqx+prbDSc9njACztewtnJsgtxiKwlZXt5rtHJjFo0Vr6u6AuBCquPY9T7p5DUKh33hQjRFtJYdRCW9cupWJyJjH1sHVQDOPe+FwmK/Mzaz+YSiLlbNH0YuzVM9WOI4RqFEXh24/mEvbcuwyzNc5JtH10TxIff5HOA4apnE6I9iWFUQvs3bGRbTffQudqF7t6hHHi258SHiG3ovqT7X//xshdJtDA3lMfo39EpNqRhFCFZcMyVs28h8ErGyfrLdMFE3H/ZM6+Il3lZEJ0DCmMjqDSVszK6yfQ09pAaVwww9/+kNj4HmrHEh6kuJzUfXoPQRqFpZFncPyZl6odSYgOV2evZvGTd9Hno18Y7Ng3J9FFYzht5guEdZKlcETgkMLoMOprq/n1ukvou7OWikgNPXNfpXs/aUb2N3998RKjHGupVsLpPUEGXIvAs9T8f1Q+9iSDdtUDUGSIYeBjTzJi9KkqJxOi40lhdAhOZwN5Ey/GsMFGXQhEPvc4hhEnqx1LeFhFWTH9/5gLQP6AWzmtX4LKiYToOMV7NvPLA7cx+MetxADVERrst17JmbfMQBsUpHY8IVQhhdFBuFwuFt0zHsOKIhq0UP/oPYw+9VK1Y4l2sOH9+0mmks2avhx/ZWDN3C4CV4OzAfNrD6J77VOGVjfOSbTt1IGc8MjLxHb3nrUohVCDFEYHsfix2zAsXgtAyZQrOfMSGXTojwr//JHEvZ+BBsrHPcGA8HC1IwnR7tYWmNn8YBYDNlUBsLdrGJ0fnME5xjSVkwnhHaQw+pfvX32Afu//CMDWG87i3FtmqZxItAdXQwPK/6ag1Sgs7WRk7CkXqB1JiHZVWVnKkkdvx/C/vxjgBHswlF51Fqff+xTB8qFACDcpjPbzu+lFOj9nAqDw/BFcOO0llROJ9lLw2XMkN2ykUomg/1VPqx1HiHajKAo///dFlKdyGGJ1ArD92K4cN+d5Rg0aqXI6IbyPFEb7rPrORPhDLxGkQOGJfThv3gdqRxLtpLykiEGrGouhlYPv4OSe/VROJET72L75Lwpm3sng/GIAbDFBBE1JJ2XCZLn7UohDkMII2PTn99RNeZDoBtgyXM/Zr35KUJD80/irjR/cTzJVFGoHcPz4qWrHEcLj6h115D1zL93f/5bBdnBpYMd5Izl11ktExsarHU8Irxbwf/13WVZRnHEHcbUKO/tEcupbnxMaJrMe+6uNK5aQbP0fADUpcwmRZV2En/njBxMlDz+GYWcdAEX9oun3yOOcc3yKysmE8A0BXRjZSnaw/sb/0K3cSXGXEEa9u5Bo+TTlt5wNDQR9fR8AS2PPY+yJZ6ucSAjPse7dwU8P3cbAJZvoDdSEa6i6+VLOvO1htMEBfakXolUC9relpsrGsmsvo8+eemydtAx44y069zCoHUu0o4L/PskYp4UKJQrDVfPUjiOER7hcLr5751EiX5rP4KrGBV+3nNCPsY+9jL6XXNOEaK2ALIwa6u18f/MlDNhcRU0YxL30NH0HJ6kdS7Qj657tDFnzHACrh93FSTKJnfADm1b/zPqZ92FYVw5ASedQYmbcz3nn/UflZEL4roArjFwuF4smX07CX8XUBwFzpzP0+HPUjiXameXDe0mmhg1BAzn+iilqxxGiTWpqylny+GT6frIcgxPqg2BP6smcPu1ZwiKi1Y4nhE8LuMLom5k3kPCDBZcGKrJu4tRzrlU7kmhn65cuItn2DS5Fg/O8eQSHhKgdSYij9vsXr1GX/TwDSxoA2D5Uz7DHn2Hk8ONVTiaEfwiowsj8zH30/+9yAHbeegFn/+d+lROJ9tbgqCd0cSYAy/QXckLyWSonEuLo7Nq2luUP3MGgpUXEAuXRWlyTryfluvtlTiIhPChgCqOf35tLj5wvAbCkHs8Fdz2pciLREQoWZnO8cws2ohl8tQy4Fr6nocHBkhcziX/7awbVgQvYZhzGqbNfITq+m9rxhPA7AVEYFXz9LjFz3kILFJ6RwPkPv6V2JNEBSnZtYfj6l0AD646ZwgldeqgdSYhW+fu3L9k56wH6bqsFYFevCHrOfpjzTrlQ5WRC+C+/L4zWLV2EMm0OIU6wjOzKOS98jFarVTuW6ABbP7yXJE0t64MHM+byu9WOI0SLlZft5ofZkzB8s5Y+CtSGQtl153HGXU8QJJOSCtGu/Low2rZuObbb7yXWDtsSOnHmm58TEhKmdizRAdb8+j+SKsy4FA2aC54mKChI7UhCHJHL5eKnD54k5Pl3GFSxb06ipJ4kPv4iif2GqZxOiMDgt4VRSVEhW26+mS5VLnZ3D2PsO58QGRWrdizRARz1dUSZpwGwrPOlnDD6VJUTCXFkW9ctZ/XMuzGstgJQGhdMeOZkzrs0XeVkQgQWvyyMXC4X+ROvom+pg1JdEMPe+QBd515qxxIdpGD+HMa6tmMlhmHXzFU7jhCHZa+rxjz3Lnot+AVDAzRoYeclYzh95gtEyIc5ITqcXw620Wq1dL/3PvZ2DqF77st07zdc7UiigxTvsDBi0ysAbDpuKrH6rionEuLQ8he/x6/nnIThg18Ia4DtA2OJ/jCXc+e8K0WRECrxyxYjgJFnjafh1EsJloGKAWXHR3eTqLGzNmQ4yZdMUjuOEAdVssvCbw9MYuDPW4kEKiM11N42AePND8jNIUKozG8LI0CKogCz+sdPSKz6AaeiIeTip9HKgGvhZZzOBr7PnUWn3E8YWKsAsPn0gZz06Mvousj6fUJ4A78ujETgsNfVEPvddACWd03jhBEnqpxIiOY25C9h8wPT6GupAmB39zA6PziD889KUzmZEGJ/UhgJv/DHR49yglJECTqGX/OE2nGEcKsqL+X7R2+n35d/0dcF9hAovuoszrz3SULCItSOJ4T4FymMhM/btXU9Ize/BhrYnJjFGF282pGEAOC3hS/geiqHBJsTgM0juzLqsecZNXCkysmEEIcihZHwebvn30MPTT1/h44g+UKZ80Wor6hwJX/OmMyAP4sBsMYGoZ0ykfMn3KVyMiHEkUhhJHzaX98uYHTNLzQoWqIuexaN3NEjVFZVXsLO1CsZUKvQoIVt5x/H6Q+8THSstGQK4QukMBI+TddzEH+HjqRSfwwnDEtWO44QRMd2Zu/5yZQVrKXfw49xwZiz1Y4khGgFKYyET+s3dDTKtO9xOOrVjiKEm/HBVwkKDiUoSC6xQvga+a0VPk+j1RIaFq52DCHcQsMi1Y4ghDhKMiBDCCGEEGIfKYyEEEIIIfaRwkgIIYQQYh8pjIQQQggh9pHCSAghhBBiHymMhBBCCCH2kcJICCGEEGIfKYyEEEIIIfaRwkgIIYQQYh8pjIQQQggh9vG5JUEURQGgoqJC5SRCiNZo+p1t+h32NXLtEcJ3teb643OFUWVlJQB9+vRROYkQ4mhUVlYSGxurdoxWk2uPEL6vJdcfjeJjH99cLhdFRUV06tQJjUZzwM8rKiro06cP27dvJyYmRoWE7UfOzTfJuTVSFIXKykp69uyJVut7vfhHuvaAvNe+Ss7N97T2vFpz/fG5FiOtVkvv3r2P+LyYmBi/+k+wPzk33yTnhk+2FDVp6bUH5L32VXJuvqc159XS64/vfWwTQgghhGgnUhgJIYQQQuzjd4VRWFgYs2bNIiwsTO0oHifn5pvk3AKHP/97yLn5Jn89t/Y8L58bfC2EEEII0V78rsVICCGEEOJoSWEkhBBCCLGPFEZCCCGEEPv43DxGLZGbm4ter8disWA0GklMTATAZDIBYLVaMRgMGI1GNWMelaZzaJKamgpAWloaWVlZAMyfP5/s7OwOz9YWhzovf3jP0tLSeO2119DpdAc87svvGRz63PzhfTta/nr98ddrD8j1x1fft3a7/ih+Jj8/X0lNTXVvG41GRVEUpbCwUElPTz/gcV9SVlamZGdnu7f3P5/ExERFp9MpRqNRKSsrUyHd0TvUefnDe1ZYWKgAik6nU3Q6nQK4z9WX3zNFOfS5+cP7drT89frjr9ceRZHrj6++b+15/fG7rjSz2YzBYGj2WEFBAWazuVlVqdPpMJvNHZyubXQ6HTk5ORQUFLi3m2RlZVFWVkZeXt4B1bO3O9R5+cN7ZrFYKCsrc3/l5OQwdepUwLffMzj0ufnD+3a0/PX646/XHpDrj6++b+15/fG7rjSDwcDy5cvd2xaLBYvFQmFhIfHx8e7H9Xo9NptNhYRtk52dTVJSEomJiSxZssT9eNM5W61WANLT01XJd7QOdl7+8J7t34Sbm5vL+PHj3du+/p4d6tz84X07Wv58/fHXaw/I9Qd8731rz+uP37UYNfUN22w2d5V4qGq46T+EL1m+fDn5+fno9XrGjRvnfjw7O5vU1FTS09PJzs72uV/gQ53Xv/niewaNfyBtNluz/4u+/p41Odi5/Zuvvm+t5c/XH3+99oBcf3z1fYP2uf74XIvR3LlzKS0tPeDx+Ph4dxPhwoULKSgoIDk5GZ1OR3Jysvsfr0nToCxvcqRzM5lMpKSkkJiYSF5eHhkZGZjNZmw2G8uXL3cPntPpdFgsFvegT7Ud7XklJCT4/HvWJCcnh5SUFPe2yWTy6vcMjv7cfOF9O1r+ev3x12sPyPUH5PrT6vfNk4OhvEFZWZl78OP+g7AKCwubDYpMTExUJV9b5OTkKPn5+e7thQsXKvn5+Up+fr6Sl5fnftxgMKgR76gd6rz84T1rYjAYlMLCQve2r79n+/v3ufnT+9Za/nr98ddrj6LI9afp576qPa4/frkkyP63y+5fWe5/C59er3c3e/uSuXPnupsM9z+HpnNbvnw5GRkZXvfJ5kiOdF6+/J4BJCUlsWTJkmbNvb7+njU53Ln5+vt2NPz1+uOv1x6Q64+vvm/QPtcfvyyMhBBCCCGOht8NvhZCCCGEOFpSGAkhhBBC7COFkRBCCCHEPlIYCSGEEELsI4WREEIIIcQ+UhgJIYQQQuwjhZEQQgghxD5SGAkhhBBC7COFkRBCCCHEPlIYCSGEEELsI4WREEIIIcQ+/w/kOepH4x6KTwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,2,1)\n", + "ax2= fig.add_subplot(1,2,2)\n", + "\n", + "ax1.plot(res1_a[:,0], np.hypot(res1_a[:,zr_index], res1_a[:,zi_index]), label=\"Mode1\")\n", + "ax1.plot(res1_a[:,0], zeta1_wkb, label=\"Mode1 - WKB\")\n", + "\n", + "ax1.plot(res2_a[:,0], np.hypot(res2_a[:,zr_index], res2_a[:,zi_index]), label=\"Mode2\")\n", + "ax1.plot(res2_a[:,0], zeta2_wkb, label=\"Mode2 - WKB\")\n", + "\n", + "ax1.set_yscale('log')\n", + "\n", + "ax2.plot(res1_a[:,0], np.hypot(res1_a[:,sr_index], res1_a[:,si_index]), label=\"Mode1\")\n", + "ax2.plot(res1_a[:,0], s1_wkb, label=\"Mode1 - WKB\")\n", + "\n", + "ax2.plot(res2_a[:,0], np.hypot(res2_a[:,sr_index], res2_a[:,si_index]), label=\"Mode2\")\n", + "ax2.plot(res2_a[:,0], s2_wkb, label=\"Mode2 - WKB\")\n", + "\n", + "ax2.set_yscale('log')\n", + "\n", + "ax1.relim()\n", + "ax1.autoscale_view()\n", + "\n", + "ax2.relim()\n", + "ax2.autoscale_view()\n", + "\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "7780e288-a7c0-436a-819a-bd1c9ae546ac", + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "1e644bda", - "metadata": { - "id": "1e644bda" - }, - "outputs": [], - "source": [ - "def test_two_fluids_wkb_spec_log() -> None:\n", - " \"\"\"Compute WKB approximation for the two-fluids model spectrum.\"\"\"\n", - "\n", - " #\n", - " # New homogeneous and isotropic cosmological model NcHICosmoQGRW\n", - " #\n", - " cosmo = Nc.HICosmoQGRW() # P1 = Cosmologia\n", - "\n", - " w = 0.00001 #P2 eq de estado da materia escura\n", - " prec = 1.0e-7\n", - "\n", - " #P3 densidade de radiação e materia escura e energia escura (1 - resto)\n", - " cosmo.props.w = w\n", - " cosmo.props.Omegar = (1.0e-8) * 1.0\n", - " cosmo.props.Omegaw = (1.0 - 1.0e-8) * 1.0\n", - " cosmo.props.xb = 1.0e30 # P4 x do bounce\n", - "\n", - " pert = Nc.HIPertTwoFluids.new()\n", - "\n", - " pert.props.reltol = prec\n", - " # pert.set_stiff_solver (True)\n", - "\n", - " lnki = math.log(1.0e-5)# P5 intervalo de momento de interesse\n", - " lnkf = math.log(1.0e5)\n", - " lnk_a = np.linspace(lnki, lnkf, 50)\n", - "\n", - " ci = Ncm.Vector.new(8)\n", - "\n", - " k_a = []\n", - " Ps_zeta1 = []\n", - " Ps_S1 = []\n", - " Ps_zeta2 = []\n", - " Ps_S2 = []\n", - " Ps_Pzeta1 = []\n", - " Ps_PS1 = []\n", - "\n", - " out_file = open(\"twofluids_spectrum_{w}.dat\", \"w\", encoding=\"utf-8\")\n", - "#alpha is related to the time variable. The log-redshift time\n", - " start_alpha1 = 1.0e-10 # P5 tempo inicial dependente do redshift.\n", - " start_alpha2 = 1.0e-14\n", - "\n", - " for lnk in tqdm(lnk_a):\n", - " k = math.exp(lnk)\n", - " pert.set_mode_k(k)\n", - " k_a.append(k)\n", - "\n", - " alphaf = cosmo.abs_alpha(1.0e20)\n", - "\n", - " # print (\"# Evolving mode %e from %f to %f\" % (k, alphai, alphaf))\n", - " #S is our variable Q.\n", - " alphai = -cosmo.abs_alpha(start_alpha1 * k**2)\n", - "\n", - " #### Ate aqui só coloca todos os parametros, define o tempo inicial, e converte o alpha1 em algum tipo de numero absoluto nessa funçao de cima.\n", - "\n", - " ##### Agora embaixo, calcula as cond iniciais, seta as condicioes iniciais e evolui no tempo.\n", - "\n", - " pert.get_init_cond_zetaS(cosmo, alphai, 1, 0.25 * math.pi, ci)\n", - "#This function does the following: Calls get_init_cond_zetaS, which calls cond_QP.\n", - "#IN cond_QP:\n", - " #Starts interface that have the equations of motion and the decomposition TV.\n", - " #Defines which case: 1 or 2, defining which momentum we assume as non-zero\n", - " #Computes all the init cond\n", - " #I believe that R and I represents each solutioon 1 and 2.\n", - "#Then we call to_zetaS, which changes from QP to zeta Q\n", - " pert.set_init_cond(cosmo, alphai, 1, False, ci)\n", - "\n", - " print(f\"# Mode 1 k {k: 21.15e}, state module {pert.get_state_mod():f}\")\n", - "\n", - " pert.evolve(cosmo, alphaf)#Evolve the system untill alphaF\n", - "\n", - "\n", - "\n", - " v, _alphac = pert.peek_state(cosmo)#Get the current time and values of the numerical solution for the modes. V é o vetor com os modos, n sei a ordem\n", - "#I believe that Delta represents the spectrum here.\n", - "\n", - "\n", - "##Aqui terminou de calcular os modos pro momento do loop. Ai agora calcula o espectro\n", - " Delta_zeta1 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", - " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_S1 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_Pzeta1 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", - " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_PS1 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - "\n", - " Ps_zeta1.append(Delta_zeta1)\n", - " Ps_S1.append(Delta_S1)\n", - " Ps_Pzeta1.append(Delta_Pzeta1)\n", - " Ps_PS1.append(Delta_PS1)\n", - "\n", - "\n", - " #### Aqui acabou o espectro pro modo 1. Ai faz de novo pro modo 2. ####3\n", - "\n", - " alphai = -cosmo.abs_alpha(start_alpha2 * k**2)\n", - " pert.get_init_cond_zetaS(cosmo, alphai, 2, 0.25 * math.pi, ci)\n", - " pert.set_init_cond(cosmo, alphai, 0, False, ci)\n", - "\n", - " pert.evolve(cosmo, alphaf)\n", - " v, _alphac = pert.peek_state(cosmo)\n", - " print(_alphac)\n", - " Delta_zeta2 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.ZETA_R),\n", - " v.get(Nc.HIPertITwoFluidsVars.ZETA_I),\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_S2 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.S_R), v.get(Nc.HIPertITwoFluidsVars.S_I)\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_Pzeta2 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.PZETA_R),\n", - " v.get(Nc.HIPertITwoFluidsVars.PZETA_I),\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - " Delta_PS2 = (\n", - " k**3\n", - " * math.hypot(\n", - " v.get(Nc.HIPertITwoFluidsVars.PS_R), v.get(Nc.HIPertITwoFluidsVars.PS_I)\n", - " )\n", - " ** 2\n", - " / (2.0 * math.pi**2 * cosmo.RH_planck() ** 2)\n", - " )\n", - "\n", - " Ps_zeta2.append(Delta_zeta2)\n", - " Ps_S2.append(Delta_S2)\n", - " Ps_zeta2.append(Delta_Pzeta2)\n", - " Ps_S2.append(Delta_PS2)\n", - "\n", - " out_file.write(\n", - " f\"{k: 20.15e} {Delta_zeta1: 20.15e} {Delta_zeta2: 20.15e} {Delta_S1: 20.15e} \"\n", - " f\"{Delta_S2: 20.15e} {Delta_Pzeta1: 20.15e} {Delta_Pzeta2: 20.15e} \"\n", - " f\"{Delta_PS1: 20.15e} {Delta_PS2: 20.15e}\\n\"\n", - " )\n", - " out_file.flush()\n", - "\n", - " out_file.close()\n", - "\n", - "###Plot\n", - "\n", - " plt.plot(np.log(k_a), np.log(Ps_zeta1), label=r\"$P_\\zeta$\")\n", - " plt.plot(np.log(k_a), np.log(Ps_S1), label=r\"$P_Q$\")\n", - " #plt.plot(k_a, Ps_zeta2, label=r\"$P^2_\\zeta$\")\n", - " # plt.plot(k_a, Ps_S2, label=r\"$P^2_Q$\")\n", - " plt.xlabel(r\"$k $\")\n", - " plt.ylabel(r\"$Spectrum$\")\n", - " plt.grid()\n", - " plt.legend(loc=\"upper left\")\n", - " #plt.xscale(\"log\")\n", - " #plt.yscale(\"log\")\n", - "\n", - "\n", - " #plt.savefig('spec')\n", - " plt.show()\n", - " return np.log(Ps_zeta1), k_a" - ] + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:00<00:00, 54.86it/s]\n" + ] }, { - "cell_type": "code", - "execution_count": null, - "id": "17f092b6", - "metadata": { - "id": "17f092b6" - }, - "outputs": [], - "source": [ - "#test_two_fluids_wkb_mode(Nc.HIPertTwoFluidsCross.MODE1MAIN, 1, 0.0, 1.0)\n", - "test_two_fluids_wkb_mode(Nc.HIPertTwoFluidsCross.MODE1MAIN, 1, 1.0, 0.0)\n", - "#test_two_fluids_wkb_mode(Nc.HIPertTwoFluidsCross.MODE1MAIN, 1, 1.0, 1.0)\n" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] + }, + "metadata": {}, + "output_type": "display_data" }, { - "cell_type": "code", - "execution_count": null, - "id": "98260fc2", - "metadata": { - "id": "98260fc2" - }, - "outputs": [], - "source": [ - "test_two_fluids_wkb_spec()" - ] + "name": "stderr", + "output_type": "stream", + "text": [ + "No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n" + ] }, { - "cell_type": "code", - "execution_count": null, - "id": "84556565", - "metadata": { - "id": "84556565" - }, - "outputs": [], - "source": [ - "test_two_fluids_wkb_spec_log()" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,1,1)\n", + "\n", + "k_a = np.geomspace(1.0e-3, 1.0e4, 10)\n", + "Pk_a = []\n", + "for k in tqdm(k_a):\n", + " res_a = integrate_mode1(k, -65.0)\n", + "\n", + " Pkt = k**(3)*np.hypot(res_a[:,zr_index], res_a[:,zi_index])**2\n", + " ax1.plot(res_a[:,0], Pkt, label=\"Mode 1\")\n", + " Pk_a.append(Pkt[-1])\n", + "\n", + "ax1.set_yscale('log')\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "fig = plt.figure()\n", + "ax1= fig.add_subplot(1,1,1)\n", + "\n", + "ax1.plot(k_a, Pk_a)\n", + "\n", + "ax1.set_xscale('log')\n", + "ax1.set_yscale('log')\n", + "plt.legend()\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "id": "41e30921-52ee-4e8d-afa2-7ab3adc6cfe5", + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": null, - "id": "f3f21975", - "metadata": { - "id": "f3f21975" - }, - "outputs": [], - "source": [ - "z1 = [-172.29336504, -171.47725159, -170.67740675, -169.40963547,\n", - " -168.3753366 , -167.40418261, -166.617099 , -165.69081201,\n", - " -164.60277739, -163.8977755 , -162.91261604, -161.89532066,\n", - " -160.95146111, -159.82933117, -158.99936059, -158.1648807 ,\n", - " -157.3978438 , -156.18665031, -155.4043561 , -154.44173584,\n", - " -153.5056154 , -152.43139744, -151.48454113, -150.74967245,\n", - " -149.71138271, -148.85570926, -147.97343268, -146.87265029,\n", - " -145.89153898, -145.029969 , -143.98543597, -143.28854835,\n", - " -142.18761254, -141.23608627, -140.32638846, -139.48824811,\n", - " -138.47120016, -137.4639825 , -136.53337746, -135.66450856,\n", - " -134.71280034, -133.5931724 , -132.540295 , -131.19474152,\n", - " -129.90695834, -128.57067396, -127.17615592, -125.87341712,\n", - " -124.6418451 , -123.48007829]\n", - "\n", - "lnki = math.log(1.0e-5)# P5 intervalo de momento de interesse\n", - "lnkf = math.log(1.0e5)\n", - "lnk_a = np.linspace(lnki, lnkf, 50)\n", - "result=np.polyfit(lnk_a[:30], z1[:30], 1)" - ] + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:00<00:00, 428.24it/s]\n" + ] }, { - "cell_type": "code", - "execution_count": null, - "id": "5618578b", - "metadata": { - "id": "5618578b" - }, - "outputs": [], - "source": [ - "print(result)" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] + }, + "metadata": {}, + "output_type": "display_data" }, { - "cell_type": "code", - "execution_count": null, - "id": "07fa8d3b", - "metadata": { - "id": "07fa8d3b" - }, - "outputs": [], - "source": [ - "ns = result[0] + 1\n", - "print(ns)" - ] + "name": "stderr", + "output_type": "stream", + "text": [ + "No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n" + ] }, { - "cell_type": "code", - "execution_count": null, - "id": "36e209f8", - "metadata": { - "id": "36e209f8" - }, - "outputs": [], - "source": [ - "12*1/3/(1+3*1/3) + 1" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "720f771b-3dc7-42b4-9342-ae3c1b16a651", - "metadata": { - "id": "720f771b-3dc7-42b4-9342-ae3c1b16a651" - }, - "outputs": [], - "source": [] + }, + "metadata": {}, + "output_type": "display_data" } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.4" - }, - "colab": { - "provenance": [], - "collapsed_sections": [ - "iiIp6-GfovaW", - "WqocAbPmfI5P", - "fuB-VSqxNTu3" + ], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1= fig.add_subplot(1,1,1)\n", + "\n", + "k_a = np.linspace(1.0, 1.0 + 1.0e-13, 10)\n", + "Pk_a = []\n", + "for k in tqdm(k_a):\n", + " res_a = integrate_mode2(k, -89.7)\n", + "\n", + " Pkt = k**(3)*np.hypot(res_a[:,zr_index], res_a[:,zi_index])**2\n", + " ax1.plot(res_a[:,0], Pkt, label=\"Mode 1\")\n", + " Pk_a.append(Pkt[-1])\n", + "\n", + "ax1.set_yscale('log')\n", + "#plt.legend()\n", + "plt.show()\n", + "\n", + "fig = plt.figure()\n", + "ax1= fig.add_subplot(1,1,1)\n", + "\n", + "ax1.plot(k_a, Pk_a)\n", + "\n", + "#ax1.set_xscale('log')\n", + "ax1.set_yscale('log')\n", + "plt.legend()\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "1e93c2af-f734-4b6c-bdf8-9078e9a22e2f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-8.97943035e+01, 5.03244272e-11, 2.98009714e-14, 4.98998640e+09,\n", + " 1.13014792e-04, 5.03244272e-11, 3.02036061e-14, -4.94554646e+09,\n", + " -1.12008002e-04])" ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" } + ], + "source": [ + "res_a[0]" + ] + } + ], + "metadata": { + "colab": { + "collapsed_sections": [ + "iiIp6-GfovaW", + "WqocAbPmfI5P", + "fuB-VSqxNTu3" + ], + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/numcosmo/perturbations/nc_hipert_two_fluids.c b/numcosmo/perturbations/nc_hipert_two_fluids.c index 5429d0ab3..5aa6f8281 100644 --- a/numcosmo/perturbations/nc_hipert_two_fluids.c +++ b/numcosmo/perturbations/nc_hipert_two_fluids.c @@ -72,6 +72,7 @@ #include "build_cfg.h" #include "math/ncm_spline_cubic_notaknot.h" +#include "math/ncm_spline_func.h" #include "perturbations/nc_hipert_two_fluids.h" #include "perturbations/nc_hipert_itwo_fluids.h" @@ -95,7 +96,7 @@ #define SUN_BAND_ACCESS SM_ELEMENT_D #endif /* NUMCOSMO_GIR_SCAN */ - +#undef HAVE_SUNDIALS_ARKODE #include "perturbations/nc_hipert_private.h" struct _NcHIPertTwoFluidsPrivate @@ -116,6 +117,9 @@ typedef struct _NcHIPertTwoFluidsArg NcHICosmo *cosmo; NcHIPertTwoFluids *ptf; gdouble prec; + guint mode; + gdouble alpha_i; + gdouble alpha; } NcHIPertTwoFluidsArg; static void @@ -132,7 +136,7 @@ nc_hipert_two_fluids_init (NcHIPertTwoFluids *ptf) self->arg = g_new0 (NcHIPertTwoFluidsArg, 1); #ifdef HAVE_SUNDIALS_ARKODE - self->arkode = ARKodeCreate (); + self->arkode = NULL; #endif /* HAVE_SUNDIALS_ARKODE */ } @@ -159,7 +163,7 @@ nc_hipert_two_fluids_finalize (GObject *object) if (self->arkode != NULL) { - ARKodeFree (&self->arkode); + ARKStepFree (&self->arkode); self->arkode = NULL; } @@ -588,7 +592,7 @@ static gint _nc_hipert_two_fluids_f_QP_mode1 (realtype alpha, N_Vector y, N_Vector ydot, gpointer f_data) { NcHIPertTwoFluidsArg *arg = (NcHIPertTwoFluidsArg *) f_data; - const gdouble k = NC_HIPERT (arg->ptf)->k; + const gdouble k = nc_hipert_get_mode_k (NC_HIPERT (arg->ptf)); NcHIPertITwoFluidsEOM *eom = nc_hipert_itwo_fluids_eom_eval (NC_HIPERT_ITWO_FLUIDS (arg->cosmo), alpha, k); const gdouble Q_R1 = NV_Ith_S (y, NC_HIPERT_ITWO_FLUIDS_VARS_Q_R1); @@ -627,7 +631,7 @@ static gint _nc_hipert_two_fluids_f_QP_mode2 (realtype alpha, N_Vector y, N_Vector ydot, gpointer f_data) { NcHIPertTwoFluidsArg *arg = (NcHIPertTwoFluidsArg *) f_data; - const gdouble k = NC_HIPERT (arg->ptf)->k; + const gdouble k = nc_hipert_get_mode_k (NC_HIPERT (arg->ptf)); NcHIPertITwoFluidsEOM *eom = nc_hipert_itwo_fluids_eom_eval (NC_HIPERT_ITWO_FLUIDS (arg->cosmo), alpha, k); const gdouble Q_R2 = NV_Ith_S (y, NC_HIPERT_ITWO_FLUIDS_VARS_Q_R2); @@ -747,7 +751,7 @@ static gint _nc_hipert_two_fluids_f_zetaS_zeta (realtype alpha, N_Vector y, N_Vector ydot, gpointer f_data) { NcHIPertTwoFluidsArg *arg = (NcHIPertTwoFluidsArg *) f_data; - const gdouble k = NC_HIPERT (arg->ptf)->k; + const gdouble k = nc_hipert_get_mode_k (NC_HIPERT (arg->ptf)); NcHIPertITwoFluidsEOM *eom = nc_hipert_itwo_fluids_eom_eval (NC_HIPERT_ITWO_FLUIDS (arg->cosmo), alpha, k); const gdouble zeta_R = NV_Ith_S (y, NC_HIPERT_ITWO_FLUIDS_VARS_ZETA_R); @@ -773,7 +777,7 @@ static gint _nc_hipert_two_fluids_f_zetaS_S (realtype alpha, N_Vector y, N_Vector ydot, gpointer f_data) { NcHIPertTwoFluidsArg *arg = (NcHIPertTwoFluidsArg *) f_data; - const gdouble k = NC_HIPERT (arg->ptf)->k; + const gdouble k = nc_hipert_get_mode_k (NC_HIPERT (arg->ptf)); NcHIPertITwoFluidsEOM *eom = nc_hipert_itwo_fluids_eom_eval (NC_HIPERT_ITWO_FLUIDS (arg->cosmo), alpha, k); const gdouble S_R = NV_Ith_S (y, NC_HIPERT_ITWO_FLUIDS_VARS_S_R); @@ -882,7 +886,7 @@ static gint _nc_hipert_two_fluids_J_QP_mode1 (realtype alpha, N_Vector y, N_Vector fy, SUNMatrix J, gpointer jac_data, N_Vector tmp1, N_Vector tmp2, N_Vector tmp3) { NcHIPertTwoFluidsArg *arg = (NcHIPertTwoFluidsArg *) jac_data; - const gdouble k = NC_HIPERT (arg->ptf)->k; + const gdouble k = nc_hipert_get_mode_k (NC_HIPERT (arg->ptf)); NcHIPertITwoFluidsEOM *eom = nc_hipert_itwo_fluids_eom_eval (NC_HIPERT_ITWO_FLUIDS (arg->cosmo), alpha, k); const gdouble gammabar11 = eom->gammabar11; @@ -960,7 +964,7 @@ static gint _nc_hipert_two_fluids_J_QP_mode2 (realtype alpha, N_Vector y, N_Vector fy, SUNMatrix J, gpointer jac_data, N_Vector tmp1, N_Vector tmp2, N_Vector tmp3) { NcHIPertTwoFluidsArg *arg = (NcHIPertTwoFluidsArg *) jac_data; - const gdouble k = NC_HIPERT (arg->ptf)->k; + const gdouble k = nc_hipert_get_mode_k (NC_HIPERT (arg->ptf)); NcHIPertITwoFluidsEOM *eom = nc_hipert_itwo_fluids_eom_eval (NC_HIPERT_ITWO_FLUIDS (arg->cosmo), alpha, k); const gdouble gammabar22 = eom->gammabar22; @@ -1100,7 +1104,7 @@ static gint _nc_hipert_two_fluids_J_zetaS_zeta (realtype alpha, N_Vector y, N_Vector fy, SUNMatrix J, gpointer jac_data, N_Vector tmp1, N_Vector tmp2, N_Vector tmp3) { NcHIPertTwoFluidsArg *arg = (NcHIPertTwoFluidsArg *) jac_data; - const gdouble k = NC_HIPERT (arg->ptf)->k; + const gdouble k = nc_hipert_get_mode_k (NC_HIPERT (arg->ptf)); NcHIPertITwoFluidsEOM *eom = nc_hipert_itwo_fluids_eom_eval (NC_HIPERT_ITWO_FLUIDS (arg->cosmo), alpha, k); /************************************************************************************************************/ @@ -1158,7 +1162,7 @@ static gint _nc_hipert_two_fluids_J_zetaS_S (realtype alpha, N_Vector y, N_Vector fy, SUNMatrix J, gpointer jac_data, N_Vector tmp1, N_Vector tmp2, N_Vector tmp3) { NcHIPertTwoFluidsArg *arg = (NcHIPertTwoFluidsArg *) jac_data; - const gdouble k = NC_HIPERT (arg->ptf)->k; + const gdouble k = nc_hipert_get_mode_k (NC_HIPERT (arg->ptf)); NcHIPertITwoFluidsEOM *eom = nc_hipert_itwo_fluids_eom_eval (NC_HIPERT_ITWO_FLUIDS (arg->cosmo), alpha, k); /************************************************************************************************************/ @@ -1238,7 +1242,7 @@ nc_hipert_two_fluids_set_init_cond (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gd #ifdef HAVE_SUNDIALS_ARKODE ARKRhsFn fE, fI; - ARKodeJacFn dfI_dy; + ARKLsJacFn dfI_dy; #endif /* HAVE_SUNDIALS_ARKODE */ if (vtype != c_vtype) @@ -1319,8 +1323,8 @@ nc_hipert_two_fluids_set_init_cond (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gd if (!pert->priv->cvode_init) { #ifdef HAVE_SUNDIALS_ARKODE - flag = ARKodeInit (self->arkode, fE, fI, alpha, pert->priv->y); - NCM_CVODE_CHECK (&flag, "ARKodeInit", 1, ); + self->arkode = ARKStepCreate (fE, fI, alpha, pert->priv->y); + NCM_CVODE_CHECK (self->arkode, "ARKodeInit", 0, ); #endif /* HAVE_SUNDIALS_ARKODE */ if (useQP) @@ -1344,7 +1348,7 @@ nc_hipert_two_fluids_set_init_cond (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gd NCM_CVODE_CHECK (&flag, "CVodeReInit", 1, ); #ifdef HAVE_SUNDIALS_ARKODE - flag = ARKodeReInit (self->arkode, fE, fI, alpha, pert->priv->y); + flag = ARKStepReInit (self->arkode, fE, fI, alpha, pert->priv->y); NCM_CVODE_CHECK (&flag, "CVodeReInit", 1, ); #endif /* HAVE_SUNDIALS_ARKODE */ } @@ -1364,19 +1368,19 @@ nc_hipert_two_fluids_set_init_cond (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gd NCM_CVODE_CHECK (&flag, "CVodeSetLinearSolver", 1, ); #ifdef HAVE_SUNDIALS_ARKODE - flag = ARKodeSStolerances (self->arkode, pert->priv->reltol, 0.0); + flag = ARKStepSStolerances (self->arkode, pert->priv->reltol, 0.0); NCM_CVODE_CHECK (&flag, "ARKodeSStolerances", 1, ); - flag = ARKodeSetMaxNumSteps (self->arkode, G_MAXUINT32); + flag = ARKStepSetMaxNumSteps (self->arkode, G_MAXUINT32); NCM_CVODE_CHECK (&flag, "ARKodeSetMaxNumSteps", 1, ); - flag = ARKodeSetLinearSolver (self->arkode, pert->priv->LS, pert->priv->A); + flag = ARKStepSetLinearSolver (self->arkode, pert->priv->LS, pert->priv->A); NCM_CVODE_CHECK (&flag, "ARKodeSetLinearSolver", 1, ); - flag = ARKodeSetJacFn (self->arkode, dfI_dy); + flag = ARKStepSetJacFn (self->arkode, dfI_dy); NCM_CVODE_CHECK (&flag, "ARKodeSetJacFn", 1, ); - flag = ARKodeSetLinear (self->arkode, 1); + flag = ARKStepSetLinear (self->arkode, 1); NCM_CVODE_CHECK (&flag, "ARKodeSetLinear", 1, ); if (useQP) @@ -1394,32 +1398,35 @@ nc_hipert_two_fluids_set_init_cond (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gd { case 1: case 2: - flag = ARKodeSetImEx (self->arkode); - NCM_CVODE_CHECK (&flag, "ARKodeSetImEx", 1, ); + /* flag = ARKStepSetImEx (self->arkode); */ + /* NCM_CVODE_CHECK (&flag, "ARKodeSetImEx", 1, ); */ - flag = ARKodeSetOrder (self->arkode, 5); - NCM_CVODE_CHECK (&flag, "ARKodeSetOrder", 1, ); + /* flag = ARKStepSetOrder (self->arkode, 5); */ + /* NCM_CVODE_CHECK (&flag, "ARKodeSetOrder", 1, ); */ /*flag = ARKodeSetARKTableNum (self->arkode, 22, 9); */ /*NCM_CVODE_CHECK (&flag, "ARKodeSetIRKTableNum", 1, ); */ break; - case 3: - flag = ARKodeSetExplicit (self->arkode); - NCM_CVODE_CHECK (&flag, "ARKodeSetExplicit", 1, ); - flag = ARKodeSetOrder (self->arkode, 6); - NCM_CVODE_CHECK (&flag, "ARKodeSetOrder", 1, ); - - flag = ARKodeSetERKTableNum (self->arkode, 10); - NCM_CVODE_CHECK (&flag, "ARKodeSetERKTableNum", 1, ); - break; - case 4: - flag = ARKodeSetImplicit (self->arkode); - NCM_CVODE_CHECK (&flag, "ARKodeSetImplicit", 1, ); - - flag = ARKodeSetIRKTableNum (self->arkode, 11 + 11); - NCM_CVODE_CHECK (&flag, "ARKodeSetIRKTableNum", 1, ); - break; +/* + * case 3: + * flag = ARKStepSetExplicit (self->arkode); + * NCM_CVODE_CHECK (&flag, "ARKodeSetExplicit", 1, ); + * + * flag = ARKStepSetOrder (self->arkode, 6); + * NCM_CVODE_CHECK (&flag, "ARKodeSetOrder", 1, ); + * + * flag = ARKStepSetERKTableNum (self->arkode, 10); + * NCM_CVODE_CHECK (&flag, "ARKodeSetERKTableNum", 1, ); + * break; + * case 4: + * flag = ARKStepSetImplicit (self->arkode); + * NCM_CVODE_CHECK (&flag, "ARKodeSetImplicit", 1, ); + * + * flag = ARKStepSetIRKTableNum (self->arkode, 11 + 11); + * NCM_CVODE_CHECK (&flag, "ARKodeSetIRKTableNum", 1, ); + * break; + */ default: g_error ("nc_hipert_two_fluids_set_init_cond: Unknown main mode %u.", main_mode); break; @@ -1462,12 +1469,12 @@ nc_hipert_two_fluids_evolve (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gdouble a if (TRUE) { - flag = ARKodeSetUserData (self->arkode, arg); + flag = ARKStepSetUserData (self->arkode, arg); NCM_CVODE_CHECK (&flag, "ARKodeSetUserData", 1, ); /*ARKodeSetDiagnostics (self->arkode, stderr); */ - flag = ARKode (self->arkode, alphaf, pert->priv->y, &alpha_i, CV_NORMAL); + flag = ARKStepEvolve (self->arkode, alphaf, pert->priv->y, &alpha_i, ARK_NORMAL); NCM_CVODE_CHECK (&flag, "CVode[nc_hipert_two_fluids_evolve]", 1, ); pert->priv->alpha0 = alpha_i; @@ -1478,6 +1485,9 @@ nc_hipert_two_fluids_evolve (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gdouble a flag = CVodeSetUserData (pert->priv->cvode, arg); NCM_CVODE_CHECK (&flag, "CVodeSetUserData", 1, ); + flag = CVodeSetStopTime (pert->priv->cvode, alphaf); + NCM_CVODE_CHECK (&flag, "CVodeSetStopTime", 1, ); + flag = CVode (pert->priv->cvode, alphaf, pert->priv->y, &alpha_i, CV_NORMAL); NCM_CVODE_CHECK (&flag, "CVode[nc_hipert_two_fluids_evolve]", 1, ); @@ -1508,6 +1518,87 @@ nc_hipert_two_fluids_evolve (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gdouble a } } +/** + * nc_hipert_two_fluids_evolve_array: + * @ptf: a #NcHIPertTwoFluids. + * @cosmo: a #NcHICosmo. + * @alphaf: the final log-redshift time. + * + * Evolve the system until @alphaf and store the results in an array. + * + * Returns: (transfer full): a #NcmMatrix + */ +NcmMatrix * +nc_hipert_two_fluids_evolve_array (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gdouble alphaf) +{ + NcHIPertTwoFluidsPrivate * const self = ptf->priv; + NcHIPert *pert = NC_HIPERT (ptf); + NcHIPertTwoFluidsArg *arg = self->arg; + gdouble *yi = NV_DATA_S (pert->priv->y); + gdouble alpha_i = 0.0; + GArray *array = g_array_new (FALSE, FALSE, sizeof (gdouble)); + gint flag; + + arg->cosmo = cosmo; + arg->ptf = ptf; + + if (NV_LENGTH_S (pert->priv->y) != NC_HIPERT_ITWO_FLUIDS_VARS_LEN) + g_error ("nc_hipert_two_fluids_evolve: cannot evolve subsidiary approximated system, use the appropriated evolve function."); + +#ifdef HAVE_SUNDIALS_ARKODE + + if (TRUE) + { + flag = ARKStepSetUserData (self->arkode, arg); + NCM_CVODE_CHECK (&flag, "ARKodeSetUserData", 1, NULL); + + g_array_append_val (array, pert->priv->alpha0); + g_array_append_vals (array, NV_DATA_S (pert->priv->y), NC_HIPERT_ITWO_FLUIDS_VARS_LEN); + + while (alphaf > pert->priv->alpha0) + { + flag = ARKStepEvolve (self->arkode, alphaf, pert->priv->y, &alpha_i, ARK_ONE_STEP); + NCM_CVODE_CHECK (&flag, "CVode[nc_hipert_two_fluids_evolve]", 1, NULL); + + pert->priv->alpha0 = alpha_i; + + g_array_append_val (array, alpha_i); + g_array_append_vals (array, NV_DATA_S (pert->priv->y), NC_HIPERT_ITWO_FLUIDS_VARS_LEN); + } + } + else +#endif /* HAVE_SUNDIALS_ARKODE */ + { + flag = CVodeSetUserData (pert->priv->cvode, arg); + NCM_CVODE_CHECK (&flag, "CVodeSetUserData", 1, NULL); + + g_array_append_val (array, pert->priv->alpha0); + g_array_append_vals (array, NV_DATA_S (pert->priv->y), NC_HIPERT_ITWO_FLUIDS_VARS_LEN); + + CVodeSetStopTime (pert->priv->cvode, alphaf); + + while (alphaf > pert->priv->alpha0) + { + flag = CVode (pert->priv->cvode, alphaf, pert->priv->y, &alpha_i, CV_ONE_STEP); + NCM_CVODE_CHECK (&flag, "CVode[nc_hipert_two_fluids_evolve_array]", 1, NULL); + + pert->priv->alpha0 = alpha_i; + + g_array_append_val (array, alpha_i); + g_array_append_vals (array, NV_DATA_S (pert->priv->y), NC_HIPERT_ITWO_FLUIDS_VARS_LEN); + } + } + + { + const guint ncols = NC_HIPERT_ITWO_FLUIDS_VARS_LEN + 1; + NcmMatrix *res = ncm_matrix_new_array (array, ncols); + + g_array_unref (array); + + return res; + } +} + /** * nc_hipert_two_fluids_peek_state: * @ptf: a #NcHIPertTwoFluids @@ -1874,3 +1965,89 @@ nc_hipert_two_fluids_get_cross_time (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, N return alpha; } +static gdouble +_nc_hipert_two_fluids_zeta_spectrum (const gdouble lnk, gpointer userdata) +{ + NcHIPertTwoFluidsArg *arg = (NcHIPertTwoFluidsArg *) userdata; + NcHIPert *pert = NC_HIPERT (arg->ptf); + NcHIPertTwoFluidsPrivate * const self = arg->ptf->priv; + NcmVector *init_cond = ncm_vector_new (NC_HIPERT_ITWO_FLUIDS_VARS_LEN); + const gdouble k = exp (lnk); + gdouble alpha_i0, alpha_i; + + nc_hipert_set_mode_k (pert, k); + + alpha_i = nc_hipert_two_fluids_get_cross_time (arg->ptf, arg->cosmo, arg->mode - 1, arg->alpha_i, arg->prec); + nc_hipert_two_fluids_get_init_cond_zetaS (arg->ptf, arg->cosmo, alpha_i, arg->mode, M_PI * 0.25, init_cond); + nc_hipert_two_fluids_set_init_cond (arg->ptf, arg->cosmo, alpha_i, arg->mode, FALSE, init_cond); + + nc_hipert_two_fluids_evolve (arg->ptf, arg->cosmo, arg->alpha); + + ncm_vector_clear (&init_cond); + + { + NcmVector *res = nc_hipert_two_fluids_peek_state (arg->ptf, arg->cosmo, &alpha_i0); + const gdouble zeta_r = ncm_vector_get (res, NC_HIPERT_ITWO_FLUIDS_VARS_ZETA_R); + const gdouble zeta_i = ncm_vector_get (res, NC_HIPERT_ITWO_FLUIDS_VARS_ZETA_I); + + return log (gsl_pow_3 (k) * (gsl_pow_2 (zeta_r) + gsl_pow_2 (zeta_i))); + } +} + +/** + * nc_hipert_two_fluids_compute_zeta_spectrum: + * @ptf: a #NcHIPertTwoFluids + * @cosmo: a #NcHICosmo + * @mode: the mode + * @alpha_i: the initial log-redshift time + * @alpha: the log-redshift time + * @ki: the initial k + * @kf: the final k + * @nnodes: number of knots + * + * Compute the spectra for the two fluids system. + * + * Returns: (transfer full): a #NcmSpline + */ +NcmSpline * +nc_hipert_two_fluids_compute_zeta_spectrum (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, guint mode, gdouble alpha_i, gdouble alpha, gdouble ki, gdouble kf, guint nnodes) +{ + NcHIPert *pert = NC_HIPERT (ptf); + NcHIPertTwoFluidsPrivate * const self = ptf->priv; + NcHIPertTwoFluidsArg *arg = self->arg; + NcmSpline *spline = NCM_SPLINE (ncm_spline_cubic_notaknot_new ()); + const gdouble lnki = log (ki); + const gdouble lnkf = log (kf); + NcmVector *xv = ncm_vector_new (nnodes); + NcmVector *yv = ncm_vector_new (nnodes); + gsl_function F; + guint i; + + F.params = arg; + + arg->cosmo = cosmo; + arg->ptf = ptf; + arg->prec = 1.0e-5; + arg->alpha_i = alpha_i; + arg->alpha = alpha; + arg->mode = mode; + + F.function = &_nc_hipert_two_fluids_zeta_spectrum; + + for (i = 0; i < nnodes; i++) + { + const gdouble lnk = lnki + (lnkf - lnki) * i / (nnodes - 1); + const gdouble y = F.function (lnk, arg); + + ncm_vector_set (xv, i, lnk); + ncm_vector_set (yv, i, y); + } + + ncm_spline_set (spline, xv, yv, TRUE); + + ncm_vector_free (xv); + ncm_vector_free (yv); + + return spline; +} + diff --git a/numcosmo/perturbations/nc_hipert_two_fluids.h b/numcosmo/perturbations/nc_hipert_two_fluids.h index fa244125a..671d6ea50 100644 --- a/numcosmo/perturbations/nc_hipert_two_fluids.h +++ b/numcosmo/perturbations/nc_hipert_two_fluids.h @@ -13,12 +13,12 @@ * under the terms of the GNU General Public License as published by the * Free Software Foundation, either version 3 of the License, or * (at your option) any later version. - * + * * numcosmo is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * See the GNU General Public License for more details. - * + * * You should have received a copy of the GNU General Public License along * with this program. If not, see . */ @@ -70,14 +70,14 @@ struct _NcHIPertTwoFluids * @NC_HIPERT_TWO_FLUIDS_CROSS_MODE2MAIN: FIXME * @NC_HIPERT_TWO_FLUIDS_CROSS_MODE1SUB: FIXME * @NC_HIPERT_TWO_FLUIDS_CROSS_MODE2SUB: FIXME - * + * * FIXME - * + * */ typedef enum /*< enum,underscore_name=NC_HIPERT_TWO_FLUIDS_CROSS >*/ { NC_HIPERT_TWO_FLUIDS_CROSS_MODE1MAIN = 0, - NC_HIPERT_TWO_FLUIDS_CROSS_MODE2MAIN , + NC_HIPERT_TWO_FLUIDS_CROSS_MODE2MAIN, NC_HIPERT_TWO_FLUIDS_CROSS_MODE1SUB, NC_HIPERT_TWO_FLUIDS_CROSS_MODE2SUB, } NcHIPertTwoFluidsCross; @@ -100,6 +100,7 @@ void nc_hipert_two_fluids_to_zeta_s (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, g void nc_hipert_two_fluids_evolve (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gdouble alphaf); NcmVector *nc_hipert_two_fluids_peek_state (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gdouble *alpha); +NcmMatrix *nc_hipert_two_fluids_evolve_array (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gdouble alphaf); void nc_hipert_two_fluids_set_init_cond_mode1sub (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gdouble alpha, NcmVector *init_cond); void nc_hipert_two_fluids_evolve_mode1sub (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, gdouble alphaf); @@ -108,10 +109,13 @@ gdouble nc_hipert_two_fluids_get_state_mod (NcHIPertTwoFluids *ptf); gdouble nc_hipert_two_fluids_get_cross_time (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, NcHIPertTwoFluidsCross cross, gdouble alpha_i, gdouble prec); -#define NC_HIPERT_TWO_FLUIDS_A2Q(Ai) (cimag (Ai)) -#define NC_HIPERT_TWO_FLUIDS_A2P(Ai) (creal (Ai)) -#define NC_HIPERT_TWO_FLUIDS_QP2A(Q,P) ((P) + I * (Q)) +NcmSpline *nc_hipert_two_fluids_compute_zeta_spectrum (NcHIPertTwoFluids *ptf, NcHICosmo *cosmo, guint mode, gdouble alpha_i, gdouble alpha, gdouble ki, gdouble kf, guint nnodes); + +#define NC_HIPERT_TWO_FLUIDS_A2Q(Ai) (cimag (Ai)) +#define NC_HIPERT_TWO_FLUIDS_A2P(Ai) (creal (Ai)) +#define NC_HIPERT_TWO_FLUIDS_QP2A(Q, P) ((P) + I * (Q)) G_END_DECLS #endif /* _NC_HIPERT_TWO_FLUIDS_H_ */ + From 4a7b33b44a3d40d73735cbb927d8f25511c1f20c Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Tue, 23 Apr 2024 11:11:34 -0300 Subject: [PATCH 04/27] New two fluids primordial object. --- docs/numcosmo-docs.sgml | 1 + numcosmo/meson.build | 2 + numcosmo/model/nc_hiprim_two_fluids.c | 214 ++++++++++++++++++++++++++ numcosmo/model/nc_hiprim_two_fluids.h | 97 ++++++++++++ numcosmo/numcosmo.h | 1 + 5 files changed, 315 insertions(+) create mode 100644 numcosmo/model/nc_hiprim_two_fluids.c create mode 100644 numcosmo/model/nc_hiprim_two_fluids.h diff --git a/docs/numcosmo-docs.sgml b/docs/numcosmo-docs.sgml index 0724d7b3c..af942236e 100644 --- a/docs/numcosmo-docs.sgml +++ b/docs/numcosmo-docs.sgml @@ -239,6 +239,7 @@ + diff --git a/numcosmo/meson.build b/numcosmo/meson.build index 4514bf398..356fa36d4 100644 --- a/numcosmo/meson.build +++ b/numcosmo/meson.build @@ -405,6 +405,7 @@ nc_headers = files( 'model/nc_hiprim_expc.h', 'model/nc_hiprim_power_law.h', 'model/nc_hiprim_sbpl.h', + 'model/nc_hiprim_two_fluids.h', 'perturbations/nc_hipert.h', 'perturbations/nc_hipert_adiab.h', 'perturbations/nc_hipert_bg_var.h', @@ -563,6 +564,7 @@ nc_sources = files( 'model/nc_hiprim_expc.c', 'model/nc_hiprim_power_law.c', 'model/nc_hiprim_sbpl.c', + 'model/nc_hiprim_two_fluids.c', 'perturbations/nc_hipert.c', 'perturbations/nc_hipert_adiab.c', 'perturbations/nc_hipert_bg_var.c', diff --git a/numcosmo/model/nc_hiprim_two_fluids.c b/numcosmo/model/nc_hiprim_two_fluids.c new file mode 100644 index 000000000..3e45a2c12 --- /dev/null +++ b/numcosmo/model/nc_hiprim_two_fluids.c @@ -0,0 +1,214 @@ +/*************************************************************************** + * nc_hiprim_two_fluids.c + * + * Tue October 27 14:13:46 2015 + * Copyright 2015 Sandro Dias Pinto Vitenti + * + ****************************************************************************/ +/* + * nc_hiprim_two_fluids.c + * Copyright (C) 2015 Sandro Dias Pinto Vitenti + * + * numcosmo is free software: you can redistribute it and/or modify it + * under the terms of the GNU General Public License as published by the + * Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * numcosmo is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. + * See the GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License along + * with this program. If not, see . + */ + +/** + * SECTION:nc_hiprim_two_fluids + * @title: NcHIPrimTwoFluids + * @short_description: Two Fluids implementation for primordial spectra. + * + * Primordial adiabatic scalar power spectrum obtained from a two fluids model. + * + */ + +#ifdef HAVE_CONFIG_H +# include "config.h" +#endif /* HAVE_CONFIG_H */ +#include "build_cfg.h" + +#include "nc_hiprim_two_fluids.h" + +typedef struct _NcHIPrimTwoFluidsPrivate +{ + NcmSpline2d *lnSA_powspec_lnk_lnw; +} NcHIPrimTwoFluidsPrivate; + + +G_DEFINE_TYPE_WITH_PRIVATE (NcHIPrimTwoFluids, nc_hiprim_two_fluids, NC_TYPE_HIPRIM) + +enum +{ + PROP_0, + PROP_LNK_LNW_SPLINE, + PROP_SIZE, +}; + +static void +nc_hiprim_two_fluids_init (NcHIPrimTwoFluids *two_fluids) +{ + NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); + + self->lnSA_powspec_lnk_lnw = NULL; +} + +static void +_nc_hiprim_two_fluids_dispose (GObject *object) +{ + NcHIPrimTwoFluids *two_fluids = NC_HIPRIM_TWO_FLUIDS (object); + NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); + + /* Chain up : end */ + G_OBJECT_CLASS (nc_hiprim_two_fluids_parent_class)->dispose (object); +} + +static void +_nc_hiprim_two_fluids_finalize (GObject *object) +{ + /* Chain up : end */ + G_OBJECT_CLASS (nc_hiprim_two_fluids_parent_class)->finalize (object); +} + +static gdouble _nc_hiprim_two_fluids_lnSA_powespec_lnk (NcHIPrim *prim, const gdouble lnk); +static gdouble _nc_hiprim_two_fluids_lnT_powespec_lnk (NcHIPrim *prim, const gdouble lnk); + +static void +nc_hiprim_two_fluids_class_init (NcHIPrimTwoFluidsClass *klass) +{ + GObjectClass *object_class = G_OBJECT_CLASS (klass); + NcHIPrimClass *prim_class = NC_HIPRIM_CLASS (klass); + NcmModelClass *model_class = NCM_MODEL_CLASS (klass); + + object_class->finalize = &_nc_hiprim_two_fluids_finalize; + + ncm_model_class_set_name_nick (model_class, "Power Law model for primordial spectra", "TwoFluids"); + ncm_model_class_add_params (model_class, NC_HIPRIM_TWO_FLUIDS_SPARAM_LEN, 0, PROP_SIZE); + + /* Set ln10e10ASA param info */ + ncm_model_class_set_sparam (model_class, NC_HIPRIM_TWO_FLUIDS_LN10E10ASA, "\\log(10^{10}A_{\\mathrm{SA}})", "ln10e10ASA", + 2.0, 5.0, 1.0e0, + NC_HIPRIM_DEFAULT_PARAMS_ABSTOL, NC_HIPRIM_TWO_FLUIDS_DEFAULT_LN10E10ASA, + NCM_PARAM_TYPE_FIXED); + + /* Set T_SA_ratio param info */ + ncm_model_class_set_sparam (model_class, NC_HIPRIM_TWO_FLUIDS_T_SA_RATIO, "A_T/A_{\\mathrm{SA}}", "T_SA_ratio", + 0.0, 10.0, 1.0e-1, + NC_HIPRIM_DEFAULT_PARAMS_ABSTOL, NC_HIPRIM_TWO_FLUIDS_DEFAULT_T_SA_RATIO, + NCM_PARAM_TYPE_FIXED); + + /* Set ln(k_0) param info */ + ncm_model_class_set_sparam (model_class, NC_HIPRIM_TWO_FLUIDS_LNK0, "\\ln(k_0)", "lnk0", + -3.0 * M_LN10, 3.0 * M_LN10, 1.0e-1, + NC_HIPRIM_DEFAULT_PARAMS_ABSTOL, NC_HIPRIM_TWO_FLUIDS_DEFAULT_LNK0, + NCM_PARAM_TYPE_FIXED); + + /* Set ln(w) param info */ + ncm_model_class_set_sparam (model_class, NC_HIPRIM_TWO_FLUIDS_LNW, "\\ln(w)", "lnw", + -5.0 * M_LN10, 0.0 * M_LN10, 1.0e-1, + NC_HIPRIM_DEFAULT_PARAMS_ABSTOL, NC_HIPRIM_TWO_FLUIDS_DEFAULT_LNW, + NCM_PARAM_TYPE_FIXED); + + /* Set N_T param info */ + ncm_model_class_set_sparam (model_class, NC_HIPRIM_TWO_FLUIDS_N_T, "n_{\\mathrm{T}}", "n_T", + -0.5, 0.5, 1.0e-2, + NC_HIPRIM_DEFAULT_PARAMS_ABSTOL, NC_HIPRIM_TWO_FLUIDS_DEFAULT_N_T, + NCM_PARAM_TYPE_FIXED); + + /* Check for errors in parameters initialization */ + ncm_model_class_check_params_info (model_class); + + nc_hiprim_set_lnSA_powspec_lnk_impl (prim_class, &_nc_hiprim_two_fluids_lnSA_powespec_lnk); + nc_hiprim_set_lnT_powspec_lnk_impl (prim_class, &_nc_hiprim_two_fluids_lnT_powespec_lnk); +} + +#define VECTOR (NCM_MODEL (prim)) +#define LN10E10ASA (ncm_model_orig_param_get (VECTOR, NC_HIPRIM_TWO_FLUIDS_LN10E10ASA)) +#define T_SA_RATIO (ncm_model_orig_param_get (VECTOR, NC_HIPRIM_TWO_FLUIDS_T_SA_RATIO)) +#define LNK0 (ncm_model_orig_param_get (VECTOR, NC_HIPRIM_TWO_FLUIDS_LNK0)) +#define LNW (ncm_model_orig_param_get (VECTOR, NC_HIPRIM_TWO_FLUIDS_LNW)) +#define N_T (ncm_model_orig_param_get (VECTOR, NC_HIPRIM_TWO_FLUIDS_N_T)) + +/**************************************************************************** + * Power spectra + ****************************************************************************/ + +static gdouble +_nc_hiprim_two_fluids_lnSA_powespec_lnk (NcHIPrim *prim, const gdouble lnk) +{ + NcHIPrimTwoFluids *two_fluids = NC_HIPRIM_TWO_FLUIDS (prim); + NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); + const gdouble ln_ka = lnk - LNK0; + const gdouble lnw = LNW; + + return LN10E10ASA - 10.0 * M_LN10 + ncm_spline2d_eval (self->lnSA_powspec_lnk_lnw, ln_ka, lnw); +} + +static gdouble +_nc_hiprim_two_fluids_lnT_powespec_lnk (NcHIPrim *prim, const gdouble lnk) +{ + const gdouble ln_ka = lnk - prim->lnk_pivot; + + return N_T * ln_ka + LN10E10ASA - 10.0 * M_LN10 + log (T_SA_RATIO); +} + +/** + * nc_hiprim_two_fluids_new: (constructor) + * + * This function instantiates a new object of type #NcHIPrimTwoFluids. + * + * Returns: (transfer full): A new #NcHIPrimTwoFluids + */ +NcHIPrimTwoFluids * +nc_hiprim_two_fluids_new (void) +{ + NcHIPrimTwoFluids *prim_pl = g_object_new (NC_TYPE_HIPRIM_TWO_FLUIDS, + NULL); + + return prim_pl; +} + +/** + * nc_hiprim_two_fluids_set_lnk_lnw_spline: + * @two_fluids: a #NcHIPrimTwoFluids + * @lnSA_powspec_lnk_lnw: a #NcmSpline2d + * + * Set the spline for the primordial adiabatic scalar power spectrum as a function of ln(k) and ln(w). + * + */ +void +nc_hiprim_two_fluids_set_lnk_lnw_spline (NcHIPrimTwoFluids *two_fluids, NcmSpline2d *lnSA_powspec_lnk_lnw) +{ + NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); + + ncm_spline2d_clear (&self->lnSA_powspec_lnk_lnw); + + self->lnSA_powspec_lnk_lnw = lnSA_powspec_lnk_lnw; +} + +/** + * nc_hiprim_two_fluids_peek_lnk_lnw_spline: + * @two_fluids: a #NcHIPrimTwoFluids + * + * Get the spline for the primordial adiabatic scalar power spectrum as a function of + * $\ln(k)$ and $\ln(w)$. + * + * Returns: (transfer none): the spline for the primordial power spectrum. + */ +NcmSpline2d * +nc_hiprim_two_fluids_peek_lnk_lnw_spline (NcHIPrimTwoFluids *two_fluids) +{ + NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); + + return self->lnSA_powspec_lnk_lnw; +} + diff --git a/numcosmo/model/nc_hiprim_two_fluids.h b/numcosmo/model/nc_hiprim_two_fluids.h new file mode 100644 index 000000000..74c344a5e --- /dev/null +++ b/numcosmo/model/nc_hiprim_two_fluids.h @@ -0,0 +1,97 @@ +/*************************************************************************** + * nc_hiprim_two_fluids.h + * + * Tue October 27 14:14:03 2015 + * Copyright 2015 Sandro Dias Pinto Vitenti + * + ****************************************************************************/ +/* + * nc_hiprim_two_fluids.h + * Copyright (C) 2015 Sandro Dias Pinto Vitenti + * + * numcosmo is free software: you can redistribute it and/or modify it + * under the terms of the GNU General Public License as published by the + * Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * numcosmo is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. + * See the GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License along + * with this program. If not, see . + */ + +#ifndef _NC_HIPRIM_TWO_FLUIDS_H_ +#define _NC_HIPRIM_TWO_FLUIDS_H_ + +#include +#include +#include +#include +#include + +G_BEGIN_DECLS + +#define NC_TYPE_HIPRIM_TWO_FLUIDS (nc_hiprim_two_fluids_get_type ()) +#define NC_HIPRIM_TWO_FLUIDS(obj) (G_TYPE_CHECK_INSTANCE_CAST ((obj), NC_TYPE_HIPRIM_TWO_FLUIDS, NcHIPrimTwoFluids)) +#define NC_HIPRIM_TWO_FLUIDS_CLASS(klass) (G_TYPE_CHECK_CLASS_CAST ((klass), NC_TYPE_HIPRIM_TWO_FLUIDS, NcHIPrimTwoFluidsClass)) +#define NC_IS_HIPRIM_TWO_FLUIDS(obj) (G_TYPE_CHECK_INSTANCE_TYPE ((obj), NC_TYPE_HIPRIM_TWO_FLUIDS)) +#define NC_IS_HIPRIM_TWO_FLUIDS_CLASS(klass) (G_TYPE_CHECK_CLASS_TYPE ((klass), NC_TYPE_HIPRIM_TWO_FLUIDS)) +#define NC_HIPRIM_TWO_FLUIDS_GET_CLASS(obj) (G_TYPE_INSTANCE_GET_CLASS ((obj), NC_TYPE_HIPRIM_TWO_FLUIDS, NcHIPrimTwoFluidsClass)) + +typedef struct _NcHIPrimTwoFluidsClass NcHIPrimTwoFluidsClass; +typedef struct _NcHIPrimTwoFluids NcHIPrimTwoFluids; + +/** + * NcHIPrimTwoFluidsSParams: + * @NC_HIPRIM_TWO_FLUIDS_LN10E10ASA: Amplitude of the adiabatic scalar mode $\ln(10^{10}\mathcal{A}_\mathrm{s})$ + * @NC_HIPRIM_TWO_FLUIDS_T_SA_RATIO: Tensor-to-scalar ratio $r$ + * @NC_HIPRIM_TWO_FLUIDS_LNK0: Logarithm of the mode $k_0$ in $\mathrm{Mpc}^{-1}$. + * @NC_HIPRIM_TWO_FLUIDS_LNW: Logarithm of the equation of state parameter $w$. + * @NC_HIPRIM_TWO_FLUIDS_N_T: Spectral index of the tensor power spectrum. + * + * Parameters for the two fluids primordial power spectrum. + * + */ +typedef enum /*< enum,underscore_name=NC_HIPRIM_TWO_FLUIDS_SPARAMS >*/ +{ + NC_HIPRIM_TWO_FLUIDS_LN10E10ASA, + NC_HIPRIM_TWO_FLUIDS_T_SA_RATIO, + NC_HIPRIM_TWO_FLUIDS_LNK0, + NC_HIPRIM_TWO_FLUIDS_LNW, + NC_HIPRIM_TWO_FLUIDS_N_T, + /* < private > */ + NC_HIPRIM_TWO_FLUIDS_SPARAM_LEN, /*< skip >*/ +} NcHIPrimTwoFluidsSParams; + +struct _NcHIPrimTwoFluidsClass +{ + /*< private >*/ + NcHIPrimClass parent_class; +}; + +struct _NcHIPrimTwoFluids +{ + /*< private >*/ + NcHIPrim parent_instance; + +}; + +GType nc_hiprim_two_fluids_get_type (void) G_GNUC_CONST; + +#define NC_HIPRIM_TWO_FLUIDS_DEFAULT_LN10E10ASA (3.179) +#define NC_HIPRIM_TWO_FLUIDS_DEFAULT_T_SA_RATIO (0.2) +#define NC_HIPRIM_TWO_FLUIDS_DEFAULT_LNK0 (0.0) +#define NC_HIPRIM_TWO_FLUIDS_DEFAULT_LNW (-4.0 * M_LN10) +#define NC_HIPRIM_TWO_FLUIDS_DEFAULT_N_T (0.0) + +NcHIPrimTwoFluids *nc_hiprim_two_fluids_new (void); + +void nc_hiprim_two_fluids_set_lnk_lnw_spline (NcHIPrimTwoFluids *two_fluids, NcmSpline2d *lnSA_powspec_lnk_lnw); +NcmSpline2d *nc_hiprim_two_fluids_peek_lnk_lnw_spline (NcHIPrimTwoFluids *two_fluids); + +G_END_DECLS + +#endif /* _NC_HIPRIM_TWO_FLUIDS_H_ */ diff --git a/numcosmo/numcosmo.h b/numcosmo/numcosmo.h index 1a39edac4..212146b29 100644 --- a/numcosmo/numcosmo.h +++ b/numcosmo/numcosmo.h @@ -98,6 +98,7 @@ #include #include #include +#include /* Large Scale Structure / Structure Formation */ #include From 3a8d8a4a5a9f355404ba34f9fc7040032ec01894 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Tue, 23 Apr 2024 20:25:18 -0300 Subject: [PATCH 05/27] New HIPrimTwoFluid model. New notebook with HIPrimTwoFluid calibration code. 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"execution_count": null, "id": "a4daed56-57bc-4993-b8ab-3468d8f83d5f", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "

" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -141,21 +130,10 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "id": "8470dc58-92f9-46ab-8ec6-982e346cda0d", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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NehfFSrKPXFP8LV4M/P470KWLVEFokZLEzZ8vm+xS8ohrgXcyu/BCWcx2wQXA6tVA//7ShTWimYbzzwc+/VS+r13rf7Bm270QJbPmjSpj/djJPnJN8eP1+muBxo2TlXBaNGiQLCpau1YmG266Se2IKFQcWWpBYaGslIvJvrknnCAP9s9/ShUiN+GlFNRazQ9RPHz+uaxmzskBWug6o7qMDP/o0pNPAnv3qhsPhY7JUisC7Zsb8Vxzt27+B9u+PcoHo3ThTZGVlKny/yDtUdoFDBsmC5K1bMQI6V+8bh0/LycTJkshUPbNveEGaSg2YYIMn0b0qSA3d/8Hu/lmdiqj/bTZN5ewPUX2G9y1axcAICsrS+VIKJVs3CjrZgBtFnY31749MHq0HCtJHmkfa5ZC1KaNrI4zGKS52KOPyieDhQtD20+rxQd75BHg55+lG2bYD0apKisrCzqdDn/88QcAoH379shQa0fQKDU0NGDLli1o3749srN52qHYmT0b2LNHNlE44QS1ownN+PHA9OnSkm/1aqnOIG3jWSsMGRlAWZnkOCNHyoq5M86QxW5hd4pVHuzII/2b8P76K/DWW9yEl3wO2/fCUhKmZJaZmYnu3bsnbcJH2rNzp/RWAvw98pJB9+7ApZfKhr9PPCGfnUnbMrwpUEhQV1eHvLw81NbWIjfshkiRWbZMSo5qaoAjjgDeeQf4xz8ifLBPPwUuuQRwu6Uv0zvvAL17xzJcSnJ79+7F7iRvanrAAQcgM7PpzL8a791YSvb4k928ecB110k5qMsFJNOg5aefyjqftm3lc3KjnXsoQcJ5/ybRS0tbTj1VVmCcd57s93PKKTI4NGhQBA+mbMJ73nlAdbW0n339deBf/4p12JSksrKyWOtD1EjjdgHjxydXogRI/77jjwdWrQKeekp2jSDtYoF3FHr2lBxn4ECgthY4+2z5pBORo46SBzv5ZOlWNmQI8PzzMYyWiCh1LF0qiUa7dv6C6WSSkeGfOpw5U+quSLuYLEUpPx+w22XJ6p49MiR8551RbML7wQeA2SwbHF19NXDffdyEl4ioGWUl2YgRgF6vbiyRuvJKOe1v2CCTCaRdTJZioG1bGQS6/Xa5fP/98gaur4/gwdq1k22zb7lFLt91FzBqFLBv2TURUbpbvx547TU5njhR3Vii0bYtoOwOpEwpkjYxWYqRzExJkp5+WubOX3hBZtJqaiJ8sIoKYNYsOZ43T+qZuJkQERFmzZI+d4MGJf+y+7Fj5W/G0qVAHHYKohhhshRjo0YB774rvSc//VQKv3/6KcIHGztWWgl06CDTcwMHAr/8EtN4iYiSyfbtwNy5cpwMTShb06ULMHSoHLNJpXYxWYoDkwn47DPppfG//0nN9mefRfhg550nWVeXLrL74oABwMqVMY2XiChZLFzo77JywQVqRxMbStL34otACrRUS0lMluKkTx/ZN7dfP+DPP2W4+OWXI3ywE06QPgWNN+F9662YxktEpHVer3/0ZcIEIFW6aQwYAJx0kpSmKk02SVuYLMXRYYcBH38szSvr64GiImDatAgXtymb8J51loxDX3KJbFtNRJQmPv4YWLNGdoUaNUrtaGJLGV2aPZvrebSIyVKcdeggLe2nTJHLt94qqx8iasacmyvbVCub8E6cGMWOvkREyUVZMTZyJKDTqRpKzA0dKh+wN2/2bwxM2sFkKQGysmTj3RkzZHHb3Lky115XF8GDKZvwlpfL5UcflXdZiuxMT0QUyLp1sg8nkNztAoI54ABZ0wOw0FuLmCwl0MSJ0nisfXvgv/+VxW0bNkTwQBkZMkT14ovyDnvtNeDMM4Hff491yEREmvDkk1LCcNZZwDHHqB1NfBQXyyn9iy/ki7SDyVKCXXgh8MknMty6ejXQv38UvTWuvFJaCuj1wJdfSpXgd9/FNF4iIrVt2yY97IDUaBcQzKGHymkd4OiS1jBZUkFhoXxq6NtX5qdPP11KkSIycKDsKVdQAPz8szR2+vjjGEZLRKSu556T/Td79gTOPVftaOJLSQZffhnYtEndWMiPyZJKuneXxW1DhgB//y0r5iJe3NZ8E96zzuImvESUEhoa/KMsEydK3WcqKywETj1V9hqdM0ftaEiR4i87bcvLA95+u+nithtvjHBxm7IJ79Ch/k14772Xm/ASUVJzOIDvvwc6dQKuvVbtaBJj8mT5PmcOsHOnurGQYLKksuaL2x57DDCbZbQpbO3aAYsWASUlcvnuu7kJLxElNWVU6brrpHtKOrjkEuDww4EtW2RfdVIfkyUNUBa3LVoE5OTIirkzzpBm3WHLzJTOl7Nn+zfhPfdcbsJLREnnxx9l9D0jQzp2p4s2bYDx4+X48cc5QaAFmkqWHA4HbDYbKioq4EnDP+5FRTKTlp8PrFghi9vWro3wwcaMkarxjh2BDz+USXBuwktESUSp4zzvPKBXL3VjSbTRo4G2bYGvvgKWLVM7GoprsuTxeFBRUYGKioom19tsNthsNlitVjgcDgCAy+WC3W6H2WyGxWKBLtXas4bo1FNlG7hevSS3OfVUSaAicu65/k14v/1W+hSsWBHTeImI4qGuDnj2WTlO5XYBweTnAyNGyLHSuZzUE9dkyeFwoKampsl1zZOiadOm+W7r8Xhgs9lQrhTwpKmePWVx28CBslz2nHP8J42wHX+89Ck49lhpWvmvf3ETXiLSvHnzgL/+Anr3llXD6UhJEl97DVi/Xt1Y0l1ckyWz2YyCgoIm1zkcjiajRjqdzje6VFBQ4LuP1WqNZ2ial58P2O3AsGGyhHTUKODOOyOcuz78cBlhOvts/ya8TzwR65CJiGKiocF/ipo0SWqW0tE//ymbM+zdC8yapXY06S3hNUvV1dXIz8/3Xdbr9fB4POjXr1+T61pSX1+Purq6Jl+pqG1baZd0++1y+f77ZVi2vj6CB8vNlRGl0aPlTDRpUhR9CoiSn8fjQXFxcZPjdKyV1KL33gN++knaq1x9tdrRqEtpIzB3LrcAVZMmCrzdbjeMRiMAqWeqqqqCxWIJevvy8nLk5eX5vrp165aoUBMuM1OSpKefBrKzgRdekCHpZrOboWnTBqisBB58UC4rfQr4DiSNC6f+MVQOhwNutxuAlAesWLECgwcPRmFhIUpLS2MWO4VPqdG5/npZo5LOLrgA6NEDcLuBhQvVjiZ9JTxZaj4t53a7YTAYAAAlJSUwm82+OqZgysrKUFtb6/vaENFutMll1Cjg3XdlgOjTT6VZ908/RfBAGRlAaen+fQq4CS9pWDj1j6Gw2Wwwm82+yzqdDitXrsTKlStRVlYW1mNRbH33nWw0nm7tAoLJyvL/HGbMYBsBtWQn+glNJlOTT20ulwsmkymsx8jJyUFOTk6sQ9M8kwn47DNZRvvjj5IwvfGGbAcXtqIioGtX2Welqkr6FLzzTupu501JzWw2w+12N5kmC1b/aDKZYLPZfKNGCr1eD7PZDKfT6RvJVigf2KxWK6644oq4/T+odUq7gIsukhEVkg/Ld90FrFkDfPQRMGiQ2hGln7gmSw6HA3a7HR6PBwaDAWazGQaDAUVFRb6TWVlZWTxDSDl9+sjitgsvlC4AgwYBCxYAEZ3fBw6UPgXnngtUV0vW9eqrUlFIpHHB6h8BNBk1CsTpdMLpdMLlcjVJnux2e4slAPX19ahvVDSYqvWSavF4gPnz5Tgd2wUEo9MBI0dKkfeMGUyW1BDXZMlkMgUcNWrtREYtO+ww4OOPgauukpGloiLA5ZLZtbBXjfTqJX0KLrlEhq3OPlsKpNK9qpKSUvPRpECMRiOMRiOsVmuTkSqPx9Pq4pLy8nJMnTo12jApiGeeka2e+vblZ7bmJk6UZOnNN+V8v28wlBJEEwXeFL4OHYBXXgGmTJHLZWWAxSJ76Iat+Sa811zDTXhJ81qqfwyFxWJBdXW1b1RJp9OhsrKyxfukY71kouzd65+CS+d2AcH07i2fZb1eYOZMtaNJP0yWklhWFvDoozIsm5kJPPWUrJyorY3gwdq2laJvpZ7s7rtl50puwksaZTKZUFVV5bscSf1juHJycpCbm9vki2JjyRJg3TpAr5dRc9qfMjX59NPAtm3qxpJumCylgIkTZVFb+/ayimTgwAi7vWZmSluBOXMkE5s/X9qHs/cMqUypf7Tb7bDZbADQpP7RarWy/jHJzZgh30ePlnMZ7e+cc6RyorZWalUpcTK83uSfa6mrq0NeXh5qa2vT+pPeypUysvTbb0DnztKDsrAwwgd7912pGt+2DfjHP2Tr7yOPjGW4REn/3k32+LVizRrpVp2VJfU43burHZF2PfGEjDAdfbRs+ZnJIY+IhfP+5Y85hRQWykq5vn2BzZuB00+PYhu4c88Fli6V9gLffiutBbgJLxHFgTKqdOmlTJRac+21QKdOwA8/yJZYlBhMllJM9+6S4wwZEoNt4I47TloLNN6E9403YhkuEaW5mhrZ1glgu4BQdOokfZcAf6dzij8mSykoL09mzW64IQbbwDXfhPfSS/0fA4mIovT008COHcDxx0u9JbVuwgRZLfjuu8D//qd2NOmByVKKatMGsFqB8nK5/NhjwOWXSw+TsCmb8Fossm518mTpWcBNeIkoCnv2+NsFTJ7MdgGh6tkTOP98OY545oDCwmQphWVkALfe6t8G7o03ZBu4336L4MHatJFVcsqeWY8/HkX2RUQk56QNG4CDDgKuvFLtaJLL5Mnyfd68CNvFUFiYLKWBoiLpOZmfLzXaAwYAa9dG8EAZGUBJSdPs68wzuQkvEUVEqbkpLpZWbxS6wYNlofK2bcCzz6odTepjspQmTj1VarV79QJ++UUuf/BBhA/WOPtSNuH99tuYxktEqe2rr6QcMjsbGDtW7WiST0aGvyD+iSdYFRFvTJbSSM+esg3cwIEybHvOOVF8Ijn1VHmwnj2Bn3+WTXg/+iiW4RJRClNqbcxm6VBC4RsxQjbZdbmAd95RO5rUxmQpzeTnS2+OYcOkuHLUKOCOOyLcBk7ZhPeUUyT7OvtstpUlolZt2QK88IIcs11A5Dp0kI7nABcpxxuTpTTUtq30Nbn9drn8wAOyF1N9fQQPdtBBMiV3xRWyCe/IkcDUqdyEl4iCslrlfHPiiTKLT5EbP166eDscEdaiUkiYLKWpzEzg/vulx0l2NvDii4DJJA3iwta2rTyAsgnvPfdIm1luwktEzezeDcyaJceTJrFdQLSOOEKaDwNsIxBPTJbS3KhR0tgsN1c6f598MvDTTxE8kLIJb2WlbPC0YIEURW3dGvOYiSh5vfIKsGkTcOihwNChakeTGpSpzAULALdb3VhSFZMlgskEfPaZbJXy448yLL5sWYQPZrEAS5YAHTtKwfepp0oBOBER/LU1Y8dKBxKK3umny+5UO3bIbAHFHpMlAgD06SOb8PbrJ1NxgwcDL70U4YOdc45/E97vvgP695cWA0SU1qqqZE1ImzbSW4lio3EbgSeflMU7FFtMlsjnsMOAjz8GLr5Yii+vvFJm1iKq1VY24T3uOOCPP7gJLxH5RpWKiuR8Q7EzfList1m/HnjzTbWjST1MlqiJDh2kpmDKFLlcViYza7t3R/Bgyia855wj48OXXsptsonS1G+/+Uer2S4g9tq2lXM1wNNsPDBZov1kZQGPPiqfAjMzgaeekk0bI9p/qFMn2YS3uFiGqKZMkU2N2G6WKK1UVsqHrpNPlpYBFHvjxsn5+5NPgFWr1I4mtTBZoqAmTgRefx1o314aWQ4cKEO8YcvOBmbP9m/CO2MGcNll3ISXKE3U18spAPBvAEux17WrdEQH2KQy1pgsUYsuvFA+pRx2GLBmjdRqr1wZwQMpm/C+9JIsgXnzTeCMM2RsnohS2uLFst92ly7yOUkTHnhAVu22axf9V+fOmhnKUZLRF16QTukUG0yWqFWFhbJSrm9fyW1OP11m1iJyxRX+TXhXrJA+BWw7S5SyvF5/Dc24cbISTnU1NZIs/f03sHNn9F+//SaPpwEDBsiq5vp66ZROscFkiULSvbt0AxgyBNi+XTrGRtwt9tRTZaVcz57AL7/I5Q8/jGW4RKQRn38un4tycvwFyKp7+mlZdHLccXIOiuZL2UD8tdcirFOIrYwM/+jSrFkRLs6h/TBZopDl5QFvvw3ccAPQ0CArWqZMibBWu2dPabhy6qn+TXjnz491yESkMqV2Zvhw4OCD1Y0FgDQhevJJOZ48WT4JRvN1xhnAmWfKiVDZx0VlQ4dKh/RNm2R1M0WPyRKFpU0bGdotL5fLjz8OXH55hLXaBx0kuz8WFckJ7NprZV85bsJLlBI2bgRsNjnWTLuAN94ANmyQ88+wYbF5TGUox2qVoXeV5eRIh3SAhd6xorlkyePxoJitXTUtIwO49VZg0SJ5U77xRhS12m3bSiXirbfK5alTgZEjuQkvUQqYPVs+B51+OnD88WpHs4+SPRQXy/knFi64AOjRQ/bCXLgwNo8ZpeJi+XC7fDk3UIiFqJIlj8eDiooKVFRUNLneZrPBZrPBarXC4XCE9ZgOhwNu7gSYFIqKmtZq9+8fYa12ZqYMVVmt0iTkuedkWo6b8BIlrZ07pbcSoKFRpVWrZHlvVpZ/6CUWsrKACRPk+PHHNTE6fthhsgsDwNGlWIgqWXI4HKipqWlyncvlgt1uh9lshsViwTSlt04IbDYbzEqTCEoKSq12r15S23jKKTKzFpHRo6UoqlMn2XfllFOAdetiGS4RJciiRcCff0pZz8UXqx3NPkrWYDZLU6JYGjVKtkBYu9Zf9K0yJUl96SVg82Z1Y0l2USVLZrMZBQUFTa5zOBzQ6XS+yzqdzje6pIw2Nf6y7ZvQdjqdMBqNIT1vfX096urqmnyRepRa7YEDgbo64NxzgWeeifDBzj5btkjp2hX4/ntZB/vllzGNl4jiq3G7gPHjpS+t6rZskSl/ID6dMXU6KSEANLPfSL9+8plz927/KB9FJuYv4erqauTn5/su6/V6eDweAGh11MjpdMLpdMLlcrWYPJWXl2Pq1Kkxi5mil58vXb5HjQJefBG4/nrgf/8D7r8/ghPlccdJY6cLLpBh8zPPBN59VwofiEjzli6Vt267drJ6VhOsVmk+1K+ffAiLh4kTZUXcW28BLhdgMMTnecIwaRLw2WdSP1ZWJnWmFL6EFHiHUoNkNBphNpvhdrt9yVUwZWVlqK2t9X1t2LAhRpFSNNq2BZ5/Hrj9drk8bZoUfkfUeqRrV6ktMJlkdcl558mIE1GMNF9MUlpaCpvNtl8NJoVPGVgZMQLQ69WNBYAMrSjL+idNklUq8dC7t4yOe73+9gQqu+wyOZ3+8Qfw8stqR5O8Yp4sNZ+Wc7vdMISRXVssFlRXV7c4JZeTk4Pc3NwmX6QNmZkymrRokZQeLVsmA0UzZ8qqmLB06iTbogwZIr0Jzj0XcDrjEjdpW7wXk9hsNhQUFMBsNjcpHaDwrV8v/RkBDRV2v/qqNB069FDZRSCelP/0008D27bF97lC0KaNdE4HNFN7npRiniyZTCZUNVqn6HK5YDKZYv00pHFFRcBXX8nu4h6PLBTp2RO4914pCA+5FUm7dtKbYNAgSZguukhOepRW4r2YpPmItpNJecRmzZKmtYMGyRZJmqAMdY0ZE/95qHPOkRUvdXWaabRrsch/e+VKqS+l8EVVs+RwOGC32+HxeGAwGGA2m2EwGFBUVASbzQa3242ysrJYxUpJpqBA5sqtVuCuu2RngLvvli9AhucPPFDyobZt/d+bf3Xo0A49z3kLx/5kwcnrFyG7qEhWy2Vlqfr/o8QJNEUfbDGJyWTynX8a0+v1MJvNAeshLRYLSktL4XA4sHLlyv1GyBX19fWor6/3Xebikqa2b/fvR6aZUaWqKskQ2rSRZCneMjOldmnSJNkTauxYuU5FBx0EXHWVLLx5/HEp+qbwRJUsmUymgKNGXP5PiuxsGQK+7jrZefzVV6X4s6YGcLvlKzTtATyP/IzHMW7pTNzywAx0uuvGOEZOWhfrxSRlZWXQ6XRwOp1B78/FJS1buFDao/XoIeszNEHZxLKoSJoPJcK110rx5g8/AP/9r4w2qWzSJEmWXnkF+PVX4PDD1Y4ouWhhQSelgXbtgGuukS+vV7aD+/VXGanesUMa2O3YIYtVlMvKl8cD/Pij1D/V1OTjPtyFF+7+Ca8c/wuOu+gItf9rpCGhLiYxGo2wWq2+5Mrj8cBqtcJgMPi+AikrK8NNN93ku1xXV4du3brFJPZk5/X62xhNmKCRgd/ffpMCSiCxQ12dOsnS4Mcflx+KBpKl444D/vUv4P/+T6ZK//MftSNKLkyWKOEyMqQlSaMZlJDs3Qu8/poXN139B6p39sQZ5m1wLAcKC+MRJWldQUFBk2m5SBaTWCwW3+WSkpJW75OTk4Mcrr0O6KOPgDVrpC/jqFFqR7NPZaWshDv5ZCmgTKQJEyRRevddGWE6+ujEPn8AkydLsmS1AnfeKR9iKTSa2xuOKJisLOBycwa++tCDU/AZPLs74vwh9fj1V7UjIzVwMYm2KKNKI0eG/0EoLnbtkuZCgDoFVD17AuefL8caaSNw0UXAEUdIGYTSn5NCw2SJko7+5KPx3uhXcCy+xu9bc3D55dx3N9Upi0nsdruv63/jxSRWq5WLSVS0bp10+QCktlkTXn4Z+P13oEsX4PLL1YlB6RQ+b57UHqis8RZ2M2awjUA4Mrze5P9x1dXVIS8vD7W1tey5lC5+/RXrDIPRb/dncCMfd90FsO42+ST7ezfZ44+Vm28GHnlE+jG+957a0UCygJNOkh2+77/f3ylXjTj69gW+/RZ49FFgyhR14mhk61Yp7t6+XaZOzzhD7YjUE877lyNLlJwOPxw9Rp2J2ZCdwx94QM6LRJRY27ZJ/0VAQ+0CvvhCTgg5OdJkSC0ZGf4fyhNPSOGlyg48UBbaAP6pU2odkyVKXrfeiisyX0ERFmHvXmlPsHu32kERpZfnnpMZpl69NLHoSyhNKIcNAw4+WN1YRoyQIi6XC3jnHXVj2UeZKn3jDeDnn1UNJWkwWaLkdeSRwKWXYibG46C2f2HNGn5SIkqkhgb/e27iRNV7L4qNG4F9dW2aGOrq0AEYPVqOlSROZf/4h+wi1dAgW1FR67Tw0iaK3KRJyIcbFXv/DUC6g3N1HFFiOBzA999LW6GRI9WOZp/Zs2UjytNOA044Qe1oxPjxkkl+8AGwdq3a0QDw55FPPSU7SVHLmCxRcjvtNOC44zBy91yceuSv+Ptv4EY29iZKCGVU6brrAE3Ut+/cKb2VAG2MKimOOAK45BI51sjw93nnyZZUHo9MpVLLmCxRcttXQJkJL2btGo2sLC9sNo2syCFKYT/+CLz9trwFNdMuYNEi4M8/gW7d/MmJVijJ23PPhbPPU9woW9gBbCMQCiZLlPyGDQN0Ohy76T1MvvgXANLehL2XiOJH6bN43nnSf1F1Xq+/Jmj8eNmYUktOP132HNmxQ+a+NOC664COHYHvvpMpVQqOyRIlv3btgKuvBgDcvedOHHoo8L//+ffPJKLYqqsDnn1WjjUz27V0KbBqlZwPbrhB7Wj217iNwMyZUlelstxcSZgAzdSeaxaTJUoN+1ab5L6zCOW3Sqfce++VBr5EFFvz5gF//QUcc4ysqtIEpRZoxAggP1/dWIIZPhw46CBg/XpZt68BylTc22/L1CoFxmSJUsM//wkMGADs2YORO+agXz/59HvbbWoHRpRaGhr8o7YTJ8qAierWrwdee02ONVNAFUDbtv4mmRop9O7VS6ZSAc1sYadJTJYodewbXcp8ei5mPNYAQKYK2NmbKHbeew/46ScgL883+62+WbOkO/aZZ8oHJy0bN042afvkE5k21ABlC7tnn5UPmbQ/JkuUOoqKpOFLdTVOrv8YI0ZIzefkyVzpQRQrSm3LDTdIcbDqtm8H5s6VY+WvvpZ17QqYzXKskdGlIUOA3r1lanXePLWj0SYmS5Q6OnSQegUAsFrx4INy1WefAS+8oG5oRKngu++A//5Xlp2PH692NPssXChL8Y88ErjgArWjCY2S1L3wArBli7qxYP8t7Boa1I1Hi5gsUWpRthV49VV0PWCLr2appEQ2/CSiyCk1LRddBPTooW4sAGTIWBmdmTBBpreSwYABQL9+QH09YLWqHQ0AmVLNy5Mp1nffVTsa7WGyRKnlhBPkJLR7N7BgAW66SU7qmzYBDz6odnBEycvjAebPl2PNtAv4+GNgzRqgfXvg+uvVjiZ0GRn+0aVZszSxA3jHjv6OC2wjsD8mS5R6lNGluXPRNseLhx+Wi9Ony8bfRBS+Z56RPcT69gXOOEPtaPZR/qqPHAnodKqGErahQ4FDD5VPcq+8onY0AGRwLjMTsNuBb79VOxptYbJEqWfYMClW+uEHYOlSXHIJMHiwjHj/+99qB0eUfPbu9bcLmDxZI+0C1q0D3nxTjrXcLiCYnBxg7Fg51shQzpFHyhQrwKa+zTFZotTTqRNw5ZVyPHcuMjKAxx6TcobXXpONv4kodEuWAD//DOj10ldRE2bOlJqls86S7pjJqLgYaNMG+Pxz4Msv1Y4GgH92cMECYOtWdWPREiZLlJqUqbjFi4GtW9G3r/9D3OTJmthpgChpKDXUo0dLeZDqtm3z76+mmQKqCBx2mP+DnUbaCPzrX8Cxx0pHhqefVjsa7WCyRKnppJOkOd3OnbK0GMDUqbILwtq1wJw5KsdHlCRWrwY+/FBGZseNUzuafZ57DqitlR18zz1X7WiioyR7L78MbN6sbixo2kbgySdlCpaYLFGqyshoUugNrxd6PXDffXLVXXcBNTXqhUeULJTalUsvBbp3VzcWAE3bBUycKBXJyaxfP+CUU2RFnEY+xQ0fLh8sf/nFXxaW7lR7ldlsNhQWFu53vcfjQXFxsQoRUcoZMUL2YvrmG6CqCoDkT//8p8zF3323yvERaVxNDfD883Ksmdkuux34/nupTbz2WrWjiQ3lhztnjqxEUVm7dprbwk51ISdLHo8HFRUVqKioaHK9zWaDzWaD1WqFw+EI+YnNZjP0ev1+1zscDrjd7pAfhyioAw/0byuwbzuE7Gz/wpPZs2WKgYgCe+opYMcOaV82cKDa0eyj/PW+7jogN1fdWGLlsstkG5Q//gBeekntaABIjWdWlrSy+uYbtaNRX8jJksPhQE2zeQuXywW73Q6z2QyLxYJp06ZFFYzNZoNZ+eNGFAvKVNyLL8rGR5C9Ni+/XFr6c984osD27JEFZ4AMfGiiXcCPPwJvvy3HEyaoG0sstWnjLwibMUMTJ6Vu3eQ8CXB0CQgjWTKbzSgoKGhyncPhgK5RIzCdTucbXVJGmxp/2Wy2oI/vdDphNBrDDJ+oFaedBhx1lHTTW7TId/VDD0mbk48+Al5/Xb3wiLTqjTeADRuAgw/2L9hSnbLfynnnAb16qRtLrFksclJauVI2tNQAZXZw4ULgzz/VjUVt2dHcubq6Gvn5+b7Ler0eHo8HACIaIXI6nXA6nXC5XC0mT/X19ahvNK9bV1cX9nNRmsjIkB7+JSUyFbdvpKlHD2lQ+cADwM03y4Katm1VjpVIQ5Tp6uJijbw36uqAZ5+VY6UZUCo56CDgqqukVfqMGcCpp6odEU45BSgslPxt7lygrEztiNQT8wLvUOuNHA4HXC6Xb7TJaDTCbDbD7Xb7Eq5gysvLkZeX5/vq1q1btGFTKhs5Uoa5q6qAr7/2XX3rrUCXLtII+NFHVYyPSGO++gr49FOp8RszRu1o9pk/X6bSe/cGhgxRO5r4UIZyXnlFhvVU1riNwMyZmtjCTjVRJUvNp+XcbjcMBkNI9zWZTKiurt5vBMpisaC6urrFKbmysjLU1tb6vjZo4EVFGnbIIcDFF8vxvkJvQDaOVMrsHngA2LhRhdiINEhpF2A2S92x6hoa/EFNnKiRAqo4OO446Qq5d6+sQNGAoiI5hW7cKDsgpKuokiWTyYSqfUuyASn4NplMUQfVmpycHOTm5jb5ImqRUuj9/PPSmnaf4cOBAQOkpCmdh5jTTWFhIYYMGYLS0lLfdcHamaSbLVuAF16QY83Mdr33nhR35+UB11yjdjTxpfzQrVZZiqiynBz/6KJGtrBTRVir4ex2O+x2u2/qzGAwoKioyFfMXca/NqRVJpPsEllbCzRaaJCZ6V/p8dxzskUTaU+sW5eUlZXBbrc3WcEbrJ1JurFapdXPiScC/furHc0+yl/p66+XIeFUdtFFwBFHSJMrJWtV2ZgxUsnw2WfAihVqR6OOkJMlk8mExYsX+1oFKMxms691AJf9k2ZlZsqJFmgyFQfIHwWlt93kyTLiT9oS69YlLpcLDoejycgSSU3KrFlyrJl2Ad99B/z3vxLM+PFqRxN/WVn+tgiPP66JNgKdOwNXXCHH6dpGIMn7xBOF4brrJGlaulROwI385z/ygfXLL/0di0k7Yt26pKSkBCaTCQUFBS22NGmuvr4edXV1Tb5SySuvAJs2yf6uyh9H1SntAi66CAixJjbpXX+97Fi8ejXwf/+ndjQA/LODixYBv/2mbixqYLJE6aNrV+D88+VY2bF8n86dgTvukOPSUl//StKw1lqXWCyWJl/KyLfD4fAlVa2tvG0u1VfiKqMGY8YABxygbiwAAI9HVsEBGtpvJQEOPNBfm6WRQqETT5T6zt27gcpKtaNJPCZLlF6UQu/58/fbg2nKFKCgQD41/ec/iQ+NohdK6xKTyQSPx+NLmBonUY3bmQSSyitxq6qA5culNkUz7QKeeUZWX/TtK63308nEifL9zTelv4kGKKNLs2cDu3apG0uiMVmi9HLuudJcqaZmv9bdOTnAI4/I8SOPANXViQ+PQhdN6xKz2QyTyYSSkhLfdcHamTSWyitxlVGlK68EDj1U3VgAyPJ5ZQpOMwVUCfSPf0g/qYYG/74zKrv8cjl9/v478PLLakeTWEyWKL1kZwOjRslxs0JvALjwQjk/7dolHb5Ju9RqXZKKfvvNv3+rZma7liyRERW9XjpbpyPll/HUU8C2berGgqZb2Gmk9jxhmCxR+rn+evmU+sEH+w0fZWRIN++sLBl4CmM1OsURW5fEV2Wl1KKccgrQr5/a0eyjDHWNHi3FzunovPOkNqC2VnqbaICyhd2KFenVaiXD603+3LCurg55eXmora1NqWFxiqOzz5blyGVlAQuUJk2ShsF9+gCrVsmAFMVesr93kz1+QEr3jjhCplYWLZKOzapbswb45z9l9eq6dUD37mpHpJ7HH5eCyt69gW+/1cR05KhRsk3flVcCL76odjSRC+f9y5ElSk8Wi3yfOzdgl9x77gHy84G1a4E5cxIbGlEiLV4siVLXrsBll6kdzT7KqNKll6Z3ogRIy5OOHYHvvwfsdrWjAeCfHbTZ0mebKCZLlJ4uvlg+Tv/5Z8Dhbb0euO8+Ob7rLqkHJ0o1Xq9/Zfq4cVKTorqaGn+zM83st6Ki3FxJmADNdIQ8/njg9NOBPXs0s4Vd3DFZovSUne0/ET/6aMC23aNHy0zA1q3A3XcnOD6iBPj8c6k9ycnxd9VQ3dNPy2jv8ccDAweqHY02KG0E3n5b9sjTAGV0qbIS2LlT3VgSgckSpa/rrwc6dZLh7ffe2++fs7OBxx6T49mzpZkuUSpRBiqGDwcOPljdWADIUEU6twsIplcvKfYG/D8flV18scyQ/vlnctcthYrJEqWv3Fz/x+np0wPeZNAgqeNoaJAay+RfDkEkNm707ymtmXYBb7wBbNgAHHQQMGyY2tFoizIS/uyzgAa22cnO9m/Vlw5tBJgsUXqbPFne9R99BCxbFvAm06fLNMWHH+7Xx5Ioac2eLQM5p58uM16aoAx1FRcDbduqG4vWDBkCHHOM7MU0b57a0QAAbrgBaNcO+Ppr4NNP1Y4mvpgsUXrr3h249lo5njo14E169PA3qLz55vSYn6fUtnOnf38vzYwqrVoFfPKJfHgZO1btaLQnI8Nfu/TEEwHrLBNNrweuvlqONbKFXdwwWSK67TY5QdvtwGefBbzJrbdKm/9166QenCiZvfii1Jp07y61J5qgjCqZzdLHgPZ3zTVAXh7w00/Au++qHQ0Af7L9+uvAL7+oGkpcMVki6tHDP7p0zz0Bb9KxIzBtmhw/8ACwaVNCIiOKOa/Xn5eMH6+RhqtbtgAvvCDHmhnq0qAOHWTuC9DMUE6fPsDgwZrawi4umCwRAcDtt/tHlz7+OOBNhg8HBgyQTdC5swYlq6VLZcarXTv/313VWa3SSrxfP3mTUXATJkhnc7tdOnprgFJ7PneunB9TEZMlIgA48kgpKgWkQClAPUBmpv/D3IIFwBdfJC48olhRXsNXXy01J6rbvRuYNUuOJ09mu4DWHHkkcNFFcvzEE6qGojjvPMBgADwefz/RVMNkiUhx113Sd2nlStkkK4CTTvLP2E2apIkaS6KQrV8PvPaaHCu1wqp79VWZ1z70UGDoULWjSQ7KUM6CBdI1V2VZWf7X04wZqdlGgMkSkeKQQ4DSUjm+7TaZFgjgP/+RGqYvv0zdT1GUmmbOlAR/0CCgb1+1o9lHGeoaO1Z6dFDr/vUv4Nhjge3bpeO5Bihb2H37LfDBB2pHE3tMlogau/FGWfb2yy9BO+V27gzccYcc33qrtD0h0rq//5aaEkBDW65VVQHLl8umdMo0OLUuI8NfCP/kk8DeverGA1mkp4y6a2QLu5hiskTUWPv2/h10778/6A66U6YABQXA5s1AeXniwiOK1PPPy4yNwQCcf77a0eyj/FUtKgIOO0zdWJLN8OFAfr58sHvzTbWjASC15wCwZAlQXa1uLLHGZImouZEjZQddjydoK4GcHODhh+X44YcBlyth0RGFrXG7gIkTpcZEdb/9Brz0khyzXUD42rUDLBY51shQztFHA+eeK683jWxhFzNMloiay8pquoPu2rUBb3bRRYDJBOzaJZ29ibTqgw+klqRjR6kt0YTKSlkJd/LJwIknqh1Ncho7Vs5XH38MfPON2tEA8Oe9zzyTWiUKTJaIAhk0CLjkEqkFuPHGgMs7MjIkp8rKku61DkeigyQKjVJDfe21Uluiuvp6+SACcFQpGt26AZdfLscaGV066ywZYaqrA+bPVzua2GGyRBTM9OnAAQdI87clSwLepE8fYNw4OZ4yRTYmJdKSn34C3n5bjjXTLmDxYuD332UxhfLHniKjJJsLF8oeNirLzGzaRiBV2qswWSIKpqBAMiBA5tl27Qp4s3vukeZ+a9f6Nycl0oonn5SB0fPOA446Su1oIMEoQ13jxslKOIrcKacAhYWyO7Ky3FFlI0cCubnAjz8C77+vdjSxoVqyZLPZYLPZUKr0tdnH4/GgmEtISStuv12a5f34Y9BuuXq9fwHdnXcGXUBHlHB1dVI7Amhotuvzz4EVK2SVhFKgTJFr3EZg5kypA1NZx47A9dfLsUa2sItayMmSx+NBRUUFKioqmlyvJD1WqxWOEIs2bDYbdDodzGYz8vPzYbVaff/mcDjgdrtDDYsovnJzpQslANx7L/DHHwFvZrHIArqtW4G7705gfEQtmDdPimx795ZaEk1QamuGDwcOPljdWFJFUZE01d240d+iXWUTJkge9/77wPffqx1N9EJOlhwOB2qafWR2uVyw2+0wm82wWCyYpmzL3gqz2QyTyQQAqK6uRr9+/QBIEmU2m0MNiSgxrr0WMBrlY/qddwa8SXZ20wV0q1cnLDqigBoa/IOhkyZpZMu1jRsBm02ONVNAlQJycoAxY+RYI0M5BgNw4YVyrJEt7KIScrJkNptRUFDQ5DqHwwGdTue7rNPpfKNLymhT4y+b8iZpdP/CwkIYjUY4nU4YjcaQYqmvr0ddXV2TL6K4ycz0Z0Jz58qW7QEMGgRcdpn8kZoyJTX3R6Lk8c47Utyt0wHXXKN2NPvMni2rIE47DTjhBLWjSS1jxkj912efyTSnBiid4ufPl7Z1ySw7mjtXV1cjPz/fd1mv18Oz7yfS2giR0+mEx+OBxWKB0+n0Xed0OuFyuVpMnsrLyzF16tRoQicKz2mnAVdcAbz8smRCH30U8KP6Qw/JyqMPPwTeeEO6DxCpQZntuuEGoEMHdWMBIAXIygoIzey3kkI6d5Zz1MKF8stfsEDtiHDmmbIH4Zo1Ujt3001qRxS5mBd4h1Jv5HK5MHToUFRWVqKwsBButxtGoxFmsxlut9uXcAVTVlaG2tpa39eGDRtiFD1RCyoqgLZtgf/7P9kpPQCDwd+g8uab5e8DUaJ9+610vMjMBMaPVzuafRYtkqXt3boBF1+sdjSpSUlCFy2SDukq0+AWdhGLKllqPi3ndrthMBhavZ/BYEB1dTXsdjtWrlzpq18CAIvFgurq6han5HJycpCbm9vkiyjujjgCuOUWOf73v4NmQmVl0j7G5QIefTSB8RHto4wqXXwxcOSRqoYiGrcLGD9eivwo9k48ERgwQFbEaaSPyVVXyYrhdeuCtqtLClElSyaTCVVVVb7LLperSeJDlHJKS4GuXYGffw6aCXXsCChrHR54ANi0KXHhUWgKCwsxZMiQJq1LlBW9zduZJBu32z8Do5nZrqVLpdavXTtg9Gi1o0ltyi999uygveESqX17/69cI03GIxLWaji73Q673e4r1DYYDCgqKvIVc5eVlcUtUCJN6NABePBBOW4hExo+XD7g/f23jDRRdGLZugSQqXy73e5bwatM/ZtMJrhcLriSeGfkp54CduwAjjsOOP10taPZR/krOWKEDDNQ/Fx+uQxt//671FhqwLhxsi3Uhx8m8Uphbwqora31AvDW1taqHQqlg717vd4BA7xewOsdOTLozb74Qm4CeL2ff5648JJJqO/dxYsXe0tKSrzTpk3zXVddXe21WCy+yyaTKeTnnTZtmtdut3tLSkqaXF9ZWbnfdS3R2rln926vt3t3ec09/bTa0ezzyy9eb1aWBLV6tdrRpIf775efd79+Xm9Dg9rReL1er9dslpBGj1Y7Er9w3r/c7oQoXJmZ/vqL+fOBL78MeLOTTpK2/4CMjKfKHklqiHXrkpKSEphMJhQUFDS53mKxwOPxJO3I0htvAOvXAwcdJKObmjBrllT2DhokS6Mo/iwW6b20YoV0TNcApdD7ueeSc5cDJktEkWicCU2aFDQTKi+XGqYvvgCefz6B8aWB1lqXWCyWJl9KOxOHw+FLqpTb22w233XNE6jGtN7jTcnhi4tl4abqtm/371emmf1W0sDBB/uzZY0UCg0cKK21du6UqeJkw2SJKFKNM6GFCwPepHNn4I475PjWW2XrCYqfUFqXmEwmeDweX3Kk7Cjg8Xhgs9lQXV2NkpKSgPctLy9HXl6e76tbt24xjT8aX30FfPqpLDQbO1btaPZZuFAqznv0AC64QO1o0ouSnNps0jldZc23sNuzR914wsVkiShSnTvLRruArJLbti3gzaZMAQoKgM2bJb+i2Ii0dQngT5CUpEjZq9JsNqOyhSXXWu7xpowqmc2yYFN1Xq9/VGPCBKnwpcQ5/nip8N+zR1bGacCVV8qg14YNwOuvqx1NeJgsEUVjyhTpRNlCJpSTAzz8sBw//LD0X6LoqdG6RKs93v74A3jxRTnWTLuAjz+W1s0dOgCjRqkdTXpShnIqKzXRIbdtW5kiBjSzhV3ImCwRRaNt25AyoYsuAkwmaXvy738nML4UwdYlLauslNfWSSdJywpNUP4ajhwpG9RR4l18MdC9u3ROV7JplY0dK1PFS5cC+3Y6SwoZXm/yb/dZV1eHvLw81NbWauaTHqURrxc46yzA4ZCddF95JeDN1q6V3jd798pNBw9OcJwalOzvXS3Ev2uXNJf/7TcpEdLEKrh162Tu2euVvVeOOUbtiNJXRYWUCRx3nBS2BdjTMtGGD5fcbeRIYN489eII5/3LkSWiaGVkSDfvrCzZM+7DDwPerE8fac4GyOxdshU4kjYtXiyJUufOUq+kCTNn+j9EMFFS1w03SOf0r7+WFQAaoEwVv/iiTCEnAyZLRLHQt69/CdLkyUEzoXvukQbGa9ZoZusmSmKNt1wbOxY44AB14wEgCx2UteGaKaBKY3o9cPXVcqyRQqH+/WXKeNeu5DkPMlkiipWpU/2ZkNUa8CZ6PXDffXJ8553J2ZyNtOPzz4GqKkmSlMJZ1T33HFBbC/TsCZxzjtrREOAv9H79deCXX1QNRaGxLexaxWSJKFb0euDee+X4zjulv0wAFosMRG3dKiNNRJFS9nIePhw45BB1YwEgzVmVdgETJ0q3e1Jfnz5SJNnQIFOkGmA2y9Tx5s3SCkrr+EomiqXiYsmE3O6gmVB2NvDYY3I8e7YMRBGF6+ef/WsJbrxR1VD8HA7g+++BTp2Aa69VOxpqTBnKmTtXdvhW2QEH+CsXNNJkvEVMlohiqXEmNGuWLIELYPBg4NJLZWXclClSe0IUjieekIECkwk49li1o9lH+at33XVAEq5uTGnnnSc94Twezey9VFwsSdMXX8iXljFZIoq1EDOh6dOlYeUHH8gGqEShqqvzb7l2003qxuLz44/A22/L6tAJE9SOhprLypKpUUCSWg18QjvkEGDYMDnW+ugSkyWieJg+XT4yORzAm28GvInBANx8sxzffLMmGuxSHFmt8kl69eroH+vpp2Wfwd69gbPPjv7xYuLJJ+X7eecBvXqpGwsFdt11sp/lt9/KpzQNUGrPX34Z2LQp+sebM0fOp7EeqWKyRBQPjTOhm24C6usD3qysTIocXS7/7B2lppdekoRp1aroHmfPHv+n8Btv1EgNdV0d8Oyzcqz89SPtycvz15JpZCjHaAQGDpTX9Zw50T/eq68CjzwCfPdd9I/VmBbeZkSpKYRMqGNHYNo0Ob7//th8siJtOvJI+f7zz9E9zuuvy2Pk5/vb56hu3jwZ6jrmGGDIELWjoZYoU6RLlgDV1erGso9Sez5nTvQj7OvXy/fu3aN7nOaYLBHFS6dOTTOhzZsD3uyqq6RJ299/S35FqSlWydIjj8j3ceOkMbPqGhqk2hyQmhgNbKdBLTj6aODcc6VmSZk6Vdkll0hys2ULsGBB5I/j9QIbNsgxkyWiZKJkQtu2Bc2EMjP9I+ILFmh/VQhFpkcP+R5NsvT558Dy5VIOp2ydo7r33gN++kmmeDQz1EUtUqZKn3lGRgRVlp3tb38xfbqsjYlETQ2wfbscH354bGJTMFkiiqfMTP8WA/PnA19+GfBmJ50km0oCMiTd0JCg+ChhlJGldesif4zGTSgPOyzqkGJDeX3fcIPMK5P2nXWWjDDV1cl5SQNuuAE48EBZVBlkTUyrXC753rkz0LZt7GIDmCwRxV///sA118jxpElBM6Hycvlb88UXsns8pRYlWdqwIbJNlNet83c61kwTyu++A/77X5l6Gz9e7WgoVJmZTdsIaODTWceO/tHSadMi62yglGDFYzEmkyWiRCgvBzp0kEzohRcC3qRzZ+D22+W4tFRm7ih1dO4MtGkjiVIkhfzTp8vftCFDNNSEUql5uegi/zwjJYeRI6Vx6I8/Au+/r3Y0ACR/y8mR0+TSpeHf/6ef5HvPnrGNC2CyRJQYXboAd9whxy1kQlOmSNeBzZslv6LUkZXlLzpVpgtC9fvvUl4CaGgRgMfjn8JRljNR8ujYEbj+ejlWplJVduih/nKEiorw789kiSgVKJnQpk3Agw8GvEnbtv7VTg8/HP4fVdK23r3l+7ffhne/xx+XJdX9+wNnnBHzsCLzzDOyhLNvXw0FRWGZMEGmUN9/X/b004Cbb5aQliwJ/33CZIkoFbRtKxkQIHMqQTKhiy6S/b7q64F//zuB8VHc9e0r34NsGRhQba1/o/hbb9XIyvy9e/1TcJMmaSQoCpvBAFx4oRwr7R9UdtRR0koAkNNkqLxe4H//k2MmS0TJ7uKLZe+4+nrgllsC3iQjQ1Y9ZWUBr72mmV0JKAb69JHva9aEfp85c2TR0jHHSCKtCUuWSMW5Xi/tMSh5KVOo8+fL1KoGlJTI9+efB375JbT7bN4M/Pmn1K4rI7ixpFqyZLVa4XA4UFpa2uR6j8eD4uJilaIiirOMDOnmnZUlffk//DDgzfr2BcaOleMpUyJbPUXa03hkKZTVPtu3+9sFlJZqZGsTwN8YbPRooH17dWOh6Jx5prww//7bXxinsgEDJKzdu4H//Ce0+3z9tXzv3Ts+zVpDfut5PB5UVFSgolnVlc1mg81m8yU/oT4WAJhMJrhcLrgaTUc4HA643e5QwyJKPiFmQlOnygf3NWtkTzFKfr17S8JTUyNF262ZNUtud8QR/t3ZVbdmjST5WVka6oxJEcvI8DepfPLJyDtCxtjUqfL9mWdCa+Sq7Ll43HHxiSfkZMnhcKCmpqbJdS6XC3a7HWazGRaLBdOUrR1aodPpYLFYYLVaYTAYYDAYAEjiZTabwwifKEkpmdDq1cDcuQFvotcD990nx3feCfAzRPJr184/RdBap/a//vKvA7j7bunarQnKqNKll8Z+TwlSx1VXyQln3TqZYtWA006T2s09e2S3qNZoJlkym80oKChocp3D4YBOp/Nd1ul0vtElZbSp8ZdN6ai2j8VigcfjgcvlgtPphNFojOK/QpRE9Hrg3nvl+I47gmZCFosMRLnd8geTkt+pp8r3Zctavt2MGTIC1auXhnYRqamRQhLAPxpBya99e5lSBfzJsAYoo0vz5rW856/X638/nXhifGKJaga8uroa+fn5vst6vd43xaaMNjX+UkaNbDabL6kqKCjwJVFOpxM2m82XPAVTX1+Purq6Jl9ESae4WCp+3W7gnnsC3iQ7W0qcAGD27PAKg0mblGSppaZ7W7YADz0kx1OnyutAE55+GtixAzj+eGDgQLWjoVgaN06mVj/8UEa8NeCUU4Czz5aZwZb6i7lcwMaN0vR1wID4xBLzcsFQ6o1MJhM8Hg9sNhuqq6tRUlICo9EIs9kMt9vtS7iCKS8vR15enu+rW7duMYqeKIGys/3N4GbNCrqefPBgmfHYu1dKnCLZBoC0Q8kxqqqCLz667TZpGXD88UBRUaIia8WePf52AZMns11AquneXU40gGbaCACy9UlmJrB4MfDxx4Fvo6yTOemk+K03iCpZaj4t53a7ffVHLdHpdDCbzTCbzaisrGzybxaLBdXV1S1OyZWVlaG2ttb3tWHDhsj+A0RqGzxYmors3SsbfgXJhKZPl20APvgg8k0mSRsKCqQNwJ49gctDqqpkAAeQv1maWQH3xhuysd3BBwNXXql2NBQPytTqc8/JlKsGHHccMGaMHE+aJCvkmnv1Vfl+7rnxiyOqt6HJZEJVVZXvssvlgslkijqo1uTk5CA3N7fJF1HSevhhqd6124G33gp4E4NBOtsCwE03STdnSl6XXy7fFy1qev2OHbLdg9crNbeamulSalmKi2O/pTtpw8CBwAknyAnmqafUjsbn3nv962GURS+KLVsAZSH+0KHxiyGs1XB2ux12u91XY2QwGFBUVOQr5i7TzKZFREmkeSZUXx/wZmVlshmry+WvY6LkNGKEfH/7bf+WDl6vbCT63XfAYYdp7He8ahXwyScydax8zKfU07iNwMyZmmnwlp8vlQoA8MAD/uQIkBx+zx4p7D7qqDgG4U0BtbW1XgDe2tpatUMhikxdndfbubPXC3i9Dz4Y9GYLFshNOnTwejduTGB8caLWe9doNHpNJpO3pKSkxetaE038l14qv8sBA7zedeu83gkT5HJGhtf73nthP1x8XXedBHfllWpHQvG2Y4fXe/DB8vtevFjtaJq49lr/+e/VV73e//s/rzcnJ/JQw3n/Zni9yV8uWldXh7y8PNTW1nJKjpLXggUyB9Oxo2xy1LnzfjdpaJAVIl98ITedNy/xYcZSqO9dj8cD677OnCXKXgiAb5RbqZcMtQwgUE+3SPq8RXPu+flnqcdovph31ix/z1JN2LIF6NZNRjyXL4/fciPSjjvvlOZGAwcCn36qdjQ+O3fKVnbN+1+fe66M0oa75iCc969WSgeJaMQIWc6xbZsshwogM9O/gG7+fODLLxMYn4pi2RRXuW/z7ZYCXRdPRx4pm70rTSp79ZIaak0lSoC0j6+vl3mO/v3VjoYSYexYmXJduhRooY1PorVtK2Wdt9winykzM2W16EsvxX9xJkeWiLTkiy/8n9y//DJoh7WRI2Ugqn9/4LPPNLRiKkzhvHetVis8Ho9vZMlqtaK6utqXJA0dOhTFxcUwmUyw2Wz7tTHR6/X7jRxZrdb9rg90naK+vh71jWrK6urq0K1bt6jOPV6v7AHXvr0GV+Pv3i1Z3aZNskJKKbai1Dd8OPDii5odwt6zRxYR5+RE/hjhnH+00uqMiADJfq65RjKhSZMkEwrwF/TBB2W57BdfAAsXaqjDcwK11hQ3GKUhrtLvTa/XB7wukPLyckxV2grHSEYG0KFDTB8ydl55RRKlww4DrrhC7WgokSZPlmTpxReBigrgkEPUjqiJ7OzENmtN0s+jRCmsvFz+en7+uWRCAXTuDNx+uxyXlsrMHYXXFFdJkMxmc8DrAkm7Hm9Ku4AxYzS0OR0lRP/+UhawaxfQrB9iOmKyRKQ1XbqElAlNmSJdBzZvlvwq3UTaFBfwJ0iNi8UDXddcWvV4q6qSgu42baS3EqWfyZPl++zZkjSlMSZLRFp0441Ajx4yBaJsPd9M27bSzxKQ7y5XAuPTALWa4qYNZVTpyitlGo7Sj9ksw9ibNwP7Vp6mKyZLRFrUOBOaPh1Yty7gzS6+WHZMqa+XFSKpik1xE+y332SJESCdMik9HXCAf3mmkjynKa6GI9IqrxcYMkQ2hLv88qCf7NaskQ1X9+6Vmw4alNgwo5Hs791kjz+oqVOBe+4BTj5ZFhlQ+vrjD+mztWuX1FGmUPsI9lkiSgUZGbLnRWamrEr66KOAN+vb1//hb/JkzexQQMmqvl5qVAB/zQqlr0MOAYYNk+M0Hl1iskSkZSFmQlOnykaTa9ZID0GiiC1eDPz+uyw0uOwytaMhLVD2i3v5ZamjTENMloi0bupU4MADZcvtuXMD3kSvl525AdmpIIQV9ET783r9LeLHjZOVcERGo2x9smcPMGeO2tGogskSkdbl54eUCRUXy0CU2y3lJkRh+/xzYMUKaYtssagdDWmJMiU7Z45s0pZmmCwRJYMxY4A+fYCaGhlpCiA7W0qcANmMdc2axIVHKUKpSRk+HDj4YHVjIW255BIp9N6yxb9SMo0wWSJKBtnZ/umRmTOBb78NeLPBg4FLL5WVcVOmyKwKUUg2bvSvuFRqVIgU2dnA+PFy/PjjaXdyYbJElCwGD5ZPd61kQtOnS3uUDz4A3nwzoRFSMps9W2pSTj9delEQNXfDDUC7dsBXXwHLlqkdTUIxWSJKJkomZLcDb70V8CYGA3DzzXJ8002yEpyoRTt3+vf/4qgSBZOfD4wYIcfKSHeaYLJElEwKCiQDAlrMhMrKZJcCl8tfx0QU1KJFwJ9/At27S1t4omCUju6vvQasX69uLAnEZIko2dx2m2RC1dVBP9116gRMmybH998vWzsRBdS4XcD48VKbQhTMP/8p2wTs3SsrSdIEkyWiZNOpk39z3fvuk328ArjqKtmZYNs2GWkiCmjpUmDVKqlFueEGtaOhZKBM1VqtwPbt6saSIEyWiJLRiBHASSdJJnTbbQFvkpnpHzCYPx/48ssExkfJQ2kXcPXV0t2UqDUXXAD06AFs3QosXKh2NAnBZIkoGTXOhJ59FqiqCniz/v2Ba66R40mTgIaGBMVHyWH9eqk9Afy1KEStycoCJkyQ4zRpI8BkiShZDRggowGAZEJBTljl5UCHDsAXXwAvvJDA+Ej7Zs2S2pNBg6T9O1GoRo2SE8vatUE3+U4lTJaIktmDD8oJ6/PPg2ZCXboAd9whx6WlMnNHhO3b/XsNKltZEIVKpwNGjpTjNGgjwGSJKJl16QLcfrscl5QEzYSmTJH+S5s2yUgTERYulI0Ee/QAzj9f7WgoGSlTt2+9JX1KUhiTJaJkd+ON8gdv0yZ/v4Bm2rYFHn5Yjh9+OOXPa9Qar9df2D1hgtSgEIWrd2/g7LPl9fTkk2pHE1dMloiSXeNM6KGHgHXrAt7s4otlx5T6euCWWxIYH2nPRx/JTssdOkjtCVGklCncp59O6Tl+VZMlj8eD4uLiVq8jolZccokU6baQCWVkSDfvzEzg1VeBDz9MaISkJcqo0siRUntCFKmzzwaOOgqoq5MeJSkq5GTJ4/GgoqICFRUVTa632Wyw2WywWq1wOBxhPbnD4YDb7W71OiJqReNM6JVXgq5O6dsXGDtWjqdMkX1TKc2sW+ffYZntAihamZn+19ETT6Rsf5KQkyWHw4Gampom17lcLtjtdpjNZlgsFkwLUi8RiM1mg9lsbvU6IgrRP/8ZUiZ0773Se3D1amnAS2nmySelxuTss6XmhChaI0cCubnADz8A//2v2tHERcjJktlsRkFBQZPrHA4HdI2GcHU6nW90SRltavxls9kAAE6nE0ajscljBboumPr6etTV1TX5IiIAU6cCBx4IfPMN8NRTAW+i10vCBAB33ikLoihNbNsmtSWAf8sKomh16uSvfVOmeFNMVDsmVldXIz8/33dZr9fD4/EAQKsjRE6nE06nEy6XC06nM+B1wZKn8vJyTJ06NZrQiVJTfr5kQhMnSnOloiJJnpopLgZmz5Z+cvfck7LnN2puwQKgthbo1Qs45xy1o6FUMmGC9Ft6910ZYTr6aLUjiqmYF3iHUm9kNBphNpvhdrt9yVWg64IpKytDbW2t72vDhg0xiJwoRYwZA/TpA9TUSCYUQHa2v4/crFmSNFGKa2jwZ8UTJ0qtCVGsFBTInnFASrYRiOrd0nxazu12w2AwhHx/i8WC6urqJiNIga5rLicnB7m5uU2+iGif7Gwp9gaAmTOBb78NeLPBg2UR3d690qopDbZ3Sm92u3ziz80Frr1W7WgoFSlTu/PmyQhmCokqWTKZTKhqtIGny+WCyWSKOigiipLJJI2V9u6VYu8gmdDDDwMHHCB/R5UFUpSilKHEUaOkxoQo1gYPBv7xD6mNe/ZZtaOJqbBWw9ntdtjtdl+htsFgQFFRka+Yu6ysLG6BElGYGmdCS5YEvInBANx8sxzfdJO0aaIU9MMPUkuSkeHfLZ4o1jIy/KNLTzwhH9ZSRIbXm/yD73V1dcjLy0NtbS2n5IgaKyuTzXZ79pSOzTk5+93kr7+kFnPzZrlpaWniwkv2927SxD9hgkzJXnghhxApvv7+G+jWDdi6VV5rF16odkRBhfP+ZYUfUSq77TbgsMOAn34KujN4p06SJAHA/fdL0pTqCgsLMWTIEJTuywyVnQNaW1ySlDweqSEB/FtTEMVLhw7ADTfIcZBzTjLiyBJRqps/Xwp6O3YEfvxRkqdmGhqAk08GvvxSbpqocoNQ37sejwfWfR00S0pKfNcrJQHK4pJQayabN8B1Op0YPXq077LJZAqpyW5SnHsefVTmWPv0kU6kGRlqR0Sp7pdfZI6/oUFGtPv0UTuigDiyRER+V18NnHSSFF3edlvAm2Rm+leVz5sHNFq3oQmx3kHA5XLB4XD4RpZ0Oh1WrlyJlStXoqysLKzH0rS9e6V2BJBaEiZKlAhHHCFLbYGUaeLGZIko1WVm+ofDn302aCbUvz9wzTVyPGmStrZ4iuUOAoCMTplMJhQUFMBms/lanlit1hZHp5Ju94AlS2QvOL0eGDFC7WgonShTvs89lxLbBETVwZuIksSAATLC9NxzchJbtizgKEN5uezD+/nnwAsvaPvva6Q7CCgJlclkgsfjgV6v9/2b3W6HxWIJet+k2z1ASZJHjwbat1c3Fkovp50GHHcc8PXXsvVSo+nzZMSRJaJ0UV4uxZfLlwMvvhjwJl26ALffLselpTJzl0xC2UFASZKUpElJrJonToEk1e4Bq1cDH30EZGUB48apHQ2lm4wM/+jSzJlBN/ZOFkyWiNJF167+mqWSElniG8CNN0pt5qZN/lVyWhTNDgJmsxkmk6lJsbhOp0NlZWWL90uq3QOUWpFLLwW6d1c3FkpPw4YBBx0ErF8PvPGG2tFEhckSUTq56SbgyCOBjRuDZkJt20o/SwCYPl1KXrSIOwi04M8/geefl2O2CyC1tG0ru3YDSV/ozWSJKJ00zoQeegj4+eeAN7v4Ytm5oL4e+Pe/ExdeMNxBIExz5wI7dwJGI3DqqWpHQ+ls7FjZr/KTT4BVq9SOJmLss0SUbrxe2Tvuww8BsxlYvDjgzdaskfrMhgbggw+AQYNiH0qyv3c1Gf/u3UCPHjJ6OH++f4kjkVqGDQMWLQKuuw545hm1o/FhnyUiCi4jA3jsMWkpYLMBH38c8GZ9+8qHQkD24k3y+sz08dprkigdcghQVKR2NET+/eJeeAHYskXdWCLEZIkoHf3zn8CYMXI8eXLQTGjqVODAA2Vh1dy5CYyPIqe0CxgzJuBegEQJN2AAcOKJMq+/rxN/smGyRJSu7r1XMqFvvpE+KAHk5wP33SfHd96ZEr3lUtuKFcBnnwFt2viHBYnUlpHhH12aNUumipMMkyWidJWfL0NHAHDHHbJLeADFxbK1U00NcM89iQuPIqCMKhUVBdwDkEg1V1whr8lNm6TzbZJhskSUzsaO9WdCQTpTZ2f7/wbPmgWsXZvA+Ch0mzcDL70kx8qneCKtOOAA/9S/ckJJIkyWiNJZdrYUewPAk08C334b8GaDB8u+mHv3StPK5F9Dm4IqK2V64+STpT6ESGvGjJEp4s8/B778Uu1owsJkiSjdmUzSWKmVTGj6dPlwaLcDb72V4BipZfX1wOzZcswmlKRVhx4KXHmlHCdZk0omS0Tkz4T++1/ZqT6AggJpAA7I9/r6BMZHLXvpJeCPP2RLm8suUzsaouCUZP7ll2XqOEkwWSIioGdPGVUCWsyEbrsN6NwZqK5OyrKD1OT1+n8Z48fLNAeRVhUWAqecIlPGc+aoHU3ImCwRkbj9dlmt8tNPQYfIO3Xybyl3331J9cEwdS1bBjidspXN6NFqR0PUOmV0ac6cpBmiZrJERKJ5JvTbbwFvNmIEcNJJwLZtMtJEKlMS26uukh3eibTu0ktlyviPP/wrODWOyRIR+V19tayk+usvGWkKIDPTP+szbx5QVZW48KiZDRuAV1+VYxZ2U7Jo00amjAFJ9pNgeS2TJSLya5wJPfusdIQOYMAAyasAaemTBOe61PTEE7KK8YwzZAsbomQxerRMHa9cKV3nNY7JEhE1dfLJMtfm9baYCT34INChg7RMeeGFBMdIMg+q7LOlLFMkShYHHSRTx0BStBFgskRE+1MyoeXLgRdfDHiTLl38M3UlJfK3mxLo2WeB2lqgVy/g/PPVjoYofEqn+VdekSllDWOyRET769rVX71dUgL8/XfAm914I9Cjh2z3pNSGUwLs3evvvH7jjTJ9SpRsjj1WppD37vU3VdUo1d5hhYWFGDJkCEpLS5tc7/F4UFxcrFJURORz003AkUcCGzcC06YFvEnbtsDDD8vx9OnAunWJCy/prF0LvPZa0FWGYXnzTcDlAg48ELjmmugfj0gtyuiS1Qrs2BH94y1fLtsM/P579I/VSMjJksfjQUVFBSoqKppcb7PZYLPZYLVa4XA4Qn7isrIy2O12TGt2EnY4HHC73SE/DhHFSeNM6KGHgJ9/DnizSy4BBg2Sdim33JKw6JLP6NHSXXvp0ugf69FH5fuYMTJdSpSsLroIOOII2cw7FsWPDz4InHWWfDCJoZCTJYfDgZqamibXuVwu2O12mM1mWCyW/RKflrhcLjgcjiYjSzabDWazOeTHIKI4u/RS4MwzgZ07g2ZCGRmygC4zU0oPPvoowTEmiyOPlO9Bks6QVVUBn34qy68nTIg2KiJ1ZWX5X8ePPx790tr16+V79+7RPU4z2aHe0Gw2w+12w+Px+K5zOBzQ6XS+yzqdDg6HAyaTCTabbb8RIr1e70uGSkpKAEjSZLPZYDAYYDQao/ivEFHMZWRIbcwJJwA2G/Dxx1Jj0EzfvsDYscDMmdLux+kEskM+u6SJWCVLyqjSlVdKlT1Rsrv+euCee4DVqwGHAxgyJPLHUjtZCqS6uhr5+fm+y3q93pdMtTRCpEzXmUwmeDwe6PV6AIDT6YTT6YTL5YLT6QyaPNXX16O+UYv0urq6aP4bRNSSY4+V6Z5Zs/yZUFbWfjebOlVG0VevBubOleSJGunRQ75Hkyxt2CAbkAL+vfyIkt2BB0rCNGMGUFERebK0bRugDNLEOFmKeYF3KPVGSpKkJE1msxlGozHg6FUg5eXlyMvL831169YtFqETUTD33isntG++AZ56KuBN8vPlZgBw553+cxbto4wsRVMF/+ST/iaUJ5wQi6iItOHGG+VDmMMBfPVVZI/xyy/yPS8PyM2NXWyIMlkqKChoctntdsNgMIR0X7PZDJPJ5JuOU1gsFlRXV7c4JVdWVoba2lrf1waN92cgSnr5+TJ0BEhzpa1bA95szBigTx+p1VRuTvs0noaLpC7jr7+Ayko5ZhNKSjVHHgkUFcnxQw9F9hg//STfe/WKSUiNRZUsmUwmVDXaGMrlcsFkMkUdVGtycnKQm5vb5IuI4mzMGOAf/2gxE8rOlhrNTp1kgQs1okwLbN8O/Pln+Pe3WqUJ5VFHsQklpSZlEcnLL0c2AqskSz17xi6mfcJaDWe322G322Gz2QAABoMBRUVFvtYBZWVlMQ+QiDSiTRt/I8QnnwS+/TbgzQYPltFwDn40k5PjL8gO9w9BfT3wyCNyXFLCJpSUmo4/XuqV9u71L2QIRxyTpZALvE0mU8BRIy71J0ojQ4ZIX5Q335Qag/fekxVzzRx4oAqxJYNevaTd+fffAyedFPr9nntO7te1q+zbR5SqSkqkqeTTTwN33y0lAKHSwsgSEREAaVR5wAHAf/8LvP222tEklz595PvataHfZ+9eWSEEyHBdTk7s4yLSisGDZYRp+3ZZgRuOH3+U70yWiEh1PXv6l63feCOwa5e68UQg0HZLpaWlsNls++1SEFN9+8r3cJKlV1+VPwIHHihdwIlSWUaGjC4B0kogyL6U+6mr86+G69075mExWSKi8N1+O3DYYTLsPWNG3J8u3tst2Ww2FBQUwGw2+5rrxoUysrRmTWi393r9OxRPnCiV80SpbuhQ6Uv255+hb7D7zTfy/fDDw5u6CxGTJSIKX6dOQHm5HN97b2w2h21BvLdbat7fzel0xiTu/SjJ0i+/SAO91rz1ljQBbd9ekiWidJCdLc3aANnEO5T3yqpV8v344+MSEpMlIorMNdcAJ54o/X9uvz2uT2U2m/fr6xZsuyUAvtGmxl/KKl5AtlsymUwoKCiAzWaDxWJBTU0NHA4HVq5cGb//SH6+FGkDkgS1pKHB/wdj0iTgoIPiFxeR1lx9NVBQIKNLM2e2fvuvv5bvxx0Xl3C4exMRRSYzU5oqnXIK8Oyzsr9Jv34Je/pYb7dUVlYGnU4Hp9MZ9P4x2Wrp5JNln71ly4DTTw9+O5tNphZyc4NuYkyUsrKzgbvuAkaOlAUO48a1PA39+efyPU6d7TmyRESRO/lkWcru9cq+cdHuGB6lSLdb8ng8vtEng8EQdCeCmGy1dOqp8n3p0uC32b1b/lAAwM03A/sSOqK0Mny4NGF1u4Hp04Pf7s8//XWAp50Wl1CYLBFRdB58UGpqPvsMWLQoYU8by+2WdDodSkpKYDabWxyVislWS0qytGyZJEWBzJwJ/PCDTL1NmRL+cxClguxs4P775biiwr/arblPP5XvxxwDHHJIXEJhskRE0enaFbjtNjm+5ZbQl/pGSY3tlmKy1ZLRCBx8sGxd8vHH+//7H39IMz4A+M9/Yr4hKFFSMZtl4+idO4NPR7/5pnyP4/ufyRIRRe+mm2QjzI0bZfVKjKXUdktZWcAll8hxo6JzADKNOX689IwpLARGjUp4eESakpEhtZGZmcDixcAbbzT99127/NfFcUeRDK9X5SKDGKirq0NeXh5qa2u5qS6RWl55RU5WbdsC330nyVMrkv29G3H8H3wgn4I7dADWr/fXJD3zDHD99TL98PnnkjARkTSqfOghWVH69df+VaXz5wPXXiv7Lq5fLx9GQhTO+5cjS0QUG5ddBpx5pgyXKx14KbBBg2SJ899/+9suvPUWMGaMHN97LxMlosbuv19WutXUAGefLb3dtm5t2l4jjEQpXEyWiCg2MjKAxx7zD5d/8IHaEWlXRoZ8SgaAOXNke4aLL5aC76IioNE2LEQE2Y/ylVdkBGntWuDoo4F//APYsEG6fU+YENenZ7JERLFz7LHSbwkA7rtP3Vi0bsgQ4JFHJLn84QepVxo3DliwQK4joqZ69AA++khGZevqZHSpc2fg9ddlSjuO2JSSiGKrvFyaxyVLwbWabrxRRpS++koSzV691I6ISNuOOgpYuVL6lP31l0z9xzlRApgsEVGsNd43jlpnMMgXEYUmKwv4178S+pQc6yUiIiJqAZMlIiIiohYwWSIiIiJqAZMlIiIiohYwWSIiIiJqAZMlIiIiohYwWSIiIiJqAZMlIiIiohYwWSIiIiJqAZMlIiIiohYwWSIiIiJqQUrsDef1egEAdXV1KkdCROFQ3rPKezjZ8NxDlLzCOf+kRLL0119/AQC6deumciREFIm//voLeXl5aocRNp57iJJfKOefDG+yfqRrpKGhAZs2bUKnTp2QkZHR4m3r6urQrVs3bNiwAbm5uQmKMHniAbQXk9biARhTrOLxer3466+/0KVLF2RmJl9VQDjnnsai/V2pfX8txJCI+8fqNrGIJZXvr1YM4Zx/UmJkKTMzE4cffnhY98nNzdXEHxSF1uIBtBeT1uIBGFMoWosnGUeUFJGcexqL9nel9v21EEMi7h+r28QillS+vxoxhHr+Sb6PckREREQJxGSJiIiIqAVplyzl5OTg7rvvRk5OjtqhANBePID2YtJaPABjCoXW4tGSaH82at9fCzEk4v6xuk0sYknl+2slhpakRIE3ERERUbyk3cgSERERUTiYLBERERG1gMkSEZFGWa1WOBwOWK3WmDyezWaDzWZDaWlpxI/h8XhQXFwc8f0dDgdsNhsqKirg8XjCvr/NZoPD4UBFRUXY9yssLGxyXTg/30D3b+nnGe7t4xFz48eJ5GfWWLS/NyC61064P7tYv3dSos9Sazwej+8HVlJS4rveZrPB7XZj5cqVGDp0KEwmk+96AHC73TAYDL7rExVToOdOREzNY1CYzeaExxBIRUUFDAaDpmJSYtDpdKr8rprHodbrOVAsiX7OZBDO+97hcGD79u1wOp1YvXo19Hp92K/7xs9nMBh8r9PXX38dxcXFKCwsbPX30zxmh8MBt9sdUQxmsxl2ux3Tpk3D/PnzfY8V6P6BflYulwuvv/46LrnkElRXV+O5557D1VdfHVLcZrMZlZWVvriXLVsGALBYLLDZbJg/fz5+//133+2V29ntdhx66KE4/PDDm2yL0fh973K5YLVaccUVVzR5zsrKSt9tly9fjoaGBpx//vnIz8+H1WqFxWJpNXa9Xu+7/q677vLF+Ouvv8Jms/leE8Eeo6amBvn5+SgpKYHH48HMmTNx6KGHxu33FuznD0jC9c033/jOVaGeG2w2G7Kzs/G///0Pq1evbvKzC/beAQCTyeRLsoL9nEKVFsmSw+HwvWAUTqcTgLxRPB4PevToga1bt8LlcsFut/te5EOGDInLiT5QTMGeO1ExAfICd7lcvhd3cXExzGZzQmMIZMiQIVi8eDF0Oh0KCws1ERMgP6/y8nKUlZUBCP47jDe1X8+NaeH3olXhvO+dTie2bduG+vp6tG3bFlVVVWG/7hs/n/LHwuVyYeXKlVi4cCGMRmOrv5/Gj6H80Xn66acjisHhcPj+YM+dOxerVq0Kev9APysA+Oyzz/D7779jyJAhWLBgQdBkKdD9t2/f7ovb5XLhpZdeAgDodDo8//zzOProo5Gfn+/7GZeWlsJut2P58uWw2+2+9zmAJn98q6urUVxcHPLv12AwtDjCEuxx3n//fTzwwAMwmUwoLCxEfX190CSg8WNUVVVhyJAhMBqN8Hg8cf29Bfs/2Gw2GI1G/P77776YQz03mM1m2Gw21NTUoKamBv369fP9TIK9d4xGIwD53drtdiZLoTCbzXC73U2GDt1ut+8HqNPpoNfr4XQ6sWLFCuh0Ot/tdDodHA5HzE/2gWJyOBwBn9vlciUkJuWxKysrYTKZYDQafc8bLLZEJQLKczudTqxcuVL1mBQvv/wyioqKfJfViknt13NjWvi9aFU473sAOPbYY+F2u+F2u1u9vfIpuvFtAUnoG//RfeKJJ9C9e/cmf0xaur9er0dBQQHWrl3r+4Pzxx9/4Nhjj40ohoKCArRp0waHHnqob4Qg2P03btyIn376yZekvfnmm+jevTtKS0tRXFyMHj16hPV/d7vdTX52BxxwgO9n3fj5vvnmG2zZsgXTpk2DTqfzxZednb3f83333Xf4+++/sWLFCt/PqqXfb319Pdq3bw+j0Rj05x3sddKuXTvfdR06dMDPP/8MAC3+3jZv3owTTzwRRqMRw4YNw/nnnx/331vz+yvJi8PhQJs2bUJ+/sajqWazGcuWLcPhhx/ue+229N6JdKowmLRIlgIxmUxNTt5utxtGoxEvvfRSkzeXXq+P+Q89mOrq6oDPHez6eJk2bRoKCwthNBrxwQcftBhbIqxYsQIulwsulwuAjHZVVlaqGhMgiZvyJleoFZOWXs9q/16STbCfl9Fo9L3md+7ciRNPPLHF2wMI+OnZarX6/t3pdGLdunUYPHiw7w9Ya/dXHkO5v9PpxMaNG7Fz586wY+jXrx8cDgeqq6txyCGHhHR/j8fju+7dd99F//79YTKZYLfbMWzYsJD/7wCwY8cO38/OaDRiyZIlvn8fMWKEL0GpqanBscce6xsZ8Xg88Hg8aNOmTZPnczqdvj/oys+zeY1M49+X0+lETk4OTj31VDidzrBGO6qrq9GrVy9fQpGTk+Pbaqel39s333yDhx56CAaDAZdddhk2bNjg+/d4/t4a31/5v7/zzjvYtm1bWK89hdPpxPbt29G/f3/f/UN573g8Ht97Jxos8Ib88Z07d27Qf2+e7SZSsOeOZ0xVVVVYuXIl9Ho9Bg8eHPR2ifq5eDwe6PV6GI1GGI1GrFixwjftpFZMgAwBKzVULUn060eLr2c130PJyO12w2QywePx4LvvvkNNTU2Lf0xC+fm6XC4MHToUq1atwuOPP97kPqHcv2vXrr4Rj8aJUjiPoYwI/PDDD9iwYUOTmp1Q7t+7d2+sXr0aDocDTqcTxxxzTMivLWUqafXq1QDkA0Z9fT2WLVsGl8vV6h/rZcuWoa6uDna7HYD/51lZWYnCwsL94lBmBX744Ycmt//uu+9w8803hxT3jz/+CJfL5ftA1qtXL3g8HjgcDtTV1eHoo49u9TGOPfZYX4H377//jv79+zf590T83oxGI8xmM3bs2LHfayec1+4nn3yy32u3ucbvHeV3EO0UHJACI0sVFRWoqanZ73qloK01NpsNQ4YM8f0wmw+hKkVjiYippeeONqZQY1N+HkajEXa73TcPH4ufS6QxGQyGJs+l1+vhcrlUjUkpNrfZbKiqqkJ1dTUMBkPcYgr1NRWP13O41HhOLQj3fa/cftWqVaivr/fdd/ny5Rg6dCgAKYy1Wq3o3Lmz737Kz1e5/8cff+wbgW7p+QwGA6qrq32f9k0mEyoqKva7f0uPAcD3hzKSGJT/0+WXXw4AvpVNyv09Hk+L58g+ffqga9eucDqdqKmpwfLly7Fjx46Qnlf5/zZ+bXbv3h3nn3/+flPEys9Y+e52uzF06FD8+uuvvt+N8vMMxmQyNfl5K7cfOnQoiouLQ5qW7tWrl++DjzLqpfz/KisrQ3pftWvXrkmBfKTvTeW1GM17+/LLL8fgwYN9yVeo9w/02gVaPtco/+eYTf9700RlZaV32rRpTa6z2+1eu93u9Xq93pUrV3qrq6u91dXVXrPZ7LuN0WhMWEzBnjvRMa1cudJ3efHixb6fTaJiaG7r1q1ek8nku2wwGLxbt25VNabGSkpKvIsXL/Z6vYn9XTWn9utZoZXfi1aF+r6P9PbRPl88HiPS+yf6eZXbK7dTviu3S8TPKpaPo/ZrJ1Y/i3g9XjjSYrsTh8OByspKePb1eFBWlDTuX+HxeHzLQhsvRWxcYBbvmFp67kTEpKioqPAVzakVQ3NK8Z/yCU0LMQHyeywtLYXBYMC0adN8o02Jjknt13Nzav9etCrc9324t4/2+eLxGJHeP9HP2/z2Crvdjo4dO+Loo4+O+88qlo+j9msnVj+LeD1euNIiWSIiIiKKFAu8iYiIiFrAZImIiIioBUyWiIiIiFrAZImIiIioBUyWiIiIiFrAZImIiIioBUyWiIiIiFrAZImIiIioBUyWiIiIiFrAZImIiIioBUyWSLNcLhcqKipgs9l8ezW5XC6VoyKidMDzDzXGveFIswoLC7Fy5UoAslmiy+WCTqeDxWJROTIiSnU8/1BjHFkiTbJarTCZTL7LOp0Odru9yXVERPHA8w81x2SJNKugoGC/6wwGgwqREFG64fmHGmOyRJp0xRVXYOXKlbDZbLDZbADk051yTEQULzz/UHOsWSIiIiJqAUeWiIiIiFrAZImIiIioBUyWiIiIiFrAZImIiIioBUyWiIiIiFrAZImIiIioBUyWiIiIiFrAZImIiIioBUyWiIiIiFrAZImIiIioBf8Pu8ye1BW1HQQAAAAASUVORK5CYII=", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -180,21 +158,10 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "id": "0fcea250-ab16-4d75-b437-254e07cb70cb", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -218,21 +185,10 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "id": "f09ef1fb-3287-4c23-953e-a9325f45a419", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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NAwAGdnl1Y2qM00XUFfKFfexhVH9QZKCdNeNyP4lEomrFv2jYQqOuUNlCQ4GBdpaOurCjaBho1BXyhX3kymNobKGdrtqrUdc66sKOgDhXqwXY5aQukdvZw75WDrRCtrPFnISmAXttnswYGNF3yGpSLBazdVzthR0N0WjUshtqdbXadq1FY6BRV9DH0Lo40PaeAf/8Sns/41c2gcHRpl9m5yTxRhd2BMS6Wi3ALid1iXxhH3mNXc5WpFIpyLKMeDxubjGZSqUwNTUFVVWRSqVw4cIFxONxyLKM2dlZAIcXdoxGowgGg1UXdIzFYg3DaXV1Faurq+bVNmqvmWa1eVKr2EKjrpAr7GG/m1toAyN6C6rdn3GERlehDQQCZgstEAhgenoaXq/X3PDI6B42OvkcEOtqtQBbaNQl8t0+y+lw6N3Bdt6OGT+LRCJIJpMIBoNYWlqyPK6ZjY1EulotwECjLqHPcnIdWiuMq9Cm0+kj98xtJXCsrlZbuTFxoz19T0tTXU5jatYo6Kg9N421K9yXk05DvrCPPXOWk4F2EsZVaAGYV6E1dne6c+cOpqenoSgKVldXMT8/j1gsZv4NW7XajKvVGgEVCoXMsbpEIoFMJtPwarU3b95sz3+kZlM6ndbm5+fNx6FQyPLYra0tLRAIaGtra3bfXstmsxoALZvN2n4NnR8//a/+r/ZTv/wbmvaOW9NWXul0Ocfa2dnR3n//fW1nZ6fTpbRVMpnUotFo3fdjsZi2tbXV8DXhcNjy/ax+bnbzwXaXMx6PV6W0JElVi+Yq3blzB3Nzc0e+X7FYRC6Xq7oRWeHCWjGJdLVaoIkxtHQ6DZ/PZz72er11A4KAPg1sp5u5tLQEj8dj3iYnxb5GPHVWvrCHnNHl3C8A+7udLYhMolytFmhxUqDRlK3d7a4ikQiy2ax529jYaKUU6nG5wj62UbEsga00YYhytVqgiUCrPd+r0UyFcZ6WMSAYi8WQSqUavp/L5YLb7a66ETVS2DvA7n4JJTihGSvhu2QtWqlU6nQJXUVrcRM627OcoVCoaupVURSza2n0l419/wD9MiPXr19va/OSzod8Yf/wwZAE7D4VPtAGBwfhdDqxubmJiYkJDA4OwnGC8yzPE03T8OjRIzgcDgwMnGxnL9uB5vf7MTc3B1mWkclkqgb2gsEgksmkOQgYj8cRj8ehKErVSmSik8gX9gAA465+OFxuAPeF73I6nU5cu3YNDx48wOZmm88Q6CEOhwNXr15FX1/fiV7f1Do0q/5v7SxHKBRCMpk8UUFEtXLlFtr4UD8wVB6a6IK1aIODg3jxxRexv7+Pg4ODTpfTFQYGBk4cZgDP5aQukNvRW2ju4YHD3Z8E73IajO7TSbtQ1Bye+kTCyxUqAq28P6foXU7qDAYaCS9rtNCGBrqqy0lnj4FGwsvt6GNonsouJ1to1AADjYRnttCGKycFumMMjc4WA42EZ4yheSrH0Bho1AADjYSXqxxDc3FSgKwx0Eh4RpdTb6Gxy0nWGGgkPGNhbdWyDc5yUgMMNBJerrKFxllOOgIDjYSXazjLmdM37yWqwEAjoWmadnimwFBFC620B+ztdLAyEhEDjYS2s3eAvQO9JeYZHgAGxwBH+deW3U6qwUAjoRlnCfQ5HRgZ7AOcTsA1rj/JiQGqwUAjoak7+t4BnuGBwwskci0aWWCgkdAy23qgeUcHD79pTgyoZ18QCY2BRkLLPGsUaFyLRo0x0EhomaflQBupCDSuRSMLDDQS2hOjyznWqMvJQKNqDDQS2la5y+mr7HIOX9Dvd+r3haXzrak9BWRZBnC4J2ejHdKNXaGSySRmZ2dt7aJOZOVJuct5obLLOXpRv99+1IGKSGS2A01RFMRiMUSjUQDAzMxMXVgZmwrPz89DVVVcu3YNW1tbp1gunTdb5UDzVXY5Ry/p908ZaFTNdpczHo+b+24C+rbu8Xi86phMJoNYLGY+7/V6LXdOLxaLyOVyVTeiWplGLbQxI9A+7UBFJDLbgZZOp+Hz+czHXq8XqqpWHRMKhcwWHKAHnNXO6UtLS/B4POZtcnKyydLpPDC6nFXLNowWGrucVKOlSYFMxnpQdmFhAe+9957l85FIBNls1rxtbGy0Ugr1IE3TGnc5xyb0+6ef8oobVMX2GNrU1FRVi8yYGGhElmXMzMxY7rQOAC6XCy6Xy36ldO7kCvvYL+mBVT0pUG6hHezqV64dls6+OBKS7RZaKBRCIpEwHyuKYk4KVAadMdYWDoeRSqWgKMrpVUvnyuPtIgBgzNWPoYG+wycGhg4X13JigCrYbqH5/X7Mzc2ZyzIikYj5XDAYRDKZRCaTwezsrPl9VVWhsUtAJ/QwWwAAXHY3aMmPTuhnCmx/Clx89YwrI1E1tQ7NqguZTqcB6DObXKZBp+VhXg+05zxD9U+OXQIyac50UhWeKUDC+iSrdzkvjzcItNHyxABnOqkCA42E9TBX7nI2aqGNP6/f5+6fYUUkOgYaCcsItOfcDQJNKq9bzN47w4pIdAw0EtYnuSMmBTxX9fss1y/SIQYaCev+lr6r0/Oe4fonPWyhUT0GGglpZ/cAn+b1SYGXfCP1BxiBln8AHOydYWUkMgYaCWlj6xkAwD3UD6nyLAHD6ATQNwhoJU4MkImBRkL66IkeaC82ap0B+nZ20kv61xmejUI6BhoJ6eOMHmgveUetD7r4mn7/+IdnUBF1AwYaCenu420AR7TQgMNTnhhoVMZAIyF98CAPAHj9uXHrg8wW2g/OoCLqBgw0Eo6mafjgEyPQ3NYHGoH26fd5XTQCwEAjAd3b2sF2cR+DfU74J44YQ7v8BuDo009Qz22eXYEkLAYaCefb97IAgFcujWGg74hf0cFR4NIb+tf3k2dQGYmOgUbC+bO7TwAA11++cPzBL5T3rLi/3saKqFsw0Eg4f3pX36vic37fMUcCePEv6/fKH7WxIuoWDDQSyqa6gw8+ycPhAN685j3+Ba+U94Z98BdA/mFbayPxMdBIKF/79gMAwPWXvbg4ZmMTnbFLwJXP6l9//7+3sTLqBgw0EkappOF3Eh8DAL74meftv/Azc/p98t9z+cY5x0AjYXztOw+QfvQU40P9+NuffcH+Cz8zB/QPAw+/C3zwP9pXIAmvqU1SZFkGcLgnp7GNXbPHENW6r+7g3d/7HgDgF//KNYwPDdh/8YgX+Pw/BP74XwBf+6fAC0HAfaVNlZLIbAeaoiiIxWKIRqMAgJmZmbqwsnMMUaVSScP/+uBT/Op/+y4eb+/ixy6P4x/89anm3+itfwJ8//eARx8A/+5vAF/8dWDqhn5VDjo3bAeasYGwQZIkxOPxqsCyc8xpeJDdwTfST8zHtcMmtaMotXuD1o2y1L2+5vhj37+119cecOz7N3t83fNHjzO1+t9z3Ov39jU82i7ggVrAn2+oyDzdBQD4L47iN798vXpTYbsGR4Ev3Qb+w88BT34E/McwMHZZnzC4cA0Y8gCucaDfBTichzdnn34PB+BwNP+5dHJePzD55qm+pe1AS6fT8PkO1wV5vd6qHdPtHmMoFosoFovm41wuZ7cUfO9+Dm/f+Zbt40ls465+fOlzL+If3XgVo66mRkGqXXgZ+KU/1Lueyd8Cth8CP/j9U6uTTlngFzoXaI1kMpkTH7O0tIR33333RJ/rHRvEX31toup7tf+2NvrHtv4YxzHPH/0Otc83+ve9/phj3uOY4495WH6P5v67mv251NdQX8VRn9Hf58DEmAsT7iG8/tw4fvKqhMH+U+oaDkvAF/4ZcOPXgHsJvQuqbui7rBdywMGufpVbTSvfV9zobE38+Km/pe1Am5qaqmptGYP+zR5jiEQiePvtt83HuVwOk5OTtmoJvHgBX/3F00126jH9LuDlt/QbnRu2/1kMhUJIJBLmY0VRzLExI8SOOqaWy+WC2+2uuhERtcKhHTdCXKFySYbX60U4HAagt8ySySQkSbI85ji5XA4ejwfZbJbhRkRV7OZDU4HWTgw0IrJiNx+4SIeIekZLs5ynyWgoNrN8g4jOByMXjutQChNo+bx+DXm7M51EdP7k83l4PB7L54UZQyuVStjc3MT4+HjdOqhGjGUeGxsbQo65sb7WiV4j62ud3Ro1TUM+n8eVK1fgPOJ0NmFaaE6nE1evXm36daIv+WB9rRO9RtbXOjs1HtUyM3BSgIh6BgONiHpG1waay+XCO++8A5fLxmWaO4D1tU70Gllf6067RmEmBYiIWtW1LTQioloMNCLqGQw0IuoZwqxDs0NVVayurgIAFhcXze/LsoxMJoNkMonZ2VnzkkWd2LDlqBob1dLJTWWMzzYYV0YRaaOblZUV85p6ItZnkGUZkiQJ8f+1ti5R/jYa1XbqNWhdZG1tTVtcXNSWl5fN7yWTSW1tbU3TNE3b2trSJEnSNE3T0um0Nj8/bx4XCoU6VqNVLZ2qUdP0n1VljUYdnaypVigU0ra2tjRN07RAIKBpmlj1Gba2trRAIGD+HopSo2h/G5XaVUNXdTnD4TCmpqp3BMpkMojFYgD0TVm8Xi9SqZTlhi2dqNGqlk7VaHxWNBpFKpUyHx9V61lLpVJmHalUCslkUqj6Kt25cwdzc3PmY1FqFO1vo1K7auiqQGskFAqZ2+YB+v/EQCDQ1IYt7WZVS6drXF5eRjAYRDAYRCQSObLWs7a+vg5FUaAoCgBgYWFBqPoMqVSqrqskSo0i/220q4auD7RKCwsLeO+99yyft7Opy1mxquUsa0wkEkgmk/B6vbhx44blcZ34uamqCq/Xi0AggEAggPX1dbM1WauT/18VRbHcN6NSp3/3uuFv4zRqEGZSYGVlBU+ePKn7vs/nqxpctyLLMmZmZqouC253w5Z213hULaddo91ajZ9XIBBALBbDwsIC4vF4W35uJ6nP7/dXfa7X64WiKGdWn50ajQkLWZaRSCSQTqfh9/uF+RkazuJvo1ltq+FURuLOUDQarRrM1jRNi8ViWiwW0zRNHwhNp9NaOp3WwuGweYwxqNyJGq1q6XSNyWTSfLy2tmb+7DpVU6Wtra2qgWK/369tbW0JU1+txcXFqkkBUWoU7W/D0K4auurUp3g8jmg0ClVVsbCwgHA4DEVREAwGzWNUVTWvannSDVtOu8ajaulEjYaVlRVzYFaUmioZSw5UVYXf7xeuPkM8HsetW7fg9/uxvLxstto6XaNofxu12lFDVwUaEdFRempSgIjONwYaEfUMBhoR9QwGGhH1DAYaEfUMBhoR9QwGGhH1DAYaEfUMBhoR9QwGGhH1DAYaCUVRFKysrECWZfMaaMY10YiOw3M5SSjBYNC8Oq0sy1AUBZIkYX5+vsOVUTdgC42Esbq6WnX1V0mSEIvFhNgEhboDA42EUrsfA4Azv/ggdS8GGgnj5s2bSCaTkGXZvFaWJEl12+0RWeEYGhH1DLbQiKhnMNCIqGcw0IioZzDQiKhnMNCIqGcw0IioZzDQiKhnMNCIqGcw0IioZzDQiKhn/H9NJhUudgHxogAAAABJRU5ErkJggg==", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=1)\n", "fig = plt.figure()\n", @@ -248,21 +204,10 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "id": "af2c3d95-97ec-4f81-b226-dfec9ae4a6f4", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -293,21 +238,10 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "id": "60453966-409d-44d7-969a-ee67005bb392", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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xPLXv1LI1uBW7zc7lh1/Oz479mbEf3XiTQplDsNkst3VVc3PzjpW04X7Y/BEtq7+i8orvUTr7eP1vLNhOy+ovqDylDDo2QP60cXt9CZ7EDmve1Zfnr39Pv19UogdNB59lbrusLH8vuPCvO0obrFsGyo3gfwDO2v7epemHn5ksv2DFbtdXdH75Jnzr9/pWQdG8uVOvgbtnw5dvwKaVsNeR5rXTJJu2beL37/yeV9e8CsCBrgO5+aSbOWryUXF9XdmiJXmUl5fvuNO9FeXVNyg79ihKz7xQX+wDKC++QNms2ZQedRg4xjf4k+BJQPt6ffRkub6vIFn58I1qmF0JmVmmNi1pTJ8JP1Zg+d/19zKgwv/N1+tCnVULkw82u4VpJSkWrJz8a70g68T9Y49P3B/2P0VfmPDVW2kVPEUiEZasWsJtS2+jM9Spb+R7dAVXHrnrRr7xICNPyUFVVYqKioz7/qXvoLV3UFFRgf/9DygtLcXv9+vHrq7G/+5blO5dMK5tkITxdBbq0XN27pq5PXCywXGXwi/9cNIvJHAaLbsdjr1Er1J+8tVgd+jTMn85EZ7/DfS0md1CYSUZmbsGTlFF21cPdWxIWHPMtqZ9DVe+eCUL31pIZ6iToyYdxWPnPcZPj/lpQgInkOApWfj9fuPiSFVV5v7gpzQ8tISy088hEAjox+bOpaGhgbKyMgLt28a9DTLylI4iEfjkaXjhP0H7Uj8243g4+xbYZ/ANmsUoZBdA+c1QeoVenfyz5+Hte/QA9cwb9AB1N/tsiTSXN0X/f+dmc9uRAP3hfh76+CHufu9uYyPfXxz3C75/2Pd3ux/deJOE8eQwcATZ7XbT0vwS9HbqFyM5eq2v6Kq8eJHgKd1s+gievx5Wv6bfz99b/6A/yiu5OeOtuAQueVSvkfX89dC6Cv75S1j6P/Dtej3nRYjBOLYnRKd4yYJVW1dx45s3suLrFQDM3ms2N51404j3oxtvMvIkRkqCp3TRFYBXa6H5fyDSDxlOfWrulF+DM2/3jxdjd5AHDnhTr87+Wp2+X979Z+n5Lp6FshxdpJ1Qf4i/rfgbjSsa6Qv3kefI49qZ13LRQRdhM/EiThLGxUhJ8JTq+vtg2f+DV/4A3Vv1Y4d9R1/hM1S+hRh/mVlw0s/h6Pnw8s3gXwQrFusFEU9dACf+AhzZZrdSiLj78OsP+d0bv+Nz7XNg7Bv5xoOMPImRkuApla1+HZ67Xq8ZAzDlcD2vyT1+FXnFKOVNhvPvgpk/gueqYc07elVp/yI46w9w6HkyfSpSUndfN/e8dw+LPl5EOBKmKLuImtk1nLX/WaaONg0kwZMYKQmeUtHWL+DF38LH/9Tv50yEb/6nXksmQ37klrD3cfCjF2CFD5pu0BP3H70UDjgdvl0HUw4zu4XCEiJmN2BcNG9s5sY3b2RNh759zbnuc6meVb3HG/mOt2jCeFdfF33hPjLt0l+KwVnmN6OxsRG3201TUxN1dXWAXuhO0zRUVaWioiJmR3QxiN5t8O874I3/hv4g2Oww88fwzd9AbtHuHy8Sy2aDo+fq2738+w548y49kf8vJ+tFN79ZY6wcEenGGiMxe6qjt4M7lt3B4s8WAzA1dyo3nHgDp00/zeSWDW7CgEKKnb2duLJd5jVGWFrcgidN02hsbAR27BEF4PP5gB37SkU34AS9sF1DQ4OxU3I0kNI0TQKn4UQiO0YwOrbvP3TAafoU3dQjzG2b2D1nHpz5O72EwYu/1ctIvNug50SdsX3EUEobiCTz+trXWfjWQjZ36eUW5h08j1+X/Zq8LOsuUMm0ZzLBMYFtoW109HZI8CSGFLfgSVEUWltbKS4uNo6pqkpTUxMNDQ2AXl7d4/HgcrmoqKgwRp/cbjeNjY3GTufNzc3GaJTYyfr39LymNW/r9137wrf+oCeFWySPQIxQ0QFw8cOgvqr/TLd8DM9cA0v/nz6Vt/8pZrdQiN0K9ASoe7eOZ1c/C8C++fty00k3MWuvWSa3bGTys/LZFtomK+4GiEQidPd1x/U1cjJzLJP7NhJxC568Xi+BQCBmF3NFUWJGkFwuF4qiGJVCKyoqqKysNEaeSkpKjOdpbGyM2VV5oGAwSDAYNO63t6fBL33nFnhpIbz3EBDRd6SWVVupwf0N+Mm/9XpQr/wBNn0I/3suHH4BfOu/9ABZCIsZbCPfKw6/gp8e+9O4beQbD/lZ+WzctlGCpwG6+7o5/pHj4/oa71zyDrmO3GHPmTt3Ln6/n8rKSqqqqoxYwT2+O6+MSEK3Z2lpaYkZiSoqKjJGlxRF3128pKQEn8/HzJkzY84bTm1tLYWFhcZtxgxzCqwlRF+vnhtzVym8twiIwFHz4BfL4LTrJHBKFRmZcHwl/OI9fWWezQ4f/QPungWv1EJvl9ktTCk+nw+fz0d1dXXMcU3TqKysNKlV6FPySWDTtk388uVfUvV6FVuDWzlo4kE8cs4jLJi5IKkCJ4B8h6y4s6LGxkbuu+8+o3K4qqooioLb7cb31POUnX1JzPlD/U2PF9MTxgOBAPPmzUNRFHw+Hy0tLca0XvTY7qbtampqWLBggXG/vb09NQOoVU3wfI1eqRpg2rHbK1XH94pAmGhCMZx3x47SBl++Aa/dAu8/rFeGP+JCmZ4dxGhyLn0+Hy6XC4/Hg6qqMaPciqIQCAQS/w0kyc90sI18K4+u5MdH/jhh+9GNN9miZVc5mTm8c8k7cX+N4QyceaqqqqK+vp7SUn07Me/5Z9Pwvw8bXx/ub3q8JDR4KikpiZnGi3ZgLpfL2Ktm4J410U5vdzuhO51OnE7n+DfYKr7+HF6ogVUv6vcnTIYzb4Rjv69vRitS315HwQ+egZVPwIu/g7Y14PuhXjH+27foXxeG0eRcDuxfWlpajJEmn8+H1+vl0UcfTWzjk8Sa9jXc9NZNvLvxXQCOnnQ0C09ayIETDzS5ZXtGaj3tymaz7XZKLdGam5tjLowGGupvejwl9JPX4/HQ3Nxs3FdV1ch3EoPoadM37733BD1wsjv0LVV+sQxKL5PAKd3YbHDkRfDzZvhGDWRmw5f/hobT4J+/gm2tZrfQMrxeLyUlJTHHhsq5HPj1srIySktL8fv9xlWtiNUf7ueBlQ9w0VMX8e7Gd8nOyOa6mdfx4LcfTPrACWSLlmRRXl4+4N7g09sD/6bHW1xX2zU1NaFpGm63G6/Xi9vtZv78+fh8PgKBADU1NfF6+eQWDuvTMi8thG1b9GMHnQVn/REmJX/nJPZQVi5843p95LHpd/po1LL/Bysfh2/8Bmb9GJJ0yiSehsq5BPD7/WiaRkVFBX6/3zjm9/tRVXXIYCrdFqvsvJHv8Xsdz40n3ciM/NRJk5CRJ+tTVXWIXOgd0907/02PdwAVt+DJ4/EMOqq0uym4tPfVO/BcFWx4X79ffKBer+mg8mEflgp6+npYumkppVNKLTdEbEmuGTD3f/WCms9dD5tWwPPVeiB19i1Q8k2zW2h5gUAAVVWZO3cubreb2tpa6urq8Hg8lJaWGiVThlJbW8vChQvj2EJrJIxbdSPfeDCCp5AET1bl9/tj4gvltTdRv1qH74kn8V5yxaB/0+PN9IRxsV37emi6EVY8pt93FsDpVTC7Ut9UNoVFIhGUrxRuW3ob6zrXccXhV3DtrGvNblby2P8UqHwNlv2vvk/elk9g0QX6Pnnf+r1eP0oMmXPpdruNFTw7q6ioGDbRNH6LVawTkKzYsoIb3rxhx0a+M77Bb4+3xka+8SAJ49a38yCM5/STaHnzKZio93XD/U2PFwmezBbqgbfugn/dDqEuwKZXmj7zBsibYnbr4u7TwKfUN9cbSacAazvXmtiiJGXP0KfrjrwIXr0F3r1Pr1S+qglO+jmcskCvZJ7GPB5PzLLl8ci5TOXFKsmwkW88yLSdGAkJnswSiegfbi/8p74pLMCM4/VK0nsfZ27bEkDr0bj7/btZ/NliwpEwzgwnx045lnc2vENbsM3s5iWvnIn671DZD+D56/Vq5f+6Dd5/RC9tcNTcpFkGvyck53LPvLPhHRa+tdDYyPc893lUzaqy3Ea+8SDBkxgJCZ7MsOkjPTdl9ev6/fy9t3+weVP+g60v3Mdjnz7GPe/fY6xmKd+vnGtmXsOX7V/yzoZ3ZJXLeJhyGFz2D/jkGXjhN3qA/vhV0Py3tAjQJedybNqCbdy29Dae+PwJwPob+caDrLYTIyHBUyJ1BeCVP+rbbkTCkOGEk38Jp/wasibs/vFJ7u0Nb1P3bp2RO3HwxIO5fvb1xp5XWlADkJGn8WKzwWHnwYEeeOtufQRqzTvQ+M3tU8M3Qt5ks1sphpOgCuORSIQXvnyB2ndqCfQEsGFj/iHzubr0aktv5BsPMvIkRkKCp0To79NXQL3yB+jeqh877Hx9n7KJ+5vatERY07GG25bexktfvQSAy+niF8f9gosOuohM+45fwcKsQkCu+MadIxtOuxaOvWTHooT3FsFHT8Lp1TC7IuUXJSSdBI5Ab9y2kT+8/QdeXfsqAO5CNzeddBPHTUnt0cmhRBPGu/u6CYVDOOxS9kPsSoKneFv9ur6MfPNK/f6Uw/Vl5O7TzW1XAnSFuvjbir/xwMoH6A33kmHLYP4h8/nZsT+j0Fm4y/nRY9193QT7gzgzUjMR1zQFe8Oc+7aXNtheDuPF/9RX6Z1dmxblMMQO4UiYRz99lDuX3UlXXxeZ9kyuOuoqrjzqSrIy0jeYnuDYMQvQ2duZFnleYvQkeIqXrV/Ai7+Fj/+p38+ZCN/8Tyj7ob7pawoLR8I8oz7DHcvuYEu3XuTzhGknUD2retgKxHmOPDJsGfRH+mkPtjM5V6aU4mLf4+GqV+D9h+Clm/W9Eh/26oVYz66F4pLdP4dIai1aCze9eRPvb3kfgGMmH8NNJ96UEhXC91SmPZMJjglsC22jo7dDgif0ad1Id3dcX8OWkzP2VZwmlENL7U9xM/Rug3/fAW/8N/QHwWaHmT+Gb/4GcgeriJpaPvz6Q2rfrWX5luUATM+bznWzruObM7652z8Mm81GQVYBW4NbaQu2SfAUT3Y7lF4Oh38XXquHd/4Kq16AlpfhhJ/CaddBdoHZrRTjrCvUxV+X/5VFKxfRF+kjNzOXX5X9ivmHzMduk+2eovKz8o3gSUCku5tPS8vi+hqH+Jdhy02e4sgSPI2XSETfHuOF30LHev3YAafpU3RTjzC3bQnwdffX3LnsTp5seRLQd8iuOLqCyw6/bFTTb4XOQj146pWk8YTILoSz/gClV+ibT3+uwJv/Dcsf1RPKj/me7KFoqvG5pI5EIrz45YvUN9ezuWszoBe7/M/j/5O9Juw1Lq+RSvKz8tm4baPkX1qIpmlcddVVaJqGqqq43W5cLheLFy82pT0SPI2HTR/pOSRf/Eu/79oXvvUHOOw7KV96oLe/l4c/fpiG5Q1sC20D4PyS87m69Gqm5I6+yGeBUx/tkBV3CTb5YPi+Dz57QQ+iAio8+TN9Zei362H6TLNbmGbGr9/4NPApty29jbc2vAXAPnn7UDO7htNnpH7e5VjlO2TF3UC2nBwO8S+L+2sMZ+nSpSxevNjYazJadsTn81H7Xzex7LlFxrk+nw+A5ubmuGzNAhI87ZmeNr2a8zsNEOnXd7k/9Ro46RfgGP4XIdlFIhFeX/s69c31fNXxFQBHTTqK6tnVHDP5mDE/b3SliwRPJrDZ4JCz9T3x3v4LvH4rrFsGfzsTjr4YPDdBwTSzWylGaH3neu55/x7+2fJPIkTIsmfxo6N+xI+P/DHZmdlmN8/SZIuWWDabzfQptWjdNp/PF1Ovzev10nDXHcZ9n8+Hy+XC4/GgqiqNjY3DbrE0VpYJngaLFKurq5k1axaqqlJVVWVm82KFw7D879B0A2zTE6I57Dv6aNPE/cxtWwKobSr179bzxvo3AJiUM4lflf6K75R8Z4/zJqIr7mS43ESZTjjlV/qU3UsL4f2H9d/3T57WLw5O/A/9HGFJa9rX8MBHD/D4qscJhUMAfGu/b3F16dXsW7Cvya1LDlLrybqampqGjQcGBlYtLS1UVlbGpR1xC540TaOxsREg5huNBknRTTk9Hs+gkWJRURElJSV4vV4aGxtRFGWP96EaFxuWwzPXwNrte7EVH6RXbD7wTHPblQDtve389YO/8n8f/x99kT4cdgeXHX4ZFUdXxCzv3RPRWk8y8mQB+VPhgnv1BQ/PVcG6pXow5X9QX5V3yLfNbmHqG2GRzEgkgn+zn0c+fgTlK4VwJAzArL1m8evSX3PU5KPi2cqUI1XGrcvlco3oPEVRKCsro7S0NC7tiFvwpCgKra2tFBcXG8dUVaWpqYmGhgYAysvL8Xg8g0aKS5cujdkB3e/3mxs89XbBa7fAm3frU3RZeXB6FRz/05QvMNgf7ueJz5/grvfuItATAPRk0+tmXjfuV7LRkScJnixkehn8uElPIlduhK2r4f8u1kdbz/kT5EvCsVk2btvIUy1P8Y/P/2HsQwdwyj6n8MMjfsisvWal9Ca+8SIjT9Y1kgRxv9+PpmlUVFTg9/vjEkDFbRmN1+ulpCS2XoyiKDFRo8vlQlGUmK9HI8WKigpaW1tRFIVly4ZPVAsGg7S3t8fcxpX6KvzlJHjjz3rgdPh34efNcPLVKR84Ldu0jIufuZiFby0k0BPAXejmr56/ctcZd8VlCsAInmS1nbXY7XDs9+AXy+DkX4E9U69hds9seO+hhG0jEi8+n4+ysrJdjimKQn19feIbNEzAE+wP8tzq56hsquRbvm9x13t3saZjDbmZuVx00EUsOX8Jf/H8hdnTZkvgNEZG8BSS4MnqFEVB/XINvqf1WEJVVebOnUtDQwNlZWUEAoG4vG5Cc55aWlpiRqKKioqM0aXBIsWamhpcLldMZv1gamtrWbhw4fg3ONSj5zW9q4+UUbAPnHtbWkxXbOjcwO3Lbuf5L54H9NUnPzv2Z8w/dH5ctyuQhHGLc+ZD+UJ9E+snf65XKX/yP2CFT5/iK9jb7BYCo0sbgO1Jp9tHxEHvgKO5lgOXRptpc9dmHlj5AE98/kTMiMjMqTO54MALKN+vnFxH8tTJsTJJGE8eHo+HlmYFtq/2drvdtLS0xP11TU8YDwQCRqTodrupra2lrq7O6PzcbrdxG0pNTQ0LFiww7re3tzNjxow9a9jmj8H3I9j8kX5/1lVw5g0pXziwu6+b//3wf7n/w/vp6e/Bhg3vwV5+ftzPKcqOf5FPmbZLEnsdBVe+BG/fo292rb4Cfz0VLmq0RP7faNIGBuN2u2lubqa8vJzy8vJhL97iLRQO8T8r/of7lt9Hb7gXgL0m7MX5JedzQckFzCjYw75O7EKm7ZJXsD9IT18P/ZF+MmwZODOcODOc4z4Km9DgqaSkJCaPKXr1N1SkONIVdk6nE6dzHFf/fPo8LPkx9HbChMlwwV/hIAskq8dRdFf125fezoZtGwAom1rG9bOv59CiQxPWDlltl0QyMvWp60POBd8PYOMKeGiOvg3RadeaWuPM6/USCARi+puh0gYGC6A0TWPWrFmUlpZSWVmJx+OJW+LpcIKRfn798tX8a51eQ650Sik/PurHnLz3yWTYMxLennQhwdMOkSSZku+22djQs4Xubb27fM1hdzA5d3LMVjt7+n0lNHjyeDxUV1cb91VVtcYKuoGW3g9PLwAisP+p4L0f8kZf7DGZfBr4lFvevYWlm5YC+lXtNTOv4az9zkp4zoSstktCkw6EHyvw/PWw7P/BK7+Hjg1wzq1goQ/44dIGdvbYY4/h9Xpxu900NTXh8/kGDZ6CwSDBYNC4P375lvrf3T2h9fxr3SayM7K56aSbOOeAcySPKQFktR04HA5sNhtbtmxh8uTJlv696wn1s85mJ9yjz5Y4M5xk2PV9Unv7egkSJJgRpIceQA+ctmzZgs1mw+EYWxpKXFfbNTU1oWkabrfb6Ijmz5+Pz+cjEAhQU1MTr5cfG/8iePrX+r9Lr9DzmzLil99jtq09W7nrvbtYsmoJ4UiY7IxsfnTkj/jBkT8gJ9OcIp/RkafOUCehcCiu+VViHDmy4Tt36lsRPXudXpk8Eobz7rB0lf1oMqmiKKiqahTgmzdvHo2NjZSWlhq5mIOJW74l0Ga381CfvpVK3Wl1nLHvGXF5HbErGXmCjIwMpk+fztq1a/niiy/Mbs6wvu7cQC8RnPZMXDnF9Nn66KMPAFvERl9/H60ZrWy1bTUeY7PZmD59OhkZY7vAi1vw5PF4Bh1VMjN3YFgtL8M/f6n/+4SfwVl/tHSnvydC4RCPfvIo935wr9E5nL3/2SwoW8C0PHMrSEc7LdA7rkTkWYlxNPsqfQNs34/1UajCffRNhi1gqLQB2J50OiB1wOVyjShtIC75ltv9OyebEBEOnniwBE4JFk0Y7+7rTuuLuLy8PA466CBCoZDZTRnSlq4tXP3+LdiJcP/hlRS5jx/R4xwOx5gDJ7BAwrgltK3TO/tIGI79fkoHTm+ue5O65jrUNhWAQ4sO5frZ11M2Nb47Zo9Upj2TfEc+HaEO2oPtEjwloyPnQFcAnr0WXv4D7Hcy7HeS2a2KS9rAuOdbDvDF9umEoyZJgctEy3PkGf/u7O2MyZVJNxkZGXsUZMTb55s/Z0PvBg4J9rK3MweyE7P1kARPAM9XQ3cAph0D596ekoHTV+1fcevSW3l1zasATHRO5Jelv+TCAy+0XOJpgbOAjlCH1HpKZrOvgvXv6Vu7PF4J//EOZCVuGX1Spg3sZF2m3j1Pz59uckvST4Y9gzxHHp2hTjp6O9I6eLK67r5uAFzhMOO5ofbuSPD0uaIX+7NlwAV/0XM3Usi20DYalzey6KNFhMIhMm2ZXHzoxfz02J8aQ9NWU+gsZF3nOkkaT3Zn3wKrX4e2r/SSBgmcvku6tIGd2Wz0bf8cMCv/MN3lZ+UbwZMQO4tbhfGkEInAq7fo/z7+J3qya4oIR8I8+fmTnPfEedz/4f2EwiFO3vtklpy/hOrZ1ZYNnEBW3KWM7AI480b93/++U5/KEyJJyIq75BDBnFIK6T3ytPp1WNsMmdn6LvIpYvmW5dzy7i2s+HoFAPvm70vVrCpOm36apZebRkmtpxRy5Bx9W6NNK/QyIKdda3aLkkZyVNdJXbLiTgwnvYOnVS/q/z/uspSo5bSlawt3+u/kqZanAJjgmEDl0ZV8/7Dvk5WRPHvwSZXxFGK3w0m/gCcqYFWTBE8iaUjwlFxsCb7cSO/g6aw/wKHngms/s1uyR3r7e3nwowe5b/l9dPV1AXDBgRdwdenVTMqZZHLrRk/2t0sxR14EWRPSYk9IkTpkf7sklMCZlfQOnsASS6jHKhKJ8MqaV/jT0j+xpmMNAEdPPpqa2TUcOelIk1s3dsbIk6y2Sw0ZDjjsPLNbIcSoSM5TcpCcJzEqLVoLde/W8daGtwCYkjOFX5X9inPd52K3Jfc6ABl5EkJynswm03bJJdHZvBI8JZm2YBv3vn8vj376KP2Rfhx2Bz844gdcedSV5DoSV0cnnoyE8aBc8QlhS/jHggDId2wPnkISPIldSfCUJPrCffg+83H3+3cbIzJnzDiDa2ddy4z88dkOwipk2k4IYTYZeUoOkcjAMVrJeRIDvL3hberereNz7XMADnQdSPXsak6YdoLJLYsPqfMkhEzbmS2aPiAj4MnBluA/GMsETz6fD4Dm5mbq6uqGPJZO1rSv4U9L/8TLa14GwOV08fNjf86cg+eQabfMj27cDazzFI6Ekz6HS4hRG7BqKBlqs6UiGXkSw4nbJ7CmaTQ2NgLE7E4eDYiiO5p7PB58Ph8ulwuPx4OqqjQ2NlJUVLTLsYqKing111J23lIlw5ahb6lyzE+NwCKVFTj1K75wJExnqNPS1dCFEKlJgicxnLgFT4qi0NraSnFxsXFMVVWamppoaGgAoLy8HI/HE7PfVEtLC5WVlZSWlu5yLNWFI2GeanmKP/v/zNfdXwNw0t4nUTWrihJXicmtSxxnhpOczBy6+7ppC7ZJ8CTSUkRGnExlBE+SMJ4UUma1ndfrJRAIoGmacUxRFFwul3Hf5XKhKIqxgaeiKJSVlcUEToMd21kwGCQYDBr329uTb476/c3vc8u7t7CydSUA+xXsx3Uzr0uaLVXGW0FWAd193Xq+Qb7ZrRGpzufzUVtby7Jly2KOgflpA7LazhzR4Km7r5tQfwhHhsPkFondSuBnZUKTSVpaWmJGooqKiozgyu/3o2kaFRUV+P3+IY8Npra2lsLCQuM2Y0byrD7buG0j1a9Xc9lzl7GydSV5jjyunXktT5z/BKfPOD0tAyeQLVrEntE0jfr6eurr62OO+3w+fD4fjY2NKIpiHPd6vRQVFcWc53K58Hq9FBcXGykIIn3kOfKMf8vok3WZVSTT9EzcQCCAqqrMnTuXhoYGysrKhjw2lJqaGtra2ozbmjVrEvgdjE1Hbwd3LruTcx8/l2dXP4sNG3MOmsPTFz7NFUdckfZXOVKuQOyJaNrAQNG0Aa/XS0VFxbCjSV6v1xgRb2lpYebMmXFt767S86LJSjLsGUYAJXlPYmcJXbJVUlISM40XTRp3u920tLTscv5gxwbjdDpxOp3j1cy4CvWHeOyzx2j4oIGtwa0AzJw6k6pZVRxWfJjJrbMOKVcg9sRY0gYGs7u0gVRIGRBDy8/KpzPUKcGT2EVCR548Hg/Nzc3GfVVVh+24Ukk4EubFL17kgicv4JZ3b2FrcCsHFB7AXWfcxf1n3S+B004GlisQYjwMlzYwmJGkDSQiZUBynswj+9uJocR1tV1TUxOapuF2u/F6vbjdbubPn4/P5yMQCFBTUxOvl7eMcCSM8qXCX5f/lVVbVwFQnF3Mz479GRcddFFK12vaE9FyBTLyJOIpmg6gKAqqquLz+fB6vUbagNvtpra2dsgpvpqaGhYsWGDcb29vT6qcSzE8KVdgfSlXYdzj8Qw6qjSwLEEq6+3v5YUvXuD+D+83KoPnOfK49PBL+cERP2CCY4LJLbQ2mbYT422otAHQ+6uBaQJDpRLsLJ4pA1Jh3HwSPCWPlClVkK42btuI7zMfiz9bTKBHv6qNBk2XHnZpWhS5HA+SMC7Gm8fjobq62rhv6bQBqTBuCdEacxI8iZ1J8DQO2oJtNH3ZxDPqMyzdtNQ4PiV3CvMPmc/8Q+ZL0DRKRs6T7CslxkDSBsR4kJEn6zOrVIEET2PUFmzj5a9e5sUvX+TtDW/TF+4zvjZz6kwuPvRiztj3DBz29C45MFYybSf2RCqkDci0nfkkYTx5yLSdhfWF+3ht7Wss/mwx76x/h77IjoDp4IkHc677XL69/7eZljfNxFamBpm2E0KYLd8hI09JJYFT3BI8jUAkEqHpyyZuX3Y76zrXGccPmXgI5fuVU75/Oe5Ct4ktTD0DK4xHIhHJ+0gim7Zt4uPAx7R2t5KVkcV+Bftx8MSDyc7MNrtpQoyKTNtZX+xqu8SR4Gk3IpEIf3znj/z9078DMNE5kQsPupALD7yQ/Qv3N7dxKSyaqBkKh+ju6ybXkWtyi8TuqG0qt7xzC29teGuXr+Vk5nCe+zxuOPEGE1qWjGwybWcBkjCePGTazmIe+eQR/v7p37Fh48qjruSqo68iJzPH7GalvJzMHDLtmfSF+2jvbZfgyeK+av+Ky5+7nLZgGzZsHDzxYKZOmEqwL8gqbRWBnoBpiZ1CjJWMPImhSPA0jFA4xH3L7wOgalYVlx5+qcktSh82m43CrEJae1ppC7ax14S9zG6SGMad/jtpC7ZxZPGR3Hr6rUzPn258LRKJ8EngE5m2GyOZsjaPBE9iKBI8DWPV1lW09rSSn5XP/EPnm92ctFPo3BE8CesKhUP8e92/Afjdib+LCZxA//CX7YdGT8bpzGcETyEJnqzONuC/iZDQve2STYumVxg+eOLBUnLABLLiLjls2raJ7r5usuxZHFp0qNnNSQ0y2mQJ0eCpu6+bUH/I5NYIK5HgaRhaUANgSs4UcxuSpqTWU3KI5jJl2jOx26RLGW+yMbB58hx5xr9l9EkMJD3dCEjOgTlkc2AhhJky7BlGACV5T9Zk1kIUywRPPp+PsrKymGNlZWWUl5fH7Ecl0odM2yUJSc6JC3lbrUGSxpODLcH1nuKWMK5pGo2NjQBUVVUZx30+H7BjR/PoFgper5eGhoaY56ipqTF1OwWzim8JXXTaTva3Sw4yQhsfMm1nrvysfDZs2yBbtCSDBP6pxC14UhSF1tZWiouLjWOqqtLU1GQESeXl5cPuaq6qqrHBZ11dXbyaulvyoWCOgVXGhUg0RVHQNA1VVamoqMDlciXw1aXPsQoZebK2lKsw7vV6CQQCaJpmHFMUJaYDcrlcKIoyZAAVHbFSVRWfzzfkKFQwGCQYDBr329vH5wpBivqZS6btkkOy/J2MZjQ8eqFXV1eHpmkJDpyElUjwJAaT0JynlpaWmJGooqKimOBqIEVRUBQFYMhzomprayksLDRuM2bMGK8mCxPJtF1ysfr0UnQ0fKBokOT1eqmoqDBGuKOjTj6fj9raWjOaKyxCtmgRgzE9YTwQCAB6ZxUdYQLweDxommYEUMPlPtXU1NDW1mbc1qxZM65ttPqHQqqSkafkkCwjT16vl5KSkphjQ42GA5SUlBiPiY5Y7SwYDNLe3h5zG2+SNmAuGXmyNrP6n4RWGC8pKYkZRYoOk4MeLLW0tMScHw2YhsuLAnA6nTidzvFtrDCdlCoQ8TbUaPjMmTONIKqoqMi4yNtZbW0tCxcujEvbIhI0WUI0eJKEcWtL6QrjHo+H5uZm476qqrsNjET6io48dfd109vfa3JrxO6kyghtIBCgtLQU0POhmpubqaioGPTcuI16S+BkGfkOGXkSu4rrarumpiY0TcPtduP1enG73cyfPx+fz0cgEKCmpiZeLz+uUuVDIdnkOfKw2+yEI2Hae9uZlDPJ7CaJQSRzSY/hRsOjSeXDpQwkYtRb+h9zybSdtaXctJ3H4xl0VMnMuk2jlcwfCqnAbrNTkFWAFtRoC7ZJ8GR1SfgZ7/F4YorwWmk0XHofa5CE8eSQ6O4noTlPyUoSNs1T6Cw0gich9kQqjYaLxJGRpySSwM9qCZ6EpcnmwNaXLKvtUmE0XCRedOGKBE9iINNLFVhZsnwopLJ8p37VJ+UKrE9yc8aTvJdWYYw8hSR4siKz0mskeBKWJiNPIl3JpZs1RIOn7r5uQv0hk1sjhpLoyw0JnoSlyf521icjtPElOZfmynPkGaOqMvokoiR4GoZ8KJgvGjxJgTrrkw95kYrsNjt5jjxA8p6sL0WLZCYryeUwj0zbiXQll27WISvurE+m7YQYQKbtkoB8yo8/GcWzFNmiRexMgqdhSJFM88nmwMlDRmjjQ95X88nIk3XJajsLk1wO80Sr+8rIk0g3culmHTLyZH0ybSfEAEbCeFA6LauShRUi1cnIU5JI4ECHBE/DkA8F80WDp45QB33hPpNbI4Yj00vxISPf5pP97azLrM9pSwdPPp8PRVGor683tR3yoWCeaKcF0nGJdCJ9jpXIyJPYWUL3ttM0jcbGRgCqqqqM4z6fD4BAIIDb7cbj8aCqKqqqUlVVhaZpqKqK2+1OZHOFBWTaM8lz5NEZ6qQt2MbE7IlmN0nsJFUXVjQ2NuJ2u1FVlYqKCrObI0wkOU9iZwkdeVIUhdbW1phjqqrS1NSE1+uloqKCuro6ANxuN83NzZSXl0vglOakUGZysPr0kqZp1NfX7zKS7fP58Pl8NDY2oigKgPF/j8dDUVGRcYFnBhn5Np+MPImdJTR48nq9lJSUxBxTFAWXy2Xcd7lcKIqCpmnMmjWL6upqGhoa8Pv9Qz5vMBikvb095jaerP6hkOpkxZ0YD6O5ePP7/cYFm8vlorm5OeHtTc3xvOQkwZN1xeY8pVHCeEtLC8XFxcb9oqIiNE3jsccew+v14vF4aGpqMq4EB1NbW0thYaFxmzFjRiKaLhJEaj1ZW7IsrBjNxRvoI1W7E+8LN2ENkjBufbYEpw+YHjwNJhAIMG/ePCNh3O/3D5tzUFNTQ1tbm3Fbs2bNuLQjVXM5ko1UGRfxMtTFW2lpKYFAAMAYBR9M3C7cZLTbUmTkSezM9OBp5yvBaNK4y+WiqqoKj8eD1+uNuTrcmdPppKCgIOY2niTnwFzR/e2k1pNIhEAggMfjQdM0FEVBVVW8Xu+g58brwk1YiwRP1mXWIEdCV9sNxuPxUF1dbdxXVRWPx2Nii4TVyLSdtSXLtN1gSkpKYqbnohdvsGNF8HD9kdPpxOl0xqVtEblms4xo8NTT30Nvfy9ZGVkmt0jsLNF/LgkNnhRFoampCU3TcLvdeL1e3G438+fPx+fzEQgEqKmpSWSThpXMHwqpRKbtkkMyjtDKxZsYiTxHHjZsRIjQ0dtBcU7x7h8kEi+B090JDZ48Hs+gHdNQQ+JCgKy2E+MjuS7ednwIyGpf89ltdvIceXSEOiR4shizBjlMn7YTYncKnNuDJ5m2s6RkWViRbBdvyfGupo/8rHwjeBLWIxsDW0iyfCikOkkYTw4yQiJSmSSNi4EkeBoB+VAwl+Q8iXSWjLlkqcjYoiUkF3FCgieRBAautgtHwia3RojEiEjQZCky8mRttgH/TQQJnoYhq+2sIZowHo6E2RbaZnJrxFBkhGQcyWi35UjwJAaS4GkE5EPBXNmZ2WRnZAMydWdFcpEh0oFs0SIGkuBJJAVZcWd9cpERH/K+WoOMPFmTWQu7JHgahlxRW4ckjQshzGQkjPdKwriQ4GlE5MrPfFKuwLqkpIdIBzLylAQSmCsowZNICjLylATkGmMcSYVxq5HgyZrMmiGS4Gk4ckFtGbI5sEg30v1YiySMW5tUGLcgufIzn0zbWZfkBop0ICNPYiBLB08+n4+ysjKzmyEsQFbbWV+q5QYqioLP56O+vh5N00xrR6q9r8lKgidris25TNzfSkI3BtY0jcbGRgCqqqqM4z6fD4BAIIDb7TY27/R6vTQ0NCSyiTHkito6JOdJ7M5o+5fhqKpKU1MTdXV1aJqGy+WKS5uHI72PtUSDp57+Hnr7e8nKyDK5RWKgRF9iJDR4UhSF1tZWiouLjWPRTioaJJWXl4+ocxPpJTptJ8GT9VjlImM8+xdFUdA0DZ/PR3NzM3V1dXFr96AkVcBy8hx52LARIUJHbwfFOcW7f5BIWQkNnrxeL4FAIGYIXFGUmKs6l8uFoiijCqCCwSDBYNC4394ueTGpJjryJDVWrMvs3MDR9i8+n49AIBDzHEVFRXi9XgBKSkqM52xsbKSiomKX15S+J33YbXbyHHl0hDokeLIQsy7eEho8DaalpSXmSrGoqGjU+QW1tbUsXLhwnFtmnStqIdN2YmyG61+iQdJgZs6ciaIoxmN2DrKi4tX3wIBpOxmEsoz8rHwjeBLWIqvtwOioFEVBVVUjZ2EoNTU1tLW1Gbc1a9aMa3skYdN8A6ftpCijxSTZj2OoQGig0tJSVqxYwTXXXMN9992H2+0e9Lx49z3CWiRp3OISOPpt+shTSUlJzEhTNKkTwOPx0NLSstvncDqdOJ3OeDVRWEB0tV1vuJee/h5yMnNMbpHYmRUvMobrX4ajqiq5ubncdtttwNC5UtL3pBdji5aQTM+mO9ODJ4/HQ3V1tXFfVVXLJIzLCId15GbmkmnLpC/SR1uwTYInMSJj7V9Gmou5JzlPT82vYN8Vb4HNRgTbgGk6Gxn0c7U9gz5bH/ypimZ+o399kHMjoB+zQXTyIgJEbDbYfm5kwBX5YOeGbXa6HNnGrTMrl00TitmQN4kvXHuzPm+yJLEDGXt1Y8+DXy9+i1+1y+dDRriffds2sH/bBvbu2IKrpx1XTwcTQt1k9Ydw9odw9PfhCIewRyLYIhFsgC0SJvrbueNYzG/2iB1DmEW2fjLIYvm9FYSHmFDbMO9HfPvGX+3Jtxsj4avtmpqa0DQNt9uN1+vF7XYzf/58I3mzpqYmkU0aEbMTYYX+MyhwFhDoCdAWbGOvCXuZ3SSxnVVyA8ezf4nmSkVX3X311VesW7dul/P2KOcp1Isz3DfMCTb0Ma3Q9pt5vs4u5N97H83TB5zIuvwpprbFTNl9TuxAf6Sb3lDY7OaYIxLhiMAXnLv6TWZu+oT8ULfZLdrOBvRvv+0q0jf48bFKaPDk8XgGveobLnFTiKhCZyGBnoCsuLMos6ftPB4PM2fOpLGxEVVVjeNerxefz2ckfo90NW9ra6tR6+npp5+OGWGKqqmpYcGCBcb99vZ2ZsyYMaL2nvjft9Ddvg2IQHSUO6L/29nyArd8fBcfZjv56ZELmDn5hB0j4Tudy1DHiWwfgtr98Uh/P2zrJLKtk0hnJxFNI7xuLeE1XxH+9BMm9bRxgfovLlj9bxwXzsH5s19imzBhRN9nKvnrh+/xpOrn8lOm8IPDvml2cxIuvGEDPXV/oP+dt3YczM8n4+BDsO93ALbJk7EVFWErKMTmdILTiS3LCVlZYLfro5fb/2+z2fT7NjvYo//Wx6NG47kv/8HfV/0/PJ1d/OjEOkJTSwc97+QpRXvwne/K9Gk7K7PKFbXQSa0nsTvjVeuppKSEF154gUmTJuHz+Xj77be59NJLdzlvT3KeJk8fZvQ0spytG2Fjjo28g6az7/6Hj+k1xkO4p4dtb7+N9vdH6Xz1VUKP+7Cv+IDp995D1ggDxVSxd/72D2B7D9Mn5prbmATr8r/H2p/+lP62NmwOB4UXfJfCCy8i55ijsWVkmNYuZ7iYrzfb2GaHae7psF9JQl5XgqcRMPuKWuikXIE1WSk3cLxqPXk8HhoaGjj++OPxer1cc801MaNZUfGs8xSxSLdjz84m/xvfIP8b32Db2++w/rrrCK5axeo5Xoouv5yJF88nc9Iks5uZEEbCeJqMfkciEbrefpvAg4vofPVViETIPvJI9r61HucBB5jdvBhjyZfaExI8iaRhBE+yv50lWTU3cKy1nubPn8/y5ctpbGwc8ry41Xmy6Hs54YTj2X/xY6z95dX0LF/O13ffTWtDAwXnnMPEyy8j54gjzG5iXBVk6at+U71UQbinh7Z//pOtDy4iuGqVcbzgnHOY9vv/wp6bXqNug7FknSersNIVtdjRccnIk9hTI6n1VFVVxdFHH01RURGZmZmDVhhPRJ0nqwWljr32Yv+HH2LvP/2J7GOOJhIK0fbkk3wxx8sX37+U9uefJ9I3XCJ88kr1Ok+hTZvYfMedfP6Nb7LxdzcQXLUKW24uE7//fdzPPcs+t99mucApbSuMJwOrdV7pSqbtrClRnVd9fT2tra27HC8uLo7ZCHhnY631BDs2GB5q5Cld6zzZHA4KzzuXwvPOpfuDDwg8uIj2F16ge9ky1i1bRua0aUy85HtMnDuXDBM2VY6XVA2eBv4M2R74OvbZh4mXXoprzkVkFBSY3ELrkeBJJA3Z3y69DRcgDcfKteRSQc4xx7DPbccwpeo6tv7f/6E9+hh9Gzaw5bbb+fqeeyk8/3yKLrsU50EHmd3UPZZK03aRUIj2F19k64OL6P7gA+N47syZTLzicvLPOMPURPAxSacK40KMlKy2syYrrUpN1lpyqcAxdSpTfvUrJv30p7Q//QyBRYsIfvIJ2mOPoT32GBNOOpGJl11G3umnY7MnZ8ZIKow89W3divbYYrY+8gh9mzYB+khiwbnnUnT5ZWQfbt7KzrGQaTsLk9V21iDTdmJ3UqmWXPQjIdn6H7vTiWvORRRedCFdzc1sXbSIjpdeZtubb7Htzbdw7LcvRd+/lMKLLiQjL8/s5o5KNHjq6e+ht7+XrIwsk1s0csFVqwg8uIi2p54isn2FaMakSUy8+OKUWDGZ6L8SCZ5E0pBpO2tLtg95EV82m40Js2czYfZseteuZevDj6D5fIS+/IpNf/wjW/78ZwrnXETRpZeSte++Zjd3RCY4JmDDRoQI7b3tTMqxdsARCYfpfO01ti5axLY3dxS2dB5+GEWXX07BOedgz0qeANBKJHgahpWmI4RM21mVrEoVu5M1fTpTq6uY/PP/QHvySbYueoje1avZ+uAiti56iLxvfIOiyy8j94QTLL1Ax26zk5eVR0dvBx29HZYNnvo7t9H2xBNsfegher/8Uj9ot5Pv8VB0+WXklJVZ+n0eDbP6HwmeRNIocOrJml19XYT6QzgyHCa3SAyUKp2xVUS2j+Sl0oiefcIEii65hIkXX8y2N94g8OAitv3rX3S+8gqdr7yC86CDmHjZpRR+5zvYc6y5+XdBVoERPFlN79q1bF30ENqSJYQ7OwGw5+fjmjuXiZdcQtb0fUxuYbxJwrglyBW1teRn5RtD5m29bZa96hNij6V4IGqz28k79VTyTj2VoKqy9aGH0P7xJMFVq9h4w41sue12XPP0D3zHtGlmNzeG1ZLGI5EIXc3NBB58kM6XX4GwvmFx1gEHMPGyS3F997vY02AfQsl5GiC6o7mqqlRUVMRssSDSj91mp8BZQFuwjfag9fMNhBC753S72euGG5j8q1+h+Zaw9eGHCa1bR+t9f6P1/v9Hfnm5PtV03HGWGN20SvAUDgZjVjVGTTjlFIouv4wJp5yStKsak8G4Bk+aptHY2AjE1mTx+XzAjuJ0I6mxEt3Ms66uDk3TTA2crPAHK3SFWYW0BdtkixYLSqXpJUtJk7c1o6CA4h/9kKIrLqfj5ZfZuughut59l47nn6fj+efJPuIIii6/jPxvf9vUJOd8h7n724U2b0b7+9/Z+vdH6d9eKd+WnU3hBd+l6LLLcJYkZmNcq0iJUgXjtaN59Lk0TcPn89Hc3ExdXd14NnVEJGHcegqdhdAhSeMi9aVr72PLyKCgvJyC8nJ6PvmEwKJFtP/zaXpWrmR99fVk3PonU5fXmzXy1P3hSgIPPkD7c89DKARA5rRpFH3/Elxeb0pVch+LpJ62G68dzaM1WUpKSoznbGxsHHRvKYjvzubCWmR/O+uRiwwRL9mHHsref/gDU665Bu2xx9j6yP/Rt3mzqRsSJzJ4ivT10aG8RODBB+n2+43jOccdR9EVl5Pv8WDLtHT2TWKlUoXxse5oPnPmTO644w58Ph/Lli0jd5jNCOO2s/l2Mh1hHdEVdxI8WY9Mb48neS8HyiwqYtJPfkLxj39M+wsvElj0ID0fLKftySdpe/JJcsrKKLrsMvI9Z8Y9mEjEFi39bW1oPh+Bhx+mb/0G/aDDQcG3z6bossvJOerIuL22GBlTQtaR7Gjucrn47LPPjH/7B0TdO6upqWHBggXG/fb2dmbMmLHH7ZQrausxaj1JzpNIcclaYTyedrsh8d7TKLokvtNY8Rx5CqoqgUWLaPvHk0S6uwHImDgR18XzmXjx93BMnTLur5kqknrabjBj3dFcURS+8Y1v4PV68Xq9zJ0715juGy9Ln3yJ9c+9SPRtj0SvnG02ItiYEPqQ7/X1k//Gv3nigfbtpw1+rvGTi7k/8By2DynaiAw4V7+vHwhnOghl5xLKyaUvewI9+YV0FU0hkiHDslErtulz/a989gUdGz42uTUWEu4npy1ATlsAR1cnju5tOHq6sPf3Yevvw97fjy3cb/zfMOD6wDbwzhBlOmyDHO8KB7g02E+WbTNPvXD9kE2ccPihnPnLH4z2OxNiUINuSLx+A5v/dBtb7r4nbhsSR4On9tD4pIdEwuGYmldRzkMOoejyyyg47zzsTue4vJYYP3H/VB7rjubR6b5o4vhXX33FunXrBj13rNN2m5e+z0GvPjXk1w8x/vXZ9lvi9dvsbMqdyEdF+/P+5IN4Y++j6MlM3z8kx8Qg2XvBR5s24X9PNbs5prGH+ynb/BkzN33Mka2rmdG5GcfAoCjBjgGgA3hyyHNWbd4ISRY8NTY24na7jXIpwnoSvSHxeI08hbu6aHvySQKLHqJX3d6X2WzknXEGRZddRu7xs2UqfARi6zEmac6Toig8++yzrFy5kuXLl/PQQw8ZO5pfc801dHZ2MnPmzBGPILW2thrlCp5++umYpPCBxjptN3XWcaz6+oIBV9mRHVfWkQhbQp8QCLVQlHkAUzIP1a/MjZ9TBCLbawAPeMyO+xFsw50b/fr2c4lARl8vjp4uMru7cPR0kd0eILM3yN7bWtl7WyueNcu4+qOnWH3S2XxaPod+pzUr8MaT2rOGtztgxiQ448Ddj2CmnHA/+73zEoe++Bg5bbHT3+GMTLoLiwjl5hHKmUAoO5dwpoOIPYNwRgZhewaRjAwi9gzjMZGBnfMgHXXM1xn83K5wK1/0/Jssex4HZp85ZNMnHHbIkF9LlNGUU1EUBcBY3OLz+UzZYFim7UZm5BsSX0RG3tiLRu5p8BRav57Aww+jLfYR3r64yT5hAi7vHCZ+//tJs8+f1ST1tJ3H40HTNJqbm2OSxEtLS0ddrqCkpIQXXniBSZMm4fP5ePvtt7n00ksHPdfpdOIcw7Bm2flnUHb+GUN+/falt/PAyi/4wRFn8KOZ14z6+fdUJBKhb/MWgp+vouvdZjqefx6+/JKDX36cwz96k2kLbyLv9NMT3i4zvbZmM2+/DMUFfdScc5jZzUmovi1bWPfrBXQtXQpAhstFwTnfJvf4E8g+4nAc06Zhy8jYzbOMv2WblvGH599i/4KpLLiwNuGvPxqjKafi9/spLS0F9LzLpqamxAVPMuIwZrEbEq9j68MPj+uGxGNJGI9EInT7/QQeXESHokC/Pkrs2Hdfii69lMKLLiQjL2/UbRHmGfdpu/EqV+DxeGhoaOD444/H6/VyzTXXoKqDT9OkaqkCm82GY+oUHFOnkHfyyUy++pd0vvoqm2pvIbRmDWsqf0L+2WdT9P1LyJk5My2GeAud6bU5cCQcpuvdd9F8S+h48UUivb3YJ0xg8tW/xHXxxbIj+iiNpn8CYs4bTKr2Pakia/o+474h8WhGniK9vbQ/9xyBBxfRs3KlcTz3xBMouuxy8k4/zZQLnlSSEkUyhzLWcgXz589n+fLlNDY2DntevEoVWG21nc1uJ/+MM5hw4ols+e+7CDzwgFF9N2u//SicM4fCC76LY0rqrsgwShWk+Gq70KZNtD3xBNqSxwmtWWMczz7iCPa+tR7nCBZdiJEZqn8qLS01Ltg0TWPWrFm7PDaeZVKM1XZpcFEUb+O5IXE0eAr2Bwn2B3Fm6LMekYienkEkQv/WrWx99FG2/v3v9G/5GgCb00nh+d9h4qWXkX3IwfH9hkXcmbaMayTlCqqqqqivr6eoqIjMzMwhEzbjVaogymo5B/acHKZWV1F4/nfY+sgjtD/zLL1ffsmW229ny5//TN5pp+HyziHvtNOwORxmN3dcRUsVdPR20B/uJ8OeOldtkVCIztdeQ1vso/Nf/zI2+LTn5VFw3rm45njJPvIIy32YpuIG2oFAAK/XS319PYqioKpqTI5UVLz7HjG+drch8aY//BGb02kEQYTDehA74D6RCI/09wGg1pXu+NoQMqdMYeIll+CaP4/MiRMT842mowjWLZJZX19Pa2vrLseLi4sH7ViixlquAHYkdQ438jTWnKdkl33YYUz7r/9i6vXX0/78C2hLltDt9xtXUxmTJuG64LsUXjQHp/sAs5s7LqIjT6AHUK5sl3mNGSfB1atpW7IE7R9P0v/118bxnJlluOZ4KTjrW9iHKRJrFWYHdfHon6KPGypHM137nlQQsyHxksfZ+tBDhNatIzLEwqSBdnxwhoc8J/vooym6/HIKzvpWyl3EilEGT8N1QMMZa7kCsyXLFbV9wgRccy7CNecigqqKtmQJbds/iFv/9j+0/u1/yCkrwzVnDgVnn5UUH8RDcdgdTHBMYFtoG229bUkbPIW7u2l/4QU0n4/upcuM4xnFxbguvCClAt5ESa3+yVqji6kso6CA4h/+gKLLL6P3q6+2j2Bsvxiw2cBuN2ry2WyA3c6lz13Ghq6N3H3m3Rw+6Qj96wNutsxMMvLzTf7O0oNZn9PjPm2nKApNTU1omobb7cbr9RrlCqLJ4TU1NeP9svGVRP2Y0+1m6nXXMeVXv9KngHxL6Hz9dbqXLaN72TI2/eEPFJxzDi7vHLKPPtr00YKxKMwqZFtoG+3B5ErOjUQi9Hy4Em2Jj/annyHc2al/YftUgmuuV69Fk2RXqVbLDRxOMvVP0WK6VksbSFW2jAycB4zsgiU8eSJbA5voKHCQOXlynFsmRsKW4H5o3IMnj8cz6FWbGfVR0pnN4SDf4yHf4yG0aTNt//gH2pIlhL76Cm3xYrTFi3EedKCeZP7d7ybVXHyhs5D129YnTdJ4v6bR9s+n0ZYsIfjJJ8Zxx4wZel2aCy/EMXWqiS0cH8nwIS/9kxgPidwcWFiT7PsxjGS6oh6OY+oUJlVWUFxxFV3NzWg+Hx0vvEhw1edsvqWOzbfdTv4ZZ+DyzmHCSSdZfulsMmwObJQYWOyjo6mJSG8vALasLPK/9S1c3jnkzp49LhWPhRCJle/YvkVLb3KNfqei2M9piyaMp6tkuKIeiYHF4/p/+1van3kGzbeEnpUr6XjhBTpeeIHMadO259xcRNb06WY3eVDG5sAWDJ6GKjHgPPRQXHPmUPid8+K2YalILVKqwLpk5Ml6krrCuEgeGQUFTPze95j4ve/R88knaL4ltP3zn/Rt2MDX9/6Fr+/9C7knnoBrjpf8co+lNqY0CmVaZNputyUGvHPJPuLwlP8QTJWLDEtI8d+VZCfBk5DgaRipMm23O9mHHspev/1Pplx3LR2KQtuSJWx78y263nqbrrfexl5YSOF55+Ga6yX70EPNbq4RPJmdMD5siQGvl4KzztptwT0hRPIZyxYtIj5SusJ4skuXK2q700nhuedSeO659K5dR9vjj6M98QR9Gzaw9eGH2frww2QfcQQu7xwKzj2XjIKC3T9pHJg5bRfu6qL9hRfRluxUYiAFa2qNVLKU9Eg28q5al4w8WY9M2wlLyJq+D5N/+Qsm/cfP2PbmW2hLltDx0kv0rFzJxpUr2XRLHflnfQvXHC+5s2cldEoq0Vu0GCUGfD7an9mpxEC0mnsSlhgYb6k+LSlEVDR4ag9JwrilJLALkuBpGHJFrdc+yTv1FPJOPYW+rVtpf+opNN8SgqtW0f7UP2l/6p849t0X10UXUXjhBQlZcp+okSejxIDPR/DTT43jeomBOQn7fq0uXaa3hYiSkScLMan7keBpBOSKWpc5cSJFV1zBxMsvp2f5cjTfEtqffZbQV1+x5c472fLf/03eqadS6J1D/je+EbeRmHiWKth9iYHtI21SYkDElY1ImqQLJCMJnqxHpu2E5dlsNnKOOYacY45has2AffWWLaPztdfofO01MoqLKfzud3F55+Ac4T6GI2UkjI9jjZXQxo07SgysXWscdx56KC6vVy8xUFg4bq8nxEilS85lMpGEcSHBk9gj9txcXBddiOuiCwmqq2l7fMfqs8D99xO4/35yjjtOTzI/+2zsEybs8WsOnLaLRCJjHhmMhEJ0vPoqbb4laV1iYE/JtJ1INzLyJCR4GgG58hsZp/sAplx7LZOvvprO11/fsa/ee+/R/d57bPrDH8k/59u45swh59hjxxyUREee+iP9bAttIy8rb1SPD6qr0Zb49M2TW1uN47kzZ1LonSMlBsZIgkyRLqLBU7A/SLA/iDPDOnXw0o1UGBcpw+ZwkH/mmeSfeSahzZtp+8eTaEt8hL78ijbfEtp8S8gqKdGTrr97PpnFxaN6/uzMbJwZToL9Qdp620YUPBklBnw+upftVGJge0X1kW4KKtKHoihomoaqqlRUVOAyoTq8BKXWM8ExARs2IkTo6O3AmSPBU7qxfPDk8/mora1l2YAPvESR6Yg955gyhUkVV1F81ZV0L12qJ5m/8AK9LS1srq9n8+23k//Nb+r76p1yyoj31SvMKmRz92bagm3sk7fPoOfElBh4+mnC27bpX4iWGJjrJe+009K+xMCeSqZVqZqm0djYCEBVVZVx3OfzARAIBHC73Xg8HlRVpampibq6OjRNS2zgJAGTpdltdvKy8ujo7aCjt4NJOZPMbpJIsIQHT6PpvEDf7byhoSHRzRTjzGazkTtrFrmzZjH1t/9J+zPPoi1ZQs+KFXQ0NdHR1ETm1KkUfve7ZO41FSIRfQlqJKLf0P8f2X78nA9DtHaH6Wn9O60F+xIJR2LOjfT20vHSy1JiIIGSYXpbURRaW1spHjDaGQ2Sov1MeXk5Ho/HGHXy+Xw0NzdTV1dnVrOFBRVkFRjBkzBP2lQYH03nJVJTRn4+Ey+ez8SL59Pz6WdoS3y0P/kUfZs20bo9sN6dc6L/eHkxm4c5z5aVRf5ZZ+GaM0dKDAi8Xi+BQABN04xjiqLEjCq5XC4URQGgpKTEeExjYyMVFRUxzxcMBgkGg8b99vbxWwFqbAycBEFpOpKkcWtJ+VIFo+m8RhpAxasDS6bpiGSVfcjB7PWb3zDl2mvpfOklOl56mUgwqE9bGDew2ewxx5ZuWsqGro0cPflo9i88IPZcux2w4Tz0EArPkxID8Zbs09stLS0xF3NFRUVomsbMmTONIKqoqIhAILDLY2tra1m4cGHC2iqsQ4InC0rgdLclcp6G6rxGKt4dmCRsxp89K4uCb3+bgm9/e0TnN7xxA098/gS/PO5MTjr6qji3ToxEKo2QBAIBvF4viqIMO21XU1PDggULjPvt7e3MmDFjHFqQOu9lqsp3bN+iZRzrzYnRM2uQwxLB02CiV3mKoqCqKj6fD6/XO+i58evAhFXFo1CmSG719fW0Dig9EVVcXByTX7mzkpKSmIu1aN4l7MjLHKrvcTqdOJ3xWWkl03bWJiNP1mJLcAw1rsFTPDovj8dDS0vLsK8brw4s2acjUlk0eIr3/nZiBCzyZzJcHzMcj8dDdXW1cV9VVcm5FLsV3SZKgqf0NK7BU6p2XnLlZz3R7REkeLKOZJjeVhSFpqYmNE3D7Xbj9Xpxu93Mnz8fn89HIBCgpqbG7GaKJBAdeZLRb3Ol1Wo76bzEnjJGnnoleBIj5/F4Br0wG2pazkwWGdATQ5D97azFNuC/iZDw4CmpOi9ZbWdZMm1nHTK9HQcDR/GsP6CXliTnKb1J0ZsRSIbpiHQT3Ry4PShD5lYh09sinURX20nwlJ4keBJJSabthBBmkpwnazBrhkiCp2HIdIR1RfMNgv1Bevp6TG5NepO/k/iIbB/IkxE9a5JpO2uxQUKLZErwNALSeVnPBMcEMmz6JsKS9ySESDRJGE9vEjyJpGSz2WTqTqQwuWCzuujIU2+4l2B/cDdni1QjwZNIWlLryRpkVWp8GBXGZcGKJeU6crHb9I9QGX0yny3B6QMSPI2ATNtZk7FFi6y4swT5kBfpxG6zk+fIAyRpPB1J8CSSlkzbCSHMJEnj5otdsCIJ45Yg0xHWFq31JNN25pLVdiJdSdJ4+pLgaSRkNsKSpMq4tcj09jgaMAUq76t1ychT+pLgSSSt6K7mMm0nxoPP56OsrGyXYz6fL2bjciGiJHgynxTJtCCZjrA2mbYTw9E0jfr6eurr62OORwOixsZGFEUxjnu9XoqKimLOc7lceL1eiouLaWxsTFjbQTYGTgZSZdw6Ej0+m/CNgUcr2oH5/X6qqqpMaYMMm1uTrLazFqv9nSiKQmtrK8XFxcYxVVVpamqioaEBgPLy8kE3KofYzcpbWlqorKyMb4OHYLX3VewgI08Wk8AVvwkPnjRNM67gBgZDPp8PgEAggNvtxuPxoKoqqqpSVVWFpmmoqorb7U50k4VFyWo7a7Dqwgqv10sgEEDTNOOYoii4XC7jvsvlQlGUIQOo6GPKysooLS3d5WvBYJBgcEeBxPZ2CeTTiQRP6Svh03bRq8GBoleDXq+XiooK6urqAHC73TQ3N1NeXm5K4CTTdtYWnbaTkSdrSIY6Ty0tLTEjUUVFRTHB1c78fj+aplFRUYHf79/l67W1tRQWFhq3GTNmjFNLrf9eClltZwVmfU4nPHjyer2UlJTEHBvqalDTNGbNmkV1dTUNDQ2Ddl6gX/21t7fH3MaTDJtbk4w8ifEQCAQAvR9SVdUYBVdVlblz59LQ0EBZWZlx3kA1NTW0tbUZtzVr1oxbuyLb+51kCErTlYw8WUda5jwNdTX42GOP4fV6cbvdNDU14fP5Bh06r62tZeHChYlssrCAaPC0LbSNUDiEw+4wuUXpyYwrv/r6+l1GsAGKi4uHzY0sKSmJGWmKpgkAeDweWlpajK+53e6Y+4NxOp04nc5Rtl6kinyHBE/pyhLB02ACgQDz5s2jsbGR0tJSY+h8MDU1NSxYsMC4397ePi7D51bN5RC6PEceNmxEiNAebKc4p3j3DxJxk8gR2rEuHvF4PDFlB1RVHTbfSYjhyGo785lVYXxcg6fxvhp0uVwj6iTjffUnw+bWlGHPID8rn/bedtp62yR4EjEURaGpqQlN03C73cYo9vz58/H5fAQCAWpqasxu5pDk0s36ZNrOOpJ62k6uBkWiFToLae9tl6RxE1l1hNbj8QzajwwsQWBZcsGWFCRhPH0lfNou2a8GhbVEOy8plGkB8nkv0kx05Kk33EuwP4gzQ/LfEs6ka7eEB0/JeDUoq+2sS1bciVRlzfE8MVCuIxe7zU44EqajtwNnjgRPZrEl+A9GtmcRSU22aDGf1EOLL7l4sy67zU6eIw+QpHFLSOB0twRPw5APBeszNgeW4Ml08iEv0pEkjZsrbYpkJiNZbWddxrSdBE8ipUifkywkadwaEv0XI8HTMKy6ikjsYEzbSc6TaWSENr7k4s3aZOQpPUnwJJJadORJShWYT6btRDqS4Ck9SfAkkppM2wkhzCRVxs3VH+kHwEaERE7eSfA0DJmOsD4pVWAB8mcy/mw2IjKQlxRk5Mlcof4QAFlSqsB6ZDrCuqRUgXVIbk58SP9jbRI8mSsU1oOnzARfxUnwJJJatFRBR28H/eF+k1sjhEg3strOXNHgyZHgBV4SPA1DVttZX3TkKUKEzlCnya1JT6kyve3z+SgrK9vlmKIo1NfXJ7w9we0jeZn2hG8EIUZBRp7M1dPXA8i0nSXJdIR1OTIc5GbmAjJ1ZzarTS9pmkZ9ff0ugY/P58Pn89HY2IiiKMZxr9dLUVGRcV9VVWOTcrfbjaqqCWt7X6SfLRkZAEzNnZqw1xWjl++Q4MlMm7o2ATClr08qjAsxGka5AlntIgZQFIXW1taYY6qq0tTUhNfrpaKigrq6uiEf73a7aW5upry8HFVVcbvd8W6y4cPOtfTbbORFYFLOpIS9rhg9WW1nnt7+Xj7b+hkA+4X6EvralgqeBhs2Lysro7y8nOrq6oS3J1WmI1KdlCswl1X/TrxeLyUlJTHHFEXB5XIZ910uV8zo00CapjFr1iyqq6tpaGjA7/ePa/s2bdvElq4tu75uj8atq/8BwDfCWWTYM8b1dcX4kmk78yxZtYTuvm6m9Ic5KBRK6GvHdTJd0zQaGxsBqKqqMo77fD4AAoEAbrcbj8cD6J1dQ0NDzHPU1NTg9Xrj2czdstp0hIglK+7ESLW0tFBcXGzcLyoqQtO0Qc997LHH8Hq9uN1umpqa8Pl8lJaWxpwTDAYJBoPG/fb2kY8+/O/K/+Whjx/iyOIjOWLSEWRnZLNh2wbeWP8G20LbyAuH+Vlf9ui+QZFwkjBujmfUZ7i1+VYAfrQtlPCRoLgGT9Fh84GdVXTYPBoklZeXG8HTYFRVRVEUmpqahh1iF+nL2BxYaj2JMQgEAoDeX6mqis/nw+v1Mm/ePBobGyktLUXTNCoqKnZ5bG1tLQsXLhzT60ZzNT5s/ZAPWz+M+dpBudP44yo/Mwb0ncKaoiNPveFegv1BnBlOk1uUurpCXTy3+jke++wxPmr9CIDy/cr53jtPbD8jcQMdcQ2evF4vgUAg5spuqGHzoQKo6IjVwE5tZ3ty9SeSn0zbmcuMVan19fW75DMBFBcXx4xy76ykpCSmP4qOfgN4PB5aWlqMr7lcrmGfC/SR8QULFhj329vbmTFjxoi+h9u/cTtburbw5vo3+bL9S0LhEC6ni+OmHMdxba3YVnpBVvxaXq4jF7vNTjgSpqO3A2eOBE/j7bOtn7H408U8rT5trKp22B1cedSVVB5did0InhIn4WtgRzNsHs1F8Hg8aJoWsxJmoD25+hsJmbazNpm2s4ZErkrdXVAzFI/HE5M/GV1NN1ZOpxOnc+wflpNzJ/PdA7+76xc6Bs/DEtZjt9nJc+TR3ttOe2+7JPiPk2B/kBe/eJHFny3mvc3vGcf3zd+XeYfM4/yS85mYPdG09lmigMhQw+Yej8eoswIMmfu0J1d/IvlFp+1ktYs5rJowHp3u1zQNt9tt5C/Nnz8fn89HIBCgpqbG7GaKFJCfla8HT7JB+R7b0LmBv3/6dx5f9ThaUAMg05bJN/f9JvMOmcfsvWZjt5m/1m3MwVMihs1hR8A03NXhaK7++vv7CY0wKz+PPKZlTcMZdtLT0zOix5jF4XCQkZGeq3Jk5Mlc4UgY0Ds4K/F4PIP2G2YvQBGppyCrgHWsk6TxPfBR60fct/w+Xl7zstGnTJswDe/BXi488EIm5042uYWxxtzbWWXYfDQ6OztZu3btiHM0Tp9wOrMPnE0BBaxevTrOrdszNpuN6dOnk5eXZ3ZTEk5ynszV298LQGaGtYInIRJFVtyN3SeBT7j3/Xt5Zc0rxrHjpx3PJYdewunTTx9hqY7tn+kJTB2I+2o7qwyb9/f3s3btWnJzc5k8efKI8jNytuXQ0dvBpJxJps6t7k4kEmHLli2sXbuWgw46KO1GoIzgSVbbmSK6t1SWPcvklqQia06JilhS62n0Nndt5s5ld/JP9Z+Anjt2zgHncOVRV1LiKtnNo80X1+DJSsPmoVCISCTC5MmTycnJGdFjMkOZ2CN2HE4H2dnWrrcyefJkvvjiC0KhUNoFT9GrPhl5Mkd05Mlhd5jcklQii1SSiRE8hSR42p3e/l4WfbSIxuWNdPV1YcPG2fufzU+O+QluV+Kq+O+ptBtnH82KoL6wXu49w2b9YCSd998ztmcJthOJRNL6vTBDoEdf8BFN3Bci3cgWLSPzr7X/4pZ3b+Grjq8AOHry0dTMruHISUea3LLRS7vgaaTCkTDdfd0AZGdYe9Qp3UWDp75IH119XUxwTDC5Rell+ZblALgLk+eqUYjxJNN2wwv0BLjl3Vt4bvVzgL5f46/Lfs157vPGZ+WcCfXQ0jp46gv3EewPkpOZE/MD7Av3sXHbRsKRMA67g+xMCZ6sLDsjmyx7Fr3hXtqCbRI8JdD7m9/n7Q1vA3Da9NNMbo0Q5pDgaXCRSIRnVz/LLe/eghbUsNvsXHbYZfz02J/GqZ9OkYRxq+vo7WB953rsNjvOTCcZtgz6w/309PcYK/L2mrCXTANZnM1mo9BZyJbuLbQF29g7b2+zm5Ty+sP9PNnyJPXN9USIcM4B57BfwX5mNyv1SL54UpDVdrvauG0j//X2f/H62tcBOHjiwdx80s0cMekIk1s2PtI2eIpEInQF++jrs9MX7qMr2Bfz9axMJ1Nzp5Jpy6Wrt2+IZxlejiNDAq8EMYInWXEXN5FIhE8Cn/CM+gzPrX6Ozd2bAZi11yx+d8LvTG5dipF+I6nIyNMO4UgY32c+bl92O9tC23DYHfzkmJ/wwyN/mFKLStI2eOoO9XNy7bu7OWvVHr3GRzefRW7W8G/x3LlzmTVrllE3a+7cuSxevHiPXjcdyYq7+FnbsZZnVz/LM+ozqG2qcbwgq4CKoyu45LBLUqpTFGK0JHjSfdH2BTe9dRPLNi0D4JjJx3DzSTcn1Sq6kUrb4MkqioqKjHIOfr/fOO7z+aitrWXZsmVmNS2pSKHM8dUWbOOFL17gny3/5P0t7xvHs+xZnD7jdM51n8up+5xKVobUdhIi3Vfb9YX7ePCjB7n3/XuNPOKrS6/m4kMuHmGRyz0lCeMJk+PI4KObz4r7a+zO0qVLaWhoAKC6utr4t9frNf4tds8oV5Cmndd4iEQivLPxHRZ/uphX17xKb1iv32TDxuxpszn3gHPx7OcxPiiEELqBOU/pVi7lk8An3PDGDXwc+BiAk/Y+iRtOvIF98vZJfGNSpcK4ldlstt1OqcXbwD3+qqurqaurM/b5E6Mj+9uNXW9/L8+tfo4HP3qQz7Z+Zhw/0HUg3y35Lt8+4NtMnTDVxBYmhs/nA6C5uZm6ujrjuKZpMRc2iSUZ48kgekERCocI9gfTYoV2sD9IwwcN3P/h/fRH+inIKqBqVhXnl5yfFsFj2gZPVrB06VLcbjc+ny+msxajJyNPoxfqD/HE50/QsLyBzV168ndOZg7nl5zPnIPmcGjRoUndCWqaRmNjIxC7F2c0SIpuSu7xePD5fLhcLjweD6qq0tjYSEVFBaBvMxUIBBLc+uR939NRbmYudpudcCRMR29HygdP721+jxveuIEv2r8AoHy/cn5z/G+YlDPJ3IYlkARPJhpq+xoxepLzNHL94X6eVp/mLx/8hXWd6wCYkjOFSw67BO/BXuO9THaKotDa2kpxcbFxTFVVmpqajFGk8vJyPB5PzJZRLS0tVFZWAnqg5fV6efTRRxPbeJFUbDYb+Vn5tAXb6OjtYHLuZLObFBfbQtv4s//P/P2TvxMhwqScSfz2+N9y5n5nmt20hJPgyaIURUFVVaPzFsOLbg0iwdPQIpEIr619jduX3c7qttUAFGcXc9XRVzH34Lkpl/zt9XoJBAIx0+OKouByuYz7LpcLRVGMixhFUSgrK6O0tBS/309paWmCWy2SVb5DD55SdfT73+v+zc1v3cyGbRsAuOigi1hQtsAaF1smzG5bKngaLOdgqDyEVOfxeGhpaTG7GUnDyHmSOk+DatFaqG+u5831bwL6SN2PjvwR3zv0e+Rkjmyj7FTQ0tISMxJVVFRkBFd+vx9N06ioqDBWvvr9fvx+P6qqDhpMBYNBgsGgcb+9PTU/OMXupWq5Aq1H49alt/JUy1MA7JO3DzeeeCMn7n2iyS0bTIokjO9pzkFRUdGQeQhCDCTTdoNrC7bxlw/+wt8/+Tv9kX4cdgeXHX4ZVx51paya2y4QCKCqKnPnzsXtdlNbW0tdXR0ej4fS0lIaGxtjRq8Gqq2tZeHChfFrnAl7domxSbUq45FIhBe/fJE/vvNHAj0BbNi49PBL+fmxPyfXkWt280wX1+BpT3MOBl7lDcxDEGJn0Y6rPShX/qDXXVny2RLufv9utKAGwBkzzuDamdcyo2CGuY0bB/X19bS2tu5yvLi4OOZCbWclJSUxgVD0As7tdg850ltRUTHkRVtNTQ0LFiww7re3tzNjxji8v0mcqJ+uUmnkaXPXZn7/9u95Zc0rAJQUlrDw5IUcM/kYk1tmHXENnvY052DgY3Y+NpAMnYvoyFNPfw89fT0pv9plOO9ueJdbmm9h1Va9Qv6BrgOpmlVl0WH2sRkuQBqOx+OhurrauK+q6h4t2nA6nTidzjE/XqQOI3gKJW/wFIlEeHzV49y29DY6Qh1k2jO56qiruPKoK1MuJ3JPJTznaTQ5B9GkzZ2P7SzuQ+fC8vIcefrGzpF+2nvb0zJ4WtuxltuW3obylQLoo3E/P+7nzD14Lpl2S6U3JoSiKDQ1NaFpGm63G6/Xi9vtZv78+fh8PgKBADU1NWY3U6SIZK8yvqZ9DQvfWsg7G98B4MjiI1l48kIOnniwyS0biTStMD5UzsFgxwYTt6FzkTRsNhsFWQVsDW6lLdjGlNwpZjcpYbpCXfxtxd94YOUD9IZ7ybBlMO+QefzsmJ/hynaZ3TzTDFUKJLlWr0rOU7JI1mm7/nA/D338EHe/dzc9/T1kZ2Tz8+N+zqWHXZqgrVXGUTJUGE9UzsFIVpzJ0LkAfeouGjylg3AkzDPqM9y57E42d+tFLo+fdjzVs6o5aOJBJrdOiPSSjMHTqq2ruPHNG1nx9QoAjt/reG488caUyIuMtzEHT1bJORizSARCXfF9DUeuJH4mkFHrKQ3KFazYsoJbmm9h+ZblAEzPm861s67ljBlnJHVVcBElP8Nkk0yr7Xr7e/nbir9x34r76Av3ke/I59pZ13LhgRdK/zFCcV9tZ9mcg1AX/HHv+L7Gb9ZD1oRhT5k7dy5+v5/KykqqqqpQVRVA9rgbg2itp1Recbelawt3+u80aq7kZOZQcXQFlx1+Gc4MGX0VwizJMvK0fMtybnzzRj7XPgfgmzO+yW9P+G1apTqMh7gGT6mRcxA/jY2N3HfffbhcLurr61FVFUVRqKiowOfzUVtby7Jly4zzBzsmdkjlWk/B/iCLPlrEfcvvo6tPHzE9v+R8ri69Wjo9ISzA6sFTV6iLu9+/m4c+eogIEYqyi/jN8b/hW/t9K/lHm0yoh2aJhHFTOHL1kaF4v8YwBtaOqaqqor6+3lhN6PV6d9nFfbBjYgcjeEqhabtIJMIra17h1uZbWdu5FoCjJx3N9bOv56jJR5ncOhF3UiQzaVh5td1b699i4VsLjb0szy85n+tmXpfWC0r2VPoGTzbbbqfUEq25uXnMuWRiwBYtKTLytGrrKuqb63l7w9uAvnnvr8p+xbnuc7Hb7Ca3TsRVso8EpKGBOU+RSMQSozltwTZuW3obT3z+BADTJkzjhhNv4JR9TjG5ZckvfYMnCyovLze7CUktVTYHbgu2cc/79/DYp4/RH+kny57FFUdcwZVHXSnbIghhUdGRp1A4RLA/aHqtuZe+fInfv/N7vu7+Ghs2Lj70Yq4uvZoJDmsNGiQrCZ4sQlVVioqKzG5GUkv2abu+cB+LP1vMPe/fYwSAnn09LJi5gBn5snRYCCvLzczFbrMTjoTp6O0wLXj6uvtr/vjOH2n6sgmA/Qv25+aTb+a4KceZ0p7EkJyntOX3+2OS6xVFQVVVfD6fkWA/2DGxQzKvtnt7w9vUvVtnrIA5aOJBVM+q5vhpx5vcMiHESNhsNvKz8mkLttHR28Hk3MkJff1IJMJTLU9R31xPe287GbYMfnTkj6g8pjK1V+JGIhDq1v/tyEnYy0rwZBE7B0Mej2eXAqGDHRM7JONquzXta/jT0j/x8pqXAf17+MWxv2DOwXPScksVEbU9XybcZ24zxKjkO/TgKdFJ4+s613HzWzfz5vo3ATis6DBuPvlmDi06NKHtMEWoCyL9+r+z8hL2stI7i5QRDZ6suNplZ9tC27hv+X08+NGDhMIhMmwZXHzoxfz0mJ8a34dIY4X76P9vWwPhfki2bTLSVKLLFfSH+/n7p3/nz/4/093XjTPDyc+O/RmXH355+lx8bf1S/7+zEJz5CXvZNHl3RTqITtt1hjoJhUM47A6TW7SrcCTM0+rT3LnsTrZ0bwHgxGknUj27mhJXicmtE5bh2k8vdRLqgg3vwz5lZrdIjEAiq4yrmsoNb97AB1s+AKBsahk3nXgT+xfuH/fXtpQv39D/P/WI5NjbTgiriV71gd55FWVbKwH/gy0fUPdunbGP1Iz8GVTNquL06adbYllzumtsbMTtdtPU1GRsQh49pqpqTF22uLNnwCHnwIc+ePUW+N6jYJfyFFaXiJGnUDjE/Svup2F5A6FwiAmOCSwoW4D3YG/6lTDp1uDN/9b/fdh5CX1pCZ5EysiwZ5CflU9HbwdtwTbLBE+buzZz57I7+af6TwAmOCZQeXQl3z/s+2RlZJncutSlaRqNjY1A7F6cPp8P2LEpucfjMTYr93g8NDQ0oKqqsVWSx+PB5/MlfqHGadfBx0/Bqhfh8Svh3Nshx5W41xejZgRPofgETyu/XskNb97AZ1s/A+C06afxuxN+x14T9orL61laYDX4fgjaV1AwHcp+kNCXl+BJpJTCrEIjeDJbsD/Igysf5L4V99Hdp68GueDAC7i69Gom5UwyuXWpT1EUWltbKS4uNo6pqkpTU5NRqb+8vByPx4PL5aKiosIYaXK73fh8PqPiv8vloqmpKbHB05RD4YK/wOMV8OESUF+DE34Cx10O+VMT1w4xYvGqMt7d181f3v8LD3z0AOFIGJfTxfWzr+ecA85Jv1HrzR/D0vth2f9Cfy/kTITvPZLwotcSPImUUuAsgE5zk8YjkQgvffUSf1r6J2M7hGMmH8P1s6/nyElHmtaudOP1egkEAsaoEugBlcvlMu67XC4URTHKhFRUVFBZWWmMOg187GCCwSDBYNC4394+zr93R3mhYB946ufQ+jm8/Ht45Y9wwOlw6LlQcgYUS66cVcRj2q55YzM3vXkTX3V8BcA5B5xD9exqy4ysx124H9a/Dy0vwafPwvr3dnztgNPh/Ltg4n4Jb5algqfocHpzc7ORc1BdXc2sWbNQVVW2LhG7ZfYWLZ9t/Yz6d+t5Z+M7AEzJncKCsgXpeYVoQS0tLTEjUUVFRWiahs/nw+Vy4fF4KCkpMUadBgZRs2bN2uX5amtrWbhwYXwbvd+J8LN3YOXj8M5fYd0yUF/RbwAT99c/RPY9EfY9HiYeINu7mGQ8g6eO3g7uWHYHiz9bDOh9yQ0n3MDpM07f4+e2tL4gbPwQ1jbDmrdBfRW6t+74uj0TDj4bZl0JJd80rZlxDZ5Gk3MwsPNSVZXGxkaKioooKSnB6/XS2NgYc4W4pyKRiDGVEi85mTm7/cCcO3cufr+fyspKqqqqjM7a7XbHtW2pyqxaT1qPxt3v383izxYTjoRxZjj5wRE/4EdH/ki2VLG4QCDAvHnzUBQFn89HS0uLMa1XX19vFKcd7OKtpqaGBQsWGPfb29uZMSMO1eAzMuHoefotoMLKJ6DlFfjqbdj6hX7zP6CfO2GKHkTNOAH2PQH2OhoyJbcuEcZrtd2ra17lv97+LzZ3bQZg3sHz+FXZr2IWxaSESEQvx7G2GdYu1f+/4QN9Om4gZwG4T4eSM+HQ8yAvsQVIBxPX4Gk0OQcDcwlaWlqorKxk6dKlMcPmO1fh3hPdfd0c/0h8qze/c8k7w35wNjY2ct999+Fyuaivr0dVVRRFoaKiAp/PR21tLcuWLTPOH2xkTsRK9BYtoXCIxz59jHvfv9eYKvzWft9iwcwF7JO3T0LakI7q6+tpbW3d5XhxcfGwI9QlJSUxfUr0As7lchl90MC+KPpcQ/U7TqcTpzPB1ZuL3HDqNfot2Alf/Bu+/Dd89Y4+pbFtM3z8T/0GkOGEacfA9FkwfaZ+K5who1NxYOQ8jXGXg0BPgFvevYXnVj8HwL75+3LTSTcxa69dRz2TUrBT/x0dGCxt27zreTlFO35f9z9V/3+GtUrPxDV4GkvOgaIolJWVUVpaSmlpKdXV1SiKwrJlyygpGXxuP+55B3EycOlzVVUV9fX1RoKq1+s1Akxg0JG5hC6dThLRK79EjDy9uf5N6t+tp6VNr/p+yMRDqJ5dnTodnYWNdQrf4/FQXV1t3FdVddwuyEzhzINDztZvoG9Tsf49fURqzTv6rXsrrH1Xv0XlTdU/nPYp0/+/93H6c4k9MtbVdpFIhGdWP0Pdu3VoQQ27zc4VR1zBz475mekbDI9ZOAytq7YHSs2wdhlsXgmRcOx59kzY66jtwdL238kit+WD+4TnPA2VcwD6yJKmaVRUVOD3+yktLaWmpgaXy4Xf7x9ypctY8g5yMnN455J3xvx9jPQ1RqO5uXnID4XBRubErhIxbfdV+1fcuvRWXl3zKgAup4tfHPcL5hw0hwypBG0ZiqLQ1NSEpmm43W68Xi9ut5v58+fj8/kIBALU1NSY3czx5ciB/U7Sb6BPiwTUAR9gS2HTh9C5CT55Wr8B2Oww5fDtI1OzYJ+ZMOlgqS01SmPJedq4bSM3v3Uz/1r3LwAOnngwN590M0dMOiIubYybroD++7Vu6Y5gabB+uGD6jhHQ6bP0UdEE7kk3XiyRMB4IBFBVlblz5+J2u6mtraWurs7ImYouHR4qD2gseQc2m81yuSjl5eW7PWfgyJzYVTyn7baFttGwvIFFHy2iL9xHpi2Tiw+9mJ8c8xPZUsWCPB7PoKNKabWpts2mr8YrLoFjLtaP9XbpeSXGh9xSaF+nB1WbPtSXgIOeZ7JPWWxANaF4yJcSO0a+23vbiUQiw+a8hiNhFn+6mDv8d7AttA2H3cFPjvkJPzzyh5bcHSFGf0j/XVm7dMf0W2CQfVczc2Cf0h0jnNNnQsHeiW9vHIw5eBrvnAO32z3oprcjGZ43Je9gnKmqSlHR8EtPBxuZE7Giq+3GmnMwmHAkzFMtT/Fn/5/5uvtrAE7e+2SqZlXhdkliv0gyWbn6Cr79TtxxrH39gFGDpbDOD8H22FV9oK/ki06vTC+DqUdJMvoA0ZGnvnAfPf09Q84+fNH2BTe+eSP+zX4Ajp18LAtPWmjd/qR9fezo5fr3oK9n1/OKDxyQWzdLH820WK7SeBlz8CQ5B+Nr52T46AqfaFXjwUbmxK7Ge9ru/c3vc8u7t7CydSUA+xXsR9WsKk7d51QpPSBSR8HecPj5+g2gvw82f7Tjw3LdUvj6M9i6Wr+teEw/L8MJex+rj0pJMjq5mblk2DLoj/TT0duxS/DUF+7jgZUPcO/799Ib7iUnM4dflf6Kiw+92Dpbq0RHJgcGSx3rdz0vu3D7zz2aq1QKuWlSe4oErLZLu5yDMdp5KsHj8cSMxA01Midijde03cZtG7nTfyfPqM8AkOfI4yfH/IRLDr0ER4peSQlhyMiEaUfrt1k/1o91b9VrTK1dpn+orluqH4smpkflTY0NpvY+LqG73ZvJZrORn5WPFtTo6O1gSu4U42ufBD7hhjdu4OPAx4A+en3DiTewd56J01hD5cSF+2LPs9n1jXeNUcdZUFSS1jlxcQ2eJOdAJFo0eGoPthOOhEd9NdfT18MDKx/gfz78H7r7urFh46KDLuLnx/1ctlQR6S1nIhzo0W8wfDL6p8/oN9A/eCcfpk/zRXOnJh+ib36cggYGT6Bv09TwQQP3f3g//ZF+CrIKqJ5dzXfc30n86HW3tj0AHpDYPbAAZVR0NWZ0Cm7asbIacyeWSBgXYrxEEzYjROjo7RhxInckEqHpyyZuW3ob67fpQ9SlU0qpnl3N4cWHx629QiStwZLRQ93bp3y2fzCvW6YXQdy8Ur/5H9TPy8qHfY7bEUxNnwl5U4Z+rSQycH87/yY/N755I1+0fwHoNeBqjq9JzIVYfx9s+Tg2qfvrT3c9b5ep11lQOD1tp15HSoInkVKyMrLIycyhu6+b9mD7iIKnTwOfUtdcR/PGZgCm5k7lmpnXcPb+Z0tekxCj4cjRq5rve8KOYx0bY4OpdX7o7YDVr+u3KNe+A3JoZuqV0R3JV+MoGjzV/KvGKJw7KWcSvz3+t5y535nxe+GOTbErKNf5IbRt1/MmHrAjSJo+U5L+x0iCJ5FyCp2FdPd109bbxgyGLlkR6Alwz3v34FvlM7ZU+dGRP+KHR/5w1DW6hBBDyN8LDjtPv8H2EZFPduRNrV2m39e+0m8rH9fPszsGFE/cPiqSBPv2TcicAOzYnPyigy5iQdmC8S1n0heEDctjp0zbvtr1vKx8PZF74BTcBEk/GA8SPImUU5hVyMZtG4csVxAKh3j0k0e594N7jbyEs/c/mwVlC5iWNy2RTRUi/WRkwl5H6reZP9SP9bQN2LZje0J619ew3q/f3t2+20Ju8Y6aQfuU6bccl2nfymCm508H9JV3fz7jz5ww7YTdPGI3IhHQvtwxere2GTau2HX/N2ww5bABo0qzthc6Tc3cMrNJ8CRSznAr7t5Y9wZ1zXWsblsNwGFFh1E9u5qyqWUJbaMQYoDsQnB/Q7/BTgHD9qBh43LoaoVVL+q3qEkHx241M+VwPUAzyU+O+QnHTTmOk/Y+aWyFmIMd+pRbdJpzbTNs27LrebmTYkfl9i6F7II9/wbEiEjwJFLOYLWevmz/klubb+W1ta8BUJRdxC+P+yUXHHiBbKkihNXYbDBxf/121PbV2X1BfcRl4EqxrV/o9ae+/gzef1g/z5Grrw4buAVIAqta52fl49lvhLULw2G97QOn3zZ/BERiz7M79LIRAxPsJ+5v+SnMVJa2wVMkEiHS3R3X17Dl5EjCsQkGbg7c0dtB4/JGHvr4IWNLlUsOu4TKYyqN84QQSSDTuSMgitr2dWwwFa2M/tWb+i0qf++d9lM7Vq+0nmjbWgckdQ9o784K991R2mH6rKRNnk9l6Rs8dXfzaWl8p2oO8S/Dljv0H6imaVx11VVomoaqqrjdblwuF4sXL45ru1JddOTpf1f+L4988giBngAAp00/jWtnXssBhQeY2TxhUdF9NJuamowK/oqiGH+fFRUVuFwucxspYk2YBIecrd9gx0jOwM1pN6/UK2R//JR+A7BlbC/6OGDfvuIDx7foY1/vgP3ftgdLW1fvep4jV59yG7gCLn+v8WuHiIu0DZ6sYOnSpSxevBhVVfH7/UbxUJ/PR21tLcuWLTPO9fl8ADQ3N8vWLLsRHVHqDHVCCPYv2F/fUmX6qSa3TCRSdGNxiN1OKvq3FN1X0+PxGPttejweGhoaUFUVwAikNE2TwCkZ2O0w5VD9dtyl+rFgJ2x4f0AQsxQ6N+o5VBuXw9L79fOyC2HqkWDPhEhYPxYJ6/lXkTAQGeT+zv+OnhPWc7YG2/8tmqMVDZYmH2ZqjpYYm7T9idlycjjEv2z3J+7hawwnWn09un9dlNfrpaGhwbjv8/lwuVx4PB5UVaWxsZGKior4NDoFzMjXyxPYsHHtzGv53qHfky1V0pCiKLS2tlJcXGwcU1WVpqYm4++rvLwcj8eDy+WioqLCGH1yu900NjaiaRo+n08uWpKZMw/2P0W/gR7gtK+LrT21/j19xd+Xb4zva2e7YssE7FOqV2oXSS99gyebbdgptURqamoadqPlgYFVS0sLlZWViWhW0vLs5+G+b93HwRMPpig7fTaqFLG8Xi+BQMAYVQI9oBo4guRyuVAUxbiQqaiooLKy0hh5KikpMZ5nsIuWYDBIMBg07re3D14eQ1iIzaZX0C6cDkdcoB/rD8GmlfD1qh3n2GyATd9exhb9v33XY9h2nD/wfv7eevV1yXtNSWkbPFnJSKcDFEWhrKyM0tLS+DYoydlt9j2vrSJSUktLS8xIVFFRkTG6FB3dLSkpwefz4fF4UBTFOC8QCOzyfLW1tSxcuDBh7RdxkuHQtyjZ+1izWyKShKW2RG5sbERRFKqrq41jiqLg8/mor6+PuYJMJSNJEPf7/WiaRkVFBX6/PwGtEiI9BAIBI+/J5/PR0tJCVVWVcZESnbYbbKq8pqaGtrY247ZmzZpEN18IYYK4jjxJwubYKIqCqqpGLpSqqsydOxe3201tba3kXoi0V19fT2tr6y7Hi4uLh50CLykpibkIi/ZBLpfLmB4fOE0efa6BxwZyOp04nc6xfAtCiCQW1+BJEjbHxuPx0NLSYtx3u90x94VId8MFSMPxeDwxI9uqqhr5TkIIMVJxnbbzer2UlJTEHBsqYTOqoqLCqKsCOxI2S0pKjFGsnQWDQdrb22NuQoj0pigKTU1NNDU1GaPdbreb+fPn4/P5aGxspKamxuRWCiGSUcITxsc7YRNGl7QZiUR2f1ISStXvS4ix8ng8g44qDTUFJ4QQI2WJ1XaBQIB58+YZyeEtLS3GtF702HDTdjU1NSxYsMC4397ezowZM2LOcTgc2Gw2tmzZwuTJk1Nq25RIJMKWLVuw2Ww4HFLPSAghhIinMQdPVknYhJElbWZkZDB9+nTWrl3LF198Mey5ychmszF9+nQyMmSTWyGEECKexhw8JWPCZl5eHgcddBChUCghr5dIDodDAichhBAiAeK+2q6pqQlN03C73Xi93piEzUAgkPCEzYyMDAkyhBBCCDFmcQ2eJGFTCCGEEKnGUhXGhRBCCCGszhKr7cZbdNm+1HsSIvlE/26TsfyG9D1CJK/R9D0pGTx1dHQA7FKuQAiRPDo6OigsLDS7GaMifY8QyW8kfY8tkoyXd7sRDodZv349+fn5I67nFK0NtWbNGgoKCkb9mnv6eCu0wezHj/Q5xuucPW2HlR9vhTaM9fGRSISOjg723ntv7PbkyiwYS98DyfuzslIbEvH4RPQ94/Ecyf54s9owmr4nJUee7HY706dPH9NjCwoKxvzDHo/HW6ENZj9+pM8xXuek8uOt0IaxPD7ZRpyi9qTvgeT8WVmtDYl4fCL6nvF4jmR/vBltGGnfk1yXdUIIIYQQJpPgSQghhBBiFCR42s7pdHLjjTfudpuXeD3eCm0w+/EjfY7xOmdP22Hlx1uhDePxPaQLs99r+X2zTt8zHs+R7I+3ShuGk5IJ40IIIYQQ8SIjT0IIIYQQoyDBkxBCCCHEKEjwNEqNjY0oikJjY+O4PJ/P58Pn81FdXb1Hz6NpGpWVlWN6rKIo+Hw+6uvr0TRt1I/3+XwoikJ9ff2oH1dWVhZzbDTv72CP3937OZbHjGebd36usbxvUXv6c4M9+72B0f/+jvffT7qxYv+zp79D6dL/7GnfMx5t3vm5krn/Gcvv7nj+/aRknafR0DTNeCOrqqqM4z6fD4BAIIDb7cbj8aAoCl1dXfj9flasWEFRUZGxyfFg5+/uNVesWMEVV1yBx+NBVVUqKyspLy/f7XMM1mZFUVi+fDk+n29Uj/d6vTQ1NVFXV8cDDzyAoihDPn6w11VVlX/84x9ccMEFtLS0sGjRIi677LIRtdvr9dLQ0GC8d2+88QYAFRUVxh+Gx+OJeUz03KamJqZOnUpXVxeKouDxePD5fLhcLuP9bGxsZN68ecO+ZlNTEyUlJVRVVRmPqaioGLL9qqrGbL2hKArLli2jqKiIZcuWccMNN3DzzTeP6H1XVZWqqiqee+457rnnHhwOR1x+bsP9DKKPG83vb5TP5yMzM5PPPvuMFStWxLx3Q/39AMbPyufzpf0m4Ynufwa+ntvtNv5e/vGPf1BZWUlZWVncf4eSpf954IEH2LRpk3H+zn3P9OnTY7bxGEn/09DQYJz71ltvEQ6HOffccykuLh6274m2P5n7nz393Boo+l7PnDmT+++/nzlz5rBkyZKYr0N8+5+0H3lSFIXW1taYY6qq0tTUhNfrpaKigrq6OgD8fj+BQIDW1lays7Npbm4e9vzdveZRRx1l/KK89957fP311yN6jp3b7PP5KC0tZdOmTaN+vKIoaJrGPffcwx133DHs4wd7rwDefPNNGhoaKCkp4cEHHxxxuwG6urqM927atGm8/vrrALhcLpqbm2MeE32fS0tLAXjrrbeYPn260Vav12u8ny0tLcycOXO3r9nQ0EBTU1PMY0bT/qamJtatW4fX62Xu3Lkj/v7dbjfNzc2cfPLJ/Pvf/+Y//uM/4vZzG+o5op1HZ2fnqH5/o7xeL319fbS2ttLa2mq8d8P9/bjdbmDHzzfdJbr/Gfh60b8XVVVZtmwZlZWVCfkdSpb+54knnhi276moqODLL780nmuk/U/0uW677TbuuOMO6urqdtv3DNX+ZOp/9vRza6Doe60oCuvXr48pTJuo/iftR568Xi+BQCBm2FFRFFwul3Hf5XIZUevRRx9NIBAgEAjs9vxohDvwXICioiJKSkqM11QUhYyMDA488MARP4emaRQXF+P3+yktLUVRFBwOx6gfD1BSUoLD4WDq1KnG1c9Qj1+3bh2ff/650Wk+9dRT7LvvvlRXV1NZWckBBxww4tcF/cpg4HuXlZVlvNeffvopJSUlxmsuX76czs5O4/12uVy0tLRQUlIS85pvvPEG27ZtY+nSpSN6TZfLRX19PWVlZaiqajxu4M/L6/UavysDff7552Rm7vgzys7OHtH3r2kas2bNYsOGDfy///f/jJ9jvH5uA7+XkpISVq5caVx1bd68maOPPjrm/djdc0Qf6/V6eeONN5g+fbrxwTLc389Yh/dTlRn9z85/D3fddRf77ruv8fNLxO9QMvQ/A19v+fLlbNmyhbq6OqPvURSFzMzMXV7v448/Nvqfnfv6wX5ewWCQ3NxcSktLh/17S4X+Z08/twb2PdHzjzzySPbZZ58h39949T9pHzwNpqWlJeYPrKioCE3TKC0tRVVVAHp6epg1a9aw5wNDDgtGhy/9fj+aprHPPvvQ09Mz4udobGw0vu73+3n22Wfp7Ow0filH+vjo1VFLSwtTpkwZ0etrmmYce+655zj++OPxeDw0NTXxve99b8TtBuju7jbeu9LSUp5++mnj65deeqnxHJqm0draSnFxsfF+a5rGp59+GtPW6JWF1+s13ovhXhP0/cg2bdpEVVUVfr9/VEO5AzsuTdOYMWPGiL7/xx57zBj5qqysRFGUuP/cBj4H6L83fr+fdevWjep3byC/309XVxfHH3+88X6P5O8n2nmLXcW7/9m571i9ejVnnnnmiPuO6HNEHz+W36Fk6X+igW1raytHH3200QdpmoamaTgcjpjX8/v9xgf8wP5noIE/L7/fj9Pp5OSTTx513wPJ1//s6efWQNHPztNOO42VK1caxxPV/6T9tN1IBQIBPB4Pmqbx8ccf09raOuwPd+eIeTCtra3MnTuXhoYGHnjgAbq6ukb9HKWlpXi9Xrq7u2M6r9E8HvRRnjVr1sTMuY/k8YceeigrVqxAURT8fj+HHXbYiB4HO4Z+V6xYAehz0cFgkDfeeANVVXf7x7Nu3To2bNiAqqoEAgFUVTXez7KyskHbsfNrRod4n3322SEfM9DHH38ck9+x//77093djaIoqKqK2+0e0fc/b948fD4fX3zxBevXrx/1+76nP7d99tnHuJLd+fdmpM8Rfb9ff/11/vznPw/7mIF/P9H3Kt3znUYjHv1P9Of3/vvv7/LzS9TvUDL3P2+88Qbt7e3GtP/u+p/o7/2nn34ac/7HH3/MNddcM6J2p0r/s6efWwPf6z/84Q+7fHbuLB79T0qPPNXX1w86R15cXByTnLnz+e+//z7BYNB47FtvvcXcuXMBPdGtsbGRadOmGY8bOCxbX1/Pq6++iqZptLS0DPua0VEU2BGRR9uw83MM1eaoOXPmcOaZZ6IoCo8++uioHl9VVcWcOXMAjJUL0cdrmjbs6x5xxBHss88++P1+Wltbeeutt+ju7h7R63o8nl1Wauy7776ce+65gyYNRt/n6P9zcnL4v//7PxoaGnC73bjd7pj3fCSv6Xa7Oeuss6isrBxRouJhhx1GdXW18YdXUlJCcXExHo8Hj8fD3LlzjdGv4bhcLuN3SdM0Y5g5muA4EgMfHzWaxwNGpzeW54i+39E2RN+/nacpBj5f9HdhJO91skt0/zPavmOwn99o+q+ogb9DY+m/kqH/2bnvCQQCzJ07l7Vr1xo/m931Px6PJ+b9jp4/d+7ctO1/op9b0WBstH0P7DqamKj+J6WDp+H+6IY7X1VVqqurjUSz6BzsUDwej/FHX1VVxaOPPsqjjz46qteOPsfixYuN1xzNc+zp42+99dZdvueRPH682h2lquqQ73X03Lq6Oqqrq41zq6urR/XHMJrXjPdzmf348XqOeD5fskp0/zMef4Nm9V9W73/Gq+8ZzWsm4rmS/fGJes7BpP32LIqi0NDQgKbp9SYGW/o7MElttOePx2ta5fFmvO7Oj4lqamoiLy+PQw45JK7vldnf/3h/L+P5fsTj+dJNovsfK/wOJUv/s6d9z3i02czv32qPT9RzjlTaB09CCCGEEKMhCeNCCCGEEKMgwZMQQgghxChI8CSEEEIIMQoSPAkhhBBCjIIET0IIIYQQoyDBkxBCCCHEKEjwJIQQQggxChI8CSGEEEKMggRPQgghhBCjIMGTEEIIIcQoSPAkkoaqqtTX1+Pz+Yy9plRVNblVQoh0IP2PGEj2thNJo6ysjGXLlgH6xo+qquJyuaioqDC5ZUKIVCf9jxhIRp5EUmhsbMTj8Rj3XS4XTU1NMceEECIepP8RO5PgSSSNkpKSXY653W4TWiKESDfS/4iBJHgSSWHevHksW7YMn8+Hz+cD9Ku/6L+FECJepP8RO5OcJyGEEEKIUZCRJyGEEEKIUZDgSQghhBBiFCR4EkIIIYQYBQmehBBCCCFGQYInIYQQQohRkOBJCCGEEGIUJHgSQgghhBgFCZ6EEEIIIUZBgichhBBCiFGQ4EkIIYQQYhT+P93RDnhOsGRkAAAAAElFTkSuQmCC", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -339,7 +273,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "id": "ab63ada8-c087-4d13-ac4a-80429306b37a", "metadata": {}, "outputs": [], @@ -359,19 +293,10 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": null, "id": "09c12f7e-052d-4d30-b3aa-e8555e9c2497", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 1min 36s, sys: 109 ms, total: 1min 36s\n", - "Wall time: 1min 37s\n" - ] - } - ], + "outputs": [], "source": [ "%%time\n", "\n", @@ -400,47 +325,10 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": null, "id": "476f9a4d-2dd3-4dbe-87fd-012d513dd66d", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "134.57836099164655 3.000000006559785\n", - "141.52141095439333 2.0000300099855415\n", - "134.57836114168347 3.000000000960305\n", - "142.2968566197709 2.0000299868417066\n", - "134.57836097984554 3.00000000632813\n", - "143.06610105865937 2.00002997116096\n", - "134.57836014857665 3.0000000340371296\n", - "143.83401935805443 2.000029878833156\n", - "134.57835645181956 3.000000157285378\n", - "144.6016525115409 2.0000297711644537\n", - "134.57834224436107 3.000000630514608\n", - "145.36922825485252 2.00002952780053\n", - "134.57831375726963 3.000001575271915\n", - "146.13680167873076 2.000028915218776\n", - "134.57831642529098 3.000001467599617\n", - "146.9043920037454 2.000027652723656\n", - "134.5783181026893 3.000001390309717\n", - "147.67202561358476 2.0000249393415572\n", - "134.57832747686788 3.000001051688091\n", - "148.43975348446267 2.0000191058865715\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -482,7 +370,7 @@ }, { "cell_type": "code", - "execution_count": 83, + "execution_count": null, "id": "1a554573-e2b6-4657-9faa-cf2a3d158a0d", "metadata": {}, "outputs": [], @@ -504,1585 +392,37 @@ }, { "cell_type": "code", - "execution_count": 84, + "execution_count": null, "id": "b6db60c6-74da-4d92-8b95-28ad8cf777a2", "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/sandro/.local/lib/python3.11/site-packages/pysr/sr.py:1281: UserWarning: Note: it looks like you are running in Jupyter. The progress bar will be turned off.\n", - " warnings.warn(\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Expressions evaluated per second: 5.940e+05\n", - "Head worker occupation: 11.2%\n", - "Progress: 1186 / 18000 total iterations (6.589%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39161 * x₀) - -184.54)\n", - "7 2.219e+01 1.490e-07 y = (184.54 + (-0.19581 * (x₀ + x₀)))\n", - "9 2.212e+01 1.662e-03 y = (((785.47 / (-2005.8 - x₀)) * x₀) - -184.54)\n", - "10 8.285e+00 9.819e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", - "12 8.184e+00 6.158e-03 y = (179.54 + (tanh(((2.3223 / 0.182) - x₀) * 0.68639) / 0.167...\n", - " 4))\n", - "13 8.178e+00 7.094e-04 y = (179.54 + (tanh(((2.3223 / 0.182) - x₀) * 0.68639) / tanh(...\n", - " 0.1674)))\n", - "14 8.065e+00 1.398e-02 y = ((179.54 + (tanh((2.1379 / 0.1674) - x₀) / 0.1674)) - (-0....\n", - " 030648 * x₀))\n", - "15 8.065e+00 1.907e-06 y = ((179.54 + (tanh((2.1379 / 0.1674) - x₀) / 0.1674)) - (tan...\n", - " h(-0.030648) * x₀))\n", - "16 7.925e+00 1.742e-02 y = (((179.54 + (tanh((2.1379 / 0.1674) - x₀) / 0.1674)) - (-0...\n", - " .030648 * x₀)) - 0.32827)\n", - "18 7.536e+00 2.518e-02 y = ((179.56 + (0.1674 * x₀)) + ((tanh(((2.5389 / 0.182) + -1....\n", - " 4805) - x₀) - 0.28773) / 0.15))\n", - "19 7.437e+00 1.326e-02 y = ((179.56 + (0.1674 * x₀)) + ((tanh(((2.5389 / 0.182) + -1....\n", - " 4805) - x₀) - 0.28773) / tanh(0.15)))\n", - "20 7.237e+00 2.720e-02 y = ((179.56 + ((0.182 * 0.69808) * x₀)) + ((tanh(((2.5389 / 0...\n", - " .182) + -1.332) - x₀) - 0.28773) / 0.15))\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.450e+05\n", - "Head worker occupation: 9.4%\n", - "Progress: 2234 / 18000 total iterations (12.411%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39161 * x₀) - -184.54)\n", - "7 2.219e+01 3.278e-07 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 1.673e+01 2.825e-01 y = ((x₀ * tanh(-17.291 / x₀)) - -189.25)\n", - "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", - "12 8.172e+00 6.875e-03 y = (179.58 + (tanh(((2.654 / 0.20935) - x₀) / 1.495) / 0.1650...\n", - " 5))\n", - "14 7.874e+00 1.856e-02 y = ((178.94 + (tanh((2.1667 / 0.17141) - x₀) / 0.12876)) + (0...\n", - " .12876 * x₀))\n", - "15 7.869e+00 6.215e-04 y = (178.94 + ((tanh((2.1667 / 0.17141) - x₀) / 0.12876) + (ta...\n", - " nh(0.12876) * x₀)))\n", - "16 6.322e+00 2.190e-01 y = (178.94 + (((tanh((2.1888 / 0.17141) - x₀) + -0.22259) / 0...\n", - " .12876) + (0.19232 * x₀)))\n", - "17 6.305e+00 2.673e-03 y = (178.94 + (((tanh((2.1888 / 0.17141) - x₀) + -0.22259) / t...\n", - " anh(0.12876)) + (0.19232 * x₀)))\n", - "18 5.812e+00 8.138e-02 y = (178.94 + (((tanh(((2.1667 / 0.17141) - x₀) / 1.9154) + -0...\n", - " .22259) / 0.12876) + (0.19232 * x₀)))\n", - "19 5.778e+00 5.904e-03 y = (178.94 + (((tanh(((2.1667 / 0.17141) - x₀) / 1.9154) + -0...\n", - " .22259) / tanh(0.12876)) + (0.19232 * x₀)))\n", - "20 5.747e+00 5.301e-03 y = (178.94 + (((tanh(((2.1667 / 0.17141) - x₀) / 1.9154) + -0...\n", - " .22259) / tanh(tanh(0.12876))) + (0.19232 * x₀)))\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.280e+05\n", - "Head worker occupation: 9.2%\n", - "Progress: 3322 / 18000 total iterations (18.456%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39161 * x₀) - -184.54)\n", - "7 2.219e+01 3.278e-07 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 1.673e+01 2.825e-01 y = ((x₀ * tanh(-17.291 / x₀)) - -189.25)\n", - "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", - "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", - " 503))\n", - "14 7.729e+00 2.786e-02 y = ((tanh((((-17.291 / 0.47296) + x₀) * 1.839) / x₀) * x₀) - ...\n", - " -189.25)\n", - "16 6.315e+00 1.011e-01 y = (178.94 + (((tanh((2.1888 / 0.17141) - x₀) + -0.228) / 0.1...\n", - " 2876) + (0.19232 * x₀)))\n", - "17 4.538e+00 3.304e-01 y = (178.94 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17141) ...\n", - " + (0.19232 * x₀)) / 0.17141))\n", - "18 4.437e+00 2.258e-02 y = (178.94 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17141) ...\n", - " + (0.19232 * x₀)) / tanh(0.17141)))\n", - "19 3.530e+00 2.287e-01 y = (178.94 + ((tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17141)...\n", - " + (0.19232 * x₀)) / 0.17141) * 1.2226))\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.470e+05\n", - "Head worker occupation: 10.1%\n", - "Progress: 4630 / 18000 total iterations (25.722%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = (184.54 + (-0.39161 * x₀))\n", - "6 2.219e+01 -0.000e+00 y = (184.54 + (tanh(-0.41372) * x₀))\n", - "7 2.219e+01 4.172e-07 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 1.673e+01 2.825e-01 y = ((x₀ * tanh(-17.291 / x₀)) - -189.25)\n", - "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", - "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", - " 503))\n", - "14 7.464e+00 4.531e-02 y = ((tanh((((-17.291 / 0.47296) + x₀) / 0.58405) / x₀) * x₀) ...\n", - " - -189.25)\n", - "16 6.313e+00 8.375e-02 y = (178.94 + (((tanh((2.1888 / 0.17141) - x₀) / 0.12876) + (0...\n", - " .19232 * x₀)) - 1.7868))\n", - "17 3.418e+00 6.136e-01 y = (178.84 + (tanh((tanh((2.1699 / 0.17585) - x₀) / 0.17704) ...\n", - " + (0.1873 * x₀)) / 0.14429))\n", - "18 3.335e+00 2.440e-02 y = (178.84 + (tanh((tanh((2.1699 / tanh(0.17585)) - x₀) / 0.1...\n", - " 7704) + (0.1873 * x₀)) / 0.14429))\n", - "19 2.429e+00 3.170e-01 y = ((178.94 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.19605)...\n", - " + (0.17757 * x₀)) / 0.1319)) + -1.2866)\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.380e+05\n", - "Head worker occupation: 10.0%\n", - "Progress: 5759 / 18000 total iterations (31.994%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = (184.54 + (-0.39161 * x₀))\n", - "6 2.219e+01 4.172e-07 y = (184.54 + (tanh(-0.41372) * x₀))\n", - "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 1.673e+01 2.825e-01 y = ((x₀ * tanh(-17.291 / x₀)) - -189.25)\n", - "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", - "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", - " 503))\n", - "14 7.155e+00 6.646e-02 y = ((tanh((((-17.294 / 0.48751) + x₀) / 0.50115) / x₀) * x₀) ...\n", - " - -189.79)\n", - "16 6.312e+00 6.264e-02 y = (178.94 + (((tanh((2.3223 / 0.182) - x₀) / 0.12876) + (0.1...\n", - " 9232 * x₀)) - 1.7868))\n", - "17 3.350e+00 6.335e-01 y = (178.84 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17704) ...\n", - " + (0.1873 * x₀)) / 0.14429))\n", - "18 3.324e+00 7.797e-03 y = (178.84 + (tanh((tanh((2.3223 / 0.1873) - x₀) / tanh(0.182...\n", - " )) + (0.1873 * x₀)) / 0.14429))\n", - "19 2.418e+00 3.181e-01 y = ((178.94 + -1.2737) + (tanh((tanh((2.1888 / 0.17141) - x₀)...\n", - " / 0.1969) + (0.17757 * x₀)) / 0.1319))\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.570e+05\n", - "Head worker occupation: 9.9%\n", - "Progress: 7012 / 18000 total iterations (38.956%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = (184.54 + (-0.39161 * x₀))\n", - "6 2.219e+01 4.172e-07 y = (184.54 + (tanh(-0.41372) * x₀))\n", - "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 1.673e+01 2.825e-01 y = ((tanh(-17.292 / x₀) * x₀) - -189.25)\n", - "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", - "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", - " 503))\n", - "14 7.155e+00 6.646e-02 y = ((tanh((((-17.294 / 0.48751) + x₀) / 0.50115) / x₀) * x₀) ...\n", - " - -189.79)\n", - "16 6.312e+00 6.264e-02 y = (178.94 + (((tanh((2.3223 / 0.182) - x₀) / 0.12876) + (0.1...\n", - " 9232 * x₀)) - 1.7868))\n", - "17 3.350e+00 6.335e-01 y = (178.84 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17704) ...\n", - " + (0.1873 * x₀)) / 0.14429))\n", - "18 3.324e+00 7.797e-03 y = (178.84 + (tanh((tanh((2.3223 / 0.1873) - x₀) / tanh(0.182...\n", - " )) + (0.1873 * x₀)) / 0.14429))\n", - "19 2.418e+00 3.184e-01 y = (178.94 + ((tanh((tanh((2.1888 / 0.17141) - x₀) / 0.1969) ...\n", - " + (0.17757 * x₀)) / 0.1319) - 1.285))\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.710e+05\n", - "Head worker occupation: 10.8%\n", - "Progress: 8207 / 18000 total iterations (45.594%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39155 * x₀) + 184.54)\n", - "6 2.219e+01 1.192e-07 y = (184.54 + (tanh(-0.41372) * x₀))\n", - "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 1.673e+01 2.825e-01 y = ((tanh(-17.292 / x₀) * x₀) - -189.25)\n", - "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", - "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", - " 503))\n", - "14 7.155e+00 6.646e-02 y = ((tanh((((-17.294 / 0.48751) + x₀) / 0.50115) / x₀) * x₀) ...\n", - " - -189.79)\n", - "16 6.312e+00 6.264e-02 y = (178.94 + (((tanh((2.3223 / 0.182) - x₀) / 0.12876) + (0.1...\n", - " 9232 * x₀)) - 1.7868))\n", - "17 3.350e+00 6.335e-01 y = (178.84 + (tanh((tanh((2.1888 / 0.17141) - x₀) / 0.17704) ...\n", - " + (0.1873 * x₀)) / 0.14429))\n", - "18 3.324e+00 7.797e-03 y = (178.84 + (tanh((tanh((2.3223 / 0.1873) - x₀) / tanh(0.182...\n", - " )) + (0.1873 * x₀)) / 0.14429))\n", - "19 2.417e+00 3.187e-01 y = (178.94 + ((tanh((tanh((2.1888 / 0.17141) - x₀) / 0.1969) ...\n", - " + (0.17757 * x₀)) / 0.1319) - 1.3127))\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.600e+05\n", - "Head worker occupation: 11.4%\n", - "Progress: 9399 / 18000 total iterations (52.217%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", - "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 1.673e+01 2.825e-01 y = ((tanh(-17.292 / x₀) * x₀) - -189.25)\n", - "10 8.285e+00 3.513e-01 y = (179.56 + (tanh((2.3223 / 0.182) - x₀) / 0.1674))\n", - "12 8.172e+00 6.877e-03 y = (179.59 + (tanh(((2.4269 / 0.19161) - x₀) * 0.6702) / 0.16...\n", - " 503))\n", - "14 7.155e+00 6.646e-02 y = ((tanh((((-17.294 / 0.48751) + x₀) / 0.50115) / x₀) * x₀) ...\n", - " - -189.79)\n", - "16 6.312e+00 6.264e-02 y = (178.94 + (((tanh((2.3223 / 0.182) - x₀) / 0.12876) + (0.1...\n", - " 9232 * x₀)) - 1.7868))\n", - "17 3.332e+00 6.389e-01 y = (178.84 + (tanh((tanh((2.3223 / 0.182) - x₀) / 0.18279) + ...\n", - " (0.18279 * x₀)) / 0.14429))\n", - "18 3.324e+00 2.539e-03 y = (178.84 + (tanh((tanh((2.3223 / 0.182) - x₀) / 0.18279) + ...\n", - " (0.18279 * x₀)) / tanh(0.14429)))\n", - "19 2.417e+00 3.186e-01 y = (178.94 + ((tanh((tanh((2.1888 / 0.17141) - x₀) / 0.1969) ...\n", - " + (0.17757 * x₀)) / 0.1319) - 1.3127))\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.620e+05\n", - "Head worker occupation: 10.8%\n", - "Progress: 10588 / 18000 total iterations (58.822%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", - "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 8.285e+00 9.852e-01 y = (179.55 + (tanh(12.762 - x₀) / 0.16742))\n", - "10 8.172e+00 6.878e-03 y = (179.58 + (tanh((12.672 - x₀) / 1.4917) / 0.16504))\n", - "14 7.155e+00 3.323e-02 y = ((tanh((((-17.294 / 0.48751) + x₀) / 0.50115) / x₀) * x₀) ...\n", - " - -189.79)\n", - "16 3.943e+00 2.979e-01 y = (178.94 + (tanh((tanh(12.672 - x₀) / 0.1969) + (tanh(0.177...\n", - " 57) * x₀)) / 0.1319))\n", - "17 2.512e+00 4.510e-01 y = (178.94 + ((tanh((tanh(12.672 - x₀) / 0.1969) + (0.17757 *...\n", - " x₀)) / 0.1319) - 1.3127))\n", - "19 2.417e+00 1.924e-02 y = (178.94 + ((tanh((tanh((2.1888 / 0.17141) - x₀) / 0.1969) ...\n", - " + (0.17757 * x₀)) / 0.1319) - 1.3127))\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.530e+05\n", - "Head worker occupation: 11.5%\n", - "Progress: 11751 / 18000 total iterations (65.283%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", - "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", - "10 8.172e+00 6.878e-03 y = (179.58 + (tanh((12.672 - x₀) / 1.4917) / 0.16504))\n", - "12 7.346e+00 5.326e-02 y = ((178.94 + (tanh(12.672 - x₀) / 0.14744)) - (-0.086907 * x...\n", - " ₀))\n", - "13 7.340e+00 8.773e-04 y = ((178.94 + (tanh(12.672 - x₀) / tanh(0.14744))) - (-0.0869...\n", - " 07 * x₀))\n", - "14 6.035e+00 1.958e-01 y = ((176.37 + (tanh(12.765 - x₀) / 0.11286)) - (0.27904 * (1....\n", - " 2977 - x₀)))\n", - "15 3.682e+00 4.942e-01 y = (178.94 + (tanh((tanh(12.377 - x₀) / 0.17757) + (0.18953 *...\n", - " x₀)) / 0.1319))\n", - "17 2.417e+00 2.104e-01 y = (178.94 + ((tanh((tanh(12.762 - x₀) / 0.19774) + (0.17757 ...\n", - " * x₀)) / 0.1319) - 1.3155))\n", - "19 1.677e+00 1.826e-01 y = (178.94 + ((tanh((tanh((12.377 - x₀) * 0.3928) / 0.19774) ...\n", - " + (0.17757 * x₀)) / 0.1319) - 1.7223))\n", - "20 1.655e+00 1.361e-02 y = (178.94 + ((tanh((tanh((12.377 - x₀) * 0.3928) / 0.19774) ...\n", - " + (0.17757 * x₀)) / tanh(0.1319)) - 1.7223))\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.560e+05\n", - "Head worker occupation: 11.7%\n", - "Progress: 12940 / 18000 total iterations (71.889%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", - "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", - "10 8.172e+00 6.878e-03 y = (179.58 + (tanh((12.672 - x₀) / 1.4917) / 0.16504))\n", - "12 7.345e+00 5.336e-02 y = ((178.94 + (x₀ / 12.672)) + (tanh(12.672 - x₀) / 0.14744))\n", - "13 7.340e+00 6.743e-04 y = ((178.94 + (tanh(12.672 - x₀) / tanh(0.14744))) - (-0.0869...\n", - " 07 * x₀))\n", - "14 6.035e+00 1.958e-01 y = ((176.37 + (tanh(12.765 - x₀) / 0.11286)) - (0.27904 * (1....\n", - " 2977 - x₀)))\n", - "15 3.525e+00 5.378e-01 y = (178.94 + (tanh((tanh(12.377 - x₀) / 0.18816) + (0.17757 *...\n", - " x₀)) / 0.14744))\n", - "16 3.505e+00 5.538e-03 y = (178.94 + (tanh((tanh(12.377 - x₀) / 0.18816) + (0.17757 *...\n", - " x₀)) / tanh(0.14744)))\n", - "17 2.405e+00 3.765e-01 y = (178.94 + ((tanh((tanh(12.785 - x₀) / 0.19774) + (0.17757 ...\n", - " * x₀)) / 0.1319) - 1.3155))\n", - "19 1.649e+00 1.889e-01 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", - " + (0.17757 * x₀)) / 0.1319)) - 1.5548)\n", - "20 1.630e+00 1.115e-02 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", - " + (0.17757 * x₀)) / tanh(0.1319))) - 1.5548)\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.420e+05\n", - "Head worker occupation: 11.6%\n", - "Progress: 14054 / 18000 total iterations (78.078%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", - "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", - "10 8.172e+00 6.878e-03 y = (179.58 + (tanh((12.674 - x₀) / 1.4857) / 0.16488))\n", - "12 7.342e+00 5.352e-02 y = (178.94 + ((tanh(12.672 - x₀) / 0.14744) + (x₀ * 0.084886)...\n", - " ))\n", - "13 7.338e+00 6.113e-04 y = (178.94 + ((tanh(12.672 - x₀) / tanh(0.14744)) + (x₀ * 0.0...\n", - " 84886)))\n", - "14 6.035e+00 1.955e-01 y = ((176.37 + (tanh(12.765 - x₀) / 0.11286)) - (0.27904 * (1....\n", - " 3155 - x₀)))\n", - "15 3.525e+00 5.378e-01 y = (178.94 + (tanh((tanh(12.377 - x₀) / 0.18816) + (0.17757 *...\n", - " x₀)) / 0.14744))\n", - "16 3.505e+00 5.538e-03 y = (178.94 + (tanh((tanh(12.377 - x₀) / 0.18816) + (0.17757 *...\n", - " x₀)) / tanh(0.14744)))\n", - "17 2.404e+00 3.770e-01 y = ((178.94 + -1.3794) + (tanh((tanh(12.785 - x₀) / 0.19774) ...\n", - " + (0.17757 * x₀)) / 0.1319))\n", - "18 2.404e+00 2.361e-04 y = ((178.94 + -1.3794) + (tanh((tanh(12.785 - x₀) / 0.19774) ...\n", - " + (0.17757 * x₀)) / tanh(0.13234)))\n", - "19 1.649e+00 3.770e-01 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", - " + (0.17757 * x₀)) / 0.1319)) - 1.5548)\n", - "20 1.630e+00 1.115e-02 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", - " + (0.17757 * x₀)) / tanh(0.1319))) - 1.5548)\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.390e+05\n", - "Head worker occupation: 11.6%\n", - "Progress: 15222 / 18000 total iterations (84.567%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", - "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", - "10 8.172e+00 6.879e-03 y = (179.58 + (tanh((12.673 - x₀) * 0.67247) / 0.16498))\n", - "12 6.102e+00 1.460e-01 y = ((176.37 + (tanh(12.765 - x₀) / 0.11286)) + (x₀ * 0.25852)...\n", - " )\n", - "14 5.293e+00 7.119e-02 y = ((176.37 + (tanh((12.765 - x₀) * 0.40616) / 0.11286)) + (x...\n", - " ₀ * 0.27904))\n", - "15 3.227e+00 4.947e-01 y = (178.62 + (tanh((tanh(12.785 - x₀) / 0.17757) + (0.18874 *...\n", - " x₀)) / 0.1319))\n", - "17 2.404e+00 1.472e-01 y = ((178.94 + -1.3794) + (tanh((tanh(12.785 - x₀) / 0.19774) ...\n", - " + (0.17757 * x₀)) / 0.1319))\n", - "18 2.404e+00 2.361e-04 y = ((178.94 + -1.3794) + (tanh((tanh(12.785 - x₀) / 0.19774) ...\n", - " + (0.17757 * x₀)) / tanh(0.13234)))\n", - "19 1.607e+00 4.025e-01 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", - " + (0.17757 * x₀)) / 0.12996)) - 1.5548)\n", - "20 1.596e+00 6.797e-03 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", - " + (0.17757 * x₀)) / tanh(0.12996))) - 1.5548)\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.390e+05\n", - "Head worker occupation: 12.2%\n", - "Progress: 16401 / 18000 total iterations (91.117%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", - "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", - "10 8.172e+00 6.879e-03 y = (179.58 + (tanh((12.673 - x₀) * 0.67247) / 0.16498))\n", - "12 4.428e+00 3.064e-01 y = (175.18 + (tanh(14.175 - x₀) * (11.229 - (0.40177 * x₀))))\n", - "14 4.195e+00 2.693e-02 y = (175.18 + ((tanh(14.175 - x₀) - 0.056134) * (11" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "[ Info: Started!\n" - ] - }, - { - "data": { - "text/html": [ - "
PySRRegressor.equations_ = [\n",
-       "\t    pick         score                                           equation  \\\n",
-       "\t0         0.000000e+00                                           179.5845   \n",
-       "\t1         3.209774e-02                             (180.22537 - tanh(x0))   \n",
-       "\t2         5.457020e-01                  ((-0.39166483 * x0) - -184.54474)   \n",
-       "\t3         4.506454e-08             ((0.60839283 * x0) - (x0 - 184.54402))   \n",
-       "\t4         9.851865e-01     (179.55518 + (tanh(12.761697 - x0) * 5.97393))   \n",
-       "\t5         6.878725e-03  (179.58165 + (tanh((12.67312 - x0) * 0.6724680...   \n",
-       "\t6         5.337357e-02  (171.31406 + (tanh(tanh(15.395343 - x0)) * (21...   \n",
-       "\t7         5.594758e-01  (175.17535 + (tanh(14.175411 - x0) * (11.22903...   \n",
-       "\t8         3.709056e-02  (169.95616 + (tanh(15.848622 - x0) * (20.68860...   \n",
-       "\t9         4.994208e-01  (172.24475 + (tanh(15.065756 - x0) * (17.05391...   \n",
-       "\t10        8.544651e-02  (173.39519 + (tanh(14.70492 - x0) * (15.266392...   \n",
-       "\t11  >>>>  8.171071e-01  (172.24475 + (tanh(15.010006 - x0) * (15.01000...   \n",
-       "\t12        1.408766e-02  (172.24475 + (tanh(15.065757 - x0) * (15.06575...   \n",
-       "\t13        1.660253e-01  (172.24475 + (tanh(15.065757 - x0) * (15.06575...   \n",
-       "\t14        1.504349e-01  (172.24477 + (tanh((15.149901 - x0) * 0.365321...   \n",
-       "\t\n",
-       "\t         loss  complexity  \n",
-       "\t0   42.167710           1  \n",
-       "\t1   38.296616           4  \n",
-       "\t2   22.190395           5  \n",
-       "\t3   22.190393           7  \n",
-       "\t4    8.285218           8  \n",
-       "\t5    8.172015          10  \n",
-       "\t6    7.747281          11  \n",
-       "\t7    4.427638          12  \n",
-       "\t8    4.266422          13  \n",
-       "\t9    2.589215          14  \n",
-       "\t10   2.377164          15  \n",
-       "\t11   1.050012          16  \n",
-       "\t12   1.035323          17  \n",
-       "\t13   0.876944          18  \n",
-       "\t14   0.754465          19  \n",
-       "]
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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" - ], - "text/plain": [ - "PySRRegressor.equations_ = [\n", - "\t pick score equation \\\n", - "\t0 0.000000e+00 179.5845 \n", - "\t1 3.209774e-02 (180.22537 - tanh(x0)) \n", - "\t2 5.457020e-01 ((-0.39166483 * x0) - -184.54474) \n", - "\t3 4.506454e-08 ((0.60839283 * x0) - (x0 - 184.54402)) \n", - "\t4 9.851865e-01 (179.55518 + (tanh(12.761697 - x0) * 5.97393)) \n", - "\t5 6.878725e-03 (179.58165 + (tanh((12.67312 - x0) * 0.6724680... \n", - "\t6 5.337357e-02 (171.31406 + (tanh(tanh(15.395343 - x0)) * (21... \n", - "\t7 5.594758e-01 (175.17535 + (tanh(14.175411 - x0) * (11.22903... \n", - "\t8 3.709056e-02 (169.95616 + (tanh(15.848622 - x0) * (20.68860... \n", - "\t9 4.994208e-01 (172.24475 + (tanh(15.065756 - x0) * (17.05391... \n", - "\t10 8.544651e-02 (173.39519 + (tanh(14.70492 - x0) * (15.266392... \n", - "\t11 >>>> 8.171071e-01 (172.24475 + (tanh(15.010006 - x0) * (15.01000... \n", - "\t12 1.408766e-02 (172.24475 + (tanh(15.065757 - x0) * (15.06575... \n", - "\t13 1.660253e-01 (172.24475 + (tanh(15.065757 - x0) * (15.06575... \n", - "\t14 1.504349e-01 (172.24477 + (tanh((15.149901 - x0) * 0.365321... \n", - "\t\n", - "\t loss complexity \n", - "\t0 42.167710 1 \n", - "\t1 38.296616 4 \n", - "\t2 22.190395 5 \n", - "\t3 22.190393 7 \n", - "\t4 8.285218 8 \n", - "\t5 8.172015 10 \n", - "\t6 7.747281 11 \n", - "\t7 4.427638 12 \n", - "\t8 4.266422 13 \n", - "\t9 2.589215 14 \n", - "\t10 2.377164 15 \n", - "\t11 1.050012 16 \n", - "\t12 1.035323 17 \n", - "\t13 0.876944 18 \n", - "\t14 0.754465 19 \n", - "]" - ] - }, - "execution_count": 84, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - ".229 - (0.4...\n", - " 0177 * x₀))))\n", - "15 2.377e+00 5.680e-01 y = (173.4 + (tanh(14.702 - x₀) * (15.274 - (tanh(tanh(tanh(x₀...\n", - " ))) * x₀))))\n", - "17 2.352e+00 5.418e-03 y = (173.4 + (tanh(14.702 - x₀) * (15.274 - (tanh(tanh(tanh(x₀...\n", - " + x₀))) * x₀))))\n", - "19 1.607e+00 1.903e-01 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", - " + (0.17757 * x₀)) / 0.12996)) - 1.5548)\n", - "20 1.596e+00 6.797e-03 y = ((178.94 + (tanh((tanh((12.377 - x₀) * 0.39528) / 0.19774)...\n", - " + (0.17757 * x₀)) / tanh(0.12996))) - 1.5548)\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n", - "\n", - "Expressions evaluated per second: 5.250e+05\n", - "Head worker occupation: 12.6%\n", - "Progress: 17491 / 18000 total iterations (97.172%)\n", - "====================================================================================================\n", - "Hall of Fame:\n", - "---------------------------------------------------------------------------------------------------\n", - "Complexity Loss Score Equation\n", - "1 4.217e+01 1.594e+01 y = 179.58\n", - "4 3.830e+01 3.210e-02 y = (180.23 - tanh(x₀))\n", - "5 2.219e+01 5.457e-01 y = ((-0.39166 * x₀) - -184.54)\n", - "7 2.219e+01 -0.000e+00 y = ((0.60839 * x₀) - (x₀ - 184.54))\n", - "8 8.285e+00 9.852e-01 y = (179.56 + (tanh(12.762 - x₀) * 5.9739))\n", - "10 8.172e+00 6.879e-03 y = (179.58 + (tanh((12.673 - x₀) * 0.67247) / 0.16498))\n", - "11 7.747e+00 5.337e-02 y = (171.31 + (tanh(tanh(15.395 - x₀)) * (21.191 - x₀)))\n", - "12 4.428e+00 5.595e-01 y = (175.18 + (tanh(14.175 - x₀) * (11.229 - (0.40177 * x₀))))\n", - "13 4.266e+00 3.709e-02 y = (169.96 + (tanh(15.849 - x₀) * (20.689 - (tanh(x₀) * x₀)))...\n", - " )\n", - "14 2.589e+00 4.994e-01 y = (172.24 + (tanh(15.066 - x₀) * (17.054 - (tanh(tanh(x₀)) *...\n", - " x₀))))\n", - "15 2.377e+00 8.545e-02 y = (173.4 + (tanh(14.705 - x₀) * (15.266 - (tanh(tanh(tanh(x₀...\n", - " ))) * x₀))))\n", - "16 1.774e+00 2.926e-01 y = (172.24 + (tanh(15.15 - x₀) * (15.15 - (tanh(tanh(x₀ / 15....\n", - " 15)) * x₀))))\n", - "17 1.529e+00 1.488e-01 y = (172.24 + (tanh(15.01 - x₀) * (15.15 - (tanh(x₀ / (15.15 +...\n", - " 15.15)) * x₀))))\n", - "18 1.073e+00 3.538e-01 y = (172.24 + (tanh(15.15 - x₀) * (15.15 - (tanh(tanh(x₀ / (15...\n", - " .15 / 0.752))) * x₀))))\n", - "19 9.611e-01 1.105e-01 y = (172.24 + (tanh((15.01 - x₀) * 0.6549) * (15.15 - (tanh(x₀...\n", - " / (15.15 + 15.15)) * x₀))))\n", - "20 8.244e-01 1.534e-01 y = (172.24 + (tanh((15.15 - x₀) * 0.56801) * (15.15 - (tanh(t...\n", - " anh((0.73638 * x₀) / 15.15)) * x₀))))\n", - "---------------------------------------------------------------------------------------------------\n", - "====================================================================================================\n", - "Press 'q' and then to stop execution early.\n" - ] - } - ], + "outputs": [], "source": [ "model.fit(lnk_a2.reshape(-1,1), lnPk_a2)" ] }, { "cell_type": "code", - "execution_count": 86, + "execution_count": null, "id": "96633b71-f2b6-4a05-9abd-a54310418289", "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
PySRRegressor.equations_ = [\n",
-       "\t    pick         score                                           equation  \\\n",
-       "\t0         0.000000e+00                                           179.5845   \n",
-       "\t1         3.209774e-02                             (180.22537 - tanh(x0))   \n",
-       "\t2         5.457020e-01                  ((-0.39166483 * x0) - -184.54474)   \n",
-       "\t3         4.506454e-08             ((0.60839283 * x0) - (x0 - 184.54402))   \n",
-       "\t4         9.851865e-01     (179.55518 + (tanh(12.761697 - x0) * 5.97393))   \n",
-       "\t5         6.878725e-03  (179.58165 + (tanh((12.67312 - x0) * 0.6724680...   \n",
-       "\t6         5.337357e-02  (171.31406 + (tanh(tanh(15.395343 - x0)) * (21...   \n",
-       "\t7         5.594758e-01  (175.17535 + (tanh(14.175411 - x0) * (11.22903...   \n",
-       "\t8         3.709056e-02  (169.95616 + (tanh(15.848622 - x0) * (20.68860...   \n",
-       "\t9         4.994208e-01  (172.24475 + (tanh(15.065756 - x0) * (17.05391...   \n",
-       "\t10        8.544651e-02  (173.39519 + (tanh(14.70492 - x0) * (15.266392...   \n",
-       "\t11  >>>>  8.171071e-01  (172.24475 + (tanh(15.010006 - x0) * (15.01000...   \n",
-       "\t12        1.408766e-02  (172.24475 + (tanh(15.065757 - x0) * (15.06575...   \n",
-       "\t13        1.660253e-01  (172.24475 + (tanh(15.065757 - x0) * (15.06575...   \n",
-       "\t14        1.504349e-01  (172.24477 + (tanh((15.149901 - x0) * 0.365321...   \n",
-       "\t\n",
-       "\t         loss  complexity  \n",
-       "\t0   42.167710           1  \n",
-       "\t1   38.296616           4  \n",
-       "\t2   22.190395           5  \n",
-       "\t3   22.190393           7  \n",
-       "\t4    8.285218           8  \n",
-       "\t5    8.172015          10  \n",
-       "\t6    7.747281          11  \n",
-       "\t7    4.427638          12  \n",
-       "\t8    4.266422          13  \n",
-       "\t9    2.589215          14  \n",
-       "\t10   2.377164          15  \n",
-       "\t11   1.050012          16  \n",
-       "\t12   1.035323          17  \n",
-       "\t13   0.876944          18  \n",
-       "\t14   0.754465          19  \n",
-       "]
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" - ], - "text/plain": [ - "PySRRegressor.equations_ = [\n", - "\t pick score equation \\\n", - "\t0 0.000000e+00 179.5845 \n", - "\t1 3.209774e-02 (180.22537 - tanh(x0)) \n", - "\t2 5.457020e-01 ((-0.39166483 * x0) - -184.54474) \n", - "\t3 4.506454e-08 ((0.60839283 * x0) - (x0 - 184.54402)) \n", - "\t4 9.851865e-01 (179.55518 + (tanh(12.761697 - x0) * 5.97393)) \n", - "\t5 6.878725e-03 (179.58165 + (tanh((12.67312 - x0) * 0.6724680... \n", - "\t6 5.337357e-02 (171.31406 + (tanh(tanh(15.395343 - x0)) * (21... \n", - "\t7 5.594758e-01 (175.17535 + (tanh(14.175411 - x0) * (11.22903... \n", - "\t8 3.709056e-02 (169.95616 + (tanh(15.848622 - x0) * (20.68860... \n", - "\t9 4.994208e-01 (172.24475 + (tanh(15.065756 - x0) * (17.05391... \n", - "\t10 8.544651e-02 (173.39519 + (tanh(14.70492 - x0) * (15.266392... \n", - "\t11 >>>> 8.171071e-01 (172.24475 + (tanh(15.010006 - x0) * (15.01000... \n", - "\t12 1.408766e-02 (172.24475 + (tanh(15.065757 - x0) * (15.06575... \n", - "\t13 1.660253e-01 (172.24475 + (tanh(15.065757 - x0) * (15.06575... \n", - "\t14 1.504349e-01 (172.24477 + (tanh((15.149901 - x0) * 0.365321... \n", - "\t\n", - "\t loss complexity \n", - "\t0 42.167710 1 \n", - "\t1 38.296616 4 \n", - "\t2 22.190395 5 \n", - "\t3 22.190393 7 \n", - "\t4 8.285218 8 \n", - "\t5 8.172015 10 \n", - "\t6 7.747281 11 \n", - "\t7 4.427638 12 \n", - "\t8 4.266422 13 \n", - "\t9 2.589215 14 \n", - "\t10 2.377164 15 \n", - "\t11 1.050012 16 \n", - "\t12 1.035323 17 \n", - "\t13 0.876944 18 \n", - "\t14 0.754465 19 \n", - "]" - ] - }, - "execution_count": 86, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "model" ] }, { "cell_type": "code", - "execution_count": 87, + "execution_count": null, "id": "c215ccee-6c88-4d55-b3bd-d00071c1507f", "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/sandro/.local/lib/python3.11/site-packages/pysr/sr.py:1121: FutureWarning: PySRRegressor.equations is now deprecated. Please use PySRRegressor.equations_ instead.\n", - " warnings.warn(\n" - ] - }, - { - "data": { - "text/plain": [ - "'(172.24475 + (tanh(15.010006 - x0) * (15.010006 - (tanh(tanh(0.051303983 * x0)) * x0))))'" - ] - }, - "execution_count": 87, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "model.equations.iloc[11]['equation']" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": null, "id": "b73ca8cc-9168-4ecf-bed5-c14f56b1e753", "metadata": {}, "outputs": [], @@ -2179,51 +519,20 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "id": "13668ef8-43cd-4a07-a777-ea5bbdf1dd96", "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n", - "Time evolution: 0%| | 0/999 [00:00" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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SCKByrRstF0MelMGrrsZsfg38RXUIl+6BpmIvCqsaUV67H5X1B6ErKoFuG/pGlComfRPRhsUuoE5UBG10zZC+QK8UPol2lNUU1UCr1qa5V7kpHAphavwSvKPnMTdxHv6pIcgzl5A3N4KipTHoguOoCntQJQRQtdaNlouhKZTDq67CXH4t/MX1CJc2QFOxF0VV+1BeewCVDfuhLyiGfjs6R7SFmPRNRKtEt9aPLiQuiEbnRzdUDK3aTRZTHNUW1bIYSpNQKISp0Yvwjp7F/MQF+DwXgZmL0MyPoGhpHOXBCVSHp6AVguveKywL8Ajl8OZVYz6/Br6ieqCsAXkVjSiqaoSu7iAq6/ZDW1C4DT0j2ho7Kum7u7sbg4ODcdd0Oh1cLldc+CURbY1QOISJxQmMzI9geG5Y+XV4fhijc6MYXRhNeWu9Ll+XcGSI02TpFwwEMDV+Ed7Rc5gfPw+/5yIwcwmahREUR6fJZA9qhBBq1rqRECmGpgTdcjEUGRlC2R5oKvagqHofdMu7yaq0BWuPMlFGhUIhBAKBTDcja2k0GqjV6k2/PmNJ30Aktyn2+BNRFCGKIk6cOAFJkiCKIgwGw1Y2kWjXC8thjC+MY2h2CBdnL2J4fjiuMBqbH0NQXn9EoTy/PK74WVkQcQF1+gQCfkyODmF69BzmJy/APzUEzAxDuzCCIt8YKpaLoVohjNq1biQAIVnAlFABKa8acwV1CBTVAWUN0OgbUVy9H7q6/ais3YdqbT6qt6uDtOXm5uZw8eJF7JJJo7QQBAF79+5FScnm8tEylvSdiMFgQH9/P9ra2tDW1haXBk5El8myjLGFMZybOYcLMxciX7MXMDQ7hKHZoXUXUucJeagtrkV9cT0aShrifo0WQ9xanx5+vx9To+chjZ7D/MQFBLyRkSHt/AiKfeOoCE6gUvaiXgijfq0bCUBQVmFS0GNaE5kmC5Q0AKUN0OobUVTdCH29AfraRtTkadYeZaIdLRQK4eLFiygqKkJ1dTWT4xOQZRkTExO4ePEiDh8+vKmRpownfceSJAmtra0wGo2wWCxKLhNRLptanMIZ6QzOSGdw2nsaZ6QzcEvuNY/nyBPysKd0D/aW7EV9ST0aihuUXxtKGlBdWA21avND05SYz7eEqZHzkMbOY2HiPALeixBmhqFZGEGJbwwVwcnlYkhetxgKyGpMqfSQ8qoxX1CLYHFkzZBWvw8l1ftQUXcAFbWNqMvLQ912dZCyUiAQgCzLqK6uRmEh15AlU11djXPnziEQCGS+YEpkraTvlR566CFlZ53D4YDdbmfSN+UUaUnCC1Mv4MXJF5VfJxYnEj43T8jD3tK92F+2H42ljdhXtg/7SiNfdSV10Kg029z63W1paRFTw+cgjZ3DwuQQgt6LEGYvQTs/ihLfOCpCE6iUJTQIMhrWupEA+GU1plSVkPKqsVBQi0BJA4SyyMhQafV+VNQfREV1A4sh2hCOLK3tSj+fjCV9A5HRJ1EUlQN3jx07BpvNBqPRqByZkgyTvmmnk2UZ4rSIwbFBDIwN4LmJ53Bp7tKq5wkQ0FjaiEO6QzhUcSjyq+4QDpQdgEbNomgrLC0uYHL4HKSxs1icHELAexGq2WHkL4wsF0OTqIKEPQD2rHUjAfDLeZhQVWJaU4PFgloEiuuhKt8DbWVjZGSo/gD01XtQr1KvPcpERFklY0nfQCTUMjbtW6fTpbwzjknftNOEwiG84n0Fg2ODGBwbhGvMBa/Pu+p5+8v249rKa3Fd1XW4ruo6HKk4wvVEV2Bxfg4Tw2cxM3YeC1NDCHmHIMwOI39hFKX+cehDE9BjBnsB7F3nXj5Zg8nlYmihMDJNJpTvRb6+EaW1+6CvOwhdVR32qNRrF1ZEu5jL5UJ3dzdEUYTFYoEkSZiamsLx48dTWmYTPUt25TrmZMt5gMubztK5u55J30RpEh1Benz4cTwx/ASeHn961bqjAnUBbqy5Ec21zbip+iZcW3UtyrTMEUvVwvwMJi5FiqHFqQsIeS9BmB1GweIoSpRiaBb7UrjXkqzBhKoaM9pqLBbUIVgSGRnKr4xMk1U2HESZvhZ7VCoWQ0RrMBqNOH78OBwOhzJTJEkSDh48CK939T8SV7Jarejp6Ul6vaenZ1XhpdPpYDKZlBmrdGDSN9EW8ix58KfhP0WKpJEnML4wHvfzUk0pbq69Gc21zWiubcY1+ms4rZbE3Ow0pobPYmb8PBYnLiAoXYR6bgT5i6Mo841BH56EDnPYn8K9FuR8TKkqMa2txVJh7XIxtBcFlY0orYkcxVFaUY1GlSrt/SJKJ1mWsRgIpfU9CjXqTa0HSrZ+OZbdbkdra+uq652dnXjggQfiNpGtZDQaYbVad0bBZDKZEo4eMR6Adit/yI9nxp/B48OP4/Hhx3HKcyru5/nqfLTUtuD2httxS90tuKriKu5OAzA/N4PJS2JMMTQE9dwIChZGUOofR1VoEmXCPFJJS1mQ8zGprsaMphqLhfUIldRDrYuMDJXVHoC+4SBKyyrRqFKBk/a02y0GQrjm8/+e1vd46UtvRpF2/fJBFEVlrbLb7Y4LqQYiRVBra6sy82Q0GuNiiKJOnjwJi8WyZrG08n3TkeGYlUnfANDf359wSI4ok2Kn2R4ffhyDY4Orjgg5UnEEr214LW5vuB3GWmPOJV0vzM9icvgspkfPYWHyAkLSRahnh5WRocrwBMoxj+K1brL8j9c5FGJKVYUZbQ2WCuuWi6HIyFBZzf5IMVReiX3cHUSUdaJB1aIooq+vDxaLRfmZzWZDZWWlMqDS1tYGh8OhbAqLNTU1taoASlQ/AEBzczNcLlf2F0xXmvQdPRYl+gHbbLY1d8oRbQfvkhd/GvmTUiStnGarKqxSCqTb6m9DVeHuPTxicWEeE5dETI+dx+LkhcgC6rlhFCyMonR5mqwixTVD8yjApKo6phhqgLpiuRiqPYjKhgMoKdOnNMpERBGFGjVe+tKb0/4eG2EwGNDW1oaenh7l7/zBwUEllxGAMkCyctrO6XSira1t1T1X1g9Ren36jnXOqqTv2Kk7t9sdV40SbZeV02wve16GjMvHDeSr89Fc26wUSYd1h3dF/onPt4iJi2chjZ3FwkRkZEiYuRSzm2w85QXUq6bJShug1u1BQeU+lNXsR+WeJpSU69ceZSKiDRMEIaXpsu2m0+kwMDAAIFIXNDc3w+12K/WAy+VK+DqXy7WhAGuPx4OWlpYrb3ACWZX0Hfua5ubmNT8kBlfSVolOsz0x/AQeH34cA2MDu3KabW52GhNDZzA96sbS5DmEvUPQzl1EyeII9MExVMle7BXkdbfWL8paTKqqYhZQN0Ct2xu3ZqisvIrTZEQ5ShRF9Pb2KmuYTCYTzGYz+vr6YLPZYDAYYDabcfLkSdhsNuj1emUKzWAwxK1BMhqN6OnpSXl3vdvtxrFjx9LSr6xK+gYi1WQ0tHKtypLBlXQl1ptmqyyoVAqk2xtu3xHTbMFAAGMXRUwNncLC6KuQp0Tkzw6h1DeCqtA4KjC79vSWEMkZmlBVYVpbc3lrva7x8m6yBgNKdVVcQE1ESRkMBvT19a267nA44h4nykyyWCxwOp3KchyTyQSHw4GKigqYTKZ1d8qJopjy4vCNyqqkb1EU0dHRAYPBgO7u7jUXfTO4kjbCH/Lj2YlnL+9mmzq1Y6fZPBMjGD79DOYuPAdMnUHB3Hnoly6iLjyKPUJozYygGRRjUl2Dmfx6+IsbIJc3Qlu5HyW1B1G5pwkV1XuwV6Vad5SJiCgdjEYjent7465Fs5c6OzuVcMqV9QMQqSnSGV2UVUnfBoMh7vFaGFxJa5FlGWenzyoFUrJptugIkrHGiIK8ggy1NjGfbxHnXxqAVxxEeOwllEy/inrfWVRBQsJljcvHcoyo6+Et2Atf6X5Ab0Bh1X6U1RtQtfcQysr0YCwmEWWzrq6uVZu+nE4nmpqalKm5lfWDJEmQJGlLgrGT2bFJ30QrRafZomuRxhbG4n6ezdNsoWAQ5199GpMv/wnhSy5UTL+AgwERVwnBhM8fEWowXmDAoq4J6somFNVdhar9V6O6/iD25+WlFOZIRJSNdDrdqh3y69UNOp0u7ZmPTPqmHSu6m+2JkSfWnGa7vT5SIF1VcVXWTLP5fIsQn/0jpFO/Q9HIkzAsvgCDsIi45BABmEYxhvKvwrzuCFS110B34AbsOXwT6ksreHArEdE2yrqkb6fTCUmSIIoizGZz2hZv0c6TyjTbVRVXRUaR6iO72bJlmm1xfg5nXL/F3Cu/R+l4P5p8p/AawX/5CUJkK/75/MOY0V8PTWMz6l5zB+oPXI3reFwHEVHGpX1KbiNhltHMpp6eHkiSxGKJduxutnAoBPHFJzHxzK9RcukPuGrpBVwvBC4/QQC8KMO54hvh33Mrqq57Aw5ccytek8dz5YiIslHaC6aNhFlGR5fsdjuPRslRvpAPz44/qxxeu9Zuttvqb8uqabaxS2dx7qlfQiX+Bwyz/TiEaRyK/lAAxqHHUFkzwvtuR+31b0Tj4RtxM0ePiIh2hLQXTBsJswQiu+qir+HRKLtfIBzAi5Mv4smRJ9E/2o9nJp6BL+SLe040NPK2htuyajfbwvwMTj/1Gyyc+g3qJp/AwfAF1Mb+XM7H6aKb4dt/F+qNb8XeQzeghgUSEe1yLpcL3d3dEEVxQ6GTUaIowuVyrVrOs1bodXQ2K1G201bJSA5TsjDLlpYWpXDS6/UJD+GLYtL3zhQKh3DKcwpPjT6Fp0afgmvMtWodUnVhNW6rvy3rptlCoRDE5x/HxLP/jrJL/4mrfC/gxphdbGFZwBnNYXjq7kD5dW/GIeMbcKM2O4o7IqLtYjQa0dbWhsHBwU3tirdarQlnmKLXe3p6VoVaR8+hjc1l2mpZc+CMx+NBe3s7nE5nSlNyTPreGeb8c3hu8jk8O/4snh5/Gs9NPof5wHzccyryK9BS14Jb625Fa30rDpYdzJpptpEhN4b6fwHh7O9waLYfhzGLw9EfCsCoUI0LFbdBc/gomm55K66qrF3rdkRE6SXLQGAhve+hKQLS9N9ou92O1tbWVdc7OzvXTfk2Go2wWq27q2BaK8wyOpy2XoeZ9J19QuEQzs+cx4tTL+LZiUiBdNp7Om4NEgCUakrRUteCW+puQWtdKw5XHIZKyI6pqrnZaZx+6tfwvexE3dQTOBAeitu+Py8X4EzxzfDtuwsNzW/DnqbrUMdpNiLKFoEF4GsN6X2PTw8D2tSPzna5XDh69Cj6+vogSRJ6e3vR1dUFj8eDvr4+WCwWZcQodn1z1MmTJ2GxWFLeCBZ7Ft1WykjBtBVhlkz6zqxgOAhxWsRLUy/h1NQpvDT1El7xvrJqeg0A9pTswU01N+Hm6ptxU81NOKQ7BLVKnYFWrxYKhXDm2ccw9dyvUTb8n7jK9yJuFkKXfy4LcGuugqfuDlRc/2Y03fwG3KjlnzsiolQZjUa0tLRAr9crO+KdTidOnDgBvV4Pq9WqFEmJluJMTU2tKoDsdju6u7sxODgYd725uRkul2tnFkwMs9z5PEsenPGewWnpNNySGy97Xsar3ldXLc4GgMK8QhypOIIbqm/ATTU34abqm1BdVJ2BVic3fP40LvT/Cnnn/gNNcwM4gtnLPxSAEaEaQxW3Q3PV8jSbviZzjSUi2ghNUWQEKN3vsQkrN3slEjv7BERqiLa2tlXPa29vXzUSBUTWP6fLthyNcqVhlrQ9ZvwzcEtunPZGCqMz0hmckc7As5R48X2xphhX66/GNZXX4DX61+Daymuxv2x/1oweRc3OeHH6yV/D98qjaJh6Avvli4gdsJ5DIc4UGeE/cBf2NL8VewzXoT5L1lAREW2IIGxoumw7xRYzqRY2Lpdr1QLvtXg8HrS0tGy4banImkXfUTabDQaDQUn6pq23EFiAOC3itPc0zkhnIkWSdHpVKGSUAAF7SvbgUMUhHNIdwmHdYVxTeQ32le3LmrVHsYKBAE4/+0d4n/s1ykf+iMP+UzCumGY7oz0Cqe51KL/+TTh00124idNsRERbwuVyweFwKFNver0eoigqUUEOh0PZ1dbb24uBgQFl3VH07//olJrRaNxQNIHb7caxY8fS0q+sSvqORgpEtwamc3tgLvCFfDg3fQ6npdM4471cGF2au5T0NbVFtThUESmKmnRNOKw7jIPlB1G0ySHY7XJJPIWhwV9Bc+53ODQ/iNcgZieeAAwLtbiovw3aq0ww3PrnOKLLrmlCIqLdwmg0oq+vL+6a2+1Wvnc4HMr3K3fDWywWOJ1OZcDEZDLB4XCgoqICJpNp3Z1yoiim7ZSQrEr6drlcmJubg8ViweTkJM6fP8+CKQXBcBAXZi4oa4zOSGdw2nsaF2YvICyHE76msqASh3SHlFGjQ7pDaNI1oVRbus2t35wZaQpn/vRL+E8/ij2eJ9Eoj2BP7M9RBLG4GYEDr8ee5reiwXAN0rxvhIiIrpDRaERvb2/ctWj2UmdnpxJO6XQ6IYpi3MCK0+lM65robUn6vnjxIn7zm98AgNJRnU4XN8p08uRJTE1Nwel0wmKxwGAw4N3vfjdHmRIIhoN42fMy+kf70T/aD9e4a1W2UVSZtkwpiGKLo4qCim1u9ZULBvx45dH/i7xnH0TTwrMwCpeLwaCswhnt1ZhueB30178ZhpvuxE08l42IaMfp6upaddKH0+lEU1OTMjVnMpniRq0kSYIkSZsKykzVtqxhOnXqFBYWLgdpRTsZHWVyOBx48MEHcfToUczOzsJgMECSJFRVVaGvry9hwbRbkr5lWYYMWfnVF/JhMbiIhcACFoOLmAvMYWJxAmPzY7g0dwkve17Gy56XV23fL8wrVKbRYouj6sLq7Q+BlGWlb4B8+ZJ8OY8pNptJDl8ufMKyjLn5eSzMTGFxVsKCNIq54VcgjDwHg/QYrsVU5IkCMCQ0YKTqdhRcbUJT61twdVn6dkcQEdH20Ol0q9Ywr1cI6XS6tA+ubEvB1NzcjMnJybhrZ86cwaFDytGk0Gg0GB4ehkqlwh/+8AeUlJSgqakpriiK9eUvfxlf/epX09ruqH/7zidR80+/gCxE/vqXBaz+XgDCy3VJeJ2fhVXAkkbAkhZY1AKL+cB8ATBZJmCyDBitEDCqB+Q1Cp3SUBg3LfnRvBSAcdGPw/4A1DgLABBiihH/itcJcSGScsz1xM8RkjxHJcSHUSYiJPl+Pfrlr0Q8KMOz9cfQcOdf4qqrr0cjd7MREdE2yFjS95NPPolbb70VQGRKrq6uDj6fD6973euwd+9eZSX9nj17Et4jGAwmvJ4OYd8iyrY8aT5RwXH52nw+cK4eOLtPxuSeEGR9CLXhEK7y+3Gt34/9gSDiNu/vsrohIKsxJxRjTlUKKX8PfLpDKL76jTh061vxhoLs3DJLRES7V8aSvr/xjW8oj0VRREtLC+bn53H48GFIkgSn04mxsbG4RPBYeXnb1/RbOz6G04ZrIcgyBAiRURdZiDwOR65BlqGShUjdIkdGZgQ5ch0yoAKAcDjy+nAYgs8PLPogLC1/zc4D41NQTXggD4+g2BfAteeAa88JAPKA4jKoj1wF9b5GCAf24dL+fZHvi+N3r10ecBGWHwsJzvwRLl8SIj2Kf03M97E3FS6XdMprhNXPi/vfmPeP/V8AEFRxY1bKexQXFkKTX4QKQUAFAB54Q0REmSbIsrz+3Moaoou1V6qsrFQWeFutVrz44oswGo148MEHAUS2Ds7Pz+POO++EXq9Hb28v7rnnHjz88MPKdsTm5uZVsedRidYwNTY2Ynp6GmVlZVfSpYyTAwEsvfoqFgddmH/ySSw89RTCs7MJn6tpaID28CHkHzqE/MOHkX/oMPKbDFAVFm5zq4mIKBOWlpZw9uxZHDx4EAUFBZluTtZK9DnNzMygvLw8pdrhigumVNlsNkiSpGQxiaKIzs7OVcVR7M45vV6f8iKujXR6p5FDISy9dApLL5+C/8wZ+E6fhu/0GQQnJhK/QBCgaWyMKaIOIf+qw9AePAiVVru9jSciorRiwZSaKy2YtmVeayPnyTFCYDVBrUbh9deh8Prr4q6HJAm+mAIq+n3I60XgwgUELlzA3G9/e/kFajW0+/ZdLqIORwoq7f79EDTcgk9ERFfO5XKhu7sboijCYrFAkiRMTU3h+PHjKR1zIooiXC7XqnrA6XQm3S0XDcmODcjeats2wpRuu3mEaaOCU1OriijfmTMIJ4te0GiQf+AA8g8fgjZmVEq7bx8EdXadC0dERPGycYTJbrfHBVRLkoSDBw/C6/Wu+9rOzs5VCeAA0NHRAUmS0NPTk7DwcrlcEEUx6cDLjhhh2iin0wlJkpTz5NIVc75b5VVWIq+yEsW33aZck2UZwfHx5SLqtFJE+U+fQXhhYbnAOh13HyE/H1qDYdXUnmbPnu3PdiIionXJsrwqp2+rFeYVburvAEmS1n2O3W5Ha2vrquudnZ3rHotiNBphtVrTNlO1LQXTRs6Tix6b0tPTA0mSWCxtEUEQoKmthaa2FiV/dodyXZZlBIeH46f2Tp+GTxQhLy3Bd+oUfKdOxd1LVVqKgte8BgXXXIOCa69BwTXXQHvgAEejiIgybDG4iFt/dGta3+PJ9zyZ0vmi0cN3RVGE2+1etYmrs7MTra2tEEURJpMJRqMxblQq6uTJk7BYLCnXA7GH926lbVvDlOp5ctHRJbvdjv7+/oTDcrR1BEGAZs8eaPbsQclddynX5VAIgUuX4ouoM2fgF0WEZ2ex8NRTWHjqqcv3KSxEwdVXLxdR16LwppugPXiAI1FERDkqdiCkr68PFotF+ZnNZkNlZaUyGtTW1gaHwwGPx7PqPlNTU6sKoOiAy8o6obm5GS6Xa+cWTO3t7fB4PHHDcdHz5KJ0Oh2cTieASLBl9DUrz5Oh7SEsLxDX7tuH0qNHletyIACf242lF1/C0kvLXy+/DHlxEYtPP43Fp59WnqvW6VB4000ovPlmFN58Ewqvv55xB0REaVSYV4gn3/Nk2t9jIwwGA9ra2tDT06MMkgwODsb9vR8telZO2zmdTrS1tcVds9vt0Ol0SjEWWyfo9ek7Iitja5jcbnfciJNer4ckSWhpaVE+QL1en7DaBHbPWXI7jaDRREaSrr4a+C/3AoiMRvnPn48UUS++iMXnn8fSCy8gJEmY+93vMPe730VerFaj4OqrUXTLLSi69RYUtbRAXVKSuc4QEe0ygiCkNF223XQ6HQYGBgBEZpiam5vhdruVXW8ulyvh61wu16oF3rFrlNxud9zIlcfjQUtLy1Y3H4ASr5wdPB6P8sFEp+SSjS51d3ejvLxc+WpsZB50pghqNfINBpTf/XbUfqoTB374II70P4UDD/WitutTKH3LW5BXUwOEQlh68UV4vv99XPzQf8ert96Gs8eOY/zvv4G5Pz6G8MKWnz9DRETbTBRF9Pb2YmBgQBkAMZvN0Ov1sNlsyoauyspK2Gw2ZXoNiIxGiaKoPDYajUmX5jidTjQ3N8cVVG63Oy3TccA2JH1HrQyuXPm4o6MDFotl3ROJo3Zz0vduJMsygiMjWBgcjKSXP/kUAkND8U/SaFB4/fUovu1WFN9xBwpvuIH5UERE68jGWIHNcrlcGBgYiBss6ezshM1mg8lkUnbKxUYIxI5CdXR0KIHYK+26pO/NYg7TzhMYHsb8k09h4cknMf/UkwgOj8T9XFVcjKJbb0XxHa9F8WtfG9mJx0XkRERxdlPBBCTPYers7FQWire1tcFgMMDj8aCnp0fZNKbX65OGY+6Igil6npwkSbBYLMr842aPQUmEBdPOJssyAhcvRoqnx5/A/OOPI7Ri8Z+moQHFd9wRKaBuuw1qRk4QEe26gkmSJDz00ENxo0zReAKTyZRwyk2SJDidzjXriB1RMG0HFky7ixwOY+mlU5h//HHMP/YYFlwuIBC4/ARBQMH116P4tbej5I47UHjjjRB4Th4R5aDdVjCly44vmOx2O7q7u+Om45LlK6yFBdPuFl5YwMLAAOYfewxzjz0G/xl33M+FoiIU33LL8gjUHcyAIqKcwYIpNVl3NMpGUr2ByPbA2FTPtfIVKHepiopQcuedKLnzTtQCCIyNYf6xyOjT/BNPIOTxxEUY5NXXo/iO16LkjjtQdNttyKuoyGj7iYhoZ9vygmkjqd6JrJWvQBSlqa2F7t53QXfvuyCHw/C9/DLmHnsM8489jsXBQQRHRjBt/wmm7T+JTN9dd52yeLzopps4fUdERBuy5QXTRlK914oQSJSvQJSIoFJFjmS55hpU/dVfIby4GJm+++NjmH/8cfhOn8bS889j6fnnMfU9K6fviIhow7Yl6TtZqncyLpcLkiTBbDYnTPkEmPRNyakKC1Hyuteh5HWvA7A8fff4E5Hpu8cfXz1911CP4tdy+o6IiJLLWNJ39MiT6FbB6BonURTR0dEBq9WK5ubmpEejMOmbUqWprYXuXe/Enq//HQ7/8T9x8Kc/Qc3//ASKbr8NgkaD4HBk+u7Sx+/D6dfegbMdxzD+v/4XFvr7Ifv9mW4+EdGO4nK50NHRgebmZiXpeyNia4JYa91LkiScPHlyw++1ERsaYUo11XulpqamuBGl6MJvADCZTHC7L+94MhgMcY+T6erqwn333ac8jiZ9E60ldvqu8oMf5PQdEdEWMxqNaGtrw+DgYMqnd8SyWq0Jd8hHr/f09KyaeYpuFrPb7VeU6biWDRVMaxVFazGZTOjs7FQeR8OnrkR+fj7y8/Ov6B5Em5m+K7njjsjicU7fEVGWkWUZ8uJiWt9DKCxM2z8c7XY7WltbV13v7OxUjkVJxmg0wmq1ZkfBlAqn0wmHwwFJkmAwGNDe3g6DwYDjx4/DbrfD4/Ggq6trq9+WaEtEp+9073qnsvtu/vHHMffYY1gcGERweARSnx1Snz1u9x3DM4koG8iLi3jF2JzW9zjiGoRQVJTy810uF44ePYq+vj5IkoTe3l50dXXB4/Ggr68PFotFGTGK3VEfdfLkSVgsljWLpViiKKblAN4tL5hMJlPC0aN0VXxE6bL29N1j8J0+Ezd9pyoqQhGn74iI4hiNRrS0tECv1ysZi06nEydOnIBer4fValWKpETrlqemplYVQMkCrpubm+FyuXZGwbRRyZK+o6cRb3YakGircfqOiLKdUFiII67NH2Sf6ntsxsp4oURW7qB3Op1oa2uLu7ZWwLVer99U21KRdUnfoihCFEWcOHECkiSlbWiN6EptePru2mtR1NqKotYWFBmNPDyYiLacIAgbmi7bTrHFTKqFTaJoobUCrj0eD1paWq6wpYllXdK3wWBAf38/2tra0NbWxqk82hFSmr574QUsvfACPN//PgAg/6qrUNTSjKKWFhQ2t0BTW5PhXhARXTmXywWHw6FMven1+riRIIfDoYwQ9fb2YmBgQBkcMRgMcQMlRqMRPT09CWuGRAHXbrcbx44dS0u/si7pW5IktLa2wmg0wmKxwGQyMe2bdpxE03cLTz6JhYFBLAwMwC+K8L36Knyvvgrvj34MANDs2YOC669H4fXXoeC661Fw7bVQlxRnshtERBtmNBrR19cXdy02LsjhcCjfr4wPsFgscDqdyhSbyWSCw+FARUUFTCaTslMuWcC1KIopLw7fqKxL+n7ooYeUnXUOhwN2u51J37TjaWprUX7PPSi/5x4AQHBqCguDkeJpYWAAvpdfQeDSJQQuXcLsr38deZEgQGswoODaa1Bw1VXIP3wY+YcPI6++novJiWhXMhqN6O3tjbsWzV7q7OyEzWZDe3s7Ojo6YDAY0N3drRRdTqczrbvwM7boO1HSd3t7O44dOwabzQaj0ahUj4l0d3fj/vvv384mE22ZvMpKlL3pTSh705sAAKHZWSy98AIWn49M2y2+8DyCwyPwu93wu92I/eeAqrgY+YcOIf+qw9AeNEB7YD+0+/ZB09gIFbPJiGiH6+rqilvIDURqhaamJphMpoQB15IkQZKkK854XIsgy7Kc6pNTTfq22WyQJEm5tvJxR0eHMt22WYlGmBobGzE9PY2ysrJN35coWwQnJ7H4wgvwnToF3+kz8J0+Dd/Zs0AwmPgFgoC8ujpo9+2LfB3YD83eRmgaGqDZ0wB1RQVHpoh2oaWlJZw9exYHDx5EQUFBppuTtRJ9TjMzMygvL0+pdmDSN1GWyquqQunrX4/S179euSb7/fCfPw/fmTNYevVVBM6fh//8BfjPn0d4bg7BkREER0aw8OSTq+4nFBZCU18fKaCiX3suf59XUwNBrd7GHhLRVtrA+EdOutLPh0nfRDuIoNUqa5nK/vzPleuyLCPk9cJ//jwCFy4oRVTg4kUEhocRnJiAvLgIvyjCL4qJb56XB01tLfLq66Cpq4emvg55tXWRX+vqoKmrg1qv5ygVUZZRL/9Dx+/3o3CTGUm5wL98mLp6k/8w3NCUXDbbyLAaUa4J+/0IjowgMDwc+bo0fPn74WEERkeTT/XFELRa5NXWQlNXFymsausuF1h1tcirr4dap2NRRbSNZFnGhQsXEAgE0NDQAJVKlekmZZ1wOIzh4WFoNBrs27dP+W/URmqHjBdMyeLNJUlCZ2fnqjNlkmHBRLR5ciiE4MREZDRqdBSBkVEExkYRHBlFYHQUwdFRBCcngRT+cyHk5yOvrvZyEaX8WgdNfT3yamtZVBFtMb/fj7NnzyIcDme6KVlLpVLh4MGD0Mac+Zm2NUyp2EjS91rx5k6nM+GZMkS09QS1GprlabdkZL8fgfEJBMciBVX018DoCIKjYwiMjiI0OQnZ50Pg/AUEzl9I/n4FBZFRquX3VAqsmOk/VVkZiyqiFGm1Whw+fFiZdqLVtFrtFY2+ZTTpO1m8eTRiYGUWAxFljqDVQrt3D7R79yR9TtjvR3B8PDL9N7o8OjUyisDYmHIt5PFAXlqC/9w5+M+dS/5+hYWX11TVRouqmCKLI1VEcVQqFXfJpVFWJH3HxpsnOjeGiHYGlVYL7d690O7dm/Q5YZ8PwbGxpKNUwZERhCQpskh9vaKqoCBSVNXVRab9oovUa+uUaUDGKRDRVsh40vfKePPoNZfLBVEUkxZQTPom2plU+flKVlQy4aWlSFE1OhY/BTg6FlljFTtSdf48/OfPJ72XoNVGCqo1RqvUFRUQuFCWiNaQ0aRvURRXxZtHz46Lhl0mw6Rvot1LVVAA7f790O7fn/Q5YZ8PwfFxBEZGlour0cujVKORacDQ5GRk7dWFCwhcWGNNlUZzefdfdLQqulh9ebRKXVnJooooh22oYEo16XulpqamuOInuvA7Ubx5lNlsTnosChCJTr/vvvuUx9GkbyLKDar8fGgbG6Fd4//3ypqq0dGko1XByUnIgUAks+rixeRvqNFAU1Oz5mhVXmUlwz+JdikmfRPRrpXKmirZ749EKoyNRUarRscikQoxo1XBiQkgEFAOSF5MdrO8POTVVEOzci1VTABoXlUViyqiHWjLc5icTiesViskSYLFYlF2wsXGCuj1+rgdcluBOUxElC5yIIDg5GTCtVTR6b/g+DiQSgaOWo28mprLi9WVdPW6y9OC1dUQ8jK2YoIoZ+yo4MqtwoKJiDJJDgYRnJxUpv+UnX+xo1Xj40AotP7NVCrkVVdHpvsS7PxTiiqNJv0dI9rFMhpcuVE2mw0GgwEOh0NJ+o5eE0VxzXVMRETZQsjLU8I/k53mJYdCCE5OJd35FxwdRWB8HAgGERwbQ3BsDEt4LskbCsirqooJ/0wQrVBTDSEm1ZiINi+jSd/RheAmkwlWqxWiKEJcPhg0mgQeDbEkItrpBLUamtoaaGprUHjDDQmfI4fDCE1NXQ7+TDRaNTYGBAIITkwgODGBpeefT/KGAtRVlZcXpycYrcqrrYWKRRXRujKa9K3T6WA2m5URJYPBALvdruQu6XQ6OBwOFkxElDOE6HRcdTUKr78+4XPkcBghj2fNnKrg6CjkQAChiUmEJiaBF15I+p7qysqYANBEo1W1UHGTDeW4rEj6NpvNsFgsyujSWvlLUQyuJKJcJahUkem4qirgumsTPkeWZYS83gQ5VfGjVbLPh9DUFEJTU8BLLyV9T3VFRfzZf6t2AtZCVZhsMpJo58to0nfs4btNTU3K6FJs4dTa2prwngyuJCJKThAE5On1yNPrgWvXKKok6fKoVPTImtGY8//GxiAvLSHk9SLk9cJ36lTS91TrdJd3/tUliFaoq4WqqChdXSZKq4wmfR87dgxOpxN2ux1ut1uZsjt58iScTidEUUya/cTgSiKiKyMIAvIqKpBXUYGC17wm4XNkWUZ4ejpJTtXlMwDlxUWEJAkhSYLv5ZeTvqeqvHy5oKqFpq5eGa3Kq6uFpr4emtpaqIqL09Vlok3LaNK3TqdT1ifFrlOK3mutcEsGVxIRpZ8gCFDrdFDrdCg4ciThc2RZRnh2NmYt1epjaoIjIwgvLCA8PQ3f9DR8r76a9D1VpaXJd/5FD1UuKUlXl4kS2rFJ30RElB0EQYC6rAzqsjLgyFVJnxeanV0jpyryODw3h/DsLHyzs/CdPp30XqqSkvjRqehoVTQAtL4eqpISCIKQji5TDmLSNxERZY3Q3NzltVRJRqvCKW7yURUVJT5MOWa0SlVWxqIqh+2opO9EwZVOpxOSJCnBlbE77JJhwURElBvC8/ORab41UtXD09Mp3UsoLIzb+ZdotEqt07Go2qUymvR9pcGVAJTiSZKklIolIiLKHariYuQbDMg3GJI+J7ywECmq1hitCkkS5MVF+M+ehf/s2aT3EgoKYnKqVoxW1dUir76eRVUOyLrgSpvNpkQO9Pf3K6NOREREqVIVFSH/4EHkHzyY9DnhpSVllCoa/LlytCrk8UBeWoL//Hn4z59Pei9Bq12VUxXd+Rc9VFldUQFBpUpHd2kbZGVwZVNTk3Ifm83G8+SIiGjLqQoKoD1wANoDB5I+J+zzXQ7+TJJTFZqaguz3I3DhAgIXLiS9l6DRxOdUJRitUldWsqjKUlkXXGkymeB0OpXneTyehPdk0jcREaWbKj8f2n37oN23L+lzwn4/guPjkQIqyWhVaHIKciCAwNAQAkNDyd9Qo4GmpuZyYVVfF7O2KhK1kFdZCUGtTkNvaS1ZGVwZvbbWlByTvomIKBuotFpo9+6Fdu/epM+R/X4ExieS51SNjiI4MQEEAghcuoTApUtYTHazvDzk1VRDs3ItVfRxXR3yqqpYVG2xrA6uXCt6gEnfRES0UwhaLbR790C7d0/S58iBAIITE8uHKCcerQpOTADBIILDIwgOjyQvqtRq5NXUXJ7+i45WRXOq6uqQV10NIS9j4yY7zo4NrmTSNxER7SaCRgNNQwM0DQ0Abk74HDkYRHByMsGhyjGjVePjQCiE4MgIgiMjyd9QpUJedXXiw5Sjo1XV1RA0mvR0eIdhcCUREdEuIodCCE5OXt4BmGi0ajwyUrUuQUBeVRXyls/5u7xYPTpaVQdNTTUErTb9HUuDHRVcuVVYMBEREaVGDoUQnJpa3vkXE6UwcnlNVWB8HAgE1r+ZIEBdVXl5cXqCs//yamuhysKiascVTJIkobOzU1n0HR2N2kgOEwsmIiKirSOHwwhNTcWNTimjVTGL1eVUiioA6srK5bVUyUaraqHa5qU2OybpO8rpdCrxAbFRA6IoMoeJiIgoA4ToGqfqauD66xI+Rw6HEfJ6Y3KqVh9TExwdhez3IzQ1hdDUFPDSS0nfU11RER+lsHw0TeHNN6PgyJF0dTUlGU36BiIFUnt7O3p7ewHE74xzu92wWCxb3UQiIiLaAoJKhbzKSuRVVgLXXpvwObIsIyRJq3Kq4karRkch+3wIeb0Ieb3wvXQq7h41n/zk7iuYNpL0rdfrYTQaE97H6XSiubk56c+JiIgo+wmCgLyKCuRVVKDgmmsSPkcpquJ2/kUWp4emp6FtSn5u4HbJaNK3Xq+Hy+WCy+WCKIpwuVwwGo1wuVyQJAlms1m5thKTvomIiHaHuKLq6qsz3ZyEMnZgjcfjgdFoXDUiJYoiOjo6YLVa0dzcnPRolO7ubpSXlytfDK0kIiKidMlo0neU2WyOW9jtdrvXbQuTvomIiGi7MOmbiIiIaB1p2SXncDggSRIMBgPa29thMBhw/Phx2O12eDwedHV1bfXbIhonxbVMRERElIpozZBKJGVWBFduhYsXL3JKjoiIiDZsaGgIe/fuXfM5u6ZgCofDGB4eRmlpKQRByHRz0iK6TmtoaCgn08zZf/Y/V/ufy30H2H/2P339l2UZs7OzaGhogEq19j64bYkV2A4qlWrd6nC3KCsry8n/00Sx/+x/rvY/l/sOsP/sf3r6X15entLzMhYrQERERLRTsGAiIiIiWgcLph0kPz8fX/jCF3I2ToH9Z/9ztf+53HeA/Wf/s6P/u2bRNxEREVG6cISJiIiIaB0smIiIiIjWwYKJiIiIaB27JocpV3R0dOCBBx6ATqeLu2632wFcPtj4Ss/qy1YnT55UDm5ub28HkDt97+joUI4V6u3tRU9PD4Dc6X+U3W6HTqdT+pkr/bfb7TAYDBgYGAAA5cDyXOq/x+PB4OAgOjo6cu73X5Ik2Gw2APHnuu72/mdV/2TaMdxutwxA1ul0sk6nkwHIPT09stvtls1ms/I8k8mUwVamj8lkkr1eryzLsmw0GmVZlnOm77Ic6bNOp4v7HHKp/7Isy16vVzYajXJfX58sy7nT/2i/o99H/9OdK/0fHBxUfs+9Xq+s0+lkWc6d/suyLPf19cknTpyQe3p6lGu7vf/Z1j9Oye0goijC6/UqX1arFSdOnIDT6YwbcdLpdHA6nZlraBq4XC6ljy6XC4ODgwCQE32P6urqgtfrhcPhUPqcS/0HgIceegjHjx9XHudK/3U6nfJnXhRF5V/ZudJ/j8cDh8MBINJHvV4Pl8uVM/0HIiPqTU1Ncdd2e/+zrX+ckttBYocibTYbjh07BgBwu92orKxUfqbX6yFJ0nY3L60GBgYgiiJEUQQAWCwWWK3WnOh7VH9/P4DIXx5AZEoml/rvcrlgMpmUIXogN/7sx7LZbHA4HOjr6wOQO/03mUxx//3zeDwwGo3o7e3Nif4ns9t//7OtfyyYdiBRFCFJ0qp1TLGif6nuFpIkQa/Xw2g0AogUUC6XK+Fzd1vfo6JrlgCgqalJKZhX2q39F0VRWbe2lt3afyBSJBsMBnR2dsJqtSZ8zm7uPxD5x9IDDzyQ9Oe7vf/r2e39z2T/WDBlkZMnT2JqamrV9crKyrhFflarFW1tbcrjpqamuKo7ujhuJ1mv7waDIa5Per0eoijuir4D6/ffbrejv79fKZp0Ol1O9T+62D/6ObjdbhgMhpzpPwDlH0kmkwkdHR3o6OjIqf4DkQXAbW1tSuGca/1fabf0P5ms619GV1DRphgMBtntdiuP3W633N7erjyOLg7dTbxeb9yCP4PBIHu93pzouyxHFr06HA7lscFgkGU5N37vVzpx4kTcou9c6L/VapVPnDihPDYYDPLg4GDO9F+WZdnhcCj/H4j2PZf6L8uRPwcrF33v5v5nW/94NMoO1NzcjEcffTRuSi5266Ver09p6mKniW4rliQJBoMhYazAbu07cLmf/f39sFgsyr+0cqX/QGQRaGdnJwwGA3p6epRRJ2B391+SJGUBrMPhiBt5yIX+i6KI5uZm5bEkSYj+1ZUL/Qcif/atViskSYLFYsmZ//5lU/9YMBERERGtg7ECREREROtgwURERES0DhZMREREROtgwURERES0DhZMREREROtgwURERES0DhZMREREROtgwURERES0DhZMREREROtgwURERES0jrxMN2CrhMNhDA8Po7S0FIIgZLo5RJQFzp49i5///Oc4cOAA/uM//gPf/OY3cfbsWRw8eDDTTSOiLCDLMmZnZ9HQ0ACVau0xpF1zltzFixfR2NiY6WYQERHRDjM0NIS9e/eu+ZxdM8JUWloKINLpsrKyDLeGiIiIst3MzAwaGxuVGmItWVUwSZKEzs5O9PT0QKfTbei10Wm4srIyFkxERESUslSW8qS9YJIkCTabDQBw4sQJ5brdbgcAeDweGAwGmEwmiKKIgYEBHD16FABgMpnQ09OT7iYSERERrSntBZPT6cTU1BQqKyuVa6IowuFwwGq1AgDa2tpgMpmg0+kwODgIIFJQtbe3b1k7QqEQAoHAlt1vN9JqtesueiMiIspFaS+Y2tvb4fF4IEmScs3pdMZNuel0OjidTphMJgCAzWbDsWPHtuT9ZVnG6Oho3PtTYiqVCgcPHoRWq810U2gDZFlGeH4eIWkaoWkJ4bl5yH4fZJ8PYZ8Pss+vPJaDQcjhMBCWATl8+ftwGLIc8304tPycFPaEpLRvJLW9JSntQdkV21SIaCNKjx5F8W23ZrQNGVnD5Ha740ac9Hp9XEHjcDhgNpvXvIfP54PP51Mez8zMJHxetFiqqalBUVERIweSiMYyjIyMYN++ffycskzQ64XvlVfge/U0ApcuIjA8DP+lSwiOjiE0PQ2EQpluIhFR2mj2NORmwZSIx+MBEFnzpNfr131+d3c37r///jWfEwqFlGIptkCjxKqrqzE8PIxgMAiNRpPp5uQsWZYROH8e8396EvNP/gmLzzyL4MjIuq8TtFqodTqoSkogFORDlV8AIT8fQr4WKm0+BK0WgkYDqFSASoAgqNb/PuUp2hQK7FSL8FSex3qeKKcU3nBDppuQmYKpqakpbkQpuvAbiEzPRdc2raWrqwv33Xef8ji6NTBWdM1SUVHRFrR694tOxYVCIRZM20yWZSy9+BJmHvkVZn/97whcurTqOZq9e5F/9RFo9+2HpqEBmj0N0NTXQ11RAXV5OVQFBRloORFRbshIwWQymdDZ2ak8FkVRWb+Uqvz8fOTn56f0XE4vpYaf0/YLTk5Csv8E0k9/isCFC5d/oNGg6MYbUXT7bShqbUXBa14DdQo5IURElB7bskvO4XBAkiQYDAa0t7fDYDDg+PHjsNvt8Hg86OrqSnczsobL5UJ3dzdEUYTFYoEkSZiamsLx48dhNBrXfb0oinC5XKt2ENpsNuj1emVqU6/Xr3pONOIhNt6BMmPh6afh/cGDmHE4gOWRUKGwECWvvwtlb/lzlLzuz6DiyCgRUdbIuqNRnE4nJEmCKIowm80pB1jOzMygvLwc09PTSnDl0tKScm5UQRZNV9jt9rhYBUmScPDgQXi93nVfGw32jGWxWOLCPjs6OvDAAw8k/OxcLhdEUUwY2ZCtn9duIcsy5h9/HFPfs2Khv1+5XnjjjdC9+y9Q9qY3sUgiItpGiWqHZLIuuNLhcKCnpweSJG047Xs9sixjMZDe3USFGvWmprZSiT2w2+1obW1ddX1lTIPFYkn62RmNRlit1i3NuKK1ybKMud//HpPf/UcsPf985KJGg/K770bFe9+DwmuvzWwDiYhoXVkVXBkdXbLb7ejv79/ylO/FQAjXfP7ft/SeK730pTejSLv+xyqKIpxOJ0RRhNvtVgI7ozo7O9Ha2qqs7zIajXGfWSyj0YiKigocO3YMHR0dKa0HE0VRWWhP6bPw9NMY//u/x+JA5PdXKCiArqMDlR/4f6Gpr89w64iIKFVpj3Vub29HU1NT3LVkwZVAZAdd9DXRkandKDqqZjKZ4HK54j4Pm82GyspKtLe348SJE8oC+ej6pJX6+vrw6KOPoqmpCR0dHRBFEUBkRKq5uXnV85ubm+Fyuba+U6TwnTmDoQ9/BOff/R4sDgxC0Gqh/8AHcOhRJ+o+82kWS0REO0xWBVe2tLQohVPsAuZEUg2ujFWoUeOlL735Clq+vkKNekPPNxgMaGtrQ09PjzJ6NDg4GFdERkfaEk3buVwuGI1G5St6LbrAPtGIVCo5V7Q5wYkJjH/zm5j+6b8C4TCgUqH83neh+iMfgaauLtPNIyKiTcqag8M8Ho/yF350Sm6ttO/u7m6Ul5crXyszmBIRBAFF2ry0fm1m/ZJOp8PAwACAyFRZdFQoOgK1lpUFkdvtXvc1sblXtDVkvx9T/+f/wP2WP8e0/SdAOIzSNhMM//YwGr7yFRZLREQ7XNYFV0YXhq+3KDmV4MpsJIoient7lTVMJpMJZrMZfX19sNlsMBgMMJvNOHnypBIVEP1sDAZD3Nojp9OpTF1GR+Q6OzvXXSzvdru37Ky+XCfLMuZ+9zuM/20P/OfPAwAKrr8etV1dKDLenOHWERHRVsmJ4MpsYjAY0NfXt+q6w+GIe5woK8liscDpdCojb6mMQCUiiuKW70DMRT5RxNjXujH/xz8CANRVVai57z6Uv/MdGzhShIiIdgIGV+4gRqMRvb29KT8/ugvPbrcrI3ZOp5Of9xUKzcxg8rvfheeHPwKCQQgaDfTv/0tUWixQl5RkunlERJQGWRdc2dzcDL1eD6PRuKFYgZ0UXHklJEnCQw89tOb6rrVe63Q6k0537sbPayvJ4TCkn/wEE9/4B4SWQ0ZL3vhG1HaegHb//gy3joiINmrHBlcCkbVJDFVMTqfTbapYir6Wn+3mLL30Ekbv/xIWn30WAKBtakJtVxdK/uyODLeMiIi2Q1YFV0Z/Fp3G2+rgSqKNCs3MYOKb34L3xz8GwmGoiopQ9T8+Cv173wtBo8l084iIaJtkXXDliRMnYDKZ0NTUpIxCEW03WZYh/exncP/5W+H94Q+BcBhlb30rDI88gsr3v5/FEhFRjsmq4Mpo0WQymSBJ0poBi5sJriRKxdKrr2L0S19SjjPRGgyo+9xnUXz77RluGRERZUrW7H32eDxKoRQtnNZab7OZ4EqitYTm5jH2tz04+657I8eZFBai+r77YPjZv7JYIiLKcVkXXBktktbLF9qpwZWUfWRZxuwjj2Dsb3sQHB8HAJS2mVDb1QVNQ0OGW0dERNmAwZXbzOVyobu7G6IooqenZ8P9FkURLpdr1ehbbNo3EJnmXPmc6I7FRKGYuconnsXYV76M+cefAABo9u1D3Wc/g5I778xwy4iIKJswuHKbGY1GtLW1YXBwcFMp3VarddXuQYvFgp6eHmUhfUdHBx544IFVr9XpdDCZTHFBlrkqvLCAye9ZMfX97wOBAIT8fFSa/wqVH/wgVDuwECciovRKe8GU7PiOtf7CliQJnZ2dqw6WvWKyDAQWtvaeK2mKgE0cwJsKu92O1tbWVddX7jq0WCxJjz4xGo2wWq05WzDJsoy5Rx/F6Ne+huDwCACg5K67UPvZz0DLKV0iIkoi64IrgUgBEJ1a2lKBBeBraV6T8ulhQFuc8tNdLheOHj2Kvr4+SJKE3t5edHV1wePxoK+vDxaLBUajEQDisqtiGY1GVFRU4NixY+jo6Ehp5Cr2EN9c4b9wAaNf/Srmf/8HAICmoQG1n/k0St74RghpKnKJiGh3SPsuuWhwZaxocGV7ezvMZnPcFFOuTRcZjUa0tLQoa45aW1vhdDphMplgsVjiCqRkRWRfXx8effRRNDU1oaOjA6IoAoh8ls3Nzaue39zcDJfLlZ4OZaHw0hImvv0diG+/O1IsaTSotFhg+OUvUHr0KIslIiJaV9pHmNrb2+HxeOJ2xSULroyeIZc2mqLICFA6aYo29bKVn0cisZ9hlMvlgtFoVL6i16LrxRKNSK2Vb7XbzP3+9xj9ylcRGBoCABS/9rWo/dxnkX/wYIZbRkREO0lWBVfq9Xq4XC64XC5lN1iyAmpTwZWCsKHpsu0UW8RspKCxWq1xRZHb7V73rDmPx4OWlpaNN3IHCVy6hNHubsw5HwUA5NXWorbrUyh985s5okRERBuWVcGVRqMx4YhUIjs1uNLlcsHhcGBgYABOp1MpDm02GyRJgsPhQG9vr7KeaWBgQJliMxgMyvdAZKSuqakJNpsNdrsdNpsNnZ2dSUeootxu965dvyT7/Zi02uB+29sjxVJeHvQf+AAMv/wlyt7yFhZLRES0KVkXXAkAZrN53VGSnRpcaTQa0dfXF3fN7XYr3zscDuX7RPEBTqdT+WyS7UBcjyiK6xZVO9H8449j9Mtfgf/sWQBAUUsL6r7weeQfPpzhlhER0U6XkREmk8mE/v5+5fFmgyvLysrivnY7o9EYV1ytx+l0QhTFuEOMnU7nrsu9CoyN4eLHP44LH/hv8J89C3VVFRpO9mDfD/4viyUiItoSDK7cYbq6umCz2dYdgQMihWlsgSVJEiRJ2tSoVDaSAwF4fvAgJr/zHYQXFgCVChXveQ+q/8dHoc6BApqIiLaPIMuynOlGxLLZbDAYDHA4HKumpNYyMzOD8vJyTE9PK6NNS0tLOHv2LA4ePIiCgoJ0NXnX2Emf10J/P0a/9GX4Tp8GABTeeCPqvvB5FFxzTYZbRkREO0Wi2iGZrAqujK5rMplMsFqtORmuSGsLTk5i/O/+DtM/fxgAoNbpUPM/P4Hye++FoMqaPQxERLTLbMuU3NTUVFyMQDS4Mrodvq2tDSaTCTqdDmazWRllYrFEUXIoBO+P/wUT3/wmwrOzgCBAd+wYqv/mY8irqMh084iIaJdL+z/J29vb0dTUFHctWXBllNlshiRJcVvoKXctPvMMznZ0YOwrX0F4dhYF116LA73/gvr7v8hiiYiItkVG5jCSBVfa7XalcGpqaorb3bWSz+fDzMxM3BftLkGvFyOf+xzO/cW74XvpFFRlZaj7wudx4KFeFN5wQ6abR0REOSRrFn14PB5lHZPdbofb7Y5b87TSTg2upPXJ4TC8Dz0E8S1/DqkvUjSXv+tdaHrkV6h497shqNUZbiEREeWarAqu1Ol0ysG76x3Au1ODK10uF7q7uyGKIiwWCyRJwtTUFI4fP57SOXrRI2NWfj42mw16vV45oDd6mG+s6AL8tQrRTFt84UWMfulLWHruOQBA/pEjqPv851CU4BBhIiKi7ZKRgslkMqGzs1N5vNngyvz8/A29RpZlLAYXN/SajSrMK1zz+A2j0Yjjx4/D4XAoWUqSJOHgwYPwer3r3t9qtSZMAO/p6VHWhXV0dOCBBx5Y9VqdTgeTyQS73b5uQbrdQtPTmPjmN+H98b8AsgxVcTGq/8dHUfHe90LIy8gfUyIiIkVOBVcuBhdx649uTet7PPmeJ1GkKdrw69Y7Ow+IRDG0trauur5yEb3FYkl69InRaITVas2agkmWZUz/7OcY/7u/Q2h5dKzsbW9DzYkT0NTWZLh1REREEWkvmJKdd5bsL+zoQu/+/v4NBVfuNKIoKkeXuN1uDA4Oxv28s7MTra2tyuib0WiMi2KIZTQaUVFRgWPHjqGjoyOl0bpsyLhaeuUVjH7py1hc7rvWYEDd5z+H4ttuy2i7iIiIVsqq4Eq73a5MG4mimPIRIKkqzCvEk+95csvul+w9UhHtsyiK6Ovrg8ViUX5ms9lQWVmpFJVtbW1wOBzK+qSV+vr64HK54HQ60dHRgcHBQRgMhqTFZ3NzM1wuV8YKptDcHCa//W14HvwhEApBKCxE1V//d1T+5V9C0Goz0iYiIqK1ZFVwZeyok9vtjisitoIgCJuaLksng8GAtrY29PT0KJ/H4OBgXDZVtNhJNG3ncrlgNBqVr+g1l8uVtPjU6/Xb0LPVZFnGzK9+hfG/7UFwYgIAUPqmN6H2U53QNDRkpE1ERESpyMrgSqfTiebm5jV3je2mHCadToeBgQEAkWKyeXlHWLLpzFgrp+jcbrdSfEZf63a70dLSojwnOqq3nXxnz2Lov/03DH/ifyI4MQHN/n1ofMCGvd/6JoslIiLKelkVXAlERkckSYLZbIbL5Up6j52awySKInp7ezEwMKAUiWazGXq9HjabDaIowmw2o7KyEjabLS6802AwxKWfO51ONDU1Kc+z2Wzo7OyMK0YTFZ9ut3vbCqbw0hImvvUtnL3nHZh//AkIWi2qPvoRGB5+GCWve922tIGIiOhKZc1+bY/HA1EU0dHRAYPBgO7u7jUXfe/UHCaDwYC+vr5V1x0OR9zjRFlJFosFTqdTmVpbbwRqZfEZLZpEUUy6i24rzf3hDxj98lcQGBoCABS/7nWo+9xnod23L+3vTUREtJWyKrjSYDDA7XandI/N5DDtdEajEb29vSk9N1nx6XQ60x7jEBgZwVj332L2N78BAOTV1qL2059G6Zva1syoIiIiylY7NrgyV3V1daW0ezBR8SlJEiRJSttnLQcC8PzgQUx85zuQFxYAtRr6//pfUfXhD0NdUpyW9yQiItoOORVcuRvodLpNRy3EHj2z1RZcLox+8X74Xn0VAFB4882o++IXUHDkSFrej4iIaDtlZXBld3f3qiBHyk5Brxfjf/d1TP/0pwAAtU6Hmk9+EuXveicEVdac7UxERHRFsiq4EogUUonSrCm7yOEwpJ/8BBNf/3uEpqcBALqODlTf93HkVVRkuHVERERbK6uCK2lnWHr5ZYx+8X4sPvMMACD/6qtR94XPo+jmmzPbMCIiojRJe8HU3t4Oj8cTtysuWXDlRoomn88Hn8+nPN7JwZU7RWhuHpPf/hY8P3gQCIehKipC9cf+Byre+14IeVmTUEFERLTlsi64MlU7NbjS5XKho6MDzc3NcenmqRJFMS7MMio2vHJl4GWUJEk4efLkht9TlmXMPPIIxLe+FZ7/7/8C4TBK//wtMDzyK+j/8i9ZLBER0a6XNatyowfLOp3OpEVBrK6uLkxPTytfQ8vhiNnOaDSira0NLS0tm5qGtFqtqxbMWywWHDt2DO3t7TCbzXA4HAnvHT1bbr3PNpZ/aAhDf2XGpY/fh+D4eORIk//9v7H3H/4BmtraDbefiIhoJ8qq4EogsqsulfDKzQRXyrIMeXFxQ6/ZKKGwMG3hjHa7Ha2trauur5zitFgsSZO8jUZjwqJrJTkQwNT3/xmT3/0uZJ8PglaLSrMZlX/1QahyLDCUiIgop4Ir5cVFvGJsTut7HHENQigqSvn5LpcLR48eRV9fHyRJQm9vL7q6uuDxeNDX1weLxaIcaRK7UD6W0WhERUUFjh07ho6OjpQ+S1EUk54nt/jiixj+4hfhO30GAFB0+22o/8IXoD1wIOV+ERER7SYMrswwo9GIlpYW6PV6mEwmiKIIp9OJEydOQK/Xw2q1KkVSdNpypb6+PrhcLjidTnR0dGBwcBAGg0GZeuvv7487l6+5uRkul2tVwSQHgwhJEoY//RmoRkagrqhAbdenUHb33TzShIiIclrWBVemk1BYiCOu9AZiCoWFm3rdyl2DiSRaGB89VDf6Fb3mcrmUNUuiKMYdp6LX61fdJzQ9Df+lSwgvLEANoLz9v6DmE59gphIREREyNCWXKYIgbGi6bDvFFjGJCppkYkeggMgORLPZHFd0ud1uWCwW5bHH40FLS4vyODQ/D//QEORwGMjLQ8PJHlQkWCtFRESUq7KuYLLZbDAYDBBFcdNnpmUzl8sFh8OhTL3p9fq4ESCHw6GMDPX29mJgYEBZbxT9XKJTaU6nE01NTbDZbNDr9fB4POjs7IwrlpxOJ5qbm5XRJyBSQB07dgxAZBoucPEiAEBVWoq8vDwUJlnbRERElKsEWZbldL7BRo5GiUYKmM1m5eepTt3NzMygvLwc09PTKCsrAwAsLS3h7NmzOHjwIAoKCrayWxnhcrkwMDCQciHpcrkgiiLa29uVqTsA6OjoQF9fH2RZRuDCBYRmZyFotZD37MG5Cxd2zedFRES0lkS1QzJpz2GKHo0SK3o0SjQ3KLogOXYhsk6nQ39/f7qbt6MYjcaUIheAyGfc0dEBq9WK5ubmuJyrrq6uSLF0aRih2VlAEKBtbISgVqez+URERDtWVh2NAiRe2EyXdXV1xS3gTsZgMKwqriRJgiRJOPrGNyJw8RJC0xIAQLt3L1SFhcDSUrqaTUREtKNlZA1TsqNRjEYjRFEEEPnLPVFIY1SuniWn0+k2vbZLp9Ph3re/Hf6zZxFeXAQEAZo9e6AuL9/iVhIREe0uWXU0islkgiRJylqmtdYv7dSz5DIlHAggMDICn9uN8OIiBLUa2v37kZckwoCIiIguy0jB1NTUFPc49mgUg8EASZLipukS2chZcuFweGsavsPIoRBCMzPwDw3B9+qrCE5NAbIMVWkptIcOQV1SEv/89K7/JyIi2rGy6miU6GLwaK5QW1tb0mM+UjlLTqvVQqVSYXh4GNXV1dBqtbsysVoOhSJfwSBknw9yIAB5yYfw0hKAy0WQqqAQ6ko9UFQEfygEhEKX7yHLmJiYgCAI0Gg0GegFERFR9sqqo1GSLQbf7DlzKpUKBw8exMjICIaHhzfdB9/iHILzc4gUH7EFl7z8SMDlwiT+51hj0GZDpZu8/PyYXyHLEOS17yMLAmSNCtCoAd8sMD2e9P7hoA+hC0/g6SemVvxQSPL9GleFxA/lmB9stHYVYv43WVNWX4q/Iggr2rD+DZK2ZCP3WPUKIfKr8ido+cOIPF798+jjuLsJgvK9LAgQEHOPFR9u9Jqw6ufC5T+iwur7JmuDjOX3E2JeH3Pfy/1a/VkQEW1U9eFbsP/ITRltQ1YdjZJsMXgiqS761mq12LdvH4LBIEIxIyob8ej3v4wDDz2xqdduF58GmC0ExnUCRvTAiE6AWC/AW3r5b6zScAjloTBqQyHsCQaxNxjEYX8ABwIBqGUZmqVJqEPcKUdERNnlT9Of2P0F02ZE075PnTqF5ubmhM/p7u7G/fffn9L9otNMm51q0jca8GL9byAv1x7Rf1HLACAsD/YIl79XrsV8j+hzln+VYx+vvA9WfC8AITUQyBMQ0AjwayK/BjQCFgqBuWI1lrRAQAjDjzD8QhgBhBEQZCwthTAvBCELwEi0QyoA2uWvIqBAVuNwsBQ3Bwy4KaBDEfISDozFjiVsbrnT6hdt7D6Jn7yRtVeXR7pWvCbBLZK823pPWPMeQsyfHmFFuyNjOXL8OKYsx79mxR0j95BX3Pvy9wLkVR+ysOI+AsJxjV3589XXYsfo5OVRz9h2rMS1cUR0ZbSV+zLdhPQnfQOpp32Looj+/n60trbCbDbj9ttvR1tbG770pS+tumeiEabGxsaU0jpzTSgcwrR/Gp5FDyaXJnFh5gLOzZzDGe8ZPD/5POYCc8pzC/MKcU/TPfjLa/8SjaXceUhERLvXRpK+t2WEKZr2HTvdlmiBt9VqxXe+8x0cP34cADA1NRVXFMVKZdE3RahVaugL9NAX6HEIh3Bb/W3Kz0LhEE5Lp/G7od/h12d/Dfe0G72v9OKnp3+K913zPvz3G/87CvJ4TAoREeW2bSmYUk37FkURN9xwAx555BGIooi/+Iu/SFow5Wpw5VZTq9S4Wn81rtZfDcsNFjw1+hT+9/P/G38a+RP+6YV/wh8u/gFfv+vraNI1rX8zIiKiXSpjwZXJFni///3vx5EjR2A2m3HDDTckTftmcOXWEwQBt9bfClubDd96w7dQWVCJM9IZvO+R98E15sp084iIiDIma5K+gY2lfW8kuJI2RhAEvGHfG2C/x46ba27GrH8WZocZz4w/k+mmERERZcQVT8mdPHkSU1Mrc3uAysrKuAXeKzU1NcVN0cWmfUdft1b+EtcwpV9VYRWsbVZ8/Hcfx2OXHsNHf/tRPPjWB7G/bH+mm0ZERLStrrhgWqsoWkuytG/KLoV5hfjGXd/AB/79A3hx6kV8/Hcfx4/e+iMuBCciopyyLVNy0bRvh8OhRAnEpn3bbDYl7ZuyT5GmCN9+47ehL9DjtPc0/vapv0UwHMx0s4iIiLbNtuQwbYeNZCnQ5jx26TF8yPkhAMCRiiP47G2fxU01N2W2UURERJu0kdohqxZ9U3a7Y88d+NqffQ3l+eV4xfsK3vfI+/DFx78IaUnKdNOIiIjSKisLJrvdnvRIFMqsu5vuxsPvfBjvOvQuAMBPTv8Ed//sbvz09E8RlsMZbh0REVF6ZNXRKLGLvtva2uBwOFJ+D07Jbb+nx5/Gl//0ZZz2ngYA3Fh9Iz532+dwRH8kwy0jIiJaX9ZNyUWPRokVPRqlvb0dZrMZPT0929EU2kI319yMh97+ED7Z8kkU5RXh2YlncfwXx9HzVA/m/HPr34CIiGiH2JaCqb29HU1N8UdrJDoaxel0bkdzaAvlqfLwX6/9r3j4nQ/jzQfejJAcwoOnHsQ7fvYO/Prcr7FL9hQQEVGOy7qjUVLl8/kwMzMT90WZU1tci6/f9XVYTVbsK92H8cVxfPL3n4TFYcG56XOZbh4REdEVyapF3x6PBwCUY1Gia5wS4Vly2em1e16Ln77jp/jwTR+GVqXFEyNP4N6H78V3nv4OloJLmW4eERHRpmTl0Sgmkwlut3vN9+3q6sJ9992nPJ6ZmWHRlCXy1fn40I0fwtsOvg1fe+pr+OOlP8L6nBW/EH+BT9/6ady5985MN5GIiGhDduzRKDxLLvs1ljXiH4/+I3574bfofqobl+Yu4cOPfhhH9x1FZ2sn6kvqM91EIiKilGxLrIDT6YTVaoUkSbBYLGhvbwcQHyug1+uV65vBWIHsthBYwPee/R5+8NIPEJSDKMwrxIdu/BDe95r3QaPWZLp5RESUgzZSO2Tl0SjRQqq/vz/luAEWTDvDae9pfOVPX4Fr3AUAaCpvwmdu+wxa61oz3DIiIso1WVcwbSS40m63Q6fTwWQy4eTJk9DpdDCbzeu+BwumnUOWZfyb+G/4+4G/h2cpstD/bsPduK/lPlQVVmW4dURElCt2dHBle3u7spbJ7XajpaVlO5pI20gQBNzTdA8efufDOH7kOAQI+Dfx33DPv96Df3n5XxAKhzLdRCIiojhZG1zpdDrR3NwMo9G4HU2kDCjPL8dnb/ssfvS2H+GaymswG5jFV5/8Kt7zq/fg+YnnM908IiIiRVYGV7pcLkiSBLPZDJfLlfD1DK7cPa6rug4/euuP8JlbP4NSTSlemnoJ7/3Ve/HFx78IaUnKdPOIiIiyL7hSFEV0dHTAarWiublZCbNcicGVu4tapcZfXP0XePhdD+OepnsgQ8ZPTv8Ed//sbvzk1Z8gLIcz3UQiIsphWRdcaTAY1g2tBBhcuVtVFVbhq3/2Vdx7+F589cmv4rT3NL74xBfx09M/xWdu+wyuqbwm000kIqIcxOBKykrNtc3ofXsvfnzqx/jHZ/8Rz00+h3f/8t04dtUxfOTmj6A8vzzTTSQiohzC4ErKeuML4/j6wNfxyNlHAAD6Aj3ua74P9zTdA0EQMtw6IiLaqbIuh2mjbDYbDAYDHA4HgytJ8dTIU/jqk1+FOC0CAIw1Rnz61k/jiP5IhltGREQ7UdblMEmShJMnT+LkyZNx1+12O+x2O2w2mxIpEF3XZDKZIIoiRFHcjibSDnBL/S2w323Hx5s/jsK8QrjGXTj+i+PoeaoHc/65TDePiIh2sawLrowme0dHmQwGw3Y0kXYIjVqDD1z3ATz8zofRtr8NITmEB089iLt/djd+Kf4SWThgSkREu0DWBleazWZIksQRJkqorrgO33j9N/A90/ewv2w/Jhcn8an//BQ++JsPwi2tv8uSiIhoI7IuuNJutyuFU1NTk7IwfCUGVxIA3LHnDvz0np/iozd/FPnqfDw1+hTaH27HNwa+gYXAQqabR0REu0TWBVeaTCalcHK73UljCxhcSVFatRbmG8z4+Tt/jtc3vh5BOYjvv/h93POze/Cbc7/hNB0REV2xrAuu1Ol0SrzAWjEDDK6klfaU7MG33/ht/H7o9+h+qhuX5i7hE7//BF7b8Fp03dKFA+UHMt1EIiLaoRhcSbvOXY134db6W/FPL/wT/s/z/wePDz+Oex++F++/9v34qxv+CoV5hZluIhER7TAMrqRd7cLMBXQ/1Y0/XvojAKChuAGdt3TiDY1vYOglEVGO2/HBlUAkj6mzsxNWqzWl57NgomRkWcZvL/wWPf09GJkfAQDcufdOfOqWT6GxlNO4RES5aiO1wxVPyaVCkiTYbDYA8VN4sSNMBoMhbkrO6XTC4/FsR/NolxMEAUf3H8XtDbfjgecfwD+/+M/4w8U/4E/Df8IHr/8gPnD9B5Cv5vQuEREll3XBlUCkkLqS6TmiRIo0RfiY8WP4yT0/wa31t8If9uMfn/1HvPNn78QfLv4h080jIqIslnXBlS6XC0ajcd17MoeJNstQbsADbQ/g7+76O9QU1uDi3EV8+NEP42O//RiG54Yz3TwiIspCWRdcCQAulwt2ux2iKMLlciV8PXOY6EoIgoC3HHgLHn7Xw3j/te9HnpCH3w79Fu/42TvwwHMPwB/yZ7qJRESURbIuuNJoNKK9vR0ejycup2mlrq4uTE9PK19DQ0Pb11DaNYo1xfhEyyfQd3cfWmpbsBRawree/hb+y8P/BU8MP5Hp5hERUZbIuuDKKLPZDLPZnPT1zGGirXSo4hD+6c3/hF+e/SW+3v91nJs5B7PDjDftfxM+2fpJ1BXXZbqJRESUQTs2uJJoqwmCgLcb3o679t6F7z7zXfz45R/jN+d/g/+89J/46xv/Gu+95r3QqDSZbiYREWUAgyuJknjF8wq+8qev4JmJZwAATeVN+Mxtn0FrXWtmG0ZERFtixwdXNjc3Q6/Xw2g0xsUNrIUFE6VDWA7j52d+jn8Y/Ad4fV4AwNsMb8Mnmj+B6qLqDLeOiIiuRNYVTBsNrtxMDhMLJkqnad80vv30t/HQKw9BhowSTQk+fNOHcfzq45ymIyLaoTZSO2RlcKUoinA6nXFrnIgyqTy/HJ+97bP48dt+jOsqr8NcYA49/T1of7gdj116LNPNIyKiNMu64EogMgplMpnQ1NSkjEKtxOBKyoRrq67FD9/2Q3z+9s+jIr8C4rSIDzk/hL92/jXOTp/NdPOIiChNsi640ul0KoXTWjlMDK6kTFEJKnRc1YFf3PsLvO+a9yFPyMN/XvpP3Pvze9HzVA+mfdOZbiIREW2xrAuuNJlMSuEEIOlaJgZXUqaVactwovUE/vUd/4q79t6FoBzEg6cexNv/9e3ofbkXwXAw000kIqItkpXBldEiaa1cJgZXUrY4UH4A3zn6HTx+6XGc7D8J97QbX3nyK/jxyz/GR40fxRsb3whBEDLdTCIiugIMriTaIq/d81rY6+3oe7UP333mu3BPu/E3//E3uKHqBnzM+DHcUn9LpptIRESbxOBKojSY8c/gn1/4Zzx46kEsBhcBALfX346P3PwR3FB9Q4ZbR0REQBbmMG2U0+mEJEkQRRFmszluN10yLJgoG00uTsL2nA19r/Ypa5purbsVH7j+A7i9/nZO1RERZVDWFUwbCa4URRFWqxU9PT2QJCmlYglgwUTZ7eLsRXzv2e/hl+IvEZQjhdM1ldfg/3nN/4M3HXgT8tVcj0dEtN12dHBldHTJbreju7t7O5pHlHZ7S/fiK3/2Ffzq3l/hva95LwrUBXhp6iV8+o+fxtG+ozjZfxJnvGcy3UwiIkoiK4Mrm5qalNdER6ZWYnAl7UT1JfX41C2fwm/af4OP3PQR1BfXY9o3jR+89AO86+F34R0/ewe+/fS3cWrqFMJyONPNJSKiZVkXXNnS0hJ3LRkGV9JOVlFQAcuNFjxy7yP47tHv4g2Nb4BGpYE4LcL2nA3HfnEMd/Xehb/5j7/BD0/9EM+MP4P5wHymm01ElLOuOFZgK3k8HrS3t8PpdMJut6O/vz/ujLlYXV1duO+++5THMzMzLJpox1Gr1Lhz7524c++dmPXP4vcXfw/HOQeeGHkCkk/CoxcexaMXHlWev6dkDw6WH0R9cT3qi+tRV1yHyoJKlOWXoVRbijJtGUq0JTwQmIhoi2VlcGX0dWvFDDC4knabUm0p3m54O95ueDsCoQBenHoRA2MDGBwbxKueVzG+OI5Lc5dwae7SuvfKU+VBq9IiX50PjVqDfHU+tCottGotVIIKAoTIr4IQ91i5hsvfC9jcTr7N7ADc9Htt5nXcoEi0Y7zr0Lvwxn1vzGgbGFxJlIU0ag1uqrkJN9XchA9e/0EAgLQk4bR0GhdmLmB0YRQjcyMYXRiFd8mLWf8sZvwzyrRdMBxEMBzEQnAhk90gItoSrbWtmW7C9kzJOZ1OOBwOSJIEg8GA9vZ2GAwGHD9+HHa7HR6PB11dXQAiEQSdnZ3o6elJOVKAKBfoCnRorWtFa13y/3AEw0HM+eewFFqCP+SPfIX9cd+H5TBkWY78CjnyPcJx18OIfB+SQ5tq63bGu8nY+HtlYfwcEa3h+urrM92E7SmYWlpa4HK5ACSfZosWR6IoYmBgAEePHgUQGYlKto6JiOLlqfKgK9BluhlERLvOto0wTU1Nxe2Ki+YwWa1WAEBbWxtMJhN0Oh0GBwcBRIItr+S4FCIiIqKtkHU5TNGF3zabjWuaiIiIKCtkXQ5TlMPhWHMNE4MriYiIaLtkXQ4TEFn4vVZoJRAJrrz//vtXXWfhRERERKmI1gypbATJyhwmnU6nrG1KZmVw5aVLl3DNNdcwvJKIiIg2ZHZ2FuXl5Ws+Z8fmMK0MriwpKcHQ0BBKS0s3FZi3E0TTzIeGhtY9VXk3Yv/Z/1ztfy73HWD/2f/09V+WZczOzqKhoWHd52ZdDtNmqVQq7N27d4tanN3Kyspy8v80Uew/+5+r/c/lvgPsP/ufnv6vN7IUtS0Fk8lkSjh6xMgAIiIi2gkytkuOiIiIaKdgwbSD5Ofn4wtf+ELOHjrM/rP/udr/XO47wP6z/9nRf0HmoUpEREREa+IIExEREdE6WDARERERrYMFExEREdE6supoFFpfR0cHHnjggVXn7NntdgCXE9N368HFJ0+eVBLho7EUudL3jo4OJa+st7cXPT09AHKn/1F2ux06nU7pZ6703263w2AwYGBgAABgNpuV60Bu9N/j8WBwcBAdHR059/svSRJsNhuA+MDo3d7/rOqfTDuG2+2WAcg6nU7W6XQyALmnp0d2u92y2WxWnmcymTLYyvQxmUyy1+uVZVmWjUajLMtyzvRdliN91ul0cZ9DLvVflmXZ6/XKRqNR7uvrk2U5d/of7Xf0++h/unOl/4ODg8rvudfrlXU6nSzLudN/WZblvr4++cSJE3JPT49ybbf3P9v6xym5HUQURXi9XuXLarXixIkTcDqdcSNOOp0OTqczcw1NA5fLpfTR5XJhcHAQAHKi71FdXV3wer1wOBxKn3Op/wDw0EMP4fjx48rjXOm/TqdT/szHHiOVK/33eDxwOBwAIn3U6/VwuVw5038gMqLe1NQUd2239z/b+scpuR0kdijSZrPh2LFjAAC3243KykrlZ3q9Pu5g491gYGAAoihCFEUAgMVigdVqzYm+R/X39wOI/OUBRKZkcqn/LpcLJpNJGaIHcuPPfiybzQaHw4G+vj4AudP/ladFeDweGI1G9Pb25kT/k9ntv//Z1j8WTDuQKIqQJGnVOqZY0b9UdwtJkqDX62E0GgFECiiXy5Xwubut71HRNUsA0NTUpBTMK+3W/ouimNJxSru1/0CkSDYYDOjs7ITVak34nN3cfyDyj6UHHngg6c93e//Xs9v7n8n+sWDKIidPnsTU1NSq65WVlXGL/KxWK9ra2pTHTU1NcVV3dHHcTrJe3w0GQ1yf9Ho9RFHcFX0H1u+/3W5Hf3+/UjTpdLqc6n90sX/0c3C73TAYDDnTfwDKP5JMJhM6OjrQ0dGRU/0HIguA29ralMI51/q/0m7pfzJZ17+MrqCiTTEYDLLb7VYeu91uub29XXkcXRy6m3i93rgFfwaDQfZ6vTnRd1mOLHp1OBzKY4PBIMtybvzer3TixIm4Rd+50H+r1SqfOHFCeWwwGOTBwcGc6b8sy7LD4VD+PxDtey71X5Yjfw5WLvrezf3Ptv7xaJQdqLm5GY8++mjclFzs1ku9Xp/S1MVOE91WLEkSDAZDwliB3dp34HI/+/v7YbFYlH9p5Ur/gcgi0M7OThgMBvT09CijTsDu7r8kScoCWIfDETfykAv9F0URzc3NymNJkhD9qysX+g9E/uxbrVZIkgSLxZIz//3Lpv6xYCIiIiJaB2MFiIiIiNbBgomIiIhoHSyYiIiIiNbBgomIiIhoHSyYiIiIiNbBgomIiIhoHSyYiIiIiNbBgomIiIhoHSyYiIiIiNbBgomIdi1RFHHy5EnY7XZYLBblGhHRRvFoFCLatZqbmzE4OAggciaVKIrQ6XQwm80ZbhkR7TQcYSKiXclms8FkMimPowfXxl4jIkoVCyYi2rWamppWXTMYDBloCRHtdCyYiGhXOnbsGAYHB2G322G32wFERpmi3xMRbQTXMBERERGtgyNMREREROtgwURERES0DhZMREREROtgwURERES0DhZMREREROtgwURERES0DhZMREREROtgwURERES0DhZMREREROtgwURERES0DhZMREREROv4/wHAtuvDj6wMYgAAAABJRU5ErkJggg==", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -2250,21 +559,10 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": null, "id": "0048f301-a4f1-48a4-9de3-c2a3ef103f59", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -2289,218 +587,10 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "id": "d8694a1e-6562-434c-b5da-9d60cdb3de4f", "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Mode evolution: 0%| | 0/100 [00:00" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -2560,19 +639,10 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": null, "id": "818e4ad0-510c-4d31-a2bf-83bde5f04c58", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-0.00017585144466178716\n", - "1.000011999964\n" - ] - } - ], + "outputs": [], "source": [ "print(np.polyfit(np.log(k_a),np.log(k_a**3 * PI_zeta2),1)[0])\n", "\n", @@ -2581,7 +651,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": null, "id": "6b2523f8", "metadata": {}, "outputs": [], @@ -2768,7 +838,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "id": "a81352e0", "metadata": {}, "outputs": [], @@ -2971,7 +1041,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "id": "1e644bda", "metadata": {}, "outputs": [], @@ -3173,50 +1243,10 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": null, "id": "17f092b6", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mode k = mode_k: 1000\n", - "# Calculating mode 1, initial time -63.10759538973279, redshift_alpha 3.91e+02]: \n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 9999/9999 [00:00<00:00, 215664.91it/s]" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "# Final values k = 1000 Ps_zeta1 = 5.115284221544647e-55 Ps_Pzeta1 = 6.634574990849296e-122 Ps_S1 = 6.566648912425620e-123 Ps_PS1 = 4.819512169162375e-100\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "#test_two_fluids_wkb_mode(Nc.HIPertTwoFluidsCross.MODE1MAIN, 1, 0.0, 1.0)\n", "test_two_fluids_wkb_mode(Nc.HIPertTwoFluidsCross.MODE1MAIN, 1, 1.0, 0.0)\n", @@ -3225,3029 +1255,27 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "id": "98260fc2", "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - " 0%| | 0/20 [00:00" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "test_two_fluids_wkb_spec()" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "id": "84556565", "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - " 0%| | 0/50 [00:00" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/plain": [ - "(array([-172.29336504, -171.47725159, -170.67740675, 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"stdout", - "output_type": "stream", - "text": [ - "3.0000712909085103\n" - ] - } - ], + "outputs": [], "source": [ "ns = result[0] + 1\n", "print(ns)" @@ -6311,21 +1323,10 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": null, "id": "36e209f8", "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "3.0" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "12*1/3/(1+3*1/3) + 1" ] @@ -6354,8 +1355,7 @@ "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.6" + "pygments_lexer": "ipython3" } }, "nbformat": 4, diff --git a/notebooks/primordial_perturbations/two_fluids_calibrate.ipynb b/notebooks/primordial_perturbations/two_fluids_calibrate.ipynb new file mode 100644 index 000000000..7f2e83285 --- /dev/null +++ b/notebooks/primordial_perturbations/two_fluids_calibrate.ipynb @@ -0,0 +1,629 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "34003942", + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "import numpy as np\n", + "from numpy.testing import assert_allclose\n", + "\n", + "from tqdm import tqdm\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from numcosmo_py import Nc, Ncm\n", + "from numcosmo_py.plotting.tools import set_rc_params_article" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b31c9f4d", + "metadata": {}, + "outputs": [], + "source": [ + "Ncm.cfg_init()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "533290e5-dc2a-467a-8319-11811d78cc2b", + "metadata": {}, + "outputs": [], + "source": [ + "cosmo = Nc.HICosmoQGRW()\n", + "cosmo.props.w = 1.0e-5\n", + "cosmo.props.Omegar = 1.0 * (1.0e-5)\n", + "cosmo.props.Omegaw = 1.0 * (1.0 - 1.0e-5)\n", + "cosmo.props.xb = 1.0e30\n", + "\n", + "k = 1.0\n", + "min_alpha_c = -120.0\n", + "max_alpha_c = -1.0\n", + "min_alpha_scale = 1.0e-12\n", + "np_plot = 1000\n", + "\n", + "# Time arrays for the contraction and bounce phases\n", + "\n", + "alpha_c = np.linspace(min_alpha_c, max_alpha_c, np_plot)\n", + "alpha_b_e = np.geomspace(min_alpha_scale, 2.0, np_plot)\n", + "alpha_b = np.concatenate((np.flip(-alpha_b_e), alpha_b_e))\n", + "\n", + "# Computing background observables in the contraction phase\n", + "\n", + "m_s_c = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_c])\n", + "m_zeta_c = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_c])\n", + "mnu2_s_c = np.array([cosmo.eom_eval(alpha, k).mnu2_s for alpha in alpha_c])\n", + "mnu2_zeta_c = np.array([cosmo.eom_eval(alpha, k).mnu2_zeta for alpha in alpha_c])\n", + "nu1_c = np.array([cosmo.eom_eval(alpha, k).nu1 for alpha in alpha_c])\n", + "nu2_c = np.array([cosmo.eom_eval(alpha, k).nu2 for alpha in alpha_c])\n", + "nu_s_c = np.sqrt(mnu2_s_c / m_s_c)\n", + "nu_zeta_c = np.sqrt(mnu2_zeta_c / m_zeta_c)\n", + "y_c = np.array([cosmo.eom_eval(alpha, k).y for alpha in alpha_c])\n", + "gamma11_c = np.array([cosmo.eom_eval(alpha, k).gammabar11 for alpha in alpha_c])\n", + "gamma22_c = np.array([cosmo.eom_eval(alpha, k).gammabar22 for alpha in alpha_c])\n", + "gamma12_c = np.array([cosmo.eom_eval(alpha, k).gammabar12 for alpha in alpha_c])\n", + "tau_c = np.array([cosmo.eom_eval(alpha, k).taubar for alpha in alpha_c])\n", + "\n", + "# Computing background observables in the bounce phase\n", + "\n", + "m_s_b = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_b])\n", + "m_zeta_b = np.array([cosmo.eom_eval(alpha, k).m_zeta for alpha in alpha_b])\n", + "mnu2_s_b = np.array([cosmo.eom_eval(alpha, k).mnu2_s for alpha in alpha_b])\n", + "mnu2_zeta_b = np.array([cosmo.eom_eval(alpha, k).mnu2_zeta for alpha in alpha_b])\n", + "nu1_b = np.array([cosmo.eom_eval(alpha, k).nu1 for alpha in alpha_b])\n", + "nu2_b = np.array([cosmo.eom_eval(alpha, k).nu2 for alpha in alpha_b])\n", + "nu_s_b = np.sqrt(mnu2_s_b / m_s_b)\n", + "nu_zeta_b = np.sqrt(mnu2_zeta_b / m_zeta_b)\n", + "y_b = np.array([cosmo.eom_eval(alpha, k).y for alpha in alpha_b])\n", + "gamma11_b = np.array([cosmo.eom_eval(alpha, k).gammabar11 for alpha in alpha_b])\n", + "gamma22_b = np.array([cosmo.eom_eval(alpha, k).gammabar22 for alpha in alpha_b])\n", + "gamma12_b = np.array([cosmo.eom_eval(alpha, k).gammabar12 for alpha in alpha_b])\n", + "tau_b = np.array([cosmo.eom_eval(alpha, k).taubar for alpha in alpha_b])\n", + "\n", + "cos2_phi_c = (nu1_c**2 * nu_zeta_c**2 - nu2_c**2 * nu_s_c**2) / (nu1_c**4 - nu2_c**4)\n", + "sin2_phi_c = (nu1_c**2 * nu_s_c**2 - nu2_c**2 * nu_zeta_c**2) / (nu1_c**4 - nu2_c**4)\n", + "\n", + "cos2_phi_b = (nu1_b**2 * nu_zeta_b**2 - nu2_b**2 * nu_s_b**2) / (nu1_b**4 - nu2_b**4)\n", + "sin2_phi_b = (nu1_b**2 * nu_s_b**2 - nu2_b**2 * nu_zeta_b**2) / (nu1_b**4 - nu2_b**4)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a4daed56-57bc-4993-b8ab-3468d8f83d5f", + "metadata": {}, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1 = fig.add_subplot(1, 2, 1)\n", + "ax2 = fig.add_subplot(2, 2, 2)\n", + "ax3 = fig.add_subplot(2, 2, 4)\n", + "\n", + "ax1.plot(alpha_c, m_s_c, c=\"r\", label=r\"$m_s$\")\n", + "ax1.plot(alpha_c, m_zeta_c, c=\"b\", label=r\"$m_\\zeta$\")\n", + "ax1.set_yscale(\"log\")\n", + "ax1.set_xlabel(r\"$\\alpha$\")\n", + "\n", + "ax2.plot(alpha_b, m_s_b, c=\"r\", label=r\"$m_s$\")\n", + "ax2.set_xscale(\"symlog\", linthresh=min_alpha_scale)\n", + "ax2.set_yscale(\"log\")\n", + "ax2.set_xlabel(r\"$\\alpha$\")\n", + "\n", + "ax3.plot(alpha_b, m_zeta_b, c=\"b\", label=r\"$m_\\zeta$\")\n", + "ax3.set_xscale(\"symlog\", linthresh=min_alpha_scale)\n", + "ax3.set_yscale(\"log\")\n", + "ax3.set_xlabel(r\"$\\alpha$\")\n", + "\n", + "ax1.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8470dc58-92f9-46ab-8ec6-982e346cda0d", + "metadata": {}, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1 = fig.add_subplot(1, 2, 1)\n", + "ax2 = fig.add_subplot(1, 2, 2)\n", + "\n", + "ax1.plot(alpha_c, mnu2_s_c / m_s_c, c=\"r\", label=r\"$\\nu_s^2$\")\n", + "ax1.plot(alpha_c, mnu2_zeta_c / m_zeta_c, c=\"b\", label=r\"$\\nu_\\zeta^2$\")\n", + "ax1.set_yscale(\"log\")\n", + "ax1.set_xlabel(r\"$\\alpha$\")\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_b, mnu2_s_b / m_s_b, c=\"r\", label=r\"$\\nu_s^2$\")\n", + "ax2.plot(alpha_b, mnu2_zeta_b / m_zeta_b, c=\"b\", label=r\"$\\nu_\\zeta^2$\")\n", + "ax2.set_xscale(\"symlog\", linthresh=min_alpha_scale)\n", + "ax2.set_yscale(\"log\")\n", + "ax2.set_xlabel(r\"$\\alpha$\")\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0fcea250-ab16-4d75-b437-254e07cb70cb", + "metadata": {}, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1 = fig.add_subplot(1, 2, 1)\n", + "ax2 = fig.add_subplot(1, 2, 2)\n", + "\n", + "ax1.plot(alpha_c, y_c * np.sqrt(m_s_c * m_zeta_c), c=\"k\", label=r\"$\\nu_s^2$\")\n", + "ax1.set_yscale(\"symlog\", linthresh=1.0e-10)\n", + "ax1.set_xlabel(r\"$\\alpha$\")\n", + "\n", + "ax2.plot(alpha_b, y_b * np.sqrt(m_s_b * m_zeta_b), c=\"k\", label=r\"$\\nu_s^2$\")\n", + "ax2.set_xscale(\"symlog\", linthresh=min_alpha_scale)\n", + "ax2.set_yscale(\"symlog\")\n", + "ax2.set_xlabel(r\"$\\alpha$\")\n", + "\n", + "ax1.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f09ef1fb-3287-4c23-953e-a9325f45a419", + "metadata": {}, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=1)\n", + "fig = plt.figure()\n", + "\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "\n", + "ax1.plot(alpha_c, cos2_phi_c, label=r\"$\\cos^2(\\phi)$\")\n", + "ax1.plot(alpha_c, sin2_phi_c, label=r\"$\\sin^2(\\phi)$\")\n", + "ax1.set_xlabel(r\"$\\alpha$\")\n", + "ax1.legend()\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "af2c3d95-97ec-4f81-b226-dfec9ae4a6f4", + "metadata": {}, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1 = fig.add_subplot(1, 2, 1)\n", + "ax2 = fig.add_subplot(1, 2, 2)\n", + "\n", + "ax1.plot(alpha_c, nu1_c, label=r\"$\\nu_1$\")\n", + "ax1.plot(alpha_c, gamma11_c, label=r\"$\\gamma_{11}$\")\n", + "ax1.plot(alpha_c, gamma12_c, label=r\"$\\gamma_{12}$\")\n", + "ax1.plot(alpha_c, tau_c, label=r\"$\\tau_{12}$\")\n", + "\n", + "ax1.set_yscale(\"symlog\", linthresh=1.0e-6)\n", + "ax1.set_xlabel(r\"$\\alpha$\")\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_c, nu2_c, label=r\"$\\nu_2$\")\n", + "ax2.plot(alpha_c, gamma22_c, label=r\"$\\gamma_{22}$\")\n", + "ax2.plot(alpha_c, gamma12_c, label=r\"$\\gamma_{12}$\")\n", + "ax2.plot(alpha_c, tau_c, label=r\"$\\tau_{12}$\")\n", + "\n", + "ax2.set_yscale(\"symlog\", linthresh=1.0e-6)\n", + "ax2.set_xlabel(r\"$\\alpha$\")\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "60453966-409d-44d7-969a-ee67005bb392", + "metadata": {}, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1 = fig.add_subplot(1, 2, 1)\n", + "ax2 = fig.add_subplot(1, 2, 2)\n", + "\n", + "ax1.plot(alpha_b, nu1_b, label=r\"$\\nu_1$\")\n", + "ax1.plot(alpha_b, gamma11_b, label=r\"$\\gamma_{11}$\")\n", + "ax1.plot(alpha_b, gamma12_b, label=r\"$\\gamma_{12}$\")\n", + "ax1.plot(alpha_b, tau_b, label=r\"$\\tau_{12}$\")\n", + "ax1.set_xscale(\"symlog\", linthresh=min_alpha_scale)\n", + "ax1.set_yscale(\"symlog\", linthresh=1.0e-6)\n", + "ax1.set_xlabel(r\"$\\alpha$\")\n", + "\n", + "ax1.legend()\n", + "\n", + "ax2.plot(alpha_b, nu2_b, label=r\"$\\nu_2$\")\n", + "ax2.plot(alpha_b, gamma22_b, label=r\"$\\gamma_{22}$\")\n", + "ax2.plot(alpha_b, gamma12_b, label=r\"$\\gamma_{12}$\")\n", + "ax2.plot(alpha_b, tau_b, label=r\"$\\tau_{12}$\")\n", + "ax2.set_xscale(\"symlog\", linthresh=min_alpha_scale)\n", + "ax2.set_yscale(\"symlog\", linthresh=1.0e-6)\n", + "ax2.set_xlabel(r\"$\\alpha$\")\n", + "ax2.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ab63ada8-c087-4d13-ac4a-80429306b37a", + "metadata": {}, + "outputs": [], + "source": [ + "def get_zeta(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.ZETA_R) + 1.0j * v.get(\n", + " Nc.HIPertITwoFluidsVars.ZETA_I\n", + " )\n", + "\n", + "\n", + "def get_S(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.S_R) + 1.0j * v.get(\n", + " Nc.HIPertITwoFluidsVars.S_I\n", + " )\n", + "\n", + "\n", + "def get_Pzeta(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.PZETA_R) + 1.0j * v.get(\n", + " Nc.HIPertITwoFluidsVars.PZETA_I\n", + " )\n", + "\n", + "\n", + "def get_PS(v):\n", + " return v.get(Nc.HIPertITwoFluidsVars.PS_R) + 1.0j * v.get(\n", + " Nc.HIPertITwoFluidsVars.PS_I\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "09c12f7e-052d-4d30-b3aa-e8555e9c2497", + "metadata": {}, + "outputs": [], + "source": [ + "%%time\n", + "\n", + "def spec_params(Omegars = 1.0e-5, w = 1.0e-3, E0 = 1.0):\n", + " cosmo.props.w = w\n", + " cosmo.props.Omegar = E0 * Omegars\n", + " cosmo.props.Omegaw = E0 * (1.0 - Omegars)\n", + " \n", + " pert = Nc.HIPertTwoFluids.new()\n", + " pert.props.reltol = 1.0e-9\n", + " \n", + " spec1 = pert.compute_zeta_spectrum(cosmo, 1, -cosmo.abs_alpha(1.0e-14), -1.0, 1.0e-3, 1.0e8, 300)\n", + " spec2 = pert.compute_zeta_spectrum(cosmo, 2, -cosmo.abs_alpha(1.0e-14), -1.0, 1.0e-3, 1.0e8, 300)\n", + "\n", + " return spec1, spec2\n", + "\n", + "specs1 = []\n", + "specs2 = []\n", + "w_a = np.geomspace(1.0e-5, 1.0e-1, 50)\n", + "for w in w_a:\n", + " spec1, spec2 = spec_params(w=w)\n", + " specs1.append(spec1)\n", + " specs2.append(spec2)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "476f9a4d-2dd3-4dbe-87fd-012d513dd66d", + "metadata": {}, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "\n", + "for spec1, spec2, w in zip(specs1, specs2, w_a):\n", + "\n", + " lnk_a1 = np.array(spec1.peek_xv().dup_array())\n", + " lnPk_a1 = np.array(spec1.peek_yv().dup_array())\n", + "\n", + " lnk_a2 = np.array(spec2.peek_xv().dup_array())\n", + " lnPk_a2 = np.array(spec2.peek_yv().dup_array())\n", + "\n", + " ax1.plot(\n", + " np.exp(lnk_a2),\n", + " (np.exp(lnPk_a2) + np.exp([spec1.eval(lnk) for lnk in lnk_a2])),\n", + " label=r\"$k^3|\\zeta|^2$\",\n", + " )\n", + "\n", + "ax1.set_xscale(\"log\")\n", + "ax1.set_yscale(\"log\")\n", + "ax1.set_xlabel(r\"$k$\")\n", + "# ax1.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "924a1ade", + "metadata": {}, + "outputs": [], + "source": [ + "lnk_v = specs1[0].peek_xv()\n", + "lnw_v = Ncm.Vector.new_array(np.log(w_a))\n", + "zm = Ncm.Matrix.new(lnw_v.len(), lnk_v.len())\n", + "\n", + "for i, (spec1, spec2, w) in enumerate(zip(specs1, specs2, w_a)):\n", + " lnPk_a1 = np.array(spec1.peek_yv().dup_array())\n", + " lnPk_a2 = np.array(spec2.peek_yv().dup_array())\n", + "\n", + " lnPk0 = np.log(np.exp(lnPk_a1[0]) + np.exp(lnPk_a2[0]))\n", + " lnPk = np.log(np.exp(lnPk_a1) + np.exp(lnPk_a2)) - lnPk0\n", + " lnPk_v = Ncm.Vector.new_array(lnPk)\n", + "\n", + " zm.set_row(i, lnPk_v)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ebd0af70", + "metadata": {}, + "outputs": [], + "source": [ + "s = Ncm.Spline2dBicubic.notaknot_new()\n", + "s.set(lnk_v, lnw_v, zm, True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "115e8f6c", + "metadata": {}, + "outputs": [], + "source": [ + "for i, (spec1, spec2, w) in enumerate(zip(specs1, specs2, w_a)):\n", + " lnk_a1 = np.array(spec1.peek_xv().dup_array())\n", + " lnPk_a1 = np.array(spec1.peek_yv().dup_array())\n", + "\n", + " lnk_a2 = np.array(spec2.peek_xv().dup_array())\n", + " lnPk_a2 = np.array(spec2.peek_yv().dup_array())\n", + " lnPk0 = np.log(np.exp(lnPk_a1[0]) + np.exp(lnPk_a2[0]))\n", + " lnPk = np.log(np.exp(lnPk_a1) + np.exp(lnPk_a2)) - lnPk0\n", + "\n", + " lnPk_eval = np.array([s.eval(lnk, np.log(w)) for lnk in lnk_a1])\n", + "\n", + " assert_allclose(lnPk, lnPk_eval, rtol=1.0e-12)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5fb3ed5b", + "metadata": {}, + "outputs": [], + "source": [ + "hiprim_2f = Nc.HIPrimTwoFluids()\n", + "hiprim_pl = Nc.HIPrimPowerLaw()\n", + "hiprim_2f.set_lnk_lnw_spline(s)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "91caee9f", + "metadata": {}, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "\n", + "lnk_a = np.linspace(np.log(1.0e-3), np.log(1.0e8), 1000)\n", + "lnw_a = np.linspace(np.log(1.0e-5), np.log(1.0e-1), 100)\n", + "\n", + "lnPk = np.array([hiprim_pl.lnSA_powspec_lnk(lnk) for lnk in lnk_a])\n", + "ax1.plot(np.exp(lnk_a) / 4000.0, np.exp(lnPk), label=r\"$k^3|\\zeta|^2$\")\n", + "hiprim_2f.props.lnk0 = 0.0\n", + "\n", + "for lnw in lnw_a[::10]:\n", + " hiprim_2f.props.lnw = lnw\n", + "\n", + " lnPk = np.array([hiprim_2f.lnSA_powspec_lnk(lnk) for lnk in lnk_a])\n", + "\n", + " ax1.plot(np.exp(lnk_a) / 4000.0, np.exp(lnPk), label=r\"$k^3|\\zeta|^2$\")\n", + "\n", + "ax1.set_xscale(\"log\")\n", + "ax1.set_yscale(\"log\")\n", + "ax1.set_xlabel(r\"$k$\")\n", + "# ax1.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a0b46cf2", + "metadata": {}, + "outputs": [], + "source": [ + "def compute_D_ell(hiprim, lmax=2500):\n", + " lmax = 2500\n", + "\n", + " cbe_prec = Nc.CBEPrecision.new()\n", + " cbe_prec.props.k_per_decade_primordial = 50.0\n", + " cbe_prec.props.tight_coupling_approximation = 0\n", + "\n", + " cbe = Nc.CBE.prec_new(cbe_prec)\n", + "\n", + " Bcbe = Nc.HIPertBoltzmannCBE.full_new(cbe)\n", + " Bcbe.set_TT_lmax(lmax)\n", + " Bcbe.set_target_Cls(Nc.DataCMBDataType.TT)\n", + " Bcbe.set_lensed_Cls(True)\n", + "\n", + " cosmo = Nc.HICosmoDEXcdm.new()\n", + " cosmo.omega_x2omega_k()\n", + " cosmo.param_set_by_name(\"Omegak\", 0.0)\n", + "\n", + " reion = Nc.HIReionCamb.new()\n", + "\n", + " cosmo.add_submodel(reion)\n", + " cosmo.add_submodel(hiprim)\n", + "\n", + " Bcbe.prepare(cosmo)\n", + "\n", + " Cls_2f = Ncm.Vector.new(lmax + 1)\n", + "\n", + " Bcbe.get_TT_Cls(Cls_2f)\n", + "\n", + " Cls_2f_a = np.array(Cls_2f.dup_array())\n", + " Cls_2f_a = np.array(Cls_2f_a[2:])\n", + "\n", + " ell = np.array(list(range(2, lmax + 1)))\n", + "\n", + " Dls_2f_a = ell * (ell + 1.0) * Cls_2f_a\n", + " return ell, Dls_2f_a" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "75daf807", + "metadata": {}, + "outputs": [], + "source": [ + "hiprim_2f.props.lnk0 = -9.0\n", + "hiprim_2f.props.lnw = np.log(1.0e-4)\n", + "\n", + "ell, Dell_2f = compute_D_ell(hiprim_2f)\n", + "_, Dell_pl = compute_D_ell(hiprim_pl)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "13483b8e", + "metadata": {}, + "outputs": [], + "source": [ + "plt.title(r\"$D_\\ell$\")\n", + "plt.plot(ell, Dell_2f, \"r\", label=\"two-fluids\")\n", + "plt.plot(ell, Dell_pl, \"b--\", label=\"power-law\")\n", + "\n", + "plt.xscale(\"log\")\n", + "plt.xlabel(r\"$\\ell$\")\n", + "plt.ylabel(r\"$\\ell(\\ell+1)C_\\ell$\")\n", + "plt.legend(loc=\"best\")\n", + "plt.savefig(\"hiprim_Dls.pdf\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "42856717", + "metadata": {}, + "outputs": [], + "source": [ + "# ser = Ncm.Serialize.new(Ncm.SerializeOpt.CLEAN_DUP)\n", + "# ser.to_binfile(s, \"hiprim_2f_spline.bin\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9a674d16", + "metadata": {}, + "outputs": [], + "source": [ + "test_hiprim_2f = Nc.HIPrimTwoFluids(use_default_calib=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7708e561", + "metadata": {}, + "outputs": [], + "source": [ + "set_rc_params_article(ncol=2)\n", + "fig = plt.figure()\n", + "\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "\n", + "lnk_a = np.linspace(np.log(1.0e-3), np.log(1.0e8), 1000)\n", + "lnw_a = np.linspace(np.log(1.0e-5), np.log(1.0e-1), 100)\n", + "hiprim_2f.props.lnk0 = -9.0\n", + "test_hiprim_2f.props.lnk0 = -9.0\n", + "\n", + "for lnw in lnw_a[::10]:\n", + " hiprim_2f.props.lnw = lnw\n", + " test_hiprim_2f.props.lnw = lnw\n", + "\n", + " lnPk_test = np.array([test_hiprim_2f.lnSA_powspec_lnk(lnk) for lnk in lnk_a])\n", + " lnPk = np.array([hiprim_2f.lnSA_powspec_lnk(lnk) for lnk in lnk_a])\n", + "\n", + " ax1.plot(np.exp(lnk_a) / 4000.0, lnPk - lnPk_test)\n", + "\n", + "ax1.set_xscale(\"log\")\n", + "ax1.set_xlabel(r\"$k$\")\n", + "# ax1.legend()\n", + "\n", + "pass" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9ca56ae9", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/primordial_perturbations/two_fluids_perturbations.ipynb b/notebooks/primordial_perturbations/two_fluids_perturbations.ipynb index 7fdd965b7..f3a25e8ac 100644 --- a/notebooks/primordial_perturbations/two_fluids_perturbations.ipynb +++ b/notebooks/primordial_perturbations/two_fluids_perturbations.ipynb @@ -3,20 +3,16 @@ { "cell_type": "markdown", "id": "152b1c34", - "metadata": { - "id": "152b1c34" - }, + "metadata": {}, "source": [ "# Two Fluid Quantum Cosmological Model" ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "id": "Xna_qd5unXpw", - "metadata": { - "id": "Xna_qd5unXpw" - }, + "metadata": {}, "outputs": [], "source": [ "# Importing the relevant libraries\n", @@ -38,9 +34,7 @@ { "cell_type": "markdown", "id": "SSYdpVinZzn1", - "metadata": { - "id": "SSYdpVinZzn1" - }, + "metadata": {}, "source": [ "# Introduction" ] @@ -48,9 +42,7 @@ { "cell_type": "markdown", "id": "eMicLj9IZ8gC", - "metadata": { - "id": "eMicLj9IZ8gC" - }, + "metadata": {}, "source": [ "In this notebook we shall analyze the predictions a two fluid quantum cosmological model where gravity is coupled though matter using the Wheeler-De Witt equation.\n", "\n", @@ -64,25 +56,10 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "id": "jgV564_mbm_v", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "jgV564_mbm_v", - "outputId": "c8412475-fc2d-4b02-b6d9-34070311921d" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "w=0 => 1.0\n", - "w=1/3 => 3.0\n" - ] - } - ], + "metadata": {}, + "outputs": [], "source": [ "def nsw(w): # defines a function that calculates the single fluid spectral index ns\n", " return 1 + 12*w/(1+3*w)\n", @@ -94,9 +71,7 @@ { "cell_type": "markdown", "id": "9VIf518scRQW", - "metadata": { - "id": "9VIf518scRQW" - }, + "metadata": {}, "source": [ "The above results mean that ordinary matter cannot describe the approximately flat red spectrum with $n_{s}$. Therefore, a natural extension of said model is to consider the two fluid coupled to geometry.\n", "\n", @@ -146,9 +121,7 @@ { "cell_type": "markdown", "id": "1et0L5cgdOyP", - "metadata": { - "id": "1et0L5cgdOyP" - }, + "metadata": {}, "source": [ "# Background Quantities" ] @@ -156,9 +129,7 @@ { "cell_type": "markdown", "id": "cmnX2kzJmRde", - "metadata": { - "id": "cmnX2kzJmRde" - }, + "metadata": {}, "source": [ "In this section we study the quantities $m_{S}, m_{Q}, \\phi, c^{2}_{S}, c^{2}_{m}$ that occur in the perturbative Hamiltonian. We also study the evolution of the eigenvalues $\\nu_{1}, \\nu_{2}$ that diagonalize the Hamiltonian tensor. Finally, we study the behavior of the coupling matrices $\\gamma_{ij}, \\tau_{ij}$, which define the dynamics of the relevant perturbative quantities.\n", "\n", @@ -167,15 +138,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "id": "1515a28b", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "1515a28b", - "outputId": "632cccd1-efb5-44fc-a6a2-aad64d411884" - }, + "metadata": {}, "outputs": [], "source": [ "cosmo = Nc.HICosmoQGRW() # defines a cosmological model, which is represented by a NumCosmo object. Then, the relevant cosmological parameters are added to this object\n", @@ -190,9 +155,7 @@ { "cell_type": "markdown", "id": "-aSx2PR7oHee", - "metadata": { - "id": "-aSx2PR7oHee" - }, + "metadata": {}, "source": [ "To study the behavior of said quantities, we shall vary our cosmological parameters. However, before we dwell into such analysis, let's perform a consistency check by considering the dust only $\\Omega_{r} = 0$ and radiation only $\\Omega_{w} = 0$ cases. The complete model shall present regimes of domination by each fluid, and we shall also check if we indeed recover the $n_{s}$ values for the single fluid case." ] @@ -200,9 +163,7 @@ { "cell_type": "markdown", "id": "KiOdkZDMoq87", - "metadata": { - "id": "KiOdkZDMoq87" - }, + "metadata": {}, "source": [ "## Consistency Check" ] @@ -210,20 +171,16 @@ { "cell_type": "markdown", "id": "iiIp6-GfovaW", - "metadata": { - "id": "iiIp6-GfovaW" - }, + "metadata": {}, "source": [ "## Evolution of ...." ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "id": "Bysmnq-koGoW", - "metadata": { - "id": "Bysmnq-koGoW" - }, + "metadata": {}, "outputs": [], "source": [ "k = 1.0\n", @@ -241,27 +198,10 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "id": "9b5ebdeb", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "9b5ebdeb", - "outputId": "b640709a-e502-41aa-8661-37d8c7d1e068" - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], + "metadata": {}, + "outputs": [], "source": [ "cosmo.eom_eval(-120,-1)\n", "#m_s_c = np.array([cosmo.eom_eval(alpha, k).m_s for alpha in alpha_c])\n", @@ -271,23 +211,10 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "id": "WuQyCqQSWpGW", - "metadata": { - "id": "WuQyCqQSWpGW" - }, - "outputs": [ - { - "data": { - "text/plain": [ - "46657882087.38496" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], + "metadata": {}, + "outputs": [], "source": [ "cosmo.eom_eval(-120,1).nu1\n", "#cosmo.props.m_s" @@ -295,11 +222,9 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "id": "533290e5-dc2a-467a-8319-11811d78cc2b", - "metadata": { - "id": "533290e5-dc2a-467a-8319-11811d78cc2b" - }, + "metadata": {}, "outputs": [], "source": [ "# Computing background observables in the contraction phase\n", @@ -344,23 +269,10 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "id": "a4daed56-57bc-4993-b8ab-3468d8f83d5f", - "metadata": { - "id": "a4daed56-57bc-4993-b8ab-3468d8f83d5f" - }, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "metadata": {}, + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -391,23 +303,10 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "id": "8470dc58-92f9-46ab-8ec6-982e346cda0d", - "metadata": { - "id": "8470dc58-92f9-46ab-8ec6-982e346cda0d" - }, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "metadata": {}, + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -432,23 +331,10 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "id": "0fcea250-ab16-4d75-b437-254e07cb70cb", - "metadata": { - "id": "0fcea250-ab16-4d75-b437-254e07cb70cb" - }, - "outputs": [ - { - "data": { - "image/png": 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KHZAej23fGKgE4yKfRERE8RfPAekAA5VwWrffnj179C82ERERxVY8V0kHGKiEu+OOO3DTTTehu7sbjY2NosshIiJKSfFcgwpgoBLOZDKx24+IiCjOGKjSgNbt19jYiEAgILgaIiKi1MMxVGngvvvuw/Tp09HZ2Ym33npLdDlEREQphy1UaSAjIwPl5eUAuMgnERFRPHBQegQ1NTWQZRlOp1N0KTGjjaPaunUrent7BVdDRESUWlKihcrn88HpdA4IQLIsQ5ZluFwuKIoS1bVkWYbdbofD4YDZbI76vGT38MMPY+LEibhw4QIOHjwouhwiIqKU0t7eDgCwWCxxuX5CApWiKPonolFVFW63Gw6HA1VVVaivr4/qWl6vFz6fTz/2eDyxLFWYrKwsrF69GgBn+xEREcWatsXbpEmT4nL9hAQqh8MBu90e9piiKDCbzfpxaGuT1moV+iHLMgCgqqoK7e3tUBQFLS0tiSg/YbTZfps3b0YwGBRcDRERUeo4f/48AOCGG26Iy/Uz43LVKLS2tsJqterHFotFb3lyOBxDnltbWwuz2QyPxzPocwOBQNgSBNpgtGS2ZMkS5OXl4fTp0/B4PCguLhZdEhERUUrQApWhW6ii5fV6h32Oz+fTW6xsNhtsNlvE59XV1aGgoED/KCwsjHW5MZebm4tly5YBYLcfERFRrASDwbgHqlG3UDmdzgHjowDAarWiurp60PPsdnvYWCiv1ztoOAplNpuHvK6mtrYWGzZs0I/9fr8hQlVlZSXeeOMNbNq0Cf/9v/930eUQEREZXldXF7q7uwEkcaCKJtxEIkkSampq9GNVVSFJ0mjL0WVnZyM7Oztm10uUFStWICsrC8eOHcMnn3yC2267TXRJREREhqa1TuXm5iIvLy8u90jYLD+32w23260PLrfZbFi3bp0+AL22tjYRpSS9goICLF68GAC7/YiIiGIh3t19QIIGpUuSFLH1abjB5+mqoqICu3fvxqZNmxg0iYiIRikRgSqpBqXTNWVlZTCZTGhubsaZM2dEl0NERGRo2hpU8VoyAWCgSkpTpkzBwoULAQBbtmwRWwwREZHBsYUqjWl7+3GzZCIiotFhoEpj2qrp+/fv15sqiYiIaOS+/vprAMDkyZPjdg8GqiQ1Z84c3Hvvvejr68O2bdtEl0MUUxcvXkRDQ4P+JkdEFE+nTp0CAMyePTtu92CgSmKhe/sRpZLdu3fjRz/6ER566CHRpRBRGmCgSnPaOKo9e/ags7NTcDVEsaP9kVBWVia4EiJKdT09Pfjiiy8AMFClrdtvvx0333wzuru7sWvXLtHlEMVEd3c3duzYAeDbVlgionhpa2tDb28vsrKyMG3atLjdh4EqiZlMJs72o5Szd+9edHR0YOrUqbj//vtFl0NEKU7r7ps1axYyMuIXexiokpz2F/zOnTtx5coVwdUQjZ72x0FZWVlc39yIiIDEjJ8CGKiS3vz58zFjxgx0dXXhrbfeEl0O0aj09vZi69atAL4dI0hEFE8MVAQAyMjIQHl5OQDO9iPje//993H27FkUFBRg0aJFosshojSgqioABirCt3/Jb926FT09PYKrIbp+2h8FK1euxNixYwVXQ0Tp4C9/+QsA4I477ojrfRioDODhhx+GxWLBhQsXcPDgQdHlEF2XYDCoj59idx8RJUJvb68eqO6888643ouBygAyMzOxevVqAOz2I+P6f//v/+HkyZPIycnB0qVLRZdDRGlAVVVcvnwZOTk5uOmmm+J6LwYqgwhdNT0YDAquhmjktD8GHn/8cYwbN05wNUSUDj7++GMAwLx58zBmzJi43suQgUqWZSiKAqfTKbqUhCktLcW4ceNw5swZtLS0iC6HaMS07j4u5klEiXL48GEA8e/uAxIUqHw+H5xO54AAJMsyZFmGy+WCoihRXUtVVaiqCkmSYLPZ9NH7qS43NxfLli0DwG4/Mp5PP/0Uf/nLX5CZmYmVK1eKLoeI0sQHH3wAALjnnnvifq+EBCpFUdDe3h72mKqqcLvdcDgcqKqqQn19fVTXstlsaGpqQmlpKVRVhc1mi0fJSUn7y56rppPRaH8ELFq0CBaLRXA1RJQOrl69igMHDgBAQpZpyYz7HQA4HA54vV74fD79MUVRYDab9WOz2QxFUSBJEmRZhtfrDbuGxWKBw+GAz+fD/PnzUVRUhPXr10OSJBQVFSXi0xBuxYoVyMrKwieffIJjx45h7ty5oksiiooWqNjdR0SJ0tzcjIsXL8JqtWLevHlxv19CAlUkra2tsFqt+rHFYtEDl8PhGPS8119/HQ6HAzabDW63G7IsRwxUgUAAgUBAP/b7/bErXpCCggIsXrwYu3fvxubNmxmoyBC+/PJL/PnPfwYAfZFaIqJ427t3L4BrrVOJ2OYqqQal92+VimTt2rX6oHSPx4OqqqqIz6urq0NBQYH+UVhYGOtyhQid7UdkBFu2bAEA3H///Zg+fbrYYogobWjvPYsXL07I/UbdQuV0OgeMjwIAq9WK6urqQc+z2+1hXYBerzeq8VBms3nI62pqa2uxYcMG/djv96dEqCorK8OPfvQjNDc34/Tp05g1a5bokoiGxO4+Ikq0EydOoKmpCWPGjMETTzyRkHuOOlBFE24ikSQJNTU1+rE2cy9WsrOzkZ2dHbPrJYspU6Zg4cKFOHjwILZs2YL/9J/+k+iSiAbl9Xr1ZncGKiJKlD/+8Y8AgCVLlmDy5MkJuWfCZvm53W59zBNwbbbeunXr9GUTamtrE1FKStC27WC3HyW7HTt2oLe3F3feeWfcVykmIgKAzs5OvPTSSwCAZ555JmH3TcigdEmSIrY+DTX4nAZXUVGBDRs2YP/+/Th//jwmTZokuiSiiLh3HxEl2gsvvIBvvvkGt956a8K6+4AkG5RO0ZkzZw7uvfde9PX1Yfv27aLLIYro4sWLePPNNwGwu4+IEuPo0aP4+7//ewDAz372s7hvNxOKgcqgONuPkt3u3btx5coV2Gw23HXXXaLLIaIU9/XXX6OsrAyBQADLly/HU089ldD7M1AZlNaFsmfPHnR2dgquhmig0Nl9JpNJcDVElMo+/PBD3H///fjss88wZ84cvPLKKwl/32GgMqjbb78dN998M7q7u7Fr1y7R5RCF6e7uxo4dOwBw/BQRxceVK1ewY8cOVFRUYMGCBTh58qS+6PfUqVMTXo+wldJpdEwmEyorK1FfX49NmzZh7dq1oksi0u3duxcdHR2YOnUqFixYILocIuFOnTqFrq4uAEAwGNQfj+bf13POaP6dTPe7evUqOjs74ff70dnZifb2dpw6dQqffPIJDh06hKtXr+rP/eu//mu88MILwvYLZaAysIqKCtTX12Pnzp24cuUKcnJyRJdEBODb2X3l5eUJ2fKBKJm98sor+MEPfiC6jJQ0depU/NVf/RWeffZZ3H777UJrYaAysPnz52PGjBloa2vDW2+9hRUrVoguiQi9vb3YunUrAM7uIwKgz3YdN24ccnNz9cdDx/jE89+Juk88/j1mzBjk5+cjPz8fEyZMgNlsxqxZs2Cz2TB//nzMmTMnacZoMlAZWEZGBioqKvCb3/wGmzZtYqCipPD+++/j7NmzKCgowKJFi0SXQyTc0aNHAQAbN27EsmXLBFdD8cK2eIPTWgC2bduGnp4ewdUQfTu7b9WqVRg7dqzgaojEunr1Kk6cOAEAuOOOOwRXQ/HEQGVwDz/8MCwWCy5cuICDBw+KLofSXDAY5OroRCE+/fRTXL16FePHj0dhYaHociiOGKgMLjMzE6tXrwbART5JvEOHDuHkyZPIzc3F0qVLRZdDJJzW3Xf77bcnzVgfig8GqhQQump6/6moRImkhfqlS5ciLy9PcDVE4h05cgQAu/vSAQNVCigtLcW4ceNw5swZtLS0iC6H0hi7+4jCaYFK9JR+ij8GqhSQm5urzxzRfqERJdqJEydw5MgRZGZmYuXKlaLLIUoKWpcfW6hSHwNVitBaBDiOikTRvvcWLVqEiRMnCq6GSDzO8EsvDFQpYsWKFcjKysInn3yCY8eOiS6H0pAWqNjdR3QNZ/ilFwaqFJGfnw9JkgCwlYoSr62tDR988AFMJhPKy8tFl0OUFDjDL70YLlD5fD6sX78ePp9PdClJR5vtx3FUlGhbtmwBACxYsADTpk0TWwxRkuAMv/SSkK1nfD4fXC4XAKC6ulp/XJZlAIDX64XNZtNbWIaiqiqam5uxePFiAIAkSaivr49D1cazevVqrF+/Hi0tLTh9+jRmzZoluiRKE1qrKPfuI/oWZ/ill4S0UCmKgvb29rDHVFWF2+2Gw+FAVVVV1KHIbDajpaUFLS0tqK2tZZgKMWXKFDz44IMA2O1HieP1evHOO+8AYKAiCsUZfuklIS1UDocDXq83rJtOURSYzWb92Gw2Q1EUSJIEWZbh9XrDrmGxWOBwOGCz2QAALpcLa9euTUT5hlJRUYEDBw5g8+bNeO6550SXQ2lg+/bt6O3txZ133ombbrpJdDlESYEz/NJPQgJVJK2trbBarfqxxWLRA5fD4Rj2fLfbjaqqqkH/fyAQQCAQ0I/9fv/1F2sgFRUV2LBhAw4cOIDz589j0qRJokuiFMfuPqKBOMMv/STVoPT+rVKD8fl8sFgsQz6nrq4OBQUF+ke6fEPPmTMH9957L/r6+rBt2zbR5VCKu3jxIt58800AXC6BKBRn+KWfUbdQOZ3OAeOjAMBqtYYNQO/PbreHdQFqA9OjYTab0dDQMORzamtrsWHDBv3Y7/enTaiqrKzERx99hE2bNuHZZ58VXQ6lsN27d+PKlSuw2Wy46667RJdDlDQ4wy/9jDpQDRWahiJJEmpqavRjVVWjmuUXrezsbGRnZ8fsekZSUVGB559/HoqiwO/3Iz8/X3RJlKJC9+7jX+FE3+IMv/STsFl+brcbbrdbXyrBZrNh3bp1kGUZLpcLtbW1iSglLdx+++245ZZb0N3djcbGRtHlUIrq7u7Gjh07AHD8FFF/bKFKPwkZlC5JUsTWp2gGn9PImUwmVFRUoL6+Hps3b8aTTz4puiRKQW+//Tb8fj+mTp2KBQsWiC6HKGlwhl96SqpB6RQ72gDhxsZGXLlyRXA1lIq02X3l5eXIyOBbCZHm008/RU9PD2f4pRm+C6aokpISzJgxA11dXVAURXQ5lGJ6e3v17WbY3UcULnT8FMcWpg8GqhSVkZGh/6LjqukUa++//z7OnTsHs9mMRx99VHQ5REmFK6SnJwaqFKYFqq1bt6Knp0dwNZRKtNl9q1atQlZWluBqiJILZ/ilJwaqFPbwww/DYrGgvb0dBw8eFF0OpYhgMMjV0YmGwBl+6YmBKoVlZmZi9erVAL5tUSAarUOHDuHkyZPIzc3F0qVLRZdDlFQ4wy99MVClOG223+bNmxEMBgVXQ6lAa516/PHHkZeXJ7gaouTCGX7pi4EqxZWWlmLcuHH44osv0NzcLLocSgFaaye7+4gG4gy/9MVAleJycnKwfPlyAOz2o9E7ceIEjhw5gszMTKxcuVJ0OURJhzP80hcDVRrg8gkUK9r30KOPPoqJEycKroYo+XCGX/pioEoDK1aswNixY3H8+HEcO3ZMdDlkYFqg0sbmEVE4zvBLXwxUaSA/Px+LFy8GwFYqun5tbW344IMPYDKZUFZWJrocoqTDGX7pjYEqTWjdfhxHRddL22pmwYIFmDZtmthiiJIQZ/ilNwaqNFFWVgaTyYSWlhacPn1adDlkQFoYZ3cfUWSc4ZfeGKjSxOTJk/Hggw8C+LalgSha7e3t2LdvHwAul0A0GM7wS28MVGlEa1lgtx+N1Pbt29Hb24s777wTdrtddDlESYkD0tObIQOVoiiQZRlOpxM+n090OYZRXl4OADhw4ADOnz8vthgyFM7uIxoel0xIb5mJuInP54PL5QIAVFdX64/LsgwA8Hq9sNlskCRp2Gupqgq32436+nr4fD6Yzea41JyK5syZg6KiIng8Hmzbtg3PPvus6JLIALq6urBnzx4ADFREg+EMP0pIC5WiKGhvbw97TAtGDocDVVVVqK+vj/paPp8Psiyjrq4uHuWmNC7ySSO1e/duXLlyBTabDXfeeafocoiSEmf4UUJaqBwOB7xeb1j3nKIoYa1LZrMZiqJAkiTIsgyv1xt2DYvFAofDAQCw2+36NV0uF6qqqhLxaaSEiooKPP/883C73fD7/cjPzxddEiW50O4+zlwiiowz/CghgSqS1tZWWK1W/dhiseiBSwtOkZSUlEBRFP2c/sFLEwgEEAgE9GO/3x+Dqo3v9ttvxy233IITJ06gsbERTz75pOiSKIl1d3djx44dADi7j2gonOFHSTUofbBwFKqoqAjAtfFXTU1Ng7ZO1dXVoaCgQP9gE+w1JpOJ3X4Utbfffht+vx9Tp07FggULRJdDlLQ4w49G3ULldDoHjI8CAKvVGjYAvT+73R7WBagNTI+Gdt2hWrJqa2uxYcMG/djv9zNU/ZvKykrU19dj586duHLlCnJyckSXRElKC93l5eXIyEiqv7+Ikgpn+NGoA9VQoWkokiShpqZGP1ZVNapZftHKzs5GdnZ2zK6XSkpKSjBjxgy0tbVBURSsXLlSdEmUhHp7e/VFYDm7j2hwnOFHQAJn+bndbrjdbn2pBJvNhnXr1kGWZbhcLtTW1iaiFAKQkZHBvf1oWO+//z7OnTsHs9mMRYsWiS6HKGlxhh8BCRqULklSxNanobrsKL4qKirwm9/8Btu2bUNPTw8yM4XNT6AkpYXtVatWISsrS3A1RMmLM/wISLJB6ZQ4Dz/8MCwWC9rb23Hw4EHR5VCSCQaD+vgpzu4jGhpn+BHAQJW2MjMzUVZWBoDdfjTQoUOHcPLkSeTm5mLp0qWiyyFKapzhRwADVVoLXT4hGAwKroaSidY69fjjjyMvL09wNUTJjTP8CBC4sCeJV1paivHjx+OLL75Ac3Mz5s+fL7okShJaqyW7+8Jdz/6jlNo4w480bKFKYzk5OVi2bBkALvJJ3zpx4gSOHDmCzMxMLqkR4nr3H6XUxhl+pGGgSnPa+kIcR0UaLVw/9thjmDhxouBqksdg+49SeuMMP9IwUKW55cuXY+zYsTh+/DiOHTsmuhxKApzdF9lQ+4/2FwgE4Pf7wz4oNXFAOmkYqNJcfn6+Pg6E3X7U1taGDz74ACaTSZ8FSoMbbP9R7iWaPrhkAmkYqIirppNO22rm/vvvx7Rp08QWk2TsdnvY8VD7j9bW1qKjo0P/OHPmTCJKJAE4w480DFSE1atXIyMjAy0tLTh9+rTockggLVRz776BJElCU1OTfjzU/qPZ2dnIz88P+6DU093dzRl+pGOgIkyePBkPPvggAHb7pbP29nbs27cPAFBeXi62mCTE/Uepv88++4wz/EjHdagIwLUWif3792Pz5s147rnnRJdDAmzfvh29vb246667BnRv0TXcf5RCcYYfhWILFQH4tkXiwIEDOH/+vNhiSAitdZLdfUTR4Qw/CsVARQCA2bNno6ioCH19fdi2bZvocijBurq68OabbwLgcglE0eIMPwrFQEU6LvKZvnbv3o1AIAC73Y4777xTdDlEhsAZfhSKgYp0WsuEoihciDDNhO7dx7EgRMPjDD/qj4GKdHPnzsWtt96K7u5uNDY2ii6HEiQQCGDnzp0A2N1HFC1tht+ECRM4w48AGDRQFRcXo7S0FDU1NaJLSSkmk4mLfKaht99+G36/H1OnTsWCBQtEl0NkCJzhR/0lZNkEn88Hl8sFAKiurtYfl2UZwLcrDg+2SF5/tbW1nL4cJ5WVlfiHf/gH7Nq1C1euXEFOTo7okijOtNl95eXlyMgw5N9YRAnH8VPUX0LePRVFQXt7e9hjqqrC7XbD4XCgqqoK9fX1UV9PVVUoisIWqjgoKSnBzJkz0dXVBUVRRJdDcdbb24utW7cC4HIJRCPBGX7UX0JaqBwOB7xeb9jO7IqiwGw268dmsxmKokCSJMiyPGDTUYvFordKaa1cqqpClmW2VsWQyWRCeXk5fvOb32DTpk1YuXKl6JIojt577z2cO3cOZrMZixYtEl0OkWFwDSrqT9hK6a2trbBarfqxxWLRA9dQAUlrNZEkCT6fDxaLJeLzAoEAAoGAfsxZa9GrrKzEb37zG2zbtg09PT3IzOSC+qlK6+5btWoVsrKyBFdDZAyhM/zY5UeapBow0b9VKhItSGnBarDwVVdXh4KCAv2DszCi99BDD8FqtaK9vR0HDhwQXQ7FSTAY1AMVZ/cRRY8z/CiSUTc9OJ3OAeOjAMBqtYYNQO/PbreHdQFqA9OjoYWooQax19bWYsOGDfqx3+/nN36UMjMzsWrVKvzud7/D5s2b8eijj4ouieLg0KFDOHnyJHJzc7F06VLR5RAZBmf4USSjDlRDhaahSJIUNqhcVdWoZ/lFIzs7G9nZ2TG7XrqprKzUA9WLL77IN40UpLVOPf7448jLyxNcDZFxcIYfRZKQwTGKosDtdsPn88Fms8HhcMBms2HdunX6APTa2tpElEJRKi0txbhx4/DFF1+gubkZ8+fPF10SxZi21hhn9xGNDGf4USQJCVSSJEVsfeLsvOSVk5OD5cuXY+PGjdi0aRMDVYo5ceIEjhw5gszMTKxYsUJ0OUSGwhl+FElSDUqn5KINVNa6hih1aF/Txx57DBMnThRcDZFxcIYfDYaBiga1YsUKjB07FsePH8exY8dEl0MxxNl9RNeHM/xoMAxUNKj8/HwsXrwYAPf2SyVtbW344IMPYDKZUFZWJrocIkPhDD8aDAMVDUkbsMxuv9SxZcsWAMD999+PadOmiS2GyGA4w48Gw0BFQ1q9ejUyMjLQ0tKC06dPiy6HYoCz+4iuH2f40WAYqGhIkydPxoMPPgiArVSpoL29Hfv27QPA8VNE14Mz/GgwDFQ0LM72Sx3bt29Hb28v7r777qh3JiCiazjDj4bCQEXD0gLVgQMHcP78ecHV0Ghwdh/R9eMMPxoKAxUNa/bs2SgqKkJfXx+2bdsmuhy6Tl1dXXjzzTcBcPwU0fXgDD8aCgMVRUX7BczlE4xr9+7dCAQCsNvtmDdvnuhyiAyHM/xoKAxUFBWti0hRFPj9fsHV0PXQwnBFRQX/uia6DpzhR0NhoKKozJ07F7feeiu6u7vR2NgouhwaoUAggJ07dwJgdx/R9eIMPxoKAxVFxWQycbafgb399tvw+/2YNm0avvOd74guh8hwOMOPhsNARVHTWjZ27tyJK1euCK6GRkILweXl5cjI4I890Uhxhh8Nh++sFLWSkhLMnDkTFy9ehNvtFl0ORam3t1ffbobdfUTXhzP8aDgMVBQ1dvsZ03vvvYfz589j4sSJeOSRR0SXQ2RInOFHwzFsoPL5fFi/fr3oMtKOFqi2bduGnp4ewdVQNLTZfatWrUJWVpbgaoiMiQPSaTiZibiJz+eDy+UCAFRXV+uPy7IMAPB6vbDZbJAkKeprKooCr9cb20JpWA899BCsViva29uxf/9+PPbYY6JLoiEEg0Gujk4UA1wygYaTkBYqRVHQ3t4e9piqqnC73XA4HKiqqkJ9fX3U15NlGQ6HI9ZlUhQyMzNRVlYGgN1+RvDRRx/h1KlTyMvLw5IlS0SXQ2RInOFH0UhIC5XD4YDX64XP59MfUxQFZrNZPzabzVAUBZIkQZblAa1PFosFDocDHo8HRUVFiSibBlFRUYHf/va32Lx5M1588UXOGktiWuh9/PHHkZeXJ7gaImP69NNPOcOPhpWQQBVJa2srrFarfmyxWPTANVzrk8fjgcfjgaqqgwasQCCAQCCgH3N179iRJAnjx49HW1sbmpubcd9994kuiQYRujo6EV0frbuPM/xoKEnVtBDNmKiioqKILV791dXVoaCgQP/gXxWxk5OTg+XLlwNgt18yO378OI4ePYrMzEysXLlSdDlEhsUB6RSNUbdQOZ3OAeOjAMBqtYYNQO/PbreHBSJtYHq0qqqqUFVVNej/r62txYYNG/Rjv9/PUBVDFRUVeP3117Fp0yb86le/4l9tSUgLu4899lhY9zoRjQyXTKBojDpQDRWahiJJEmpqavRjVVVHNMtvONnZ2cjOzo7Z9Sjc8uXLMXbsWJw4cQLHjh3jG00S0gIVF/MkGh3O8KNoJGyWn9vthtvt1pdKsNlsWLduHWRZhsvlQm1tbSJKoRjJz8/XA7A2ToeSxxdffIEPP/wQJpNJn5VJRCMXOsOPgYqGkpBB6ZIkRWx94tIHxlZZWYnGxkZs3rwZP/3pT0WXQyG0rWYeeOABTJ06VWwxRAYWOsNv5syZosuhJJZUg9LJWFavXo2MjAx4PB6cPHlSdDkUgrP7iGKDM/woWgxUdN0mTZqEhx56CMC3LSIknraKPcBARTRanOFH0WKgolHRfmFzHFXy2L59O3p7e3H33XePaOYsEQ3EGX4ULQYqGpXy8nIAwMGDB3H27FmxxRAAdvcRxRJn+FG0GKhoVGbPno3i4mIEg0Fs27ZNdDlpr6urC3v27AHA5RKIRosz/GgkGKho1Njtlzx27dqFQCAAu92OefPmiS6HyNA4w49GgoGKRk1rCXnrrbfQ0dEhuJr0FrqYJ2ckEY0OZ/jRSAjbHJlSx9y5c3Hrrbfi+PHjaGxsxFNPPSW6pLQUCASwc+dOABw/la66urpw6NAhnDp1Cm1tbfjqq6/Q1dWFS5cu4fLly/pHb28vgsEggsEg+vr69H9HOk5n586dA8DuPooOAxXFRGVlJerq6rB582YGKkHefvtt+P1+TJs2Dd/5zndEl0MJ8tVXX+H3v/89XnvtNXz88cfo6+sTXVLKefDBB0WXQAbAQEUxUVFRgbq6OjQ2NuLy5cvIzc0VXVLa0br7KioqkJHB3vxU19XVhb/7u7/DSy+9hN7eXv3xwsJC3HTTTZgxYwamT5+O/Px85ObmIi8vD7m5ucjJyUFmZiZMJhNMJhMyMjL0f4d+hD6ezvLz83HfffeJLoMMgIGKYqKkpAQzZ87EF198AUVRsGrVKtElpZXe3l59cVV296W+06dPY/ny5foaSQ888ACeffZZLFu2DNOmTRNcHVF64p+xFBMmk0n/Ra61lFDivPfeezh//jwmTpyIRx55RHQ5FEfnz5+HJEk4cuQIpk6dijfffBPvvvsuvv/97zNMEQnEQEUxowWqrVu3oqenR3A16UVbsmLVqlXIysoSXA3FSzAYxPe//318+umnmD17Nj788EMsWbJEdFlEBAYqiqGHHnoIVqsVXq8XBw4cEF1O2ggGg2HLJVDq+td//Vfs2LEDY8eOxfbt21FYWCi6JCL6NwxUFDOZmZlYvXo1AC7ymUgfffQRTp06hby8PLZWpLCenh78/Oc/BwD89Kc/xZ133im4IiIKxUBFMaW1kGzevJnTtxNEa51atmwZZ1emsNdffx2fffYZbrjhBvzN3/yN6HKIqB8GKoopSZIwfvx4tLW1obm5WXQ5aYGbIaeHV155BQDwH//jf8T48eMFV0NE/RkyULlcLiiKgpqaGtGlUD85OTlYvnw5AM72S4Tjx4/j6NGjyMrKwooVK0SXQ3HS1taGvXv3AgC++93vCq6GiCJJSKDy+XxwOp1wOp1hj8uyDFmW9YAU7bWAay0hqqpCVdVYl0ujpHX7bdq0Ke23rog3LbQ+9thjMJvNYouhuHn99dcRDAaxcOFCzJkzR3Q5RBRBQhb2VBQF7e3tsFqt+mOqqsLtdqOhoQEAUFpaCkmShr2W2WxGVVUVXC4XbDYbbDZb3Oqm67Ns2TKMHTsWJ06cwNGjR7kPVhyxuy897NmzBwDwxBNPCK6EiAaTkEDlcDjg9Xr11iXgWsgK/YvabDZDURRIkgRZluH1esOuYbFY4HA49OOqqiqsX78eqqoyVCWZ/Px8lJaWYufOndi8eTMDVZycOXMGTU1NMJlMKCsrE10OxcnVq1f1ZUgee+wxwdUQ0WCEbT3T2toa1mJlsVj0wBUanPqTZRlmsxmSJMFut0OWZVRXVw94XiAQQCAQ0I/9fn/siqdhVVRU6IHqpz/9qehyUpK21cwDDzyAqVOnii2G4qa5uRkXL16E1WrlUglESSypBqX3b5WKRJIk+Hw+yLKM1tbWiGEKAOrq6lBQUKB/cAG8xFq9ejUyMjLg8Xhw8uRJ0eWkJC7mmR7eeecdAMAjjzzCTa+JktioW6icTifa29sHPG61WgcNOwBgt9vDugC9Xm9UXXdms1lvwRqqJau2thYbNmzQj/1+P0NVAk2aNAkPPfQQ9u3bhy1btuAnP/mJ6JJSyoULF7Bv3z4AHD+V6j766CMAwIIFCwRXQkRDGXWgGio0DUWSpLBlD1RVjWpQerSys7ORnZ0ds+vRyFVWVmLfvn3YtGkTA1WMbd++HX19fbj77rtx4403ii6H4ujjjz8GANx9992CKyGioSSk/VhRFLjdbrjdbsiyDACw2WxYt26dvmxCbW1tIkqhBCovLwcAHDx4EGfPnhVbTIrRZvexuy+1Xb58GZ9++ikAcPwUUZJLyKB0SZIitj4N1WVHxjdr1iyUlJSgubkZ27Ztww9/+EPRJaWEzs5OuN1uAOzuS3VHjx5FX18fbrjhBk48IEpyHOFIcaX9wueq6bGza9cuBAIB3HTTTZg3b57ociiODh8+DAC46667YDKZBFdDRENhoKK40gKVoijo6OgQXE1q0MJpRUUFf8mmuCNHjgAAgzORATBQUVzNnTsXt912G65evYrGxkbR5RheIBDAzp07AXD8VDr4/PPPAVybFU1EyY2BiuJOa6XSBlLT9XvrrbfQ2dmJadOm4b777hNdDsXZqVOnAACzZ88WXAkRDYeBiuJOC1S7du3C5cuXBVdjbKHdfVzkMfVpgYobIhMlP74jU9yVlJRg5syZuHjxoj47jUaut7cXW7duBcDZfeng0qVLOH/+PAC2UBEZAQMVxZ3JZGK3Xwy8++67OH/+PCZOnIhHHnlEdDkUZ6dPnwZwbbPx0I3kiSg5MVBRQmgDqLdv346enh7B1RiT1t23atUqZGVlCa6G4k3bA5OtU0TGwEBFCfHggw/CarXC6/Vi//79ossxnGAwyNXR0wwHpBMZCwMVJURmZibKysoAcJHP6/HRRx/h9OnTyMvLw5IlS0SXQwmgdfkxUBEZAwMVJUzoqul9fX2CqzEWrXVq2bJlyM3NFVwNJcLXX38NAJg+fbrgSogoGgxUlDCSJGH8+PFoa2tDc3Oz6HIMJXS5BEoP2gy/SZMmCa6EiKLBQEUJk5OTg+XLlwNgt99IHD9+HEePHkVWVhZWrFghuhxKEC1Q3XDDDYIrIaJoMFBRQmkDqjdt2oRgMCi4GmPQwudjjz3G6fNp5MKFCwDYQkVkFAxUlFDLli3D2LFjceLECRw7dkx0OYbA2X3piS1URMbCQEUJlZ+fj9LSUgBc5DMaZ86cQVNTE0wmkz5LklJfd3c3Ojo6ALCFisgoDBmoZFmGLMuoqakRXQpdh9DZfjS0LVu2AAAWLlyIKVOmiC2GEkbr7svIyMDEiRMFV0NE0chMxE18Ph9cLhcAoLq6Wn9clmUAgNfrhc1mgyRJw15LlmWYzWZIkgRVVeFyuVBVVRWfwikuVq9ejYyMDHg8Hpw8eZIbvw6Bs/vSkxaorFYrN8EmMoiE/KQqioL29vawx1RVhdvthsPhQFVVFerr66O6lsPh0INXa2srSkpKYl4vxdekSZPw0EMPAfi2BYYGunDhAvbt2weAgSrdcMkEIuNJSAuVw+GA1+uFz+fTH1MUJWzGktlshqIokCQJsizD6/WGXcNiscDhcISdX1xcjKKioniXT3FQWVmJffv2YdOmTfjJT34iupyktH37dvT19eGee+7BjTfeKLocSiAGKiLjSUigiqS1tRVWq1U/tlgseuAKDU6ReDwe+Hw+VFVVwePxRAxVgUAAgUBAP/b7/bEpnGKivLwczz33HA4ePIizZ89yfFAE2qB9tk6lH87wIzKepOqc798qFYmqqlizZg0aGhpQXFw86Dl1dXUoKCjQPwoLC2NdLo3CrFmzUFJSgmAwiG3btokuJ+l0dnbC7XYD4HIJ6YgtVETGM+oWKqfTOWB8FHBtMGXoAPT+7HZ7WBegNjB9ODabDa2trcM+r7a2Fhs2bNCP/X4/Q1WSqaioQHNzMzZv3owf/vCHostJKrt27UIgEMBNN92EO+64Q3Q5lGDaH4qhrfhElNxGHaiGCk1DkSQpbNkDVVWjmuUXrezsbGRnZ8fsehR7lZWV+Lu/+zsoioKOjg4UFBSILilpaLP7KisrYTKZBFdDiaYNUcjPzxdcCRFFK2Gz/NxuN9xut75Ugs1mw7p16yDLMlwuF2praxNRCiWR2267DbfddhuuXr2KxsZG0eUkjUAggJ07dwLg+Kl01dnZCQCYMGGC4EqIKFoJGZQuSVLE1qfhBp9T6qusrMSvfvUrbNq0CU899ZTocpLCW2+9hc7OTkybNg333Xef6HJIAC1QsYWKyDiSalA6pR+tBWbXrl24fPmy4GqSgza7r7y8nIs6pim2UBEZD9+tSaji4mLMmjULFy9exJ49e0SXI1xvby+2bt0KgLP70hkDFZHxMFCRUCaTCeXl5QC4tx8AHDx4EBcuXMDEiRPxyCOPiC6HBGGgIjIeBioSTmuJ2b59O65evSq4GrG0ULlq1SpkZWUJroZE4Sw/IuNhoCLhHnzwQdxwww3wer3Yv3+/6HKECQaDYcslUHoKBoPo6uoCwBYqIiNhoCLhxowZg9WrVwNI724/j8eD06dPIy8vD0uWLBFdDgly6dIl9PX1AWCgIjISBipKClqLzObNm/VfJulGC5PLli1Dbm6u4GpIFG38lMlkwrhx4wRXQ0TRYqCipLB48WKMHz8eX375JT788EPR5QjBzZAJCB+QzlXyiYyDgYqSQk5ODlasWAEgPbv9PvnkExw7dgxZWVlYuXKl6HJIIM7wIzImBipKGlrLzKZNmxAMBgVXk1haiFy8eDH3NExz2gw/BioiY2GgoqSxfPlyjB07Fp999hmOHDkiupyE4uw+0rCFisiYGKgoaUyYMEGf3ZZO3X6nT59GU1MTTCaTPtuR0hf38SMyJgYqSiqh3X7pYsuWLQCurcc1ZcoUscWQcGyhIjImBipKKqtXr0ZGRgYOHTqEzz//XHQ5CcHuPgrFQEVkTAxUlFRuuOEGfQ+7dOj2O3/+vL46vLanIaU3BioiY2KgoqSjdfulQ6Datm0b+vr6UFRUhDlz5oguh5IAAxWRMTFQUdLRWmreffddfP3112KLiTNtrBi7+0hz6dIlAOAq6UQGY8hAJcsyiouLRZdBcVJYWIj77rsPwWBQH7Cdijo6OqAoCgAGKvrWlStXAFxb7JaIjCMhgcrn88HpdMLpdIY9LssyZFmGy+XSf7FEw+FwwGKxxLpMSiJawEjl2X6NjY3o7u7Gbbfdhrlz54ouh5IEAxWRMSUkUCmKgvb29rDHVFWF2+2Gw+FAVVUV6uvrE1EKGYQ2jmrv3r3wer2Cq4kPdvdRJAxURMaUmYibOBwOeL1e+Hw+/TFFUWA2m/Vjs9kMRVEgSRJkWR7wS9RiscDhcCSiXEoCt9xyC+bNm4e//OUv2LFjB7773e+KLimmLl++jMbGRgAMVBSOgYrImBISqCJpbW2F1WrVjy0Wix64YhGcAoEAAoGAfqztj0XGUVlZib/85S944403Ui5Qvfnmm7h06RJmzZqFoqIi0eVQEmGgIjKmpBqUHm3XjqIoUFUVsiwP+py6ujoUFBToH4WFhbEqkxJEa7nZs2cPurq6BFcTW2+88QaAa5+jyWQSXA0lEwYqImMadQuV0+kcMD4KAKxWK6qrqwc9z263h3UBer1e2Gy2qO4pSRJaW1uHfE5tbS02bNigH/v9foYqg7nrrrtgt9vR2tqKxsZGrF27VnRJMdHd3Y3t27cDAJ544gnB1VCyYaAiMqZRB6qhQtNQJElCTU2NfqyqKiRJGm05uuzsbGRnZ8fsepR4JpMJDocD9fX1eOONN1ImUL311lvo6OjA1KlT8cADD4guh5IMAxWRMSVslp/b7Ybb7da76Ww2G9atW6cvm1BbW5uIUshgtBacnTt34vLly4KriQ2tu6+8vBwZGUnV605JgIGKyJgSMihdkqSIrU+ctUfDKSkpwaxZs3D69Gm8+eabht/vrqenR1+slN19FAkDFZEx8c9jSmomk0kfnK617BjZgQMH0N7eDovFom8CTRRKC1QcskBkLAxUlPS0lpzt27eHLYVhRBs3bgQAlJWVISsrS3A1lIy073G2UBEZCwMVJb0HHngA06dPR0dHB/bs2SO6nOvW09Ojt7KtW7dOcDWUjILBILv8iAyKgYqSXkZGBtasWQMAeO211wRXc/327duHc+fOwWq14rHHHhNdDiWh7u5u/d8MVETGwkBFhqAtmbB161bDzvZ7/fXXAVxbzJPdfRSJ1joFMFARGQ0DFRnCggULUFhYiK6uLuzevVt0OSMW2t2XKutpUexpgcpkMjF0ExkMAxUZQkZGhh5EjNjt9/bbb6O9vR2TJk3CokWLRJdDSSp0/BS3JCIyFgYqMgxtIPf27dtx8eJFwdWMzP/9v/8XwLUZi5mZwvYkpyTHAelExsVARYZRUlICu92OS5cuYdOmTaLLiVpXV5c+furpp58WXA0lMwYqIuNioCLDMJlMeOaZZwAAr7zyithiRmDjxo24ePEibr75ZixcuFB0OZTEGKiIjIuBigzlmWeeQUZGBvbt24dPP/1UdDlRefXVVwEA3/ve9zguhobEQEVkXAxUZCgzZ87E448/DgD47W9/K7ia4Z04cQIHDhxARkYGvvvd74ouh5IcAxWRcTFQkeE8++yzAIDf/e53uHr1quBqhva73/0OALB06VLMmDFDbDGU9BioiIyLgYoMZ+XKlZg8eTK+/vprbNu2TXQ5g+rs7MTLL78M4Fp3H9FwGKiIjIuBigxn7Nix+OEPfwgA+NnPfoaenh7BFUX24osv4sKFC7j55ptRUVEhuhwyAAYqIuNioCJD+s//+T/DYrHg6NGjerdaMvF6vfjHf/xHAMAvf/lLrj1FUWGgIjIuQwYql8sFRVHgcrlEl0KCmM1mPP/88wCutVIl20Kf//iP/wi/34+77rqLW81Q1BioiIwrKQKVz+eD0+mE0+kMe1yWZciyrAcoAPp/JUmCxWKBLMsJr5eSw49//GPceOON+Oqrr1BdXY1gMCi6JADXvkf/x//4HwCA//bf/hsyMpLix4wMgIGKyLiS4p1eURS0t7eHPaaqKtxuNxwOB6qqqlBfXw8A8Hg8sNlsAK61UjQ1NSW8XkoO2dnZ+PWvfw0A+F//63/hxz/+Mfr6+oTWtH//fqxevRqBQACVlZVYtWqV0HrIWBioiIwrKQKVw+GA3W4Pe0xRFJjNZv3YbDbrrVM+ny+B1VEyq6iowMsvvwyTyYSGhgY88sgj+MMf/oBvvvkmYTUEAgF88MEH+MEPfoClS5fi8uXLWL58Of70pz9xIU8aES1QZWdnC66EiEYqaUfKtra2wmq16scWiwU+nw9FRUVQVRXAtWA1f/78iOcHAgEEAgH92O/3x7dgEuYHP/gBxo8fj+9+97s4ePAgDh48CAAoKCjAtGnTMG7cOOTk5CAzMxNjxoyByWTSP6IRDAb1j76+PvT09ODq1au4ePEifD4f2trawrobly1bhjfeeIO/FGnE2EJFZFxJG6gi8Xq9cDgccDqdUBQFqqqiuro64nPr6urwi1/8IsEVkihPPvkk7r//fvzhD3/AH//4R3z66afo6OhAR0dHQu4/YcIErFq1Cj/+8Y+xcOFCtkzRdWGgIjKuuAcqp9M5YHwUAFit1kHDEADY7fawrj2v16uPndLOkyRp0PNra2uxYcMG/djv96OwsHCk5ZOBzJ49G88//zyef/55XLx4EadOncLZs2dx+fJlXL58Gb29vejt7dVbmwAMO5BdC0ahrVpZWVnIysrCuHHjMGHCBMyZMweTJk1iiKJR+/73v4+FCxfizjvvFF0KEY1Q3APVUKFpKJIkoaamRj9WVXXIANVfdnY2u1zS2Lhx43D77bfj9ttvF10KUdTmz58/6DAGIkpuSdHlpygK3G43fD4fbDYbHA4HbDYb1q1bB1mW4fV6UVtbK7pMIiIiooiSIlBJkhSx9cnhcAiohoiIiGhkkmLZBCIiIiIjY6AiIiIiGiUGKiIiIqJRYqAiIiIiGiUGKiIiIqJRYqAiIiIiGiUGKiKiEaipqYEsy3A6naJLIaIkwkBFRAPIsgxFUSL+vzVr1oRtCxV6jsfjgcvlgsvlCnvc5XJh/fr1Ea/Z/14+nw9OpzNmgWWw68myrNc22OcaqVa73Q6HwwGz2Rz1eUSU+hioiCiMz+dDXV1dxNCkqipkWcaNN96IiRMnwmQywel06ucUFRVh7dq1WL9+PQDA4/EAAKqqqlBfX481a9YMey9FUSLu/3m9Il1PVVW43W44HA69tmh4vd6wWrXPj4goKVZKTwRtE1y/3y+4EqLk9vvf/x5lZWW4dOnSgJ+Xw4cP49SpUzCbzQCAV199Fd/73vcAAHv37oXf78fHH3+MRYsWwe/348yZM9i5cyeWLFmCjIwMmM1m7N+/H/fcc8+g91qyZAna2trQ0dGhP6b9NxgMwufzweVyhe0T6nK5IEmSvoF6KIfDMSAIKYqifw4A9NYmSZL07a5CWSwWPXzV1NRAURS0tLTAbrdHfA0DgQACgYB+3NHREfZ5EJExhL73DCdtAlVnZycAoLCwUHAlRKnlJz/5ScTHCwoK9H//7ne/0//9yCOPRH3tn//852HHnZ2dmDlzJoqKiuB0OlFdXQ1ZlmGxWCKGqcG0trbCarXqxxaLRQ9cw215VVtbC7PZDI/HM+hz6+rq8Itf/GLA43z/ITKmzs7OsPe0SNImUE2fPh1nzpzBhAkTYDKZhnyu3+9HYWEhzpw5g/z8/ARVaJx6ANZkxHqA4WvasmULysvL8cILL2DOnDkoLy+PeJ3PP/8cW7dujRim9u7diy1btuDFF18Me/y5557Do48+ql9Tu1d9fT1+9atfhdX06quvoqOjQ79+MBhEZ2cnpk+fDgD63p/r169HcXExqqqqruPVCNe/VSoSrXXMZrPpH5HU1tZiw4YN+nFfXx+8Xi+sVuuw7z+a0X7/iD4/GWpIxPmxek4saknm85Ohhus5v/97z1DSJlBlZGRg5syZIzonPz8/aX4RAslXD8CaopEs9TidTnz55ZcAgH/6p39CdnY2AMBqtaK6uhpOpxM2mw179uzB4cOH0dbWhnnz5qGoqGjAtf70pz+htLQ07PPy+Xwwm80oKyvDM888g6effloPPrIsY8WKFXqLTui9jhw5AuDauKaHH34YAJCbm4tAIBB2/Uh/HXq9XlgslhG/Fna7PawL0Ov1RtXCZTabw7oaB5Odna2/vqHnXo/Rfv+IPj8ZakjE+bF6TixqSebzk6GGkZ4/XMuUJm0CFVG6q66uht/vx4svvohf/vKXA95QQoNCU1MT5s+fr4cpLSxpZFnWB54D18Ywtba26oO7LRaLHnS08UqSJMHj8QwIJQcPHgQAfVxVNDweDzweDzZu3AiXywVZloftqgslSRJqamr0Y1VV9fBHRHQ9GKiIKIyiKFAUBaqqoqioCDabDcXFxWhpadFDldlsDmsZWrt2rX6e2+3G+vXrUVRUBFVVw2b2+Xy+sMGdiqLgnXfeAXCtG/Huu+/Wr+Hz+WCz2QYEJZ/Ph9dee00Pb1VVVXC5XFBVNWIrU6Tr2Ww2rFu3Th+AXltbG6uXj4jSVZAGuHLlSvDnP/958MqVK6JLCQaDyVdPMMiaopFs9QSDrMlIRvu6iD4/GWpIxPmxek4saknm85Ohhni/15iCwSjmAhIRERHRoLiwJxEREdEoMVARERERjRIDFRGRgWl7EYbunzga2h6HobMgR8rn84XNAh0pRVH0DagjbYE0HG1/yJHuBynLMoqLi8MeG8nrG+n84V7P6zknljX3v9b1vG6a0X7dgNF971zP924sf344y+/faAv2AeHTx7VZQC0tLVizZk3YujrAt+vXxGPK9VA1Rbp3ImoKpd1Po83GSnQdobT1jZKlHo0sy/rSASJrEvn9PFg9Iu6bzEbyc68oCi5dugSPx4PDhw/rW+QM9vzh7mez2fTv0y1btugLpw73telfs6Io8Hq911WDw+GA2+1GfX09fv/73+vXinR+pNdKVVV90djW1lb88Y9/xF//9V9HVbfD4UBDQ4Ne97vvvgvg2kxS7Ze1JElh52jPdbvdmDJlCi5duhS2jZH2eqqqCpfLhbVr1w55T7fbDbvdjurqav2cwRau9fl8UFU1bEsjbVski8WClpYW/OxnP8Mvf/nLqF53VVVRXV2NXbt24aWXXkJWVlZcvm6Dvf5a/R9//LH+XhXt+4L2WpeUlOC3v/0tnnjiCbzxxhth/x8Y+PMDQP9ajXT5lf4YqP6NtoFq6HYUoRu7+nw+3Hjjjfjmm2/0jVUbGhoAAKWlpXH5RRCppsHunaiaNNoPsvZDsH79ev0HMpF1hCotLcXGjRthNptRXFwsvB6NtgGwNjVfVE2iv5/7S4avTTIayc+9x+NBV1cXAoEAcnJy0NTUNOLv+9D7ab9MVFVFS0sL/uVf/gVFRUXDfm1Cr6H9UnrllVeuqwZFUeDz+fDSSy/h5ZdfxqFDhwY9P9JrBQDvvfcezp49i9LSUvzhD38YNFBFOv/SpUt63aqq4rXXXgNwbakQt9sNAPo52utcU1MDt9uN999/HzNnzkR9fT0kSQr75dza2or169cPe0+Hw4HS0lJUV1fr5wz3uodyu91oa2uDw+GA2WzGD37wg0EDVWgtNpsNTU1NWLhwIXp6evDrX/960Nc90vkj+boN9vrLsoyioiKcPXtWf+2ifV8I/UPiyy+/DNviaqifH22tPe3ry0AVA5E2UPV6vfoLrK274/F40NzcPOjGqvGuabBNXVVVTUhNoddvaGiAJEkoKirS7z3UprPxpC0Yqf27paVFaD2hXn/9daxbt04/FlWT6O/n/pLha5OMRvJzDwB33XUXvF5v2NY5I9382efzhf2C/5//839i1qxZYb9shts82m6348iRI/ovpHPnzuGuu+66rhrsdjuysrIwZcoUvYVmsPPb2trw2Wef6UFu27ZtmDVrFmpqarB+/XrceOONI/rcvV5v2Gs3duxY/bU+fvw47Ha7fs+PP/4YXV1d+uttNpvR2toKu90eds93330XFy9eRHNzc1T3NJvNcDqdKC4uhqqq+nmhr7fD4dC/V0J99tlnyMz89ld7Tk5OVJ+/z+fD/Pnz8dVXX+HVV1/Vw0a8vm79z9fupygKsrKywl6LaDYuD33+vHnzMGPGDP2xoX5+rrdrMhIGqiFIkhT25u71elFUVITXXntt0I1V422wTV2H2uw1Xurr61FcXIyioiK89dZbQ9YXb83NzVBVFaqqArjWYtbQ0CCsHo3H49HfCDSiakq272fRXxsjGey10hZPBYArV65g/vz5Qz4fiLz5s8vl0v+/x+PB559/jsWLF+u/5KLZPFrrutFWsW9ra8OVK1dGXENJSQkURUFraysmT54c1fk+n09/bNeuXfjOd74DSZLgdrvx1FNPRf25A8Dly5f1166oqAg7duzQ//+/+3f/Tr+Gz+fTW1e019vn8+H48eNhtYYOQdBez6HuCVzb+/Hs2bOorq4echPuSELDlM/nQ2FhYVSf/+uvv653P2otadF87UfzdQs9H7j2vdPY2Iiurq4Rfe9pPB4PfD4fHn74YX1LKyC6nx8tUI4GB6VHaf369Xj55ZcH/f/RbKwaL4PdO941NTU16X31ixcvHvR5iXhtfD4fLBYLioqKUFRUhObmZr2LS0Q9msFW7+4v0d8/yfr9LPLnyGi8Xi8kSYLP58OxY8fQ3t4+5C+caF5bbWX7Q4cO4cUXXww7J5rzZ8yYobeahIapkVxDaxU7fvw4zpw5EzZ+KJrzb7vtNhw+fBiKosDj8WDu3LlRf19p3VaHDx8GcO2PkEAggHfffReqqg77C72trQ1fffUVVFWF1+vVX8+GhgYUFxdHrKP/PbXuqcbGxkHPCXXs2LGw8Wpz5szB5cuX9Z4Lm80W1ee/du1ayLKMkydP4ssvvxzx6z7ar1tRUREcDgcuX7484HtnJN+7DQ0N+Pu//3tcunRpyOeH/vxor9VouvuANGmhcjqdA/qZgW83hR2OLMsoLS3VX+zr3Vg1FjUNde/R1jSS+rTXpKioSN9qRFGUmLw211OPzWYLu4/FYoGqqnGrJ5qatAHysiyjqakJra2tsNlswl4jTTy+n6+HqPuKNNKfe+35hw4dQiAQ0M99//339S19qqur4XK5MG3aNP087bXVzn/nnXf0luyh7mez2dDa2qq3GkiSBKfTOeD8oa4BQP9lej01aJ/TE088AQD6jC3tfJ/PN+R75B133IEZM2bA4/Ggvb0d77//Pi5fvhzVfbXPN/T7ctasWVixYkXErmjtddb+m5ubi3/9139FQ0OD/p4U+ppFc0+bzYalS5di/fr1UXV/z507FzU1NWE/z1arVW+RXrNmzYg2/ta+9loX2Uh+LkPP14z05/qJJ57A4sWL9YAW7fmhr3X/GoZ6r9G+F2Iy1CAu668bVENDQ7C+vj7sMbfbHXS73cFgMBhsaWkJtra2BltbW4MOh0N/TlFRUcJqGuzeiaxJq6ulpUU/3rhxo/76JLIOzTfffBOUJEk/ttlswW+++UZYPf1VV1cHN27cGAwGE/+1CiX6+zlUsnxtklG0P/fX+/zR3i8e17je80XcVztHe672X+25iXi9Y3Uto5+fqGtGg1vP/BtFUdDQ0ADfv62Boc2UCV3fwxeysWvoFMz+g+LiWdNQ905ETaGcTqf+V4zIOjTagEVfv011RdWjURQFNTU1sNlsqK+v11utEl2T6O/nSER/bZLRSH/uR/r80d4vHte43vNF3Lf/ORq3243x48fj1ltvjfvrLfLzT6bzE3XNaDFQEREREY0SB6UTERERjRIDFREREdEoMVARERERjRIDFREREdEoMVARERERjRIDFREREdEoMVARERERjRIDFREREdEoMVARERERjRIDFRmaqqpwOp2QZVnfBkJVVcFVEVE64PsPheLWM2RoxcXFaGlpAXBtryZVVWE2m/Xd7omI4oXvPxSKLVRkWC6XC5Ik6cdmsxlutzvsMSKieOD7D/XHQEWGZrfbBzxms9kEVEJE6YbvPxSKgYoMa+3atWhpaYEsy5BlGcC1vxK1fxMRxQvff6g/jqEiIiIiGiW2UBERERGNEgMVERER0SgxUBERERGNEgMVERER0SgxUBERERGNEgMVERER0SgxUBERERGNEgMVERER0SgxUBERERGNEgMVERER0SgxUBERERGN0v8PuE5vuhFx7HwAAAAASUVORK5CYII=", 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "metadata": {}, + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -551,23 +411,10 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "id": "60453966-409d-44d7-969a-ee67005bb392", - "metadata": { - "id": "60453966-409d-44d7-969a-ee67005bb392" - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "metadata": {}, + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -600,20 +447,16 @@ { "cell_type": "markdown", "id": "WqocAbPmfI5P", - "metadata": { - "id": "WqocAbPmfI5P" - }, + "metadata": {}, "source": [ "# Perturbative Quantities" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": null, "id": "ab63ada8-c087-4d13-ac4a-80429306b37a", - "metadata": { - "id": "ab63ada8-c087-4d13-ac4a-80429306b37a" - }, + "metadata": {}, "outputs": [], "source": [ "def get_zeta(v):\n", @@ -631,7 +474,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "id": "70436600-32f4-4325-9b1f-049325be6471", "metadata": {}, "outputs": [], @@ -683,9 +526,7 @@ "cell_type": "code", "execution_count": null, "id": "13668ef8-43cd-4a07-a777-ea5bbdf1dd96", - "metadata": { - "id": "13668ef8-43cd-4a07-a777-ea5bbdf1dd96" - }, + "metadata": {}, "outputs": [], "source": [ "res1_a = integrate_mode1(1.0e8, -1.0)\n", @@ -694,7 +535,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": null, "id": "e8992080-d34e-47e8-ae91-556e2e0c2a40", "metadata": {}, "outputs": [], @@ -771,7 +612,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": null, "id": "194fd91b-c10e-4895-b54e-2437dfe5b5b5", "metadata": {}, "outputs": [], @@ -782,7 +623,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": null, "id": "543d7fe5-0e28-436c-a7cd-b4498e08e7ab", "metadata": {}, "outputs": [], @@ -799,15 +640,7 @@ "execution_count": null, "id": "2aa32a26-3337-4fcd-9a31-87b09cbe63aa", "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - " 1%|██ | 1/100 [00:03<05:17, 3.21s/it]" - ] - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -838,31 +671,10 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": null, "id": "9ffc96e2-346c-4c7a-9a7a-eb1a09cb00af", "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'k_a' is not defined", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[20], line 4\u001b[0m\n\u001b[1;32m 1\u001b[0m set_rc_params_article(ncol\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m2\u001b[39m)\n\u001b[1;32m 2\u001b[0m fig \u001b[38;5;241m=\u001b[39m plt\u001b[38;5;241m.\u001b[39mfigure()\n\u001b[0;32m----> 4\u001b[0m b, a \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mpolyfit(np\u001b[38;5;241m.\u001b[39mlog(\u001b[43mk_a\u001b[49m), np\u001b[38;5;241m.\u001b[39mlog(Pk2), \u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m 6\u001b[0m ax1 \u001b[38;5;241m=\u001b[39m fig\u001b[38;5;241m.\u001b[39madd_subplot(\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m 7\u001b[0m ax1\u001b[38;5;241m.\u001b[39mplot(k_a, Pk2)\n", - "\u001b[0;31mNameError\u001b[0m: name 'k_a' is not defined" - ] - }, - { - "data": { - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -881,40 +693,18 @@ }, { "cell_type": "code", - "execution_count": 77, + "execution_count": null, "id": "63ab0826-e401-424e-a6fb-0ef10443823c", "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([-8.13964193e-03, 1.06259987e+02])" - ] - }, - "execution_count": 77, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [] }, { "cell_type": "code", - "execution_count": 37, + "execution_count": null, "id": "d2940da2-4e1a-4e49-8a06-30a5db9a4cd5", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -934,25 +724,17 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": null, "id": "b2d4b0fd-2cba-4881-a5a0-e391eb0a237d", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of time steps: Mode1 (207222, 9) Mode2 (153237, 9)\n" - ] - } - ], + "outputs": [], "source": [ "print(f\"Number of time steps: Mode1 {res1_a.shape} Mode2 {res2_a.shape}\")\n" ] }, { "cell_type": "code", - "execution_count": 39, + "execution_count": null, "id": "7373590b-1669-45d8-97e7-e5c9614f6365", "metadata": {}, "outputs": [], @@ -966,21 +748,10 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": null, "id": "e4ee0de8-36b0-4da0-b494-f7047f88284f", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -1045,7 +805,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": null, "id": "378c8f1f-8f53-4de8-b63c-5a20ddb89421", "metadata": {}, "outputs": [], @@ -1078,31 +838,10 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": null, "id": "14f3527d-fd7f-493e-8d64-1bf8e1b3cf8f", "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -1137,45 +876,10 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": null, "id": "7780e288-a7c0-436a-819a-bd1c9ae546ac", "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:00<00:00, 54.86it/s]\n" - ] - }, - { - "data": { - "image/png": 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SJBqeMbIde8bI9r20RH6RmcSauOn5i06HlxvZ5k4a2b4XUiPbkZERrl+/jt1uV+y4AHJycjCbzRQWFhIRMX/7MC0asTTqHaXss7Kw7lH7YS0xrzHTPXjwIEePHlU6mttsNsxmc9g93axWK0eOHKG3tzes+wgEAoEgwPCUkW1bD3eGA0a2RbFR/HVmMj9LC4ORbdtvaW//Ao+nHwCVSkNycjnZWR+G1MhWkiSam5ux2+3cuXMHn0/u+xQZGcm6deswmUykp6eHZK/ZZtGIpbnCoUOH2LNnjyKWrFYrhw8fxmazKWsqKyuVxxUVFYpH3pS/25R/3rfXG41GrFar4hsnEAgEgtnh9jNGtu5njGz/KjWRv85MYkN8aI1se3pqaG39jL7+i8q4TpdBVubPycw8gE6XFpK9QLbFunnzJna7na6uLmU8IyMDs9nMmjVrFlx7n0UjlqK10dR+WBv2PaaD2WymoaGB/Pz8567GqqqqcLlc1NfLYdPy8nLMZjN2ux1A6UV1/PhxZb3T6aS+vh6Xy0VlZaXiuycQCASCmWPE5+fvu/r5TVsvDYPBRra/yEzmQHpojWzHxtpobfstbW3HZ8TItq2tDbvdzq1bt/B45L5PWq2WtWvXYjabycqaH55w34dFI5ZUKtVrr8hmioqKCqxWKyaTiYqKiqC56upqysvLlcclJSXYbDYcDkfQuNFoVNZPdT8HRFRJIBAIZpiHipFtPwNe+Spqysj2F5nJbDaE2sj2HK2tn9HTewYmOzEFjGwPEh2dHZK9ACYmJrh9+zZ2u522tjZlPCUlBbPZTHFxMdHR0wsUzGcWjViaS5SUlGC327Hb7dTU1ATNmUwmrFar0l6hqqoKq9WKwWCgurpauZKbSqAzmUz09fVx4sQJgLDnPgkEAoFANrI92T3A37X1cNk1Q0a27Sdoa/0tY+MB0RIwst2DWh06y5POzk7q6+u5ceOGYlyv0WgoLCzEbDaTm5sbMgH4LP4JH6O3e9Aao9AtSQj5839fhFiaJSoqKnA4HM9VwR06dAiHw0FBQQEg5yNN9aqqrq6moKAAi8WiRJCm1ptMJoxGIyUlJS9sDTCV7wRy1/QpcSUQCASC6dOoGNn20euRjWXVwDvJ4TOybW39nO6e6rAb2Xo8Hu7du4fdbqepqUkZT0xMxGw2s379evT60HXznkKSJCYaB3HbOxm91YM07iOqMGlOiSWVNNVKcx4zODhIQkICAwMDxMfLDbXGxsZ48uQJS5cuJSoqdE29FjridRMIBIJgvH6J6t4BftPWy+m+gJFtemQEH2Ua+SgjKaRGth5PP23tU0a2T5XxhIQSsjI/JDV1HxpN6H4/TxnZXrt2jdFRucWOSqVi1apVmM1mli5dGhafNq9rnJGGTkbqO/H2BioFNcYo9BvTid+VE/I9n+VF2uFliMiSQCAQCAQvoG1sgk/be/n0GSNbgF3GOH6RmUR5UkIYjGw/p6v7L/j9ASPb9PSfkJX1AXGxq0KyF8hGtvfv38dut/PkyRNlPD4+HpPJxIYNG14rIL4PksfH6J1e3PWdjD92wWS4RhWpJnptCnpTKpFLElCF6HUNFUIsCQQCgUAwyauMbD/IkC1IQm9k+4dJI9uHynhcbBFZWR+SlvajkBvZTkWRXmRku3z58pBHkSRJYqJ5iJH6TkZudCON+ZS5yKUJ6E1pRK9NRq2bewa6UwixJBAIBIJFz5SR7X9u66XpGSPbzQY9f52ZzL6UBHQhNbK9RWvrZ88Z2aal/YjsrA+Ji1sbUguSR48eKUa2U0wZ2ZpMprC4SPgGx3E3dMnXbN0BBw2NQUeMKQ19SSrapPlRSSfEkkAgEAgWJa8ysn0/PZF/mJnMihAb2XZ2/pmW1s8YGrqljOv1y8nK/ID09J+G3Mi2oaGB+vp6BgcHlfH8/HxMJhOrVq1CowltNEfy+hm928tIfSdjD/sD12wRaqLXJBNjSkOXP/eu2V6HEEsCgUAgWFS8zMi2JD6GX2Qm8ePURGJCbWTb9jnt7cFGtqmpe8nK+hBDgjmkUaQnT55gt9t58OCBYmQbHR2tGNkmJSWFZK9nmWh3M1LXwcj1LvwjXmU8Mi8evXnymi1q/kqO+XtygUAgEAi+IzeGRvirhkeKkW2MRs3+tET+YWYSa0NsZNvd/RUtrZ8xMGBXxqOjc8nK/ICMjPeIjAydaHG73Vy/fp36+vogI9vc3FzMZjOrV68OuZGtf8zLyI1u3HUdeFoC+U+ahEhiStKIMaURkTw/rtlehxBLM0hBQQH5+flUV1cHjR85coTKykr6+/unfW9sMpmoqamZ9nqXy4XNZqOuru6FfZgEAoFgMVCoj8ag1WKM0PCLrGTeS0skbkaMbC1kZX2IMXFLSI1sm5qasNvt3L17VzGy1el0ipFtWlroPOGm9pxoHMR9tUPuieSZTIHXqIguTEJvTkO3PHHeXbO9DiGWZpi+vj5cLleQyDl27FhYkuuepbKy8jkfOoFAIFhsRKhVfG1eQWqkdgaMbNMnjWzfD6mR7ejoqGJk293drYxnZmYqRraRkaHr+wTgG5pgpKELt70jKFlbmxqDfmMaMRtS0cSGds+5xKIRS5IkIY2Ovn7hG6CKjn7tP76DBw9y9OhRPv74YwBsNhtmsznsNiVWq5UjR47Q29sb1n0EAoFgrpOmC8111MuNbHeSlfUhScadqNWhe5ttbW1VjGy9XjkvKCIigrVr12IymUJuZCv5JcYe9jNS18HovT6YvLpURaqJLk5BvzGdyNy4sNiezDUWj1gaHeVBiSmse6xsqEcV8+o770OHDrFnzx5FLFmtVg4fPozNZlPWVFZWKo8rKioUP7gpyxKLxYLT6XxuvdFoxGq1CjNdgUAgCBOKkW3b5/T0nGbKyDYiIomszPfJzPx5SI1sx8fHFSPb9vZ2ZTw1NVUxsg2124K3bwy3vYOR+k58A4E2CpG5cejN6USvS0atWzTyAVhEYmkuYTabaWhoID8//7mrsaqqKqVpGEB5eTlmsxm7XU4QdDgcABw/flxZ73Q6qa+vx+VyUVlZidVqneHvSCAQCBY24+PdtLefoLXtt4yNtSrjiYmbJ41sLSE3srXb7dy4cYOJialu3hqKioowm83k5OSENKIjefyM3u3BXTfZWXsSdYyWmJI09BvTiEgLvS/cfGHRiCVVdDQrG+rDvsd0qKiowGq1YjKZqKioCJqrrq6mvLxceVxSUoLNZsPhcASNG41GZb3T6eTAgQMAIqokEAgEIUKSJNnItu1zuru/ecbINoHMjP1kZv4cvT50v3M9Hg93797FbrfT3NysjBuNRsXINuY1txffec8ON+6r3yr5V4FumQH9xnSiC5NQaUPvCzffWDxiSaV67RXZTFFSUoLdbsdut1NTUxM0ZzKZsFqt7N+/H5AjR1arFYPBQHV1tXIlN1UaajKZ6Ovr48SJEwBhz30SCASChY7H0097++9obfuckZGAb1q4jGx7enqor6/n+vXripGtWq1WjGyXLFkSUgsS//hUyX8nnuaAMbAmQUeMOQ29KQ2tURipP8uiEUtzjYqKChwOx3NVcIcOHcLhcFBQUADI+UgWiwWQo0gFBQVYLBYlgjS13mQyYTQaKSkpeWFrgKl8JwCn06mIK4FAIBBMGtkONtDa+hldXeE3svV6vTx48OA5I9uEhATFyDYuLi5k+wFMtA7jrm1n5Ho30sSkP5tGRfRqI/qN6Quy5D9UqCRpsr/7PGZwcJCEhAQGBgYUl+SxsTGePHnC0qVLQ578tpARr5tAIFhMeL1DdHT8kdbWzxh2P1DGZSPbD0hL+3FIjWz7+/tpaGigoaEBt9sNyDcfU0a2y5YtC20UacLH6I1uhq92BEWRtCnR6DemE1Myt0r+Jb+fDscjInQ6knOXhHWvF2mHlyEiSwKBQCBYdAwO3aa19TM6O/+EzzcCBIxss7I+ID6uOOxGtrGxsZSUlFBSUhLyXnueDjfDte2MXOtCGnsmirQmmdiydCKXJsyZkn/P+BhNt2/gsNfiqL/KyICLop0W9v7z/262j6YgxJJAIBAIFgWyke2XtLZ+xuDQTWU8XEa2g4ODShTp20a2ZrOZlStXhtTIVvL4Gbndg/tKOxONgf00SVHElqYTY0qbM1GkkcEBnPVXeWy/QuPN63gnAh59kdHRaEPcVPNNmVNi6ejRo4odiLDkEAgEAkEoGB5+SGvb53R0/B6vV76KCqeRrdPpVIxspzJdwmlk6+kewV3bwUhDZ6CiTY1sP1KWga7AMCdykVydHTyuu4zDXkvr/btIkl+Zi0tOocBURoG5jJzCNWi0ofWxe1PeSCy5XC6OHj0KoDRZBLmCC+SKrfz8fCVB+XXPBWCxWLBarTidTlEGLxAIBILvhd8/TlfX17S2foZroE4ZD6eR7bVr16ivr6e/v18ZnzKyLSwsRKsNXXxC8voZvduL+0o7484BZVxj0KEvTUdvTkcTP7vRGUmS6Hri4LH9Co/rrtDT9DRoPnVJAQXmMpZt3ERK3tI5cy34It7ob85ms9Hb2xukkp1OJ9XV1UpjxPLy8mmJJYPBwKFDh5TokhBKAoFAIPiujIw8fcbIVm6xEk4j28bGRux2O/fu3XvOyNZsNpOamhqSvabw9o7iruvAbe/EP+yRB1UQtcqIviyDqBWzW9Hm83ppvX+Hx3VXeGy/wlBPwLtOpVaTvXoNyzZuYpl5E/EpoX1twskbiaX9+/crxrBT2Gy2oEQ1g8GAzWbDYrFQVVWl9Aeawmg0Kj2FQC6Fr6ioeGVkaXx8nPHxwP3ms3fBAoFAIFhcyEa2pyaNbC8o4+E0sr1x4wZ2u52enh5lPCsrC7PZTFFRUUiNbCWfxNj9XoZrOxh/1A+TNezquEg5irQxHa1BF7L9viuesTGe3mjgcd1lnA11jLmHlTmtTsfSdSYKzGXkl2wkOi50OWEzSchzlhwOR1CkyWg0KmLqWVH0baqqqjAYDFgsFgoKCqiqqgq62nuWTz75hF/96lchPbdAIBAI5heyke2xSSPbrslRFUlJO8jK/JCkpLdCZmQrSZJiZHv79u0gI9vi4mJMJhOZmZkh2WsKr2tcjiLVdeAfDHi06VYkEluaTtRqIyrN7HTXHhkcwFFfy+O6KzTdvI7XEzhfdFy8cr2Wu3Y9EZGzJ+RCxYwkeH87mvQiLBYLNpuNqqoqHA7HK/3NDh8+zC9/+Uvl8eDgIDk5OSE5azgpKChQEtif5ciRI1RWVtLf3z/t8lGTyURNTc2017tcLmw2G3V1dSJ5XiAQzFskyUdv33laWz+np+cUzxrZZma+T1bmQaKjQ/d+MD4+zq1bt7Db7XR0dCjjqampbNy4kbVr14a0J53klxh72I+7tp2x+32BKJI+Av3GNDmKlDQ9a61QM9zXy6O6yzy6cpGWe3eCErQT0tJZZt7Eso2byFy5GrU6dFV+c4GQi6WCgoKga7mpJO/XYTAYlMjTqyJQIN8H63TfTalKkoR3wv/6hW+ANlL92gS1qWvLZ0XOsWPHQt5j49tUVlY+Z9orEAgE84XxiR7a26aMbFuU8UTDJtnINqU8pEa2HR0d2O12bt68GWRku2bNGsxmM9nZ2SFNSPYNTihRJJ8rkGaiy09Avylj1jzaBru7eHT1Eg+vXKTt0X14po916pIClpVuYtnGzSTn5M3pBO03JeRiyWKxUFlZqTx2Op3TSvAON94JP0f/27Nh3ePQv91JhO7VavrgwYMcPXpUuWK02WyYzeawe7pZrVaOHDlCb29vWPcRCASCUCFJEv2uK7S2fvackW1GxntkZf4cvb4gZPt5PB7u3LmD3W6npSUgyJKSkjCbzaxbty6kRraSX2Lc4cJ9pZ3Re33gl4WIOkZLTEka+rJ0IlJm3tO0v6ONR7WXeFR7kQ7Ho6C5jBWrWFG6heVlW0hITZ/xs80Wb1wNV11djcvlIj8/n/3795Ofn8/BgweVZO7Dhw+H6qwLgkOHDrFnzx5FLFmtVg4fPozNZlPWVFZWKo8rKioU89wpfzeLxYLT6XxuvdFoxGq1ikpCgUAwr/F4XJNGtp8FG9nGbyAr60NSU38QUiPb7u5uxch2bGwMkI1sV69erRjZhjSKNDzBSH0nw1c78PWOKeORefHoN2UQsyYZVcTMRpF6W5p4WHuRR7WX6G4MvOaoVGSvLmJ56VaWl24mLil5Rs81V3gjsWSxWF4YNXrdNdpsoI1Uc+jf7gz7HtPBbDbT0NBAfn7+c1djVVVVuFwu6uvrAbn1gtlsxm63A3ICPcDx48eV9U6nk/r6elwuF5WVla/M9xIIBIK5iCRJDA5eo6X1M7q6vnzGyFYvG9lmfkBc3OqQ7ef1erl//z52u52nT58q4waDAZPJxPr160NqZCtJEhNPBhiu7WD0dg/45CiSSqchpiSV2LIMItJD50E3nfN0Nz7hUe1FHtZeoq+1WZlTqdXkrlnH8tItLNu4Cb0hccbONVeZUx28w4lKpXrtFdlMUVFRgdVqxWQyUVFRETRXXV1NeXm58rikpASbzYbD4QgaNxqNynqn08mBAwcARFRJIBDMK2Qj27+nte0zhofvK+OxsYVkZ31IWtqP0GpjQ7Zff38/9fX1XLt2LcjIdsWKFZjNZgoKCkJrZDviwd3Qhbu2HW/3qDIekR1LbFkG0etSUEfOzHvTlEB6cOkcD69cxNXZrsypNVryitezomwrBeayeVviHy4WjViaS5SUlGC327Hb7dTU1ATNmUwmrFarEp2rqqrCarViMBiorq5WruSmKgxNJhN9fX2cOHECIOy5TwKBQBAKhobu0NL6GZ2df/8tI9t3ycr6MKRGtj6fTzGyffz4sTIeFxenGNkmJCSEZC+YjCI1DeGubWfkZg945eIiVaSamPWp6MsyiMwKnQB8HT1NT3lw5QIPLp2nv71VGddGRLJkfQkryraSbypFFzNzka35hhBLs0RFRQUOh+O5KrhDhw7hcDgoKJCTFisrK5WrzurqagoKCrBYLEoEaWq9yWTCaDRSUlLywtYAU/lOICfdT4krgUAgmCl8vlHZyLbtMwYHbyjjMTHLyM6aMrINnWiZMrKtr69naGhIGS8oKMBsNrNixYqQGtn6x7yMXJOjSJ6OEWU8IkOPviyDmPUpqKNm5m23r62FB5fO8+DyeXpbmpRxbUQkSzeYWbF5G/klG4mMmp02BPMNlSQ9Uwc4TxkcHCQhIYGBgQHi4+XQ4djYGE+ePGHp0qUh7YGx0BGvm0AgCDXD7ke0tn5OR8fvnjGyjZCNbDM/xGDYGHYj25iYGMXIdiqNIVRMtAzJRrbXu5A8k1GkCDXRxSnoy9KJzImbkbJ6V2cHDy6d48Hl80FJ2hqtlrx1JazavJ0CcxmR0TNfYTcXeZF2eBkisiQQCASCkKMY2bZ9jst1VRmPjsolK+vnk0a2oausGh4e5vr169jt9qB0hLy8PMxmM6tXrw6pka1/3MfojW6Ga9vxtD5j75EaQ2xZOjElaaijw/8WO9jTxYPL8hVbpzNQ5q/WaMhbu56VW3ZQYC4jSj9z134LESGWBAKBQBAyRkYaaWv7LW3tVd8yst1DVuaHGI1bQ25kW1dXx7179/D75ahOVFSUYmSbkpISkr2mmGh3y7lI17qQxmXjXDQqYtYmy7lIS+LDHkUa7u/j4eXz3L90jvZHD5RxlUpNzppiVm7ezvLSzSJJO4QIsSQQCASCkHD/wb+itfVT5bFOl05m5s/JzDxAlC50DQxHRka4ceMG9fX1M2Nk6/ExcrMHd207E02B3CdtcjT60nRiTGlo9BEh2+9FjI+4eVR7iXsXztB851bAakSlImf1GlZs3s6Ksi3EJBjCeo7FihBLAoFAIAgJMTFLARVJxu1kZX1AUtLukBrZtrS0YLfbuXPnznNGtmazmYyMjJDsNYWnawR3bTvuhi6kUXk/1Cqii5LQl2Wgy09ApQ5fFMk7McGTa3buXTyDs6EOn8ejzGWsWMWqLTtZsWkrsYmhzcESPI8QSwKBQCAICZkZ+0lJ3kN0dG7InnN8fJybN29it9vp7OxUxtPS0jCbzaE3svX6Gb3dw3BtBxNPBpRxTaIOfWkGenMamrjQRa2+jd/vo+Xube5dOMOj2kuMj7iVuaTsXFZve4tVW3csaKsRSZLmnM+cEEsCgUAgCAlabRxabWi6Xre3t2O327l165ZiZKvVaikqKgqLka23Z5Thqx2M1Hfgd09GkVQQtTqJ2LJ0dMsTwxZFkiSJricO7l04w4NL5xju71PmYpOSWbVlB6u3vUVK3tI5JyJCxUD3KM13e2m628eY28PP/o+m2T5SEEIszSAFBQXk5+dTXV0dNH7kyBEqKyvp7+9/ru/SyzCZTNTU1Ex7vcvlwmazUVdX98I+TAKBQDDbTExMKEa2ra2B5onJycmYTKbQG9n6/Ize7cN9tZ3xRy5lXBMfKecibUxHm6AL2X7fpr+jjfsXznLv4ln62wLGvTq9nhWbtrF621tkrypCFcKO4nOFiTEvrQ/6abrbR/PdPgae6W4O4B4YRx/G1/67IsTSDNPX14fL5QoSOceOHZu26Pm+VFZWPudDJxAIBHOB7u5u7HY7N27cCDKyLSwsxGw2k5eXF9ooUv8Y7qsduO0d+Icm84BUELUiEX1ZBlErjag04YngjA4Ncv/SOe6dO03740AlmzYiknxzGau37mTJehPaiPAmjM80kl+ip2WYpru9NN3po8M5gN8XaPOoVqtIL0ggp9BIbqGRmDBedX4fFo1YkiQJ7/h4WPfQ6nSv/Qd98OBBjh49yscffwyAzWbDbDaH3abEarVy5MgRent7w7qPQCAQTAev18u9e/ew2+00NjYq4waDAbPZzPr164mNDV1vIMkvMXa/D3dtO2MP+2HyfVodG4F+Yzr6jelojeFpxOvzenA21HH33CmcDXb8PvmaT6VSk7t2Hau3vcWyjZvRhTBqNhdwD4zTfK+Ppjt9tNzvY3TIEzQfnxJNbqGRnNVGslcmEjkDfam+L3P3ZCHGOz7O//uv94d1j//m76qIeE2i4aFDh9izZ48ilqxWK4cPH8ZmsylrKisrlccVFRWKH9yUZYnFYsHpdD633mg0YrVahZmuQCCYs/T19SlGtiMjsiWISqVi5cqVmM1m8vPzQ2pk6xsYx13XgbuuA9/AhDKuW2ZAX5ZOdGESKk3or7kkSaLD8ZC7505x/+I5xoYDLQdSlxRQuGM3q7buQG9IDPnes4XP46fN4aL5Th9N9/robRkOmo/QachamUhuoZHcIiMJKfNHHC4asTSXMJvNNDQ0kJ+f/9zVWFVVFS6Xi/r6egDKy8sxm83Y7XYAHA4HAMePH1fWO51O6uvrcblcVFZWYrVaZ/g7EggEgpfj8/l4+PAhdrtd+R0GspGtyWRiw4YNoTWy9UuMP+pnuLaDsfu9MNmSSB2jJcachr40g4jk8HiiDfZ0ce/8Ge6cOxWUh6RPNLJ621sU7thNSu6SsOw900iSxEDXqHK11vqwH++EP7BABSk5cYo4SstPQBMGYToTLBqxpNXp+G/+rirse0yHiooKrFYrJpOJioqKoLnq6mrKy8uVxyUlJdhsNhwOR9D4lLdRdXU1TqeTAwcOAIiokkAgmDMMDAzQ0NBAQ0NDkJHtsmXLMJvNLF++PKRGtr6hCdz1nbivduDrG1PGI5fGE1uWQXRRMqqI0L9ZT4yO8LD2EnfPnaL5zk1lXBupY3npZgp37CZ37TrU6tB9r7PFxJiX1ocumu700nSnl8GesaD5mIRIclcbySkykrPKSPQcyz36viwasaRSqV57RTZTlJSUYLfbsdvt1NTUBM2ZTCasViv798tXhlVVVVitVgwGA9XV1cqVXF9fn7K+r6+PEydOAIQ990kgEAhehd/vx+FwYLfbefjwYZCRbUlJCSUlJSE1spUkiXHnAO7adkbv9MJk0rAqSou+JBV9WToRafqQ7TeF3++j6dYN7p47xaOrl/FOBHJicwrXUrhzD8tLt8z7PCRJkuhrc9N0p4/GO720P3YFJ2ZrVGQuN0wmZieRlKVfkO0NFo1YmmtUVFTgcDieq4I7dOgQDoeDgoICQM5HslgsgBxFKigowGKxKBGkqfVTTtolJSUvbA0wle8E4HQ6FXElEAgEoWB4eJhr164pKQFTLFmyBLPZzKpVq0JqZOtzexhp6MRd24G3J1B2Hpkbh740g+jiZNSRoY/k9LY2c+eMjXvnTwf1Q0rMyKJwx24Kt+8iPiU15PvOJOMjHprv9SvXa25XcHFUfHIUuUVJ5BYlkbXCQGTUwpcSKmlK9s9jBgcHSUhIYGBggPh42ThwbGyMJ0+esHTp0pB2d13oiNdNIBBMF0mSePr0KXa7/Tkj2/Xr12MymUJqZCtJEhONg7hrOxi51Q3eySiSTkPMhlT0pelEZoaugm6K8ZERHlw+x+0zNtof3lfGo/SxrNy6k6Idu0lftmLeRlQkv0R389Dk1VofHU8GkfwBaaCNUMuJ2UVy9CghNXrefq/P8iLt8DIWvhwUCAQCQUiZMrK12+1B7Uiys7MVI9uIEPYJ8o96GWnoZPhqB97OEWU8IlOPflMGMetSUetCG0WS/H5a7t3m9ulqHtZeUq7ZVGo1SzeYWbPTwtKSjfO2H9Lo0ARNd/touttL893ny/oT02Mmo0dGMpcZ0IYhSjefEGJJIBAIBK/lWSPb27dv4/P5AIiMjFSMbNPTQ+dXJkkSnpZhhq+0M3qzG8kjR61UEWqi16UQW5ZBRHZsyCMcgz1d3Dlbw52zNQx0dijjxsxs1uwqp3DH7nlZ7u/3+el8OqQkZnc1DSm9pkAu689elUjemiRyCo3EJ4WnWnC+IsSSQCAQCF7K2NgYt27des7INj09XTGy1U2zEng6+Me9jFzvxl3bjqctYCKrTYshdlMGMRtSUYc4R8Y7McHjusvcPmOj8dZ1mMxOiYyOZuWWHax5y0LG8lXz7uppuH9cyTtqud/H+Ig3aD45J5bcQjl6lJ6fgEY7P8v6ZwIhlgQCgUDwHG1tbYqRrccjX9FotVrWrFmD2WwmKysrpOJhom0Yd207I9e6kSbkqBVaFTFrU9BvyiAyNy6k+02Z1946Xc39i2cYdweEWU7hWtbsKmd56ZY5U0U9HXw+Px2PB2iczD3qbQ1uCqmL0SpVa7lFxjnlvTbXEWJJIBAIBIBsZHv79m3sdjttbW3KeHJyMmazmXXr1hEdHbrrGf+Ej9Gb3QzXduBpDvRh0iZHoy/LIKYkFY0+tDlBI4MD3Dt/httnqulpeqqMxyWlUPTWHop2WjCkhe46Mdy4B8blsv7bPTTf7WNizBeYVEFqXjy5RUbyipJIXRKPWj2/omNzBSGWBAKBYJHT1dWlGNmOT3pohtPI1tPpxl3bgbuhE2nqzV2jIrooCX1ZBrr8hJDu5/f5eHqjgdunq3HUX1W82TQRESwv3ULRWxZy1xTPi6aRkl+is3GQxtu9NN3upatxKGg+KjZCFkdrkshZbSQ6dmE0hZxthFgSCASCRYjX6+Xu3bvY7XaampqU8cTEREwmU+iNbD1+Rm/3MFzbzsTTQWVcY4xCX5qO3pyGJsRv7ANdHdw6Vc2dM9VBPZHS8pezZlc5q7bsICqE32O4GHN7aL7XR+OtXpru9j5XuZaSG0fe2iTy1iSRmieiR+FgTomlqqoqDAYDDQ0NitHsQqKgoID8/Hyqq6uDxo8cOUJlZSX9/f3PNal8GSaTiZqammmvd7lc2Gw26urqXti0UiAQLA56e3upr6/n+vXrM2Jk6+kewX21g5H6TvxTCcZqiFqdRGxZBrplBlQhfHP3ejw47Fe4deobGm9eU8aj4+Ip3LGLorfK57w321TX7Ke3emi83UuHM7jvUWSUhpxCOXqUW5Qkco9mgDcSSy6Xi6NHjwIEiZuqKtmDra+vj/z8fKUD9atwOp04nU4+/vhjXC4XTqczpD5nkiQppafhQhWhfm3ouK+vD5fLFSRyjh07Nm3R832prKx8zrRXIBAsDnw+Hw8ePMBut+N0OpXx+Ph4xcj2dU35vguS18/o3V7cte2MOwaUcU2CTo4ibUxDEx/aN/jelmZunfqau+dOMToUiFzlFW9g7e53KDCXzemeSJ5xHy33+2i83Uvj7V6G+4O7Zidm6FmyRo4epS+bv4a085U3Eks2m43e3l6SkpKUMafTSXV1NVarFYDy8vJpiaX8/Hzq6uooLy+nvLxc8UYLFZLHT9u/uhTS5/w2mf96C6rXNO46ePAgR48eVcSlzWbDbDaH3dPNarVy5MiRoAZyAoFgYeNyuRQj2+HhQGXU8uXLMZvNLFu2LKRGtt6+MdxXO3DbO/APT14VqSBqpRF9WTpRK40hjSJ5xsd4eOUiN2u+pu3BXWU8NtHIml3lrNlVTkLq3E3WdnWNKOKo9WE/fu+3umavSiSvSBZI8cmi79Fs8kZiaf/+/UqkZAqbzRYUJTEYDNhsNiwWC1VVVYoB7BRGo5H9+/fjcrnYuHEjJSUlVFRUYLFYXhoFGR8fV5IQQW5ZPl84dOgQe/bsUcSS1Wrl8OHD2Gw2ZU1lZaXyuKKiQjHPnfJ3s1gsQZ8Op9YbjUasVmtII3ICgWB+4ff7efz4MXa7nUePHilGtnq9XjGyTUwMXVNFyScxdr+X4doOxh/1K40O1XGR6DemoS9NR2sIbfl95xMHt2q+5t6FM0yMTl4lqtXkl2xk7e53WLrehDqEIjBU+H1+2h0DPL3Zw9Nbvbie6UYOEJcUJUeP1iaTtUJ0zZ5LhDxnyeFwBEWajEajIqZeFS06fvw4+/fvV3J6qqqqXiqWPvnkE371q199p3OpItRk/ust3+lrviuqiOmFRc1mMw0NDeTn5z93NVZVVYXL5aK+vh6QI3Nmsxm73Q7Iry/Ir9fUeqfTqZhXVlZWKlE9gUCweBgaGlKMbAcGAldfS5cuxWw2s3LlypAa2Xpd47jrOhip68A3OKGM65YbiC3LIGq1EVUIr4rGR9zcv3iWmzVf0/XEoYwnpKaxdvc7FO3cQ6wx6RXPMDuMj3pputPL05ty/tGzjSHVahUZyw3krUliydokDGkx867xZTjxuVxIkoQ2hOL++zIjCd7fjia9iPfff5+jR49SUlKCy+VSoikv4vDhw/zyl79UHg8ODpKTk/PK51epVK+9IpspKioqsFqtmEwmKioqguaqq6spLy9XHpeUlGCz2XA4HEHjRqNRWe90Ojlw4ACAiCoJBIsIv9+vGNnev38/yMh2w4YNmEwmkpOTQ7af5JcYe9iPu7adsft9gSiSPgK9eTKKFEKbDEmSaHtwj1unvuHBlfN4J28UNFotyzZuZu2ed8gtKkYVwoT0UDDQPcLTm708udlD+yMX/meSs6P0EbI4Kk4mt9BIZPScqrOaVfwTE4w2XMN96RLuS5cYu3OH5H/+z0n5l/9ito8WerFUUFAQdC03leT9OgwGw7Qr4HQ6XUjb6880JSUl2O127HY7NTU1QXMmkwmr1apE4aqqqrBarRgMBqqrqxUROSVATSYTfX19nDhxAiDsuU8CgWD2GRkZ4fr169jt9qAPozk5OZjNZgoLC0NqZOsbnMBt78B9tQOfK5ACoctPQF+WQXRREqoQWmXIjSNPc+vUN/S2BNoaGLNyKN7zDqu37yImPiFk+70pfr9Ep3OAp7d6eHKzl/52d9B8YnoMS4qTWVKcTHp+gijtn0SSJMYfPlLE0YjdjjQ6GrRm4pm2FrNJyMWSxWKhsrJSeex0OqeV4L3YqKiowOFwPFcFd+jQIRwOBwUFBYCcjzT1+lVXV1NQUIDFYlEE6NR6k8mE0WikpKTkha0BpvKdQP47mRJXAoFgfiBJEs3Nzdjtdu7cuRNkZLtu3TpMJlNojWz9EuMOF+7adkbv9sFkdEQVrUVvkqNIEakxIdzPT9Ptm9w69TWP6y7j88rXVdpIHSs3b2ftnnfIXDF3/Nkmxrw03+2T849u9zI2HOh9pFKryFyewJK1skAyhPB1mu94OrtwX5bFkfvyZXzdPUHzmuRk9Js3o9+yBf2WzUSkpc3SSYNRSVPZf98Dm82G1WrF5XJRUVERFA0BOfoxlcAdTgYHB0lISGBgYEApfx0bG+PJkycsXbqUqHnk7TPbiNdNIJh79PT0cPz4cbq6upSx9PR0Nm7cyJo1a0IaafcNTzBS34X7ajve3jFlPDIvHn1ZOjFrk1FFhC6lwe3q5/bpam6d+pqBroBRb+rSAor3vMOqrTvRxehDtt+bMNQ3xtObPTy52fNc9ZouRktuURJLipPILUwiKsQ2LfMVv9vNiN2uRI/GHz0OmldFRRFjNsviaOsWdCtWzJggfpF2eBlvFFmyWCwvjBqFWxwJBALBYiIhIYHBwUG0Wi1r167FbDaTmZkZsjcVSZKYeDLIcG07o7d7wDcZRdJpiClJJbYsg4j00AkWye+n8dZ1btq+wlFfi38qShYdw+ptb7F299uk5S8L2X7fF0mS6G118+RGN87r3fQ0BxvTJqREs6Q4maXFyaL30SSSz8fYnTu4L17EffESIzdugOeZjuMqFVFFRZORoy1El2xAHTn3LVlEZplAIBDMcSIiIvjggw9ITU0NrZHtiAd3w2QUqSuQKxKRHUtsWQbR61JQh7Awxu3q5/YZmxxF6uxQxjNWrKJ4z15WbtpGxCxHtP1+iQ7HAM4b3Ty53s1gTyC6plJBekGCIpBE9ZrMREurLI4uXcJ95Qr+Z6oxASKyspTIUUxZ2ZyobvuuCLEkEAgE84C8vLyQPI8kSUw0DeGubWfkZg945Qo6VaSamPWp6EvTicyOC8leMJmLdOcmN21f8bjuimJiGxkdQ+GOXRRb9s26/YjX46PlXj/OG908vdkT5L2miVCTs9pI/vpklqxNJjpu7kdBwo1vaIiR2lrcly4xfPEinsbgJGx1XBz6TWVK9CgiN3fei0ohlgQCgWAR4B/zMnK9C/eVDjwdgWqtiHQ9+k3pxKxPRR0VureEkcEB7pyxcbPmK1wd7cp4+rIVFFv2smrzjlmNIo2PeHh6q5cnN7ppvNOHd9ynzOlitCxZm8zS9cnkFiYRoZsbbWdmC8nrZfTmLSV6NHrzJvgCrxcaDdHr16PfspnYrVuJWrMGVQh7es0FFtZ3IxAIBIIgJlqGZCPb611IE5P+mFo1MetS0JelE5kTF9Lcp5a7t7hh+4rHVy8pFW2R0dGs3vYWxZZ9pC6ZvV5ww/3jPLnRzZMb3bQ+CO5/FJuoY+m6FJauTyZzuWFR5x9JkoSnqYnhSXE0cqUW/3BwvlbkkiVy5GjbVmJKS9HExs7SaWcGIZYEAoFggeGf8DF6o5vh2nY8LYE3OW1qNPrSDPQlqahjQletNTo0yJ2zNdys+Zr+thZlPC1/mRxF2rqTyKjZ8TZzdY7guNaF83oPXU+DrbESM/Tkr08mf30KKbmhE43zEZ/LhfuKfLXmvngRT2tr0LwmIYGYzZvRb91C7JYtRGRlzdJJZwchlmaQgoICxc7lWY4cOUJlZSX9/f3P9V16GSaTiZqammmvd7lc2Gw26urqXtiHSSAQzH88HW6Ga9sZaehCmrpW0qiIXpNMbFkGkUvjQxpFar1/h5u2r3hYexHfZMVThC5qMoq0d9Yq2vra3DiudeFo6Ka39ZmIiArSl8azdH0K+etSMKQt3v5H0sQEozduTEaPLjN2+zZMdoAHICKCmA0bJhOztxJVuBrVHPTbmymEWJphpoyHnxU5x44dm7bo+b5UVlY+50MnEAjmP5LHx8jNHtxXO5hoDEROtElR6EsziDGlookNXVLy2PAwd8/JUaRnu2unLimg2LKX1dt2Ehk9syJkqsTf0dCFo6GL/o6AQa1KrSJ7VSL561NYui4ZfcL8dX94E+T2EE9wX5isWrt6FWkk2Mg3clkB+i1biN26lRizGbV+bvS3mgssGrEkSRKeZ3s9hIGIiIjXfmo7ePAgR48eVaxdbDYbZrM57DYlVquVI0eO0NvbG9Z9BALBzODpGsFd2467oQtpdNKcVa0iuigJfWk6ugIDqhDZakiSRNvD+9y0neTh5Qt4PbJxrlanY9WWnayz7CWtYPmMXmNJkkR30xCOhm4c17oYeKb1gVqjIqfQSMGGFJYWpxAVuzgbRHr7+5VmkO6Ll/B2dATNa4xGpWJNv2UzESHsAL/QWDRiyePx8Ld/+7dh3eNv/uZviHxNc61Dhw6xZ88eRSxZrVYOHz6MzWZT1lRWViqPKyoqFD+4KcsSi8WC0+l8br3RaMRqtQozXYFggSJ5/Yze6WH4SgcTTwK9bDQGHfqydPTmdDQhLG0fcw9z7/xpbtq+oqe5URlPyV1CsWUfq7e/NaPdtSW/ROfTQTmCdK2boWc6jGu0anKLjBSUpLJkbRK6EOZkzRdkI9oGpSHk2L178IxJhyoykhizSbla061cOedMiOcqi0YszSXMZjMNDQ3k5+c/dzVWVVWFy+Wivr4egPLycsxmM3a7HQCHwwHA8ePHlfVOp5P6+npcLheVlZVYrdYZ/o4EAkE48faOMny1gxF7J373ZIRcBVGrjOg3ZRC1PDGkUaSOxw+5YTvJg0vn8U7IxrlTHm3Flr1kLF85Y1EkyS/R7hzA0dCF81o3w/0BI19tpJq8NUkUlKSStyaJyBC2PpgPSJLE+KNHuC9OGtHW1SGNjQWt0a1cqYijGLMJtbCx+l4smp+siIgI/uZv/ibse0yHiooKrFYrJpOJioqKoLnq6mrKy8uVxyUlJdhsNhwOR9C40WhU1judTg4cOAAgokoCwQJB8vkZu9fHcG07449cyrg6PhL9xnT0G9PRGkKXfzM+MsK9C2e4aTtJd+MTZTwpO5diyz4Kd+wiSj8z5eGSJEeQHtu7eFzfhdsVEEgROg1LipMpKEkhtyiJiBB2GJ8PeLu7cV++rAgkb3d30LwmJZnYLVvRb92CfvNmtCkps3TShcWiEUsqleq1V2QzRUlJCXa7HbvdTk1NTdCcyWTCarUGmRJbrVYMBgPV1dXKlVxfX5+yvq+vjxMnTgCEPfdJIBCEF69rDPfVDtx1nfiH5NwgVKBbnkhsWQZRq4yoNKGL6nQ4HnGj+iT3L53FOy6LEk1EBCs3baPYso/MlatnJIokSRI9zcM8snfyuL4r6IotMkrD0nUpFJhSyVmdiDaERr5zHf/YGCP2eqUh5PiDB0HzqqgoYjZuDBjRLp/Z3LHFwqIRS3ONiooKHA7Hc1Vwhw4dwuFwUFBQAMj5SFNmxdXV1RQUFGCxWJQI0tR6k8mE0WikpKTkha0BpvKdAJxOpyKuBALB7CP5JcYe9OGu7WDsQR9MppmoYyPQm9PRl6ajNYbu+mRidIR7F85ys+Yrup44lHFjZrYcRdq5m+jY0FmevIretmEe27t4ZO8MStLW6jQsLU5mmSmV3CLjohFIkt/P+IMHijgasdcjTUwErYkqLES/VY4eRW/YgFq3OCv8ZhKVJD2T/TVPGRwcJCEhgYGBAeLj4wEYGxvjyZMnLF26lChxRzttxOsmEMwcvsFx3HWduK924BsIXDXpChLQl2UQXZiEShu6BNxO52Nu2r7i3sWzeMZkYaLRalletpV1ln1krS6akaiEq3NEiSD1tQWsVzQRapasSWKZOY28tYvnis3T2alcq7kvXcI3eXMwhTY9Xb5W2zJ5tTaZhrFQ6R7pJiUm/NeHL9IOL0NElgQCgWAGkfwS449dDNe2M3avFyb7AKpjtMSY0tCXphOREro+RRNjo9y/eI6btq/odD5SxhMzsii27KVwx25i4hNCtt/LGOwZ5XG9HEHqaQ40ilRrVOQWJbHMlMrSdcmLIknbPzLCSF2dYkQ78dgRNK+OiSGmtFSxE4lcunTBX611uDv4+unXfPXkK+703uGb/d+Qrp87rQwW/k+lQCAQzAF8wxO47ZNRpL5n8nGWxBNblkH0mmRUEaGLInU9dcpRpAunmRiVo0hqjZblZVtYZ9lLduHasL8BjwxO8MjeyaO6TjqfBBpmqtQqclYlssycRv765AVf5i9Jkny1duECwxcvMmqvR3q2759aTdSaNYqVSPS6dajmSI5tOOkZ7eHrp1/z9dOvudZ1TRlXq9Rc777OXv3eWTxdMEIsCQQCQZiQJIlx5wDu2nZG7/SCT856UEVp0JekoS9LJyItdH2KPONjPLh8gZvVJ2l/HEgENqRnULxnL0VvWcIeRZoY8/LkejcPr3bSfL8facqsVgVZKwwsN6eRvyGF6BB2FZ+LeHt75Wu1CxcYvngJX09P0HxEZuZk3tFW9JvK0ITZxWGu0D/WT3VjNV8//Zq6jjqkyQQ9FSpK0krYu2QvljwLydHJs3zSYIRYEggEghDjc3sYaZCjSN7uQNJyZE4c+rJ0ootTUIcwH6e3pZmbtpPcOVfDuFvOAVJrNCzbuJliy15yi4rD2nzQ5/PTfKePh1c7eHKjB68n4DGWuiSeFaVpLDOlLmirEWligpGGa7gvXmT44gXG794LmldFR6MvLUW/bZt8tbZkyYK/WptiYHyAU02n+OrpV9S21+KTfMpccUoxe5fs5e28t0nTp83iKV+NEEsCgUAQAiRJYqJxEHdtByO3usE7+Yk5UkPMhhT0ZRlEZoauT5HX4+HR1UvctJ2k5e5tZTw+JY3iPe+wZlc5ekNiyPb7NpIk0eEY4OFVOVF7zB24VkpIjWZFaTorNqYtWLNaSZKYePpU9lq7cAF3Xd1zXmu6wtXEbt2Kfus2oks2oF4EV2tTDE8Mc7r5NF8//ZqLbRfx+r3K3GrjavYt3cc7S94hMzZzFk85fYRYEggEgjfAP+ZlpKGL4dp2vJ2BN8uITD36sgxi1qeg1oXuV62ro52bNV9x+3Q1o0NyHpBKpSbfVMq68n0sKd4Q1ihSX5ubh1c7eFjXGdQLKTo+kuXmVFaUppOaF7cgoya+wUHcV64oAsnT1hY0r0lOJnbrFjl6tHkz2uS5dZUUbgYnBjnbfJbqxmoutl5kwh9oebA8cTl7l+xl75K95MbnvvxJ/H7ouAGZG2bgxNNHiCWBQCD4jkiShKdlmOHadkZvdCNNXjupItREr0shtiyDiOzYkAkGn9eLs+EqN6pP0ngzkAgba0xi7e53WLv7beKSwvfGPNw/zqO6Th7WdQRVskXoNORvSGFFaRrZKxNRaxaWz5jk8zF26xbDFy7ivniR0Zs3wRe4QlJFRBBtMhG7bSv6bdvQrVix6LzW+sf6Od18mm8av6G2vTYogrQkfgl7l8oCqcBQ8OonGumDa/8F7P8J+p/Cf3sdEpeE8+jfCSGWZpCCggLy8/Oprq4OGj9y5AiVlZX09/c/16TyZZhMJmpqaqa93uVyYbPZqKure2HTSoFA8Hr84z5GrnfhvtqBpzUgGrRpMcSWphNTkoY6OnS/Vgd7url16htun/qa4f7J3jsqFUvWlbDOso/8ko2oNeHpReQZ9+G83s39y+20POgPNMpUq8hdk8SK0jSWFCcvuF5InvZ2hi9ckKNHly/jHxwMmo/Mz0e/bSuxW7cSs3Ej6piFec34KnpGe6hprKG6sRp7pz0oB2mZYRmWPAuWXAsrEle8+gODJEFrPdT9B7j9O/BN9hrTxUPnXSGWZgNJkvD7R1+/8A1Qq6Nf+0myr68Pl8sVJHKOHTs2bdHzfamsrHzOtFcgEEyPiXY37tp2Rq51IY1PvjFoVcSsTUFflk5kXnzIokh+v4+nNxq4afsKZ30dkiRHraLjE1i7q5y1e/ZiSAtP/xnJL9H2yMX9K+04GrrxjAfeBDOWJbCiNJ1lJalExS6cUv+pnkfDFy/ivnCRCaczaF4dH49+82ZFIEVkzo8cm1DT4e7A1mijurGaa13XlCo2kHOQLHkWLHkW8hOm4U86MQK3q2SR1H4jMJ5eDBv/Caw9AJGhqxINBYtGLPn9o5w5uzase7y18xYazas/ZRw8eJCjR4/y8ccfA2Cz2TCbzWH3dLNarRw5coTe3t6w7iMQLBQkj4+RWz24r7Qz0TSkjGuTo9GXphNjSkOjD51ocLv6uX26mps1XzHY3aWM5xSupbh8H8tLN6PRhkekuDpHeFDbwYMrHQw90wMqPjmKVZszWFGaTkJKdFj2nmmm0/Moet069Fu3ErttK1Fr16IKU/RurtM82IytSRZIt3puBc0VJxcrAiknLmd6T9jzGOz/Ea5/CmMD8phGB2t+Bhv/KWSZYI7mui0asTRXOHToEHv27FHEktVq5fDhw9hsNmVNZWWl8riiokIxz53yd7NYLDif+fQztd5oNGK1WhXfOIFA8N3xdI/IFW0NnfhHJvMv1Cqii5LQl2WgK0gIWRRJkiSa79zkRvVJHtddxj+ZDxOlj6XorT2s3bOXpKxpvhF9R8ZHPDyyd/HgSjsdzsBVU2SUhmXmNFZuSicjhN/rbOLt759Myj7/8p5H27bJPY82b0LzGuuLhYokSdztvUtNUw2nm0/z2PVYmVOhYkPqBsrzyrHkWabfXdvnhYdfyVEk5+nAuCFPjiJt+IcQM/ftWxaNWFKro3lr563XL3zDPaaD2WymoaGB/Pz8567GqqqqcLlc1NfXA1BeXo7ZbMZutwPgcMht8Y8fP66sdzqd1NfX43K5qKysxGq1hvLbEggWPJLXz+jdXty17Yw7BpRxjUGHviwdvTkdTVzoyr5Hhwa5c8bGzZqv6W9vVcYzVqxinWUfKzZvIyIy9D2J/D4/TXf7uH+5g6c3e/B5JxPTVZBTmMSqzeksLU5GO8/zkCSfj9GbN3Gfv8Dw+fOM3b4t58dMsph7Hn0bj89DXWcdp5pOcab5DJ0jncqcRqXBnG6mPLecPXl7vlujyKFOaPgN1P+vMDj1M66CFe/IUaSCPTCPkuFnTSxVVVXxySefKKIA4OjRo0oCdKiTkFUq1WuvyGaKiooKrFYrJpOJioqKoLnq6mrKy8uVxyUlJdhsNhwOR9C4cdJIsbq6GqfTyYEDBwBEVEkg+I4MXWhl6Ewz/uHJqxgVRK0yoi/LIGpFIip16KJIbQ/uccN2kodXLuCbvPqJiIqmcPsuii17SV0Snn+/PS1D3L/cwcOrHYwOBa6ckrL0rNyUwYrStHnfMNLb3S1XrZ0/x/DFS/gHBoLmdatWEbt926LsefRthieGudB6gVPNpzjfcp5hT6BYIVobzbasbezK2cWO7B0k6L5Dx3dJgqbLchTp7t+Df/JnLSZJjiCZ//G0k7ZdIxNU1bfwh+utfPbPNhEfNbt5ctMWSy6Xi6NHjwIoV0ggix6QE5fz8/OxWCzTer79+/cHRUCmcnYsFgtWqxWn07lg3/hLSkqw2+3Y7XZqamqC5kwmE1arlf379wPy62u1WjEYDFRXVytXcn2TrtQmk4m+vj5OnDgBEPbcJ4FgoSGN+/APe1DHRaLfKBvZag1RIXv+8RE3d8+f5mb1SXqaG5Xx1CUFrCvfx6qtO4iMDv0HudGhCR7UdnD/Sge9Lc+8GcZFsGJjOis3pZOcE7r2BjON5PEwev06w5PRo/F7wR2z1fHxstfa9h3ot24lIi11lk46N+ga6eJM8xlONZ96rsQ/KSqJt3LeYnfubsoyytBpvqNwHh+Cm8eg7j9C193AeHapHEUq/CuIeP2/KUmSaGhy8WltI3++2c7EZOTzD9da+cXmJd/tTCFm2mLJZrPR29tLUlKSMuZ0OqmurlZET3l5+bTF0rcxGAwcOnRIiS4tVKE0RUVFBQ6H47kquEOHDuFwOCgokHtSVFZWKq9pdXU1BQUFWCwW5fWZWm8ymTAajZSUlLwwKjeV7wTy39uUuBIIFjv60nS0qTFEFxpRhbBPUKfzMTeq/8K9i2fxjssl0dpIHau27qDYspf0gteUVX8Ppq7Z7l1q5+mNHvyTvmxqrYqlxcms2pRBTpERzTzth+Tp6GD4/Hnc587LZf3Dw0HzUWvWELtjO/pt24kuXotKu2gyTZ5DkiScA05ON5/mVNOp5xK0l8QvYXfubnbl7KI4pRi16nv8THTdkwXSjd/CxGQRRESMXM228Z9AxrppPc3QmIc/XG/j0yuN3O8IFFMUZsTzDzbl8eP1s1+BOO2fpP379ytl71PYbLagN3uDwYDNZsNisVBVVaVEP6YwGo1KxORlHDp0iIqKigUZWZrKNwKUCNGL5n7961+/UPC8TOBM58pSiCOB4MVo4iKJWRuaho6esTHuXTzLTdtXdDofKeNJ2bkUW/ZRuGMXUfrQWZ5M4eoc4d6ldu5faWdkINA1OXVJPKs3p7PMnEZUCCv3Zgr/xASj9fUMn7+A+/x5xh89CprXJCai37Zt8nptK9pnPswvRjw+Dw1dDZxtOcvZ5rM0DTUFzRenFLM7Zze7cndNr8T/RXgn4P6fZZHUeCEwnrRMjiKt+wCiDdN6qtutA3xa28Qfr7cyMiEXN+i0an68LpOPNuWxLnvuFBi8kex2OBxBkSaj0aiIqdeJom9TVVWFwWDAYrFQUFBAVVVV0HXfs4yPjzM++UkNYPBbTcMEAoFgJuluespN20nunjvNxKhseaLRalletpV15fvIWlUU8l/6E2NeHA1d3LvUTvvjQH5OVGwEKzels3pzBklZoRdm4WaipQX3+fMMnzuPu7Y22G9NrSa6uBj9ju3Ebt9OVFHRouuY/W36xvq40HqBs81nudR2KSj/KEIdwaaMTezK3cVb2W+REpPy/TcaaIX6/w0a/g6GJ5PAVRpY9QNZJC3dOa2y/9EJH3+62cantU3caHYp4wUpej4qy+O9kmwSYuaesA95jPLb0aSXYbPZcDqdVFVVsX//fiwWCzabjaqqKhwOxysruj755BN+9atfherIAoFA8J3xTkzwsPYiN6pP0vYgkKdhSMug2LKXorcsxMR/h+TYaTBlXnvvUjuP6rvwTjaNVKkgd00Sq7dksGRtMhrt/BEQ/rExuSnk5PXaxNOnQfOalGRit22Xo0dbtqAJcwPfuY4kSTzsf8i5lnOcbTnLze6bQQ0ijVFGdmTvYGf2TjZnbkYf8QbNHSUJnpyVE7bv/wWmOnXHpkHJX4PpH0FC1rSe6nHXEJ/WNvFFfQuDY3K+VIRGxd41GXxUlkvZUuOciSK9iDcSSwUFBUHXclNJ3tPBYrEEXT0ZDAYlGvW6qNThw4f55S9/qTweHBwkJyc8vUgEAoHgWfraWrlpO8mdszWMDcv5FSq1mmUbN1Fs2UfemnUhj3a4B8Z5cKWDe5facT1j1puQGs3qLRms2pSB3jB/qtkmmpoYPnOW4fPnGbl6FemZmwK0WmLWr0e/Ywex27ehW7VqTr+JzgRj3jGudlxVBFKHuyNofrVxtSKQipKLvl/+0bOMuuDG5/JVW+8zV5952+RcpFXvgvb11YTjXh9f3+nk0yuN1D4JBFJyjNF8WJrHAXM2ybHz4+f2jcSSxWKhsrJSeex0Or93gvd3QafTodPNjxdYIBDMf3xeD4/rarlp+wtNt28q43FJKRTveYc1u8qJNYY2X8bn89N4q5d7l9ppvN2LNJmsrdVpWGZKZfWWjHnTNFKamGCkvp7hs+cYPnuWiSdPgua16enEbt+Ofsd29Js2oYmLm6WTzh063Z2cbz3P2eazXGm/wpgv0Fk9ShPFpoxN7MjZwfas7dNvEPk62m/KUaRbJ8AzKcojY2Hdz+WrttTV03qapt4RPrvaxAl7M71uOYdOrQLL6jQ+2pTH9mXJqEPUkmOm+E7VcNXV1bhcLvLz89m/fz/5+fkcPHhQSeY+fPhwOM8qEAgEM8pAVye3Tn3NrVPfMDLgkgdVKvI3mCm27GPpBhNqdWgbOPa2DXP/UjsPaoN7ImUUJLBqSwbLTKlERs39Ki9vdzfD584xfOYs7kuX8LvdgUmtlhiTidgdO4jdsZ3IZcvmhegLJ37Jz93eu0py9r2+4FYIaTFp7Mzeyc6cnZSmlxKlDVF7C88Y3P2jLJJargbGUwvlKFLxQdC9Xrx6fX5q7nfxaW0T5x52B84dr+PnG3P5eWkOGQnz1zJn2v/iLBbLC6NG3zWRWyAQCOYyfr+PJ9fs3Kg+yZPr9UrnZ70hkbW732bt7neITwltz56JMS+P67u4e6GNzieBgpWY+EhWbU5n1eYMEtPnlrHot5H8fsZu3VKiR2N37gTNa5KTid2+ndidO9Fv3SKiR8DA+ACX2y5zvvU8F1sv0jsW8O5UoWJtylpZIGXvZEViiFtN9DfK3bUbfgMjk/uqtXJPpI3/FHI3Tythu31glN9ebeZYXTMdg4Ho144VKXxUlsueValo52mrimeZ+x9PFhAFBQVKh/JnOXLkCJWVlfT39z/Xd+llmEwmampqpr3e5XJhs9moq6sLeXd0gWAhMNTXw+1T1dw69Q1DvYFPxrlr17OufB8FpjI0IezbI0kS3U1D3LnQxqOrnXgmk7XVahV5a5NYvTWTvCIj6jn8RuMbHMR98aKSf+T7VoFP1Nq1xO7cSezOnUQVFS76yjVJkrjfd5/zree50HqBG9038Et+ZV4foWdL5hZ2Zu9kW9Y2kqJD3ArB7wfHKaj79/Dwa5hKDI/PAtM/hpJfQFzaNJ5G4tyjbj6tbaLmXieTN8Qk6SM5YM7hw9JccpPmhmNGqBBiaYaZ6lX1rMg5duzYtEXP96WysvI5HzqBYLEj+f003rrOjeqTOOprkfzyG1dUXDxr3rJQvOcdEjOmV+0zXcZHvTys7eDuxTZ6mgNl3gmp0RRuzWTV5gxi4uemFYckSUw8fszw2bMMnz3HSEMDTJr/AqhjY9Fv3SoLpB3b0SaHpn/VfGZwYpDLbZe50HqBC60X6BkNNvEtSChge/Z2tmVtoyS1hAhNGMrmR11w/TNZJPUFTNjJ3yVHkVbsBc3r5UDP8Dgn7C18drWR5r5RZbxsqZGPNuXxTlEaOu389hV8GYtGLEmSxIjf//qFb0CMWv3aMOnBgwc5evSo0kPKZrNhNpvDblNitVo5cuQIvb29r18sECxwRgYHuH26mps1XzHQGagsylpVyDrLPpaXbUUbQu+wqZL/uxfaeFzfhdcj/y7SaNXkb0ihaFsmmSsMczJvxz82xkhtrSyQzpzF09YWNB9ZUKBEj2JKNqCKmHs9cmYSSZJ40P+AC60XON9ynhvdN/BJAUEZrY2mLKOM7VmyQMqMDWN36s67skC6cQw8kzljugRY/6Gcj5S8/LVPIUkStU/6+LS2ia9ut+PxyWGk+Cgt75my+agsl2WpC/9KddGIpRG/n4Jzt16/8A1w7FiLXvNqVX3o0CH27NmjiCWr1crhw4ex2WzKmsrKSuVxRUWF0u17yrLEYrHgdDqfW280GrFarQuu87lAEAokSaL13p1JI9uL+H1yr5fI6BiKdu6h2LKX5Jy8kO45Nuzh/pV27l5sp789kOBszNRTuDWTlZvS52RnbU9XF8NnzjB8+gzuy5eRxgK5KKrISGLKymSB9NZOIrOzZ/Gkc4OhiSGutF/hfIuce9Q12hU0n5+Qz7asbWzP3k5JagmRmjBGDn1eePAlXP338PR8YDxlNZQdgrXvg+71zUoHRjx80dDCp7WNOLoDP7vrcwx8VJbLu8WZREcuzCjSi1g0YmkuYTabaWhoID8//7mrsaqqKlwuF/X19YDst2c2m7Hb7UDAFuX48ePKeqfTSX19PS6Xi8rKylc29BQIFhtjw8PcPVfDDdtX9LU2K+PpBcspLt/Hqs07iIgKnXGu5JdofdjP3QttOK534/dOlvxHqllmTqNoWyZpS+PnVBRJkiTGHz5k+NQphk6fYezmzaB5bXq6Ej3SbypDHbOw8lG+K1ONIS+0XuB863ludN3AKwWMaaO10ZSll7EtaxvbsreRFRvaq9wXMtwtd9e2/ycYbJXHVBpY9UMoPQRLtr02YVuSJK43u/i0tok/3WhjfNLINiZSw082ZPFhaS5rskLbaHW+sGjEUoxajWPH2rDvMR0qKiqwWq2YTCYqKiqC5qqrqykvL1cel5SUYLPZcDgcQeNGo1FZ73Q6OXDgAICIKgkETF57PX7IjeqTPLh0Dq9H7vWi1elYve0t1ln2kZa/LKR7ugfGuX9ZjiINdgfyOVJy4yjclsnyjWnooufOr1xpYgJ3XR3Dp04zfPr0c9drUcXFxO3eReyuXehWhN70d74xPDHMlfYrikDqGgmOHi2JX6JEj0xpJnSaGeoF2FIPV4/Cnd+Bb9IXMCZZ7q5t/seQ8PrI3/C4lz9eb+XTK03cbQ9UY65Kj+OjTXn8ZH0mcVFzLwI6k8ydf7lhRqVSvfaKbKYoKSnBbrdjt9upqakJmjOZTFitVqUlQ1VVFVarFYPBQHV1tXIlN2UrYzKZ6OvrU4xyw537JBDMZSZGR7h34Sw3bCfpfhq4qk7OXcI6yz5Wb38LXUzoSvD9fonmu33cvdDG05s9+CfLgiKiNKwoTadoWyYpuXMnn8PncjF87hxDp0/jPnc+qPeRSqdDv2ULsbt3EbtzJxGpoW2PMN/wS37u993nUtsluXLtW9GjKE0UpRmlcvQoaxs5cTPoIuEdhzu/h1ortDUExrNMchSp6Kegfb1Yu9s2yGdXG/nDtTaGxyevpbVq3i3O4KOyPEpy52Ye3WywaMTSXKOiogKHw/FcFdyhQ4dwOBwUFBQAcj7SVH+r6upqCgoKsFgsSgRpar3JZMJoNFJSUvLC1gBT+U4gd1qfElcCwUKg66lTNrI9fwbPmBzV0UREsHLzdoot+8hcEVrLjKG+Me5daufepTaG+wJWHen58RRuy2SZKY0I3dz4cDbx9ClDk9Gjb1evaZKTidv1FrG7dqPfvAl19PxtGhgKekd7udR2iYttF7ncdpm+seBWCFPRo21Z2zCnm2cuejTFQIt8zVb/dzAyWVWniYQ178HGfwbZptc+xZjHx5c32/m0tpGGJpcynp+s58OyXPabsjHEzM1qzNlEJUmS9Pplc5vBwUESEhIYGBggPj4egLGxMZ48ecLSpUuJCmE+wkJHvG6C+YJnYpyHly9wo/ovtD96oIwnZmSxrnwfhTt2Ex0XH7L9puxH7l5oo+lO71SvSnQxWlZuSqdwayZJWa9PnA03ks/H6PXrDJ8+zdCp00w8UwwCoFuxgtjdu4jbvZuoNWsWde8jj8/D9e7rXGy9yKW2S891zY7RxlCaUcrWzK1szdxKTvwseJBKEjy9AFetwWa28Vlg/q9kQ9vYlNc+jaN7mM9qm6iqb2FgVO4Mr1WreGdNOh+V5bI5P2nRRZFepB1ehogsCQSCeUVvazM3bV9x56yN8clrJLVGw7LSLayz7CWnqDikv/QHe0e5e6GNexfbGRmcUMazVhgo3JZJ/oYUtBGzG0XyT0zgvnSJIZuN4VOng5tDarXoSzcSu2s3sbt2EZk9A8nGc5jmoWYutl7kYttFrrZfZcQ7EjS/2riaLZlb2Jq1lfUp68PT92g6jA/DzWNyVVv3MyJuyXb5qm3lD17bG2nC6+ebux18eqWJy85A25gsQzQfluVywJxNapz4UDwdhFgSCARzHp/Xw6Orl7lZfZLmu4EWIPEpqRTv2cuaXeXoDYkh28/v8/P0Vi93zrfRdLdXaXQcHRfBqs0ZFG7NxJA2uxVhvuFhhs+eZchmw332HP6RwJu+Oj6e2J07idu9C/22bYvaWmTEM8LVjqtK9KhpqClo3hhlZHPmZrZmbmVz5maSo2e5kWavQ/Zpu/YpjA/IYxF62cy29J9Ny8y2uW+Ez682cdzeTM9wwMh296o0PtqUy47lKWjmmZHtbCPEkkAgmLO4Oju4VfMVt05XMzoov3GoVGryTRtZZ9lH3roNITWyHe4f4+6FNu5ebMftCuQiZa9KpGh7FkvXJaPRzt61lbenh6FTpxiy2Ri5fAXJEzDa1aalEbdnD3GWPcRs3Lhom0NONYWcEkcNXQ14/YHEbK1Ky7rUdWzL2saWzC2sMq5CrZrlq0hJAucZqP1fgm1IjAWyQFr3AUQbXvkUXp+f0w+6+bS2kbMPu5Vr4tQ4HT/fmMPB0lyyDIs7J+1NWPBiaQGkZM0o4vUSzDZ+nw9nQx03bCd5eqMhYGSbaGTt7ndYu/tt4pNfn6Mx7f38Ek135ChS460e5U0mKjaC1ZszKNyeiSF19qJIEy0tDFXbGLLZGG0IvB4AkUuXEmexEFduWdT5R31jfVxuu8yltktcarv0nKVIVmyWIo5K00uJjZz93DIAJkbkq7Zaa/BV2/K3obQCCnbDa/5OOwfH+O3VZn5b10T7QKB56PblybKR7eo0Iuawv+B8YcGKpYiICFQqFd3d3aSkpCy6xLXvgyRJdHd3o1KpiFikn0oFs8dQXw+3ar7h1qmvGe4L5FfkFW9gXfk+8ktKQ2pk6x4Y597FNu5cCK5oy1phoGh7FvnrU9BEzPybzFSDyCmBNH7/ftB81Jo1ikDSTVbNLjY8fg83u28q0aO7vXeRCIjIaG00pemlSu5Rblzu3HoPGGiRc5Ea/g5G++WxyFjZhqS0ApJf3QPM75e46Ojh0ytNVN/rxDfZsiIxJoL3zTl8UJrLkuTQtcgQLGCxpNFoyM7OpqWlhadPn872ceYNKpWK7OxsNHOkJ5VgYSP5/TTevMYN20kc9VcVI9vouHjW7Cpn7Z53SEwPnXeW5Jdovt/HnfNtPLnRgzT5JqOL0bJqcwZF2zNJTJ/5NxlJkhi7eZPBr79hqLoaT3Og0zgaDTFmsyyQLHuIyMiY8fPNBVqHWxVxVNtey7BnOGh+ZeJKtmRtYWvmVjakbgivpcj3QZKguRau/Du496dAVZshD8oqYMM/gKhXd8fuHR6nqr6Fz6420dgbyFErXWLko025vFOUTtQsFxssVBasWAKIjY1l+fLleJ651xe8moiICCGUBGFnZMDF7TM2btpOMtDVqYxnr15Dcfk+lpduQRvC6ObI4AT3LrVx90Ibgz2Bq4qMggSKtmdSUJKKdoZ9riS/n9HrNxj6+msGv/kGb3u7MqfS6dBv20acxULsWzvRJoYueX2+MOIZwd5pl/setV7k6eDToHmDzqAkZm/J3EJKTOiuZkPKVAPJK/8O2q8Hxpdsh03/NazYC6/Iu5Mkibqn/Xxa28jJWx1M+OQPFHE62cj2w7JcVqQt3gT+mWJBiyWQI0zizV8gmH0kSaLl3m1ufPMXHl29rBjZ6mL0FO7czTrLPpKyc0O6X+uDfu6cb8N5vRv/pFt6ZLTcF6lo28z3RZL8fkYbGuQI0jff4O0MCEV1TAyxu3YR9/bbxG7ftuj81yRJ4pHrEZdaL3Gh7QINnQ14/IEPuhqVhnUp65SrtdXG1WhCmNwfcoa75AaSdf8R3JPWKBodFL8PZf87SF/zyi8fGPXw+4YWPq1t4lFXIIq2LjuBj8ryeHddBjGRC/4tfM4gXmmBQBBWFCPb6pP0tbUo4+nLVrDOso+VW7YToQtdr5fR4QnuX+7gzvlWBroCHm1pS+Mp2p7JMnMaETMYRZJ8Pkbq6xn66muGqqvxdncrc+rYWGJ37yL+nXfQb9uGWjfDHaFnGdeYS/Fbu9x2ma7RYL+1TH2mcrVWllFGXOQ8iKC0XZer2m5/EfBqi8uAjf8UTP8Y9Emv/PIbzS4+rW3k72+0MeaZvJaO0PBX6zP5qCyPtdmL08h2thFiSSAQhIXhvl4u/PY/BxnZRuiiWL3tLYote0NqZCtJEu2PXdw+14bjWhd+77c82rZnkpIzc2+0ktfLiN3O4FdfMVRtw9cbSFhXx8XJJf7vvI1+61bUkXMstyaMeP1ebvfc5mLbRS62XuR2z+2gxOwoTRTmdLN8tZa1haXxS+dWYvbL8HnhwZdw5X+BpkuB8SyzfNVW+FfwiuaW7nEvf7rRxqe1TdxqHVDGV6bF8dGmXH6yIYv4RW5kO9sIsSQQCMJCRFQ0D69cwOuZkI1sy3/A6m1voQvh9dKY28ODK3IUqb8jkPCakhtH0fZMlm9MIzJqZn7NSV4v7tpahr7+hiGbLaiLtjohgTjLHjmCtGkTqkUkkDrcHUrH7CvtVxiaGAqaX2ZYpogjU5pp5v3W3oSxAdmn7epRGJhMyldrofAnskjKNr/yy+93DPJZbRO/b2hl6Bkj2x+uzeCjslxMeYnzQywuAoRYEggEYUEXE8Puf1yBMSubjOWhM7KVJInOJ4PcPtfK4/oufJNXFdpINSs2plG0I4vUvNB5wr3yLFM5SH/5C4NffR0kkDQGA3HlFuLe2Yu+rHTRNIkc845R31nPhdYLXGq7hHMg2JsuPjI+qGN2uj59lk76Bria5au2+r+DKfEXkyRfs238JxD/8grOMY+Pk7fb+fRKE/bGfmV8SVIMH5Xl8Z4pG6N+8Yjp+YIQSwKBIGys2VUesucaH/XysFaOIvW2upXxpKxYirZnsqIsHV10+H+lSZLE2O3bDH75FwZPngxK0tYkJhJXXk783neIKS1FFcK+UHMVSZJwuBxcbJPL+us76xn3BfpWqVVq1iavVaJHa5LWzO3E7FfR2gCX/79w5w+B0v+UVbD5fw9r34eIl+fePelx81ltIyfqW3CNBIxs3y5K46OyPDbnJ6EWFiRzloX/L1kgEMxbJEmiq3GIO+daeWTvxDshR5E0EWqWm1Mp2p5F2tL4sF9VTDWKHPzLSQb/8pegPkjquDhZIP3gB+g3lS0KgTQwPsDl9stcapU7ZneOdAbNp8WksTVLLunflLGJBN08Tkr2++HR13Dp/wONFwPjS3fCln8JBXte2mXb4/NTfbeTT2sbufg42Mj2g9Ic3jfnkBovjGznAwv/X7VAIJh3TIx5eXi1kzvnW+lpDpRNJ2boKdqeycqydKL04b/WGn/yRL5i+8tJJhwOZVwVHU3c7t3E//AHchXbAs9BejYx+1LrJW733sYv+ZV5nUaHOc2slPXnJ+TP/1wbzyjc+Bwu/8/Q+0geU2thzXuw+V9ARvFLv7TVNcrntU0cszfTPSRH2VQq2LUylY/KcnlrZaowsp1nCLEkEAjmDN1NQ9w538rDq514xuVrDo1WTUFJCkU7ssgoSAj7m7CntZXBkycZ+MtfGL8b8OtSRUYSu3MH8T/4AbE7dy74PkjTSczekimX9ZeklRClXSARkuFuqPv3UPcfYGQyGqRLAPM/kq1IErJe+GU+v8TZh118eqWJ0w+6mGwOT3KsbGT789IcshMX9s/MQkaIJYFAMKt4xn08sndy51wrXY2BN2RDWgxF2zNZtSmDqNjwRpG8/f0MnjzJ4J/+zOi1a4EJrRb9ls3E/+AHxO3ZgyZuHvT5+Z6Mecewd9oVS5EXJWZvytikXK/Ny8TsV9H9UM5HuvFbmMq5SsiFzf9ctiLRvfjvvmtwjOP2Zj6/2kyrK9DXa+uyJD4qy6O8UBjZLgRmTSxVVVXxySefUF9fHzRmMBhoaGjg448/nq2jCQSCGaC3dZg751p5UNvBxJgcRVJrVORvSKFoexZZKwxhjSL5R0cZPn2agb//E8MXLoBXLt1GpSKmtFQWSG+XL1irEUmSeOx6rNiJ1HfWM+GfUOYXVGL2y5AkaLwEF/+tnJc0RWaJnI+0+segef5t0u+XuOzs5dPaRr6504l3MoxkiInggCmbD0pzyU+Z2e7wgvAybbHkcrk4evQoQJCQqaqqAqCvr4/8/HwsFsu0nm///v1YrVblsdPpxOl08vHHH+NyuXA6neTn50/3eAKBYB7gnfDxuKGLO+fa6HAGmu/FJ0dRtD2LVZsziIkPX/6P5PMxUlvLwN//iaHqavzuQFVdVGEh8T/+EfH7fkBEWmrYzjCbTCVmT0WPukaCO2an69MVr7WyjLL5nZj9Kvx+ePgVXPh/QcvVyUEVrPwBbPkXkLtZTjL6Fv3uCcXI9klP4GfHnJfIR5ty2bcmQxjZLlCmLZZsNhu9vb0kJQVatTudTqqrqxXRU15ePm2x9G3y8/Opq6ujvLyc8vJy9u/f/72eRyAQzD362t3cOd/KgysdjI/IERyVWkX+umSKtmeRvSoRVZgSXiVJYvzePQb+9GcG//znILuRiKws4n/0Lgk/+hG6goKw7D+bTCsxe7Jj9tbMrSxNmCcds78vPo9sQ3Lhf4LuyXw0jQ7WfygnbSc/31VekiTqG/v5tLaJL2+1M+GVX79YnZaflWTxYVkuq9Jnpq+XYPaYtljav38/fX19uFwuZcxms2EwGJTHBoMBm82GxWKhqqqKvmcatAEYjcaXiiCXy8XGjRspKSmhoqICi8VCSUnJd/tuBALBnMHn8eO41sWd8220PXIp43HGKAq3ZbJ6awb6hPB1a/a0tjLw5y8Z+NPfM/E4UMmmTkggft9eEn78Y6I3bFhw4qB9uF3pebSoErNfxcQIXPsvcvn/QJM8FhknN5Dc9F9D3PP5V4NjHv5wrZVPrzTxoDPwGhZlxvMPNuXx43WZ6HUi7Xex8EZ/0w6HIyjSZDQaFTH1XSNDx48fZ//+/eTn51NdXU1VVdVLxdL4+Djj44GmZ4ODg9/98AKBICy4Oke4c6GN+5faGXPLzfdUKshbm8yaHVnkFBrD1nzP53Ix+PU3DPzp7xm1B/IhVZGRxO7eTcKPf0Tstm0Lym5k1DuKvcMu5x61XeTJwJOg+QXRMfv7MtoPV/8D1P67QGWbPgU2/XMw/1cQbXjuS263DvBpbSN/vN7GyIScSxcVoebH62Qj2+Ls8FdkCuYeIZfF344mvQybzYbT6aSqqor9+/fz/vvvc/ToUUpKSnC5XBw6dOilX/vJJ5/wq1/9KlRHFggEb4jP6+fJjR5un2ul9UHAwiE2UcfqrZkUbs0gNjE8EQzJ42H4/HkGfv97hs6cBY8s0FCpiCkrI+FH7xL39tsLppJtOonZxcnFbMmSo0dFSUULLzH7dQy2w5X/H9j/V5iY7NNlyIOt/w2s/wgiooOWj0x4+fONdj6tbeRGSyCXbnlqLB+V5fLTkmwSoheHXY3gxbyRWCooKAi6lptK8p4OFosFxzNN3gwGw7Qr4A4fPswvf/lL5fHg4CA5OTnTO7RAIAgZgz2j3LnQxr2LbYwOTYkUyCtKomh7JnlrklCHqWx67N49XL//PYN//jLIk023ahUJP3qX+B/+kIj0hRFFcY25uNJ+Rble+3ZidoY+Q2kIWZZRRnzkIs2hcTXB+f8nXP8UfJMCMm0NbPs/yOa236pse9g5xGe1TXzR0MLQ2KSRrUbNvrXpfFSWx8YlwshWIPNGYslisVBZWak8djqd3zvB+7ug0+nQ6eaRM7VAsIDw+/w03u7l9rk2mu72wmTzvZj4SFZvzaBwWybxSdGvfpLvibenh4E//ZmBP/yB8QcPlHFNcjIJP/oRCT/5K6JWrgzL3jOJz+/jbu9dLrRe4ELrBW713EKaeqGBKE0UpnSTnJidtZWl8Qs8Mft19D+dFEmfgX9StOdukUXS8vKgyrZxr4+vbnfw6ZUmrj4NiOy8pBg+LM1lvymbpFjx/iII5jtVw1VXV+NyucjPz1fyiw4ePKgkcx8+fDicZxUIBLPIcP849y61cfdCG8P9gZzB7FWJrNmRxZJ1yWjCEEXyT0wwfOo0A3/4A8Pnz4NPziNRRUQQu2cPCT/5KzkPaZ57svWO9nKp7RIXWi9wqe0SrnFX0PwywzKl55EpzYROI97Q6XsC5/9HuZGkf7JP1tKdsLMSlmwNWvq0x83nV5s4Ud9Cn1uOOmnUKspXp/HRply2FiQLI1vBS1FJkiS9ftncZnBwkISEBAYGBoiPX6ThZ4EgDEh+ieZ7fdw+18rTW71Ik833ovQRrN6SQeH2TAypobdwkCSJsVu3GPjDHxj48i/4BwJ5JFHrijH85CfE79uH5plq3PnGVFn/+dbzXGy9yJ3eO0HzcRFxbMrcxLasbWzN3EqaPm2WTjoH6XXA+f+HLJIkWTxTsFsWSbmblGUen5+ae118WtvI+Uc9ynhGQhQflOZycGMOacLIdtHyXbTD/P4oJhAIwsLI4AT3L7dz53wrgz1jynjGsgTW7Mgif0MK2jA03/N0djLw93/PwB/+GGRcq01LI+HHPybhpz9BN4+b1XaPdHOh9QIX2y5yue0ygxPBlbyrjavZlrWNbVnbWJuylgi1SCoOoucxnPs3cOs4TPWLWmaRRVJOqbKszTXKb+uaOVbXROdgwMh254oUPirLY9fKFLTCgkTwHRBiSSAQAHI0p+2RizvnWnFc68bvk6NIkdFaVm5Kp2h7JkmZobdw8I+NMWSrYeAPf8B96ZLcXRlQ6XTElZeT8NOfoN+0CZVm/lV0efwebnTdUATS/b77QfMJugS2ZMiJ2VuztpIcnTxLJ53jdD+URdLtqoBIWv62LJKyzYBsZHvuUTefXmni1P3OZ4xsI3nfnMMHpbnkGIWRreD7IcSSQLDIGXN7eHClgzvnW+nvGFHGU5fEs2ZHJsvMaUREhlaoSJLE2N27DHzxBQN//hL/M73Sok0mEn7yV8Tv3Tsvy/073B1cbL3IhdYLXGm/wrBnWJlToaIoqYht2fLV2trktYuvrP+70OeEM/93uHkcpZJgxT7Y+TFkyX34uofGJ41sm2jpDxjZbs5P4qNNubxdmE6kVkSRBG+GEEsCwSJEkiQ6nwxy51wrj+q78HnkT+tanYYVpWms2Z5FSm7ohYq3v5/BP3+J64svGL8fiLJoMzMw/OQnJPzVXxGZlxfyfcOJx+ehoatBqVx77HocNJ+oS2RL1ha2ZW1jS+YWjFHGWTrpPGKwHc4dgYbfBBK3V/5QFkmZ65EkicuOHj6tbeLr2x2KkW1CdAT7J41sl6UKI1tB6BBiSSBYREyMeXl4tZPb51rpbQlEPJKy9KzZkcWK0nQio0P7a0Hy+3FfvszAF18wVG1DmmwaqYqIkK/Z3vsZ+s2bUannz6f/9uF2zree53zreWrbaxn1BiIaapWatclrldyjwqRC1Kr5873NKiN9srnt1aPgncyVW2aB3f89ZG6g3z3BF+edfFbbhPMZI9uSXAMfleXxw2JhZCsID0IsCQSLgO6mIe6cb+Xh1U4843L1kCZCzTJTKmt2ZJG2ND7kfXomWloZ+P3vcf3+d3jb2pVx3apVGN57j4QfvTtvqtm8fi83um9wruUc51rOPRc9SopKYmvWVrZnbWdz5mYSdAmzdNJ5yvgQXP6fZe+2KS+7nE2w518h5W2hoamfT49d58/PGNnqIzX8tCSLD0vzKMwUVdCC8CLEkkCwQPFM+Hhs7+T2uTa6ngZyggxpMazZkcXKTelE6UNbbeUfH2fIZmPgiy9wX74Ck51J1PHxJLz7Lgnv/YzooqKQ7hku+sb6uNh6kXMt57jYdjHIkFatUrMuZR3bs7azLWsbK40rRfTo++AZA/t/lNsATHm3pa2FPf+KoZy3+MP1Nj79w3nudwQb2X5UlseP12cSK4xsBTOE+EkTCBYYfW1u7pxv5f6VDiZG5XwPtUZF/oYU1mzPInOFIeRRpLG7d3F98TsG/vznoJ5IMZs3YfjZe8SVW1BHze1+NpIkca/vHudaznG+9Ty3uoO7Zht0BrZmbWVH1g62Zm0V0aM3weeRLUnOHoHBVnnMWAC7/8/cStjNZ3XN/PG/nHrOyPbDsjzWCSNbwSwgxJJAsADwefw4rndx51wbbY9cynhcUhRF2zNZvSWTmPjI0O45MMDAn/8sJ2vfvaeMazMyMPz0JyT87GdEZmeHdM9Q4/a4udJ2hXOt5zjfcp7u0e6g+VXGVWzP2s6O7B2ici0U+P1w53dw+m+hb7KPVnwW49s+5o/SDv7LmTZutlxSlgsjW8FcQYglgWAeM9A9wp3zbdy71M7Y8GTitAqWFCezZkcWOauNqEJo4SBJEiO1V3GdOMFQdTXShGwboYqIINayB8PP3kO/ZfOc7on0dOCpnHvUeo76znq8U9VWQLQ2mk0Zm9iRvYPtWdtF1+xQIUnw4C9w6n+ArslO5TFJdK3/l1jdOzj+ZQ9D47LgFka2grmIEEsCwTyk8XYvN2qaaL7Xr4zpDToKt2VSuDWD2MTQXnl5e3sZ+P3v6T9xAk9jkzKuW7ECw/73iP/Rj9AmJoZ0z1Ax4ZvA3mHnfOt5zrWco2moKWg+Ny5XFkfZ2zGnmYnUhDYCt6iRJHCcglP/N2hrkId0cdxf+o/42763OH9qHOgAhJGtYG4jxJJAMA9pe9QvCyUV5BYaKdqexZK1SahDaOEwVfLvOn6CoVOnYLLkX63XE//uuxj27ydqTdGc/OTfM9rDuZZznGk+w5X2K0Gl/Vq1FnOaWbleW5KwZNbOuaBpvAyn/q/QeBEAvzaayynv8zcdO2m8HgWMCyNbwbxBiCWBYB5SuC0LUFG4LZOElOiQPrenq4uB3/0eV1UVnpYWZTyquJjE9w8Qv28far0+pHu+KZIk8dj1mDPNZzjTfIabPTeD5lOiU9ievZ0dWTvYlLkJfcTcOv+CorUBTv8P8NgGgE8dyTcxP+T/0vM2PcNyUnxmQhQ/F0a2gnmEEEsCwTwkISWazT8tCNnzST4f7osX5VykU6fBJ1chqWNjSfjxjzG8f4CoVatCtl8o8Pg81HfVKwKpdbg1aL4oqYidOTvZmb2T1cbVczICtmCQJHCekfskOWoA8Kk0/FG1m38z8mPaR5JQqWD3ylQ+KsvlrZWpaEQUSTCPEGJJIFjEeDo7cX3xBa6qqqDGkdEbNmB4/33i976DOjq0kas3YWB8gAutFzjTfIYLrReCfNd0Gh1lGWW8lfMWO7N3khqTOnsHXSz4PHD7d7JI6rwFgB81f/Bt4X/yvkeTlEZyrI5/sTGHn5fmkJ0ojGwF8xMhlgSCRYbk9TJ8/jyu4ycYPntWLucG1AkJJPzVj0k8cADd8uWzfMoAzYPNnG4+zZmWMzR0NuCTfMqcMcrIzuydvJXzFpsyNhETId6Mw44kQft1uPFbuFUFIz0AjKLjt963+I++fbRIqWxdlsT/qSyP8sI0IkKYSycQzAZCLAkEiwRPWxuuqi9wffEF3s5OZTzGbMZw8H3iysvnRONIn9/HrZ5bskBqPoNzwBk0v8ywjLdy3uKtnLdYm7xWdM6eCfx+6Lgp5yHdPA49D5SpLsnA/+Z9m099FtQxiYqRbX6KMLIVLByEWBIIFjCSx8Pw2bP0Hz+O+/wFxX5EYzCQ8JOfYHj/ALr8/Fk+JYx5x7jcdplTzac413KOvrE+ZU6j0mBOM8vXazk7yYnLmcWTLhL8Puh5BE2X5VykJ+dgNPB3Mk4k3/hK+MK3nQv+tWxYksKvyvLYuyZdGNkKFiRCLAkEC5CJlhZcJ6oY+N3v8HYHulLHbNqE4cB+OYoUObv9hAYnBjnXco5TTae40HohqLw/LiKObdnbeCv7LWEtEk78PnA1ycKo9xH0PISu+9BxCzzuoKVj6hgueVfxlc/ESV8Z6OL5mTmLw2V5rEyPm6VvQCCYGYRYEggWCNLEBEOnTuM6cQL3pUuBKFJSEoaf/gTD/v1ELlkyq2fsHunmdPNpappquNp+Fa8U6J6drk9nd85uduXuwpRmIkIt7C1CxtjgpBia+vMQeh9DrwN84y/8EilCT2fsKr4eWckfB1dwU8rHi5bi7AT++7JcfrQuk5hI8RYiWByIn3SBYJ4z0diIq6oK1+9+j6+3VxnXb9mC4f33idu9C9UsRpGaBpuoaaqhpqmGm903g8xp8xPy2ZO7hz25eyhMKhTl/W+C3w8DzcFRoilxNNzx8q/T6CBpGSQvQ0paTpM6mxOtRv7TAy0jQ/KS6AgN+9dn8mFZLsXZhhn5dgSCuYQQSwLBPMQ/McGwzUb/8ROMXLmijGtSkjH87D0M+98jMmd2cnskSeJ+331FID12PQ6aL04uZnfubnbn7mZpwtJZOeO8RpLA1Qidd+Q/XXcnBdJj8I69/Oti0yB5xaQwWgHJy+U/CTm4PRJ/vN7GZ1cbud06qHzJyrQ4PtqUy082ZBEfJSJ9gsWLEEsCwTxi3PkE14kTDPzhD/j6J33hVCr027eR+P77xO7ciSpi5t/UfH4f17quUdNUw+nm00ENIrUqLeZ0M3ty97ArZ5cwp/0ujA1C1z25h9GUOOq8CxNDL16viQRjASRPCqKk5ZPCaBlEPZ/3da99kE/P3uUP19oYHpevRCO1at5dm8FHm3IpyRVGtgIBCLEkEMx5/BMTDH1TjevYMUbq6pRxbVoahvfew/Dez4jIyprxc3n9XuyddqqfVmNrsgVVsEVpotiatZU9uXvYkb1DJGhPh9F+aLsu9zBquyb/v6vxxWs1kZCyEtLWQGqh/P9Jy8CQB5pX/1of8/j48mY7n9Y20tDkUsaXJuv5qCyX90qySdQLM2GB4FmEWBII5igTjY30Hz/OwO9+H4giqdXE7tyJ4f0DxG7fjko7s/+EPX4PdR11fPP0G041naJ/vF+Zi4+M562ct9idu5stmVuI1s6dzt9zjrFBaL8xKYom//Q/efHauExIK4L0NbI4SiuShZHmu0UQHd3DfFbbRFV9CwOjsimyVq3inaJ0PirLZXNBkogiCQQvQYglgWAOIXk8DNWcov/Ybxm5HMhF0qalYdi/H8P+94jIyJjRM3n8Hq62X+WbRlkgucZdypxBZ2BP7h7eznubjRkbRQXbi/B5ofM2tNRB81Voa5Dzi15E4hLI3CD/yVgP6Wshxvi9t57w+vn6Tgef1TZx2RlI/s8yRPNhWS4HzNmkxs1+I1KBYK4za2KpqqoKgLq6On79618DcPToUfLz86murlbGBILFwERLC67jJ3D97nf4emT7CFQq9Du2k3jwILE7dsxoFMnj83C5/TLVjdWcajrF4EQg6dcYZWRP7h7K88rZmL4RrVp85grC3SOLopar0FwniyPPyPPrEnIhc/2kOFovi6M3EEbP0tw3wmdXmzhhb6ZneAIAtQp2r0rjo0257FieIoxsBYLvwLR/y7lcLo4ePQrAxx9/rIxPiZ6+vj7y8/OxWCyvfa6qqioMBgMWiwWn08nRo0d5//33AbBYLFitVpxOJ/lzoLOwQBAuJK+X4TNn6D92HPeFZ7prpyTLuUj7DxCZPXO5SBO+CS63Xeabxm843XSaIU8giTgpKglLnoXyvHJMaSYhkKbweeVqtJarskBqvvri6zRdAmSbILsUss2yQNInh/QoXp+fU/e7+LS2iXOPuqd+nEiN0/Hz0lx+vjGHTIO4GhUIvg/T/o1ns9no7e0lKSlJGXM6nVRXV2O1WgEoLy+flljav3+/8v8Oh4OKigoMBgOHDh1SoktCKAkWKrJHWxWuqi/wdnUp4/otWzAcPCj3RZqhirYJ3wQXWy/yTeM3nGk+w7BnWJlLjk7Gkmvh7SVvU5JagkYtbCwYG5QFUdNlaK6F1obnOl0DkLwScjbK4iinVH6sDo+HXcfAGL+ta+K3V5vpGAy0Dti+PJmPyvLYszpVGNkKBG/ItMXS/v376evrw+VyKWM2mw2DwaA8NhgM2Gw2LBYLVVVV9PX1BT2H0WgMEko2mw2TyURJSYkydujQISoqKkRkSbCgkHw+hs+fx/XbYwyfOyc3EAQ0RiOG936G4cABInNzZ+QsXr+Xq+1XOfn0JDWNNUERpNToVCx5skBan7JeCKThbmi6BI2X5f923ALJH7xGFw9ZJlkUZZfKEaToxLAey+eXOP+om89qm6i534XPL4eRjPpIDpiz+bA0l7wkfVjPIBAsJt4olu5wOIIiTUajURFTz4qiF9HQ0IDL5eLQoUM0NDTgdDqVq7mCggKqqqqCrvueZXx8nPHxQIv+wcHBF64TCGYbT2cXri+qcFVV4W1rV8ZjyspIPPg+cRbLjHTX9kt+rnVd4+STk1Q3VgeV+adEp/DOknd4e8nbrEtZh1q1SKMQkiT7pDVeCgik3kfPrzPkQd4WyCmT/6SshBkSlV2DYxy3N/P51WZaXQEvvdKlRj4qy2XvmnR02kUucAWCMBDyxINvR5NehNPp5MCBA+Tn5/PJJ5/w61//GovFgs1mo6qqCofDoVztvYhPPvmEX/3qV6E8tkAQMiS/H/fFS7iOH2Po1Gnw+QDQJCSQ8NOfYnj/fXT54e9cLUkSd3vvcvLJSb56+hWdI53KnEFn4O28t9m7dO/ivWKTJOi+D40XJyNHl2Gw9fl1qYWyOMrdLP83PnNGj+n3S5x/3MNntY3Y7gWiSPFRWn5Wks1HZbksTxNGtgJBOHkjsVRQUBB0LTeV5P068vPzcTgcz41PRaNeF5U6fPgwv/zlL5XHg4OD5MyStYNAMIW3pwfX736P68QJPM3Nyni02UTiwYPEvf02ap0u7Od43P+Yk09P8tWTr2gaalLGYyNi2Z27m31L91GWUbb4yvwlCbofwNPzk38uwkhP8Bq1Vk6+nhJGOWUhq1D7rnQNjnGivoXPrzbR0h+IIpnzEvmgNJcfFmcQFbEIRa5AMAu8kViyWCxUVlYqj51O57QSvN8UnU6HbgbedASC1yFJEiO1tfQfO8aQrQY8crM/dVwcCT/5CYnvH0C3fHnYz9E82MzJpyc5+eRkkBdblCaKnTk72bdkH9uyt6HTLKJ/N5Ik9zN6cm5SHF0Ad3fwGm20nGs0FTnKNkPk7OX6+P0SFx738FltE7Z7nXi/FUX6oDSXlekiiiQQzDTfqRquuroal8tFfn4++/fvJz8/n4MHDyrJ3IcPHw7nWQWCOYO3v5+B3/0e1/HjTDQGLCmi163DcPAg8fv2oo4Ob5l2z2gPXz35ii+dX3K797YyrlVr2Za5jb1L97IrZxcxETFhPcecQZKgzzkpji7If4Y7gtdoo+Ro0ZLtsHQ7ZJaAdvatPbqGxjhhb+G3dU009wWiSKapKNLaDKIjRRRJIJgtVJI01Y1j/jI4OEhCQgIDAwPEx8fP9nEECxRJkhipq8N17DhD33yDNBVF0uuJ//GPSDx4kKhVq8J6hhHPCDVNNXzp/JLL7ZfxT1ZmqVVqStNL+cHSH7A7d/fi8GKTJLmn0dML8GQycjTUFrxGo5MjR0u2w5JtcuRIOzeia36/xEWHHEWqvhuIIsVFaXmvJJufl+awKl38PhMIwsV30Q6is5xA8Bq8/f0M/PGPuI6fYMLpVMaj1qzBcPB9En7wA9T68F3deP1eLrdd5ssnX3Kq6RSj3kDkoTi5mB/k/4B3lrxDcnRomxzOSfqfBoujwZbgeU0kZG+UhdGS7fL/R8wtO4/uoXFO1Dfz26vNNPUFOnuX5Br4oDSXd4szRRRJIJhjCLEkELwASZIYra+n/9hxhr7+GmlCtoxQxcSQ8O67GA6+T3RRUVj3v9N7hz87/8zJJyeDSv1z43L5Yf4P+WH+D8mLzwvbGeYEw13gPAtPzoDzHAw0Bc+rI+QeR0u3B8RR5Ny7dvT7JS45evnsaiPf3AmOIv1sQxYflOWKKJJAMIcRYkkgeAbfsJuB331B//HjTDwOVGzqCleT+P5B4t99F01s+KJIzUPNfOn8ki+dX/J08KkynqhLZO/Svbyb/y5rk9cuXHf48SG5z5HzjPyn627wvFor5xktnbxWyymb1YTs19EzPK7kIjX2BqJIGyajSD8SUSSBYF4gxJJA8AySZ4Kuf/M/Ink8qKKjif/hD+RcpDVrwiZQ+sf6+frp1/zZ+WdudN9QxqM0UezK3cW7+e+yOXPzwiz1//+3d6dPUV39vsC/NEPL3HTTzGDYzSCCEzhETSKRJtHgfFGf+5xbp+rcQd6dF6lbWr56Kq8srfsP4FP33Pvi1HPjsaPRGIfQGDWjQVAjKlO3yjw2TTNPve+LDbtpB0AFdnfz/VRR0GsRXWS74cvav7XWxBjQcm8qHN2WPnZOuH9O3BpAyAdS84GUDwF12NKP8y04nSJ+s/bgH3cb8cOTdoxPTs0iqQNwMDcRf9mUgtUJnEUi8iYMS0QzBERFQfc//jv8o6MRuXcv/MMXZ5n2yMQIbjXfwveW7/Fzy8+YEKWAoPJTYUvcFuwx7EFBSgFCAz131uSdOJ1A52MpGFlvSbNIL5+tFvXBVDjaAaR+suAHzi6W7oFRmCqb8fUfjXg+YxZpfbIGf92cgj3r4hESxG+5RN6Idy7RS/T/+q+L8ueKooj7nfdx2XIZN57fcDu0NkubhT3CHuxO3Q19iH5R/n7F9L5wPVZ7dufVjSBDoqVQJOQDwg4pLHmJ6RVtX1c04YfHrlmkMHUADmxIwF83r+QsEpEPYFgiWmQtAy24bLmM7yzfoanftbN3QmiCXKht0BgUHOECG+wBnt9xBaTe5+79gaHSJpDT4SgmG1B513l0bX3DOH+vGecq3M9oW5eswV83J2PvugTOIhH5EN7NRItgaHwIP7z4AZctl1HRXiG3BwcE47OVn2F/2n7kxeb5xqG1E6NA013AchNoKAfa/3Tv9/OXVqkJO6SAlLjRIzaCfFvjk06UP+3EuYpG3K7rwtSCNkSsCMDBDYk4sikZ2QnLYH8romWIYYlogThFJyraK3Cp4RLMjWZ5PyQ/+GFz/GbsN+xHQUqB9++oLYpAdz1gKZcC0vOfgfEh98+JyXaFo5XbALX3HtHxrHsQX1c04pvKFnQPjMrtHwpa/GVTCnblxPGMNiIfx7BE9J5eOF7gUsMlXLFeQdtgm9y+MmIl9hn2Ya+wF/Fh8QqOcAEM2aRHapabgOXHVzeDDI0BDDulNyEfCI9VYpQLZmR8Eteq2/D1H024+8y1x1V0mBrFeUk4uikZqdE+VnxPRG/EsET0DhxjDtx4fgOXGi65LfcPDwzHrtRd2GfYh3X6dd67H9LkONBcMRWObgItVQBmnIzkrwZWbp0KSAVAbDbgrV/rDI9b+3CuogkX77egf2R6hSKQnxmDo5uSsXNVDAL9feDRKRG9FYYlonlyik7cbbuLi/UXUd5YjjGntKu3yk+FbQnbsN+wH/nJ+VgR4FnHa8ybzSrVHFl+lFatjfW79+uzgLQCwPApkLLNI3fKfheOkXFcftCKcxVNeNTSJ7cnRQXj6MZkFG9MQnzk4h6KTESejWGJaA7tg+34tuFbfNvwLVoGWuT2NE0a9hv2o0go8s7l/iN9Uiianj16edVaiA4QPp2aPfoUiEhQZJiLYfr4kfOVTbhe3Y7RCelA4iB/FT7LjsVfNqVgm0EHlcr7Z8uI6P0xLBG9xvjkOG4338Y39d/g19Zf4RSlH6ZhgWEoEopwMO0gVutWe9djNqcTaL0PNJilcNRcAYiTrn5VAJD8IZA2VXsUt87rlvTP5UXPIEyVzfimshmtfSNye0ZsGI5uSsHBDYnQhnrfSj0iWlwMS0QzWPusuFh/EZctl90Or90YuxGH0g/BuNKI4AAveiQz2COtWqsvk94P9bj369KkmiPDTuCD7V69au1NBkcn8P2jNpgqm/HHjGLtiBUB2L8+EcV5SVibFOldwZeIlhTDEi17Q+NDuPH8Bi7UX8CDrgdye3RwNPYb9uNg+kGsjFip3ADfhnNSmj2qLwMayl4tzFZHSEv604zSI7YoL/m63pLTKeKP5zacv9eMa9VtGBqTZtBUfsDH6Xoc3pgEY1Ysl/wT0bwwLNGyJIoiqrur8U39N7j27BqGJqR9gvz9/PFx4sc4lH4IHyV95B2H1w52S4XZDWXS+2Gbe39sjhSO0guB5C2Avxd8Te+ouXcI31S24JuqZjTaXHs/CdGhKN6YhEMbkhAX6aUF+ESkGIYlWlZ6R3pxxXoFF+ovoMHeILcnhyfjUPoh7DPsQ0xIjIIjnAfnpDRj1FAmzSC13sers0f5UjhKM/pUYfbrDIxO4Hp1Oy7eb8avlh6IU/8rwtQB2LsuHsV5SchNieJjNiJ6ZwxL5POcohO/t/6OCw0XcLPxJsad4wAAtb8ahSsLcSj9kOcfPTLQNaP26Oars0dxa4C0QikgJW3y6dkjQDp65Of6bly434KyJ+0YGXfKfdvTdCjOS8Ku7HgEB/ExGxG9P4Yl8lmtA63ykv+ZO2tnabNwMP0gioQiRAR56Inw0yvX6q5LM0it99371ZHScv7p2aPwOGXGuYREUcTD5j58e78F3z1sRc/gmNwn6ENxYH0iDuUmIinKN/Z/IiLPwbBEPmVscgw3G2/iQv0F/N72O8Spx1PhQeEoSi3CofRDyNJlKTzKNxjtlzaErLsB1N8ABrvc++PWToWj6dmj5XH7vugZxLf3W/HtgxY86x6U26PDgrB3XQIObkjEmkSuZiOixbM8vtuSz6vrrcPF+ou4Yr0C+6hdbt8StwUH0w+iIKXAM3fWtj2TwlHddelA2qlHhACAoHBpz6P0z6Wds5fB7NE02+AYvv+zFRfvt6Cq0S63Bwf64/PsWBzYkIiP0qIRwKNHiGgJMCyR1xqeGMb1Z9dxvu48HnU/kttjQmJwIO0ADqQdQHJ4soIjfI3JCaDprhSO6m4A3bXu/VoByNgNZHwOpGwFApbPBomDoxMwP+3Adw9bcau2CxNOaVZQ5Qd8lK7HwQ0J+Gx1HELV/LZFREuL33XI61j7rDhfex6XLJfQP3V+WYBfAPKT83Ew/SC2J2yHv8qDCnuHbNKS/un6oxHX+WNQBUihKGOX9Badptw4FTA8Nokfaztx5c9WlD/tlI8dAYA1iZE4sCERe9fFIybcA2cFiWjZYFgirzDuHMePjT/iXO05/NH+h9yeFJaEw5mHsd+wH7pgnYIjnEEUga4a1+xR011AdIUABGuB9M+k2SPDTiBYo9hQlTA6MYnbtV248mcbzE875A0jASA1OhR71sZj37oEpMf63m7iROSdGJbIo7UPtsNUZ8KF+gvoGpYKnlV+KnyS9AmOZh7FtoRtnrHkf3IcePErUHsVqL0G2F+498dkS+EoYxeQtBHwpJmvJTA24cQvDd347s9WlD3uQP/ohNyXFBWMPWsTsGdtPLITIlioTUQeR7GwZDKZAAAVFRU4ffq03KbRaFBVVYXjx48rNTRS2PS+SOdqz+F2821MTh32qluhw6H0QziccRjxYfEKjxLS6rWGcikg1d0ARuyuPn+1dKxIxudSgbbGw2qnlsDYhBO/WXtw7VEbrlW3o2/YVbweF7ECRWvjsXddAtbxXDYi8nDzDkt2ux1nz54FALcgMx16bDYbBEGA0Wic88+aDkVGoxFWqxVnz56VPz5+/DjsdjusVisEQXjbr4e8mH3EjkuWS/iP2v9AY3+j3L4pbhOOZB5BQXIBApXebLG/XZo5qr0KWG8Bk669fhCik4qzV30h7aAdFKrUKBUzPDaJO/VduF7dDvPTDvSPuGaQosPUKFoThz3rEpCXEgWVigGJiLzDvMOS2WxGT08PdDpXXYjVakVZWRlKS0sBAIWFhfMKS8XFxfLHFosFJSUlEAQBFRUVKCwsRGFhodvnkO8amRjBneY7uPrsKu4035F31w4LDMM+wz4cyTwCg8ag3ABFEeiuA2q+l95a7rn3awUg8wtg1R4gefOye7wGAP0j47hZ04nr1e24VduF4XFXDVJ0mBqfZ8eiaG08tqTq4M+AREReaN5hqbi4GDabDXa7XW4zm83QaDTya41GA7PZDKPRCJPJBJvN/UgGrVbrFoLMZjPy8vKQm5sLu92OTZs2ITc3FyUlJTAajcjNzX33r4w81qRzEnfb7+Kq9SrKG8sxMD4g92Vps3A08yh2p+5GSKBCOzE7J4HmCqDmClBzFbBZ3PsT81wBSZ8JLMNHSD0DozA/7cD16nb80tCDsUlXAXuiJhi7cuKwOycOG1KiGJCIyOu9V82SxWJxm2nSarVymJprZqiqqgp2ux3Hjh1DVVUV7t27h+LiYgiCgLKyMphMpjeGpdHRUYyOjsqvHQ7H+3wZtERqbDW41HAJ155dQ89Ij9weHxqPL1K/wBfCF8iIylBmcOPD0mO1mitA7XVgqNvV5x8EpH4CrCqSHrNFeEC9lAJa7cMoeyIFpLvPeuCccXavQR+K3Tnx2JUTxyJtIvI5C17g/fJs0utYrVYcPnwYgiDg1KlTOH36NI4cOYKzZ8/Ks0zHjh17439/6tQpfPXVVws5bFoCV59dxb8//XcAgEatwecffI4vUr/A+pj1yqxoGx0A6n8Anl4G6n4Axl1HaUAdCWR8JgUkQwGwwkPPkFtEoijicasDZU86YH7agcet7r+U5CRGYFd2HHblxCEthsv8ich3vVdYMhgMbo/lpou85yIIAiwWyyvt810Bd/LkSXz55Zfya4fDgeTk5bfayNsUpRahfbAdRalF2JawTZli7eFeaeXak8uApRyYGHH1RSRK4WhVEbByO6B0MbkCRsYn8Zu1B+VPO2B+0ol2h+v/j58fkJcShV05cfg8Ow7JWh5YS0TLw3uFJaPRiBMnTsivrVbrvAq835darYZarV70v4cWVqY2E2c+ObP0f/Fgt/R47cll4NltwOlaoYWoVGD1PiBrP5CYuyzrj2yDY7hZ0wnzkw7cqe9y2yQyJMgfn6TrYVwdi08z9dCF8b4jouXnrVbDlZWVwW63QxAEub7o6NGjcjH3yZMnF3OsRPPnaAWeXpEesb34xX0Hbf0qIGufFJJic5ZdQBJFEZauAZQ/7YT5aQcqX/S61R/FRqhhzIqFcXUstgo6rAhcfiv8iIhm8hNFUZz70zybw+FAZGQk+vr6EBGx/GpLaErvc2n26OllaTXbTPHrpICUtQ/QK1RErqCB0Qn82tCNW3VduF3bhRb7sFv/6vgIGFfHojArFjmJLNAmIt/3NtmBx52Qd+t9ATy+KL21PXDvS9o89YhtLxD1gRKjU4woiqjt6MetWikc3Xthw/ik6/eiIH8VtghaFK6ORUFWLBI1wQqOlojIszEskffpawYefws8vgC0VLra/VRSYXbWPiBrDxCRoNgQldA3PI5fGrpxu7YLt+u63IqzAWClLgT5GXrsyNTjQ0GHkCDe/kRE88HvluQdHG3Ak0tSQGq6O6PDD/jgIyD7oBSSwvSKDXGpOZ0inrQ5cKu2E7frulDVaMfkjOKjFYEqbBV0yM+MwY4MPT6IXn7HrxARLQSGJfJcA51TAeki8OJXANNBwA9I2QrkHJICUniskqNcUr2DY7hTL80c3anrRvfAqFu/QR8qh6PNqVoWZxMRLQCGJfIsg91Sgfbji8Dzn91XsSVvkWaQVu9fNo/YJp0i/my243ZdF27VduFhsx0zl2SEBvljW1o0dmTosSNDz72PiIgWAcMSKW+0X1rm/+i8dOSI6NrnB4l5QPYhKSBplsfGo139o/ipXgpHP9V3oXdo3K1/VVy4FI4y9di4UougAAV2PyciWkYYlkgZE2NAg1kKSLXXgIkZS9nj10szSNkHlsUqtolJJx402aWVa3VdeNTS59Yfrg7AR+nRyM/U45MMPeIjuXKNiGgpMSzR0nE6gcbfpID05Fvp6JFpujRgzRFgTTGgMyg2xKXS4RiRV639VN8Fx8iEW392QgTyM/XYkRGDDSkaBPpz9oiISCkMS7T42qulgFT9DdDX5GoPiwNy/hOw9rA0m+TDGyGOTThR+aJ3qvaoEzXt/W79mpBAfJwu1R19khGNmPAVCo2UiIhexrBEi6O/HfjzHPDwa6DziatdHSGtYFt7GPjgY0Dlu6u1WuzDuF0rhaNfLT0YGHXNHvn5AWuTNNiRoUd+ph7rkjTwV/luWCQi8mYMS7RwJkal+qMH/5DqkaYLtf2DgPTPgLVHpPeBvllzMzoxiT+e2eTHa/WdA279utAguTD7o7RoHkpLROQlGJbo/YiidMzIg39Ij9pm1iElbwHW/WepUDs4SqkRLqoXPYPysv7fLD0YHnet5FP5AbkpUVOzRzHIToiAirNHREReh2GJ3s1gD/Dw/0khqfOxqz08AVj3F2D9PwHRacqNb5EMj03i92c98uzRs+5Bt/6YcLUcjj5Ki0ZkSKBCIyUiooXCsETzJ4pA4+/AvX+TVrNNjknt/mrpLLb1/wQI+T5VhySKIqzdg/Ky/rvWHoxOuDbKDFD5IW9llLxrdlZ8OPx8uFCdiGg5YliiuY04pGLte//mXqwdvx7I/WdpRVuwRqnRLbjB0Qn8aunB7bpO3KrtQnPvsFt/QuQK7JgKR9vTdAhfwdkjIiJfxrBEb9b2UApIf54HxqceNwUES3shbfyvQGKusuNbIKIooq5jQA5HFc9tGJ90nSkS5K/C5lStvHItLSaMs0dERMsIwxK5Gx+WzmWr+N9Ayz1Xe3QmsOm/AWuP+sQskmNkHL82dMuP19r6Rtz6k7XByM+IQX6mHh8KOoSqeasQES1X/AlAkq46oPL/SAXbI3apTRUIrN4nzSKt3O7Vm0aKoojHrQ7crpPCUdWLXkw4XbNH6gAVthp08oG0qdGhnD0iIiIADEvL28Qo8PQ7oPL/As9/crVrUoC8fwE2/BcgLEax4b0v+9AYfqqXZo/u1Hehq3/UrV/Qh8or17akarEi0HcK04mIaOEwLC03ogi0Vkl1SI/OA0PdUrufCsjYDWz8F8Cw0ytXtDmdIqpb+3BratfsB012zJg8QkiQP7YZdFJxdroeKboQ5QZLREReg2FpOZickOqP6m4ATy4BNourLzxBWtGW+89AZKJyY3xH9qEx3Knvxq3aTtyp60L3wJhbf0ZsmLysf+MHUVAHeF8IJCIiZTEs+aKxQWklW/M9KSRZb7vqkAAgMATI/EI6fsRQAPh7zz8Dp1PEkzYHfqzpxK26Ltxv7HWbPQoN8sf2tGjkZ0rF2Qka3zxahYiIlo73/JSkNxsflh6ptVQCzZXSXkjipPvnrNAAaUYgYxeQuRtQhyky1HfRNzSOnxq6ph6vdaF7wL32aHr2KD9Tj40rtQgKUCk0UiIi8kUMS77Azx/4/n8CkzNCRHg8kJgHJG0EUrZJ772kDmnmyrUfazpxv8mOyRnTRyHy7JFUnJ3I2SMiIlpEDEu+ICBIqjkKCgESN0rBKCJB6VG9lb7hcfw8VXt0q+7VlWvpMWFyOGLtERERLSWGJV9R9L+UHsFbEUWp9uhWbRdu13ahsrHXbfYoOHDm7JEeSVFcuUZERMpQLCydPXsWgiCgrKwMp0+ffmMb+Y7B0Qn83NCNm087cauuEx0O99kjgz4Un2bGID8zBptSOXtERESeYd5hyW634+zZswCA48ePy+0mkwkAYLPZIAgCjEbjvP4sADAajSgtLYXVaoVWq32lTRCEeX8h5JmabEO4WdOJ8ppO/G7pwdikU+4LDpT2PcpfFYP8DD2StZw9IiIizzPvsGQ2m9HT0wOdTie3Wa1WlJWVobS0FABQWFg4r7Ck0Whw7NgxeSZpOhS9ro28y8SkE1WNdpTXdODHmk7UdQy49adoQ7BzVQx2rorBZu6aTUREXmDeYam4uBg2m02eFQKkAKXRaOTXGo0GZrMZRqMRJpMJNpvN7c/QarUoLi6WXx87dgwlJSVus0ivayPPZh8aw+26Ltys6cSt2i70DY/Lff4qP2xcGYWCrBjsXBULg55nrhERkXd5r5oli8XiNtOk1WrlMDUzFL3MZDJBo9HAaDTCYDDAZDJBEIRX2mY+7ptpdHQUo6OueheHw/E+Xwa9g4bOAZQ/7UB5TScqX7gXZ2tCApGfocfOrFjsSNcjMiRQwZESERG9nwUv8H55Nul1jEYjzGYzTCYTLBYLSktLYbfbX2l7k1OnTuGrr75ayGHTHCadIu439qLsSQfKnnTA2j3o1p8ZG45PV8WgICsGG5I1CPDnxpBEROQb3issGQwGt8dy00Xec9FoNPLM0/T717W9ycmTJ/Hll1/Krx0OB5KTk992+DSHkfFJ/FTfjbIn7Sh/2omeQde5a4H+fthqiIYxKwafZsawOJuIiHzWe4Ulo9GIEydOyK+tVuu8Crzfl1qthlqtXvS/ZzmyDY6h/Kk0e/RTfTeGx13HpoSvCMDOVTEoXB2LHRl6hK/g4zUiIvJ9b7UarqysDHa7HYIgoLi4GIIg4OjRo3Ix98mTJxdzrLRInncPyo/X7r2wuR1Mm6gJRuHqWBSujsXmVC0C+XiNiIiWGT9RFMW5P82zORwOREZGoq+vDxEREUoPxyvUd/TjWnU7rj5qQ017v1vf6vgIFK6OxWfZsVgdH8HVa0RE5HPeJjvwuJNlQhRF1LT349qjNlytbkdDp2v/owCVH7YIWhRmxcK4OpZHixAREc3AsOTDRFFEdYsDV6vbcL26Hc9mrGAL9PfDx+l67M6JQ+HqWGhCghQcKRERkediWPIxoijiQZNdfsTW3Dss9wUFqJCfocfuNXEoyIpFBAu0iYiI5sSw5CNq2/tx+WELLj9sRZPNFZCCA/2xc1UMduXE4dNVMQhT85ITERG9Df7k9GJNtiF892crLj9odSvSDgnyR0FWLIrWxGFHRgyCg3j+GhER0btiWPIy3QOjuPqoDZcetKLyRa/cHuSvwo5MPfavT0DBqlgGJCIiogXCsOQF+kfGceNxBy4/bMUvDd3yOWx+fsBWQYf96xOwKzueZ7AREREtAoYlDzU24cSt2k5cetAK89MOjE445b51SZHYtz4Re9bGIzZihYKjJCIi8n0MSx7E6RRR2diLi/dbcPVRG+xD43KfoA/FgfWJ2LsuAanRoQqOkoiIaHlhWPIA9R39uHi/BZcetKLF7lrJFhOuxr51CTiwIRHZCdxJm4iISAkMSwp53j2I64/bcflBK560OeT2MHUAduXE4cD6RGw16OCvYkAiIiJSEsPSEhFFEbUd/bhe3Y7r1e1uS/0D/f2wIyMGBzYkwJgVixWBXMlGRETkKRiWFlF73wh+aeiW3izd6HCMyn3+Kj9sFXTYlROHojXxiArlcSNERESeiGFpAQyNTaC5dxjPuwfxuNWBx619eNzqQFvfiNvnqQNU+Dhdj105cTBmxfA8NiIiIi/AsDSHFz2DeNLqgG1oDPahcdgGx9A7NIbewTHYBsfQ3DuMnsGx1/63Kj9gTWIktqdFY3taNPJWRvERGxERkZdhWJrD9ep2nLpWM+fnha8IQIo2BKviIpCTGIHshEhkxYcjnIfVEhEReTWGpTms1IVi0wdR0IQEISokEFGhQYia/jgkCAmaYCRrQxAZzFBERETkixiW5rArJw67cuKUHgYREREpRKX0AIiIiIg8GcMSERER0SwYloiIiIhmwbBERERENAuGJSIiIqJZMCwRERERzYJhiYiIiGgWDEtEREREs2BYIiIiIpoFwxIRERHRLBiWiIiIiGbhE2fDiaIIAHA4HAqPhIiIiLzBdGaYzhCz8Ymw1N/fDwBITk5WeCRERETkTfr7+xEZGTnr5/iJ84lUHs7pdKK1tRXh4eHw8/NTejhwOBxITk5GU1MTIiIilB4OvSdeT9/C6+lbeD19y1JeT1EU0d/fj4SEBKhUs1cl+cTMkkqlQlJSktLDeEVERARvXh/C6+lbeD19C6+nb1mq6znXjNI0FngTERERzYJhiYiIiGgWDEuLQK1W429/+xvUarXSQ6EFwOvpW3g9fQuvp2/x1OvpEwXeRERERIuFM0tEREREs2BYIiIiIpoFwxIRERHRLHxinyVPZDKZ3F4XFxcDAA4fPoyTJ08CAM6dO4fTp08v+djo7b3pek6322w2CIIAo9G45GOjt3f48GH8/e9/h0ajeaWd96d3edO15L3pvc6cOQNBEAB40M9OkRZcb2+vePr0afn1sWPH5I9zc3NFjUYjGo1Gsbe3V4HR0dt60/W0WCxu19ZoNC752OjtWSwWEYCo0WhEjUYjApCvL+9P7/Kma8l703vNvPdyc3PldqXvTT6GWwQajQalpaWoqqqSX087efIkent7UVZW9spvQuSZ3nQ9zWaz2zXUaDQwm80KjJDehtVqRW9vr/xWWlqK48ePA+D96W3edC15b3qnqqoq+bpVVVWhsrJS7lP63uRjuEVy+vRp5OXlITc3F+Xl5XJ7RUUFAGlqGACOHTumyPjo7bzuelosFuh0OvlztFot7Ha7QiOk+Zr5OObs2bM4cuSI/Jr3p3d507Xkvemd7t27B6vVCqvVCgAoKSlBaWkpAOXvTYalRVJRUYHKykqcOHECBQUFckKe+ZzVYDDgyJEj/A3WC7zper5s+kYmz2e1WmG3293uP96f3ul11/JlvDc9n91uh1arRW5uLgApPFVVVSE3N1fxe5Nh6R2cOXMGPT09r7TrdDocP34cJpMJhYWFyM3NRVlZGUpKSmA2m2G321FRUSFfdI1GA6vVKv/DIGW86/U0GAxuv61OF5KSsua6ntNKS0tRWFgovzaZTLw/Pcy7Xkvem55pruspCILbddJqtfJMk9L3JsPSO5h5k77OyzdmYWEhtFottFqtWxK22+38RuwB3vV6CoKAEydOyO1Wq5UrbjzAXNdzmslkQklJifxaEATenx7mXa+l0WjkvemB5rqeRqNRfuwGuK6b1WpV/N7kcSeL5MyZM/LF1Wq1ryw1r6ioQElJCX/b8RJzXU+bzebWTp4vLy8P5eXlbt+EeX96p9muJe9N72IymWCz2WC32yEIgsf87GRYIiIiIpoFtw4gIiIimgXDEhEREdEsGJaIiIiIZsGwRERERDQLhiUiIiKiWTAsEREREc2CYYmIiIhoFgxLRERERLNgWCIiIiKaBcMSERER0SwYloiIiIhm8f8BHKh8pu5HlLEAAAAASUVORK5CYII=", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -1209,45 +913,10 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": null, "id": "41e30921-52ee-4e8d-afa2-7ab3adc6cfe5", "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:00<00:00, 428.24it/s]\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n" - ] - }, - { - "data": { - "image/png": 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xSfF4cMUspcsJSypZlmWli4g1LS0tSE9PR3NzM9LS0kLe/n+9tg/Txo/BLQsmY1Qiu6yJiCh6NJ7twOcffg/N57vwi5tm476leUqXNGKCyQ9cCTDKHGtsw6Nbj0CWgd+9fgCrF+fgq1fmIkfDmUVERBT5/vuNA2g+34XZk9LwtatylS4nbHGrsigjjE7Aui/ORI5mFJrPd8Hyvohr/udd3P9kJd7/9AzcbnbYEhFRZKo86kR59XEAwEMr5yJezRjTHw7RKmC4h2gBwOWW8Z+Dp/HEtqPYcqjBd1w7bjS+dmUu7tBnIzU5YViuTUREFGpdLjdu+vNWHDzVii9fnoP1t89XuqQRF0x+YMBTwEgEvJ4cZ87iqQ9rYK0+jrMd3QCA0Ylq3KHPxteuysW08anDXgMREdFQbHxfxH+9vh+a0Yl4+/9di7GjE5UuacQx4IW5kQ54Xmc7urHZfhxPfliDw6fP+o5fPS0DX7tqKgyzJkAdxy1eiIgovNRJ52H4w3to63TBbJyPVQU5SpekCAa8MKdUwPOSZRnbHI14cttR2PafgvexvMnCKNx1ZS5WL86BJgb/MiIiovD0zaer8caekyjIHYvnTFchLkY7IxjwwpzSAa+n401teObjY3j2k2NoausCACTGx+HWBVm4e8lUzJ2crmh9REQU2949eBr3Pl4JdZwKr35nKWZNUvb3ppIY8MJcOAU8r/YuF17ZWYcnPzyKPSdafMd1UwTcvWQqvjh3EhLjOVuJiIhGTnuXC1945H0cc7bhgWV5+NmK2UqXpCgGvDAXjgHPS5Zl2I9J+MeHR/H67np0uTzfHpljkvCVK6bgziumYEJassJVEhFRLPhDxaf489uHMDEtGbYfXosxSbG9fC8DXpgL54DX0+nWdvzr41o883ENTrd2AADi41S4Ye5E3L1kKgpyx0Klis3nIIiIaHgdaTiH5Y+8j06XG3+7U4cb501SuiTFMeCFuUgJeF5dLjf+vfckntx2FJVHm3zHZ09Kw91LcrklGhERhZQsy/ja3z/BlkMNuPaycXji3sXsUAADXtiLtIDX0966Zjz1YQ1e3HEC7V1uAED6qASsXpyDu67IxZQMbolGRERD8+quOnz7n9uRGB+Ht75/DaZmjla6pLDAgBfmIjngeUltnXiuqhb/+LAGx5vOAwBUKuD6mePxtaumYum0zJidxk5ERIPX2t6F6x9+D6dbO/B9w3R833CZ0iWFDQa8MBcNAc/L5Zbx7oHTePLDi7ZEyxyNr13FLdGIiCg4v311Hx7begRTM1Lw5vevQXICHwHyYsALc9EU8Hrqb0u023XZuHsJt0QjIqKB7atrwc1/3QqXW8Y/7rsc11w2TumSwgoDXpiL1oDnxS3RiIgoWG63DOP/bYP9mIQV8yZhw506pUsKOwx4YS7aA54Xt0QjIqJAbao8hrXP78boRDXe/uHnMDGda65ejAEvzMVKwOup1nlhS7TKY5C4JRoREfXgPNeJzz/8H0htXXhwxSzcv0yrdElhiQEvzMViwPNq73Lh5Z11eHLbUeyt45Zo0aaj24Vv/3M74uNU+OtXdByKJ6KArLXuwqaqWsycmIpXv7MU8Wr+HvAnmPwQ23t+0IhLTlBjVUEOivTZsB+T8OQ2z5Zo9mMS7Md24Ldj9nNLtAj28FufomLfKQBAxb5TuGHuRIUrIqJwV13jxKaqWgDAQ7fNZbgLEfbgKSCWe/D8Od3Sjn990ndLtOVzJ+IebokWMbYdbsCdj30M70+URVMEvPDNJfzaEVG/ul1u3PSXrThwshWrC3JQapyvdElhLZj8wJhMihuflozvGaZj69rP4y9fXoTFU8ei2y3jtV31KPq/D3Hjn7fi2U+O4XynS+lSqR/NbV34YflOyDKwYp5nmH37MQlVNU2XfjERxawnth3FgZOtEFISsPaLM5UuJ6ow4FHYSIyPw80LslD+jSV47btLsbogB0nxcdhf34KfvLAbN/zpfTjPdSpdJl1ElmX87MXdqG9uR17maPxP0XzcoZsMACh7T1S4OiIKVyeb2/FIxacAgJ/cMJOrKoQYAx6FpTlZ6Sg1zsfHP70eP71xJsanJqGmsQ3/77kdcLv5VEE4eWlHHV7dVQ91nAqPrF6IlMR43L9MC5UKsO0/1WstRCIiwPOH4W9e3YtznS7opghYVZCjdElRhwGPwpqQkojia/Lx5H2XIyk+Dv85eAb/+55D6bLoglpnG37+4h4AwPeun46FOQIAIH/cGBTOmgAA2Pg+e/GIqLey90W8vvsk4lTAQ7fN497lw4ABjyLCrElp+PUtcwAAD791EB+JjQpXRC63jB8+txOtHd3Q547Ftz6X3+vjpms961ht3n4Cp1valSiRiMLQSztO4L/fOAAAeHDFbMzO4mTD4cCARxFj9eIc3L5oMtwy8N1/bceZCzNuSRll7zvwyVEnRieq8ciqhX2WNtDnaqDPHYtOlxtPbDuqTJFEFFa2ORrwo/KdAID7l+bhvqV5ClcUvRjwKGKoVCo8tHIupo0fg9OtHfjBph1w8Xk8Rew50Yw/vOV5OPpXt8zBlIwUv+eZrvH04j31UQ3OdnSPWH1EFH4OnmyF6alqdLlkrJg3CT+9cZbSJUU1BjyKKCmJ8fjfO3UYlaDG1sMN+Ms7h5QuKeac73The89uR7dbxhfnToRRn93vuYZZE6AdNxqt7d149pNjI1glEYWTk83tuOfxT9Da3o3FU8fi4VUL+NzdMGPAo4gzfUIqHrptLgDgT28fwgeHGxSuKLb87vX9cJw5hwlpSfjdynkDLmQcF6fCAxf2lPz71iPocrlHqkwiChOt7V245/FPUN/cjvxxo7HxawVITlArXVbUY8AbJKvVCqvVirVr1/Y6ptfrFawqdtyhz8bqghzIMvC9Z7fzIf4R8u6B03jqoxoAwO+LFmBsAOtWrVw0GZljklDX3I5Xd9UNd4lEFEY6u9345tN2HDjZinGpSXji3sshpHC9u5EQsoBnNpt9occfSZJgNpthNpsDOl5UVARJkkJVXr/X8dZssVhgs9kCastqtUIQBBiNRmRkZMBisQAAjEYjNBpNyGqmgf361jmYOTEVDWc78Z1/bUc3e4eGVcPZDvzY6nk4+r6r87Bs+riAXpecoMa9V08F4Fn4mLsjEsUGWZbxkxd2YevhBqQkqvH4PYuRo/H/vC6FXkgCXmFhIYqLi2E0GrF+/Xq/59hsNjQ29l3awt9xURRhtVqRl5eHsWM9+5BeHMyC1d91KioqYDQaUVxcjNLS0oDaMhqNMBgMAACHw4GCgoIh1UaDk5ygxoY7dRidqMbHR5z4o43P4w0XWZbxk+d3o+FsJy6bMAYlN8wI6vV3XZGLlEQ1DpxsxZZDHFInigV/qPgUL9hPQB2nwt/u1GHu5HSlS4opQw54drsdgiD4/l1dXe33PKPRiPz8/ICOi6KIpqYm31tZWRlKSkp6nePtkevJYrFAFP0vqurvOjabzVc7AAiC4OvF8/bq9Xy7uHfSZrNBr9dDp9P5vebFNmzYgNmzZ2Px4sUBnU+Xlj9uDH53+zwAwF/fPYz/HDytcEXR6dnKWtj2n0KiOg5/XL0o6Odn0lMS8KXFUwAAFi58TBT1/vnxMfzlncMAgN+tnIvPzRivcEWxZ8gBr6qqCqIo+oKVyWQaclEGg8EXvCwWC1atWtXnHEEQoNPpfCHParVCo9FAq9UGfB2Hw4GMjAzf+xqNxjcs7O3V6/lmNBp959rtdkiShOLiYtjt9oCut2bNGuzbtw+VlZUB10iXduvCybjzCk94+MGmHaiTzitcUXQRz5zFb17ZBwD48fIZg16U9L6lU6GOU2Hr4QbsOdEcyhKJKIy8c+AUfv6SZ4eb714/Hasv/HFHI2vIAU+SJGg0Guh0Ouh0OlRVVQUceC5FFEVIktSrl60ng8EAnU4Hk8kEp9PZK4ANltPpDKiuoqIilJWVQa/X+15js9l8w8s0sn5+02zMyUpDU1sXvvOv7ZytGSJdLjd+sGkHzne5sCQ/A18fwqKk2WNTcNP8SQDYi0cUrXYdl7Dmme1wuWUY9dn4gWG60iXFrCEHPK1W26vXTKPR9DtMGqyysrKAhj+dTuegJjdcPGTrdDoD6gHUarVwOByoqKhAdXW173k8g8EAh8MRkqBJwUlOUONvd+qQmhSP6pom/P7fB5UuKSr85e1D2Hm8GWnJ8SFZt6r4wsLHr+2uR62zLRQlElGYONbYhvueqMT5LheWTc/E+tsHXkaJhteQA57BYOgV6ERR9AWeoc6CtVqtAwYuu90Ou92O8vJyOJ3OoHvODAZDr+HSnrVT5MnNGA2zcT4Az0bWtn2nFK4oslXXOPHXdy88Q3P7PExKHzXkNudkpWPZ9Ey43DIe23pkyO0RUXhoOteJex7/BA1nOzF7Uhr+9y49EtRciU1JQ777giDAZDLBYrHAbDajtLTUN6Sq1+t9Ic9ms6GiogIVFRW9glh/x71t99czJ0kSNm3a5Jt8UVxcDKfT2W/vob/raLVarF692jehYt26dUO5FRQGvjhvEu5ZMhUA8MPynTjexF6iwTjb0Y3vb9oBtwzcvmgybpqfFbK2vb14myprIbV1hqxdIlJGe5cL9/+jCmLDOUwWRuHxexdjTFK80mXFPJXMRalGXEtLC9LT09Hc3Iy0tME9sE796+x2o6jsQ+yslbAgR0C56SokxvMvyWD8qHwnrNXHMVkYhTe+vwxpyQkha1uWZaz481bsq2/Bj75wGb79eT6jQxSpXG4Za56x4829J5GWHI/nv7kE0yekKl1W1AomP/C3HkWdxPg4/PXLi5CWHI+dtRLWv7Ff6ZIiyuu762GtPo44FfDI6oUhDXcAoFKpYLrW04v3xLajaO9yhbR9Iho5D722D2/uPYlEdRwsXytguAsjDHgUlXI0KXh41UIAwOMfHMWbe+qVLShCnGxux0837wYAfPNz+bg8b3h2Zrlx3iRMFkah4WwnXrCfGJZrENHwenSLiMc/OAoA+P2qBbhSmzHwC2hEMeBR1CqcPcH3vNePy3ehpvGcwhWFN7dbxo+tOyG1dWHe5HR87/rLhu1aCeo43HdhyZVHt4hwufmkCFEkeW1XPR56zTM68tMbZ+KWBaF7TpdCgwGPotqPl8+APncsWju6seafdg4HDuCJbUex5VADkhPi8MjqhcP+3OKXFucgfVQCxIZzqOCMZ6KI8ckRJ37w3A4AwD1LpuKBZYFvMEAjhwGPolqCOg5/+fIijE1JwJ4TLXjotX1KlxSWDpxswX+/eQAA8LMVszFt/Jhhv+bopHjcdaV3+zLHsF+PiIbu8OlWPPCPKnR2u7F8zgT8/KbZXOsuTDHgUdTLEkbhD6sXAgCe/ugYXtlZp2xBYaa9y4XvP7sDnd1ufH7meNx1xchtK3T3kqlIVMfBfkxC1dFL7yJDRMo53dKOu/9eiebzXdBNEfCnLy2CeoiLn9PwYcCjmHDdjPFYc51n55KfPL8L4pmzClcUPh5+6yAOnGxFxuhElN4xf0T/Gh+fmozbdZMBeBanJqLwdLajG/c9WYkT0nnkZY7Go3cvRnKCWumyaAAMeBQzfmC4DFfkaXCu04VvPcPn8QDgg8MN2LjFs6NE6R3zMS41acRreOAaLVQqoGLfKRw+zeBNFG66XG6secaOPSdakDE6EU/cuxia0YlKl0WXwIBHMSNeHYc/f3kRMkYn4sDJVvzq5b1Kl6So5rYu/PC5nQCAr1wxBYbZExSpI3/cGBhmea796Bb24hGFE1mW8eDmPXjv0zNITojDY/csRm7GaKXLogAw4FFMmZCWjD99aRFUKuDZylq8YD+udEmKkGUZP31xN062tCMvczQeXDFL0XpMF5azecF+Aqdb2xWthYg+8+e3D2NTVS3iVMBfv6zDwhxB6ZIoQAx4FHOWTs/Edy9sj/WzzXtw6FSrwhWNvM3bT+C1XfWIj1Phj6sXIiVR2X0jC6ZqoM8di06XG09cWDiViJRVXlWLR2yfAgB+e9tcxXr5aXAY8Cgmfff66bh6WgbOd3mex2vr7Fa6pBFT62zDL17yDE9/3zAdC8LkL3LvotRPf1SDsx2x8/UgCkfvfXoG617w7Grzrc/l484rchWuiILFgEcxSR2nwh9XL8K41CQcOn0WD764B7Ic/bspuNwy/t9zO3C2oxsFuWPxzc9NU7okn8JZE6DNHI2W9m5sqqxVuhyimLXnRDO+9XQ1ut0yVi6ajB8vn6F0STQIDHgUs8alJuEvX16EOJXn2a/yquh/Hu//3nOg8mgTxiTF45HVC8NqDau4OBUeuNCL99gWEV0ut8IVEcWe401tuO+JSpzrdGFJfsaIL51EocOARzHtSm0GfvgFz1+nP39pD/bXtyhc0fDZdVzCIxWe52l+dcsc5GhSFK6or5WLJiNzTBLqmtvx2q56pcshiinNbV245/FKnG7twMyJqfi/r+qHfctCGj78ylHM++a1+bj2snHo6Pas9RSNz3+1dXbj+8/uQLdbxo3zJuKOC4sLh5vkBDXuWeJ51qfsfTEmhs2JwkFHtwsPPFWFw6fPYmJaMh6/dzHSkhOULouGgAGPYl5cnAqPrF6ISenJEBvOYd0Lu6MuWPzu9f0QG85hQloSfrdyXlgPudx1ZS5SEtXYX9+CrYcblC6HKOq53TJ++NxOfHLEidSkeDxx32JMSh+ldFk0RAx4RAA0oxPxly979lV8ZWcdnvn4mNIlhcw7B07h6Y88n8/DRQshpIT3CvRCSiJWL84BAJS9x4WPiYbbf795AK/uqkeCWoWyr+oxc2Ka0iVRCDDgEV1QMFWDtTd4nsf7zSv7sOdEs8IVDV3D2Q6UWHcBAL6+NA9Lp2cqXFFgvr40D+o4FbYeboiKrwNRuHrigyOwXNgH2mycjyXTIuNnBF0aAx5RDw8s08Iwazw6XW586xk7Wtq7lC5p0GRZxlrrLjSc7cSMCakRtdRB9tgUrJg3CQCwkduXEQ2LN/ecxK9f3QcA+PHyGVi5KFvhiiiUGPCIelCpVPh90QJMFkbhmLMNa627IvZ5vH9+cgxvHziNRHUc/vilhUhOUCtdUlC8Cx+/uqsex5vaFK6GKLpU1zThe89uhyx79qL+1ufylS6JQowBj+giQkoiNtypQ4JahTf2nMQT244qXVLQHGfO4rcX/jIvuWEGZk2KvGdq5k5Ox9JpmXC5ZTy29YjS5RBFDfHMWdz/ZCU6ut24fuZ4/OaWOWE98YoGhwGPyI+FOQJ+euMsAJ4ZqDtqJWULCkKXy40fbNqB9i43rp6WgfuuzlO6pEHz9uJtqqyF1NapcDVEka/hbAfuebwSTW1dWJCdjr98ZRHi1YwC0YhfVaJ+3LNkKr44dyK6XDLWPGOPmIDx57cPYdfxZqSPSsDvixYgLox2qwjWsumZmDUpDW2dLjz9UY3S5RBFtLbObnz9iUocc7ZhiiYFj92zGCmJ8UqXRcOEAY+oHyqVCqXG+ZiiScEJ6Tx+VL4z7J/HqzzqxIZ3DwMAfrdyXsSvZaVSqWC60Iv3xLYatHe5FK6IKDJ1u9z4zj+3Y+fxZoxNScAT9y5G5pgkpcuiYcSARzSAtOQE/O1OHRLVcbDtPx3WMzpb27vwg0074JaB23WTsWL+JKVLCokV8ychKz0ZDWc7sHn7CaXLIYo4sizjFy/vxdsHTiMpPg6P3r0Y2nFjlC6LhhkDHtElzJ2cjp/fPBsAUPrmQVTXOBWuyL9fvbwPx5vOI3vsKPz6ljlKlxMyCeo43LfU8xzhxvdFuN3h3YtKFG7+9h8H/vnxMahUwJ++tAj63LFKl0QjgAGPKAB3XTEFNy/Igsst49v/3A7nufB6Hu+1XfV43n4ccSrgkdULkRple0h+6fIpSEuOh9hwDhX7TyldDlHE2Lz9OP7n3wcBAL+8aTZumDtR4YpopDDgEQVApVJh/e3zoM0cjfrmds9QaJj0JJ1sbsdPN+8GAHzrc9OweKpG4YpCb0xSPO66MhcAfKvuE9HAPjjc4NvJpvgaLe6J4Bn1FDwGvEGyWq2wWq1Yu3Ztr2N6vV7Bqmg4jUmKx4Y7dUiKj8N7n57B/77nULokzybh5TvQfL4L87PT8T3DdKVLGjb3LJmKRHUcqmuaUHU0PIfJicLFgZMt+MZT1ehyybhp/iT85IaZSpdEIyzogGc2m33hxh9JkmA2m2E2mwM63l+bFosFVqsVZrMZdrs92DIDrst7XYvFApvNFlBbVqsVgiDAaDQiIyMDFosFAGA0GqHRRF/vCX1m1qQ0/OZWz/NtD791EB+JjYrW8/cPjuCDw41ITojDI6sXIiGK17Man5aM23WTAQBl7MUj6ld983nc8/dKtHZ04/I8DR5eFdnLJdHgBLUATmFhIcrLyyEIAvR6PYxGY59zbDYbGhsbkZGREdBxf23a7XZUVFSgvLzcd05FRUWwn9slry+KIioqKlBWVua7jsFguGRbPT9vh8MBk8k0pNoosqwqyMHHR5x4wX4C3/3Xdrz23WUYlzryyw0cONkC85ueZ2seXDEb+TEwK+7+ZVo8W1kL2/5TcJw5GxOfM1EwWtq7cM/fK3GypR3Txo/Bxq8WICk+srYppNAI+M99u90OQRB8/66urvZ7ntFoRH5+3z3t/B3vr02bzQatVtvn3J68PXI9WSwWiKL/v+z9Xd9ms/muDwCCIPh68by9ej3fLu61tNls0Ov10Ol0fq9J0UmlUuGh2+Zi+vgxON3age9v2g7XCD+P197lwvef3YFOl2eroTuvmDKi11fKtPFjYJg1AbIMPBrGS9YQKaGz241vPFWNg6daMS41CU/cuxjpKdE14YoCF3DAq6qqgiiKvgAVil6r/trUarW9glrPc7wEQYBOp/OFPKvVCo1G0ycYDsThcPTq0dNoNJAkCYAnEBYXF/d669lzZ7fbIUkSiouLAx5C3rBhA2bPno3FixcHXCOFp5TEePztTh1GJajxweFG/OWdQyN6/d//+yAOnGxF5phElBrnx9Q+kt+41vN//PnqEzjd2q5wNUThQZZlrH1+F7Y5GjE6UY3H71mM7LEpSpdFCgo44EmSBI1GA51OB51Oh6qqqiE/G9dfm94gJUmSr0etZ0+bl8FggE6ng8lkgtPp9DtkHCyn89IPb4uiiKKiIpSVlUGv1/teY7PZIIpiv88nrlmzBvv27UNlZeWQ6yTlTZ+Qiv9aORcA8Ke3D2HroYYRue7WQw14dOsRAEDpHfNjbjX6gqka6KYI6HS58eS2o0qXQxQWfv/WQWzefgLqOBX+dpcecyenK10SKSzggKfVanv1jmk0mn6HQ0PRZnl5OURRREFBAQRBQEFBQb/tOJ3OQU1uuHjI1ul0BtQDqNVq4XA4UFFRgerqat9zewaDAQ6HIyRBkyLD7bpsrC7IgSwD39+0HadbhrdHSWrrxA/LdwAA7rxiCq6fNWFYrxeuiq/x/N996sManOvoVrgaImU9/VENNrzrmdW//vZ5uPaycQpXROEg4IBnMBj6DJt6g413WDNY/bUpSRKKioqg0+ngdDp9Ie9idrsddrsd5eXlcDqd/facDXT9nr1pPT8nokD9+tY5mDkxFQ1nO/Gdf21Ht8s9LNeRZRk/3bwbp1o6oM0cjZ+tmDUs14kEhbMnIC9zNFrau/FsZa3S5RApxrbvFH7x0h4AwA8Ml2FVQY7CFVG4UMlB7J5utVrhdDohSRK0Wq2vpyo/Px/V1dW+SQplZWWQJAkmk8l3Tn/H+2vTYrH4evRKSkr61CJJEtavX4/S0lLfMYvFAoPB4LcXbqDrA5/1Ao5E71tLSwvS09PR3NyMtLS0Yb8eDT/xzFnc/JetONfpwprr8vHj5aFfc+r56uP4YflOxMep8MK3lmB+thDya0SSf358DD/dvBuThVH4z48/F9VLxBD5s6NWwpctH+F8lwurC3Lw33fMi6nncWNRMPkhqIBHocGAF51e2VmH7/xrOwDg8XsX47oZ40PWdq2zDV/80xac7ejGj5fPwJrrpoWs7UjV3uXC0tJ30HC2E3/60kLcunCy0iURjZiaxnO4/W/b0HiuE9deNg6P3l3AP3JiQDD5gd8NRCFy84Is3HWlZ7mS/7dpB+qk8yFpt9vlxg827cDZjm4U5I7FN67tuwxRLEpOUOPuq6YCAP7vPRH8W5VihfNcJ+55vBKN5zoxJysNG+7UMdxRH/yOIAqhB1fMxtzJaWhq68J3/rUdXSF4Hu//3nOgqqYJY5Li8cjqhVBzRXqfr16Vi1EJauyvb8HWwyMzi5lISec7Xfj6k5U40nAOk4VRePyexRiTFNSeBRQjGPCIQig5QY0NX9EhNSke1TVN+J9/HxxSeztrJfzR5llj79e3zEGOhuta9SSkJGL1Ys9D5RZuX0ZRzuWW8b1nt2P7MQnpoxLw5H2LMT4tWemyKEwx4BGFWG7GaJiN8wF4Qodt36lBtdPW2Y0fbNqBbreMFfMn+fZhpd6+vjQP6jgVthxqwN66ZqXLIRoWsizjN6/sxVv7TiFRHYeNXyvAtPGpSpdFYYwBj2gYfHHeJNx79VQAwA/Ld6LW2RZ0G//12n6IDecwMS0Z/3XbXM6O60eOJgUr5k0CwF48il4bt4h48sMaAMAjqxfi8rzg136l2MKARzRM1n1xFhbkCGg+34Vv/2s7OrsDfx7Ptu8Unvn4GADg4VULIKQkDleZUaH4Gs/SSK/uqsfxpuDDNFE4e3lnHX73+gEAwIMrZmHF/EkKV0SRgAGPaJgkxsfhr19ehPRRCdhZK2H9G/sDet2Z1g6sfX4XAOD+pXm4elrmcJYZFeZOTsfV0zLgcsv4+9ajSpdDFDLNbV0ose4EANx79VR8fWmewhVRpGDAIxpGOZoUPFy0AADw+AdH8cbu+gHP924Y3niuEzMnpuJHy2eMRJlRwXRh+7JnK4+hua1L4WqIQuPV3XVo73Ljsglj8OCK2XxUgwLGgEc0zAyzJ8B0YQixxLoLNY3n+j33mY+P4Z0Dp5EYH4c/fmkhkhPUI1VmxFs2PROzJqWhrdOFpz+uUbocopDYbD8BALhDl80lkigoDHhEI+BHy2dAnzsWrR3d+NYzdrR3ufqc4zhzFg+9tg8AsPaGmZg5kbucBEOlUqH4Gs/w1eMfHPV7j4kiybHGNlTVNEGlAndqoaAx4BGNgAR1HP76lUUYm5KAvXUtviDn1dntxvef3YH2LjeWTsvEvUumKlNohLtpfhay0pPRcLYDm7efULocoiF5cYfne3hJfgYmpnO9OwoOAx7RCJmUPgqPrF4IAHj6o2N4eWed72N/evtT7D7RjPRRCfh90QLEcShmUBLUcbjvwkPoG7eIcLu5fRlFJlmWfX+krFyUrXA1FIkY8IhG0OdmjMea6zyTAdY9vwuOM2fxyREn/vYfBwBg/e3z+Jf6EH3p8ilITY6HeOYcbPsHt8g0kdJ2Hm/GkYZzSE6Iww1zJypdDkUgBjyiEfYDw2W4Ik+Dc50urHnGjh9s2gFZ9jxEfeM8rm81VGOS4nHXlbkAgDIufEwRarP9OADgC7Mncq9ZGhQGPKIRFq+Ow1++vAiZYxJx4GQrTkjnkaMZhV/dMlvp0qLGvUumIlEdh+qaJlTXOJUuhygoXS43XtnlWVJpJbcopEFiwCNSwPi0ZPzpS4ugUgFxKuCRVQuRmpygdFlRY3xaMlYu8vxiLHuPvXgUWd7/9Ayc5zqROSYRy7jQOQ0S+32JFHL1tEw8c/8VUEGFgqncVzLUHrgmD5uqalGx/xQcZ84if9wYpUsiCsgLFyZX3LwgC/Fq9sPQ4PA7h0hBS/IzcVV+htJlRKVp41NhmDUBsgw8uoW9eBQZWtq7YNvnmRx0O2fP0hAw4BFR1DJd69lB5Hn7CZxp7VC4GqJLe3P3SXR0uzFt/BjMnczFzmnwGPCIKGoV5I7FoikCOrvdeHLbUaXLIbqkF7Z7Zs+uXDSZ+87SkDDgEVHUUqlUvn2An/qoBuc6uhWuiKh/J6Tz+Ej0zPq+dWGWwtVQpGPAI6KoVjh7IvIyR6P5fBc2VdYqXQ5Rv166sDXZFXkaZI9NUbgainQMeEQU1dRxKty/zLN92WNbj6DL5Va4IqK+ZFnGZrt3azKufUdDx4BHRFHvDl02MkYn4oR0Hq/vrle6HKI+9ta14NDps0iMj8MXuaMNhQADHhFFveQENe5ZMhWAZ+FjWZaVLYjoIpsvrH1XOGsC0kdx0XMaOgY8IooJd12Zi1EJauyrb8EHhxuVLofIp9vlxks76gAAt3F4lkKEAY+IYsLY0YlYvTgHAFD2vkPhaog+84GjEQ1nOzA2JQHXXjZO6XIoSjDgEVHM+PrSPKjjVNhyqAF765qVLocIALDZ7ln77uYFWUiM569lCg1+JxFRzMjRpODGCw+wb3yf25eR8s51dOPfez1bk3F4lkKJAY+IYop34eNXdtXjeFObwtVQrPv33pM43+VCXuZoLMoRlC6HoggD3iBZrVZYrVasXbu21zG9Xq9gVUR0KXMnp2NJfgZcbhl/33pU6XIoxnlnz962kFuTUWjFB/sCs9kMrdbzF7DRaOzzcUmSYLFYAAAlJSWXPN5fm1artdc5/q4VjP6u772O0+mEVquFwWC4ZFtWqxWCIMBgMEAURVgsFhQXF8NoNKKsrGxIdRLR8DNdm49tjkY8W3kM37t+OtJTuCwFjbxTLe344HADAOC2RdyajEIrqIBXWFiI8vJyCIIAvV7vN3TZbDY0NjYiIyMjoOP+2pQkCaIo+oKYyWQacsDzd31RFFFRUeELZYWFhQEFvJ61OBwOmEymIdVGRCPrmumZmDkxFQdOtuLpj2uw5rppSpdEMejlHXVwy4A+dyxyM0YrXQ5FmYCHaO12OwRB8P27urra73lGoxH5+fkBHe+vTUEQUFZWBrvd7nv/YpIkwWw29zpmsVggiv4fnPZ3fZvN1qttQRBgs9kAeHrpLBZLr7eLexVtNhv0ej10Op3fa15sw4YNmD17NhYvXhzQ+UQ0PFQqFYovPIv3+AdH0d7lUrgiikUveIdnObmChkHAPXhVVVUQRdEXoEwm05CHIwdqs7S01Bee3n777T6vFQQBOp0OZrMZJSUlsFqt0Gg0vqHeQDgcjl49ehqNBpIkAbj0kLDdbockSSguLobdbg8o5K1ZswZr1qxBS0sL0tPTA66TiELv5gVZ+P2/D6KuuR0vbj+BL10+RemSRowsy7Afk/DyjhOYJIzCN67t+0c5Da8DJ1uwv74FCWoVbuLWZDQMAu7BkyQJGo0GOp0OOp0OVVVVvh62wRqozcrKSlRXV0Oj0eD666/3+3qDwQCdTgeTyQSn0znkYVzA8yzepYiiiKKiIpSVlUGv1/teY7PZIIpin54+Igo/Ceo43Lc0DwBg2SLC7Y7+7ctOtbTjb/85jOv/8B7u+N9tePLDGvz3GwdgP9akdGkxxzu54roZ4zF2dKLC1VA0CrgHT6vV9uod02g0EEUx4OHJYNoURRGFhYXQ6XSoqKiAyWSCzWbr9/k4p9MJjUYT9PXz8/N9PXbedgLpAdRqtXA4+q6EbzAY/B4novD0pcun4E9vH4J45hxs+0/hC3MmKl1SyHV0u/D2/tMor6rFe5+egTfHjkpQY2J6Mo40nMOjW0T87U6uADBSXG4ZL233bE22ksOzNEwC7sHzzhj1EkXRF7h6hqRg9NfmxYGtsLDQb4Cz2+2w2+0oLy+H0+kMuufMYDCgsrKyz/WJKDaMSYrHXVfmAgAsUbbw8Z4TzfjVy3txxe/exreesePdg55wt3jqWJjvmI/KBw0o+6on1L255ySONXJNwJHykdiIky3tSEuOx+dnjVe6HIpSAffgCYIAk8kEi8UCSZJQWlrqm6Cg1+tRXV3tm6RQUVEBSZKg1Wp9w6b+jvfXZnFxMcxmM6qqqgDAN4zbkyRJ2LRpE0pLSwEAxcXFvkkW/nrh/F1fq9Vi9erVsFqtcDqdWLdu3aBuIhFFrnuXTMVjW46gqqYJ1TVN0OeOVbqkQXOe68SL20+gvPo49te3+I5PTEvGHfrJMOpzkJf52WzNyyak4trLxuG9T8/g7x8cwa9umaNE2THHOzy7Yn4WkuLVCldD0Uoly3L0P3gSZryTLJqbm5GWlqZ0OUQxr8S6E89VHcfyORNQ9tUCpcsJSrfLjfc+PYPyquN4+8ApdLk8P9IT4+PwhdkTYNRnY9n0cVDH+V9Ed+uhBtz12MdISVTjw59czzUBh9n5ThcKHqrAuU4XnjNdhcvzgn+8iGJXMPkh6IWOiYiiTfE1WjxXdRxv7TsF8cxZaMeNUbqkSzp8uhXlVcfxwvYTONPa4Ts+b3I6igqyccuCLAgpl354/+ppGb41AZ/5pAbf+hzXBBxOb+07iXOdLmSPHYWCCO4tpvDHgEdEMW/a+FQYZo2Hbf9pbNxyBOtvn6d0SX61tHfhlZ11KK86jh21ku94xuhE3LZoMooKsjFzYnCjAiqVCg8s0+KH5Tvx5LajuH+pFonx3MVyuLx4YXh25aLJiOunV5UoFBjwiIgAFF+TD9v+03jefhz/r/AyjEtNUrokAIDbLWOboxHl1bV4c89JdHS7AQDqOBWumzEeRQXZuG7G+CGFspsXZMH87wM41dKBV3bW4Q59dqjKpx7OtHbg/UPerck4e5aGFwMeERE8s0sX5gjYUSvhyW1H8aPlMxSt51hjG6zVtXjefgInpPO+45dNGIMifQ5uWzQ5ZCE0MT4O9yzJQ+mbB7Bxi4jbddz4fji8srMOLreMBdnpyI+AxwAosjHgERHBM1T5jWu1+MbTdjz1UQ2++bl8jE4a2R+RbZ3deH33SZRX1eLjI58tup6WHI9bFmahSJ+D+dnpwxK+vnL5FPzlnUM4cLIVWw83YNn0cSG/Rqx7ccdnw7NEw40Bj4jogsLZEzE1IwVHG9vwXFUt7r06b9ivKcsyqmqaUF5Vi9d21eNcp2dfXJUKWDotE0UFOfjC7AlIThje5TTSUxKwqiAHT2w7io1bjjDghdjh02ex63gz1HEq3LQgS+lyKAYw4BERXaCOU+H+ZVo8+OIePLrlCL56ZS7i1cMz4aC++TxesJ+Atfo4jjSc8x3PzUhBkT4bt+uykSWMGpZr9+frS/Pwjw+P4v1Pz+DgyVbMmJg6otePZt7JFddeNg6ZY8Lj+U6Kbgx4REQ9GPXZeKTiU5yQzuO13fW4dWHohtPau1yo2HcK5dXHsfXQZ9uGpSSqsWLeJBQV5GDx1LGKPf+Wo0nBDXMn4vXdJ/HoFhH/U7RAkTqijdst+xY35vAsjRQGPCKiHpIT1Lh7yVT8oeJTWN4XccuCrCEFLlmWsedEC8qra/HSjjo0n+/yfezyPA2K9Nm4cd6kEX/erz/3L9Pi9d0n8dKOOvx4+QyMT0tWuqSIV3nUiRPSeYxJikfh7AlKl0MxIjx+ohARhZGvXpmL//2PA3vrWvDB4UYsnZ4ZdBsNZzvw4nbPEOyBk62+45PSk3GHLhtGfTam9tg2LFzopoxFQe5YVNU04ckPj+LHy2cqXVLE806u+OLcicP+LCWRFwMeEdFFxo5OxKqCbDz5YQ3K3ncEHPC6XG785+AZlFfV4p0Dp9Ht/mzbsOVzJqJIn42rp2X2u21YuLh/mRZVNdV4+qNjWHPdNKQk8lfFYLV3ufDqrnoAwEodh2dp5PB/LRGRH/cv0+Kpj2qw5VAD9tW1YHZW/ztEfHqqFeVVtdi8/QQaznb6ji/IToexIAe3zM+KqD1eC2dPQG5GCmoa22CtPo6vXTVV6ZIi1jsHTqO1vRuT0pNxZV6G0uVQDGHAIyLyI0eTghvnTcKru+qxcYuIR1Yv7PXx5rYuvLyrDtaqWuw83uw7njkmESsXTUZRQQ4umxCZs1DVcSp8fWkefvHSXjy29QjuvCI37Hsdw5V3csWtC7k1GY0sBjwion6YrsnHq7vq8fLOOvxo+QxMTEvGB4cbUF59HP/eexKdF7YNi49T4fMzx6OoIAefmzEOCcO0tMpIMuqz8fBbn6KmsQ0V+07hhrkTlS4p4jSd68R/Dp4GANzO4VkaYQx4RET9mJedjiX5GdjmaMR3/mlHfXM76pvbfR+fOTEVRn02bls0OerWNktJjMddV07BhncdeHSLyIA3CK/uqkOXS8bsSWkR25tLkYsBj4hoAMXXaLHN0Qj7MQkAkD4qAbde2DZs7uS0qN6z9e6rpmLj+0dQVdME+7Em6KaMVbqkiOIdnmXvHSmBAY+IaADXXjYOX7sqF3VSO25blAXDrOHfNixcjE9Lxq0Ls1BefRyPbhHxtzv1SpcUMY42nIP9mIQ4FXALtyYjBTDgERENQKVS4Te3zlW6DMXcv0yL8urjeHPPSdQ625CjSVG6pIjg7b27elomF4smRUT+k8BERDRsZkxMxTWXjYNbBh7bekTpciKCLMu+xY05PEtKYcAjIqIBPbAsDwDwXFUtmtu6LnE22Y9JqGlsQ0qiGsvncHIKKYMBj4iIBrR0WiZmTkxFW6cL//zkmNLlhL3N248DAJbPmchdQEgxDHhERDQglUqFB5ZpAQBPbDviW/+P+ursdn+2NdkiDs+SchjwiIjokm5ekIUJaUk41dKBV3bWKV1O2PrPwdOQ2rowLjUJV08LbA9jouHAgEdERJeUGB+Hu5dMBQBs3CJClmVlCwpTvq3JFmRxezdSFAMeEREF5M7Lc5GSqMaBk6344HCj0uWEnebzXXh7v2drspWcPUsKY8AjIqKApKckYFVBDgBPLx719vruenS63LhswhjMnpSmdDkU4xjwiIgoYPddnYc4FfDep2dw8GSr0uWElc12z/DsykXZUb2FHUUGBjwiIgrYlIwU3DDXs7bbo+zF86l1tuGTo06oVMCtC7k1GSmPAY+IiIJy/4UlU17aUYfTre0KVxMeXrqwc8WVeRnIEkYpXA0RA96gWa1WWK1WrF27ttcxvZ6bcRNRdNNNGQt97lh0utz4x7YapctRnCzLeOHC7FlOrqBwEXTAM5vNvnDjjyRJMJvNMJvNAR3vr82ioiJIkhRsef3q7/re61osFthstoDaslqtEAQBRqMRGRkZsFgsAACj0QiNRhOymomIwpV3+7KnP65BW2e3wtUoa/eJZohnziEpPg5fnMutySg8BBXwCgsLUVxcDKPRiPXr1/s9x2azobGx7/T5/o77a1MURVitVuTl5WHs2LFQqVR+g2Ew/F1fFEVUVFTAaDSiuLgYpaWlAbVlNBphMBgAAA6HAwUFBUOqjYgo0hTOnojcjBRIbV14vvq40uUo6oULkysKZ09AanKCwtUQeQS8SZ7dbocgCL5/V1dX+z3PaDTC6XT26X3zd7y/NkVRRFNTk+9jFosFxcXFvdqTJAkWiwUlJSW+YxaLBQaDAVqtNqC6bDab7xoAIAgCbDYbDAYDrFYrnE5nrzY0Gg2MRmOv1+v1euh0Or/3gogoWqnjVLjv6jz88uW9eGzrEXzlityYXNi3y+X27exxO4dnKYwEHPCqqqogiiJE0TNrymQyoaysbEgX769Nb+8Y4Altq1at6vNaQRCg0+lgNptRUlICq9UKjUbjN9z1x+FwICMjw/e+RqPxBcCeQc4fu90OSZJQXFwMu90eUMjbsGEDNmzYAJfLFXCNREThqqggG3+o+BRHG9tQse+Ub3ZtLNl6qAGN5zqRMToRy6aPU7ocIp+Ah2glSYJGo4FOp4NOp0NVVRXsdvuQLn6pNkVRhCRJvXrZejIYDNDpdDCZTHA6nZcMZYG4uNfOH1EUUVRUhLKyMuj1et9rbDabb3jZnzVr1mDfvn2orKwccp1EREpLSYzHXVdOARC7S6Z4J1fcvCALCWrOW6TwEXAPnlar7dU7ptFoIIrikIYnL9VmWVkZCgsLL9mO0+kc1OSG/Pz8XkO2TqczoB5ArVYLh8PR57jBYPB7nIgoWt191VRsfP8IqmqasP1YExZNGat0SSOmtb0Lb+09CQBYuYjDsxReAv5zw2Aw+IZSAU8vlncodbCzXQdqE/DMVh0ocNntdtjtdpSXl8PpdPbbczbQ9Xv2pl18fSIiGtj4tGTccmFh30e3HFG4mpH15p6T6Oh2QztuNOZnpytdDlEvAffgCYIAk8kEi8UCSZJQWlrqGzrV6/Worq72TVKoqKiAJEnQarW+YVN/xwdq03vN/nrmJEnCpk2bfDNfi4uLYbFYIIqi31Do7/parRarV6/2TahYt25doLeDiIguuH9ZHqzVx/HGnnrUOtuQo0lRuqQRsdm79t3CydyajMKOSpZlWekiYk1LSwvS09PR3NyMtDRuSE1Eke+rj32MLYcacO/VU/HLm+coXc6wq28+jyX//Q5kGdhScl3MhFpSVjD5gU+EEhHRkBVf4xk52VRZi+a2LoWrGX4v7aiDLAOXT9Uw3FFYYsAjIqIhWzotEzMnpqKt04V/fnJM6XKGlSzL2HxhcePbOLmCwhQDHhERDZlKpcL9yzy9eE9sO4LObrfCFQ2f/fWtOHiqFYnqOKyYN0npcoj8YsAjIqKQuGVBFsanJuFUSwde3VWndDnDZvN2z9Zs188aj/QUbk1G4YkBj4iIQiIxPg53L5kKANi45QiicQ6fyy3jpR2e8MrhWQpnDHhERBQyd14xBaMS1Nhf34Jtjkalywm5bY4GnG7tgJCSgOtmjFe6HKJ+MeAREVHICCmJWL04BwBgeT/6ti/zTq64af4kJMbzVyiFL353EhFRSN13dR7iVMB7n57Bp6dalS4nZNo6u/EmtyajCMGAR0REITUlIwXL50wEADy6JXp68d7aewptnS7kZqRAF0N77lJkYsAjIqKQ8y6Z8uL2OpxubVe4mtB44cLWZLdxazKKAAx4REQUcvrcsdBNEdDpcuOpD2uULmfITre0Y+uhMwA4e5YiAwMeERENiwcu9OI99VEN2jq7Fa5maF7eWQe3DCyaIiAvc7TS5RBdEgMeERENiy/MmYgpmhRIbV14vvq40uUMyeYLw7O3s/eOIgQDHhERDQt1nApfX5oHAHhs6xG43JG58PGnp1qxt64F8XEqrJifpXQ5RAFhwCMiomFTVJCN9FEJONrYBtv+U0qXMyje3rvPzRgPzehEhashCgwDHhERDZuUxHjcecUUAJG5ZIrbLeMl7/CsjsOzFDkY8IiIaFjdvWQqEtQqVB5twvZjTUqXE5SPjjSirrkdqcnx+PxMbk1GkYMBj4iIhtWEtGTcssDT+/XoliMKVxOcFy/03q2YNwnJCWqFqyEKHAMeERENuweu8Uy2eGNPPWqdbQpXE5j2Lhfe2O3Zmoxr31GkYcAjIqJhN3NiGpZNz4RbBv7+QWT04tn2n0JrRzcmC6Nw+VSN0uUQBYUBj4iIRoR34ePnKmvRfL5L4WoubbP9wtZki7IQF8etySiyMOAREdGIWDY9EzMnpuJcpwv/+uSY0uUMqPFsB9771LM12UoOz1IEYsAjIqIRoVJ9tvDxEx8cRWe3W+GK+vfqrnp0u2XMm5yOaeNTlS6HKGgMeERENGJuWZiFcalJONnSjld31SldTr9euDB7lr13FKkY8IiIaMQkxatxz5KpAICNW45AlsNv+zLHmbPYWStBHafCzQu4NRlFJgY8IiIaUXdeMQWjEtTYX9+CbY5Gpcvpw7tzxbLpmRiXmqRwNUSDw4BHREQjSkhJxKqCbADAxjDbvkyWZWzeweFZinwMeERENOLuW5oHlQr4z8EzOHSqVelyfKpqmlDrPI/RiWp8YfZEpcshGjQGPCIiGnG5GaOx/EKACqftyzZfGJ69Ye4kjErk1mQUuRjwiIhIEd7tyzZvP4HTre0KVwN0dLvw2q56AMDtOg7PUmRjwBskq9UKq9WKtWvX9jqm1+sVrIqIKHLoczXQTRHQ6XLjqQ9rlC4H7x44jebzXZiQloQrtRlKl0M0JEEHPLPZ7As3/kiSBLPZDLPZHNDxgdq81LWC0d/1ve1bLBbYbLaA2rJarRAEAUajERkZGbBYLAAAo9EIjYb7FRIRBcq7fdnTH9XgfKdL0Vq8w7O3LZwMNbcmowgXH8zJhYWFKC8vhyAI0Ov1MBqNfc6x2WxobGxERkZGQMf7azOQawXD3/VFUURFRQXKysp81zQYDJdsq2ctDocDJpNpSLUREcWqL8yZiCmaFBxztsFqP46vXpmrSB1SWyfeOXAaALCSw7MUBQLuwbPb7RAEwffv6upqv+cZjUbk5+cHdLy/NgO5lrdHrieLxQJR9D/l3t/1bTab7zoAIAiCrxfP26vX8+3inkSbzQa9Xg+dTuf3mhfbsGEDZs+ejcWLFwd0PhFRtFPHqXDf1VMBAH/fegRutzILH7+6qx5dLhkzJ6Zi5sQ0RWogCqWAA15VVRVEUfQFqFD0WvXXZiDXEgQBOp3OF/KsVis0Gg20Wm3A13c4HL169DQaDSRJAuAJhMXFxb3eevbc2e12SJKE4uJi2O32gK63Zs0a7Nu3D5WVlQHXSEQU7YoKcpCWHI8jDedg239KkRpevDA8y8kVFC0CDniSJEGj0UCn00Gn06GqqirgYBNsm4Fey2AwQKfTwWQywel0DnkYFwCcTuclzxFFEUVFRSgrK4Ner/e9xmazQRTFkDwzSEQUK0YnxePOC0OzSix8fKyxDVU1TVCpgFsXMuBRdAj4GTytVturd0yj0UAUxYCHJ4NpM9hrOZ3OQU1uyM/P9/XYedsJpAdQq9XC4XD0OW4wGPweJyKigd2zZCoe3SKi8mgTdtRKWJgjjNi1vZMrrs7PxIS05BG7LtFwCrgHz2Aw9Hq+TRRF34SEniEpGP21OdC1erLb7bDb7SgvL4fT6Qy658xgMPQaLu3vOkRENLwmpCXjlgWe3rOR7MWTZRkvcmsyikIqWZYDfqLVarXC6XRCkiRotVrfkGh+fj6qq6t9kxTKysogSRJMJpPvnP6O99dmf8e9JEnC+vXrUVpa6jtmsVhgMBj89sINdH3gs17AUAzzXkpLSwvS09PR3NyMtDQ+zEtEBAD761vwxT9tQZwKeO/H1yFHkzLs19x+rAkr/7YNoxLUqHrQgNFJQS0uQTSigskPQQU8Cg0GPCIi/7762MfYcqgB912dh1/cPHvYr/eLl/bgHx/W4NaFWfjTlxYN+/WIhiKY/MCdLIiIKGzcf2Hh402Vx9B8vmtYr9XlcuOVnXUAODxL0YcBj4iIwsY10zMxY0IqznW68K9Pjg3rtd47eAZNbV3IHJOEpdMyh/VaRCONAY+IiMKGSqXC/cvyAABPfHAUnd3uYbuWd/bsLQuyEK/mr0OKLvyOJiKisHLLwiyMS03CyZZ2vLa7bliu0dLehYoLiypzcWOKRgx4REQUVpLi1bhnyVQAwMb3j2A45gK+sbsend1uTB8/BnOyONmNog8DHhERhZ07r5iCUQlq7KtvwYeOxpC37x2evW3RZKhUqpC3T6Q0BjwiIgo7QkoiigqyAYR+4eMT0nl8JHq2mLyNs2cpSjHgERFRWLrv6jyoVMC7B8/g0KnWkLX74oXeuyu1GkwWRoWsXaJwwoBHRERhaWrmaCyfPREA8OiWIyFpU5Zl3/As176jaMaAR0REYeuBazxLpmzefgJnWjuG3N7euhYcPn0WSfFx+OK8SUNujyhcMeAREVHY0udqsGiKgE6XG099eHTI7b1g9/TeGWZPQFpywpDbIwpXDHhERBTWHriwfdlTH9XgfKdr0O10u9x42bs12UIOz1J0Y8AjIqKwtnzORORoRqGprQvP248Pup2thxvQcLYDY1MScO2McSGskCj8MOAREVFYU8epcN/VnmfxHtt6BG734BY+9k6uuHlBFhK4NRlFOX6HExFR2FtVkIO05HgcaTgH24UtxoJxtqMb/957EgBnz1JsYMAjIqKwNzopHndemQtgcEum/HvPSbR3uZGXORoLc4QQV0cUfhjwiIgoItyzZCoS1Cp8ctSJnbVSUK/1bU22kFuTUWxgwCMioogwIS0ZNy/IAhDc9mWnWtrxgaMBAIdnKXYw4BERUcS4f6lnyZQ39pxErbMtoNe8tOMEZBkoyB2LKRkpw1keUdhgwCMioogxOysNS6dlwuWW8fgHRwN6jXdx49vYe0cxhAGPiIgiygPXeHrxNlUeQ/P5rgHP3V/fggMnW5GojsNN87k1GcUOBjwiIooo10zPxIwJqTjX6cKznxwb8NwXL0yuuG7mOAgpiSNRHlFYYMAjIqKIolKp8PVlnoWPn9h2FF0ut9/zXG4ZL+7wBDxOrqBYw4BHREQR59aFWRiXmoT65na8tqve7zkfiY041dKB9FEJuG7m+BGukEhZDHhERBRxkuLVuPsqz8LHG7eIkOW+25d5J1esmD8JSfHqEa2PSGkMeEREFJHuvCIXyQlx2FvXgg8djb0+dr7ThTf3eHr2ODxLsYgBj4iIItLY0YlYVZADoO/Cx2/tO4lznS7kaEahIHesEuURKYoBj4iIItZ9V+dBpQLePXgGh0+3+o57tyZbya3JKEYx4BERUcSamjkaX5g9AQDw6JYjAIAzrR3YcsizNRkXN6ZYxYA3SFarFVarFWvXru11TK/XK1gVEVHseWCZZ+HjF7afwJnWDryysw4ut4wFOQK048YoXB2RMoIOeGaz2Rdu/JEkCWazGWazOaDj/bVZVFQEu90Ou93eK0QNVn/X917XYrHAZrMF1JbVaoUgCDAajcjIyIDFYgEAGI1GaDSaIddKRESB0+eOxcIcAZ3dbjz1UY1vePZ29t5RDIsP5uTCwkKUl5dDEATo9XoYjcY+59hsNjQ2NiIjIyOg4/21KYoirr/+ehQUFKC8vDzYzyugukRRREVFBcrKyny1GAyGS7bV8/N2OBwwmUxDro+IiAZHpVLhgWVarPmnHY9tEXGu04X4OBW3JqOYFnDAs9vtEATB9+/q6mq/5xmNRjidTkiSdMnjA7W5bt06vwHSS5IkWCwWlJSU+I5ZLBYYDAZotdqA6rLZbL7rA4AgCLDZbDAYDLBarXA6nb3a0Gg0vWqy2WzQ6/XQ6XT91klERMNv+ZwJyNGMQq3zPADg2svGIWNMksJVESkn4IBXVVUFURQhip6p6CaTydfzNVgDtVlZWQkAvpBVXFzc67WCIECn08FsNqOkpARWqxUajcZvuOuPw+Ho1aOn0Wh8AXCgcAl4AqkkSSguLobdbg8o5G3YsAEbNmyAy+UKuEYiIrq0eHUc7rs6D79+ZR8AYKWOw7MU2wJ+Bk+SJGg0Guh0Ouh0OlRVVcFutw/p4gO1WVpaCqPRiOLiYpSWlvbpEQQAg8EAnU4Hk8kEp9N5yVAWiIt77fwRRRFFRUUoKyuDXq/3vcZms0EUxX6fT1yzZg327dvnC69ERBQ6qwpyMFkYheyxo2CYNUHpcogUFXAPnlar7dU7ptFoIIrikIYn+2tTFEVUVlaitLQUgKe3bqBrOZ3OQU1uyM/P7xUcnU5nQD2AWq0WDoejz3GDweD3OBERDb/RSfF46wfXQKUCkhO4NRnFtoB78AwGg28oFfD0YnknJPjrXRtKm1qtFoWFhb7jkiT5DXfeWbbl5eVwOp399pwNdP2evWk9PyciIoo8o5PikZIY1PxBoqikkv3t0NwP78QDSZKg1Wp9Q6L5+fmorq72TVIoKyuDJEkwmUy+c/o73l+b3rBWWVkJk8nUp2dNkiSsX7/e18sHDDzJYqDrA5/1AoZimPdSWlpakJ6ejubmZqSlpQ379YiIiCjyBZMfggp4FBoMeERERBSsYPIDd7IgIiIiijIMeERERERRhgGPiIiIKMow4BERERFFGQY8IiIioijDgEdEREQUZRjwiIiIiKIMAx4RERFRlGHAIyIiIooy3LBPAd7NQ1paWhSuhIiIiCKFNzcEsgkZA54CWltbAQA5OTkKV0JERESRprW1Fenp6QOew71oFeB2u1FXV4fU1FSoVKphuUZLSwtycnJQW1vL/W4VwPuvLN5/ZfH+K4v3X1nDef9lWUZrayuysrIQFzfwU3bswVNAXFwcsrOzR+RaaWlp/A+uIN5/ZfH+K4v3X1m8/8oarvt/qZ47L06yICIiIooyDHhEREREUYYBL0olJSXhl7/8JZKSkpQuJSbx/iuL919ZvP/K4v1XVrjcf06yICIiIooy7MEjIiIiijIMeERERERRhsukhDGr1QoAcDqd0Gq1MBgMAZ8TquOxLJB7IkkSLBYLAKCkpMR33GKxQKPRQBRFGAwG6HS6AY97r+VlNBqH5XOKJIF+/2u1WlRVVQEAiouLAQR//4uKirBx40YIgjACn1lkCOT+FxUVYd26dQCATZs2obS0FMDg7r+/dmJZoPff3/dtsPe/5zUFQeDPfwR2/4O9zwP9/Hc6naiurkZRUVHo7r9MYcnhcMjFxcW+9w0GQ8DnhOp4LAv0npSXl8slJSVyaWmp71h1dbVsNBr7vLa/401NTb1e3/O6sSqQ+9/U1CTrdDrfv70/zoK9/w6HQwYgC4IgC4IgA+j19YhFgX7/63Q6WRAE2WAwyE1NTbIsB3//+2snlgX689/f9+1g7r8sf/b/qby8PNSfTsQJ5P4He58HOu69501NTbIgCCH7PDhEG6ZsNluvv8oEQYDNZgvonFAdj2WB3hOj0Yj8/Pw+r9Vqtb2O2e32fo8LgoCysjLY7XbftWJdIPdfEARUV1cDgO8vYu9rg7n/oiiiqanJ91ZWVtarNzYWBfr9v27dOjQ1NaGiosJ3frD3v792Ylkg97+/79vB3H8AeO6557B69erQfzIRKNDfv8Hc5/6OO51OVFRU+K6j0Wh6fV2GgkO0YcrhcCAjI8P3vkajgSRJAZ0TquOxbCj3RKvVorKy0ve+KIoQRbHf4zqdDqWlpdDr9dDpdHj77bdD9nlEqmDuv8ViQUVFBcrLywEEf/97DodbLBasWrUqxJ9N5An0/nvvp9PpBOAZIh/M97+/dmJZIPe/5zBez+/bwdx/u90Og8HQ51GRWBXI/Q/2Pg/086fn19LpdPYZOh8s9uBFEO8Pv8GcE6rjsSzQe+INDJIk+f7qEwSh3+OA5xdldXU1NBoNrr/++hBXHh36u//FxcUwmUxYu3YtgMHdf8DzA1eSJPYg9cPf/S8tLYXRaERxcTFKS0shSdKg7r+/dqi3/r7/L/6+Hcz99wYQ6t/F9z/Y+3ypnz8AYDKZsHHjxpDVzIAXpi4e9vM+6BnIOaE6HsuGek/Ky8shiiIKCgogCAIKCgr6PW61WlFYWAidToeKigoUFBTE/BB5oPffGwQMBgOee+45330L5v57lZWVhewv50gXyP23Wq2+UA14flmJoggg+O///tqJVcH8/PH3fRvM/TebzQA8X8/KykpUVFSEbIgwUgV6/4P9OTPQzx/v74FQTrBjwAtTBoOhT3eutxu35y81f+eE6ngsC+T+90eSJBQVFUGn08HpdPr+M/d33Ol0QqPR+F5fWFjY6/1YFMj9t1gsWL9+ve8cjUbjG0oJ5v57eWfkUmD3X6vVorCw0HeOJEnQ6XRB3//+2ollwfz8ufj7Ntj7X1JSAqPRCKPR6Pta8P5f+v4He58H+vnjfebPaDT6ngsOBe5kEcZ6TtPWaDS+ZJ+fn4/q6moIgtDvOaE6HssCuf82mw1lZWWQJAkmk8l3Ts/p8P0tn9LzuNls9v1n5/33uNT9Bz77wVhRUYGMjAzfPQ32/gOAXq/H22+/zSHaC4L5+VNZWQmTyeQLGsHe//7aiWWB3H/A//ftYL7/bTYb1q5dC61Wi9LS0pj/GgRy/4O9z/6Oi6IIvV7vO0eSJIQqljHgEREREUUZDtESERERRRkGPCIiIqIow4BHREREFGUY8IiIiIiiDAMeERERURCsVmuv2a+AZ5asdzZyOGDAIyIioqgmSRLMZrNvYWcvq9UKq9XqC2eBMhqNvdYr7bk+rXcbsuGqOVAMeERERBTVbDYbGhsbex0TRREVFRW9tskbLEEQUFxcDIvFAq1We8l1BC0Wy6BqDkb8oF9JREREpDBJkmCxWPosKmwwGHxBy2g0wul09toJxLtQupd38XqDwQCr1dpn/9lAFqH37o19qf19A9lv2V/NwWDAIyIiooglCAJ0Oh3MZjNKSkpgtVqh0Wgu2YvmcDiQkZHhe9+71SGAoHcTslqtEAQBBoMB+fn5sFqtfXYLGWkcoiUiIqKIZjAYoNPpYDKZ4HQ6B73d48W9dv2x2WwQRdG3pZnBYIAkSbBarXA4HIqHO4A9eERERBQlvHvHBiI/P7/X8KfT6Qx4D16DwQCHw+F7XxAEX6j0Fy4lScL69et971/8fN1w7MHMgEdEREQRzW63w263o7y8HBaLBVar9ZK9eAaDodeSJqIowmAwDEt9giD0msThHU4eTgx4REREFLEkScKmTZt8Aco7m7XnRAebzYaKigpIkgStVguj0QitVovVq1f7JlSsW7dOyU+jD381B0Mly7I8TLURERER0UVGogePAY+IiIgoynAWLREREVGUYcAjIiIiijIMeERERERRhgGPiIiIKMow4BERERFFGQY8IiIioijDgEdEREQUZRjwiIiIiKIMAx4RERFRlGHAIyIiIooyDHhEREREUeb/A7A6Y69pUJNAAAAAAElFTkSuQmCC", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "set_rc_params_article(ncol=2)\n", "fig = plt.figure()\n", @@ -1281,23 +950,10 @@ }, { "cell_type": "code", - "execution_count": 67, + "execution_count": null, "id": "1e93c2af-f734-4b6c-bdf8-9078e9a22e2f", "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([-8.97943035e+01, 5.03244272e-11, 2.98009714e-14, 4.98998640e+09,\n", - " 1.13014792e-04, 5.03244272e-11, 3.02036061e-14, -4.94554646e+09,\n", - " -1.12008002e-04])" - ] - }, - "execution_count": 67, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "res_a[0]" ] @@ -1326,8 +982,7 @@ "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.6" + "pygments_lexer": "ipython3" } }, "nbformat": 4, diff --git a/numcosmo/model/nc_hiprim_two_fluids.c b/numcosmo/model/nc_hiprim_two_fluids.c index 3e45a2c12..fd1e1924b 100644 --- a/numcosmo/model/nc_hiprim_two_fluids.c +++ b/numcosmo/model/nc_hiprim_two_fluids.c @@ -1,13 +1,13 @@ /*************************************************************************** * nc_hiprim_two_fluids.c * - * Tue October 27 14:13:46 2015 - * Copyright 2015 Sandro Dias Pinto Vitenti + * Tue April 27 11:14:53 2024 + * Copyright 2024 Sandro Dias Pinto Vitenti * ****************************************************************************/ /* * nc_hiprim_two_fluids.c - * Copyright (C) 2015 Sandro Dias Pinto Vitenti + * Copyright (C) 2024 Sandro Dias Pinto Vitenti * * numcosmo is free software: you can redistribute it and/or modify it * under the terms of the GNU General Public License as published by the @@ -37,11 +37,14 @@ #endif /* HAVE_CONFIG_H */ #include "build_cfg.h" -#include "nc_hiprim_two_fluids.h" +#include "model/nc_hiprim_two_fluids.h" +#include "math/ncm_serialize.h" +#include "math/ncm_cfg.h" typedef struct _NcHIPrimTwoFluidsPrivate { NcmSpline2d *lnSA_powspec_lnk_lnw; + gboolean use_default_calib; } NcHIPrimTwoFluidsPrivate; @@ -51,6 +54,7 @@ enum { PROP_0, PROP_LNK_LNW_SPLINE, + PROP_USE_DEFAULT_CALIB, PROP_SIZE, }; @@ -60,6 +64,47 @@ nc_hiprim_two_fluids_init (NcHIPrimTwoFluids *two_fluids) NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); self->lnSA_powspec_lnk_lnw = NULL; + self->use_default_calib = FALSE; +} + +static void +_nc_hiprim_two_fluids_set_property (GObject *object, guint prop_id, const GValue *value, GParamSpec *pspec) +{ + NcHIPrimTwoFluids *two_fluids = NC_HIPRIM_TWO_FLUIDS (object); + NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); + + switch (prop_id) + { + case PROP_LNK_LNW_SPLINE: + nc_hiprim_two_fluids_set_lnk_lnw_spline (two_fluids, g_value_get_object (value)); + break; + case PROP_USE_DEFAULT_CALIB: + nc_hiprim_two_fluids_set_use_default_calib (two_fluids, g_value_get_boolean (value)); + break; + default: /* LCOV_EXCL_LINE */ + G_OBJECT_WARN_INVALID_PROPERTY_ID (object, prop_id, pspec); /* LCOV_EXCL_LINE */ + break; /* LCOV_EXCL_LINE */ + } +} + +static void +_nc_hiprim_two_fluids_get_property (GObject *object, guint prop_id, GValue *value, GParamSpec *pspec) +{ + NcHIPrimTwoFluids *two_fluids = NC_HIPRIM_TWO_FLUIDS (object); + NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); + + switch (prop_id) + { + case PROP_LNK_LNW_SPLINE: + g_value_set_object (value, nc_hiprim_two_fluids_peek_lnk_lnw_spline (two_fluids)); + break; + case PROP_USE_DEFAULT_CALIB: + g_value_set_boolean (value, nc_hiprim_two_fluids_get_use_default_calib (two_fluids)); + break; + default: /* LCOV_EXCL_LINE */ + G_OBJECT_WARN_INVALID_PROPERTY_ID (object, prop_id, pspec); /* LCOV_EXCL_LINE */ + break; /* LCOV_EXCL_LINE */ + } } static void @@ -89,7 +134,10 @@ nc_hiprim_two_fluids_class_init (NcHIPrimTwoFluidsClass *klass) NcHIPrimClass *prim_class = NC_HIPRIM_CLASS (klass); NcmModelClass *model_class = NCM_MODEL_CLASS (klass); - object_class->finalize = &_nc_hiprim_two_fluids_finalize; + object_class->finalize = &_nc_hiprim_two_fluids_finalize; + object_class->dispose = &_nc_hiprim_two_fluids_dispose; + model_class->set_property = &_nc_hiprim_two_fluids_set_property; + model_class->get_property = &_nc_hiprim_two_fluids_get_property; ncm_model_class_set_name_nick (model_class, "Power Law model for primordial spectra", "TwoFluids"); ncm_model_class_add_params (model_class, NC_HIPRIM_TWO_FLUIDS_SPARAM_LEN, 0, PROP_SIZE); @@ -108,13 +156,13 @@ nc_hiprim_two_fluids_class_init (NcHIPrimTwoFluidsClass *klass) /* Set ln(k_0) param info */ ncm_model_class_set_sparam (model_class, NC_HIPRIM_TWO_FLUIDS_LNK0, "\\ln(k_0)", "lnk0", - -3.0 * M_LN10, 3.0 * M_LN10, 1.0e-1, + -4.0 * M_LN10, 4.0 * M_LN10, 1.0e-1, NC_HIPRIM_DEFAULT_PARAMS_ABSTOL, NC_HIPRIM_TWO_FLUIDS_DEFAULT_LNK0, NCM_PARAM_TYPE_FIXED); /* Set ln(w) param info */ ncm_model_class_set_sparam (model_class, NC_HIPRIM_TWO_FLUIDS_LNW, "\\ln(w)", "lnw", - -5.0 * M_LN10, 0.0 * M_LN10, 1.0e-1, + -5.0 * M_LN10, -1.0 * M_LN10, 1.0e-1, NC_HIPRIM_DEFAULT_PARAMS_ABSTOL, NC_HIPRIM_TWO_FLUIDS_DEFAULT_LNW, NCM_PARAM_TYPE_FIXED); @@ -127,6 +175,21 @@ nc_hiprim_two_fluids_class_init (NcHIPrimTwoFluidsClass *klass) /* Check for errors in parameters initialization */ ncm_model_class_check_params_info (model_class); + g_object_class_install_property (object_class, + PROP_LNK_LNW_SPLINE, + g_param_spec_object ("lnk-lnw-spline", + NULL, + "Spline for the primordial adiabatic scalar power spectrum as a function of ln(k) and ln(w)", + NCM_TYPE_SPLINE2D, + G_PARAM_READWRITE | G_PARAM_STATIC_NAME | G_PARAM_STATIC_BLURB)); + g_object_class_install_property (object_class, + PROP_USE_DEFAULT_CALIB, + g_param_spec_boolean ("use-default-calib", + NULL, + "Use default calibration", + FALSE, + G_PARAM_READWRITE | G_PARAM_CONSTRUCT | G_PARAM_STATIC_NAME | G_PARAM_STATIC_BLURB)); + nc_hiprim_set_lnSA_powspec_lnk_impl (prim_class, &_nc_hiprim_two_fluids_lnSA_powespec_lnk); nc_hiprim_set_lnT_powspec_lnk_impl (prim_class, &_nc_hiprim_two_fluids_lnT_powespec_lnk); } @@ -177,6 +240,57 @@ nc_hiprim_two_fluids_new (void) return prim_pl; } +/** + * nc_hiprim_two_fluids_set_use_default_calib: + * @two_fluids: a #NcHIPrimTwoFluids + * @use_default_calib: a #gboolean + * + * Set the use_default_calib flag. + * + */ +void +nc_hiprim_two_fluids_set_use_default_calib (NcHIPrimTwoFluids *two_fluids, gboolean use_default_calib) +{ + NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); + + if ((use_default_calib && self->use_default_calib) || (!use_default_calib && !self->use_default_calib)) + return; + + if (use_default_calib) + { + NcmSerialize *ser = ncm_serialize_new (NCM_SERIALIZE_OPT_CLEAN_DUP); + gchar *default_calib_file = ncm_cfg_get_data_filename ("hiprim_2f_spline.bin", TRUE); + + ncm_spline2d_clear (&self->lnSA_powspec_lnk_lnw); + + self->lnSA_powspec_lnk_lnw = NCM_SPLINE2D (ncm_serialize_from_binfile (ser, default_calib_file)); + g_assert_nonnull (self->lnSA_powspec_lnk_lnw); + g_assert (NCM_IS_SPLINE2D (self->lnSA_powspec_lnk_lnw)); + g_assert (ncm_spline2d_is_init (self->lnSA_powspec_lnk_lnw)); + + g_free (default_calib_file); + ncm_serialize_free (ser); + } + + self->use_default_calib = use_default_calib; +} + +/** + * nc_hiprim_two_fluids_get_use_default_calib: + * @two_fluids: a #NcHIPrimTwoFluids + * + * Get the use_default_calib flag. + * + * Returns: a #gboolean + */ +gboolean +nc_hiprim_two_fluids_get_use_default_calib (NcHIPrimTwoFluids *two_fluids) +{ + NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); + + return self->use_default_calib; +} + /** * nc_hiprim_two_fluids_set_lnk_lnw_spline: * @two_fluids: a #NcHIPrimTwoFluids @@ -190,6 +304,13 @@ nc_hiprim_two_fluids_set_lnk_lnw_spline (NcHIPrimTwoFluids *two_fluids, NcmSplin { NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); + if (self->use_default_calib) + { + g_error ("nc_hiprim_two_fluids_set_lnk_lnw_spline: Cannot set spline when use_default_calib is TRUE."); + + return; + } + ncm_spline2d_clear (&self->lnSA_powspec_lnk_lnw); self->lnSA_powspec_lnk_lnw = lnSA_powspec_lnk_lnw; diff --git a/numcosmo/model/nc_hiprim_two_fluids.h b/numcosmo/model/nc_hiprim_two_fluids.h index 74c344a5e..719da4c49 100644 --- a/numcosmo/model/nc_hiprim_two_fluids.h +++ b/numcosmo/model/nc_hiprim_two_fluids.h @@ -1,13 +1,13 @@ /*************************************************************************** * nc_hiprim_two_fluids.h * - * Tue October 27 14:14:03 2015 - * Copyright 2015 Sandro Dias Pinto Vitenti + * Tue Apr 23 11:14:19 2024 + * Copyright 2024 Sandro Dias Pinto Vitenti * ****************************************************************************/ /* * nc_hiprim_two_fluids.h - * Copyright (C) 2015 Sandro Dias Pinto Vitenti + * Copyright (C) 2024 Sandro Dias Pinto Vitenti * * numcosmo is free software: you can redistribute it and/or modify it * under the terms of the GNU General Public License as published by the @@ -52,8 +52,8 @@ typedef struct _NcHIPrimTwoFluids NcHIPrimTwoFluids; * @NC_HIPRIM_TWO_FLUIDS_LNW: Logarithm of the equation of state parameter $w$. * @NC_HIPRIM_TWO_FLUIDS_N_T: Spectral index of the tensor power spectrum. * - * Parameters for the two fluids primordial power spectrum. - * + * Parameters for the two fluids primordial power spectrum. + * */ typedef enum /*< enum,underscore_name=NC_HIPRIM_TWO_FLUIDS_SPARAMS >*/ { @@ -76,7 +76,6 @@ struct _NcHIPrimTwoFluids { /*< private >*/ NcHIPrim parent_instance; - }; GType nc_hiprim_two_fluids_get_type (void) G_GNUC_CONST; @@ -89,9 +88,13 @@ GType nc_hiprim_two_fluids_get_type (void) G_GNUC_CONST; NcHIPrimTwoFluids *nc_hiprim_two_fluids_new (void); +void nc_hiprim_two_fluids_set_use_default_calib (NcHIPrimTwoFluids *two_fluids, gboolean use_default_calib); +gboolean nc_hiprim_two_fluids_get_use_default_calib (NcHIPrimTwoFluids *two_fluids); + void nc_hiprim_two_fluids_set_lnk_lnw_spline (NcHIPrimTwoFluids *two_fluids, NcmSpline2d *lnSA_powspec_lnk_lnw); NcmSpline2d *nc_hiprim_two_fluids_peek_lnk_lnw_spline (NcHIPrimTwoFluids *two_fluids); G_END_DECLS #endif /* _NC_HIPRIM_TWO_FLUIDS_H_ */ + diff --git a/numcosmo_py/app/generate.py b/numcosmo_py/app/generate.py index efc9c75dc..e29ba9bbf 100644 --- a/numcosmo_py/app/generate.py +++ b/numcosmo_py/app/generate.py @@ -47,8 +47,10 @@ @dataclasses.dataclass class GeneratePlanck: - """Common block for commands that load an experiment. All commands that load an - experiment should inherit from this class.""" + """Common block for commands that load an experiment. + + All commands that load an experiment should inherit from this class. + """ experiment: Annotated[ Path, typer.Argument(help="Path to the experiment file to fit.") @@ -64,7 +66,6 @@ class GeneratePlanck: def __post_init__(self): """Generate Planck 2018 TT baseline experiment.""" - Ncm.cfg_init() if self.experiment.suffix != ".yaml": @@ -97,8 +98,10 @@ def __post_init__(self): @dataclasses.dataclass class GenerateJpasForecast: - """Common block for commands that load an experiment. All commands that load an - experiment should inherit from this class.""" + """Common block for commands that load an experiment. + + All commands that load an experiment should inherit from this class. + """ experiment: Annotated[ Path, typer.Argument(help="Path to the experiment file to fit.") @@ -209,7 +212,6 @@ class GenerateJpasForecast: def __post_init__(self): """Generate JPAS 2024 forecast experiment.""" - Ncm.cfg_init() if self.experiment.suffix != ".yaml": diff --git a/numcosmo_py/experiments/planck18.py b/numcosmo_py/experiments/planck18.py index 8497323da..0eba5cb4b 100644 --- a/numcosmo_py/experiments/planck18.py +++ b/numcosmo_py/experiments/planck18.py @@ -38,9 +38,8 @@ class Planck18Types(str, Enum): EXP_PARAMETERS: dict[str, dict[str, float]] = { Planck18Types.TT: { "NcHICosmo:H0": 66.86, - "NcHICosmo:Omegac": 0.12068 / 0.6686**2, - "NcHICosmo:Omegab": 0.022126 / 0.6686**2, - "NcHICosmo:w": -1.0, + "NcHICosmo:omegac": 0.12068, + "NcHICosmo:omegab": 0.022126, "NcHIPrim:ln10e10ASA": 3.0413, "NcHIPrim:n_SA": 0.9635, "NcHIReion:z_re": 7.54, @@ -62,9 +61,8 @@ class Planck18Types(str, Enum): }, Planck18Types.TTTEEE: { "NcHICosmo:H0": 67.32, - "NcHICosmo:Omegac": 0.12010 / 0.6732**2, - "NcHICosmo:Omegab": 0.022377 / 0.6732**2, - "NcHICosmo:w": -1.0, + "NcHICosmo:omegac": 0.12010, + "NcHICosmo:omegab": 0.022377, "NcHIPrim:ln10e10ASA": 3.0447, "NcHIPrim:n_SA": 0.96589, "NcHIReion:z_re": 7.68, @@ -108,10 +106,10 @@ def create_cosmo_for_cmb(massive_nu: bool = False) -> Nc.HICosmo: cosmo = Nc.HICosmoDEXcdm() cosmo.params_set_default_ftype() - cosmo.omega_x2omega_k() + cosmo.cmb_params() cosmo.param_set_by_name("H0", 70.0) - cosmo.param_set_by_name("Omegab", 0.05) - cosmo.param_set_by_name("Omegac", 0.25) + cosmo.param_set_by_name("omegab", 0.022) + cosmo.param_set_by_name("omegac", 0.12) if massive_nu: cosmo.orig_param_set(Nc.HICosmoDESParams.ENNU, 2.0328) @@ -121,7 +119,7 @@ def create_cosmo_for_cmb(massive_nu: bool = False) -> Nc.HICosmo: cosmo.set_property("H0_fit", True) cosmo.set_property("Omegac_fit", True) cosmo.set_property("Omegab_fit", True) - cosmo.set_property("w_fit", True) + cosmo.set_property("w_fit", False) cosmo.param_set_by_name("Omegak", 0.00) cosmo.set_property("Omegax_fit", False) diff --git a/numcosmo_py/nc.pyi b/numcosmo_py/nc.pyi index dd0584ea2..4fbc29c50 100644 --- a/numcosmo_py/nc.pyi +++ b/numcosmo_py/nc.pyi @@ -193,6 +193,11 @@ HIPRIM_SBPL_DEFAULT_N_SA: float = 0.9742 HIPRIM_SBPL_DEFAULT_N_T: float = 0.0 HIPRIM_SBPL_DEFAULT_RA: float = 0.8 HIPRIM_SBPL_DEFAULT_T_SA_RATIO: float = 0.2 +HIPRIM_TWO_FLUIDS_DEFAULT_LN10E10ASA: float = 3.179 +HIPRIM_TWO_FLUIDS_DEFAULT_LNK0: float = 0.0 +HIPRIM_TWO_FLUIDS_DEFAULT_LNW: int = 0 +HIPRIM_TWO_FLUIDS_DEFAULT_N_T: float = 0.0 +HIPRIM_TWO_FLUIDS_DEFAULT_T_SA_RATIO: float = 0.2 HIREION_CAMB_DEFAULT_HEIII_REION_DELTA: float = 0.5 HIREION_CAMB_DEFAULT_HEIII_Z: float = 3.5 HIREION_CAMB_DEFAULT_HII_HEII_REION_DELTA: float = 0.5 @@ -11532,8 +11537,19 @@ class HIPertTwoFluids(HIPert): ): ... @staticmethod def clear(ptf: HIPertTwoFluids) -> None: ... + def compute_zeta_spectrum( + self, + cosmo: HICosmo, + mode: int, + alpha_i: float, + alpha: float, + ki: float, + kf: float, + nnodes: int, + ) -> NumCosmoMath.Spline: ... def eom(self, cosmo: HICosmo, alpha: float) -> HIPertITwoFluidsEOM: ... def evolve(self, cosmo: HICosmo, alphaf: float) -> None: ... + def evolve_array(self, cosmo: HICosmo, alphaf: float) -> NumCosmoMath.Matrix: ... def evolve_mode1sub(self, cosmo: HICosmo, alphaf: float) -> None: ... def free(self) -> None: ... def get_cross_time( @@ -12479,6 +12495,136 @@ class HIPrimSBPLClass(GObject.GPointer): parent_class: HIPrimClass = ... +class HIPrimTwoFluids(HIPrim): + r""" + :Constructors: + + :: + + HIPrimTwoFluids(**properties) + new() -> NumCosmo.HIPrimTwoFluids + + Object NcHIPrimTwoFluids + + Properties from NcHIPrimTwoFluids: + lnk-lnw-spline -> NcmSpline2d: lnk-lnw-spline + Spline for the primordial adiabatic scalar power spectrum as a function of ln(k) and ln(w) + use-default-calib -> gboolean: use-default-calib + Use default calibration + ln10e10ASA -> gdouble: ln10e10ASA + \log(10^{10}A_{\mathrm{SA}}) + T-SA-ratio -> gdouble: T-SA-ratio + A_T/A_{\mathrm{SA}} + lnk0 -> gdouble: lnk0 + \ln(k_0) + lnw -> gdouble: lnw + \ln(w) + n-T -> gdouble: n-T + n_{\mathrm{T}} + ln10e10ASA-fit -> gboolean: ln10e10ASA-fit + \log(10^{10}A_{\mathrm{SA}}):fit + T-SA-ratio-fit -> gboolean: T-SA-ratio-fit + A_T/A_{\mathrm{SA}}:fit + lnk0-fit -> gboolean: lnk0-fit + \ln(k_0):fit + lnw-fit -> gboolean: lnw-fit + \ln(w):fit + n-T-fit -> gboolean: n-T-fit + n_{\mathrm{T}}:fit + + Properties from NcHIPrim: + k-pivot -> gdouble: k-pivot + Pivotal value of k + + Properties from NcmModel: + name -> gchararray: name + Model's name + nick -> gchararray: nick + Model's nick + scalar-params-len -> guint: scalar-params-len + Number of scalar parameters + vector-params-len -> guint: vector-params-len + Number of vector parameters + implementation -> guint64: implementation + Bitwise specification of functions implementation + sparam-array -> NcmObjDictInt: sparam-array + NcmModel array of NcmSParam + params-types -> GArray: params-types + Parameters' types + reparam -> NcmReparam: reparam + Model reparametrization + submodel-array -> NcmObjArray: submodel-array + NcmModel array of submodels + + Signals from GObject: + notify (GParam) + """ + + class Props: + T_SA_ratio: float + T_SA_ratio_fit: bool + ln10e10ASA: float + ln10e10ASA_fit: bool + lnk_lnw_spline: NumCosmoMath.Spline2d + lnk0: float + lnk0_fit: bool + lnw: float + lnw_fit: bool + n_T: float + n_T_fit: bool + use_default_calib: bool + k_pivot: float + implementation: int + name: str + nick: str + params_types: list[None] + reparam: NumCosmoMath.Reparam + scalar_params_len: int + sparam_array: NumCosmoMath.ObjDictInt + submodel_array: NumCosmoMath.ObjArray + vector_params_len: int + + props: Props = ... + parent_instance: HIPrim = ... + def __init__( + self, + T_SA_ratio: float = ..., + T_SA_ratio_fit: bool = ..., + ln10e10ASA: float = ..., + ln10e10ASA_fit: bool = ..., + lnk_lnw_spline: NumCosmoMath.Spline2d = ..., + lnk0: float = ..., + lnk0_fit: bool = ..., + lnw: float = ..., + lnw_fit: bool = ..., + n_T: float = ..., + n_T_fit: bool = ..., + use_default_calib: bool = ..., + k_pivot: float = ..., + reparam: NumCosmoMath.Reparam = ..., + sparam_array: NumCosmoMath.ObjDictInt = ..., + submodel_array: NumCosmoMath.ObjArray = ..., + ): ... + def get_use_default_calib(self) -> bool: ... + @classmethod + def new(cls) -> HIPrimTwoFluids: ... + def peek_lnk_lnw_spline(self) -> NumCosmoMath.Spline2d: ... + def set_lnk_lnw_spline( + self, lnSA_powspec_lnk_lnw: NumCosmoMath.Spline2d + ) -> None: ... + def set_use_default_calib(self, use_default_calib: bool) -> None: ... + +class HIPrimTwoFluidsClass(GObject.GPointer): + r""" + :Constructors: + + :: + + HIPrimTwoFluidsClass() + """ + + parent_class: HIPrimClass = ... + class HIQG1D(GObject.Object): r""" :Constructors: @@ -18903,6 +19049,13 @@ class HIPrimSBPLSParams(GObject.GEnum): RA: HIPrimSBPLSParams = ... T_SA_RATIO: HIPrimSBPLSParams = ... +class HIPrimTwoFluidsSParams(GObject.GEnum): + LN10E10ASA: HIPrimTwoFluidsSParams = ... + LNK0: HIPrimTwoFluidsSParams = ... + LNW: HIPrimTwoFluidsSParams = ... + N_T: HIPrimTwoFluidsSParams = ... + T_SA_RATIO: HIPrimTwoFluidsSParams = ... + class HIReionCambSParams(GObject.GEnum): HEIII_Z: HIReionCambSParams = ... HII_HEII_Z: HIReionCambSParams = ... From f41c48e449b99fceec9df5222aeb730b37d19390 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Tue, 23 Apr 2024 21:00:37 -0300 Subject: [PATCH 06/27] Including two_point model in the app experiment generator. --- numcosmo/model/nc_hiprim_two_fluids.c | 3 + numcosmo_py/app/generate.py | 16 +++- numcosmo_py/experiments/planck18.py | 113 +++++++++++++++++++++++--- 3 files changed, 118 insertions(+), 14 deletions(-) diff --git a/numcosmo/model/nc_hiprim_two_fluids.c b/numcosmo/model/nc_hiprim_two_fluids.c index fd1e1924b..e80b6dc4f 100644 --- a/numcosmo/model/nc_hiprim_two_fluids.c +++ b/numcosmo/model/nc_hiprim_two_fluids.c @@ -330,6 +330,9 @@ nc_hiprim_two_fluids_peek_lnk_lnw_spline (NcHIPrimTwoFluids *two_fluids) { NcHIPrimTwoFluidsPrivate * const self = nc_hiprim_two_fluids_get_instance_private (two_fluids); + if (self->use_default_calib) + return NULL; + return self->lnSA_powspec_lnk_lnw; } diff --git a/numcosmo_py/app/generate.py b/numcosmo_py/app/generate.py index e29ba9bbf..5ae0bca14 100644 --- a/numcosmo_py/app/generate.py +++ b/numcosmo_py/app/generate.py @@ -33,6 +33,7 @@ from numcosmo_py import Ncm from numcosmo_py.experiments.planck18 import ( Planck18Types, + Planck18HIPrimModel, generate_planck18_tt, generate_planck18_ttteee, set_mset_parameters, @@ -60,6 +61,11 @@ class GeneratePlanck: Planck18Types, typer.Option(help="Data type to use.", show_default=True) ] = Planck18Types.TT + prim_model: Annotated[ + Planck18HIPrimModel, + typer.Option(help="Primordial model to use.", show_default=True), + ] = Planck18HIPrimModel.POWER_LAW + massive_nu: Annotated[ bool, typer.Option(help="Use massive neutrinos.", show_default=True) ] = False @@ -74,13 +80,17 @@ def __post_init__(self): ) if self.data_type == Planck18Types.TT: - exp, mfunc_array = generate_planck18_tt(massive_nu=self.massive_nu) + exp, mfunc_array = generate_planck18_tt( + massive_nu=self.massive_nu, prim_model=self.prim_model + ) elif self.data_type == Planck18Types.TTTEEE: - exp, mfunc_array = generate_planck18_ttteee(massive_nu=self.massive_nu) + exp, mfunc_array = generate_planck18_ttteee( + massive_nu=self.massive_nu, prim_model=self.prim_model + ) else: raise ValueError(f"Invalid data type: {self.data_type}") - set_mset_parameters(exp.peek("model-set"), self.data_type) + set_mset_parameters(exp.peek("model-set"), self.data_type, self.prim_model) ser = Ncm.Serialize.new(Ncm.SerializeOpt.CLEAN_DUP) diff --git a/numcosmo_py/experiments/planck18.py b/numcosmo_py/experiments/planck18.py index 0eba5cb4b..259188e56 100644 --- a/numcosmo_py/experiments/planck18.py +++ b/numcosmo_py/experiments/planck18.py @@ -25,6 +25,8 @@ from enum import Enum +import numpy as np + from numcosmo_py import Ncm, Nc @@ -35,8 +37,15 @@ class Planck18Types(str, Enum): TTTEEE = "TTTEEE" -EXP_PARAMETERS: dict[str, dict[str, float]] = { - Planck18Types.TT: { +class Planck18HIPrimModel(str, Enum): + """Planck 18 primordial model.""" + + POWER_LAW = "power-law" + TWO_FLUIDS = "two-fluids" + + +EXP_PARAMETERS: dict[tuple[str, str], dict[str, float]] = { + (Planck18Types.TT, Planck18HIPrimModel.POWER_LAW): { "NcHICosmo:H0": 66.86, "NcHICosmo:omegac": 0.12068, "NcHICosmo:omegab": 0.022126, @@ -59,7 +68,7 @@ class Planck18Types(str, Enum): "NcPlanckFI:calib_217T": 0.99825, "NcPlanckFI:A_planck": 1.00046, }, - Planck18Types.TTTEEE: { + (Planck18Types.TTTEEE, Planck18HIPrimModel.POWER_LAW): { "NcHICosmo:H0": 67.32, "NcHICosmo:omegac": 0.12010, "NcHICosmo:omegab": 0.022377, @@ -88,17 +97,79 @@ class Planck18Types(str, Enum): "NcPlanckFI:galf_TE_A_143_217": 0.664, "NcPlanckFI:galf_TE_A_217": 2.081, }, + (Planck18Types.TT, Planck18HIPrimModel.TWO_FLUIDS): { + "NcHICosmo:H0": 66.86, + "NcHICosmo:omegac": 0.12068, + "NcHICosmo:omegab": 0.022126, + "NcHIPrim:ln10e10ASA": 3.0413, + "NcHIPrim:lnk0": 0.0, + "NcHIPrim:lnw": np.log(1.0e-4), + "NcHIReion:z_re": 7.54, + "NcPlanckFI:A_cib_217": 48.5, + "NcPlanckFI:xi_sz_cib": 0.32, + "NcPlanckFI:A_sz": 7.03, + "NcPlanckFI:ps_A_100_100": 254.9, + "NcPlanckFI:ps_A_143_143": 49.8, + "NcPlanckFI:ps_A_143_217": 47.3, + "NcPlanckFI:ps_A_217_217": 119.9, + "NcPlanckFI:ksz_norm": 0.00, + "NcPlanckFI:gal545_A_100": 8.86, + "NcPlanckFI:gal545_A_143": 10.80, + "NcPlanckFI:gal545_A_143_217": 19.43, + "NcPlanckFI:gal545_A_217": 94.8, + "NcPlanckFI:calib_100T": 0.99965, + "NcPlanckFI:calib_217T": 0.99825, + "NcPlanckFI:A_planck": 1.00046, + }, + (Planck18Types.TTTEEE, Planck18HIPrimModel.TWO_FLUIDS): { + "NcHICosmo:H0": 67.32, + "NcHICosmo:omegac": 0.12010, + "NcHICosmo:omegab": 0.022377, + "NcHIPrim:ln10e10ASA": 3.0447, + "NcHIPrim:lnk0": 0.0, + "NcHIPrim:lnw": np.log(1.0e-4), + "NcHIReion:z_re": 7.68, + "NcPlanckFI:A_cib_217": 47.2, + "NcPlanckFI:xi_sz_cib": 0.42, + "NcPlanckFI:A_sz": 7.23, + "NcPlanckFI:ps_A_100_100": 250.5, + "NcPlanckFI:ps_A_143_143": 47.4, + "NcPlanckFI:ps_A_143_217": 47.3, + "NcPlanckFI:ps_A_217_217": 119.8, + "NcPlanckFI:ksz_norm": 0.01, + "NcPlanckFI:gal545_A_100": 8.86, + "NcPlanckFI:gal545_A_143": 11.10, + "NcPlanckFI:gal545_A_143_217": 19.83, + "NcPlanckFI:gal545_A_217": 95.1, + "NcPlanckFI:calib_100T": 0.99969, + "NcPlanckFI:calib_217T": 0.99816, + "NcPlanckFI:A_planck": 1.00061, + "NcPlanckFI:galf_TE_A_100": 0.1142, + "NcPlanckFI:galf_TE_A_100_143": 0.1345, + "NcPlanckFI:galf_TE_A_100_217": 0.482, + "NcPlanckFI:galf_TE_A_143": 0.224, + "NcPlanckFI:galf_TE_A_143_217": 0.664, + "NcPlanckFI:galf_TE_A_217": 2.081, + }, } -def set_mset_parameters(mset: Ncm.MSet, exp_type: Planck18Types): +def set_mset_parameters( + mset: Ncm.MSet, exp_type: Planck18Types, prim_model: Planck18HIPrimModel +): """Set the experiment parameters.""" - for param, value in EXP_PARAMETERS[exp_type].items(): + for param, value in EXP_PARAMETERS[(exp_type, prim_model)].items(): pi = mset.fparam_get_pi_by_name(param) + if pi is None: + raise ValueError(f"Invalid parameter: {param}") + mset.param_set(pi.mid, pi.pid, value) -def create_cosmo_for_cmb(massive_nu: bool = False) -> Nc.HICosmo: +def create_cosmo_for_cmb( + massive_nu: bool = False, + prim_model: Planck18HIPrimModel = Planck18HIPrimModel.POWER_LAW, +) -> Nc.HICosmo: """Create a cosmology for CMB experiments.""" if massive_nu: cosmo = Nc.HICosmoDEXcdm(massnu_length=1) @@ -123,9 +194,17 @@ def create_cosmo_for_cmb(massive_nu: bool = False) -> Nc.HICosmo: cosmo.param_set_by_name("Omegak", 0.00) cosmo.set_property("Omegax_fit", False) - prim = Nc.HIPrimPowerLaw.new() - prim.set_property("ln10e10ASA_fit", True) - prim.set_property("n_SA_fit", True) + if prim_model == Planck18HIPrimModel.POWER_LAW: + prim = Nc.HIPrimPowerLaw.new() + prim.set_property("ln10e10ASA_fit", True) + prim.set_property("n_SA_fit", True) + elif prim_model == Planck18HIPrimModel.TWO_FLUIDS: + prim = Nc.HIPrimTwoFluids(use_default_calib=True) + prim.set_property("ln10e10ASA_fit", True) + prim.set_property("lnk0_fit", True) + prim.set_property("lnw_fit", True) + else: + raise ValueError(f"Invalid primordial model: {prim_model}") reion = Nc.HIReionCamb.new() reion.set_property("z_re_fit", True) @@ -168,10 +247,16 @@ def create_mfunc_array_for_cmb(cbe: Nc.CBE) -> Ncm.ObjArray: def generate_planck18_tt( massive_nu: bool = False, + prim_model: Planck18HIPrimModel = Planck18HIPrimModel.POWER_LAW, ) -> tuple[Ncm.ObjDictStr, Ncm.ObjArray]: """Generate Planck 2018 TT baseline experiment dictionary.""" # Likelihood cbe_boltzmann = Nc.HIPertBoltzmannCBE.new() + if prim_model == Planck18HIPrimModel.TWO_FLUIDS: + cbe = cbe_boltzmann.peek_cbe() + cbe_prec = cbe.peek_precision() + # Increase the precision for the two-fluids model + cbe_prec.props.k_per_decade_primordial = 30.0 b18_lowl_EE = Nc.DataPlanckLKL.full_new_id( Nc.DataPlanckLKLType.BASELINE_18_LOWL_EE, cbe_boltzmann @@ -192,7 +277,7 @@ def generate_planck18_tt( planck_model = Nc.PlanckFICorTT() planck_model.params_set_default_ftype() - cosmo = create_cosmo_for_cmb(massive_nu=massive_nu) + cosmo = create_cosmo_for_cmb(massive_nu=massive_nu, prim_model=prim_model) mset = Ncm.MSet.new_array([planck_model, cosmo]) mset.prepare_fparam_map() @@ -213,10 +298,16 @@ def generate_planck18_tt( def generate_planck18_ttteee( massive_nu: bool = False, + prim_model: Planck18HIPrimModel = Planck18HIPrimModel.POWER_LAW, ) -> tuple[Ncm.ObjDictStr, Ncm.ObjArray]: """Generate Planck 2018 TT baseline experiment dictionary.""" # Likelihood cbe_boltzmann = Nc.HIPertBoltzmannCBE.new() + if prim_model == Planck18HIPrimModel.TWO_FLUIDS: + cbe = cbe_boltzmann.peek_cbe() + cbe_prec = cbe.peek_precision() + # Increase the precision for the two-fluids model + cbe_prec.props.k_per_decade_primordial = 30.0 b18_lowl_EE = Nc.DataPlanckLKL.full_new_id( Nc.DataPlanckLKLType.BASELINE_18_LOWL_EE, cbe_boltzmann @@ -239,7 +330,7 @@ def generate_planck18_ttteee( planck_model = Nc.PlanckFICorTTTEEE() planck_model.params_set_default_ftype() - cosmo = create_cosmo_for_cmb(massive_nu=massive_nu) + cosmo = create_cosmo_for_cmb(massive_nu=massive_nu, prim_model=prim_model) mset = Ncm.MSet.new_array([planck_model, cosmo]) mset.prepare_fparam_map() From df0b73ab1b12f142004813554068b6a555395a6b Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Tue, 23 Apr 2024 21:06:37 -0300 Subject: [PATCH 07/27] Registring two_fluids model. --- numcosmo/math/ncm_cfg.c | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/numcosmo/math/ncm_cfg.c b/numcosmo/math/ncm_cfg.c index c2e813b81..4c434d403 100644 --- a/numcosmo/math/ncm_cfg.c +++ b/numcosmo/math/ncm_cfg.c @@ -106,11 +106,12 @@ #include "model/nc_hicosmo_Vexp.h" #include "model/nc_hicosmo_de_reparam_ok.h" #include "model/nc_hicosmo_de_reparam_cmb.h" -#include "model/nc_hiprim_power_law.h" #include "model/nc_hiprim_atan.h" -#include "model/nc_hiprim_expc.h" #include "model/nc_hiprim_bpl.h" +#include "model/nc_hiprim_expc.h" +#include "model/nc_hiprim_power_law.h" #include "model/nc_hiprim_sbpl.h" +#include "model/nc_hiprim_two_fluids.h" #include "lss/nc_window_tophat.h" #include "lss/nc_window_gaussian.h" #include "lss/nc_growth_func.h" @@ -622,11 +623,12 @@ ncm_cfg_init_full_ptr (gint *argc, gchar ***argv) ncm_cfg_register_obj (NC_TYPE_HICOSMO_IDEM2_REPARAM_OK); ncm_cfg_register_obj (NC_TYPE_HICOSMO_IDEM2_REPARAM_CMB); - ncm_cfg_register_obj (NC_TYPE_HIPRIM_POWER_LAW); ncm_cfg_register_obj (NC_TYPE_HIPRIM_ATAN); - ncm_cfg_register_obj (NC_TYPE_HIPRIM_EXPC); ncm_cfg_register_obj (NC_TYPE_HIPRIM_BPL); + ncm_cfg_register_obj (NC_TYPE_HIPRIM_EXPC); + ncm_cfg_register_obj (NC_TYPE_HIPRIM_POWER_LAW); ncm_cfg_register_obj (NC_TYPE_HIPRIM_SBPL); + ncm_cfg_register_obj (NC_TYPE_HIPRIM_TWO_FLUIDS); ncm_cfg_register_obj (NC_TYPE_CBE_PRECISION); From 544ba991812389d0d7457d1415547cbc8705bc23 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Wed, 24 Apr 2024 13:13:53 -0300 Subject: [PATCH 08/27] Extending calibration to w = 1.0e-7. --- data/hiprim_2f_spline.bin | Bin 123352 -> 171592 bytes .../two_fluids_calibrate.ipynb | 21 ++++++++++-------- 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zDbDZX{1MI{G zP>{%naPEk6Pn@5?c{t9=I6sf`Oq^fG`7NAR;k*Io?Ktnj`Aht}o0}&Me#o3*3eq-I zl0=AGbjZnAN&Nq9{^jHE6S`R`NbXxVYgoupSvL<4{F^(i0si?8&($!HNN3+rkh1W1 KG5+3({r>^3%Ezw& diff --git a/notebooks/primordial_perturbations/two_fluids_calibrate.ipynb b/notebooks/primordial_perturbations/two_fluids_calibrate.ipynb index 7f2e83285..5d3d5c8d5 100644 --- a/notebooks/primordial_perturbations/two_fluids_calibrate.ipynb +++ b/notebooks/primordial_perturbations/two_fluids_calibrate.ipynb @@ -318,8 +318,8 @@ " pert = Nc.HIPertTwoFluids.new()\n", " pert.props.reltol = 1.0e-9\n", " \n", - " spec1 = pert.compute_zeta_spectrum(cosmo, 1, -cosmo.abs_alpha(1.0e-14), -1.0, 1.0e-3, 1.0e8, 300)\n", - " spec2 = pert.compute_zeta_spectrum(cosmo, 2, -cosmo.abs_alpha(1.0e-14), -1.0, 1.0e-3, 1.0e8, 300)\n", + " spec1 = pert.compute_zeta_spectrum(cosmo, 1, -cosmo.abs_alpha(1.0e-14), -1.0, 1.0e-3, 1.0e8, 100)\n", + " spec2 = pert.compute_zeta_spectrum(cosmo, 2, -cosmo.abs_alpha(1.0e-14), -1.0, 1.0e-3, 1.0e8, 100)\n", "\n", " return spec1, spec2\n", "\n", @@ -417,7 +417,7 @@ "\n", " lnPk_eval = np.array([s.eval(lnk, np.log(w)) for lnk in lnk_a1])\n", "\n", - " assert_allclose(lnPk, lnPk_eval, rtol=1.0e-12)" + " # assert_allclose(lnPk, lnPk_eval, rtol=1.0e-12)" ] }, { @@ -462,6 +462,7 @@ "ax1.set_yscale(\"log\")\n", "ax1.set_xlabel(r\"$k$\")\n", "# ax1.legend()\n", + "ax1.grid()\n", "\n", "pass" ] @@ -518,7 +519,7 @@ "metadata": {}, "outputs": [], "source": [ - "hiprim_2f.props.lnk0 = -9.0\n", + "hiprim_2f.props.lnk0 = -1.8\n", "hiprim_2f.props.lnw = np.log(1.0e-4)\n", "\n", "ell, Dell_2f = compute_D_ell(hiprim_2f)\n", @@ -577,9 +578,9 @@ "ax1 = fig.add_subplot(1, 1, 1)\n", "\n", "lnk_a = np.linspace(np.log(1.0e-3), np.log(1.0e8), 1000)\n", - "lnw_a = np.linspace(np.log(1.0e-5), np.log(1.0e-1), 100)\n", - "hiprim_2f.props.lnk0 = -9.0\n", - "test_hiprim_2f.props.lnk0 = -9.0\n", + "lnw_a = np.linspace(np.log(1.0e-7), np.log(1.0e-1), 100)\n", + "hiprim_2f.props.lnk0 = 0.0\n", + "test_hiprim_2f.props.lnk0 = 0.0\n", "\n", "for lnw in lnw_a[::10]:\n", " hiprim_2f.props.lnw = lnw\n", @@ -588,9 +589,11 @@ " lnPk_test = np.array([test_hiprim_2f.lnSA_powspec_lnk(lnk) for lnk in lnk_a])\n", " lnPk = np.array([hiprim_2f.lnSA_powspec_lnk(lnk) for lnk in lnk_a])\n", "\n", - " ax1.plot(np.exp(lnk_a) / 4000.0, lnPk - lnPk_test)\n", + " ax1.plot(np.exp(lnk_a) / 4000.0, np.exp(lnPk_test))\n", + " # ax1.plot(np.exp(lnk_a) / 4000.0, np.exp(lnPk))\n", "\n", "ax1.set_xscale(\"log\")\n", + "ax1.set_yscale(\"log\")\n", "ax1.set_xlabel(r\"$k$\")\n", "# ax1.legend()\n", "\n", @@ -600,7 +603,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9ca56ae9", + "id": "87556e55", "metadata": {}, "outputs": [], "source": [] diff --git a/numcosmo/model/nc_hiprim_two_fluids.c b/numcosmo/model/nc_hiprim_two_fluids.c index e80b6dc4f..80c952503 100644 --- a/numcosmo/model/nc_hiprim_two_fluids.c +++ b/numcosmo/model/nc_hiprim_two_fluids.c @@ -162,7 +162,7 @@ nc_hiprim_two_fluids_class_init (NcHIPrimTwoFluidsClass *klass) /* Set ln(w) param info */ ncm_model_class_set_sparam (model_class, NC_HIPRIM_TWO_FLUIDS_LNW, "\\ln(w)", "lnw", - -5.0 * M_LN10, -1.0 * M_LN10, 1.0e-1, + -7.0 * M_LN10, -1.0 * M_LN10, 1.0e-1, NC_HIPRIM_DEFAULT_PARAMS_ABSTOL, NC_HIPRIM_TWO_FLUIDS_DEFAULT_LNW, NCM_PARAM_TYPE_FIXED); From 284ed7e97e26a3ffcfbc8c77fcb3ad6cf32b7dac Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Wed, 24 Apr 2024 15:24:44 -0300 Subject: [PATCH 09/27] Added option to skip catalog validation when continuing a MCMC. --- numcosmo/math/ncm_fit_esmcmc.c | 73 +++++++++++++++++++++++++++++----- numcosmo/math/ncm_fit_esmcmc.h | 3 ++ numcosmo_py/app/esmcmc.py | 10 +++++ numcosmo_py/ncm.pyi | 2 + 4 files changed, 78 insertions(+), 10 deletions(-) diff --git a/numcosmo/math/ncm_fit_esmcmc.c b/numcosmo/math/ncm_fit_esmcmc.c index 6d905961a..0807fe432 100644 --- a/numcosmo/math/ncm_fit_esmcmc.c +++ b/numcosmo/math/ncm_fit_esmcmc.c @@ -75,6 +75,7 @@ typedef struct _NcmFitESMCMCPrivate gdouble max_runs_time; gdouble log_time_interval; guint interm_log; + gboolean skip_check; GPtrArray *full_theta; GPtrArray *full_thetastar; GPtrArray *full_thetastar_inout; @@ -123,6 +124,7 @@ enum PROP_TRIM_TYPE, PROP_MIN_RUNS, PROP_MAX_RUNS_TIME, + PROP_SKIP_CHECK, PROP_LOG_TIME_INTERVAL, PROP_INTERM_LOG, PROP_MTYPE, @@ -165,8 +167,10 @@ ncm_fit_esmcmc_init (NcmFitESMCMC *esmcmc) self->min_runs = 0; self->max_runs_time = 0.0; self->log_time_interval = 0.0; + self->interm_log = 0; self->nadd_vals = 0; self->fparam_len = 0; + self->skip_check = FALSE; self->m2lnL = g_ptr_array_new (); self->theta = g_ptr_array_new (); @@ -348,6 +352,9 @@ _ncm_fit_esmcmc_set_property (GObject *object, guint prop_id, const GValue *valu case PROP_MAX_RUNS_TIME: self->max_runs_time = g_value_get_double (value); break; + case PROP_SKIP_CHECK: + ncm_fit_esmcmc_set_skip_check (esmcmc, g_value_get_boolean (value)); + break; case PROP_LOG_TIME_INTERVAL: self->log_time_interval = g_value_get_double (value); break; @@ -433,6 +440,9 @@ _ncm_fit_esmcmc_get_property (GObject *object, guint prop_id, GValue *value, GPa case PROP_MAX_RUNS_TIME: g_value_set_double (value, self->max_runs_time); break; + case PROP_SKIP_CHECK: + g_value_set_boolean (value, ncm_fit_esmcmc_get_skip_check (esmcmc)); + break; case PROP_LOG_TIME_INTERVAL: g_value_set_double (value, self->log_time_interval); break; @@ -603,6 +613,13 @@ ncm_fit_esmcmc_class_init (NcmFitESMCMCClass *klass) "Maximum time between runs", 1.0, G_MAXDOUBLE, 2.0 * 60.0 * 60.0, G_PARAM_READWRITE | G_PARAM_CONSTRUCT | G_PARAM_STATIC_NAME | G_PARAM_STATIC_BLURB)); + g_object_class_install_property (object_class, + PROP_SKIP_CHECK, + g_param_spec_boolean ("skip-check", + NULL, + "Skip check", + FALSE, + G_PARAM_READWRITE | G_PARAM_CONSTRUCT | G_PARAM_STATIC_NAME | G_PARAM_STATIC_BLURB)); g_object_class_install_property (object_class, PROP_LOG_TIME_INTERVAL, g_param_spec_double ("log-time-interval", @@ -1032,6 +1049,39 @@ ncm_fit_esmcmc_set_max_runs_time (NcmFitESMCMC *esmcmc, gdouble max_runs_time) self->max_runs_time = max_runs_time; } +/** + * ncm_fit_esmcmc_set_skip_check: + * @esmcmc: a #NcmFitESMCMC + * @skip_check: a boolean + * + * Set whether to skip the check of the last ensemble in the catalog when continuing a + * run. + */ +void +ncm_fit_esmcmc_set_skip_check (NcmFitESMCMC *esmcmc, gboolean skip_check) +{ + NcmFitESMCMCPrivate * const self = ncm_fit_esmcmc_get_instance_private (esmcmc); + + self->skip_check = skip_check; +} + +/** + * ncm_fit_esmcmc_get_skip_check: + * @esmcmc: a #NcmFitESMCMC + * + * Get whether to skip the check of the last ensemble in the catalog when continuing a + * run. + * + * Returns: the value of the skip_check property. + */ +gboolean +ncm_fit_esmcmc_get_skip_check (NcmFitESMCMC *esmcmc) +{ + NcmFitESMCMCPrivate * const self = ncm_fit_esmcmc_get_instance_private (esmcmc); + + return self->skip_check; +} + /** * ncm_fit_esmcmc_has_rng: * @esmcmc: a #NcmFitESMCMC @@ -1626,22 +1676,25 @@ ncm_fit_esmcmc_start_run (NcmFitESMCMC *esmcmc) const guint len = ncm_mset_catalog_len (self->mcat); const guint start = len > self->nwalkers ? len - self->nwalkers : 0; - if (!ncm_fit_esmcmc_validate (esmcmc, start, len)) + if (!self->skip_check) { - if (self->mtype > NCM_FIT_RUN_MSGS_NONE) + if (!ncm_fit_esmcmc_validate (esmcmc, start, len)) { - ncm_cfg_msg_sepa (); - g_message ("# NcmFitESMCMC: Last ensemble failed in the m2lnL check, the catalog may be corrupted, removing last ensemble and retrying...\n"); - } + if (self->mtype > NCM_FIT_RUN_MSGS_NONE) + { + ncm_cfg_msg_sepa (); + g_message ("# NcmFitESMCMC: Last ensemble failed in the m2lnL check, the catalog may be corrupted, removing last ensemble and retrying...\n"); + } - ncm_fit_esmcmc_end_run (esmcmc); + ncm_fit_esmcmc_end_run (esmcmc); - ncm_mset_catalog_remove_last_ensemble (self->mcat); + ncm_mset_catalog_remove_last_ensemble (self->mcat); - self->cur_sample_id -= (len - start); - self->started = FALSE; + self->cur_sample_id -= (len - start); + self->started = FALSE; - ncm_fit_esmcmc_start_run (esmcmc); + ncm_fit_esmcmc_start_run (esmcmc); + } } } diff --git a/numcosmo/math/ncm_fit_esmcmc.h b/numcosmo/math/ncm_fit_esmcmc.h index 5b755cb5c..2cefe4c47 100644 --- a/numcosmo/math/ncm_fit_esmcmc.h +++ b/numcosmo/math/ncm_fit_esmcmc.h @@ -60,6 +60,9 @@ void ncm_fit_esmcmc_set_auto_trim_div (NcmFitESMCMC *esmcmc, guint div); void ncm_fit_esmcmc_set_auto_trim_type (NcmFitESMCMC *esmcmc, NcmMSetCatalogTrimType ttype); void ncm_fit_esmcmc_set_min_runs (NcmFitESMCMC *esmcmc, guint min_runs); void ncm_fit_esmcmc_set_max_runs_time (NcmFitESMCMC *esmcmc, gdouble max_runs_time); +void ncm_fit_esmcmc_set_skip_check (NcmFitESMCMC *esmcmc, gboolean skip_check); + +gboolean ncm_fit_esmcmc_get_skip_check (NcmFitESMCMC *esmcmc); gboolean ncm_fit_esmcmc_has_rng (NcmFitESMCMC *esmcmc); diff --git a/numcosmo_py/app/esmcmc.py b/numcosmo_py/app/esmcmc.py index 696ab1323..9e6330e9b 100644 --- a/numcosmo_py/app/esmcmc.py +++ b/numcosmo_py/app/esmcmc.py @@ -199,7 +199,15 @@ class RunMCMC(RunCommonOptions): ), ] = 0 + skip_check: Annotated[ + bool, + typer.Option( + help="Skip the check of the last ensemble when continuing a run.", + ), + ] = True + def __post_init__(self) -> None: + """Run the ESMCMC algorithm.""" super().__post_init__() self.fit.log_info() @@ -312,6 +320,8 @@ def __post_init__(self) -> None: self.output.absolute().with_suffix(".mcmc.fits").as_posix() ) + esmcmc.set_skip_check(self.skip_check) + esmcmc.start_run() esmcmc.run(self.nsamples) esmcmc.end_run() diff --git a/numcosmo_py/ncm.pyi b/numcosmo_py/ncm.pyi index 121a6cfee..d1d98880b 100644 --- a/numcosmo_py/ncm.pyi +++ b/numcosmo_py/ncm.pyi @@ -3333,6 +3333,7 @@ class FitESMCMC(GObject.Object): def get_catalog(self) -> MSetCatalog: ... def get_offboard_ratio(self) -> float: ... def get_offboard_ratio_last_update(self) -> float: ... + def get_skip_check(self) -> bool: ... def has_rng(self) -> bool: ... def mean_covar(self) -> None: ... @classmethod @@ -3373,6 +3374,7 @@ class FitESMCMC(GObject.Object): def set_nthreads(self, nthreads: int) -> None: ... def set_rng(self, rng: RNG) -> None: ... def set_sampler(self, sampler: MSetTransKern) -> None: ... + def set_skip_check(self, skip_check: bool) -> None: ... def start_run(self) -> None: ... def use_mpi(self, use_mpi: bool) -> None: ... def validate(self, pi: int, pf: int) -> bool: ... From 6253c46f5618b77020833a327ff887d7a48a5eef Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Wed, 24 Apr 2024 16:29:02 -0300 Subject: [PATCH 10/27] Better logic to use skip_check. --- numcosmo/math/ncm_fit_esmcmc.c | 27 +++++++++++++-------------- 1 file changed, 13 insertions(+), 14 deletions(-) diff --git a/numcosmo/math/ncm_fit_esmcmc.c b/numcosmo/math/ncm_fit_esmcmc.c index 0807fe432..1e8a716bf 100644 --- a/numcosmo/math/ncm_fit_esmcmc.c +++ b/numcosmo/math/ncm_fit_esmcmc.c @@ -1671,30 +1671,29 @@ ncm_fit_esmcmc_start_run (NcmFitESMCMC *esmcmc) } } - if (read_from_cat) + if (read_from_cat && !self->skip_check) { const guint len = ncm_mset_catalog_len (self->mcat); const guint start = len > self->nwalkers ? len - self->nwalkers : 0; - if (!self->skip_check) + if (!ncm_fit_esmcmc_validate (esmcmc, start, len)) { - if (!ncm_fit_esmcmc_validate (esmcmc, start, len)) + if (self->mtype > NCM_FIT_RUN_MSGS_NONE) { - if (self->mtype > NCM_FIT_RUN_MSGS_NONE) - { - ncm_cfg_msg_sepa (); - g_message ("# NcmFitESMCMC: Last ensemble failed in the m2lnL check, the catalog may be corrupted, removing last ensemble and retrying...\n"); - } + ncm_cfg_msg_sepa (); + g_message ("# NcmFitESMCMC: Last ensemble failed in the m2lnL check, the " + "catalog may be corrupted, removing last ensemble and " + "retrying...\n"); + } - ncm_fit_esmcmc_end_run (esmcmc); + ncm_fit_esmcmc_end_run (esmcmc); - ncm_mset_catalog_remove_last_ensemble (self->mcat); + ncm_mset_catalog_remove_last_ensemble (self->mcat); - self->cur_sample_id -= (len - start); - self->started = FALSE; + self->cur_sample_id -= (len - start); + self->started = FALSE; - ncm_fit_esmcmc_start_run (esmcmc); - } + ncm_fit_esmcmc_start_run (esmcmc); } } From f7991d2e73be7edf1aeae12c473aabfb14a0c3e5 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Sat, 4 May 2024 22:43:20 -0300 Subject: [PATCH 11/27] Fixed bug in calc_param_ensemble_evol. Updated docstring and added more catalog related tools. --- numcosmo/math/ncm_mset_catalog.c | 8 +- numcosmo_py/app/__init__.py | 22 +++++- numcosmo_py/app/catalog.py | 131 ++++++++++++++++++++++++++++++- numcosmo_py/app/esmcmc.py | 2 +- numcosmo_py/app/fisher.py | 13 +-- numcosmo_py/app/from_cosmosis.py | 15 ++-- numcosmo_py/app/generate.py | 4 +- numcosmo_py/app/loading.py | 20 +++-- numcosmo_py/app/run_fit.py | 14 +++- 9 files changed, 197 insertions(+), 32 deletions(-) diff --git a/numcosmo/math/ncm_mset_catalog.c b/numcosmo/math/ncm_mset_catalog.c index 48573a670..4b84baa32 100644 --- a/numcosmo/math/ncm_mset_catalog.c +++ b/numcosmo/math/ncm_mset_catalog.c @@ -4861,6 +4861,7 @@ _ncm_mset_catalog_calc_ensemble_evol (NcmMSetCatalog *mcat, guint vi, guint nste NcmVector *pv = ncm_vector_new (nsteps); const gdouble pmin = ncm_vector_get (self->params_min, vi); const gdouble pmax = ncm_vector_get (self->params_max, vi); + const guint div = max_t > 100 ? max_t / 100 : 1; guint i, t; @@ -4910,14 +4911,13 @@ _ncm_mset_catalog_calc_ensemble_evol (NcmMSetCatalog *mcat, guint vi, guint nste ncm_stats_dist1d_epdf_reset (epdf1d); - if (t % (max_t / 100) == 0) - if (mtype > NCM_FIT_RUN_MSGS_NONE) - ncm_message ("="); + if ((mtype > NCM_FIT_RUN_MSGS_NONE) && (t % div == 0)) + ncm_message ("="); } if (mtype > NCM_FIT_RUN_MSGS_NONE) { - if (t % (max_t / 100) != 0) + if (t % div != 0) ncm_message ("="); ncm_message ("|\n"); diff --git a/numcosmo_py/app/__init__.py b/numcosmo_py/app/__init__.py index 8f10456cb..f4758b680 100644 --- a/numcosmo_py/app/__init__.py +++ b/numcosmo_py/app/__init__.py @@ -32,7 +32,13 @@ from .run_fit import RunFit, RunTest from .fisher import ComputeTheoryVector, RunFisher, RunFisherBias from .esmcmc import RunMCMC -from .catalog import AnalyzeMCMC, CalibrateCatalog, PlotCorner +from .catalog import ( + AnalyzeMCMC, + CalibrateCatalog, + PlotCorner, + VisualHW, + ParameterEvolution, +) from .generate import GeneratePlanck, GenerateJpasForecast app = typer.Typer(no_args_is_help=True, help="NumCosmo command line interface.") @@ -113,6 +119,18 @@ "help": "Plots the corner plot for a given catalog.", } +CAT_VISUAL_HW_CMD: CMDArg = { + "name": "visual-hw", + "no_args_is_help": True, + "help": "Visualizes the Heidelberger and Welch convergence test.", +} + +CAT_PARAM_EVOLUTION_CMD: CMDArg = { + "name": "param-evolution", + "no_args_is_help": True, + "help": "Plots the parameter evolution for a given catalog.", +} + GEN_PLANCK_CMD: CMDArg = { "name": "planck18", "no_args_is_help": True, @@ -147,6 +165,8 @@ app_cat.command(**CAT_ANALYZE_CMD)(AnalyzeMCMC) app_cat.command(**CAT_CALIBRATE_CMD)(CalibrateCatalog) app_cat.command(**CAT_PLOT_CORNER_CMD)(PlotCorner) +app_cat.command(**CAT_VISUAL_HW_CMD)(VisualHW) +app_cat.command(**CAT_PARAM_EVOLUTION_CMD)(ParameterEvolution) # ------------------------------------------------------------------------------ # Installing experiment generation subcommands app_generate.command(**GEN_PLANCK_CMD)(GeneratePlanck) diff --git a/numcosmo_py/app/catalog.py b/numcosmo_py/app/catalog.py index f01cfc57f..705026397 100644 --- a/numcosmo_py/app/catalog.py +++ b/numcosmo_py/app/catalog.py @@ -31,6 +31,7 @@ from rich.text import Text import numpy as np import matplotlib.pyplot as plt +from matplotlib.colors import LogNorm import getdist import getdist.plots @@ -46,7 +47,7 @@ from .loading import LoadCatalog -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class AnalyzeMCMC(LoadCatalog): """Analyzes the results of a MCMC run.""" @@ -363,7 +364,7 @@ def __post_init__(self) -> None: self.end_experiment() -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class CalibrateCatalog(LoadCatalog): """Calibrate the APES sampler using a given catalog.""" @@ -605,7 +606,7 @@ def __post_init__(self) -> None: plt.show() -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class PlotCorner(LoadCatalog): """Plots the corner plot of the catalog.""" @@ -667,3 +668,127 @@ def __post_init__(self) -> None: plt.show() self.end_experiment() + + +@dataclasses.dataclass(kw_only=True) +class ParameterAnalysis(LoadCatalog): + """Plots the corner plot of the catalog.""" + + plot_name: Annotated[ + Optional[str], + typer.Option(help="Name of the plot file."), + ] = None + + param_name: Annotated[ + str, + typer.Option(help="Name of the plot file."), + ] + + def __post_init__(self) -> None: + """Parameter analysis.""" + super().__post_init__() + + if self.plot_name is None: + self.plot_name = str(self.mcmc_file) + + pi = self.mset.fparam_get_pi_by_name(self.param_name) + if pi is not None: + pindex = self.mset.fparam_get_fpi(pi.mid, pi.pid) + self.nadd_vals + elif self.param_name.isnumeric(): + total_len = self.mset.fparams_len() + self.nadd_vals + pindex = int(self.param_name) + if pindex >= total_len or pindex < 0: + raise ValueError( + f'Invalid parameter index "{self.param_name}"=={pindex}.' + ) + if pindex >= self.nadd_vals: + pi = self.mset.fparam_get_pi(pindex) + else: + raise ValueError(f"Parameter {self.param_name} not found.") + + self.pi: Ncm.MSetPIndex = pi + self.pindex: int = pindex + self.symbol: str = self.mcat.col_symb(pindex) + + +@dataclasses.dataclass(kw_only=True) +class VisualHW(ParameterAnalysis): + """Visual Heidelberger and Welch.""" + + def __post_init__(self) -> None: + """Visual Heidelberger and Welch.""" + super().__post_init__() + + cumsum_vec, mean, var = self.stats.visual_heidel_diag(self.pindex, 0) + cumsum = np.array(cumsum_vec.dup_array()) + mean_a = (np.array(range(len(cumsum))) + 1.0) * mean + + set_rc_params_article(ncol=2) + _, ax = plt.subplots() + + ax.title.set_text("Visual Heidelberger and Welch.") + ax.plot(cumsum, label=f"Cumulative sum -- ${self.symbol}$") + ax.plot(mean_a, label=f"Mean, standard deviation = {np.sqrt(var):.2f}") + + ax.set_xlabel("Iterations") + ax.set_ylabel("Cumulative sum") + ax.legend(loc="best") + if self.output is not None: + filename = self.output.with_suffix(".corner.pdf").absolute().as_posix() + plt.savefig(filename, bbox_inches="tight") + + plt.show() + + self.end_experiment() + + +@dataclasses.dataclass(kw_only=True) +class ParameterEvolution(ParameterAnalysis): + """Parameter evolution.""" + + grid_size: Annotated[ + int, + typer.Option(help="Grid size."), + ] = 200 + + def __post_init__(self) -> None: + """Parameter evolution.""" + super().__post_init__() + + mcat = self.mcat + if self.pi is not None: + param_vec, evol_matrix = mcat.calc_param_ensemble_evol( + self.pi, self.grid_size, Ncm.FitRunMsgs.NONE + ) + else: + param_vec, evol_matrix = mcat.calc_add_param_ensemble_evol( + self.pindex, self.grid_size, Ncm.FitRunMsgs.NONE + ) + + param = np.array(param_vec.dup_array()) + evol_a = np.abs(evol_matrix.dup_array()) + min_evol_a = min(evol_a[evol_a > 0.0]) + max_evol_a = max(evol_a) + evol_a[evol_a == 0.0] = min_evol_a + evol = evol_a.reshape((-1, self.grid_size)) + print(f"min_evol_a={min_evol_a}, max_evol_a={max_evol_a}") + + set_rc_params_article(ncol=2) + _, ax = plt.subplots() + + ax.title.set_text(f"Parameter evolution -- ${self.symbol}$") + cax = ax.matshow( + evol.T, + aspect="auto", + origin="lower", + cmap="viridis", + extent=[0, evol.shape[0], param[0], param[-1]], + norm=LogNorm(), + ) + ax.set_xlabel("Iterations") + ax.set_ylabel(f"${self.symbol}$") + plt.colorbar(cax, label=rf"$p_t\left({self.symbol}\right)$") + + plt.show() + + self.end_experiment() diff --git a/numcosmo_py/app/esmcmc.py b/numcosmo_py/app/esmcmc.py index 9e6330e9b..1673a9d52 100644 --- a/numcosmo_py/app/esmcmc.py +++ b/numcosmo_py/app/esmcmc.py @@ -54,7 +54,7 @@ class Parallezation(str, Enum): THREADS = "threads" -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class RunMCMC(RunCommonOptions): """Computes the MCMC using APES.""" diff --git a/numcosmo_py/app/fisher.py b/numcosmo_py/app/fisher.py index bb1c8959f..b88c39c63 100644 --- a/numcosmo_py/app/fisher.py +++ b/numcosmo_py/app/fisher.py @@ -36,11 +36,12 @@ from .run_fit import RunCommonOptions -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class ComputeTheoryVector(LoadExperiment): - """Computes theory vectory for a given experiment.""" + """Compute theory vectory for a given experiment.""" def __post_init__(self) -> None: + """Compute theory vector for a given experiment.""" super().__post_init__() dset: Ncm.Dataset = self.likelihood.peek_dataset() @@ -57,9 +58,9 @@ def __post_init__(self) -> None: self.end_experiment() -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class RunFisher(RunCommonOptions): - """Computes the Fisher matrix of the model to the data.""" + """Compute the Fisher matrix of the model to the data.""" fisher_type: Annotated[ FisherType, @@ -69,6 +70,7 @@ class RunFisher(RunCommonOptions): ] = FisherType.OBSERVED def __post_init__(self) -> None: + """Compute the Fisher matrix of the model to the data.""" super().__post_init__() if self.fisher_type == FisherType.OBSERVED: self.fit.obs_fisher() @@ -86,7 +88,7 @@ def __post_init__(self) -> None: self.end_experiment() -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class RunFisherBias(RunCommonOptions): """Computes the Fisher matrix of the model to the data and the bias.""" @@ -98,6 +100,7 @@ class RunFisherBias(RunCommonOptions): ] = None def __post_init__(self) -> None: + """Compute the Fisher matrix of the model to the data and the bias.""" super().__post_init__() if self.product_file and self.theory_vector is not None: diff --git a/numcosmo_py/app/from_cosmosis.py b/numcosmo_py/app/from_cosmosis.py index a75d2bc00..6e5c85280 100644 --- a/numcosmo_py/app/from_cosmosis.py +++ b/numcosmo_py/app/from_cosmosis.py @@ -21,7 +21,7 @@ # You should have received a copy of the GNU General Public License along # with this program. If not, see . -"""NumCosmo APP subcommand to convert CosmoSIS likelihoods to NumCosmo""" +"""NumCosmo APP subcommand to convert CosmoSIS likelihoods to NumCosmo.""" from typing import Optional, Annotated from pathlib import Path @@ -82,12 +82,17 @@ def numcosmo_from_cosmosis( ), ] = False, ): - """Converts a Cosmosis ini file to a NumCosmo yaml file, containing - the same information. The NumCosmo yaml file can be used to run the - same likelihoods in NumCosmo. + """Convert a Cosmosis ini file to a NumCosmo yaml file. - """ + The NumCosmo yaml will contain the model builders and experiment matching the + Cosmosis ini file. The NumCosmo yaml file can be used to run the same + likelihoods in NumCosmo. + Due to the differences between the two frameworks, some likelihoods may not be + converted correctly, usually due to the different parameter names or the + different parameterizations of the models. In this case, the user should + manually adjust the model builders. + """ Ncm.cfg_init() if outfile is None: diff --git a/numcosmo_py/app/generate.py b/numcosmo_py/app/generate.py index 5ae0bca14..b4ca59eb9 100644 --- a/numcosmo_py/app/generate.py +++ b/numcosmo_py/app/generate.py @@ -46,7 +46,7 @@ ) -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class GeneratePlanck: """Common block for commands that load an experiment. @@ -106,7 +106,7 @@ def __post_init__(self): ) -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class GenerateJpasForecast: """Common block for commands that load an experiment. diff --git a/numcosmo_py/app/loading.py b/numcosmo_py/app/loading.py index 2793ac3f2..0e2bd1c5e 100644 --- a/numcosmo_py/app/loading.py +++ b/numcosmo_py/app/loading.py @@ -24,6 +24,7 @@ """NumCosmo APP dataclasses and subcommands to load data. +This module contains dataclasses and subcommands to load data from files. """ import dataclasses @@ -36,10 +37,12 @@ from numcosmo_py.sampling import set_ncm_console -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class LoadExperiment: - """Common block for commands that load an experiment. All commands that load an - experiment should inherit from this class.""" + """Common block for commands that load an experiment. + + All commands that load an experiment should inherit from this class. + """ experiment: Annotated[ Path, typer.Argument(help="Path to the experiment file to fit.") @@ -79,6 +82,7 @@ class LoadExperiment: ] = None def __post_init__(self) -> None: + """Load the experiment file and prepare the experiment.""" ser = Ncm.Serialize.new(Ncm.SerializeOpt.CLEAN_DUP) builders_file = self.experiment.with_suffix(".builders.yaml") @@ -167,9 +171,10 @@ def __post_init__(self) -> None: self.mset = mset def _load_saved_mset(self) -> Optional[Ncm.MSet]: - """Loads the saved model set from the starting point file " - "or the product file.""" + """Load the saved model-set. + Loads the model-set from the starting point file or the product file. + """ if self.starting_point is not None: if not self.starting_point.exists(): raise RuntimeError( @@ -199,7 +204,7 @@ def _load_saved_mset(self) -> Optional[Ncm.MSet]: return None def end_experiment(self): - """Ends the experiment and writes the output file.""" + """End the experiment and writes the output file.""" if self.output is not None: ser = Ncm.Serialize.new(Ncm.SerializeOpt.CLEAN_DUP) ser.dict_str_to_yaml_file( @@ -207,7 +212,7 @@ def end_experiment(self): ) -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class LoadCatalog(LoadExperiment): """Analyzes the results of a MCMC run.""" @@ -227,6 +232,7 @@ class LoadCatalog(LoadExperiment): ] = 0 def __post_init__(self) -> None: + """Load the MCMC file and prepare the catalog.""" super().__post_init__() if self.mcmc_file is None: raise RuntimeError("No MCMC file given.") diff --git a/numcosmo_py/app/run_fit.py b/numcosmo_py/app/run_fit.py index 902fc1d53..db6e75c01 100644 --- a/numcosmo_py/app/run_fit.py +++ b/numcosmo_py/app/run_fit.py @@ -39,7 +39,7 @@ ) -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class RunCommonOptions(LoadExperiment): """Common options for the run command.""" @@ -69,6 +69,10 @@ class RunCommonOptions(LoadExperiment): ] = FitRunMessages.SIMPLE def __post_init__(self) -> None: + """Create common objects for the run command. + + Create the fit object and set the logger. + """ super().__post_init__() check_runner_algorithm(self.runner, self.algorithm) @@ -92,7 +96,7 @@ def __post_init__(self) -> None: self.fit = fit -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class RunFit(RunCommonOptions): """Computes the best fit of the model to the data.""" @@ -110,6 +114,7 @@ class RunFit(RunCommonOptions): ) # type: ignore def __post_init__(self) -> None: + """Compute the best fit of the model to the data.""" super().__post_init__() self.fit.log_info() @@ -139,11 +144,12 @@ def __post_init__(self) -> None: self.end_experiment() -@dataclasses.dataclass +@dataclasses.dataclass(kw_only=True) class RunTest(RunCommonOptions): - """Loads the experiment file and computes the likelihood once.""" + """Load the experiment file and computes the likelihood once.""" def __post_init__(self) -> None: + """Load the experiment file and computes the likelihood once.""" super().__post_init__() self.mset.param_set_all_ftype(Ncm.ParamType.FIXED) self.mset.prepare_fparam_map() From 3ae61deca193400c5f101722bc0596850abc1e6a Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Sat, 4 May 2024 22:52:41 -0300 Subject: [PATCH 12/27] Save plot option. --- numcosmo_py/app/catalog.py | 12 ++++-------- 1 file changed, 4 insertions(+), 8 deletions(-) diff --git a/numcosmo_py/app/catalog.py b/numcosmo_py/app/catalog.py index 705026397..e55393df1 100644 --- a/numcosmo_py/app/catalog.py +++ b/numcosmo_py/app/catalog.py @@ -688,9 +688,6 @@ def __post_init__(self) -> None: """Parameter analysis.""" super().__post_init__() - if self.plot_name is None: - self.plot_name = str(self.mcmc_file) - pi = self.mset.fparam_get_pi_by_name(self.param_name) if pi is not None: pindex = self.mset.fparam_get_fpi(pi.mid, pi.pid) + self.nadd_vals @@ -733,9 +730,8 @@ def __post_init__(self) -> None: ax.set_xlabel("Iterations") ax.set_ylabel("Cumulative sum") ax.legend(loc="best") - if self.output is not None: - filename = self.output.with_suffix(".corner.pdf").absolute().as_posix() - plt.savefig(filename, bbox_inches="tight") + if self.plot_name is not None: + plt.savefig(self.plot_name, bbox_inches="tight") plt.show() @@ -768,10 +764,8 @@ def __post_init__(self) -> None: param = np.array(param_vec.dup_array()) evol_a = np.abs(evol_matrix.dup_array()) min_evol_a = min(evol_a[evol_a > 0.0]) - max_evol_a = max(evol_a) evol_a[evol_a == 0.0] = min_evol_a evol = evol_a.reshape((-1, self.grid_size)) - print(f"min_evol_a={min_evol_a}, max_evol_a={max_evol_a}") set_rc_params_article(ncol=2) _, ax = plt.subplots() @@ -789,6 +783,8 @@ def __post_init__(self) -> None: ax.set_ylabel(f"${self.symbol}$") plt.colorbar(cax, label=rf"$p_t\left({self.symbol}\right)$") + if self.plot_name is not None: + plt.savefig(self.plot_name, bbox_inches="tight") plt.show() self.end_experiment() From a7cfea2ecf4ffcee1f3e98f3004dae99a18084c3 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Sun, 5 May 2024 12:16:04 -0300 Subject: [PATCH 13/27] Calibrating model. --- numcosmo/model/nc_hiprim_two_fluids.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/numcosmo/model/nc_hiprim_two_fluids.c b/numcosmo/model/nc_hiprim_two_fluids.c index 80c952503..1ccad05b4 100644 --- a/numcosmo/model/nc_hiprim_two_fluids.c +++ b/numcosmo/model/nc_hiprim_two_fluids.c @@ -156,7 +156,7 @@ nc_hiprim_two_fluids_class_init (NcHIPrimTwoFluidsClass *klass) /* Set ln(k_0) param info */ ncm_model_class_set_sparam (model_class, NC_HIPRIM_TWO_FLUIDS_LNK0, "\\ln(k_0)", "lnk0", - -4.0 * M_LN10, 4.0 * M_LN10, 1.0e-1, + -5.0 * M_LN10, -2.0 * M_LN10, 1.0e-1, NC_HIPRIM_DEFAULT_PARAMS_ABSTOL, NC_HIPRIM_TWO_FLUIDS_DEFAULT_LNK0, NCM_PARAM_TYPE_FIXED); From 001d514412a2738705e7d11ec7f69fd3a82b69d7 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 6 May 2024 10:57:21 -0300 Subject: [PATCH 14/27] mcmc_file is now non-optional. --- numcosmo_py/app/loading.py | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/numcosmo_py/app/loading.py b/numcosmo_py/app/loading.py index 0e2bd1c5e..30db2c81a 100644 --- a/numcosmo_py/app/loading.py +++ b/numcosmo_py/app/loading.py @@ -217,11 +217,11 @@ class LoadCatalog(LoadExperiment): """Analyzes the results of a MCMC run.""" mcmc_file: Annotated[ - Optional[Path], + Path, typer.Argument( help="Path to the MCMC file.", ), - ] = None + ] burnin: Annotated[ int, @@ -234,8 +234,6 @@ class LoadCatalog(LoadExperiment): def __post_init__(self) -> None: """Load the MCMC file and prepare the catalog.""" super().__post_init__() - if self.mcmc_file is None: - raise RuntimeError("No MCMC file given.") if not self.mcmc_file.exists(): raise RuntimeError(f"MCMC file {self.mcmc_file} not found.") From 7c48d1068117e3b9988afd628df85b7e91777aca Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Thu, 9 May 2024 11:03:21 -0300 Subject: [PATCH 15/27] Fixed default value. --- numcosmo/model/nc_hiprim_two_fluids.h | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/numcosmo/model/nc_hiprim_two_fluids.h b/numcosmo/model/nc_hiprim_two_fluids.h index 719da4c49..30edc03b7 100644 --- a/numcosmo/model/nc_hiprim_two_fluids.h +++ b/numcosmo/model/nc_hiprim_two_fluids.h @@ -82,7 +82,7 @@ GType nc_hiprim_two_fluids_get_type (void) G_GNUC_CONST; #define NC_HIPRIM_TWO_FLUIDS_DEFAULT_LN10E10ASA (3.179) #define NC_HIPRIM_TWO_FLUIDS_DEFAULT_T_SA_RATIO (0.2) -#define NC_HIPRIM_TWO_FLUIDS_DEFAULT_LNK0 (0.0) +#define NC_HIPRIM_TWO_FLUIDS_DEFAULT_LNK0 (-5.0 * M_LN10) #define NC_HIPRIM_TWO_FLUIDS_DEFAULT_LNW (-4.0 * M_LN10) #define NC_HIPRIM_TWO_FLUIDS_DEFAULT_N_T (0.0) From 1f9264a98a8e779cfc4bbd7119950821b84b97d1 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Thu, 9 May 2024 11:42:30 -0300 Subject: [PATCH 16/27] Adding log_file option to numcosmo. --- numcosmo_py/app/loading.py | 25 +++++++++++++++++++++---- numcosmo_py/sampling/__init__.py | 17 +++++++++-------- 2 files changed, 30 insertions(+), 12 deletions(-) diff --git a/numcosmo_py/app/loading.py b/numcosmo_py/app/loading.py index 30db2c81a..fac5e60e7 100644 --- a/numcosmo_py/app/loading.py +++ b/numcosmo_py/app/loading.py @@ -55,8 +55,9 @@ class LoadExperiment: help=( "If given, the product file is written, the file name is the same as " "the experiment file with the extension .product.yaml. " - "This option is incompatible with the output and starting-point options " - "since the product file contains the output and starting point." + "This option is incompatible with the output and starting-point " + "options since the product file contains the output and starting " + "point." ), ), ] = False @@ -81,6 +82,15 @@ class LoadExperiment: ), ] = None + log_file: Annotated[ + Optional[Path], + typer.Option( + "--log-file", + "-l", + help="Path to the file where the log should be written.", + ), + ] = None + def __post_init__(self) -> None: """Load the experiment file and prepare the experiment.""" ser = Ncm.Serialize.new(Ncm.SerializeOpt.CLEAN_DUP) @@ -103,7 +113,11 @@ def __post_init__(self) -> None: # this is necessary because when using MPI, the model builders # should be created in all processes before initializing NumCosmo. Ncm.cfg_init() - console = set_ncm_console() + self.console_io = None + if self.log_file: + self.console_io = open(self.log_file, "w", encoding="utf-8") + + console = set_ncm_console(self.console_io) experiment_objects = ser.dict_str_from_yaml_file( self.experiment.absolute().as_posix() @@ -129,7 +143,8 @@ def __post_init__(self) -> None: ) if self.starting_point is not None: raise RuntimeError( - "The product file option is incompatible with the starting-point option." + "The product file option is incompatible with the starting-point " + "option." ) self.output = self.experiment.with_suffix(".product.yaml") @@ -210,6 +225,8 @@ def end_experiment(self): ser.dict_str_to_yaml_file( self.output_dict, self.output.absolute().as_posix() ) + if self.console_io is not None: + self.console_io.close() @dataclasses.dataclass(kw_only=True) diff --git a/numcosmo_py/sampling/__init__.py b/numcosmo_py/sampling/__init__.py index 5e543d218..8e6635f4a 100644 --- a/numcosmo_py/sampling/__init__.py +++ b/numcosmo_py/sampling/__init__.py @@ -23,7 +23,7 @@ """Sampling module for numcosmo.""" -from typing import Optional, Union, Type +from typing import Optional, Union, Type, IO from enum import Enum from rich.console import Console @@ -83,7 +83,6 @@ def get_algorithms( ] ]: """Get algorithms for a given runner.""" - if runner == FitRunner.NLOPT: return Ncm.FitNloptAlgorithm if runner == FitRunner.LEVMAR: @@ -99,7 +98,6 @@ def get_algorithms( def check_runner_algorithm(runner: FitRunner, algorithm: Optional[str]): """Check if algorithm is valid.""" - if algorithm is not None: algorithms = get_algorithms(runner) if algorithms is None: @@ -123,7 +121,7 @@ class NcmHighlighter(RegexHighlighter): ] -def set_ncm_console() -> Console: +def set_ncm_console(file: Optional[IO[str]]) -> Console: """Set console for Ncm.Fit.""" theme = Theme( { @@ -135,7 +133,9 @@ def set_ncm_console() -> Console: "Ncm.percentage": "bold magenta", } ) - console = Console(highlighter=NcmHighlighter(), theme=theme) + console = Console( + highlighter=NcmHighlighter(), theme=theme, soft_wrap=True, file=file + ) Ncm.cfg_set_log_handler(lambda msg: console.print(msg, end="")) @@ -155,9 +155,10 @@ def render(self, task: Task) -> Text: class NcmFitLogger: - """Class implementing logging functions for Ncm.Fit""" + """Class implementing logging functions for Ncm.Fit.""" def __init__(self, console: Optional[Console]) -> None: + """Initialize NcmFitLogger.""" self.console = console if console is not None else Console() self.progress = Progress( TextColumn("# [progress.description]{task.description}: "), @@ -189,14 +190,14 @@ def update_progress(self, _fit: Ncm.Fit, n: Union[int, float]): self.progress.update(self.task, completed=n) def start_update(self, _fit: Ncm.Fit, start_message: str): - """Starting updates.""" + """Start updates.""" self.task = self.progress.add_task(start_message) self.progress.start() self.progress.start_task(self.task) self.progress.update(self.task, completed=0, total=10) def end_update(self, _fit: Ncm.Fit, _end_message: str): - """Ending updates""" + """End updates.""" assert self.task is not None self.progress.stop_task(self.task) From c3bdac641291f23d092ba12a07248fa59e9a2a66 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Sat, 18 May 2024 23:27:52 -0300 Subject: [PATCH 17/27] Fixed merge. --- numcosmo_py/app/loading.py | 20 -------------------- 1 file changed, 20 deletions(-) diff --git a/numcosmo_py/app/loading.py b/numcosmo_py/app/loading.py index 584ee66c1..34e71987b 100644 --- a/numcosmo_py/app/loading.py +++ b/numcosmo_py/app/loading.py @@ -39,16 +39,10 @@ @dataclasses.dataclass(kw_only=True) class LoadExperiment: -<<<<<<< HEAD - """Common block for commands that load an experiment. - - All commands that load an experiment should inherit from this class. -======= """Load an experiment file. Common block for commands that load an experiment. All commands that load an experiment should inherit from this class. ->>>>>>> master """ experiment: Annotated[ @@ -99,11 +93,7 @@ class LoadExperiment: ] = None def __post_init__(self) -> None: -<<<<<<< HEAD """Load the experiment file and prepare the experiment.""" -======= - """Initialize the experiment and load the data.""" ->>>>>>> master ser = Ncm.Serialize.new(Ncm.SerializeOpt.CLEAN_DUP) builders_file = self.experiment.with_suffix(".builders.yaml") @@ -197,15 +187,9 @@ def __post_init__(self) -> None: self.mset = mset def _load_saved_mset(self) -> Optional[Ncm.MSet]: -<<<<<<< HEAD - """Load the saved model-set. - - Loads the model-set from the starting point file or the product file. -======= """Load the saved model. Load the saved model-set from the starting point file or the product file. ->>>>>>> master """ if self.starting_point is not None: if not self.starting_point.exists(): @@ -280,11 +264,7 @@ class LoadCatalog(LoadExperiment): ] = None def __post_init__(self) -> None: -<<<<<<< HEAD """Load the MCMC file and prepare the catalog.""" -======= - """Initialize the MCMC file and load the data.""" ->>>>>>> master super().__post_init__() if not self.mcmc_file.exists(): From a98dd3713ddf9366bab6e6c164d378e51749320c Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 20 May 2024 00:13:30 -0300 Subject: [PATCH 18/27] Tests for nc_hiprim_two_fluids. --- numcosmo/model/nc_hiprim_two_fluids.c | 47 ++++++- numcosmo/model/nc_hiprim_two_fluids.h | 3 + tests/meson.build | 26 ++-- tests/test_ncm_generic.c | 20 +++ tests/test_py_hiprim_two_fluids.py | 195 ++++++++++++++++++++++++++ 5 files changed, 277 insertions(+), 14 deletions(-) create mode 100644 tests/test_py_hiprim_two_fluids.py diff --git a/numcosmo/model/nc_hiprim_two_fluids.c b/numcosmo/model/nc_hiprim_two_fluids.c index 1ccad05b4..d6e258f3e 100644 --- a/numcosmo/model/nc_hiprim_two_fluids.c +++ b/numcosmo/model/nc_hiprim_two_fluids.c @@ -240,6 +240,46 @@ nc_hiprim_two_fluids_new (void) return prim_pl; } +/** + * nc_hiprim_two_fluids_ref: (skip) + * @two_fluids: a #NcHIPrimTwoFluids + * + * Increases the reference count of the object. + * + * Returns: (transfer full): the same object. + */ +NcHIPrimTwoFluids * +nc_hiprim_two_fluids_ref (NcHIPrimTwoFluids *two_fluids) +{ + return NC_HIPRIM_TWO_FLUIDS (g_object_ref (two_fluids)); +} + +/** + * nc_hiprim_two_fluids_free: (skip) + * @two_fluids: a #NcHIPrimTwoFluids + * + * Decreases the reference count of the object. When its reference count drops to 0, the + * object is finalized. + */ +void +nc_hiprim_two_fluids_free (NcHIPrimTwoFluids *two_fluids) +{ + g_object_unref (two_fluids); +} + +/** + * nc_hiprim_two_fluids_clear: (skip) + * @two_fluids: a #NcHIPrimTwoFluids + * + * If *@two_fluids is not %NULL, the reference count of the object is decreased and the + * pointer is set to %NULL. + */ +void +nc_hiprim_two_fluids_clear (NcHIPrimTwoFluids **two_fluids) +{ + g_clear_object (two_fluids); +} + /** * nc_hiprim_two_fluids_set_use_default_calib: * @two_fluids: a #NcHIPrimTwoFluids @@ -256,13 +296,13 @@ nc_hiprim_two_fluids_set_use_default_calib (NcHIPrimTwoFluids *two_fluids, gbool if ((use_default_calib && self->use_default_calib) || (!use_default_calib && !self->use_default_calib)) return; + ncm_spline2d_clear (&self->lnSA_powspec_lnk_lnw); + if (use_default_calib) { NcmSerialize *ser = ncm_serialize_new (NCM_SERIALIZE_OPT_CLEAN_DUP); gchar *default_calib_file = ncm_cfg_get_data_filename ("hiprim_2f_spline.bin", TRUE); - ncm_spline2d_clear (&self->lnSA_powspec_lnk_lnw); - self->lnSA_powspec_lnk_lnw = NCM_SPLINE2D (ncm_serialize_from_binfile (ser, default_calib_file)); g_assert_nonnull (self->lnSA_powspec_lnk_lnw); g_assert (NCM_IS_SPLINE2D (self->lnSA_powspec_lnk_lnw)); @@ -314,6 +354,9 @@ nc_hiprim_two_fluids_set_lnk_lnw_spline (NcHIPrimTwoFluids *two_fluids, NcmSplin ncm_spline2d_clear (&self->lnSA_powspec_lnk_lnw); self->lnSA_powspec_lnk_lnw = lnSA_powspec_lnk_lnw; + + if (!ncm_spline2d_is_init (self->lnSA_powspec_lnk_lnw)) + ncm_spline2d_prepare (self->lnSA_powspec_lnk_lnw); } /** diff --git a/numcosmo/model/nc_hiprim_two_fluids.h b/numcosmo/model/nc_hiprim_two_fluids.h index 30edc03b7..3828788ac 100644 --- a/numcosmo/model/nc_hiprim_two_fluids.h +++ b/numcosmo/model/nc_hiprim_two_fluids.h @@ -87,6 +87,9 @@ GType nc_hiprim_two_fluids_get_type (void) G_GNUC_CONST; #define NC_HIPRIM_TWO_FLUIDS_DEFAULT_N_T (0.0) NcHIPrimTwoFluids *nc_hiprim_two_fluids_new (void); +NcHIPrimTwoFluids *nc_hiprim_two_fluids_ref (NcHIPrimTwoFluids *two_fluids); +void nc_hiprim_two_fluids_free (NcHIPrimTwoFluids *two_fluids); +void nc_hiprim_two_fluids_clear (NcHIPrimTwoFluids **two_fluids); void nc_hiprim_two_fluids_set_use_default_calib (NcHIPrimTwoFluids *two_fluids, gboolean use_default_calib); gboolean nc_hiprim_two_fluids_get_use_default_calib (NcHIPrimTwoFluids *two_fluids); diff --git a/tests/meson.build b/tests/meson.build index 336dbd64e..511fdcafb 100644 --- a/tests/meson.build +++ b/tests/meson.build @@ -1,4 +1,3 @@ - c_tests = [ { 'name': 'ncm_cfg', @@ -281,8 +280,7 @@ if mpi_c_dep.found() mpiexec_args = ( [ - '-n', - '2', + '-n', '2', executable_test.full_path(), ] ) @@ -311,6 +309,10 @@ python_tests = [ 'name': 'py_hicosmo_Vexp', 'source': 'test_py_hicosmo_Vexp.py', }, + { + 'name': 'py_hiprim_two_fluids', + 'source': 'test_py_hiprim_two_fluids.py', + }, { 'name': 'py_hipert_em', 'source': 'test_py_hipert_em.py', @@ -522,8 +524,7 @@ if enable_gir if py_tap.found() and get_option('pytest_tap') r = run_command( python, - '-c', - 'import importlib.metadata; import sys; sys.stdout.write(importlib.metadata.version("pytest-tap"))', + '-c', 'import importlib.metadata; import sys; sys.stdout.write(importlib.metadata.version("pytest-tap"))', check: true, ) message('pytest-tap version: @0@'.format(r.stdout().strip())) @@ -536,7 +537,6 @@ if enable_gir pytest_protocol = 'tap' endif - foreach python_test : python_tests if python_test.has_key('timeout') timeout = python_test['timeout'] @@ -547,7 +547,8 @@ if enable_gir test( python_test['name'], python, - args: pytest_args + join_paths( + args: pytest_args + + join_paths( meson.current_source_dir(), python_test['source'], ), @@ -563,10 +564,10 @@ if enable_gir if mpiexec.found() mpiexec_args = ( [ - '-n', - '2', + '-n', '2', python.full_path(), - ] + pytest_args + ] + + pytest_args ) foreach python_test : python_tests if python_test.has_key('mpi') and python_test['mpi'] @@ -578,7 +579,8 @@ if enable_gir test( 'mpiexec_' + python_test['name'], mpiexec, - args: mpiexec_args + join_paths( + args: mpiexec_args + + join_paths( meson.current_source_dir(), python_test['source'], ), @@ -591,4 +593,4 @@ if enable_gir endforeach endif endif -endif +endif \ No newline at end of file diff --git a/tests/test_ncm_generic.c b/tests/test_ncm_generic.c index e29e66d6f..8d837831a 100644 --- a/tests/test_ncm_generic.c +++ b/tests/test_ncm_generic.c @@ -52,6 +52,7 @@ void test_nc_hicosmo_qgw_basic (void); void test_nc_hipert_adiab_basic (void); void test_nc_hipert_em_basic (void); void test_nc_hipert_gw_basic (void); +void test_nc_hiprim_two_fluids_basic (void); gint main (gint argc, gchar *argv[]) @@ -81,6 +82,7 @@ main (gint argc, gchar *argv[]) g_test_add_func ("/nc/hipert/adiab/basic", test_nc_hipert_adiab_basic); g_test_add_func ("/nc/hipert/em/basic", test_nc_hipert_em_basic); g_test_add_func ("/nc/hipert/gw/basic", test_nc_hipert_gw_basic); + g_test_add_func ("/nc/hiprim/two_fluids/basic", test_nc_hiprim_two_fluids_basic); g_test_run (); } @@ -448,3 +450,21 @@ test_nc_hipert_gw_basic (void) NCM_TEST_FREE (nc_hipert_gw_free, gw); } +void +test_nc_hiprim_two_fluids_basic (void) +{ + NcHIPrimTwoFluids *tf = nc_hiprim_two_fluids_new (); + NcHIPrimTwoFluids *tf2; + + g_assert_true (tf != NULL); + g_assert_true (NC_IS_HIPRIM_TWO_FLUIDS (tf)); + + tf2 = nc_hiprim_two_fluids_ref (tf); + nc_hiprim_two_fluids_clear (&tf2); + g_assert_true (tf2 == NULL); + + g_assert_true (NC_IS_HIPRIM_TWO_FLUIDS (tf)); + + NCM_TEST_FREE (nc_hiprim_two_fluids_free, tf); +} + diff --git a/tests/test_py_hiprim_two_fluids.py b/tests/test_py_hiprim_two_fluids.py new file mode 100644 index 000000000..0c552310e --- /dev/null +++ b/tests/test_py_hiprim_two_fluids.py @@ -0,0 +1,195 @@ +#!/usr/bin/env python +# +# test_py_hiprim_two_fluids.py +# +# Sun May 19 23:27:08 2024 +# Copyright 2024 Sandro Dias Pinto Vitenti +# +# +# test_py_hiprim_two_fluids.py +# Copyright (C) 2024 Sandro Dias Pinto Vitenti +# +# numcosmo is free software: you can redistribute it and/or modify it +# under the terms of the GNU General Public License as published by the +# Free Software Foundation, either version 3 of the License, or +# (at your option) any later version. +# +# numcosmo is distributed in the hope that it will be useful, but +# WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +# See the GNU General Public License for more details. +# +# You should have received a copy of the GNU General Public License along +# with this program. If not, see . + +"""Tests on NcHIPrimTwoFluids cosmological model.""" + +import pytest +from numpy.testing import assert_allclose +import numpy as np + +from numcosmo_py import Ncm, Nc + +Ncm.cfg_init() + + +@pytest.fixture(name="two_fluids") +def fixture_two_fluids() -> Nc.HIPrimTwoFluids: + """Fixture for NcHIPrimTwoFluids.""" + two_fluids = Nc.HIPrimTwoFluids.new() + + return two_fluids + + +def test_init(two_fluids): + """Test NcHIPrimTwoFluids initialization.""" + assert two_fluids is not None + assert isinstance(two_fluids, Nc.HIPrimTwoFluids) + assert isinstance(two_fluids, Nc.HIPrim) + assert isinstance(two_fluids, Ncm.Model) + assert two_fluids.get_use_default_calib() is False + + +def test_set_use_default_calib(two_fluids): + """Test NcHIPrimTwoFluids set_use_default_calib.""" + two_fluids.set_use_default_calib(True) + assert two_fluids.get_use_default_calib() is True + assert two_fluids.peek_lnk_lnw_spline() is None + + two_fluids.set_use_default_calib(False) + assert two_fluids.get_use_default_calib() is False + assert two_fluids.peek_lnk_lnw_spline() is None + + two_fluids.set_use_default_calib(True) + assert two_fluids.get_use_default_calib() is True + assert two_fluids.peek_lnk_lnw_spline() is None + + +def test_set_lnk_lnw_spline_init(two_fluids): + """Test NcHIPrimTwoFluids set_lnk_lnw_spline.""" + lnk = np.log(np.geomspace(1.0e-5, 1.0e1, 1000)) + lnw = np.log(np.geomspace(1.0e-7, 1.0e-1, 330)) + + lnk_v, lnw_v = np.meshgrid(lnk, lnw) + + lnPk = 2.0 * lnk_v + lnw_v + + lnPk2d = Ncm.Spline2dBicubic( + init=True, + spline=Ncm.SplineCubicNotaknot.new(), + x_vector=Ncm.Vector.new_array(lnk.tolist()), + y_vector=Ncm.Vector.new_array(lnw.tolist()), + z_matrix=Ncm.Matrix.new_array(lnPk.flatten().tolist(), len(lnk)), + ) + + two_fluids.set_lnk_lnw_spline(lnPk2d) + assert two_fluids.peek_lnk_lnw_spline() is not None + assert two_fluids.peek_lnk_lnw_spline() is lnPk2d + + eval_lnSA = np.array([two_fluids.lnSA_powspec_lnk(lnki) for lnki in lnk]) + + assert_allclose( + eval_lnSA, + two_fluids.props.ln10e10ASA + - 10.0 * np.log(10.0) + + 2.0 * (lnk - two_fluids.props.lnk0) + + two_fluids.props.lnw, + rtol=1.0e-8, + ) + + +def test_set_lnk_lnw_spline_no_init(two_fluids): + """Test NcHIPrimTwoFluids set_lnk_lnw_spline.""" + lnk = np.log(np.geomspace(1.0e-5, 1.0e1, 1000)) + lnw = np.log(np.geomspace(1.0e-7, 1.0e-1, 330)) + + lnk_v, lnw_v = np.meshgrid(lnk, lnw) + + lnPk = 2.0 * lnk_v + lnw_v + + lnPk2d = Ncm.Spline2dBicubic( + spline=Ncm.SplineCubicNotaknot.new(), + x_vector=Ncm.Vector.new_array(lnk.tolist()), + y_vector=Ncm.Vector.new_array(lnw.tolist()), + z_matrix=Ncm.Matrix.new_array(lnPk.flatten().tolist(), len(lnk)), + ) + + two_fluids.set_lnk_lnw_spline(lnPk2d) + assert two_fluids.peek_lnk_lnw_spline() is not None + assert two_fluids.peek_lnk_lnw_spline() is lnPk2d + + eval_lnSA = np.array([two_fluids.lnSA_powspec_lnk(lnki) for lnki in lnk]) + + assert_allclose( + eval_lnSA, + two_fluids.props.ln10e10ASA + - 10.0 * np.log(10.0) + + 2.0 * (lnk - two_fluids.props.lnk0) + + two_fluids.props.lnw, + rtol=1.0e-8, + ) + + +def test_set_lnk_lnw_spline_serialize(two_fluids): + """Test NcHIPrimTwoFluids set_lnk_lnw_spline.""" + lnk = np.log(np.geomspace(1.0e-5, 1.0e1, 1000)) + lnw = np.log(np.geomspace(1.0e-7, 1.0e-1, 330)) + + lnk_v, lnw_v = np.meshgrid(lnk, lnw) + + lnPk = 2.0 * lnk_v + lnw_v + + lnPk2d = Ncm.Spline2dBicubic( + spline=Ncm.SplineCubicNotaknot.new(), + x_vector=Ncm.Vector.new_array(lnk.tolist()), + y_vector=Ncm.Vector.new_array(lnw.tolist()), + z_matrix=Ncm.Matrix.new_array(lnPk.flatten().tolist(), len(lnk)), + ) + + two_fluids.set_lnk_lnw_spline(lnPk2d) + assert two_fluids.peek_lnk_lnw_spline() is not None + assert two_fluids.peek_lnk_lnw_spline() is lnPk2d + + eval_lnSA = np.array([two_fluids.lnSA_powspec_lnk(lnki) for lnki in lnk]) + + assert_allclose( + eval_lnSA, + two_fluids.props.ln10e10ASA + - 10.0 * np.log(10.0) + + 2.0 * (lnk - two_fluids.props.lnk0) + + two_fluids.props.lnw, + rtol=1.0e-8, + ) + + ser = Ncm.Serialize.new(Ncm.SerializeOpt.CLEAN_DUP) + two_fluids2 = ser.dup_obj(two_fluids) + + assert two_fluids2.peek_lnk_lnw_spline() is not None + assert two_fluids2.peek_lnk_lnw_spline() is not lnPk2d + + eval_lnSA = np.array([two_fluids2.lnSA_powspec_lnk(lnki) for lnki in lnk]) + + assert_allclose( + eval_lnSA, + two_fluids.props.ln10e10ASA + - 10.0 * np.log(10.0) + + 2.0 * (lnk - two_fluids.props.lnk0) + + two_fluids.props.lnw, + rtol=1.0e-8, + ) + + +def test_lnT_powespec_lnk(two_fluids): + """Test the tensorial power spectrum.""" + lnk = np.log(np.geomspace(1.0e-5, 1.0e1, 1000)) + + eval_lnT = [two_fluids.lnT_powspec_lnk(lnki) for lnki in lnk] + + assert_allclose( + eval_lnT, + two_fluids.props.ln10e10ASA + - 10.0 * np.log(10.0) + + np.log(two_fluids.props.T_SA_ratio) + + two_fluids.props.n_T * (lnk - np.log(two_fluids.props.k_pivot)), + rtol=1.0e-8, + ) From 5374c764395e47a689e4d0cff7efc44e1c131479 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 20 May 2024 00:56:35 -0300 Subject: [PATCH 19/27] Adding tests for hipert_two_fluids. --- tests/meson.build | 4 + tests/test_ncm_generic.c | 20 +++++ tests/test_py_hipert_two_fluids.py | 114 +++++++++++++++++++++++++++++ 3 files changed, 138 insertions(+) create mode 100644 tests/test_py_hipert_two_fluids.py diff --git a/tests/meson.build b/tests/meson.build index 511fdcafb..c84257ca4 100644 --- a/tests/meson.build +++ b/tests/meson.build @@ -321,6 +321,10 @@ python_tests = [ 'name': 'py_hipert_gw', 'source': 'test_py_hipert_gw.py', }, + { + 'name': 'py_hipert_two_fluids', + 'source': 'test_py_hipert_two_fluids.py', + }, { 'name': 'py_de_cont', 'source': 'test_py_de_cont.py', diff --git a/tests/test_ncm_generic.c b/tests/test_ncm_generic.c index 8d837831a..115a7ddfa 100644 --- a/tests/test_ncm_generic.c +++ b/tests/test_ncm_generic.c @@ -52,6 +52,7 @@ void test_nc_hicosmo_qgw_basic (void); void test_nc_hipert_adiab_basic (void); void test_nc_hipert_em_basic (void); void test_nc_hipert_gw_basic (void); +void test_nc_hipert_two_fluids_basic (void); void test_nc_hiprim_two_fluids_basic (void); gint @@ -82,6 +83,7 @@ main (gint argc, gchar *argv[]) g_test_add_func ("/nc/hipert/adiab/basic", test_nc_hipert_adiab_basic); g_test_add_func ("/nc/hipert/em/basic", test_nc_hipert_em_basic); g_test_add_func ("/nc/hipert/gw/basic", test_nc_hipert_gw_basic); + g_test_add_func ("/nc/hipert/two_fluids/basic", test_nc_hipert_two_fluids_basic); g_test_add_func ("/nc/hiprim/two_fluids/basic", test_nc_hiprim_two_fluids_basic); g_test_run (); @@ -450,6 +452,24 @@ test_nc_hipert_gw_basic (void) NCM_TEST_FREE (nc_hipert_gw_free, gw); } +void +test_nc_hipert_two_fluids_basic (void) +{ + NcHIPertTwoFluids *tf = nc_hipert_two_fluids_new (); + NcHIPertTwoFluids *tf2; + + g_assert_true (tf != NULL); + g_assert_true (NC_IS_HIPERT_TWO_FLUIDS (tf)); + + tf2 = nc_hipert_two_fluids_ref (tf); + nc_hipert_two_fluids_clear (&tf2); + g_assert_true (tf2 == NULL); + + g_assert_true (NC_IS_HIPERT_TWO_FLUIDS (tf)); + + NCM_TEST_FREE (nc_hipert_two_fluids_free, tf); +} + void test_nc_hiprim_two_fluids_basic (void) { diff --git a/tests/test_py_hipert_two_fluids.py b/tests/test_py_hipert_two_fluids.py new file mode 100644 index 000000000..10690fc1d --- /dev/null +++ b/tests/test_py_hipert_two_fluids.py @@ -0,0 +1,114 @@ +#!/usr/bin/env python +# +# test_py_hipert_two_fluids.py +# +# Mon May 20 00:24:30 2024 +# Copyright 2024 Sandro Dias Pinto Vitenti +# +# +# test_py_hipert_two_fluids.py +# Copyright (C) 2024 Sandro Dias Pinto Vitenti +# +# numcosmo is free software: you can redistribute it and/or modify it +# under the terms of the GNU General Public License as published by the +# Free Software Foundation, either version 3 of the License, or +# (at your option) any later version. +# +# numcosmo is distributed in the hope that it will be useful, but +# WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +# See the GNU General Public License for more details. +# +# You should have received a copy of the GNU General Public License along +# with this program. If not, see . + +"""Tests on NcHIPertTwoFluids perturbations module.""" + +from itertools import product +import pytest +from numpy.testing import assert_allclose +import numpy as np + +from numcosmo_py import Ncm, Nc + +Ncm.cfg_init() + + +@pytest.fixture(name="two_fluids") +def fixture_two_fluids() -> Nc.HIPertTwoFluids: + """Fixture for NcHIPertTwoFluids.""" + two_fluids = Nc.HIPertTwoFluids.new() + + return two_fluids + + +@pytest.fixture(name="cosmo_qgrw") +def fixture_cosmo_qgrw() -> Nc.HICosmo: + """Fixture for NcCosmoQGrw.""" + cosmo = Nc.HICosmoQGRW() + cosmo.props.w = 1.0e-5 + cosmo.props.Omegar = 1.0 * (1.0e-5) + cosmo.props.Omegaw = 1.0 * (1.0 - 1.0e-5) + cosmo.props.xb = 1.0e30 + + return cosmo + + +def test_init(two_fluids): + """Test NcHIPertTwoFluids initialization.""" + assert two_fluids is not None + assert isinstance(two_fluids, Nc.HIPertTwoFluids) + assert isinstance(two_fluids, Nc.HIPert) + + +def test_compute_full_spectrum(two_fluids, cosmo_qgrw): + """Test NcHIPertTwoFluids compute_full_spectrum.""" + two_fluids.props.reltol = 1.0e-9 + + def spec_params(Omegars=1.0e-5, w=1.0e-3, E0=1.0): + cosmo_qgrw.props.w = w + cosmo_qgrw.props.Omegar = E0 * Omegars + cosmo_qgrw.props.Omegaw = E0 * (1.0 - Omegars) + + spec1 = two_fluids.compute_zeta_spectrum( + cosmo_qgrw, 1, -cosmo_qgrw.abs_alpha(1.0e-14), -1.0, 1.0e-3, 1.0e8, 10 + ) + spec2 = two_fluids.compute_zeta_spectrum( + cosmo_qgrw, 2, -cosmo_qgrw.abs_alpha(1.0e-14), -1.0, 1.0e-3, 1.0e8, 10 + ) + + return spec1, spec2 + + specs1 = [] + specs2 = [] + w_a = np.geomspace(1.0e-5, 1.0e-1, 6) + for w in w_a: + spec1, spec2 = spec_params(w=w) + specs1.append(spec1) + specs2.append(spec2) + + lnk_v = specs1[0].peek_xv() + lnw_v = Ncm.Vector.new_array(np.log(w_a)) + zm = Ncm.Matrix.new(lnw_v.len(), lnk_v.len()) + + for i, (spec1, spec2, w) in enumerate(zip(specs1, specs2, w_a)): + lnPk_a1 = np.array(spec1.peek_yv().dup_array()) + lnPk_a2 = np.array(spec2.peek_yv().dup_array()) + + lnPk0 = np.log(np.exp(lnPk_a1[0]) + np.exp(lnPk_a2[0])) + lnPk = np.log(np.exp(lnPk_a1) + np.exp(lnPk_a2)) - lnPk0 + lnPk_v = Ncm.Vector.new_array(lnPk) + + zm.set_row(i, lnPk_v) + + s = Ncm.Spline2dBicubic.notaknot_new() + s.set(lnk_v, lnw_v, zm, True) + + ser = Ncm.Serialize.new(Ncm.SerializeOpt.CLEAN_DUP) + default_calib_file = Ncm.cfg_get_data_filename("hiprim_2f_spline.bin", True) + s_calib = ser.from_binfile(default_calib_file) + + for w, lnk in product(w_a, lnk_v.dup_array()): + Pk0 = s.eval(lnk, np.log(w)) + Pk1 = s_calib.eval(lnk, np.log(w)) + assert_allclose(Pk0, Pk1, rtol=1.0e-3) From 3de07ef2269064350907268991ef2579351901ca Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 20 May 2024 11:04:34 -0300 Subject: [PATCH 20/27] Testing new ensemble evol methods. --- tests/test_ncm_mset_catalog.c | 132 +++++++++++++++++++++++++++++++++- 1 file changed, 131 insertions(+), 1 deletion(-) diff --git a/tests/test_ncm_mset_catalog.c b/tests/test_ncm_mset_catalog.c index 23d33f0d7..9c931641d 100644 --- a/tests/test_ncm_mset_catalog.c +++ b/tests/test_ncm_mset_catalog.c @@ -52,6 +52,8 @@ void test_ncm_mset_catalog_bestfit (TestNcmMSetCatalog *test, gconstpointer pdat void test_ncm_mset_catalog_percentile (TestNcmMSetCatalog *test, gconstpointer pdata); void test_ncm_mset_catalog_autocorrelation (TestNcmMSetCatalog *test, gconstpointer pdata); void test_ncm_mset_catalog_accept_ratio_array (TestNcmMSetCatalog *test, gconstpointer pdata); +void test_ncm_mset_catalog_calc_param_ensemble_evol (TestNcmMSetCatalog *test, gconstpointer pdata); +void test_ncm_mset_catalog_calc_add_param_ensemble_evol (TestNcmMSetCatalog *test, gconstpointer pdata); void test_ncm_mset_catalog_invalid_run (TestNcmMSetCatalog *test, gconstpointer pdata); typedef struct _TestNcmMSetCatalogTests @@ -81,6 +83,8 @@ TestNcmMSetCatalogTests tests[] = {"percentile", test_ncm_mset_catalog_percentile}, {"autocorrelation", test_ncm_mset_catalog_autocorrelation}, {"accept_ratio_array", test_ncm_mset_catalog_accept_ratio_array}, + {"calc_param_ensemble_evol", test_ncm_mset_catalog_calc_param_ensemble_evol}, + {"calc_add_param_ensemble_evol", test_ncm_mset_catalog_calc_add_param_ensemble_evol}, {NULL, NULL} }; @@ -175,7 +179,7 @@ test_ncm_mset_catalog_new_2_chains (TestNcmMSetCatalog *test, gconstpointer pdat ncm_mset_param_set_all_ftype (mset, NCM_PARAM_TYPE_FREE); ncm_mset_prepare_fparam_map (mset); - mcat = ncm_mset_catalog_new (mset, 1, 2, FALSE, + mcat = ncm_mset_catalog_new (mset, 1, 20, FALSE, "m2lnL", "-2\\ln(L)", NULL); @@ -666,6 +670,132 @@ test_ncm_mset_catalog_accept_ratio_array (TestNcmMSetCatalog *test, gconstpointe } } +void +test_ncm_mset_catalog_calc_param_ensemble_evol (TestNcmMSetCatalog *test, gconstpointer pdata) +{ + NcmData *data = NCM_DATA (test->data_mvnd); + NcmDataGaussCov *cov = NCM_DATA_GAUSS_COV (test->data_mvnd); + NcmMSet *mset = ncm_mset_catalog_peek_mset (test->mcat); + const guint nt = g_test_rand_int_range (NTESTS_MIN, NTESTS_MAX); + NcmVector *y = ncm_data_gauss_cov_peek_mean (cov); + guint i; + + if (ncm_mset_catalog_nchains (test->mcat) == 1) + { + g_test_skip ("Single chain"); + + return; + } + + for (i = 0; i < nt; i++) + { + gdouble m2lnL = 0.0; + + ncm_data_resample (data, mset, test->rng); + ncm_data_m2lnL_val (data, mset, &m2lnL); + + ncm_mset_catalog_add_from_vector_array (test->mcat, y, &m2lnL); + } + + { + NcmVector *pval = NULL; + NcmMatrix *t_evol = NULL; + const NcmMSetPIndex *pindex = ncm_mset_fparam_get_pi (mset, 0); + guint i; + + ncm_mset_catalog_calc_param_ensemble_evol (test->mcat, pindex, 100, NCM_FIT_RUN_MSGS_NONE, &pval, &t_evol); + + g_assert_nonnull (pval); + g_assert_nonnull (t_evol); + g_assert_cmpuint (ncm_vector_len (pval), ==, ncm_matrix_ncols (t_evol)); + + for (i = 0; i < ncm_vector_len (pval); i++) + { + const gdouble pval_i = ncm_vector_get (pval, i); + + g_assert_cmpfloat (pval_i, >=, 0.0); + g_assert_cmpfloat (pval_i, <=, 3.0); + } + + for (i = 0; i < ncm_matrix_nrows (t_evol); i++) + { + guint j; + + for (j = 0; j < ncm_matrix_ncols (t_evol); j++) + { + const gdouble tval_ij = ncm_matrix_get (t_evol, i, j); + + g_assert_cmpfloat (tval_ij, >=, 0.0); + } + } + + ncm_vector_clear (&pval); + ncm_matrix_clear (&t_evol); + } +} + +void +test_ncm_mset_catalog_calc_add_param_ensemble_evol (TestNcmMSetCatalog *test, gconstpointer pdata) +{ + NcmData *data = NCM_DATA (test->data_mvnd); + NcmDataGaussCov *cov = NCM_DATA_GAUSS_COV (test->data_mvnd); + NcmMSet *mset = ncm_mset_catalog_peek_mset (test->mcat); + const guint nt = g_test_rand_int_range (NTESTS_MIN, NTESTS_MAX); + NcmVector *y = ncm_data_gauss_cov_peek_mean (cov); + guint i; + + if (ncm_mset_catalog_nchains (test->mcat) == 1) + { + g_test_skip ("Single chain"); + + return; + } + + for (i = 0; i < nt; i++) + { + gdouble m2lnL = 0.0; + + ncm_data_resample (data, mset, test->rng); + ncm_data_m2lnL_val (data, mset, &m2lnL); + + ncm_mset_catalog_add_from_vector_array (test->mcat, y, &m2lnL); + } + + { + NcmVector *pval = NULL; + NcmMatrix *t_evol = NULL; + guint i; + + ncm_mset_catalog_calc_add_param_ensemble_evol (test->mcat, 0, 100, NCM_FIT_RUN_MSGS_NONE, &pval, &t_evol); + + g_assert_nonnull (pval); + g_assert_nonnull (t_evol); + g_assert_cmpuint (ncm_vector_len (pval), ==, ncm_matrix_ncols (t_evol)); + + for (i = 0; i < ncm_vector_len (pval); i++) + { + const gdouble pval_i = ncm_vector_get (pval, i); + + g_assert_true (gsl_finite (pval_i)); + } + + for (i = 0; i < ncm_matrix_nrows (t_evol); i++) + { + guint j; + + for (j = 0; j < ncm_matrix_ncols (t_evol); j++) + { + const gdouble tval_ij = ncm_matrix_get (t_evol, i, j); + + g_assert_cmpfloat (tval_ij, >=, 0.0); + } + } + + ncm_vector_clear (&pval); + ncm_matrix_clear (&t_evol); + } +} + void test_ncm_mset_catalog_traps (TestNcmMSetCatalog *test, gconstpointer pdata) { From 983a9bab7bb9d7f58bf4fa5e3b92b1a72ce225fe Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 20 May 2024 11:32:23 -0300 Subject: [PATCH 21/27] Adding tests for output. --- tests/test_ncm_mset_catalog.c | 128 ++++++++++++++++++++++++++++------ 1 file changed, 105 insertions(+), 23 deletions(-) diff --git a/tests/test_ncm_mset_catalog.c b/tests/test_ncm_mset_catalog.c index 9c931641d..b2d527ce5 100644 --- a/tests/test_ncm_mset_catalog.c +++ b/tests/test_ncm_mset_catalog.c @@ -54,6 +54,7 @@ void test_ncm_mset_catalog_autocorrelation (TestNcmMSetCatalog *test, gconstpoin void test_ncm_mset_catalog_accept_ratio_array (TestNcmMSetCatalog *test, gconstpointer pdata); void test_ncm_mset_catalog_calc_param_ensemble_evol (TestNcmMSetCatalog *test, gconstpointer pdata); void test_ncm_mset_catalog_calc_add_param_ensemble_evol (TestNcmMSetCatalog *test, gconstpointer pdata); +void test_ncm_mset_catalog_calc_add_param_ensemble_evol_short (TestNcmMSetCatalog *test, gconstpointer pdata); void test_ncm_mset_catalog_invalid_run (TestNcmMSetCatalog *test, gconstpointer pdata); typedef struct _TestNcmMSetCatalogTests @@ -85,6 +86,7 @@ TestNcmMSetCatalogTests tests[] = {"accept_ratio_array", test_ncm_mset_catalog_accept_ratio_array}, {"calc_param_ensemble_evol", test_ncm_mset_catalog_calc_param_ensemble_evol}, {"calc_add_param_ensemble_evol", test_ncm_mset_catalog_calc_add_param_ensemble_evol}, + {"calc_add_param_ensemble_evol/short", test_ncm_mset_catalog_calc_add_param_ensemble_evol_short}, {NULL, NULL} }; @@ -751,49 +753,129 @@ test_ncm_mset_catalog_calc_add_param_ensemble_evol (TestNcmMSetCatalog *test, gc return; } - for (i = 0; i < nt; i++) + if (g_test_subprocess ()) { - gdouble m2lnL = 0.0; + for (i = 0; i < nt; i++) + { + gdouble m2lnL = 0.0; - ncm_data_resample (data, mset, test->rng); - ncm_data_m2lnL_val (data, mset, &m2lnL); + ncm_data_resample (data, mset, test->rng); + ncm_data_m2lnL_val (data, mset, &m2lnL); - ncm_mset_catalog_add_from_vector_array (test->mcat, y, &m2lnL); + ncm_mset_catalog_add_from_vector_array (test->mcat, y, &m2lnL); + } + + { + NcmVector *pval = NULL; + NcmMatrix *t_evol = NULL; + guint i; + + ncm_mset_catalog_calc_add_param_ensemble_evol (test->mcat, 0, 100, NCM_FIT_RUN_MSGS_FULL, &pval, &t_evol); + + g_assert_nonnull (pval); + g_assert_nonnull (t_evol); + g_assert_cmpuint (ncm_vector_len (pval), ==, ncm_matrix_ncols (t_evol)); + + for (i = 0; i < ncm_vector_len (pval); i++) + { + const gdouble pval_i = ncm_vector_get (pval, i); + + g_assert_true (gsl_finite (pval_i)); + } + + for (i = 0; i < ncm_matrix_nrows (t_evol); i++) + { + guint j; + + for (j = 0; j < ncm_matrix_ncols (t_evol); j++) + { + const gdouble tval_ij = ncm_matrix_get (t_evol, i, j); + + g_assert_cmpfloat (tval_ij, >=, 0.0); + } + } + + ncm_vector_clear (&pval); + ncm_matrix_clear (&t_evol); + } + + return; } - { - NcmVector *pval = NULL; - NcmMatrix *t_evol = NULL; - guint i; + g_test_trap_subprocess (NULL, 0, 0); + g_test_trap_assert_passed (); + g_test_trap_assert_stdout ("*Calculating evolution to time*"); +} - ncm_mset_catalog_calc_add_param_ensemble_evol (test->mcat, 0, 100, NCM_FIT_RUN_MSGS_NONE, &pval, &t_evol); +void +test_ncm_mset_catalog_calc_add_param_ensemble_evol_short (TestNcmMSetCatalog *test, gconstpointer pdata) +{ + NcmData *data = NCM_DATA (test->data_mvnd); + NcmDataGaussCov *cov = NCM_DATA_GAUSS_COV (test->data_mvnd); + NcmMSet *mset = ncm_mset_catalog_peek_mset (test->mcat); + const guint nt = g_test_rand_int_range (NTESTS_MIN, NTESTS_MAX); + NcmVector *y = ncm_data_gauss_cov_peek_mean (cov); + guint i; - g_assert_nonnull (pval); - g_assert_nonnull (t_evol); - g_assert_cmpuint (ncm_vector_len (pval), ==, ncm_matrix_ncols (t_evol)); + if (ncm_mset_catalog_nchains (test->mcat) == 1) + { + g_test_skip ("Single chain"); - for (i = 0; i < ncm_vector_len (pval); i++) + return; + } + + if (g_test_subprocess ()) + { + for (i = 0; i < ncm_mset_catalog_nchains (test->mcat) * 5; i++) { - const gdouble pval_i = ncm_vector_get (pval, i); + gdouble m2lnL = 0.0; - g_assert_true (gsl_finite (pval_i)); + ncm_data_resample (data, mset, test->rng); + ncm_data_m2lnL_val (data, mset, &m2lnL); + + ncm_mset_catalog_add_from_vector_array (test->mcat, y, &m2lnL); } - for (i = 0; i < ncm_matrix_nrows (t_evol); i++) { - guint j; + NcmVector *pval = NULL; + NcmMatrix *t_evol = NULL; + guint i; - for (j = 0; j < ncm_matrix_ncols (t_evol); j++) + ncm_mset_catalog_calc_add_param_ensemble_evol (test->mcat, 0, 100, NCM_FIT_RUN_MSGS_FULL, &pval, &t_evol); + + g_assert_nonnull (pval); + g_assert_nonnull (t_evol); + g_assert_cmpuint (ncm_vector_len (pval), ==, ncm_matrix_ncols (t_evol)); + + for (i = 0; i < ncm_vector_len (pval); i++) { - const gdouble tval_ij = ncm_matrix_get (t_evol, i, j); + const gdouble pval_i = ncm_vector_get (pval, i); - g_assert_cmpfloat (tval_ij, >=, 0.0); + g_assert_true (gsl_finite (pval_i)); + } + + for (i = 0; i < ncm_matrix_nrows (t_evol); i++) + { + guint j; + + for (j = 0; j < ncm_matrix_ncols (t_evol); j++) + { + const gdouble tval_ij = ncm_matrix_get (t_evol, i, j); + + g_assert_cmpfloat (tval_ij, >=, 0.0); + } } + + ncm_vector_clear (&pval); + ncm_matrix_clear (&t_evol); } - ncm_vector_clear (&pval); - ncm_matrix_clear (&t_evol); + return; } + + g_test_trap_subprocess (NULL, 0, 0); + g_test_trap_assert_passed (); + g_test_trap_assert_stdout ("*Calculating evolution to time*"); } void From c0a93d90d7cb50d6e7474e4e50571cadafc40e8e Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 20 May 2024 12:00:00 -0300 Subject: [PATCH 22/27] More tests for ncm_fit_esmcmc. --- tests/test_ncm_fit_esmcmc.c | 63 ++++++++++++++++++++++++++++++++++++- 1 file changed, 62 insertions(+), 1 deletion(-) diff --git a/tests/test_ncm_fit_esmcmc.c b/tests/test_ncm_fit_esmcmc.c index c9a7f9a37..90824b938 100644 --- a/tests/test_ncm_fit_esmcmc.c +++ b/tests/test_ncm_fit_esmcmc.c @@ -44,6 +44,7 @@ void test_ncm_fit_esmcmc_new_apes (TestNcmFitESMCMC *test, gconstpointer pdata); void test_ncm_fit_esmcmc_traps (TestNcmFitESMCMC *test, gconstpointer pdata); void test_ncm_fit_esmcmc_free (TestNcmFitESMCMC *test, gconstpointer pdata); +void test_ncm_fit_esmcmc_properties (TestNcmFitESMCMC *test, gconstpointer pdata); void test_ncm_fit_esmcmc_run (TestNcmFitESMCMC *test, gconstpointer pdata); void test_ncm_fit_esmcmc_run_lre (TestNcmFitESMCMC *test, gconstpointer pdata); void test_ncm_fit_esmcmc_run_burnin (TestNcmFitESMCMC *test, gconstpointer pdata); @@ -74,9 +75,10 @@ TestNcmFitEsmcmcFunc walkers[TEST_NCM_FIT_ESMCMC_NWALKERS] = {test_ncm_fit_esmcmc_new_apes, "apes/kde/gauss", GINT_TO_POINTER (5)}, }; -#define TEST_NCM_FIT_ESMCMC_TESTS 7 +#define TEST_NCM_FIT_ESMCMC_TESTS 8 TestNcmFitEsmcmcFunc tests[TEST_NCM_FIT_ESMCMC_TESTS] = { + {test_ncm_fit_esmcmc_properties, "properties", NULL}, {test_ncm_fit_esmcmc_run, "run", NULL}, {test_ncm_fit_esmcmc_run_lre, "run/lre", NULL}, {test_ncm_fit_esmcmc_run_burnin, "run/burnin", NULL}, @@ -335,6 +337,65 @@ test_ncm_fit_esmcmc_free (TestNcmFitESMCMC *test, gconstpointer pdata) NCM_TEST_FREE (ncm_rng_free, test->rng); } +void +test_ncm_fit_esmcmc_properties (TestNcmFitESMCMC *test, gconstpointer pdata) +{ + /* auto_trim */ + ncm_fit_esmcmc_set_auto_trim (test->esmcmc, TRUE); + + { + gboolean auto_trim; + + g_object_get (G_OBJECT (test->esmcmc), "auto-trim", &auto_trim, NULL); + g_assert_true (auto_trim); + } + + ncm_fit_esmcmc_set_auto_trim (test->esmcmc, FALSE); + + { + gboolean auto_trim; + + g_object_get (G_OBJECT (test->esmcmc), "auto-trim", &auto_trim, NULL); + g_assert_false (auto_trim); + } + + /* max_runs_time */ + ncm_fit_esmcmc_set_max_runs_time (test->esmcmc, 123.0); + { + gdouble max_runs_time; + + g_object_get (G_OBJECT (test->esmcmc), "max-runs-time", &max_runs_time, NULL); + g_assert_cmpfloat (max_runs_time, ==, 123.0); + } + + /* skip_check */ + ncm_fit_esmcmc_set_skip_check (test->esmcmc, TRUE); + g_assert_true (ncm_fit_esmcmc_get_skip_check (test->esmcmc)); + { + gboolean skip_check; + + g_object_get (G_OBJECT (test->esmcmc), "skip-check", &skip_check, NULL); + g_assert_true (skip_check); + } + ncm_fit_esmcmc_set_skip_check (test->esmcmc, FALSE); + g_assert_false (ncm_fit_esmcmc_get_skip_check (test->esmcmc)); + { + gboolean skip_check; + + g_object_get (G_OBJECT (test->esmcmc), "skip-check", &skip_check, NULL); + g_assert_false (skip_check); + } + + /* log-time-interval */ + g_object_set (G_OBJECT (test->esmcmc), "log-time-interval", 54321.0, NULL); + { + gdouble log_time_interval; + + g_object_get (G_OBJECT (test->esmcmc), "log-time-interval", &log_time_interval, NULL); + g_assert_cmpfloat (log_time_interval, ==, 54321.0); + } +} + #define TEST_NCM_FIT_ESMCMC_TOL (2.5e-1) void From 9daa3cb6adba2152f7c9945603893084160f1ad5 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 20 May 2024 12:08:10 -0300 Subject: [PATCH 23/27] More testing for hipert_two_fluids. --- tests/test_py_hipert_two_fluids.py | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/tests/test_py_hipert_two_fluids.py b/tests/test_py_hipert_two_fluids.py index 10690fc1d..078a10070 100644 --- a/tests/test_py_hipert_two_fluids.py +++ b/tests/test_py_hipert_two_fluids.py @@ -112,3 +112,11 @@ def spec_params(Omegars=1.0e-5, w=1.0e-3, E0=1.0): Pk0 = s.eval(lnk, np.log(w)) Pk1 = s_calib.eval(lnk, np.log(w)) assert_allclose(Pk0, Pk1, rtol=1.0e-3) + + +def test_evolve_array(two_fluids, cosmo_qgrw): + """Test NcHIPertTwoFluids evolve_array.""" + two_fluids.props.reltol = 1.0e-9 + m = two_fluids.evolve_array(cosmo=cosmo_qgrw, alphaf=-1.0e-1) + + assert all(np.isfinite(m.dup_array())) From 1433df8d7337b29c26c83bbc14b94b48cfa423b9 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 20 May 2024 12:30:26 -0300 Subject: [PATCH 24/27] Increasing number of point in fftlog jljm. --- tests/test_ncm_fftlog.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tests/test_ncm_fftlog.c b/tests/test_ncm_fftlog.c index e6a720454..f2b70278f 100644 --- a/tests/test_ncm_fftlog.c +++ b/tests/test_ncm_fftlog.c @@ -406,7 +406,7 @@ test_ncm_fftlog_sbessel_j_q0_5_new (TestNcmFftlog *test, gconstpointer pdata) void test_ncm_fftlog_sbessel_jljm_new (TestNcmFftlog *test, gconstpointer pdata) { - const guint N = 1 * g_test_rand_int_range (1000, 2000); + const guint N = 1 * g_test_rand_int_range (7800, 8000); const guint ell = g_test_rand_int_range (0, 10); const gint dell = ell > 1 ? g_test_rand_int_range (-2, 2) : g_test_rand_int_range (-ell, ell + 2); const gdouble lnw = 1.0 / 4.0 * log (g_test_rand_double_range (0.4, 1.0)); From 9dfaa92baac1315c6df2afcc71e36907e872011d Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 20 May 2024 13:57:49 -0300 Subject: [PATCH 25/27] Fixed old edge case. --- numcosmo/math/ncm_mset_catalog.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/numcosmo/math/ncm_mset_catalog.c b/numcosmo/math/ncm_mset_catalog.c index 4b84baa32..5e2236b5d 100644 --- a/numcosmo/math/ncm_mset_catalog.c +++ b/numcosmo/math/ncm_mset_catalog.c @@ -2766,7 +2766,7 @@ _ncm_mset_catalog_post_update (NcmMSetCatalog *mcat, NcmVector *x) if (self->nchains > 1) { - if ((self->cur_id + 1) % self->nchains + 1 == self->nchains) + if ((self->cur_id + 1) % self->nchains == 0) { NcmVector *e_mean = ncm_stats_vec_peek_mean (self->e_stats); const guint len = ncm_vector_len (e_mean); From 79a5b532a55a7cb5e1f83713f8556efefbf18f89 Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 20 May 2024 14:08:40 -0300 Subject: [PATCH 26/27] Added extra safe-guard. --- numcosmo/math/ncm_mset_catalog.c | 2 ++ 1 file changed, 2 insertions(+) diff --git a/numcosmo/math/ncm_mset_catalog.c b/numcosmo/math/ncm_mset_catalog.c index 5e2236b5d..33bf112f1 100644 --- a/numcosmo/math/ncm_mset_catalog.c +++ b/numcosmo/math/ncm_mset_catalog.c @@ -2778,6 +2778,8 @@ _ncm_mset_catalog_post_update (NcmMSetCatalog *mcat, NcmVector *x) ncm_vector_set (e_var, i, ncm_stats_vec_get_var (self->e_stats, i)); } + g_assert_cmpuint (ncm_stats_vec_nitens (self->e_stats), ==, self->nchains); + ncm_stats_vec_append (self->e_mean_stats, e_mean, TRUE); g_ptr_array_add (self->e_var_array, e_var); From 3737ded7e00d8372aee908feacd123d0eaef9b8f Mon Sep 17 00:00:00 2001 From: Sandro Dias Pinto Vitenti Date: Mon, 20 May 2024 14:24:54 -0300 Subject: [PATCH 27/27] Removing coveralls upload. --- .github/workflows/build_check.yml | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/.github/workflows/build_check.yml b/.github/workflows/build_check.yml index 80bf2da0a..0b622f2be 100644 --- a/.github/workflows/build_check.yml +++ b/.github/workflows/build_check.yml @@ -247,11 +247,11 @@ jobs: # # ninja coverage -C build -v -d stats -d explain # run: | # gcovr --root . --object-directory build --config gcovr.cfg --xml-pretty -o build/meson-logs/coverage.xml - - name: Coveralls - uses: coverallsapp/github-action@v2 - with: - files: ./numcosmo-coverage.info - format: lcov - github-token: ${{ secrets.GITHUB_TOKEN }} + #- name: Coveralls + # uses: coverallsapp/github-action@v2 + # with: + # files: ./numcosmo-coverage.info + # format: lcov + # github-token: ${{ secrets.GITHUB_TOKEN }}