p5_err_p_cor_asy.ipynb

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   "source": [
    "# Error propagration with asymmetric distributions\n",
    "\n",
    "The errorbars on $\\phi_*$ are highly asymmetric (from the literature). It may be possible that this could be the source of large errorbars. In the following notebook, we check this.\n",
    "\n",
    "In the following notebook, we use data from [Bouwens+15](https://ui.adsabs.harvard.edu/abs/2015ApJ...803...34B/abstract)."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import astropy.constants as con\n",
    "import os\n",
    "import corner\n",
    "import utils as utl\n",
    "import posdef as pdf\n",
    "from tqdm import tqdm\n",
    "import scipy.integrate as inte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Redshift\n",
    "z_bou = np.array([3.8,4.9,5.9,6.8,7.9])\n",
    "\n",
    "# Characteristic absolute magnitude\n",
    "mst_bou = np.array([-20.88, -21.17, -20.94, -20.87, -20.63])\n",
    "msterr_bou = np.array([0.08, 0.12, 0.2, 0.26, 0.36])\n",
    "\n",
    "# Characteristic luminosity\n",
    "lst_bou = np.array([])\n",
    "lsterr_bou = np.array([])\n",
    "\n",
    "for i in range(len(mst_bou)):\n",
    "    mst1 = np.random.normal(mst_bou[i], msterr_bou[i], 10000)\n",
    "    lst1 = utl.m_to_l_wave(mst1, 1500)\n",
    "    lst_bou = np.hstack((lst_bou, np.mean(lst1)))\n",
    "    lsterr_bou = np.hstack((lsterr_bou, np.std(lst1)))\n",
    "\n",
    "# Alpha\n",
    "alp_bou = np.array([-1.64, -1.76, -1.87, -2.06, -2.02])\n",
    "alperr_bou = np.array([0.04, 0.05, 0.1, 0.13, 0.23])\n",
    "\n",
    "# Normalisation constant\n",
    "phi_bou = np.array([1.97, 0.74, 0.50, 0.29, 0.21])*0.001\n",
    "phi_pos_err_bou = np.array([0.34, 0.18, 0.22, 0.21, 0.23])*0.001\n",
    "phi_neg_err_bou = np.array([0.29, 0.14, 0.16, 0.12, 0.11])*0.001\n",
    "phi_avg_err_bou = (phi_pos_err_bou + phi_neg_err_bou)/2\n",
    "\n",
    "# Kappas\n",
    "sol_lum = (con.L_sun*1e7).value\n",
    "kap_uv = 2.2e-10/sol_lum\n",
    "kap_ir = 4.5*10**(-44)\n",
    "\n",
    "# Range of Luminosities (or absolute magnitudes) used\n",
    "mags_bou = np.linspace(-24, -13, 1000)\n",
    "lums_bou = utl.m_to_l_wave(mags_bou, 1500)\n",
    "\n",
    "#print(np.log10(lst_bou))\n",
    "#print(np.log10(lsterr_bou))\n",
    "#print(np.log10(lums_bou))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# SFRD without error propagation\n",
    "sfrd_wo_errs = np.zeros(z_bou.shape)\n",
    "\n",
    "for i in range(len(z_bou)):\n",
    "    sfrd_wo_errs[i] = utl.sfrd_wo_err(lum=lums_bou, lum1=lst_bou[i], phi1=phi_bou[i], alpha=alp_bou[i], kappa=kap_uv, limit=0.03, Auv=0.0)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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     "name": "stderr",
     "text": [
      "100%|██████████| 10000/10000 [02:03<00:00, 80.98it/s]\n",
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     ]
    }
   ],
   "source": [
    "sfrd_bou = np.zeros(z_bou.shape)\n",
    "sfrd_err_bou = np.zeros(z_bou.shape)\n",
    "\n",
    "for i in range(len(z_bou)):\n",
    "    sfrd_bou[i], sfrd_err_bou[i] = utl.sfrd_w_err(lum=lums_bou, lum1=lst_bou[i], lum1err=lsterr_bou[i], phi1=phi_bou[i], phi1err=phi_avg_err_bou[i], alpha=alp_bou[i], alphaerr=alperr_bou[i], kappa=kap_uv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "log_sfrd_bou, log_sfrd_bou_err =  utl.log_err(sfrd_bou, sfrd_err_bou)\n",
    "log_sfrd_wo_bou = np.log10(sfrd_wo_errs)\n",
    "\n",
    "plt.figure(figsize=(15,7.5))\n",
    "plt.errorbar(z_bou, log_sfrd_bou, yerr=log_sfrd_bou_err, fmt='.')\n",
    "plt.scatter(z_bou, log_sfrd_wo_bou, marker='s', c='orangered', label='Without errors', alpha=0.5)\n",
    "plt.xlabel('Redshift')\n",
    "plt.ylabel('SFRD')\n",
    "plt.ylim([-2.7, -0.5])\n",
    "plt.grid()"
   ]
  },
  {
   "source": [
    "## Using asymmetric distributions\n",
    "\n",
    "Till now, we have been using a symmetric Gaussian distribution generated from `numpy.random.normal` module to sample the distribution of various parameters. However, that is not the case always -- often, especially for the parameter $\\phi_*$, the errorbars are not exactly symmetric. Hence, we want to sample asymetric distributions for those parameters. We wrote a special function to do so in `util.py` script, namely `asymmetric_gausian_distribution` -- we would implement the same function to compute the luminosity density below,"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lum_den22(lum, lum1, lum1err, phi1, phi1errp, phi1errn, alpha, alphaerr, limit=0.03):\n",
    "    \"\"\"\n",
    "    Function to calculate luminosity density\n",
    "    ----------------------------------------\n",
    "    Parameters:\n",
    "    -----------\n",
    "    lum : float, numpy.ndarray\n",
    "        luminosity range\n",
    "    phi1 : float\n",
    "        normalisation constant\n",
    "    phi1errp : float\n",
    "        Positive error in normalisation constant\n",
    "    phi1errn : float\n",
    "        Negative error in normalisation constant\n",
    "    lum1 : float\n",
    "        characteristic luminosity\n",
    "        the 'knee' of the function\n",
    "    lum1err : float\n",
    "        Error in characteristic luminosity\n",
    "    alpha : float\n",
    "        the faint-end slope of power law\n",
    "    alphaerr : float\n",
    "        Error in the faint-end slope of power law\n",
    "    limit : float\n",
    "        lower limit of the intensity\n",
    "        as a function of L*\n",
    "        default is 0.03 (from Madau&Dickinson)s\n",
    "    -----------\n",
    "    return\n",
    "    -----------\n",
    "    numpy.ndarray :\n",
    "        an array of luminosity density\n",
    "    \"\"\"\n",
    "    # Values of Parameters\n",
    "    log_phi1, log_phip = utl.log_err(phi1, phi1errp)\n",
    "    log_phi1, log_phin = utl.log_err(phi1, phi1errn)\n",
    "    log_phi2 = utl.asymmetric_gausian_distribution(log_phi1, log_phip, log_phin, 10000)\n",
    "    phi2 = 10**log_phi2\n",
    "    lum2 = np.random.normal(lum1, lum1err, 10000)\n",
    "    alp2 = np.random.normal(alpha, alphaerr, 10000)\n",
    "    # Values of luminosities\n",
    "    nor_lum = np.linspace(limit*lum1, np.max(lum), 100000)\n",
    "    # Integration array\n",
    "    rho2 = np.array([])\n",
    "    # Integration starts\n",
    "    for i in tqdm(range(len(phi2))):\n",
    "        if lum2[i] < 0 :#alp2[i] != alp2[i] or lum2[i] != lum2[i] or lum2[i] == 0 or phi2[i] != phi2[i]:\n",
    "            continue\n",
    "        else:\n",
    "            nor_sc1 = utl.schechter(nor_lum, lum1=lum2[i], phi1=phi2[i], alpha=alp2[i])\n",
    "            nor_sc = nor_lum*nor_sc1#/phi2[j]\n",
    "            rho_nor = inte.simps(nor_sc, nor_lum)\n",
    "            rho2 = np.hstack((rho2, rho_nor))\n",
    "    return rho2\n",
    "\n",
    "\n",
    "def sfrd_w_err(lum, lum1, lum1err, phi1, phi1errp, phi1errn, alpha, alphaerr, kappa, limit=0.03):\n",
    "    \"\"\"\n",
    "    Function to calculate luminosity density\n",
    "    ----------------------------------------\n",
    "    Parameters:\n",
    "    -----------\n",
    "    lum : float, numpy.ndarray\n",
    "        luminosity range\n",
    "    phi1 : float\n",
    "        normalisation constant\n",
    "    phi1errp : float\n",
    "        Positive error in normalisation constant\n",
    "    phi1errn : float\n",
    "        Negative error in normalisation constant\n",
    "    lum1 : float\n",
    "        characteristic luminosity\n",
    "        the 'knee' of the function\n",
    "    lum1err : float\n",
    "        Error in characteristic luminosity\n",
    "    alpha : float\n",
    "        the faint-end slope of power law\n",
    "    alphaerr : float\n",
    "        Error in the faint-end slope of power law\n",
    "    kappa : float\n",
    "        conversion factor b/w luminosity density and\n",
    "        star formation rate\n",
    "    limit : float\n",
    "        lower limit of the intensity\n",
    "        as a function of L*\n",
    "        default is 0.03 (from Madau&Dickinson)\n",
    "    -----------\n",
    "    return\n",
    "    -----------\n",
    "    float\n",
    "        mean star formation rate\n",
    "    float\n",
    "        error in star formation rate\n",
    "    \"\"\"\n",
    "    lum_den2 = lum_den22(lum, lum1, lum1err, phi1, phi1errp, phi1errn, alpha, alphaerr, limit)\n",
    "    kpp1 = kappa\n",
    "    sfr2 = kpp1*lum_den2\n",
    "    sfr_m, sfrp, sfrn = utl.get_quantiles(sfr2)\n",
    "    return sfr_m, sfrp-sfr_m, sfr_m-sfrn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "100%|██████████| 10000/10000 [01:46<00:00, 94.34it/s]\n",
      "100%|██████████| 10000/10000 [02:03<00:00, 80.67it/s]\n",
      "100%|██████████| 10000/10000 [01:43<00:00, 96.85it/s]\n",
      "100%|██████████| 10000/10000 [01:50<00:00, 90.21it/s]\n",
      "100%|██████████| 10000/10000 [01:55<00:00, 86.27it/s]\n"
     ]
    }
   ],
   "source": [
    "sfrd_bou_asy = np.zeros(z_bou.shape)\n",
    "sfrd_perr_bou_asy = np.zeros(z_bou.shape)\n",
    "sfrd_nerr_bou_asy = np.zeros(z_bou.shape)\n",
    "\n",
    "for i in range(len(z_bou)):\n",
    "    sfrd_bou_asy[i], sfrd_perr_bou_asy[i], sfrd_nerr_bou_asy[i] = sfrd_w_err(lum=lums_bou, lum1=lst_bou[i], lum1err=lsterr_bou[i], phi1=phi_bou[i], phi1errp=phi_pos_err_bou[i], phi1errn=phi_neg_err_bou[i], alpha=alp_bou[i], alphaerr=alperr_bou[i], kappa=kap_uv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 1080x540 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "log_sfrd_bou_asy, log_sfrd_bou_perr_asy =  utl.log_err(sfrd_bou_asy, sfrd_perr_bou_asy)\n",
    "log_sfrd_bou_asy, log_sfrd_bou_nerr_asy =  utl.log_err(sfrd_bou_asy, sfrd_nerr_bou_asy)\n",
    "\n",
    "plt.figure(figsize=(15,7.5))\n",
    "plt.errorbar(z_bou, log_sfrd_bou_asy, yerr=[log_sfrd_bou_perr_asy, log_sfrd_bou_nerr_asy], fmt='.')\n",
    "plt.scatter(z_bou, log_sfrd_wo_bou, marker='s', c='orangered', label='Without errors', alpha=0.5)\n",
    "plt.xlabel('Redshift')\n",
    "plt.ylabel('SFRD')\n",
    "plt.legend(loc='best')\n",
    "plt.ylim([-2.7, -0.5])\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "--------------------------------------------------------------------------------\nAt redshift 3.8\n--------------------------------------------------------------------------------\nWithout Error Propagation:\n--------------------------\nValue of SFRD is: 3.75e-02\nValue of log(SFRD) is: -1.43e+00\n--------------------------------------------------------------\nWith Error Propagation (wo taking into account of correlations)\n--------------------------------------------------------------\nValue of SFRD is: 3.76e-02 +/- 7.07e-03\nValue of log(SFRD) is: -1.42e+00 +/- 8.16e-02\n--------------------------------------------------------------\nWith Error propagation and with asymmetric distribution\n--------------------------------------------------------------\nValue of SFRD is: 3.76e-02 +/- 7.72e-03\nValue of log(SFRD) is: -1.42e+00 +/- 8.90e-02\n--------------------------------------------------------------------------------\n--------------------------------------------------------------------------------\nAt redshift 4.9\n--------------------------------------------------------------------------------\nWithout Error Propagation:\n--------------------------\nValue of SFRD is: 2.18e-02\nValue of log(SFRD) is: -1.66e+00\n--------------------------------------------------------------\nWith Error Propagation (wo taking into account of correlations)\n--------------------------------------------------------------\nValue of SFRD is: 2.20e-02 +/- 5.84e-03\nValue of log(SFRD) is: -1.66e+00 +/- 1.15e-01\n--------------------------------------------------------------\nWith Error propagation and with asymmetric distribution\n--------------------------------------------------------------\nValue of SFRD is: 2.19e-02 +/- 7.07e-03\nValue of log(SFRD) is: -1.66e+00 +/- 1.40e-01\n--------------------------------------------------------------------------------\n--------------------------------------------------------------------------------\nAt redshift 5.9\n--------------------------------------------------------------------------------\nWithout Error Propagation:\n--------------------------\nValue of SFRD is: 1.43e-02\nValue of log(SFRD) is: -1.84e+00\n--------------------------------------------------------------\nWith Error Propagation (wo taking into account of correlations)\n--------------------------------------------------------------\nValue of SFRD is: 1.47e-02 +/- 7.11e-03\nValue of log(SFRD) is: -1.83e+00 +/- 2.11e-01\n--------------------------------------------------------------\nWith Error propagation and with asymmetric distribution\n--------------------------------------------------------------\nValue of SFRD is: 1.46e-02 +/- 9.35e-03\nValue of log(SFRD) is: -1.84e+00 +/- 2.79e-01\n--------------------------------------------------------------------------------\n--------------------------------------------------------------------------------\nAt redshift 6.8\n--------------------------------------------------------------------------------\nWithout Error Propagation:\n--------------------------\nValue of SFRD is: 1.09e-02\nValue of log(SFRD) is: -1.96e+00\n--------------------------------------------------------------\nWith Error Propagation (wo taking into account of correlations)\n--------------------------------------------------------------\nValue of SFRD is: 1.15e-02 +/- 8.61e-03\nValue of log(SFRD) is: -1.94e+00 +/- 3.26e-01\n--------------------------------------------------------------\nWith Error propagation and with asymmetric distribution\n--------------------------------------------------------------\nValue of SFRD is: 1.15e-02 +/- 1.29e-02\nValue of log(SFRD) is: -1.94e+00 +/- 4.89e-01\n--------------------------------------------------------------------------------\n--------------------------------------------------------------------------------\nAt redshift 7.9\n--------------------------------------------------------------------------------\nWithout Error Propagation:\n--------------------------\nValue of SFRD is: 6.05e-03\nValue of log(SFRD) is: -2.22e+00\n--------------------------------------------------------------\nWith Error Propagation (wo taking into account of correlations)\n--------------------------------------------------------------\nValue of SFRD is: 7.08e-03 +/- 9.05e-03\nValue of log(SFRD) is: -2.15e+00 +/- 5.55e-01\n--------------------------------------------------------------\nWith Error propagation and with asymmetric distribution\n--------------------------------------------------------------\nValue of SFRD is: 6.62e-03 +/- 1.41e-02\nValue of log(SFRD) is: -2.18e+00 +/- 9.23e-01\n--------------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "f23 = open(os.getcwd() + '/Results/Bou15_asy.dat','w')\n",
    "f23.write('#Redshift\\tSFRD(asy)\\tperr\\tnerr\\n')\n",
    "\n",
    "for i in range(len(sfrd_bou)):\n",
    "    print('--------------------------------------------------------------------------------')\n",
    "    print('At redshift {:.1f}'.format(z_bou[i]))\n",
    "    print('--------------------------------------------------------------------------------')\n",
    "    print('Without Error Propagation:')\n",
    "    print('--------------------------')\n",
    "    print('Value of SFRD is: {:.2e}'.format(sfrd_wo_errs[i]))\n",
    "    print('Value of log(SFRD) is: {:.2e}'.format(log_sfrd_wo_bou[i]))\n",
    "    print('--------------------------------------------------------------')\n",
    "    print('With Error Propagation (wo taking into account of correlations)')\n",
    "    print('--------------------------------------------------------------')\n",
    "    print('Value of SFRD is: {:.2e} +/- {:.2e}'.format(sfrd_bou[i], sfrd_err_bou[i]))\n",
    "    print('Value of log(SFRD) is: {:.2e} +/- {:.2e}'.format(log_sfrd_bou[i], log_sfrd_bou_err[i]))\n",
    "    print('--------------------------------------------------------------')\n",
    "    print('With Error propagation and with asymmetric distribution')\n",
    "    print('--------------------------------------------------------------')\n",
    "    print('Value of SFRD is: {:.2e} +/- {:.2e}'.format(sfrd_bou_asy[i], sfrd_perr_bou_asy[i]))\n",
    "    print('Value of log(SFRD) is: {:.2e} +/- {:.2e}'.format(log_sfrd_bou_asy[i], log_sfrd_bou_perr_asy[i]))\n",
    "    print('--------------------------------------------------------------------------------')\n",
    "    f23.write(str(z_bou[i]) + '\\t' + str(sfrd_bou_asy[i]) + '\\t' + str(sfrd_perr_bou_asy[i]) + '\\t' + str(sfrd_nerr_bou_asy) + '\\n')\n",
    "f23.close()"
   ]
  }
 ]
}