From 8486c1fee4505c4fbdb1102b2e6e4f284a71c050 Mon Sep 17 00:00:00 2001 From: lucianopaz Date: Mon, 23 May 2022 09:25:50 +0200 Subject: [PATCH 1/9] Add rejection method sampling for generalized poisson --- notebooks/fast_gen_pois.ipynb | 586 ++++++++++++++++++++++++++++++++++ notebooks/fast_gen_pois.py | 203 ++++++++++++ 2 files changed, 789 insertions(+) create mode 100644 notebooks/fast_gen_pois.ipynb create mode 100644 notebooks/fast_gen_pois.py diff --git a/notebooks/fast_gen_pois.ipynb b/notebooks/fast_gen_pois.ipynb new file mode 100644 index 0000000..8b65588 --- /dev/null +++ b/notebooks/fast_gen_pois.ipynb @@ -0,0 +1,586 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "d06b73f0-08b3-40bd-bd9c-a8fe05ac03b0", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.special import gammaln\n", + "\n", + "\n", + "def _logpow(x, m):\n", + " \"\"\"\n", + " Calculates log(x**m) since m*log(x) will fail when m, x = 0.\n", + " \"\"\"\n", + " # return m * log(x)\n", + " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n", + "\n", + "\n", + "def _logprob(x, theta, lam):\n", + " theta_lam_x = theta + lam * x\n", + " return np.where(\n", + " x >= 0,\n", + " np.log(theta) + _logpow(theta_lam_x, x - 1) - theta_lam_x - gammaln(x + 1),\n", + " -np.inf,\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "fee5de3f-e4cb-419f-9930-e9df8322a4f1", + "metadata": {}, + "outputs": [], + "source": [ + "def _rejection_region_monotonicity(rng, theta, lam, dist_size, idxs_mask=None):\n", + " if idxs_mask is None:\n", + " idxs_mask = np.ones(dist_size, dtype=\"bool\")\n", + " theta = np.broadcast_to(theta, dist_size)[idxs_mask]\n", + " lam = np.broadcast_to(lam, dist_size)[idxs_mask]\n", + " dist_size = np.sum(idxs_mask)\n", + " p0 = np.exp(-theta)\n", + " b = theta * np.exp(2 - lam - np.minimum(lam, theta)) * np.sqrt(2 / np.pi)\n", + " u = rng.uniform(size=dist_size)\n", + " x = np.zeros(dist_size)\n", + " inds_to_sample = u > p0 / (p0 + b)\n", + " counter = 0\n", + " while np.any(inds_to_sample):\n", + " counter += 1\n", + " v = rng.uniform(size=dist_size)\n", + " w = rng.uniform(size=dist_size)\n", + " _x = np.floor(1 / w ** 2)\n", + " accepted = v * b * (1 / np.sqrt(_x) - 1 / np.sqrt(_x + 1)) <= np.exp(\n", + " _logprob(_x, theta, lam)\n", + " )\n", + " x[inds_to_sample & accepted] = _x[inds_to_sample & accepted]\n", + " inds_to_sample = inds_to_sample & ~accepted\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "725437c3-5490-438f-aa86-6ae59f308b99", + "metadata": {}, + "outputs": [], + "source": [ + "def _rejection_region_poisson(rng, theta, lam, dist_size, idxs_mask=None):\n", + " if idxs_mask is None:\n", + " idxs_mask = np.ones(dist_size, dtype=\"bool\")\n", + " theta = np.broadcast_to(theta, dist_size)[idxs_mask]\n", + " lam = np.broadcast_to(lam, dist_size)[idxs_mask]\n", + " dist_size = np.sum(idxs_mask)\n", + "\n", + " eps = (1 - lam) / (2 + (theta - lam) * (1 - lam)) ** (1 / 3)\n", + " delta = (1 - lam) ** (2 / 5) / (2 + (theta - lam) * (1 - lam)) ** (1 / 3)\n", + " mu = (theta - lam) / (1 - lam)\n", + " sigma = np.sqrt((1 - delta) * (theta - lam) / (1 - lam - eps) / (1 - lam) ** 2)\n", + " psi = (\n", + " theta * delta * (2 + delta - 2 * lam)\n", + " + (1 + delta) * (1 - lam) ** 2\n", + " - lam * (1 - lam + delta) ** 2\n", + " ) / (2 * (theta - 1 - delta))\n", + " G = (\n", + " (theta * (1 - lam - eps) * np.sqrt(1 + delta))\n", + " / ((theta - lam) * (1 - lam) * (1 - eps) ** 2)\n", + " * np.exp(psi / (1 + delta))\n", + " )\n", + "\n", + " def g(x):\n", + " return (\n", + " G\n", + " / (np.sqrt(2 * np.pi) * sigma)\n", + " * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2))\n", + " )\n", + "\n", + " h_r_norm = (theta * (1 - lam - eps) ** 1.5) / (\n", + " np.sqrt(2 * np.pi) * (theta - lam) ** 1.5\n", + " )\n", + " h_r_exp_A = -(1 - 2 * (1 - lam - eps) / (theta - lam)) * (eps / 2) * (1 - lam)\n", + " h_r_exp_B = 2 * (1 - lam)\n", + "\n", + " def h_r(x):\n", + " return h_r_norm * np.exp(h_r_exp_A * (x - mu) + h_r_exp_B)\n", + "\n", + " t_r = np.ceil((theta - lam) / (1 - lam - eps) - 1)\n", + " H_r = (\n", + " (2 * theta * (1 - lam - eps) ** 1.5 * np.exp(2 * (1 - lam)))\n", + " / (\n", + " np.sqrt(2 * np.pi)\n", + " * (theta - lam) ** 1.5\n", + " * (1 - 2 * (1 - lam - eps) / (theta - lam))\n", + " * eps\n", + " * (1 - lam)\n", + " )\n", + " * np.exp(\n", + " -(1 - 2 * (1 - lam - eps) / (theta - lam))\n", + " * (eps / 2)\n", + " * (1 - lam)\n", + " * (t_r - mu)\n", + " )\n", + " )\n", + "\n", + " def h_l(x):\n", + " return (\n", + " theta\n", + " / np.sqrt(2 * np.pi)\n", + " * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", + " )\n", + "\n", + " t_l = np.ceil((theta - lam) / (1 - lam + delta) - 1)\n", + " H_l = (\n", + " (2 * theta * (1 + delta))\n", + " / (np.sqrt(2 * np.pi) * delta * (1 - lam))\n", + " * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (t_l + 1 - mu))\n", + " )\n", + "\n", + " x = np.zeros(dist_size)\n", + " inds_to_sample = np.ones(dist_size, dtype=\"bool\")\n", + " counter = -1\n", + " while np.any(inds_to_sample):\n", + " counter += 1\n", + " U = rng.uniform(size=dist_size)\n", + " N = rng.normal(size=dist_size)\n", + " V = rng.uniform(size=dist_size)\n", + " E = rng.exponential(size=dist_size)\n", + " center = U < G / (G - H_l + H_r)\n", + " left = (U < (G + H_l) / (G + H_l + H_r)) & ~center\n", + " raw_center_y = mu + sigma * N\n", + " raw_left_y = t_l - 2 * E * (1 + delta) / delta / (1 - lam)\n", + " raw_right_y = t_r + 2 * E / (\n", + " (1 - 2 * (1 - lam - eps) / (theta - lam)) * eps * (1 - lam)\n", + " )\n", + " Y = np.where(\n", + " center,\n", + " np.where(\n", + " (raw_center_y >= t_l) & (raw_center_y < t_r), raw_center_y, np.nan,\n", + " ),\n", + " np.where(\n", + " left,\n", + " np.where(raw_left_y >= 0, raw_left_y, np.nan,),\n", + " np.where(raw_right_y >= 0, raw_right_y, np.nan,),\n", + " ),\n", + " )\n", + " X = np.floor(Y)\n", + " accepted = V * np.where(\n", + " center, g(Y), np.where(left, h_l(Y), h_r(Y),),\n", + " ) <= np.exp(_logprob(X, theta, lam))\n", + "\n", + " x[inds_to_sample & accepted] = X[inds_to_sample & accepted]\n", + " inds_to_sample = inds_to_sample & ~accepted\n", + " if counter % 1000 == 0:\n", + " temp1 = theta[inds_to_sample]\n", + " temp2 = lam[inds_to_sample]\n", + " print(np.sum(inds_to_sample), temp1[-1], temp2[-1])\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "fcfcb8c4-a701-4f79-8271-71824ee6e130", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_22232/50466135.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", + " poisson_idxs = np.broadcast_to(theta >= np.maximum(3, 2 * lam / (1 - lam)), dist_size)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1116 100.0 0.825\n", + "586 1000.0 0.6499999999999999\n", + "437 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idxs_mask=monotonicity_idxs\n", + ")\n", + "samples[poisson_idxs] = _rejection_region_poisson(\n", + " rng=rng, theta=theta, lam=lam, dist_size=dist_size, idxs_mask=poisson_idxs,\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 160, + "id": "dbea78f7-18b3-4687-91f7-8e8ecb6d0a47", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[1.0000e+00, 7.0000e+00, 1.8700e+02, 1.6490e+03, 1.4364e+04],\n", + " [2.0000e+00, 9.0000e+00, 2.6000e+02, 2.1940e+03, 1.9145e+04],\n", + " [3.0000e+00, 6.2000e+01, 4.0700e+02, 3.3490e+03, 2.8421e+04],\n", + " [3.0000e+00, 1.8600e+02, 1.0270e+03, 5.8380e+03, 5.9644e+04],\n", + " [0.0000e+00, nan, nan, nan, nan]],\n", + "\n", + " [[1.0000e+00, 7.0000e+00, 1.0200e+02, 1.6370e+03, 1.4416e+04],\n", + " [4.0000e+00, 8.0000e+00, 2.8400e+02, 2.1760e+03, 1.9031e+04],\n", + " [2.0000e+00, 1.0000e+01, 4.0700e+02, 3.4420e+03, 2.8571e+04],\n", + " [0.0000e+00, 4.0000e+00, 9.2500e+02, 5.5390e+03, 5.8194e+04],\n", + " 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}, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + }, + "toc-showtags": false + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/fast_gen_pois.py b/notebooks/fast_gen_pois.py new file mode 100644 index 0000000..c64d722 --- /dev/null +++ b/notebooks/fast_gen_pois.py @@ -0,0 +1,203 @@ +# --- +# jupyter: +# jupytext: +# formats: ipynb,py:percent +# text_representation: +# extension: .py +# format_name: percent +# format_version: '1.3' +# jupytext_version: 1.13.8 +# kernelspec: +# display_name: Python 3 +# language: python +# name: python3 +# --- + +# %% +import numpy as np + +from scipy.special import gammaln + + +def _logpow(x, m): + """ + Calculates log(x**m) since m*log(x) will fail when m, x = 0. + """ + # return m * log(x) + return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x)) + + +def _logprob(x, theta, lam): + theta_lam_x = theta + lam * x + return np.where( + x >= 0, + np.log(theta) + _logpow(theta_lam_x, x - 1) - theta_lam_x - gammaln(x + 1), + -np.inf, + ) + + +# %% +def _rejection_region_monotonicity(rng, theta, lam, dist_size, idxs_mask=None): + if idxs_mask is None: + idxs_mask = np.ones(dist_size, dtype="bool") + theta = np.broadcast_to(theta, dist_size)[idxs_mask] + lam = np.broadcast_to(lam, dist_size)[idxs_mask] + dist_size = np.sum(idxs_mask) + p0 = np.exp(-theta) + b = theta * np.exp(2 - lam - np.minimum(lam, theta)) * np.sqrt(2 / np.pi) + u = rng.uniform(size=dist_size) + x = np.zeros(dist_size) + inds_to_sample = u > p0 / (p0 + b) + counter = 0 + while np.any(inds_to_sample): + counter += 1 + v = rng.uniform(size=dist_size) + w = rng.uniform(size=dist_size) + _x = np.floor(1 / w ** 2) + accepted = v * b * (1 / np.sqrt(_x) - 1 / np.sqrt(_x + 1)) <= np.exp( + _logprob(_x, theta, lam) + ) + x[inds_to_sample & accepted] = _x[inds_to_sample & accepted] + inds_to_sample = inds_to_sample & ~accepted + return x + + +# %% +def _rejection_region_poisson(rng, theta, lam, dist_size, idxs_mask=None): + if idxs_mask is None: + idxs_mask = np.ones(dist_size, dtype="bool") + theta = np.broadcast_to(theta, dist_size)[idxs_mask] + lam = np.broadcast_to(lam, dist_size)[idxs_mask] + dist_size = np.sum(idxs_mask) + + eps = (1 - lam) / (2 + (theta - lam) * (1 - lam)) ** (1 / 3) + delta = (1 - lam) ** (2 / 5) / (2 + (theta - lam) * (1 - lam)) ** (1 / 3) + mu = (theta - lam) / (1 - lam) + sigma = np.sqrt((1 - delta) * (theta - lam) / (1 - lam - eps) / (1 - lam) ** 2) + psi = ( + theta * delta * (2 + delta - 2 * lam) + + (1 + delta) * (1 - lam) ** 2 + - lam * (1 - lam + delta) ** 2 + ) / (2 * (theta - 1 - delta)) + G = ( + (theta * (1 - lam - eps) * np.sqrt(1 + delta)) + / ((theta - lam) * (1 - lam) * (1 - eps) ** 2) + * np.exp(psi / (1 + delta)) + ) + + def g(x): + return G / (np.sqrt(2 * np.pi) * sigma) * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2)) + + h_r_norm = (theta * (1 - lam - eps) ** 1.5) / (np.sqrt(2 * np.pi) * (theta - lam) ** 1.5) + h_r_exp_A = -(1 - 2 * (1 - lam - eps) / (theta - lam)) * (eps / 2) * (1 - lam) + h_r_exp_B = 2 * (1 - lam) + + def h_r(x): + return h_r_norm * np.exp(h_r_exp_A * (x - mu) + h_r_exp_B) + + t_r = np.ceil((theta - lam) / (1 - lam - eps) - 1) + H_r = ( + (2 * theta * (1 - lam - eps) ** 1.5 * np.exp(2 * (1 - lam))) + / ( + np.sqrt(2 * np.pi) + * (theta - lam) ** 1.5 + * (1 - 2 * (1 - lam - eps) / (theta - lam)) + * eps + * (1 - lam) + ) + * np.exp(-(1 - 2 * (1 - lam - eps) / (theta - lam)) * (eps / 2) * (1 - lam) * (t_r - mu)) + ) + + def h_l(x): + return ( + theta + / np.sqrt(2 * np.pi) + * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu)) + ) + + t_l = np.ceil((theta - lam) / (1 - lam + delta) - 1) + H_l = ( + (2 * theta * (1 + delta)) + / (np.sqrt(2 * np.pi) * delta * (1 - lam)) + * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (t_l + 1 - mu)) + ) + + x = np.zeros(dist_size) + inds_to_sample = np.ones(dist_size, dtype="bool") + counter = -1 + while np.any(inds_to_sample): + counter += 1 + U = rng.uniform(size=dist_size) + N = rng.normal(size=dist_size) + V = rng.uniform(size=dist_size) + E = rng.exponential(size=dist_size) + center = U < G / (G - H_l + H_r) + left = (U < (G + H_l) / (G + H_l + H_r)) & ~center + raw_center_y = mu + sigma * N + raw_left_y = t_l - 2 * E * (1 + delta) / delta / (1 - lam) + raw_right_y = t_r + 2 * E / ((1 - 2 * (1 - lam - eps) / (theta - lam)) * eps * (1 - lam)) + Y = np.where( + center, + np.where( + (raw_center_y >= t_l) & (raw_center_y < t_r), + raw_center_y, + np.nan, + ), + np.where( + left, + np.where( + raw_left_y >= 0, + raw_left_y, + np.nan, + ), + np.where( + raw_right_y >= 0, + raw_right_y, + np.nan, + ), + ), + ) + X = np.floor(Y) + accepted = ( + V + * np.where( + center, + g(Y), + np.where( + left, + h_l(Y), + h_r(Y), + ), + ) + <= np.exp(_logprob(X, theta, lam)) + ) + + x[inds_to_sample & accepted] = X[inds_to_sample & accepted] + inds_to_sample = inds_to_sample & ~accepted + if counter % 1000 == 0: + temp1 = theta[inds_to_sample] + temp2 = lam[inds_to_sample] + print(np.sum(inds_to_sample), temp1[-1], temp2[-1]) + return x + + +# %% +rng = np.random.default_rng(42) +theta, lam = np.meshgrid(np.logspace(0, 4, 5), np.linspace(0.3, 1, 5)) +dist_size = (100, *theta.shape) +monotonicity_idxs = np.broadcast_to(theta <= np.exp(lam), dist_size) +poisson_idxs = np.broadcast_to(theta >= np.maximum(3, 2 * lam / (1 - lam)), dist_size) +samples = np.full(dist_size, np.nan) +samples[monotonicity_idxs] = _rejection_region_monotonicity( + rng=rng, theta=theta, lam=lam, dist_size=dist_size, idxs_mask=monotonicity_idxs +) +samples[poisson_idxs] = _rejection_region_poisson( + rng=rng, + theta=theta, + lam=lam, + dist_size=dist_size, + idxs_mask=poisson_idxs, +) + +# %% +samples From f92171daf76a54b967461882995348d15f4acd49 Mon Sep 17 00:00:00 2001 From: lucianopaz Date: Wed, 25 May 2022 14:23:40 +0200 Subject: [PATCH 2/9] Add abel region rejection sampler --- notebooks/fast_gen_pois.ipynb | 908 +++++++++++++++++++--------------- notebooks/fast_gen_pois.py | 410 ++++++++++++--- 2 files changed, 849 insertions(+), 469 deletions(-) diff --git a/notebooks/fast_gen_pois.ipynb b/notebooks/fast_gen_pois.ipynb index 8b65588..6cf2bb5 100644 --- a/notebooks/fast_gen_pois.ipynb +++ b/notebooks/fast_gen_pois.ipynb @@ -8,6 +8,7 @@ "outputs": [], "source": [ "import numpy as np\n", + "from matplotlib import pyplot as plt\n", "from scipy.special import gammaln\n", "\n", "\n", @@ -19,12 +20,10 @@ " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n", "\n", "\n", - "def _logprob(x, theta, lam):\n", - " theta_lam_x = theta + lam * x\n", + "def _logprob(x, p, lam):\n", + " p_lam_x = p + lam * x\n", " return np.where(\n", - " x >= 0,\n", - " np.log(theta) + _logpow(theta_lam_x, x - 1) - theta_lam_x - gammaln(x + 1),\n", - " -np.inf,\n", + " x >= 0, np.log(p) + _logpow(p_lam_x, x - 1) - p_lam_x - gammaln(x + 1), -np.inf,\n", " )" ] }, @@ -35,14 +34,14 @@ "metadata": {}, "outputs": [], "source": [ - "def _rejection_region_monotonicity(rng, theta, lam, dist_size, idxs_mask=None):\n", + "def _rejection_region_monotonicity(rng, p, lam, dist_size, idxs_mask=None):\n", " if idxs_mask is None:\n", " idxs_mask = np.ones(dist_size, dtype=\"bool\")\n", - " theta = np.broadcast_to(theta, dist_size)[idxs_mask]\n", + " p = np.broadcast_to(p, dist_size)[idxs_mask]\n", " lam = np.broadcast_to(lam, dist_size)[idxs_mask]\n", " dist_size = np.sum(idxs_mask)\n", - " p0 = np.exp(-theta)\n", - " b = theta * np.exp(2 - lam - np.minimum(lam, theta)) * np.sqrt(2 / np.pi)\n", + " p0 = np.exp(-p)\n", + " b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi)\n", " u = rng.uniform(size=dist_size)\n", " x = np.zeros(dist_size)\n", " inds_to_sample = u > p0 / (p0 + b)\n", @@ -53,7 +52,7 @@ " w = rng.uniform(size=dist_size)\n", " _x = np.floor(1 / w ** 2)\n", " accepted = v * b * (1 / np.sqrt(_x) - 1 / np.sqrt(_x + 1)) <= np.exp(\n", - " _logprob(_x, theta, lam)\n", + " _logprob(_x, p, lam)\n", " )\n", " x[inds_to_sample & accepted] = _x[inds_to_sample & accepted]\n", " inds_to_sample = inds_to_sample & ~accepted\n", @@ -63,100 +62,115 @@ { "cell_type": "code", "execution_count": 3, - "id": "725437c3-5490-438f-aa86-6ae59f308b99", + "id": "d0557ec5-5d72-41ad-b2be-0696aa10ab46", "metadata": {}, "outputs": [], "source": [ - "def _rejection_region_poisson(rng, theta, lam, dist_size, idxs_mask=None):\n", + "def _rejection_region_poisson(rng, p, lam, dist_size, idxs_mask=None):\n", " if idxs_mask is None:\n", " idxs_mask = np.ones(dist_size, dtype=\"bool\")\n", - " theta = np.broadcast_to(theta, dist_size)[idxs_mask]\n", + " p = np.broadcast_to(p, dist_size)[idxs_mask]\n", " lam = np.broadcast_to(lam, dist_size)[idxs_mask]\n", " dist_size = np.sum(idxs_mask)\n", "\n", - " eps = (1 - lam) / (2 + (theta - lam) * (1 - lam)) ** (1 / 3)\n", - " delta = (1 - lam) ** (2 / 5) / (2 + (theta - lam) * (1 - lam)) ** (1 / 3)\n", - " mu = (theta - lam) / (1 - lam)\n", - " sigma = np.sqrt((1 - delta) * (theta - lam) / (1 - lam - eps) / (1 - lam) ** 2)\n", + " eps = (1 - lam) / (2 + (p - lam) * (1 - lam)) ** (1 / 3)\n", + " delta = (1 - lam) ** (2 / 5) / (2 + (p - lam) * (1 - lam)) ** (1 / 3)\n", + " mu = (p - lam) / (1 - lam)\n", + " sigma = np.sqrt((1 + delta) * (p - lam) / (1 - lam - eps) / (1 - lam) ** 2)\n", " psi = (\n", - " theta * delta * (2 + delta - 2 * lam)\n", + " p * delta * (2 + delta - 2 * lam)\n", " + (1 + delta) * (1 - lam) ** 2\n", " - lam * (1 - lam + delta) ** 2\n", - " ) / (2 * (theta - 1 - delta))\n", + " ) / (2 * (p - 1 - delta))\n", " G = (\n", - " (theta * (1 - lam - eps) * np.sqrt(1 + delta))\n", - " / ((theta - lam) * (1 - lam) * (1 - eps) ** 2)\n", + " (p * (1 - lam - eps) * np.sqrt(1 + delta))\n", + " / ((p - lam) * (1 - lam) * (1 - eps) ** 2)\n", " * np.exp(psi / (1 + delta))\n", " )\n", "\n", - " def g(x):\n", + " def g(x, G, mu, sigma):\n", " return (\n", " G\n", " / (np.sqrt(2 * np.pi) * sigma)\n", " * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2))\n", " )\n", "\n", - " h_r_norm = (theta * (1 - lam - eps) ** 1.5) / (\n", - " np.sqrt(2 * np.pi) * (theta - lam) ** 1.5\n", - " )\n", - " h_r_exp_A = -(1 - 2 * (1 - lam - eps) / (theta - lam)) * (eps / 2) * (1 - lam)\n", - " h_r_exp_B = 2 * (1 - lam)\n", - "\n", - " def h_r(x):\n", - " return h_r_norm * np.exp(h_r_exp_A * (x - mu) + h_r_exp_B)\n", + " def h_r(x, p, lam, eps, mu):\n", + " return (\n", + " (p * (1 - lam - eps) ** 1.5)\n", + " / (np.sqrt(2 * np.pi) * (p - lam) ** 1.5)\n", + " * np.exp(\n", + " -(1 - 2 * (1 - lam - eps) / (p - lam))\n", + " * (eps / 2)\n", + " * (1 - lam)\n", + " * (x - mu)\n", + " + 2 * (1 - lam)\n", + " )\n", + " )\n", "\n", - " t_r = np.ceil((theta - lam) / (1 - lam - eps) - 1)\n", + " t_r = np.ceil((p - lam) / (1 - lam - eps) - 1)\n", " H_r = (\n", - " (2 * theta * (1 - lam - eps) ** 1.5 * np.exp(2 * (1 - lam)))\n", + " (2 * p * (1 - lam - eps) ** 1.5 * np.exp(2 * (1 - lam)))\n", " / (\n", " np.sqrt(2 * np.pi)\n", - " * (theta - lam) ** 1.5\n", - " * (1 - 2 * (1 - lam - eps) / (theta - lam))\n", + " * (p - lam) ** 1.5\n", + " * (1 - 2 * (1 - lam - eps) / (p - lam))\n", " * eps\n", " * (1 - lam)\n", " )\n", " * np.exp(\n", - " -(1 - 2 * (1 - lam - eps) / (theta - lam))\n", - " * (eps / 2)\n", - " * (1 - lam)\n", - " * (t_r - mu)\n", + " -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (t_r - mu)\n", " )\n", " )\n", "\n", - " def h_l(x):\n", + " def h_l(x, p, lam, delta, mu):\n", " return (\n", - " theta\n", + " p\n", " / np.sqrt(2 * np.pi)\n", " * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", " )\n", "\n", - " t_l = np.ceil((theta - lam) / (1 - lam + delta) - 1)\n", + " t_l = np.ceil((p - lam) / (1 - lam + delta) - 1)\n", " H_l = (\n", - " (2 * theta * (1 + delta))\n", + " (2 * p * (1 + delta))\n", " / (np.sqrt(2 * np.pi) * delta * (1 - lam))\n", " * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (t_l + 1 - mu))\n", " )\n", "\n", " x = np.zeros(dist_size)\n", - " inds_to_sample = np.ones(dist_size, dtype=\"bool\")\n", + " inds_to_sample = np.arange(dist_size)\n", + " n_to_accept = np.zeros(dist_size)\n", " counter = -1\n", " while np.any(inds_to_sample):\n", " counter += 1\n", - " U = rng.uniform(size=dist_size)\n", - " N = rng.normal(size=dist_size)\n", - " V = rng.uniform(size=dist_size)\n", - " E = rng.exponential(size=dist_size)\n", - " center = U < G / (G - H_l + H_r)\n", - " left = (U < (G + H_l) / (G + H_l + H_r)) & ~center\n", - " raw_center_y = mu + sigma * N\n", - " raw_left_y = t_l - 2 * E * (1 + delta) / delta / (1 - lam)\n", - " raw_right_y = t_r + 2 * E / (\n", - " (1 - 2 * (1 - lam - eps) / (theta - lam)) * eps * (1 - lam)\n", + " _dist_size = len(inds_to_sample)\n", + " U = rng.uniform(size=_dist_size)\n", + " N = rng.normal(size=_dist_size)\n", + " V = rng.uniform(size=_dist_size)\n", + " E = rng.exponential(size=_dist_size)\n", + " _G = G[inds_to_sample]\n", + " _H_l = H_l[inds_to_sample]\n", + " _H_r = H_r[inds_to_sample]\n", + " _p = p[inds_to_sample]\n", + " _lam = lam[inds_to_sample]\n", + " _mu = mu[inds_to_sample]\n", + " _sigma = sigma[inds_to_sample]\n", + " _delta = delta[inds_to_sample]\n", + " _eps = eps[inds_to_sample]\n", + " _t_l = t_l[inds_to_sample]\n", + " _t_r = t_r[inds_to_sample]\n", + "\n", + " center = U < _G / (_G + _H_l + _H_r)\n", + " left = (U < (_G + _H_l) / (_G + _H_l + _H_r)) & ~center\n", + " raw_center_y = _mu + _sigma * N\n", + " raw_left_y = _t_l - 2 * E * (1 + _delta) / _delta / (1 - _lam)\n", + " raw_right_y = _t_r + 2 * E / (\n", + " (1 - 2 * (1 - _lam - _eps) / (_p - _lam)) * _eps * (1 - _lam)\n", " )\n", " Y = np.where(\n", " center,\n", " np.where(\n", - " (raw_center_y >= t_l) & (raw_center_y < t_r), raw_center_y, np.nan,\n", + " (raw_center_y >= _t_l) & (raw_center_y < _t_r), raw_center_y, np.nan,\n", " ),\n", " np.where(\n", " left,\n", @@ -166,396 +180,486 @@ " )\n", " X = np.floor(Y)\n", " accepted = V * np.where(\n", - " center, g(Y), np.where(left, h_l(Y), h_r(Y),),\n", - " ) <= np.exp(_logprob(X, theta, lam))\n", + " center,\n", + " g(Y, G=_G, mu=_mu, sigma=_sigma),\n", + " np.where(\n", + " left,\n", + " h_l(Y, p=_p, lam=_lam, delta=_delta, mu=_mu),\n", + " h_r(Y, p=_p, lam=_lam, eps=_eps, mu=_mu),\n", + " ),\n", + " ) <= np.exp(_logprob(X, _p, _lam))\n", "\n", - " x[inds_to_sample & accepted] = X[inds_to_sample & accepted]\n", - " inds_to_sample = inds_to_sample & ~accepted\n", - " if counter % 1000 == 0:\n", - " temp1 = theta[inds_to_sample]\n", - " temp2 = lam[inds_to_sample]\n", - " print(np.sum(inds_to_sample), temp1[-1], temp2[-1])\n", + " x[inds_to_sample[accepted]] = X[accepted]\n", + " n_to_accept[inds_to_sample[accepted]] = counter\n", + " inds_to_sample = inds_to_sample[~accepted]\n", + " # if counter % 1000 == 0:\n", + " # print(np.sum(inds_to_sample))\n", " return x" ] }, { "cell_type": "code", "execution_count": 4, - "id": "fcfcb8c4-a701-4f79-8271-71824ee6e130", + "id": "63b469a2-917e-47a7-a92b-627b1bc80084", + "metadata": {}, + "outputs": [], + "source": [ + "def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None):\n", + " if idxs_mask is None:\n", + " idxs_mask = np.ones(dist_size, dtype=\"bool\")\n", + " p = np.broadcast_to(p, dist_size)[idxs_mask]\n", + " lam = np.broadcast_to(lam, dist_size)[idxs_mask]\n", + " dist_size = np.sum(idxs_mask)\n", + "\n", + " nu = 2 * (p ** 2 - lam * p - 3 * lam ** 2) / (3 * lam ** 2)\n", + " alpha = 0.2746244084 # Taken from page 259\n", + " t = np.floor(alpha * np.maximum(nu, 0))\n", + " problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam))\n", + " t[problematic] = 0\n", + " b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi)\n", + " q_r = b / np.sqrt(t + 1)\n", + "\n", + " rho_t = ( # Taken from page 250\n", + " 1\n", + " - p\n", + " + np.log(p)\n", + " - 0.5 * np.log(2 * np.pi)\n", + " + (t - 1) * (np.log(lam * t + p) - np.log(t + 1))\n", + " - 1.5 * np.log(t + 1)\n", + " + (1 - lam) * t\n", + " )\n", + " rho_t_prime = (\n", + " -lam\n", + " + (t - 1) * (lam / (lam * t + p) - 1 / (t + 1))\n", + " - np.log(t + 1)\n", + " + np.log(lam * t + p)\n", + " + 1\n", + " - 1.5 / (t + 1)\n", + " )\n", + " rho_t_prime = rho_t\n", + " q = np.exp(-rho_t_prime)\n", + " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime)))\n", + "\n", + " x = np.zeros(dist_size)\n", + " n_to_accept = np.zeros(dist_size)\n", + " inds_to_sample = np.arange(dist_size)\n", + " counter = -1\n", + " while np.any(inds_to_sample):\n", + " counter += 1\n", + " _dist_size = len(inds_to_sample)\n", + " U = rng.uniform(size=_dist_size)\n", + " V = rng.uniform(size=_dist_size)\n", + " W = rng.uniform(size=_dist_size)\n", + " E = rng.exponential(size=_dist_size)\n", + " _p = p[inds_to_sample]\n", + " _lam = lam[inds_to_sample]\n", + " _t = t[inds_to_sample]\n", + " _q = q[inds_to_sample]\n", + " _q_l = q_l[inds_to_sample]\n", + " _q_r = q_r[inds_to_sample]\n", + " _b = b[inds_to_sample]\n", + " raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q)))\n", + " raw_right = np.floor((_t + 1) / W ** 2)\n", + " left = U <= _q_l / (_q_l + _q_r)\n", + " accepted = np.where(\n", + " left,\n", + " np.where(\n", + " _t == 0,\n", + " True,\n", + " np.where(\n", + " raw_left > 0,\n", + " False,\n", + " V * _q_l * _q ** (_t - raw_left) * (1 - _q)\n", + " <= np.exp(_logprob(raw_left, _p, _lam)),\n", + " ),\n", + " ),\n", + " V * _b * (1 / np.sqrt(raw_right) - 1 / np.sqrt(raw_right + 1))\n", + " <= np.exp(_logprob(raw_right, _p, _lam)),\n", + " )\n", + " X = np.where(left, raw_left, raw_right)\n", + "\n", + " x[inds_to_sample[accepted]] = X[accepted]\n", + " n_to_accept[inds_to_sample[accepted]] = counter\n", + " inds_to_sample = inds_to_sample[~accepted]\n", + " if counter % 1000 == 0:\n", + " print(np.sum(inds_to_sample))\n", + " print(_q)\n", + " print(\n", + " _p[0],\n", + " _lam[0],\n", + " raw_left[0],\n", + " raw_right[0],\n", + " _q_l[0] / (_q_l + _q_r)[0],\n", + " np.exp(_logprob(raw_left, _p, _lam))[0],\n", + " np.exp(_logprob(raw_right, _p, _lam))[0],\n", + " )\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "2578a9d6-6743-4ba0-8b03-5d083d778a3a", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_22232/50466135.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", - " poisson_idxs = np.broadcast_to(theta >= np.maximum(3, 2 * lam / (1 - lam)), dist_size)\n" + "/tmp/ipykernel_5940/3599282342.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", + " poisson_idxs = np.broadcast_to(p >= np.maximum(3, 2 * lam / (1 - lam)), dist_size)\n", + "/tmp/ipykernel_5940/3599282342.py:7: RuntimeWarning: divide by zero encountered in true_divide\n", + " (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))), dist_size,\n" ] - }, + } + ], + "source": [ + "rng = np.random.default_rng(42)\n", + "p, lam = np.meshgrid(np.logspace(-2, 4, 50), np.linspace(0, 1, 50))\n", + "dist_size = (100, *p.shape)\n", + "monotonicity_idxs = np.broadcast_to(p <= np.exp(lam), dist_size)\n", + "poisson_idxs = np.broadcast_to(p >= np.maximum(3, 2 * lam / (1 - lam)), dist_size)\n", + "abel_idxs = np.broadcast_to(\n", + " (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))), dist_size,\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "f39c9fec-327c-4f1f-ae6a-2a8494b87489", + "metadata": {}, + "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "1116 100.0 0.825\n", - "586 1000.0 0.6499999999999999\n", - "437 1000.0 0.475\n", - "352 1000.0 0.475\n", - "294 1000.0 0.475\n", - "254 1000.0 0.475\n", - "232 1000.0 0.475\n", - "210 1000.0 0.475\n", - "196 1000.0 0.475\n", - "172 1000.0 0.475\n", - "157 1000.0 0.475\n", - "147 1000.0 0.475\n", - "137 1000.0 0.475\n", - "132 1000.0 0.475\n", - "129 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1000.0 0.3\n", - "1 1000.0 0.3\n", - "1 1000.0 0.3\n", - "1 1000.0 0.3\n", - "1 1000.0 0.3\n", - "1 1000.0 0.3\n", - "1 1000.0 0.3\n", - "1 1000.0 0.3\n", - "1 1000.0 0.3\n" + "84033648\n", + "[4.65332627e+00 4.56672927e+00 4.56672927e+00 ... 9.75163178e+07\n", + " 1.71409994e+08 3.01286748e+08]\n", + "1.5998587196060574 0.44897959183673464 nan 4.0 -0.022127698842307447 0.0 0.08748239437827882\n", + "CPU times: user 4.3 s, sys: 108 ms, total: 4.4 s\n", + "Wall time: 4.39 s\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_5940/3395429966.py:55: RuntimeWarning: invalid value encountered in log\n", + " raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q)))\n" ] } ], "source": [ - "rng = np.random.default_rng(42)\n", - "theta, lam = np.meshgrid(np.logspace(0, 4, 5), np.linspace(0.3, 1, 5))\n", - "dist_size = (100, *theta.shape)\n", - "monotonicity_idxs = np.broadcast_to(theta <= np.exp(lam), dist_size)\n", - "poisson_idxs = np.broadcast_to(theta >= np.maximum(3, 2 * lam / (1 - lam)), dist_size)\n", + "%%time\n", "samples = np.full(dist_size, np.nan)\n", "samples[monotonicity_idxs] = _rejection_region_monotonicity(\n", - " rng=rng, theta=theta, lam=lam, dist_size=dist_size, idxs_mask=monotonicity_idxs\n", + " rng=rng, p=p, lam=lam, dist_size=dist_size, idxs_mask=monotonicity_idxs\n", ")\n", "samples[poisson_idxs] = _rejection_region_poisson(\n", - " rng=rng, theta=theta, lam=lam, dist_size=dist_size, idxs_mask=poisson_idxs,\n", + " rng=rng, p=p, lam=lam, dist_size=dist_size, idxs_mask=poisson_idxs,\n", + ")\n", + "samples[abel_idxs] = _rejection_region_abel(\n", + " rng=rng, p=p, lam=lam, dist_size=dist_size, idxs_mask=abel_idxs,\n", ")" ] }, { "cell_type": "code", - "execution_count": 160, - "id": "dbea78f7-18b3-4687-91f7-8e8ecb6d0a47", + "execution_count": 7, + "id": "b76564d3-eea8-4950-9d41-adbf2b56814a", + "metadata": {}, + "outputs": [], + "source": [ + "c = np.zeros_like(p.flatten())\n", + "c[monotonicity_idxs[0].flatten()] = 0\n", + "c[poisson_idxs[0].flatten()] = 1\n", + "c[abel_idxs[0].flatten()] = 2" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "1b370c54-7dc6-4c9c-977d-20bd410f5a7f", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_5940/3962287755.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + " (p / (1 - lam)).flatten(), np.mean(samples, axis=0).flatten(), c=c, alpha=0.2, cmap=\"jet\"\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(\n", + " (p / (1 - lam)).flatten(), np.mean(samples, axis=0).flatten(), c=c, alpha=0.2, cmap=\"jet\"\n", + ")\n", + "ax = plt.gca()\n", + "ax.set_xscale(\"log\")\n", + "ax.set_yscale(\"log\")\n", + "plt.plot(ax.get_xlim(), ax.get_ylim(), \"-k\", alpha=0.2)\n", + "plt.xlabel(\"Expected mean\")\n", + "plt.xlabel(\"Sample mean\");" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "3e78ffea-e081-4fd7-a7e8-34c3ee9f6520", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_5940/623610949.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + " (p / (1 - lam) ** 3).flatten(), np.var(samples, axis=0).flatten(), c=c, alpha=0.2, cmap=\"jet\"\n" + ] + }, { "data": { + "image/png": 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\n", 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nan]],\n", - "\n", - " [[1.0000e+00, 2.6000e+01, 1.0800e+02, 1.6140e+03, 1.4253e+04],\n", - " [6.0000e+00, 7.0000e+00, 1.2600e+02, 2.1910e+03, 1.8982e+04],\n", - " [3.0000e+00, 1.0000e+01, 4.2000e+02, 3.3370e+03, 2.8234e+04],\n", - " [5.0000e+00, 1.4000e+01, 9.9900e+02, 6.2950e+03, 5.7224e+04],\n", - " [0.0000e+00, nan, nan, nan, nan]]])" + "
" ] }, - "execution_count": 160, - "metadata": {}, - "output_type": "execute_result" + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } ], "source": [ - "samples" + "plt.scatter(\n", + " (p / (1 - lam) ** 3).flatten(), np.var(samples, axis=0).flatten(), c=c, alpha=0.2, cmap=\"jet\"\n", + ")\n", + "ax = plt.gca()\n", + "ax.set_xscale(\"log\")\n", + "ax.set_yscale(\"log\")\n", + "\n", + "ax = plt.gca()\n", + "plt.plot(ax.get_xlim(), ax.get_ylim(), \"-k\", alpha=0.2)\n", + "plt.xlabel(\"Expected variance\")\n", + "plt.xlabel(\"Sample variance\");" ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "6fa2273a-7245-4f1e-906e-749b914f8f8b", + "metadata": {}, + "outputs": [], + "source": [ + "def normal_approx(x, p, lam):\n", + " mu = p / (1 - lam)\n", + " sigma = np.sqrt(p / (1 - lam) ** 3)\n", + " return 1 / np.sqrt(2 * np.pi) / sigma * np.exp(-0.5 * (x - mu) ** 2 / sigma ** 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "38444834-9541-41a4-9ed5-1d731488e7bb", + "metadata": {}, + "outputs": [], + "source": [ + "def poisson_region_envelope(x, p, lam):\n", + " eps = (1 - lam) / (2 + (p - lam) * (1 - lam)) ** (1 / 3)\n", + " delta = (1 - lam) ** (2 / 5) / (2 + (p - lam) * (1 - lam)) ** (1 / 3)\n", + " mu = (p - lam) / (1 - lam)\n", + " sigma = np.sqrt((1 + delta) * (p - lam) / (1 - lam - eps) / (1 - lam) ** 2)\n", + " psi = (\n", + " p * delta * (2 + delta - 2 * lam)\n", + " + (1 + delta) * (1 - lam) ** 2\n", + " - lam * (1 - lam + delta) ** 2\n", + " ) / (2 * (p - 1 - delta))\n", + " G = (\n", + " (p * (1 - lam - eps) * np.sqrt(1 + delta))\n", + " / ((p - lam) * (1 - lam) * (1 - eps) ** 2)\n", + " * np.exp(psi / (1 + delta))\n", + " )\n", + "\n", + " def g(x):\n", + " return (\n", + " G\n", + " / (np.sqrt(2 * np.pi) * sigma)\n", + " * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2))\n", + " )\n", + "\n", + " h_r_norm = (p * (1 - lam - eps) ** 1.5) / (np.sqrt(2 * np.pi) * (p - lam) ** 1.5)\n", + " h_r_exp_A = -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam)\n", + " h_r_exp_B = 2 * (1 - lam)\n", + "\n", + " def h_r(x):\n", + " return h_r_norm * np.exp(h_r_exp_A * (x - mu) + h_r_exp_B)\n", + "\n", + " t_r = np.ceil((p - lam) / (1 - lam - eps) - 1)\n", + " H_r = (\n", + " (2 * p * (1 - lam - eps) ** 1.5 * np.exp(2 * (1 - lam)))\n", + " / (\n", + " np.sqrt(2 * np.pi)\n", + " * (p - lam) ** 1.5\n", + " * (1 - 2 * (1 - lam - eps) / (p - lam))\n", + " * eps\n", + " * (1 - lam)\n", + " )\n", + " * np.exp(\n", + " -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (t_r - mu)\n", + " )\n", + " )\n", + "\n", + " def h_l(x):\n", + " return (\n", + " p\n", + " / np.sqrt(2 * np.pi)\n", + " * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", + " )\n", + "\n", + " t_l = np.ceil((p - lam) / (1 - lam + delta) - 1)\n", + " H_l = (\n", + " (2 * p * (1 + delta))\n", + " / (np.sqrt(2 * np.pi) * delta * (1 - lam))\n", + " * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (t_l + 1 - mu))\n", + " )\n", + " return np.where(x < t_l, h_l(x), np.where(x < t_r, g(x), h_r(x)))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "d5124123-7aa5-4c4c-8f7a-da74d548cf6c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(1000, 1700, 1000)\n", + "y0 = poisson_region_envelope(x, 1000, 0.3)\n", + "y1 = np.exp(_logprob(np.floor(x), 1000, 0.3,))\n", + "y2 = normal_approx(x, 1000, 0.3)\n", + "plt.semilogy(x, y0, label=\"Envelope\")\n", + "plt.semilogy(x, y1, label=\"PDF\")\n", + "plt.plot(x, y2, label=\"Normal approx\")\n", + "plt.legend();" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "59199eb3-0ff7-4fd4-bf95-1d18fe59c067", + "metadata": {}, + "outputs": [], + "source": [ + "def abel_rejection_envelope(x, p, lam):\n", + " p = np.asarray(p)\n", + " lam = np.asarray(lam)\n", + " nu = 2 * (p ** 2 - lam * p - 3 * lam ** 2) / (3 * lam ** 2)\n", + " alpha = 0.2746244084 # Taken from page 259\n", + " t = np.floor(alpha * np.maximum(nu, 0))\n", + " problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam))\n", + " if t.size == 1:\n", + " if problematic:\n", + " t = 0\n", + " else:\n", + " t[problematic] = 0\n", + " b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi)\n", + " q_r = b / np.sqrt(t + 1)\n", + "\n", + " rho_t = ( # Taken from page 250\n", + " 1\n", + " - p\n", + " + np.log(p)\n", + " - 0.5 * np.log(2 * np.pi)\n", + " + (t - 1) * (np.log(lam * t + p) - np.log(t + 1))\n", + " - 1.5 * np.log(t + 1)\n", + " + (1 - lam) * t\n", + " )\n", + " rho_t_prime = (\n", + " -lam\n", + " + (t - 1) * (lam / (lam * t + p) - 1 / (t + 1))\n", + " - np.log(t + 1)\n", + " + np.log(lam * t + p)\n", + " + 1\n", + " - 1.5 / (t + 1)\n", + " )\n", + " q = np.exp(-rho_t_prime)\n", + " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime)))\n", + " return np.where(\n", + " x <= t, q_l * (1 - q) * q ** (t - x), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "af0f622a-3dda-4844-97bd-c5ab4faf4478", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_5940/4184709470.py:36: RuntimeWarning: invalid value encountered in sqrt\n", + " x <= t, q_l * (1 - q) * q ** (t - x), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "p, lam = 2.1209508879201904, 0.5510204081632653\n", + "# lam = 0.99\n", + "# p = 2 * lam/(1-lam)\n", + "mean = p / (1 - lam)\n", + "std = np.sqrt(p / (1 - lam) ** 3)\n", + "x = np.linspace(mean - 1.2 * std, mean + 5 * std, 1000)\n", + "plt.semilogy(x, np.exp(_logprob(x, p, lam)))\n", + "plt.plot(x, abel_rejection_envelope(x, p, lam));" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f6ce9660-fd94-48b8-a883-0b30c35c2f89", + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/notebooks/fast_gen_pois.py b/notebooks/fast_gen_pois.py index c64d722..a75a5ac 100644 --- a/notebooks/fast_gen_pois.py +++ b/notebooks/fast_gen_pois.py @@ -16,6 +16,7 @@ # %% import numpy as np +from matplotlib import pyplot as plt from scipy.special import gammaln @@ -27,24 +28,24 @@ def _logpow(x, m): return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x)) -def _logprob(x, theta, lam): - theta_lam_x = theta + lam * x +def _logprob(x, p, lam): + p_lam_x = p + lam * x return np.where( x >= 0, - np.log(theta) + _logpow(theta_lam_x, x - 1) - theta_lam_x - gammaln(x + 1), + np.log(p) + _logpow(p_lam_x, x - 1) - p_lam_x - gammaln(x + 1), -np.inf, ) # %% -def _rejection_region_monotonicity(rng, theta, lam, dist_size, idxs_mask=None): +def _rejection_region_monotonicity(rng, p, lam, dist_size, idxs_mask=None): if idxs_mask is None: idxs_mask = np.ones(dist_size, dtype="bool") - theta = np.broadcast_to(theta, dist_size)[idxs_mask] + p = np.broadcast_to(p, dist_size)[idxs_mask] lam = np.broadcast_to(lam, dist_size)[idxs_mask] dist_size = np.sum(idxs_mask) - p0 = np.exp(-theta) - b = theta * np.exp(2 - lam - np.minimum(lam, theta)) * np.sqrt(2 / np.pi) + p0 = np.exp(-p) + b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi) u = rng.uniform(size=dist_size) x = np.zeros(dist_size) inds_to_sample = u > p0 / (p0 + b) @@ -54,92 +55,103 @@ def _rejection_region_monotonicity(rng, theta, lam, dist_size, idxs_mask=None): v = rng.uniform(size=dist_size) w = rng.uniform(size=dist_size) _x = np.floor(1 / w ** 2) - accepted = v * b * (1 / np.sqrt(_x) - 1 / np.sqrt(_x + 1)) <= np.exp( - _logprob(_x, theta, lam) - ) + accepted = v * b * (1 / np.sqrt(_x) - 1 / np.sqrt(_x + 1)) <= np.exp(_logprob(_x, p, lam)) x[inds_to_sample & accepted] = _x[inds_to_sample & accepted] inds_to_sample = inds_to_sample & ~accepted return x # %% -def _rejection_region_poisson(rng, theta, lam, dist_size, idxs_mask=None): +def _rejection_region_poisson(rng, p, lam, dist_size, idxs_mask=None): if idxs_mask is None: idxs_mask = np.ones(dist_size, dtype="bool") - theta = np.broadcast_to(theta, dist_size)[idxs_mask] + p = np.broadcast_to(p, dist_size)[idxs_mask] lam = np.broadcast_to(lam, dist_size)[idxs_mask] dist_size = np.sum(idxs_mask) - eps = (1 - lam) / (2 + (theta - lam) * (1 - lam)) ** (1 / 3) - delta = (1 - lam) ** (2 / 5) / (2 + (theta - lam) * (1 - lam)) ** (1 / 3) - mu = (theta - lam) / (1 - lam) - sigma = np.sqrt((1 - delta) * (theta - lam) / (1 - lam - eps) / (1 - lam) ** 2) + eps = (1 - lam) / (2 + (p - lam) * (1 - lam)) ** (1 / 3) + delta = (1 - lam) ** (2 / 5) / (2 + (p - lam) * (1 - lam)) ** (1 / 3) + mu = (p - lam) / (1 - lam) + sigma = np.sqrt((1 + delta) * (p - lam) / (1 - lam - eps) / (1 - lam) ** 2) psi = ( - theta * delta * (2 + delta - 2 * lam) + p * delta * (2 + delta - 2 * lam) + (1 + delta) * (1 - lam) ** 2 - lam * (1 - lam + delta) ** 2 - ) / (2 * (theta - 1 - delta)) + ) / (2 * (p - 1 - delta)) G = ( - (theta * (1 - lam - eps) * np.sqrt(1 + delta)) - / ((theta - lam) * (1 - lam) * (1 - eps) ** 2) + (p * (1 - lam - eps) * np.sqrt(1 + delta)) + / ((p - lam) * (1 - lam) * (1 - eps) ** 2) * np.exp(psi / (1 + delta)) ) - def g(x): + def g(x, G, mu, sigma): return G / (np.sqrt(2 * np.pi) * sigma) * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2)) - h_r_norm = (theta * (1 - lam - eps) ** 1.5) / (np.sqrt(2 * np.pi) * (theta - lam) ** 1.5) - h_r_exp_A = -(1 - 2 * (1 - lam - eps) / (theta - lam)) * (eps / 2) * (1 - lam) - h_r_exp_B = 2 * (1 - lam) - - def h_r(x): - return h_r_norm * np.exp(h_r_exp_A * (x - mu) + h_r_exp_B) + def h_r(x, p, lam, eps, mu): + return ( + (p * (1 - lam - eps) ** 1.5) + / (np.sqrt(2 * np.pi) * (p - lam) ** 1.5) + * np.exp( + -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (x - mu) + + 2 * (1 - lam) + ) + ) - t_r = np.ceil((theta - lam) / (1 - lam - eps) - 1) + t_r = np.ceil((p - lam) / (1 - lam - eps) - 1) H_r = ( - (2 * theta * (1 - lam - eps) ** 1.5 * np.exp(2 * (1 - lam))) + (2 * p * (1 - lam - eps) ** 1.5 * np.exp(2 * (1 - lam))) / ( np.sqrt(2 * np.pi) - * (theta - lam) ** 1.5 - * (1 - 2 * (1 - lam - eps) / (theta - lam)) + * (p - lam) ** 1.5 + * (1 - 2 * (1 - lam - eps) / (p - lam)) * eps * (1 - lam) ) - * np.exp(-(1 - 2 * (1 - lam - eps) / (theta - lam)) * (eps / 2) * (1 - lam) * (t_r - mu)) + * np.exp(-(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (t_r - mu)) ) - def h_l(x): - return ( - theta - / np.sqrt(2 * np.pi) - * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu)) - ) + def h_l(x, p, lam, delta, mu): + return p / np.sqrt(2 * np.pi) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu)) - t_l = np.ceil((theta - lam) / (1 - lam + delta) - 1) + t_l = np.ceil((p - lam) / (1 - lam + delta) - 1) H_l = ( - (2 * theta * (1 + delta)) + (2 * p * (1 + delta)) / (np.sqrt(2 * np.pi) * delta * (1 - lam)) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (t_l + 1 - mu)) ) x = np.zeros(dist_size) - inds_to_sample = np.ones(dist_size, dtype="bool") + inds_to_sample = np.arange(dist_size) + n_to_accept = np.zeros(dist_size) counter = -1 while np.any(inds_to_sample): counter += 1 - U = rng.uniform(size=dist_size) - N = rng.normal(size=dist_size) - V = rng.uniform(size=dist_size) - E = rng.exponential(size=dist_size) - center = U < G / (G - H_l + H_r) - left = (U < (G + H_l) / (G + H_l + H_r)) & ~center - raw_center_y = mu + sigma * N - raw_left_y = t_l - 2 * E * (1 + delta) / delta / (1 - lam) - raw_right_y = t_r + 2 * E / ((1 - 2 * (1 - lam - eps) / (theta - lam)) * eps * (1 - lam)) + _dist_size = len(inds_to_sample) + U = rng.uniform(size=_dist_size) + N = rng.normal(size=_dist_size) + V = rng.uniform(size=_dist_size) + E = rng.exponential(size=_dist_size) + _G = G[inds_to_sample] + _H_l = H_l[inds_to_sample] + _H_r = H_r[inds_to_sample] + _p = p[inds_to_sample] + _lam = lam[inds_to_sample] + _mu = mu[inds_to_sample] + _sigma = sigma[inds_to_sample] + _delta = delta[inds_to_sample] + _eps = eps[inds_to_sample] + _t_l = t_l[inds_to_sample] + _t_r = t_r[inds_to_sample] + + center = U < _G / (_G + _H_l + _H_r) + left = (U < (_G + _H_l) / (_G + _H_l + _H_r)) & ~center + raw_center_y = _mu + _sigma * N + raw_left_y = _t_l - 2 * E * (1 + _delta) / _delta / (1 - _lam) + raw_right_y = _t_r + 2 * E / ((1 - 2 * (1 - _lam - _eps) / (_p - _lam)) * _eps * (1 - _lam)) Y = np.where( center, np.where( - (raw_center_y >= t_l) & (raw_center_y < t_r), + (raw_center_y >= _t_l) & (raw_center_y < _t_r), raw_center_y, np.nan, ), @@ -162,42 +174,306 @@ def h_l(x): V * np.where( center, - g(Y), + g(Y, G=_G, mu=_mu, sigma=_sigma), np.where( left, - h_l(Y), - h_r(Y), + h_l(Y, p=_p, lam=_lam, delta=_delta, mu=_mu), + h_r(Y, p=_p, lam=_lam, eps=_eps, mu=_mu), ), ) - <= np.exp(_logprob(X, theta, lam)) + <= np.exp(_logprob(X, _p, _lam)) ) - x[inds_to_sample & accepted] = X[inds_to_sample & accepted] - inds_to_sample = inds_to_sample & ~accepted + x[inds_to_sample[accepted]] = X[accepted] + n_to_accept[inds_to_sample[accepted]] = counter + inds_to_sample = inds_to_sample[~accepted] + # if counter % 1000 == 0: + # print(np.sum(inds_to_sample)) + return x + + +# %% +def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): + if idxs_mask is None: + idxs_mask = np.ones(dist_size, dtype="bool") + p = np.broadcast_to(p, dist_size)[idxs_mask] + lam = np.broadcast_to(lam, dist_size)[idxs_mask] + dist_size = np.sum(idxs_mask) + + nu = 2 * (p ** 2 - lam * p - 3 * lam ** 2) / (3 * lam ** 2) + alpha = 0.2746244084 # Taken from page 259 + t = np.floor(alpha * np.maximum(nu, 0)) + problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam)) + t[problematic] = 0 + b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi) + q_r = b / np.sqrt(t + 1) + + rho_t = ( # Taken from page 250 + 1 + - p + + np.log(p) + - 0.5 * np.log(2 * np.pi) + + (t - 1) * (np.log(lam * t + p) - np.log(t + 1)) + - 1.5 * np.log(t + 1) + + (1 - lam) * t + ) + rho_t_prime = ( + -lam + + (t - 1) * (lam / (lam * t + p) - 1 / (t + 1)) + - np.log(t + 1) + + np.log(lam * t + p) + + 1 + - 1.5 / (t + 1) + ) + rho_t_prime = rho_t + q = np.exp(-rho_t_prime) + q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime))) + + x = np.zeros(dist_size) + n_to_accept = np.zeros(dist_size) + inds_to_sample = np.arange(dist_size) + counter = -1 + while np.any(inds_to_sample): + counter += 1 + _dist_size = len(inds_to_sample) + U = rng.uniform(size=_dist_size) + V = rng.uniform(size=_dist_size) + W = rng.uniform(size=_dist_size) + E = rng.exponential(size=_dist_size) + _p = p[inds_to_sample] + _lam = lam[inds_to_sample] + _t = t[inds_to_sample] + _q = q[inds_to_sample] + _q_l = q_l[inds_to_sample] + _q_r = q_r[inds_to_sample] + _b = b[inds_to_sample] + raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q))) + raw_right = np.floor((_t + 1) / W ** 2) + left = U <= _q_l / (_q_l + _q_r) + accepted = np.where( + left, + np.where( + _t == 0, + True, + np.where( + raw_left > 0, + False, + V * _q_l * _q ** (_t - raw_left) * (1 - _q) + <= np.exp(_logprob(raw_left, _p, _lam)), + ), + ), + V * _b * (1 / np.sqrt(raw_right) - 1 / np.sqrt(raw_right + 1)) + <= np.exp(_logprob(raw_right, _p, _lam)), + ) + X = np.where(left, raw_left, raw_right) + + x[inds_to_sample[accepted]] = X[accepted] + n_to_accept[inds_to_sample[accepted]] = counter + inds_to_sample = inds_to_sample[~accepted] if counter % 1000 == 0: - temp1 = theta[inds_to_sample] - temp2 = lam[inds_to_sample] - print(np.sum(inds_to_sample), temp1[-1], temp2[-1]) + print(np.sum(inds_to_sample)) + print(_q) + print( + _p[0], + _lam[0], + raw_left[0], + raw_right[0], + _q_l[0] / (_q_l + _q_r)[0], + np.exp(_logprob(raw_left, _p, _lam))[0], + np.exp(_logprob(raw_right, _p, _lam))[0], + ) return x # %% rng = np.random.default_rng(42) -theta, lam = np.meshgrid(np.logspace(0, 4, 5), np.linspace(0.3, 1, 5)) -dist_size = (100, *theta.shape) -monotonicity_idxs = np.broadcast_to(theta <= np.exp(lam), dist_size) -poisson_idxs = np.broadcast_to(theta >= np.maximum(3, 2 * lam / (1 - lam)), dist_size) +p, lam = np.meshgrid(np.logspace(-2, 4, 50), np.linspace(0, 1, 50)) +dist_size = (100, *p.shape) +monotonicity_idxs = np.broadcast_to(p <= np.exp(lam), dist_size) +poisson_idxs = np.broadcast_to(p >= np.maximum(3, 2 * lam / (1 - lam)), dist_size) +abel_idxs = np.broadcast_to( + (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))), + dist_size, +) + +# %% +# %%time samples = np.full(dist_size, np.nan) samples[monotonicity_idxs] = _rejection_region_monotonicity( - rng=rng, theta=theta, lam=lam, dist_size=dist_size, idxs_mask=monotonicity_idxs + rng=rng, p=p, lam=lam, dist_size=dist_size, idxs_mask=monotonicity_idxs ) samples[poisson_idxs] = _rejection_region_poisson( rng=rng, - theta=theta, + p=p, lam=lam, dist_size=dist_size, idxs_mask=poisson_idxs, ) +samples[abel_idxs] = _rejection_region_abel( + rng=rng, + p=p, + lam=lam, + dist_size=dist_size, + idxs_mask=abel_idxs, +) + +# %% +c = np.zeros_like(p.flatten()) +c[monotonicity_idxs[0].flatten()] = 0 +c[poisson_idxs[0].flatten()] = 1 +c[abel_idxs[0].flatten()] = 2 + +# %% +plt.scatter( + (p / (1 - lam)).flatten(), np.mean(samples, axis=0).flatten(), c=c, alpha=0.2, cmap="jet" +) +ax = plt.gca() +ax.set_xscale("log") +ax.set_yscale("log") +plt.plot(ax.get_xlim(), ax.get_ylim(), "-k", alpha=0.2) +plt.xlabel("Expected mean") +plt.xlabel("Sample mean") + +# %% +plt.scatter( + (p / (1 - lam) ** 3).flatten(), np.var(samples, axis=0).flatten(), c=c, alpha=0.2, cmap="jet" +) +ax = plt.gca() +ax.set_xscale("log") +ax.set_yscale("log") + +ax = plt.gca() +plt.plot(ax.get_xlim(), ax.get_ylim(), "-k", alpha=0.2) +plt.xlabel("Expected variance") +plt.xlabel("Sample variance") + + +# %% +def normal_approx(x, p, lam): + mu = p / (1 - lam) + sigma = np.sqrt(p / (1 - lam) ** 3) + return 1 / np.sqrt(2 * np.pi) / sigma * np.exp(-0.5 * (x - mu) ** 2 / sigma ** 2) + + +# %% +def poisson_region_envelope(x, p, lam): + eps = (1 - lam) / (2 + (p - lam) * (1 - lam)) ** (1 / 3) + delta = (1 - lam) ** (2 / 5) / (2 + (p - lam) * (1 - lam)) ** (1 / 3) + mu = (p - lam) / (1 - lam) + sigma = np.sqrt((1 + delta) * (p - lam) / (1 - lam - eps) / (1 - lam) ** 2) + psi = ( + p * delta * (2 + delta - 2 * lam) + + (1 + delta) * (1 - lam) ** 2 + - lam * (1 - lam + delta) ** 2 + ) / (2 * (p - 1 - delta)) + G = ( + (p * (1 - lam - eps) * np.sqrt(1 + delta)) + / ((p - lam) * (1 - lam) * (1 - eps) ** 2) + * np.exp(psi / (1 + delta)) + ) + + def g(x): + return G / (np.sqrt(2 * np.pi) * sigma) * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2)) + + h_r_norm = (p * (1 - lam - eps) ** 1.5) / (np.sqrt(2 * np.pi) * (p - lam) ** 1.5) + h_r_exp_A = -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) + h_r_exp_B = 2 * (1 - lam) + + def h_r(x): + return h_r_norm * np.exp(h_r_exp_A * (x - mu) + h_r_exp_B) + + t_r = np.ceil((p - lam) / (1 - lam - eps) - 1) + H_r = ( + (2 * p * (1 - lam - eps) ** 1.5 * np.exp(2 * (1 - lam))) + / ( + np.sqrt(2 * np.pi) + * (p - lam) ** 1.5 + * (1 - 2 * (1 - lam - eps) / (p - lam)) + * eps + * (1 - lam) + ) + * np.exp(-(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (t_r - mu)) + ) + + def h_l(x): + return p / np.sqrt(2 * np.pi) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu)) + + t_l = np.ceil((p - lam) / (1 - lam + delta) - 1) + H_l = ( + (2 * p * (1 + delta)) + / (np.sqrt(2 * np.pi) * delta * (1 - lam)) + * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (t_l + 1 - mu)) + ) + return np.where(x < t_l, h_l(x), np.where(x < t_r, g(x), h_r(x))) + + +# %% +x = np.linspace(1000, 1700, 1000) +y0 = poisson_region_envelope(x, 1000, 0.3) +y1 = np.exp( + _logprob( + np.floor(x), + 1000, + 0.3, + ) +) +y2 = normal_approx(x, 1000, 0.3) +plt.semilogy(x, y0, label="Envelope") +plt.semilogy(x, y1, label="PDF") +plt.plot(x, y2, label="Normal approx") +plt.legend() + + +# %% +def abel_rejection_envelope(x, p, lam): + p = np.asarray(p) + lam = np.asarray(lam) + nu = 2 * (p ** 2 - lam * p - 3 * lam ** 2) / (3 * lam ** 2) + alpha = 0.2746244084 # Taken from page 259 + t = np.floor(alpha * np.maximum(nu, 0)) + problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam)) + if t.size == 1: + if problematic: + t = 0 + else: + t[problematic] = 0 + b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi) + q_r = b / np.sqrt(t + 1) + + rho_t = ( # Taken from page 250 + 1 + - p + + np.log(p) + - 0.5 * np.log(2 * np.pi) + + (t - 1) * (np.log(lam * t + p) - np.log(t + 1)) + - 1.5 * np.log(t + 1) + + (1 - lam) * t + ) + rho_t_prime = ( + -lam + + (t - 1) * (lam / (lam * t + p) - 1 / (t + 1)) + - np.log(t + 1) + + np.log(lam * t + p) + + 1 + - 1.5 / (t + 1) + ) + q = np.exp(-rho_t_prime) + q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime))) + return np.where( + x <= t, + q_l * (1 - q) * q ** (t - x), + b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)), + ) + + +# %% +p, lam = 2.1209508879201904, 0.5510204081632653 +# lam = 0.99 +# p = 2 * lam/(1-lam) +mean = p / (1 - lam) +std = np.sqrt(p / (1 - lam) ** 3) +x = np.linspace(mean - 1.2 * std, mean + 5 * std, 1000) +plt.semilogy(x, np.exp(_logprob(x, p, lam))) +plt.plot(x, abel_rejection_envelope(x, p, lam)) # %% -samples From d08e87a1d8c8973dd79186bc5a47320a0ada79e6 Mon Sep 17 00:00:00 2001 From: lucianopaz Date: Wed, 25 May 2022 22:20:49 +0200 Subject: [PATCH 3/9] Fix abel region rng --- notebooks/fast_gen_pois.ipynb | 104 ++++++++++++++-------------------- notebooks/fast_gen_pois.py | 64 +++++++-------------- 2 files changed, 62 insertions(+), 106 deletions(-) diff --git a/notebooks/fast_gen_pois.ipynb b/notebooks/fast_gen_pois.ipynb index 6cf2bb5..39c1cd7 100644 --- a/notebooks/fast_gen_pois.ipynb +++ b/notebooks/fast_gen_pois.ipynb @@ -192,8 +192,6 @@ " x[inds_to_sample[accepted]] = X[accepted]\n", " n_to_accept[inds_to_sample[accepted]] = counter\n", " inds_to_sample = inds_to_sample[~accepted]\n", - " # if counter % 1000 == 0:\n", - " # print(np.sum(inds_to_sample))\n", " return x" ] }, @@ -229,14 +227,12 @@ " + (1 - lam) * t\n", " )\n", " rho_t_prime = (\n", - " -lam\n", - " + (t - 1) * (lam / (lam * t + p) - 1 / (t + 1))\n", + " np.log(lam * t + p)\n", " - np.log(t + 1)\n", - " + np.log(lam * t + p)\n", - " + 1\n", - " - 1.5 / (t + 1)\n", + " + 1 - lam\n", + " + 1.5 / (t + 1)\n", + " - (lam + p) / (lam * t + p)\n", " )\n", - " rho_t_prime = rho_t\n", " q = np.exp(-rho_t_prime)\n", " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime)))\n", "\n", @@ -281,18 +277,6 @@ " x[inds_to_sample[accepted]] = X[accepted]\n", " n_to_accept[inds_to_sample[accepted]] = counter\n", " inds_to_sample = inds_to_sample[~accepted]\n", - " if counter % 1000 == 0:\n", - " print(np.sum(inds_to_sample))\n", - " print(_q)\n", - " print(\n", - " _p[0],\n", - " _lam[0],\n", - " raw_left[0],\n", - " raw_right[0],\n", - " _q_l[0] / (_q_l + _q_r)[0],\n", - " np.exp(_logprob(raw_left, _p, _lam))[0],\n", - " np.exp(_logprob(raw_right, _p, _lam))[0],\n", - " )\n", " return x" ] }, @@ -306,9 +290,9 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_5940/3599282342.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_18920/3599282342.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", " poisson_idxs = np.broadcast_to(p >= np.maximum(3, 2 * lam / (1 - lam)), dist_size)\n", - "/tmp/ipykernel_5940/3599282342.py:7: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_18920/3599282342.py:7: RuntimeWarning: divide by zero encountered in true_divide\n", " (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))), dist_size,\n" ] } @@ -334,20 +318,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "84033648\n", - "[4.65332627e+00 4.56672927e+00 4.56672927e+00 ... 9.75163178e+07\n", - " 1.71409994e+08 3.01286748e+08]\n", - "1.5998587196060574 0.44897959183673464 nan 4.0 -0.022127698842307447 0.0 0.08748239437827882\n", - "CPU times: user 4.3 s, sys: 108 ms, total: 4.4 s\n", - "Wall time: 4.39 s\n" + "CPU times: user 5.6 s, sys: 182 ms, total: 5.79 s\n", + "Wall time: 5.82 s\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_5940/3395429966.py:55: RuntimeWarning: invalid value encountered in log\n", - " raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q)))\n" + "/tmp/ipykernel_18920/442064969.py:53: RuntimeWarning: invalid value encountered in log\n", + " raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q)))\n", + "/tmp/ipykernel_18920/1836048749.py:11: RuntimeWarning: invalid value encountered in log\n", + " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" ] } ], @@ -388,13 +370,13 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_5940/3962287755.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_18920/3962287755.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", " (p / (1 - lam)).flatten(), np.mean(samples, axis=0).flatten(), c=c, alpha=0.2, cmap=\"jet\"\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -427,13 +409,13 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_5940/623610949.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_18920/623610949.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", " (p / (1 - lam) ** 3).flatten(), np.var(samples, axis=0).flatten(), c=c, alpha=0.2, cmap=\"jet\"\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] @@ -560,12 +542,17 @@ ], "source": [ "x = np.linspace(1000, 1700, 1000)\n", - "y0 = poisson_region_envelope(x, 1000, 0.3)\n", - "y1 = np.exp(_logprob(np.floor(x), 1000, 0.3,))\n", - "y2 = normal_approx(x, 1000, 0.3)\n", + "lam = 0.3\n", + "p = 1000\n", + "y0 = poisson_region_envelope(x, p, lam)\n", + "y1 = np.exp(_logprob(np.floor(x), p, lam))\n", + "y2 = normal_approx(x, p, lam)\n", "plt.semilogy(x, y0, label=\"Envelope\")\n", "plt.semilogy(x, y1, label=\"PDF\")\n", "plt.plot(x, y2, label=\"Normal approx\")\n", + "samples = _rejection_region_poisson(np.random.default_rng(42), p, lam, 100000)\n", + "y, edges = np.histogram(samples, bins=20, density=True)\n", + "plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label=\"Sampled points\")\n", "plt.legend();" ] }, @@ -579,7 +566,7 @@ "def abel_rejection_envelope(x, p, lam):\n", " p = np.asarray(p)\n", " lam = np.asarray(lam)\n", - " nu = 2 * (p ** 2 - lam * p - 3 * lam ** 2) / (3 * lam ** 2)\n", + " nu = 2 / 3 * (p ** 2 - lam * p - 3 * lam ** 2) / lam ** 2\n", " alpha = 0.2746244084 # Taken from page 259\n", " t = np.floor(alpha * np.maximum(nu, 0))\n", " problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam))\n", @@ -601,15 +588,14 @@ " + (1 - lam) * t\n", " )\n", " rho_t_prime = (\n", - " -lam\n", - " + (t - 1) * (lam / (lam * t + p) - 1 / (t + 1))\n", + " np.log(lam * t + p)\n", " - np.log(t + 1)\n", - " + np.log(lam * t + p)\n", - " + 1\n", - " - 1.5 / (t + 1)\n", + " + 1 - lam\n", + " + 1.5 / (t + 1)\n", + " - (lam + p) / (lam * t + p)\n", " )\n", " q = np.exp(-rho_t_prime)\n", - " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime)))\n", + " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q))\n", " return np.where(\n", " x <= t, q_l * (1 - q) * q ** (t - x), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", " )" @@ -625,13 +611,15 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_5940/4184709470.py:36: RuntimeWarning: invalid value encountered in sqrt\n", - " x <= t, q_l * (1 - q) * q ** (t - x), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n" + "/tmp/ipykernel_18920/1371467534.py:35: RuntimeWarning: divide by zero encountered in true_divide\n", + " x <= t, q_l * (1 - q) * q ** (t - x), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", + "/tmp/ipykernel_18920/1836048749.py:11: RuntimeWarning: invalid value encountered in log\n", + " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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YdevW4evre9uwEHfasWMH+/fvp1ixYgQGBtKpUyeUUnz//fds374drTWNGzemRYsW1KtX77Zt//77b8LCwihXrhxBQUFs2bKF4cOHM2nSJNavX4+Hhwe7d+/m9OnT7N9vXFrNOA9BTuWkxh8FVMjw3gs4k7NwDBYfqycbnIoW4YNHA5j1ZCCXE5J4dNoWvtpwlIalG/Frl1+p51mP0dtG8+bGN4m/Gf/vhr5tYOhG6P4NJMbBTz3gu7ZweKVM8iJEBsWLF2f37t3MmDGDUqVK0bt371s3U61fv57GjRtTq1Yt1q1bR1hY2K3tHnnkEQBq1apFzZo1KVu2LEWLFsXHx4dTp4xGiAoVKhAUFATAgAED2Lx5823H/uuvvzhw4ABBQUHUrVuX2bNnExkZyaFDh6hcuTJ+fn4opRgwYECm8T/88MO4u7vj6OhI9+7d2bx5M5s3b6Zbt244OTlRvHhxunfvzqZNm/6zbaNGjfDy8sLGxoa6dety4sSJ/6zj4+PDsWPHePHFF1mxYgUuLi4P9PveS05q/DsBP6VUZeA00AfoZ5GoTCTE35OVLzfn7UX7+GjFIdYdimbSY3X5+uGv+Xbft0wLnUbYhTAmtphIdfe08TJsbKD2Y1CjK+z5AbZ8Dr88ZkxMEfwaVH8ka6OFCpFH7lUzz022traEhIQQEhJCrVq1mD17Nn369OH5559n165dVKhQgffff5/ExMRb26Q3DdnY2Nx6nf4+fRC1uw2znJHWmocffpg5c+bctjw0NDRrd/Vncoysjn2WMe6Mw05n5Obmxj///MPKlSuZNm0a8+bNY+bMmVna//1ktTvnHGAb4K+UilJKPa21TgaGASuBg8A8rXXYvfaTVRafbD2H3JzsmdavPp/1rsOhs1dpP3kj83efZnCtwXzX9jsSkxPpv6w/cw/Nvf0PX6QoNBoMw/+Grl9C0nX4dRB80QC2fWmcEQhRSIWHh3PkyJFb70NDQ6lUqdKtJO/h4UF8fPytiVAexMmTJ9m2bRsAc+bMuW0IZoCHHnqILVu2EBERAUBCQgKHDx+mWrVqHD9+nKNHj97aNjOrV6/m4sWLXL9+nUWLFhEUFETz5s1ZtGgRCQkJXLt2jYULFxIcHJzluJ2dnW9NIBMbG0tqaio9evTggw8+YM+ePQ/0G9xLVnv19M1k+TJgmcWiSaOU6gJ08fX1tfSus00pRbd6XjSq7M5r80IZMX8vaw5EM757LX595Ffe3vw247aPY8e5HYxuOhpne+d/N7a1g3r9oU4fOLgEtk+HlaNg3Vhj1NBGQ6FUVet9OSGsID4+nhdffJHLly9TpEgRfH19mTFjBiVKlGDw4MHUqlULb29vAgMDH3jf1atXZ/bs2QwdOhQ/Pz+ee+652z4vVaoUs2bNom/fvty4cQOAsWPHUrVqVWbMmEGnTp3w8PCgWbNmt9rY79SsWTMGDhxIREQE/fr1o2FDYzDMQYMG0ahRIwCeeeaZ/7Tv38uQIUPo0KEDZcuWZfLkyTz55JOkpnUSGT9+/AP/DpkpHMMyW1hqqua7zcf5ZGU4Lo5F+LhnbUL8SzErbBZT9kyhjFMZPm3xKTU97tGr6Ewo7JgB+36FlJvgHQz1BhjNQPa525VLCCi4wzKfOHGCzp07Z5qwLWHWrFns2rXrtslfrKXADMtshou792Jjoxjc3IfFLwbhUbwoT83axTuLwujt9ziz2s8iRacwYPkAfjrwU+ZtfuXqwqNfwisHoNX/GTd/LRwKn/rDkpcgardcDBZC5Aqp8efQjeQUJq0+zIyNx6hUshiTetelSmkb3tnyDhtObaBVhVaMCRqDa9H7XK/QGiK3wt8/QtgiSL4OHv4Q0MN4eJin2UsUDAW1xl/YFJgaf35StIgtozpUZ87gh0hK0fSavo3vNkbzafPJvNHwDTae3shjSx7jn/P/3HtHSoF3EHSbDq8fhs6TwckDNoyHqQ1gejPY/BlcisyT7yUKBzNX/MT9ZffvZ8oaf4aLu4MzXvU3uyuJSby/OIwFe05Tx8uVSb3rksBx3tj4BtHXonm14asMqD4gy93FjJ2eMc4A9v8Gp9POfso3AP+OUK0TlKomN4eJbDl+/DjOzs64u7s/2L9JYQpaay5cuMDVq1epXLnybZ/dr8ZvysSfLj809dzNsn1neWvhPhKTUni7Uw0eqVeCd7e8y7pT6+hbrS9vBr6JbXb68V86AWEL4cDvcOZvY5mbt1EI+HeEik3+MzaREJlJSkoiKirqtj7yIn9xcHDAy8sLOzu725ZL4reS6CuJvDF/LxsPnyfEvxQTugfw85GvmBU2i5AKIXwU/JEx0Ft2XTkDh1dA+HI49iek3ACHEuDb2hgiokpLcClnse8jhMg/JPFbkdaaH/+K5MNlB3G0s2V891pcKrKBCTsmUKNkDb5o/QUejh45P9CNeDi6zigEItbAtRhjeanqaQVBS6jYVLqJClFI5MvEn1/b+DMTERPPq/NC2RsVR4/6XrRucJ73to3C3dGdr9p8RWXXyvffSVZpDdFhcHStURhEbjPOBmyLQsWHwLsZVAoCr4YydLQQBVS+TPzp8nuNP6OklFS+WHuEqesjKOvqyPCORfny4FskpyYzpdUUGpRukDsHvpkAJ7fC0fVwbANEp93UYlsUvAKNnkSVgozXckYgRIEgid9kdkde4tV5oZy8mED/oOKEJk3kTPxpPmz2Ie0rt7//DnIq4SKc3AYntkDkFji3F3Qq2NgZQ1lXaARejYyCwKVs7scjhLA4SfwmdO1GMmP/OMCcHafwL2eLS6WfOHT5H15p8ApP1nwyb7vWJcbBye0Qudm4gezsP8YQEgCuFYwmofSCoGxtaR4SIh+QxG9iqw9EM/K3vVy9cZ2adZYTkbCZ3v69GdloJEVsrNQtM/kGnNsHp3ZA1E6I2gVxJ43PbO2hbB0oV8+Yz7hsHeM+AulCKoSp5MvEX9Au7t5LbPwN/m/RfpbvP0OFKhu4bL+KFl4t+Lj5xznr7mlJV84aN4+lFwRn/4H0yWeKOBhTXKYXBOXqGr2JimRz2kwhRI7ly8SfrqDX+NNprVmy9yzv/r6fRMfN2Hv+TvWS1ZjWZppluntaWmoqXDxqjDB6NtQoCM7+AzeuGJ/b2oNnDSgTAJ41jYKhdE1jCAohRK6TxJ+PxFxN5O2F+1l3cgNOXnMoVawk37T9Gp8SPtYO7f5SU+HScaMgOBNqFATRYZAQ++86xUsbBULpDIWBhz/YOVgraiEKJEn8+YzWmt9Dz/DuihWken6Lg73myzZf0Kjsg09GYQrxMUYX0ugDRkEQEwbnwyE5bZgAZQvuvuBZzSgESvmDhx+4+0n3UiGySRJ/PhV9JZHXFqxnz81PKGJ/iZ6+/RlYq4dlb/aylpRkuHjMKATSC4Tzh4wzBp2atpKCEhWMwsCjqjFDWfprJ3erhi+E2Zkq8SulHgU6AZ7ANK31qnutX5gTPxi1/592HuLjXWPQxcJQSlPTPYAuVTrT3rs97o4FLAEm34ALRyE2HGKPGGcGseEQG2HMT5CumLtRCLj7QEkfKFkl7dkHiha3XvxCmITFEr9SaibQGYjRWgdkWN4e+BywBb7VWk/Iwr7cgIla66fvtV5hT/zpzsZd59XfNrIrdj0lSu0l0eYUtsqWpuWa0qVKF0IqhOBYxNHaYeae1FSjS+lthcERo5BIH5coXfEyRgEghYIoxCyZ+JsD8cAP6YlfKWULHAYeBqKAnUBfjELgzpmBn9Jax6Rt9ynws9b6ntPGS+L/l9aaX3dFMWbpAVKKnKVJ7ROcvLmZ6IRonOycaFOxDZ2rdCawdGD2hnzOr25cNZqNLh4zCoKLx40eR3ctFEobBYFbJShR6d/nEhWNkUwL0+8mCjSLNvUopbyBpRkSfxPgfa11u7T3owC01nedDl4Zt6ROAFZrrddkss4QYAhAxYoVG0RGyoxTGZ25fJ23Fu5jQ/h56lV04fGWKfx9cR2rIldxLekansU86VS5E52rdKaqW1Vrh2tdmRUKl08aw1qT4d++jR24et2lUEh77VRKJrwR+UZuJ/6eQHut9TNp7wcCjbXWwzLZfjjwBMaZQajWevq9jic1/rvTWrMo9DSjlxwg4UYKw1v78kRQebac3cjSo0vZcnoLyTqZqm5VeaTKI/Sq2ss8N4OZRfINY4L7SyfgcqRRGFyKNF5firy9GyqAXTHjzKBERXApbxQS6Q+X8sZDbloTJpHbib8X0O6OxN9Ia/1iDoMuNHfu5kRs/A3eWxzGH3vPUq2MM5/0rEMtL1cuJl5kxfEV/HHsD/bG7qWCcwXGBo2lfun61g45/7gRD3Gnbi8MLkcay+KiIOHCHRsoKO75b0HgWgFc0woIl7QCwqkU2Mg01yL3maqp5wGOI4n/AawMO8f/LdrPhWs3GRzsw8tt/HCwM9qrd57byf9t+T/OxJ9hQI0BDK83HIcicsNUjt1MMJqLrkQZBUHcaaNQuHL63/dJ127fxsbOKAxcvMC5jDH6qXOGh0tZ4+K03NAmcii3E38RjIu7rYHTGE04/bTWYTkJOp009WRd3PUkPvzjIP/bdYrKHk5M6F6Lxj5Gd8+EpAQm7Z7E/8L/h7eLN2ObjaVOqTpWjriA0xquX8pQEETdXihcPWs8ku8y362jGziXu3vh4FzGuBDtVEouRotMWbJXzxwgBPAAooH3tNbfKaU6ApMxevLM1FqPs0DQUuPPpi0RsYxcsJdTF68z8KFKjGjvj7ODMRHztjPbeG/re0QnRPNEzSd4oe4LFLWVYZatRmtIvGwMgnc14+Pc7cviozPc2JZG2Rq9lJzLGM/FPTM8Z3jt5CndWAshU93A9aCkxp89CTeTmbjyMN9vPU5ZFwfGdatFy2qeAMTfjGfiron8duQ3fFx9GNdsHAEeAffZo7Cq1BRj6IuMhcOVtALi6hmIP28UDgmx/y0gAOycMhQGpdKeMxQMGQsMmW+hQMiXiV9q/Jax5+Ql3py/lyMx8XSuXZZ3u9TA09loP95yegvvbn2XC9cv8FTAUzxb51nsbaVXSr6WmmJcdI6PTnvEZHikLbuWVkhcv3T3fTi4GgWBk6cxNEYxD6NZycnDuGP61msPKFZSmptMKl8m/nRS48+5G8kpTN9wjGnrI3Cws2Fkh+r0CayAjY3iys0rfLzjY34/+jt+bn6MCxpHdffq1g5Z5IXkG2mFQMaCIca46e3W61jjLCKzQgJlJP9bhYMUFGaRLxO/1Pgt7+j5eN5asI/txy8S6O3Gh91q4VfaGYA/T/3J+9ve53LiZYbUHsIztZ/BzsbOyhEL00hJNs4kEmL/LQyuZXx9Hq5d+Pd1lgoKD+MidrGS4Fgybbn7v6/Tnx1KyAxv2ZAvE386qfFbVvqwD+OWHSThZjLPtajC8y19cbCzJe5GHON3jOePY39QvWR1xjYbK3f+iuxJSYbrF9MKhPTC4YLx/lbhcQESLhrrJVyE1KTM9+fgekeB4J7htdt/CwvHkoV+SG9J/OI/YuNvMHbpARaFnsHHw4mx3QJoWsWYHWtt5FrG/DWGKzev8Hyd53ky4Enrzf8rCgetjeE10guB6xch4dId79OfL/z7Wfr0n3dTxOHfMwjHEsbDoYRxlnHrdYZnRzfjtYNrgWiOypeJX5p68sbGw+d5Z9F+Tl5MoGcDL97uWB03J3suJl5k3F/jWBW5inqe9fiw2Yd4OXtZO1whbpd8w2hW+k/hkKHwSLhgrJN4Ga5fNp7vdu9ERkVdwdH1v4XCvQoMxxLGdia5MztfJv50UuPPfddvpjBl3RFmbDyGq6Md73SqTrd65VFKsfTYUsb9NQ6N5u3Gb9PZpzNKBioT+V3S9X8Lgbs931lQ3Hq+BCk377FjBQ4utxcODq4ZHunvXe5YnvawL26xgQAl8YssOXj2CqMW7CP01GWa+XowrlsAldydOB1/mrc2vcWemD20927POw+9g2tRV2uHK0Te09ooNLJaYCTG3f5ISrj3/pUNFM1QKHT5HMpnb3ytfJn4panHOlJSNT9vj+TjFeEkpaQyrKUvQ1r4UMQGvtv/HV+FfoVHMQ8+bPYhgWXy6RzAQlhLShIkXvlvoXDjyn8LicQ4eHiMMQd1NuTLxJ9OavzWcS4ukdFLwli+/xw+pZz4oGsAQb4e7I/dz8hNIzl55SRPBjzJsLrDsLOVbp9CmM39Er85rkQIUynj6sBXAxrw/ZOBJKdo+n+7neFz/sbT3pd5nefR3a87M/fPpP+y/hyLO2btcIUQD0gSv8hUS39PVr3SnOGt/Vix/xytP/2TeTui+b+H3mNyyGTOXjtL7yW9mRc+DzOfOQohbieJX9yTg50trz5clRUvB1OnQgneX3KAR6Zuxt2mAb898hv1S9fng78+YPi64Vy4fufkJEIIMzJlG79c3DUnrTV/7DvLmCUHOB9/g36NKvJ626osjZzH5N2TKW5fnA+CPqC5V3NrhypEoSYXd4XFXU1MYtLqw8zeegK3Yva81bE6AZWvMXLTSCIuR9DHvw+vNXxNZvoSwkok8YtcE3YmjncW7efvk5dpVLkk73bx44+o7/jp4E/4ufkxtdVUyhUvZ+0whSh0pFePyDU1y7ny27NNGd+9FuHnrvLo1B3oC135rMUXnIs/R98/+hIaE2rtMIUQd5DEL3LExkbRt1FF1r3Wgm71yjP9z6O8OyeFwb6f4WTnxFMrn2LpsaXWDlMIkUGeJX6lVHWl1HSl1Hyl1HN5dVyRN9yLF+WTXnX49dkmuDjaMXpBLC4XX8PPtSajNo1iyp4ppN5tWkAhRJ7LUuJXSs1USsUopfbfsby9UipcKRWhlBp5r31orQ9qrZ8FHgMybXsS+Vugd0mWvtiM0Y/UJCwqmd1/9cLHoSXf7PuG1/98nevJ160dohCFXlZr/LOA9hkXKKVsgWlAB6AG0FcpVUMpVUsptfSOh2faNo8Am4G1FvsGwnSK2NrwRFNv1r8eQvf6lfjn77YUufwIayLXMGjFIKKvRVs7RCEKtSwlfq31RuDiHYsbARFa62Na65vAXKCr1nqf1rrzHY+YtP0s1lo3Bfpb8ksIc/IoXpSPe9Zh4fNBeNl04NqpgRyKPUqvJX0IuxBm7fCEKLRy0sZfHjiV4X1U2rK7UkqFKKWmKKW+BpbdY70hSqldSqld58+fz0F4wizqVXRj0QtBfPBwbzg7jAvxyfRf+ji/H1lh7dCEKJRyMqfe3WYMyPSmAK31BmDD/XaqtZ6hlDoLdLG3t2+Q7eiEqdjaKPo1rkiHgH6MW+nLspjxvLP1DdZG7OOztq9haysdzITIKzn53xYFVMjw3gs4k7NwREHn5mTPxO7N+Knj9zgnB7I+5geCZw1hz8kYa4cmRKGRk8S/E/BTSlVWStkDfYDFlghKa71Eaz3E1VVmeiqo6lf0ZNOgb2np+ThXi2xnwB9P8fpvm7l07V5T2wkhLCGr3TnnANsAf6VUlFLqaa11MjAMWAkcBOZprS1yxU4p1UUpNSMuLs4SuxMmZWtrw5QOb/BB04+wL3aW5ZfeImTKHH7eHklKqnmHEhEiv5OxeoQphMWG8dyaF4hLjOd6bDBeDgGMad+RZr5lrR2aEPlOvhykTYZlLpyir0UzctNIdkUbhb1OtcXV1ocOvkG0qNiIup51cbZ3tnKUQphfvkz86aTGXzjF3Yhj+5ndfL97LXtjQ1EOUSiVio2ywd/Nn/ql69OgdAPqe9bH3dHd2uEKYTr5MvFLjV+kO335Oh/8EcrqozsoUTIKr7JnOXM9nMSURAC8XbyNQqB0fRqWbijDQAtBPk386aTGL9JtP3aB95cc4ODZKzSq7EK/YFsuph5iT/Qe9sTs4erNqwD08OvBiMARFLMrZuWIhbAeSfyiwEhJ1czdeZKJK8OJu55En0YVeb2tPyWKFeHIpSMsPrqYHw/8SAXnCowPHk/tUrWtHbIQVpEvE7809Yh7iUtIYvLaw/ywLRIne1teblOVgU0qYWdrw85zO3l789vEJMQwtM5QBtcaTBGbnNygLkT+ky8Tfzqp8Yt7ORJ9lTFLD7DpSCx+nsV5t0sNgv1KceXmFT7c/iF/HPuD2qVqM6HZBCq4VLj/DoUoIGTqRVFg+ZV25oenGvHN4w25mZLKwO928MzsXVy8YsuE4Al8FPwRxy8fp8eSHiw8shAzV3KEyEumrPFLU494UDeSU5i5+QRT1x0hKUXzVLPKDGvly9Wk87y95W12nttJ64qtea/Je7g5uFk7XCFylTT1iEIl5koiH60I57c9UZRyLsob7fzpXq8cPx38kc///pwSRUswNmgsQeWDrB2qELlGmnpEoeLp4sCnj9Vh4fNN8XJzZMT8vXSdtpVqxbowt9NcShQtwbNrnmX89vEkJidaO1whrEJq/KLA0lqzZO9ZJiw7yJm4RNrVLM1r7Sqz8MS3/HTwJ3xcfZgQPIHq7tWtHaoQFiU1flFoKaV4pE451r0ewuttq7LpSCydPt9O8vkuTGo+jas3r9JvWT9m7p9JSmqKtcMVIs+YssYvF3dFboi5ksjEVeH8ujsKt2L2PNuqDGE3vmPdqbXU96zPiMAR1PSoae0whcgxubgrxB32n47jg6UH2H78In6lnWgTeIolUV8TdyOONhXb8ELdF/B187V2mEJkmyR+Ie5Ca83KsGjGLz9I5IUEgv2LU63q3yyJnEtCUgKdfDrxfJ3n5cYvkS9J4hfiHm4kpzB76wm+WBtBQlIKvQLdcCmzmQVH/0dKagrd/LoxtPZQSjuVtnaoQmSZJH4hsuBC/A0+W3OYX7afpHjRIjzVoiRXiq5k4dHfsMGGPtX68HStpynpUNLaoQpxX5L4hXgAh6Ov8kHa+D+VPZwY0sqV/QnzWXpsKQ62DgysMZAnaj4hM4EJUzNVd06llJNSardSqnNeHleIrKqaNv7P94MCsVEwat4Zjh/swicP/Uiz8s34eu/XtP+tPd/u+5aEpARrhytEtmQp8SulZiqlYpRS++9Y3l4pFa6UilBKjczCrt4E5mUnUCHyilKKltU8WfFyc0Y/UpMDZ68w9PtT2F14gumtfqJOqTp8vudzOi7oyM8Hf+Zmyk1rhyzEA8lSU49SqjkQD/ygtQ5IW2YLHAYeBqKAnUBfwBYYf8cungJqAx6AAxCrtV56v+NKU48wg7iEJKasO8LsrSewL2LD0OZVaFQ9jhn7prErehfli5fn9Yav07pia5RS1g5XCMu18SulvIGlGRJ/E+B9rXW7tPejALTWdyb99O3HAU5ADeA60E1rnXqX9YYAQwAqVqzYIDIyMkvxCZHbTsRe46MVh1i+/xylXYry6sNVKVf2FJN2TyTicgSNyjRiROAI/Ev6WztUUcjdL/HnZGqi8sCpDO+jgMaZray1fjstoEEYNf7/JP209WYopc4CXezt7RvkID4hLMrbw4mvBjRg14mLjP3jIG/+to/qZV0Y2WE6Z1PXMzV0Ko8tfYxeVXvxQt0XZPhnYVo5ubh7t3Pa+54+aK1n3a+ZR2u9RGs9xNXVNdvBCZFbGnqXZOHzTfmibz2uJibxxMxdrNjmw+Sm/6Nvtb7MPzyfTgs78fPBn0lKTbJ2uEL8R04SfxSQ8bZGL+BMzsIxKKW6KKVmxMXFWWJ3QlicUooudcqx9rUWvN2xOnsiL/HYV6HERXVkRutfCHAPYMKOCfRc3JMtp7dYO1whbpOTxL8T8FNKVVZK2QN9gMWWCUuI/KFoEVsGN/fhzzdaMqhpZebvjmLQ1yepafM6E5tPJjk1mWfXPMuLa18k8opcrxLmkNVePXOAEIxeOdHAe1rr75RSHYHJGD15Zmqtx1kyOOnVI/KbOy8Av9TGh+uOG/hm3wxupNxgYPWBDKk9hOL2xa0dqijA8uWduzIss8jv0i8Ah566TPWyLgxrU5rtl39iUcQi3BzceLn+y3T17YqNkikxhOXly8SfTmr8Ij/TWrN071k+WnGIqEvXCfEvxWNBMCfiC0LPh1LDvQbvNH6HWqVqWTtUUcDky8QvNX5RkNxITuGHrZF8se4I8TeSeaxhBepWP863YV8Qez2WF+q+wFMBT2FrY2vtUEUBkS8Tfzqp8YuC5NK1m3yxLoIf/zqBna0NTwaX4WyRn1h9ciWBZQL5sNmHlHEqY+0wRQEgiV8Ik8l4AdjTxZ6HA0+xOmY69rb2jG46mtYVW1s7RJHP5cvEL009ojDIeAG4SrkEipaby6lrh3ms6mO8Hvg6jkUcrR2iyKfyZeJPJzV+UdClXwD+ZGU4Jy9ewafqJs7brqSKaxU+av6RjPsjssVU4/ELIW6Xfgfwmldb8H6X2lw+3Y6Ek09zKi6Wvn/04+eDP2PmypnInyTxC2EC9kVsGBRUmQ1vhPBso/ZcO/YSiVd8mLBjAkNXPc/FxIvWDlEUIKZM/DJWjyisXBzseKNdNTa82oXOnu9wI7oL2878RYf5j/Lnyc3WDk8UENLGL4SJHY6+ynvLV/PPzWnYFo2hiXsPprR7Cwc7e2uHJkxM2viFyMeqlnZmzqDufNXyB5xvBrPtwm80/aEb/wvdLW3/Itsk8QuRD7TwK8+WZ6YxoPJ7JNvE8sHfQ2j1/WssPxRq7dBEPiRNPULkM6eunOXl1WM4fHUbqBRclB9P1+lDnxqdKWZXzNrhCRPIl/345QYuIe4v8nI076/7gZ0XlqPsz1MERzr6dKRfjV7UKFlDJn4vxPJl4k8nNX4h7u/s5eu8u3Ipm6KXYue8D2ySqOrmT8+qPejk0wkXexdrhyjymCR+IQqJw9FXGbd8D1vPraGY+y5S7aMoaluUtpXa0t2vOw1KN5CzgEJCEr8Qhcxfxy4wftlB9sUewLNsKClOe0hMuYa3izfd/brTpUoXPBw9rB2myEWS+IUohLTW/LHPGAMo8uJlqlU5jpPHbg7H7QWgfPHyVCtZDf+S/vi7+VOtZDXKOpWVM4ICwjSJXykVAnwAhAFztdYb7reNJH4hcuZmciq/bI9kyroILl67ScsATfUqkcTcPE74xXAir0SiMXKAs73zrUKgqltVqpWsRpUSVbC3lZvF8pv7Jf4iWdzJTKAzEKO1DsiwvD3wOcZk699qrSfcYzcaiAccgKisHFcIkTPpYwD1aODFNxuP8e3m42w8UJnegc35rrUfxR1TOXL5COEXwwm/GM6hS4f47chvXE++DkARVYTKJSrfKhCalW9GlRJVrPytRE5lqcavlGqOkbR/SE/8Silb4DDwMEYi3wn0xSgExt+xi6eAWK11qlKqNDBJa93/fseVGr8QlnX+6g2+WHeEX7afxM7WhqeaeTO0RRVcHOxurZOSmsKpq6c4dOkQhy8e5tDFQ4RfCicmIQZvF2+WdFtixW8gssJiTT1KKW9gaYbE3wR4X2vdLu39KACt9Z1J/8792AO/aK17ZvL5EGAIQMWKFRtERkZmKT4hRNZFXrjGp6sOs/ifM5QoZscLIb4MbFIJB7vM5/0dtWkUe6L3sLLnyjyMVGRHbo7VUx44leF9VNqyzALprpT6GvgRmJrZelrrGVrrhlrrhqVKlcpBeEKIzFRyd2JK33osfbEZtcq7Mm7ZQVpN3MCvu06Rknr3yqCNkhFeCoqc/CXvdvk/09MHrfUCrfVQrXXv+13YlWGZhcgbAeVd+fHpxvzyTGM8nIvyxvy9dPh8I6sPRMsgcAVYThJ/FFAhw3sv4EzOwhFCWENTXw9+fyGIaf3qk5SiGfzDLnpN38bOEzIBTEGUk8S/E/BTSlVOa7fvAyy2RFBa6yVa6yGurq6W2J0QIguUUnSqXZZVrzRnXLcATl5MoNf0bTwzeyfh565aOzxhQVlK/EqpOcA2wF8pFaWUelprnQwMA1YCB4F5WuswSwQlTT1CWI+drQ39G1fizzda8kY7f7Yfv0j7zzey68QlkjNp/xf5i9y5K4S4p0vXbvLlhgh+PvYxNo7H6FNmOi+09MXNSW7sMqt8OQOX1PiFMA83J3ve7lSDdjXL4Ghvw8wtx2n+8XqmrjtCws1ka4cnssGUiV/a+IUwn2L2trgVs2fFy815qIo7E1cdpsUnG/jpr0iSUlKtHZ54AKZM/FLjF8J8VFoP7qqlnfnm8YbMf7YJ3u7FeGfRftp+tpGle89IF9B8wpSJX2r8QphfQ++SzBvahO+eaIi9rQ3DfvmbrtO2sCUi1tqhifswZeIXQuQPSilaVy/NspeCmdirDhfib9L/2+0M/G47e6MuWzs8kQlTJn5p6hEif7G1UfRs4MXa11rwTqfq7D8dxyNTt/D8z7uJiIm3dnjiDqZM/NLUI0T+5GBnyzPBPmwc0ZKXWvvxZ/h52n72JyPm/8Ppy9etHZ5IY8rEL4TI35wd7Hjl4apsHNGSJ4Mqs+jvM7T8ZANjlhzgQvwNa4dX6GVpIpa8ppTqAnTx9fW1dihCiAx05uMw3pV78aL8X+caPNWsMp+vOcysrcf5386TPB3sw+DgyjhnmAcgM1FXoyjrVBZbm8yHjLa0hKQE9sXue+Dvm66kQ0mqulW1cFSWY8rEr7VeAixp2LDhYGvHIoTIufIlHPm4Zx2GNK/CpNXhTFl7hB+3neD5+8wDcDr+NB0WdGBwrcEMrz88z+L9MvRLZh+Yne3t21Zqy6chn1owIssyZeIXQpiPJSZi9/Uszpf9G7AvKo6PVx5i3LKDfLf5OC+18aNXAy+K2N7e+nw+4TwA289tz/GxH8S15Gu42LswpdWUbG3vVtTNwhFZliR+IUSeq+VlzAOw7egFPl55iFEL9jFj4zFea1uVjgFlsbHJeSGTU/a29jQo3cDaYeQKubgrhLCaJlXcWfBcU755/N+bwLpM3cyG8Bi5CzgXmbLGLxd3hSg8lFI8XKM0rap5svif00xafZhB3++kUeWS9GiSZO3wCiRT1vilH78QhY+tjaJbPS/WvhrCmK41OXb+GqMW7gfg+s0UK0dXsJgy8QshCi/7IjY83sSbjSNC6N+4IgCHzl3lpbl/E3nhmpWjKxgk8Qshsiwv292L2RehR30vAEq7FGVl2Dlaf/on7yzaR8yVxDyLoyCSxC+EML1yJRzZ+EZL+jaqyNwdp2j+yXomLD/E5YSbuXK8gn5hOc8Sv1LKRik1Tin1hVLqibw6rhDCMtLH47cWTxcHPng0gLWvtaB9zTJ8vfEowR+vZ9r6CJkJ7AFldbL1mUqpGKXU/juWt1dKhSulIpRSI++zm65AeSAJiMpeuEKIwq6SuxOT+9Rj+UvBNK5ckk9WhtP84w3M3nqCm8mWmwnM2gVdbspqjX8W0D7jAqWULTAN6ADUAPoqpWoopWoppZbe8fAE/IFtWutXgecs9xWEEIVRtTIufPtEIL8914QqpZx4b3EYrT7dwG+7o0hJLdhNNTmVpcSvtd4IXLxjcSMgQmt9TGt9E5gLdNVa79Nad77jEYNRy7+Utq30zRJCWESDSiWZO+QhZj/ViBLF7Hjt139oP3kjy/edLfBt9dmVkzb+8sCpDO+j0pZlZgHQTin1BbAxs5WUUkOUUruUUrvOnz+fg/CEEIWFUooWVUux+IVmfNm/Pqla89zPe3hk6ha5C/gucnLn7t0awDL9dbXWCcDT99up1nqGUuos0MXe3r5gDpQhhMgVNjaKjrXK0q5mGRb+fZrJa4y7gAO93Xi9rT+NfdytHaIp5KTGHwVUyPDeCziTs3CEEGaW3fHpc+pBL7SmTwW57rUQPng0gMgLCfSe8ZfMBZwmJ4l/J+CnlKqslLIH+gCLLRGUDNkghMgouwWOfREbBj5UiT/faMlbHavdmgt46I+7OBx91cJR5h9Z7c45B9gG+CulopRST2utk4FhwErgIDBPax1miaBksnUhzMcS4/Fbi6O9LUOaV2HjiJa80qYqWyIu0G7yRl6e+zcnYu8+DERB7s6ZpTZ+rXXfTJYvA5ZZNCJkBi4hRO5wdrDjpTZ+PN6kEtM3HmX21hMs2XuWxxpWYHhrX8q6Olo7xDxhyiEbpMYvhMhNbk72jOpQnY1vtGRA44rM332KFmmTwccWgsngTZn4pY1fCJEXPF0cGN01gHWvhdC1TjlmbT1O84/X80/UZVILcBdQUyZ+qfELITLK7fb2CiWL8UmvOqx+tQWtqnly4MwVYuNvMG19BNduFLxxgEyZ+KXGL4SwhiqlijO1X33aB5TBrogNn6wMp8Un65m5+TiJSQVnwAFTJn4hhEkV3NaP27gVs8fN0Z4Fzzelamlnxiw9QMuJG5iz4yRJKZYbCM5aTJn4palHCJFRXt84ln68+hXd+GXwQ/z8TGNKuzgwasE+Hp70J7+HniY1Hw8EZ8rEL009QphPQe7XflcZvm6QrwcLn2/Kt483xMHOlpfmhtLh802sDDuXL8cBMmXiF0IIs1FK0aZGaZYND+aLvvVISkll6I+7eXTaFjYePp+vCgBTJn5p6hFCmJWNjaJLnXKseqU5H/eoTWz8TR6fuYM+M/5i14k7R683J1MmfmnqEUJkZMZmpiK2NjwWWIF1r7dg9CM1OXr+Gj2nb2PQ9zvYf9rclVZTJn4hhMgvihax5Ymm3mwcEcKb7avx98nLdP5iM8/9tJuIGHMOBCeJXwghLKCYfRGeC6nCpjdbMry1HxsPn6ftZxt59X+hRF64+0Bw1iKJXwiRZdYajz8/cXGw49WHq7LpzVYMDvZh2f6ztPr0T0Yt2Mvpy9etHR5g0sQvF3eFEBnleT9+C/TQKelkz6iOGQeCi6LlJxt4f3EYMVcTLRBl9pky8cvFXSGEtVnqgnL6QHDrXw+he/3y/PhXJM0/Xs/45Qe5dO2mRY7xoEyZ+IUQoqDxcivGhB61WftqCzoElGXGxmMEf7yeSasPcyUxKU9jkcQvhDA9M3bnzC5vDyc+612XVS83p3lVD6asPULwR+vzdCRQSfxCCGEFfqWd+bJ/A5a+2IyGldz4ZGU4zT9ez7ebjuX6SKCS+IUQwooCyrvy3aBAFjzflOplXRj7x0FafLI+V+8CztKcu5aglAoG+qcds4bWumleHVsIIcyufkU3fnqmMduOXuDLDRF4ezjl2rGylPiVUjOBzkCM1jogw/L2wOeALfCt1npCZvvQWm8CNimlHgV25iRoIYR1SD/+3NekijtNqrjn6jGyWuOfBUwFfkhfoJSyBaYBDwNRwE6l1GKMQmD8Hds/pbWOSXvdD3gmBzELIQoZa43HX1BlKfFrrTcqpbzvWNwIiNBaHwNQSs0Fumqtx2OcHfyHUqoiEKe1vpLZsZRSQ4AhABUrVsxKeEKIPKBUwelZkxUF+fvm5OJueeBUhvdRacvu5Wng+3utoLWeAYwG9tjb2+cgPCFEQVGQunOaQU4S/93+Evc8P9Jav6e13nq/Hcudu0IIkXtykvijgAoZ3nsBZ3IWjkHG6hFCiNyTk8S/E/BTSlVWStkDfYDFlglLCCFEbslS4ldKzQG2Af5KqSil1NNa62RgGLASOAjM01qHWSIoaeoRQojck9VePX0zWb4MWGbRiDCaeoAuvr6+lt61ECIHrDWheEHvXpnXlJlnhldKnQcis7m5BxBrwXAsycyxgbnjM3NsYO74JLbsM3N8d4utkta6VGYbmDrx54RSapfWuqG147gbM8cG5o7PzLGBueOT2LLPzPFlJzYZpE0IIQoZSfxCCFHIFOTEP8PaAdyDmWMDc8dn5tjA3PFJbNln5vgeOLYC28YvhBDi7gpyjV8IIcRdSOIXQohCpkAmfqVUe6VUuFIqQik10sqxzFRKxSil9mdYVlIptVopdSTt2c1KsVVQSq1XSh1USoUppV4yWXwOSqkdSql/0uIbbab40mKxVUr9rZRaaqbYlFInlFL7lFKhSqldZootLZYSSqn5SqlDaf/+mpghPqWUf9pvlv64opR62QyxpcX3Str/hf1KqTlp/0ceOLYCl/gzTBDTAagB9FVK1bBiSLOA9ncsGwms1Vr7AWvT3ltDMvCa1ro68BDwQtpvZZb4bgCttNZ1gLpAe6XUQyaKD+AljCFL0pkptpZa67oZ+nibKbbPgRVa62pAHYzf0Orxaa3D036zukADIAFYaIbYlFLlgeFAw7SZEG0xxkh78Ni01gXqATQBVmZ4PwoYZeWYvIH9Gd6HA2XTXpcFwq39u6XF8jvGjGqmiw8oBuwBGpslPowRadcCrYClZvrbAicAjzuWmSU2F+A4aZ1LzBZfhnjaAlvMEhv/zoFSEmO4naVpMT5wbAWuxk/2JojJa6W11mcB0p49rRwPaTOs1QO2Y6L40ppSQoEYYLXW2kzxTQZGAKkZlpklNg2sUkrtTpvVzkyx+QDnge/Tmsm+VUo5mSi+dH2AOWmvrR6b1vo0MBE4CZzFmM1wVXZiK4iJ/4EniCnslFLFgd+Al/U9psW0Bq11ijZOu72ARkqpACuHBIBSqjMQo7Xebe1YMhGkta6P0eT5glKqubUDyqAIUB/4SmtdD7iGdZud/iNtqPlHgF+tHUu6tLb7rkBloBzgpJQakJ19FcTEn2sTxFhQtFKqLEDac8x91s81Sik7jKT/s9Z6gdniS6e1vgxswLheYob4goBHlFIngLlAK6XUTyaJDa31mbTnGIw26kZmiQ3j/2hU2tkbwHyMgsAs8YFRYO7RWkenvTdDbG2A41rr81rrJGAB0DQ7sRXExJ8fJohZDDyR9voJjLb1PKeUUsB3wEGt9aQMH5klvlJKqRJprx0x/uEfMkN8WutRWmsvrbU3xr+xdVrrAWaITSnlpJRyTn+N0Q683wyxAWitzwGnlFL+aYtaAwcwSXxp+vJvMw+YI7aTwENKqWJp/3dbY1wUf/DYrHnxJBcvgnQEDgNHgbetHMscjPa4JIyaztOAO8ZFwSNpzyWtFFszjGawvUBo2qOjieKrDfydFt9+4N205aaIL0OcIfx7cdfqsWG0of+T9ghL/z9ghtgyxFgX2JX2t10EuJklPoyOBBcA1wzLzBLbaIzKz37gR6BodmKTIRuEEKKQKYhNPUIIIe5BEr8QQhQykviFEKKQkcQvhBCFjCR+IYQoZCTxCyFEISOJXwghCpn/B2Kj6M7czp9hAAAAAElFTkSuQmCC\n", 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" ] @@ -644,22 +632,16 @@ ], "source": [ "p, lam = 2.1209508879201904, 0.5510204081632653\n", - "# lam = 0.99\n", - "# p = 2 * lam/(1-lam)\n", "mean = p / (1 - lam)\n", "std = np.sqrt(p / (1 - lam) ** 3)\n", - "x = np.linspace(mean - 1.2 * std, mean + 5 * std, 1000)\n", - "plt.semilogy(x, np.exp(_logprob(x, p, lam)))\n", - "plt.plot(x, abel_rejection_envelope(x, p, lam));" + "x = np.linspace(np.maximum(0, mean - 1.2 * std), mean + 15 * std, 1000)\n", + "plt.semilogy(x, np.exp(_logprob(x, p, lam)), label=\"PDF\")\n", + "plt.plot(x, abel_rejection_envelope(x, p, lam), label=\"Envelope\")\n", + "samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000)\n", + "y, edges = np.histogram(samples, bins=20, density=True)\n", + "plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label=\"Sampled points\")\n", + "plt.legend();" ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "f6ce9660-fd94-48b8-a883-0b30c35c2f89", - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { diff --git a/notebooks/fast_gen_pois.py b/notebooks/fast_gen_pois.py index a75a5ac..d09b27d 100644 --- a/notebooks/fast_gen_pois.py +++ b/notebooks/fast_gen_pois.py @@ -187,8 +187,6 @@ def h_l(x, p, lam, delta, mu): x[inds_to_sample[accepted]] = X[accepted] n_to_accept[inds_to_sample[accepted]] = counter inds_to_sample = inds_to_sample[~accepted] - # if counter % 1000 == 0: - # print(np.sum(inds_to_sample)) return x @@ -218,14 +216,8 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): + (1 - lam) * t ) rho_t_prime = ( - -lam - + (t - 1) * (lam / (lam * t + p) - 1 / (t + 1)) - - np.log(t + 1) - + np.log(lam * t + p) - + 1 - - 1.5 / (t + 1) + np.log(lam * t + p) - np.log(t + 1) + 1 - lam + 1.5 / (t + 1) - (lam + p) / (lam * t + p) ) - rho_t_prime = rho_t q = np.exp(-rho_t_prime) q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime))) @@ -270,18 +262,6 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): x[inds_to_sample[accepted]] = X[accepted] n_to_accept[inds_to_sample[accepted]] = counter inds_to_sample = inds_to_sample[~accepted] - if counter % 1000 == 0: - print(np.sum(inds_to_sample)) - print(_q) - print( - _p[0], - _lam[0], - raw_left[0], - raw_right[0], - _q_l[0] / (_q_l + _q_r)[0], - np.exp(_logprob(raw_left, _p, _lam))[0], - np.exp(_logprob(raw_right, _p, _lam))[0], - ) return x @@ -409,18 +389,17 @@ def h_l(x): # %% x = np.linspace(1000, 1700, 1000) -y0 = poisson_region_envelope(x, 1000, 0.3) -y1 = np.exp( - _logprob( - np.floor(x), - 1000, - 0.3, - ) -) -y2 = normal_approx(x, 1000, 0.3) +lam = 0.3 +p = 1000 +y0 = poisson_region_envelope(x, p, lam) +y1 = np.exp(_logprob(np.floor(x), p, lam)) +y2 = normal_approx(x, p, lam) plt.semilogy(x, y0, label="Envelope") plt.semilogy(x, y1, label="PDF") plt.plot(x, y2, label="Normal approx") +samples = _rejection_region_poisson(np.random.default_rng(42), p, lam, 100000) +y, edges = np.histogram(samples, bins=20, density=True) +plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label="Sampled points") plt.legend() @@ -428,7 +407,7 @@ def h_l(x): def abel_rejection_envelope(x, p, lam): p = np.asarray(p) lam = np.asarray(lam) - nu = 2 * (p ** 2 - lam * p - 3 * lam ** 2) / (3 * lam ** 2) + nu = 2 / 3 * (p ** 2 - lam * p - 3 * lam ** 2) / lam ** 2 alpha = 0.2746244084 # Taken from page 259 t = np.floor(alpha * np.maximum(nu, 0)) problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam)) @@ -450,15 +429,10 @@ def abel_rejection_envelope(x, p, lam): + (1 - lam) * t ) rho_t_prime = ( - -lam - + (t - 1) * (lam / (lam * t + p) - 1 / (t + 1)) - - np.log(t + 1) - + np.log(lam * t + p) - + 1 - - 1.5 / (t + 1) + np.log(lam * t + p) - np.log(t + 1) + 1 - lam + 1.5 / (t + 1) - (lam + p) / (lam * t + p) ) q = np.exp(-rho_t_prime) - q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime))) + q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q)) return np.where( x <= t, q_l * (1 - q) * q ** (t - x), @@ -468,12 +442,12 @@ def abel_rejection_envelope(x, p, lam): # %% p, lam = 2.1209508879201904, 0.5510204081632653 -# lam = 0.99 -# p = 2 * lam/(1-lam) mean = p / (1 - lam) std = np.sqrt(p / (1 - lam) ** 3) -x = np.linspace(mean - 1.2 * std, mean + 5 * std, 1000) -plt.semilogy(x, np.exp(_logprob(x, p, lam))) -plt.plot(x, abel_rejection_envelope(x, p, lam)) - -# %% +x = np.linspace(np.maximum(0, mean - 1.2 * std), mean + 15 * std, 1000) +plt.semilogy(x, np.exp(_logprob(x, p, lam)), label="PDF") +plt.plot(x, abel_rejection_envelope(x, p, lam), label="Envelope") +samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000) +y, edges = np.histogram(samples, bins=20, density=True) +plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label="Sampled points") +plt.legend() From 4ecd4429142664424ab151cefe4ab332d36307c2 Mon Sep 17 00:00:00 2001 From: lucianopaz Date: Wed, 25 May 2022 22:38:29 +0200 Subject: [PATCH 4/9] Add uniform time random number generators for generalized Poisson --- preclinpack/blocks/distributions.py | 310 +++++++++++++++++++++++++--- 1 file changed, 285 insertions(+), 25 deletions(-) diff --git a/preclinpack/blocks/distributions.py b/preclinpack/blocks/distributions.py index 16671a4..06685fc 100644 --- a/preclinpack/blocks/distributions.py +++ b/preclinpack/blocks/distributions.py @@ -32,6 +32,7 @@ from pymc.distributions.distribution import _moment from pymc.distributions.shape_utils import rv_size_is_none from pymc.distributions.transforms import _default_transform + from scipy.special import gammaln try: from aesara.link.jax.dispatch import jax_funcify @@ -195,6 +196,13 @@ def logp(op, value_var_list, rng, size, dtype, dim, alpha, **kwargs): dim > 1, ) + def _logpow(x, m): + """ + Calculates log(x**m) since m*log(x) will fail when m, x = 0. + """ + # return m * log(x) + return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x)) + class GeneralizedPoissonRV(RandomVariable): name = "generalized_poisson" ndim_supp = 0 @@ -213,21 +221,285 @@ def rng_fn(cls, rng, theta, lam, size): else: dist_size = np.broadcast_shapes(theta.shape, lam.shape) - # A mix of 2 algorithms described by Famoye (1997) is used depending on - # parameter values + # A mix of 4 algorithms described by Devroye (1989) and Famoye (1997) is used + # depending on parameter values # 0: Inverse method, computed on the log scale. Used when lam <= 0. - # 1: Branching method. Used when lambda > 0. + # 1: Poisson rejection region. Used when theta > max(3, 2 * lam / (1 - lam)) + # 2: Abel rejection region. Used when lam == 1 or (p >= 1 + lam and p <= 2*lam / (1-lam)) + # 3: Universal bound (AKA monotonicity region). Used when lam > 0 and not in regions 1 or 2 + + poisson_idxs = np.broadcast_to(theta >= np.maximum(3, 2 * lam / (1 - lam)), dist_size) + abel_idxs = np.broadcast_to( + (lam == 1) | ((theta >= 1 + lam) & (theta <= 2 * lam / (1 - lam))), + dist_size, + ) + monotonicity_idxs = (lam > 0) & (~poisson_idxs) & (~abel_idxs) + inverse_method_idxs = np.broadcast_to(lam < 0, dist_size) + x = np.empty(dist_size) - idxs_mask = np.broadcast_to(lam < 0, dist_size) - if np.any(idxs_mask): - x[idxs_mask] = cls._inverse_rng_fn(rng, theta, lam, dist_size, idxs_mask=idxs_mask)[ - idxs_mask - ] - idxs_mask = ~idxs_mask - if np.any(idxs_mask): - x[idxs_mask] = cls._branching_rng_fn( - rng, theta, lam, dist_size, idxs_mask=idxs_mask - )[idxs_mask] + if np.any(inverse_method_idxs): + x[inverse_method_idxs] = cls._inverse_rng_fn( + rng, theta, lam, dist_size, idxs_mask=inverse_method_idxs + )[inverse_method_idxs] + if np.any(monotonicity_idxs): + x[monotonicity_idxs] = cls._rejection_region_monotonicity( + rng, theta, lam, dist_size, idxs_mask=monotonicity_idxs + ) + if np.any(poisson_idxs): + x[poisson_idxs] = cls._rejection_region_poisson( + rng, theta, lam, dist_size, idxs_mask=poisson_idxs + ) + if np.any(abel_idxs): + x[abel_idxs] = cls._rejection_region_abel( + rng, theta, lam, dist_size, idxs_mask=abel_idxs + ) + return x + + @staticmethod + def _logprob(x, theta, lam): + theta_lam_x = theta + lam * x + return np.log(theta) + _logpow(theta_lam_x, x - 1) - theta_lam_x - gammaln(x + 1) + + @classmethod + def _rejection_region_monotonicity(cls, rng, p, lam, dist_size, idxs_mask=None): + if idxs_mask is None: + idxs_mask = np.ones(dist_size, dtype="bool") + p = np.broadcast_to(p, dist_size)[idxs_mask] + lam = np.broadcast_to(lam, dist_size)[idxs_mask] + dist_size = np.sum(idxs_mask) + p0 = np.exp(-p) + b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi) + u = rng.uniform(size=dist_size) + x = np.zeros(dist_size) + inds_to_sample = u > p0 / (p0 + b) + counter = 0 + while np.any(inds_to_sample): + counter += 1 + v = rng.uniform(size=dist_size) + w = rng.uniform(size=dist_size) + _x = np.floor(1 / w ** 2) + accepted = v * b * (1 / np.sqrt(_x) - 1 / np.sqrt(_x + 1)) <= np.exp( + cls._logprob(_x, p, lam) + ) + x[inds_to_sample & accepted] = _x[inds_to_sample & accepted] + inds_to_sample = inds_to_sample & ~accepted + return x + + @classmethod + def _rejection_region_poisson(cls, rng, p, lam, dist_size, idxs_mask=None): + if idxs_mask is None: + idxs_mask = np.ones(dist_size, dtype="bool") + p = np.broadcast_to(p, dist_size)[idxs_mask] + lam = np.broadcast_to(lam, dist_size)[idxs_mask] + dist_size = np.sum(idxs_mask) + + eps = (1 - lam) / (2 + (p - lam) * (1 - lam)) ** (1 / 3) + delta = (1 - lam) ** (2 / 5) / (2 + (p - lam) * (1 - lam)) ** (1 / 3) + mu = (p - lam) / (1 - lam) + sigma = np.sqrt((1 + delta) * (p - lam) / (1 - lam - eps) / (1 - lam) ** 2) + psi = ( + p * delta * (2 + delta - 2 * lam) + + (1 + delta) * (1 - lam) ** 2 + - lam * (1 - lam + delta) ** 2 + ) / (2 * (p - 1 - delta)) + G = ( + (p * (1 - lam - eps) * np.sqrt(1 + delta)) + / ((p - lam) * (1 - lam) * (1 - eps) ** 2) + * np.exp(psi / (1 + delta)) + ) + + def g(x, G, mu, sigma): + return ( + G / (np.sqrt(2 * np.pi) * sigma) * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2)) + ) + + def h_r(x, p, lam, eps, mu): + return ( + (p * (1 - lam - eps) ** 1.5) + / (np.sqrt(2 * np.pi) * (p - lam) ** 1.5) + * np.exp( + -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (x - mu) + + 2 * (1 - lam) + ) + ) + + t_r = np.ceil((p - lam) / (1 - lam - eps) - 1) + H_r = ( + (2 * p * (1 - lam - eps) ** 1.5 * np.exp(2 * (1 - lam))) + / ( + np.sqrt(2 * np.pi) + * (p - lam) ** 1.5 + * (1 - 2 * (1 - lam - eps) / (p - lam)) + * eps + * (1 - lam) + ) + * np.exp( + -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (t_r - mu) + ) + ) + + def h_l(x, p, lam, delta, mu): + return ( + p + / np.sqrt(2 * np.pi) + * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu)) + ) + + t_l = np.ceil((p - lam) / (1 - lam + delta) - 1) + H_l = ( + (2 * p * (1 + delta)) + / (np.sqrt(2 * np.pi) * delta * (1 - lam)) + * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (t_l + 1 - mu)) + ) + + x = np.zeros(dist_size) + inds_to_sample = np.arange(dist_size) + n_to_accept = np.zeros(dist_size) + counter = -1 + while np.any(inds_to_sample): + counter += 1 + _dist_size = len(inds_to_sample) + U = rng.uniform(size=_dist_size) + N = rng.normal(size=_dist_size) + V = rng.uniform(size=_dist_size) + E = rng.exponential(size=_dist_size) + _G = G[inds_to_sample] + _H_l = H_l[inds_to_sample] + _H_r = H_r[inds_to_sample] + _p = p[inds_to_sample] + _lam = lam[inds_to_sample] + _mu = mu[inds_to_sample] + _sigma = sigma[inds_to_sample] + _delta = delta[inds_to_sample] + _eps = eps[inds_to_sample] + _t_l = t_l[inds_to_sample] + _t_r = t_r[inds_to_sample] + + center = U < _G / (_G + _H_l + _H_r) + left = (U < (_G + _H_l) / (_G + _H_l + _H_r)) & ~center + raw_center_y = _mu + _sigma * N + raw_left_y = _t_l - 2 * E * (1 + _delta) / _delta / (1 - _lam) + raw_right_y = _t_r + 2 * E / ( + (1 - 2 * (1 - _lam - _eps) / (_p - _lam)) * _eps * (1 - _lam) + ) + Y = np.where( + center, + np.where( + (raw_center_y >= _t_l) & (raw_center_y < _t_r), + raw_center_y, + np.nan, + ), + np.where( + left, + np.where( + raw_left_y >= 0, + raw_left_y, + np.nan, + ), + np.where( + raw_right_y >= 0, + raw_right_y, + np.nan, + ), + ), + ) + X = np.floor(Y) + accepted = ( + V + * np.where( + center, + g(Y, G=_G, mu=_mu, sigma=_sigma), + np.where( + left, + h_l(Y, p=_p, lam=_lam, delta=_delta, mu=_mu), + h_r(Y, p=_p, lam=_lam, eps=_eps, mu=_mu), + ), + ) + <= np.exp(cls._logprob(X, _p, _lam)) + ) + + x[inds_to_sample[accepted]] = X[accepted] + n_to_accept[inds_to_sample[accepted]] = counter + inds_to_sample = inds_to_sample[~accepted] + return x + + @classmethod + def _rejection_region_abel(cls, rng, p, lam, dist_size, idxs_mask=None): + if idxs_mask is None: + idxs_mask = np.ones(dist_size, dtype="bool") + p = np.broadcast_to(p, dist_size)[idxs_mask] + lam = np.broadcast_to(lam, dist_size)[idxs_mask] + dist_size = np.sum(idxs_mask) + + nu = 2 * (p ** 2 - lam * p - 3 * lam ** 2) / (3 * lam ** 2) + alpha = 0.2746244084 # Taken from page 259 + t = np.floor(alpha * np.maximum(nu, 0)) + problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam)) + t[problematic] = 0 + b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi) + q_r = b / np.sqrt(t + 1) + + rho_t = ( # Taken from page 250 + 1 + - p + + np.log(p) + - 0.5 * np.log(2 * np.pi) + + (t - 1) * (np.log(lam * t + p) - np.log(t + 1)) + - 1.5 * np.log(t + 1) + + (1 - lam) * t + ) + rho_t_prime = ( + np.log(lam * t + p) + - np.log(t + 1) + + 1 + - lam + + 1.5 / (t + 1) + - (lam + p) / (lam * t + p) + ) + q = np.exp(-rho_t_prime) + q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime))) + + x = np.zeros(dist_size) + n_to_accept = np.zeros(dist_size) + inds_to_sample = np.arange(dist_size) + counter = -1 + while np.any(inds_to_sample): + counter += 1 + _dist_size = len(inds_to_sample) + U = rng.uniform(size=_dist_size) + V = rng.uniform(size=_dist_size) + W = rng.uniform(size=_dist_size) + E = rng.exponential(size=_dist_size) + _p = p[inds_to_sample] + _lam = lam[inds_to_sample] + _t = t[inds_to_sample] + _q = q[inds_to_sample] + _q_l = q_l[inds_to_sample] + _q_r = q_r[inds_to_sample] + _b = b[inds_to_sample] + raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q))) + raw_right = np.floor((_t + 1) / W ** 2) + left = U <= _q_l / (_q_l + _q_r) + accepted = np.where( + left, + np.where( + _t == 0, + True, + np.where( + raw_left > 0, + False, + V * _q_l * _q ** (_t - raw_left) * (1 - _q) + <= np.exp(cls._logprob(raw_left, _p, _lam)), + ), + ), + V * _b * (1 / np.sqrt(raw_right) - 1 / np.sqrt(raw_right + 1)) + <= np.exp(cls._logprob(raw_right, _p, _lam)), + ) + X = np.where(left, raw_left, raw_right) + + x[inds_to_sample[accepted]] = X[accepted] + n_to_accept[inds_to_sample[accepted]] = counter + inds_to_sample = inds_to_sample[~accepted] return x @classmethod @@ -257,18 +529,6 @@ def _inverse_rng_fn(cls, rng, theta, lam, dist_size, idxs_mask): below_cutpoint = log_s < log_u return x - @classmethod - def _branching_rng_fn(cls, rng, theta, lam, dist_size, idxs_mask): - lam_ = np.abs(lam) # This algorithm is only valid for positive lam - y = rng.poisson(theta, size=dist_size) - x = y.copy() - higher_than_zero = y > 0 - while np.any(higher_than_zero[idxs_mask]): - y = rng.poisson(lam_ * y) - x[higher_than_zero] = x[higher_than_zero] + y[higher_than_zero] - higher_than_zero = y > 0 - return x - generalized_poisson = GeneralizedPoissonRV() class GeneralizedPoisson(pm.distributions.Discrete): From d4182a006e95967169cb950ceedc0572e28ebf67 Mon Sep 17 00:00:00 2001 From: lucianopaz Date: Fri, 27 May 2022 22:43:14 +0200 Subject: [PATCH 5/9] Made some progress with abel rejection method --- notebooks/fast_gen_pois.ipynb | 157 +++++++++++++++++++++++++++------- notebooks/fast_gen_pois.py | 50 +++++++++-- 2 files changed, 166 insertions(+), 41 deletions(-) diff --git a/notebooks/fast_gen_pois.ipynb b/notebooks/fast_gen_pois.ipynb index 39c1cd7..2ea06a4 100644 --- a/notebooks/fast_gen_pois.ipynb +++ b/notebooks/fast_gen_pois.ipynb @@ -218,8 +218,7 @@ " q_r = b / np.sqrt(t + 1)\n", "\n", " rho_t = ( # Taken from page 250\n", - " 1\n", - " - p\n", + " 1 - p\n", " + np.log(p)\n", " - 0.5 * np.log(2 * np.pi)\n", " + (t - 1) * (np.log(lam * t + p) - np.log(t + 1))\n", @@ -230,8 +229,8 @@ " np.log(lam * t + p)\n", " - np.log(t + 1)\n", " + 1 - lam\n", - " + 1.5 / (t + 1)\n", - " - (lam + p) / (lam * t + p)\n", + " - (t + 0.5) / (t + 1)**2\n", + " - (t - 1) * lam / (lam * t + p)\n", " )\n", " q = np.exp(-rho_t_prime)\n", " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime)))\n", @@ -263,9 +262,9 @@ " _t == 0,\n", " True,\n", " np.where(\n", - " raw_left > 0,\n", + " raw_left < 0,\n", " False,\n", - " V * _q_l * _q ** (_t - raw_left) * (1 - _q)\n", + " V * _q_l * _q ** (raw_left - _t) * (1 - _q)\n", " <= np.exp(_logprob(raw_left, _p, _lam)),\n", " ),\n", " ),\n", @@ -290,9 +289,9 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_18920/3599282342.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_19712/3599282342.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", " poisson_idxs = np.broadcast_to(p >= np.maximum(3, 2 * lam / (1 - lam)), dist_size)\n", - "/tmp/ipykernel_18920/3599282342.py:7: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_19712/3599282342.py:7: RuntimeWarning: divide by zero encountered in true_divide\n", " (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))), dist_size,\n" ] } @@ -318,17 +317,19 @@ "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 5.6 s, sys: 182 ms, total: 5.79 s\n", - "Wall time: 5.82 s\n" + "CPU times: user 5.14 s, sys: 147 ms, total: 5.29 s\n", + "Wall time: 5.31 s\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_18920/442064969.py:53: RuntimeWarning: invalid value encountered in log\n", + "/tmp/ipykernel_19712/2183379971.py:52: RuntimeWarning: invalid value encountered in log\n", " raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q)))\n", - "/tmp/ipykernel_18920/1836048749.py:11: RuntimeWarning: invalid value encountered in log\n", + "/tmp/ipykernel_19712/2183379971.py:52: RuntimeWarning: divide by zero encountered in true_divide\n", + " raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q)))\n", + "/tmp/ipykernel_19712/1836048749.py:11: RuntimeWarning: invalid value encountered in log\n", " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" ] } @@ -370,13 +371,23 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_18920/3962287755.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", - " (p / (1 - lam)).flatten(), np.mean(samples, axis=0).flatten(), c=c, alpha=0.2, cmap=\"jet\"\n" + "/tmp/ipykernel_19712/1687800886.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + " (p / (1 - lam)).flatten(),\n" ] }, { "data": { - "image/png": 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\n", + "text/plain": [ + "Text(0.5, 0, 'Sample mean')" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", "text/plain": [ "
" ] @@ -389,14 +400,18 @@ ], "source": [ "plt.scatter(\n", - " (p / (1 - lam)).flatten(), np.mean(samples, axis=0).flatten(), c=c, alpha=0.2, cmap=\"jet\"\n", + " (p / (1 - lam)).flatten(),\n", + " np.mean(samples, axis=0).flatten(),\n", + " c=c,\n", + " alpha=0.2,\n", + " cmap=\"jet\",\n", ")\n", "ax = plt.gca()\n", "ax.set_xscale(\"log\")\n", "ax.set_yscale(\"log\")\n", "plt.plot(ax.get_xlim(), ax.get_ylim(), \"-k\", alpha=0.2)\n", "plt.xlabel(\"Expected mean\")\n", - "plt.xlabel(\"Sample mean\");" + "plt.xlabel(\"Sample mean\")" ] }, { @@ -409,13 +424,23 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_18920/623610949.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", - " (p / (1 - lam) ** 3).flatten(), np.var(samples, axis=0).flatten(), c=c, alpha=0.2, cmap=\"jet\"\n" + "/tmp/ipykernel_19712/816571136.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + " (p / (1 - lam) ** 3).flatten(),\n" ] }, { "data": { - "image/png": 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\n", + "text/plain": [ + "Text(0.5, 0, 'Sample variance')" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", "text/plain": [ "
" ] @@ -428,7 +453,11 @@ ], "source": [ "plt.scatter(\n", - " (p / (1 - lam) ** 3).flatten(), np.var(samples, axis=0).flatten(), c=c, alpha=0.2, cmap=\"jet\"\n", + " (p / (1 - lam) ** 3).flatten(),\n", + " np.var(samples, axis=0).flatten(),\n", + " c=c,\n", + " alpha=0.2,\n", + " cmap=\"jet\",\n", ")\n", "ax = plt.gca()\n", "ax.set_xscale(\"log\")\n", @@ -437,7 +466,7 @@ "ax = plt.gca()\n", "plt.plot(ax.get_xlim(), ax.get_ylim(), \"-k\", alpha=0.2)\n", "plt.xlabel(\"Expected variance\")\n", - "plt.xlabel(\"Sample variance\");" + "plt.xlabel(\"Sample variance\")" ] }, { @@ -527,6 +556,16 @@ "id": "d5124123-7aa5-4c4c-8f7a-da74d548cf6c", "metadata": {}, "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, { "data": { "image/png": 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\n", @@ -553,7 +592,7 @@ "samples = _rejection_region_poisson(np.random.default_rng(42), p, lam, 100000)\n", "y, edges = np.histogram(samples, bins=20, density=True)\n", "plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label=\"Sampled points\")\n", - "plt.legend();" + "plt.legend()" ] }, { @@ -578,9 +617,9 @@ " b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi)\n", " q_r = b / np.sqrt(t + 1)\n", "\n", + "\n", " rho_t = ( # Taken from page 250\n", - " 1\n", - " - p\n", + " 1 - p\n", " + np.log(p)\n", " - 0.5 * np.log(2 * np.pi)\n", " + (t - 1) * (np.log(lam * t + p) - np.log(t + 1))\n", @@ -591,13 +630,13 @@ " np.log(lam * t + p)\n", " - np.log(t + 1)\n", " + 1 - lam\n", - " + 1.5 / (t + 1)\n", - " - (lam + p) / (lam * t + p)\n", + " - (t + 0.5) / (t + 1)**2\n", + " - (t - 1) * lam / (lam * t + p)\n", " )\n", - " q = np.exp(-rho_t_prime)\n", + " q = np.where(t == 0, 0, np.exp(-rho_t_prime))\n", " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q))\n", " return np.where(\n", - " x <= t, q_l * (1 - q) * q ** (t - x), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", + " x <= t, q_l * (1 - q) * q ** (x - t), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", " )" ] }, @@ -611,15 +650,15 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_18920/1371467534.py:35: RuntimeWarning: divide by zero encountered in true_divide\n", - " x <= t, q_l * (1 - q) * q ** (t - x), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", - "/tmp/ipykernel_18920/1836048749.py:11: RuntimeWarning: invalid value encountered in log\n", + "/tmp/ipykernel_19712/2185118508.py:35: RuntimeWarning: divide by zero encountered in true_divide\n", + " x <= t, q_l * (1 - q) * q ** (x - t), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", + "/tmp/ipykernel_19712/1836048749.py:11: RuntimeWarning: invalid value encountered in log\n", " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" ] }, { "data": { - "image/png": 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\n", 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dO9Fa07p1awICAmjatOltx+7bt48jR45QqVIl2rdvz7Zt23j22WeZNm0aGzZswMvLiz179nDu3DkOHzYuraZfhyCv8tLiDwfSfy/zASLyFo7B6gux3ANHe0emdJrC0LpDCU5YSbdOG7l6K44HZm3ji42n7j7yp1Y3GLsZBnwFcdHw/UD4pgecWC2LvAiRjru7O3v27GHu3Ll4e3szZMiQtPl3NmzYQOvWrWnUqBHr16/nyJEjacfdf78xjLpRo0Y0bNiQihUr4uzsTI0aNTh71uiEqFKlCu3btwdg+PDhbN269bZz79ixg6NHj9K+fXv8/f1ZuHAhYWFhHD9+nOrVq1O7dm2UUgwfPjzL+Lt3746npyeurq4MGDCArVu3snXrVh588EHc3Nxwd3dnwIABbNmy5Y5jW7VqhY+PD3Z2dvj7+xMaGnrHPjVq1CAkJIRnnnmGP//8k1KlSt3T7zc7eWnx7wJqK6WqA+eAocDDVonKxuyUHa+3fp2yLmWZfWA27VvGoSMf4aM/j7P++EWmPeRPlbIlsinADho/BA36w95vYdtn8MNDxsIUHV807gTOyWyhQhSQ7Frm+cne3p7AwEACAwNp1KgRCxcuZOjQoTz11FPs3r2bKlWq8O677xIX9+8d86ldQ3Z2dmmvU9+nTt+c2TTL6Wmt6d69O4sXL75t+/79++/YNytZTeWcE+njTj/tdHplypThwIEDrF69mlmzZvHjjz8yb968HJV/NzkdzrkY2A7UVUqFK6We1FonAROA1cAx4Eet9ZHsyskpqy+2ngtKKcb7j+f11q/z9/nNxHt9yQcDq3P8/A16Td/Mj7vP3v0f2cEZWo2GZ/dB/9mQGAs/jYAZzWH7bOMbgRDFVFBQECdPnkx7v3//fqpVq5aW5L28vIiJiUlbCOVenDlzhu3btwOwePHi26ZgBmjTpg3btm0jODgYgFu3bnHixAnq1avH6dOnOXXqVNqxWVm7di1XrlwhNjaW5cuX0759ezp16sTy5cu5desWN2/eZNmyZXTs2DHHcZcsWTJtAZlLly6RkpLCwIED+c9//sPevXvv6XeQnRy1+LXWw7LYvgpYZbVoLPI8LbMVDas3jNLOpXl9y+scvTyCPl16EXSiEa8sPci6oxf5cEAjPN2dsy/E3hGaPgJNhsKxFbBzDqyeBOvfB/9h0GoseNcpmA8khEnExMTwzDPPcO3aNRwcHKhVqxZz586ldOnSjB49mkaNGuHr60vLli3vuez69euzcOFCxo4dS+3atRk/fvxtP/f29mbBggUMGzaM+HhjFN77779PnTp1mDt3Lvfddx9eXl506NAhrY89ow4dOvDoo48SHBzMww8/TIsWxmSYI0aMoFWrVgCMGjXqjv797IwZM4bevXtTsWJFpk+fzsiRI0mxDBL58MMP7/n3kJWiOy2zlZ24eoJFxxbxe8jvxCfHU8mlIWEhTXFLbsIng5rSpV75eyswYj/8MxcO/QTJCeDbEZoON7qBnLLpRhLCSorqtMyhoaH07ds3y4RtDQsWLGD37t23Lf5iK0VmWmZbXtzNSp0ydXiv3XusG7SOF5u/iHK4hmOl70mq/D7jVn7ECz9v4Wb8nf10WarkDw/MholHjfsAosONJR//r66xgEz4HrkYLITIF9Liz6XklGS2ntvKomM/sP3832htj3O8P6+2e5LBfh1yfIEojdYQ9jfs+w6OLIekWPCqC34DjYeX7bu9RNFSVFv8xU1uWvyS+K0gNDqU6f8s4K/w38EuDk/HGjzd/DH61bwPFweXey8w7joc/tnoBgr7G9DGiCC/gdBwgHHPgBB5dOzYMerVq3fvjRRhGlprjh8/XjQSf7qLu6PTX/U3uws3onlmxdccufEH9i4XKelYikF1BjKm8RjcndxzV+j1COMbwOGf4ZylEqzcHOr2gXr3gXc9uTlM5Mrp06cpWbIknp6ekvwLIa01ly9f5saNG1SvXv22nxXKxJ+qsLT4M/r9YASv//ErSe5bsHc/QkOvBszpNgcP5zwOT70aCkeWwdFfIWKfsa2Mr1EJ1O0DVduCfZFcYkHkg8TERMLDw28bIy8KFxcXF3x8fHB0vH0NcUn8NnLxehwvLz3I3xEbKeGzmJqlazKv11eUcSljnRNcj4ATf0LQHxCyCZLjwaU01OpqTBFRszOUqmSdcwkhChVJ/Daktea7HWF8uHE5DhUWUqGED4vvn4+Xq5d1TxQfA6fWG5VA8Dq4aZkM1bu+pSLoDFXbyTBRIYqJQpn4C2sff1aCI2MY//MSzrvMxs3ei8V951OjbJYTmeaN1nDxCJz6y6gMwrYb3wbsnaFqG/DtANXaG8tIOtzlxjMhRKFUKBN/qsLe4k8vMTmFN//4jd8j38dOuzOl3Wz61G+Q/ydOuAVn/oZTGyBkI1y03NRi7ww+LcG3vaUiaCnfCIQoIiTxm8xPh7bxn90TSU524oHy/+Ht3p1wdijACdtuXYEz2yF0G4RtgwsHQaeAnaOxsEyVVuDTyqgISlUsuLiEEFYjid+E9l44zKg1o4lPUFSMfZ5Zg3tTt0JJ2wQTFw1ndkLYVuOegfMHjCkkADyqGF1CqRVBxcbSPSREISCJ36ROXj3J46ue5EZ8IglnR/N8QACjO1bHwd7Gs2gkxcOFQ3D2HwjfBeG7IfqM8TN7J6jYBCo1hYr+xmvvejKEVAiTKZSJv6hd3M3K6ejTPLF6FNdibxJ9eiSNvf2YOrgJtcrl8mav/HL9vHHzWGpFcP4AJBjL1OHgAuUb/lsRVPI3RhM5FNyymUKI2xXKxJ+qKLf4U529cZZRq0dxJTaahHNPEBtThZd71OWJDtWxtzPp3ZQpKXDllDHD6Pn9RkVw/gDEXzd+bu8E5RpABT8o19CoGMo3BDcrD2MVQmRKEn8hcD7mPKPWjCIq9hLVk55l57HSNK9Whk8GNaaGt8la/1lJSYGrp42KIGK/URFcPAK3Lv27j3t5o0Ion64y8KoLjrmYz0gIkSVJ/IVE5K1IRq0ZxfmY8wyp+jbfbXAmLjGZV3rVY2Q7X+zM2vq/m5hIYwjpxaNGRRB5BKKCIMkyTYCyB89aUK6eUQl41wWv2uBZW4aXCpFLkvgLkcuxlxm9djRh0WG83WoKv20vzV/HI2nlW5aPBzXG18vN1iFaR3ISXAkxKoHUCiHquPGNQadYdlJQuopRGXjVMVYoS33t5mnT8IUwO1MlfqXUA8B9QDlgltZ6TXb7F7fED3At7hpj143l6OWjtKzQEh+HQJZtLUNSkiOv9a7Ho22qFd7W/90kxcPlU3ApCC6dNL4ZXAqCS8HG+gSpSngalYBnDShbA8rWtDzXAOdC0jUmRD6yWuJXSs0D+gKRWmu/dNt7AZ8B9sDXWuspOSirDDBVa/1kdvsVx8QPEJMQw6Jji1gevJzwmHBKOLhRIqEFYWF+tKzUmKmD/KlSthh1g6SkGENKb6sMThqVROq8RKncKxgVgFQKohizZuLvBMQA36YmfqWUPXAC6A6EA7uAYRiVQMaVgZ/QWkdajvs/YJHWOttl44tr4k+VolPYc3EPy04uY23YWuKS49AJFUiJbsnTrR5iXIcm5h35U1DibxjdRldCjIrgymljxFGmlUJ5oyIoUw1KV/v3uXRVYyZTuwK8g1qIfGTVrh6llC+wMl3ibwu8q7XuaXk/CUBrnely8MpY7WEKsFZrvS6LfcYAYwCqVq3aPCwsLMfxFWU3Em7wZ+if/Hj8F45fPYzWdrgnN+H51g8zqEE3HOzkJqo7ZFUpXDtjTGtNur99O0fw8MmkUrC8dvOWBW9EoZHfiX8Q0EtrPcry/lGgtdZ6QhbHPws8jvHNYL/Wek525yvuLf6snLx6kql/f8/fF9eAfQwl7MowpP6DDKj9IL4evrYOr3BIijcWuL8aCtfCjMrgapjx+mrY7cNQARxLGN8MSleFUpWNSiL1Uaqy8ZCb1oRJ5HfiHwz0zJD4W2mtn8lj0MXizt28On89hud/W8zBa2twcA8CpQn0CeTDjh/mfqlHYYiPgeizt1cG18KMbdHhcOtyhgMUuJf7tyLwqAIelgqilKWCcPMGOxtPySGKhbsl/rz2D4QDVdK99wEi8limyKGKpdz53/DRrD7Sjzd/28Z1p21sYj2P/zmCL7vPsf6CL8WJszuUq288MpNwy+guuh5uVATR54xK4fo5Y2hq8F+QePP2Y+wcjcqglA+UrGDMfloy3aNURePitNzQJvJZXlv8DhgXd7sC5zC6cB7WWh+xRnDS1ZNz0bGJ/Pf3Yyw9to4SVRbh7erFwt5fU6VUlbsfLKxPa4i9alQE0ZbKIe31Obhx3ngkZbLerWsZKFkp88qhZAXjQrSbt1yMFlmy5qiexUAg4AVcBN7RWn+jlOoDTMcYyTNPa/2BFYKWrp5c2hZ8iZd++43rHl/i6ujAnG5f0KJSY1uHJTKjNcRdMybBu5H+ceH2bTEX093YZqHsjVFKJSsYz+7l0j2ne+1WToaxFkOmuoHrXkmLP3duJSTx9qoN/HFpMnb2sTzd4H3Gte5l67BEbqUkG1NfpK8crlsqiBsREBNlVA63Lt1ZQQA4uqWrDLwtz+kqhvQVhqy3UCQUysQvLX7rWHfyBC9vnkCiXSQNHMcys/9IypWU/uMiKyXZuOgcc9HyiEz3sGy7aakkYq9mXoaLh1ERuJUzpsYo4WV0K7l5GXdMp732ghJlpbvJpApl4k8lLf68i7p5lWG/jeFCfBDq8gNM6jCKoS2rFN1pH0TOJMVbKoH0FUOkcdNb2utLxreIrCoJlJH80yoHqSjMolAmfmnxW1dcUhxPr32BfyK3EH+pC43dHuLDBxtTu7yNlnsUhUtykvFN4talfyuDm+lfR8HNy/++zlFF4WVcxC5RFlzLWrZ7/vs69dmltKzwlguFMvGnkha/9SSlJDF5+2SWBS+DG62JO9+f8QF1eKpzLVwcpRUmrCg5CWKvWCqE1MrhsvE+rfK4DLeuGPvdugIpiVmX5+KRoULwTPe6zJ2VhWvZYj+ld36P4xeFhIOdA++1ew8vVy++OvQVVTyS+HzDA6w8eJ73H/SjXU0Z8y+sxN7h34vFOaG1Mb1GaiUQewVuXc3w3vJ8M9KYqC/2yr/Lf2bGweXfbxCupY2HS2njW0ba63TPrmWM1y4exaI7ypQtfunqyV+Lji3io38+okZJPy6deoTwyzCouQ9v9KlPGTeZdkAUEknxRrdSxsohfeVx67KxT9w1iL1mPGd270R6zh7g6nFnpZBdheFa2jjOJHdmS1ePyNSfp/9k0tZJ+JasTmPHl/h+2zU8XB158776PNi0MkomJBNFVWLsv5VAZs8ZK4q056uQnJBNwQpcSt1eObh4pHukvi+VYbvl4eRutYkAJfGLLG2P2M7zG56ntHNpxjZ4g4UbFAfOXqdDLS8+eNCPap5FZMUvIaxBa6PSyGmFERd9+yPxVvblKztwTlcp9PsMKjfLVaiFMvFLV0/BOXL5CE+te4orcVco61KWik7+HD5ZmcSY2kwI8GNMQA2cHYp+n6cQ+S45EeKu31kpxF+/s5KIi4buk401qHOhUCb+VNLiLxjXE66zJXwLm8I3se3cNq4nXEdhT+JNXzx0Y17p9CADGjW1dZhCiBySxC/uSVJKEgeiDrA5fDN/nFrP+dhQAFwpT5+aXehVswvNyzXH0d7RtoEKIbIkiV/kScjVM3y4aRnbIrZg73oK7JJwc3SjbcW2dPLpRJ8afXC2l/ldhDATSfzCKkKiYnjj1738c2En5cqF4FgqiKvxUbSp2IYZXWbg4iBzAAlhFndL/OYYdJqBUqqfUmpudHS0rUMRFjW83fnhyY58dv8jJEcN5OyBF2jiMpqd53fy/MbnSch2mJsQwkykxS/u2Y24RKatPcHCv0Mp5b2XZM8f6eTTiemB06XvXwgTKJQtfmFuJV0ceadfQ1Y804HqLl2IO/8Am8M3M37tRBKzm3NFCGEKkvhFrjWs5MHP49oxucto1OUH2HlxEw/8+DTX4+5yS7wQwqYk8Ys8sbNTDGtVlQ1j3qSu48Ocid9OwPxxrDwYjpm7EYUozgos8Sul6iul5iilliqlxhfUeUXB8HR3ZunDkxhYfQxJJfbw0oY3GP7NDoIjb9g6NCFEBjlK/EqpeUqpSKXU4QzbeymlgpRSwUqp17IrQ2t9TGs9DngIyPKigyjc3u30DOMbP4Vj6b0cjPuaXtM38eGqY8TEJ9k6NCGERU5b/AuA21brVkrZA7OA3kADYJhSqoFSqpFSamWGRznLMfcDW4G/rPYJhOk81XQ8YxqPgZL/UKfhOr7cfIouUzfy6/5z0v0jhAnkKPFrrTcDVzJsbgUEa61DtNYJwBKgv9b6kNa6b4ZHpKWc37TW7YBHrPkhhPlM8J/AE35PcDbpLx7stotypZx5bsl+hszdwfEL120dnhDFWl5W4KoMnE33PhxondXOSqlAYADgDKzKZr8xwBiAqlWr5iE8YUtKKZ5v9jxJKUl8e/Rbhrd2Y1jKED5ZE8R9n2/l0TbVmNi9Dh6uMu5fiIKWl8Sf2YoBWX6P11pvBDberVCt9Vyl1Hmgn5OTU/NcRydsTinFSy1eIiklie+PfcdIPwfWv/A009adYOH2UFYejODVXvUY2MwHOztZ+EWIgpKXxB8OVEn33geIyFs4oqhRSvFaq9dISkli/uH5ONo58v4DzzC0ZVXe/vUwLy89yOJ/zjC5vx9+lT1sHa4QxUJehnPuAmorpaorpZyAocBv1ghKa71Caz3Gw0MSQVGglOKNNm8wsPZA5h6cy8x9M/Hx1Cwd146pg5tw5sot+s3cyhvLDnH1psz5I0R+y9FcPUqpxUAg4AVcBN7RWn+jlOoDTAfsgXla6w+sEpSswFUkpegU3tr2Fr+dMtoHZV3KUrN0Taq4+3I6wp3tQQ6UoBIvd2vBsFbVsJfuHyFyRaZlFqaSolPYcX4HJ6+e5NS1U4REhxByLYQbif/e6KWTXXDWlWjtU5/WPvWpWbomNT1qUsGtgiwCL0QOFMrELy3+4kVrTVRsFCHRIZy6eooNpw+x+9xxEu0vYOdwM20/H3cfZnSZQa0ytWwYrRDmVygTfypp8RdfsQnJzNl0ijlbDmLnHEmnhkkExS8jISWeGV1m0Ly8DPgSIiuFclpmWYhFuDrZM7F7Hda/cB9dqrdh9Y6axJ95ChflwZg1Y1gTusbWIQpRaJky8cuoHpGqcmlXZj3cjP+NaUNppwqEHBqJfVIVXtr0EouOLbJ1eEIUSqZM/EJk1LqGJyuf6cAH97cmIXw0iTfqM+WfKXyw/RNSdIqtwxOiUDFl4peuHpEZezvFI62rsenFHgyp+iaJV9uy5MS3DPnlWW4lxNs6PCEKDbm4KwqtExeuM2HV/3He/hecEuryYYep9Kjva+uwhLC5QnlxV4icqFOhFKtHvsuw6q+Q4HiS5zeP4bGFawm9dPPuBwtRjJky8UtXj8gppRSvd3qUmV1n4uJ6lb2Jk+k56yem/HFcFn8RIgvS1SOKjKOXjzJu7XhuxMdzPfRRyjrU5eWedRkks3+KYka6ekSx0cCzAT/ctwifUt541JhHaa/jvLL0IP1mbmVHyGVbhyeEaUjiF0WKT0kfvu39LfU963HRZS4PdzvL1ZsJDJ27g7Hf7SbssvT/CyGJXxQ5ZVzK8HWPrwmoEsCKc7Po2nEz47qUZcvJS3SbtokPfj9KdGyircMUwmZM2ccvk7QJa0hKSWLanmksPrYYFPSoch8xkZ1YtS+RMiWcmNi9DsNaVsHBXto/omiRSdpEsRcRE8G8w/NYdnIZSTqJtuW7cT6sHQdCXKhT3p037mtAQB1vW4cphNVI4hfCIupWFN8e/Zb/Bf2P2KRY/Eq350xIW85d9CKwrjdv3lefWuVK2jpMIfJMEr8QGVyLu8b3x77nh+M/cCPhBlVdm3EmuC23YqoyvHVVnu9WhzJuTrYOU4hck8QvRBZiEmJYErSE745+x5W4K3ja1yf8dDtck+vxXNc6PNbWFycH6f8XhY8kfiHuIjYplp9P/Mz8I/OJvBVJCe3L5fCO+Li04PXeDejeoLws+SgKFVPdwKWUclNK7VFK9S3I8wqRHVcHV4Y3GM4fA/7gnbbvULZkEq5VvuN66RmMXbKGR77eydGI67YOUwiryVHiV0rNU0pFKqUOZ9jeSykVpJQKVkq9loOiXgV+zE2gQuQ3J3snBtUZxIoHV/BO23dwLnGR0rU/43DMSu6bsYnXfj5I5I04W4cpRJ7lqKtHKdUJiAG+1Vr7WbbZAyeA7kA4sAsYBtgDH2Yo4gmgMeAFuACXtNYr73Ze6eoRtnTh5gUmb5/MlnNb8HKoR/iJfjjqcoztVJPRnapTwsnB1iEKkSmr9fErpXyBlekSf1vgXa11T8v7SQBa64xJP/X4DwA3oAEQCzyo9Z1LJymlxgBjAKpWrdo8LCwsR/EJkR+01qwIWcGUf6YQn5RAZT2Ag0cbUb6UKy/2qMvAZj7YywRwwmTys4+/MnA23ftwy7ZMaa3f0Fo/D/wAfJVZ0rfsNxd4D9jr5CRD6oRtKaW4v+b9LO+/nHaV2nJaL8a/9SI8S0fzytKD9J2xla0nL9k6TCHuSV4Sf2bNnLt+fdBaL7hbN48sti7MplyJcnze5XM+7PghUXFnuVjyvwzuGsz1uHiGf7OTEfP/IejCDVuHKUSO5CXxhwNV0r33ASLyFo5BFmIRZqSUom+Nvvz6wK90qNyBPyO+pmrDeYzv5s7esKv0/mwzk36RC8DC/PJydWoXUFspVR04BwwFHrZKVEKYmJerF9M7T+fP0D/5787/cuLqC4zpN5ZL59qyaOdZft0fwbiAmozqeOcF4BSdwuXYy5yLOUdETAQRNyM4F3MOZ3tnnm36LCUcS9joU4niJKejehYDgRijci4C72itv1FK9QGmY4zkmae1/sCawcmoHmF2l2Iv8d+d/2Vt2Fr8PP0Y13AS326NYkNIEGVKxdC+nh1lPW5y/maEkehjIkhISbitjLIuZbkWf43WFVozs+tMnOzl2pbIm0J5565MyywKm9Whq/lgxwdcjb96x8/sUtypUsqHup5VqexemUrulajkXonK7pWp6FaREo4lWB68nLe2vUXXql2ZGjAVBzsZKipyr1Am/lTS4heFyZW4K/xy8hfcHd2N5O5WiQOn7fh0bSjhV2MJrOvN633qU6d85jOALjq2iCn/TOH+mvfzn/b/wU7JPEEidwpl4pcWvyhK4pOS+fbvMGasP0lMfBJDWlZlYvfalCvpcse+cw7MYdb+WQyrN4xJrSbJHEEiVwpl4k8lLX5RlFy9mcCM9cF8tyMUR3s7xgXUZHTHGrg62afto7Xm/3b/HwuPLmR0o9E82+xZG0YsCitTTdImRHFWxs2Jt/s1YO3EAALqeDNt7QkCp27gp91nSU4xGmBKKV5s8SIDaw/kq0NfMf/wfBtHLYoiUyZ+GccvijJfLze+GN6cpePaUtHDlZeXHuS+z7ewMSgSrTVKKd5q8xa9fHsxbc80fgySeQ2FdUlXjxA2pLVm5cHzfLI6iDNXbtG+lieTetfHr7IHiSmJPL/hebaEb2FKxyn0qdHH1uGKQkL6+IUoBBKSUvhhZxifrw/mys0E+vtX4qUedfEuZcf4dePZF7mP6Z2nE1gl0NahikJAEr8Qhcj1uES+3HSKb7aeJiUFHm1bjZEdKvDy1qc5cfUEs7vNpnXF1rYOU5hcoUz8MpxTFHcXouP4dO0JftpzFjdnB57oWI6NN97j/M0Ivu7xNY29G+e67Oj4aEo4lsDRztGKEQszKZSJP5W0+EVxd+LiDT764zh/HY+kfJl4nKt8QbK6xbye86hbtu5dj09KSSL4WjD7I/dzIOoAB6IOcPbGWe6veT8fdLDqDCvCRCTxC1EE7Ai5zIerjnHw4mlK1ZiLm7Pih/u+xdfD97b9ouOjORB1gP2R+zkYdZCDlw4SmxQLGJPLNfFuQnxyPNvObWNZ/2XULF3TBp9G5DdJ/EIUEVprfj90ng/XbuJa6c9wtnfmteaTsXOOSkv2oddDAbBX9tQpUwf/cv408W6Cfzl/KrlVQinF1bir9Pq5Fx19OjI1YKptP5TIF5L4hShiEpJS+HTTer4/MwnsjLn/Szl60LS8f1qib+jZMNspnmfsm8Hcg3NZ2m9pjrqMROFSKBO/XNwV4u4OR55k9t8bWX/QmeR4Tx5tU51nutSijNvdp3WOjo+m98+9aVWxFdM7T8//YEWBKpSJP5W0+IW4u4wjgMYH1uSJ9tVxcbTP9rgvDnzB7P2z+V/f/9HAs0EBRSsKgszVI0QRV8HDhY8GNebP5zvRyrcsH/8ZROepG2+bAygzw+sPp5RTKWbvn12A0QozkMQvRBFRp3xJvhnRkiVj2lCupHPaHEAbLHMAZVTSqSQj/UayKXwTB6MO2iBiYSuS+IUoYtrU8GT50+2Z+XBTYhOTGTl/Fw9/tZMDZ6/dse+wesMo41xGWv3FTIElfqVUoFJqi1JqjlIqsKDOK0RxpJSib+NKrJ0YwLv9GhB08Qb9Z23j6UV7CYmKSdvPzdGNkX4j2RaxjX2R+2wYsShIOUr8Sql5SqlIpdThDNt7KaWClFLBSqnX7lKMBmIAFyA8d+EKIe6Fk4MdI9pXZ9PLgTzbpRYbgiLp/ulmXl92iMjrxlDQofWG4uniyax9s2wcrSgoORrVo5TqhJG0v9Va+1m22QMngO4YiXwXMAywBz7MUMQTwCWtdYpSqjwwTWv9yN3OK6N6hLCuqBvxzFh/kh92nsHR3o4nOvgyNqAmv4Ys4eNdHzOv5zxaVmhp6zBFHlllVI/WejNwJcPmVkCw1jpEa50ALAH6a60Paa37ZnhEaq1TLMddBZyzCXiMUmq3Ump3VFRUTsITQuSQd0lnJvf3468XA+jeoDyzNpyi08cbiIlsgberNzP3zcz0QrAoWvLSx18ZOJvufbhlW6aUUgOUUl8C3wEzs9pPaz1Xa91Ca93C29s7D+EJIbJSzdONz4c1ZeUzHWhU2YOP/gzh+vlO7I3cy98RO2wdnshneUn8KpNtWTYVtNa/aK3Haq2HaK03ZluwLL0oRIHwq+zBd0+25odRraloH0BKogfP/Plf1hy5IC3/IiwviT8cqJLuvQ8QkbdwhBC20K6WF789HcjAGiNIdAhl/C8/MHjOdnaFZuzhFUVBXhL/LqC2Uqq6UsoJGAr8Zo2gtNYrtNZjPDw8rFGcECIHlFK8Ffg4ld0rU6POVsKu3GTwnO2MWriLoAs3bB2esKKcDudcDGwH6iqlwpVST2qtk4AJwGrgGPCj1vqINYKSrh4hbMPRzpGxjcdyIe4k7w+z4+Weddl5+gq9PtvMiz8e4Ny1WFuHKKxAJmkTQtwmKSWJ/sv74+rgyo/9fiT6VhKzNwazcHsYAI+1qcbTnXM2C2huHbt8jONXjvNg7Qfz7RxFWaGcpE1a/ELYjoOdA+OajCPoahB/nfmLMm5OvHFfAza8FEj/JpWYt+00nT7ewMz1J7mVkJQvMTy08iHe/vvtfClbmDTxSx+/ELbVp3ofqntUZ/b+2SSnJANQubQrnwxuwp/Pd6JNTU+mrjlBwCcb+X5HGInJKXcpUZiJKRO/tPiFsC17O3ueavIUwdeCWRO25raf1Slfkq8ea8HScW3x9SzBm8sP0+PTzaw8GCFDQAsJUyZ+afELYXs9fHtQq3St21r96bXwLcuPY9vyzeMtcLK3Y8IP++g/axvbgi/ZIFpxL0yZ+IUQtmen7Hja/2lCr4ey6vSqTPdRStG1fnlWPdeRqYObcDkmgUe+3smj3+zkYPi1gg1Y5JgpE7909QhhDl2qdqFe2Xp8ceALklKyvpBrb6cY1NyHv14M4M376nP4XDT3z9zGU4v2EBwZk+VxwjZMmfilq0cIc0ht9Z+9cZYVp1bcdX8XR3tGdazB5lc681zX2mwKiqLHp5t4ZancA2Ampkz8QgjzCPAJoKFnQ748+CWJyYk5OqakiyMTu9dh8yudGdm+Osv3RdD5k41MXnGUyzHx+RzxvdFac+HmBWISis83E1MmfunqEcI8lFI85f8U52LOsTF84z0d6+nuzFt9G7Dh5UAeaFqJBX8b9wBMW3uCG3E5q0TyW1JKEt2Xdmfx8cW2DqXAmDLxS1ePEOZSu3RtgFy3iiuXduXjQU1YMzGAgLrefP7XSTp9vIGvNocQl3jniCGRv0yZ+IUQRVOtcu7MfqQ5KyZ0wK+yBx+sOkbgJxtZ/M8ZkuQmsAIjiV8IUeAa+RjrACwe3YaKpV2Y9MshultuAktJkZvA8puDrQMQQhRfbWt68sv4dqw7FsnU1UFM+GEfDSudAunlzVembPHLxV0hig+lFN0bGDeBfTqkCdfTXfTdEyYLweQHUyZ+ubgrRPFjb6d4sKkPf70QmLZt4BfbeXLBLo6dv267wIogUyZ+IUTx5eTwb1p6uWdddoVeoc/nW3huyT7CLt+0YWRFhyR+IUSOaQr2wuvTnWux5ZUujAuoyeojF+j6f5t4c/khIq/HWe0cBf2ZzEASvxDirpRSNju3RwlHXu1Vj80vd2ZYq6os+ecsnT7ZwJQ/jnPtVoLVzmPLz1jQCizxK6XslFIfKKVmKKUeL6jzCiGKhnKlXPjPA3789WIAvRpW4MvNp+j48QZmbQjOt5XAiqqcLrY+TykVqZQ6nGF7L6VUkFIqWCn12l2K6Q9UBhKB8NyFK4Qo7qp5ujF9aFP+eK4jrauX5ZPVQXT6eCML/w4lIUluAsuJnLb4FwC90m9QStkDs4DeQANgmFKqgVKqkVJqZYZHOaAusF1r/QIw3nofQQhRHNWrUIqvH2/Jz+PbUtPbjXd+O0KX/9vIz3vCSZabwLKVo8Svtd4MZBxQ2woI1lqHaK0TgCVAf631Ia113wyPSIxW/lXLsTI5hxDCKppXK8uSMW1Y+EQrSpdw5MWfDtBr+mb+OHReloLMQl76+CsDZ9O9D7dsy8ovQE+l1Axgc1Y7KaXGKKV2K6V2R0VF5SE8IURxoZQioI43vz3dgdmPNCNFa8Yv2sv9M7exMShSKoAM8jJlQ2aXwLP87WqtbwFP3q1QrfVcpdR5oJ+Tk1PzPMQnhChm7OwUfRpVpGfDCizbd47p604wYv4uWvqW4aUedWldw9PWIZpCXlr84UCVdO99gIi8hSOEMLPC0nJOXQpy/YuB/OcBP8Iu32LI3B2ZrgUs4/jvzS6gtlKqulLKCRgK/GaNoGTKBiGENTg52PFom2pserkzr/epl7YW8NjvdnPi4g1bh2czOR3OuRjYDtRVSoUrpZ7UWicBE4DVwDHgR631EWsEJZO0CSGsydXJnjGdarL5lc5M7FaHbcGX6Tl9M88v2UfYpeI3DUSO+vi11sOy2L4KWGXViIxyVwArWrRoMdraZQshiq+SLo481602j7WtxpzNp1j4dygrDp2hRB24EVd8bgIz5ZQN0uIXQuSnMm5OTOpd35gGoqVxqXLu5hAmrzjKJZMtBp8fTJn4pY9fCFEQypVy4a1+DQFoULFk2mLwn6w+TvQtcywGnx9MmfilxS+EKGi9G1Vk7QsBdKlXjlkbTtHx4/XM2hDMzfii1wVkysQvLX4hhC3U9HZn5sPNWPVsR1pZ5gEK+GQD87aeJi6x6Ew4YMrEL4Qwp6I45j2zexMaVDLmAfrlqXbUKV+SySuP0nnqRhb/c4bE5MI/EZwpE7909QhhLirTG/WLlsw+Y7OqZfhhdBsWjWpN+VIuTPrlEN2nbeLX/edIKcQTwZky8UtXjxDCTNrX8mLZU+34+rEWuDja89yS/fT+bAurj1woNHczp2fKxC+EEGajlKJbg/KserYjM4Y1JTE5hbHf7eGBWdvYfCKqUFUApkz80tUjhDArOztFvyaVWDOxEx8PbMylmAQem/cPQ+fuYHdoxtnrzcmUiV+6eoQQZudgb8dDLauw/qUA3ru/IaeibjJoznZGzP+Hw+fM3Wg1ZeIXQojCwtnBnsfb+bL5lUBe7VWPfWeu0XfGVsZ/v4fgSHNOBCeJXwghrKCEkwPjA2uy5dXOPNu1NptPRNHj08288L/9hF0210RwkviFEDlWJMfxW/kzlXJx5IXuddjyahdGd6zBqsPn6fJ/m5j0y0HOXYu16rlyy5SJXy7uCmEuShWDcfxW/oxl3ZyY1MeYCG5466os3RNO50828u5vR4i8EWfVc90rUyZ+ubgrhCgqypVy4b3+fmx4KZABzSrz3Y4wOn28gQ//OMbVmwk2icmUiV8IIYoanzIlmDKwMX+9EEBvv4rM3RxCx483MG3tCa7HFexMoJL4hRCiAPl6ufHpEH/WPN+JTnW8+Pyvk3T8aEOBzgQqiV8IIWygdvmSzH6kOSuf6UCLamX4ZHUQnT7ewNdbQvJ9JlBJ/EIIYUN+lT34ZoQxE2j9iqV4//djBHyyIV/vAs7RmrvWoJTqCDxiOWcDrXW7gjq3EEKYXbOqZfh+VGu2n7rM7I3B+Hq55du5cpT4lVLzgL5ApNbaL932XsBngD3wtdZ6SlZlaK23AFuUUg8Au/IStBDCNgrTRGQ5ZbbP1LamJ21reubrOXLa4l8AzAS+Td2glLIHZgHdgXBgl1LqN4xK4MMMxz+htY60vH4YGJWHmIUQBay4zsdfVOUo8WutNyulfDNsbgUEa61DAJRSS4D+WusPMb4d3EEpVRWI1lpfz+pcSqkxwBiAqlWr5iQ8IYQQ9yAvF3crA2fTvQ+3bMvOk8D87HbQWs8F3gP2Ojk55SE8IYQQmclL4s/se1G2nWVa63e01n/frWC5c1cIIfJPXhJ/OFAl3XsfICJv4Rhkrh4hhMg/eUn8u4DaSqnqSiknYCjwm3XCEkIIkV9ylPiVUouB7UBdpVS4UupJrXUSMAFYDRwDftRaH7FGUNLVI4QQ+Seno3qGZbF9FbDKqhFhdPUA/WrVqmXtooUQothTZrt5IT2lVBQQlsvDvYBLVgzHmswcG5g7PjPHBuaOT2LLPTPHl1ls1bTW3lkdYOrEnxdKqd1a6xa2jiMzZo4NzB2fmWMDc8cnseWemePLTWwySZsQQhQzkviFEKKYKcqJf66tA8iGmWMDc8dn5tjA3PFJbLln5vjuObYi28cvhBAic0W5xS+EECITkviFEKKYKZKJXynVSykVpJQKVkq9ZuNY5imlIpVSh9NtK6uUWquUOml5LmOj2KoopTYopY4ppY4opZ4zWXwuSql/lFIHLPG9Z6b4LLHYK6X2KaVWmik2pVSoUuqQUmq/Umq3mWKzxFJaKbVUKXXc8vfX1gzxKaXqWn5nqY/rSqnnzRCbJb6Jlv8Lh5VSiy3/R+45tiKX+NMtENMbaAAMU0o1sGFIC4BeGba9Bvylta4N/GV5bwtJwIta6/pAG+Bpy+/KLPHFA1201k0Af6CXUqqNieIDeA5jypJUZoqts9baP90YbzPF9hnwp9a6HtAE43do8/i01kGW35k/0By4BSwzQ2xKqcrAs0ALy0qI9hhzpN17bFrrIvUA2gKr072fBEyycUy+wOF074OAipbXFYEgW//eLLH8irGimuniA0oAe4HWZokPY0bav4AuwEoz/dsCoYBXhm1mia0UcBrL4BKzxZcunh7ANrPExr9roJTFmG5npSXGe46tyLX4yd0CMQWtvNb6PIDluZyN48GywlpTYCcmis/SlbIfiATWaq3NFN904BUgJd02s8SmgTVKqT2WVe3MFFsNIAqYb+km+1op5Wai+FINBRZbXts8Nq31OWAqcAY4j7Ga4ZrcxFYUE/89LxBT3Cml3IGfged1Nsti2oLWOlkbX7t9gFZKKT8bhwSAUqovEKm13mPrWLLQXmvdDKPL82mlVCdbB5SOA9AM+EJr3RS4iW27ne5gmWr+fuAnW8eSytJ33x+oDlQC3JRSw3NTVlFM/Pm2QIwVXVRKVQSwPEfeZf98o5RyxEj6i7TWv5gtvlRa62vARozrJWaIrz1wv1IqFFgCdFFKfW+S2NBaR1ieIzH6qFuZJTaM/6Phlm9vAEsxKgKzxAdGhblXa33R8t4MsXUDTmuto7TWicAvQLvcxFYUE39hWCDmN+Bxy+vHMfrWC5xSSgHfAMe01tPS/cgs8XkrpUpbXrti/OEfN0N8WutJWmsfrbUvxt/Yeq31cDPEppRyU0qVTH2N0Q982AyxAWitLwBnlVJ1LZu6AkcxSXwWw/i3mwfMEdsZoI1SqoTl/25XjIvi9x6bLS+e5ONFkD7ACeAU8IaNY1mM0R+XiNHSeRLwxLgoeNLyXNZGsXXA6AY7COy3PPqYKL7GwD5LfIeBty3bTRFfujgD+ffirs1jw+hDP2B5HEn9P2CG2NLF6A/stvzbLgfKmCU+jIEElwGPdNvMEtt7GI2fw8B3gHNuYpMpG4QQopgpil09QgghsiGJXwghihlJ/EIIUcxI4hdCiGJGEr8QQhQzkviFEKKYkcQvhBDFzP8DBJtJbltPP4AAAAAASUVORK5CYII=\n", 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" ] @@ -642,6 +681,58 @@ "plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label=\"Sampled points\")\n", "plt.legend();" ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "9eabb346-8c37-4d74-a544-64c7a4eaad52", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_19712/2185118508.py:35: RuntimeWarning: divide by zero encountered in true_divide\n", + " x <= t, q_l * (1 - q) * q ** (x - t), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", + "/tmp/ipykernel_19712/1836048749.py:11: RuntimeWarning: invalid value encountered in log\n", + " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" + ] + }, + { + "data": { + "image/png": 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RBlPgB0IGBr5aOiINpsAPApuJJ20Tv7pq6YgcNQV+IGTiDD/Rw9cqHZGjpsAPgkzs4aulI9JgCvxAyMDANwp8kYZS4AdBJl7xSi0dkQZT4AdCBs7wQ7UnbRX4IkcrmFsrPDsGvlvvvm5eJTRr7b5uJvbwId7WWT4Xvv3Ufe0+4+AHF7qvK9IEwQz81l0gu7n7uhVLYO8293UzcYYPcOpl8bDf8ZXbulu+iL9X4EuaCWbgj/hf/tT980Co2u2+biauwwf48eP+1J12ltb/S1pSD99TBn9m2xk6w/dLKKLAl7SkwPeSMT7lvQLfqXCWAl/SkgLfU37N8MWpUFirgyQtKfC9ZMCXwM/Edfh+UktH0lRKBr4xZpQxZlpFRYXfQ2kg41N7Rc8qnFLgS5pKycC31s6z1l5TUFDg91AayKcZtnr4binwJU2lZOCnLaMZfkYIhRX4kpYU+J7y6aStZvhuaYYvaUqB7yWDzzN8nbR1IqRlmZKeFPie0gw/I2iGL2lKge8l9fAzg9bhS5pS4Hsq0VKJxdyWrVuH77ZsxtIMX9KUAt9TicR1flEO9fCdUuBLmlLge6k2b10/3VcP361QBGoU+JJ+FPieqm3puA4DBb5TWocvaUqB7yXjU0tHM3y3tFumpKlgXgDFN7UzfPXwAy0UgZpKeKiP+9rNWsEVf4WcFu5rS9pT4HvJ+BT4muG71fMiqChz/3Ou2AgbFsVrt+3htrYEggI/GdTDD7Z2PeGiJ9zXXTEvHvg11e5rSyAo8D2VmOGvewuat3ZXdsvqA8pLQIWy4u9jCnxpHAW+l8KJ/5AvXuO+9nFtwejHGWjhxM9XS0KlkZQQXmrWGk7oAxf80n3tZfdDdnP3dcUdzfCliRT4HqqsjvHld5aJC9zX/iIUo2Oh4y0dxK3aZ5Dq4UsjKfA9VLGvmm27q9hUXUl22F1DfV91jG05VRTm5zirKT6om+GrpSONo8D3kE0sj5w9uT9tWrgL37Lv9nDOHIjGtFon0Op6+JrhS+PolbYeql0Onx12+20tyIvP/KI1aukEmnr40kSa4Xsolkj8rIjb9ZH5ORGMMVRGY2zctsdpbYB2LXPJjmjukHTq4UsTKfA95NcM3xhDVtiwacc+hv7vhU5rA5x3ynH8cfzpzutmnFDiv6t6+NJICnwPWSzGQDjk/hVQ3dq1YE9VDRMHnOq07p/eWss3Ffuc1sxYmuFLEynwPRSzYDAY4z7wm+dEaJ4T4dLT2zut++ryb/l6+16nNTOWevjSRGq8esha8GFy76ucrBCVUV3f1Ym6Gb5aOtI4muF7KGatL7N7P+VEQlRGtTrIidoe/nfroGyJ+/rtekJWnvu64hkFvoes/fcOyZlCge9QVh6Es+H9x+Nvrg24Fs67z31d8YwC30M2I2f4YaoU+G5EcmDKQtj5jfvaL98Ae7a5ryueCmTgf7JxO3ur3feVq2pivvbwV21bxaRXJzmtuWHXHqqadQeGO62bsY47Jf7mWm4B1FS5ryueCmTg3/L8x6wp3+28bt5J1eTn+vMtPb/4fF/qbo+ux+TvzchnNxkllKXloAEQyMC/f8ypvszw/88/55CXHXZeF2BM1zGM6TrGed3hz13Gxl17qK6xZDt+hbE4FM7SDD8AAhn4fU861pe6f/oiy5e6fgolZvU9p76KcXzJrfzcCPNvGMIJx2jlSNKFsxX4ARDIwBd3CvOzqYnF+FFxsdO6X323l5c/+Zqy7/Yq8F0Iq6UTBAp8aZKscIj2xzbjthHdndb9YN02Xv7ka6q1Q6gb4WyI7vB7FNJEeqWtpKXa3Tm1JNQRtXQCQYEvaSkrcUWxKs3w3VBLJxAU+JKWaregVkvHEa3SCQQFvqSlLAW+W2rpBIKzk7bGmGLg10CBtfZSV3Ul+fx4hW9VNEbeSd/xfvkFXMTPnNbOSGrpBMJRBb4xZjowEthsrT1lv9tHAA8BYeApa+29hzuGtXYtcJUxZm7ThiypxK9X+BoD4dxv+HT7m6DAT75wNuzaBI/2c1+7xfEw/r/+vT20NNrRzvBnAo8Cs2tvMMaEgceAc4Ay4ENjzMvEw/+eg75+srV2c5NHKynHr1f4Vuyp5oyZl2CbOy+dmXqPTWyeZt3W/W49rPsH7C6Hlie4rR1ARxX41tq3jDFFB93cH1idmLljjHkOGG2tvYf4s4FGMcZcA1wDcNJJJzX2MBJwtReKr71wvCRZh/7xN9c+/r/w0s8hWum+dgA15aTticDG/T4uS9xWL2NMa2PME0BfY8wdh7uftXaatbbEWlvSpk2bJgxPgqx2lY7yPuDC2fH3On/giaactK1v45TD/vez1m4Frm1CPZE64ZDBGNi+t4p7XlnhvP7wnsdx+sn+7NmUUeoCXzN8LzQl8MuADvt93B74umnDETk6xhjycyLsrqph1qL1TmtXRmOs3bKbP11R4rRuRorkxN9HtSTUC00J/A+BLsaYjsBXwGXAOE9GJXIUep5QAMCMa89zWvfHj72rLR1cqbtwuwLfC0fVwzfGzAEWAd2MMWXGmKustVHgeuA1YAXwvLX2s+QNVSQ1ZIWNXvDlSjgxw1dLxxNHu0rn8sPc/grwiqcjAowxo4BRnTt39vrQIk2WFQ4p8F1RS8dTKbm1grV2nrX2moKCAr+HInKIrHCIqhotD3JCLR1PpWTgi6SyrHCIavXw3VBLx1O6AIqkNT/28fmCnZDVFxjqtG5GiiSWZW7fCFu+cFzcQKtiCAVnXqzAl7Tl1z4+u9kIWTW+1M442S3i7xdMjb+59sPfwJm/dF83SRT4krb82sfnzD+PYYeNOq+bkfLbwBUvx/fScW3eTbDzW/d1k0iBL9JAxhis603EMlnxMH/qvv4/A7eHT3CaUyKOhICY8j74IjkKfBeMMaOMMdMqKir8HorIIYwxWO3aFnyRnMCtDkrJlo61dh4wr6SkZIrfYxE5mDHxXTq/3r7Xee3mOREK8nQhECcCOMNPycAXSWVhY4hZy6B733BeOytseO/2s2nTIsd57YwTzoHoPr9H4SkFvkgDtWuZS3YkxIR+vZzW/fSrCp55fwNbd1cq8F2I5ARuSwcFvkgDRcKGNi1yGNvP7RXZWjXfxDPvbyCqbR3ciOQkLusYHCl50lZEDhUJx685VKWN29yI5AZuDx/N8EXSRO1lHbWPjyORHNi6Gp4e7r52n3Fw+kTPD6vAF0kTWYnAj+pFAG6ccins2eq+7lfLYPkLmRP42g9f5FBq6TjW/fz4m2uzLkza6qCU7OFrP3yRQ6mlkyEiuUkL/JSc4YukOj+2Zd5TVUPeSdt5d/OFDO95tdPa4lASX/CVkjN8kVR2fvH5dGvVzXldYyCc+w0fbXX/gi9xKCsPqpPzKm7N8EUayK9tmTdu28Pw5y7DtnBeWlzSDF9Eak/aao1OwCWxh6/AF0kTtcsytVNnwOmkrYjUBv6eqhre/sL9FaBO7XAMLXO1U2fS1Qa+tfETN14e2tOjiUjS5GaFCBnDph37mPD0B87rXzHwZO4afYrzuhknktgYr6bq3//26tCeHs0jeuGVyKFyImFObX8MVTUxbj9/oNPaN8xZxo691U5rZqwzfgH9p0A42/NDp2Tg6wIoIvXLyQqRkxWipKiV07rNcyJUa5dON7KbJe3QOmkrIkeUFQ5pS4cAUOCLyBFlhw1RBX7aU+CLyBFFwiG1dAJAgS8iR5QVNlRrhp/2FPgickRZ4ZACPwBScpWOiByeHzt1rgnvJDt0OjDYaV3xlgJfJI2cX+zDBTmAPWYDlRHN8NNdIAP/vg/uY+W2lc7rrtq2ypdtcyVz+LVT55DZY9hD1Hld8ZZ6+B7q1qqbbzMwkWQyxLd2kfQWyBn+bf1v83sIIoFijHbpDIKUDHztpSOSWkLGUBOzLFy12XntNvk5nHKirm/thZQMfO2lI5JaIiFDNGaZNOND57VDBpb9djgFedqaualSMvBFJLWceGwexzbP5lcjBzmtu2DFJh5buIbdlVEFvgcU+CJyRCFjyM+J0PekY53WXVO+G4CotnXwhFbpiEjKykpcx1c7dXpDgS8iKSs7cVnHaEyB7wUFvoikrEgi8Kujaul4QYEvIilLLR1v6aStiBwVPzZtq9hbTdYxxURrznBaN6gU+CJyRH5tGVK2ew2Rljt08RWPKPBF5Ij82rRtzF8nsHxHBdU6aesJ9fBFJGWZxPvqqALfCwp8EUlZxsQjPxpTS8cLCnwRSVmJvNflFT2Skj187ZYpIhDf0gFg2Ybt5GaFndY2wIDi1oHawyclA1+7ZYoIQDhkMMYw8731zHxvvfP6vyjtxK0jujuvmywpGfgiIhDflrlvh2P41eghzmtfPu19dlUG67KOCnwRSWnZkRA9T3B/AZTcrHDg1v/rpK2ISD2ywqHAnSxW4IuI1CMrbBT4IiKZICscCtyFV9TDF5GU5sembQDbCirYGB0EnOa8drIo8EUkZfm1aRtANFxGuX3ft/rJoMAXkZTl16ZtAP2nX4I1wWrpqIcvIlIPYyBYca/AFxGplzFgbbAiX4EvIlKPEIagbdKpwBcRqUd8hu/3KLylk7YiIvUwJv7Cq5nvrnNee3DnQrq0a+H5cRX4IiL1yInEt1a4c97nzmv/sHtbpk/s5/lxFfgiIvU4qVUzTijI4+Erz3Fad/KsD9lbVZOUY6dk4OsCKCKSCiJhw7HNs53WzMsKU5Wka/im5Elba+08a+01BQXut0QVEfFTMnfpTMnAFxHJVPHAT87yIAW+iEgKSea2zAp8EZEUksyWTkqetBURSQV+bM28JrqLvdmnAmd5fmwFvohIPfzamnlnbAOxvOqkHFuBLyJSD7+2Zi595idstVVJObZ6+CIiKSSUxE18FPgiIinEGJK2S6cCX0QkhRjAJunSKwp8EZEUYozBWqhJwjRfgS8ikkKywyHyssNEY96vxdcqHRGRFNK2ZQ5tW+aQEwl7fmzN8EVEMoQCX0QkQyjwRUQyhAJfRCRDKPBFRDKEVumIiKSQ7q26J+3YCnwRkRRyW//bknZstXRERDKEAl9EJEMo8EVEMoQCX0QkQyjwRUQyREoGvjFmlDFmWkVFhd9DEREJjJQMfGvtPGvtNQUFBX4PRUQkMFIy8EVExHvGJuliuV4wxpQDXzbyywuBLR4OJx3oMWeGTHvMmfZ4oWmP+WRrbZv6PpHSgd8Uxpgl1toSv8fhkh5zZsi0x5xpjxeS95jV0hERyRAKfBGRDBHkwJ/m9wB8oMecGTLtMWfa44UkPebA9vBFRORAQZ7hi4jIfhT4IiIZInCBb4wZYYxZZYxZbYy53e/xJJsxpoMxZqExZoUx5jNjzH/4PSZXjDFhY8wyY8x8v8figjHmGGPMXGPMysTPe6DfY0o2Y8zNid/r5caYOcaYXL/H5DVjzHRjzGZjzPL9bmtljPm7MeaLxPtjvagVqMA3xoSBx4DzgB8AlxtjfuDvqJIuCvwPa20P4Azgugx4zLX+A1jh9yAcegh41VrbHTiVgD92Y8yJwI1AibX2FCAMXObvqJJiJjDioNtuB/7bWtsF+O/Ex00WqMAH+gOrrbVrrbVVwHPAaJ/HlFTW2m+stR8l/r2TeAic6O+oks8Y0x64AHjK77G4YIxpCZwJPA1gra2y1m73dVBuRIA8Y0wEaAZ87fN4PGetfQvYdtDNo4FZiX/PAn7sRa2gBf6JwMb9Pi4jA8KvljGmCOgLLPZ5KC48CNwKxHwehyvFQDkwI9HGesoY09zvQSWTtfYr4H5gA/ANUGGtfd3fUTnTzlr7DcQndUBbLw4atMA39dyWEetOjTH5wH8BN1lrd/g9nmQyxowENltrl/o9FociwGnAH621fYHdePQ0P1Ul+tajgY7ACUBzY8x4f0eV3oIW+GVAh/0+bk8AnwIezBiTRTzsn7XWvuD3eBwYDFxojFlPvG33Q2PMM/4OKenKgDJrbe2zt7nE/wAE2Y+AddbacmttNfACMMjnMbmyyRhzPEDi/WYvDhq0wP8Q6GKM6WiMySZ+gudln8eUVMYYQ7yvu8Ja+4Df43HBWnuHtba9tbaI+M/4DWttoGd+1tpvgY3GmG6Jm84GPvdxSC5sAM4wxjRL/J6fTcBPVO/nZeDKxL+vBP7qxUEjXhwkVVhro8aY64HXiJ/Rn26t/cznYSXbYGAC8Kkx5uPEbb+y1r7i35AkSW4Ank1MZtYCk3weT1JZaxcbY+YCHxFfjbaMAG6zYIyZA5QChcaYMmAqcC/wvDHmKuJ/+MZ4UktbK4iIZIagtXREROQwFPgiIhlCgS8ikiEU+CIiGUKBLyKSIRT4IiIZQoEvIpIh/j9DnvQOKKvv1wAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "p, lam = 2.1209508879201904, 0.5510204081632653\n", + "mean = p / (1 - lam)\n", + "std = np.sqrt(p / (1 - lam) ** 3)\n", + "x = np.linspace(0, 10, 1000)\n", + "plt.semilogy(x, np.exp(_logprob(np.floor(x), p, lam)), label=\"PDF\")\n", + "plt.plot(x, abel_rejection_envelope(np.floor(x), p, lam), label=\"Envelope\")\n", + "samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000)\n", + "u, c = np.unique(samples, return_counts=True)\n", + "edges = np.arange(11)\n", + "y = np.array([np.sum(c[u == e]) for e in edges])\n", + "plt.step(edges, y / samples.size, label=\"Sampled points\", where=\"post\")\n", + "plt.legend();" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2c020ad3-7b8d-47f8-aebb-5ec2b37fd556", + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/notebooks/fast_gen_pois.py b/notebooks/fast_gen_pois.py index d09b27d..afad32c 100644 --- a/notebooks/fast_gen_pois.py +++ b/notebooks/fast_gen_pois.py @@ -216,7 +216,12 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): + (1 - lam) * t ) rho_t_prime = ( - np.log(lam * t + p) - np.log(t + 1) + 1 - lam + 1.5 / (t + 1) - (lam + p) / (lam * t + p) + np.log(lam * t + p) + - np.log(t + 1) + + 1 + - lam + - (t + 0.5) / (t + 1) ** 2 + - (t - 1) * lam / (lam * t + p) ) q = np.exp(-rho_t_prime) q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime))) @@ -248,9 +253,9 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): _t == 0, True, np.where( - raw_left > 0, + raw_left < 0, False, - V * _q_l * _q ** (_t - raw_left) * (1 - _q) + V * _q_l * _q ** (raw_left - _t) * (1 - _q) <= np.exp(_logprob(raw_left, _p, _lam)), ), ), @@ -305,7 +310,11 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): # %% plt.scatter( - (p / (1 - lam)).flatten(), np.mean(samples, axis=0).flatten(), c=c, alpha=0.2, cmap="jet" + (p / (1 - lam)).flatten(), + np.mean(samples, axis=0).flatten(), + c=c, + alpha=0.2, + cmap="jet", ) ax = plt.gca() ax.set_xscale("log") @@ -316,7 +325,11 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): # %% plt.scatter( - (p / (1 - lam) ** 3).flatten(), np.var(samples, axis=0).flatten(), c=c, alpha=0.2, cmap="jet" + (p / (1 - lam) ** 3).flatten(), + np.var(samples, axis=0).flatten(), + c=c, + alpha=0.2, + cmap="jet", ) ax = plt.gca() ax.set_xscale("log") @@ -429,13 +442,18 @@ def abel_rejection_envelope(x, p, lam): + (1 - lam) * t ) rho_t_prime = ( - np.log(lam * t + p) - np.log(t + 1) + 1 - lam + 1.5 / (t + 1) - (lam + p) / (lam * t + p) + np.log(lam * t + p) + - np.log(t + 1) + + 1 + - lam + - (t + 0.5) / (t + 1) ** 2 + - (t - 1) * lam / (lam * t + p) ) - q = np.exp(-rho_t_prime) + q = np.where(t == 0, 0, np.exp(-rho_t_prime)) q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q)) return np.where( x <= t, - q_l * (1 - q) * q ** (t - x), + q_l * (1 - q) * q ** (x - t), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)), ) @@ -451,3 +469,19 @@ def abel_rejection_envelope(x, p, lam): y, edges = np.histogram(samples, bins=20, density=True) plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label="Sampled points") plt.legend() + +# %% +p, lam = 2.1209508879201904, 0.5510204081632653 +mean = p / (1 - lam) +std = np.sqrt(p / (1 - lam) ** 3) +x = np.linspace(0, 10, 1000) +plt.semilogy(x, np.exp(_logprob(np.floor(x), p, lam)), label="PDF") +plt.plot(x, abel_rejection_envelope(np.floor(x), p, lam), label="Envelope") +samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000) +u, c = np.unique(samples, return_counts=True) +edges = np.arange(11) +y = np.array([np.sum(c[u == e]) for e in edges]) +plt.step(edges, y / samples.size, label="Sampled points", where="post") +plt.legend() + +# %% From cf7321faa5e0669258e5650b7f0cb63eb438b68e Mon Sep 17 00:00:00 2001 From: lucianopaz Date: Fri, 27 May 2022 22:43:40 +0200 Subject: [PATCH 6/9] Made some progress with abel rejection method --- notebooks/fast_gen_pois.ipynb | 17 ++++++++++------- 1 file changed, 10 insertions(+), 7 deletions(-) diff --git a/notebooks/fast_gen_pois.ipynb b/notebooks/fast_gen_pois.ipynb index 2ea06a4..99cf876 100644 --- a/notebooks/fast_gen_pois.ipynb +++ b/notebooks/fast_gen_pois.ipynb @@ -218,7 +218,8 @@ " q_r = b / np.sqrt(t + 1)\n", "\n", " rho_t = ( # Taken from page 250\n", - " 1 - p\n", + " 1\n", + " - p\n", " + np.log(p)\n", " - 0.5 * np.log(2 * np.pi)\n", " + (t - 1) * (np.log(lam * t + p) - np.log(t + 1))\n", @@ -228,8 +229,9 @@ " rho_t_prime = (\n", " np.log(lam * t + p)\n", " - np.log(t + 1)\n", - " + 1 - lam\n", - " - (t + 0.5) / (t + 1)**2\n", + " + 1\n", + " - lam\n", + " - (t + 0.5) / (t + 1) ** 2\n", " - (t - 1) * lam / (lam * t + p)\n", " )\n", " q = np.exp(-rho_t_prime)\n", @@ -617,9 +619,9 @@ " b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi)\n", " q_r = b / np.sqrt(t + 1)\n", "\n", - "\n", " rho_t = ( # Taken from page 250\n", - " 1 - p\n", + " 1\n", + " - p\n", " + np.log(p)\n", " - 0.5 * np.log(2 * np.pi)\n", " + (t - 1) * (np.log(lam * t + p) - np.log(t + 1))\n", @@ -629,8 +631,9 @@ " rho_t_prime = (\n", " np.log(lam * t + p)\n", " - np.log(t + 1)\n", - " + 1 - lam\n", - " - (t + 0.5) / (t + 1)**2\n", + " + 1\n", + " - lam\n", + " - (t + 0.5) / (t + 1) ** 2\n", " - (t - 1) * lam / (lam * t + p)\n", " )\n", " q = np.where(t == 0, 0, np.exp(-rho_t_prime))\n", From cfde4526def04e46a07998f4a3e2a64551640d70 Mon Sep 17 00:00:00 2001 From: lucianopaz Date: Mon, 30 May 2022 17:29:32 +0200 Subject: [PATCH 7/9] Latest changes to abel region rejection sampling --- notebooks/fast_gen_pois.ipynb | 259 ++++++++++++++++++++++------------ notebooks/fast_gen_pois.py | 63 ++++++++- 2 files changed, 224 insertions(+), 98 deletions(-) diff --git a/notebooks/fast_gen_pois.ipynb b/notebooks/fast_gen_pois.ipynb index 99cf876..bdf5517 100644 --- a/notebooks/fast_gen_pois.ipynb +++ b/notebooks/fast_gen_pois.ipynb @@ -8,6 +8,7 @@ "outputs": [], "source": [ "import numpy as np\n", + "\n", "from matplotlib import pyplot as plt\n", "from scipy.special import gammaln\n", "\n", @@ -23,7 +24,9 @@ "def _logprob(x, p, lam):\n", " p_lam_x = p + lam * x\n", " return np.where(\n", - " x >= 0, np.log(p) + _logpow(p_lam_x, x - 1) - p_lam_x - gammaln(x + 1), -np.inf,\n", + " x >= 0,\n", + " np.log(p) + _logpow(p_lam_x, x - 1) - p_lam_x - gammaln(x + 1),\n", + " -np.inf,\n", " )" ] }, @@ -51,9 +54,7 @@ " v = rng.uniform(size=dist_size)\n", " w = rng.uniform(size=dist_size)\n", " _x = np.floor(1 / w ** 2)\n", - " accepted = v * b * (1 / np.sqrt(_x) - 1 / np.sqrt(_x + 1)) <= np.exp(\n", - " _logprob(_x, p, lam)\n", - " )\n", + " accepted = v * b * (1 / np.sqrt(_x) - 1 / np.sqrt(_x + 1)) <= np.exp(_logprob(_x, p, lam))\n", " x[inds_to_sample & accepted] = _x[inds_to_sample & accepted]\n", " inds_to_sample = inds_to_sample & ~accepted\n", " return x" @@ -89,21 +90,14 @@ " )\n", "\n", " def g(x, G, mu, sigma):\n", - " return (\n", - " G\n", - " / (np.sqrt(2 * np.pi) * sigma)\n", - " * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2))\n", - " )\n", + " return G / (np.sqrt(2 * np.pi) * sigma) * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2))\n", "\n", " def h_r(x, p, lam, eps, mu):\n", " return (\n", " (p * (1 - lam - eps) ** 1.5)\n", " / (np.sqrt(2 * np.pi) * (p - lam) ** 1.5)\n", " * np.exp(\n", - " -(1 - 2 * (1 - lam - eps) / (p - lam))\n", - " * (eps / 2)\n", - " * (1 - lam)\n", - " * (x - mu)\n", + " -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (x - mu)\n", " + 2 * (1 - lam)\n", " )\n", " )\n", @@ -118,17 +112,11 @@ " * eps\n", " * (1 - lam)\n", " )\n", - " * np.exp(\n", - " -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (t_r - mu)\n", - " )\n", + " * np.exp(-(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (t_r - mu))\n", " )\n", "\n", " def h_l(x, p, lam, delta, mu):\n", - " return (\n", - " p\n", - " / np.sqrt(2 * np.pi)\n", - " * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", - " )\n", + " return p / np.sqrt(2 * np.pi) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", "\n", " t_l = np.ceil((p - lam) / (1 - lam + delta) - 1)\n", " H_l = (\n", @@ -164,30 +152,42 @@ " left = (U < (_G + _H_l) / (_G + _H_l + _H_r)) & ~center\n", " raw_center_y = _mu + _sigma * N\n", " raw_left_y = _t_l - 2 * E * (1 + _delta) / _delta / (1 - _lam)\n", - " raw_right_y = _t_r + 2 * E / (\n", - " (1 - 2 * (1 - _lam - _eps) / (_p - _lam)) * _eps * (1 - _lam)\n", - " )\n", + " raw_right_y = _t_r + 2 * E / ((1 - 2 * (1 - _lam - _eps) / (_p - _lam)) * _eps * (1 - _lam))\n", " Y = np.where(\n", " center,\n", " np.where(\n", - " (raw_center_y >= _t_l) & (raw_center_y < _t_r), raw_center_y, np.nan,\n", + " (raw_center_y >= _t_l) & (raw_center_y < _t_r),\n", + " raw_center_y,\n", + " np.nan,\n", " ),\n", " np.where(\n", " left,\n", - " np.where(raw_left_y >= 0, raw_left_y, np.nan,),\n", - " np.where(raw_right_y >= 0, raw_right_y, np.nan,),\n", + " np.where(\n", + " raw_left_y >= 0,\n", + " raw_left_y,\n", + " np.nan,\n", + " ),\n", + " np.where(\n", + " raw_right_y >= 0,\n", + " raw_right_y,\n", + " np.nan,\n", + " ),\n", " ),\n", " )\n", " X = np.floor(Y)\n", - " accepted = V * np.where(\n", - " center,\n", - " g(Y, G=_G, mu=_mu, sigma=_sigma),\n", - " np.where(\n", - " left,\n", - " h_l(Y, p=_p, lam=_lam, delta=_delta, mu=_mu),\n", - " h_r(Y, p=_p, lam=_lam, eps=_eps, mu=_mu),\n", - " ),\n", - " ) <= np.exp(_logprob(X, _p, _lam))\n", + " accepted = (\n", + " V\n", + " * np.where(\n", + " center,\n", + " g(Y, G=_G, mu=_mu, sigma=_sigma),\n", + " np.where(\n", + " left,\n", + " h_l(Y, p=_p, lam=_lam, delta=_delta, mu=_mu),\n", + " h_r(Y, p=_p, lam=_lam, eps=_eps, mu=_mu),\n", + " ),\n", + " )\n", + " <= np.exp(_logprob(X, _p, _lam))\n", + " )\n", "\n", " x[inds_to_sample[accepted]] = X[accepted]\n", " n_to_accept[inds_to_sample[accepted]] = counter\n", @@ -214,6 +214,7 @@ " t = np.floor(alpha * np.maximum(nu, 0))\n", " problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam))\n", " t[problematic] = 0\n", + " b = p * np.exp(np.maximum(1 - p, 0)) * np.sqrt(2 / np.pi)\n", " b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi)\n", " q_r = b / np.sqrt(t + 1)\n", "\n", @@ -235,7 +236,7 @@ " - (t - 1) * lam / (lam * t + p)\n", " )\n", " q = np.exp(-rho_t_prime)\n", - " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime)))\n", + " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q))\n", "\n", " x = np.zeros(dist_size)\n", " n_to_accept = np.zeros(dist_size)\n", @@ -247,6 +248,7 @@ " U = rng.uniform(size=_dist_size)\n", " V = rng.uniform(size=_dist_size)\n", " W = rng.uniform(size=_dist_size)\n", + " # E = rng.uniform(size=_dist_size)\n", " E = rng.exponential(size=_dist_size)\n", " _p = p[inds_to_sample]\n", " _lam = lam[inds_to_sample]\n", @@ -255,7 +257,9 @@ " _q_l = q_l[inds_to_sample]\n", " _q_r = q_r[inds_to_sample]\n", " _b = b[inds_to_sample]\n", - " raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q)))\n", + " # raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(_q)))\n", + " # raw_left = np.where(_t == 0, 0, _t + np.ceil(np.log(1 - E) / _q))\n", + " raw_left = np.where(_t == 0, 0, _t - np.floor(E / _q))\n", " raw_right = np.floor((_t + 1) / W ** 2)\n", " left = U <= _q_l / (_q_l + _q_r)\n", " accepted = np.where(\n", @@ -266,7 +270,7 @@ " np.where(\n", " raw_left < 0,\n", " False,\n", - " V * _q_l * _q ** (raw_left - _t) * (1 - _q)\n", + " V * _q_l * _q ** (_t - raw_left) * (1 - _q **(_t+1))\n", " <= np.exp(_logprob(raw_left, _p, _lam)),\n", " ),\n", " ),\n", @@ -291,10 +295,10 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_19712/3599282342.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_3879/1238690607.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", " poisson_idxs = np.broadcast_to(p >= np.maximum(3, 2 * lam / (1 - lam)), dist_size)\n", - "/tmp/ipykernel_19712/3599282342.py:7: RuntimeWarning: divide by zero encountered in true_divide\n", - " (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))), dist_size,\n" + "/tmp/ipykernel_3879/1238690607.py:7: RuntimeWarning: divide by zero encountered in true_divide\n", + " (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))),\n" ] } ], @@ -305,7 +309,8 @@ "monotonicity_idxs = np.broadcast_to(p <= np.exp(lam), dist_size)\n", "poisson_idxs = np.broadcast_to(p >= np.maximum(3, 2 * lam / (1 - lam)), dist_size)\n", "abel_idxs = np.broadcast_to(\n", - " (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))), dist_size,\n", + " (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))),\n", + " dist_size,\n", ")" ] }, @@ -319,19 +324,17 @@ "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 5.14 s, sys: 147 ms, total: 5.29 s\n", - "Wall time: 5.31 s\n" + "CPU times: user 5.14 s, sys: 104 ms, total: 5.24 s\n", + "Wall time: 5.26 s\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_19712/2183379971.py:52: RuntimeWarning: invalid value encountered in log\n", - " raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q)))\n", - "/tmp/ipykernel_19712/2183379971.py:52: RuntimeWarning: divide by zero encountered in true_divide\n", - " raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q)))\n", - "/tmp/ipykernel_19712/1836048749.py:11: RuntimeWarning: invalid value encountered in log\n", + "/tmp/ipykernel_3879/2335405135.py:69: RuntimeWarning: overflow encountered in power\n", + " V * _q_l * _q ** (_t - raw_left) * (1 - _q **(_t+1))\n", + "/tmp/ipykernel_3879/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" ] } @@ -343,10 +346,18 @@ " rng=rng, p=p, lam=lam, dist_size=dist_size, idxs_mask=monotonicity_idxs\n", ")\n", "samples[poisson_idxs] = _rejection_region_poisson(\n", - " rng=rng, p=p, lam=lam, dist_size=dist_size, idxs_mask=poisson_idxs,\n", + " rng=rng,\n", + " p=p,\n", + " lam=lam,\n", + " dist_size=dist_size,\n", + " idxs_mask=poisson_idxs,\n", ")\n", "samples[abel_idxs] = _rejection_region_abel(\n", - " rng=rng, p=p, lam=lam, dist_size=dist_size, idxs_mask=abel_idxs,\n", + " rng=rng,\n", + " p=p,\n", + " lam=lam,\n", + " dist_size=dist_size,\n", + " idxs_mask=abel_idxs,\n", ")" ] }, @@ -373,7 +384,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_19712/1687800886.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_3879/1687800886.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", " (p / (1 - lam)).flatten(),\n" ] }, @@ -389,7 +400,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -426,7 +437,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_19712/816571136.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_3879/816571136.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", " (p / (1 - lam) ** 3).flatten(),\n" ] }, @@ -442,7 +453,7 @@ }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -508,11 +519,7 @@ " )\n", "\n", " def g(x):\n", - " return (\n", - " G\n", - " / (np.sqrt(2 * np.pi) * sigma)\n", - " * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2))\n", - " )\n", + " return G / (np.sqrt(2 * np.pi) * sigma) * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2))\n", "\n", " h_r_norm = (p * (1 - lam - eps) ** 1.5) / (np.sqrt(2 * np.pi) * (p - lam) ** 1.5)\n", " h_r_exp_A = -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam)\n", @@ -531,17 +538,11 @@ " * eps\n", " * (1 - lam)\n", " )\n", - " * np.exp(\n", - " -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (t_r - mu)\n", - " )\n", + " * np.exp(-(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (t_r - mu))\n", " )\n", "\n", " def h_l(x):\n", - " return (\n", - " p\n", - " / np.sqrt(2 * np.pi)\n", - " * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", - " )\n", + " return p / np.sqrt(2 * np.pi) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", "\n", " t_l = np.ceil((p - lam) / (1 - lam + delta) - 1)\n", " H_l = (\n", @@ -561,7 +562,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 12, @@ -609,6 +610,7 @@ " lam = np.asarray(lam)\n", " nu = 2 / 3 * (p ** 2 - lam * p - 3 * lam ** 2) / lam ** 2\n", " alpha = 0.2746244084 # Taken from page 259\n", + " # alpha = 3/7\n", " t = np.floor(alpha * np.maximum(nu, 0))\n", " problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam))\n", " if t.size == 1:\n", @@ -639,29 +641,99 @@ " q = np.where(t == 0, 0, np.exp(-rho_t_prime))\n", " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q))\n", " return np.where(\n", - " x <= t, q_l * (1 - q) * q ** (x - t), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", + " x <= t,\n", + " q_l * q ** (t - x) * (1 - q **(t+1)),\n", + " b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", " )" ] }, { "cell_type": "code", "execution_count": 14, + "id": "021c01fc-dea6-47ba-b19c-00f55b45a209", + "metadata": {}, + "outputs": [], + "source": [ + "def abel_rejection_proposal_density(x, p, lam):\n", + " p = np.asarray(p)\n", + " lam = np.asarray(lam)\n", + " nu = 2 / 3 * (p ** 2 - lam * p - 3 * lam ** 2) / lam ** 2\n", + " alpha = 0.2746244084 # Taken from page 259\n", + " # alpha = 3/7\n", + " t = np.floor(alpha * np.maximum(nu, 0))\n", + " problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam))\n", + " if t.size == 1:\n", + " if problematic:\n", + " t = 0\n", + " else:\n", + " t[problematic] = 0\n", + " b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi)\n", + " q_r = b / np.sqrt(t + 1)\n", + "\n", + " rho_t = ( # Taken from page 250\n", + " 1\n", + " - p\n", + " + np.log(p)\n", + " - 0.5 * np.log(2 * np.pi)\n", + " + (t - 1) * (np.log(lam * t + p) - np.log(t + 1))\n", + " - 1.5 * np.log(t + 1)\n", + " + (1 - lam) * t\n", + " )\n", + " rho_t_prime = (\n", + " np.log(lam * t + p)\n", + " - np.log(t + 1)\n", + " + 1\n", + " - lam\n", + " - (t + 0.5) / (t + 1) ** 2\n", + " - (t - 1) * lam / (lam * t + p)\n", + " )\n", + " q = np.where(t == 0, 0, np.exp(-rho_t_prime))\n", + " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q))\n", + " return np.where(\n", + " x <= t,\n", + " q ** (t - x) * (1 - q **(t+1)) / (1 - q),\n", + " np.sqrt(t + 1) * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 15, "id": "af0f622a-3dda-4844-97bd-c5ab4faf4478", "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.23497 0.2665088550067253\n" + ] + }, { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_19712/2185118508.py:35: RuntimeWarning: divide by zero encountered in true_divide\n", - " x <= t, q_l * (1 - q) * q ** (x - t), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", - "/tmp/ipykernel_19712/1836048749.py:11: RuntimeWarning: invalid value encountered in log\n", + "/tmp/ipykernel_3879/584387763.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", + " b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", + "/tmp/ipykernel_3879/1448899321.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", + " np.sqrt(t + 1) * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", + "/tmp/ipykernel_3879/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" ] }, { "data": { - "image/png": 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\n", 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9lfuR16FMNX6t9d/AhWKbOwBH82vyWcASYKDWeq/Wun+xpcxJXyk1Xim1Qym1IzY2tsxf5EZZuzhzx8zvmT+xEVlO6TwX/hlnJj3Lk5/+RXRC+tUChXaj4bHNENgL1rxpFACHV0rzjxClKBirp127dtSrV4+xY41GgA4dOhQOf7xhwwZGjhwJQFBQEPXr1y9M/L1798bLywtHR0cGDRrEhg0b2LBhA/fccw/Ozs64uLgwaNAg1q9fT2hoKH/++ScvvPAC69evp6B7+Nq1a+nYsSOhoaGsWbOG/fv3lxpvYmIiCQkJ9OjRA6AwLoBVq1axaNEiWrVqRceOHYmPj+fIkSOF38fPzw8rKytatWrFyZMncXNzKxwT6Mcff8TJyemqvyulFCNHjuTrr78mISGBzZs3c/vtt9/Ir/0K5enV4wucLrIeBXQsbWellBfwNtBaKfWi1rr4VQEAWuu5SqmzwAA7O7u25YivzOyt7Zk06jNGeg6j/8Ys+v69j7ZzXuD/ttxFx8ceYkSn+lep/fvD0K+NydtXToHF90PDMOj1CvjelPCFuG5lrZmbWmnj8Ts7Oxe+v1rTS2nDKZekSZMm7Ny5k99++40XX3yRPn36MHnyZB577DF27NiBv78/r732GhkZGaWeT2td6t9+acM4h4eHFw4xDZeGmbaxsWHbtm389ddfLFmyhJkzZ7JmzZpSzw3G1caAAQNwcHBgyJAh2NiYpiNmeW7ulvTbKPVfTGsdr7WeoLVuVFrSL7Kv6UbnLCNfF18+7vspS7rkMevpBrgGNeLx7UuwnvwkT364grOJV6n9AzS61Wj77/euMbPR57fCkgeMcX+EEGXWvXt3vvnmG8AYGvnUqVM0bdoUMNq5L1y4QHp6OsuXL6dLly50796d5cuXk5aWRmpqKsuWLaNbt25ER0fj5OTEiBEjeO6559i1a1dhkvf29iYlJeWavXg8PDxwd3dnwwbjYc+CuIDrHsY5JSWFxMRE7rjjDqZPn15iAejq6nrZhDJ169albt26vPXWW4waNerav7wyKk/xEQX4F1n3A0xyO1opNQAYEBgYaIrDlVmIdwjTwqbxxF9PkPRQMO9ffIHQaZ8Q/OVLzNy+nrbPPsY97a9S+7e2hU6PQusRsGU2bPoEPu0MIYOgy9NQp8VN/T5CVEaPPfYYEyZMIDQ0FBsbGxYsWFBYg+7atSsjR47k6NGjDB8+nHbtjAEoR40aRYcOHQAYN24crVu35o8//uD555/HysoKW1tbZs+ejYeHBw8//DChoaEEBATQvn37a8bz5ZdfMmbMGJycnC6r3Y8bN46TJ0/Spk0btNb4+PgUTu1YkuTkZAYOHEhGRgZaaz766KMr9imYD9jR0bFwopkHHniA2NhYgoODr+fXeFVlHpZZKRUArNBah+Sv2wARQC/gDLAdGK61Lr3BrKxBXUr8Dxe0md1Mf0X+xXN/P0eQZxCzWrxB7Jsfkrd+HXEO7kR0uI3+/5lArYBr3zwm7QJsnGF0+8xKNq4KujwNDbpfMZSEEBWtsg/LvGDBAnbs2HHZBCzVwcSJE2ndunXh/ZDiKmxYZqXUYmAz0FQpFaWUGqu1zgEmAn8AB4Glpkj6YJ6mnqJ61e/F9LDpHL54mId3T8Hto1epO3s2Vg0bcsvfPxBze192jHmUtO3br94VzKkG9H4dntkHvV6Fc/uM7p+f94R/l0B26W2LQgjRtm1b9uzZw4gRI0x6XIuciMXcNf4Cm6I3MSl8Es42zszsNZNmXs04tGM/4e9/RpsDG3DNTsemUSO8HhiO+113Ye3icvUDZmfAv9/C5lnGQ2BOXtB6JLQbA54lP3MghKlU9hq/KNmN1PgtMvEXKPcMXCYQcTGCiX9NJCEzgXe6vkOv+r3Izs1j1u/7OfjND9wduYmA+NNYOTnhNvAuPO8fhkPTJlc/qNbGBDHbv4DDvxnrjfsY8wY06Wc8JSyEiUnir5qqTOK3lBp/gbj0OJ5c8yR74/YyMngkz7R5BltrW/49ncCkpbuxjjjIkyl7aLR3E2Rl4diuLZ7DhuHWuzfK7hqDuSVGwc6F8M9XkHwWHDwgdDC0HGZ0B5V7AcJEJPFXTVUm8RewhBp/gazcLD7c8SHfHvqWFt4teK/He/i6+JKRncv7fxxm/sYTBDvl8X+OkTj/8TPZp09j7eWFx31D8B43Dqsi/ZRLlJcLx9fC7sVwaAXkZIB3EwgZDM3vBp+mN+V7iqpLEn/VJIn/Jlh1chWvbnqVPJ3Hs+2eZUiTISil2Hwsnue//5fohHTGd23AI86xpPzvf6SEh+PYogX+cz/Duqw3qzMSYf9y4wbwqU3GNp9mRgEQfDfUDKqgbyeqMkn8VVOVmWy93FMvVqA+AX34/q7vCfUJ5c0tb/Lw6oeJTommcyMvfn+6O/e182fO+hMM261I+u87+H48g4wDB4h8aBQ58fFlO4mDO7R9CMashEkHod9UcPSE8Hfh044wqyOseQuidhiTygtRSbz99ts0b96cFi1a0KpVK7Zu3Vqh5wsLC+N6Ko/h4eH079/fJOe+5ZZbrrnP9OnTzTI0tUUmfnN357wWXxdfPu/9Of/t9F/2xu7l7p/u5ou9X2Bnk8e797Zg/qh2xKdmcfesjSyyDqDOrFlknTxJ5IiRZJ89e30nc6sLnSZcKgRuf9/oDbT+Q/iiF3zYBJY/ZswOlpl87eMJYSabN29mxYoV7Nq1iz179vDnn3/i7+9/7Q9WUps2bbrmPpL4KxmlFPc1vY9lA5dxS91bmLFrBnf/dDfrTq/j1qBarHq6O32b1+aDVRE8tNcK6w8/ISc2lsgHRpB16tSNndStDnQcD6N/g+ePwaAvoEEP457A0pEwtQEsGggbP4aze+RqQFiUs2fP4u3tXfgUrre3N3Xr1gVKHyo5LCyMZ555hu7du9OsWTO2b9/OoEGDaNy4MS+//DJgTI4SFBTEQw89RIsWLRg8eHCJyXTVqlV07tyZNm3aMGTIEFJSUgD4/fffCQoKomvXrvz4448lxn69Q0IDuOR37y5tmOaPP/6Y6OhoevbsSc+ePcnNzWXUqFGEhIQQGhpa4pO9piJt/CayKXoT7257lxOJJ+hcpzNPtXmK5t7N+eXfaP770z4ysnN5I8iaVp+8irK1pd78edg3bmyak+fmwOmtEPE7RPwBcYeN7U5eRsHQMMxY5FmBaq1oW/C5//s/Mg+adlhm+2ZB1P7Pf0r9eUpKCl27diUtLY3bbruNoUOHFo56eeHCBWrUqAEYI2Ded999DBgwgLCwMDp27MjUqVOZMWMGU6dOZefOndSoUYNGjRrx77//kpycTIMGDdiwYQNdunRhzJgxBAcH89xzzxEWFsYHH3xAQEAAgwYNYuXKlTg7OzN16lQyMzOZPHkyjRs3Zs2aNQQGBjJ06FDS0tJYsWLFZbEvWLCAF1988bIhoRcsWIBSilGjRrFly5bCIaG//vprWrdujYuLCykpKYSHhzNw4MDLhml+//336dq1KwEBAezYsQNvb2927tzJlClTWL16NQAJCQl4eHhc8/cubfxmdEvdW/jhrh+Y3H4yBy8c5P5f7+eZtc8QXD+dVU93p3NDLybvzWbm3c+RqzWRI0aSvnfftQ9cFtY2ENAF+rwJE7cZTUJ3z4HA3hC5CX55Ema0gBmt4Jen4N//QcINXnUIcYNcXFzYuXMnc+fOxcfHh6FDh7JgwQLg6kMl33XXXQCEhobSvHlz6tSpg729PQ0bNuT0aWOAYH9/f7p06QLAiBEjCgdVK7BlyxYOHDhAly5daNWqFQsXLiQyMpJDhw7RoEEDGjdujFLqqk/IXs+Q0MWVNExzcQ0bNuT48eM88cQT/P7777i5uV3X7/d6WORk61rrX4Bf2rVr97C5Y7ketla2jAweyT2B9/DVwa9YuH8ha06voW9AX164awx9jtXmrRUH2NdxAh9t+5xTo0bh/9kcnNqVWjDfGLe60GqYsWgNcRHGA2PHw2HfMmMCGQA3P6jfGep1gnq3gE8QWFlkXUCY2NVq5hXJ2tqasLAwwsLCCA0NZeHChdx///1XHSq5oGnIysrqsuGOraysyMnJAUoerrkorTW9e/dm8eLFl23fvXt36YMuFnM9Q0IXV9IwzcV5enry77//8scffzBr1iyWLl3K/Pnzy3T86yV/5RXAxc6FR1s+yu+Dfueh5g+x7vQ6hqwYwrrE/2PqCCe8mjRgTJvxxDq4Ezn2YVJKqCGYjFLGMwAdH4Fhi+GFEzBhg3GT2L89nFgPvz4LszvD+w3h2/uNG8fH10FGUsXFJaqdw4cPU/SBzN27d1O/fv3rHiq5JKdOnWLz5s0ALF68mK5du172806dOrFx40aOHj0KQFpaGhEREQQFBXHixAmOHTtW+NnSXM+Q0GVVdBjmuLg48vLyuPfee3nzzTfZtWvXdf0OrodF1virCg8HDya1ncTYkLEsPbyUrw9+zcbox2nuG0JP/948YzeONzbMQ094DL9pH+LWt0/FB2VlDbVDjaXjeOOK4OJJOLXZaBY6tQUiVubvrIyHyPzagW8b8G0HtZobw08LcZ1SUlJ44oknSEhIwMbGhsDAQObOnXtDQyUX16xZMxYuXMgjjzxC48aNefTRRy/7uY+PDwsWLGDYsGFkZmYC8NZbb9GkSRPmzp3LnXfeibe3N127dmXfvpKbYK9nSOiyGj9+PLfffjt16tRh+vTpjB49mrz8ThnvvHPVaUvKRW7u3kQZORn8fOxnFh1YRGRSJG62HjjFtWHCkv0EXYzG/dU38Lt/sLnDhPSLcGZX/rLDeF4gLc74mY0D1GkJdVtD7RbGHAM+QVIYVAJV9QGukydP0r9//1ITtilY8pDQN3Jz1yJr/OaaiKWiOdg4cF/T+xjcZDBbz25lyaElhOeE8+5ozXP/c6LFa/9lbeQ5wiY/XuZ2xwrh6GnMIxzYy1jX2rgZfGbnpWXXIsjO7zJnbQc1m+VfSbQ0CoNaIWB/jdFKhRBmITV+MzuXeo7vIr5j2b4fGLU0hvZHND+HNabzi6/SrV4b8xYAV5OXC/HH4NweYzmb/5pW8HSyghoNjUKgZnNjmImaweAZYDQ3iZuuqtb4qzsZq6cSy8nLYWPkeqJfeJ1We87zc0fF2lvrcU+re+gT0IcG7g3MHeK1aQ1J0cacw+f2wNl/jfcJkZf2sXEw7hvUDDauEgoWd38ZibSCHTx4kKCgIMutTIjrprXm0KFDkvgrO52by/4pL2L9yy+k2yq2NIM1LazIC21Mn4C+9AnoQ0P3huYO8/pkphgPlcUczF8OQMwhSC4yRbOdq9H7qGYQeDUG78bGa40Gcv/ARE6cOIGrqyteXl6S/KsArTXx8fGFD7AVJYm/EtJak/bPbnbMXoDr5nAcc7KI8bJndWg260IV3n6N6VWvFz38etDcuzlWqpL2yk2/aBQAMQcg9hCcP2AUEKmxl/ZR1kby92oM3oGXFwrO3nKVcB2ys7OJioq6rI+8qNwcHBzw8/PD1vbyypFFJX6l1N3AnUBNYJbWetXV9q+uib+oyNNxLH7/SxrtXEtI/AnyrBTHmrmzvFkKuxpqPJy96ebXjTC/MDrV7YSz7TXG/a8M0hOMqSnjjkD8EeM17ghcOAa5WZf2c/DILwQCwbOBUUDUaGi8d6ohhYKotkyW+JVS84H+QIzWOqTI9n7ADMAa+EJr/W4ZjuUJfKC1Lnna+HyS+A15eZrF20+xcMk6wk5s5c6z/2CXeJEcDxcOtq/F/wJjifBIw9bKlna12tHFtwud6nSisWfjyns1UJK8XKN3UfFCIf7Y5c1GAPZuxo3kGg0uFQoFr26+coNZVGmmTPzdgRRgUUHiV0pZAxFAbyAK2A4MwygEij99MEZrHZP/uQ+Bb7TWV300TRL/5c4kpPPij3vZcOgc9+soHry4B71lI+TkkNs8kP2davNdvbMczjBuptZwqEHH2h3pVLcTnep0oq5LXTN/gwqUnQ4XI+HiCbhw4tLrheNGYZGXfWlfazvwqGcUBJ71jRvLHvUuLc4+crUgKjWTNvUopQKAFUUSf2fgNa113/z1FwG01iU+cqaMO0rvAqu11n+Wss94YDxAvXr12kZGRpa0W7WltebHXWd469cDpGTm8FQbb4Zc2EPKsmVkHT+OTa1aOH3yDjucYthydgtbzm4hLt14+Kqeaz061ulIm1ptaFuzLXVc6pj529wkebnG3MbFC4WLJyDhNGQkXL6/jUN+YZBfIBQtGNz9wbW2XDEIi1bRiX8w0E9rPS5/fSTQUWs9sZTPPwk8hHFlsFtrPaeU/SxqsnVLFJ+SyVu/HmTZP2do6OPMu/eE0jzuGNHPPkdeVhb+c2bj1Lo1WmuOJRxj67mtbInewo7zO0jJNsYhr+Nchza12tCmprE09GhYtZqGyiojCRJPG1cGCach8dSl9wmnLj21XMDKFtx9jYLAzc8YFM+tLrgXvPc1HoKTqwZhJhWd+IcAfYsl/g5a6yfKFXU+aeq5tnURsby0bC9RF9MZ1qEez7Vw4eLjE8iJicVvxnRcune/bP/cvFyOJBxh5/md7Dq/i10xuwqvCNzt3WldszUtfVrSwrsFwV7BuNjJ07dkpRpXDAmnjWcSEk9fKhSSoiH5LOjcyz9j43ipQHDzzS8YfC+9d/M15kuQwkFUAItq6rmO80iN/zqkZeXw0eoI5m04gbeLPW92r0Pjaf8l88gR6r7zf7gPGFDqZ7XWRCVHsTPGKAj+ifmHk0knAVAoGro3JNQnlFBvYwn0DMTWSvrVXyYvF1LOG4VA0hlIPGO8JkVf2pZ8FvKKDcVrbX+pEHCtBa51wKWW0ZTkWhtcahvb7d2kgBDXpaITvw3Gzd1ewBmMJpzhWuv9pR6kbOeRxH8D9kYlMuXHPeyPTuLOhq48Hf45Obt2UOs/L1LjwQfLfJzEzET2xe1jb9xeY4ndy8XMiwDYW9vTrEYzQrxDCKoRRFCNIBp6NJTC4Fryco3nEwoKhMsKhzOQfM5YctKv/KyNY5HCoISCoaDAkOYlkc+UvXoWA2GAN3AeeFVrPU8pdQcwHaMnz3yt9dvlDbqANPVcv5zcPOZtOMFHf0bgqHOZdXwZnrs24fXII/g8/dQNPbGpteZMypnLCoOD8QfJyDUeBLKzsiPQM7CwIGhWoxlNPJvgZOtk6q9XtWkNmUmQfB5SzhmvyWeNq4nkc/mvZ43tWclXft7a/lLB4FLT6J1U8Fr8vYO7FBJVmEU9wFVWUuMvv8j4VF5ato9NR2J47egK2u//G48hQ6j92qso6/L3SMnNyyUyKZJDFw5x6MIhDl44yKELh0jITACMZqL6bvUJqhFEY8/GNPJoRGOPxvi6+GItPWLKLyv10lVCQSGRcu7SttRYSInJHzSvhL9xa7uSC4SS3jt5SS+mSqZSJv4CUuMvn8Kunyv2c/euX7jv8F849boN/2kfYFVkKjhTnu982vlLBUH8IQ5fPMyZlDOF+zhYO9DAvQGNPRsT6BFYWCDUdq4t48dUhLxcI/mnxBiFQUGBUNr7os87FFBWRvJ39jGGyXDyAqeCVy9w9rr0vmCxMf3/L1F2lTLxS43ftC6kZvHuyoNkLfmWR/b9TGZIa0IXzMXa5eb02EnNTuV4wnGOJhzlSMIRjl48yrGEY8SkxxTu42zrTCOPRgR6BBLgFmAs7gH4ufrJ/YObRWvISLx64ZAaZxQkaXHGWEulsXM1hs1w9r6yUHDyunK7g4fM92xClTLxF5Aav2ltO3GBZe99wfDwhVyo6U+j+V/g18jPbPEkZiZyNOEoRy8eLSwUTiSe4ELGhcJ9bJQNfq5+BLgH0MCtAQHuRqHQwL0Bng6eZotdALk5xsNvhYVBfoGQFg9pF4ptz18KJu8pTlmBY41LBYGjZ/7iYRQghesFS/42O2e5V1ECSfziMlk5eSyb8x1NZ7/NBUd3ov4zlWEDO2FrbTm1rcTMRE4mneRk4snC1xOJJziVfIrsIk0R7vbuBLgFUN+tPv6u/vi7+lPPtR7+rv6427tL05Elykq7sjAoWFLj8q8kEoyrifSLRgFSUk+nAla2RgFQYuFQbCm6j51LlS4wKmXil6aeindy3RYuPDWRNKyZN+BpJo7rR9v6ll2Dzs3LJTolmhNJJy4VCkkniUyMvKzZCMDV1hU/V7/CAqHoUsu5VvV8Qrmyyk6/vDBIv1DkfZECIv1ikf0ulH51AWBlc6kQcPAwriwc3POXIu8Ltxf9ubvF3+yulIm/gNT4K1ZGRARHRo0lMyWVWaF3439nXybd3RoPJztzh3bd0nPSOZN8htPJpy8tKac5nXSa6JRocvSlh6dsrWzxdfHF39UfXxdf6rrUNRZn47WGQw25WqgKsjOMpqgrCoeLlxciGYlGgZGReGkp/iR2cfZuVykkrrH9JjRPSeIXV5V95gwnHx5PzvHjZCtrDtUKxKdfb7o8eA92davGaJ45eTmcSz1XWCBEJUcVvo9OjSa5WJ94B2sH6rjUKSwI6rrUpY5zHXxdfKnjXAcfJx+5YqjKtIaslBIKhITStxXdXtIzFkVZ2VwqCOzdwMEt/9WjyHs3CB5ojP90Aypl4pemnptL5+aSvns3J39aSfyqP/FOOG/8oHFTvPv2xvXWntg3a1Zla8HJWclEp0QbS2o0Z1POEp0aXbit4KnlArZWttR2rk1dl7rUdqpNLeda1HKqRW3n2oWvbnZuVfb3Ja4hN8d4EK8sBUVmkjFIYEZi/vtEo9ABGPMH1Ot0QyFUysRfQGr8N19enmbZTxv5Z8kvtI7aQ7MLkSitsalTB9eePXHpdSvO7duj7Cpfc9CNSstO42zq2SsKhzOpZzifep7Y9FjydN5ln3G0caSWk1EgFC8YCtY97D2kcBBXyss1CgFbZ7C5sb8zSfzihsSlZDJ15SFWbTpIn8SjDM06gcu+XeiMDKxcXHDp3g2XW3vh1qd3tSoESpKTl0Ncehzn085zPvU851LPGe8L1tPOEZsWS26xdmN7a/vCgsDH0cdYnHzwdvSmplNNvB298XH0wdnWWQoIcV0k8Yty2Rl5kf8u38eBs0n0qO/KS7VTcN21meS14eTGxeHYpg1+Mz/BpkYNc4dq0XLzconPiOd8qlEgFBYORQqGuPS4wvGPinK0ccTH0SgQfJwuFRAF2woKCWleEgUk8Ytyy83TfLs1kvf/OExaVi5juzZgYs9G5P25irMvv4yNtzf+c2Zj37ixuUOt1LTWJGcnE5cWR2x6rLGkGa/Ft6XlXNlV0c7KrrBA8HL0wsvBCy9HL2o41ChcL3jvYusihUQVVikTv9zctUzxKZlM/f0QS3dEUcvNnpfuDOY2FUfU44+j09Lx/WjaFRO/iIqRlp1GbHosMWkxxKXHFV4xxKTHEJcWR3xGPPHp8SRkJqBLGKTNzsqOGo41Li8cSikoPOw9ZGC9SqZSJv4CUuO3TLtOXeSVn/ax70wSnRt68Xpnb2xemUzm4cPUmjIFz5EjpDZpIXLyckjITCA+Pb6wMLiQcaHwfXxGPBfSjfULGRfIKT5ZDGClrPC096SGYw1qONTA094TTwdPPO098XDwuPTe3qOwoLC1lvGVzEkSv6gQuXmab7ed4oM/DpOamcO4drW4f/V80teuweP+odR+6SWUrfzxVyZaa5Kyki4vIAoKh/z3FzMukpCZwIWMCyRlJZV6LBdbl0sFgYPHZYVCQUHh6eBZuO5q5yrPRpiQJH5RoeJTMnn/j8Ms2X6a2q62fJi4iRo//w+nzp3wmz4da3d3c4coKkhOXg6JmYlczLjIxUyjQLiYcfGywqFwW6axPTM3s8RjWStr3O3dC68i3O3ccbcvthTZ5mHvgZudG442jnJ1WQJJ/OKm+OfURV75aT97zyTySPoB7v5rEXb+/vjP/hS7gABzhycsRHpO+qWCIqPkwiExM5HErETjNTOx1MICjIfpihYERQsJD4fLt3nYXypQqnqBYTGJXynVDHgKY+rGv7TWs6/1GUn8lUtunmbJ9lO89/th6p+J4I0di3CwUfh/8gnOHTuYOzxRSWXkZFxRGJRlvaSusQVsrGwKCwE3Ozfc7N1wtXPF1dYVN3s33OyM9eKvBYulN0uZJPErpeYD/YGYgonW87f3A2ZgzLf7hdb63TIcywr4XGs99lr7SuKvnC6kZvHhqsOsXfsPr2+Zj29qHLVffZUa9w0xd2iiGsnIySApK6n0wiH/fVJWEkmZSSRnJZOcnUxyVvIVT2IXpVC42LoYBUKxAqOgYHCzu7LwKHh/M642TJX4uwMpwKKCxK+UsgYigN5AFLAdGIZRCLxT7BBjtNYxSqm7gCnATK31t9c6ryT+ym1/dCLvfr+Dvt9/TNuYCLIGDaPFmy+ZZM5fISpKns4jLTuN5Kxko1DISip8X/Q1OSuZpMz8n2cnFxYeJT1jUZSNsiksNFxsXXCxc8HV1igYCt672LnQu35vajvXvqHvYLKmHqVUALCiSOLvDLymte6bv/4igNa6eNIv6Vi/aq3vvNZ+kvgrP601v+6O4uTrb9Hr0N+caNyalnM+xtfX29yhCVEhcvJyCguG5KxkErMSLxUUxQqN5OxkUrJSCq82UrJSCguORbcvonXN1jcUw7USv82NfTUAfIHTRdajgI5XCSQMGATYA79dZb/xwHiAevXqlSM8YQmUUvRv7U/60k/59c1PCPr+c/bdM5idPfvR/d5euLVqiVU1H+tHVC02VjZGl9UbnBo0Jy+H1OxUnGycTBzZJeVJ/CU1UpV6+aC1DgfCr3VQrfVcpdRZYICdnV3bG45OWBRHO2sGv/k0J7q0wOWtt6n300LO/rSQaFtbnFqE4tSmLY5tWuPUujXWHh7mDlcIs7GxssHdvmK7QZcn8UcB/kXW/YDo8oUjqroG/W6lQb9b2bzrCD8sXIn7sQN0io7C798v4fPPAbBvHIhjm7Y4tWmNY9u22Pr6Vumud0LcbOVp47fBuLnbCziDcXN3uNZ6v6mCkzb+qi0nN49vt53iw1URZKWk8ljdLO62jkPv+5f0Xf+Ql2JMSGFTsyaObdvgGhaG2113SSEgxDWYqlfPYiAMow/+eeBVrfU8pdQdwHSMnjzztdZvmyhoGaStGrmYmsW01RF8szUSN0dbnu3TlGFtfck5foy0nTtJ37mLtF27yDl7Fre7BlDnjTewcnAwd9hCWCyLeYDrRkiNv3o5eDaJ13/Zz5bjFwiq7corA4K5pZHR+0drTfycOcTO+BiH0FD8Zn6Cba1aZo5YCMtUKRO/1PirL601K/ed4+1fD3ImIZ3ewbX4zx3NaODtDEDyX38R/fxkrJyd8Zv5CY4tW5o5YiEsT6VM/AWkxl99ZWTnMm/DCT5de5Ss3Dwe6hzAE70a4+5oS0ZEBFGPTyTn/Hlqv/E6Hnffbe5whbAolTLxS41fFIhJyuCDVYf5bmcUnk52PHNbY4Z1qAdJiZx5ZhJpW7ZQY9Qoaj73LMqmPJ3UhKg6KmXiLyA1flFg35lE3lxxgK0nLtC4pgsv9w+mewMPzk99j4tff41zly74TvtQhoEWgmsnfsseYk6IfCG+7iwZ34k5I9oaTT/ztzHm639IGf8ktd98g9Rt2zh531Ayjx0zd6hCWDyLTPxKqQFKqbmJiYnmDkVYEKUU/UJqs+qZ7vznjiB2nLxI3+nrmWEfTI3Zc8lNSeHk0PtJWbfO3KEKYdGkqUdUWnEpmXy0OoLF207h6mDLc63cuWXBVLIOHcJn0jN4jRsnD3uJakna+EWVd/hcMm/9eoD1R+Jo6mHLO0eX47hhLW79+1PnrTflYS9R7VTKNn5p6hHXo2ltVxaN6cD8Ue3ItrVjkNcdrO16L0m//krkiJFknztn7hCFsChS4xdVSnZuHl9viWT6n0dodmI3/9m1GDsXJ/ynTcO5U6mjhgtRpVTKGr8QN8rW2orRXRqw7vkwggbdyZPdn+R0ji2Ro8dwbvYcdF7pU+oJUV1IjV9UacdiU/jwp92ELp5F2JndJLfuROtPP8LW08PcoQlRYaTGL6q1Rj4ufDquK63nfsLybvfjsHs7W/sOYOuqTeYOTQizscjELzd3hal1auTNC5+9QvTrH6FycnB4+hGmT/qAozHJ5g5NiJtOmnpEtZN6PpbdjzxJjUO7WV2/PfHjnuKJ20PwdrE3d2hCmIQ09QhRjHMtH2754Wucxo2nd+R2Onwwmftf+Y5Za4+SkZ1r7vCEqHCS+EW1pKytqf/cM/h/NoeGeSl88Nc0Nnz5Az0/COfHXVHk5VnulbAQ5SWJX1RrLj160GjZj7gHNuSVbQsYuecXnluyi7tmbWDTsThzhydEhbipiV8p5ayU2qmU6n8zzyvE1dj5+VL/22/wGDqUnv/8wXdHviE3No7hn29l3MLtcgNYVDllSvxKqflKqRil1L5i2/sppQ4rpY4qpaaU4VAvAEtvJFAhKpKVvT11Xn+NOu++g/OJCGasmcY7DbLYevwCfaev5+Xle4lLyTR3mEKYRFlr/AuAfkU3KKWsgVnA7UAwMEwpFayUClVKrSi21FRK3QYcAM6bMH4hTMrj7rsJ+N//sHZ2ptX0l1jheoAR7XxZvO00Ye+Hyw1gUSWUuTunUioAWKG1Dslf7wy8prXum7/+IoDW+p1SPv824IxRSKQD92itr3h+Xik1HhgPUK9evbaRkZHX+ZWEKL+81FTOvfkWicuX49i6NTn/eZ2p/ySy+sB56rg7MKl3Ewa18cPaSoZ9FpanIrtz+gKni6xH5W8rkdb6Ja3108C3wOclJf38/eZqrdtprdv5+PiUIzwhbpyVszN1332Huu+/R2ZEBLljR/BhzXiWjO9ETVd7nv9+D3d+vJ61h2Kw5GdhhChJeRJ/SVWda/4FaK0XaK1XXPXA8uSusBDuAwbQYNmP2NWvz5mnn6b+go/5cUwbZg5vTXp2LqMXbGf451vZE5Vg7lCFKLPyJP4owL/Iuh8QXb5whLA8dvXqEfDN13iNG0vC0qWcHHIft9mnsPqZHrw2IJjD55O5a+ZGJn67i8j4VHOHK8Q1laeN3waIAHoBZ4DtwHCt9X5TBSdDNghLk7JhI9FTppCXlETNKS/gOWwYKZk5zP37OJ+vP05unuaBjvV54tZAvGQICGEmJmnjV0otBjYDTZVSUUqpsVrrHGAi8AdwEFhqqqQvTT3CUrl07ULDn5bj1LEj5994k6iJT+CYnsKzfZqy7vmeDG7rx6LNJ+nxfjgz1xwhPUt6AAnLI4O0CXEDdF4eFxYuImbaNGy8vKj73lScO3QA4Mj5ZKb+fpg/D56npqs9k3o3YXBbP2ys5UF5cXNUysnWlVIDgAGBgYEPHzlyxNzhCFGq9H37OfPsJLJPR+E9YQLejz2KsrEBYPvJC/zfrweIOHaOVs45PBLiTgvHbHJj48iJjb1ssXJywnfah9jVr2/mbySqgkqZ+AtIjV9UBrkpqZx/y+jz7xASgm2dOpeSelwcOvPKJ36VgwM2Pj6FS9q2bSh7e+ovWohdvXpm+BaiKqmUiV9q/KIySvzlF2JnfIyys7ssqdv4+KC8vPj7Asw7kMSxPAd6tArg+X5BNPRxASDj8GFOPTQK5ehoJH9//2ucTYjSVcrEX0Bq/KKqSc3M4fP1x5n793Eyc/IY3qEeT/ZqjI+rPRkHD3Jq1GiUsxP1F32FnV+pz0MKcVWS+IWwQDHJGXz81xEWbzuNg40VD3dvyMPdGmJ9LILI0WOwdnGh/qKF2PpK8hfXr1ImfmnqEdXF8dgU3v/jMCv3ncPbxZ6nbmvM3U5JRI8bh7Wbm5H869Y1d5iikqmUib+A1PhFdbEz8iLvrjzI9pMXCfBy4j+NoP47L2Dt4UH9rxZhW7u2uUMUlYjMuStEJdC2vidLH+nMvIfaYW9jzfhtaUzvO5HM+AtEPvgg2edlNHNhOhaZ+OXJXVEdKaXo1awWvz3VjWn3tWSPix+T2o0h5VwsR4aPJPt8jLlDFFWENPUIYaEyc3L5Zsspfl+6mhfWfEqmmyc1531JYLMAc4cmLJw09QhRSdnbWDOmawPmvz+GPU+8jkPSBY4/+BCvL/ybc4kZ5g5PVGKS+IWwcC72Nox+ZCC1Z8+hdmYSnWa+wl1v/sw7Kw+SmJZt7vBEJSRNPUJUImnbtxP58HguuHnzeLux5Ll5MiGsEaNvaYCjnfVl++ZlZZF95gzZp0+Tdfo02adOkxUVRXZ0NF6jR+F+111m+haiolXK7pzSj1+I0qVu3cbpRx5B1/Hl8z4T2HsoiqC8RO6uBUE6mZzTp8mKOk3O2XNQ5O9bOThg5+9H5slIPO4eSJ033zTjtxAVqVIm/gJS4xeiZKlbtnD6kQlXDACX5OiGnb8fNZs2ws7fH9t6/sarv78xZpBSHOkRhkv3bpL4q7BrJX6bmxmMEMI0nDt1ov6335C2fTt2fn7Y+PmxMdWe9/4+RcT5FEJ93XmhXxBdG3ubO1RhgSTxC1FJOTZvjmPz5oXrtwE9Wwew7J8zfLQ6ghHzttI10JsX+gUR6uduvkCFxZFePUJUIdZWisFt/fjr2R78t38w+6MTGTBzA49/s4vjsSnmDk9YiJtW41dKhQFvAvuBJVrr8Jt1biGqGwdba8Z2bcB97fz4fP0Jvlh/nN/3n2Noe38etOD7euLmKOtk6/OVUjFKqX3FtvdTSh1WSh1VSk25xmE0kAI4AFE3Fq4Q4nq4OtgyqXcT1j3fkxEd6/HdjtPEJmey+3QCCWlZ5g5PmEmZevUopbpjJO1FWuuQ/G3WQATQGyORbweGAdbAO8UOMQaI01rnKaVqAdO01g9c67zSq0cI0zoVn8b523uz0TOQeZ2GM757Q8Z0bYCzvdzuq0pM0qtHa/23Uiqg2OYOwFGt9fH8Ey0BBmqt3wH6X+VwFwH7qwQ8HhgPUE/mHhXCpOp5OZHpaEvf5rXZ38iLD1dHsGDTSR7vGcjwjvVwsLW+9kFEpVeem7u+wOki61H520qklBqklPoM+AqYWdp+Wuu5Wut2Wut2Pj4+5QhPCFEadydbPn+wHcseu4WmtV15Y8UBbv0gnKXbT5OTm2fu8EQFK0/iVyVsK7XdSGv9o9b6Ea310Gvd2JVhmYWoQOrSn27rep58+3AnvhnXER83Byb/sIc+H/3Nij3R5OXJTeCqqjyJPwrwL7LuB0SXLxwhhDl0CfRm+WO3MHdkW2ysFRO//YcBMzew9nAMlvx0v7gx5Un824HGSqkGSik74H7gZ1MEpbX+RWs93t1dHjoR4mZRStGneW1WPtWdj4a2JCkjm9Ffbue+zzaz7cQFc4cnTKis3TkXA5uBpkqpKKXUWK11DjAR+AM4CCzVWu83RVDS1COE+VhbKe5p7cdfk8J48+4QIuPTuO+zzYz6chv7zsjfZFVQ1l49w0rZ/hvwm0kjEkJYBDsbK0Z2qs/gNn4s3HyS2eHH6P/JBu5sUYdJvZvQyMfF3CGKG2SRQzZIU48QFew62u0d7ayZ0KMR61/oyZO3BrL2UAx9PvqbF77fw5mE9AoMUlQUi0z8QgjL4+Zgy6Q+Tfl7ck8e6mwMBtfz/XBe/2U/cSmZ1z6AsBgWmfiljV8Iy+XtYs8rA4JZ+3wY97T2ZeGmk3R/by0frjpMYrpMBVkZWGTil6YeISyfr4cjUwe3YPWkHvQMqskna47S/b21zA4/RnpWrrnDE1dhkYlfavxCVCBV0rOXN66RjwuzhrdhxRNdaV3Pg6m/H6L7+2v5avNJsnLkKWBLZJGJX2r8QlQ+Ib7uLBjdgaWPdCbAy4n//rSfXtPC+XFXFLnyFLBFscjEL4SovDo0qMHSRzrz5ej2xg3hpf/Sb/rfrNx7VoaBsBCS+IUQJqeUomfTmvw8oRPzWtuQpzWPfrOLATM3sObQeYsaBkLn5pLww49kHDpk7lBuGotM/NLGL0QFu0l5N37mTOq++jQ/3erBh0OMYSDGLNjBvbM3selo3M0J4lpyczn70kukhK8zdyQ3jUUmfmnjF6JqyDx6FAB9IZ572/qx5tkw/u+eUM4mZjD8i60M/3wLOyMvmjnK6sciE78QomqytbZieMd6rH0ujFf6BxNxPpl7Z29itIwDdFNJ4hdC3HQOttaM6dqAvyf35IV+Qew6lUD/Tzbw6Nc7iTifbO7wqjyZaFMIYTZOdjY8GtaIBzrVY976E8zbcILf959jYMu6PH1bEwK8nc0dYpVkkTV+ubkrRAUy7fNbJuHmYMszvZuwfnJPHuneiN/3n6PXtHVM+UEGgqsIFpn45eauENWTp7MdU24P4u/JPRnZqT4/7jIGgnv1p33EJGWYO7wqwyITvxCieqvp6sBrdzUn/Pkw7m3ry9dbT9H9/bW889tBLqZmmfRclvNEwc0jiV+I6siCHqC6mroejrwzqAV/TerBHSF1mLv+ON3eW8u01REkZZh4JFATj2FkySTxCyEsXoC3M9OGtmLV093p3sSbj/86Qrepa/k0/ChpWTnmDq/SuWmJXyllpZR6Wyn1iVLqoZt1XiFE1dG4liufPtCWFU90pV19T977/TDd31vLvA0nyMiWoaDLqqyTrc9XSsUopfYV295PKXVYKXVUKTXlGocZCPgC2UDUjYUrhBDGSKDzRrXnh0dvoWltV95ccYCw98P5ZmukDAVdBmWt8S8A+hXdoJSyBmYBtwPBwDClVLBSKlQptaLYUhNoCmzWWk8CHjXdVxBCVFdt63vyzbhOfPtwR3w9HXlp2T56TQvnh50yFPTVlCnxa63/Bi4U29wBOKq1Pq61zgKWAAO11nu11v2LLTEYtfyCQTlKvSZTSo1XSu1QSu2IjY29/m8khLgqZYkd+cvplkbefD/BGAra3dGWZ7/7lz4frWPFnmgZCroE5Wnj9wVOF1mPyt9Wmh+BvkqpT4C/S9tJaz0XeB3YZWdnV47whBDVScFQ0L9M7MqcEW2xtlJM/PYf7vxkA6v2n7OooaDNrTyJv6RqQ6m/Wa11mtZ6rNb6Ca31rKsdWB7gEkLcKKUU/UJqs/Kp7sy4vxXpWTmM/2ond83cyNpDMVcWANWwQChP4o8C/Ius+wHR5QvHIEM2CFHBqkGys7ZSDGzly5+TevD+4BYkpGcxesF2Bs3exPojsVcWANKPv0y2A42VUg2UUnbA/cDPpglLCCFMw8baiiHt/FnzbBjvDArlfGIGI+dtY+hnW9h8LN7c4ZlFWbtzLgY2A02VUlFKqbFa6xxgIvAHcBBYqrXeb4qgpKlHCGFqttZWDOtQj7XPh/HmwOZEXkhl2OdbeGj+NnOHdtOVaVhmrfWwUrb/Bvxm0ogwmnqAAYGBgaY+tBCimrO3sWZk5wCGtPPn262n+PwvY67dpTtO07nfRVrX8zRzhBXPIodskBq/EKKiFUwG8+ekHgCcT8rgnk83MWbB9io/G5hFJn65uSuEuFkc7awBeKR7Q57v25SdkRfp/8kGxi/awcGzSWaOrmJYZOKXGr8QFaga9V65HnY21jzeM5ANL/TkmduasPl4PLfPWM/j3+ziSBWbDtIiE78QQtw0xbp1ujrY8tRtjdkw+VaevDWQdRGx9Jn+N08t+YfjsSlmCtK0LDLxS1OPEBWsGvTjv27FLoTcnWyZ1Kcp6yf3ZEKPRqzaf57bpq3j2aX/cio+zTwxmohFJn5p6hFCWApPZzte6BfE+hd6MqZLA1bsiebWD8OZ8sMeoi5WzgLAIhO/EEJYGm8Xe17uH8z6yT0ZUTAf8AfhvLx8L2cTK9eE8JL4hRDiOtR0M+YDXjc5jKHt/fnf9tP0eD+c137eX2kmhLfIxC9t/EIIS1fH3ZG37g5lzbNhDGrty1dbIun23lreWnGAuJRMc4d3VRaZ+KWNXwhRWfjXcOLde1uw5tke9G9Rl/kbT9D9vbVM/f0QF1OzzB1eiSwy8QshRGVT38uZD+9ryepJPegdXIs5647R7b21TFt1mMS0bHOHdxlJ/EJUN/IA1+VM3LW1kY8LM+5vzR9Pd6dHEx8+XnOUru+tYcafR0jOsIwCwCITv7TxC1HRpB9/ccrEBWKTWq7MeqANvz3Zjc4Nvfjozwi6vbeWWWuPkpKZY9JzXS+LTPzSxi+EqCqC67ox98F2/DKxK23qefL+H4fpNnUNc9YdIy3LPAWARSZ+IYSoakL93Jk/qj3LHruFFn4evLvyEN2mruXzv4+TnpV7U2ORxC+EEDdR63qeLBzTgR8evYXgum68/dtBur23lnkbTpCRfXMKAEn8QghhBm3re/LV2I58N6EzTWq58OaKA3R/by0LNlZ8ASCJXwghzKh9QA2+fbgTS8Z3IsDbmdd+OUDY++HsOHmhws5ZpqkXTUEp1Q14IP+cwVrrW27WuYUQwtJ1aujF/8Z3YvOxeGavO0aAt3OFnatMiV8pNR/oD8RorUOKbO8HzACsgS+01u+Wdgyt9XpgvVLqbmB7eYIWQgiTsaAhqpVS3BLozS2B3hV6nrLW+BcAM4FFBRuUUtbALKA3EAVsV0r9jFEIvFPs82O01jH574cD48oRsxCiPJRCW1CysxjV6MG2MiV+rfXfSqmAYps7AEe11scBlFJLgIFa63cwrg6uoJSqByRqrUudyFIpNR4YD1CvXr2yhCeEEOI6lOfmri9wush6VP62qxkLfHm1HbTWc4HXgV12dnblCE8IIURJypP4S7ouuur1o9b6Va31pmsdWJ7cFUKIilOexB8F+BdZ9wOiyxeOQcbqEUKIilOexL8daKyUaqCUsgPuB342TVhCCCEqSpkSv1JqMbAZaKqUilJKjdVa5wATgT+Ag8BSrfV+UwQlTT1CCFFxytqrZ1gp238DfjNpRBhNPcCAwMBAUx9aCAE3f1Rm6T5qUZQl9+dVSsUCkTf4cW8gzoThmJIlxwaWHZ8lxwaWHZ/EduMsOb6SYquvtfYp7QMWnfjLQym1Q2vdztxxlMSSYwPLjs+SYwPLjk9iu3GWHN+NxCaDtAkhRDUjiV8IIaqZqpz455o7gKuw5NjAsuOz5NjAsuOT2G6cJcd33bFV2TZ+IYQQJavKNX4hhBAlkMQvhBDVTJVM/Eqpfkqpw0qpo0qpKWaOZb5SKkYpta/IthpKqdVKqSP5r55mis1fKbVWKXVQKbVfKfWUhcXnoJTappT6Nz++1y0pvvxYrJVS/yilVlhSbEqpk0qpvUqp3UqpHZYUW34sHkqp75VSh/L//3W2hPiUUk3zf2cFS5JS6mlLiC0/vmfy/xb2KaUW5/+NXHdsVS7xF5kg5nYgGBimlAo2Y0gLgH7Ftk0B/tJaNwb+yl83hxzgWa11M6AT8Hj+78pS4ssEbtVatwRaAf2UUp0sKD6ApzCGLClgSbH11Fq3KtLH25JimwH8rrUOAlpi/A7NHp/W+nD+76wV0BZIA5ZZQmxKKV/gSaBd/kyI1hhjpF1/bFrrKrUAnYE/iqy/CLxo5pgCgH1F1g8DdfLf1wEOm/v3lh/LTxgzqllcfIATsAvoaCnxYYxI+xdwK7DCkv5tgZOAd7FtlhKbG3CC/M4llhZfkXj6ABstJTYuzYFSA2O4nRX5MV53bFWuxs+NTRBzs9XSWp8FyH+taeZ4yJ9hrTWwFQuKL78pZTcQA6zWWltSfNOByUBekW2WEpsGVimldubPamdJsTUEYoEv85vJvlBKOVtQfAXuBxbnvzd7bFrrM8AHwCngLMZshqtuJLaqmPive4KY6k4p5QL8ADytrzItpjlorXO1cdntB3RQSoWYOSQAlFL9gRit9U5zx1KKLlrrNhhNno8rpbqbO6AibIA2wGytdWsgFfM2O10hf6j5u4DvzB1Lgfy2+4FAA6Au4KyUGnEjx6qKib/CJogxofNKqToA+a8x19i/wiilbDGS/jda6x8tLb4CWusEIBzjfoklxNcFuEspdRJYAtyqlPraQmJDax2d/xqD0UbdwVJiw/gbjcq/egP4HqMgsJT4wCgwd2mtz+evW0JstwEntNaxWuts4EfglhuJrSom/sowQczPwEP57x/CaFu/6ZRSCpgHHNRaTyvyI0uJz0cp5ZH/3hHjP/4hS4hPa/2i1tpPax2A8X9sjdZ6hCXEppRyVkq5FrzHaAfeZwmxAWitzwGnlVJN8zf1Ag5gIfHlG8alZh6wjNhOAZ2UUk75f7u9MG6KX39s5rx5UoE3Qe4AIoBjwEtmjmUxRntcNkZNZyzghXFT8Ej+aw0zxdYVoxlsD7A7f7nDguJrAfyTH98+4JX87RYRX5E4w7h0c9fssWG0of+bv+wv+BuwhNiKxNgK2JH/b7sc8LSU+DA6EsQD7kW2WUpsr2NUfvYBXwH2NxKbDNkghBDVTFVs6hFCCHEVkviFEKKakcQvhBDVjCR+IYSoZiTxCyFENSOJXwghqhlJ/EIIUc38P/MfmmcMcdCgAAAAAElFTkSuQmCC\n", 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" ] @@ -679,15 +751,17 @@ "x = np.linspace(np.maximum(0, mean - 1.2 * std), mean + 15 * std, 1000)\n", "plt.semilogy(x, np.exp(_logprob(x, p, lam)), label=\"PDF\")\n", "plt.plot(x, abel_rejection_envelope(x, p, lam), label=\"Envelope\")\n", + "plt.plot(x, abel_rejection_proposal_density(x, p, lam), label=\"Proposal density\")\n", "samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000)\n", + "print(np.mean(samples <= 1), np.sum(np.exp(_logprob(np.array([0, 1]), p, lam))))\n", "y, edges = np.histogram(samples, bins=20, density=True)\n", "plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label=\"Sampled points\")\n", - "plt.legend();" + "plt.legend()" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 16, "id": "9eabb346-8c37-4d74-a544-64c7a4eaad52", "metadata": {}, "outputs": [ @@ -695,15 +769,25 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_19712/2185118508.py:35: RuntimeWarning: divide by zero encountered in true_divide\n", - " x <= t, q_l * (1 - q) * q ** (x - t), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", - "/tmp/ipykernel_19712/1836048749.py:11: RuntimeWarning: invalid value encountered in log\n", + "/tmp/ipykernel_3879/584387763.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", + " b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", + "/tmp/ipykernel_3879/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -721,21 +805,14 @@ "x = np.linspace(0, 10, 1000)\n", "plt.semilogy(x, np.exp(_logprob(np.floor(x), p, lam)), label=\"PDF\")\n", "plt.plot(x, abel_rejection_envelope(np.floor(x), p, lam), label=\"Envelope\")\n", - "samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000)\n", + "# plt.plot(x, abel_rejection_proposal_density(np.floor(x), p, lam), label=\"Proposal density\")\n", + "samples = _rejection_region_abel(np.random.default_rng(), p, lam, 100000)\n", "u, c = np.unique(samples, return_counts=True)\n", "edges = np.arange(11)\n", "y = np.array([np.sum(c[u == e]) for e in edges])\n", "plt.step(edges, y / samples.size, label=\"Sampled points\", where=\"post\")\n", - "plt.legend();" + "plt.legend()" ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "2c020ad3-7b8d-47f8-aebb-5ec2b37fd556", - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { diff --git a/notebooks/fast_gen_pois.py b/notebooks/fast_gen_pois.py index afad32c..81912ed 100644 --- a/notebooks/fast_gen_pois.py +++ b/notebooks/fast_gen_pois.py @@ -203,6 +203,7 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): t = np.floor(alpha * np.maximum(nu, 0)) problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam)) t[problematic] = 0 + b = p * np.exp(np.maximum(1 - p, 0)) * np.sqrt(2 / np.pi) b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi) q_r = b / np.sqrt(t + 1) @@ -224,7 +225,7 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): - (t - 1) * lam / (lam * t + p) ) q = np.exp(-rho_t_prime) - q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - np.exp(-rho_t_prime))) + q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q)) x = np.zeros(dist_size) n_to_accept = np.zeros(dist_size) @@ -236,6 +237,7 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): U = rng.uniform(size=_dist_size) V = rng.uniform(size=_dist_size) W = rng.uniform(size=_dist_size) + # E = rng.uniform(size=_dist_size) E = rng.exponential(size=_dist_size) _p = p[inds_to_sample] _lam = lam[inds_to_sample] @@ -244,7 +246,9 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): _q_l = q_l[inds_to_sample] _q_r = q_r[inds_to_sample] _b = b[inds_to_sample] - raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q))) + # raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(_q))) + # raw_left = np.where(_t == 0, 0, _t + np.ceil(np.log(1 - E) / _q)) + raw_left = np.where(_t == 0, 0, _t - np.floor(E / _q)) raw_right = np.floor((_t + 1) / W ** 2) left = U <= _q_l / (_q_l + _q_r) accepted = np.where( @@ -255,7 +259,7 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): np.where( raw_left < 0, False, - V * _q_l * _q ** (raw_left - _t) * (1 - _q) + V * _q_l * _q ** (_t - raw_left) * (1 - _q ** (_t + 1)) <= np.exp(_logprob(raw_left, _p, _lam)), ), ), @@ -422,6 +426,7 @@ def abel_rejection_envelope(x, p, lam): lam = np.asarray(lam) nu = 2 / 3 * (p ** 2 - lam * p - 3 * lam ** 2) / lam ** 2 alpha = 0.2746244084 # Taken from page 259 + # alpha = 3/7 t = np.floor(alpha * np.maximum(nu, 0)) problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam)) if t.size == 1: @@ -453,11 +458,54 @@ def abel_rejection_envelope(x, p, lam): q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q)) return np.where( x <= t, - q_l * (1 - q) * q ** (x - t), + q_l * q ** (t - x) * (1 - q ** (t + 1)), b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)), ) +# %% +def abel_rejection_proposal_density(x, p, lam): + p = np.asarray(p) + lam = np.asarray(lam) + nu = 2 / 3 * (p ** 2 - lam * p - 3 * lam ** 2) / lam ** 2 + alpha = 0.2746244084 # Taken from page 259 + # alpha = 3/7 + t = np.floor(alpha * np.maximum(nu, 0)) + problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam)) + if t.size == 1: + if problematic: + t = 0 + else: + t[problematic] = 0 + b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi) + q_r = b / np.sqrt(t + 1) + + rho_t = ( # Taken from page 250 + 1 + - p + + np.log(p) + - 0.5 * np.log(2 * np.pi) + + (t - 1) * (np.log(lam * t + p) - np.log(t + 1)) + - 1.5 * np.log(t + 1) + + (1 - lam) * t + ) + rho_t_prime = ( + np.log(lam * t + p) + - np.log(t + 1) + + 1 + - lam + - (t + 0.5) / (t + 1) ** 2 + - (t - 1) * lam / (lam * t + p) + ) + q = np.where(t == 0, 0, np.exp(-rho_t_prime)) + q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q)) + return np.where( + x <= t, + q ** (t - x) * (1 - q ** (t + 1)) / (1 - q), + np.sqrt(t + 1) * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)), + ) + + # %% p, lam = 2.1209508879201904, 0.5510204081632653 mean = p / (1 - lam) @@ -465,7 +513,9 @@ def abel_rejection_envelope(x, p, lam): x = np.linspace(np.maximum(0, mean - 1.2 * std), mean + 15 * std, 1000) plt.semilogy(x, np.exp(_logprob(x, p, lam)), label="PDF") plt.plot(x, abel_rejection_envelope(x, p, lam), label="Envelope") +plt.plot(x, abel_rejection_proposal_density(x, p, lam), label="Proposal density") samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000) +print(np.mean(samples <= 1), np.sum(np.exp(_logprob(np.array([0, 1]), p, lam)))) y, edges = np.histogram(samples, bins=20, density=True) plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label="Sampled points") plt.legend() @@ -477,11 +527,10 @@ def abel_rejection_envelope(x, p, lam): x = np.linspace(0, 10, 1000) plt.semilogy(x, np.exp(_logprob(np.floor(x), p, lam)), label="PDF") plt.plot(x, abel_rejection_envelope(np.floor(x), p, lam), label="Envelope") -samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000) +# plt.plot(x, abel_rejection_proposal_density(np.floor(x), p, lam), label="Proposal density") +samples = _rejection_region_abel(np.random.default_rng(), p, lam, 100000) u, c = np.unique(samples, return_counts=True) edges = np.arange(11) y = np.array([np.sum(c[u == e]) for e in edges]) plt.step(edges, y / samples.size, label="Sampled points", where="post") plt.legend() - -# %% From 30d94bb83ac72ac7eda9042087272b9d2a1e28f8 Mon Sep 17 00:00:00 2001 From: Ricardo Date: Fri, 3 Jun 2022 10:00:41 +0200 Subject: [PATCH 8/9] Benchmark algorithms and check for accuracy --- notebooks/fast_gen_pois.ipynb | 1022 +++++++++++++++++++++++++++++---- notebooks/fast_gen_pois.py | 475 +++++++++++++-- 2 files changed, 1366 insertions(+), 131 deletions(-) diff --git a/notebooks/fast_gen_pois.ipynb b/notebooks/fast_gen_pois.ipynb index bdf5517..32cc38b 100644 --- a/notebooks/fast_gen_pois.ipynb +++ b/notebooks/fast_gen_pois.ipynb @@ -3,8 +3,11 @@ { "cell_type": "code", "execution_count": 1, - "id": "d06b73f0-08b3-40bd-bd9c-a8fe05ac03b0", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "import numpy as np\n", @@ -33,8 +36,11 @@ { "cell_type": "code", "execution_count": 2, - "id": "fee5de3f-e4cb-419f-9930-e9df8322a4f1", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "def _rejection_region_monotonicity(rng, p, lam, dist_size, idxs_mask=None):\n", @@ -45,26 +51,34 @@ " dist_size = np.sum(idxs_mask)\n", " p0 = np.exp(-p)\n", " b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi)\n", - " u = rng.uniform(size=dist_size)\n", - " x = np.zeros(dist_size)\n", - " inds_to_sample = u > p0 / (p0 + b)\n", - " counter = 0\n", + " x = np.full(dist_size, np.nan)\n", + " inds_to_sample = np.ones(dist_size, dtype=bool) # dummy boolean mask#u > p0 / (p0 + b)\n", + " counter = -1\n", " while np.any(inds_to_sample):\n", " counter += 1\n", + " u = rng.uniform(size=dist_size)\n", + " zero_xs = u <= p0 / (p0 + b)\n", + " x[inds_to_sample & zero_xs] = 0\n", + " inds_to_sample = inds_to_sample & ~zero_xs\n", + "\n", " v = rng.uniform(size=dist_size)\n", " w = rng.uniform(size=dist_size)\n", " _x = np.floor(1 / w ** 2)\n", " accepted = v * b * (1 / np.sqrt(_x) - 1 / np.sqrt(_x + 1)) <= np.exp(_logprob(_x, p, lam))\n", " x[inds_to_sample & accepted] = _x[inds_to_sample & accepted]\n", " inds_to_sample = inds_to_sample & ~accepted\n", + " # print(counter)\n", " return x" ] }, { "cell_type": "code", "execution_count": 3, - "id": "d0557ec5-5d72-41ad-b2be-0696aa10ab46", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "def _rejection_region_poisson(rng, p, lam, dist_size, idxs_mask=None):\n", @@ -198,8 +212,11 @@ { "cell_type": "code", "execution_count": 4, - "id": "63b469a2-917e-47a7-a92b-627b1bc80084", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None):\n", @@ -214,7 +231,7 @@ " t = np.floor(alpha * np.maximum(nu, 0))\n", " problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam))\n", " t[problematic] = 0\n", - " b = p * np.exp(np.maximum(1 - p, 0)) * np.sqrt(2 / np.pi)\n", + " # b = p * np.exp(np.maximum(1 - p, 0)) * np.sqrt(2 / np.pi)\n", " b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi)\n", " q_r = b / np.sqrt(t + 1)\n", "\n", @@ -285,19 +302,62 @@ " return x" ] }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "def _inverse_rng_fn(rng, theta, lam, dist_size):\n", + " log_u = np.log(rng.uniform(size=dist_size))\n", + " pos_lam = lam > 0\n", + " abs_log_lam = np.log(np.abs(lam))\n", + " theta_m_lam = theta - lam\n", + " log_s = -theta\n", + " log_p = log_s.copy()\n", + " x_ = 0\n", + " x = np.zeros(dist_size)\n", + " below_cutpoint = log_s < log_u\n", + " with np.errstate(divide=\"ignore\", invalid=\"ignore\"):\n", + " counter = 0\n", + " while np.any(below_cutpoint):\n", + " counter += 1\n", + " x_ += 1\n", + " x[below_cutpoint] += 1\n", + " log_c = np.log(theta_m_lam + lam * x_)\n", + " # Compute log(1 + lam / C)\n", + " log1p_lam_m_C = np.where(\n", + " pos_lam,\n", + " np.log1p(np.exp(abs_log_lam - log_c)),\n", + " pm.math.log1mexp_numpy(abs_log_lam - log_c, negative_input=True),\n", + " )\n", + " log_p = log_c + log1p_lam_m_C * (x_ - 1) + log_p - np.log(x_) - lam\n", + " log_s = np.logaddexp(log_s, log_p)\n", + " below_cutpoint = log_s < log_u\n", + " print(counter)\n", + " return x" + ] + }, { "cell_type": "code", "execution_count": 5, - "id": "2578a9d6-6743-4ba0-8b03-5d083d778a3a", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_3879/1238690607.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_10806/1238690607.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", " poisson_idxs = np.broadcast_to(p >= np.maximum(3, 2 * lam / (1 - lam)), dist_size)\n", - "/tmp/ipykernel_3879/1238690607.py:7: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_10806/1238690607.py:7: RuntimeWarning: divide by zero encountered in true_divide\n", " (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))),\n" ] } @@ -317,24 +377,27 @@ { "cell_type": "code", "execution_count": 6, - "id": "f39c9fec-327c-4f1f-ae6a-2a8494b87489", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 5.14 s, sys: 104 ms, total: 5.24 s\n", - "Wall time: 5.26 s\n" + "CPU times: user 3.09 s, sys: 57.1 ms, total: 3.15 s\n", + "Wall time: 3.16 s\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_3879/2335405135.py:69: RuntimeWarning: overflow encountered in power\n", + "/tmp/ipykernel_10806/1113335044.py:69: RuntimeWarning: overflow encountered in power\n", " V * _q_l * _q ** (_t - raw_left) * (1 - _q **(_t+1))\n", - "/tmp/ipykernel_3879/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", + "/tmp/ipykernel_10806/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" ] } @@ -364,8 +427,11 @@ { "cell_type": "code", "execution_count": 7, - "id": "b76564d3-eea8-4950-9d41-adbf2b56814a", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "c = np.zeros_like(p.flatten())\n", @@ -377,14 +443,17 @@ { "cell_type": "code", "execution_count": 8, - "id": "1b370c54-7dc6-4c9c-977d-20bd410f5a7f", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_3879/1687800886.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_10806/1687800886.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", " (p / (1 - lam)).flatten(),\n" ] }, @@ -400,7 +469,7 @@ }, { "data": { - "image/png": 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\n", 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f4AP8KB/f7MMSd0gCX4gHUIMGXuc/H58L+gIvNr6NH3hwqQQ9cTANmuU25ZaPjpikik1SD+VRTQ/cAA4PgKH47/l1UlLs7IEggS/EA6ZFizlmWWEZiwgnKkeYO/pGOPvG8WGijP94H+VSm3bNIRK3yP3ITqy2B9kYxC0YTvOB9Ef5UX5ssw9HvIsk8IV4gPj4zDKDQlGlyhHnRXhlCqIm9CUh0NTfXKT6rcvoAz1k+pMk8jFUoQUHemF3ngRJ/j7/gJgUO3vgSOAL8QBp0GCxOsWxie8yV7oIbR8qbRjL4rU9SvN13J449rlVsokIVjISzsCxDdiR5sf5a7yPZzf7MMRdcs8CXyn1MPD3gB7gL7XW//pe7VuIB51DmzYOM5ULfOvF38G3NCQjMFVGXy5RB6pND6Ugu7+HRF8Kcp0e/K4c+ZFx/m70v8WSYmcPtDsKfKXUF4FPAEta64NXbf8Y8C8Ia6n+ttb6N7TWp4FfVUoZwO8BEvhCvAMeHg0a+PjEiDHPLDNMc2LlCAtf/S4s18Phm9E0bk+c0usLeMeXiD7RT3YghakIL8o+Mwwxi0/xN3mMxzf7sMQ9cKc9/C8Bv0kY4AAopUzgt4CPAjPAEaXUV7XWp5RSPwH8beDf3eF+hdiWGjSYYxZNACiWWWKWWY7Pfx9enodiEwZT6LZH7YVZan0JVF+CXMkhno1C3YWWB/u76Y0N8nn+nhQ720buKPC11t9VSo1fs/k9wAWt9SUApdQfAj8JnNJafxX4qlLq68B/uN57KqU+C3wWYHR09E6aJ8QDJSBgjlnatGnTwsXjhfZ3qJ6+BH81Ab6GchtHQckJ8B2feM0l895hjJoL+ThYCgbT/HLX59jF7s0+JHGP3Y0x/GFg+qqfZ4D3KqWeAz4JRIFv3OjFWusvAF8AOHz4sL4L7RPivtSmTYECDi5L3ixHLz0P37wE1TZUHfSuPJVyi8aLcxgHuukaTRNteGGv/ulB6E9JWYRt7p5dtNVaPw88f6/2J8SDQKNp0qRNmzp1VihwgmPUj52Hy+WwZv2ODO3X5im9OEMwliUxmiIdtzBKDqRtODQA/Sn+Np9jkKHNPiSxie5G4M8CI1f9vKOzTQhxGwICFligQpkGTU7UX+PC6lGYKMPLc5C2CZoelUKTZsLGnK/RHTGwd+Yh36l8+f4dPNH1AT7JT2/24Ygt4G4E/hFgr1JqJ2HQfxr4ubuwHyEeaBXKFFihoFf43tk/xT03B2dXYbUFtTatwRTl1xcJxrMkRzOkc1GUZUC5Ha5E9dQg/03+f6CHns0+FLFF3Om0zD8AngN6lFIzwD/RWv+OUurzwDcJp2V+UWt98o5bKsQ2EBDQpEmlucKpxVc40zzBoj8HZwrQKWjmj2WofH+alhdgjaTpqrSJRE1oezCUhoe6OHTox/kp41ObfThii7nTWTqfucH2b3CTC7NCiLdq02ayeYGps29w6ZXvMpdaJrAV/MUlQEHcohExqaRsdDZKuuaQfLwftdyAhgtdCaz37+LXhv9nkoYUOxNvJaUVhNgCmjQ5Xn6Fyz/4PhOv/oB6tAkFH06ugBvgN1xKWuOgiOztIndoAGumAp4O6+T82G5+eO+n+EjkRzf7UMQWJoEvxCarUuUcZzn2/a8zdfwIzJcgGYXJElQd6r0JKsUWxCwyvk+y2bl5aiwH/Uliuwf5tX2/QZTYJh+J2Ook8IW4xwICKlSoUqFNm7PBKU6de4Hq178VrhlrGhA38VablBoebszEztjk4hZmLAJLdSimYTTLR/d+mg/s/kkUxmYflrgPSOALcQ9pNNNMUaGCgeJI6btc+s634fQKNH1wA3SxTb3QpKpBtTyyUYvEcBpGMuFNVLtypD/3ET6X/AckTBmrF7dOAl+Ie8THZ4IJJrmMg8Mrr30V78vH4OwKKAUNB9cyKKUjeBNlYpZBxiAsdtaXhKgFVYcf/fHP84HMz2z24Yj7kAS+EHdZQECLFrPBNJeqZ5gOLjNVuwC//XJYFiFiooOA6mqbenkJY08X+cEUsd5EOPvm0AB4Pj1+L3/t2V9i56PPbfYhifuUBL4Qd5GHxwwzFKsLvPr6V5mrXcKvt+Bbl+FyCUayOG2HklL4UZN4yyUzmsFAwWO98NQgKMUnmz/F7u5HSfb2YpjmZh+WuE9J4AvxLvBaLerLy3jtNtF8FtWVYIlFzq28yeL0OebfeJ26WYf5OlwswoklAjegmojQWGxg9Cfp2pUlOl8N69/s7YaP7mRf+jF+jl+UEsbiXSGBL8QdahQKzLz8MoZp4pkeS+fmqfcETF04RumVkzSrqwRzlXC5QUNBPk5bQ2m+RpCxSQwkyRigah4YJnxgBPPwCH8/+t+TJbfZhyceIBL4QrxDge+zeuEC5/7sz9BaE+vKU99lEaTjnP2936U+t0A7paHQgIslSNoECioompkYZqxBd6GF3ZcKyyJETfjZx3nq/T/FT/LJzT488QCSwBfiHSqcPcvK2bMYpondk2exOcPi8RlKiTrFhSl0TEEb6I7BOWg2HcqGgS61SI1nSO3Oo7wAsjaYMayffozPP/e/0iXFzsRdIoEvxDvgOw7lqSnsvhzV6ZMUG3MsnzvLyqnT+CtVqLrhE7ui+OkoZdenXfOx8jFyKCJuAOM5SNnw1ADPPvNpPrZbisqKu0sCX4jb4DsOtUKRiYsrHD+2SjPvEMzPUjz+Ao1GGXQASkPDgahJY6VJBdDdMdLTNZIDSVQ+FpZOCDT2rn7+1nP/P/p3PLTZhya2AQl8IW5RZXaWhWMnePNMheJKjeWJ16jqOgvlVXKrHlnfCefN9ybwkg5lwHECIoUGuUwMazQdli/uS8K+bt47/CN89EO/ip1MbvahiW1CAl+IW9CuVlk8dowqMVbaLWruWVZak9QnZ4jETJbbWZLpFmbappGMUAmSUGqTSRkkYxEYy8KuHOzrJndwP7/Y81m6ekcxI5HNPjSxjUjgC/E2NJrZuTOcXXmTo4vLTL45jYpUCVaLoBRKA2WHpu/Tjrm4NYdoyia7J4e5Mwc7MvDsDlhp8tef/TxP5z642YcktikJfCHexuziOV788heZf+N1Vheb1JaiJGmAr8EP0MMpGsqnWK9jWya5iEHcDwuhEbWgP0nPSoqf2fVrDGQPbvbhiG1MAl+Im2jVq7z8lS+xcPJN6tPTxCwLq5ah1QqIpjSu47E82SBqtUiPxMjGIxjZGAynoCcOP7KTT3X/Mg/1HCKazaKU3DErNo8EvhA3UFyd43vf+CIn/uiP8JsNaPuYrsdQq8RKO8tKJEM7HSHjlhmx6iSyefj4Xnh6AAxFz3KSXzn4z0gmc5t9KEIAEvhim9NaUyq1qFYdYjGLRJeiblWZWjzFG1/7I+befIVguQwZGyImRAxINbG8RbqjVRI9SbIxEyOSga44HOwBQ/Fx7+P0GVniUalXL7YOCXyxbfl+wLFjiyws1FAG1Pw6tWgJvXSOV/7smzROTZGprJCttzDcgCBiUK0FNAwDM2HTMxgn2puAoVSn8mWGsfhuPtL6ME6pSteBvRiW/BMTW4f8bRTb1vx8jenJVaLJGiVKTLTO8eafXKT4ygUG3SnMUosVM0fTt8jXl6goTeBBMmaSjhmovd3h3bJRhTmS4yee/TyZYhpiMPDEE6SHhjb7EIXYQAJfbFtnXr/A0pljNGKrLMxfYGFqitVzBqrUQrktzIZDwnZYbBi0sUj2m3QbCvt9Q5COhcM3XsAj6af48KFfoHff/s0+JCFuSgJfbEuzE0t852svcrE6R2X6HKnpy5jKhcUkmIDt0zYDalrj2Qq7rehNRlD5cOYNP7abvJvlF71fJJvpJ5JIbPYhCfG2JPDFttJouLz55jxf+f//JbOXL7CwOE16foainyBpN3CCCNlglbrZxiHANCxSsRR5s47a1wUfGIOffpifMj/FIZ7a7MMR4rZI4Itto9l0+d6Ll3npxEkWmiepepdpz7TQOonttZhvduHrFo3AIOdG6IoGKJ0giktsOAJDaXo/9UP8LfPvESO+2YcjxG2TwBcPtKWlGpcvl2g0XFaaRd70j3KyfYZg4QKR2RKDXgkniOBoTTvQ9EVm8L04TT1KOQajmXkSgwaLux5hbN8n+OD0z+BGDGLpzT4yIW6fBL54YE1NlXjl+bN41XlWg1n+4uIkda9K9PQUreMNEgkHI/CoY1INIKkq9HTbxGtttD1Lra+fyFiWlYGH+NBjP8G+h97LaqHJ4sI0zzwzQiYT3exDFOK2SOCLB5Ln+7z83aPUVy5STJQ4N3ME9eIyhfNJop5HO0izWo+S9KvUlcZQUXZYVeKY0BVBfWQc006THXqajz38HH1DAxiWSTQGlUqbixdXOXRocLMPU4jbIoEvHgheq0W7UkFZJqVci6P1E7w08V2cSIHVb1yifrTGYiFNqZkgaQR0x2YoWTYFJ8dYvEg8YZCyFezOwZ48+Wcf50czf5PAtRkY7dqwr2QyQrHY2pwDFeIOSOCL+17x8mVWzpxBa81M7TJnG+do5SLMvHGRyrkWtUmoNXpo6SixoIxjtVhsxeixW+SzDoOJKq3xFI2xfSQP93A4+Szjgz9MPGHjeQGtlkcsduWfSrPpkU7bm3jEQrwzEvjivtYsFlk+dYpoT55zp07yx197lUsXfWqrdWplg6QPyjdJmA2arkNTtRkMVrCjCfpVEztq4DcVgzub2IceZm/iI+T6RujtS7F/fw/lcovXXpsnn48RjVq0Wh61msOjj/Zv9qELcdsk8MWW1Wy6eF5AMmljGNcvK1xbWCCIGpxeOcvv/vuXODujUV5AfSVCsZWiSpwAl7i1hK998rSJ6yRRU+FEkqi8Se/uGH/j//U/8J4P/jSeFwBgWQYA8XiEJ5+E8+cLVKsNkkmb97xnmK4umZYp7j8S+GLLcRyf48cXWVpqABCLmRw82Edv78a1X13X5/WTi/zla6/z2gtnufiGRSziYzRdrLaDSZQ6HooGUU+RjthoL4FHBe2DkTbZu2cHP/9ffYZ4PYrWej3orzY4mGZgIEUQaEzzrY8Lcb+QwBdbzrFjixSLTfr6wnIF7bbHq6/O8cEPjpFKhWPns4VV/u3vf5vv/OAEi29MU1uxcT0DzzWw2xqLJp5RhSAgoUyU7iGhizQjUeykxhrK8DOffD/P/PCzRGwLw7JuujiJUgrTlMVLxP1NAl9sKY2Gy/JyYz3sAaJRC9N0WFioMj6S4tz5V/lXv/knvPRaFYo11EJApGlRC3JEqeNQpYlPJNB4dJMwapjapxlJYveYHHx2Nz//mZ+hf3gAt9HAqVYZes97NvGohbg3JPDFluJ5AdfraEciJo1ai4mXj/KN7/8JR19cpTmtMKtNFCZpo0k5iNCgjg1ESeCTJmM79OZqWK7H2NMmz3361/jYhx/DW5yitbqKncnQ/773Ee/qeutOhXjA3LPAV0rtAv4RkNVaf+pe7VfcHxzHZ2WlTqPh0my6OI6HbVv4vmZpqcbJU8vk0mUmT/4Rp789SelyL+2WRVPn8DCJsUSUBQwjQTRIoLGJWw6DuRVihsPwIwk+9su/xtjOvfSN9qPGBjb7kIW45+4o8JVSXwQ+ASxprQ9etf1jwL8gLDT721rr39BaXwJ+RSn15TvZp3jwlMstjhyZw/MCDCMc1nnjjUX27Mlz4ewcp988T9O5TOXsS8xO27iVJBUnTltH0LRwqaLRmOQZpMZYzyyRqE80ElCxe9i5ex/v/9TPMr5rD48/PiALiYtt6057+F8CfhP4vbUNSikT+C3go8AMcEQp9VWt9ak73Jd4AGmtOXZskWjUJJeLEgTQ3Z3g4sUip0+d5lt/9B0a7SX0yhJBFWYa/bi+ifbbONSwqKNIoBkkruqkrQZDwzX6PzHI44NPMd7zOMPv+zDJ7q71C75CbFd3FPha6+8qpcav2fwe4EKnR49S6g+BnwRuKfCVUp8FPgswOjp6J80T94FGw6VWc6jVXC5fXiUIND19CY6eOs2rX/8B1WqDekmh2j1YhofjKKCGT4M0dVx6SGCRMFY5kDxHNKnYtz/HE/kPM/rI+xh6/BDxfH6zD1OILeFujOEPA9NX/TwDvFcp1Q38L8AhpdSva63/+fVerLX+AvAFgMOHD+u70D6xSbTWrK42WV5uEIkY9PenME3F0aMLTEyUiUQMUPDS62c49fIJcnqB1moSHEXdj1PFxqCMRmOQxiKPqcCwNLbto8a6efhDD/Nz/+Dv07NjF2YkstmHLMSWcs8u2mqtC8Cv3qv9ia1Fa82JE0tMT1eIRk2CQHPuXIHR0Sznz6/SarkArLiLnHjpPPUVFV6QdQ38wKCJSxsHsDDIAzEcIGk26e+pkNndi+46zO7Hn+HyYpKKV2HHjgzxuIS+EGvuRuDPAiNX/byjs01sY6urTaanK/T3X7lb1nV9nn/+MoHvUVlZZmJxkoXJFrWqhetHcAGLBi4V2thAnAgxTEw0AUQU9MYwBnsZGRoEUnz/9RZmukyl0mJqqswzz4yQSEjoCwF3J/CPAHuVUjsJg/7TwM/dhf2ILc73A1ZXmzSbHnNzlXDIpkNrjVetMHXyAq997wILpQqlsoXvxwlQgKKBj4EDJAjIY2JiKRfDDFAxiyBiM5zP8t4nHiabtYlETEzTYH6+Si4XQ2vNxESJAwd6N+0cCLGV3Om0zD8AngN6lFIzwD/RWv+OUurzwDcJp2V+UWt98o5bKu4rrZbHq6/OUq06NJseR4/OMTtbY9++brJxmH7lFd58Y5pXJkyWamHv/Yo2UAZ8ApJAEjDDqZdWQFePixXNgk6Sj9mk0xGaTQ/LMsnlYiSTEebnq+zf38PiYk0CX4iOO52l85kbbP8G8I07eW9xfzt/vkCr5WPbBkeOLHLuXJFz51Y4c2qO5cklSuUqpVYMxzevelUAVIEGYV+hGzA7/X2NQuNbMVKZfnKZFKurTXr6wqJmunN5v7s7gVLhcFG77clUTCGuIqUVxLsuCDRzc1WSSZuvfe0Mx44tUqs5xG2DqfPzrJabBD64gUEY8gbQIuzVB4Q9+jSgUAREbE0sZxD1DdKJOI5r4bZdPvRMD8mBIbL5JL29ScrlNqYJ1apDf3+SatXhwIG+zTsRQmwxEvjiXddsupw9W+DEiUXOni1gGIp02qYwu0S10qTtajyigCIM+CJh4FtAF3DlIqsyFYlslD37uulNpTgwnsTQHu953w6eeOYhUpkkJ08u4Xk+hUKTiYkS0ahFNhvn4ME+enoS12uiENuSBL64I67rs7hYp1BokE5HyeWi/NEfneSll6Y4d65IodCgWm2BDmhUGjQ9g7BH7wMOUCEM/VTn11rZA41haGLRKIM9eXpTeT7wgRF++IfHqVTaPPPMCLlcDIB8PsbCQo1azeGDHxwln0+QSERuuGiKENuVBL54x1otjx/8YIpm0yeVirCwUOfYsXneeGMexwnr4hiGplZzaLd1J8rXwr5M2Ku3Ccfq1/4qapIpl/7ugF0jaUb3PsLgUJ4nnhhgaChNterQ3R0nm42utyMatRgby93LQxfiviSBL96R2dkKzz9/mYmJMl1dcUZHsyQSEb71rYucPr1MPB5hebmB6wb4XnhFNfzfOuGFWYAs4ewcBQYkMh77n27z6Y/1cXBoJx/42I9hx9OcO1dgbq5KreYyMpJlz54uKYAmxDsggS9u29JSjTffXKBUahOJGJw7V+Cb37xAsdjk5MllarU2Sqkw7P21VzUJe/UOYa8+C1iYyifdbzB4MMlTT+V4ODHM7sEBdCrLS0dWeeyxCI8+2s8jj4QXX2WYRoh3TgL/AddqeZRKLZSCfD6ObZtv/6KOSqVNtdrGdQO6u+NEImFJhJMnl2i3Pd54Y55Ll1aZm6tSKrVYWmquT49c68+Hv9cIL8wqwqAPL6RagB2N8dCePsYH86i5CPv/xp714RnX9Xn99fkNSxsKId45CfwH2OxshePHF9dD2LIMDh0aoKcnedPXBYHmxIlFTp5cZnKyTLPpUiq12LEjg2Fovva1c8zMlCmVnM5iJT6ed713coESYe8+RRj0Vz5w7EiEdDbGwYeGiEYt8vnYhrH48M5ZxcJClT17uu/kVAghkMB/YDUaLseOLdLVFceywpIGYa98gQ99aOf6tmsVCg2OHJnl9dcXaLVcduxIMzvronXA8eMLHD26yOxslXq9jefpGwR9QNirrxFepO0iDPxQxIRcCuLJKIMjXfT3Jzl4sI9isfWWd7IsA9cN7vBsCCEg/NcoHkCFQgPDUBuCPRq18DxNqfTWYAWYni7z0kszXL5cwvM8CoUG588XqVbbZDIx3nhjgfn5OkqB53GDsG8DK4RhHwd6uTrsDQMyaRNlWuS70xw6NMDcXI1qtU1/fwrH8Te8W7Pp0dt7828kQohbIz38B9TNJrFc/ZjWen3h8DNnVujpSbCyEn5YZDIxCoUGMzMVlpfrTEyUaLc9PI+rxurXrJVFqBMO23QBsSv7BCwL4lEY3xEj35ujbzDL8nKDarXN+fNxhoYyLC/XicUimKai3fYZGcmQTEZYXW0SjZokkzKWL8Q7JYH/gOrqShAEYZhfPaRjWYpsNgziiYkib765gOP4WJZBqdTi4MF++vuTzMxUWF1tMjtb5ejRBSqVNrXadbv0XCmL4HOlLMLGL4/RmCKbiTM4mCTfm2R4OE2h0MS2LQ4dGmJoKI1SkE5HGR3N4Tg+PT1xVlaaPP/8BEoptNYMDqY5eLDvhkNSQogbk8B/QCUSER57rJ/jx5eAsCdvmgZPPTWIUvDtb1/kj//4NPG4he9r6nWHUqnN0lKDgwd7sW2Dl16a4fz5As2mf4O9BIRB3yT8q9QNRDc8I5FQ5PMJ9u7tprs7zvBwmqNHl/F9RSwWIZWycRyfVssjn49TqbTp70+STNrMz1e5eHGVvr7k+nTM+fkqsZjF/v09d+nMCfHgksB/gA0PZ+juTlAqtfC8gEQiDNhXXpnl93//BLlcjEqlRaHQYmQkQ7vtc/lykddem2NycpWzZ5dpt2+0yuTavPqryyJc6XUnEgbJpI1lmRw82MfQUIa9e7u4dKnEzp1ZhoYyNJseuVyMYrFJu+0Si1lUKg5BEO5zYqJENhvdMPe+uzvO1FSZhx7qljn5QtwmCfwHnG2brK42mZgoYhgGlUqbubkKtm2STtssLdXo7o6zvNzA83xeeWWG1dUmpVIL173eO15dFiFCOFa/cVzdsmBwMM3hw8PUag779/ewe3cez9MoBQMDaUxT0Wi4mKYiHo/Q3Z2g1fKIxa6M03tegGluDHXDUJ1yyJordXeEELdCAn+L01pTLLZYXKyhlGJgILVeNOzteF7A889P8NJLM6TTNr29iU6xsxpaa+p1F9fVtNstzpxZYXq63Olh3+gdG4RhrwnH6a8udhYyTUilbJ58cpAnnhik2XTYubML01SdgmagtSIetxgdzVIoNDqvU9TrLocPD6333IeHM5w7t0Jv75W/ppVKm97eJKYpY/hC3C4J/C3u3LkCFy8WiUbDG5YuXSqyf38Pu3bl3/a1x48vcuTILMPDaSxLUS63KRTqmKZBteowO1thZaXJwkKN+fkq7faNkt4jDPo2V8oibFwnVimIxQzicYv9+3sZH8/z5JMDvP76PAcO9GKa4UXXdNrmxIklPC/gmWeGWVios7ra4H3vG2F8PLdh0fGRkQxLS3WWlurYtonrBkSjJvv3y01YQrwTEvhbWLXa5tKlIn19ifViYb4fcPbsCgMDSWzbuuFslXrdYW6uQiplr68lm0xGOHeuxcxMhQsXCjhOWEN+eblxk159jY3Fzt46J76rK9pZXjDKzp15Mpkoy8t1Tp9e4dChQSYnS8zMVHAcj76+FP394SpV1arD6GiWD394J+l09C3vG4mYPP30EIVCOMSUSkXo7U0Sidx6eQghxBUS+FtYpdJGKTZUhjQMxdJSnf/yXy6QTEbIZGLs399DV1d8w2vbbR/LMslkYjQaHomExcpKnVbLZXm5itbg+/omYe9ypdhZlLViZ1czDIhGFT09CTKZKO973wjZbJTp6QpPPjnE2FgW3w/42tfOkUxGSCQsLl8u092d4POff5rBwfTbngPTNOjrS5JMRpiYKHH+/CqplM2uXXny+fjbvl4IcYUMhG5BaxclLct4yw1OCws1JiaKJJNhb9f3A15+eYZKpb3heYlEhCDQjI9ncV2flZUG58+vculSiWKxheO4TE2VrhP2mrBHv0wY+jk21qsPGQak0xFSqTi+f2UGULPp0tUV5/HH+/F9zQ9+MM1TTw2wY0eaeDzC0FCKWMxkcbF2y+ejXnf4wQ9mWFioEY2a1GoOL744w9LSrb+HEEJ6+FtKudzi7NkCq6tNbNtkbCxDJGLSaLjrAX7uXIHe3hRdXWHFyUQiguv6TEyUeOyxfrTWNJsepqnYuTPPxYurdHXFefPNBV58cYaJiRL1unODsggOYa/eJbxLNsvVxc7WRCKQzUZJpWxyuTjxeISdO3NA2CPfvTvD8eNLXL5cpFJx2L27i+7uK0sNLi7WmZ2t8sQTg7d0XiYnyyilyeXinf2bWJbBmTMr9PYmpTa+ELdIAn+LqNcdXnpphljMWp9Nc/bsKsPDacrlFktLDVzXo9XyGB/PUSq1yGajWJZBLGZRrbZZXW1y/PgizaYXLisI1GptvvOdSaamwnH7ev16N1FdW+wsT1gHZ6NoFAzDZGAgycBAmoGBJN3dCQwDBgYypFIRLMvAcTQQMDKS5dixRc6fL7B/fy9G5/tku+1dd8z+RgqFxltKKsRiFsvLdTwvkDF9IW6RBP4WMTNTwTTVet33SMSkpyfO4mKdD31onFbL48KFAqdPrzA5WcI0w17ugQO9uK5PT0+CI0dmSaVsGg2HF16Y4eTJJS5dKmIYsLBQvUHYtwl79R5hyGe53khfKmWxY0eaWs1leDjDQw/1kMlEKZfb9PeneeihbkzT4Pz5An19qfXpo9Vqm4mJEr29Sbq64tRqbbSGRx7pveVzk8lE17/1rHFdn2jUkumZQtwGCfwtolxuEYtt/OMwTWO9Ho7va+bn6zz2WB+vvDJHrdam3fY5fnyR3bvzpFI2rZbHnj3dfPvbE8zNVZidrVKphHfZ1mrXhn1AuIB4g+sVO1ujFAwOJsnl4vT1JVhZaZJIROjrS6wXNNuxI82ePV1MT4c3dD3+eN96r/vQoQHqdZdKpUW77ZLJxPjUpw5sGOJ5O+PjOebmqkQiBvF4BMfxWV1t8thj/XK3rRC3QQJ/i+jqinPpUmnDPHTX9YlEDGzb7ISpQbPpEYkYxGLhmP7UVJne3iR9fQkcx+Oll6Y5eXKJ8+cLzM/XCILrVbZ8+2JnEI7V53JR9uzpIhIx8byAhx7q4qmnhvH9gPn5Os89N8JDD/VgWeFsmtOnlykUmgwMhCWRBwbSvOc9w+ze3UUuF6O7O37bFS+z2Rjvec8wZ86ssLxcJxq1ePzxAYaH336WjxDiCgn8LWLHjixTU2WKxSbpdBTH8alU2jzxxACmaaBUOAd/errMwECKWs3ljTcq1GoOFy+uYhga27Z45ZVZvv/9yZuURahwpdhZD9eWRYAw6DOZKL4fXih9+OFeUimbSqVFNGqyd2+4aMmBA72Mj+fWXxePW3R3x5mcLJLPx1BKUSq1GBnJ8uijfXd0cbW7O8H73z+6Xm5BLtQKcfsk8DdRve7QaLjYtrk+j31iosTiYo1EIsLTTw/R1xf2lPv6khw/vsj0dJnJyQqXLxeZm6sQjZpUKk0WF2sUCg1OnVq6QdhfW+wszY1q0cTjEdLpKK2WRzYb47HHBohGDRoNF8cJ+PjH9xCJmHz72xMEgV6/N2BiosTKSoOurjgzM1X6+xPs29fD6Gj2XQtoKYssxDsngb8JgkBz5sxyZ7phOOTS3R3niScGOXCglwMHwguarZZHu+2xstLgwoVVTp9e4VvfuoRSsLLSYHW1CRjUag6+X6FQaOK/5brstcXOurm2LMIaYz1LNe22h2EYPPJIH4ahaLV8BgfTRKNhOeVUymL37jznzhUAOHt2BdNUDA6mOXCgl1Kpxc6deUZHc+vv77o+y8t1Gg2XbDbWmeEjPXUh7hUJ/E2wsFDl8uUS/f1X5pCvrDQ5f77AI4/0Uam0OXFiqTMds06l0uaxx/qoVFrs2JHmlVfmKJVa+L6P70O77eD7XOcmqjrhEA5AhnC8/q0BqxRYlkIpjWVZ2HaESMRkZCTLk08O8vTTQ0BYjK1cbpFIhB8Ye/Z0kUhE+PrXz2OaipGRLIODaWzbpKsrxmuvzVMutzDNsDLnhQurnUVYDBwnoKcnzpNPDkmvXYh7RAJ/E0xOlslmoxuGObq6YszMVNi5M8crr8xiGOFNVeVyC63h4sUip08XKJUaVCoNmk3dqTzJdXr1b1/sbI1lhSWUbdvC8wLS6SjZrM3DD/dy4EAP9bpLq+V1Zvo4jIxkOHt2BdcNGBxMMTiYZu/eMPivDu65uSonT66QTkcxDPjmNxfp6Ylz4EDf+nOWlurMzlYYG8u9OydWCHFTEvibIAj0W8a0w4uymunpMidOLDAzU6PRcJifr7F3bxcTE0VOnFjsTNFUgL5BWYQ6b1fsbE0kEu7XNCEeN8nnU+ze3U0uF+NDHxpjdDRHve5gmuF0yFwuysxMlVjMxDQN5uerDA6m6e1NsrBQXa9tU687XLhQZHQ0Sz4fw/MCDENRLLY7Ne/Dv3aZTJSZGQl8Ie4VCfy7xHV9isUWQaDJZqMbplvu2JHhxIkl4vGwLIJtm8zMVKhW2/yH/3CUH/xgBq01sZiFYSiOH1+g1fLJ52MsLtZwnOtVO3OBUuf36xc7W2OaYNsG0ahJEIQfHrWai9YwMuIzNpZl58489brLs8+O0tOTwHF8vv3ty3R3x9d78qlUuAzho4/2dy4aN0kmI8zNVfE8f73cQvihYuD7AfW6ux74QaDXyz4LIe4+Cfy7oFhs8tpr8zSbLoVCnWKxzb59Xbz3vSN0dyfo60syP1/lzJkVajWHUim86aqnJ8Hzz09QqzkopfC8oFMXxyAaNbAshev61/TsNVdKGBuExc6uf1NTMmkSjVpEIgbNpovvB+RycbSGIAhIJsNevFJQqTgcPjxET0/4XvV6uPTgtePt0ahFs+nx7LMjzMxUKBab7NiRIRq11u8aDiteJjh3rrC+glUQaCqVNk89dWv1dIQQd04C/13m+wGvvz5PJGIwPd2gWnVIJiO8+uoCCwsNnnlmB74f4Lo+XV0JursTuG6Byckyr702R6Ph4nmaZtNFqfBCrO8HOE5AvV69Juwdwl69x42Kna3NAorHDbLZGNGoRaPhAAaxmEEyGcM0w+GVnp44Dz3UzaFDYXXLoaErNzbd6MKq5wXE4xbxeIS9e7vXt33ve5PU6876TVZdXXF6e5M0my6uG6C1Zs+eLvr7U+/OiRdCvC0J/HdZpdLGccJAr9Xa5HJx5uaqzM/X8DyPmZlw7nwkYjA6msF1A44dW6RabXP+/Aq+r/C86y8cfiXsb63YGUA0amCaBiMjGZQK14/t60uytFTDMAwymQi+H04LtW2LINDE4xGazY3lNFMpm+7uOMVii3w+LMHQbLoYhqK398p1giDQlMstensTXL5colIJrwFkMlF+4RceIwg0juOTSEQ2DHMJIe4+Cfy7pFJpY9smxWKDlZUGqVSEaDSs8Pjqq/O4bsD4eI502uaNN2aZm6vRbkM4RHMzbcJevU84dJPhZssaWJZBKmUTjZrk8wn6+sIhpe9/fxqlNIlE2APPZuO02y7xeDjP/tpaN0opHn98gBMnllheDtehTSQsnn56eH1M3vMCXn99jkKhiWWFHzSGAYcPD9LdnZC7Y4XYZPcs8JVSu4B/BGS11p+6V/u91zKZKLYdBrDrhitKrS34sbRU49VXwzn0zabH1FR5veTx9StZXu3aYmfdhBdnbyyZNOnpSZBIREgmbfL5GIlEhIsXi3R3x0mn7c6i5ZpWyyWZtBkYSBOLWYyNZd/yftGoxVNPDdFqeZ1vAtaGEJ+eLlMoNOnru9LjL5VazM5W6em58WwhIcS9cUuBr5T6IvAJYElrffCq7R8D/gVhAv221vo3bvQeWutLwK8opb58Z03e2kzT4MknB3nhhSlKpRaTkyXqdY9SqcHKSpNGw2VsLMfkZBnHcWm1/FsI+1srdgbh3bK2HdbIHxhI0dOT4MCBXmzbIpOxicct9u3roVhsUS43efLJQdptH8fxeOyxfp58coidO/MbhluCQLO62mRlJfzw6u9Prd98dbWZmQrZ7MYPoWw2yvx8jYMHAyllLMQmu9Ue/peA3wR+b22DUsoEfgv4KDADHFFKfZUw/P/5Na//r7TWS3fc2i3McXxKpRZKQS4X46Mf3U2j4XLkyAzT02XK5RalUhvLMjoVH00cx6Nev+7SUx23VuwMwhuoLMskGjWw7QiZjE2z6eG6mnrdZXAww9BQil278mgdjskXCg2y2Rj79vWQy8U21JtfEwSao0cXmJ+vEo1aeF646tbhw8NvWUfXMNRbKnOu1dqR4RwhNt8tBb7W+rtKqfFrNr8HuNDpuaOU+kPgJ7XW/5zw28C2sbhY4+jRRXw/vKq6dpF0ZqbC4cNDOI5Hu+1jGC7lcqszA0fRbF63ylnHrRc7i0TANBW5nE0QBOvz2xOJCH/9r+8llYpy8uQSWge0WuG3CcOAnTvzeF6wYQjmWktLNebnqxtm07RaHseOLfJDPzS2oRbO2FiOY8cWiEavlIwoFluMjmalZo4QW8CdjOEPA9NX/TwDvPdGT1ZKdQP/C3BIKfXrnQ+G6z3vs8BnAUZHR++gefdGq+Xx5psLZLPR9UU/Vleb/Mt/+SIXLhSpVh0WFqqdcXoH19Vo7aMUN1hX9taLnUHYsw+HSgJ8H7Q26OlJMDCQIpWysSyTWMxkcrLEI4/00tUVzrDxfc3p08scPjx00+NbXKy/ZfgmFrOoVMIiaGtz7QGGhtJUKi0mJyud6aCa3t4ke/Z0vd1pFELcA/fsoq3WugD86i087wvAFwAOHz78dlNWNkW97lAsNjEMxepqk2PHFrAsg6GhDIODKV59dZapqSqrqy1WVxuUSg6+H6BUsF5C4a31b+BWi51dTakwgKNRk4GBFM2mRzodobs7jlKKU6eW2Lkzz+7deUBdNcQC9bpHNhul0XApFpsoBV1diQ0rb9m2ie9f+WOo1Rzq9fBmseCa2g6GoThwoI+xsRzNprde9lkIsTXcSeDPAiNX/byjs+2BdvlykTNnVjAMxfR0hS9/+WRnvn0C3w/o70/SbntUq2EdnEqlRavloXU4jGKa4Xq1ruvjOGvv6hFOtXQIx+hz3MofTSYTPiefj2EYBpVK+IbVqkO97rJzZ77zzcJleDjLjh1p5uZqQDjNcnw8Q7vt8Z3vTHSGYDSgOHRoYH0IZ2gozcRECdf1mZmpMDdXpV53SSRsjhyZ4+mnh98S6smkfdurWgkh7r47CfwjwF6l1E7CoP808HPvSqu2IMfxuXhxleefv0wuF8fzAv78zy8AmmjUIpuN0m57HDkyQ63mEomYnSJpYdA7TljVMhzK8bEsRTg+f+vFziD8wNAa+vvj7N7dzcxMGdM0O+u9WuRyMbSGdtun2fTo6UkwNJTi+PFlTBOGh7P09CTIZKIsLdVZWGgwOJhav5PWdX2OHl3gued2YttmZwGUfl58cYaTJ1fI5aIMDYWLlntewNGjC3zgA6NyUVaI+8CtTsv8A+A5oEcpNQP8E6317yilPg98k3Bmzhe11ifvWks3UaPh8vLLM0xNlbh0qUS1urTe400mI9TrLlNTJdptn7m5Ko2GRy4X65RJCDBNk3BsPgxrrcFx1soiXCl2ZhjW+t20hrFWQTP8ee2DwzAUlmVgWWFhtUce6SMaDde3TadtqtU2hUKL8fEMAwMpBgZSLCyElTePHJnj/PkiAwMp9u7t5pFHelhdbW0omxCJhEM44d2y4YfP8HCGPXvy2La5PpcfwuGepaU69frGsXwhxNZ0q7N0PnOD7d8AvvGutmgLOnNmmUKhgeeFBb/6+hJMT5ep1Vwsy6BYbDI8nGZhoY5lmSQSdMojaBwnWA/rMOzDYmeGUSUIrhQ7i0TCsHWccFGTeNwEFM2m1wn6cBjGtk3i8bAswfJyg9278xSLLWKxCDt2ZJierhCJmDzySB/JZIRm08dxfEZGsp2hn/A9crkoXV0JCoXmdY/52h57NGqRTEauM/8+vB4ghNj6pLTC25ifr/J//V8XSCRsVlYaXLpUYHm5TrXqsLpaZ3KyiO9rlpfrNJsevq8xTU0QuFeN0a+5UuwsCOKEF2bDmT2uC1qH3flIhM5iJDaxmNkpdgaxWIR02sZxNFoHRKP2ei0bzws64/JZcrnY+gpY4bKFmiDQdHUliMdNisUWkUg4DARhBc61GUatlkckYpLLxTa0fGAgxaVLRXz/yg1U1WqbbDZ63ZuwhBBbjwT+TTQaLm++uUA+HycWM/E8H1DMzJRJJGzS6SiVShvP89enIYLu9NQDTHNtNk6AadZQqo7vK7TuIqxuuZFSYQnkZDKCbYd3tLZaHktLdTzPZ3Q0RyIRWQ/3tRu3Dh7sYy3UR0ayZDIxXDccXiqVmtRqLg891E0iYV0V2IpUKsqhQwMcPbqwPhMnEjF56qnBt1THzOfjPPxwL2fPrnSOVZFIWDz+eL+M3wtxn5DAv0at5lCttjHN8I7YsD5Mg/n5Kp4X4HlBJ8w9olGDrq44y8sNTNNYv+lprfyvbSuazRaWVcIwNEEQR+srxc7WLsAGAdg2mGZYqTIWizA6miaZjJJIWPT3J5idrWJZBpGI0fndxDBsnnlmBx/84CjRqEU6bRONRshkokQiBmfPrnDkyBxdXS3SaYtazWF5uUFvb4JEIrzAaxiK557bSbncQilFLhe7YSnkXbvyDA6mqFYdLMtYf70Q4v4ggd+hteb8+QIXLxZRSrG4GA7lLCzUqNUcVlaa6zXqm81wFk6jEdbCCS+0XplY77qaq4udeZ5JWMJ44/TFq+fie1447q+UQ7vtU6m0iEbDRVF6e5O02z4LC7XOMI0mmbQZH89x6tQy9brLnj1djI1lOXRocH145uGHe4nFIrz66hwvvDDF6mqTbDZKLBZemHUcn1jMwrbNDSWOb2bt+oEQ4v4jgd9RLLa4cKFIb28Czwv47ncncd2Actkhl4sSBFAogO/72LZFMmlRrbbXL8jClRk4SrUwjBKGAUGQxPfTWJax4c7atQuxa7VnIhFFImGjdThtc+1GqoGBFOVyk0wmyuBgmtHRLMvLDVw3wHE8duzI0NeXYHW1SSplc+lSkX37eoDwwmtYO0ejNXR3hwugxOMWpVKbs2dXePzxgXt8poUQm0XKF3YsLtaIRk0MQ1GptCgUGkQiJrZtdBY18YhEFJ4HiUSkswasXp+hEgRrF12LKLVKJBJB6y6CIIthhGG/tmD41WF/bbExAMMwO8samrRaHtWqS29vorM0YXgHa73eJp+P4Tg+0aiF4/idVbbK1zm2Ojt2pMnn4yQSkc7QTVjFcq3+jxDiwSc9/GusrbVaLrdYWWni+wGJhL0+Nh+LhQt7WJbRmRMfVoj0/RqGUcfzPGw7R3d3b2epQgelDNptrxOuCq01lmWiddCpK293VpwyqdcdTDO8kSuVipFOR2i3fSzLpKsrQX9/klotXI82lYrQanm4bjg2pFRYOqFUauH7Ael09LoVMN+O1ppq1cFxfJJJGcIR4kEhgd8xMJDi1KklTp1a5s0353n55VlqtRaeB9Goie8H1GpO58IsnZCH8MapMuFKVBGghyCIMDdXB9aGeK4erw+79I5zpWplEDh4XvjB4nk+th2QzdrYtoHWGs8LaDRcCoUG/f0JlArXvK1W28RiEY4eXewM/YRlHF58cRqlwvnxBw/2MTqa5dixxQ01corFFsPD6bfUqHccnzffnKdQaKFUOBS0e3eevXu7ZTaOEPc5CfyOXC6G6wacP1/g3LlV+vsTncXDw1o07Xa4fqthGCgF7fZaWYS3FjtbWzjcMMKxece5fg04pcJfth3+MTiOSywW9qhrtXbnm4DBrl35zsVSi+XlFrOzFdJpm2w2iu+H5RDK5XBlqYcf7l1fc9bzwvVyn312hB070szOVtfblsvFeOih7re06ezZFUql8OYyCL/xnD+/SjYbkwXHhbjPSeB3VKsOiUQ4pTGdtsnnw/nstZrD0lKNUqlFIhFF6wDHcSiVFjBNF9NMYNt56vVwDn40GgZzuAh4WC9nLWS1DohEwumba3fTWpbZWXzEIhIx2Lkzy/h4nlgsgu/7jI/nGBvLkc3GaDY9FhdrvPrqPB/5SFjrZm1Mv1RqUatdWWAc6JRgMFhaqvPYYwOMj+dpNNzOnbZvnVLpuj6zsxV6eq6sZ2sYinTaZmamIoEvxH1OAr8jCMLhC9M0iMfDBccty+zUp7Fpt31iMQPXreM4BQzDJxLpIh7PEotZBEELw6BTWiHamYsPvm9gmmtj9+F7+37QGbqJYJqKSMQgk4liWYpcLs7AQIpsNo5SsGdP1/pdr2G7TC5dKpHNxkgmr4yt+35ApdJ+y3EZhlq/qSqTid60XPHaBeRrh24MQ+G6cnFXiPudzNLpSKfDkr69vQkgLF1gmooggETCwjA8TLMAlLHtJIbRh2EkOxdvw5k7WofvA7oTtOFFXqBTxmBtmCccmzfNsBBaOh2l1QpLDofj7OFdrA8/3EO77Xfu4A0ppchk7A31a8LZQor+/iStlrdhe6vl3XRFq6vZdnhh+NoPjkrFYXg4/U5OqxBiC5EefodpGjzxRD/Vant9qb5wrnuAZdUZHGxRqWgsqxvPs4lG27iuxvN8DEMRj1tkMjGiUYPl5SZaB+tTL1MpG8fxse2wOFr4/ChKhYt8u65PEOhObz+scTMykuXpp4e5dKnI1FS58+GjMU2Dn/qphzl3rkC97qz34HfuzDEwkOK11+apVtvr23ftym8Y5nk7jzzSyyuvzLK8XMc0DTwvrPE/NCSBL8T9TunrTQTfIg4fPqxfffXVe7Ivx/GZmiozM1OmUmlRq7VZXi6xvLyAbQfs2TNMpRLl9OkVarU22WyCRMKm3XbJ5aLk8+EQzOxsheXlsAJlJhNB67AcQk9PCq19CoUGQWAwOJjsjMu7eB7kcjbd3UlyuRi5XIzh4Qy5XAzH8ZicLLO4WCOfj7FrVxfxeIR222NlpUG97qzfL9BshmvnFosNlFLs29dDd3fitmfXuK7PykqDZjNcESufj0sJBSHuE0qp17TWh6/7mAQ+XLq0yu/+7lFefXWWlZUmnueSTLZx3QqWZWPbeebmXBoNh3rdw/d94vEIAwMpDhzoo1BosrgYLvYdzqMPb5oyTUU6HWVgIE02a9Pfn2Z4OE2j4dFouICm3Q5794ODKQxD0dWVYO/eLpRSGIaiUGgyMVEiCALi8QiPPtrHs8+OkkqFF1JPnlzi5Mkljh5dolptUy43SaWiHDjQy+Bgik9+8mF27Mje9XMohNgabhb4235Ip1Rq8ad/epbTp5eIRCyyWajVily4UCCZzLFr1xBLS03qdZfV1RaJRIRIJCyBUC63+Ku/ukwqZeN5AVqr9WGQIAg/SMMbrDQrK03K5TbtdjimXq+71GoOvu+za1c35XJ7fWZPo+HS25vkL/7iIr6v2bu3i0jEpFZzuHixSDRq8dhj/Rw/vkir5XH2bIHe3jgTE0XSaZtEwmJ1NVzJ6k//9Cy/8iuH5OYpIYRctJ2eLjM5WURrqNUWcd0lfB8MoxelchSLLSqVcMHusLKlxrIUSinqdY9Wy6VWa3eGZvzOilF0Fi03CALNwkId2zZptwMWF+udgmsB1WoL2zZRKvxASKdt2m2PhYUaS0s1LMukXG53VswKrwW4bsDqapNz5wrYtsnERLFTG6fVWVYxXFO2UGgSiYTTNWdmKm9zFoQQ28G27+E7jk+7XaNancZxWiSTXWgdxbLCkPR9jdaqc8es2lD7RuvgLfVwrh0uD6dm6vXXhj3/sHZ9uN1YnxK6VhohLKAWzhJaK3x2tbDMQ3jxt9321y/ori1Evvb8oLNeYljHXwix3W3rHr7ruvh+AaWKgCKbHcEwssTj0c5drqqzhqvVqZkTYJprhdLCMfVIxCCZjBCJmFiWwvM0phnO+tE6wLIU3d3x9Vk6uVyMSMTq3HAVpd0Ob4TKZGzqdZdYzCKfj9HXl6Ld9jvFzsIED2vqhAuk7NqVp9l02bkzR63mks+Hi56YpsJxwmsMpmlg2wZDQ5nNPdFCiC1h2wZ+oVDg1KlTGIbDj//4U4yO7qXVUiwv15ifr9HbmyCVCqdO9vTECQJNIhHBcQJqtXZnjn1kfSZMImHhebpzMfbqipga2zZQStHdHWVsLNsZHtLEYhFs22Jurra+8EgkYqzPztm5M8f4eJ7p6QozM2UWFmr09iZ5/PEBBgbSjIxkicctenvj69U+y+U2i4s1BgaSFApNPvKRnWSztz4tUwjx4Np2s3Qcx2FqaopyuUwymWR8fJxoNMrCQpUjR2aZmCgRj4c96EzGZna2Qr3uEY9brKw0uHChSL3eprs7zqOP9vPoo/3U6y5vvDHP5curtFoeWiuy2Sj9/eHMG9MM6+EMDYUzdMLhGAMI5/E3Gj6xmMngYArbtmg0XJLJCD09Cep1l4mJIrVaWCJ5ZCRLMmkD4YdJsdhiebnG0lKDcrm1PhSUy8XZt6+bvj4phyDEdiLTMjuWl5eZmZkBYHh4mN7eXqkAKYR4oGz7aZmtVovJyUlqtRqZTIaxsTFs297sZgkhxD31QAe+1prFxUXm5uYwDIPx8XG6u99aElgIIbaDBzbwG40Gk5OTNBoNcrkco6OjRCJy85EQYvt64AJfa83c3ByLi4tYlsWuXbvI5/Ob3SwhhNh0D1zgh3fA1unq6mLHjh1Y1gN3iEII8Y48kGm4d+9emX0jhBDXeCBvvJKwF0KIt3ogA18IIcRbSeALIcQ2IYEvhBDbhAS+EEJsExL4QgixTUjgCyHENiGBL4QQ28SWLo+slFoGJje7HZusB1jZ7EZsYXJ+bk7Oz809iOdnTGvde70HtnTgC1BKvXqj2tZCzs/bkfNzc9vt/MiQjhBCbBMS+EIIsU1I4G99X9jsBmxxcn5uTs7PzW2r8yNj+EIIsU1ID18IIbYJCXwhhNgmJPCFEGKbkMC/Tymldimlfkcp9eXNbstWIefk5pRSDyul/o1S6stKqb+92e3ZapRSzymlvtc5R89tdnvuBgn8TaCU+qJSakkpdeKa7R9TSp1VSl1QSv1/bvYeWutLWutfubst3Xy3c662yzm52m2en9Na618F/ibw/s1o7712m//WNFADYsDMvW7rvSCBvzm+BHzs6g1KKRP4LeDjwAHgM0qpA0qpR5VSf3bNr7573+RN8yVu8Vzd+6ZtCV/iNs6PUuongK8D37i3zdw0X+LWz8/3tNYfB/4h8E/vcTvvCQn8TaC1/i6wes3m9wAXOr1UB/hD4Ce11se11p+45tfSPW/0Jrmdc3XPG7cF3O750Vp/tRNqP39vW7o5bvPfWtB5vAhE72Ez7xkJ/K1jGJi+6ueZzrbrUkp1K6X+DXBIKfXrd7txW8x1z9U2PydXu9H5eU4p9X8opf5Ptk8P/3pudH4+2Tk3/w74zU1p2V1mbXYDxDujtS4Av7rZ7dhK5JzcnNb6eeD5TW7GlqW1/grwlc1ux90kPfytYxYYuernHZ1t4q3kXN2cnJ+b27bnRwJ/6zgC7FVK7VRK2cCnga9ucpu2KjlXNyfn5+a27fmRwN8ESqk/AF4E9imlZpRSv6K19oDPA98ETgN/pLU+uZnt3ArkXN2cnJ+bk/OzkRRPE0KIbUJ6+EIIsU1I4AshxDYhgS+EENuEBL4QQmwTEvhCCLFNSOALIcQ2IYEv7jtKqX+klDqplDqmlHpTKfXeu7y/55VSh+/mPoS4F6SWjrivKKWeAT4BPKm1biulegB7k5slxH1BevjifjMIrGit2wBa6xWt9RyAUup/VEodUUqdUEp9QSmlOtufV0r970qpV5VSp5VSTyulvqKUOq+U+v92njOulDqjlPr3ned8WSmVuHbnSqkfVUq9qJR6XSn1x0qp1HWe87b76zzvF5RSr3S+pfyfnTrtKKX+dee1J5VS//Sq508opf5pZ9/HlVL73+VzKx5wEvjifvPnwIhS6pxS6l8ppX74qsd+U2v9tNb6IBAn/CawxtFaHwb+DfCfgc8BB4FfVkp1d56zD/hXWuuHgQrwd67ecefbxD8GfkRr/STwKvDf3qCdN92fUuph4GeB92utnwB8rtSo/0ed1z4G/LBS6rGr3nels+9/Dfx3b3u2hLiKBL64r2ita8BTwGeBZeA/KqV+ufPwh5RSLyuljgMfBh656qVrxbGOAye11vOdbwmXuFI5cVpr/ULn//8+8IFrdv8+whWSXlBKvQn8EjB2g6a+3f4+0jmOI533+giwq/Oav6mUeh14o3MMV6/mtVa+9zVg/Ab7FuK6ZAxf3He01j5hXffnO+H+S0qpPwT+FXBYaz2tlPqfCNcmXdPu/B5c9f/Xfl77d3BtYalrf1bAt7TWn7mFZr7d/hTwu1rrDQu1KKV2Evbcn9ZaF5VSX7rBcfjIv19xm6SHL+4rSql9Sqm9V216ApjkSiiudMbVP/UO3n60c1EY4OeA71/z+EvA+5VSezptSSqlHnoH+wH4S+BTqrM+sVKqSyk1BmSAOlBWSvUTrrsqxLtCegjifpMC/qVSKgd4wAXgs1rrklLq3wIngAXCmue36yzwOaXUF4FThOPk67TWy53hoz9QSq2tefqPgXO3uyOt9Sml1D8G/lwpZQAu8Dmt9UtKqTeAM4TL8L1ws/cR4nZIeWQhCGfpAH/WueArxANJhnSEEGKbkB6+EEJsE9LDF0KIbUICXwghtgkJfCGE2CYk8IUQYpuQwBdCiG1CAl8IIbaJ/xsZfdvFERVF9AAAAABJRU5ErkJggg==\n", 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" ] @@ -430,14 +499,17 @@ { "cell_type": "code", "execution_count": 9, - "id": "3e78ffea-e081-4fd7-a7e8-34c3ee9f6520", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_3879/816571136.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_10806/816571136.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", " (p / (1 - lam) ** 3).flatten(),\n" ] }, @@ -453,7 +525,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -485,8 +557,11 @@ { "cell_type": "code", "execution_count": 10, - "id": "6fa2273a-7245-4f1e-906e-749b914f8f8b", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "def normal_approx(x, p, lam):\n", @@ -498,8 +573,34 @@ { "cell_type": "code", "execution_count": 11, - "id": "38444834-9541-41a4-9ed5-1d731488e7bb", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "def monotonicity_region_envelope(x, p, lam):\n", + " return p * np.exp(\n", + " 2 \n", + " - lam \n", + " - np.minimum(lam, p) \n", + " * np.sqrt(2 / np.pi) \n", + " * (\n", + " (1/np.sqrt(x)) \n", + " - (1 / np.sqrt(x + 1))\n", + " )\n", + " ) + (x == 0) * np.exp(-p) # Extra probability for x==0" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "def poisson_region_envelope(x, p, lam):\n", @@ -555,23 +656,26 @@ }, { "cell_type": "code", - "execution_count": 12, - "id": "d5124123-7aa5-4c4c-8f7a-da74d548cf6c", - "metadata": {}, + "execution_count": 13, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 12, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -600,9 +704,12 @@ }, { "cell_type": "code", - "execution_count": 13, - "id": "59199eb3-0ff7-4fd4-bf95-1d18fe59c067", - "metadata": {}, + "execution_count": 14, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "def abel_rejection_envelope(x, p, lam):\n", @@ -649,9 +756,12 @@ }, { "cell_type": "code", - "execution_count": 14, - "id": "021c01fc-dea6-47ba-b19c-00f55b45a209", - "metadata": {}, + "execution_count": 15, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "def abel_rejection_proposal_density(x, p, lam):\n", @@ -698,42 +808,34 @@ }, { "cell_type": "code", - "execution_count": 15, - "id": "af0f622a-3dda-4844-97bd-c5ab4faf4478", - "metadata": {}, + "execution_count": 16, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.23497 0.2665088550067253\n" - ] - }, { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_3879/584387763.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", - " b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", - "/tmp/ipykernel_3879/1448899321.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", - " np.sqrt(t + 1) * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", - "/tmp/ipykernel_3879/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", - " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" + "/tmp/ipykernel_10806/584387763.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", + " b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n" ] }, { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 15, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -752,44 +854,286 @@ "plt.semilogy(x, np.exp(_logprob(x, p, lam)), label=\"PDF\")\n", "plt.plot(x, abel_rejection_envelope(x, p, lam), label=\"Envelope\")\n", "plt.plot(x, abel_rejection_proposal_density(x, p, lam), label=\"Proposal density\")\n", - "samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000)\n", - "print(np.mean(samples <= 1), np.sum(np.exp(_logprob(np.array([0, 1]), p, lam))))\n", + "# samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000)\n", + "# print(np.mean(samples <= 1), np.sum(np.exp(_logprob(np.array([0, 1]), p, lam))))\n", "y, edges = np.histogram(samples, bins=20, density=True)\n", - "plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label=\"Sampled points\")\n", + "# plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label=\"Sampled points\")\n", "plt.legend()" ] }, { "cell_type": "code", - "execution_count": 16, - "id": "9eabb346-8c37-4d74-a544-64c7a4eaad52", - "metadata": {}, + "execution_count": 18, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_3879/584387763.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", - " b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", - "/tmp/ipykernel_3879/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", + "/tmp/ipykernel_10806/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" ] }, { "data": { + "image/png": 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\n", "text/plain": [ - "" + "
" ] }, - "execution_count": 16, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "p, lam = 2.1209508879201904, 0.5510204081632653\n", + "\n", + "mean = p / (1 - lam)\n", + "std = np.sqrt(p / (1 - lam) ** 3)\n", + "x = np.linspace(0, 10, 1000)\n", + "\n", + "plt.figure(figsize=(16, 6))\n", + "plt.semilogy(x, np.exp(_logprob(np.floor(x), p, lam)), label=\"PMF\")\n", + "\n", + "# plt.plot(x, abel_rejection_envelope(np.floor(x), p, lam), label=\"Envelope\")\n", + "# plt.plot(x, abel_rejection_proposal_density(np.floor(x), p, lam), label=\"Proposal density\")\n", + "samples_monot = _rejection_region_monotonicity(np.random.default_rng(), p, lam, 100000)\n", + "samples_abel = _rejection_region_abel(np.random.default_rng(), p, lam, 100000)\n", + "for samples, algo in zip((samples_monot, samples_abel), (\"monoticity\", \"abel\")):\n", + " u, c = np.unique(samples, return_counts=True)\n", + " edges = np.arange(11)\n", + " y = np.array([np.sum(c[u == e]) for e in edges])\n", + " plt.step(edges, y / samples.size, label=f\"Sampled points ({algo})\", where=\"post\")\n", + " plt.legend(loc=(1, 0))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.11991754613423761" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.exp(_logprob(0, p, lam))" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_10806/4253790774.py:8: RuntimeWarning: divide by zero encountered in true_divide\n", + " poisson_idxs = p >= np.maximum(3, 2 * lam / (1 - lam))\n", + "/tmp/ipykernel_10806/4253790774.py:10: RuntimeWarning: divide by zero encountered in true_divide\n", + " abel_idxs = (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam)))\n" + ] + } + ], + "source": [ + "p_range = np.logspace(-2, 4, 50)\n", + "lam_range = np.linspace(0, 1, 60)\n", + "p, lam = np.meshgrid(p_range, lam_range)\n", + "dist_size = p.shape\n", + "# monotonicity_idxs = p <= (1 + lam)\n", + "# monotonicity_idxs = p <= np.exp(lam)\n", + "# poisson_idxs = p > np.maximum(1 + lam, 2 * lam / (1 - lam))\n", + "poisson_idxs = p >= np.maximum(3, 2 * lam / (1 - lam))\n", + "# poisson_idxs = p > np.maximum(np.exp(lam), 2 * lam / (1 - lam))\n", + "abel_idxs = (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam)))\n", + "# abel_idxs = (lam == 1) | ((p > np.exp(lam)) & (p <= 2 * lam / (1 - lam)))\n", + "# abel_idxs = (lam == 1) | ((p >= 3) & (p <= 2 * lam / (1 - lam)))" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.54,)" + ] + }, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" + } + ], + "source": [ + "idxs = np.full((lam_range.size, 50), 0, dtype=int)\n", + "# idxs[monotonicity_idxs] = 0\n", + "idxs[poisson_idxs] = 1\n", + "idxs[abel_idxs] = 2\n", + "np.mean(idxs==1)," + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_10806/2366160465.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", + " poisson_idxs = p >= np.maximum(3, 2 * lam / (1 - lam))\n", + "/tmp/ipykernel_10806/2366160465.py:6: RuntimeWarning: divide by zero encountered in true_divide\n", + " abel_idxs = (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam)))\n", + "/tmp/ipykernel_10806/294563780.py:8: RuntimeWarning: divide by zero encountered in true_divide\n", + " (1/np.sqrt(x))\n", + "/tmp/ipykernel_10806/294563780.py:5: RuntimeWarning: invalid value encountered in multiply\n", + " - np.minimum(lam, p)\n", + "/tmp/ipykernel_10806/3405323858.py:41: RuntimeWarning: overflow encountered in exp\n", + " return p / np.sqrt(2 * np.pi) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", + "/tmp/ipykernel_10806/3405323858.py:41: RuntimeWarning: overflow encountered in multiply\n", + " return p / np.sqrt(2 * np.pi) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", + "/tmp/ipykernel_10806/584387763.py:38: RuntimeWarning: overflow encountered in power\n", + " q_l * q ** (t - x) * (1 - q **(t+1)),\n", + "/tmp/ipykernel_10806/584387763.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", + " b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", + "/tmp/ipykernel_10806/584387763.py:38: RuntimeWarning: divide by zero encountered in power\n", + " q_l * q ** (t - x) * (1 - q **(t+1)),\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Poisson envelope is not higher than pmf for p=3.7, lam=0.475, xs=[4]\n", + "Poisson envelope is not higher than pmf for p=3.7, lam=0.492, xs=[3 4 5]\n", + "Poisson envelope is not higher than pmf for p=3.7, lam=0.508, xs=[3 4 5]\n", + "Poisson envelope is not higher than pmf for p=3.7, lam=0.525, xs=[3 4 5 6]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.525, xs=[6]\n", + "Poisson envelope is not higher than pmf for p=3.7, lam=0.542, xs=[3 4 5 6]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.542, xs=[6 7]\n", + "Poisson envelope is not higher than pmf for p=3.7, lam=0.559, xs=[3 4 5 6]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.559, xs=[5 6 7 8]\n", + "Poisson envelope is not higher than pmf for p=3.7, lam=0.576, xs=[3 4 5 6 7]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.576, xs=[5 6 7 8]\n", + "Poisson envelope is not higher than pmf for p=3.7, lam=0.593, xs=[3 4 5 6 7]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.593, xs=[5 6 7 8]\n", + "Poisson envelope is not higher than pmf for p=3.7, lam=0.610, xs=[3 4 5 6 7]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.610, xs=[5 6 7 8 9]\n", + "Poisson envelope is not higher than pmf for p=3.7, lam=0.627, xs=[3 4 5 6 7 8]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.627, xs=[5 6 7 8 9]\n", + "Poisson envelope is not higher than pmf for p=3.7, lam=0.644, xs=[3 4 5 6 7 8]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.644, xs=[5 6 7 8 9]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.661, xs=[ 5 6 7 8 9 10]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.678, xs=[ 5 6 7 8 9 10]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.695, xs=[ 5 6 7 8 9 10]\n", + "Poisson envelope is not higher than pmf for p=4.9, lam=0.712, xs=[ 6 7 8 9 10]\n" + ] }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_10806/584387763.py:38: RuntimeWarning: overflow encountered in multiply\n", + " q_l * q ** (t - x) * (1 - q **(t+1)),\n", + "/tmp/ipykernel_10806/584387763.py:38: RuntimeWarning: invalid value encountered in multiply\n", + " q_l * q ** (t - x) * (1 - q **(t+1)),\n" + ] + } + ], + "source": [ + "p_range = np.logspace(-2, 4, 50)\n", + "lam_range = np.linspace(0, 1, 60)\n", + "p, lam = np.meshgrid(p_range, lam_range)\n", + "\n", + "poisson_idxs = p >= np.maximum(3, 2 * lam / (1 - lam))\n", + "abel_idxs = (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam)))\n", + "\n", + "idxs = np.full((lam_range.size, 50), 0, dtype=int)\n", + "# idxs[monotonicity_idxs] = 0\n", + "idxs[poisson_idxs] = 1\n", + "idxs[abel_idxs] = 2\n", + "\n", + "xs = np.concatenate([np.arange(10), np.logspace(1, 4.5)]).astype(int)\n", + "for i in range(p.shape[0]):\n", + " for j in range(p.shape[1]):\n", + " if idxs[i, j] == 0:\n", + " proposal = monotonicity_region_envelope(xs, p[i, j], lam[i, j])\n", + " pmf = np.exp(_logprob(xs, p[i, j], lam[i, j]))\n", + " bad_xs = xs[proposal < pmf + 0.00]\n", + " if len(bad_xs):\n", + " print(\n", + " f\"Monotonicity envelope is not higher than pmf for p={p[i, j]:.1f}, \"\n", + " f\"lam={lam[i, j]:.3f}, xs={bad_xs}\"\n", + " )\n", + " \n", + " elif idxs[i, j] == 1:\n", + " proposal = poisson_region_envelope(xs, p[i, j], lam[i, j])\n", + " pmf = np.exp(_logprob(xs, p[i, j], lam[i, j]))\n", + " bad_xs = xs[proposal < pmf - 0.03]\n", + " if len(bad_xs):\n", + " print(\n", + " f\"Poisson envelope is not higher than pmf for p={p[i, j]:.1f}, \"\n", + " f\"lam={lam[i, j]:.3f}, xs={bad_xs}\"\n", + " )\n", + " \n", + " elif idxs[i, j] == 2:\n", + " proposal = abel_rejection_envelope(xs, p[i, j], lam[i, j])\n", + " pmf = np.exp(_logprob(xs, p[i, j], lam[i, j]))\n", + " bad_xs = xs[proposal < pmf - 0.0 + 0.00]\n", + " if len(bad_xs):\n", + " print(\n", + " f\"Abel envelope is not higher than pmf for p={p[i, j]:.1f}, \"\n", + " f\"lam={lam[i, j]:.3f}, xs={bad_xs}\"\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] }, "metadata": { @@ -799,30 +1143,516 @@ } ], "source": [ - "p, lam = 2.1209508879201904, 0.5510204081632653\n", - "mean = p / (1 - lam)\n", - "std = np.sqrt(p / (1 - lam) ** 3)\n", - "x = np.linspace(0, 10, 1000)\n", - "plt.semilogy(x, np.exp(_logprob(np.floor(x), p, lam)), label=\"PDF\")\n", - "plt.plot(x, abel_rejection_envelope(np.floor(x), p, lam), label=\"Envelope\")\n", - "# plt.plot(x, abel_rejection_proposal_density(np.floor(x), p, lam), label=\"Proposal density\")\n", - "samples = _rejection_region_abel(np.random.default_rng(), p, lam, 100000)\n", - "u, c = np.unique(samples, return_counts=True)\n", - "edges = np.arange(11)\n", - "y = np.array([np.sum(c[u == e]) for e in edges])\n", - "plt.step(edges, y / samples.size, label=\"Sampled points\", where=\"post\")\n", - "plt.legend()" + "data = idxs.T\n", + "\n", + "fig, ax = plt.subplots(figsize=(7, 7))\n", + "\n", + "# get discrete colormap\n", + "cmap = plt.get_cmap('coolwarm', np.max(data) - np.min(data) + 1)\n", + "# set limits .5 outside true range\n", + "mat = ax.imshow(data, cmap=cmap, vmin=0, vmax=2,origin=\"lower\",)\n", + "# tell the colorbar to tick at integers\n", + "cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038)\n", + "cbar.ax.set_yticklabels([\"monotonicity\", \"poisson\", \"abel\"])\n", + "\n", + "ax.set_xlabel(\"lam\")\n", + "every = 8\n", + "plt.xticks(range(0, lam_range.size)[::every], np.round(lam_range[::every], 2));\n", + "\n", + "ax.set_ylabel(\"p\")\n", + "every = 8\n", + "plt.yticks(range(0, p_range.size)[::every], np.round(p_range[::every], 2));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Benchmark algorithms" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "import signal\n", + "import time" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "class TimeOutError(RuntimeError):\n", + " pass\n", + "\n", + "def handler(signum, frame):\n", + " raise TimeOutError\n", + "\n", + "signal.signal(signal.SIGALRM, handler)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "rng = np.random.default_rng(42)\n", + "dist_size = (100, *p.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "duration_monot = np.full_like(p, np.nan)\n", + "for i in range(p.shape[0]):\n", + " for j in range(p.shape[1]):\n", + " signal.setitimer(signal.ITIMER_REAL, .05)\n", + " try:\n", + " start = time.time()\n", + " _rejection_region_monotonicity(rng, p=p[i, j], lam=lam[i, j], dist_size=100)\n", + " end = time.time()\n", + " except TimeOutError:\n", + " continue\n", + " duration_monot[i, j] = end - start\n", + "signal.alarm(0)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_10806/2133065621.py:11: RuntimeWarning: invalid value encountered in sqrt\n", + " sigma = np.sqrt((1 + delta) * (p - lam) / (1 - lam - eps) / (1 - lam) ** 2)\n", + "/tmp/ipykernel_10806/2133065621.py:41: RuntimeWarning: invalid value encountered in power\n", + " * (p - lam) ** 1.5\n", + "/tmp/ipykernel_10806/2133065621.py:29: RuntimeWarning: invalid value encountered in power\n", + " / (np.sqrt(2 * np.pi) * (p - lam) ** 1.5)\n", + "/tmp/ipykernel_10806/2133065621.py:10: RuntimeWarning: divide by zero encountered in true_divide\n", + " mu = (p - lam) / (1 - lam)\n", + "/tmp/ipykernel_10806/2133065621.py:11: RuntimeWarning: divide by zero encountered in true_divide\n", + " sigma = np.sqrt((1 + delta) * (p - lam) / (1 - lam - eps) / (1 - lam) ** 2)\n", + "/tmp/ipykernel_10806/2133065621.py:18: RuntimeWarning: invalid value encountered in true_divide\n", + " (p * (1 - lam - eps) * np.sqrt(1 + delta))\n", + "/tmp/ipykernel_10806/2133065621.py:36: RuntimeWarning: divide by zero encountered in true_divide\n", + " t_r = np.ceil((p - lam) / (1 - lam - eps) - 1)\n", + "/tmp/ipykernel_10806/2133065621.py:46: RuntimeWarning: invalid value encountered in subtract\n", + " * np.exp(-(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (t_r - mu))\n", + "/tmp/ipykernel_10806/2133065621.py:52: RuntimeWarning: divide by zero encountered in true_divide\n", + " t_l = np.ceil((p - lam) / (1 - lam + delta) - 1)\n", + "/tmp/ipykernel_10806/2133065621.py:54: RuntimeWarning: divide by zero encountered in true_divide\n", + " (2 * p * (1 + delta))\n", + "/tmp/ipykernel_10806/2133065621.py:56: RuntimeWarning: invalid value encountered in subtract\n", + " * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (t_l + 1 - mu))\n", + "/tmp/ipykernel_10806/2133065621.py:85: RuntimeWarning: divide by zero encountered in true_divide\n", + " raw_left_y = _t_l - 2 * E * (1 + _delta) / _delta / (1 - _lam)\n", + "/tmp/ipykernel_10806/2133065621.py:86: RuntimeWarning: divide by zero encountered in true_divide\n", + " raw_right_y = _t_r + 2 * E / ((1 - 2 * (1 - _lam - _eps) / (_p - _lam)) * _eps * (1 - _lam))\n", + "/tmp/ipykernel_10806/2133065621.py:86: RuntimeWarning: invalid value encountered in add\n", + " raw_right_y = _t_r + 2 * E / ((1 - 2 * (1 - _lam - _eps) / (_p - _lam)) * _eps * (1 - _lam))\n", + "/tmp/ipykernel_10806/2133065621.py:38: RuntimeWarning: invalid value encountered in true_divide\n", + " (2 * p * (1 - lam - eps) ** 1.5 * np.exp(2 * (1 - lam)))\n", + "/tmp/ipykernel_10806/2133065621.py:84: RuntimeWarning: invalid value encountered in add\n", + " raw_center_y = _mu + _sigma * N\n", + "/tmp/ipykernel_10806/2133065621.py:85: RuntimeWarning: invalid value encountered in subtract\n", + " raw_left_y = _t_l - 2 * E * (1 + _delta) / _delta / (1 - _lam)\n", + "/tmp/ipykernel_10806/2133065621.py:24: RuntimeWarning: invalid value encountered in subtract\n", + " return G / (np.sqrt(2 * np.pi) * sigma) * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2))\n", + "/tmp/ipykernel_10806/2133065621.py:50: RuntimeWarning: invalid value encountered in subtract\n", + " return p / np.sqrt(2 * np.pi) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", + "/tmp/ipykernel_10806/2133065621.py:31: RuntimeWarning: invalid value encountered in subtract\n", + " -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (x - mu)\n", + "/tmp/ipykernel_10806/2468484780.py:19: RuntimeWarning: invalid value encountered in subtract\n", + " np.log(p) + _logpow(p_lam_x, x - 1) - p_lam_x - gammaln(x + 1),\n" + ] + }, + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "duration_poisson = np.full_like(p, np.nan)\n", + "for i in range(p.shape[0]):\n", + " for j in range(p.shape[1]):\n", + " signal.setitimer(signal.ITIMER_REAL, .05)\n", + " try:\n", + " start = time.time()\n", + " _rejection_region_poisson(rng, p=p[i, j], lam=lam[i, j], dist_size=100)\n", + " end = time.time()\n", + " except TimeOutError:\n", + " continue\n", + " duration_poisson[i, j] = end - start\n", + "signal.alarm(0)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_10806/1113335044.py:8: RuntimeWarning: divide by zero encountered in true_divide\n", + " nu = 2 * (p ** 2 - lam * p - 3 * lam ** 2) / (3 * lam ** 2)\n", + "/tmp/ipykernel_10806/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", + " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n", + "/tmp/ipykernel_10806/1113335044.py:69: RuntimeWarning: overflow encountered in power\n", + " V * _q_l * _q ** (_t - raw_left) * (1 - _q **(_t+1))\n" + ] + }, + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "duration_abel = np.full_like(p, np.nan)\n", + "for i in range(p.shape[0]):\n", + " for j in range(p.shape[1]):\n", + " signal.setitimer(signal.ITIMER_REAL, .05)\n", + " try:\n", + " start = time.time()\n", + " _rejection_region_abel(rng, p=p[i, j], lam=lam[i, j], dist_size=100)\n", + " end = time.time()\n", + " except TimeOutError:\n", + " continue\n", + " duration_abel[i, j] = end - start\n", + "signal.alarm(0)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True)\n", + "\n", + "# Region\n", + "data = idxs.T\n", + "cmap = plt.get_cmap('coolwarm', np.max(data) - np.min(data) + 1)\n", + "mat = ax[0].imshow(data, cmap=cmap, vmin=0, vmax=2,origin=\"lower\",)\n", + "cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0])\n", + "cbar.ax.set_yticks([0.3, 1, 1.7])\n", + "cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", + "\n", + "# Timings\n", + "data = duration_monot.T\n", + "mat = ax[1].imshow(data, cmap=\"viridis\", origin=\"lower\",)\n", + "cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1])\n", + "\n", + "\n", + "for axi in ax:\n", + " axi.set_xlabel(\"lam\")\n", + " every = 8\n", + " axi.set_xticks(range(0, lam_range.size)[::every])\n", + " axi.set_xticklabels(np.round(lam_range[::every], 2));\n", + "\n", + " axi.set_ylabel(\"p\")\n", + " every = 8\n", + " axi.set_yticks(range(0, p_range.size)[::every])\n", + " axi.set_yticklabels(np.round(p_range[::every], 2))\n", + " \n", + " axi.axhline(20.5, color=\"white\")\n", + " \n", + "fig.suptitle(\"Monotonicity region performance\", y=0.85, fontsize=18);" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True)\n", + "\n", + "# Region\n", + "data = idxs.T\n", + "cmap = plt.get_cmap('coolwarm', np.max(data) - np.min(data) + 1)\n", + "mat = ax[0].imshow(data, cmap=cmap, vmin=0, vmax=2,origin=\"lower\",)\n", + "cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0])\n", + "cbar.ax.set_yticks([0.3, 1, 1.7])\n", + "cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", + "\n", + "# Timings\n", + "data = duration_poisson.T\n", + "mat = ax[1].imshow(data, cmap=\"viridis\", origin=\"lower\",)\n", + "cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1])\n", + "\n", + "\n", + "for axi in ax:\n", + " axi.set_xlabel(\"lam\")\n", + " every = 8\n", + " axi.set_xticks(range(0, lam_range.size)[::every])\n", + " axi.set_xticklabels(np.round(lam_range[::every], 2));\n", + "\n", + " axi.set_ylabel(\"p\")\n", + " every = 8\n", + " axi.set_yticks(range(0, p_range.size)[::every])\n", + " axi.set_yticklabels(np.round(p_range[::every], 2))\n", + " \n", + " axi.axhline(20.5, color=\"k\")\n", + " \n", + "fig.suptitle(\"Poisson region performance\", y=0.85, fontsize=18);" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True)\n", + "\n", + "# Region\n", + "data = idxs.T\n", + "cmap = plt.get_cmap('coolwarm', np.max(data) - np.min(data) + 1)\n", + "mat = ax[0].imshow(data, cmap=cmap, vmin=0, vmax=2,origin=\"lower\",)\n", + "cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0])\n", + "cbar.ax.set_yticks([0.3, 1, 1.7])\n", + "cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", + "\n", + "# Timings\n", + "data = duration_abel.T\n", + "mat = ax[1].imshow(data, cmap=\"viridis\", origin=\"lower\",)\n", + "cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1])\n", + "\n", + "\n", + "for axi in ax:\n", + " axi.set_xlabel(\"lam\")\n", + " every = 8\n", + " axi.set_xticks(range(0, lam_range.size)[::every])\n", + " axi.set_xticklabels(np.round(lam_range[::every], 2));\n", + "\n", + " axi.set_ylabel(\"p\")\n", + " every = 8\n", + " axi.set_yticks(range(0, p_range.size)[::every])\n", + " axi.set_yticklabels(np.round(p_range[::every], 2))\n", + " \n", + " axi.axhline(20.5, color=\"w\")\n", + " \n", + "fig.suptitle(\"Abel region performance\", y=0.85, fontsize=18);" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "nan_to_inf = lambda x: np.nan_to_num(x, nan=np.inf)\n", + "\n", + "d = 0.00\n", + "best_duration = np.full_like(duration_monot, np.nan)\n", + "best_duration[\n", + " (duration_monot + d < nan_to_inf(duration_poisson)) & (duration_monot + d < nan_to_inf(duration_abel))\n", + "] = 0\n", + "\n", + "best_duration[\n", + " (duration_poisson + d < nan_to_inf(duration_monot)) & (duration_poisson + d < nan_to_inf(duration_abel))\n", + "] = 1\n", + "\n", + "best_duration[\n", + " (duration_abel + d < nan_to_inf(duration_monot)) & (duration_abel + d < nan_to_inf(duration_poisson))\n", + "] = 2" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "data": { + "image/png": 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rJlJVZwIPBEiyPnAp8GXghcD/qap/m2fRdwNH9Ly+AXh8VV2XZEPg+0mOqKrj+pa7CNgfeG1f+2+BF1TV2UnuAfw4yZFVdc3IOydJkiRJYzSpqo97AedW1YXJ/NUzkzwVOB/4zVxbVRVwXftyw/ZR/ctW1QXtOm7taz+r5/llSa4AtgGuGWlPJEmSJGnMJnWP2n7AZ3tev6K9DPGjSe4CkGRz4O+B1S5tTLJ+kpOAK4BvVdXxowSR5GHARsC5A947IMnKJCuvvvrqUVYvSdJYOVZJ0vIx9kQtyUbAU4Avtk0fAHakuSzycuBdbftBNJdEXte3Cqrqlqp6ILAd8LAku40Qx92BQ4AXVtWt/e9X1Yqq2qOq9thyyy2HXb0kSWPnWCVJy8ckLn38Y+DEqvo5wNxPgCQfAr7Wvnw48Mwk7wDuDNya5Pqqet9c/6q6JslRwN7ATxcaQJI7Av8N/OOAe9skSZIkqVMmkag9h57LHpPcvaoub18+jTbhqqpH9/Q5CLiuqt6XZBvgpjZJuwPwRODtC914O6P3ZeCTVXXoYndGkiRJksZtrJc+JtmMJrH6Uk/zO5KcmuQUYE/gb9eymrsDR7X9T6C5R+1r7frfkuQp7fOHJrkE+DPgg0lOa5d/FvAYYP+erwR44BLtoiRJkiQtubHOqFXVb4Ct+tqev4DlDup5fgrwoHn6vbHn+Qk097D19/kU8KkFBy1JkiRJUzapqo+SJEmSpAUyUZMkSZKkjpnUF15LkqQx23HHHQe2n3vual8fKknqOGfUJEmSJKljTNQkSZIkqWNM1CRJkiSpY0zUJEmSJKljTNQkSZIkqWOs+ihJ0gzaeOON563y2G+h/eYzqGqkFSYlabycUZMkSZKkjjFRkyRJkqSOMVGTJEmSpI4xUZMkSZKkjrGYiCRJWqNBhUPmKxoyTF9J0vycUZMkSZKkjjFRkyRJkqSOMVGTJEmSpI4xUZMkSZKkjrGYiCRJGtqgoiHjWse4ipFMu/DJfPtv8RVJYKImSZpBSV69pver6t2TikWSpH5LMU6ZqEmSZtEW0w5AkqQ1WPQ4ZaImSZo5VfXmaccgSdJ8lmKcspiIJGlmJdk5ybeT/LR9vXuSf5p2XJIkweLGKRM1SdIs+xBwIHATQFWdAuw31YgkSbrdyOOUlz5KkmbZplX1oyS9bTdPKxgNthQVIhe63vkqJk67wuMg096+pIkYeZxyRk2SNMt+kWRHoACSPBO4fLohSZJ0m5HHKWfUJEldtnWSlT2vV1TVip7XLwdWAPdNcilwPvDcSQYoSVrWxjZOmahJkrrsF1W1x3xvVtV5wBOSbAasV1W/nlxokiSNb5zy0kdJ0sxKslWSfwe+Bxyd5L1Jtpp2XJIkweLGKWfUJEmz7HPAMcAz2tfPBT4PPGFqEWnJDVOMZL6+gwp3LLbIyTCFS4ZZfph1WpBE6ryRxykTNUnSLLt7Vf1zz+t/SfLsqUUjSdKqRh6nvPRRkjTLvplkvyTrtY9nAUdOOyhJklojj1POqEmSZk6SX9OUOg7wKuCQ9q31geuA104nMkmSlmacMlGTJM2cqtpi7nmSLYGdgE2mF5EkSbdbinGqU5c+JtklyUk9j18leVWS309ybJJTkxye5I49yxyY5JwkZyb5o3nWmyRvTXJWkjOS/M3k9kqSNC5JXgJ8F/gGcFD7843TjEmSpDmLGac6NaNWVWcCDwRIsj5wKfBl4FDgtVX13SQvAl4HvCHJrsB+wP2BewD/k2Tnqrqlb9X7A/cE7ltVtya56yT2R5I0dq8EHgocV1V7Jrkv8LYpx6QOWmyFx2HWudAKk0sR06B1WAlS6pSRx6lOzaj12Qs4t6ouBHamKWsJ8C1uL2+5L/C5qrqhqs4HzgEeNmBdLwXeUlW3AlTVFWONXJI0KddX1fUASTauqp8Bu0w5JkmS5ow8TnU5UdsP+Gz7/DSapAzgz2hmxwC2BS7uWeaStq3fjsCzk6xMckSSnfo7JDmgfX/l1VdfvSQ7IEkau0uS3Bn4CvCtJF8FLpxqRGPUO1ZdeeWV0w5HkrR2I49TnUzUkmwEPAX4Ytv0IuBlSX4MbAHcOOQqN6bJZvcAPgR8tL9DVa2oqj2qao8tt9xy9OAlSRNTVU+rqmuq6iDgDcBHgKdONagx6h2rttlmm2mHI0lai8WMU526R63HHwMnVtXPAdopwicBJNkZeHLb71Jun10D2K5t63cJ8KX2+ZeBj40hZknSFFXVd6cdgyRJ8xl2nOpqovYcbr/skSR3raorkqwH/BPwX+1bhwGfSfJummIiOwE/GrC+rwB7AucDjwXOGl/okiRpOVtokZD5in4MUyBkoUVKLDAizZ7OXfqYZDPgidw+AwbwnCRnAT8DLqOdEauq04AvAKfTlLp8+VzFxyRfT3KPdvl/BZ6R5FTgYOAlk9gXSZIkSRpF52bUquo3wFZ9be8F3jtP/7cCbx3Qvk/P82u4/XJJSZIkSeq0zs2oSZIkSdJyZ6ImSZIkSR3TuUsfJUmSloOFFh0Ztu9ilx9X4RGLnEjDcUZNkiRJkjrGRE2SJEmSOsZETZIkSZI6xkRNkiRJkjrGRE2SJEmSOsaqj5IkSbrNfBUiB1VoHKaSoxUepeE4oyZJkiRJHWOiJkmSJEkdY6ImSZIkSR1joiZJkiRJHWMxEUmSJK3VfEVGRu03rIUWM1mK9Upd4IyaJEmSJHWMiZokSZIkdYyJmiRJkiR1jImaJEmSJHWMiZokSZIkdYxVHyVJkjR2i63aOKjvfBUbx9V3HMtL83FGTZIkSZI6xkRNkiRJkjrGRE2SJEmSOsZETZIkSZI6xmIikiRJWucttnDJUmxroQVVFlvMZNh1TNswx/uMMcbRNc6oSZIkSVLHmKhJkiRJUseYqEmSJElSx5ioSZIkSVLHWExEkpaZM3bZZ9ohSFqGFlugY1LrnM98xTmmXaTkUX/63UWtcz4HHnHAam1/cvOZA/suNoYfHL76fn1tg10Wtc51gTNqkiRJktQxJmqSJEmS1DEmapIkSZLUMd6jJkkau01224n7ffWrwy84wftPJEnLVxfHqc7NqCX52ySnJflpks8m2STJp5Oc2bZ9NMmG8yz7jnbZM5L8e5K07RslWZHkrCQ/S/KMye6VJEmSJC1cp2bUkmwL/A2wa1X9LskXgP2ATwPPa7t9BngJ8IG+ZR8JPArYvW36PvBY4GjgH4ErqmrnJOsBW455VyRJkjRm81Ub/MHhj11w38UaVLFwGMPFdcmA7a++r8Ovd3UH//GK1Rvnq8Q4qO8QBsV64KLWuG7oVKLW2gC4Q5KbgE2By6rqm3NvJvkRsN2A5QrYBNgICLAh8PP2vRcB9wWoqluBX4wtekmSJElapE5d+lhVlwL/BlwEXA5c25ekbQg8H/jGgGWPBY5ql7scOLKqzkhy57bLPyc5MckXk9ytf/kkByRZmWTl1VdfvdS7JknSovWOVVdeeeW0w5EkjVGnErUkdwH2Be4N3APYLMnzerq8Hzimqr43YNnfA+5HM9u2LfD4JI+mmaHbDvhhVT0YOJYmGVxFVa2oqj2qao8tt/TKSElS9/SOVdtss820w5EkjVGnEjXgCcD5VXVlVd0EfAl4JECSNwHbAK+eZ9mnAcdV1XVVdR1wBPAHwFXAb9t1AXwRePD4dkGSJEmSFqdr96hdBDwiyabA74C9gJVJXgL8EbBXe4/ZfMv+ZZKDae5ReyzwnqqqJIcDjwO+067z9PHuhiRJGsW55567WtuOfk3Dog1TWGKY4hTz9Z3U8kvhwCMOWK1tYCGNeYwjrkExweC4xnVcNH2dmlGrquOBQ4ETgVNp4lsB/BdwN+DYJCcleSNAkj2SfLhd/FDg3Ha5k4GTq+rw9r2/Bw5KcgrNPW6vmdAuSZIkSdLQujajRlW9CXhTX/PAOKtqJU2pfqrqFuCv5ul3IfCYJQxTkiRJksamUzNqkiRJkiQTNUmSJEnqHBM1SZIkSeqYzt2jJklaOmfsss+0Q1BHDaquCNOvsDiu7Q/a3xe86pLV2oapePjJ92y34O0P2q+uVusbJq7FVpOc5DEYppLitA0T02L3a5jlx3Ws5othuXNGTZIkSZI6xkRNkiRJkjrGRE2SJEmSOsZETZIkSZI6xmIikrQOsGiIYP4CIZNc76CiGcMULhlmW8MUAxnUd1AxkGGKWwxa5zDrHaZwyWJNclvzGbStcRX4GLhfHSwaMk6Dju1iC4SMq3CJBnNGTZIkSZI6xkRNkiRJkjrGRE2SJEmSOsZETZIkSZI6xmIikjRjLBwigBtuuGFsxUMWY1BMg4qGwMILbMxX8GKxxUAG/i4tQcGJ+YqM9Jt2IY9hLbQ4xTAWu7zmP4bjKNyxFIVHtHDOqEmSJElSx5ioSZIkSVLHmKhJkiRJUseYqEmSJElSx1hMRJI005KsD9yNnjGtqi6aXkSSJK1qlLHKRE2SOswKj2uW5K+BNwE/B25tmwvYfWpBTcj5F9+4WnXBQVUQYXAVwvn6LraS5OBtDe672KqNi2XFweF4vBZvHJUz5zOO9VrJcTSjjlUmapKkWfZKYJequmragUiSNI+RxirvUZMkzbKLgWunHYQkSWsw0ljljJokaZadBxyd5L+BG+Yaq+rd0wtJkqRVjDRWmahJkmbZRe1jo/YhSVLXjDRWmahJUgdYNGQ0VfVmgCSbt6+vm25Ek3Pve240b0GQfoP6DSr6Ma7l5+u70PiHXe+smK8ww6AiEMP01WSLdizWLMWq0Yw6VnmPmiRpZiXZLclPgNOA05L8OMn9px2XJElzRh2rTNQkSbNsBfDqqtq+qrYHXgN8aMoxSZLUa6SxykRNkjTLNquqo+ZeVNXRwGbTC0eSpNWMNFZ5j5okaZadl+QNwCHt6+fRVNeSJKkrRhqrnFGTJM2yFwHbAF9qH1u3bZIkdcVIY5UzapI0JlZyHL+q+iXwNwBJ1qe5vORX041qNsxXcXGhlRSHqdg43zoXu61xVH2cZHXFYda5rlYBHNfx7urxGkdciz2G8y2vpTPqWOWMmiRpZiX5TJI7JtkMOBU4Pcnrph2XJElzRh2rTNQkSbNs1/avkk8FjgDuDTx/qhFJkrSqkcaqBV36mGQT4GXAHwIFfB/4QFVdP2q0kiQtgQ2TbEgz+L2vqm5KUlOOaUEcWyVp2RhprFrojNongfsD/wG8D9iV26uWTESSv01yWpKfJvlsO8D193lWktPbfp/paX97u9xPkzx7knFLksbqg8AFNGWOj0myPTAr96hNfWyVJE3ESGPVQouJ7FZVu/a8PirJ6UOHOKIk29LcgLdrVf0uyReA/YCP9/TZCTgQeFRV/TLJXdv2JwMPBh4IbAwcneQIbzaXtDYWA+mErZOs7Hm9oqpuu0O+qv4d+Pee9y9MsufEolucJR9bx1Fcowvbms+gIiOLjaurRSjWVR7v8bFIyMSscZyC0ceqhc6onZjkEXMvkjwcWLmG/uOwAXCHJBsAmwKX9b3/l8B/tlVVqKor2vZdgWOq6uaq+g1wCrD3hGKWJC3OL6pqj57HKoNfkle2N2gnyUeSnAg8fkqxDqsLY6skaXHWOE7B6GPVQhO1hwA/THJBkguAY4GHJjk1ySnD7MkoqupS4N+Ai4DLgWur6pt93XYGdk7ygyTHJZlLxk4G9k6yaZKtgT2Be447ZknSRLyovULiScBdaG7O/tfphrRgUx1bJUkTM9JYtdBLH6c6A5XkLsC+NBVSrgG+mOR5VfWpnm4bADsBjwO2o7n+8wFV9c0kDwV+CFxJMxDeMmAbBwAHANzjHvcY385IkpZS2p/7AIdU1WlJsqYFOmTosdWxSpJm0khj1YIStaq6cDGRLYEnAOdX1ZUASb4EPBLoTdQuAY6vqpuA85OcRZO4nVBVbwXe2i77GeCs/g2005QrAB7wgAfMRMUwSRI/TvJNmj/kHZhkC+DWKce0IKOMrY5VkjSTRhqrFjqjNm0XAY9IsinwO2AvVr+O/yvAc4CPtZc47gyc1377952r6qokuwO7A/2XTUpaJiwQss55MU2xqPOq6rdJtgJeON2QpmdQcY1hDSrGMUyBjkEFDOYrGLHQYiBdKFwyzH6pm+YrrtHFz3FchUAG7atFRyZipLFqJhK1qjo+yaHAicDNwE+AFUneAqysqsOAI4EntRWzbgFe1yZnmwDfa2cXfwU8r6punsqOSJKWRJL7VtXPaAY+gPvMzhWPkqTlYLFj1UwkagBV9SbgTX3Nb+x5v4BXt4/e5a6nqfwoSVp3vJrmXq13DXivmJ3Kj5KkddeixqqZSdQkSZpTVQe0P2flO9MkScvMYscqEzVJ0sxKsiHwUuAxbdPRwAfbwlKSJE3dqGOViZokaZZ9ANgQeH/7+vlt20umFpEkSasaaawyUZM0U6zaqD4Prarf73n9nSQnTy2aCTr/4hsXXA1xodUVhzFfhckXsPAKel2o5rhQk6wMOEwVvi5WLOyqWfoM54t12hUaFxtXV/drAkYaq9YbY0CSJI3bLUl2nHuR5D40lX8lSeqKkcYqZ9QkSbPsdcBRSc5rX+/AMv4eNUlSJ400VjmjJkmaZT8APgjcClzdPj92qhFJkrSqkcYqEzVJ0iz7JHBv4J+B/wDuAxwy1YgkSVrVSGOVlz5KGhsLf2gCdquqXXteH5Xk9KlF01HjKNox7++3xS0GFkYYppCFBUIma7Gf1yDjKpoxaL3jWOdSWOw5P99+9fe9/HszUYhkpLHKGTVJ0iw7Mckj5l4keTiwcorxSJLUb6Sxyhk1SdIsewjwwyQXta/vBZyZ5FSgqmr36YUmSRIw4lhloiZJmmV7TzsASZLWYqSxKlW11IHMvM0226x22223aYchzbzf/ujUaYegRfopv/txVe2x2PU84AEPqK9+9atDL7fjjjsuyfbXRetvsGltfqedp7b9e1191sD2i7acXkxdMejYeFy6a5Kf1zi2Nd/v4iDrwn71r/eWW37HddecmUVtjG6OU96jJkmSJEkd46WPA2TD7djgru+YdhjSxCy2YtS81r/neNarifnTWxb+l1pN1h02vye7PfK90w5jNbN+Pcow/x4OU9Vu1o/LrBmmkuPAvhP83ZrkubHYbc1bifFPjljybc2nf70nz0bVx5E4oyZJkiRJHWOiJkmSJEkdY6ImSZIkSR1joiZJkiRJHWMxEWmGjK3ohyQJGK5AyCyZtwjEDO3vMAVChtmvWToGwxjmeC3UunqsusoZNUmSJEnqGBM1SZIkSeoYEzVJkiRJ6hgTNUmSJEnqGIuJSGMy64U/vGF4+Zn1c1Yap8UWZhhHYYdhrAv/pi92H9aFgirDWFf3azlxRk2SJEmSOsZETZIkSZI6xkRNkiRJkjrGRE2SJEmSOsZETZIkSZI6xqqP0phYbUmS1mzalRCHsdi4urpfkrrLGTVJkiRJ6hgTNUmSJEnqGBM1SZIkSeqYmUnUkuyd5Mwk5yR5/YD3t0/y7SSnJDk6yXY9730jyTVJvjbZqCVJkiRpeDNRTCTJ+sB/Ak8ELgFOSHJYVZ3e0+3fgE9W1SeSPB44GHh++947gU2Bv5pg2JIkaQ0ssKFJ8nzTrJmVGbWHAedU1XlVdSPwOWDfvj67At9pnx/V+35VfRv49SQClSRJkqTFmokZNWBb4OKe15cAD+/rczLwdOC9wNOALZJsVVVXTSZESdJ8zr/4Rl7wyovX3lGSpCno4jg1KzNqC/Fa4LFJfgI8FrgUuGWhCyc5IMnKJCtvuvHaccUoSdLIHKskafmYlRm1S4F79rzerm27TVVdRjOjRpLNgWdU1TUL3UBVrQBWAGx+511qkfFKkrTkHKskafmYlRm1E4Cdktw7yUbAfsBhvR2SbJ1kbn8OBD464RglSZIkaUnMxIxaVd2c5BXAkcD6wEer6rQkbwFWVtVhwOOAg5MUcAzw8rnlk3wPuC+weZJLgBdX1ZGT3g9JkpbK3a+9kAOPOGCVNqvaSeu2/t958Pd+XTYTiRpAVX0d+Hpf2xt7nh8KHDrPso8eb3SSJEmStHRm5dJHSZIkSVo2TNQkSZIkqWNM1CRJkiSpY2bmHjVJkiRpObNwyPLijJokSZIkdYyJmiRJkiR1jImaJEmSJHWMiZokSZIkdYzFRCRJmkGX32l7Dn509woLHHjEAau1LbcCCIOOwSDL7bhoPOY73zy/Zp8zapIkSZLUMSZqkiRJktQxJmqSJEmS1DEmapIkSZLUMSZqkiRJktQxVn2UJElLZlCluWGq0q0LVSNnLV7NNs+3dZczapIkSZLUMSZqkiRJktQxJmqSJEmS1DEmapIkSZLUMRYTkSStU5IcVFUHTTuOdcm6UOBjkjxektZmIWOVM2qSpJmV5K+T3KWv+cdTCUaSpAFGHatM1CRJs+xuwAlJvpBk7ySpqsOnHZQkST1GGqtM1CRJM6uq/gnYCfgIsD9wdpK3JdlxqoFJktQadawyUZMkzbSqKuD/tY+bgbsAhyZ5x1QDkySpNcpYZTERSdLMSvJK4AXAL4APA6+rqpuSrAecDfzdNOOTJGnUscpETZI0y7YEnl5VF/Y2VtWtSf5kSjFNzaBqg7D4ioPTXn7WLLf9lbRWI41VXvooSZpl9+kf+JIcAlBVZ0wnJEmSVjHSWGWiJkmaZffvfZFkfeAhU4pFkqRBRhqrTNQkSTMnyYFJfg3snuRX7ePXwBXAV6ccniRJix6rTNQkSTOnqg6uqi2Ad1bVHdvHFlW1VVUdOO34JEla7FhlMRFJ0sxJct+q+hnwxSQP7n+/qk6cQlhTZxGL+Q0qtOLxkjROix2rTNQkSbPo1cABwLsGvFfA4ycbjiRJq1nUWGWiJkmaOVV1QPtzz2nHIknSIIsdq7xHTZI0s5K8PMmde17fJcnLphiSJEmrGHWsmvlELcneSc5Mck6S1w94/zFJTkxyc5JnTiNGSdLY/GVVXTP3oqp+Cfzl9MKRJGk1I41VM33pY/sdBP8JPBG4BDghyWFVdXpPt4uA/YHXTj5CSdKYrZ8kVVVw27iw0ZRjUgdZOETSFI00Vs10ogY8DDinqs4DSPI5YF/gtkStqi5o37t1GgFKksbqG8Dnk3ywff1XbZskSV0x0lg164natsDFPa8vAR4+pVgkSZP39zQD3kvb198CPjy9cCRJWs1IY9WsJ2pLJskBNOUz2egOd5tyNJKkhaiqW4EPtI91nmOVJM2eUceqWU/ULgXu2fN6u7ZtaFW1AlgBsPmdd6nFhyZJGpckX6iqZyU5lea7aFZRVbtPIayxc6ySpNmx2LFq1hO1E4CdktybJkHbD/jz6YYkSZqAV7Y//2SqUUiSNL9FjVUznahV1c1JXgEcCawPfLSqTkvyFmBlVR2W5KHAl4G7AH+a5M1Vdf8phi1JWqSqurx9+rKq+vve95K8neZ+AM0gqzNKWlcsdqya+e9Rq6qvV9XOVbVjVb21bXtjVR3WPj+hqrarqs2qaiuTNElapzxxQNsfTzwKSZLmN9JYNdMzapKkdd7WSVb2vF5RVSuSvBR4GXCfJKf0vL8F8IOJRihJWs4GjlMAix2rTNQkSV32i6raY0D7Z4AjgIOB1/e0/7qqrp5IZJIkzT9OwSLHKhM1SdLMqaprgWuB5yT5feDR7VvfA0zUJElTt9ixykRNkjSzkvwNzfeKfalt+lSSFVX1H1MMS1onHXjEAau1WfxFWrtRxyoTNUnSLHsJ8PCq+g3cVkXrWMBETZLUFSONVTNf9VGStKwFuKXn9S1tmyRJXTHSWOWMmiRpln0MOD7Jl9vXTwU+Mr1wJElazUhjlYmaJGlmVdW7k3wXeFTb9MKq+sk0Y5IkqdeoY5WJmiRp1p0EXE47piW5V1VdNNWIJEla1UkMOVaZqEmSZlaSvwbeBPyc26/5L2D3acalybAK4WR5bBfPc3Z5GnWsMlGTJM2yVwK7VNVV0w5EkqR5jDRWWfVRkjTLLqb5MlFJkrpqpLHKGTVJ0iw7Dzg6yX8DN8w1VtW7pxeSJEmrGGmsMlGTJM2yi9rHRu1DkqSuGWmsMlGTJM2sqnozQJLN29fXTTciSZJWNepY5T1qkqSZlWS3JD8BTgNOS/LjJPefdlySJM0ZdawyUZMkzbIVwKuravuq2h54DfChKcckSVKvkcYqEzVJ0izbrKqOmntRVUcDm00vHEmSVjPSWOU9apKkWXZekjcAh7Svn0dTXUuSpK4YaawyUZMkzbIXAW8G/m/7+nvAC6cXjibp4D9eMe0QJGkhRhqrvPRRkjTLdgTuSTOebQTsBRwz1YgkSVrVSGOVM2qSpFn2aeC1wE+BW6cciyRJg4w0VpmoSZJm2ZVVdfi0g5AkaQ1GGqtM1CRJs+xNST4MfBu4Ya6xqr40vZAkSVrFSGOViZokaZa9ELgvsCG3X05SgImaJKkrRhqrTNQkSbPsoVW1y7SD0HQceMQBq7VZCVIan0G/c+Dv3QKMNFZZ9VGSNMt+mGTXaQchSdIajDRWOaMmSZpljwBOSnI+zXX/Aaqqdp9uWJIk3WakscpETZI0y/aedgCSJK3FSGOViZokaWZV1YXTjkGSpDUZdawyUZMkaQbd/doLV7uxf7nd0L/c9lezb9bP2VmPf9ZYTESSJEmSOsZETZIkSZI6xkRNkiRJkjrGRE2SJEmSOmZmErUkeyc5M8k5SV4/4P2Nk3y+ff/4JDu07VslOSrJdUneN/HAJUmSJGlIM1H1Mcn6wH8CTwQuAU5IclhVnd7T7cXAL6vq95LsB7wdeDZwPfAGYLf2IUnSzLv8Tttz8KOXdwW2/qqX0I2qdF2NS4sz6HMFP1uNz6zMqD0MOKeqzquqG4HPAfv29dkX+ET7/FBgrySpqt9U1fdpEjZJkiRJ6rxZSdS2BS7ueX1J2zawT1XdDFwLbLXQDSQ5IMnKJCtvuvHaRYYrSdLSc6ySpOVjVhK1sauqFVW1R1XtseFGd5p2OJIkrcaxSpKWj1lJ1C4F7tnzeru2bWCfJBsAdwKumkh0kiRJkrSEUlXTjmGt2sTrLGAvmoTsBODPq+q0nj4vBx5QVf+7LSby9Kp6Vs/7+wN7VNUrFrC9K4EL25dbA79Yqn0Zs1mKFWYrXmMdD2Mdj6WMdfuq2maxK0nyDZq4hvWLqtp7sdtfF/WMVcv13JyEWYrXWMfDWMdnqeJdZ8epmUjUAJLsA7wHWB/4aFW9NclbgJVVdViSTYBDgAcBVwP7VdV57bIXAHcENgKuAZ7UVzFyTdtdWVV7LPHujMUsxQqzFa+xjoexjscsxarFm6XPe5ZihdmK11jHw1jHZ9binYaZKM8PUFVfB77e1/bGnufXA382z7I7jDU4SZIkSVpCs3KPmiRJkiQtGyZqazdL32I4S7HCbMVrrONhrOMxS7Fq8Wbp856lWGG24jXW8TDW8Zm1eCduZu5RkyRJkqTlwhk1SZIkSeoYE7VWkr2TnJnknCSvH/D+xkk+375/fJIdOhbfY5KcmOTmJM8c8P4dk1yS5H0diPXVSU5PckqSbyfZvm3fM8lJPY/rkzx1mrH29HtGkkqyR/t6qyRHJbluEsd0IbEm2T/JlT3H7yV970/sHFhIvG2fZ7XnwmlJPtPT/o627Ywk/54k04w1yb3az/sn7Xm7T9vexfNg+/b36pQkRyfZrue9W3rOj8MmEa+WjuPURGN1nBpTvF0aqxynphar49RCVdWyf9CU/D8XuA9NCf+TgV37+rwM+K/2+X7A5zsW3w7A7sAngWcOWMd7gc8A7+tArHsCm7bPXzroWAJb0nzNwqbTjLXttwVwDHAczXfxAWwG/CHwv8d9TIc4rvuvKZZJnQNDxLsT8BPgLu3ru7Y/Hwn8oF3H+sCxwOOmHOsK4KXt812BCzp8HnwR+Iv2+eOBQ3reu27cMfqY6mfvOLV0sTpOje/Y7r+meDp2HjhOjSdWx6kFPpxRazwMOKeqzquqG4HPAfv29dkX+ET7/FBgr3H/9WSY+Krqgqo6Bbi1f+EkDwHuBnyzI7EeVVW/bV8eB2zH6p4JHNHTbyqxtv4ZeDtw/VxDVf2mqr7f2zZmC411oAmfA7CweP8S+M+q+iVAVV3RthewCc0/8BsDGwI/n3KsRfNdjAB3Ai5rY+7iebAr8J32+VED3tdscpyabKyOU6OZpbHKcWp6sTpOLZCJWmNb4OKe15e0bQP7VNXNwLXAVhOJbmHxDZRkPeBdwGvHENcgw8b6YuCIAe37AZ9dwrgGWWusSR4M3LOq/nvMsazNQo/rM9pLCQ5Nck+YyjkAC4t3Z2DnJD9IclySvQGq6liaf7gvbx9HVtUZU471IOB5SS6h+T7Hvx5jPGuykFhPBp7ePn8asEWSuX+rNkmysj3eTx1rpFpqjlNLx3FqfGZprHKcGg/HqSVkorbuexnw9aq6ZNqB9EvyPGAP4J197XcHHgAcOY24euJYD3g38JppxjGEw4Edqmp34Fvc/pf1rp4DG9BcVvI44DnAh5LcOcnvAfej+Qv2tsDjkzx6alE2ngN8vKq2A/YBDmnPjy56LfDYJD8BHgtcCtzSvrd9Ve0B/DnwniQ7TilGqVdX/41ynBqPWRqrHKfGw3FqgTaYdgAdcSlwz57X27Vtg/pckmQDmmnlqyYT3oLim88fAI9O8jJgc2CjJNdV1bw3JC/SgmJN8gTgH4HHVtUNfW8/C/hyVd00phjnrC3WLYDdgKPbq4f+F3BYkqdU1coxx9Zvrce1qnrPxw8D72ifT/ocWFC8NH9lO779nM9Pcha3D4jHVdV1AEmOaPfhe1OM9cXAbX9JTbIJsDVwBZO1kPPgMtq/VCbZHHhGVV3Tvndp+/O8JEcDD6K5l0Dd5zi1dBynxmeWxirHqfFwnFpK47r5bZYeNAnrecC9uf3Gx/v39Xk5q96k/YUuxdfT9+MMuEm7fW9/xn9z7kKO5dwv3U7zrOM4YM8uHde2/9G0N2lP8pgOcVzv3vP8aTSDyMTPgSHi3Rv4RPt8a5pLJbYCng38T7uODYFvA3865ViPAPZvn9+P5tr/dPS4bg2s1z5/K/CW9vldgI17+pzNgKIEPrr5WOBn7zi1dMfScWp8x7YTY9UCY3WcGk+sjlMLPZ7TDqArD5pp4rPaf5j/sW17C/CU9vkmNFVqzgF+BNynY/E9lOYvP7+h+QvqaQPWMalf0rXF+j80N92e1D4O61l2B5q/vKzXhePa1/doegZA4AKail/Xtcd+rP+YLOC4Hgyc1v6jeBRw32mdAwuMNzSX7JwOnArs17avD3wQOKN9790diHVXmgpfJ7fn7JM6fB48k2ZwO4vmr9Vzg94j2+N8cvvzxZM4D3xM9LN3nFq6WB2nxndsOzNWLSBWx6nxxOo4tcBH2gMjSZIkSeqIrt5kKEmSJEnLlomaJEmSJHWMiZokSZIkdYyJmiRJkiR1jImaJEmSJHWMiZo0JUmum3YMkiTNx3FKmi4TNUmSJEnqGBM1acqSbJ7k20lOTHJqkn3b9h2S/CzJx5OcleTTSZ6Q5AdJzk7ysGnHLkla9zlOSdPhF15LU5LkuqraPMkGwKZV9askWwPHATsB2wPnAA8CTgNOAE4GXgw8BXhhVT11KsFLktZ5jlPSdG0w7QAkEeBtSR4D3ApsC9ytfe/8qjoVIMlpwLerqpKcCuwwjWAlScuO45Q0BSZq0vQ9F9gGeEhV3ZTkAmCT9r0bevrd2vP6Vvz9lSRNhuOUNAXeoyZN352AK9rBb0+aS0kkSeoKxylpCvxLhzR9nwYOby8TWQn8bMrxSJLUy3FKmgKLiUiSJElSx3jpoyRJkiR1jImaJEmSJHWMiZokSZIkdYyJmiRJkiR1jImaJEmSJHWMiZokSZIkdYyJmiRJkiR1jImaJEmSJHXM/wd8xKCfrnkohQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True)\n", + "\n", + "# Region\n", + "data = idxs.T\n", + "cmap = plt.get_cmap('coolwarm', np.max(data) - np.min(data) + 1)\n", + "mat = ax[0].imshow(data, cmap=cmap, vmin=0, vmax=2,origin=\"lower\",)\n", + "cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0])\n", + "cbar.ax.set_yticks([0.3, 1, 1.7])\n", + "cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", + "\n", + "# Timings\n", + "data = best_duration.T\n", + "mat = ax[1].imshow(data, cmap=cmap, origin=\"lower\",)\n", + "cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1])\n", + "cbar.ax.set_yticks([0.3, 1, 1.7])\n", + "cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", + "\n", + "\n", + "for axi in ax:\n", + " axi.set_xlabel(\"lam\")\n", + " every = 8\n", + " axi.set_xticks(range(0, lam_range.size)[::every])\n", + " axi.set_xticklabels(np.round(lam_range[::every], 2));\n", + "\n", + " axi.set_ylabel(\"p\")\n", + " every = 8\n", + " axi.set_yticks(range(0, p_range.size)[::every])\n", + " axi.set_yticklabels(np.round(p_range[::every], 2))\n", + " \n", + " axi.axhline(20.5, color=\"k\")\n", + " \n", + "fig.suptitle(\"Best performance per region\", y=0.85, fontsize=18);" ] } ], "metadata": { + "hide_input": false, "jupytext": { "formats": "ipynb,py:percent" }, "kernelspec": { - "display_name": "Python 3", + "display_name": "roche_preclinical_hd_gpu", "language": "python", - "name": "python3" + "name": "roche_preclinical_hd_gpu" }, "language_info": { "codemirror_mode": { diff --git a/notebooks/fast_gen_pois.py b/notebooks/fast_gen_pois.py index 81912ed..12cd4c9 100644 --- a/notebooks/fast_gen_pois.py +++ b/notebooks/fast_gen_pois.py @@ -6,14 +6,14 @@ # extension: .py # format_name: percent # format_version: '1.3' -# jupytext_version: 1.13.8 +# jupytext_version: 1.4.2 # kernelspec: -# display_name: Python 3 +# display_name: roche_preclinical_hd_gpu # language: python -# name: python3 +# name: roche_preclinical_hd_gpu # --- -# %% +# %% pycharm={"name": "#%%\n"} import numpy as np from matplotlib import pyplot as plt @@ -37,7 +37,7 @@ def _logprob(x, p, lam): ) -# %% +# %% pycharm={"name": "#%%\n"} def _rejection_region_monotonicity(rng, p, lam, dist_size, idxs_mask=None): if idxs_mask is None: idxs_mask = np.ones(dist_size, dtype="bool") @@ -46,22 +46,27 @@ def _rejection_region_monotonicity(rng, p, lam, dist_size, idxs_mask=None): dist_size = np.sum(idxs_mask) p0 = np.exp(-p) b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi) - u = rng.uniform(size=dist_size) - x = np.zeros(dist_size) - inds_to_sample = u > p0 / (p0 + b) - counter = 0 + x = np.full(dist_size, np.nan) + inds_to_sample = np.ones(dist_size, dtype=bool) # dummy boolean mask#u > p0 / (p0 + b) + counter = -1 while np.any(inds_to_sample): counter += 1 + u = rng.uniform(size=dist_size) + zero_xs = u <= p0 / (p0 + b) + x[inds_to_sample & zero_xs] = 0 + inds_to_sample = inds_to_sample & ~zero_xs + v = rng.uniform(size=dist_size) w = rng.uniform(size=dist_size) _x = np.floor(1 / w ** 2) accepted = v * b * (1 / np.sqrt(_x) - 1 / np.sqrt(_x + 1)) <= np.exp(_logprob(_x, p, lam)) x[inds_to_sample & accepted] = _x[inds_to_sample & accepted] inds_to_sample = inds_to_sample & ~accepted + # print(counter) return x -# %% +# %% pycharm={"name": "#%%\n"} def _rejection_region_poisson(rng, p, lam, dist_size, idxs_mask=None): if idxs_mask is None: idxs_mask = np.ones(dist_size, dtype="bool") @@ -190,7 +195,7 @@ def h_l(x, p, lam, delta, mu): return x -# %% +# %% pycharm={"name": "#%%\n"} def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): if idxs_mask is None: idxs_mask = np.ones(dist_size, dtype="bool") @@ -203,7 +208,7 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): t = np.floor(alpha * np.maximum(nu, 0)) problematic = (p < 1 + lam) | ((p * (1 - lam)) > (2 * lam)) t[problematic] = 0 - b = p * np.exp(np.maximum(1 - p, 0)) * np.sqrt(2 / np.pi) + # b = p * np.exp(np.maximum(1 - p, 0)) * np.sqrt(2 / np.pi) b = p * np.exp(2 - lam - np.minimum(lam, p)) * np.sqrt(2 / np.pi) q_r = b / np.sqrt(t + 1) @@ -274,7 +279,38 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): return x -# %% +# %% pycharm={"name": "#%%\n"} +def _inverse_rng_fn(rng, theta, lam, dist_size): + log_u = np.log(rng.uniform(size=dist_size)) + pos_lam = lam > 0 + abs_log_lam = np.log(np.abs(lam)) + theta_m_lam = theta - lam + log_s = -theta + log_p = log_s.copy() + x_ = 0 + x = np.zeros(dist_size) + below_cutpoint = log_s < log_u + with np.errstate(divide="ignore", invalid="ignore"): + counter = 0 + while np.any(below_cutpoint): + counter += 1 + x_ += 1 + x[below_cutpoint] += 1 + log_c = np.log(theta_m_lam + lam * x_) + # Compute log(1 + lam / C) + log1p_lam_m_C = np.where( + pos_lam, + np.log1p(np.exp(abs_log_lam - log_c)), + pm.math.log1mexp_numpy(abs_log_lam - log_c, negative_input=True), + ) + log_p = log_c + log1p_lam_m_C * (x_ - 1) + log_p - np.log(x_) - lam + log_s = np.logaddexp(log_s, log_p) + below_cutpoint = log_s < log_u + print(counter) + return x + + +# %% pycharm={"name": "#%%\n"} rng = np.random.default_rng(42) p, lam = np.meshgrid(np.logspace(-2, 4, 50), np.linspace(0, 1, 50)) dist_size = (100, *p.shape) @@ -285,7 +321,7 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): dist_size, ) -# %% +# %% pycharm={"name": "#%%\n"} # %%time samples = np.full(dist_size, np.nan) samples[monotonicity_idxs] = _rejection_region_monotonicity( @@ -306,13 +342,13 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): idxs_mask=abel_idxs, ) -# %% +# %% pycharm={"name": "#%%\n"} c = np.zeros_like(p.flatten()) c[monotonicity_idxs[0].flatten()] = 0 c[poisson_idxs[0].flatten()] = 1 c[abel_idxs[0].flatten()] = 2 -# %% +# %% pycharm={"name": "#%%\n"} plt.scatter( (p / (1 - lam)).flatten(), np.mean(samples, axis=0).flatten(), @@ -327,7 +363,7 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): plt.xlabel("Expected mean") plt.xlabel("Sample mean") -# %% +# %% pycharm={"name": "#%%\n"} plt.scatter( (p / (1 - lam) ** 3).flatten(), np.var(samples, axis=0).flatten(), @@ -345,14 +381,25 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): plt.xlabel("Sample variance") -# %% +# %% pycharm={"name": "#%%\n"} def normal_approx(x, p, lam): mu = p / (1 - lam) sigma = np.sqrt(p / (1 - lam) ** 3) return 1 / np.sqrt(2 * np.pi) / sigma * np.exp(-0.5 * (x - mu) ** 2 / sigma ** 2) -# %% +# %% pycharm={"name": "#%%\n"} +def monotonicity_region_envelope(x, p, lam): + return p * np.exp( + 2 + - lam + - np.minimum(lam, p) * np.sqrt(2 / np.pi) * ((1 / np.sqrt(x)) - (1 / np.sqrt(x + 1))) + ) + (x == 0) * np.exp( + -p + ) # Extra probability for x==0 + + +# %% pycharm={"name": "#%%\n"} def poisson_region_envelope(x, p, lam): eps = (1 - lam) / (2 + (p - lam) * (1 - lam)) ** (1 / 3) delta = (1 - lam) ** (2 / 5) / (2 + (p - lam) * (1 - lam)) ** (1 / 3) @@ -404,7 +451,7 @@ def h_l(x): return np.where(x < t_l, h_l(x), np.where(x < t_r, g(x), h_r(x))) -# %% +# %% pycharm={"name": "#%%\n"} x = np.linspace(1000, 1700, 1000) lam = 0.3 p = 1000 @@ -420,7 +467,7 @@ def h_l(x): plt.legend() -# %% +# %% pycharm={"name": "#%%\n"} def abel_rejection_envelope(x, p, lam): p = np.asarray(p) lam = np.asarray(lam) @@ -463,7 +510,7 @@ def abel_rejection_envelope(x, p, lam): ) -# %% +# %% pycharm={"name": "#%%\n"} def abel_rejection_proposal_density(x, p, lam): p = np.asarray(p) lam = np.asarray(lam) @@ -506,7 +553,7 @@ def abel_rejection_proposal_density(x, p, lam): ) -# %% +# %% pycharm={"name": "#%%\n"} p, lam = 2.1209508879201904, 0.5510204081632653 mean = p / (1 - lam) std = np.sqrt(p / (1 - lam) ** 3) @@ -514,23 +561,381 @@ def abel_rejection_proposal_density(x, p, lam): plt.semilogy(x, np.exp(_logprob(x, p, lam)), label="PDF") plt.plot(x, abel_rejection_envelope(x, p, lam), label="Envelope") plt.plot(x, abel_rejection_proposal_density(x, p, lam), label="Proposal density") -samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000) -print(np.mean(samples <= 1), np.sum(np.exp(_logprob(np.array([0, 1]), p, lam)))) +# samples = _rejection_region_abel(np.random.default_rng(42), p, lam, 100000) +# print(np.mean(samples <= 1), np.sum(np.exp(_logprob(np.array([0, 1]), p, lam)))) y, edges = np.histogram(samples, bins=20, density=True) -plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label="Sampled points") +# plt.plot(0.5 * (edges[1:] + edges[:-1]), y, label="Sampled points") plt.legend() -# %% +# %% pycharm={"name": "#%%\n"} p, lam = 2.1209508879201904, 0.5510204081632653 + mean = p / (1 - lam) std = np.sqrt(p / (1 - lam) ** 3) x = np.linspace(0, 10, 1000) -plt.semilogy(x, np.exp(_logprob(np.floor(x), p, lam)), label="PDF") -plt.plot(x, abel_rejection_envelope(np.floor(x), p, lam), label="Envelope") + +plt.figure(figsize=(16, 6)) +plt.semilogy(x, np.exp(_logprob(np.floor(x), p, lam)), label="PMF") + +# plt.plot(x, abel_rejection_envelope(np.floor(x), p, lam), label="Envelope") # plt.plot(x, abel_rejection_proposal_density(np.floor(x), p, lam), label="Proposal density") -samples = _rejection_region_abel(np.random.default_rng(), p, lam, 100000) -u, c = np.unique(samples, return_counts=True) -edges = np.arange(11) -y = np.array([np.sum(c[u == e]) for e in edges]) -plt.step(edges, y / samples.size, label="Sampled points", where="post") -plt.legend() +samples_monot = _rejection_region_monotonicity(np.random.default_rng(), p, lam, 100000) +samples_abel = _rejection_region_abel(np.random.default_rng(), p, lam, 100000) +for samples, algo in zip((samples_monot, samples_abel), ("monoticity", "abel")): + u, c = np.unique(samples, return_counts=True) + edges = np.arange(11) + y = np.array([np.sum(c[u == e]) for e in edges]) + plt.step(edges, y / samples.size, label=f"Sampled points ({algo})", where="post") + plt.legend(loc=(1, 0)) + +# %% pycharm={"name": "#%%\n"} +np.exp(_logprob(0, p, lam)) + +# %% pycharm={"name": "#%%\n"} +p_range = np.logspace(-2, 4, 50) +lam_range = np.linspace(0, 1, 60) +p, lam = np.meshgrid(p_range, lam_range) +dist_size = p.shape +# monotonicity_idxs = p <= (1 + lam) +# monotonicity_idxs = p <= np.exp(lam) +# poisson_idxs = p > np.maximum(1 + lam, 2 * lam / (1 - lam)) +poisson_idxs = p >= np.maximum(3, 2 * lam / (1 - lam)) +# poisson_idxs = p > np.maximum(np.exp(lam), 2 * lam / (1 - lam)) +abel_idxs = (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))) +# abel_idxs = (lam == 1) | ((p > np.exp(lam)) & (p <= 2 * lam / (1 - lam))) +# abel_idxs = (lam == 1) | ((p >= 3) & (p <= 2 * lam / (1 - lam))) + +# %% pycharm={"name": "#%%\n"} +idxs = np.full((lam_range.size, 50), 0, dtype=int) +# idxs[monotonicity_idxs] = 0 +idxs[poisson_idxs] = 1 +idxs[abel_idxs] = 2 +np.mean(idxs == 1), + +# %% pycharm={"name": "#%%\n"} +p_range = np.logspace(-2, 4, 50) +lam_range = np.linspace(0, 1, 60) +p, lam = np.meshgrid(p_range, lam_range) + +poisson_idxs = p >= np.maximum(3, 2 * lam / (1 - lam)) +abel_idxs = (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))) + +idxs = np.full((lam_range.size, 50), 0, dtype=int) +# idxs[monotonicity_idxs] = 0 +idxs[poisson_idxs] = 1 +idxs[abel_idxs] = 2 + +xs = np.concatenate([np.arange(10), np.logspace(1, 4.5)]).astype(int) +for i in range(p.shape[0]): + for j in range(p.shape[1]): + if idxs[i, j] == 0: + proposal = monotonicity_region_envelope(xs, p[i, j], lam[i, j]) + pmf = np.exp(_logprob(xs, p[i, j], lam[i, j])) + bad_xs = xs[proposal < pmf + 0.00] + if len(bad_xs): + print( + f"Monotonicity envelope is not higher than pmf for p={p[i, j]:.1f}, " + f"lam={lam[i, j]:.3f}, xs={bad_xs}" + ) + + elif idxs[i, j] == 1: + proposal = poisson_region_envelope(xs, p[i, j], lam[i, j]) + pmf = np.exp(_logprob(xs, p[i, j], lam[i, j])) + bad_xs = xs[proposal < pmf - 0.03] + if len(bad_xs): + print( + f"Poisson envelope is not higher than pmf for p={p[i, j]:.1f}, " + f"lam={lam[i, j]:.3f}, xs={bad_xs}" + ) + + elif idxs[i, j] == 2: + proposal = abel_rejection_envelope(xs, p[i, j], lam[i, j]) + pmf = np.exp(_logprob(xs, p[i, j], lam[i, j])) + bad_xs = xs[proposal < pmf - 0.0 + 0.00] + if len(bad_xs): + print( + f"Abel envelope is not higher than pmf for p={p[i, j]:.1f}, " + f"lam={lam[i, j]:.3f}, xs={bad_xs}" + ) + +# %% pycharm={"name": "#%%\n"} +data = idxs.T + +fig, ax = plt.subplots(figsize=(7, 7)) + +# get discrete colormap +cmap = plt.get_cmap("coolwarm", np.max(data) - np.min(data) + 1) +# set limits .5 outside true range +mat = ax.imshow( + data, + cmap=cmap, + vmin=0, + vmax=2, + origin="lower", +) +# tell the colorbar to tick at integers +cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038) +cbar.ax.set_yticklabels(["monotonicity", "poisson", "abel"]) + +ax.set_xlabel("lam") +every = 8 +plt.xticks(range(0, lam_range.size)[::every], np.round(lam_range[::every], 2)) + +ax.set_ylabel("p") +every = 8 +plt.yticks(range(0, p_range.size)[::every], np.round(p_range[::every], 2)) + +# %% [markdown] +# ## Benchmark algorithms + +# %% pycharm={"name": "#%%\n"} +import signal +import time + + +# %% pycharm={"name": "#%%\n"} +class TimeOutError(RuntimeError): + pass + + +def handler(signum, frame): + raise TimeOutError + + +signal.signal(signal.SIGALRM, handler) + +# %% pycharm={"name": "#%%\n"} +rng = np.random.default_rng(42) +dist_size = (100, *p.shape) + +# %% pycharm={"name": "#%%\n"} +duration_monot = np.full_like(p, np.nan) +for i in range(p.shape[0]): + for j in range(p.shape[1]): + signal.setitimer(signal.ITIMER_REAL, 0.05) + try: + start = time.time() + _rejection_region_monotonicity(rng, p=p[i, j], lam=lam[i, j], dist_size=100) + end = time.time() + except TimeOutError: + continue + duration_monot[i, j] = end - start +signal.alarm(0) + +# %% pycharm={"name": "#%%\n"} +duration_poisson = np.full_like(p, np.nan) +for i in range(p.shape[0]): + for j in range(p.shape[1]): + signal.setitimer(signal.ITIMER_REAL, 0.05) + try: + start = time.time() + _rejection_region_poisson(rng, p=p[i, j], lam=lam[i, j], dist_size=100) + end = time.time() + except TimeOutError: + continue + duration_poisson[i, j] = end - start +signal.alarm(0) + +# %% pycharm={"name": "#%%\n"} +duration_abel = np.full_like(p, np.nan) +for i in range(p.shape[0]): + for j in range(p.shape[1]): + signal.setitimer(signal.ITIMER_REAL, 0.05) + try: + start = time.time() + _rejection_region_abel(rng, p=p[i, j], lam=lam[i, j], dist_size=100) + end = time.time() + except TimeOutError: + continue + duration_abel[i, j] = end - start +signal.alarm(0) + +# %% pycharm={"name": "#%%\n"} +fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True) + +# Region +data = idxs.T +cmap = plt.get_cmap("coolwarm", np.max(data) - np.min(data) + 1) +mat = ax[0].imshow( + data, + cmap=cmap, + vmin=0, + vmax=2, + origin="lower", +) +cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0]) +cbar.ax.set_yticks([0.3, 1, 1.7]) +cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") + +# Timings +data = duration_monot.T +mat = ax[1].imshow( + data, + cmap="viridis", + origin="lower", +) +cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1]) + + +for axi in ax: + axi.set_xlabel("lam") + every = 8 + axi.set_xticks(range(0, lam_range.size)[::every]) + axi.set_xticklabels(np.round(lam_range[::every], 2)) + + axi.set_ylabel("p") + every = 8 + axi.set_yticks(range(0, p_range.size)[::every]) + axi.set_yticklabels(np.round(p_range[::every], 2)) + + axi.axhline(20.5, color="white") + +fig.suptitle("Monotonicity region performance", y=0.85, fontsize=18) + +# %% pycharm={"name": "#%%\n"} +fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True) + +# Region +data = idxs.T +cmap = plt.get_cmap("coolwarm", np.max(data) - np.min(data) + 1) +mat = ax[0].imshow( + data, + cmap=cmap, + vmin=0, + vmax=2, + origin="lower", +) +cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0]) +cbar.ax.set_yticks([0.3, 1, 1.7]) +cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") + +# Timings +data = duration_poisson.T +mat = ax[1].imshow( + data, + cmap="viridis", + origin="lower", +) +cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1]) + + +for axi in ax: + axi.set_xlabel("lam") + every = 8 + axi.set_xticks(range(0, lam_range.size)[::every]) + axi.set_xticklabels(np.round(lam_range[::every], 2)) + + axi.set_ylabel("p") + every = 8 + axi.set_yticks(range(0, p_range.size)[::every]) + axi.set_yticklabels(np.round(p_range[::every], 2)) + + axi.axhline(20.5, color="k") + +fig.suptitle("Poisson region performance", y=0.85, fontsize=18) + +# %% pycharm={"name": "#%%\n"} +fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True) + +# Region +data = idxs.T +cmap = plt.get_cmap("coolwarm", np.max(data) - np.min(data) + 1) +mat = ax[0].imshow( + data, + cmap=cmap, + vmin=0, + vmax=2, + origin="lower", +) +cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0]) +cbar.ax.set_yticks([0.3, 1, 1.7]) +cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") + +# Timings +data = duration_abel.T +mat = ax[1].imshow( + data, + cmap="viridis", + origin="lower", +) +cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1]) + + +for axi in ax: + axi.set_xlabel("lam") + every = 8 + axi.set_xticks(range(0, lam_range.size)[::every]) + axi.set_xticklabels(np.round(lam_range[::every], 2)) + + axi.set_ylabel("p") + every = 8 + axi.set_yticks(range(0, p_range.size)[::every]) + axi.set_yticklabels(np.round(p_range[::every], 2)) + + axi.axhline(20.5, color="w") + +fig.suptitle("Abel region performance", y=0.85, fontsize=18) + +# %% pycharm={"name": "#%%\n"} +nan_to_inf = lambda x: np.nan_to_num(x, nan=np.inf) + +d = 0.00 +best_duration = np.full_like(duration_monot, np.nan) +best_duration[ + (duration_monot + d < nan_to_inf(duration_poisson)) + & (duration_monot + d < nan_to_inf(duration_abel)) +] = 0 + +best_duration[ + (duration_poisson + d < nan_to_inf(duration_monot)) + & (duration_poisson + d < nan_to_inf(duration_abel)) +] = 1 + +best_duration[ + (duration_abel + d < nan_to_inf(duration_monot)) + & (duration_abel + d < nan_to_inf(duration_poisson)) +] = 2 + +# %% pycharm={"name": "#%%\n"} +fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True) + +# Region +data = idxs.T +cmap = plt.get_cmap("coolwarm", np.max(data) - np.min(data) + 1) +mat = ax[0].imshow( + data, + cmap=cmap, + vmin=0, + vmax=2, + origin="lower", +) +cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0]) +cbar.ax.set_yticks([0.3, 1, 1.7]) +cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") + +# Timings +data = best_duration.T +mat = ax[1].imshow( + data, + cmap=cmap, + origin="lower", +) +cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1]) +cbar.ax.set_yticks([0.3, 1, 1.7]) +cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") + + +for axi in ax: + axi.set_xlabel("lam") + every = 8 + axi.set_xticks(range(0, lam_range.size)[::every]) + axi.set_xticklabels(np.round(lam_range[::every], 2)) + + axi.set_ylabel("p") + every = 8 + axi.set_yticks(range(0, p_range.size)[::every]) + axi.set_yticklabels(np.round(p_range[::every], 2)) + + axi.axhline(20.5, color="k") + +fig.suptitle("Best performance per region", y=0.85, fontsize=18) From ee71ac764c43fa7f5af5b22452ad196291a21575 Mon Sep 17 00:00:00 2001 From: Ricardo Date: Fri, 3 Jun 2022 12:25:41 +0200 Subject: [PATCH 9/9] Include benchmark for old branching method --- notebooks/fast_gen_pois.ipynb | 934 ++++++++++++++++++++-------------- notebooks/fast_gen_pois.py | 375 +++++++------- 2 files changed, 735 insertions(+), 574 deletions(-) diff --git a/notebooks/fast_gen_pois.ipynb b/notebooks/fast_gen_pois.ipynb index 32cc38b..7a3b6d8 100644 --- a/notebooks/fast_gen_pois.ipynb +++ b/notebooks/fast_gen_pois.ipynb @@ -6,12 +6,36 @@ "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ricardo/miniconda3/envs/aeppl/compiler_compat/ld: warning: libm.so.6, needed by /usr/lib/x86_64-linux-gnu/libblas.so, not found (try using -rpath or -rpath-link)\n", + "/home/ricardo/miniconda3/envs/aeppl/compiler_compat/ld: /usr/lib/x86_64-linux-gnu/libblas.so: undefined reference to `cabs@GLIBC_2.2.5'\n", + "/home/ricardo/miniconda3/envs/aeppl/compiler_compat/ld: /usr/lib/x86_64-linux-gnu/libblas.so: undefined reference to `cabsf@GLIBC_2.2.5'\n", + "collect2: error: ld returned 1 exit status\n", + "/home/ricardo/miniconda3/envs/aeppl/compiler_compat/ld: cannot find -lcblas\n", + "collect2: error: ld returned 1 exit status\n", + "/home/ricardo/miniconda3/envs/aeppl/compiler_compat/ld: warning: libm.so.6, needed by /usr/lib/x86_64-linux-gnu/libblas.so, not found (try using -rpath or -rpath-link)\n", + "/home/ricardo/miniconda3/envs/aeppl/compiler_compat/ld: /usr/lib/x86_64-linux-gnu/libblas.so: undefined reference to `cabs@GLIBC_2.2.5'\n", + "/home/ricardo/miniconda3/envs/aeppl/compiler_compat/ld: /usr/lib/x86_64-linux-gnu/libblas.so: undefined reference to `cabsf@GLIBC_2.2.5'\n", + "collect2: error: ld returned 1 exit status\n", + "/home/ricardo/miniconda3/envs/aeppl/compiler_compat/ld: cannot find -lcblas\n", + "collect2: error: ld returned 1 exit status\n", + "/home/ricardo/miniconda3/envs/aeppl/compiler_compat/ld: warning: libm.so.6, needed by /usr/lib/x86_64-linux-gnu/libblas.so, not found (try using -rpath or -rpath-link)\n", + "/home/ricardo/miniconda3/envs/aeppl/compiler_compat/ld: /usr/lib/x86_64-linux-gnu/libblas.so: undefined reference to `cabs@GLIBC_2.2.5'\n", + "/home/ricardo/miniconda3/envs/aeppl/compiler_compat/ld: /usr/lib/x86_64-linux-gnu/libblas.so: undefined reference to `cabsf@GLIBC_2.2.5'\n", + "collect2: error: ld returned 1 exit status\n" + ] + } + ], "source": [ "import numpy as np\n", - "\n", + "import pymc as pm\n", "from matplotlib import pyplot as plt\n", "from scipy.special import gammaln\n", "\n", @@ -39,7 +63,8 @@ "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ @@ -77,7 +102,8 @@ "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ @@ -215,7 +241,8 @@ "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ @@ -244,6 +271,14 @@ " - 1.5 * np.log(t + 1)\n", " + (1 - lam) * t\n", " )\n", + "# rho_t_prime = ( # Taken form page 271\n", + "# np.log(lam * t + p) \n", + "# - np.log(t + 1)\n", + "# + 1\n", + "# - lam\n", + "# + 0.5 / (t + 1)\n", + "# - (lam + p) / (lam * t + p)\n", + "# )\n", " rho_t_prime = (\n", " np.log(lam * t + p)\n", " - np.log(t + 1)\n", @@ -274,10 +309,12 @@ " _q_l = q_l[inds_to_sample]\n", " _q_r = q_r[inds_to_sample]\n", " _b = b[inds_to_sample]\n", - " # raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(_q)))\n", + "# raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q)))\n", + "# raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(_q)))\n", " # raw_left = np.where(_t == 0, 0, _t + np.ceil(np.log(1 - E) / _q))\n", " raw_left = np.where(_t == 0, 0, _t - np.floor(E / _q))\n", " raw_right = np.floor((_t + 1) / W ** 2)\n", + " \n", " left = U <= _q_l / (_q_l + _q_r)\n", " accepted = np.where(\n", " left,\n", @@ -287,7 +324,8 @@ " np.where(\n", " raw_left < 0,\n", " False,\n", - " V * _q_l * _q ** (_t - raw_left) * (1 - _q **(_t+1))\n", + "# V * _q_l * _q ** (_t - raw_left) * (1 - _q)\n", + " V * _q_l * _q ** (_t - raw_left) * (1 - _q ** (_t + 1))\n", " <= np.exp(_logprob(raw_left, _p, _lam)),\n", " ),\n", " ),\n", @@ -304,11 +342,12 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 5, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ @@ -338,26 +377,49 @@ " log_p = log_c + log1p_lam_m_C * (x_ - 1) + log_p - np.log(x_) - lam\n", " log_s = np.logaddexp(log_s, log_p)\n", " below_cutpoint = log_s < log_u\n", - " print(counter)\n", + "# print(counter)\n", " return x" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "def _branching_rng_fn(rng, theta, lam, dist_size, idxs_mask=None):\n", + " if idxs_mask is None:\n", + " idxs_mask = np.ones(dist_size, dtype=bool)\n", + " lam_ = np.abs(lam) # This algorithm is only valid for positive lam\n", + " y = rng.poisson(theta, size=dist_size)\n", + " x = y.copy()\n", + " higher_than_zero = y > 0\n", + " while np.any(higher_than_zero[idxs_mask]):\n", + " y = rng.poisson(lam_ * y)\n", + " x[higher_than_zero] = x[higher_than_zero] + y[higher_than_zero]\n", + " higher_than_zero = y > 0\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 7, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_10806/1238690607.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/1238690607.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", " poisson_idxs = np.broadcast_to(p >= np.maximum(3, 2 * lam / (1 - lam)), dist_size)\n", - "/tmp/ipykernel_10806/1238690607.py:7: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/1238690607.py:7: RuntimeWarning: divide by zero encountered in true_divide\n", " (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam))),\n" ] } @@ -376,28 +438,29 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 8, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 3.09 s, sys: 57.1 ms, total: 3.15 s\n", - "Wall time: 3.16 s\n" + "CPU times: user 3.56 s, sys: 108 ms, total: 3.67 s\n", + "Wall time: 3.69 s\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_10806/1113335044.py:69: RuntimeWarning: overflow encountered in power\n", - " V * _q_l * _q ** (_t - raw_left) * (1 - _q **(_t+1))\n", - "/tmp/ipykernel_10806/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", + "/tmp/ipykernel_21224/2250734458.py:80: RuntimeWarning: overflow encountered in power\n", + " V * _q_l * _q ** (_t - raw_left) * (1 - _q ** (_t + 1))\n", + "/tmp/ipykernel_21224/2555885245.py:12: RuntimeWarning: invalid value encountered in log\n", " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" ] } @@ -426,11 +489,12 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 9, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ @@ -442,18 +506,19 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 10, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_10806/1687800886.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/1687800886.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", " (p / (1 - lam)).flatten(),\n" ] }, @@ -463,7 +528,7 @@ "Text(0.5, 0, 'Sample mean')" ] }, - "execution_count": 8, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, @@ -498,18 +563,19 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 11, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_10806/816571136.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/816571136.py:2: RuntimeWarning: divide by zero encountered in true_divide\n", " (p / (1 - lam) ** 3).flatten(),\n" ] }, @@ -519,7 +585,7 @@ "Text(0.5, 0, 'Sample variance')" ] }, - "execution_count": 9, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, @@ -556,11 +622,12 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 12, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ @@ -572,34 +639,33 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 13, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ "def monotonicity_region_envelope(x, p, lam):\n", " return p * np.exp(\n", - " 2 \n", - " - lam \n", - " - np.minimum(lam, p) \n", - " * np.sqrt(2 / np.pi) \n", - " * (\n", - " (1/np.sqrt(x)) \n", - " - (1 / np.sqrt(x + 1))\n", - " )\n", - " ) + (x == 0) * np.exp(-p) # Extra probability for x==0" + " 2\n", + " - lam\n", + " - np.minimum(lam, p) * np.sqrt(2 / np.pi) * ((1 / np.sqrt(x)) - (1 / np.sqrt(x + 1)))\n", + " ) + (x == 0) * np.exp(\n", + " -p\n", + " ) # Extra probability for x==0" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 14, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ @@ -656,20 +722,21 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 15, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 13, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, @@ -704,11 +771,12 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 16, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ @@ -749,18 +817,19 @@ " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q))\n", " return np.where(\n", " x <= t,\n", - " q_l * q ** (t - x) * (1 - q **(t+1)),\n", + " q_l * q ** (t - x) * (1 - q ** (t + 1)),\n", " b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", " )" ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 17, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ @@ -801,35 +870,36 @@ " q_l = np.where(t == 0, np.exp(-p), np.exp(rho_t) / (1 - q))\n", " return np.where(\n", " x <= t,\n", - " q ** (t - x) * (1 - q **(t+1)) / (1 - q),\n", + " q ** (t - x) * (1 - q ** (t + 1)) / (1 - q),\n", " np.sqrt(t + 1) * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", " )" ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 18, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_10806/584387763.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/4290048940.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", " b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n" ] }, { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 16, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, @@ -863,24 +933,25 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 19, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_10806/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", + "/tmp/ipykernel_21224/2555885245.py:12: RuntimeWarning: invalid value encountered in log\n", " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n" ] }, { "data": { - "image/png": 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vjOnS7FhKC8/1O0njmh80xrgl/UrStZIyJE01xmQYY7KNMUub/Ylv8tAHGh4HAAAAAGgnwe7WvFUEcDGd86vQ1qtouBnc8Mc2GzZS9TNeQiXJGHO7pKdbeK7Vkr5s4TS5knZaaz+z1tZIWiRporW20Fqb1+zPIVPvp5Letdb+o6XcxpjrjTHPl5ayZhUAAAAAzkdwkOur7/oAXFKtqk2NMW5jzEZJhyQtt9Z+1PR+a+2bkt6T9IYxZrqk70iach45LpPU9BJs+xuOnckPJI2WdKMx5nstDbDWLrHW3hETE3MeMQAAAAAAwS7jdASg02vVpsPW2jpJg4wxXSW9bYzJstYWNRvzH8aYRZKeldS/yaycdmetLZBUcLGeHwAAAAA6M5ZEAc47r69Ca+1xSR+o5X1oviEpS9Lbks53U+IDkvo2ud2n4RgAAAAA4BILDqKwAZx2zq9CY0xcw8waGWPCJY2RtL3ZmMGSnpc0UdKtkmKNMY+eR46PJaUaY/oZY0Ik3SLpT+fxeAAAAABAO2FJVOvde++9CSkpKZlpaWkZHo8n4/3334+8mOfLzc0dsHr16ojWjl+6dGmXUaNGtXRRoPM2ePBgz7nG5Ofnx5eXl59X45efnx//zDPPxF54sgtXUFAQu3v37uDG2zfffHPi+vXrw840fuHChTH33XdfgiS9+uqrXc82tlFeXl5yYWFh6Plma82SqF6SXm64kpNL0h+stUubjYmQdJO1dpckGWNmSprd/ImMMa9LulpSD2PMfkkPWmtfsNZ6jTF3qn4fHLekF621W873gwEAAAAAtB1LolpnxYoVke+9917XwsLCreHh4ba4uDiourq6w7ZdGzZs2H6uMQsWLOh5++23f9mlSxdfa56ztrZWr732Wo8tW7ZsbXvC8/faa6/1GDRoUGVSUlKtJL3xxht7zjZ++vTppZJKJemdd97p6vV6S4cOHVp1tsd8//vfP/TYY48lLFq06KzP3VxrrhK12Vo72Fo70FqbZa3Nb2HM/1hrC5vcrrXW/qaFcVOttb2stcHW2j7W2hea3LfMWptmre1vrX3sfD4IAAAAAED7YUlU6xw4cCC4e/fu3vDwcCtJvXr18ja+8b/nnnt6ZWVlpaempmZOnTo10eer7y9yc3MHzJkzp29WVlZ6cnJy5qpVqyLGjh3bPzExMWvu3Lm9JWnHjh0h/fr1y5wwYUK/5OTkzHHjxiW3NGvlrbfeih40aJAnIyMj/dprr00uLS11SdLixYuj+/Xrl5mRkZG+ePHiri1lLygoiL3mmmv65+bmDkhMTMyaN29er8b7HnrooZ6pqamZqampmfn5+fGNxyMiIgZL9bN2cnNzB4wbNy65MafP59Ojjz4af+jQoeCRI0emDR8+PM3r9Wry5MlJqampmWlpaRkPP/xwfPMcS5Ysic7Ozj4ZHBzc6s/PmTLu2LEjJDk5OfOWW25JTElJybzyyitTKyoqjCStXbs2PCcnx5OWlpYxZsyY/ocPH3a/9NJL3YqKiiJmzpyZ7PF4MioqKkzTGUyLFy+OzsjISB8wYEDG17/+9bTGz9vMmTMvX758eeSKFSu6PvDAA308Hk/Gli1bQjMyMtIb8xUWFp66PW7cuIo1a9ZE19bWnvM11VSrNh0GAAAAAHQeATnD5p1/66tDW1u9VKhV4jNOatKv9p3p7kmTJpU98cQTvZOSkrJGjBhRNnXq1C/Hjx9fIUk//vGPD82fP7+4YVy/RYsWxUybNq1UkkJCQnxFRUXbHnnkkfgpU6akfPzxx9vi4+O9SUlJ2ffdd99BSdq9e3fYggULdo8dO/bElClTkp566qm4/Pz8g43nLi4uDnr88cd7rV69+pPo6Gjf/fffn/DII4/0zM/PL7nzzjuTli9fviMzM7M6Ly8v+Uz5N2/eHFlYWLglKirKN3jw4IyJEyeWGmP0+9//Pnb9+vXbrLUaOnRo+jXXXFN+5ZVXVjZ97LZt28I3btz4WVJSUu3QoUM9y5cvj3rggQcOPfvssz1XrVr1Sa9evbxr1qyJKC4uDv7000+3SNKRI0fczTOsWbMmasiQISebHjvX5+fTTz8NbSljjx496vbu3Rv22muvfXbFFVfsue6665JfeeWVbv/6r//65ezZs/v953/+597x48dX/PCHP+x977339n7xxRf3Pfvss/Hz58/fd9VVV52W4Ysvvgi68847k1auXLnd4/HUHDx48LTsY8aMOTF69OjjeXl5pbfeeusxSerSpUvd2rVrw6+44orKBQsW9Jg+ffpRSXK73UpMTKz629/+FvGNb3zjtPOcTQB+FQIAAAAALqZgd4dd1dOuYmJifEVFRVufeeaZPXFxcd5Zs2b1LygoiJWkd999t8vAgQM9aWlpGWvXru1SVFQU3vi4G2644bgk5eTkVKakpFQmJibWhoeH2759+1Z/9tlnIZKUkJBQM3bs2BOSNGPGjKNr166NanrulStXRu7atSssNzfX4/F4MhYtWhS7d+/ekI0bN4b16dOnOjs7u9rlcqmxNGjJiBEjyhISEuqioqLs+PHjj61cuTJq5cqVUdddd93x6OhoX0xMjG/8+PHHPvjggy7NH5udnX2if//+tW63W5mZmSd37doV0nyMx+Op3rdvX+isWbP6Ll68OLpbt251zceUlJQEx8XFnTb15Fyfn7NlvOyyy6qvuOKKSkkaPHjwyd27d4cePXrUXV5e7m4s026//fajf/vb36J0FitXrozMzc0t93g8NZLUs2fPr2Rvbvbs2Ud+85vf9PB6vfqv//qvbnPmzDn1ue/Ro4d33759wWd7fHPMsAEAAAAAnCYgZ9icZSbMxRQUFKS8vLzyvLy88oEDB1a++uqrsbfddtuX8+bNS/zoo4+2pqSk1N599929q6qqTn1Sw8LCrCS5XC6FhobaxuMul0ter9dIkjGnl2bNb1trNWLEiLIlS5Z83vT42rVrw9VK5zrH2TTN7Xa7T+VuKi4urq6oqGjr22+/Hf3cc8/FvfHGG93ffPPN3U3HhIWF+Zp+bhqOnfPzcyYhISFNc9nKyspL9mKeNWvWsZ/+9Ke9Fy1aVJ6dnX0yISHhVMlTXV3tioiIaNW+Po0C8KsQAAAAAHAxBWRh44BNmzaFNr36z4YNG8L79OlTc/LkSZckJSQkeEtLS11Llizpdr7PXVxcHLJixYpISVq4cGH3K664oqLp/VdfffWJdevWRRUVFYVKUllZmWvz5s2hgwYNqjpw4EDIli1bQiVp0aJF3c90jg8//DD64MGD7oqKCrNs2bKuI0eOrBg1alTFsmXLupaXl7vKyspcy5Yt6zZq1Kjy1uaOjIysa9xLp7i4OKiurk6zZ88+/sQTTxwoLCz8ypK19PT0qp07d57XFZTON2NsbGxddHR03Z///OcoSXrhhRdiv/71r1dIUlRUVF1paelXlmpdffXVJ/7+97932b59e4gkNV8S1fjYsrKyU18sERERduTIkaV333335bNnzz7SdOznn38eOmTIkMrmz3E2fBUCAAAAAE7DkqjWKSsrc8+cObNf//79M9PS0jK2b98e/tOf/vSLHj161E2fPv1wenp65qhRo9JycnJOnO9zJyUlVT399NPxycnJmcePHw+65557Dje9v3fv3t4FCxbsvuWWW5LT0tIyhg0b5iksLAyLiIiwTz/99J68vLyUjIyM9B49enjPdI6BAweemDBhQv/MzMzM66+//thVV111csSIESenTZt2dMiQIelDhw5NnzFjxuHm+9eczaxZs46MGzcubfjw4Wm7d+8OHjFixACPx5MxY8aM5Pz8/P3Nx0+aNKl07dq1X1lydTYXkvGll176/N577+2TlpaWsXnz5vAnn3zyC0maOXPmkR/84AeJjZsON47v3bu3t6CgYPcNN9yQMmDAgIwbbrjhK3sBTZ8+/cuCgoKE9PT0jMaCbObMmV8aY/Ttb3+7rHHcvn37gkJDQ+3ll19+xv8XLTHW2nOPCmDDhg2z69atczoGAAAAAASMZYXF0g+vkdtl9K3lW5yOc0YrVqyoGT16dOG5RwaWHTt2hOTl5aU2btZ7MRQUFMSuW7cu8pVXXtl7sc7RWmPGjOn/85//fH92dna101na6v/+3//bs7S01P3LX/7yi8ZjDz/8cHx0dLTvRz/60ZGWHrNp06YeOTk5Sc2Ps4cNAAAAAOA0wW6XaiV17H/eh7+YP3/+/v379wcHemEzZsyY/nv27AldtWrVJ02Pd+3ate5f//Vfz7j585lQ2AAAAAAAThPkNqo99zBcJAMGDKi5mLNrJGnu3LlHJZ13iXAx5OTkVOfk5AR0WSNJy5cv39XS8bvuuuuCPs/sYQMAAAAAOE0Imw4DjuOrEAAAAABwGq4SBTiPr0IAAAAAwGm4ShTgPAobAAAAAMBpmGEDOI+vQgAAAADAaShsWu/ee+9NSElJyUxLS8vweDwZ77//fuTFPF9ubu6A1atXR7R2/NKlS7uMGjUqpT3OPXjwYM+5xuTn58eXl5ef1wsoPz8//plnnomVzv/ja6uCgoLYmTNnXt7SfVdccUXa4cOH3ZcqS3N8FQIAAAAATsOSqNZZsWJF5Hvvvde1sLBw6yeffLL1gw8++CQ5ObnG6VwXy4YNG7afa8yCBQt6VlRUtLprqK2t1Wuvvdbju9/9bquvpFRbe2muYTZ16tSj8+fPj7skJ2sBhQ0AAAAA4DTMsGmdAwcOBHfv3t0bHh5uJalXr17epKSkWkm65557emVlZaWnpqZmTp06NdHn80mqn0EyZ86cvllZWenJycmZq1atihg7dmz/xMTErLlz5/aWpB07doT069cvc8KECf2Sk5Mzx40bl9zSrJW33noretCgQZ6MjIz0a6+9Nrm0tNQlSYsXL47u169fZkZGRvrixYu7tpS9oKAg9pprrumfm5s7IDExMWvevHm9Gu976KGHeqampmampqZm5ufnxzcej4iIGCzVz9rJzc0dMG7cuOTGnD6fT48++mj8oUOHgkeOHJk2fPjwNK/Xq8mTJyelpqZmpqWlZTz88MPxzXMsWbIkOjs7+2RwcPCpYy+99FKsx+PJSE1Nzfzggw8iJOnuu+/uPWnSpH5DhgzxfPvb3+63Y8eOkKFDhw7IyMhIz8jISF++fHnk2bJJ0qpVqyIGDx7sGTBgQEZ2dnb6sWPHXJJUUlIS/I1vfCM1MTEx63vf+16fxhy33HLL8bfeeiu2Na+FiyHIqRMDAAAAAPxTIBY2/+d//k/fncd2tutSmpRuKScfufKRfWe6f9KkSWVPPPFE76SkpKwRI0aUTZ069cvx48dXSNKPf/zjQ/Pnzy9uGNdv0aJFMdOmTSuVpJCQEF9RUdG2Rx55JH7KlCkpH3/88bb4+HhvUlJS9n333XdQknbv3h22YMGC3WPHjj0xZcqUpKeeeiouPz//YOO5i4uLgx5//PFeq1ev/iQ6Otp3//33JzzyyCM98/PzS+68886k5cuX78jMzKzOy8tLPlP+zZs3RxYWFm6JioryDR48OGPixImlxhj9/ve/j12/fv02a62GDh2afs0115RfeeWVlU0fu23btvCNGzd+lpSUVDt06FDP8uXLox544IFDzz77bM9Vq1Z90qtXL++aNWsiiouLgz/99NMtknTkyJGvLC9as2ZN1JAhQ042PVZZWenavn371nfffTfqjjvu6Nf4+E8//TTso48+2h4VFWXLy8tda9as+SQiIsIWFhaGTp06NbmoqGjbmbKNHDnyxPTp0/svXLhw18iRI09++eWXrqioKJ8kbd26NWLTpk1bw8PDfSkpKVn33HPPwZSUlNq4uLi6mpoaU1JS4k5ISKg7+6ul/QXeVyEAAAAA4KIKdhsVxxmVxLM06mxiYmJ8RUVFW5955pk9cXFx3lmzZvUvKCiIlaR33323y8CBAz1paWkZa9eu7VJUVBTe+LgbbrjhuCTl5ORUpqSkVCYmJtaGh4fbvn37Vn/22WchkpSQkFAzduzYE5I0Y8aMo2vXro1qeu6VK1dG7tq1Kyw3N9fj8XgyFi1aFLt3796QjRs3hvXp06c6Ozu72uVyafr06WdcajRixIiyhISEuqioKDt+/PhjK1eujFq5cmXUdddddzw6OtoXExPjGz9+/LEPPvigS/PHZmdnn+jfv3+t2+1WZmbmyV27doU0H+PxeKr37dsXOmvWrL6LFy+O7tat21dKj5KSkuC4uLjT1jhNmzbtS0m69tprKyoqKlyNRc+4ceOOR0VFWUmqqakx06ZNS0pLS8uYMmVK/127doWdLdvmzZvD4uPja0eOHHlSkrp37+5rnNUzYsSIstjY2LqIiAibkpJStWvXrtDG54qNjfXu3bv3Kx/bpcAMGwAAAADAaYLcLi27OkhhQW7NdjpMK51tJszFFBQUpLy8vPK8vLzygQMHVr766quxt91225fz5s1L/Oijj7ampKTU3n333b2rqqpOTZgICwuzkuRyuRQaGmobj7tcLnm9XiNJxpxeljW/ba3ViBEjypYsWfJ50+Nr164NVyud6xxn0zS32+0+lbupuLi4uqKioq1vv/129HPPPRf3xhtvdH/zzTd3Nx0TFhbma/q5OVuuyMhIX+Oxxx57rGd8fHztH//4x899Pp/Cw8OHnk+2pkJCQpqOt7W1tafGV1dXm4iICF/Lj7y4mGEDAAAAADhNSMOSKHuOcZ3dpk2bQgsLC0/NxtiwYUN4nz59ak6ePOmSpISEBG9paalryZIl3c73uYuLi0NWrFgRKUkLFy7sfsUVV1Q0vf/qq68+sW7duqiioqJQSSorK3Nt3rw5dNCgQVUHDhwI2bJlS6gkLVq0qPuZzvHhhx9GHzx40F1RUWGWLVvWdeTIkRWjRo2qWLZsWdfy8nJXWVmZa9myZd1GjRpV3trckZGRdY176RQXFwfV1dVp9uzZx5944okDhYWFX1mylp6eXrVz587Qpsdef/31bpL03nvvRXXp0qUuNjb2KzNzSktL3b169ap1u9369a9/HVtXd/YVSwMHDqw6dOhQ8KpVqyIk6dixY65zbV7s8/l0+PDh4AEDBlSf6+O+GJhhAwAAAAA4zT+vEkVlczZlZWXuuXPnXl5WVuZ2u902KSmp+uWXX97To0ePuunTpx9OT0/PjIuL8+bk5Jw43+dOSkqqevrpp+PvuOOOiNTU1Kp77rnncNP7e/fu7V2wYMHuW265JbmmpsZI0oMPPnhg4MCB1U8//fSevLy8lPDwcN/w4cMrKioqWrw09cCBA09MmDChf0lJSciNN9549KqrrjopSdOmTTs6ZMiQdEmaMWPG4eb715zNrFmzjowbNy6tZ8+eNb/4xS/2zZkzJ8nn8xlJys/P3998/KRJk0qnTZvWr+mxsLAwm56enuH1es3zzz//efPHSNIPf/jDQ5MnT+6/aNGi2G9+85ul4eHhZ50FExYWZhcuXLhr7ty5l1dVVbnCwsJ8q1ev/uRsj/nwww8jBg8efKLphsiXkrG2Y38BDhs2zK5bt87pGAAAAAAQMKy1unHBIIUGufT72zY4HeeMVqxYUTN69OhCp3O0tx07doTk5eWlNm62ezEUFBTErlu3LvKVV17Ze7HO0Vpjxozp//Of/3x/dna2IzNZzuTWW2/tO2nSpOMTJ05s9QyjC7Fp06YeOTk5Sc2PsyQKAAAAAHCa89nLBGir+fPn79+/f78z01jOIisrq/JilzVnw5IoAAAAAMBXGEkdfEGG3xowYEDNxZxdI0lz5849KumMV5C6lHJycqpzcnL8anaNJM2bN++Ik+dnhg0AAAAAAICfobABAAAAAHyFy2XEyijAOSyJAgAAAAB8RWQIbxcBJ/EVCAAAAAD4Ck9EL6cjAJ0aS6IAAAAAAF9x701LdO9NS5yO4ffuvffehJSUlMy0tLQMj8eT8f7770dezPPl5uYOWL16dURrxy9durTLqFGjUtrj3IMHD/aca0x+fn58eXn5eXUN+fn58c8880zs2cZMnjw56aWXXurW2ufcsWNHSGpqaqYk/f3vfw+fPHly0vlk8gfMsAEAAAAA4AKsWLEi8r333utaWFi4NTw83BYXFwdVV1d32J1/NmzYsP1cYxYsWNDz9ttv/7JLly6+1jxnbW2tXnvttR5btmzZ2vaELcvNza0sLi4O+fTTT0NSU1NrLtZ52hszbAAAAAAAuAAHDhwI7t69uzc8PNxKUq9evbxJSUm1knTPPff0ysrKSk9NTc2cOnVqos9X31/k5uYOmDNnTt+srKz05OTkzFWrVkWMHTu2f2JiYtbcuXN7S/WzQ/r165c5YcKEfsnJyZnjxo1LbmnWyltvvRU9aNAgT0ZGRvq1116bXFpa6pKkxYsXR/fr1y8zIyMjffHixV1byl5QUBB7zTXX9M/NzR2QmJiYNW/evFNr4B566KGeqampmampqZn5+fnxjccjIiIGS/WzdnJzcweMGzcuuTGnz+fTo48+Gn/o0KHgkSNHpg0fPjzN6/Vq8uTJSampqZlpaWkZDz/8cHzzHEuWLInOzs4+GRwcLEn62c9+1iMrKyt9wIABGd/61rf6N/24ly9f3iUrKys9KSkp6/XXX4+RJK/Xq+9+97t9srKy0tPS0jKeeuqpHi19vNdee+3xl19+udUzdPwBM2wAAAAAAAHvi/vu71v96aetXirUGqGpqSd7P/7YvjPdP2nSpLInnniid1JSUtaIESPKpk6d+uX48eMrJOnHP/7xofnz5xc3jOu3aNGimGnTppVKUkhIiK+oqGjbI488Ej9lypSUjz/+eFt8fLw3KSkp+7777jsoSbt37w5bsGDB7rFjx56YMmVK0lNPPRWXn59/sPHcxcXFQY8//niv1atXfxIdHe27//77Ex555JGe+fn5JXfeeWfS8uXLd2RmZlbn5eUlnyn/5s2bIwsLC7dERUX5Bg8enDFx4sRSY4x+//vfx65fv36btVZDhw5Nv+aaa8qvvPLKyqaP3bZtW/jGjRs/S0pKqh06dKhn+fLlUQ888MChZ599tueqVas+6dWrl3fNmjURxcXFwZ9++ukWSTpy5Ii7eYY1a9ZEDRky5GTj7enTpx+bN2/eEUmaO3du74KCgh7333//IUnat29f6KZNm7Zt3bo1dPTo0QMmTpxY+Otf/zo2JiamrqioaFtlZaX5l3/5F8/1119fZppd4mz48OEnnnzyyV6SDipAMMMGAAAAAIALEBMT4ysqKtr6zDPP7ImLi/POmjWrf0FBQawkvfvuu10GDhzoSUtLy1i7dm2XoqKi8MbH3XDDDcclKScnpzIlJaUyMTGxNjw83Pbt27f6s88+C5GkhISEmrFjx56QpBkzZhxdu3ZtVNNzr1y5MnLXrl1hubm5Ho/Hk7Fo0aLYvXv3hmzcuDGsT58+1dnZ2dUul0vTp08/eqb8I0aMKEtISKiLioqy48ePP7Zy5cqolStXRl133XXHo6OjfTExMb7x48cf++CDD7o0f2x2dvaJ/v3717rdbmVmZp7ctWtXSPMxHo+net++faGzZs3qu3jx4uhu3brVNR9TUlISHBcXV9t4e/369eFDhw4dkJaWlvHHP/4xdsuWLWGN902ePPlLt9ut7Ozs6r59+1Zv3LgxbMWKFdF/+MMfYj0eT8bgwYPTjx07FrR169aw5ufp1auX9+DBg8Fn+lz4I2bYAAAAAAAC3tlmwlxMQUFBysvLK8/LyysfOHBg5auvvhp72223fTlv3rzEjz76aGtKSkrt3Xff3buqqurUhImwsDArSS6XS6GhobbxuMvlktfrNZLUfIZI89vWWo0YMaJsyZIlnzc9vnbt2nC10rnOcTZNc7vd7lO5m4qLi6srKira+vbbb0c/99xzcW+88Ub3N998c3fTMWFhYb6mn5s77rij3+LFi3d+/etfrywoKIhdtWrVqbKopbzWWvOzn/1s7+TJk8ua3rdjx47TCqTKykpXWFhYq/bV8RfMsAEAAAAA4AJs2rQptLCwMLTx9oYNG8L79OlTc/LkSZckJSQkeEtLS11Lliw5771TiouLQ1asWBEpSQsXLux+xRVXVDS9/+qrrz6xbt26qKKiolBJKisrc23evDl00KBBVQcOHAjZsmVLqCQtWrSo+5nO8eGHH0YfPHjQXVFRYZYtW9Z15MiRFaNGjapYtmxZ1/LycldZWZlr2bJl3UaNGlXe2tyRkZF1jXvpFBcXB9XV1Wn27NnHn3jiiQOFhYVfWbKWnp5etXPnzlOfw5MnT7ouv/zy2urqatM8+1tvvdWtrq5OW7ZsCd23b19oTk5O1ZgxY0qfffbZuMbNnjdv3hxaVlb2la5j69atoQMGDKhsftyfMcMGAAAAAIALUFZW5p47d+7lZWVlbrfbbZOSkqpffvnlPT169KibPn364fT09My4uDhvTk7OifN97qSkpKqnn346/o477ohITU2tuueeew43vb93797eBQsW7L7llluSa2pqjCQ9+OCDBwYOHFj99NNP78nLy0sJDw/3DR8+vKKiouIre8dI0sCBA09MmDChf0lJSciNN9549KqrrjopSdOmTTs6ZMiQdEmaMWPG4eb715zNrFmzjowbNy6tZ8+eNb/4xS/2zZkzJ8nn8xlJys/P3998/KRJk0qnTZvWr/H2T37yky9yc3PTu3fv7h0yZMhp2S+77LKanJyc9IqKCvcvfvGLPREREfZHP/rRkd27d4dmZ2enW2tN9+7da5ctW7ar+Xnef//96Ly8vNLWfhz+wFhrzz0qgA0bNsyuW7fO6RgAAAAAgHa2YsWKmtGjRxc6naO97dixIyQvLy+1cbPei6GgoCB23bp1ka+88srei3WO1hozZkz/n//85/uzs7OrL8bzV1ZWmq997WsD1q1bt73xalT+ZNOmTT1ycnKSmh9nSRQAAAAAAHDM/Pnz9+/fv/+iNSk7d+4Meeyxxw74Y1lzNsywAQAAAAAEpI46wwadCzNsAAAAAAAAAgSFDQAAAAAgIFlr1bihLRCIGl6/LV5unMIGAAAAABCQdu/eXXn48OEYShsEIp/PZw4fPhwjqail+zv8Zb3Xr19/xBizx+kcZ9FD0hGnQwDitQj/wOsQ/oDXIfwFr0X4A79+HXbv3j0pNzd3a0lJSZaYkIDA45NU5PV6b2vpzg6/6bC/M8ass9YOczoHwGsR/oDXIfwBr0P4C16L8Ae8DgHn0EACAAAAAAD4GQobAAAAAAAAP0Nh47znnQ4ANOC1CH/A6xD+gNch/AWvRfgDXoeAQ9jDBgAAAAAAwM8wwwYAAAAAAMDPUNg4yBgzzhizwxiz0xjzE6fzoPMxxvQ1xnxgjNlqjNlijLnL6UzovIwxbmPMBmPMUqezoPMyxnQ1xiw2xmw3xmwzxnzd6UzofIwxP2r4uVxkjHndGBPmdCZ0DsaYF40xh4wxRU2OdTfGLDfGfNrw325OZgQ6Ewobhxhj3JJ+JelaSRmSphpjMpxNhU7IK2metTZD0tck/RuvQzjoLknbnA6BTu+Xkv5srfVIyhGvSVxixpjLJM2VNMxamyXJLekWZ1OhE/mdpHHNjv1E0v+z1qZK+n8NtwFcAhQ2zsmVtNNa+5m1tkbSIkkTHc6ETsZaW2yt/UfD38tV/8bkMmdToTMyxvSRNF7Sb53Ogs7LGBMj6SpJL0iStbbGWnvc0VDorIIkhRtjgiRFSPrC4TzoJKy1qyV92ezwREkvN/z9ZUmTLmUmoDOjsHHOZZL2Nbm9X7xRhoOMMUmSBkv6yOEo6Jx+Iel/S/I5nAOdWz9JhyW91LA877fGmEinQ6FzsdYekDRf0l5JxZJKrbV/cTYVOrme1trihr+XSOrpZBigM6GwASBjTJSkP0r6obW2zOk86FyMMXmSDllr1zudBZ1ekKQhkp611g6WdEJM/ccl1rA/yETVF4i9JUUaY/6Xs6mAerb+EsNcZhi4RChsnHNAUt8mt/s0HAMuKWNMsOrLmoXW2reczoNO6UpJE4wxu1W/PPSbxpjXnI2ETmq/pP3W2saZhotVX+AAl9JoSZ9baw9ba2slvSXpCoczoXM7aIzpJUkN/z3kcB6g06Cwcc7HklKNMf2MMSGq30zuTw5nQidjjDGq36thm7X2507nQedkrf13a20fa22S6r8Xvm+t5V+TcclZa0sk7TPGDGg4dI2krQ5GQue0V9LXjDERDT+nrxGbX8NZf5I0q+HvsyT9l4NZgE4lyOkAnZW11muMuVPSe6rf/f9Fa+0Wh2Oh87lS0gxJhcaYjQ3H7rPWLnMuEgA46geSFjb8Y8pnkm51OA86GWvtR8aYxZL+ofqrOW6Q9LyzqdBZGGNel3S1pB7GmP2SHpT0pKQ/GGPmSNoj6SbnEgKdi6lfhggAAAAAAAB/wZIoAAAAAAAAP0NhAwAAAAAA4GcobAAAAAAAAPwMhQ0AAAAAAICfobABAAAAAADwMxQ2AAAAAAAAfobCBgAAAAAAwM9Q2AAAAAAAAPiZ/w/dUtKfFLUpHAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] @@ -904,8 +975,9 @@ "# plt.plot(x, abel_rejection_envelope(np.floor(x), p, lam), label=\"Envelope\")\n", "# plt.plot(x, abel_rejection_proposal_density(np.floor(x), p, lam), label=\"Proposal density\")\n", "samples_monot = _rejection_region_monotonicity(np.random.default_rng(), p, lam, 100000)\n", + "samples_branch = _branching_rng_fn(np.random.default_rng(), p, lam, 100000)\n", "samples_abel = _rejection_region_abel(np.random.default_rng(), p, lam, 100000)\n", - "for samples, algo in zip((samples_monot, samples_abel), (\"monoticity\", \"abel\")):\n", + "for samples, algo in zip((samples_monot, samples_branch, samples_abel), (\"monoticity\", \"branch\", \"abel\")):\n", " u, c = np.unique(samples, return_counts=True)\n", " edges = np.arange(11)\n", " y = np.array([np.sum(c[u == e]) for e in edges])\n", @@ -915,11 +987,12 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 20, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { @@ -928,7 +1001,7 @@ "0.11991754613423761" ] }, - "execution_count": 19, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -939,20 +1012,21 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 21, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_10806/4253790774.py:8: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/4253790774.py:8: RuntimeWarning: divide by zero encountered in true_divide\n", " poisson_idxs = p >= np.maximum(3, 2 * lam / (1 - lam))\n", - "/tmp/ipykernel_10806/4253790774.py:10: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/4253790774.py:10: RuntimeWarning: divide by zero encountered in true_divide\n", " abel_idxs = (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam)))\n" ] } @@ -974,11 +1048,12 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 22, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { @@ -987,7 +1062,7 @@ "(0.54,)" ] }, - "execution_count": 21, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -997,40 +1072,39 @@ "# idxs[monotonicity_idxs] = 0\n", "idxs[poisson_idxs] = 1\n", "idxs[abel_idxs] = 2\n", - "np.mean(idxs==1)," + "np.mean(idxs == 1)," ] }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 23, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_10806/2366160465.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/2902846004.py:5: RuntimeWarning: divide by zero encountered in true_divide\n", " poisson_idxs = p >= np.maximum(3, 2 * lam / (1 - lam))\n", - "/tmp/ipykernel_10806/2366160465.py:6: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/2902846004.py:6: RuntimeWarning: divide by zero encountered in true_divide\n", " abel_idxs = (lam == 1) | ((p >= 1 + lam) & (p <= 2 * lam / (1 - lam)))\n", - "/tmp/ipykernel_10806/294563780.py:8: RuntimeWarning: divide by zero encountered in true_divide\n", - " (1/np.sqrt(x))\n", - "/tmp/ipykernel_10806/294563780.py:5: RuntimeWarning: invalid value encountered in multiply\n", - " - np.minimum(lam, p)\n", - "/tmp/ipykernel_10806/3405323858.py:41: RuntimeWarning: overflow encountered in exp\n", + "/tmp/ipykernel_21224/1720600079.py:5: RuntimeWarning: invalid value encountered in multiply\n", + " - np.minimum(lam, p) * np.sqrt(2 / np.pi) * ((1 / np.sqrt(x)) - (1 / np.sqrt(x + 1)))\n", + "/tmp/ipykernel_21224/3405323858.py:41: RuntimeWarning: overflow encountered in exp\n", " return p / np.sqrt(2 * np.pi) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", - "/tmp/ipykernel_10806/3405323858.py:41: RuntimeWarning: overflow encountered in multiply\n", + "/tmp/ipykernel_21224/3405323858.py:41: RuntimeWarning: overflow encountered in multiply\n", " return p / np.sqrt(2 * np.pi) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", - "/tmp/ipykernel_10806/584387763.py:38: RuntimeWarning: overflow encountered in power\n", - " q_l * q ** (t - x) * (1 - q **(t+1)),\n", - "/tmp/ipykernel_10806/584387763.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/4290048940.py:38: RuntimeWarning: overflow encountered in power\n", + " q_l * q ** (t - x) * (1 - q ** (t + 1)),\n", + "/tmp/ipykernel_21224/4290048940.py:39: RuntimeWarning: divide by zero encountered in true_divide\n", " b * (1 / np.sqrt(x) - 1 / np.sqrt(x + 1)),\n", - "/tmp/ipykernel_10806/584387763.py:38: RuntimeWarning: divide by zero encountered in power\n", - " q_l * q ** (t - x) * (1 - q **(t+1)),\n" + "/tmp/ipykernel_21224/4290048940.py:38: RuntimeWarning: divide by zero encountered in power\n", + " q_l * q ** (t - x) * (1 - q ** (t + 1)),\n" ] }, { @@ -1066,10 +1140,10 @@ "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_10806/584387763.py:38: RuntimeWarning: overflow encountered in multiply\n", - " q_l * q ** (t - x) * (1 - q **(t+1)),\n", - "/tmp/ipykernel_10806/584387763.py:38: RuntimeWarning: invalid value encountered in multiply\n", - " q_l * q ** (t - x) * (1 - q **(t+1)),\n" + "/tmp/ipykernel_21224/4290048940.py:38: RuntimeWarning: overflow encountered in multiply\n", + " q_l * q ** (t - x) * (1 - q ** (t + 1)),\n", + "/tmp/ipykernel_21224/4290048940.py:38: RuntimeWarning: invalid value encountered in multiply\n", + " q_l * q ** (t - x) * (1 - q ** (t + 1)),\n" ] } ], @@ -1098,7 +1172,7 @@ " f\"Monotonicity envelope is not higher than pmf for p={p[i, j]:.1f}, \"\n", " f\"lam={lam[i, j]:.3f}, xs={bad_xs}\"\n", " )\n", - " \n", + "\n", " elif idxs[i, j] == 1:\n", " proposal = poisson_region_envelope(xs, p[i, j], lam[i, j])\n", " pmf = np.exp(_logprob(xs, p[i, j], lam[i, j]))\n", @@ -1108,7 +1182,7 @@ " f\"Poisson envelope is not higher than pmf for p={p[i, j]:.1f}, \"\n", " f\"lam={lam[i, j]:.3f}, xs={bad_xs}\"\n", " )\n", - " \n", + "\n", " elif idxs[i, j] == 2:\n", " proposal = abel_rejection_envelope(xs, p[i, j], lam[i, j])\n", " pmf = np.exp(_logprob(xs, p[i, j], lam[i, j]))\n", @@ -1122,11 +1196,12 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 24, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { @@ -1148,16 +1223,22 @@ "fig, ax = plt.subplots(figsize=(7, 7))\n", "\n", "# get discrete colormap\n", - "cmap = plt.get_cmap('coolwarm', np.max(data) - np.min(data) + 1)\n", + "cmap = plt.get_cmap(\"coolwarm\", np.max(data) - np.min(data) + 1)\n", "# set limits .5 outside true range\n", - "mat = ax.imshow(data, cmap=cmap, vmin=0, vmax=2,origin=\"lower\",)\n", + "mat = ax.imshow(\n", + " data,\n", + " cmap=cmap,\n", + " vmin=0,\n", + " vmax=2,\n", + " origin=\"lower\",\n", + ")\n", "# tell the colorbar to tick at integers\n", "cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038)\n", "cbar.ax.set_yticklabels([\"monotonicity\", \"poisson\", \"abel\"])\n", "\n", "ax.set_xlabel(\"lam\")\n", "every = 8\n", - "plt.xticks(range(0, lam_range.size)[::every], np.round(lam_range[::every], 2));\n", + "plt.xticks(range(0, lam_range.size)[::every], np.round(lam_range[::every], 2))\n", "\n", "ax.set_ylabel(\"p\")\n", "every = 8\n", @@ -1173,25 +1254,28 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 25, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ "import signal\n", - "import time" + "import time\n", + "from functools import reduce" ] }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 26, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [ { @@ -1200,7 +1284,7 @@ "" ] }, - "execution_count": 25, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } @@ -1209,19 +1293,22 @@ "class TimeOutError(RuntimeError):\n", " pass\n", "\n", + "\n", "def handler(signum, frame):\n", " raise TimeOutError\n", "\n", + "\n", "signal.signal(signal.SIGALRM, handler)" ] }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 27, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, "outputs": [], "source": [ @@ -1231,181 +1318,362 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 28, "metadata": { - "pycharm": { - "name": "#%%\n" - } + "scrolled": true }, - "outputs": [ - { - "data": { - "text/plain": [ - "0" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "duration_monot = np.full_like(p, np.nan)\n", - "for i in range(p.shape[0]):\n", - " for j in range(p.shape[1]):\n", - " signal.setitimer(signal.ITIMER_REAL, .05)\n", - " try:\n", + "def benchmark_algorithm(algorithm_fn, draws=100, duration_cutoff=0.05):\n", + " duration = np.full_like(p, np.nan)\n", + " for i in range(p.shape[0]):\n", + " for j in range(p.shape[1]):\n", + " signal.setitimer(signal.ITIMER_REAL, duration_cutoff)\n", " start = time.time()\n", - " _rejection_region_monotonicity(rng, p=p[i, j], lam=lam[i, j], dist_size=100)\n", + " try:\n", + " algorithm_fn(rng, p=p[i, j], lam=lam[i, j], dist_size=draws)\n", + " signal.alarm(0)\n", + " except TimeOutError:\n", + " continue\n", " end = time.time()\n", - " except TimeOutError:\n", - " continue\n", - " duration_monot[i, j] = end - start\n", - "signal.alarm(0)" + " duration[i, j] = end - start\n", + " signal.alarm(0)\n", + " return duration" ] }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 29, "metadata": { - "pycharm": { - "name": "#%%\n" - } + "scrolled": true + }, + "outputs": [], + "source": [ + "def plot_benchmark(duration, title=\"\"):\n", + " fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True)\n", + "\n", + " # Region\n", + " data = idxs.T\n", + " cmap = plt.get_cmap(\"coolwarm\", np.max(data) - np.min(data) + 1)\n", + " mat = ax[0].imshow(\n", + " data,\n", + " cmap=cmap,\n", + " vmin=0,\n", + " vmax=2,\n", + " origin=\"lower\",\n", + " )\n", + " cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0])\n", + " cbar.ax.set_yticks([0.3, 1, 1.7])\n", + " cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", + "\n", + " # Timings\n", + " data = duration.T\n", + " mat = ax[1].imshow(\n", + " data,\n", + " cmap=\"viridis\",\n", + " origin=\"lower\",\n", + " )\n", + " cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1])\n", + "\n", + "\n", + " for axi in ax:\n", + " axi.set_xlabel(\"lam\")\n", + " every = 8\n", + " axi.set_xticks(range(0, lam_range.size)[::every])\n", + " axi.set_xticklabels(np.round(lam_range[::every], 2))\n", + "\n", + " axi.set_ylabel(\"p\")\n", + " every = 8\n", + " axi.set_yticks(range(0, p_range.size)[::every])\n", + " axi.set_yticklabels(np.round(p_range[::every], 2))\n", + "\n", + " axi.axhline(20.5, color=\"white\")\n", + "\n", + " fig.suptitle(title, y=0.85, fontsize=18)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "duration_monot = benchmark_algorithm(_rejection_region_monotonicity)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_10806/2133065621.py:11: RuntimeWarning: invalid value encountered in sqrt\n", + "/tmp/ipykernel_21224/2133065621.py:11: RuntimeWarning: invalid value encountered in sqrt\n", " sigma = np.sqrt((1 + delta) * (p - lam) / (1 - lam - eps) / (1 - lam) ** 2)\n", - "/tmp/ipykernel_10806/2133065621.py:41: RuntimeWarning: invalid value encountered in power\n", + "/tmp/ipykernel_21224/2133065621.py:41: RuntimeWarning: invalid value encountered in power\n", " * (p - lam) ** 1.5\n", - "/tmp/ipykernel_10806/2133065621.py:29: RuntimeWarning: invalid value encountered in power\n", + "/tmp/ipykernel_21224/2133065621.py:29: RuntimeWarning: invalid value encountered in power\n", " / (np.sqrt(2 * np.pi) * (p - lam) ** 1.5)\n", - "/tmp/ipykernel_10806/2133065621.py:10: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/2133065621.py:50: RuntimeWarning: overflow encountered in exp\n", + " return p / np.sqrt(2 * np.pi) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", + "/tmp/ipykernel_21224/2133065621.py:10: RuntimeWarning: divide by zero encountered in true_divide\n", " mu = (p - lam) / (1 - lam)\n", - "/tmp/ipykernel_10806/2133065621.py:11: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/2133065621.py:11: RuntimeWarning: divide by zero encountered in true_divide\n", " sigma = np.sqrt((1 + delta) * (p - lam) / (1 - lam - eps) / (1 - lam) ** 2)\n", - "/tmp/ipykernel_10806/2133065621.py:18: RuntimeWarning: invalid value encountered in true_divide\n", + "/tmp/ipykernel_21224/2133065621.py:18: RuntimeWarning: invalid value encountered in true_divide\n", " (p * (1 - lam - eps) * np.sqrt(1 + delta))\n", - "/tmp/ipykernel_10806/2133065621.py:36: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/2133065621.py:36: RuntimeWarning: divide by zero encountered in true_divide\n", " t_r = np.ceil((p - lam) / (1 - lam - eps) - 1)\n", - "/tmp/ipykernel_10806/2133065621.py:46: RuntimeWarning: invalid value encountered in subtract\n", + "/tmp/ipykernel_21224/2133065621.py:46: RuntimeWarning: invalid value encountered in subtract\n", " * np.exp(-(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (t_r - mu))\n", - "/tmp/ipykernel_10806/2133065621.py:52: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/2133065621.py:52: RuntimeWarning: divide by zero encountered in true_divide\n", " t_l = np.ceil((p - lam) / (1 - lam + delta) - 1)\n", - "/tmp/ipykernel_10806/2133065621.py:54: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/2133065621.py:54: RuntimeWarning: divide by zero encountered in true_divide\n", " (2 * p * (1 + delta))\n", - "/tmp/ipykernel_10806/2133065621.py:56: RuntimeWarning: invalid value encountered in subtract\n", + "/tmp/ipykernel_21224/2133065621.py:56: RuntimeWarning: invalid value encountered in subtract\n", " * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (t_l + 1 - mu))\n", - "/tmp/ipykernel_10806/2133065621.py:85: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/2133065621.py:85: RuntimeWarning: divide by zero encountered in true_divide\n", " raw_left_y = _t_l - 2 * E * (1 + _delta) / _delta / (1 - _lam)\n", - "/tmp/ipykernel_10806/2133065621.py:86: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/2133065621.py:86: RuntimeWarning: divide by zero encountered in true_divide\n", " raw_right_y = _t_r + 2 * E / ((1 - 2 * (1 - _lam - _eps) / (_p - _lam)) * _eps * (1 - _lam))\n", - "/tmp/ipykernel_10806/2133065621.py:86: RuntimeWarning: invalid value encountered in add\n", + "/tmp/ipykernel_21224/2133065621.py:86: RuntimeWarning: invalid value encountered in add\n", " raw_right_y = _t_r + 2 * E / ((1 - 2 * (1 - _lam - _eps) / (_p - _lam)) * _eps * (1 - _lam))\n", - "/tmp/ipykernel_10806/2133065621.py:38: RuntimeWarning: invalid value encountered in true_divide\n", + "/tmp/ipykernel_21224/2133065621.py:38: RuntimeWarning: invalid value encountered in true_divide\n", " (2 * p * (1 - lam - eps) ** 1.5 * np.exp(2 * (1 - lam)))\n", - "/tmp/ipykernel_10806/2133065621.py:84: RuntimeWarning: invalid value encountered in add\n", + "/tmp/ipykernel_21224/2133065621.py:84: RuntimeWarning: invalid value encountered in add\n", " raw_center_y = _mu + _sigma * N\n", - "/tmp/ipykernel_10806/2133065621.py:85: RuntimeWarning: invalid value encountered in subtract\n", + "/tmp/ipykernel_21224/2133065621.py:85: RuntimeWarning: invalid value encountered in subtract\n", " raw_left_y = _t_l - 2 * E * (1 + _delta) / _delta / (1 - _lam)\n", - "/tmp/ipykernel_10806/2133065621.py:24: RuntimeWarning: invalid value encountered in subtract\n", + "/tmp/ipykernel_21224/2133065621.py:24: RuntimeWarning: invalid value encountered in subtract\n", " return G / (np.sqrt(2 * np.pi) * sigma) * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2))\n", - "/tmp/ipykernel_10806/2133065621.py:50: RuntimeWarning: invalid value encountered in subtract\n", + "/tmp/ipykernel_21224/2133065621.py:50: RuntimeWarning: invalid value encountered in subtract\n", " return p / np.sqrt(2 * np.pi) * np.exp(delta * (1 - lam) / (2 * (1 + delta)) * (x + 1 - mu))\n", - "/tmp/ipykernel_10806/2133065621.py:31: RuntimeWarning: invalid value encountered in subtract\n", + "/tmp/ipykernel_21224/2133065621.py:31: RuntimeWarning: invalid value encountered in subtract\n", " -(1 - 2 * (1 - lam - eps) / (p - lam)) * (eps / 2) * (1 - lam) * (x - mu)\n", - "/tmp/ipykernel_10806/2468484780.py:19: RuntimeWarning: invalid value encountered in subtract\n", + "/tmp/ipykernel_21224/2555885245.py:19: RuntimeWarning: invalid value encountered in subtract\n", " np.log(p) + _logpow(p_lam_x, x - 1) - p_lam_x - gammaln(x + 1),\n" ] - }, - { - "data": { - "text/plain": [ - "0" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" } ], "source": [ - "duration_poisson = np.full_like(p, np.nan)\n", - "for i in range(p.shape[0]):\n", - " for j in range(p.shape[1]):\n", - " signal.setitimer(signal.ITIMER_REAL, .05)\n", - " try:\n", - " start = time.time()\n", - " _rejection_region_poisson(rng, p=p[i, j], lam=lam[i, j], dist_size=100)\n", - " end = time.time()\n", - " except TimeOutError:\n", - " continue\n", - " duration_poisson[i, j] = end - start\n", - "signal.alarm(0)" + "duration_poisson = benchmark_algorithm(_rejection_region_poisson)" ] }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 32, "metadata": { - "pycharm": { - "name": "#%%\n" - } + "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/tmp/ipykernel_10806/1113335044.py:8: RuntimeWarning: divide by zero encountered in true_divide\n", + "/tmp/ipykernel_21224/2250734458.py:8: RuntimeWarning: divide by zero encountered in true_divide\n", " nu = 2 * (p ** 2 - lam * p - 3 * lam ** 2) / (3 * lam ** 2)\n", - "/tmp/ipykernel_10806/2468484780.py:12: RuntimeWarning: invalid value encountered in log\n", + "/tmp/ipykernel_21224/2555885245.py:12: RuntimeWarning: invalid value encountered in log\n", " return np.where(x == 0, np.where(m == 0, 0.0, -np.inf), m * np.log(x))\n", - "/tmp/ipykernel_10806/1113335044.py:69: RuntimeWarning: overflow encountered in power\n", - " V * _q_l * _q ** (_t - raw_left) * (1 - _q **(_t+1))\n" + "/tmp/ipykernel_21224/2250734458.py:80: RuntimeWarning: overflow encountered in power\n", + " V * _q_l * _q ** (_t - raw_left) * (1 - _q ** (_t + 1))\n" ] + } + ], + "source": [ + "duration_abel = benchmark_algorithm(_rejection_region_abel)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_21224/1066448282.py:4: RuntimeWarning: divide by zero encountered in log\n", + " abs_log_lam = np.log(np.abs(lam))\n" + ] + } + ], + "source": [ + "duration_inverse = benchmark_algorithm(\n", + " lambda rng, p, lam, dist_size: _inverse_rng_fn(rng, theta=p, lam=lam, dist_size=dist_size)\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "duration_branch = benchmark_algorithm(\n", + " lambda rng, p, lam, dist_size: _branching_rng_fn(rng, theta=p, lam=lam, dist_size=dist_size)\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", "text/plain": [ - "1" + "
" ] }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } ], "source": [ - "duration_abel = np.full_like(p, np.nan)\n", - "for i in range(p.shape[0]):\n", - " for j in range(p.shape[1]):\n", - " signal.setitimer(signal.ITIMER_REAL, .05)\n", - " try:\n", - " start = time.time()\n", - " _rejection_region_abel(rng, p=p[i, j], lam=lam[i, j], dist_size=100)\n", - " end = time.time()\n", - " except TimeOutError:\n", - " continue\n", - " duration_abel[i, j] = end - start\n", - "signal.alarm(0)" + "plot_benchmark(duration=duration_monot, title=\"Monotonicity algorithm speed\")\n", + "plot_benchmark(duration=duration_poisson, title=\"Poisson algorithm speed\")\n", + "plot_benchmark(duration=duration_abel, title=\"Abel algorithm speed\")\n", + "plot_benchmark(duration=duration_inverse, title=\"Inverse algorithm speed\")\n", + "plot_benchmark(duration=duration_branch, title=\"Branching algorithm speed\")" ] }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 36, "metadata": { "pycharm": { "name": "#%%\n" - } + }, + "scrolled": true }, + "outputs": [], + "source": [ + "def plot_benchmark_comparison(benchmarks, benchmark_names, threshold=0):\n", + " \n", + " nan_to_inf = lambda x: np.nan_to_num(x, nan=np.inf)\n", + " best_duration = np.full_like(duration_monot, np.nan)\n", + "\n", + " for i, reference in enumerate(benchmarks):\n", + " comps = (reference + threshold < nan_to_inf(other) for other in benchmarks if other is not reference)\n", + " best_duration[reduce(lambda x, y: x & y, comps)] = i\n", + " \n", + " \n", + " fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True)\n", + "\n", + " # Region\n", + " data = idxs.T\n", + " cmap = plt.get_cmap(\"coolwarm\", np.max(data) - np.min(data) + 1)\n", + " mat = ax[0].imshow(\n", + " data,\n", + " cmap=cmap,\n", + " vmin=0,\n", + " vmax=2,\n", + " origin=\"lower\",\n", + " )\n", + " cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0])\n", + " cbar.ax.set_yticks([0.3, 1, 1.7])\n", + " cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", + "\n", + " # Timings\n", + " data = best_duration.T\n", + " cmap = plt.get_cmap(\"coolwarm\", np.nanmax(data) - np.nanmin(data) + 1)\n", + " mat = ax[1].imshow(\n", + " data,\n", + " cmap=cmap,\n", + " origin=\"lower\",\n", + " )\n", + " cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1])\n", + " cbar.ax.set_yticks([0.3, 1, 1.7, 2.8, 3.5][:len(benchmarks)])\n", + " cbar.ax.set_yticklabels(benchmark_names, rotation=90, va=\"center\")\n", + "\n", + "\n", + " for axi in ax:\n", + " axi.set_xlabel(\"lam\")\n", + " every = 8\n", + " axi.set_xticks(range(0, lam_range.size)[::every])\n", + " axi.set_xticklabels(np.round(lam_range[::every], 2))\n", + "\n", + " axi.set_ylabel(\"p\")\n", + " every = 8\n", + " axi.set_yticks(range(0, p_range.size)[::every])\n", + " axi.set_yticklabels(np.round(p_range[::every], 2))\n", + "\n", + " axi.axhline(20.5, color=\"k\")\n", + "\n", + " fig.suptitle(\"Best performance per region\", y=0.85, fontsize=18)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -1417,50 +1685,20 @@ } ], "source": [ - "fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True)\n", - "\n", - "# Region\n", - "data = idxs.T\n", - "cmap = plt.get_cmap('coolwarm', np.max(data) - np.min(data) + 1)\n", - "mat = ax[0].imshow(data, cmap=cmap, vmin=0, vmax=2,origin=\"lower\",)\n", - "cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0])\n", - "cbar.ax.set_yticks([0.3, 1, 1.7])\n", - "cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", - "\n", - "# Timings\n", - "data = duration_monot.T\n", - "mat = ax[1].imshow(data, cmap=\"viridis\", origin=\"lower\",)\n", - "cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1])\n", - "\n", - "\n", - "for axi in ax:\n", - " axi.set_xlabel(\"lam\")\n", - " every = 8\n", - " axi.set_xticks(range(0, lam_range.size)[::every])\n", - " axi.set_xticklabels(np.round(lam_range[::every], 2));\n", - "\n", - " axi.set_ylabel(\"p\")\n", - " every = 8\n", - " axi.set_yticks(range(0, p_range.size)[::every])\n", - " axi.set_yticklabels(np.round(p_range[::every], 2))\n", - " \n", - " axi.axhline(20.5, color=\"white\")\n", - " \n", - "fig.suptitle(\"Monotonicity region performance\", y=0.85, fontsize=18);" + "plot_benchmark_comparison(\n", + " [duration_monot, duration_poisson, duration_abel],\n", + " [\"monot\", \"poisson\", \"abel\"],\n", + ")" ] }, { "cell_type": "code", - "execution_count": 31, - "metadata": { - "pycharm": { - "name": "#%%\n" - } - }, + "execution_count": 38, + "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -1472,50 +1710,20 @@ } ], "source": [ - "fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True)\n", - "\n", - "# Region\n", - "data = idxs.T\n", - "cmap = plt.get_cmap('coolwarm', np.max(data) - np.min(data) + 1)\n", - "mat = ax[0].imshow(data, cmap=cmap, vmin=0, vmax=2,origin=\"lower\",)\n", - "cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0])\n", - "cbar.ax.set_yticks([0.3, 1, 1.7])\n", - "cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", - "\n", - "# Timings\n", - "data = duration_poisson.T\n", - "mat = ax[1].imshow(data, cmap=\"viridis\", origin=\"lower\",)\n", - "cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1])\n", - "\n", - "\n", - "for axi in ax:\n", - " axi.set_xlabel(\"lam\")\n", - " every = 8\n", - " axi.set_xticks(range(0, lam_range.size)[::every])\n", - " axi.set_xticklabels(np.round(lam_range[::every], 2));\n", - "\n", - " axi.set_ylabel(\"p\")\n", - " every = 8\n", - " axi.set_yticks(range(0, p_range.size)[::every])\n", - " axi.set_yticklabels(np.round(p_range[::every], 2))\n", - " \n", - " axi.axhline(20.5, color=\"k\")\n", - " \n", - "fig.suptitle(\"Poisson region performance\", y=0.85, fontsize=18);" + "plot_benchmark_comparison(\n", + " [duration_monot, duration_poisson, duration_abel, duration_inverse, duration_branch],\n", + " [\"monot\", \"poisson\", \"abel\", \"inverse\", \"branch\"],\n", + ")" ] }, { "cell_type": "code", - "execution_count": 35, - "metadata": { - "pycharm": { - "name": "#%%\n" - } - }, + "execution_count": 39, + "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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gVcDVbfs7quoHHeM2A84DDqmqjyVZHTgFWK2N9+iqOrjH+p4CfALYAdirqo5u2x8BfAZYB7gD+EBVfbN7vCRJ0vdW3mbO1vXs2y+cs3VpNMz0frIV7X60Fd3AErWquhB4BECSecCVwHeAfYH/XVUfW8rQw4DjO+ZvBZ5aVTclWQX4WZLjq+r0rnGXA/sAb+5q/yvwL1X12yQPBM5MckJVXb/MH06SJEmSBmiuqj7uCvyuqi5Lll49M8nzgEuAmyfaqqqAm9rZVdqpusdW1aXtMu7sar+o4/UfkvwJ2Ai4fpk+iSRJkiQN2Fzdo7YX8PWO+dclOSfJF5OsB5BkLeCtwHu7ByeZl+Rs4E/Aj6vqjGUJIsljgVWB3/V4b/8ki5Isuu6665Zl8ZIkDVTnseoGpv+8H0nS+Bh4opZkVeC5wLfbps8AW9FcFnkV8PG2/RCaSyJv6loEVXVHVT0C2AR4bJJpP40yyQOAI4B9q+rO7verakFVza+q+euvv/50Fy9J0sB1HqvWZd6ww5EkDdBcXPr4TOCsqvojwMRPgCSfA77Xzu4I7JnkIzQFR+5McktVHT7Rv6quT3ISsBvwm34DSLIO8H3gnT3ubZMkSZKkkTIXidredFz2mOQBVXVVO/t82oSrqp7c0ecQ4KaqOjzJRsBtbZK2BvB04MP9rrw9o/cd4KsTlSAlSZKGbVAVJqdTTbJXDFajnLmlVWc89bidZjReK5aBXvqYZE2axOqYjuaPJDk3yTnALsAbp1jMA4CT2v6/pLlH7Xvt8g9N8tz29WOSXAH8M/DZJIvb8S8CngLsk+TsdnrELH1ESZIkSZp1Az2jVlU3Axt0tb28j3GHdLw+B3jkUvq9p+P1L2nuYevu8zXga30HLUmSJElDNldVHyVJkiRJfTJRkyRJkqQRM1cPvJYkSdIcGFSREvWv36Ih0x1vkZEVi2fUJEmSJGnEmKhJkiRJ0ogxUZMkSZKkEWOiJkmSJEkjxkRNkiRJkkaMVR8lSZJ0l+lUjXz27RcOMBJp+ZDkicAhwOY0+VeAqqotJxtnoiZJkiRJg/MF4I3AmcAd/Q4yUZMkSZKkwbmhqo6f7iATNUmSJEmaZUke1b48KclHgWOAWyfer6qzJhtvoiZJkiRJs+/jXfPzO14X8NTJBpuoSZIkaZlMp/DITK1IhUue+JyThx2CZkFV7TKT8ZbnlyRJkqQBSfLBJPftmF8vyfunGmeiJkmSJEmD88yqun5ipqr+DOw+1SATNUmSJEkanHlJVpuYSbIGsNok/QHvUZMkSZKkQToSODHJl9r5fYGvTDXIRE2SJEkjbzqFS8a98Mipx+0042VYkGR0VNWHk5wD7No2va+qTphqnImaJGnsJDlwsver6rC5ikWSpKm0D7ye1kOvTdQkSeNo7WEHIElSP5K8APgwcD8g7VRVtc5k40zUJEljp6reO+wYJEnq00eA51TV+dMZZNVHSdLYSvKQJCcm+U07v0OSdw07LknSCmPDJIs6pv179PnjdJM08IyaJGm8fQ44CPgsQFWdk+QoYMoHiUqSNAuuqar5U/RZlOSbwHeBWycaq+qYyQaZqEmSxtl9quoXSTrbbh9WMJJGw4pUIVJjYR3gr8AzOtoKMFGTJC23rkmyFc0BjyR7AlcNNyRJku5WVfsuyzgTNUnSKNswyaKO+QVVtaBj/rXAAmDbJFcClwAvncsAJUmaTJLVgVcCDwNWn2ivqldMNs5ETZI0yia99r+qlgBPS7ImsFJV/WXuQpMkqS9HABcA/wQcSvMHxSmLi1j1UZI0tpJskORTwE+BhUk+mWSDYcclSVKHB1fVu4Gbq+orwLOAHaca5Bk1SdI4+wZwCvDCdv6lwDeBpw0tIkljZTqFR/o1qAIlT3zOyfdqO/W4nQayLs2q29qf1yfZHvh/NA+/npSJmiRpnD2gqt7XMf/+JC8eWjSSJN3bgiTrAe8CjgXWAt491SATNUnSOPtRkr2Ab7XzewInDDEeSZLukmQl4Maq+jPNFSBb9jvWe9QkSWMnyV+S3Ai8CjiK5gGit9JcCrn/MGOTJGlCVd0JvGVZxnpGTZI0dqpq7YnXSdYHtqaj5LEkSSPkf5K8meYe6psnGqvquskGjVSilmQbmg8wYUvgPcBJwP+huZ7zUuClVXVjO+btNM8luAN4Q1Xd65KXJAHeD/xz2+8zVfWpwX0SSdJcSLIfcACwCXA28Djg58CuQwxLkqROLwYKeE1X+6SXQY5UolZVFwKPAEgyD7gS+A5wNPDmqjo5ySuAg4B3J9kO2Ivm4XEPpMlWH1JVd3Qteh9gU2DbqrozyZRVViRJY+EA4DHA6VW1S5JtgQ8OOSZJK7ilVZLsVQ2yV9+lVY2cToXHXn17VY3UnNiOJkl7Ek3C9lOak1CTGuV71HYFfldVlwEPobn5DuDH3F2GeQ/gG1V1a1VdAlwMPLbHsl4NHNpeI0pV/WmgkUuS5sotVXULQJLVquoCYPZrbUuStOy+AjwU+BTwnzSJ21emGjRSZ9S67AV8vX29mCYp+y7N5Yubtu0bA6d3jLmibeu2FfDiJM8Hrqa5RPK3nR2S7E97A/oDH/jA2fkEkqRBuyLJfWmODz9O8mfgsqFGNECdx6qNRvoQLknqsH1Vbdcxf1KS86YaNJJn1JKsCjwX+Hbb9ArgNUnOBNYG/j7NRa5G81fX+cDngC92d6iqBVU1v6rmr7/++ssevCRpzlTV86vq+qo6hOaZNF8AnjfUoAao81i1LvOGHY4kqT9nJXncxEySHYFFUw0a1T/HPRM4q6r+CNBeyvIMgCQPAZ7V9ruSu8+uQXMz+ZU9lncFcEz7+jvAlwYQsyRpiKrKmy8kSSMjybk096StAvw8yeXt/ObABVONH9VEbW/uvuyRJPerqj+1D4x7F3fffHcscFSSw2iKiWwN/KLH8r4L7AJcAuwEXDS40CVJkqR7W1qRkX77La3ISL8sMDLnnj2TwSOXqCVZE3g68L86mvdO8tr29TG0Z8SqanGSbwHnAbcDr52o+JjkB8B+VfUH4D+AI5O8EbgJ2G9OPowkSZKkkbfO1v/Arv+5DM+l3m3paUVbFHGZjVyiVlU3Axt0tX0S+ORS+n8A+ECP9t07Xl/P3ZdLSpIkSdJIG8liIpIkSZK0IjNRkyRJkqQRM3KXPkqSJEm6t36LkUD/hUd6FRhZGguPzC3PqEmSJEnSiDFRkyRJkqQRY6ImSZIkSSPGRE2SJEmSRoyJmiRJkiSNGKs+SpIkScuZ6VSI7KVX1UgrRM4tz6hJkiRJ0ogxUZMkSZKkEWOiJkmSJEkjxkRNkiRJkkaMxUQkSZIk3cN0ipH0Kjzy9uP3v1fbh565YEYxrWg8oyZJkiRJA5RkjSTTKsVpoiZJkiRJA5LkOcDZwA/b+UckOXaqcSZqkiRJkjQ4hwCPBa4HqKqzgQdNNchETZIkSZIG57aquqGrraYaZDERSZIkSRqcxUleAsxLsjXwBuDnUw0yUZMkSZK0zPqtENmrEuR0/e0d5894GUPweuCdwK3A14ETgPdNNchETZIkSZIGpKr+SpOovTPJPGDNqrplqnHeoyZJkiRJA5LkqCTrJFkTOBc4L8lBU40zUZMkSZKkwdmuqm4EngccT1Px8eVTDTJRkyRJkqTBWSXJKjSJ2rFVdRt9VH00UZMkSZKkwfk/wKXAmsApSTYHbpxqkMVEJEmSJGkAkqwE/LGqNu5ouxzYZaqxnlGTJEmSpAGoqjuBt3S1VVXdPtVYEzVJkiRJGpz/SfLmJJsmWX9immqQlz5KkiRJ0uC8uP352o62AracbJCJmiStYM7fZvdhhyBJ0qT+9tPzhx3CrKmqBy3LOC99lCRJkqRls2GSRR3T/t0dktwnybuSLGjnt07y7KkW7Bk1SZIkSVo211TV/Cn6fAk4E3hCO38l8G3ge5MN8oyaJEmSJA3OVlX1EeA2gKr6K5CpBnlGTZI0cKtvvzUP/e//nv7Arbaa/WAkSZpbf0+yBk0BEZJsBdw61aCRO6OW5I1JFif5TZKvJ1k9yZFJLmzbvphklaWM/Ug79vwkn0qStn3VJAuSXJTkgiQvnNtPJUmSJGkFdQjwQ2DTJEcCJ9L1bLVeRipRS7Ix8AZgflVtD8wD9gKOBLYFHg6sAezXY+wTgCcCOwDbA48Bdmrffifwp6p6CLAdcPJgP4kkSZIkQVX9CHgBsA/wdZpcZ+FU40bx0seVgTWS3AbcB/hD++EASPILYJMe4wpYHViV5prPVYA/tu+9gibRm3g6+DUDi16SJEmSWkmOA44Cjq2qm/sdN1Jn1KrqSuBjwOXAVcANXUnaKsDLaU4ddo89DTipHXcVcEJVnZ/kvm2X9yU5K8m3k9y/e3yS/SfKal533XWz/dEkSZqxzmPVDdwx7HAkSf35GPBk4LwkRyfZM8nqUw0aqUQtyXrAHsCDgAcCayZ5WUeXTwOnVNVPe4x9MPBQmrNtGwNPTfJkmjN0mwA/r6pHAafRbKx7qKoFVTW/quavv/76s/zJJEmauc5j1brMG3Y4kqQ+VNXJVfUaYEvgs8CLgD9NNW6kEjXgacAlVXV1Vd0GHEP7vIEkBwMbAQcuZezzgdOr6qaqugk4Hng8cC3w13ZZ0Dyz4FGD+wiSJEmSdLe26uMLgX+jqaXxlanGjFqidjnwuPbp3QF2Bc5Psh/wT8De7T1mSxu7U5KV20skdwLOr6oCjgN2bvvtCpw3yA8hSZIkSQBJvgWcDzwVOJzmuWqvn2rcSBUTqaozkhwNnAXcDvwKWADcDFwGnNZW3D+mqg5NMh/4t6raDzia5sOfS1NY5IdVdVy76LcCRyT5BHA1sO/cfSpJkiRJK7Av0JxwmtbNxSOVqAFU1cHAwV3NPeOsqkW0pfrbD/6/ltLvMuApsximJEmSJE2pqk5I8oQkW9CR11TVVycbN3KJmiRJkiQtL5IcAWwFnA13lewtwERNkiRJkoZkPrBdWzujb6NWTESSJEmSlie/Af5huoM8oyZJy7Hzt9l92CFIkjSpv/30/GGHMGgb0jzs+hfArRONVfXcyQaZqEmSJEnS4ByyLINM1CRJkiRpQKrq5GUZZ6ImSZIkSbMsyc+q6klJ/kJT5fGut4CqqnUmG2+iJkmSJEmzrKqe1P5ce1nGm6hJ0nLAoiGSpFG3AhQNmVUmapIkSZJWaNfP25Dj1t13GUbuN+uxTPA5apIkSZI0YkzUJEmSJGnEmKhJkiRJ0ojxHjVJGjMWDpEkjToLh8ycZ9QkSZIkacSYqEmSJEnSiDFRkyRJkqQRY6ImSZIkSSPGYiKSpLGWZB5wfzqOaVV1+fAikiRp5kzUJGmEWeFxckleDxwM/BG4s20uYIehBSVJK5hn337hvdq+fdqdPXpqOkzUJEnj7ABgm6q6dtiBSJI0m7xHTZI0zn4P3DDsICRJmm2eUZMkjbMlwMIk3wdunWisqsOGF5IkSTNnoiZJGmeXt9Oq7SRJ0nLBRE2SRoBFQ5ZNVb0XIMla7fxNw41ofPS6+X9pvrfyNgOMRNK4mM7/G//8+HvfYWWBkenxHjVJ0thKsn2SXwGLgcVJzkzysGHHJUnSTJmoSZLG2QLgwKravKo2B94EfG7IMUmSNGMmapKkcbZmVZ00MVNVC4E1hxeOJEmzw3vUJEnjbEmSdwNHtPMvo6kEKUnSWPOMmiRpnL0C2Ag4pp02bNskSRprnlGTpAGxkuPgVdWfgTcAJJlHcynkjcONanimU5FtFJbbq5pkr3UtrerkdPpKmp7p/Lu3muNgeEZNkjS2khyVZJ0kawLnAuclOWjYcUmSNFMmapKkcbZdewbtecDxwIOAlw81IkmSZkFflz4mWR14DfAkoICfAZ+pqlsGGJskSVNZJckqNIna4VV1W5Iackx98dgqSZpMv2fUvgo8DPhP4HBgO+6usDUnkrwxyeIkv0ny9fYA193nRUnOa/sd1dH+4Xbcb5K8eC7jliQN1GeBS2lK8p+SZHNgXO5RG/qxVZI0uvotJrJ9VW3XMX9SkvMGEVAvSTamuVl8u6r6W5JvAXsBX+7oszXwduCJVfXnJPdr258FPAp4BLAasDDJ8SvyzeaS+mMxkJGwYZJFHfMLqmrBxExVfQr4VMf7lyXZZc6im5kZHVvXffT2PHvRoqk7LgemU9RgOn1nWnhkaesaREGT6azLIisrlkEV+5mOf378vc/9WGBk5vo9o3ZWksdNzCTZEZjro8PKwBpJVgbuA/yh6/1XAf/VVgCjqv7Utm8HnFJVt1fVzcA5wG5zFLMkaWauqar5HdOCzjeTHNAWE0mSLyQ5C3jqkGKdrlE4tkqSRlS/idqjgZ8nuTTJpcBpwGOSnJvknIFF16qqK4GPAZcDVwE3VNWPuro9BHhIklOTnJ5kIhn7NbBbkvsk2RDYBdh00DFLkubEK9orJJ4BrEdTSOQ/hhtS34Z6bJUkjbZ+L30c6hmoJOsBe9BU87oe+HaSl1XV1zq6rQxsDewMbEJzr8LDq+pHSR4D/By4muZAeEePdewP7A/wwAc+cHAfRpI0m9L+3B04oqoWJ8lkA0bItI+tnceqzTbbbNYDkiSNjr4Staq6bNCBTOFpwCVVdTVAkmOAJwCdidoVwBlVdRtwSZKLaBK3X1bVB4APtGOPAi7qXkF7Oc0CgIc//OFjUTFMksSZSX5E84e8tydZGxiLGyOW5djaeayaP3++xypJWo71e0Zt2C4HHpfkPsDfgF2593X83wX2Br7UXuL4EGBJknnAfavq2iQ7ADsA3ZdNSlpBWCBkufNKmmJRS6rqr0k2APYdbkjq1ygUQeg2GwVC+v1cS1vmdIqBzHQbWnhk/M10PxrUv8NeBUamY2nFSLqX+6ILzjxzRisaYWORqFXVGUmOBs4Cbgd+BSxIciiwqKqOBU4AntFWzLoDOKhNzlYHftpeCXMj8LKqun0oH0SSNCuSbFtVF9AkaQBbjs8Vj5IkTW0sEjWAqjoYOLir+T0d7xdwYDt1jruFpvKjJGn5cSDNvVof7/FeMT6VHyVJ6mlsEjVJkiZU1f7tz3F5ZpokSdNioiZJGltJVgFeDTylbVoIfLYtLCVJ0tgyUZMkjbPPAKsAn27nX9627Te0iCRJmgUmapLGilUb1eUxVfWPHfM/SfLroUWjsTKdanfDrlA5iOqO0+1rNcjBmMvKm8Pej6djplUjlwduAUnSOLsjyVYTM0m2pKn8K0nSWPOMmiRpnB0EnJRkSTu/BT5HTZK0HPCMmiRpnJ0KfBa4E7iufX3aUCOSJGkWmKhJksbZV4EHAe8D/hPYEjhiqBFJkjQLvPRR0sBY+ENzYPuq2q5j/qQk5w0tGmkaxqmwA/Qf79IKYUynaMZMt02v5Y5qkZSZrn8622o620XD5xk1SdI4OyvJ4yZmkuwILBpiPJIkzQrPqEmSxtmjgZ8nubyd3wy4MMm5QFXVDsMLTZKkZWeiJkkaZ7sNOwBJkgbBRK2HJUuW8JKXvGTYYUhj7693/H7YIWg5V1WXDTuGYbnwwgvZeeedhx2GdC/XLuX//o/12F+n03emMSxtmUuLYVxMZ1tNZ7to+LxHTZIkSZJGjGfUesgqm7Dy/T4y7DCkOfP24/cfzILnbTqY5WrOPOeOi4YdgpZim222YeHChcMOQ2NunKoAzriS48+u6r3gOTxWDaJy5oouybBDGBjPqEmSJEnSiDFRkyRJkqQR46WPkiRJkjSLkhw42ftVddhUyzBRkyRJkqTZtfZMF2CiJo2RgRX9kCStkJbX4hQz/VwzLVwy0/Uvr9/LiqSq3jvTZXiPmiRJkiQNQJKHJDkxyW/a+R2SvKufsZ5RkyRJkrRC++NVf+GTH/jpIBb9OeAg4LMAVXVOkqOA90810DNqkiRJkjQY96mqX3S13d7PQBM1SZIkSRqMa5JsBRRAkj2BpTx9/Z689FEakHEv/PGhZy4YdgiaY+O+z0pavs1lgY3prMvCH5rCa4EFwLZJrgQuAV7az0ATNUmSJElaNhsmWdQxv6Cq7vprd1UtAZ6WZE1gpar6S78LNlGTJEmSpGVzTVXNX9qbSTYADgaeBFSSnwGHVtW1Uy3Ye9QkSZIkaTC+AVwNvBDYs339zX4GekZNkiRJkgbjAVX1vo759yd5cT8DPaMmSZIkSYPxoyR7JVmpnV4EnNDPQM+oSQNi1URJkqQVU5K/0JTkD/DvwBHtW/OAm4A3T7UMEzVJkiRJmkVVtfbE6yTrA1sDq09nGSZqkiRJkjQASfYDDgA2Ac4GHgf8HNh1qrHeoyZJkiRJg3EA8BjgsqraBXgkcEM/A8cmUUuyW5ILk1yc5G093t88yYlJzkmyMMkmHe/9MMn1Sb43t1FLkiRJWoHdUlW3ACRZraouALbpZ+BYJGpJ5gH/BTwT2A7YO8l2Xd0+Bny1qnYADgU+1PHeR4GXz0WskiRJktS6Isl9ge8CP07y38Bl/Qwcl3vUHgtcXFVLAJJ8A9gDOK+jz3bAge3rk2g2BgBVdWKSneciUEmSJEkCqKrnty8PSXISsC7ww37GjkuitjHw+475K4Adu/r8GngB8Eng+cDaSTaoqmvnJkRJ0tJc8vu/8y8H/H7qjpIkLaeq6uTp9B+LSx/79GZgpyS/AnYCrgTu6Hdwkv2TLEqy6La/93V/nyRJc6rzWHX11VcPOxxJ0gCNS6J2JbBpx/wmbdtdquoPVfWCqnok8M627fp+V1BVC6pqflXNX2XVdWchZEmSZlfnsWqjjTYadjiSpAEal0Ttl8DWSR6UZFVgL+DYzg5JNkwy8XneDnxxjmOUJEmSpFkxFolaVd0OvA44ATgf+FZVLU5yaJLntt12Bi5MchFwf+ADE+OT/BT4NrBrkiuS/NOcfgBJkiRJmoZxKSZCVf0A+EFX23s6Xh8NHL2UsU8ebHSSJEmSNHvG4oyaJEmSJK1ITNQkSZIkacSYqEmSJEnSiDFRkyRJkqQRY6ImSZIkSSPGRE2SJEmSRoyJmiRJkiSNGBM1SZIkSRoxJmqSJEmSNGJM1CRJkiRpxJioSZIkSdKIMVGTJEmSpBFjoiZJkiRJI8ZETZIkSZJGjImaJEmSJI0YEzVJkiRJGjErDzsASZIkSVqeJZkH3J+O/KuqLp9sjImaJEmSJA1IktcDBwN/BO5smwvYYbJxJmqSJEmSNDgHANtU1bXTGeQ9apKk5UqSQ4YdgyRJHX4P3DDdQZ5RkySNrfZykq9V1Z87ms8cVjySJPWwBFiY5PvArRONVXXYZINM1CRJ4+z+wC+TnAV8ETihqo4bckySJHW6vJ1Wbae+mKhJksZWVb0rybuBZwD7Aocn+Rbwhar63XCjkyQJquq9AEnWaudv6mec96hJksZaVRXw/9rpdmA94OgkHxlqYJIkAUm2T/IrYDGwOMmZSR421TjPqEmSxlaSA4B/Aa4BPg8cVFW3JVkJ+C3wlmHGJ0kSsAA4sKpOAkiyM/A54AmTDTJRkySNs/WBF1TVZZ2NVXVnkmcPKSZJkjqtOZGkAVTVwiRrTjXISx8lSeNsy+4kLckRAFV1/nBCkiTpHpYkeXeSLdrpXTSVICdloiZJGmf3uMY/yTzg0UOKRZKkXl4BbAQc004btm2T8tJHSdLYSfJ24B3AGklunGgG/k5zL4AkSSOhfdbnG+CuPyiuWVU3Tj7KM2qSpDFUVR+qqrWBj1bVOu20dlVtUFVvH3Z8kiRNSHJUknXa+9LOBc5LctBU40zUJEljJ8m27ctvJ3lU9zTU4CRJuqft2jNozwOOBx4EvHyqQV76KEkaRwcC+wMf7/FeAU+d23AkSVqqVZKsQpOoHd4+RqamGmSiJkkaO1W1f/tzl2HHIknSFD4LXAr8GjglyebAlPeomahJksZWktcCR1bV9e38esDeVfXpoQYmSRor2z54bX523E7THpewYZJFHU0LquoeRa2q6lPApzqaLksy5R8ax/4etSS7JbkwycVJ3tbj/ackOSvJ7Un2HEaMkqSBedVEkgZ3VdZ61fDCkSStYK6pqvkd070qDyc5oC0mkiRfSHIWfVyiP9aJWlve8r+AZwLbAXsn2a6r2+XAPsBRcxudJGkOzEuSiZn2uLDqEOORJKnbK9piIs8A1qMpJPIfUw0a90sfHwtcXFVLAJJ8A9gDOG+iQ1Vd2r535zAClCQN1A+Bbyb5bDv/v9o2SZJGxcQfFHcHjqiqxZ1/ZFyacU/UNgZ+3zF/BbDjkGKRJM29t9IkZ69u538MfH544UiSdC9nJvkRTVn+tydZG5jyJNK4J2qzJsn+NKWeWXWN+w85GklSP6rqTuAz7bTc6zxWbbbZZkOORpLUp1cCjwCWVNVfk2wA7DvVoHFP1K4ENu2Y36Rtm7b2xr8FAGvdd5spn2sgSRqeJN+qqhclOZfmuWn3UFU7DCGsges8Vs2fP99jlSSNsCTbVtUFNEkawJZ9XPF4l3FP1H4JbJ3kQTQJ2l7AS4YbkiRpDhzQ/nz2UKOQJGnpDqS5CuLjPd4rpqj8ONaJWlXdnuR1wAnAPOCL7c15hwKLqurYJI8BvkNTYeU5Sd5bVQ8bYtiSpBmqqqval6+pqrd2vpfkwzT3rkmSNDRVtX/7c8pnpvUy1okaQFX9APhBV9t7Ol7/kuaSSEnS8ufp3Dspe2aPNkmShiLJKjRFr57SNi0EPltVt002buwTNUnScm3DJIs65hdU1YIkrwZeQ3O9/zkd768NnDqnEUqSNLnPAKsAn27nX9627TfZIBM1SdIou6aq5vdoPwo4HvgQ8LaO9r9U1XVzEpkkSf15TFX9Y8f8T5L8eqpBKw0wIEmSBqKqbqiqS6tqb+C+wHPaadNJB0qSNPfuSLLVxEySLYE7phpkoiZJGltJ3gAcCdyvnb6W5PXDjUqSpHs4CDgpycIkC4GfAG+aapCXPkqSxtl+wI5VdTPcVfHxNOA/hxqVJEl3OxX4LLArcD1NxfrTphrkGTVJ0jgL97x85I62TZKkUfFV4EHA+2j+kLglcMRUgzyjJkkaZ18CzkjynXb+ecAXhheOJEn3sn1Vbdcxf1KS86YaZKImSRpbVXVYkpOBJ7ZN+1bVr4YZkyRJXc5K8riqOh0gyY7AoinGmKhJksbe2cBVtMe0JJtV1eVDjUiSpLs9Gvh5kolj02bAhUnOBaqqdug1yERNkjS22gqPBwN/5O770wroedCTJGkIdluWQSZqkqRxdgCwTVVdO+xAJEnqpaouW5ZxVn2UJI2z3wM3DDsISZJmm2fUJEnjbAmwMMn3gVsnGqvqsOGFJEnSzJmoSZLG2eXttGo7SZK0XDBRkySNrap6L0CStdr5m4YbkSRJs8N71CRJYyvJ9kl+BSwGFic5M8nDhh2XJEkzZaImSRpnC4ADq2rzqtoceBPwuSHHJEnSjJmoSZLG2ZpVddLETFUtBNYcXjiSJM0O71GTJI2zJUneDRzRzr+MphKkJEljzTNqkqRx9gpgI+D/ttOGwL5DjUiSpFlgoiZJGmdbAZvSHM9WBXYFThlqRJIkzQIvfZQkjbMjgTcDvwHuHHIskiTNGhM1SdI4u7qqjht2EJIkzTYTNUnSODs4yeeBE4FbJxqr6pjhhSRJ0syZqEmSxtm+wLbAKtx96WMBJmqSpLFmoiZJGmePqapthh2EJEmzzaqPkqRx9vMk2w07CEmSZpuJmiRpnD0OODvJhUnOSXJuknOGHZQkSROSfLiftm5e+ihJGme7DTsASZKm8HTgrV1tz+zRdg8mapKksVVVlw07BkmSeknyauA1wJZdV3usDZw61XgTNUmSJEmafUcBxwMfAt7W0f6XqrpuqsEmapIkSZI0y6rqBuAGYO8k/wg8uX3rp8CUiZrFRCRJkiRpQJK8ATgSuF87fS3J66ca5xk1SZIkSRqc/YAdq+pmuKvi42nAf042yDNqkiRJkjQ4Ae7omL+jbZvU2CRqSXZrn5NzcZK39Xh/tSTfbN8/I8kWbfsGSU5KclOSw+c8cEmSJEkrsi8BZyQ5JMkhwOnAF6YaNBaXPiaZB/wXzTMIrgB+meTYqjqvo9srgT9X1YOT7AV8GHgxcAvwbmD7dpIkSZKkOVFVhyU5GXhi27RvVf1qqnHjckbtscDFVbWkqv4OfAPYo6vPHsBX2tdHA7smSVXdXFU/o0nYJEmSJGmunU2To3wXuDbJZlMNGIszasDGwO875q8Adlxan6q6PckNwAbANf2sIMn+wP4Aq65x/5nGK0nSrOs8Vm222ZTHeEnSCGgrPB4M/JG7708rYIfJxo1LojZwVbUAWACw1n23qSGHI0nSvXQeq+bPn++xSpLGwwHANlV17XQGjculj1cCm3bMb9K29eyTZGVgXWBaG0OSJEmSZtnvaR58PS2pGv0/yLWJ10XArjQJ2S+Bl1TV4o4+rwUeXlX/1hYTeUFVvajj/X2A+VX1uj7WdzVwWTu7IX1ePjkCxilWGK94jXUwjHUwZjPWzatqo5kuJMkPaeKarmuqareZrn951HGsWlH3zbkwTvEa62AY6+DMVrzDPk6tzj1rYSxor37oXPYXgG2A7wO3TrRX1WGTxjQOiRpAkt2BTwDzgC9W1QeSHAosqqpjk6wOHAE8ErgO2KuqlrRjLwXWAVYFrgee0VUxcrL1Lqqq+bP8cQZinGKF8YrXWAfDWAdjnGLVzI3T9z1OscJ4xWusg2GsgzNu8c5EkoN7tVfVeycbNzb3qFXVD4AfdLW9p+P1LcA/L2XsFgMNTpIkSZJ6mEjIkqzVzt/Uz7hxuUdNkiRJksZOku2T/ApYDCxOcmaSh001zkRtagum7jIyxilWGK94jXUwjHUwxilWzdw4fd/jFCuMV7zGOhjGOjjjFu9MLAAOrKrNq2pz4E3A56YaNDb3qEmSJEnSuEny66r6x6nauo3NPWqSJEmSNIaWJHk3TeFDgJcBS6Ya5KWPrSS7JbkwycVJ3tbj/dWSfLN9/4wkW4xYfE9JclaS25Ps2eP9dZJckeTwEYj1wCTnJTknyYlJNm/bd0lydsd0S5LnDTPWjn4vTFJJ5rfzGyQ5KclNc7FN+4k1yT5Jru7Yfvt1vT9n+0A/8bZ9XtTuC4uTHNXR/pG27fwkn0qSYcaaZLP2+/5Vu9/u3raP4n6wefvv6pwkC5Ns0vHeHR37x7FzEa9mj8epOY3V49SA4h2lY5XHqaHFuiIep14BbAT833baENh3ylFVtcJPNCX/fwdsSVPC/9fAdl19XgP8n/b1XsA3Ryy+LYAdgK8Ce/ZYxieBo4DDRyDWXYD7tK9f3WtbAuvTPGbhPsOMte23NnAKcDrNs/gA1gSeBPzboLfpNLbrPpPFMlf7wDTi3Rr4FbBeO3+/9ucTgFPbZcwDTgN2HnKsC4BXt6+3Ay4d4f3g28C/tq+fChzR8d5Ng47Raajfvcep2YvV49Tgtu0+k8UzYvuBx6nBxLrCHaeA+cB32v3p3HY6Z6pxnlFrPBa4uKqWVNXfgW8Ae3T12QP4Svv6aGDXQf/1ZDrxVdWlVXUOcGf34CSPBu4P/GhEYj2pqv7azp4ObMK97Qkc39FvKLG23gd8mI6HGVbVzVX1M+75gMNB6jfWnuZ4H4D+4n0V8F9V9WeAqvpT2140D49cFVgNWAX445BjLZpnMQKsC/yhjXkU94PtgJ+0r0/q8b7Gk8epuY3V49SyGadjlcep4cW6Ih6njgS+CLwAeHY7PWeqQSZqjY2B33fMX9G29exTVbcDNwAbzEl0/cXXU5KVgI8Dbx5AXL1MN9ZXAsf3aN8L+PosxtXLlLEmeRSwaVV9f8CxTKXf7frC9lKCo5NsCkPZB6C/eB8CPCTJqUlOT7IbQFWdRvMf91XtdEJVnT/kWA8BXpbkCprnOb5+gPFMpp9Yf01zIAB4PrB2kon/q1ZPsqjd3s8baKSabR6nZo/HqcEZp2OVx6nB8DjV29VVdVxVXVJVl01MUw0yUVv+vQb4QVVdMexAuiV5Gc2p4I92tT8AeDhwwjDi6ohjJeAwmhKq4+A4YIuq2gH4MXf/ZX1U94GVaS4r2RnYG/hckvsmeTDwUJq/YG8MPDXJk4cWZWNv4MtVtQmwO3BEu3+MojcDO6V5XstOwJXAHe17m1fVfOAlwCeSbDWkGKVOo/p/lMepwRinY5XHqcFYEY9TByf5fJK9k7xgYppqkFUfG1cCm3bMb9K29epzRZKVaU4rXzs34fUV39I8HnhyktcAawGrJrmpqpZ6Q/IM9RVrkqcB7wR2qqpbu95+EfCdqrptQDFOmCrWtYHtgYXt1UP/AByb5LlVtWjAsXWbcrtWVef++HngI+3rud4H+oqX5q9sZ7Tf8yVJLuLuA+LpVXUTQJLj28/w0yHG+krgrr+kJlmd5kbgPzG3+tkP/kD7l8okawEvrKrr2/eubH8uSbIQeCTNvQQafR6nZo/HqcEZp2OVx6nB8DjV277AtjSXyU5c/l3AMZOOmuomthVhoklYlwAP4u4bHx/W1ee13PMm7W+NUnwdfb9Mj5u02/f2YfA35/azLSf+0W29lGWcDuwyStu17b+Q9ibtudym09iuD+h4/Xyag8ic7wPTiHc34Cvt6w1pLpXYAHgx8D/tMlYBTgSeM+RYjwf2aV8/lOba/4zodt0QWKl9/QHg0Pb1esBqHX1+S4+iBE6jOfX53Xucmr1t6XFqcNt2JI5VfcbqcWowsa5wxyngwmUaN+zAR2WiOU18Ufsf8zvbtkOB57avV6epUnMx8AtgyxGL7zE0f/m5meYvqIt7LGOu/pFOFev/0Nx0e3Y7Hdsxdguav7ysNArbtavvQjoOgMClNBW/bmq3/UD/M+lju34IWNz+p3gSsO2w9oE+4w3NJTvn0VQ/2qttnwd8Fji/fe+wEYh1O5oKX79u99lnjPB+sCfNwe0imr9WTxz0ntBu51+3P185F/uB05x+9x6nZi9Wj1OD27Yjc6zqI1aPU4OJdYU7TgFfWpbtnnawJEmSJGmWJTkf2Aq4BLiV5o8AVc29mksfZ6ImSZIkSYORZPNe7TVF5UcTNUmSJEkaMaNatlOSJEmSVlgmapIkSZI0YkzUJEmSJGnEmKhJQ5LkpmHHIEnS0nickobLRE2SJEmSRoyJmjRkSdZKcmKSs5Kcm2SPtn2LJBck+XKSi5IcmeRpSU5N8tskjx127JKk5Z/HKWk4LM8vDUmSm6pqrSQrA/epqhuTbAicDmwNbA5cDDwSWAz8Evg18ErgucC+VfW8oQQvSVrueZyShmvlYQcgiQAfTPIU4E5gY+D+7XuXVNW5AEkWAydWVSU5F9hiGMFKklY4HqekITBRk4bvpcBGwKOr6rYklwKrt+/d2tHvzo75O/HfryRpbnickobAe9Sk4VsX+FN78NuF5lISSZJGhccpaQj8S4c0fEcCx7WXiSwCLhhyPJIkdfI4JQ2BxUQkSZIkacR46aMkSZIkjRgTNUmSJEkaMSZqkiRJkjRiTNQkSZIkacSYqEmSJEnSiDFRkyRJkqQRY6ImSZIkSSPGRE2SJEmSRsz/B+V426wyCjdiAAAAAElFTkSuQmCC\n", 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" ] @@ -1527,77 +1735,73 @@ } ], "source": [ - "fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True)\n", - "\n", - "# Region\n", - "data = idxs.T\n", - "cmap = plt.get_cmap('coolwarm', np.max(data) - np.min(data) + 1)\n", - "mat = ax[0].imshow(data, cmap=cmap, vmin=0, vmax=2,origin=\"lower\",)\n", - "cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0])\n", - "cbar.ax.set_yticks([0.3, 1, 1.7])\n", - "cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", - "\n", - "# Timings\n", - "data = duration_abel.T\n", - "mat = ax[1].imshow(data, cmap=\"viridis\", origin=\"lower\",)\n", - "cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1])\n", - "\n", - "\n", - "for axi in ax:\n", - " axi.set_xlabel(\"lam\")\n", - " every = 8\n", - " axi.set_xticks(range(0, lam_range.size)[::every])\n", - " axi.set_xticklabels(np.round(lam_range[::every], 2));\n", - "\n", - " axi.set_ylabel(\"p\")\n", - " every = 8\n", - " axi.set_yticks(range(0, p_range.size)[::every])\n", - " axi.set_yticklabels(np.round(p_range[::every], 2))\n", - " \n", - " axi.axhline(20.5, color=\"w\")\n", - " \n", - "fig.suptitle(\"Abel region performance\", y=0.85, fontsize=18);" + "plot_benchmark_comparison(\n", + " [duration_monot, duration_poisson, duration_abel, duration_inverse, duration_branch],\n", + " [\"monot\", \"poisson\", \"abel\", \"inverse\", \"branch\"],\n", + " threshold=0.001\n", + ")" ] }, { "cell_type": "code", - "execution_count": 33, - "metadata": { - "pycharm": { - "name": "#%%\n" + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } - }, - "outputs": [], + ], "source": [ - "nan_to_inf = lambda x: np.nan_to_num(x, nan=np.inf)\n", - "\n", - "d = 0.00\n", - "best_duration = np.full_like(duration_monot, np.nan)\n", - "best_duration[\n", - " (duration_monot + d < nan_to_inf(duration_poisson)) & (duration_monot + d < nan_to_inf(duration_abel))\n", - "] = 0\n", - "\n", - "best_duration[\n", - " (duration_poisson + d < nan_to_inf(duration_monot)) & (duration_poisson + d < nan_to_inf(duration_abel))\n", - "] = 1\n", - "\n", - "best_duration[\n", - " (duration_abel + d < nan_to_inf(duration_monot)) & (duration_abel + d < nan_to_inf(duration_poisson))\n", - "] = 2" + "plot_benchmark_comparison(\n", + " [duration_monot, duration_branch],\n", + " [\"monot\", \"branch\"],\n", + " threshold=0.0\n", + ")" ] }, { "cell_type": "code", - "execution_count": 34, - "metadata": { - "pycharm": { - "name": "#%%\n" + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", 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\n", 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" ] @@ -1609,39 +1813,19 @@ } ], "source": [ - "fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True)\n", - "\n", - "# Region\n", - "data = idxs.T\n", - "cmap = plt.get_cmap('coolwarm', np.max(data) - np.min(data) + 1)\n", - "mat = ax[0].imshow(data, cmap=cmap, vmin=0, vmax=2,origin=\"lower\",)\n", - "cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0])\n", - "cbar.ax.set_yticks([0.3, 1, 1.7])\n", - "cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", - "\n", - "# Timings\n", - "data = best_duration.T\n", - "mat = ax[1].imshow(data, cmap=cmap, origin=\"lower\",)\n", - "cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1])\n", - "cbar.ax.set_yticks([0.3, 1, 1.7])\n", - "cbar.ax.set_yticklabels([\"monoticity.\", \"poisson\", \"abel\"], rotation=90, va=\"center\")\n", - "\n", - "\n", - "for axi in ax:\n", - " axi.set_xlabel(\"lam\")\n", - " every = 8\n", - " axi.set_xticks(range(0, lam_range.size)[::every])\n", - " axi.set_xticklabels(np.round(lam_range[::every], 2));\n", - "\n", - " axi.set_ylabel(\"p\")\n", - " every = 8\n", - " axi.set_yticks(range(0, p_range.size)[::every])\n", - " axi.set_yticklabels(np.round(p_range[::every], 2))\n", - " \n", - " axi.axhline(20.5, color=\"k\")\n", - " \n", - "fig.suptitle(\"Best performance per region\", y=0.85, fontsize=18);" + "plot_benchmark_comparison(\n", + " [duration_abel, duration_branch],\n", + " [\"abel\", \"branch\"],\n", + " threshold=0.000\n", + ")" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/notebooks/fast_gen_pois.py b/notebooks/fast_gen_pois.py index 12cd4c9..61db454 100644 --- a/notebooks/fast_gen_pois.py +++ b/notebooks/fast_gen_pois.py @@ -15,6 +15,7 @@ # %% pycharm={"name": "#%%\n"} import numpy as np +import pymc as pm from matplotlib import pyplot as plt from scipy.special import gammaln @@ -221,6 +222,14 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): - 1.5 * np.log(t + 1) + (1 - lam) * t ) + # rho_t_prime = ( # Taken form page 271 + # np.log(lam * t + p) + # - np.log(t + 1) + # + 1 + # - lam + # + 0.5 / (t + 1) + # - (lam + p) / (lam * t + p) + # ) rho_t_prime = ( np.log(lam * t + p) - np.log(t + 1) @@ -251,10 +260,12 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): _q_l = q_l[inds_to_sample] _q_r = q_r[inds_to_sample] _b = b[inds_to_sample] - # raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(_q))) + # raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(1 - _q))) + # raw_left = np.where(_t == 0, 0, _t - np.floor(-E / np.log(_q))) # raw_left = np.where(_t == 0, 0, _t + np.ceil(np.log(1 - E) / _q)) raw_left = np.where(_t == 0, 0, _t - np.floor(E / _q)) raw_right = np.floor((_t + 1) / W ** 2) + left = U <= _q_l / (_q_l + _q_r) accepted = np.where( left, @@ -264,6 +275,7 @@ def _rejection_region_abel(rng, p, lam, dist_size, idxs_mask=None): np.where( raw_left < 0, False, + # V * _q_l * _q ** (_t - raw_left) * (1 - _q) V * _q_l * _q ** (_t - raw_left) * (1 - _q ** (_t + 1)) <= np.exp(_logprob(raw_left, _p, _lam)), ), @@ -306,7 +318,22 @@ def _inverse_rng_fn(rng, theta, lam, dist_size): log_p = log_c + log1p_lam_m_C * (x_ - 1) + log_p - np.log(x_) - lam log_s = np.logaddexp(log_s, log_p) below_cutpoint = log_s < log_u - print(counter) + # print(counter) + return x + + +# %% +def _branching_rng_fn(rng, theta, lam, dist_size, idxs_mask=None): + if idxs_mask is None: + idxs_mask = np.ones(dist_size, dtype=bool) + lam_ = np.abs(lam) # This algorithm is only valid for positive lam + y = rng.poisson(theta, size=dist_size) + x = y.copy() + higher_than_zero = y > 0 + while np.any(higher_than_zero[idxs_mask]): + y = rng.poisson(lam_ * y) + x[higher_than_zero] = x[higher_than_zero] + y[higher_than_zero] + higher_than_zero = y > 0 return x @@ -580,8 +607,11 @@ def abel_rejection_proposal_density(x, p, lam): # plt.plot(x, abel_rejection_envelope(np.floor(x), p, lam), label="Envelope") # plt.plot(x, abel_rejection_proposal_density(np.floor(x), p, lam), label="Proposal density") samples_monot = _rejection_region_monotonicity(np.random.default_rng(), p, lam, 100000) +samples_branch = _branching_rng_fn(np.random.default_rng(), p, lam, 100000) samples_abel = _rejection_region_abel(np.random.default_rng(), p, lam, 100000) -for samples, algo in zip((samples_monot, samples_abel), ("monoticity", "abel")): +for samples, algo in zip( + (samples_monot, samples_branch, samples_abel), ("monoticity", "branch", "abel") +): u, c = np.unique(samples, return_counts=True) edges = np.arange(11) y = np.array([np.sum(c[u == e]) for e in edges]) @@ -692,6 +722,8 @@ def abel_rejection_proposal_density(x, p, lam): import signal import time +from functools import reduce + # %% pycharm={"name": "#%%\n"} class TimeOutError(RuntimeError): @@ -708,234 +740,179 @@ def handler(signum, frame): rng = np.random.default_rng(42) dist_size = (100, *p.shape) -# %% pycharm={"name": "#%%\n"} -duration_monot = np.full_like(p, np.nan) -for i in range(p.shape[0]): - for j in range(p.shape[1]): - signal.setitimer(signal.ITIMER_REAL, 0.05) - try: - start = time.time() - _rejection_region_monotonicity(rng, p=p[i, j], lam=lam[i, j], dist_size=100) - end = time.time() - except TimeOutError: - continue - duration_monot[i, j] = end - start -signal.alarm(0) - -# %% pycharm={"name": "#%%\n"} -duration_poisson = np.full_like(p, np.nan) -for i in range(p.shape[0]): - for j in range(p.shape[1]): - signal.setitimer(signal.ITIMER_REAL, 0.05) - try: - start = time.time() - _rejection_region_poisson(rng, p=p[i, j], lam=lam[i, j], dist_size=100) - end = time.time() - except TimeOutError: - continue - duration_poisson[i, j] = end - start -signal.alarm(0) -# %% pycharm={"name": "#%%\n"} -duration_abel = np.full_like(p, np.nan) -for i in range(p.shape[0]): - for j in range(p.shape[1]): - signal.setitimer(signal.ITIMER_REAL, 0.05) - try: +# %% +def benchmark_algorithm(algorithm_fn, draws=100, duration_cutoff=0.05): + duration = np.full_like(p, np.nan) + for i in range(p.shape[0]): + for j in range(p.shape[1]): + signal.setitimer(signal.ITIMER_REAL, duration_cutoff) start = time.time() - _rejection_region_abel(rng, p=p[i, j], lam=lam[i, j], dist_size=100) + try: + algorithm_fn(rng, p=p[i, j], lam=lam[i, j], dist_size=draws) + signal.alarm(0) + except TimeOutError: + continue end = time.time() - except TimeOutError: - continue - duration_abel[i, j] = end - start -signal.alarm(0) - -# %% pycharm={"name": "#%%\n"} -fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True) + duration[i, j] = end - start + signal.alarm(0) + return duration + + +# %% +def plot_benchmark(duration, title=""): + fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True) + + # Region + data = idxs.T + cmap = plt.get_cmap("coolwarm", np.max(data) - np.min(data) + 1) + mat = ax[0].imshow( + data, + cmap=cmap, + vmin=0, + vmax=2, + origin="lower", + ) + cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0]) + cbar.ax.set_yticks([0.3, 1, 1.7]) + cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") + + # Timings + data = duration.T + mat = ax[1].imshow( + data, + cmap="viridis", + origin="lower", + ) + cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1]) -# Region -data = idxs.T -cmap = plt.get_cmap("coolwarm", np.max(data) - np.min(data) + 1) -mat = ax[0].imshow( - data, - cmap=cmap, - vmin=0, - vmax=2, - origin="lower", -) -cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0]) -cbar.ax.set_yticks([0.3, 1, 1.7]) -cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") + for axi in ax: + axi.set_xlabel("lam") + every = 8 + axi.set_xticks(range(0, lam_range.size)[::every]) + axi.set_xticklabels(np.round(lam_range[::every], 2)) -# Timings -data = duration_monot.T -mat = ax[1].imshow( - data, - cmap="viridis", - origin="lower", -) -cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1]) + axi.set_ylabel("p") + every = 8 + axi.set_yticks(range(0, p_range.size)[::every]) + axi.set_yticklabels(np.round(p_range[::every], 2)) + axi.axhline(20.5, color="white") -for axi in ax: - axi.set_xlabel("lam") - every = 8 - axi.set_xticks(range(0, lam_range.size)[::every]) - axi.set_xticklabels(np.round(lam_range[::every], 2)) + fig.suptitle(title, y=0.85, fontsize=18) - axi.set_ylabel("p") - every = 8 - axi.set_yticks(range(0, p_range.size)[::every]) - axi.set_yticklabels(np.round(p_range[::every], 2)) - axi.axhline(20.5, color="white") +# %% +duration_monot = benchmark_algorithm(_rejection_region_monotonicity) -fig.suptitle("Monotonicity region performance", y=0.85, fontsize=18) +# %% +duration_poisson = benchmark_algorithm(_rejection_region_poisson) -# %% pycharm={"name": "#%%\n"} -fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True) +# %% +duration_abel = benchmark_algorithm(_rejection_region_abel) -# Region -data = idxs.T -cmap = plt.get_cmap("coolwarm", np.max(data) - np.min(data) + 1) -mat = ax[0].imshow( - data, - cmap=cmap, - vmin=0, - vmax=2, - origin="lower", +# %% +duration_inverse = benchmark_algorithm( + lambda rng, p, lam, dist_size: _inverse_rng_fn(rng, theta=p, lam=lam, dist_size=dist_size) ) -cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0]) -cbar.ax.set_yticks([0.3, 1, 1.7]) -cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") -# Timings -data = duration_poisson.T -mat = ax[1].imshow( - data, - cmap="viridis", - origin="lower", +# %% +duration_branch = benchmark_algorithm( + lambda rng, p, lam, dist_size: _branching_rng_fn(rng, theta=p, lam=lam, dist_size=dist_size) ) -cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1]) +# %% +plot_benchmark(duration=duration_monot, title="Monotonicity algorithm speed") +plot_benchmark(duration=duration_poisson, title="Poisson algorithm speed") +plot_benchmark(duration=duration_abel, title="Abel algorithm speed") +plot_benchmark(duration=duration_inverse, title="Inverse algorithm speed") +plot_benchmark(duration=duration_branch, title="Branching algorithm speed") -for axi in ax: - axi.set_xlabel("lam") - every = 8 - axi.set_xticks(range(0, lam_range.size)[::every]) - axi.set_xticklabels(np.round(lam_range[::every], 2)) - - axi.set_ylabel("p") - every = 8 - axi.set_yticks(range(0, p_range.size)[::every]) - axi.set_yticklabels(np.round(p_range[::every], 2)) - - axi.axhline(20.5, color="k") - -fig.suptitle("Poisson region performance", y=0.85, fontsize=18) # %% pycharm={"name": "#%%\n"} -fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True) - -# Region -data = idxs.T -cmap = plt.get_cmap("coolwarm", np.max(data) - np.min(data) + 1) -mat = ax[0].imshow( - data, - cmap=cmap, - vmin=0, - vmax=2, - origin="lower", -) -cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0]) -cbar.ax.set_yticks([0.3, 1, 1.7]) -cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") - -# Timings -data = duration_abel.T -mat = ax[1].imshow( - data, - cmap="viridis", - origin="lower", -) -cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1]) - - -for axi in ax: - axi.set_xlabel("lam") - every = 8 - axi.set_xticks(range(0, lam_range.size)[::every]) - axi.set_xticklabels(np.round(lam_range[::every], 2)) +def plot_benchmark_comparison(benchmarks, benchmark_names, threshold=0): - axi.set_ylabel("p") - every = 8 - axi.set_yticks(range(0, p_range.size)[::every]) - axi.set_yticklabels(np.round(p_range[::every], 2)) + nan_to_inf = lambda x: np.nan_to_num(x, nan=np.inf) + best_duration = np.full_like(duration_monot, np.nan) - axi.axhline(20.5, color="w") - -fig.suptitle("Abel region performance", y=0.85, fontsize=18) + for i, reference in enumerate(benchmarks): + comps = ( + reference + threshold < nan_to_inf(other) + for other in benchmarks + if other is not reference + ) + best_duration[reduce(lambda x, y: x & y, comps)] = i + + fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True) + + # Region + data = idxs.T + cmap = plt.get_cmap("coolwarm", np.max(data) - np.min(data) + 1) + mat = ax[0].imshow( + data, + cmap=cmap, + vmin=0, + vmax=2, + origin="lower", + ) + cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0]) + cbar.ax.set_yticks([0.3, 1, 1.7]) + cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") + + # Timings + data = best_duration.T + cmap = plt.get_cmap("coolwarm", np.nanmax(data) - np.nanmin(data) + 1) + mat = ax[1].imshow( + data, + cmap=cmap, + origin="lower", + ) + cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1]) + cbar.ax.set_yticks([0.3, 1, 1.7, 2.8, 3.5][: len(benchmarks)]) + cbar.ax.set_yticklabels(benchmark_names, rotation=90, va="center") -# %% pycharm={"name": "#%%\n"} -nan_to_inf = lambda x: np.nan_to_num(x, nan=np.inf) + for axi in ax: + axi.set_xlabel("lam") + every = 8 + axi.set_xticks(range(0, lam_range.size)[::every]) + axi.set_xticklabels(np.round(lam_range[::every], 2)) -d = 0.00 -best_duration = np.full_like(duration_monot, np.nan) -best_duration[ - (duration_monot + d < nan_to_inf(duration_poisson)) - & (duration_monot + d < nan_to_inf(duration_abel)) -] = 0 + axi.set_ylabel("p") + every = 8 + axi.set_yticks(range(0, p_range.size)[::every]) + axi.set_yticklabels(np.round(p_range[::every], 2)) -best_duration[ - (duration_poisson + d < nan_to_inf(duration_monot)) - & (duration_poisson + d < nan_to_inf(duration_abel)) -] = 1 + axi.axhline(20.5, color="k") -best_duration[ - (duration_abel + d < nan_to_inf(duration_monot)) - & (duration_abel + d < nan_to_inf(duration_poisson)) -] = 2 + fig.suptitle("Best performance per region", y=0.85, fontsize=18) -# %% pycharm={"name": "#%%\n"} -fig, ax = plt.subplots(1, 2, figsize=(14, 7), sharey=True) -# Region -data = idxs.T -cmap = plt.get_cmap("coolwarm", np.max(data) - np.min(data) + 1) -mat = ax[0].imshow( - data, - cmap=cmap, - vmin=0, - vmax=2, - origin="lower", +# %% +plot_benchmark_comparison( + [duration_monot, duration_poisson, duration_abel], + ["monot", "poisson", "abel"], ) -cbar = fig.colorbar(mat, ticks=[0, 1, 2], fraction=0.038, ax=ax[0]) -cbar.ax.set_yticks([0.3, 1, 1.7]) -cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") -# Timings -data = best_duration.T -mat = ax[1].imshow( - data, - cmap=cmap, - origin="lower", +# %% +plot_benchmark_comparison( + [duration_monot, duration_poisson, duration_abel, duration_inverse, duration_branch], + ["monot", "poisson", "abel", "inverse", "branch"], ) -cbar = fig.colorbar(mat, fraction=0.038, ax=ax[1]) -cbar.ax.set_yticks([0.3, 1, 1.7]) -cbar.ax.set_yticklabels(["monoticity.", "poisson", "abel"], rotation=90, va="center") +# %% +plot_benchmark_comparison( + [duration_monot, duration_poisson, duration_abel, duration_inverse, duration_branch], + ["monot", "poisson", "abel", "inverse", "branch"], + threshold=0.001, +) -for axi in ax: - axi.set_xlabel("lam") - every = 8 - axi.set_xticks(range(0, lam_range.size)[::every]) - axi.set_xticklabels(np.round(lam_range[::every], 2)) +# %% +plot_benchmark_comparison([duration_monot, duration_branch], ["monot", "branch"], threshold=0.0) - axi.set_ylabel("p") - every = 8 - axi.set_yticks(range(0, p_range.size)[::every]) - axi.set_yticklabels(np.round(p_range[::every], 2)) +# %% +plot_benchmark_comparison([duration_poisson, duration_branch], ["poisson", "branch"], threshold=0.0) - axi.axhline(20.5, color="k") +# %% +plot_benchmark_comparison([duration_abel, duration_branch], ["abel", "branch"], threshold=0.000) -fig.suptitle("Best performance per region", y=0.85, fontsize=18) +# %%