diff --git a/examples/examples-Stein.ipynb b/examples/examples-Stein.ipynb new file mode 100644 index 00000000..421d6d4a --- /dev/null +++ b/examples/examples-Stein.ipynb @@ -0,0 +1,192 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "f07fa1f2-187e-4ce0-af95-31d6120977fe", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.integrate import odeint\n", + "\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "\n", + "from gMLV import *\n", + "#import importlib\n", + "# import gMLV_ML\n", + "# import gMLV_sim\n", + "#importlib.reload(gMLV_ML);\n", + "#importlib.reload(gMLV_sim);" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "f24a82c9-f85e-49db-979d-f23fae68f172", + "metadata": {}, + "outputs": [], + "source": [ + "# some plotting functions\n", + "def plot_fit_gLV(yobs, y0, nsp, m_h, M_h):\n", + " # plot the fit\n", + " cols = [\"red\", \"green\", \"blue\", \"royalblue\",\"black\"]\n", + " #cols = [1,2,3,4,5]\n", + " yobs_pred = odeint(gLV, y0, times, args=(nsp, mu_h, M_h))\n", + " for i in range(nsp):\n", + " plt.plot(times, yobs[:, i], color=cols[i])\n", + " plt.plot(times, yobs_pred[:, i], '--', color=cols[i])\n", + "\n", + "def plot_params(mu_h, M_h, e_h ):\n", + " print(\"\\ninferred params:\")\n", + " print(\"mu_hat/mu:\")\n", + " print(np.array(mu_h))\n", + " print(\"\\nM_hat/M:\")\n", + " print(np.round(np.array(M_h),decimals=2))\n", + " print(\"e_hat/e:\")\n", + " print(np.array(e_h))\n", + "\n", + " # plot the params\n", + " plt.figure(figsize=(6.4*3,4.8))\n", + " plt.subplot(1, 3, 1)\n", + " plt.stem(np.arange(0,nsp, dtype=\"int32\"), np.array(mu_h), markerfmt=\"D\")\n", + "\n", + " plt.subplot(1, 3, 2)\n", + " plt.stem(np.arange(0,nsp*nsp), np.array(M_h).flatten(), markerfmt=\"D\")\n", + " \n", + " plt.subplot(1, 3, 3)\n", + " plt.stem(np.arange(0,nsp), np.array(e_h), markerfmt=\"D\")\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "27f9ef3f-7097-401a-80ab-fe8e92ff7eba", + "metadata": {}, + "source": [ + "## Repeat Stein et al. 2013 analysis\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "6cc88f5d-7f4e-4383-a111-52d19c10ba6f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum found: a0/a1/a2/error: 12.915496650148826 0.002154434690031882 0.21544346900318823 1.4660751017719924\n", + "unconstrained error : 1.6421125900699798\n", + "\n", + "inferred params:\n", + "mu_hat/mu:\n", + "[0.33892799 0.83096483 0.36935479 0.55465898 0.29951778 0.27150347\n", + " 0.45721187 0.3397222 0.77567307 0.27205209 0.54286798]\n", + "\n", + "M_hat/M:\n", + "[[-0.36 0.07 -0.2 0.04 0.09 -0.12 0.21 0.03 -0.21 -0.01 -0.09]\n", + " [ 0.07 -0.58 -0.16 -0. -0.11 -0.35 0.05 -0.03 0.25 0.05 -0.03]\n", + " [-0.26 -0.12 -0.13 0.03 0.01 -0.28 0.22 0.02 -0.2 -0.01 -0.08]\n", + " [-0.27 0.16 -0.07 -0.28 -0.04 -0.09 0.14 -0.02 -0.22 -0.02 -0.06]\n", + " [-0.19 -0.14 -0.01 0.03 -0.08 -0.25 0.18 -0.02 -0.2 -0. -0.07]\n", + " [-0.05 0.1 -0.07 -0.08 -0.1 -0.53 -0.12 -0.03 0.65 0.06 0.13]\n", + " [-0.03 -0.11 -0.05 0.02 -0.05 -0.11 -0.03 -0.02 -0.15 -0. -0.09]\n", + " [-0.2 -0.13 0.03 0.02 -0.12 -0.27 0.19 -0.03 -0.37 -0.02 -0.08]\n", + " [-0.29 -0.31 -0.08 0.14 -0.04 -0.34 0.29 -0. -2.03 -0.12 -0.32]\n", + " [-0.03 -0.2 -0.04 0.02 -0.02 -0.01 0.06 -0. -0.97 -0.07 -0.11]\n", + " [-0.39 -0.07 0.05 0.11 0.02 -0.17 0.33 -0.01 -0.52 -0.03 -0.38]]\n", + "e_hat/e:\n", + "[ 3.63313199 -1.48653717 -3.35645376 -1.18023161 -3.03370139 -0.94431557\n", + " -0.36861886 -2.05988454 -0.77805889 1.07734836 -1.95212351]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "nsp = 11\n", + "# read in \n", + "F = pd.read_csv('data/Stein_example_F.csv', delimiter = ',')\n", + "X = pd.read_csv('data/Stein_example_Y.csv', delimiter = ',')\n", + "\n", + "#print(F)\n", + "#print(X)\n", + "\n", + "F = F.drop(F.columns[[0, 1]], axis=1) \n", + "X = X.drop(X.columns[[0, 1]], axis=1) \n", + "\n", + "colnames = F.columns.to_list()\n", + "\n", + "#print(F.shape)\n", + "#print(X.shape)\n", + "\n", + "# get the best lambda/alpha values on a grid via cross validation\n", + "a0, a1, a2 = fit_alpha_Ridge2(X.to_numpy(), F.to_numpy(), nsp=nsp, n_a0=10, n_a1=10, n_a2=10)\n", + "\n", + "# do final fit\n", + "mu_h, M_h, e_h = do_final_fit_Ridge2(X.to_numpy(), F.to_numpy(), nsp, a0=a0, a1=a1, a2=a2)\n", + "\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h,\n", + " epsilon=e_h)\n", + "\n", + "# this does the stem plots with orange crosses the actual parameters\n", + "plot_params(mu_h, M_h, e_h)\n", + "\n", + "# plot interaction matrix\n", + "plt.figure(figsize=(6.4*2,6.4*2))\n", + "lims = np.max( [np.max(M_h), np.abs(np.min(M_h)) ] )\n", + "sns.heatmap(M_h, xticklabels=colnames, yticklabels=colnames, square=True, vmin=-lims, vmax=lims, annot=True, fmt=\".2f\", cmap='coolwarm');\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/examples-mcmc-maria.ipynb b/examples/examples-mcmc-maria.ipynb new file mode 100644 index 00000000..de101150 --- /dev/null +++ b/examples/examples-mcmc-maria.ipynb @@ -0,0 +1,920 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "53eb7b1a-08b4-4878-bb14-bc1073082119", + "metadata": { + "tags": [] + }, + "source": [ + "# Full Bayesian inference using linear approximation of dynamics" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "593af750-956c-4d93-b8ab-8e830d57d5c2", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import random\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "from scipy.integrate import odeint\n", + "\n", + "from gMLV import *\n", + "\n", + "def set_all_seeds(seed):\n", + " np.random.seed(seed)\n", + " random.seed(seed)\n", + "\n", + "# some plotting functions\n", + "\n", + "cols = [\"red\", \"green\", \"blue\", \"royalblue\",\"orange\", \"black\", \"salmon\", \"forestgreen\", \"steelblue\", \"slateblue\",\"gold\", \"palegreen\"]\n", + "\n", + "def plot_gMLV(yobs, sobs, timepoints):\n", + " #fig, axs = plt.subplots(1, 2, layout='constrained')\n", + " fig, axs = plt.subplots(1, 2)\n", + " for species_idx in range(yobs.shape[1]):\n", + " axs[0].plot(timepoints, yobs[:, species_idx], color=cols[species_idx])\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]')\n", + " if sobs.shape[1] > 0:\n", + " for metabolite_idx in range(sobs.shape[1]):\n", + " axs[1].plot(timepoints, sobs[:, metabolite_idx], color=cols[metabolite_idx])\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]');\n", + "\n", + "def plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, timepoints):\n", + " # plot the fit\n", + " #fig, axs = plt.subplots(1, 2, layout='constrained')\n", + " fig, axs = plt.subplots(1, 2) \n", + " for species_idx in range(yobs.shape[1]):\n", + " axs[0].plot(timepoints, yobs[:, species_idx], color=cols[species_idx])\n", + " axs[0].plot(timepoints, yobs_h[:, species_idx], '--', color=cols[species_idx])\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]');\n", + "\n", + " for metabolite_idx in range(sobs.shape[1]):\n", + " axs[1].plot(timepoints, sobs[:, metabolite_idx], color=cols[metabolite_idx])\n", + " axs[1].plot(timepoints, sobs_h[:, metabolite_idx], '--', color=cols[metabolite_idx])\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]');\n", + "\n", + "def compare_params(mu=None, M=None, alpha=None, e=None):\n", + " # each argument is a tuple of true and predicted values\n", + " if mu is not None:\n", + " print(\"mu_hat/mu:\")\n", + " print(np.array(mu[1]))\n", + " print(np.array(mu[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0,len(mu[0]), dtype=\"int32\"), np.array(mu[1]), markerfmt=\"D\")\n", + " ax.stem(np.arange(0,len(mu[0]), dtype=\"int32\"), np.array(mu[0]), markerfmt=\"X\")\n", + " ax.set_xlabel('i')\n", + " ax.set_ylabel('mu[i]');\n", + "\n", + " if M is not None:\n", + " print(\"\\nM_hat/M:\")\n", + " print(np.round(np.array(M[1]), decimals=2))\n", + " print(\"\\n\",np.array(M[0]))\n", + "\n", + " #fig, ax = plt.subplots()\n", + " #ax.stem(np.arange(0, M[0].shape[0] ** 2), np.array(M[1]).flatten(), markerfmt=\"D\")\n", + " #ax.stem(np.arange(0, M[0].shape[0] ** 2), np.array(M[0]).flatten(), markerfmt=\"X\")\n", + " #ax.set_ylabel('M[i,j]');\n", + "\n", + " fig, ax = plt.subplots()\n", + " Ns = M[0].shape[0]\n", + " ax.stem(np.arange(0, Ns), np.array(M[1]).diagonal(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, Ns), np.array(M[0]).diagonal(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]');\n", + " \n", + " fig, ax = plt.subplots()\n", + " Ns = M[0].shape[0]\n", + " \n", + " count = 0\n", + " Mij = np.zeros([Ns*Ns - Ns])\n", + " Mij_h = np.zeros([Ns*Ns - Ns])\n", + " for i in range(Ns):\n", + " for j in range(Ns):\n", + " if i != j:\n", + " Mij[count] = np.array(M[0])[i,j]\n", + " Mij_h[count] = np.array(M[1])[i,j]\n", + " count = count + 1\n", + " \n", + " ax.stem(np.arange(0, Ns*Ns - Ns), Mij.flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, Ns*Ns - Ns), Mij_h.flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]');\n", + " \n", + " if alpha is not None:\n", + " print(\"\\na_hat/a:\")\n", + " print(np.round(np.array(alpha[1]), decimals=2))\n", + " print(\"\\n\",np.array(alpha[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, alpha[0].shape[0] * alpha[0].shape[1]), np.array(alpha[1]).flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, alpha[0].shape[0] * alpha[0].shape[1]), np.array(alpha[0]).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('a[i,j]');\n", + "\n", + " if e is not None:\n", + " print(\"\\ne_hat/e:\")\n", + " print(np.round(np.array(e[1]), decimals=2))\n", + " print(\"\\n\",np.array(e[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, e[0].shape[0]), np.array(e[1]).flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, e[0].shape[0]), np.array(e[0]).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('e[i]');\n", + "\n", + "def print_params(mu=None, M=None, e=None):\n", + " # each argument is a tuple of true and predicted values\n", + " if mu is not None:\n", + " print(\"mu_hat:\")\n", + " print(np.array(mu))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0,len(mu), dtype=\"int32\"), np.array(mu), markerfmt=\"X\")\n", + " ax.set_xlabel('i')\n", + " ax.set_ylabel('mu[i]');\n", + "\n", + " if M is not None:\n", + " print(\"\\nM_hat:\")\n", + " print(np.round(np.array(M), decimals=2))\n", + "\n", + " fig, ax = plt.subplots()\n", + " Ns = M.shape[0]\n", + " ax.stem(np.arange(0, Ns), np.array(M).diagonal(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]');\n", + " \n", + " fig, ax = plt.subplots()\n", + " Ns = M.shape[0]\n", + " \n", + " count = 0\n", + " Mij_h = np.zeros([Ns*Ns - Ns])\n", + " for i in range(Ns):\n", + " for j in range(Ns):\n", + " if i != j:\n", + " Mij_h[count] = np.array(M)[i,j]\n", + " count = count + 1\n", + " \n", + " ax.stem(np.arange(0, Ns*Ns - Ns), Mij_h.flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]');\n", + " \n", + " if e is not None:\n", + " print(\"\\ne_hat:\")\n", + " print(np.round(np.array(e), decimals=2))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, e.shape[0]), np.array(e).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('e[i]');\n", + "\n", + "\n", + "# some MCMC analysis functions\n", + "\n", + "def make_trace_plot(var,istart,iend):\n", + " plt.figure()\n", + " post = df[var][istart:iend]\n", + " plt.plot(range(0,(iend-istart)),post)\n", + " #print(var, np.median(post))\n", + " return\n", + " \n", + "def make_hist_plot(var,istart,iend):\n", + " plt.figure()\n", + " post = df[var][istart:iend]\n", + " plt.hist(post)\n", + " print(var, np.median(post))\n", + " return\n", + " \n", + "def get_Rhat(N,p1,p2):\n", + " M = 2\n", + " mean1 = np.mean(p1,axis=0) \n", + " mean2 = np.mean(p2,axis=0) \n", + " var1 = np.var(p1,axis=0) \n", + " var2 = np.var(p2,axis=0)\n", + " \n", + " meanM = (1/M)*(mean1 + mean2)\n", + " \n", + " B = (N/(M-1)) * (mean1-meanM)*(mean1-meanM) + (mean2-meanM)*(mean2-meanM)\n", + " W = (1/M)*(var1 + var2)\n", + " \n", + " Vhat = ((N-1)/N)*W + ((M+1)/(M*N))*B\n", + " \n", + " Rhat = Vhat/W\n", + " \n", + " return Rhat\n", + "\n", + "def get_horseshoe_tau(p0,D,sigma,n):\n", + " return p0*sigma/( np.sqrt(n)*(D-p0) )\n", + "\n", + "# extract gLV vectors and matrix from posterior sample\n", + "def extract_gLV_pars(est, num_species, e=False):\n", + "\n", + " # fill mu_h\n", + " #mu_h = mu # if mu is fixed\n", + " mu_h = est[0:num_species]\n", + " est = est[num_species:]\n", + "\n", + " # fill M_h\n", + " M_h = np.zeros([num_species,num_species])\n", + " #np.fill_diagonal(M_h, M.diagonal() ) # if Md fixed\n", + " np.fill_diagonal(M_h, -est[0:num_species])\n", + " est = est[num_species:]\n", + "\n", + " count = 0\n", + " #print(\"est:\", est)\n", + " for i in range(num_species):\n", + " for j in range(num_species):\n", + " if i != j:\n", + " #M_h[i,j] = est[2*num_species + count]\n", + " #M_h[i,j] = est[num_species + count]\n", + " M_h[i,j] = est[count]\n", + " count = count + 1\n", + "\n", + " #print(mu_h)\n", + " #print(M_h)\n", + " \n", + " if e==False:\n", + " return mu_h, M_h\n", + " else:\n", + " est = est[num_species*(num_species-1):]\n", + " E_h = np.reshape(est[0:num_species],(num_species,1))\n", + "\n", + " return mu_h, M_h, E_h\n", + "\n", + "def get_signal_matrix(npert, tp):\n", + " # calculate signal matrix\n", + " u = np.zeros([npert,len(times)])\n", + " for i in range(npert):\n", + " ui = (times >= tp[i][0]) & (times <= tp[i][1]) \n", + " u[i,:] = ui\n", + "\n", + " # remove last column of signal matrix\n", + " u = u[:,:(u.shape[1]-1)]\n", + " print('signal matrix:\\n', u)\n", + " return u\n", + " \n", + "def visualise_chains():\n", + " print(\"mu:\",mu)\n", + " for i in range(num_species):\n", + " make_trace_plot(\"mu.\"+str(i+1),istart,iend)\n", + " make_hist_plot(\"mu.\"+str(i+1),istart,iend)\n", + "\n", + " print(\"Md:\",M.diagonal())\n", + " for i in range(num_species):\n", + " make_trace_plot(\"Md.\"+str(i+1),istart,iend)\n", + " make_hist_plot(\"Md.\"+str(i+1),istart,iend)\n", + "\n", + " for i in range( num_species*(num_species - 1)):\n", + " make_trace_plot(\"M.\"+str(i+1),istart,iend)\n", + " make_hist_plot(\"M.\"+str(i+1),istart,iend)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "b828f96e-f573-4fca-a14f-3e05402267b3", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + " \n", + "set_all_seeds(1234)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "1b6d7776-a94f-41e5-b359-6c0377423869", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'sigma')" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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1N/CeqhqpO3uTvAV4DvhiVf3JsOuZjSTHAcdV1Q+TvAK4BzhvBP8tAhxRVc8lORT4AXBxVd0x5NJmLMnfAcuAV1bVucOuZzaSbAaWVdVI35iVZC3w/aq6us1YfHlVPT3Mmkb1TP93j3Ooqt8Aux/nMFKq6nvAzmHXsS+q6rGq+mFbfhbYyODO65FSA8+11UPba+TOiJIsBs4Brh52Lb1LchTwFmANQFX9ZtiBD6Mb+nt7nMPIBc3BJsk4cCJw55BLmZV2WeQ+YDuwvqpGcRyfAT4M/HbIdeyrAr6T5J72aJZRdAKwA/jXdrnt6iRHDLuoUQ19HWCSHAlcD3yoqn457Hpmo6peqKo3MLhT/OQkI3XJLcm5wPaqumfYtcyBN1fVSQyeyHtRuxQ6ahYAJwFfqKoTgf8Bhv7946iGvo9zOIC0a+DXA1+pqm8Ou5591X4Fvx1YPuRSZupU4B3tevg64LQkXx5uSbNTVdvaz+3Atxhc0h01W4GtE35jvI7Bh8BQjWro+ziHA0T7AnQNsLGqPj3semYryViShW35ZQwmCfx0qEXNUFVdWlWLq2qcwf+J26rqr4dc1owlOaJNCqBdDjkDGLkZblX1OLAlyeta0+kcAI+RP+Cesjkd++lxDvMuydeAtwLHJNkKXFZVa4Zb1YydCrwPuL9dDwf4aFXdPLySZuU4YG2bGfYS4NqqGtkpjyPuWOBbg/MJFgBfrar/GG5Js/ZB4Cvt5PQR4IIh1zOaUzYlSbMzqpd3JEmzYOhLUkcMfUnqiKEvSR0x9CWpI4a+JHXE0Jekjvw/qRNVQ5NJt1UAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Prior visualisation\n", + "# mu\n", + "x_mu = np.random.lognormal(0.01,0.5,size=10000)\n", + "plt.figure()\n", + "plt.hist(x_mu);\n", + "plt.title('mu') \n", + "\n", + "# Md\n", + "x_Md = np.random.normal(0.1,0.05,size=10000)\n", + "plt.figure()\n", + "plt.hist(x_Md);\n", + "plt.title('M[i,i]') \n", + " \n", + "# Shrinkage, M\n", + "tau0 = 0.001;\n", + "x_M = np.zeros([1000])\n", + "for i in range(1000):\n", + " tau = np.random.standard_cauchy(size=1)\n", + " lam = np.random.standard_cauchy(size=1)\n", + " x_M[i] = np.random.normal(0,np.abs(lam)*np.abs(tau),size=1)\n", + "#print(x_M)\n", + "plt.figure()\n", + "plt.hist(x_M, range=(-5,5));\n", + "plt.title('M[i,j]'); \n", + "\n", + "# sigma\n", + "x_sig = np.random.lognormal(0.01,0.5,size=10000)\n", + "plt.figure()\n", + "plt.hist(x_sig);\n", + "plt.title('sigma')" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "669fa5ab", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "times:\n", + " [30 31 33 35 37 38 39 40 42]\n", + "data:\n", + " [[0.47631602 0.26044127 0.17864191 0.07372655 0.01025256]\n", + " [0.45207895 0.28747275 0.17551302 0.07165977 0.0128983 ]\n", + " [0.28421813 0.48382345 0.13831214 0.07655341 0.01692193]\n", + " [0.36339726 0.35112692 0.19059864 0.0838785 0.00903618]\n", + " [0.31838096 0.3106749 0.18080888 0.14558753 0.02740991]\n", + " [0.27745952 0.38180248 0.14157038 0.13615221 0.03989606]\n", + " [0.28601618 0.35548334 0.12251251 0.14709761 0.06777072]\n", + " [0.31935078 0.2658713 0.13219171 0.17374702 0.09364685]\n", + " [0.41944114 0.18780501 0.16822927 0.1595578 0.05752771]]\n", + "X:\n", + " [[0.47631602 0.26044127 0.17864191 0.07372655 0.01025256 1. ]\n", + " [0.45207895 0.28747275 0.17551302 0.07165977 0.0128983 1. ]\n", + " [0.28421813 0.48382345 0.13831214 0.07655341 0.01692193 1. ]\n", + " [0.36339726 0.35112692 0.19059864 0.0838785 0.00903618 1. ]\n", + " [0.31838096 0.3106749 0.18080888 0.14558753 0.02740991 1. ]\n", + " [0.27745952 0.38180248 0.14157038 0.13615221 0.03989606 1. ]\n", + " [0.28601618 0.35548334 0.12251251 0.14709761 0.06777072 1. ]\n", + " [0.31935078 0.2658713 0.13219171 0.17374702 0.09364685 1. ]]\n", + "F:\n", + " [[-0.0522247 0.09875072 -0.01767007 -0.02843356 0.22956838]\n", + " [-0.23205742 0.26029599 -0.11910011 0.0330296 0.13575756]\n", + " [ 0.12287731 -0.16028616 0.16032843 0.0456903 -0.31368732]\n", + " [-0.06612397 -0.06120036 -0.02636465 0.27570409 0.55483426]\n", + " [-0.13757364 0.20615637 -0.24464359 -0.06700404 0.37537307]\n", + " [ 0.03037334 -0.07142502 -0.14458383 0.07732293 0.52985272]\n", + " [ 0.11024176 -0.29046601 0.07604012 0.16650398 0.3234005 ]\n", + " [ 0.13631653 -0.17380407 0.12053725 -0.04259706 -0.24363199]]\n" + ] + } + ], + "source": [ + "data = pd.read_csv(\"data/data-top5-M40.csv\")\n", + "times = data.iloc[:,0].to_numpy()\n", + "print(\"times:\\n\",times)\n", + "yobs = data.drop(columns=['timepoint', 'subjectID']).to_numpy()\n", + "yobs[yobs == 0] = 1\n", + "\n", + "#print(data)\n", + "print(\"data:\\n\",yobs)\n", + "\n", + "num_species=5\n", + "\n", + "# linearise\n", + "X, F = linearize_time_course_16S(yobs, times)\n", + "print(\"X:\\n\",X)\n", + "print(\"F:\\n\",F)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "a0cb0a60", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0.47631602, 0.26044127, 0.17864191, 0.07372655, 0.01025256],\n", + " [0.45207895, 0.28747275, 0.17551302, 0.07165977, 0.0128983 ],\n", + " [0.28421813, 0.48382345, 0.13831214, 0.07655341, 0.01692193],\n", + " [0.36339726, 0.35112692, 0.19059864, 0.0838785 , 0.00903618],\n", + " [0.31838096, 0.3106749 , 0.18080888, 0.14558753, 0.02740991],\n", + " [0.27745952, 0.38180248, 0.14157038, 0.13615221, 0.03989606],\n", + " [0.28601618, 0.35548334, 0.12251251, 0.14709761, 0.06777072],\n", + " [0.31935078, 0.2658713 , 0.13219171, 0.17374702, 0.09364685]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X[:,:(X.shape[1]-1)]" + ] + }, + { + "cell_type": "markdown", + "id": "76c0b50c", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "## M40 (no perturbations)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8aa25185-e3bf-4d85-9535-ff7e11ce3260", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# Read in data\n", + "data = pd.read_csv(\"data/data-top5-M40.csv\")\n", + "times = data.iloc[:,0].to_numpy()\n", + "print(\"times:\\n\",times)\n", + "yobs = data.drop(columns=['timepoint', 'subjectID']).to_numpy()\n", + "yobs[yobs == 0] = 1\n", + "\n", + "#print(data)\n", + "print(\"data:\\n\",yobs)\n", + "\n", + "num_species=5\n", + "\n", + "# linearise\n", + "X, F = linearize_time_course_16S(yobs, times)\n", + "\n", + "#print(X[:,:(X.shape[1]-1)])\n", + "X = X[:,:(X.shape[1]-1)]\n", + "#print(F)\n", + "\n", + "import nest_asyncio\n", + "nest_asyncio.apply()\n", + "import stan\n", + "\n", + "f = open(\"model_nopert.txt\", \"r\")\n", + "gLV_code=f.read()\n", + "\n", + "obs_data_lin = {\"N\": 5,\n", + " \"T\": len(times)-1, \n", + " \"y\": F,\n", + " \"x\": X,\n", + " \"tau0\": 0.01,\n", + " \"sigma\": 0.1,\n", + " } \n", + "\n", + "posterior = stan.build(gLV_code, data=obs_data_lin, random_seed=1)\n", + "\n", + "sample_kwargs = {\"num_samples\": 1000, \"num_chains\": 2, \"num_warmup\": 5000 }\n", + "#fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\n", + "fit = posterior.sample(**sample_kwargs);\n", + "\n", + "#print(fit)\n", + "\n", + "df = fit.to_frame()\n", + "#print(df.describe().T)\n", + "#print(df.head())\n", + "\n", + "post1 = df[df.columns[7:]][0:500].to_numpy()\n", + "post2 = df[df.columns[7:]][500:1000].to_numpy()\n", + "Rhat = get_Rhat(500, post1, post2)\n", + "print(\"Rhat:\", Rhat)\n", + "istart = 0\n", + "iend = 2000\n", + "\n", + "# plot the fit using median values of parameters\n", + "post1 = df[df.columns[7:]][0:iend].to_numpy()\n", + "est = np.median(post1,axis=0)\n", + " \n", + "mu_h, M_h = extract_gLV_pars(est, num_species)\n", + " \n", + "print_params(mu=mu_h, M=M_h)\n", + "\n", + "# make the plot and comparison\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=0,\n", + " M=M_h,\n", + " mu=mu_h)\n", + "\n", + "init_species = yobs[0,:]\n", + "\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "## PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)" + ] + }, + { + "cell_type": "markdown", + "id": "1f291e8f-67b8-4de0-b13a-a6d2c6ebd530", + "metadata": {}, + "source": [ + "## Q160 (no perturbations)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "725dc3c8-2782-4baf-9f61-d69c76bd52f6", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# Read in data\n", + "data = pd.read_csv(\"maria_multiomics/processed/data-top5-Q160.csv\")\n", + "times = data.iloc[:,0].to_numpy()\n", + "print(\"times:\\n\",times)\n", + "yobs = data.drop(columns=['timepoint', 'subjectID']).to_numpy()\n", + "yobs[yobs == 0] = 1\n", + "\n", + "#print(data)\n", + "print(\"data:\\n\",yobs)\n", + "\n", + "num_species=5\n", + "\n", + "# linearise\n", + "X, F = linearize_time_course_16S(yobs, times)\n", + "\n", + "#print(X[:,:(X.shape[1]-1)])\n", + "X = X[:,:(X.shape[1]-1)]\n", + "\n", + "import nest_asyncio\n", + "nest_asyncio.apply()\n", + "import stan\n", + "\n", + "f = open(\"model_nopert.txt\", \"r\")\n", + "gLV_code=f.read()\n", + "\n", + "obs_data_lin = {\"N\": 5,\n", + " \"T\": len(times)-1, \n", + " \"y\": F,\n", + " \"x\": X,\n", + " \"sigma\": 0.01,\n", + " \"tau0\": 0.01,\n", + " } \n", + "\n", + "posterior = stan.build(gLV_code, data=obs_data_lin, random_seed=1)\n", + "\n", + "sample_kwargs = {\"num_samples\": 1000, \"num_chains\": 2, \"num_warmup\": 5000 }\n", + "#fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\n", + "fit = posterior.sample(**sample_kwargs);\n", + "\n", + "#print(fit)\n", + "\n", + "df = fit.to_frame()\n", + "#print(df.describe().T)\n", + "#print(df.head())\n", + "\n", + "post1 = df[df.columns[7:]][0:500].to_numpy()\n", + "post2 = df[df.columns[7:]][500:1000].to_numpy()\n", + "Rhat = get_Rhat(500, post1, post2)\n", + "print(\"Rhat:\", Rhat)\n", + "istart = 0\n", + "iend = 2000\n", + "\n", + "# plot the fit using median values of parameters\n", + "post1 = df[df.columns[7:]][0:iend].to_numpy()\n", + "est = np.median(post1,axis=0)\n", + " \n", + "mu_h, M_h = extract_gLV_pars(est, num_species)\n", + " \n", + "print_params(mu=mu_h, M=M_h)\n", + "\n", + "# make the plot and comparison\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=0,\n", + " M=M_h,\n", + " mu=mu_h)\n", + "\n", + "init_species = yobs[0,:]\n", + "\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "## PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "e12fba85-815e-4178-8975-4a08833c6e1a", + "metadata": {}, + "source": [ + "## M114 (w perturbation)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "733868c8-26e5-4cef-8dc4-e18a2d843e3b", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# Read in data\n", + "num_species=5\n", + "\n", + "data = pd.read_csv(\"maria_multiomics/processed/data-top5-M114.csv\")\n", + "npert = 1\n", + "tp = [[15, 23]]\n", + "\n", + "times = data.iloc[:,0].to_numpy()\n", + "print(\"times:\\n\",times)\n", + "yobs = data.drop(columns=['timepoint', 'subjectID']).to_numpy()\n", + "yobs[yobs == 0] = 1\n", + "\n", + "print(\"data:\\n\",yobs)\n", + "\n", + "u = get_signal_matrix(npert, tp)\n", + "\n", + "# linearise\n", + "X, F = linearize_time_course_16S(yobs, times)\n", + "\n", + "#print(X[:,:(X.shape[1]-1)])\n", + "X = X[:,:(X.shape[1]-1)]\n", + "\n", + "import nest_asyncio\n", + "nest_asyncio.apply()\n", + "import stan\n", + "\n", + "f = open(\"model_pert.txt\", \"r\")\n", + "gLV_code=f.read()\n", + "\n", + "obs_data_lin = {\"N\": num_species,\n", + " \"T\": len(times)-1, \n", + " \"Np\": 1,\n", + " \"y\": F,\n", + " \"x\": X,\n", + " \"u\": u.T,\n", + " \"sigma\": 0.1,\n", + " \"tau0\": 0.01,\n", + " } \n", + "\n", + "posterior = stan.build(gLV_code, data=obs_data_lin, random_seed=1)\n", + "\n", + "sample_kwargs = {\"num_samples\": 1000, \"num_chains\": 2, \"num_warmup\": 5000 }\n", + "#fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\n", + "fit = posterior.sample(**sample_kwargs);\n", + "\n", + "#print(fit)\n", + "\n", + "df = fit.to_frame()\n", + "#print(df.describe().T)\n", + "#print(df.head())\n", + "\n", + "post1 = df[df.columns[7:]][0:500].to_numpy()\n", + "post2 = df[df.columns[7:]][500:1000].to_numpy()\n", + "#post1 = np.random.normal(size=500)\n", + "#post2 = np.random.normal(size=500)\n", + "Rhat = get_Rhat(500, post1, post2)\n", + "print(\"Rhat:\", Rhat)\n", + "istart = 0\n", + "iend = 2000\n", + "\n", + "# plot the fit using median values of parameters\n", + "\n", + "post1 = df[df.columns[7:]][0:iend].to_numpy()\n", + "est = np.median(post1,axis=0)\n", + "\n", + "mu_h, M_h, E_h = extract_gLV_pars(est, num_species, e=True)\n", + "\n", + " \n", + "print_params(mu=mu_h, M=M_h, e=E_h)\n", + "\n", + "init_species = yobs[0,:]\n", + "\n", + "# make the plot and comparison\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " num_perturbations=1,\n", + " M=M_h,\n", + " mu=mu_h,\n", + " epsilon=E_h)\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)), tp=tp)\n", + "\n", + "## PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)\n" + ] + }, + { + "cell_type": "markdown", + "id": "5b8ffe84-cba2-41bb-b147-a1dd76b352e3", + "metadata": {}, + "source": [ + "## Q99 (w single perturbation)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c0754482-2f0f-4d82-925a-fed885c57c61", + "metadata": {}, + "outputs": [], + "source": [ + "# Read in data\n", + "num_species=5\n", + "\n", + "data = pd.read_csv(\"maria_multiomics/processed/data-top5-Q99.csv\")\n", + "npert = 1\n", + "tp = [[15, 23]]\n", + "\n", + "times = data.iloc[:,0].to_numpy()\n", + "print(\"times:\\n\",times)\n", + "yobs = data.drop(columns=['timepoint', 'subjectID']).to_numpy()\n", + "yobs[yobs == 0] = 1\n", + "\n", + "print(\"data:\\n\",yobs)\n", + "\n", + "u = get_signal_matrix(npert, tp)\n", + "\n", + "# linearise\n", + "X, F = linearize_time_course_16S(yobs, times)\n", + "\n", + "#print(X[:,:(X.shape[1]-1)])\n", + "X = X[:,:(X.shape[1]-1)]\n", + "\n", + "import nest_asyncio\n", + "nest_asyncio.apply()\n", + "import stan\n", + "\n", + "f = open(\"model_pert.txt\", \"r\")\n", + "gLV_code=f.read()\n", + "\n", + "obs_data_lin = {\"N\": num_species,\n", + " \"T\": len(times)-1, \n", + " \"Np\": 1,\n", + " \"y\": F,\n", + " \"x\": X,\n", + " \"u\": u.T,\n", + " \"sigma\": 0.1,\n", + " \"tau0\": 0.01,\n", + " } \n", + "\n", + "posterior = stan.build(gLV_code, data=obs_data_lin, random_seed=1)\n", + "\n", + "sample_kwargs = {\"num_samples\": 1000, \"num_chains\": 2, \"num_warmup\": 5000 }\n", + "#fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\n", + "fit = posterior.sample(**sample_kwargs);\n", + "\n", + "#print(fit)\n", + "\n", + "df = fit.to_frame()\n", + "#print(df.describe().T)\n", + "#print(df.head())\n", + "\n", + "post1 = df[df.columns[7:]][0:500].to_numpy()\n", + "post2 = df[df.columns[7:]][500:1000].to_numpy()\n", + "#post1 = np.random.normal(size=500)\n", + "#post2 = np.random.normal(size=500)\n", + "Rhat = get_Rhat(500, post1, post2)\n", + "print(\"Rhat:\", Rhat)\n", + "istart = 0\n", + "iend = 2000\n", + "\n", + "# plot the fit using median values of parameters\n", + "\n", + "post1 = df[df.columns[7:]][0:iend].to_numpy()\n", + "est = np.median(post1,axis=0)\n", + "\n", + "mu_h, M_h, E_h = extract_gLV_pars(est, num_species, e=True)\n", + "\n", + " \n", + "print_params(mu=mu_h, M=M_h, e=E_h)\n", + "\n", + "init_species = yobs[0,:]\n", + "\n", + "# make the plot and comparison\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " num_perturbations=1,\n", + " M=M_h,\n", + " mu=mu_h,\n", + " epsilon=E_h)\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)), tp=tp)\n", + "\n", + "## PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d05dea30-2fce-4e65-bf32-4793e0a44eaf", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/examples-mcmc-ode.ipynb b/examples/examples-mcmc-ode.ipynb new file mode 100644 index 00000000..9560a9f6 --- /dev/null +++ b/examples/examples-mcmc-ode.ipynb @@ -0,0 +1,554 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "f07fa1f2-187e-4ce0-af95-31d6120977fe", + "metadata": {}, + "outputs": [], + "source": [ + "import random\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.integrate import odeint\n", + "from gMLV import *" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1ac7d4f5", + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "def set_all_seeds(seed):\n", + " np.random.seed(seed)\n", + " random.seed(seed)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f24a82c9-f85e-49db-979d-f23fae68f172", + "metadata": {}, + "outputs": [], + "source": [ + "# some plotting functions\n", + "\n", + "cols = [\"red\", \"green\", \"blue\", \"royalblue\",\"orange\", \"black\", \"salmon\", \"forestgreen\", \"steelblue\", \"slateblue\",\"gold\", \"palegreen\"]\n", + "\n", + "def plot_gMLV(yobs, sobs, timepoints):\n", + " #fig, axs = plt.subplots(1, 2, layout='constrained')\n", + " fig, axs = plt.subplots(1, 2)\n", + " for species_idx in range(yobs.shape[1]):\n", + " axs[0].plot(timepoints, yobs[:, species_idx], color=cols[species_idx])\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]')\n", + " if sobs.shape[1] > 0:\n", + " for metabolite_idx in range(sobs.shape[1]):\n", + " axs[1].plot(timepoints, sobs[:, metabolite_idx], color=cols[metabolite_idx])\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]');\n", + "\n", + "def plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, timepoints):\n", + " # plot the fit\n", + " #fig, axs = plt.subplots(1, 2, layout='constrained')\n", + " fig, axs = plt.subplots(1, 2) \n", + " for species_idx in range(yobs.shape[1]):\n", + " axs[0].plot(timepoints, yobs[:, species_idx], color=cols[species_idx])\n", + " axs[0].plot(timepoints, yobs_h[:, species_idx], '--', color=cols[species_idx])\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]');\n", + "\n", + " for metabolite_idx in range(sobs.shape[1]):\n", + " axs[1].plot(timepoints, sobs[:, metabolite_idx], color=cols[metabolite_idx])\n", + " axs[1].plot(timepoints, sobs_h[:, metabolite_idx], '--', color=cols[metabolite_idx])\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]');\n", + "\n", + "def compare_params(mu=None, M=None, alpha=None, e=None):\n", + " # each argument is a tuple of true and predicted values\n", + " if mu is not None:\n", + " print(\"mu_hat/mu:\")\n", + " print(np.array(mu[1]))\n", + " print(np.array(mu[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0,len(mu[0]), dtype=\"int32\"), np.array(mu[1]), markerfmt=\"D\")\n", + " ax.stem(np.arange(0,len(mu[0]), dtype=\"int32\"), np.array(mu[0]), markerfmt=\"X\")\n", + " ax.set_xlabel('i')\n", + " ax.set_ylabel('mu[i]');\n", + "\n", + " if M is not None:\n", + " print(\"\\nM_hat/M:\")\n", + " print(np.round(np.array(M[1]), decimals=2))\n", + " print(\"\\n\",np.array(M[0]))\n", + "\n", + " #fig, ax = plt.subplots()\n", + " #ax.stem(np.arange(0, M[0].shape[0] ** 2), np.array(M[1]).flatten(), markerfmt=\"D\")\n", + " #ax.stem(np.arange(0, M[0].shape[0] ** 2), np.array(M[0]).flatten(), markerfmt=\"X\")\n", + " #ax.set_ylabel('M[i,j]');\n", + "\n", + " fig, ax = plt.subplots()\n", + " Ns = M[0].shape[0]\n", + " ax.stem(np.arange(0, Ns), np.array(M[1]).diagonal(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, Ns), np.array(M[0]).diagonal(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]');\n", + " \n", + " fig, ax = plt.subplots()\n", + " Ns = M[0].shape[0]\n", + " \n", + " count = 0\n", + " Mij = np.zeros([Ns*Ns - Ns])\n", + " Mij_h = np.zeros([Ns*Ns - Ns])\n", + " for i in range(Ns):\n", + " for j in range(Ns):\n", + " if i != j:\n", + " Mij[count] = np.array(M[0])[i,j]\n", + " Mij_h[count] = np.array(M[1])[i,j]\n", + " count = count + 1\n", + " \n", + " ax.stem(np.arange(0, Ns*Ns - Ns), Mij.flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, Ns*Ns - Ns), Mij_h.flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]');\n", + " \n", + " if alpha is not None:\n", + " print(\"\\na_hat/a:\")\n", + " print(np.round(np.array(alpha[1]), decimals=2))\n", + " print(\"\\n\",np.array(alpha[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, alpha[0].shape[0] * alpha[0].shape[1]), np.array(alpha[1]).flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, alpha[0].shape[0] * alpha[0].shape[1]), np.array(alpha[0]).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('a[i,j]');\n", + "\n", + " if e is not None:\n", + " print(\"\\ne_hat/e:\")\n", + " print(np.round(np.array(e[1]), decimals=2))\n", + " print(\"\\n\",np.array(e[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, e[0].shape[0]), np.array(e[1]).flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, e[0].shape[0]), np.array(e[0]).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('e[i]');\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a6a3a8c1-dbf9-40a7-8f83-997340de77d0", + "metadata": {}, + "outputs": [], + "source": [ + "# some MCMC analysis functions\n", + "\n", + "def make_trace_plot(var,istart,iend):\n", + " plt.figure()\n", + " post = df[var][istart:iend]\n", + " plt.plot(range(0,(iend-istart)),post)\n", + " #print(var, np.median(post))\n", + " return\n", + " \n", + "def make_hist_plot(var,istart,iend):\n", + " plt.figure()\n", + " post = df[var][istart:iend]\n", + " plt.hist(post)\n", + " print(var, np.median(post))\n", + " return\n", + " \n", + "def get_Rhat(N,p1,p2):\n", + " M = 2\n", + " mean1 = np.mean(p1,axis=0) \n", + " mean2 = np.mean(p2,axis=0) \n", + " var1 = np.var(p1,axis=0) \n", + " var2 = np.var(p2,axis=0)\n", + " \n", + " meanM = (1/M)*(mean1 + mean2)\n", + " \n", + " B = (N/(M-1)) * (mean1-meanM)*(mean1-meanM) + (mean2-meanM)*(mean2-meanM)\n", + " W = (1/M)*(var1 + var2)\n", + " \n", + " Vhat = ((N-1)/N)*W + ((M+1)/(M*N))*B\n", + " \n", + " Rhat = Vhat/W\n", + " \n", + " return Rhat\n", + "\n", + "def get_horseshoe_tau(p0,D,sigma,n):\n", + " return p0*sigma/( np.sqrt(n)*(D-p0) )" + ] + }, + { + "cell_type": "markdown", + "id": "76c0b50c", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "# Single time course: three species" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "17afad1f-293b-4f8b-bc99-f9dd3fed4ac1", + "metadata": {}, + "outputs": [], + "source": [ + "set_all_seeds(1234)\n", + "\n", + "## SETUP MODEL\n", + "# establish size of model\n", + "num_species = 3\n", + "num_metabolites = 0\n", + "\n", + "# construct interaction matrix\n", + "M = np.zeros((num_species, num_species))\n", + "np.fill_diagonal(M, [-0.05, -0.1, -0.15])\n", + "M[0, 2] = -0.1\n", + "M[2, 0] = 0.1\n", + "\n", + "# construct growth rates matrix\n", + "mu = np.random.lognormal(0.01, 0.5, num_species)\n", + "\n", + "# instantiate simulator\n", + "simulator = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M,\n", + " mu=mu)\n", + "simulator.print()\n", + "\n", + "## PRODUCE SIMULATED RESULTS\n", + "# initial conditions\n", + "init_species = 10 * np.ones(num_species)\n", + "init_metabolites = 10 * np.ones(num_metabolites)\n", + "\n", + "times = np.arange(0, 5, 0.1)\n", + "yobs, sobs, sy0, mu, M, _ = simulator.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# add some gaussian noise\n", + "yobs_x = yobs + np.random.normal(loc=0, scale=0.1, size=yobs.shape)\n", + "plot_gMLV(yobs_x, sobs, times)\n", + "\n", + "# add some gaussian noise on log scale\n", + "#yobs_lnx = np.log(yobs) + np.random.normal(loc=0, scale=0.01, size=yobs.shape)\n", + "#plot_gMLV(yobs_lnx, sobs, times)\n" + ] + }, + { + "cell_type": "markdown", + "id": "18b896ec-c198-48cb-ae38-ea5935f4e353", + "metadata": {}, + "source": [ + "## Full Bayesian inference using ODEs" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1b6d7776-a94f-41e5-b359-6c0377423869", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# Prior visualisation\n", + "# mu\n", + "x_mu = np.random.lognormal(0.01,0.5,size=10000)\n", + "plt.figure()\n", + "plt.hist(x_mu);\n", + "plt.title('mu') \n", + "\n", + "# Md\n", + "x_Md = np.random.normal(0.1,0.05,size=10000)\n", + "plt.figure()\n", + "plt.hist(x_Md);\n", + "plt.title('M[i,i]') \n", + " \n", + "# Shrinkage, M\n", + "tau0 = 0.001;\n", + "x_M = np.zeros([1000])\n", + "for i in range(1000):\n", + " tau = np.random.standard_cauchy(size=1)\n", + " lam = np.random.standard_cauchy(size=1)\n", + " x_M[i] = np.random.normal(0,np.abs(lam)*np.abs(tau),size=1)\n", + "#print(x_M)\n", + "plt.figure()\n", + "plt.hist(x_M, range=(-5,5));\n", + "plt.title('M[i,j]') " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2dd734a5", + "metadata": {}, + "outputs": [], + "source": [ + "import nest_asyncio\n", + "nest_asyncio.apply()\n", + "import stan\n", + "\n", + "gLV_code = \"\"\"\n", + "functions {\n", + " vector lotka_volterra(real t, vector y, vector mu, vector Md, vector M) {\n", + " vector[2] dydt;\n", + " dydt[1] = mu[1]*y[1] - Md[1]*y[1]*y[1] + M[1]*y[1]*y[2];\n", + " dydt[2] = mu[2]*y[2] - Md[2]*y[2]*y[2] + M[2]*y[2]*y[1];\n", + " return dydt;\n", + " }\n", + "\n", + " vector lotka_volterra_dln(real t, vector y, vector mu, vector Md, vector M) {\n", + " vector[2] dydt;\n", + " dydt[1] = mu[1] - Md[1]*y[1] + M[1]*y[2];\n", + " dydt[2] = mu[2] - Md[2]*y[2] + M[2]*y[1];\n", + " return dydt;\n", + " }\n", + "\n", + " vector lotka_volterra_N(real t, vector y, int N, vector mu, vector Md, vector M) {\n", + " vector[N] dydt;\n", + " \n", + " int countM = 1;\n", + " \n", + " for(i in 1:N){\n", + " dydt[i] = mu[i]*y[i] - Md[i]*y[i]*y[i];\n", + " \n", + " for(j in 1:N){\n", + " if ( i != j ){\n", + " dydt[i] += M[countM]*y[i]*y[j];\n", + " countM += 1; \n", + " //print(\"loop iteration: \", i, j, countM);\n", + " }\n", + " }\n", + " }\n", + " \n", + " return dydt;\n", + " }\n", + "\n", + "\n", + "}\n", + "\n", + "data {\n", + " int N;\n", + " int T;\n", + " real t0;\n", + " array[T] real ts;\n", + " array[T,N] real y;\n", + " vector[N] y0;\n", + " real sigma;\n", + " //real tau;\n", + " \n", + " //vector[2] M;\n", + " //vector[2] Md;\n", + "}\n", + "\n", + "parameters {\n", + " vector[N] mu;\n", + " vector[N] Md;\n", + " vector[N*N - N] M;\n", + " \n", + " vector[N*N - N] lambda;\n", + " real tau;\n", + " \n", + " //vector[N] y0;\n", + " //real sigma;\n", + "}\n", + "\n", + "model {\n", + " //target += double_exponential_lpdf(mu | 0, 1.0);\n", + " //target += double_exponential_lpdf(Md | 0, 0.1);\n", + " \n", + " //target += normal_lpdf(mu | 1.0, 0.2);\n", + " target += lognormal_lpdf(mu | 0.01, 0.5);\n", + " \n", + " target += normal_lpdf(Md | 0.1, 0.02);\n", + " \n", + " // Laplace\n", + " //target += double_exponential_lpdf(M | 0, 0.1);\n", + "\n", + " // exponential / normal\n", + " //target += exponential_lpdf(lambda | 10);\n", + " //target += normal_lpdf(M | 0, lambda);\n", + "\n", + " // hierarchical exponential\n", + " //for(i in 1:2){\n", + " // target += exponential_lpdf(lambda[i] | 10); // parameterised as 1/scale\n", + " // target += normal_lpdf(M[i] | 0, lambda[i]);\n", + " //}\n", + " \n", + " // Horsehoe prior\n", + " real tau0 = 0.001;\n", + " target += cauchy_lpdf(tau | 0, tau0);\n", + "\n", + " for(i in 1:(N*(N-1))){\n", + " target += normal_lpdf(M[i] | 0, lambda[i]*tau);\n", + " target += cauchy_lpdf(lambda[i] | 0, 1);\n", + " }\n", + " \n", + " vector[N] y_hat[T] = ode_bdf_tol(lotka_volterra_N, y0, t0, ts, 1e-6, 1e-6, 100000, N, mu, Md, M );\n", + "\n", + " for (t in 1:T) {\n", + " for (s in 1:N){\n", + " target += normal_lpdf(y[t,s] | y_hat[t,s],sigma);\n", + " }\n", + " }\n", + "}\n", + "\n", + "\"\"\"\n", + "\n", + "#obs_data_log = {\"T\": len(times)-1,\n", + "# \"t0\": 0.0,\n", + "# \"ts\": times[1:], \n", + "# \"y\": yobs_lnx[1:,:],\n", + "# \"y0\": np.log(init_species),\n", + "# \"sigma\": 0.01,\n", + "# #\"Md\": np.array([-M[0,0],-M[1,1] ]),\n", + "# #\"M\": np.array( [M[0,1],M[1,0]] )\n", + "# } \n", + "\n", + "obs_data = {\"N\": 3,\n", + " \"T\": len(times)-1,\n", + " \"t0\": 0.0,\n", + " \"ts\": times[1:], \n", + " \"y\": yobs_x[1:,:],\n", + " \"y0\": init_species,\n", + " \"sigma\": 0.1,\n", + " #\"tau:\": 1.0\n", + " #\"Md\": np.array([-M[0,0],-M[1,1] ]),\n", + " #\"M\": np.array( [M[0,1],M[1,0]] )\n", + " } \n", + "\n", + "#posterior = stan.build(gLV_code, data=obs_data_log, random_seed=1)\n", + "posterior = stan.build(gLV_code, data=obs_data, random_seed=1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e0cd6d62-4f37-467c-a3ea-58689641e2d7", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "sample_kwargs = {\"num_samples\": 500, \"num_chains\": 2, \"num_warmup\": 5000 }\n", + "#fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\n", + "fit = posterior.sample(**sample_kwargs)\n", + "\n", + "#print(fit)\n", + "\n", + "df = fit.to_frame()\n", + "print(df.describe().T)\n", + "#print(df.head())\n", + "\n", + "post1 = df[df.columns[7:]][0:500].to_numpy()\n", + "post2 = df[df.columns[7:]][500:1000].to_numpy()\n", + "#post1 = np.random.normal(size=500)\n", + "#post2 = np.random.normal(size=500)\n", + "Rhat = get_Rhat(500, post1, post2)\n", + "print(\"Rhat:\", Rhat)\n", + "istart = 0\n", + "iend = 1000" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "632446f0-0e5d-4d92-9031-02d2806efc27", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "print(\"mu:\",mu)\n", + "for i in range(num_species):\n", + " make_trace_plot(\"mu.\"+str(i+1),istart,iend)\n", + " make_hist_plot(\"mu.\"+str(i+1),istart,iend)\n", + "\n", + "\n", + "print(\"Md:\",M.diagonal())\n", + "for i in range(num_species):\n", + " make_trace_plot(\"Md.\"+str(i+1),istart,iend)\n", + " make_hist_plot(\"Md.\"+str(i+1),istart,iend)\n", + "\n", + "\n", + "for i in range( num_species*(num_species - 1)):\n", + " make_trace_plot(\"M.\"+str(i+1),istart,iend)\n", + " make_hist_plot(\"M.\"+str(i+1),istart,iend)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d6a562cc-b068-47d9-863c-9708f0b2ecd9", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# plot the fit using median values of parameters\n", + "\n", + "post1 = df[df.columns[7:]][0:iend].to_numpy()\n", + "est = np.median(post1,axis=0)\n", + "\n", + "# fill mu_h and M-H\n", + "mu_h = est[0:num_species]\n", + "M_h = np.zeros([num_species,num_species])\n", + "np.fill_diagonal(M_h, -est[num_species:2*num_species])\n", + "\n", + "count = 0\n", + "print(\"est:\", est)\n", + "for i in range(num_species):\n", + " for j in range(num_species):\n", + " if i != j:\n", + " M_h[i,j] = est[2*num_species + count]\n", + " count = count + 1\n", + "\n", + "#print(mu_h)\n", + "#print(M_h)\n", + "\n", + "# make the plot and comparison\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h)\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "## PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)\n", + "\n", + "# this does the stem plots with orange crosses the actual parameters\n", + "compare_params(mu=(mu,mu_h), M=(M, M_h))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/examples-mcmc.ipynb b/examples/examples-mcmc.ipynb new file mode 100644 index 00000000..1233d9da --- /dev/null +++ b/examples/examples-mcmc.ipynb @@ -0,0 +1,3324 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "53eb7b1a-08b4-4878-bb14-bc1073082119", + "metadata": { + "tags": [] + }, + "source": [ + "# Full Bayesian inference using linear approximation of dynamics" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "3bb0bf7a-adbe-45d2-939a-4a08bd18a689", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import random\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.integrate import odeint\n", + "from gMLV import *\n", + "\n", + "\n", + "def set_all_seeds(seed):\n", + " np.random.seed(seed)\n", + " random.seed(seed)\n", + "\n", + "# some plotting functions\n", + "\n", + "\n", + "cols = [\"red\", \"green\", \"blue\", \"royalblue\", \"orange\", \"black\",\n", + " \"salmon\", \"forestgreen\", \"steelblue\", \"slateblue\", \"gold\", \"palegreen\"]\n", + "\n", + "\n", + "def plot_gMLV(yobs, sobs, timepoints):\n", + " # fig, axs = plt.subplots(1, 2, layout='constrained')\n", + " fig, axs = plt.subplots(1, 2)\n", + " for species_idx in range(yobs.shape[1]):\n", + " axs[0].plot(timepoints, yobs[:, species_idx], color=cols[species_idx])\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]')\n", + " if sobs.shape[1] > 0:\n", + " for metabolite_idx in range(sobs.shape[1]):\n", + " axs[1].plot(timepoints, sobs[:, metabolite_idx],\n", + " color=cols[metabolite_idx])\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]')\n", + "\n", + "\n", + "def plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, timepoints):\n", + " # plot the fit\n", + " # fig, axs = plt.subplots(1, 2, layout='constrained')\n", + " fig, axs = plt.subplots(1, 2)\n", + " for species_idx in range(yobs.shape[1]):\n", + " axs[0].plot(timepoints, yobs[:, species_idx], color=cols[species_idx])\n", + " axs[0].plot(timepoints, yobs_h[:, species_idx],\n", + " '--', color=cols[species_idx])\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]')\n", + "\n", + " for metabolite_idx in range(sobs.shape[1]):\n", + " axs[1].plot(timepoints, sobs[:, metabolite_idx],\n", + " color=cols[metabolite_idx])\n", + " axs[1].plot(timepoints, sobs_h[:, metabolite_idx],\n", + " '--', color=cols[metabolite_idx])\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]')\n", + "\n", + "\n", + "def compare_params(mu=None, M=None, alpha=None, e=None):\n", + " # each argument is a tuple of true and predicted values\n", + " if mu is not None:\n", + " print(\"mu_hat/mu:\")\n", + " print(np.array(mu[1]))\n", + " print(np.array(mu[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, len(mu[0]), dtype=\"int32\"),\n", + " np.array(mu[1]), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, len(mu[0]), dtype=\"int32\"),\n", + " np.array(mu[0]), markerfmt=\"X\")\n", + " ax.set_xlabel('i')\n", + " ax.set_ylabel('mu[i]')\n", + "\n", + " if M is not None:\n", + " print(\"\\nM_hat/M:\")\n", + " print(np.round(np.array(M[1]), decimals=2))\n", + " print(\"\\n\", np.array(M[0]))\n", + "\n", + " # fig, ax = plt.subplots()\n", + " # ax.stem(np.arange(0, M[0].shape[0] ** 2), np.array(M[1]).flatten(), markerfmt=\"D\")\n", + " # ax.stem(np.arange(0, M[0].shape[0] ** 2), np.array(M[0]).flatten(), markerfmt=\"X\")\n", + " # ax.set_ylabel('M[i,j]');\n", + "\n", + " fig, ax = plt.subplots()\n", + " Ns = M[0].shape[0]\n", + " ax.stem(np.arange(0, Ns), np.array(M[1]).diagonal(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, Ns), np.array(M[0]).diagonal(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]')\n", + "\n", + " fig, ax = plt.subplots()\n", + " Ns = M[0].shape[0]\n", + "\n", + " count = 0\n", + " Mij = np.zeros([Ns*Ns - Ns])\n", + " Mij_h = np.zeros([Ns*Ns - Ns])\n", + " for i in range(Ns):\n", + " for j in range(Ns):\n", + " if i != j:\n", + " Mij[count] = np.array(M[0])[i, j]\n", + " Mij_h[count] = np.array(M[1])[i, j]\n", + " count = count + 1\n", + "\n", + " ax.stem(np.arange(0, Ns*Ns - Ns), Mij.flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, Ns*Ns - Ns), Mij_h.flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]')\n", + "\n", + " if alpha is not None:\n", + " print(\"\\na_hat/a:\")\n", + " print(np.round(np.array(alpha[1]), decimals=2))\n", + " print(\"\\n\", np.array(alpha[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, alpha[0].shape[0] * alpha[0].shape[1]),\n", + " np.array(alpha[1]).flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, alpha[0].shape[0] * alpha[0].shape[1]),\n", + " np.array(alpha[0]).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('a[i,j]')\n", + "\n", + " if e is not None:\n", + " print(\"\\ne_hat/e:\")\n", + " print(np.round(np.array(e[1]), decimals=2))\n", + " print(\"\\n\", np.array(e[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, e[0].shape[0]), np.array(\n", + " e[1]).flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, e[0].shape[0]), np.array(\n", + " e[0]).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('e[i]')\n", + "\n", + "\n", + "# some MCMC analysis functions\n", + "\n", + "def make_trace_plot(var, istart, iend):\n", + " plt.figure()\n", + " post = df[var][istart:iend]\n", + " plt.plot(range(0, (iend-istart)), post)\n", + " # print(var, np.median(post))\n", + " return\n", + "\n", + "\n", + "def make_hist_plot(var, istart, iend):\n", + " plt.figure()\n", + " post = df[var][istart:iend]\n", + " plt.hist(post)\n", + " print(var, np.median(post))\n", + " return\n", + "\n", + "\n", + "def get_Rhat(N, p1, p2):\n", + " M = 2\n", + " mean1 = np.mean(p1, axis=0)\n", + " mean2 = np.mean(p2, axis=0)\n", + " var1 = np.var(p1, axis=0)\n", + " var2 = np.var(p2, axis=0)\n", + "\n", + " meanM = (1/M)*(mean1 + mean2)\n", + "\n", + " B = (N/(M-1)) * (mean1-meanM)*(mean1-meanM) + (mean2-meanM)*(mean2-meanM)\n", + " W = (1/M)*(var1 + var2)\n", + "\n", + " Vhat = ((N-1)/N)*W + ((M+1)/(M*N))*B\n", + "\n", + " Rhat = Vhat/W\n", + "\n", + " return Rhat\n", + "\n", + "\n", + "def get_horseshoe_tau(p0, D, sigma, n):\n", + " return p0*sigma/(np.sqrt(n)*(D-p0))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# some MCMC analysis functions\n", + "\n", + "def make_trace_plot(var, istart, iend):\n", + " plt.figure()\n", + " post = df[var][istart:iend]\n", + " plt.plot(range(0, (iend-istart)), post)\n", + " # print(var, np.median(post))\n", + " return\n", + "\n", + "\n", + "def make_hist_plot(var, istart, iend):\n", + " plt.figure()\n", + " post = df[var][istart:iend]\n", + " plt.hist(post)\n", + " print(var, np.median(post))\n", + " return\n", + "\n", + "\n", + "def get_Rhat(N, p1, p2):\n", + " M = 2\n", + " mean1 = np.mean(p1, axis=0)\n", + " mean2 = np.mean(p2, axis=0)\n", + " var1 = np.var(p1, axis=0)\n", + " var2 = np.var(p2, axis=0)\n", + "\n", + " meanM = (1/M)*(mean1 + mean2)\n", + "\n", + " B = (N/(M-1)) * (mean1-meanM)*(mean1-meanM) + (mean2-meanM)*(mean2-meanM)\n", + " W = (1/M)*(var1 + var2)\n", + "\n", + " Vhat = ((N-1)/N)*W + ((M+1)/(M*N))*B\n", + "\n", + " Rhat = Vhat/W\n", + "\n", + " return Rhat\n", + "\n", + "\n", + "def get_horseshoe_tau(p0, D, sigma, n):\n", + " return p0*sigma/(np.sqrt(n)*(D-p0))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "## Single time course: three species, no perturbation" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of species: 3\n", + "specific growth rates: [1.27853844 0.55683415 2.06752757]\n", + "interaction matrix: \n", + "[[-0.05 0. -0.1 ]\n", + " [ 0. -0.1 0. ]\n", + " [ 0.1 0. -0.15]]\n", + "metabolite production: \n", + "None\n", + "perturbation matrix: \n", + "[]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "set_all_seeds(1234)\n", + "\n", + "# SETUP MODEL\n", + "# establish size of model\n", + "num_species = 3\n", + "num_metabolites = 0\n", + "\n", + "# construct interaction matrix\n", + "M = np.zeros((num_species, num_species))\n", + "np.fill_diagonal(M, [-0.05, -0.1, -0.15])\n", + "M[0, 2] = -0.1\n", + "M[2, 0] = 0.1\n", + "\n", + "# construct growth rates matrix\n", + "mu = np.random.lognormal(0.01, 0.5, num_species)\n", + "\n", + "# instantiate simulator\n", + "simulator = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M,\n", + " mu=mu)\n", + "simulator.print()\n", + "\n", + "# PRODUCE SIMULATED RESULTS\n", + "# initial conditions\n", + "init_species = 10 * np.ones(num_species)\n", + "init_metabolites = 10 * np.ones(num_metabolites)\n", + "\n", + "times = np.arange(0, 5, 0.1)\n", + "yobs, sobs, sy0, mu, M, _ = simulator.simulate(\n", + " times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# add some gaussian noise\n", + "yobs_x = yobs + np.random.normal(loc=0, scale=0.1, size=yobs.shape)\n", + "plot_gMLV(yobs_x, sobs, times)\n", + "\n", + "# add some gaussian noise on log scale\n", + "# yobs_lnx = np.log(yobs) + np.random.normal(loc=0, scale=0.01, size=yobs.shape)\n", + "# plot_gMLV(yobs_lnx, sobs, times)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Full Bayesian inference using ODEs" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'M[i,j]')" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Prior visualisation\n", + "# mu\n", + "x_mu = np.random.lognormal(0.01, 0.5, size=10000)\n", + "plt.figure()\n", + "plt.hist(x_mu)\n", + "plt.title('mu')\n", + "\n", + "# Md\n", + "x_Md = np.random.normal(0.1, 0.05, size=10000)\n", + "plt.figure()\n", + "plt.hist(x_Md)\n", + "plt.title('M[i,i]')\n", + "\n", + "# Shrinkage, M\n", + "tau0 = 0.001\n", + "x_M = np.zeros([1000])\n", + "for i in range(1000):\n", + " tau = np.random.standard_cauchy(size=1)\n", + " lam = np.random.standard_cauchy(size=1)\n", + " x_M[i] = np.random.normal(0, np.abs(lam)*np.abs(tau), size=1)\n", + "# print(x_M)\n", + "plt.figure()\n", + "plt.hist(x_M, range=(-5, 5))\n", + "plt.title('M[i,j]')" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'times' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 121\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 122\u001b[0m obs_data = {\"N\": 3,\n\u001b[0;32m--> 123\u001b[0;31m \u001b[0;34m\"T\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtimes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 124\u001b[0m \u001b[0;34m\"t0\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 125\u001b[0m \u001b[0;34m\"ts\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtimes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mNameError\u001b[0m: name 'times' is not defined" + ] + } + ], + "source": [ + "import stan\n", + "import nest_asyncio\n", + "nest_asyncio.apply()\n", + "\n", + "gLV_code = \"\"\"\n", + "functions {\n", + " vector lotka_volterra(real t, vector y, vector mu, vector Md, vector M) {\n", + " vector[2] dydt;\n", + " dydt[1] = mu[1]*y[1] - Md[1]*y[1]*y[1] + M[1]*y[1]*y[2];\n", + " dydt[2] = mu[2]*y[2] - Md[2]*y[2]*y[2] + M[2]*y[2]*y[1];\n", + " return dydt;\n", + " }\n", + "\n", + " vector lotka_volterra_dln(real t, vector y, vector mu, vector Md, vector M) {\n", + " vector[2] dydt;\n", + " dydt[1] = mu[1] - Md[1]*y[1] + M[1]*y[2];\n", + " dydt[2] = mu[2] - Md[2]*y[2] + M[2]*y[1];\n", + " return dydt;\n", + " }\n", + "\n", + " vector lotka_volterra_N(real t, vector y, int N, vector mu, vector Md, vector M) {\n", + " vector[N] dydt;\n", + " \n", + " int countM = 1;\n", + " \n", + " for(i in 1:N){\n", + " dydt[i] = mu[i]*y[i] - Md[i]*y[i]*y[i];\n", + " \n", + " for(j in 1:N){\n", + " if ( i != j ){\n", + " dydt[i] += M[countM]*y[i]*y[j];\n", + " countM += 1; \n", + " //print(\"loop iteration: \", i, j, countM);\n", + " }\n", + " }\n", + " }\n", + " \n", + " return dydt;\n", + " }\n", + "\n", + "\n", + "}\n", + "\n", + "data {\n", + " int N;\n", + " int T;\n", + " real t0;\n", + " array[T] real ts;\n", + " array[T,N] real y;\n", + " vector[N] y0;\n", + " real sigma;\n", + " //real tau;\n", + " \n", + " //vector[2] M;\n", + " //vector[2] Md;\n", + "}\n", + "\n", + "parameters {\n", + " vector[N] mu;\n", + " vector[N] Md;\n", + " vector[N*N - N] M;\n", + " \n", + " vector[N*N - N] lambda;\n", + " real tau;\n", + " \n", + " //vector[N] y0;\n", + " //real sigma;\n", + "}\n", + "\n", + "model {\n", + " //target += double_exponential_lpdf(mu | 0, 1.0);\n", + " //target += double_exponential_lpdf(Md | 0, 0.1);\n", + " \n", + " //target += normal_lpdf(mu | 1.0, 0.2);\n", + " target += lognormal_lpdf(mu | 0.01, 0.5);\n", + " \n", + " target += normal_lpdf(Md | 0.1, 0.02);\n", + " \n", + " // Laplace\n", + " //target += double_exponential_lpdf(M | 0, 0.1);\n", + "\n", + " // exponential / normal\n", + " //target += exponential_lpdf(lambda | 10);\n", + " //target += normal_lpdf(M | 0, lambda);\n", + "\n", + " // hierarchical exponential\n", + " //for(i in 1:2){\n", + " // target += exponential_lpdf(lambda[i] | 10); // parameterised as 1/scale\n", + " // target += normal_lpdf(M[i] | 0, lambda[i]);\n", + " //}\n", + " \n", + " // Horsehoe prior\n", + " real tau0 = 0.001;\n", + " target += cauchy_lpdf(tau | 0, tau0);\n", + "\n", + " for(i in 1:(N*(N-1))){\n", + " target += normal_lpdf(M[i] | 0, lambda[i]*tau);\n", + " target += cauchy_lpdf(lambda[i] | 0, 1);\n", + " }\n", + " \n", + " vector[N] y_hat[T] = ode_bdf_tol(lotka_volterra_N, y0, t0, ts, 1e-6, 1e-6, 100000, N, mu, Md, M );\n", + "\n", + " for (t in 1:T) {\n", + " for (s in 1:N){\n", + " target += normal_lpdf(y[t,s] | y_hat[t,s],sigma);\n", + " }\n", + " }\n", + "}\n", + "\n", + "\"\"\"\n", + "\n", + "# obs_data_log = {\"T\": len(times)-1,\n", + "# \"t0\": 0.0,\n", + "# \"ts\": times[1:],\n", + "# \"y\": yobs_lnx[1:,:],\n", + "# \"y0\": np.log(init_species),\n", + "# \"sigma\": 0.01,\n", + "# #\"Md\": np.array([-M[0,0],-M[1,1] ]),\n", + "# #\"M\": np.array( [M[0,1],M[1,0]] )\n", + "# }\n", + "\n", + "obs_data = {\"N\": 3,\n", + " \"T\": len(times)-1,\n", + " \"t0\": 0.0,\n", + " \"ts\": times[1:],\n", + " \"y\": yobs_x[1:, :],\n", + " \"y0\": init_species,\n", + " \"sigma\": 0.1,\n", + " # \"tau:\": 1.0\n", + " # \"Md\": np.array([-M[0,0],-M[1,1] ]),\n", + " # \"M\": np.array( [M[0,1],M[1,0]] )\n", + " }\n", + "\n", + "# posterior = stan.build(gLV_code, data=obs_data_log, random_seed=1)\n", + "posterior = stan.build(gLV_code, data=obs_data, random_seed=1)" + ] + }, + { + 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(10900/11000)\n", + "Sampling: 100% (11000/11000)\n", + "Sampling: 100% (11000/11000), done.\n", + "Messages received during sampling:\n", + " Gradient evaluation took 0.008988 seconds\n", + " 1000 transitions using 10 leapfrog steps per transition would take 89.88 seconds.\n", + " Adjust your expectations accordingly!\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[1] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[1] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[3] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: CVODES: CVode At t = 0 and h = 6.77849e-78, the corrector convergence test failed repeatedly or with |h| = hmin. Error code: -4 (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: CVODES: CVode Internal t = 1.62365e-13 and h = 9.40514e-30 are such that t + h = t on the next step. The solver will continue anyway. Error code: 99 (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[1] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[1] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[2] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: CVODES: CVode At t = 0 and h = 4.33234e-159, the corrector convergence test failed repeatedly or with |h| = hmin. Error code: -4 (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Rejecting initial value:\n", + " Error evaluating the log probability at the initial value.\n", + " Exception: CVODES: CVode Internal t = 0.549976 and h = 4.54297e-17 are such that t + h = t on the next step. The solver will continue anyway. Error code: 99 (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " Gradient evaluation took 0.005395 seconds\n", + " 1000 transitions using 10 leapfrog steps per transition would take 53.95 seconds.\n", + " Adjust your expectations accordingly!\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[3] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[3] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[3] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[1] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: CVODES: CVode At t = 0 and h = 1.54297e-138, the corrector convergence test failed repeatedly or with |h| = hmin. Error code: -4 (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: CVODES: CVode Internal t = 6.69317e-07 and h = 2.84001e-23 are such that t + h = t on the next step. The solver will continue anyway. Error code: 99 (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: CVODES: CVode Internal t = 1.72502e-06 and h = 7.73949e-23 are such that t + h = t on the next step. The solver will continue anyway. Error code: 99 (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: CVODES: CVode Internal t = 0.308751 and h = 2.59364e-17 are such that t + h = t on the next step. The solver will continue anyway. Error code: 99 (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[3] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: ode_bdf_tol: ode parameters and data[3] is inf, but must be finite! (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: CVODES: CVode Internal t = 3.95148e-34 and h = 3.21359e-50 are such that t + h = t on the next step. The solver will continue anyway. Error code: 99 (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " count mean std min 25% \\\n", + "parameters \n", + "lp__ 1000.0 117.433683 3.692656 102.907785 115.044616 \n", + "accept_stat__ 1000.0 0.914092 0.112074 0.010149 0.885708 \n", + "stepsize__ 1000.0 0.006181 0.000596 0.005585 0.005585 \n", + "treedepth__ 1000.0 8.967000 0.703140 5.000000 9.000000 \n", + "n_leapfrog__ 1000.0 679.747000 279.227181 37.000000 511.000000 \n", + "divergent__ 1000.0 0.022000 0.146757 0.000000 0.000000 \n", + "energy__ 1000.0 -108.030745 4.746861 -120.496056 -111.396687 \n", + "mu.1 1000.0 1.038334 0.254799 0.264083 0.843853 \n", + "mu.2 1000.0 0.584282 0.079729 0.351767 0.530817 \n", + "mu.3 1000.0 2.058561 0.182956 0.752671 2.013040 \n", + "Md.1 1000.0 0.067797 0.017203 0.038047 0.052107 \n", + "Md.2 1000.0 0.106826 0.012209 0.072545 0.099930 \n", + "Md.3 1000.0 0.151070 0.002968 0.142121 0.149058 \n", + "M.1 1000.0 0.043436 0.041431 -0.024744 0.002957 \n", + "M.2 1000.0 -0.099149 0.005729 -0.115923 -0.103061 \n", + "M.3 1000.0 0.001728 0.005064 -0.011999 -0.000853 \n", + "M.4 1000.0 0.000724 0.002972 -0.008506 -0.000916 \n", + "M.5 1000.0 0.097769 0.013329 0.000334 0.095874 \n", + "M.6 1000.0 0.005588 0.032009 -0.157640 -0.003941 \n", + "lambda.1 1000.0 4.130152 9.151473 0.010859 0.777804 \n", + "lambda.2 1000.0 15.838088 36.853520 0.334075 2.989416 \n", + "lambda.3 1000.0 0.737174 1.096954 0.002142 0.173587 \n", + "lambda.4 1000.0 0.676978 0.961032 0.001282 0.156302 \n", + "lambda.5 1000.0 15.122997 38.581515 0.350504 2.926250 \n", + "lambda.6 1000.0 2.167148 6.147883 0.005775 0.410052 \n", + "tau 1000.0 0.022622 0.023356 0.000579 0.007148 \n", + "\n", + " 50% 75% max \n", + "parameters \n", + "lp__ 117.621338 120.017812 128.884140 \n", + "accept_stat__ 0.952614 0.985306 1.000000 \n", + "stepsize__ 0.006181 0.006777 0.006777 \n", + "treedepth__ 9.000000 9.000000 10.000000 \n", + "n_leapfrog__ 511.000000 1023.000000 1023.000000 \n", + "divergent__ 0.000000 0.000000 1.000000 \n", + "energy__ -108.069604 -104.772752 -91.203940 \n", + "mu.1 1.073550 1.250482 1.596807 \n", + "mu.2 0.577178 0.628535 0.960956 \n", + "mu.3 2.080439 2.139313 2.940395 \n", + "Md.1 0.065205 0.081463 0.124525 \n", + "Md.2 0.104764 0.111622 0.157341 \n", + "Md.3 0.151006 0.153128 0.160781 \n", + "M.1 0.035570 0.076119 0.178392 \n", + "M.2 -0.098924 -0.095486 -0.081306 \n", + "M.3 0.000649 0.003892 0.024477 \n", + "M.4 0.000436 0.002512 0.010561 \n", + "M.5 0.099688 0.102163 0.164227 \n", + "M.6 0.000602 0.009762 0.238262 \n", + "lambda.1 1.919702 4.420762 172.310158 \n", + "lambda.2 6.412602 14.731355 561.515904 \n", + "lambda.3 0.423504 0.890145 19.045252 \n", + "lambda.4 0.385120 0.820975 11.082444 \n", + "lambda.5 6.271278 14.855242 718.700700 \n", + "lambda.6 0.885267 1.773426 98.971107 \n", + "tau 0.014730 0.029587 0.174891 \n", + "Rhat: [1.00090049 1.00491347 1.03021133 1.00100226 1.00281728 1.00013836\n", + " 1.00142407 0.99804158 1.0032546 1.00028299 1.03216088 1.0313435\n", + " 0.99992213 0.99884678 0.99800527 0.99806259 0.99820738 0.9994468\n", + " 1.01447472]\n" + ] + } + ], + "source": [ + "sample_kwargs = {\"num_samples\": 500, \"num_chains\": 2, \"num_warmup\": 5000}\n", + "# fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\n", + "fit = posterior.sample(**sample_kwargs)\n", + "\n", + "# print(fit)\n", + "\n", + "df = fit.to_frame()\n", + "print(df.describe().T)\n", + "# print(df.head())\n", + "\n", + "post1 = df[df.columns[7:]][0:500].to_numpy()\n", + "post2 = df[df.columns[7:]][500:1000].to_numpy()\n", + "# post1 = np.random.normal(size=500)\n", + "# post2 = np.random.normal(size=500)\n", + "Rhat = get_Rhat(500, post1, post2)\n", + "print(\"Rhat:\", Rhat)\n", + "istart = 0\n", + "iend = 1000" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mu: [1.27853844 0.55683415 2.06752757]\n", + "mu.1 1.0735504503919286\n", + "mu.2 0.577177936149171\n", + "mu.3 2.080438875628536\n", + "Md: [-0.05 -0.1 -0.15]\n", + "Md.1 0.06520512994929438\n", + "Md.2 0.10476419560401126\n", + "Md.3 0.15100562655495003\n", + "M.1 0.0355697515549101\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/neythen/anaconda3/lib/python3.7/site-packages/matplotlib/cbook/__init__.py:1402: FutureWarning: Support for multi-dimensional indexing (e.g. `obj[:, None]`) is deprecated and will be removed in a future version. Convert to a numpy array before indexing instead.\n", + " x[:, None]\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:278: FutureWarning: Support for multi-dimensional indexing (e.g. `obj[:, None]`) is deprecated and will be removed in a future version. Convert to a numpy array before indexing instead.\n", + " y = y[:, np.newaxis]\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "M.2 -0.0989240552204592\n", + "M.3 0.000649072235231638\n", + "M.4 0.000436062108010005\n", + "M.5 0.09968803108607185\n", + "M.6 0.000602284864370995\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:4: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).\n", + " after removing the cwd from sys.path.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:11: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).\n", + " # This is added back by InteractiveShellApp.init_path()\n" + ] + }, + { + "data": { + "image/png": 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", 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", 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", 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", 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", 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JdEFqmeITrxwtASOfOI2TzJ343QCPMxn/eX+VnXfyljE/opR6KxXS39HcgrvfWO5aYEhGmu851OZQJtVJKWS3oTwI89du7YihG2QfR9AHs/DTjXhszirXOUnmPXSo1O8vtQR1vTPGqzYrRDTVa1gDDdIxxg6yZ761sQXbFe0/n20ItlXolkblfAZw68vLcP3zH0efm2KrHVY3Zaq1UmBGDmWAaiUgABN+k3wpRpEn53+KGRIjbxRZ6vPDUpY9q3veXA7A+uBacoyPPt+U346ift1W3PdWXX47ymNFxDk1y5HD9qYW36zkqF61tlopqPwxWieZnLzmPwtwyO9f1EpHZhyOHUZDsk9Mfp1k7ev3JOrSNN+yikFaLOMna7fgry/XpliCaIxwaGWs2ZyuIfqyB97H5Q/6A9ZNf/ojnHPH25HXJzWabW9qwWK7MXfQFTxOXJocM24UeoAqyZx357uY+sRCrLMN/B0q1e/HESRZ2hwuvHs2Jv1WPivZm6t4v7e8VIvH3/cv9f7qxw04/sbXXCqUoPI3NuewxzVPa3mkBb073XqbyoS0BI4JX894cmNYiWTLhJ5757u4btZirNm8I9NyiSgJByI6jogWE1EtEU2RHJ9MRHOIqJmITvccayGiufa/GcL+e4houXBsnL2fiOgmO6/5RLRv0pssd0pteJJx6ytL8UZt9kt3X/WveTj2Bnegs/iB1oD5guFeZeTg9BoLwefU+0tODz5LbyVnnWFXvhHXEKx4XVc8PNd37OrHPsCHn23EasHVNEy2NbbksFXDJTitECZxvok3a9fgjtcKa0/nZ0iHXcTqwiPNwXJYnjKb29bG5tTLEEXkl0BElQBuAXA8gDEAziKiMZ7TVgC4AMADkiS2MfM4+98pnmM/EY45Nfl4ACPtf5cC+Jvy3bRSVHvf10kC9G3Y2oSfPjovX3laG28t9Td+4d5KwMerN0mP5ZjRLOg1Lrx7tnZ5qjRGDk7vtlxWCYw7WSxN0pKTcUakZ9/xDn7z1If57fzoIyR8RsDhANTPvOH5j7Hv/wargHXVSqUwUqt0kyYBqGXmZczcCOAhAKeKJzBzHTPPB5BG1TgVwH1s8TaAnkQ0MIV0Wz2btvsFwI0vLMEjNfV48N2Vmef/ydr0F4Npkdb68C/hmOvlIZWZrZ6uw1qNuSDOKKCDxsihMj9ySP7lLmvYjG/c+hY275AL+Q8/888PCGow0h6J6jRMaY8cxB62rnooP3M+4rosGt4bnl+iPRfJuT+ZK6tOXU4LlS9hEACx5am396nSiYhqiOhtIjrNc+y3turoeiKq1smPiC61061paGidYSIc0viYizHh6xxhoZ60OssyTx8dbyX3ORzpjui7RrgW0DVIp2dz+P2sj/Bu3Zd4LSB21fE3FuYHlKMa0iHtaphkyVgltRLUBVq6aqXgfYVjVvlXx5xtnpRiGKR3Y+YJAM4GcAMR7W7vvxrAKAATAfQG8DOdRJn5dmaewMwT+vXrl2qBWxNJfPpVGDrlqfzaCeLIJS+MEjZUspFDqLdSSH45hr5w8MyR0DFIV9gPvzlFV1ad9s+rRoodZiJFYSMfCepTmKMgTlLTTQN2GuHnqZY4VW8lSWpLGzbjxueX+I6sTdkJRRUV4bAKwBBhe7C9TwlmXmX/XQbgZQDj7e3PbNXRDgB3w1JfJc4vDa546H38TRLgLSs+27A97y2jw4q1W5WHzklwZkO7lm5MKW1Zrzt2GAiPzUGHOLNSS21zCFQrhTSjWU+eTKseVuTrdfw0VMJnMDhTfX5QaBJZnmf9/W1c//zHeXWUU/4tJbInqgiH2QBGEtEwIuoI4EwAMyKuAQAQUS9HXUREfQEcDGCRvT3Q/ksATgOwwL5sBoDzbK+lAwBsYOaiLm77+NxP8ftZhaBmxVDZ/PTf87WvmfyHl/IuglmW0ElbVLmk9UhkjYnsY1YxtjLcNofAPHOMe95Y7pqY5XzDOvflPI9ix1YKKmNU0dcKbpCiiiZSHmo8k7TqRcGWnCRB+Z0tWb0Jq+0Oj1VefbVSY3MOU59Y4HqmMoLsUbK9zuJK+Y6KvV+0QxXT6SByhjQzNxPRZQCeAVAJ4C5mXkhE0wDUMPMMIpoI4D8AegE4mYiuZeaxAEYDuI2IcrAE0XRmXmQnfT8R9YP1DOYC+K69fyaAEwDUAtgK4MK0bjYuD83O3ti7abs/YNmtr0SPXjbaq7IVw5tBbFDSWudW9vF47+WBd1bkQzyE9YpVbQ4z5n2KX/93Ub6BAKz7WbJ6ExZ+Gh4YbtP2Jlw3azF+fsLo/PMo9siBPX/9x+VHxGfNzMjlGNNnfRQ5897qXavdY3oGaUnoC8XKtvDTDRi7S4/8trdIR3scGlSLLD7Xpxd8hvve+gSbtzfjz98cF3hNUN2QPU+vitNh644W3znFQCl8BjPPhNVoi/umCr9nw1L/eK97E8BeAWkeEbCfAXxfpVzFIsh1Mk28htCN25sCQzKLFILMZVdrnIqchVpJVmzvcpU//88HSmnlWE3/v8nuiW3Y1uQK2udtNPp06ei79paXluIfb3+CXXt3TmWG9LotjZi/aoPWRx/UUPsNmm68beuSLzbj9leXSc/1pqsqANP2VoqT3ok3vY666ScKaqVwlIWDcJ7zPKLKZ40qK/1pydK393rrk6hWKqt5DoZ0Xkjdmi34IsTrwBsuQDVPJxSQas/uz899jGsUG9t8WZy8JCOHLPjH2/EWigkaOcxdud4V1VYm7FQ1Q84IJsecirfShffMxvl3vau19oSOgfX1JWuk+wG9Bl/V0JzePAeLJNWsQjGROKqawlyE8OFMUGdFViTndTiLODmniO+pmOukG+FQJA7748uYFLI4u7eSqRpGw9bJlXHTC0tw/zsrNEMiOGVKd+jw2Jx6SV7hCUd5K8kWZDntljdwkhDi3DESVkQIuyivKef6JCOHJfao9DWhEVfFW2SnkRP3vxqyGqBqo8hQb/TTss+lMSJ2vo3rZi3G5yEB/VRfn6woiyLUkMF1Q7Lf3uWdzyRWeSMcWgGySUkiuRzjvrfqsK1RrUcYN5aMM2dLt8r838xolVVQXlZ+ySvplY/M8+1Lqr/3Xr5hm9+W45wiPvJ73qxznTOif9fIhs55HkEhr1WIc7eBxXLUSkKqt7+6DOfeac1P8VYxHXWKaqOUlvmloFYq7ItaqS0ojU07mvEjSSgRwHpkcWwOzq/Fqzdh1oLPA68JclaQznNQcE02aqUy4rE59dIGRtawidz1xnJMfWIhrntGrRGu9KqVFNubuOGp35bE7AnGSlssY1aVNGnj4m3Qf/qo/z2JIyHnbK9wCGqGWNJYJZnnoPve6tZsEaKIWkblo//8ims9aW+Sry1Zg+1NLbj2v4sQB4aGWknjfj7fsB0rBWO46PZZITEY6M7HEE8P82KL09ER73P5muDIAUF1Q1bP1SZ6Rp+TFkY4hPDR5xtx5SPz8guQiIT1KuvWbMnHeFGNRukNsKb6kTmG7CwdZpyiVBRFOESolSKu917dsMnvavj0AsszuoIosOteIQgOeTkoLyxbcoz73/kEI34+U3vk47/d8Ds87I8v49Rb3shvN7bksOSLzfjxI/NCvZjWbW10rZkhzzu4jEH++l5UTnuz1lKhHfC7F3DodS/l94sCyHkKYn3QHzlEn88M5eFbweDPuE5wdQ9bAiTQW0mSqb/uO0bvsHOywwiHEFRVQl7eX1mIBa+qg93qyUu1EuSrf8j5DZt24D/vu/X7caqY+K1lVUkjXVEjPnhvuWTf5uy6dZFJEUU3ns71Lcy49r+L0Jxj/PUlvZj7mTxFScG9jRSzhs2B1dV9KvX97Dve8U363N7UIn33YmpZRQ3RfQeLV29ydfq8Qku8Dx21kvcR54WRRJ1VDMxKcDEJ+wY+Xb9d6bwwVDugTsUMOv3Fj1bjxhdqMW/lele5dHDSdhtwrb/eBvbWV5bi/RXrcNu5E2Lltdevn411nYPPSBvyAsIamwqiaJuD6K1kn/qn5z7GD44cqVJUu4Dqp/ouZbVGBkg2E91SK/n3P7dotT8fxUS93lmjfjkLR40eIORpIQp7bbWSslOHGk5RbnvF7f7rdUN/4cPCcr6Bk+A03rt4rhk5tALCel2invGNpWswdMpTamkKL151xBHl1fHte2rw+QYrZMIfhJDfH362Edf+d6FSfs4h94cvP3/60x/hmYX+RsOLo1rQRVetFCZkK0K8AIIaFjG5SiG2kvj8Z37wGcZOnaW0NGaSj93Vq3aFd/an6W2k3qhd41JPhZFjubfSb57y2zBU1U8yYfX8h4V6U5gQJgoH/0tJ6h0Vx97gVTN7hYO4GejKqjLjX1BjFfYZ4VD2hL0jsUKv3+o3ZgdfJ/+te62XoLLe/UZd/vddwm/f9Y7u0zXDVq1cq9Zvk05ieyUg+mjahKlD6tdtDVzIxmtzeHL+p/jJv+bl01vx5VbUr9smzeO3T32ILY0tUnuHlySfOjO7VQ72S5Gl6W20ZXa0sHxkI4Iko5EoNVX+voTTZLI8LD+3jSzkRMWhQ1CD7lUrdagqNKuykcPDs1dI1zEJzlf4XUS9klErxSTsHcXtDeaYUYl43kdJK83rSxpw0SHDQs8RGwixzl/5yFycNm4QJu/hj47700fn+VaUq6n7Uis0thae5xD2HGd+EOyCSORO67IHrKVUT9rbWlpEnKjXnIvv2OtttMJGAK9KBKp4Ckv2iWUMyie6jPLGVTZKUK23LYq9YVfIbk8r/vLiL1D7xebAa5VvUVW9FnCety5XCxZqmZvzz/6tNglV1ikrZqQWM3KISViF3ihxfVVLs/BbVzhsb2rBjuZ4BnQAqK7yT/F3yA/xhXpeiK1EeGzOKpx317uh14qcfutbqIopHKKeSlqBySjAW0m2ryWXkw79VRrgoI/9oXdXYNjVrog1uPQfNZLrC+8hvIwe4aBh3g2a5yAdTai6vEY0eDJjrPg8313+JS64e7Zr5Tcv4vmOSkq2NkJSPb63Kovqyh1NyaeMi6UzNodWQNArYmbc+1a88A/ii39WQW9vlcO65p4367DvNPmyhCrV6fON26XzOQC5/jdpFdVZq1kH77fjCj2QY5z997eV0gme5yDX54sNnPNTd3EaEVnQxSaP/pqFvHLM+dnhsjL6hIPOyAEsVQPJHMtU5wOKIxlZ2tubWnDM9a+41C+i+mb91mgXcfKoldZvbcT+kigFqtNUgk7zqpXE+9kS0+MREL87/z4HFdVlXIxwiEtATYka9j3+/qrIwGkAMO1J/QlLSSri3JXrcdJfXpMeW7+1EXVrtrgqfVLDWJhveBK8pRIF2ubGZrypqOutILVGVrYvP8lOku7vZ32EaQqT0WSeZWE6/h3NOTwdOlM3mVpJGl5EKijVpMNpgjFclvbShi34ePVm/OqJhb5jANCxKroCibc4Z8V6+Wz5gHuTEVTnvW7o4rPeErDsqw5ivmJZZy34DBN/+zzeXBrPuSMKIxxCCDMmB1WnqIp2xcNzA715nGuDGmkVFqza4KvEqu34yi/lC8Gcfcc7OOyPLyuvvaBC7JFDxM3EvXcvQZPgZMLf2/CGPZO/vbwUd72xPPC406CprEsRZAuQ3XOSsCQ5ZukoQWZsVc1mhxADS142Fv63EKuMinDwSmdnfos3F1UPq6CzfjXDLcBEO8PcleuV0g7Lz2VXEn7X2PezcFV4KJ+4GOEQwoX3zA48Jn6UR//5FWF/dLr167biAMnwNseM7U0tWJDgZZ/0l9e1PFF0SDM6ZFb2aJHh/bq4VWEaRRZ71s8vEl0s1UcOxdAOy+5JJpy8gRa9TgKheUBtxBQX6VKxElWmqL5RmS3ttatc9S95yJu01+MQ3VfvebMOQ6c8ha0JVnMT3+c7y3XC3iTDCIeYiNVpieAxodJovrP8S3wuNYxZgiMpS0I8OJLg1t9bf6NuN+j47xTWqoiDmJ2lMoiXDhFha2MLFqzagIvvKxiCpSMHiS0AUO+Ryq5Ncr4sqKLKSCQwjwDVS1rGUdlzKvj4F/aJTb1KPCtV1Zm6Win42Hf+UZNff0U2olq9Ud82IHsGMgN8VqvDtWvhsG5LI+asWBcrTEaS76JjgMKdmV3D7XJDZgaimvMAACAASURBVHQtRu9YJCo/r8eXe+SgXlpnZCOG+nbS9OJ1V5R91Kps2t6sXE723F8YSYIDAvJ8Uhs5hKTjircktPZNEbaNppacsj+W+m0En/jMwtV5JwL56oZJ1Hry/Qn8HZRo18LhjaVr8LW/vomVMXrrQdJa5WPtUCl/qznOasnJ9D/ifGUvtnTQIOcRtjq95yBXTxWbg/NQ4vSsr/rXPNymsDobAGzc3oyDpr+odK7K8qlBBNXLtEYOYR0isVHVGTmMvOZpzJj3aeg5Dml/c05nYfyuPROlk1+fwxfKuzgfnZJwIKLjiGgxEdUS0RTJ8clENIeImonodM+xFiKaa/+bIey/305zARHdRUQd7P2HEdEG4Zqp3vzSIh+XKMazDrpGJa1nJTFpAOtjS7JwTBBZ6IYLI4fiSgedd7Xyy20uVz+vK2gYYq9MnOQkU4EE2RziNp5Pzf8s+iQb2eJGMpoS1IHAeQ4p1SuZ95Zs4SLxnaisoeHMYA9FY/T19b+9pXSeI7iqVYzmCoS5Z2dJZOmJqBLALQCOBzAGwFlENMZz2goAFwB4QJLENmYeZ/87Rdh/P4BRsNaY3gnAxcKx14RrpinfjSbONy9Wjg2K4S6C6pNKRfO6volpar94hdPTqkyuiUv5NXQLx8Nmq5YD9V+qjxBFg6eoBpS93yCBPrvuSwyd8hRWrPXnu2p9cMOVpJcfmGYCdaU1z8G/P6026t26L/15SgamLrVSIjWZm/RHDlZ6HYR68/Yy6x617FB59aT7miw6kDJURNskALXMvIyZGwE8BOBU8QRmrmPm+QCUayAzz2QbAO8CGKxR7pTwh6q45D7/LFQdkry2Vz5u0G4YVIRRWqNQWfgMseIe5fLayqYCJ/kwvnm72gQ4wN1LFdWAKj1oZ+uRGitM+hsSP/SDQ9RBWXz8cdflBizngyx7q2FLtAbVb9X5FFFwSB5xcUZpm4U5Dk58MdUZ5CLeR+9znc7o1agIh0EAVgrb9fY+VToRUQ0RvU1Ep3kP2uqkcwHMEnYfSETziOhpIhorS5SILrXTrWloiBfEzRk5iA/34y82KV0bOJEtQZ29SgjsporK6WlVfq+xFwgWhlk1JlHLs6aFOHKoco0c/Od6GyqnbsR97jrre6uSzN+eM9Vzy+rKglUbrLwDsk1mYC/ArD6rW5UW+/11kMzl0fku8qpbr1rJvvckM/BVKEbgvd2YeRURDQfwIhF9wMxibIC/AniVmZ2ZX3PsazYT0QkAHgfgC5DPzLcDuB0AJkyYEKumkMTmoBxyOEg4JNTB6/YaVXoiWbTTUQ1fC3OrjuoofneudSxUbA7OuRHPPajBTVNlkgbM8Xq8Oul7+ehzfydNfF5pja5yrL4EqipO2WTBJeN0GLxtSpSnVlqojBxWARgibA+29ynBzKvsv8sAvAxgvHOMiH4FoB+AK4XzNzLzZvv3TAAdiKivan46eG0Ov3x8ATZuV5usElQ3k9bZFs2GQUWYZfFhO/kGJb11R/xQHgDQuWNwIMBiUOHSbxc+RqnNwTvPIUBX7OXlxfIRb1oqk7SIZQvTQHmegfA7rdFVkLE9Cc6zqpJ4JeoItcIIVJ7+7YpebXFREQ6zAYwkomFE1BHAmQBmRFwDACCiXkRUbf/uC+BgAIvs7YsBHAvgLOaCMoaIdia7S09Ek+wyZjItUFxFrbklp6WXDfZWSjpy0Kv0Kh9tnMlYkflKDIYi37t/TrL0ixmbWIL4WYuL9siK5fdWUlMrBc3AT0tlkhZrtuzINBqo6rtuyXE+VlFaIwdG+t+HU7YOkvlMsfLyPPssHBZkRAoHZm4GcBmAZwB8COARZl5IRNOI6BQAIKKJRFQP4AwAtxGRE2xkNIAaIpoH4CUA05nZ8Vu7FcAAAG95XFZPB7DAvuYmAGdyVgpPuwW49eWl2KLZ0w0q0gG/84fF0EG30qt8tFl82FGv5K1lyeR5kVy5AxHVSqIfvsoqa3m1UsxvuFgfvyoX3j1b6q2UFqrv+pO1WzH2V88ASNPmkIFayS6bLCy91sjB/uu9JGjEmTZKamFbvTPTs2+q8Hs2JN5GzPwmLFdVWZrSvJn5ZgA3q5QrKc7IYdbCz/GLk0ZrXRtUoZLqi7MxSMcsTGiaed1J+okjG4GmQ5Cxb179Bt8+3zuzN/NGe81bKTebA5DtSC5O45ym3l1H8H22IXruREsuB6IAm0OskCrua37x+AJ864DdtNPRpV3PkBbfnc7IgZkzUdUA+g2D7KMtQky7gitrRulnaQBVQScwoM9byXNc10lhm8La02kTdb/bmpKHng5Cu0OU41S9lXQUEwf+LnxG+ptL1+CmF2vBLA9voWdzsP7KF0PK/vto18JBDJGwWSPueo6zU3uozPx0l8VfkGI0q3F7xaqUWq2kEvXTIcjmUOp70CGqzdqc0MEgTVpSjCQQtJCRw5DeO2ml95cXavO/ZSFY4ozAZPWoGKPLdi0c3CMHdeFgLeyeDdqurCUy3BZmSIfnX+zwGmmh40IeaHNoTdLBg/f+N223Igdcffyo0OuG9+2SVZHytOQ4VW+lsFGqznKqANC1U7imPtY8B8k3lCTKrirtWjiI713HS4iR3Yevb3MoTQNUZjbT1NGZYKQSW2l7Uwv+/NzHqZStGAzs3sm1vdl28a6KWsKvCDrNNGOQ5TjcDqA7z6x7pw7Cxf7jcdSlskvEmFpZtQDtWjiIqgOdd5bj9HSeXnSHizKZVhybQ+tTneig8wz96zlY20sbtuT33fXGctz0wpI0iqbNLj06RZ/kocJjhNjkCIdirNIUQXOaNgdwqEpN9267CSMH2bU6tsqCetJ/zY7m7NV8RjjY6DRyzNkN63RtDtJVtNIqTAj5iluEvEqB1+YQ1iZ6Rw6y739HU+mGWh1iRAf13r9jk/MKDS9F6ZjkOL3YSpyualaMwyVLNU5WsmtUo/EmoV0LB7H+67yzLHvLui+9ZDaHvCdr2xQPXnVCVcia176GSvJIdAzcaSObjBWF1w1TdeRQjPtsyTGaWjiVpWb/VbMS67c2Bh7XjV8Udv/MjONvfFU5rbzNwVOfBvXcSXteVhxac/ibxIiVS6eRy9LIuk4xZLhDyWwOCvl+vHqTtkGvXPCNHCoABHyPXgEtG1XGaJ9TI45w8Da8m3dY9VLmu+++rjjCobklh45VFdiecERWJwmnLqJ7N2ELNQ27embgsTC83/iq9dsC18NOk3YtHMRXv1qypnMQWbbH67YE92JkzJdMyioXm8Mx16v3ksoNbxtXGdLoqRhHs46gGUZjDP10kFopaBVDh2LcZgtb7qcdKpMLh7ImpFotEqITlzJkd5tF7AT98omFwSd6yLK3/mXIEFeVYowlnMVLWqurahTeEU9Yj1lFtRfV484S0TCuyhLPwk2Ot1JliHqtWLTkGE05DlyLPU0SCbuEn4bzbZVKO1D6N11C4g6Bs3xVG7fpqZXSpvaLTfiLglfNPHt9gDZqcvCpVcIad6WRQ9ICJaB3l46J0ygnbyVRrZQ1pRzxrVq3DY+/vwrMQI+dOuD7h++O3fp0Llr+7Vo4xH3vWTaIaRiYk1Tnqx/7AH/S8MeXlbZn5w6Sva0Lb8chrMes8s50g+l1i5hMpcPPjtszcRqbdjgjh/KwOXyxaUdRRmOlFIXz6jfgiofnIseMqgrCT44dhb5dq4uWf7sWDrFHDhlKh1IHXQvzypEhexY7ddBbi+HCg4f69v2/w3bXSiNt/N5KwXVl+ZpwtQ2zvheaLL8/nL43vn+4/nPppPk+ZDjlD7O9AMWxOazd0oj3PlmH+nX+IHhn779rqnmVcOCQJ8ecL0d1EUZLDu1aOMQly5GD6BY57VTpCqmRJCnedk3jpSwvXeGwz+Ceru1fnDga5x2YfdTJMHwG6QS9VIY77LcKspFKBRE6Vek39GkIB4fKCIN0MUYOm0MW5Eo6mPBer+Nt512gKi17XHML59VbMuGQld2vXQuHuBX5neWZrD0EwD1yiNMQJCXpCm6AfkPqfQ0VRCV3gfXqmpOqMHQnTcqyI4rXk02ztxllcyhGTzvMQJtUOCWxMXStzsb5syXH+a8hTUEfRfsWDjHv/rv/TLbKWRiibjpqNmoQST6PrZqhmZdJPGF0vy9vw1sRsxFME++jT2qI1R1tBt1/nMYr1ZFDGcyQDlPRJRYO3m2N5LJapKk5x/n7Kqa6tV0Lh1L3TmWIFSxu6RKplVLwG9d1dxzZv5tru6Ki9G/GPwnOvf2LEzUXh9J0NEjzCaTpIBBlc8hKqouPP2wUlnzkEP9aMd7T9d/cJ1E5RFpyBZvD3h4VbJYofcVEdBwRLSaiWiKaIjk+mYjmEFEzEZ3uOdZiLwM6l4hmCPuHEdE7dpoP2+tTg4iq7e1a+/jQZLcYTCm98vYf1lu6v6mF8Y0Jg1E3/cTYI5skNpE0Hsneg3ooN0hzpx6NQb3cMfNL6T6YL4Nn29so9u+uF8xO11dd9gjiqpVUXFmPHTtAKS3n3fQJSPN8RVtRzS+OUjrPQYwG69hvZDa5pN+0t+7p1EVndbobzxyH/xnvWxgzNqJaqZhENj9EVAngFgDHAxgD4CwiGuM5bQWACwA8IEliGzOPs/+dIuz/PYDrmXkEgHUALrL3XwRgnb3/evu8TChlIzR2lx7S/U3NuXzPO27vUcdA5fUUSuORtDDj2lPUjOkVFSQxAqI4+okQ/I2E+3hkD9qDrodyUOpx6kTvztHC4ajRqsIh+NiDlxwQWK9Frj1lrLZ+XnzejlpJJvSS1l9pXVSkKb92dLoKmeYcl6StUrmLSQBqmXkZMzcCeAjAqeIJzFzHzPMBKOkkyLrTIwA8au+6F8Bp9u9T7W3Yx4+kjJ5MKTuoQXk35XJ5/bZO+VznajREVxy5h2s7DW+TxuacsscSQW82crHwPgZvx19rci5zpPvzYXv2ixxtEShWnY1cgwFAVYQXUqEMFrK7UR3ZDOherX0fos3n9SVrAMgFdFJPQm/91ymnozpMu/46a1IHUcrwGYMArBS26+19qnQiohoiepuIHAHQB8B6Znasn2Ka+fzs4xvs810Q0aV2ujUNDQ0axSmQtCHcY0DXRNfLaGrhfOXSkYk3n7Vv/rdWXUnQUwqiqSWHLoo9QyJ/g6fbK88Cr8DyjsZ06k6Oo9VK3tR269MFXxnUPfK8tBDv58kfHBJ4XthtE1TLR+ig2bsWXWhnLfzc2ic0wnHWrJCRRDg4OIIsrUZbNEgXk2IYpHdj5gkAzgZwAxGlYm5n5tuZeQIzT+jXr1+sNHQf97kHuPWpQ/vEXxIxKO+WHBdGDhrp7Sx8HDqT9HzD6ASV8MS9BwKwRw4dNUYOXlfWCiraQhE3nTVeuj+q8xf1sR45qn/+d47DF5RxEFOsqiT87Zz9/Odk1EaIDe1XBoWphpyGT35DKuUjst7x+F3VjasybzGxzBcePMwql+Tav583QTkfn7dSDHEcNRdEF9EgXUxUhMMqAEOE7cH2PiWYeZX9dxmAlwGMB7AWQE8icrqXYpr5/OzjPezzU0dXGu812P3RDEzQWwnL2qlcUeUTv5degkpC/G4P3zNccHrzWLXeP+tUlc62KqlZIygakb8MWcTvCTKU7jNY3hB6vZOSuKKqjBx8+RP5Qm0TZedhp/rMndPkaiVN1ZSQyI1njgu9RqaqEfc5Wcse84TdeimVS0wnaFuFtOtvOY8cZgMYaXsXdQRwJoAZEdcAAIioFxFV27/7AjgYwCK2uh0vAXA8m84H8IT9e4a9Dfv4i5xRvIqo511ZQa6Zut4XdMo4He2aN+/gzFVtDmJ5xA/ljteXAwB+cuye2GeI1Tv7zuThGNnfrwZLs845azx036mDst5VNt2tooJSGThcd/re+d8HjegrPSfoo/Pu3tnTEYh+boUTmDlyeUiZAVz2DLNqI1Qbn7B6S4qeBLI0To34lmRGXtnzkTlj6DSsaZg30zZIl623kq33vwzAMwA+BPAIMy8komlEdAoAENFEIqoHcAaA24jIiX89GkANEc2DJQymM/Mi+9jPAFxJRLWwbAp32vvvBNDH3n8lAJ/rbFqo1ANxwXDx9P1264X9dusV23Uu7DLHW0lHtSH7AIiAyw4fgRmXHYyrTxgtnQyVZo/EiSjbq3MHjcZGMhtZs0xBPbXJIwujJt379Iqsft2q8dpPDw883zvvwT1yUFQred5nMSOgqgtzC1l3TaYilBHntmTrSDhljnSf1cgvibeSg2PcT6tL25JjV0HSDMoYhlIuzDwTwEzPvqnC79mwVEPe694EsFdAmstgeUJ592+HJWQyJ6rByHFhKcJ+3dweFnsMsCZuVVVUpL6edKFRiKiawuGgj7uqsiI/cUam2kizJzpxaG88/+EXOHGvgcrePJZayb1PN0x/RQVJfUXFdIMapKBZ6LIYO6KR3fvceuzk9jSqcAkHNbWSmGQFkVR3nZVLo+ps/Mg5cCmkIUOqViJC3fQTAQB3vBa8AptOfr42IUZh01YBtXjUSi/8+KuY9NsXUs1DRvueIR3xDpmtj/G1nx6O53/0VdcL6mh/uKo9rm/bBjMAuPiQYaEfeaWyWkn8LWlIPJ+qrPeqqsMe1rcLXv9ZcM8ZAPYZ0hPLf3cC9h/eR33kAJLEMarQ6nUF9rAjno/nFBe+GdISIRaG+FxvfrEWT87/LOJ8b/6QevRkFRFYdbTm3JesHLJRYGgaGuWTqWpE91snX9nj0VMrebaVryywtVEvBE0UzR61UtpqqyDatXBQqTQVRBjSuzN6dO7gqjhOT0t16L/vblbvfc8B3XDNiaNDG34nzajyiQ2QrL74ffXDe9eheREwuFf4QiMVVGjoldUUktN0Rw5BDZv4/IIeparNQbw3IFqoitc7S2xGIV4TZHPIiiTvSziq1pjGuC3ZyMb1ftPNrnBtjIsP2l1u34pLSy4XaF/MknYtHHT1o7LGQdVtzXm5Kr2r/MghIk0xGVkDudwTFE+m2khzCCw26rJ0B/XcybdPlrtumYLegbg36IMKysrXk6+I/iinf62gQd0UElY6GEHYB9gcsprwpNvgJClGnBon6zCIPeiCt1KyOu69XLesI/t3zT/LtEJpN2za4RolGeFQBFT6Oa7enLDfeT/aLoDsT8uL8/KjRo8VRPj6voNd14js8KzN4MzgdAu88DziIiuPfHQj0SVrVv6gkYPXwCs/R56mv1yeMB/eURmAMycVFpqZV78+oLRB+bm3K4h8vWUiyix2fxojB6vjo5KGfqWTvT9V7YpOdt6nq1tWr/uxKhOHBrvbrtva5GpnijVJtF0LB5XvoVLSOwEKw1zVjypq5qXocVEYOUSplYA/fWMfO0hfdDkcwSSuvavrm66SPhDghilJRZZuZQVJvVOCCHoHKkIw6BnLbQ7qZdJd8MhXLklWBP2Rg6pni46NKPiYYodLKafoa8pxmdBFn20UrlW/Oupc8V6LZHJo38JBpWEUJbZMh60qxZ1rnZ6ftzKM2aUQKiFfrki9UuGnSjmcdkU3dEEcglxrVfZVEqFP12rccva+uOCgoZF5BfXWXDaZQLuEPE25zUFMO5w4ayi4Oh+S8nbqUKk9bnj2R5OVztMeOQQURPaYLz9ihGs7f28akk48U7Z4UVixkqhOk3TSdUZ5zrmDeu6ED359jO+4uCSqGTkUAZXvQeyRu9VK1paqsdFpj53vwZmcVkhbbMjceQCIXDZT9gF4q6ajVupQhHVopSuZSc4LUyuduPdApXDTgfaECoVzFIUGkd5Hqb/6WvjI8pcnjcGRo/prjxx6eSKyPnW5PG6S995+fPQe0vPC1Uryg4cLoUSi0ghCvO/h/azJnOL6CWHeSlpqJU8CKr3/7inMO3DKv1PHSnTr5A/A+MWmHfnfxuZQBIIqs7gWrDhycPfsrL9Tjldb9MXbeB89ZgDenHIE5v/6GMz71TGeXqmjVopAqMcqgwHHIK2jssmXSWNkAgTYHFRVF5rFu+rYPeXpRJTHKlNQGdwHqioqQsu/tycMRwWR9jrYss6Hw0WHDLNnjiezOXSrlkd+9dafIwNCeIe5oRLk787r5Za0aXO+SdHBYt9dLZ39V/fwh4vRMkjHKE/NL46OcZWb3Xp3xvcO2x13KMSBKlb47nYuHAL2C7/d8Vv8aoqz998Vx43dOTKvglqpwC49d0L3Th0CJ1BFVWpXY6zSeNsXxDWa6SC1gSjWad3Kf8iIvujb1T/CEJ9fkOMAEWHuVP/H7S1Cx6oKt3eYnd7he/bDx785HqN2dkdQZTCmnfoV7ByxKNAlhw7L5+d1ZZURN8bTv//fQfjlSWMCPbt8S7UGVJE47VK/btWom34ihvezA1UmbNu67+Tvqe81uAcW/+Y4HDXGL9TE7M7ef1ecs/+u+PbBwzB6oD/qbejFAXSsqlCOJRaYDQE/PW4UhvbVD+aZ1dyX4szDLlOC3rvYOFUGqJV0G7CooaC4jKTo9pokfe+kN6en1TEjtZLLIC2zOSimo9t2EAIm+EXo8J1zeuwkWTTGU4qOle55Dgft3hffPngYvvPV4aHPU3asT5eOuOLoPfCNCYPx8uIG/P215b5z0nIxdu7DCffyxcbt0vO8wjNq0mCcSXCU/6t/b+KI6fpvjsND767EXp7osdVVcjuPWKSxu3THOfsXRnRDpzzlziemK2uHSkKj2zlQS5CXfmFcP+165BD07kQ7QmWAQVpX7Rf1rTeJrRupXSN+oLKPsiXnDuuRFw4xejm6VTeJWkk3X6Jo//agxWx0DdUOlRWEqSePwYCAkYFTnKCQJecesBuqqyoDG5Cg/MX7PP4r0SNW7+0FdVK8636rGupdxyKaOPJ0ery3/sGvj8F8iTH2Jx61Yf9unXD5kSPVPe2KoIZJasfLykU5Ce1aOKgg9oBldgHA/WIPHdlXukaAc36Qa2GzEJ/JabCiGtMpJ4TbO7yL2jub3t7sCEm01jiIDZeqt5KMOB9zVGC7QLVSwPne8qt+ul6dsehl4iAPY+Ldjn4GQbaWsHSDVoXz5R840gqxOVD4O3ZeQdAp3Tp1cAW6dPj+4SMkZ5cXUSEtwuYxlCvtWjio9GTd8VvEawu/xd5fVQXhlH128aXjxFvpuZPcIOhWK9n5RZTNu/hQWJoA8mGjvQ3l6fultxi6g+o8Bxn6aiXK99DFyKlRUWvD9sftbBZmxwYTuFCOJBzKsz+ajLeuPkK4Vjw/Gm8jH+SM4O0wyJ7LqJ27CWqlgPxC50E4I4cYaqUiday9RVMtquydXn7kSPV8jVqpvOhaXYWpJ40JPccVMkNsbAJ6ok4V6detGmMEg9e6rVY4654Bi703udzyrL9ed9fbz90Pd12gvqqVf+TgeCupqRB0EXOT2qND8vnHRZOUzpNChcbD5XospBPUswt0SvCOHBQbp4ILf/AF/buJqij/exfz32NANwzssZPkbLVG1nuGTGjXTT9RYnPwp/XwpQe68hTXy1DBuTROfdMRDn/QLJdI3E9Bpj4MX1EvPUq5hnSb5tuHDAs9TkG/A3XC1t/Z1xyFmT88NL9/tz6WO99hASuzifYBp9fWqUMlrj1lbD7dY8bujCNGyV0MZTR7hIOz5e0lHjg8nUBh/bpV53/LGi5nn9ftE7DCfefP0/xEiYA9d7ZCqIs9Y9fIQdP7xtuAqeqEVRrs+y7yRar3lePMiUN85wBxRg7u7cAJkJ7zZCOHHp07CJPNGN+YMAS/OrnQuYpSK3ltDllxxoQhOHGvgbGujesI4HTEnO+1LdDuhYMOQWoKsdkIits/cWhvvHX1EYErXjVJJvQkxTtycLYdg/TgXlaPdK/BPTDvV35DoA6XHzkSu/dTs12MG+JfO1jFjTOMO8+fgAcu3h+dOwprLgjHA0cO9lmXTh7uGkV6i6CyWA8gxNAKOSfIiO3k+fyVX82vweGFA0YaQXjrUtCI1yuQA8/zql186YSUxfMrS1WRzN01S5x7kc2zyDzvjNI1wiEC9zC+8Ftmc+jdpSOmfz14SCuqB7yIDbnsA4vTYPpGDh6D9JHCzNU4E+Me//7BGGX32Hfvp++fHYRKqO3vTB5eOAeWuu6gEX0DR3dRk+B+fsJoHCE8j7hqJW/P07tCnBfXSEChZ+0eOaTXBVd2FoiyKSgJLMVCCeg2gN1t257X0ymIU8ftgrMmDcGBu/fRzMnC6RQGzsQPeDA/P2FUrPxEjFqpDIiK1fO7r+0lDUutQpNErSQSpwJ41y322hxahESj5mHIPuhxQ3rm1Tl6Pt1+HHVHv27VGD2wW35/ULriZCEKECZB81VcZQm4NrZaybM9flc1LxWVOFBWOQqkOV/FN1Ly1B1ntFmwqUjSoHDh4QzeimF6vfTQ4Th6zACcLUTKBYLr08AeO+F3X9s79jN1HlfYd3SRRIWdxnyWrNxglZ4EER1HRIuJqJaIfGs6E9FkIppDRM1EdLrkeHciqieim+3tbkQ0V/i3hohusI9dQEQNwrGLk95kWgSt7ZAGYpyYtEJqe0cOXuEgHo4bzMu5SmUZzDAqKqwlH2dfc5T2s3XbhdzXjh7YHX/+xj5qkVtFxYenDIeMULPL5K+zH0ecdaBDrxCec9LIr648PffrrTsf//Z4peui5kHIrsmCPl2r8ffzJqCXQmwuEdXv4Lf/8xXXdtTIAbDiY3Wrlqu7kjySrEYOkYo5IqoEcAuAowHUA5hNRDOYeZFw2goAFwC4KiCZ/wXwqrPBzJsAjBPyeA/AY8L5DzPzZYr3UDwCe5bsPayNOM9BrChJXvykYb1d24V5DlYGYu8wbjCvfFgQhXI6Hjw6jUOU4d9Lpw7u/s7TtlPAloAAicEjB3fGh45U0yWrTjpzCJovoHJ+p47ZjRy89qr8eSE2lajXmqwBzNaXNR8t2VPGXRQ1ASrCISuyejYqtWsSgFpmXsbMjQAeAnCqeAIz1zHzfAA578VEtB+AAQCe+J8L4QAAGY1JREFUlSVORHsA6A/gNc2yF52gZQnzC/gkqP09BBfXtHpWP/XoW9mrVhLtHET4zWnu3pAKTllVRg55d9OUe45BqiQRlY82qVEc8MfQUg3dHTTB0ov4mJPG8wnKH7C86w4d6R8thY0UVGdIO5TlrGBPGc87cKjUAylofXbdEbjqtx42ia6UBulBAFYK2/X2vkiIqALAnxA8ogCAM2GNFMR7/DoRzSeiR4lI6tNHRJcSUQ0R1TQ0NKgUJxauEBXCfpXFdXT4/uG7F9KOMMjuMUDNK8g7G9bxiHLUES2eBl2MRqtKmA7ai5NfGo/O5bXj+VCfv3IynrnCvY6BmnAQ9f7xylVY8c8q3+79ukTOpSnk7/4rw+2tlKJB2vMMO1RW4B8X7S85L18QeTohZXKORPV0s+x9B+Yc0MGrJJIG8/Nd7tTtwPlP1vFqz8hW9U7vudDv/lzIWzERTbI2SH8PwExmrg8550wADwrb/wUwlJn3BvAcgHtlFzHz7cw8gZkn9OtXHPexoAlxaVBdVZn3/49KecZlh2DBtcfGzmv8rpabpFePHidaa/6DV+i/5Fg+dI9D2Acxon+3vKHcQaVHp2JTuuaE0bjnwomBafhn2FLoXBq3t5J/X9j5IlHRXyOx845ql8PnMUS4soaopERKoJkJzVvcFRRqxhk5RNmYHrr0APzoqMJaGarfQpcAWwVQWoP0KgBi732wvU+FAwFcRkR1AP4I4Dwimu4cJKJ9AFQx83vOPmZey8zOyhZ3ANhPMa/MEd+7y5XV/pu0TjvXy1zyxQrQqUMluoZUlij23bUX5k49Gl/b1x02I45w0LE5BPXOkqKSnMpIz7VgfcA5l0wejsP27B9wtHBvup+ry84U42N/5DsHurYrKwi3nav+6Tj5R8UI8o4wyPM73CBtETVySMtbTwcn+SiV54Du1kTPoNOiXFlH9O+GHx41Utgfj16dC2F4SjlymA1gJBENI6KOsHr6M1QSZ+ZzmHlXZh4KS7V0HzOL3k5nwT1qABGJUxtPAfChSl7FIMhgySn2iK104iU08/JDo08CUN2hUhrGwzFUS8sUUI2dtkRmv7zw4KGu7RbhOc264lD8RRKg0JdvETxbHERjdtx8de0pXxlkhVg5ee9dlOYtBLUD3nUadunZCccGrDPy65PH4NZv7eva51yt6tIsE2BRrqze1dqCGrVSGnV1w7540S17XPX0+1MLk1ZVJ2jqEikcmLkZwGUAnoHVUD/CzAuJaBoRnQIARDSRiOoBnAHgNiJaqJj/N+ARDgAuJ6KFRDQPwOWwvKBKxtEufWNynbQKsqRVGg5xHeowgpawlI0cHPuE84F4l0TUMUjn1UogjNq5O06WBChUJWhyYhLE9QDivt+gy2oDXEF369MFddNPxPGK4R6cx+xdZc6rNgt7HRccPAzHfcWdn6papND7d3a4z/fq1KXXhuYgVwE6wug7Xx3uO6ZFRD2Vhn2RvNWgp6RtkNY6W444LyhNlHQTzDwTwEzPvqnC79mw1E1hadwD4B7PPt+bZuarAVytUq5iIIZjyHKeg0ja3jxedIRD546V2NZUWMVk/q+PdS2QoqoqAABnnl8qgjWDsbQ4SzwotHUUQWo2nfRCbQ52I7lzD7eNwasN0n08zvvrXB3ulBCuNqNQ7yzn2Xgn2PnOk1QQ537+Z7ySL4w2BY9D/zGdzzHuSCDJJx8UkicpZoa0BrJlQgHB5iB5wT84YgSOGh2so5Yh1bmmaHQKEmyyEBpRjYUTcmLckOiZwE7Y8rRln2oYiRu+OS70uPhcOsYIJ2KlEesy17Whb9ppxLyxkBI+1J6dO+KqY/bAg5ccEHpelEE6/GLrTxKDdFahrVVtDvlyeE4bo7LkqEpCHh685ABcfXzyEBtxaNfLhOrink1bgAM+WAD48TFqsV1EiqhmdyEbOXQKWHrR4cjRA7D4N8cFLtEo4oQtT+MDj6NWOm38IFzx8Fylc6MMs0GE6eTv/fYkrPxya/C1CukHdUS818rW1I7isiP86w+cvt9gjBXUld58dN6kTyUVQJjePutvI+7S5w9ecgBWhLzbIKLSPnD3PrHjPSXFCAcNZIuxZJKPtIJmLzF6SY3U1o0GLbMJBK/d6+XwPfvhpcUN6cxzEF1AkyfnI+x+wwjz3lKN2Bmmoss7P3j2e0eDfz9Pfd2PMP54xj7SfKRrSNt/Lz9yJG56YYn/uEdwBnnHqdanNAmaoEkEaQXzfo89OnfAXp31128oVUdQBaNW0iBoFmt/ex2DOJPIZBlkpVZ67keTce+3gyfTDOndGf/6rtsl0hEO3jWGVRDbj4E9OhXCUJfzF2EjjhxuPDNcHSWSTK0Ups+3CNKNewVu/6TzHgLwCyXxt7Vx5dF7QAZ59Eo3ny33VpO5aSet/d86YNfokxBtS+zTpTr0eHDC8S4rJUY4QD1srlhvRO+cX58yFtd9fW9fLKO4BIXpSMrIAd0ie6/iojtAwXgdJ4Ccl4JeN3FSLrJwDnBUG5OG9dYy+GnN+4hBYU6Np4dbpNZHdSKbyrWDe3WWntclxM6V1V06nS+5Wsna2bdrx0LU1tQLUn7SwwgHuBvjE/cOdikUP0AxamWX6ip8Y+KQ1Bop94So4iPOAHaG+El9zwmiSiR+WqeOs9xfg8KapAFRQa0UFIAuiCSPyZlgFRYzKdCrpkhtS/h6Dn5u/VZhIp6q4Ozayb/OeuaB9xTjfk3YzXK8UF3YSqMEKaeXHGNz8HDL2fviqflPSY+JmhXdRkMFp1qWMnwAABy2Z39ccNBQ3PNmXd6DKenIgYjyo60kSfW0F3GJO89hzi+PRkuOMfG3z0uP1/ziKFRVEJat2QIgznuOf3N/PWc/vLz4CwzpLe9RA8HqxaLVGaf3H+KEIXLcVwoT8Zz3FDUnpqtk5BDmEahDHE8p8Zl/c+IQHDKyb+Copy1hRg4auEYOLb4AtIkpfADZqJV0aLLvzymLOHI4a9IQjAyIMRNGvneWoCVLOjrr3aUj+nWrxuEBa3n37VqNnp075iczFXPk0LtLR19IEy9BEYCLNZM8PChgOBcfak1rGhsxWfOkvcMmR8Z0MVa9LvQ5EogoI8Ggf19OjLSsMCMHqH9YYo/HuxhKW8MRDk5jJ44cfve14KVQRS46ZBjuebMuvx3nkQW9Gtnymjrccf7E0B6sIwx133PWjfR3vjocCz/dgK95JoMVeeBQ2NbI+Kt79EPd9BMjzzthr4EY3Gsn1K/bple4BISFz0gDMdheWjx4yQHY2tgSfWJMjHCA+oe1o7kwWshSrVQONDY7wsEZOegPMr3qkYLRL915DnGorCBUhjzxgs1Bb4ToDdmdNgN77IR/ffcg3/5iOYAVa4Tim2ldpL6YtG6mkHcWcxU6dahUXi8kDkatBPUPa7sQRqKppTxHDv+UxOCPQ6MzcqhwhEPyNMNCFKhSrEbQGSnpq5Wi3VGzII7AnXHZwXjgEr36EpZL1kZjoDST4IqVd7lhhAPUe+ziOs9Z2BwcknxjTpTPpIwbYukzd7V7/3FnDIsETeBKklZWVMS0ObQm9h7cEwftrrY2tkPYzOy28KSKGQUYyD4UeRKMWgnqBlJxaJiFzSHU2KeYXVqV++JDhuPoMTtjfv16AOmEUU5jmdBi+fM7wlD3PTt1qdgffdHUSsWaT+HZzvpxOunvNcg/y7kYr7IcRyVm5AD1nmxlBeHH9uzPcu1RplXJKioIw/p2yY+W0pgEl0tBrVQs+nevRseqCvz0OL2gZ6W6tawj+Tqk0YGJk0+ao04ZTtkn79EPBwwvTARNsqhWEn5+wihcfqQ/1lUxMSMHTQbYYQl6d9EPbFYM0m4kHCEYd+TwpzP2wY//NQ9AwSCtM7rxzQT2+NlnRacOlfj4N/I1GMIoleArmreSV61U5PtNOjJWqTcDe+wEAPja+EEY2rcLVm/cbuWdKGc9Lp28e/RJGWOEA6BVw0/fbzCqO1RE+GKnj2oR03bFa7K9deIGohNDihQmTsVHvHbsLt2x8NONCVLLjqzW9Q2CiPDdr+6OW19Zmm0+ZeVTp07U9yN7XwePCLfH3PftSb51NdoSRjhAT2VSUUGZLa4RhrLNwf540xISzsghVYN0SmV7+DsH4tP1xfOFV6FUjWcFAVOOH5W9cPAZpItjks7c5hAS5Tfo25usGGW3taL0xRPRcUS0mIhqiWiK5PhkIppDRM1EdLrkeHciqieim4V9L9tpzrX/9bf3VxPRw3Ze7xDR0Pi3p0ZWq0vFxzXDS+tK5/S01Esn7jUQo3buhksOTbg8I/QXVAlPi9G1ugp7DMhmicSkFN8gXRpDcRAH7d4Hlxw6LEE+8pyKcZfeV9erixWy5apj9ddm0c2rnIgcORBRJYBbABwNoB7AbCKawcyLhNNWwFrr+aqAZP4XwKuS/ecwc41n30UA1jHzCCI6E8DvAXwzqpxJyHIiiQ7Sih+zlUlLOPTpWo1ZV0xOJa1cCiOHYtkc4pIkamlrQFUIPRCxolx0Pu7trN+3LHmnDNVVlUozu9saKiOHSQBqmXkZMzcCeAjAqeIJzFzHzPMB+Jz/iWg/AAMAPKtYplMB3Gv/fhTAkVRs5+NWjCMUxqY03yEtiERvpdLFVsqa8i5dcnz3V3SDdLLrdebHlGsHpFioCIdBAFYK2/X2vkiIqALAnxA8orjbVin9UhAA+fyYuRnABgC+uedEdCkR1RBRTUNDg0pxWg2uSqn5NXSsqsAj3zkQ91wQvKhPMenXzXIJ/dlxo2LFrylzWRBIW21YiuXK6ks74VgsqhqV+n2VYzXPep7D9wDMZOZ6ybFzmHkvAIfa/87VSZiZb2fmCcw8oV+/tmEYSqtXPGlYb/To7I+JXwocl9CT99lFOcxzEOcduFthHeJ0ipc+5fiVp4gvGmyx889wuR9fXkW4uV1sb6ehfbpkn5kmKsJhFYAhwvZge58KBwK4jIjqAPwRwHlENB0AmHmV/XcTgAdgqa9c+RFRFYAeANYq5mcoYwozpPWv/c7k4Zh26ld86wkY2iZpqw8vPnQ4xu7SHSfvU1wX9CiOHD0A91+8Py46JL7xPitUhMNsACOJaBgRdQRwJoAZKokz8znMvCszD4WlWrqPmacQURUR9QUAIuoA4CQAC+zLZgA43/59OoAXuRgRvcoAZwnPAcL6v8eOGYDeXTri/IOGlqhU6ZGGQbrc6WC7/O7Ss+36vweR5UeatAUY0rsznrr8UPTpKl8DupQtzMEj+iZa4yQrIoWDrfe/DMAzAD4E8AgzLySiaUR0CgAQ0UQiqgdwBoDbiGhhRLLVAJ4hovkA5sIaLfzdPnYngD5EVAvgSgA+19m2ymWHj8A7Pz/SFeq6f/dOmPPLo8vWZVMH2WJGutcWtsuzv9CrS0fcfPZ43HXBxOiTM+CA4b0L6xxnyHe/as3gzdpB4IS9rJXkphw/Ch2rKtC/u7xxT4ooHBzX9v3sJUHbK0qT4Jh5JoCZnn1Thd+zYambwtK4B8A99u8tAPYLOG87LCHT7qioINeooa2RixEfx3uuo3Mu57FksWfPizx06YGZ5xHk1tmpKj2XcOe9f++wEQCsZ1qs5zpZcVGito6ZIW0oHjFcWb0yYIDdc+zbtTxjW7U3HI1vt+oq7NpHf/nMey6ciM4d/c1QsVWP5ToSLSVGOBiKRi6GK6uX8w4cir5dq3HiXgNTKpUhCU6TeszYnWNdf9ie/dMrTALKeSRaKoxwsHnmislY1rC51MVo0zgLB/UNMArK8MqRygoqO48TQ+t3MvjZ8Xqh2dsDRjjY7LlzN+y5c+s3+pYzPzhyJMbt2rPNByxrV2TU4y52mBSdDosOMy47OJOFwYqBEQ6GotGhsgJHjBoQ69p24s3cakl74JB3PGjltoC9B/csdRFiY4SDwWCITWtvvK85YXTZRBMoN4xwMBgMsXFUJlWVrXPF4UsmJw9F31ZpnW/UYDCUBYVlZNNN15kxbLSJpcMIB0NZ09q9YNo6aa4UKHLzWeNxwUFDsdegHqmma1DHqJUMrQLTgyxPHOGQ1uJSDkN6d8avTxmbapoGPczIwWAwxCY/cqg0Q7y2hhEOhlaBUS+VJ815m4N5QTocNXpAUQIkJsGolQytAqNWKk/yBmkjvbW44/wJpS5CJOUtukrEuCGtd+JKWyO7lb8MadBiRg5tFiMcJNx/8f6lLoLBpmsna3DbfSczUakcMcKh7WLUShK6VJvHUi58Y8IQ7Ghqwdn771bqohgktLARDm0V0woayprKCsIFB5ff+rrlwktXHYbVG7eXLP/CPAcjHNoaRjgYDK2YYX27YFjfLiXLv7nFjBzaKko2ByI6jogWE1EtEfnWdCaiyUQ0h4iaieh0yfHuRFRPRDfb252J6Cki+oiIFhLRdOHcC4iogYjm2v8uTnKDBoMhO3JGrdRmiRQORFQJ4BYAxwMYA+AsIhrjOW0FgAsAPBCQzP8CeNWz74/MPArAeAAHE9HxwrGHmXmc/e+O6NswGAyloDmXA2CEQ1tEZeQwCUAtMy9j5kYADwE4VTyBmeuYeT6AnPdiItoPwAAAzwrnb2Xml+zfjQDmABgc+y4MBkNJaLG/eCMc2h4qwmEQgJXCdr29LxIiqgDwJwBXhZzTE8DJAF4Qdn+diOYT0aNENCTgukuJqIaIahoaGlSKYzAYUqbFHjkYg3TbI+t5Dt8DMJOZ62UHiagKwIMAbmLmZfbu/wIYysx7A3gOwL2ya5n5dmaewMwT+vUzy04aDKWgOaPAe4bSo+KttAqA2HsfbO9T4UAAhxLR9wB0BdCRiDYzs2PUvh3AEma+wbmAmdcK198B4DrFvFLld1/by4QLNhgiyJnAe20WFeEwG8BIIhoGSyicCeBslcSZ+RznNxFdAGCCIxiI6DcAegBweSMR0UBm/szePAXAhyp5pc1Zk3YtRbYGQ6vCWQGuY2VliUtiSJtI4cDMzUR0GYBnAFQCuIuZFxLRNAA1zDyDiCYC+A+AXgBOJqJrmTkwGDsRDQZwDYCPAMwha0h6s+2ZdDkRnQKgGcCXsLygDAZDGfKLE0ejb9dqHDt2QKmLYkgZ4jYQ7nLChAlcU1NT6mIYDAZDq4KI3mNmaYhYE3jPYDAYDD6McDAYDAaDDyMcDAaDweDDCAeDwWAw+DDCwWAwGAw+jHAwGAwGgw8jHAwGg8HgwwgHg8FgMPhoE5PgiKgBwCcxL+8LYE2KxWkNmHtuH5h7bh8kuefdmFkaubRNCIckEFFN0AzBtoq55/aBuef2QVb3bNRKBoPBYPBhhIPBYDAYfBjhYK0p0d4w99w+MPfcPsjkntu9zcFgMBgMfszIwWAwGAw+jHAwGAwGg492LRyI6DgiWkxEtUQ0JfqK1gERDSGil4hoEREtJKIf2vt7E9FzRLTE/tvL3k9EdJP9HOYT0b6lvYN4EFElEb1PRE/a28OI6B37vh4moo72/mp7u9Y+PrSU5U4CEfUkokeJ6CMi+pCIDmzL75mIfmTX6QVE9CARdWqL75mI7iKiL4hogbBP+70S0fn2+UuI6HydMrRb4UBElQBuAXA8gDEAziKiMaUtVWo0A/gxM48BcACA79v3NgXAC8w8EsAL9jZgPYOR9r9LAfyt+EVOhR/Cveb47wFcz8wjAKwDcJG9/yIA6+z919vntVZuBDCLmUcB2AfW/bfJ90xEgwBcDmst+q/AWrb4TLTN93wPgOM8+7TeKxH1BvArAPsDmATgV45AUYKZ2+U/AAcCeEbYvhrA1aUuV0b3+gSAowEsBjDQ3jcQwGL7920AzhLOz5/XWv4BGGx/MEcAeBIAwZo1WuV937DWQz/Q/l1ln0elvocY99wDwHJv2dvqewYwCMBKAL3t9/YkgGPb6nsGMBTAgrjvFcBZAG4T9rvOi/rXbkcOKFQ0h3p7X5vCHkqPB/AOgAHM/Jl96HMAzqrwbeFZ3ADgpwBy9nYfAOuZudneFu8pf7/28Q32+a2NYQAaANxtq9PuIKIuaKPvmZlXAfgjgBUAPoP13t5D23/PDrrvNdH7bs/Coc1DRF0B/BvAFcy8UTzGVleiTfgxE9FJAL5g5vdKXZYiUwVgXwB/Y+bxALagoGoA0Obecy8Ap8ISirsA6AK/6qVdUIz32p6FwyoAQ4Ttwfa+NgERdYAlGO5n5sfs3auJaKB9fCCAL+z9rf1ZHAzgFCKqA/AQLNXSjQB6ElGVfY54T/n7tY/3ALC2mAVOiXoA9cz8jr39KCxh0Vbf81EAljNzAzM3AXgM1rtv6+/ZQfe9Jnrf7Vk4zAYw0vZ06AjLsDWjxGVKBSIiAHcC+JCZ/ywcmgHA8Vg4H5Ytwtl/nu31cACADcLwtexh5quZeTAzD4X1Hl9k5nMAvATgdPs07/06z+F0+/xW17tm5s8BrCSiPe1dRwJYhDb6nmGpkw4gos52HXfut02/ZwHd9/oMgGOIqJc96jrG3qdGqY0uJTb4nADgYwBLAVxT6vKkeF+HwBpyzgcw1/53Aix96wsAlgB4HkBv+3yC5bm1FMAHsLxBSn4fMe/9MABP2r+HA3gXQC2AfwGotvd3srdr7ePDS13uBPc7DkCN/a4fB9CrLb9nANcC+AjAAgD/AFDdFt8zgAdh2VWaYI0QL4rzXgF8277/WgAX6pTBhM8wGAwGg4/2rFYyGAwGQwBGOBgMBoPBhxEOBoPBYPBhhIPBYDAYfBjhYDAYDAYfRjgYDAaDwYcRDgaDwWDw8f8BuD3JlEplTHUAAAAASUVORK5CYII=", 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", 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", 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", 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Zzpitmhic/h//g62urU93EDINKUzHKX0dSTnMlXweuWmjvLe6RoxRkY8K8v99xEMf4rKnZ3mUYeXhOq7TP1Gg0WzlZPmmSvSe8DZWf6tn0ybdfkxdy5MYzaOJkkTn8qgjBl9mlnGQaWv26m34f/+an9XpSmseSS1PIrmuFOCheUQoO+u+KJ0XoVABsusiBhVbvmU3Pl7xrVLZMubRN0WLCQqIa57Ha1+k1it7z+XojovV3+7xHby5H5cz5ccrvs2ZiClLk9A8iGg0ES0nonIimiD4vZSIXrF+n0VEvR2/3WYdX05EoxzH11jbzc4jojLH8Y5ENJWIVlj/O+i4Bh0wMzZYIXlRO6m91f6hsQBQsSsjMPZUBztHg178cU9+hn/NXS8cYQddT2JmKzVPde6hCBUN+67qFqyyPo+w17pjb3V6gU13HjLCY4VkZ5iJtlKrXxDpmfjWfYozAHL5pl04408z8cSH3oEqObju6T9mfR2q7EbvMCeiQgCPATgbwEAAFxPRQFeyKwFsZ+Z+AB4G8IB17kAA4wAcAWA0gMet/GzOYObBzDzUcWwCgOnM3B/AdOt7g+DFz79G5f5Upx9lNDWpbB0G3jElUO1WLUJ1QT8g0/EFnSpbld1VtfhKcbazE3tDJBlE1xvldctymOcxZFjabBUy/1+8Mg+flIs1Er1agh3RpfcG1aa36/W+T35F1tczdu3PrAPnd7s37EgNFmUmItrvkltYhvXJqC6ToxsdmsfxAMqZeRUzVwN4GcBYV5qxAJ63Pr8KYDil3oCxAF5m5ipmXg2g3MrPD2dezwM4X8M1aGHWqkwDknc0Mz78qiJLBX3fihwJUmdV37kgk4/dKTmzVbkOGX7yzGyMDDnbGcjtvP7z5QZPLU3U0enq/GRycd6Tnftq0suLRMVeJiXILBP2Urc45rC4s5CaKyRZsMwEcxkN3I3tC/jwq3D7vfx5+gocddf76e8yXbuSGdOVOuz2LLrNfaroEB49AKxzfF9vHROmYeZaADsBdAo4lwG8T0RziegaR5puzGzvfbkJQDdRpYjoGiIqI6KyiopomwbJkv0w5R7sWws2Yvwzs/Hi5+qqq6o5RFbNzZrPIF2XDH7zC8oiRgC5R1s/f2Uervu/LwLrlD4WyWEe7mQGMOju93HjP8X1VMUeUV/3fwETN8PW1+e0Hu1bhspThIzP43f/UQ83rlPQTkW8tUDOZ6NKehVh1xgi7OZeKlp4HDRkh/nJzHwsUuawG4joVHcCTr0dwjvIzE8y81BmHtqlS5eYq5rC2bHJvrff7EjtwxFmO0pls5X0mkzq5hlnsl+9Grw7mny+jNv/vRBfrk0JHZEA/HyleAKj7pGZarSVneQ6a3a+cy5CFGQ7Gy1WDVceOu9p2ufho5BtqtynnG+NX4Y+eLVJXVecMVtl5xjWJdMUzFYbAPRyfO9pHROmIaIiAO0AbPU7l5nt/1sA/BsZc9ZmIupu5dUdwBYN16AFZ6NQfa5OO7asg0+16Ugv6BdK88iklIngke2D9tXU4R+z1uLSp1IhpUoRJkKHufzpboI0S2bGVsFidbo36JIdqOro6N3arc7+KrOfh3emMpfwxynLsr67R+T53DwrVX7Q76kEa7fuxXH3TZMeSIoGUsyMV+asTWS5dh3CYw6A/kTUh4hKkHKAT3almQxgvPX5QgAfWFrDZADjrGisPgD6A5hNRK2J6AAAIKLWAEYCWCTIazyANzRcgxayR6ayo/wUqypy/RtBTrioDvO6esZD7y9Pr4clmuAoXYYjnU4bcXrfbr+NmDwKFIfqhu/93Pdit2uxyKc/WY0h907DGk3zC7yQ7cDDyg6/03RpHjv2VmP7Xu912NJ1kSjusRnZkU5R5z+4z45yyc7BhJ2P+x7ag4FXytaiYlcV/iO5NbJoIPXOwk349WsL8edpK8JVWIHIwsPyYdwIYAqApQAmMfNiIppIROdZyZ4G0ImIygHcAitCipkXA5gEYAmA9wDcwMx1SPkxPiGi+QBmA3ibmd+z8rofwFlEtALACOt7gyB7+Qo57FOmLc1VoP720SoNtcrgbrQfr6jAIx+U43f/WZR1PKuDle2oItbFM51lgbBfMLX9PEQjs+DzKvfXoPeEt/HUx9n33zkg+GzVNhx55xR85HDKzlye+rx2217pssIgOzAJ7aOJqAnIMHji1PSy8flw/IpK9NJQwvqOVn+7B0PunYZJZdlL0wetFyZbnEhIVlpRYn4LpOqiSEcmzPwOgHdcx+5wfN4P4CKPc+8DcJ/r2CoAgzzSbwUwPGKVI8PMmFS2Dhcc0xMlRSkZ7OzYgl6IDTv2YdPOfVi0YWf4Oqg6zF2mYFu9dy8vbld9/rod6NFBzkGqOmtW/gWxwi7tvTQEJ3oVF3aS4NbdqRfvxc+/xlWn9BXmN8taKHLOmm049bCUT00memjaks0YMVAY4yGNrPzUYraK0eeRydOn/JgmnyYhr+xBhA0RsK+6LseMabcbncuoJHF9WoRHc+StBRvx69cWYv32fbh15AAArhcr4OGddP8H0mXtqapFi+LCnMlhsc3zALDkm0qMfexTjDuuV2D61DnOvINfAtlOwb31qqzmsWt/Df743rKc4zKjSK+ysn1aqc+q9vSrXihD2W9HoHObUqXzvOrhny50EZ7E4aSN6vMIImqX7FcFlQ6fGfjh3z7Drv3Z5k67Da3YEn7+U6Y+ydGQo60aNLZ66NzNyxnkEabNZxx/2U3giDun4NevBUcwBSHvMGds3ZO6rvnr5TQjP81j8Tc7c2bRynYKNfXZnbRsx/nAe8vwn3m5IZcyZ9s79bltys6i3ea07HT+pUSd7yHv8whrtgr3WzqNYnkvzVqLB99fHpju5dlrURvi3kkHoNgDgpzjauWt/nYPPlgmjqxbKLA0PDJ9BU5+4APlaLw8xwEY4aETp0nFr8F5rXb6pMDHYTfoV+fmbump2jk8NPWrrJmzXmyurEprOV4v62crt6LasdWpX03OeeQT3P5vl19Fsup2zH5hukOXO29/TXbC17+wl9sIPtdOU8eM+nrGQkuAOu93XbqjcUbJyb3NUffEkH3uYbWE7FDt7N/iMFv9a+56/OUD8X7cztImvL4Qp/1xZmxrOnnlqlraGX+aiSueK/Nd08rN+u3qIcl+JLHWnBEekck0ERaYNUT84In/Co+LOhXfUaBE7dz4zbq1ix/x0IcosobfIqfcog07cfHfP8f/vLMUALB9TzU+WaE2EVO2E6pxLTUheilk+uL0dUsUa19zXT3wxIcr8b1HP8EXa7dnjfjr01Fguedz+r+4sKgDxnyarRJ3bruK27BjH95ZtBHbY3AIe12aruVTfm+9L4H1kMxv0YZKvLNwY9axJLURIzw04nxZP1u1VXlJ6CJBT+TXkMK0aVEZIuyRfq1gqG9HctjLp/zk2dn49WsL0797bnQXIhrNHaobtUOU6fzsMuuZ0wENG3fszxIGdj7OCXvS5o6IL7jszGLd8zz2Vddpm+gYhZ+9PA/H3DM1lAnLj7hH65X75ZZaqa6tl15p9/p/6Fm1IAxGeGjEaSZ4YuZKnPGnmUrni8wevmGTSrmnkDWZpOdVSHRUX23ObuheRdQ48pIdzdn+AdsPEbU/lDm9Lq15ZFLf8M8vsrS2DdbKAML7GVRIxGuoqauXun9hzTte83xk/BKydD1ALmBA1KHbz6VaUnjYIdTunGUOAclELjl5dEY5Rjz0oXDCqSxJ1NkID41EHellIngyx/w1D/XyigrlhIdttqoRdEBhVWOno1i2X3NHW8les7uKmQmQwefb2lZ9PeNdx+KDizZUpj/bAtOpyGVCdf3LUJokL6hvdV29VOeg22xVKeEvk6W4UK7r8btOp88tiLlfb8PwB2f6LrTo7fNIWHpYuCehNjSM8NBI1DBG0YuiewRRWCD3yO1kItNA2DplRRnJRlvVZZutRKc5ndZrt+7Fox94z66VKda21MksJOnUPGRlqsogQ9Skqmvr5a4jbLSVx/Go8xBq6+ox8c0lqNhVpcWPUKUgPO59eylWVuzB0o3e4bB2ldw1k1FwRJcT1f8Q5hYlueWumeehkagjPeGMaJ9uIkxxhY4W7Xe+3Sn6LfVAlFpBN3ehN3EDzo7OUosYsn0LQZ3OT56bjVUVe3BK/87C32VeSFvzkFnmQmi14uz/blQ6daHmUStntgrbHL18U/Ihr+LjHyzbgmc+XY3NlftDrdbspqpGXnjIhRiLE+Vr6fMopSaxZqLRPDQSdTSlrHmEGZkQ8PjMcqH6TlmRY6n/fs7ZemYM+O17OSNAr07GaaMecu80qa1zbc2npq4et72+ULjoorO8vVXiBeHIJ1rLxn5+dmch8zyzNA9Ne4s7cXcCxYWEqtp6qc5B9yZLUbEHArX1cmY3wP8aVBb/kxEAXknyvfS5TeX+Gjw+UxzS7Oa1L9bjn7PWxlofIzw0EnX1TtUmGsYW+/bCjfjDe8vxpylfSeUtmtBml7rbI3rE6y44HeZ19Ywpi4P3mLZH/19v3YuXZq8N1AYC74nPz7NWpxaitDsLGTOkeJKg/zlqZqvstC2KCi2zlYTDPGSf5zwtlOkkYKHKAiItfgQVs5X9LP18Hl7PJV/bvboF592Tl+AP7wUELTju/StzjPBoPlhtxfnuRZ3t68Zex2pPgDMurXn49EA794kdqF5C1C2IZEStKFTYD7venovc+Zw77snPsblyf7qzkIlME4XqBj2WKCaF0uJC1Naz1GTJfO33kB2tlflS77iv0pqHz29qmkfq/2VPz05PGJUtq07iZicxv8LrffOiU4QlcGQwwqMBoezzCNE3ZC0jon561nmqjVklOsamRsJkIHRWKqR1Mm/dDkyxIqxkOgS/fVi8TC5RNI9SaxHOMPfSiSiooLau3lfghOkghcu9kbyW7XerVHweFbsyJtIZyyvE+XqZrSSEsLgNRrdEMDMefH851m3bKyXEnNdQIhnRFhbjMNdI5AXYVH0eocqw7PkBr6+4LgwiSp8pO+nJJsyaTjL2Zpml8DNagX9+176Y2do1JRj804vMVmVrtuEsn5VzVXwR7s68ZUlqD/H9ETb72V9Thz+9n2u27Hf7uzjioLauS47ox3N+VtDoZFAxW327OzMj3WuerKfDPI879q2s2IO/fFCOaUu3SM+NsSktjld4GM1DA7v212iJyVYYDAEA3pPwGXjlF9R/iV6kJRsrs76rmkVyRssSnYgtcNwrCjtRuW8qwlhmMr6oIwzah0XltrnTtrA6BJVRN+B//5ws/qYyss/DSZZgd5hlkzZbOSkgwt7q3HO96hR2Ivu0pdFm4zNzWuBWC6IahTges62lxoXRPDRw1F3vo01pEQ7u2CpSPsWCCXy3vb5QkDI8vh2Xc3JiBC3ISyaEcTzaAqeQCHUeXYn9gi3asBM799ZkHctJq1wDf7L7ZLkOWsls5XpgLYpSmse+GrWOMytEO/RN8L8+ZkblvlrXMcdn6+6nqpKsw9xJAZHw/ukIrXby3H/XhDovU272HVeN+iqJWXgYzUMTu6tqIzvNxhzVHUB25/vm/Nxlxddt2xt6m8l0GGpAOtHvka0NId7BahnNw8r33L98kk6f88Jbp6uYIKQGeo6Z78s2VQaktusgXYUcgduqNDXe212l5m9y3r9gk6X496Dn/7ePVmHQxPfxzc7MCrGiFXpVHOZ+VNXUhwpH9boOu0run/2CNuKcA+LU7IlIuazCmL34WoQHEY0mouVEVE5EEwS/lxLRK9bvs4iot+O326zjy4lolHWsFxHNIKIlRLSYiH7mSH8XEW0gonnW3xgd1xAWpynG/axUn52sg+2aF+fi4Wn+obaeiByYAkQNVdZWHRSqmU4nkVda8/ARHqK6it6zC5/4L8579BOJUuUpIMKLn3+NPre9k7Osttf9jeIwb1Wc0jzcGwoF4bx/QfKTPT4HYYdeb9yRcU47q2+XG+xJclbAO+XGnfvxm3+ra+ZeGgt7DKxEZqv3rKCKOKN4ncKjfMvunJ0JRTjfkrhdNZGFBxEVAngMwNkABgK4mIgGupJdCWA7M/cD8DCAB6xzBwIYB+AIAKMBPG7lVwvgVmYeCGAYgBtceT7MzIOtv+uVuvQAACAASURBVKztb5PGL+TVGe3w6tz1WPJNpf/aOpItMaytF8iMBAN9HjE4790d4b7qusBteNMLI/pIGlG1RB102dfbsX2vvvWZgNTLetfkxUrnKE0SdHVctsNcdcVm5/1z3xtmxr1vLRHWb9f+GulAh/Q8DkevIgzbJfm27pcq7KZaIm3eryyRtvrYjHIs2rATOxQjDlVgzq7Txp3Bk2qdxD0zXofP43gA5da+4yCilwGMBbDEkWYsgLusz68CeJRS+v5YAC8zcxWA1URUDuB4Zv4MwEYAYOZdRLQUQA9Xng0CPzu+02H1y3/NBwDPZTMA+YcdRR3NrN+jbrga88jH+OuPj0XLEv9m46VBuXO8z9rfYNHdo9CmNDvPHXurQaC05lHkE3bInNsZ5Wo58ajwjJSvShQ8oMOG7m5fLSzN4+431V4F5/1jV5+7ced+PPXJauF5c9Zsx/X/+AJ/v3xoYBn2M/i0fGvmmNNsZf0vcETsRSHqjoxuvB5LjcBsVVNXj3P/oleLdRN1cmKD1zyQ6tTXOb6vt44J0zBzLYCdADrJnGuZuI4BMMtx+EYiWkBEzxBRB1GliOgaIiojorKKCrWNilRwjkrcHVSp9aI7+Wzl1pxj6bwCHvYWK1ZdNnJGXIbkiM8j2buLNgWOGr3NVuLzagRmhMETp2LQxPeVR702SS3NUc+MYsnFJm1klmVJ5+8O1RW0KRmyzVZq92bqklTUUFCrCzIfOrd5lV+exPs31aCBIH77n4XCdiOaa5TEBMx6ZmVtn7ICI+KtY4N2mBNRGwCvAfg5M9veyCcAHApgMFLayYOic5n5SWYeysxDu3TpElsdnaMDd6fZQhBnLeNn8Boll2/ejZq6+ojCw7siWTPbPc6P1B49zvVTpKos4RG08Y+749LxbrdtWRyciIFixaiWaxxzSYJwX5dXBM1/V36L2Wu2eebj1FZzFrJ0T270eFBBCq/Ir1ybtYdLJh95s5V3umWbvFfIDcO3u6uFAqlKcCwR4RGxjLjNVjqExwYAvRzfe1rHhGmIqAhAOwBb/c4lomKkBMc/mPl1OwEzb2bmOmauB/B3pMxmecOvEdlhlbLYz9pr/sYlT83ChX/9LJLwyJit/PnCY591mQbpVbswjdk2WwW9R+7noOPFkYmTZ7Dn7ow61m9yX5dXnpf8fZbwuI2Kwzwsons+aOL76c+6zVazV3sLy7CImo1o0ymRKUs3qs9p594aTHb4cxqD2WoOgP5E1IeISpBygE92pZkMYLz1+UIAH3Bq6DEZwDgrGqsPgP4AZlv+kKcBLGXmh5wZEVF3x9cLACzScA2h8eukWiiaGGQ6vPnrdig7zrKRa1Fz1oiFB0vk4LWulFdj9vNH2GaroJGe+9bl+DxCyFuZkV89y29sFIacKoTsELJCdd2ah+v+ezXDIL+R13nVtfXYU1WbvdmZBrNVHIjeQdGEzCRW2q2rZ6UByM0vf4mPHLtdNniHOTPXEtGNAKYAKATwDDMvJqKJAMqYeTJSguBFyyG+DSkBAyvdJKQc4bUAbmDmOiI6GcBlABYS0TyrqN9YkVV/IKLBSDW/NQCujXoNUciKxXb9Zo9cZVV02YddsUt9e8oCSnVEdnWZOTfqRiIfdoeAKBDGBmtrHkHOQ/fv89ftUC7LyUHtWkg5LJnFkzt1EeYZibCFx6INO3McvW7B6g45lsWr/f746VmYvXob7j3/SLtELWtbxYFw8y2R5qHZWS9C9X2xt0bOnK+zNrlomWFudervuI7d4fi8H8BFHufeB+A+17FP4GH9YObLotZXJ36DU1vzkFUf41QzCwsI9XWc1SBzGqdE+fX14c0xfte3YP0O3DV5MSaOPRJH9miXPi67PPr0iEtBOOnftQ36dW2DOT4+BJt65lg1jxyzlUePMOSQDpjrYWoEMqG6zn3YdTDkkEy8itcTss1LGbOV1ipoxWvzLZljupGNtqqv56zVndPHG4HPo1njZ9qwR3uyzrU4oyPsCX4zlqc6D0buyCRbKIjrwgheDtx7RVvv63v9iw34Yu2OHDu2/QIF3cOfvTzP93eV/qqACERyq6k+8+lqfLMj3EjdjzlrtmFfde56Rl5VOqST/9I4tilR9yJ/oiXXg9KqOcyTpV5glxXNq3K3jTjqWc9y2sMqjzk/jcHn0azJGh249H/7F1nhMW3pFqzYrDeCxMY9O5w5t3Flh1WK80mZvgKuJ2D5h9zjjG17qq16Zv8m04HrhijV2dZJ2LVXVezBHsEie0D4l3fDjn246K+fYcLrC6SXMgl6JH7L0pRv2S1VhshvVC/RZty/e84DYsaSbyr9teOYEbVtkZaRhNlKVtCPeOhD8flG82jYOB+ws+Pr1LoEzIwde6uVJvvc8M8vdFYvjShCy9Y0pi/bguWbdmU1tunLtgjzSflK/MtSjbZiBrbvTQkPt7DIx3LYRIQCosiTtMKGc9o7NC7buCunDioTD1tZs9F7tG8JMDBj+RbhHiyXPuUfqWUjeq7OUr8N8MVlNoMSC7EpizdhzCMfZ0UMJY288EjIYR6hmGY9z6OhsbuqNr0Tn43z5XaO7g/p1Aofr/gWgydOxec+EwPdxBU/7pYdjOyXYtT/fiTpMA/fKL0ujYG05uF2TurSPFSirQip+xW17LAjP6f5MNdsJc5T1G6KCwvQs0NLDDmkAyp2VeGnz87B0x4zyUNj1Wfy/G+wK2BbAruO5LEw4lebd1v/49G+ZZAN1fXivUUbtdUlquYQdzSxER4KHHnnlHSkiv1cne3Ka1Oiq14oyxwPihqKSXiINI9bJs3P+i7TVhkR9sb21DwY2y3hUVObncae3ZwkBQUpARL1WfidLx2B58rD1iZkyqqvZ8sEF23zKD/sUj9b+W1g2tq08BAHXYiEddLRVif8z/ScY7JLv5dv2Y3r/k+f5UBFeEwTvCfGbNXAsO3D9mNZ6tggyfmsvlwbLlQ0qqnEC7fwCK89BMeee83z8HJq13NmpzfVPcvjgGCZrSIID2b2Nbld8dwcqQ3E3HW46cz+wnSijqKOOeX8h561vUTPdcH6nfhX2TpB6lxsTbeASDgAeWR6uG0GtOO4zHYti6WFxz4P31dYVJqfc4Aa5vwwGOERFuE6PtGfVlx9Z47DPGQ+zrkiXqh2U1W1dWnTgIqJQK0M+XwLyFsAetG3c+us73X17DsQmLG8Ah8uF4fNrtySip4hyr3XLT01j9xjtfVsmeDU94JQ4YH3lkHmqdvCI7W2lWy0VfI+LyddDyhNJCxXhOokQTcfrajAVc/Pwe+tBUh1Y3YSDImoA9Uh6Sv3x7PEc5QlTZw4t8b0QnU2t3N07TZb6eKNeQpOWCtUVwX3mlO19cEhzW1bil8/O2iipq5eYWFIsaN3X00doMF/40eB5JRxO+RVJBS9SNps5SbsboU6qGfGOY/Ir9zr1lKra+sxbemWnBWrdWE0j5CIXlYdozvVTX5kkd3IKQiWCNX9avNujPnzxwDk/AbOjq1hmK3UJ7K518EK0jyA4CUuVlbsweXPzJYq3+s+b66s0mKyeuGzNZ6/yQ5M/v5xyllfUBCvJiTLIxcfE5imc5uSBGoiRjWiy0tDKlVcY08WIzwk2enaREj0rsq8D+kNcxKeZZuzanjId7eeg0fUALDE8gXd81bwvhNZmkcC8fNBFJC6sHXP8K1jDhSc7si9KPiVpaOt/XXmSk9tTPleSWxDu3brXrwyZ22sRqvzBh0UmEZ1fTpZbj6zX2Aa1fbh9e6UClb31oERHpI4VwcFxDZbezR1xEFtA/NTtalHxb2BVFhb6n9XbsWt/5ofnBCpaJ/X5q4PTOccgVfHZLZSgUKYrdz3V2aCoc79KPyEh46m5rUUPJC7plIQMlrHBY9/il+/tlBaQ/mLhBYhjaNIXRq7G5n3X9UK4WViK4lp+RwjPAKo2FWFZZsqc46L2vSyTbtwSv/OePvmUwLzTV7zSH5BIVk7e10DM1uFcZi7TTff7g5evNIpPJgZf5m+AlslzhPhZyLTYbYKWr9rqxUtJ4OMYN1qhW6vqpDbbrd7uxbS5ceF7ra7bY9aW0ha8zAO8wDO+NNMYUil14jo4xXB8e6A/UInN8p2j4yTWFK6XrByrwjn3ggNwWyVCtVVO8ctPM56+KPAc/Y7lvqevXobHpz6Feav99/T3Qu/sGDFjQ6FBMlSlUAP3eHoj11ybGyLU8pq6MyMCx7/r9aybQEqi6fwiMnnYYRHAF6x+FGbf8JWq5zO7f0EJt/V1su9ek7NY9mmXdixV+2l0U1tfb2yuSJMNJvTpm07R/dWhwuY8Nfyoje2rzbvTs8AF6ESzKV74KJbqXYuNCgr51S3SZBpXtuUhYe4sn4mxygYs1VIokaLJC084rLd+lFXJ7c2j7MzWVWxJ2e/ibi55azDsr5/sXaHcncre3+P7plZbv6PU5Zj8TcpTSPqfIZ5PvuXJPHoVXb1023esWfR5xPdW+IC6sLDC5kdMcNghEdIomreSXfmOkwXqtTW10sJWVvz6NmhJYDwmxGF5ebhubO2VX0eXlvRunHH3Ntx/PZt+q/COmiyNLT9M16a7T8jfe02/+f/ixGH4ZiD26e/E5GyX+f/jRqglD4JBnbPDrTZrkkDN6G6DYyos8mTFh5un0cS1Mmarax72aFV/mLq3ag+H9mQzrhMCH7obGtEwG1nH64tPxGVgpV/nfxsRH8c1L5lpk6IT/NIajpKzw4t8bfLhmQdWxcgRGVp0JoHEY0mouVEVE5EEwS/lxLRK9bvs4iot+O326zjy4loVFCe1l7ps6zjr1j7pseCXwhimAm7HVtnqpp0V550aDCQEgoyQrbOMmO01BxT77zfqqjeLq9lQ9zEFTbph07h0bqkCEUxX4NMdZ2DoTBtO9/Lo7g1pV+PPhy9Ovpv6BWWopi2SY7cCoioEMBjAM4GMBDAxUQ00JXsSgDbmbkfgIcBPGCdOxCp/cyPADAawONEVBiQ5wMAHrby2m7lHQvbfMIPFyhGxUTpyLx46eph0ml1LU+iQq2kz8N29A3t3SEgpRq2GSwMqrdLVvB5aR5+t8k+Z9K1J6pVykLnuGF3VS1i3LIdgNzAytme42zaJ/TpFF/mDuK0RMQViaYj1+MBlDPzKmauBvAygLGuNGMBPG99fhXAcEoNF8YCeJmZq5h5NYByKz9hntY5Z1p5wMrzfA3XIMTrRV9VsRvTFPfMLiB9DjAblc4xH3bvunq5UF3b5zG4V3uldXiGH97V9/dT+neWzsuN6sssrXl4CQ+f+2T7U9q3KlaqU1zEPWdIRpNwJonTYS7yh8VBnLdU1h+nig7h0QOA0wO23jomTMPMtQB2Aujkc67X8U4Adlh5eJUFACCia4iojIjKKirEq5cG4WUrDOfI0rOqbVaOKhsc5cFsJRuqa4eZFhaQ1DLlNoN7tce5R3f3/P2Wswbg0wlnSueXheLtkvZ5eIwC/e5TPvxVfsTdlmTm+kQ3W2V/v2hIT3E5BYTiuFUt6L2nQw/J1uAbrNmqocLMTzLzUGYe2qVLl1B5eM3MfGjqV8p5xSH8VRpcProf2W00bZ+Hyoh22i2n4YYz+uHRS471TFNYQKktWEOgqnl4bdLkJozD3K5KQxEhcWuxVTUSwsNRiSj7lXRuU4IrTuqDMT6DkDhwNy+d9/SFK4/P+l4YU6iljkmCGwD0cnzvaR0TpVlPREUA2gHYGnCu6PhWAO2JqMjSPkRlacMrxO3TcvVwStWBRVEBxbqMNpDq8PZq3sDGyb+/lHs09jwPlRF2v65tQtVJlkUb1Hxa0j4PgebBzL6qRz78VX7ErQnJ7HpYkOXzUF+LzKbst2cBAGYs2+KZJq7VILq3a4GNO/cD0OfzKCksQKuS7G69uAGbreYA6G9FQZUg5QCf7EozGcB46/OFAD7glJF3MoBxVjRWHwD9Acz2ytM6Z4aVB6w839BwDUJ0hripjoxuG/Md77xCjERFbfOqk/so1UmVZyT3y7Z9HiLb7FE92uXEvyfBum17ldJH8Xm8NHudb1SPqvBwLyOuO9zU7ujiei5SmkeW2Up9cOa+JfnYdOqz24anP+uWx3ecm4lZimvwEbl3tDSAGwFMAbAUwCRmXkxEE4noPCvZ0wA6EVE5gFsATLDOXQxgEoAlAN4DcAMz13nlaeX1awC3WHl1svKOBZ3CQ3mtJJ/0i+4ahUV3j1LzeQhETdy2a9k1jGos4SEyW6X2u04e1fWX2raQU+JFwmPW6q2+HbzdWcs+rrifq519XM9FZjfJbLOV9/Wec5ScOSrf24vojra64uQ+OMhaLDIun4eWta2Y+R0A77iO3eH4vB/ARR7n3gfgPpk8reOrkIrGih2d8ezuFzrICee1/M8Tlx6L1lZE0m6FJZtFbTNuP6xomfDvDToIb87P3tWvzuosRCMkktylTjcyK786aVMqFwnl5fPw34/Dvi9yD8x9G3U/Z7s+fhFiJ/TpiNvGfAfnP/apcv4y2746O9sC8hYgD/5wEN5euFG5DlkkYTWMoQz76RTF5PNosg7zhob7BQ6a9+G1SmrfLhlbv1q0Ve6xAiLcM/YI+Uw0IHJg276dsKOvOISgqrvpAFnNQ+jz8F8rTdXsEPfqBXZ9/Op87Wl9MbhXe8/f/ZDZH6TzAY73x8ds5RUF594IKmnNw13dqCtWeGaMBmy2MsghatzH+UyK83KWh1VBRVpKAQGXndgbFx9/cKg8wyBS5uocobpu4h703WotivjcT4/Dwz8alKmT4svcRlJ4eJlC/YIjGprwSJutJExtcXH1KX0jldW7c+us76pdd1/r/GF9OyqXLSLqWpGigA37+ZhQ3UaCe1LRyIHdAIjVar+dwk4fIA4vdo5cVZqEaJ8I25TmtxeEbkRhg+l5HmE1jwj1ucl6XqcP6IqRAw9MH1e9J7KTG8OYrVSFh8xtPL63XKcn2i7V7qx1akuqFBcWpCPuCNEHGaojf/sef09iK1sZou5xItqV0g4CaMiTBJs0/9/ph0qnvfbUvjnLe9uNy/38igoKPJ15b998Mr7jEcmStdRAxDaRcXwmJzxEDXnjzpSZQmSaTXJ+nLPDU32ZW0iuXBpGeKQ9HpL3wj0SF12K7O5yt4zMXX024/PwPi+JiY324wraNlhmpQHVNyCMtjOoZztc6RHhqM1sJcD4PBoBItOD3Vm6HeYFBYQbz+yHB35wVM45fg3T6WiPur2oTCegG9GI9P8+X+v5GyH3xTr1sGytTFd0kfO+X3iseMaxF15C4bBu2fNRSgrFQsZPeKg+HpnbESWS0B6/+NXLHTnnpUlHwX5eqaK8L/p357qX2svF7x0Q5Sz77lxxUkZYvHHjyWhhCW33M4pjA027bsbnkSdUOtZaQQsoSAuP7OOFBalO7weCTspXeDhe+qh9pt2mgi7xQo+lG8KV6V1pmX0H3v/FqXjStXS1Lpwv2W985tmI8Iqe++HQXlnfvYSMzBpgso9bJl2UPR4o3XHKm638nvvSiaMj1SPoPZDrO8OZrYLO6thaLgrP/fxP7hd+XTabdLSV8XnkBxWTjkjzsNV39+NLHxe0fL8IYZ3mANnRk2wkkQx+K+eKOlb3/el2QIucCJrHLjlGS92cnYzq4n9eYd3uTtRLePg5zOMwaciarURkfB7BaWz8NCvRBMszAxa9BJzmPH+zlYxmekALtUUn09cX8GzcPj6v5Lbw+PO4wfj5iP74++VD8fGvzpCuz/mDvX0vcZkQjfDQiGhv5kKH2er7x/TIPS7IR9TYfzzsYHyne9usqApdTUKnz6Nb21LfF9lvrSmRKcWdFQla7Ogj9axLFMfkOrePx0tDkXHQ66yfDrOVn7bkvu4gp60z0g0ABvUMDvO1++Ugh7lM5/ndQzvh8AMPEP4mDHOXMN0BwfO5bOx7OXZwD/x8xGFoWVKYs7+Hn++mf7fcusdtjjbCIwiFB1Ajirez2k4BAQ/9aHD6cKGHOQsQN/ZRRxyId392StaIOGpnQrK6twJv3nQyZtx6uufvfvZXofBwJU/Qf64Ftwbj1ZF5jcyvFwRsXH2K2OnqhajIKJtSkYTG6n7OB7Zrgccv9V7Esn3L7HlPMoqf7fMLeg9knNtEhPN8Ru9eZQPAkEO8tWnZSCcZn4ffbHnx87QeUEwvjREeEbnutMzLLeoA0ktLuJ6gXycqauzC5UWka+lPkOwgEGb88nQ8f0XwxP4CIt9r83uPZezwQR3FH35wdGAeSeIWFl732mtC+69G5275etvZav4YEZsq94c+V6YzttOc0CcTEjzG0fl999DsTZZyVpmV6HSdSfzahewYS2WknvYXMvCCz3tR6CGk3fWV0TxlA2ls7j3/KPTs0DK27Z2N8Agg6JFOOPtw/OXilM1dZLfO2GWzjzvNWTnnSDb2qFYM+3QZm3qfzq1zNp968KJBOekKiDwddD3at/Q1IYheALfQDOpTRh1xoH+ChHELUq9b7fcM3L8EdaxnWXOL/Mq84Yzc+RteZhs3dvFOs9Ud5w7EfRccmf5uX7e934r7sT95+VBXnvIOdhv73amrZ9+BVNTNq/zWhWPm9HJBItyah9dTdk9a9KiIJyWCgdfoIw/EJ78+s0HvJNikkelY7QYijLbycIz7vRyikbvILxE1VNfOUXZFWHdpPxBEYRHE9e/dqRUm33iSp1ZSWlQgt4NcwDWLfCJRGCCwJavgFqSi57h2217fUS9LWh9uHt4fZb8dgQkOzcTrlh7dsz2ecnXgssvc2wMAp/C44uQ+WVqGu79yX597EJErPILrkRn9s/A6H7P2eonDYSwbqRh0T08f0AU/Pak3ju8TPGlTRvNI0qxrhIcG7Al9o4/MHfXaz9v9UFXNVnFOAp8wWs4MImuuEE1KOqJHO3RqU+o5CvR04Lp9HgFV0NlRLL57FCbfdFKkPHJm1DMw2qUdzVu3Ax/47Cdh43dpJ/TpiFvOOgyd25RKx/W7Hd6yPjQZn0e6rXjk6b4t7u8y15COFvT4/RxL64ljmoM7UvHZnxyXFczy/WN6YOFdI9PLmNjYvgn7/3M/PR53fk9ufTm/ywizyVhUjPAIQMYO2rtza3x179m44BjBSNx2mLvutJ8jTTQhVGgT1WS2ateqGL07tfJO598PZKct8OjArep7CaBKj6Va3KmDY/r19RStS4tQWlSI/7kgdyKnLCKfx18F81SWbKz0zKOP1QH5+YTcrcNe8NLvfrjPkb1zGbOVd5qgzt9dL7dGqbKPeX09+2qkcUTRubM84/CuOMT5DlEq/Nd9ndeddiiuO+1QXHbiIcpl+k0Uj8s05YcRHgH4yY5/Xn1C+rOX5PdymPu91GLNQ2C2ivhOOHP0e8EyZhO50WChwHdh276jagZBddCxEsNIl8/gkhO8F44c1Kt9et8EYX1c1Q3j8/jLJcfg2Z8chwN9ynEzytKC/e6We0AivfxJ+qIklpH3uK5coZqdTirayqF5+NU9jhnWFKD12Lg17ZYlhZhw9uHSe95nlenzNPOx26S+2V/NkG5tg19m+5Haz/aOcwdi4ltLtJitdDYXmbykNA+IG/LZVqSNaueeE6obs9lq9e/HKI1U37hBzazlNTfCrxNq26IYZ0hMmnMis4GUu03Jax62z8M7TaDmERBIYJ9/Yt9O+GyVeNtnkePeL11YnPfQ3rrZnq/UybG1gqjd6OzT/Z5llNDrsEQqkYg6EtFUIlph/RcGPBPReCvNCiIa7zg+hIgWElE5ET1C1t0noj8S0TIiWkBE/yai9tbx3kS0j4jmWX9/jVJ/GcJOtDmqRzsAjpfEevKdrC1C/V4uUQco1jx0tkyfnxTMVkGhukFmJWfETqpabvNGcPlRiHsXPs/mFNWn5TrfeR+8Lil3tC937U5HtRe2WXaQtaeHzOKETlSCJ4LeUXdeXsuoBwXHvH3zyemIwytP7oPHLjkWYwPmhujUCPzuSVxLkPgRVVxNADCdmfsDmG59z4KIOgK4E8AJSO0AeKdDyDwB4Gqk9i7vD8Be5GYqgCOZ+WgAXwG4zZHlSmYebP1dF7H+kfBra5OuPRFlvx2RCdW1/ttCwHcuhOCpxLFEBXl89kIufDJX+DlHZ0GawSWuvUWIsu9zUB2ihmXGjf0c7z0/W0jKrG2lQnrMAvJZEiP7u1fnNPOXp2PGL0935B2sedh5Hd2zPRbfPSpwFYCgaCwR6VneLG+2Wv37MXjp6mGBeYtwDmSKCgnnHN1dywRFP5xLAxUQcPHxvXI2sgK8N72Kk6jCYyyA563PzwM4X5BmFICpzLyNmbcjJRhGE1F3AG2Z+XNOvVEv2Ocz8/vWPuYA8DkAfSvzKRJ26Y6WJYXo3KY0/d1uv90OSJm6DvMJARVrHrnpnKlm3z4c0245TamOzixlBUMQBUQoKMhea8g5kTKocw96GWNWDGLHfu7HHpytpOseGqTvo8/9cg9IvO5t786t0057wBlplH1+x9a57R2A7zwIG7fwdCnsQpz7ivi1G/dkQlXtMj0AdOYjuLGisNyo7fWdm09Jfy4pLMDvv380Hrk4dy23ttbaXEm+H1F9Ht2Y2d4geBOAboI0PQCsc3xfbx3rYX12H3dzBYBXHN/7ENGXACoB/JaZPw5Zdyn8B4TBr7ydwm6w3+3XGS9fMwzH+WzGE8Zh3vWAFgCHnzVs53Xu0d3x1gLxns8yDnM7n6ICQk0d4/ADD8BVistpePHAD46SevEnXXsi2rVUW+guLuzqjhzYLWdinBN7M5+7vjcQd725JHK5BR6y46Yz+6UFgbtJBd3Znh1a4vzBPdLX1KF1SVaUXMcA+78fOZFfjjK8IIfw8CPs6N/tR3BmIxpU3v/9o0AAJs//Jn0sqg/Oub6VV1BOn86tYwlHDiJQ8yCiaUS0SPA31pnO0h60DqCI6HYAtQD+YR3aCOBgZj4GwC0A/klEwl2TiOgaIiojorKKigqdhd8GZQAAF9hJREFU1VLCbtfOhzusbyflJTzEmofbm6xWt2yzVerb9afnzjy208lN3Eolsq+vqFB9pOfcr8N56iDJPbGP79MRAyRnS8dN5vn73wM73Y+HHYI195+jXg7cWoTYYX7ryAH4vrUNQO5o37+On/z6TPxy1ABs3VMNQLzIpS20vdrKmzeejDu/l7u/Ro4WZLW6VsWFnotpXj4sFe468KC2/jPMJdufWwa5/QhBg6fWpUU5e83oDB33CtX2miQZN4HCg5lHMPORgr83AGy2zE+w/otmOm0A4NzUoKd1bAOyzVH2cVj5/QTAuQAutQQTmLmKmbdan+cCWAkge+u+TL2fZOahzDy0Sxf9G9EAQKsSeXVcZTa4SLCI5nnkRCJFiL+6/oyUaalXx9wXNV2ylPBI/bcnCkZ2YIPQt0tqpNyquPEFB9qPTToMVlMvkPG1eeeX6/OQy3twz/bo0b4lJpydu+5Wur17ZHZUz3b4qWODJBt363YKQy/NYsTAblhz/znoekCLAPOW929+2HMnnIJY9R3T6YPzWkb/wHYtYg/0EBHV5zEZgB09NR7AG4I0UwCMJKIOlqN8JIAplrmrkoiGWVFWl9vnE9FoAL8CcB4z77UzIqIuRFRofe6LlJN9VcRrCM1BPsuL26TbvcKzLU7PPj0ufUxqsyDF9uPMcezgHlhz/zm++xrIma1SaZxbhKriHIUSAX+6aBCe/elxONhnImNDxX5uskIhbB/gHp1nzKXe57g3KpItu12rYnw64UwcLVg2/a8/HoLTDuuCAyT3dLfxXdsroj0jrEC230NOP8No9YiKKBz3z+MG4/FLh+RltemowuN+AGcR0QoAI6zvIKKhRPQUADDzNgD3AJhj/U20jgHA9QCeAlCOlBbxrnX8UQAHAJjqCsk9FcACIpoH4FUA1znyigWvRt3JxxYrOl+24f3jqszEw9MHdMX3j025gWSWJ7GL6NCqGEccJN4DPQwqZisbe3MkHS9c69IinDFAbZ5DQyEzEpdLH0bYPn7psbjPNQveDpX1W+zwjAFd8dcfZ5ZJ1zF6PalfZzx/xfHKI+5c/4uqUzvYDOzcT0eGkpzw1+A6xbkXeQuB5jF2cA90bF2i1TwmSyQ7gGVCGi44XgbgKsf3ZwA845HuSMHxXMN76vhrAF6LUOXEySgecg/XHZnijChxkzuBLnPg6J7tsPgb7yUvUnVSQ6VzsU1vSTXqrgeUYsuuqkTKCuLwAw/Ask27so7FaVYYI9jnoUVxIf559Qk4ons7PDztK+F5RJQVQtsiwta0UXFPuHWarWQiHv1uLxFh/p0j0TpgAVB3KfaWz7Lb3caN0+dxaJfWWFmxJ/29Qfo8mjtezVZ2fJF2mEreaXcb8JuQ5SWQ4hr7qLTPEkXNwyvMWLbTffdnp2SFNeaTCxwj3Po8mjy+e2hntGtVjFaSqybLpouDI3u0w1s3nSz8TUXr9qJdy2LPrYJt3K+Ye70omUcY5yDBGW31xo0n4/PbMuP29MZYCRqwjPAIIKoWquowd7e9YX1Tm+aItpnMdZjL5xsGFS3CjlSRfZm8lq6WLbFTm1IM1Giq04XXcuodJc2eOrjpzP5S6WSX5o+LI61VGYDs9+WyYeqLCOogR3jkWfVwrjzdprQoa60zo3k0ImRtmzKOSyduIfP9Y3ti9m+G50wqU+WVa04MfW667io+j7TZSr28uMzGrUq8wz7jwjbfucMsD2zXImvWdpzICgXZLVOTwGmquunMflj9+zH+J8RQdfceGfm+O37LrudDeDS+2MeECTvD3CYodNGNKFlXjwUYVdqLjnXTVBqoPWoThR1/8buzcOw9U9PfkzKXzL9zJPZW1+HyZ2Zj/rodiZQ55qjuWPxNJW4QzJ/pI7N7XJ447bAu6XXY4uKlq4ehjURUlo5NwsIw/PDsOc/59nn4+aQancO8OSMtUjzMFjrweqnEI/fctKpiUaWBFhd6z/Nwb/w0yBXy6RTYOt+JAiK0a1mMgd3bJiY8igsL8Jsx0fccTxqZ/eoBYOovTg29UdmJrn3MnUQVBkMOUdfUne3ufy44CuOO65X1e5Q69ZfcpdEPvwg2o3k0QKKaUOy5IMf1jmZ2EpETSOgbcaK/PD9UfB6+9VYoM7AcjXn5ocPq9uxPj/PeXbEBIfLF6UBV43e2oeX3jo68LEjXAxy7XqbnLAXXS2TO/u+EM9E25uVy8qF5NPzWmWeuPfXQ4EQ+DDjwAHxw62nCZT+iotJeREnVQ3Xl0xYXeEdb5YYY+5Wp76WIktXVmtbnkuWMAV3x3UPVljEPy2XDDsGxB8st/dJQcT7a0qLCwMiqwPw09sUHtW8pZZ6LQmOcJNjk8ZrVrKKR9O3SJpalwv071uzfonTCmVnj3nmUFhXg3Z9lQmWLi7zPCVwjSGLZlzBEuQe3n5O7HlNT4Z7zj8Tr10fbq103ypMENfT2F3hMIkw7zCm4XnmLyDJmK4MOxHNCBOkk85PZ0KZb2xb4TvdMqGyRiubhqt39PzgaAw5cjTlrtsXkL9ATzuVcDcCghz9dNAiLNuyMHKgShkM6tcaZh3fFB8uyl+iza5IP05AsMjtH6sYIjwbAx786A5c+NQtrt+0NTizgR0NTjj2ZJRpUaFVSiB8O7YUbzugXmIdz0xrAEeYYwufRsXUJbh05QK2yCdOjfUuc1C8Zs1Jz4sIhPXHhkJ54Zc5aACoh7vHTgGVHXsxWRniEROcaNr06tkp3vqrZLrtndDqyyY7nv/a0Q7F++76sdCLBEtTgWhYX4q7zjkh/9xt5/fXHQ7K+q2geBkNUdLcp53uYmeeRn4b7xg0nBW4za0J1GxH6d34Ld55z+8mSooL0XhC3vb5QS/5ZeTg+3+4yJzk3rQEy6wLJ+DzyPXM3DH5VjnFtvNB0al2S3ofD4E3cqzSEQWYfGzPD3BAbupcnufrUvr5pi+0Z5gLVI9+yQkfnnm8BYe/DPahnu4CUKT761RmYf8dI3zT2DOaxg3P3yG4otPTYq1u3ViB6vA15iJOPAZjRPJoJYV4ulZBaN7aaLbU3ukqlGhEXDekZnCgkJx7aSWnHQZl9xC854WBU7KrCjWfqDyvXwaRrT0TPDh7Ly2hqRKLm6twP/tyju2P51F3o0qY0N2EeMZpHY6IBmib8UGlcJ/QR76+uMrrx289DZXJjQ8Wvzmccntq58tI8LegXltKiQvxq9OFSO2Tmg+P7dPTcgC2JNkQg3HhmPyy6exQ6NTThkYcyjfBoJohersEeE8P+d9xg+6zQ5dkzfIU+D9expBu+1wq+ujj8wLZYc/85GCy557qh4SEMd6dU2417wl8YGuM2tM2We87P2cOqQeM2W/mt1KvDfmzPDRGaAdzfE274Vwj20NbB5ScegmF9xVqbIV7ibEEOq5XBQSThQUQdiWgqEa2w/gt7IyIab6VZQUTjHceHENFCIionokesvcxBRHcR0QZrC9p5RDTGcc5tVvrlRDQqSv3Dcv3ph+J8xS0tkybIX9HKZ/Skoy/320kw6UHSr0YPQF/HCrY6ZvuLrmHi2CPxcoSl7w3h0T0AEeXXGKMC4ySq5jEBwHRm7g9guvU9CyLqCOBOACcAOB7AnQ4h8wSAqwH0t/5GO059mJkHW3/vWHkNBDAOwBFW2seJKPEdbOJsQ3HNrM0Z7UukjXKdfvt5JG22uv70fvggob0zDHo42lpp+UzXsuhJEede5E2FqMJjLIDnrc/PAzhfkGYUgKnMvI2ZtwOYCmA0EXUH0JaZP+fUk3rB43x3eS8zcxUzrwZQjpRAavTEPQFJJXJKx2tToLCHuRnQGdx8p3tbfHXv2Rh95IFS6fU1IZ9VGrSVoZ8WVpi17K6ROojq+enGzButz5sAiIYJPQCsc3xfbx3rYX12H7e5kYguB1AG4FZL8PQA8LnPOQYPwqjcUV6WIp95HnpLSpauB5Riy66qfFejWeC3c54b7TPMJY81FIoKC5RCt3UQ+HSIaBoRLRL8jXWms7QHXff3CQCHAhgMYCOAB1UzIKJriKiMiMoqKio0Vavxkmu2Cve2jfhONzx6yTGB6dILtUnk2Vg0j6UTR+O9n58KALjgmPjmcBjU0aW5ywR4GFIEah7MPMLrNyLaTETdmXmjZYbaIki2AcDpju89Acy0jvd0Hd9glbnZUcbfAbzlyKuX6BxBvZ8E8CQADB06tCEPGmIhKKIp7PIaT40fKlW+rXnI3PgjDmobnKgB0LKkEC1LCrF04mi0KDaBiobmTdQ3YDIAO3pqPIA3BGmmABhJRB0sR/lIAFMsc1clEQ2zoqwut8+3BJHNBQAWOcobR0SlRNQHKSf77IjXoEyc/om4/HQE4LfnqC1vHkUjsM1VXo5HO6R1wtmHJ2qntXnwokH4zZjDQ53bsqTQRN40MOJcGDFzrNmNQX2J6vO4H8AkIroSwNcAfggARDQUwHXMfBUzbyOiewDMsc6ZyMzbrM/XA3gOQEsA71p/APAHIhqM1MB1DYBrAYCZFxPRJABLANQCuIGZ6yJeQ4Mg7r6ICLjqlL649+2lgeXpiPhKax4BWR3ds53UfiG6+UGMS4cYGi+ilmgGCmIiCQ9m3gpguOB4GYCrHN+fAfCMR7qc2XbMfJlPmfcBuC9klRssp/bvggXrd6LLAfEsexBqbasoM8wtgVDvIT3MIM4QB3H085ccfzAenVEutT7Ydw/tBAC49ISD9VekgdHw5tk3U35x1mG4dNjB6N7OY+G3iATt3qebQknNI197JBiaFvqFRqbh3jryMPxsRP/0vjl+HNS+ZeJRT/nCCI8QxDG6KSyg2ASHiLj3o8hoHtHzMhiCsAchUduu16q6xQGbMTVHTMhIE8X9ErjnW/i9Cm2sXQ1HDOwauvy05tGgo+MNTYUkHOaGbIzm0UxQebfatijG7N8MR8fWJaHLs1fVNbLDkCRRhYgxo8pjhEczIXd5Ev+XpGvbFpHKK1SY52EwRMV0+cljzFYhaIwNNWff8MTKFWOEikEnusNpTfsMxgiPZkKULWXDsLc6Nf0mKLzRhNAbdGKaU3IY4dFMSPql2l1VC0Bu72yDISp2+/7uoZ215mfwxrzZzQXrbbj8xEPwwmdfxz5r1hYebUoT327F0AwpKCBMu+U0HNQ+mq/OxpitgjGaRwgO7tQ6OFEDw/Z53H3eEVhx39mxl7cvwGw1/PBUGHCP9snNbTE0bfp1bYNWJdHGw8aMKo/RPBR5+EeDcP7gxreFSHof5oQmPN10Zj/s2l+LHx3XS/j7Naf2xUVDe0UKBzYY4sLM8wjGCA9FTuzbuVEulJZ0jTu1KcWDPxzk+TsRGcFhaHD07JDShNu3Ks5zTRo+Rngo0gjlBgCzMqjBIMMvRw3AsQd3wEn99DjemzLG56FIY+mCzUxZg0Gd0qJCnH1U9+CEBiM8lDF9ssFgMBjhoYoZ0RsMBoMRHso0FtfB6QO65LsKBoOhCRNJeBBRRyKaSkQrrP8dPNKNt9KsIKLxjuNDiGghEZUT0SPWXuYgoleIaJ71t4aI5lnHexPRPsdvf41S/zA0EtmB4d/phuX3jkYHEzViMBhiIKrmMQHAdGbuD2C69T0LIuoI4E4AJwA4HsCdDiHzBICrAfS3/kYDADP/iJkHM/NgAK8BeN2R5Ur7N2a+LmL9lWlMUUulRWZ2t8FgiIeowmMsgOetz88DOF+QZhSAqcy8jZm3A5gKYDQRdQfQlpk/Z2YG8IL7fEsT+SGAlyLWUxuNR3SkMHOdDAZDHEQVHt2YeaP1eROAboI0PQCsc3xfbx3rYX12H3dyCoDNzLzCcawPEX1JRB8S0SleFSOia4iojIjKKioqJC+n6dGxVWoiXmEj0pgMBkPDJ3CSIBFNA3Cg4KfbnV+YmYlI90D3YmRrHRsBHMzMW4loCID/ENERzFzpPpGZnwTwJAAMHTq02Q7AX7zqBMxcvgXtjO/DYDBoJFB4MPMIr9+IaDMRdWfmjZYZaosg2QYApzu+9wQw0zre03V8gyPvIgDfBzDEUZcqAFXW57lEtBLAYQDKgq5DF41tAN+jfUtcesIh+a6GwWBoYkQ1W00GYEdPjQfwhiDNFAAjiaiD5SgfCWCKZe6qJKJhlm/jctf5IwAsY+a0aYuIuhBRofW5L1JO9lURr8FgMBgMikQVHvcDOIuIViDV2d8PAEQ0lIieAgBm3gbgHgBzrL+J1jEAuB7AUwDKAawE8K4j73HIdZSfCmCBFbr7KoDrHHkZDAaDISEiLYzIzFsBDBccLwNwleP7MwCe8Uh3pEfePxEcew2p0N1EObpnOyxYvzPpYg3NjNvOPjzfVTAYpDEzzCWYfOPJaNvCLEBsiJcLjml8+8QYmi9GeChi1rYy6OSaU/uipLAAa+4/B13b6tlC1WBIAiM8DIY88psx38FXCWwLbDDoxggPg8FgMChjhIck6S1TjdXKYDAYzDa0svzj6mH4cHkF2rU0M7WdPH/F8di1vybf1TAYDAljhIckPdq3xCUnHJzvajQ4TjvM7BtiMDRHjNnKYDAYDMoY4WEwGAwGZYzwMBgMBoMyRngYDAaDQRkjPAwGg8GgjBEeBoPBYFDGCA+DwWAwKGOEh8FgMBiUIeamv703EVUA+DpCFp0BfKupOo2B5na9gLnm5oK5ZjUOYWbhTOBmITyiQkRlzDw03/VIiuZ2vYC55uaCuWZ9GLOVwWAwGJQxwsNgMBgMyhjhIceT+a5AwjS36wXMNTcXzDVrwvg8DAaDwaCM0TwMBoPBoIwRHgaDwWBQxggPH4hoNBEtJ6JyIpqQ7/rogoh6EdEMIlpCRIuJ6GfW8Y5ENJWIVlj/O1jHiYgese7DAiI6Nr9XEA4iKiSiL4noLet7HyKaZV3XK0RUYh0vtb6XW7/3zme9o0BE7YnoVSJaRkRLiejEZvCcf2G160VE9BIRtWhqz5qIniGiLUS0yHFM+bkS0Xgr/QoiGq9SByM8PCCiQgCPATgbwEAAFxPRwPzWShu1AG5l5oEAhgG4wbq2CQCmM3N/ANOt70DqHvS3/q4B8ETyVdbCzwAsdXx/AMDDzNwPwHYAV1rHrwSw3Tr+sJWusfJnAO8x8+EABiF1/U32ORNRDwA3AxjKzEcCKAQwDk3vWT8HYLTrmNJzJaKOAO4EcAKA4wHcaQscKZjZ/An+AJwIYIrj+20Abst3vWK61jcAnAVgOYDu1rHuAJZbn/8G4GJH+nS6xvIHoKf1Qp0J4C0AhNSs2yL38wYwBcCJ1uciKx3l+xpCXHM7AKvddW/iz7kHgHUAOlrP7i0Ao5riswbQG8CisM8VwMUA/uY4npUu6M9oHt7YjdBmvXWsSWGp6ccAmAWgGzNvtH7aBKCb9bkp3Iv/BfArAPXW904AdjBzrfXdeU3p67V+32mlb2z0AVAB4FnLXPcUEbVGE37OzLwBwJ8ArAWwEalnNxdN/1kD6s810vM2wqMZQ0RtALwG4OfMXOn8jVNDkSYRx01E5wLYwsxz812XhCkCcCyAJ5j5GAB7kDFlAGhazxkALLPLWKQE50EAWiPXvNPkSeK5GuHhzQYAvRzfe1rHmgREVIyU4PgHM79uHd5MRN2t37sD2GIdb+z34iQA5xHRGgAvI2W6+jOA9kRUZKVxXlP6eq3f2wHYmmSFNbEewHpmnmV9fxUpYdJUnzMAjACwmpkrmLkGwOtIPf+m/qwB9eca6Xkb4eHNHAD9rSiNEqScbpPzXCctEBEBeBrAUmZ+yPHTZAB2xMV4pHwh9vHLraiNYQB2OtTjBg8z38bMPZm5N1LP8QNmvhTADAAXWsnc12vfhwut9I1udM7MmwCsI6IB1qHhAJagiT5ni7UAhhFRK6ud29fcpJ+1hepznQJgJBF1sDS2kdYxOfLt9GnIfwDGAPgKwEoAt+e7Phqv62SkVNoFAOZZf2OQsvVOB7ACwDQAHa30hFTk2UoAC5GKZMn7dYS89tMBvGV97gtgNoByAP8CUGodb2F9L7d+75vveke43sEAyqxn/R8AHZr6cwZwN4BlABYBeBFAaVN71gBeQsqnU4OUhnllmOcK4Arr2ssB/FSlDmZ5EoPBYDAoY8xWBoPBYFDGCA+DwWAwKGOEh8FgMBiUMcLDYDAYDMoY4WEwGAwGZYzwMBgMBoMyRngYDAaDQZn/H15/mkTH/bypAAAAAElFTkSuQmCC", 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", 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", 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "print(\"mu:\", mu)\n", + "for i in range(num_species):\n", + " make_trace_plot(\"mu.\"+str(i+1), istart, iend)\n", + " make_hist_plot(\"mu.\"+str(i+1), istart, iend)\n", + "\n", + "\n", + "print(\"Md:\", M.diagonal())\n", + "for i in range(num_species):\n", + " make_trace_plot(\"Md.\"+str(i+1), istart, iend)\n", + " make_hist_plot(\"Md.\"+str(i+1), istart, iend)\n", + "\n", + "\n", + "for i in range(num_species*(num_species - 1)):\n", + " make_trace_plot(\"M.\"+str(i+1), istart, iend)\n", + " make_hist_plot(\"M.\"+str(i+1), istart, iend)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "est: [ 1.07355045e+00 5.77177936e-01 2.08043888e+00 6.52051299e-02\n", + " 1.04764196e-01 1.51005627e-01 3.55697516e-02 -9.89240552e-02\n", + " 6.49072235e-04 4.36062108e-04 9.96880311e-02 6.02284864e-04\n", + " 1.91970196e+00 6.41260220e+00 4.23503528e-01 3.85119833e-01\n", + " 6.27127779e+00 8.85267318e-01 1.47299637e-02]\n", + "mu_hat/mu:\n", + "[1.07355045 0.57717794 2.08043888]\n", + "[1.27853844 0.55683415 2.06752757]\n", + "\n", + "M_hat/M:\n", + "[[-0.07 0.04 -0.1 ]\n", + " [ 0. -0.1 0. ]\n", + " [ 0.1 0. -0.15]]\n", + "\n", + " [[-0.05 0. -0.1 ]\n", + " [ 0. -0.1 0. ]\n", + " [ 0.1 0. -0.15]]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:42: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:43: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:59: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:60: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:76: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:77: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n" + ] + }, + { + "data": { + "image/png": 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", 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", 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the fit using median values of parameters\n", + "\n", + "post1 = df[df.columns[7:]][0:iend].to_numpy()\n", + "est = np.median(post1, axis=0)\n", + "\n", + "# fill mu_h and M-H\n", + "mu_h = est[0:num_species]\n", + "M_h = np.zeros([num_species, num_species])\n", + "np.fill_diagonal(M_h, -est[num_species:2*num_species])\n", + "\n", + "count = 0\n", + "print(\"est:\", est)\n", + "for i in range(num_species):\n", + " for j in range(num_species):\n", + " if i != j:\n", + " M_h[i, j] = est[2*num_species + count]\n", + " count = count + 1\n", + "\n", + "# print(mu_h)\n", + "# print(M_h)\n", + "\n", + "# make the plot and comparison\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h)\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(\n", + " times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)\n", + "\n", + "# this does the stem plots with orange crosses the actual parameters\n", + "compare_params(mu=(mu, mu_h), M=(M, M_h))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Try fitting to one sample" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[]\n", + "[]\n", + "[]\n", + "[]\n", + "[]\n", + "(20, 94)\n", + "(20, 16)\n", + "Building...\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "Building: found in cache, done.Messages from stanc:\n", + "Warning in '/tmp/httpstan_0_opiy5t/model_v6qcrrkq.stan', line 97, column 35: The variable lotka_volterra_N may not have been assigned a value before its use.\n", + "Sampling: 0%" + ] + }, + { + "ename": "RuntimeError", + "evalue": "Exception during call to services function: `ValueError(\"Exception: CVODES: CVode Internal t = 50.1858 and h = 3.47331e-15 are such that t + h = t on the next step. The solver will continue anyway. Error code: 99 (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\")`, traceback: `[' File \"/home/neythen/anaconda3/lib/python3.7/asyncio/tasks.py\", line 249, in __step\\n result = coro.send(None)\\n', ' File \"/home/neythen/anaconda3/lib/python3.7/site-packages/httpstan/services_stub.py\", line 160, in call\\n future.result()\\n', ' File \"/home/neythen/anaconda3/lib/python3.7/asyncio/futures.py\", line 178, in result\\n raise self._exception\\n']`", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mRuntimeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 67\u001b[0m \u001b[0msample_kwargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m\"num_samples\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m500\u001b[0m\u001b[0;34m,\u001b[0m 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"\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/stan/model.py\u001b[0m in \u001b[0;36msample\u001b[0;34m(self, num_chains, **kwargs)\u001b[0m\n\u001b[1;32m 87\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 88\u001b[0m \"\"\"\n\u001b[0;32m---> 89\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhmc_nuts_diag_e_adapt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum_chains\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnum_chains\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 90\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 91\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mhmc_nuts_diag_e_adapt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_chains\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m 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num_chains, **kwargs)\u001b[0m\n\u001b[1;32m 309\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 310\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 311\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0masyncio\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgo\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 312\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mKeyboardInterrupt\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 313\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;31m# type: ignore\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/nest_asyncio.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(main, debug)\u001b[0m\n\u001b[1;32m 33\u001b[0m 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"\u001b[0;32m~/anaconda3/lib/python3.7/asyncio/futures.py\u001b[0m in \u001b[0;36mresult\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 176\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__log_traceback\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 177\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_exception\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 178\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_exception\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 179\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_result\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 180\u001b[0m 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\u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmessage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 237\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 238\u001b[0m \u001b[0mresp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mawait\u001b[0m \u001b[0mclient\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"/{fit_name}\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mRuntimeError\u001b[0m: Exception during call to services function: `ValueError(\"Exception: CVODES: CVode Internal t = 50.1858 and h = 3.47331e-15 are such that t + h = t on the next step. The solver will continue anyway. Error code: 99 (in '/tmp/httpstan_0ntnjtzg/model_v6qcrrkq.stan', line 97, column 2 to column 100)\")`, traceback: `[' File \"/home/neythen/anaconda3/lib/python3.7/asyncio/tasks.py\", line 249, in __step\\n result = coro.send(None)\\n', ' File \"/home/neythen/anaconda3/lib/python3.7/site-packages/httpstan/services_stub.py\", line 160, in call\\n future.result()\\n', ' File \"/home/neythen/anaconda3/lib/python3.7/asyncio/futures.py\", line 178, in result\\n raise self._exception\\n']`" + ] + } + ], + "source": [ + "'''\n", + "first fit to one sample (M88) which has no perturbations\n", + "'''\n", + "\n", + "from load_data import *\n", + "import os\n", + "import sys\n", + "import matplotlib.pyplot as plt\n", + "\n", + "sys.path.append('data_analysis')\n", + "\n", + "\n", + "data = load_subject_ID_dict(\n", + " trimmed_path='/home/neythen/Desktop/Projects/gMLV/data/maria_multiomics/processed/trimmed.csv')\n", + "# extract the taxa data ordered by subject and time\n", + "X, subjects = get_X_subjects(data)\n", + "perts = load_perturbations_dict(\n", + " pert_path='/home/neythen/Desktop/Projects/gMLV/data/maria_multiomics/processed/trimmed.csv')\n", + "\n", + "combined_dict = combine_taxa_pert_dicts(data, perts)\n", + "\n", + "\n", + "ts = []\n", + "X = []\n", + "for t, x, p in sorted(combined_dict['M88']):\n", + "\n", + " ts.append(t)\n", + " X.append(x)\n", + "\n", + "X = np.array(X)\n", + "print(X.shape)\n", + "# plt.spy(X)\n", + "\n", + "\n", + "# remove all species that are 0 at every timepoint\n", + "\n", + "mask = ~np.all((X == 0), axis=0)\n", + "\n", + "column_indices = np.where(mask)[0]\n", + "X = X[:, mask]\n", + "print(X.shape)\n", + "# plt.figure()\n", + "# plt.spy(X)\n", + "\n", + "\n", + "# SETUP MODEL\n", + "# establish size of model\n", + "num_species = X.shape[1]\n", + "num_metabolites = 0\n", + "\n", + "\n", + "obs_data = {\"N\": X.shape[1],\n", + " \"T\": len(ts)-1,\n", + " \"t0\": 0.0,\n", + " \"ts\": ts[1:],\n", + " \"y\": X[1:, :],\n", + " \"y0\": X[0, :],\n", + " \"sigma\": 0.1,\n", + " # \"tau:\": 1.0\n", + " # \"Md\": np.array([-M[0,0],-M[1,1] ]),\n", + " # \"M\": np.array( [M[0,1],M[1,0]] )\n", + " }\n", + "\n", + "# posterior = stan.build(gLV_code, data=obs_data_log, random_seed=1)\n", + "posterior = stan.build(gLV_code, data=obs_data, random_seed=1)\n", + "\n", + "\n", + "sample_kwargs = {\"num_samples\": 500, \"num_chains\": 2, \"num_warmup\": 5000}\n", + "# fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\n", + "fit = posterior.sample(**sample_kwargs)\n", + "\n", + "# print(fit)\n", + "\n", + "df = fit.to_frame()\n", + "print(df.describe().T)\n", + "# print(df.head())\n", + "\n", + "post1 = df[df.columns[7:]][0:500].to_numpy()\n", + "post2 = df[df.columns[7:]][500:1000].to_numpy()\n", + "# post1 = np.random.normal(size=500)\n", + "# post2 = np.random.normal(size=500)\n", + "Rhat = get_Rhat(500, post1, post2)\n", + "print(\"Rhat:\", Rhat)\n", + "istart = 0\n", + "iend = 1000\n", + "\n", + "print(\"mu:\", mu)\n", + "for i in range(num_species):\n", + " make_trace_plot(\"mu.\"+str(i+1), istart, iend)\n", + " make_hist_plot(\"mu.\"+str(i+1), istart, iend)\n", + "\n", + "\n", + "print(\"Md:\", M.diagonal())\n", + "for i in range(num_species):\n", + " make_trace_plot(\"Md.\"+str(i+1), istart, iend)\n", + " make_hist_plot(\"Md.\"+str(i+1), istart, iend)\n", + "\n", + "\n", + "for i in range(num_species*(num_species - 1)):\n", + " make_trace_plot(\"M.\"+str(i+1), istart, iend)\n", + " make_hist_plot(\"M.\"+str(i+1), istart, iend)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Full Bayesian inference using linear approximation of dynamics" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Building...\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "Building: 23.3s, done." + ] + } + ], + "source": [ + "# linearise\n", + "import stan\n", + "import nest_asyncio\n", + "X, F = linearize_time_course_16S(yobs_x, times)\n", + "\n", + "# print(X[:,:(X.shape[1]-1)])\n", + "X = X[:, :(X.shape[1]-1)]\n", + "\n", + "nest_asyncio.apply()\n", + "\n", + "gLV_code = \"\"\"\n", + "functions {\n", + " vector lotka_volterra_N_red(real[] x, int N, vector mu, vector Md, vector M) {\n", + " // Models Y = dlnX/dt = f ( X )\n", + " \n", + " vector[N] dydt;\n", + " \n", + " int countM = 1;\n", + " \n", + " for(i in 1:N){\n", + " dydt[i] = mu[i] - Md[i]*x[i];\n", + " \n", + " for(j in 1:N){\n", + " if ( i != j ){\n", + " dydt[i] += M[countM]*x[j];\n", + " countM += 1; \n", + " //print(\"loop iteration: \", i, j, countM);\n", + " }\n", + " }\n", + " }\n", + " \n", + " return dydt;\n", + " }\n", + "\n", + "}\n", + "\n", + "data {\n", + " int N;\n", + " int T;\n", + " \n", + " array[T,N] real y;\n", + " array[T,N] real x;\n", + " \n", + " real sigma;\n", + "\n", + " //vector[N] mu;\n", + " //vector[N] Md;\n", + "}\n", + "\n", + "parameters {\n", + " vector[N] mu;\n", + " vector[N] Md;\n", + " vector[N*N - N] M;\n", + "\n", + " vector[N*N - N] lambda;\n", + " real tau;\n", + "}\n", + "\n", + "model {\n", + " //target += normal_lpdf(mu | 1.0, 0.2);\n", + " target += lognormal_lpdf(mu | 0.01, 0.5);\n", + " \n", + " target += normal_lpdf(Md | 0.1, 0.05);\n", + " \n", + " // Laplace\n", + " //target += double_exponential_lpdf(M | 0, 0.1);\n", + "\n", + " // Horsehoe prior\n", + " real tau0 = 0.001;\n", + " target += cauchy_lpdf(tau | 0, tau0);\n", + "\n", + " for(i in 1:(N*(N-1))){\n", + " target += normal_lpdf(M[i] | 0, lambda[i]*tau);\n", + " target += cauchy_lpdf(lambda[i] | 0, 1);\n", + " }\n", + "\n", + " for (t in 1:T) {\n", + " vector[N] y_hat = lotka_volterra_N_red(x[t,:], N, mu, Md, M);\n", + " for (s in 1:N){\n", + " target += normal_lpdf(y[t,s] | y_hat[s], sigma);\n", + " }\n", + " }\n", + "}\n", + "\n", + "\"\"\"\n", + "\n", + "obs_data_lin = {\"N\": 3,\n", + " \"T\": len(times)-1,\n", + " \"y\": F,\n", + " \"x\": X,\n", + " \"sigma\": 0.1,\n", + " # \"mu\": mu,\n", + " # \"Md\": np.array([-M[0,0],-M[1,1],-M[2,2]]),\n", + " }\n", + "\n", + "posterior = stan.build(gLV_code, data=obs_data_lin, random_seed=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: 0%\n", + "Sampling: 0% (1/12000)\n", + "Sampling: 0% (2/12000)\n", + "Sampling: 1% (101/12000)\n", + "Sampling: 2% (200/12000)\n", + "Sampling: 2% (300/12000)\n", + "Sampling: 3% (400/12000)\n", + "Sampling: 4% (500/12000)\n", + "Sampling: 5% (600/12000)\n", + "Sampling: 6% (700/12000)\n", + "Sampling: 7% (800/12000)\n", + "Sampling: 8% (900/12000)\n", + "Sampling: 8% (1000/12000)\n", + "Sampling: 9% (1100/12000)\n", + "Sampling: 10% (1200/12000)\n", + "Sampling: 11% (1300/12000)\n", + "Sampling: 12% (1400/12000)\n", + "Sampling: 12% (1500/12000)\n", + "Sampling: 13% (1600/12000)\n", + "Sampling: 14% (1700/12000)\n", + "Sampling: 15% (1800/12000)\n", + "Sampling: 16% (1900/12000)\n", + "Sampling: 17% (2000/12000)\n", + "Sampling: 18% (2100/12000)\n", + "Sampling: 18% (2200/12000)\n", + "Sampling: 19% (2300/12000)\n", + "Sampling: 20% (2400/12000)\n", + "Sampling: 21% (2500/12000)\n", + "Sampling: 22% (2600/12000)\n", + "Sampling: 22% (2700/12000)\n", + "Sampling: 23% (2800/12000)\n", + "Sampling: 24% (2900/12000)\n", + "Sampling: 25% (3000/12000)\n", + "Sampling: 26% (3100/12000)\n", + "Sampling: 27% (3200/12000)\n", + "Sampling: 28% (3300/12000)\n", + "Sampling: 28% (3400/12000)\n", + "Sampling: 29% (3500/12000)\n", + "Sampling: 30% (3600/12000)\n", + "Sampling: 31% (3700/12000)\n", + "Sampling: 32% (3800/12000)\n", + "Sampling: 32% (3900/12000)\n", + "Sampling: 33% (4000/12000)\n", + "Sampling: 34% (4100/12000)\n", + "Sampling: 35% (4200/12000)\n", + "Sampling: 36% (4300/12000)\n", + "Sampling: 37% (4400/12000)\n", + "Sampling: 38% (4500/12000)\n", + "Sampling: 38% (4600/12000)\n", + "Sampling: 39% (4700/12000)\n", + "Sampling: 40% (4800/12000)\n", + "Sampling: 41% (4900/12000)\n", + "Sampling: 42% (5000/12000)\n", + "Sampling: 42% (5100/12000)\n", + "Sampling: 43% (5200/12000)\n", + "Sampling: 44% (5300/12000)\n", + "Sampling: 45% (5400/12000)\n", + "Sampling: 46% (5500/12000)\n", + "Sampling: 47% (5600/12000)\n", + "Sampling: 48% (5700/12000)\n", + "Sampling: 48% (5800/12000)\n", + "Sampling: 49% (5900/12000)\n", + "Sampling: 50% (6000/12000)\n", + "Sampling: 51% (6100/12000)\n", + "Sampling: 52% (6200/12000)\n", + "Sampling: 52% (6300/12000)\n", + "Sampling: 53% (6400/12000)\n", + "Sampling: 54% (6500/12000)\n", + "Sampling: 55% (6600/12000)\n", + "Sampling: 56% (6700/12000)\n", + "Sampling: 57% (6800/12000)\n", + "Sampling: 58% (6900/12000)\n", + "Sampling: 58% (7000/12000)\n", + "Sampling: 59% (7100/12000)\n", + "Sampling: 60% (7200/12000)\n", + "Sampling: 61% (7300/12000)\n", + "Sampling: 62% (7400/12000)\n", + "Sampling: 62% (7500/12000)\n", + "Sampling: 63% (7600/12000)\n", + "Sampling: 64% (7700/12000)\n", + "Sampling: 65% (7800/12000)\n", + "Sampling: 66% (7900/12000)\n", + "Sampling: 67% (8000/12000)\n", + "Sampling: 68% (8100/12000)\n", + "Sampling: 68% (8200/12000)\n", + "Sampling: 69% (8300/12000)\n", + "Sampling: 70% (8400/12000)\n", + "Sampling: 71% (8500/12000)\n", + "Sampling: 72% (8600/12000)\n", + "Sampling: 72% (8700/12000)\n", + "Sampling: 73% (8800/12000)\n", + "Sampling: 74% (8900/12000)\n", + "Sampling: 75% (9000/12000)\n", + "Sampling: 76% (9100/12000)\n", + "Sampling: 77% (9200/12000)\n", + "Sampling: 78% (9300/12000)\n", + "Sampling: 78% (9400/12000)\n", + "Sampling: 79% (9500/12000)\n", + "Sampling: 82% (9800/12000)\n", + "Sampling: 85% (10200/12000)\n", + "Sampling: 94% (11300/12000)\n", + "Sampling: 98% (11800/12000)\n", + "Sampling: 100% (12000/12000)\n", + "Sampling: 100% (12000/12000), done.\n", + "Messages received during sampling:\n", + " Gradient evaluation took 6.1e-05 seconds\n", + " 1000 transitions using 10 leapfrog steps per transition would take 0.61 seconds.\n", + " Adjust your expectations accordingly!\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Gradient evaluation took 0.000237 seconds\n", + " 1000 transitions using 10 leapfrog steps per transition would take 2.37 seconds.\n", + " Adjust your expectations accordingly!\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_x1c4xo8w/model_mjoxdnzg.stan', line 70, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " count mean std min 25% \\\n", + "parameters \n", + "lp__ 2000.0 -1166.774642 3.377001 -1182.397101 -1168.820677 \n", + "accept_stat__ 2000.0 0.923051 0.104009 0.007482 0.900339 \n", + "stepsize__ 2000.0 0.018728 0.000469 0.018259 0.018259 \n", + "treedepth__ 2000.0 7.534500 0.617252 4.000000 7.000000 \n", + "n_leapfrog__ 2000.0 247.936500 107.532577 31.000000 179.750000 \n", + "divergent__ 2000.0 0.009500 0.097028 0.000000 0.000000 \n", + "energy__ 2000.0 1176.291720 4.529114 1163.118401 1173.272371 \n", + "mu.1 2000.0 0.242487 0.075614 0.074745 0.186961 \n", + "mu.2 2000.0 1.147137 0.274798 0.450161 0.946634 \n", + "mu.3 2000.0 1.541302 0.424721 0.448673 1.244155 \n", + "Md.1 2000.0 0.201747 0.014099 0.149019 0.192593 \n", + "Md.2 2000.0 0.203734 0.045002 0.091594 0.173607 \n", + "Md.3 2000.0 0.132734 0.010390 0.101816 0.125687 \n", + "M.1 2000.0 0.311801 0.028551 0.197604 0.293525 \n", + "M.2 2000.0 -0.133039 0.008765 -0.161383 -0.138660 \n", + "M.3 2000.0 0.044022 0.020079 -0.006673 0.030393 \n", + "M.4 2000.0 -0.002544 0.008005 -0.034688 -0.007299 \n", + "M.5 2000.0 0.063707 0.029684 -0.016063 0.042121 \n", + "M.6 2000.0 0.055028 0.068576 -0.177891 0.001991 \n", + "lambda.1 2000.0 10.108121 16.965367 0.162134 2.834777 \n", + "lambda.2 2000.0 4.494129 7.273105 0.151455 1.419391 \n", + "lambda.3 2000.0 1.815915 3.474209 0.027030 0.572277 \n", + "lambda.4 2000.0 0.591383 1.310292 0.000860 0.110019 \n", + "lambda.5 2000.0 2.558952 4.337804 0.006383 0.683282 \n", + "lambda.6 2000.0 2.241214 5.596299 0.006319 0.403792 \n", + "tau 2000.0 0.075597 0.079251 0.002209 0.033698 \n", + "\n", + " 50% 75% max \n", + "parameters \n", + "lp__ -1166.356880 -1164.295553 -1158.688009 \n", + "accept_stat__ 0.961452 0.989016 1.000000 \n", + "stepsize__ 0.018728 0.019197 0.019197 \n", + "treedepth__ 8.000000 8.000000 9.000000 \n", + "n_leapfrog__ 255.000000 255.000000 991.000000 \n", + "divergent__ 0.000000 0.000000 1.000000 \n", + "energy__ 1176.007643 1179.013428 1193.285759 \n", + "mu.1 0.235429 0.285916 0.594249 \n", + "mu.2 1.135665 1.332415 2.187224 \n", + "mu.3 1.617340 1.858275 3.045667 \n", + "Md.1 0.201579 0.210762 0.246479 \n", + "Md.2 0.202524 0.232989 0.351099 \n", + "Md.3 0.132438 0.139705 0.168269 \n", + "M.1 0.311929 0.329949 0.412835 \n", + "M.2 -0.133078 -0.127432 -0.099785 \n", + "M.3 0.043578 0.056877 0.102524 \n", + "M.4 -0.001503 0.002082 0.025781 \n", + "M.5 0.073069 0.085962 0.162349 \n", + "M.6 0.032077 0.104058 0.238695 \n", + "lambda.1 5.180528 10.053074 243.087721 \n", + "lambda.2 2.489539 4.793287 103.936959 \n", + "lambda.3 1.056599 1.982183 79.441594 \n", + "lambda.4 0.297678 0.677918 39.727408 \n", + "lambda.5 1.344241 2.709882 63.458191 \n", + "lambda.6 0.977767 2.132445 168.665988 \n", + "tau 0.056697 0.097715 1.867568 \n", + "Rhat: [1.00018567 1.00293448 1.01315865 1.00367648 1.00240808 1.00281039\n", + " 1.0068997 1.00383495 1.00293438 0.99898331 1.0081874 1.01058108\n", + " 0.99823442 1.00109035 0.99904652 1.00044712 1.00934418 1.0007776\n", + " 0.99837552]\n" + ] + } + ], + "source": [ + "sample_kwargs = {\"num_samples\": 1000, \"num_chains\": 2, \"num_warmup\": 5000}\n", + "# fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\n", + "fit = posterior.sample(**sample_kwargs)\n", + "\n", + "# print(fit)\n", + "\n", + "df = fit.to_frame()\n", + "print(df.describe().T)\n", + "# print(df.head())\n", + "\n", + "post1 = df[df.columns[7:]][0:500].to_numpy()\n", + "post2 = df[df.columns[7:]][500:1000].to_numpy()\n", + "# post1 = np.random.normal(size=500)\n", + "# post2 = np.random.normal(size=500)\n", + "Rhat = get_Rhat(500, post1, post2)\n", + "print(\"Rhat:\", Rhat)\n", + "istart = 0\n", + "iend = 2000" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/neythen/anaconda3/lib/python3.7/site-packages/matplotlib/cbook/__init__.py:1402: FutureWarning: Support for multi-dimensional indexing (e.g. `obj[:, None]`) is deprecated and will be removed in a future version. Convert to a numpy array before indexing instead.\n", + " x[:, None]\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:278: FutureWarning: Support for multi-dimensional indexing (e.g. `obj[:, None]`) is deprecated and will be removed in a future version. Convert to a numpy array before indexing instead.\n", + " y = y[:, np.newaxis]\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mu: [1.27853844 0.55683415 2.06752757]\n", + "mu.1 0.2354294822298929\n", + "mu.2 1.1356648466037305\n", + "mu.3 1.6173400498441022\n", + "Md: [-0.05 -0.1 -0.15]\n", + "Md.1 0.20157901496719516\n", + "Md.2 0.20252358600618933\n", + "Md.3 0.13243796008973757\n", + "M.1 0.31192927482929844\n", + "M.2 -0.13307799568887915\n", + "M.3 0.04357827972561585\n", + "M.4 -0.0015027250570411885\n", + "M.5 0.07306918405147098\n", + "M.6 0.03207688071576908\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:4: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).\n", + " after removing the cwd from sys.path.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:11: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).\n", + " # This is added back by InteractiveShellApp.init_path()\n" + ] + }, + { + "data": { + "image/png": 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", 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", 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", 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", 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", 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", 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", 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ujqjvZhV+ptprvA+YAn5nhDKPajnei0mb4BweBdYmWdOO3hd1K5ceTsvsBra19jbghkVu/8/AK1v7V4FvjamuxRhpDu1DQ+ZS8QLgrrFWN7wlz6OqbqqqF1XVdFVNA09NItiHsOQ5ZM6pz7SB1wHfHHuFwxn1M/U24DXAm6vqh2OubVij/ts+Fozyb6KY+w7qwqVsv+xfMEzgC4uTmfsW+l7gM8BJrX8G+ODAuM8DB4H/Y+5o/TWtfy1wE/A14N+BM1bhHG5p9d8F/B3w/NX4XhzyWiv1heqS58DcwdIXBt6L64AXrLZ5tP6ngW8Dd7THH6/COby9LT8N/PfgNqtoDj/L3EUfs8A/AicMu29vPyBJHerhtIwk6RCGuyR1yHCXpA4Z7pLUIcNdkjpkuEtShwx3SerQ/wOiICOp0wwtWwAAAABJRU5ErkJggg==", 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", 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", 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", 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "print(\"mu:\", mu)\n", + "for i in range(num_species):\n", + " make_trace_plot(\"mu.\"+str(i+1), istart, iend)\n", + " make_hist_plot(\"mu.\"+str(i+1), istart, iend)\n", + "\n", + "\n", + "print(\"Md:\", M.diagonal())\n", + "for i in range(num_species):\n", + " make_trace_plot(\"Md.\"+str(i+1), istart, iend)\n", + " make_hist_plot(\"Md.\"+str(i+1), istart, iend)\n", + "\n", + "\n", + "for i in range(num_species*(num_species - 1)):\n", + " make_trace_plot(\"M.\"+str(i+1), istart, iend)\n", + " make_hist_plot(\"M.\"+str(i+1), istart, iend)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "est: [ 3.11929275e-01 -1.33077996e-01 4.35782797e-02 -1.50272506e-03\n", + " 7.30691841e-02 3.20768807e-02 5.18052758e+00 2.48953934e+00\n", + " 1.05659903e+00 2.97677805e-01 1.34424114e+00 9.77766819e-01\n", + " 5.66967848e-02]\n", + "mu_hat/mu:\n", + "[0.23542948 1.13566485 1.61734005]\n", + "[1.27853844 0.55683415 2.06752757]\n", + "\n", + "M_hat/M:\n", + "[[-0.2 0.31 -0.13]\n", + " [ 0.04 -0.2 -0. ]\n", + " [ 0.07 0.03 -0.13]]\n", + "\n", + " [[-0.05 0. -0.1 ]\n", + " [ 0. -0.1 0. ]\n", + " [ 0.1 0. -0.15]]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:42: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:43: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:59: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:60: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:76: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:77: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n" + ] + }, + { + "data": { + "image/png": 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", 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", 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the fit using median values of parameters\n", + "\n", + "post1 = df[df.columns[7:]][0:iend].to_numpy()\n", + "est = np.median(post1, axis=0)\n", + "\n", + "# fill mu_h\n", + "# mu_h = mu # if mu is fixed\n", + "mu_h = est[0:num_species]\n", + "est = est[num_species:]\n", + "\n", + "# fill M_h\n", + "M_h = np.zeros([num_species, num_species])\n", + "# np.fill_diagonal(M_h, M.diagonal() ) # if Md fixed\n", + "np.fill_diagonal(M_h, -est[0:num_species])\n", + "est = est[num_species:]\n", + "\n", + "count = 0\n", + "print(\"est:\", est)\n", + "for i in range(num_species):\n", + " for j in range(num_species):\n", + " if i != j:\n", + " # M_h[i,j] = est[2*num_species + count]\n", + " # M_h[i,j] = est[num_species + count]\n", + " M_h[i, j] = est[count]\n", + " count = count + 1\n", + "\n", + "# print(mu_h)\n", + "# print(M_h)\n", + "\n", + "# make the plot and comparison\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h)\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(\n", + " times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)\n", + "\n", + "# this does the stem plots with orange crosses the actual parameters\n", + "compare_params(mu=(mu, mu_h), M=(M, M_h))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Single time course: three species, with perturbation\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of species: 10\n", + "specific growth rates: [1.79502305 1.65859857 1.62687674 0.3676487 0.854671 1.01112056\n", + " 1.23704653 1.16712793 1.95536934 0.46605446]\n", + "interaction matrix: \n", + "[[-0.12 0. -0.025 0. 0. 0. 0. 0. 0. 0. ]\n", + " [ 0. -0.04 0. 0.05 0. 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. -0.17 0. 0. 0. 0. 0. 0. -0.05 ]\n", + " [ 0. 0. 0. -0.08 0. 0. 0. 0. 0. 0. ]\n", + " [ 0.02 0. 0. 0. -0.06 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0.02 0. 0. -0.14 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. 0. -0.14 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. 0. 0. -0.07 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. 0. -0.05 0. -0.1 0. ]\n", + " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. -0.01 ]]\n", + "metabolite production: \n", + "None\n", + "perturbation matrix: \n", + "[]\n", + "(50, 10)\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "set_all_seeds(1234)\n", + "\n", + "# SETUP MODEL\n", + "# establish size of model\n", + "num_species = 10\n", + "num_metabolites = 0\n", + "\n", + "# construct interaction matrix\n", + "# TODO do this programmatically\n", + "M = np.zeros((num_species, num_species))\n", + "\n", + "# np.fill_diagonal(M, [-0.05, -0.1, -0.15, -0.01, -0.2, -0.05, -0.1, -0.15, -0.01, -0.2])\n", + "np.fill_diagonal(\n", + " M, -np.round(np.abs(np.random.normal(0.1, 0.05, size=num_species)), decimals=2))\n", + "\n", + "M[0, 2] = -0.025\n", + "M[1, 3] = 0.05\n", + "M[2, 9] = -0.05\n", + "M[4, 0] = 0.02\n", + "M[5, 2] = 0.02\n", + "M[8, 6] = -0.05\n", + "\n", + "# construct growth rates matrix\n", + "mu = np.random.lognormal(0.01, 0.5, num_species)\n", + "\n", + "# instantiate simulator\n", + "simulator = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M,\n", + " mu=mu) # , epsilon=epsilon)\n", + "simulator.print()\n", + "\n", + "# PRODUCE SIMULATED RESULTS\n", + "# initial conditions\n", + "init_species = 10 * np.ones(num_species)\n", + "init_metabolites = 10 * np.ones(num_metabolites)\n", + "\n", + "times = np.arange(0, 5, 0.1)\n", + "yobs, sobs, sy0, mu, M, _ = simulator.simulate(times=times,\n", + " sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# add some gaussian noise\n", + "yobs = yobs + np.random.normal(loc=0, scale=0.1, size=yobs.shape)\n", + "print(yobs.shape)\n", + "# plot simulation\n", + "plot_gMLV(yobs, sobs, times)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "# linearise\n", + "X, F = linearize_time_course_16S(yobs, times)\n", + "# print(X[:,:(X.shape[1]-1)])\n", + "X = X[:, :(X.shape[1]-1)]\n", + "\n", + "# time dependent perturbation\n", + "u = (times >= 2) & (times < 3)\n", + "u = u.astype(int)\n", + "u = u[:len(u)-1]\n", + "print('perturbation:\\n', u)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "# Horseshoe prior: work out choice for t0\n", + "D = (10*10)-10\n", + "p0 = 6\n", + "n = 50\n", + "sigma = 0.1\n", + "print(get_horseshoe_tau(p0, D, sigma, n))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Building...\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "Building: 23.4s, done." + ] + } + ], + "source": [ + "import stan\n", + "import nest_asyncio\n", + "nest_asyncio.apply()\n", + "\n", + "gLV_code = \"\"\"\n", + "functions {\n", + " vector lotka_volterra_N_red_u(real[] x, real[] u, int N, vector mu, vector Md, vector M, vector eps) {\n", + " // Models Y = dlnX/dt = f ( X )\n", + " \n", + " vector[N] dydt;\n", + " \n", + " int countM = 1;\n", + " \n", + " for(i in 1:N){\n", + " dydt[i] = mu[i] - Md[i]*x[i];\n", + " \n", + " for(j in 1:N){\n", + " if ( i != j ){\n", + " dydt[i] += M[countM]*x[j];\n", + " countM += 1; \n", + " //print(\"loop iteration: \", i, j, countM);\n", + " }\n", + " }\n", + " }\n", + " \n", + " return dydt;\n", + " }\n", + "\n", + " vector lotka_volterra_N_red(real[] x, int N, vector mu, vector Md, vector M) {\n", + " // Models Y = dlnX/dt = f ( X )\n", + " \n", + " vector[N] dydt;\n", + " \n", + " int countM = 1;\n", + " \n", + " for(i in 1:N){\n", + " dydt[i] = mu[i] - Md[i]*x[i];\n", + " \n", + " for(j in 1:N){\n", + " if ( i != j ){\n", + " dydt[i] += M[countM]*x[j];\n", + " countM += 1; \n", + " //print(\"loop iteration: \", i, j, countM);\n", + " }\n", + " }\n", + " }\n", + " \n", + " return dydt;\n", + " }\n", + "\n", + "}\n", + "\n", + "data {\n", + " int N;\n", + " int T;\n", + " \n", + " array[T,N] real y;\n", + " array[T,N] real x;\n", + " \n", + " real sigma;\n", + "\n", + " //vector[N] mu;\n", + " //vector[N] Md;\n", + "}\n", + "\n", + "parameters {\n", + " vector[N] mu;\n", + " vector[N] Md;\n", + " vector[N*N - N] M;\n", + "\n", + " vector[N*N - N] lambda;\n", + " real tau;\n", + "}\n", + "\n", + "model {\n", + " //target += normal_lpdf(mu | 1.0, 0.2);\n", + " target += lognormal_lpdf(mu | 0.01, 0.5);\n", + " \n", + " target += normal_lpdf(Md | 0.1, 0.05);\n", + " \n", + " // Laplace\n", + " //target += double_exponential_lpdf(M | 0, 0.1);\n", + "\n", + " // Horsehoe prior\n", + " real tau0 = 0.001;\n", + " //real tau0 = 0.01;\n", + " target += cauchy_lpdf(tau | 0, tau0);\n", + "\n", + " for(i in 1:(N*(N-1))){\n", + " target += normal_lpdf(M[i] | 0, lambda[i]*tau);\n", + " target += cauchy_lpdf(lambda[i] | 0, 1);\n", + " }\n", + "\n", + " for (t in 1:T) {\n", + " vector[N] y_hat = lotka_volterra_N_red(x[t,:], N, mu, Md, M);\n", + " for (s in 1:N){\n", + " target += normal_lpdf(y[t,s] | y_hat[s], sigma);\n", + " }\n", + " }\n", + "}\n", + "\n", + "\"\"\"\n", + "\n", + "obs_data_lin = {\"N\": 10,\n", + " \"T\": len(times)-1,\n", + " \"y\": F,\n", + " \"x\": X,\n", + " \"sigma\": 0.1,\n", + " # \"mu\": mu,\n", + " # \"Md\": np.array([-M[0,0],-M[1,1],-M[2,2]]),\n", + " }\n", + "\n", + "posterior = stan.build(gLV_code, data=obs_data_lin, random_seed=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: 0%\n", + "Sampling: 0% (1/12000)\n", + "Sampling: 0% (2/12000)\n", + "Sampling: 1% (101/12000)\n", + "Sampling: 2% (200/12000)\n", + "Sampling: 2% (300/12000)\n", + "Sampling: 3% (400/12000)\n", + "Sampling: 4% (500/12000)\n", + "Sampling: 5% (600/12000)\n", + "Sampling: 6% (700/12000)\n", + "Sampling: 7% (800/12000)\n", + "Sampling: 8% (900/12000)\n", + "Sampling: 8% (1000/12000)\n", + "Sampling: 9% (1100/12000)\n", + "Sampling: 10% (1200/12000)\n", + "Sampling: 11% (1300/12000)\n", + "Sampling: 12% (1400/12000)\n", + "Sampling: 12% (1500/12000)\n", + "Sampling: 13% (1600/12000)\n", + "Sampling: 14% (1700/12000)\n", + "Sampling: 15% (1800/12000)\n", + "Sampling: 16% (1900/12000)\n", + "Sampling: 17% (2000/12000)\n", + "Sampling: 18% (2100/12000)\n", + "Sampling: 18% (2200/12000)\n", + "Sampling: 19% (2300/12000)\n", + "Sampling: 20% (2400/12000)\n", + "Sampling: 21% (2500/12000)\n", + "Sampling: 22% (2600/12000)\n", + "Sampling: 22% (2700/12000)\n", + "Sampling: 23% (2800/12000)\n", + "Sampling: 24% (2900/12000)\n", + "Sampling: 25% (3000/12000)\n", + "Sampling: 26% (3100/12000)\n", + "Sampling: 27% (3200/12000)\n", + "Sampling: 28% (3300/12000)\n", + "Sampling: 28% (3400/12000)\n", + "Sampling: 29% (3500/12000)\n", + "Sampling: 30% (3600/12000)\n", + "Sampling: 31% (3700/12000)\n", + "Sampling: 32% (3800/12000)\n", + "Sampling: 32% (3900/12000)\n", + "Sampling: 33% (4000/12000)\n", + "Sampling: 34% (4100/12000)\n", + "Sampling: 35% (4200/12000)\n", + "Sampling: 36% (4300/12000)\n", + "Sampling: 37% (4400/12000)\n", + "Sampling: 38% (4500/12000)\n", + "Sampling: 38% (4600/12000)\n", + "Sampling: 39% (4700/12000)\n", + "Sampling: 40% (4800/12000)\n", + "Sampling: 41% (4900/12000)\n", + "Sampling: 42% (5000/12000)\n", + "Sampling: 42% (5100/12000)\n", + "Sampling: 43% (5200/12000)\n", + "Sampling: 44% (5300/12000)\n", + "Sampling: 45% (5400/12000)\n", + "Sampling: 46% (5500/12000)\n", + "Sampling: 47% (5600/12000)\n", + "Sampling: 48% (5700/12000)\n", + "Sampling: 48% (5800/12000)\n", + "Sampling: 49% (5900/12000)\n", + "Sampling: 50% (6000/12000)\n", + "Sampling: 51% (6100/12000)\n", + "Sampling: 52% (6200/12000)\n", + "Sampling: 52% (6300/12000)\n", + "Sampling: 53% (6400/12000)\n", + "Sampling: 54% (6500/12000)\n", + "Sampling: 55% (6600/12000)\n", + "Sampling: 56% (6700/12000)\n", + "Sampling: 57% (6800/12000)\n", + "Sampling: 58% (6900/12000)\n", + "Sampling: 58% (7000/12000)\n", + "Sampling: 59% (7100/12000)\n", + "Sampling: 60% (7200/12000)\n", + "Sampling: 61% (7300/12000)\n", + "Sampling: 62% (7400/12000)\n", + "Sampling: 62% (7500/12000)\n", + "Sampling: 63% (7600/12000)\n", + "Sampling: 64% (7700/12000)\n", + "Sampling: 65% (7800/12000)\n", + "Sampling: 66% (7900/12000)\n", + "Sampling: 67% (8000/12000)\n", + "Sampling: 68% (8100/12000)\n", + "Sampling: 68% (8200/12000)\n", + "Sampling: 69% (8300/12000)\n", + "Sampling: 70% (8400/12000)\n", + "Sampling: 71% (8500/12000)\n", + "Sampling: 72% (8600/12000)\n", + "Sampling: 72% (8700/12000)\n", + "Sampling: 73% (8800/12000)\n", + "Sampling: 74% (8900/12000)\n", + "Sampling: 75% (9000/12000)\n", + "Sampling: 76% (9100/12000)\n", + "Sampling: 77% (9200/12000)\n", + "Sampling: 78% (9300/12000)\n", + "Sampling: 78% (9400/12000)\n", + "Sampling: 79% (9500/12000)\n", + "Sampling: 80% (9600/12000)\n", + "Sampling: 81% (9700/12000)\n", + "Sampling: 82% (9800/12000)\n", + "Sampling: 90% (10800/12000)\n", + "Sampling: 91% (10900/12000)\n", + "Sampling: 92% (11000/12000)\n", + "Sampling: 92% (11001/12000)\n", + "Sampling: 92% (11100/12000)\n", + "Sampling: 93% (11200/12000)\n", + "Sampling: 94% (11300/12000)\n", + "Sampling: 95% (11400/12000)\n", + "Sampling: 96% (11500/12000)\n", + "Sampling: 97% (11600/12000)\n", + "Sampling: 98% (11700/12000)\n", + "Sampling: 98% (11800/12000)\n", + "Sampling: 99% (11900/12000)\n", + "Sampling: 100% (12000/12000)\n", + "Sampling: 100% (12000/12000), done.\n", + "Messages received during sampling:\n", + " Gradient evaluation took 0.001336 seconds\n", + " 1000 transitions using 10 leapfrog steps per transition would take 13.36 seconds.\n", + " Adjust your expectations accordingly!\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Scale parameter is 0, but must be positive! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 86, column 8 to column 55)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Gradient evaluation took 0.001157 seconds\n", + " 1000 transitions using 10 leapfrog steps per transition would take 11.57 seconds.\n", + " Adjust your expectations accordingly!\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Scale parameter is 0, but must be positive! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 86, column 8 to column 55)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n", + " Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n", + " Exception: normal_lpdf: Location parameter is -inf, but must be finite! (in '/tmp/httpstan_yeidpn1r/model_3iulvkbn.stan', line 93, column 8 to column 56)\n", + " If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n", + " but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " count mean std min 25% \\\n", + "parameters \n", + "lp__ 2000.0 408.441556 33.456099 3.568690e+02 383.131114 \n", + "accept_stat__ 2000.0 0.543468 0.426689 1.347946e-14 0.125012 \n", + "stepsize__ 2000.0 0.001062 0.000619 4.431824e-04 0.000443 \n", + "treedepth__ 2000.0 6.116000 3.857069 1.000000e+00 2.000000 \n", + "n_leapfrog__ 2000.0 507.973000 505.732855 3.000000e+00 7.000000 \n", + "... ... ... ... ... ... \n", + "lambda.87 2000.0 0.988865 1.591306 1.148732e-01 0.123705 \n", + "lambda.88 2000.0 1.895879 7.778969 2.663123e-02 0.294140 \n", + "lambda.89 2000.0 2.005513 2.801532 7.569663e-02 0.784112 \n", + "lambda.90 2000.0 5.471772 4.240155 3.883579e-02 0.919418 \n", + "tau 2000.0 0.000728 0.000223 1.743457e-04 0.000529 \n", + "\n", + " 50% 75% max \n", + "parameters \n", + "lp__ 388.091069 434.643899 517.288517 \n", + "accept_stat__ 0.410712 0.994824 1.000000 \n", + "stepsize__ 0.001062 0.001680 0.001680 \n", + "treedepth__ 4.500000 10.000000 10.000000 \n", + "n_leapfrog__ 36.500000 1023.000000 1023.000000 \n", + "... ... ... ... \n", + "lambda.87 0.142555 1.127831 13.343088 \n", + "lambda.88 0.305211 0.666858 120.518386 \n", + "lambda.89 0.859297 1.616165 22.249590 \n", + "lambda.90 9.052702 9.401340 24.010723 \n", + "tau 0.000856 0.000883 0.001593 \n", + "\n", + "[208 rows x 8 columns]\n", + "Rhat: [1.00557055 1.4847695 1.13340618 1.01452217 1.0247589 1.12406367\n", + " 1.00477907 1.04288392 1.00906595 1.05789725 1.00827127 1.04041743\n", + " 1.01779083 1.03349051 1.0062909 1.1002946 1.00319255 0.99912493\n", + " 1.00057411 1.01665094 1.01874937 1.04493805 1.00001347 1.00043549\n", + " 1.00647231 1.00631142 0.99811246 1.01817072 1.01160872 1.0072603\n", + " 1.00519759 1.16158429 1.0205272 1.00121296 1.53188193 1.00634844\n", + " 0.99979344 1.02945402 1.10061487 0.99814066 0.998002 1.01098236\n", + " 1.06622589 1.11240878 0.99812711 1.01542401 1.17731465 1.02353228\n", + " 1.08118693 1.03068687 0.99807133 1.04072523 1.01021837 1.01776973\n", + " 0.99800267 0.99992804 1.01447138 1.07260265 1.28988349 0.99962526\n", + " 0.99969016 1.0161132 1.07037166 1.00996425 1.02292892 1.00708356\n", + " 0.99936737 1.01082879 1.02584046 1.05949955 0.9996035 0.99813928\n", + " 1.03401448 1.02937812 1.00231616 1.01228178 1.03096111 0.99837608\n", + " 1.01687797 1.01551327 0.99828722 0.99801301 1.00270106 1.00413549\n", + " 0.99854859 0.998 1.00904111 1.18179473 1.00003417 1.00229348\n", + " 1.01292731 1.0006958 0.9981959 1.0356404 0.99808487 1.00932929\n", + " 0.99800323 0.99801228 1.02597455 1.02081931 1.01264891 1.01497946\n", + " 0.9986791 1.06023265 1.00714825 1.01007503 1.00378555 1.01511833\n", + " 1.00829373 1.05457118 1.03174215 1.04327011 1.0277287 1.01344691\n", + " 1.03224089 1.00136364 1.03829232 1.20935347 1.19087179 1.00855326\n", + " 1.15320054 1.0655779 1.10597197 1.00105295 1.02281902 1.06490309\n", + " 1.05561221 1.0412013 1.0470823 1.02049338 0.99800568 1.04110423\n", + " 1.01451907 1.06479447 1.04204179 1.1427486 1.00427449 1.01464306\n", + " 1.1399531 1.0169368 1.00268951 1.10434803 1.13237586 1.0507091\n", + " 1.00286339 1.07097043 1.02754194 1.05416644 1.1484819 1.059896\n", + " 1.04836425 1.05648591 1.10760845 1.02827445 1.00742196 1.01146939\n", + " 1.00536322 1.15147423 1.07664816 1.02862436 1.05179074 0.99955705\n", + " 1.01862706 1.07176254 0.99973156 1.00831592 1.00903049 1.01954159\n", + " 1.00855692 1.03112612 0.99800045 1.18731157 1.35128813 1.00076656\n", + " 1.004563 1.00210971 1.10947991 1.08169152 1.21514948 1.15782765\n", + " 1.15396575 1.01966672 1.09118606 1.03634108 1.055454 1.12047827\n", + " 0.99800038 1.07346889 1.00210672 1.18671489 1.04650152 1.03030615\n", + " 1.03708592 1.00809585 1.08724275 1.02413684 1.01669878 1.06134637\n", + " 1.01603391 0.99802401 0.99837853]\n", + "max Rhat: 1.5318819340066943\n" + ] + } + ], + "source": [ + "sample_kwargs = {\"num_samples\": 1000, \"num_chains\": 2, \"num_warmup\": 5000}\n", + "fit = posterior.sample(**sample_kwargs)\n", + "\n", + "# print(fit)\n", + "\n", + "df = fit.to_frame()\n", + "print(df.describe().T)\n", + "# print(df.head())\n", + "\n", + "post1 = df[df.columns[7:]][0:500].to_numpy()\n", + "post2 = df[df.columns[7:]][500:1000].to_numpy()\n", + "# post1 = np.random.normal(size=500)\n", + "# post2 = np.random.normal(size=500)\n", + "\n", + "Rhat = get_Rhat(500, post1, post2)\n", + "print(\"Rhat:\", Rhat)\n", + "print(\"max Rhat:\", np.max(Rhat))\n", + "istart = 0\n", + "iend = 2000" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mu_hat/mu:\n", + "[1.32140972 2.069643 0.77343921 1.25995822 0.89959829 1.80188942\n", + " 1.63174592 1.27787552 1.58540722 0.49833113]\n", + "[1.79502305 1.65859857 1.62687674 0.3676487 0.854671 1.01112056\n", + " 1.23704653 1.16712793 1.95536934 0.46605446]\n", + "\n", + "M_hat/M:\n", + "[[-0.1 0. -0. -0. 0. 0. -0. 0. 0. 0. ]\n", + " [-0. -0.05 -0. 0. -0. 0. -0. 0. 0.01 -0. ]\n", + " [ 0. 0. -0.24 0.17 0. -0. 0. 0. -0. -0.04]\n", + " [-0. 0. -0. -0.13 -0.01 0. 0. 0. -0.02 -0. ]\n", + " [ 0. -0. -0. 0. -0.06 -0. 0.01 0. 0. 0. ]\n", + " [-0. -0.01 0.01 -0. -0. -0.2 0. -0. -0. -0. ]\n", + " [-0. 0. 0. -0. -0. -0. -0.18 -0. 0. -0. ]\n", + " [ 0. 0. 0.01 0. 0. 0. 0. -0.1 0. 0. ]\n", + " [ 0. 0. -0. -0. 0.02 0. 0. 0. -0.13 -0. ]\n", + " [-0. -0. -0. 0. -0. -0. 0. -0. 0. -0.01]]\n", + "\n", + " [[-0.12 0. -0.025 0. 0. 0. 0. 0. 0. 0. ]\n", + " [ 0. -0.04 0. 0.05 0. 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. -0.17 0. 0. 0. 0. 0. 0. -0.05 ]\n", + " [ 0. 0. 0. -0.08 0. 0. 0. 0. 0. 0. ]\n", + " [ 0.02 0. 0. 0. -0.06 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0.02 0. 0. -0.14 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. 0. -0.14 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. 0. 0. -0.07 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. 0. -0.05 0. -0.1 0. ]\n", + " [ 0. 0. 0. 0. 0. 0. 0. 0. 0. -0.01 ]]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:42: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:43: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:59: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:60: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:76: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n", + "/home/neythen/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:77: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n" + ] + }, + { + "data": { + "image/png": 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9MZyFpem/jr58Q58bPBiJoihK61NPDGdhcfpijDojQ6KHkBSc5OlwFEVRWpV6YviNGh2NLD+0HLvLzvV9rvd0OIqiKK1OJYbfaHXOahocDVyZfCVTe071dDiKoiitThUl/UaLDy7G2+DNp9d/iq/R19PhKIqitDr1xPAbSClZmLaQQVGD1LhIiqJ0Wiox/AZp5WnkVOewPm89O4p2eDoc5Qzqah18+HY2uVkWT4eiKB2KKkr6DZYcXAJAjH8Mg6IGeTga5XR2bqni4//lUl/nILGbGS8vHZEx6ilPUVpCPTH8BovSFiEQXNvrWtWxrZ2qr3Mw980sZr+cSWCQkWtujmXl0mLe+k8GTqeaYU9RWkIlhhaqt9Wz7vA6JJKre17t6XCUU1j3UxlbN1Qy/rJwAoMMfDEvH4NBx42/i0OvV8lcUVpCFSW10Oqc1TilEz+TH2Pix3g6HKUZq9VJeUkjsfG+TLw8Ej9/Aws/LcBuczH15ljGXxqB3qCSgqK0lEoMLbQicwUmnYlV01dh1Bs9HY7SJDO9jg/ezMbhkDz1Uh82rC7nsw8OExbhxR+eTFH1CopyFlRiaKEVmSsYkzCGITFDPB2KAjgdku++KWTZN0UEh5qYfm8iCz/J56dlpfTuH8Cd9yfia1Zfb0U5G+ovpwWK6orYU7KH8MRwpJSq4tnDLPUOXn/uEDmZFoaPCWHKDTF8Mucwu7ZWM/6yCK65JRadTv0fKcrZUomhBX7I/AGA8oZylRTaAR9fPRHR3gwfG4JOJ3jzhQzycxu4/vYujLs0wtPhKUqHpxJDCyxKWwTAtb2u9XAk5y9LvYMv5+dzxdQodDpBWXEjm9dVABAabuKeh7vSb3CQh6NUlM5BJYYzkFLyfcb3AExKnuThaM5PmQfr+N/r2VRX2YiM9uLn5aVYrU6uuSWWvgMDiYj2Uk9yitKKVGI4g32l+6hurCbAK4BB0aq3c1tyuSTLFxax9KtCQsJMTLs9joWfFmAy6fjzkyl0SVCDGCqKO6jEcAYrMlcAcE3Pa9AJ1R+wLa1cUsziLwpJvSCYxO5mPvvwMOGRXvzxL90JDff6zcfr37//qVb1FkLsavq9VEo58WxjVpTOQCWGM1iesZyU0BTmXD3H06GcN+x2F0ajjjEXhxMYZCQzvY4v5uWdczNUp9PJ0qVLT1iemJh4CLgKEMCicwpeUToBlRhOo95Wz4+ZP3Lf0Ps8Hcp5wemULP2qkF1bq3js6Z6UFTey6vtScjItXDQpgik3nlsz1HfeeYeEhISTrbJJKXMAhBAn/c8WQlwGvALogfeklM+dZJtpwFOABHZKKW8+62AVxYNUYjiNn7J/wuaysbtkt6dD6fSqK+3MeSOL9P11DB8TwuLPC/hpeQlmPwN3/SmJwcODz/kco0ePPvp7Q0MDubm59OjR45htpJRrj99PCKEH3gAuBvKAzUKIRVLKfc22SQYeB0ZJKSuFEKrdrNJhuS0xCCG8gdWAV9N5vpBS/lMIkQR8AoQCW4HbpJQ2d8VxLr7c9yUAF3S5wMORdG5pe2uZ83oWjY0urro+mq3rKynIszLiwlCuuTkWs1/rfk0XLVrEY489hs1mIysrC8Cn6UI/+RS7DAMOSSkzAYQQnwBTgH3NtrkbeENKWQkgpSxp1aAVpQ25sza1EZggpRwADAQuE0KMAJ4HXpZSdgcqgbvcGMNZk1KyOH0xAFckX+HhaDovl0uy8NN8zH4Gxl0SznffFFFb6+C+x7px24yEVk8KAE8//TSbNm0iKOhov4cGIOk0u8QCh5u9z2ta1lwKkCKEWCeE2NBU9HQCIcQMIcQWIcSW0tLSs/wEiuJebksMUlPX9NbY9JLABOCLpuUfAO1yDOu9pXsps5ThY/BhaOxQT4fT6dTVOmiwONHpBJOnxeDtq+P7b4vp2cefv/+7F30GBrrt3EajkcDAE45/rpM1GIBkYBxwE/CuEOKEHndSytlSylQpZWp4ePg5nlJR3MOtdQxNZbNbge5oZbQZQJWU0tG0ycnuvI7sOwOYARAfH+/OME9qcZr2tDA2YSwGnaqKaU05GfW8+0oWid18CY/04oelxfj46Ll1RgIjxoa4vbNanz59WLBgAU6nk/T0dIA44OvT7JLftM0RXZqWNZcHbJRS2oEsIcRBtESxufUiV5S2cdornhDi4RYco15K+c7JVkgpncDApjunr4GeLQ1MSjkbmA2Qmpra5lNvLT20lPjAeB4d+Whbn7rTklKy7qdyPv/gMP6BBurrHGzfVMWIC0OZelMsfv5tk4Bfe+01nn32Wby8vLj55psBnMCDp9llM5DcVD+WD9wIHN/i6Bu0J4U5QogwtKKlzFYPXlHawJmKkh4D/AD/07weOdNJpJRVwE/ABUCQEOLIFeBkd14eV9lQyS+Hf+HWfrdyUdeLPB1Op2Czufjo3Vw+fj+Xbj38iIj24uC+Oq65JZbbZiS0WVIAWLJkCc8++yybN29m8+bNAAXAqSqeaXrCvR9YDuwHPpNS7hVCzBJCHNlvOVAuhNiH9l1/TEpZ7tYPoihucqa/xnlSylmn20AIYT7F8nDALqWsEkL4oDX1ex7tj+Y6tJZJ04GFvzlqN1uRuQKndDIwaqCnQ+k0LPUO9u2sZtSEUPJzG8jJsHDTXfGMnhDW5rH8+9//5vrrrz9+8ePA56faR0q5FFh63LJ/NPtdAg83vRSlQzttYpBS/uVMBzjNNtHAB031DDq0u6zFTXdUnwgh/gVsB97/jTG73ZFhtpdnLOf6PidcQJTfICejnrgkX3Q6Qa++/vzyUzm+Zj13/jGRIReEtGks3333HUuXLiU/P58//elPzVcloop9FOWoFj2/CyEeBOYAtcB7wCBgppTy+1PtI6Xc1bTd8csz0dqFt1vLM5YDcFn3k7Y4VFpASsmKxcUs+rSA3v0DOJRWh93uYtylEVw+NcotzVDPJCYmhtTUVBYtWsSQIcfMxFcFXNrmASlKO9XSv87fSSlfEUJcCgQDtwHzgFMmho6quK6Y3OpcBIIJSRM8HU6HZLU6+eidHLZvqsJoFOzdWcOA1ECm3BhLZLTn5mAeMGAAAwYM4JZbbsFg+PWrf8cdd1Qd6ZimKErLE8OR9oNXoNU77BWddAD8NblrAEgJTSHEp22LOjqDkiIr776cSWG+FYNBEBxm5JbfJ9K9p5+nQ2PatGl89tlnDBo06Pgmsb2FELuklKccflVRzictTQxbhRDfo/UOfVwI4Q+43BeW56zMXAnApBQ1Kc/ZqKtxUFvjwD/QiJSSB2amEBJm8nRYALzyyisALF68+JjlzUZXVRSFlieGu9CGtciUUlqEEKHAne4Ly3PWHV7HhQkX8tjIxzwdSochpeTQgTqSe/mT0NVMVKw3Wen1PPhEcrtJCgDR0dEAJxth9ejoqoqitDwxSKA3cCUwCzADnissdpNySzm7S3bzr/H/IsovytPhdAi2RhcfvZvD1vWV3PNwV35aVkL6/jpuuyeBrsmeLz5qzt/f/5giJCnlkfeDhBA1UsoAjwWnKO1ISxPDm2hFRxPQEkMt8CXQqQYROlK/4JROD0fSMVSU2Zj9cgZ5OQ2MGh/KgvdzsDa4uO2eBEaMDfV0eCeora096XIhxHYpZWobh6Mo7VZLE8NwKeVgIcR2gKbx5ttPGUErWX5Ia6Zqd9o9HEn7d+hAHe++konD7mLMxDDW/lhGWKQXD8zsSmy8j6fDO6OdO3eyZs2aI2/bf8CK0oZaOrqqvamjmoSjvZo7XeXzkf4Ll3S7xMORtH8lRVZ8ffUMHBrE6h/K6N0/gL/M6tkhksIrr7zCLbfcQklJCSUlJQBJQogHPB2XorQXLX1ieBVtELwIIcSzaENaPOG2qDygylpFVlUWRp2R4V2GezqcdsnpkOTlWEjoZqbPwEB2bqliw+oKLrwknGtv7YJe3zFaML///vts3LgRs1kbzeWZZ545gDbRzmseDUxR2okWJQYp5XwhxFZgIlqfhqullPvdGlkb++XwLwAMjBqISd/pSsnOWV2tg/dfzSTrUD2XXBXFyqXF2G2S627rwvjLOtYsllJK9Hr9MYv4ta+Oopz3zjTsdoCUskYIEQKUAB83Wxcipaxwd4BtZU2OVt58ba9rPRxJ+1NwuIG3X8ygutJOUKiRJV8W0qufP9dPj/NoT+azdeeddzJ8+HCmTp2KNvYdvYC/eTgsRWk3zvTEsACtiepWjp3hSjS97+qmuNrc5oLNDIoaxF9H/9XTobQru7dVMeeNbEwmHWERJkqLbdxxXyKpI4PdPqGOuzz88MOMGzeOtWvXHvkMWVLK/3o6LkVpL840uuqVTT9PNx9uh+d0OdmQt4HpA6Z7OpR2J21vLeGRXrikpDi/kbsfSqLf4BNmrOyQmvVj6JgZTlHcpEWtkoQQU4UQgc3eBwkh2uVczWdjT8ke6u315NXkeTqUdsFuc1FSZAUguZcflnpHp0oKs2bNYvr06VRWVlJWVgaQKIToVI0pFOVctLRV0j+llEfnxG2afOefaNMZdniLD2pj5wyMVhPzVFfZmf1SBpUVdmLjvNm3q5aoWG/+9LekdjEQXmuYP38+O3fuxNtbqx+ZNWvWfrQRg//l0cAUpZ1oaWI42ZNF2w+o7yZL0pcAcF2v6zwciWcdzrbw9osZ1Nc5MJn0HEqrZ+rNsYy/NAK9ofOUtsTExGC1Wo8mBrTvd7ubYlZRPKWlF/ctQoiXgDea3v8RrUK6U9hTsgeT3kTfiL6eDsVjdmyu5IO3cvD21mE06RACHv5HCnGJvp4OrdU88MADCCEIDAykT58+XHzxxUfqGPoAi8+wu6KcN1qaGB4AngQ+RWuNtAItOXR4JXUl1Npq6R/Zv8O2sjlXUkrW/FBGaLiJqnIbXt56HvhbMlExHa8p6umkpmrDIQ0ZMoSpU6ceXT537tx82uHc44riKS3t4FYPzBRCmJt+7zTWHV4HwC39bvFwJG3PZnNha3Th529g1IRQPnw7h8BgEw/M7E5YhJenw2t106efvNXZHXfcUS6l/KCNw1GUdqulcz6PRJvr2Q+IF0IMAO6RUt7nzuDawqb8TRh0Bh4Ydn4NlVNVaWP2S5kYjIJR40P56N1cYuN8uO8v3QkINHo6PLdKT0/n8ccfZ9++fVitVoB+QohMKWWn6ZejKOeipYPovYw2WXo5gJRyJzDWXUG1peUZy+kX0Q8fY/sf/K215GZZeOHJNArzrURGe/Ph27l07+nPg39P6fRJAbSez/feey8Gg4GffvoJtO/1Rx4OS1HajZYmBqSUh49b1OEnLbA5bGwv2o7FbvF0KG1m28ZKXpqVhtDB0FHB/LKqnIFDg7jvsW74+OrPfIBOoKGhgYkTJyKlPDKbWwGg5nJVlCYtrXw+3FScJIUQRuBBoMMPojd/93wALup6kYcjaRt2u4tvPysgNs6HiGhv1v1YzogLQ7n5rvgOMzJqa/Dy8sLlcpGcnMzrr78OEEQnuNFRlNbS0ieGP6C1QopFu7saSCdolfTRLq304N7Uez0ciXvZbC7sdhcGg2DiFZFUVdrZtLaCiyZFcOvd51dSAG0+BovFwquvvsrWrVsBQoHbPRyWorQbLW2VVAZ0umY7mwo24WPwoU9EH0+H4jbVlXbeeSmDyBgvGq0udm6pJibOmzv/2Hl6Mv9W2dnZDB06FD8/P+bMmcPcuXMzgHhgo6djU5T2oKVjJXUVQnwrhCgVQpQIIRYKITp0C460sjTqbHUMjOq8w2DkZln4f08eoCCvgf27a9m9vZqpN8cy89le521SAPj3v/99ssWPt3UcitJetbSOYQFar+cjvYJuRJubocNOdbY0fSkAz0x4xsORuMe2jZV8+LY2XLaUoBOCh/6eQrce529C+O6771i6dCn5+fn86U9/ar4qEcj0TFSK0v60NDH4SinnNXv/kRDiMXcE1FaWpC+hd3hvJiZN9HQora6+zsH8d3Mw+xmoqrDTNdnM7x/sSmBw52+KejoxMTGkpqayaNEihgwZ0nxVFVpzbEVRaHli+E4IMRP4BG1IjBuApU0zu9HRZnKraazhp+yfuLpHpxk5HOBoBbPRpCOpu5n9u2sZPiaEm+6Kx2hsccvkTmvAgAEMGDCAm1kPEeoAACAASURBVG++GYfDQW5uLj169OCOO+6oklJWejo+RWkvWpoYpjX9vOe45TfSAWdyW5K+BJd0eTqMVlVVYeOdlzJJ6ePPvh3VFORZmTwthksmR563Y0CdyrJly3j00Uex2WxkZWUB+AghFkkpJ3s6NkVpD1raKqlTzeD24Y4PAbip300ejqR1ZGfU885LGVjqnOTlWjCbDdz3WDf6DAw8887noaeeeopNmzYxbty4I4sagE71HVeUc9HSsZKuB5ZJKWubZroaDDwjpdzu1ujcQErJmtw1AExImuDhaM7d5nUVfPRuDgaDwOGQ9BkYwG0zEvA/D4a2OFtGo5HAwBOSpjzZtopyPmppwfOTTUlhNHAR8D7wtvvCcp99pfuot9eTEJhAiE+Ip8M5J8UFVj54KxuznwFrg4vxl0Vw76PdVFI4gz59+rBgwQKcTifp6ekAccAvHg5LUdqNliaGI8MFTAJmSymXACb3hOReK7NWAnBJt0s8HMnZc7m0m9vQCBO9+wdQXWln4qQIrr01VtUntMBrr73G3r178fLy4qabbgJwAQ+dbh8hxGVCiDQhxKGmhhin2u5aIYQUQqS2ctiK0mZaWvmcL4R4B7gYeF4I4cUZkooQIg74EIhEe0yfLaV8pakl06dobcezgWlt2SLk55yfSQhM4M1Jb7bVKVtVaXEj7/43kwvGhfLLj2UU5Fm5+KpIptwQo5JCC/n6+vLss8/y7LPPAiCEyJdSWk+1vRBCj9aP52IgD9jcVFm977jt/NHGEVM9qJUOraVPDNOA5cClUsoqIAQ4Uz8GB/CIlLI3MAL4oxCiNzATWCmlTAZWNr1vEy7pYlX2KsYnjceg63hTVh/YU8P/e/IAxYVWvvgwD4vFyR8e6cbVN6onhd9iy5YtXHPNNQwePJj+/fsD9BZC7DrNLsOAQ1LKTCmlDa3Z9pSTbPcM8DxwyiSjKB3Baa+OQohtUsrBUkoL8NWR5VLKQqCw+TbH79t8m6b6if1og/BNAcY1bfYBsAr46zl/khbYXbybioYKqqxVbXG6ViOl5OfvS/niozwMeoHDLhk9MYyrb4w9b4bKbk233HILL7zwAv369UOn05GYmHgIuOo0u8QCzYedz+O4Xv9CiMFAnJRyyek6fwohZgAzAOLj48/6MyiKO53ptrnXGe6kBHDGNpFCiERgENojdmRT0gAoQitqOtk+rf4H9O3BbwFIDkluleO1lb07a/j8wzx0OtAbBHfen8SA1CBPh9VhhYeHM3nyMV0WbFLKnLM9nhBCB7wE3HGmbaWUs4HZAKmpqaollNIunSkx9GzBMU47jr0Qwg/4EnhISlnTvMhDSimFECf943DHH9A3B74B4Npe17bG4dzO5ZIIAQW52kRCXRJ9+P2fuhIa3vnmY25LTz/9NL///e+ZOHEiXl5eAEFCiGuklF+dYpd8tJZLR3RpWnaEP9AXWNX0/Y4CFgkhJkspt7T+J1AU9zptYjiXuyiApkl9vgTmN/ujKxZCREspC4UQ0UDJuZyjpZwuJ7uKd2HSmxgSM+TMO3hY1qF65s/OIbqLN9s2VjFkRDC33ZOA0aSGtjhXc+bM4cCBA9jtdnQ6HWgT9VxJs+LS42wGkoUQSWgJ4Ubg5iMrpZTVQNiR90KIVcCjKikoHZXbamCFduv0PrBfSvlSs1WLgOnAc00/F7orhua2F27H7rKTGp3a7iue1/9czsfv5yJ0UJhv5bIpUUy6LhqdTlUwn5GUcIaK+M2bN5OWlnb0/dy5c7OllL879SGlQwhxP1oDDD3wPynlXiHELGCLlHJR6wSvKO2DO6+Qo4DbgN1CiB1Ny/6GlhA+E0LcBeTw6zhMbvVD1g8AzBgyoy1Od1acDslXC/JYtbwUnQ4MOsGt9yUydFQ77YhnLQWjP+i9z25/lx2sxWAKBYNP0zInVO+B6v0g7SBdYC2Byh1QtQMc9WAKBlMI+HWD4IHgnwwVm6FgKZRt1GIyhYJXCBjMoDeDfzcY8l8ARo4cyb59++jdu3eLQ5VSLgWWHrfsH6fYdtzZ/YMoSvvgtsQgpVyLVjl9Mm0+1vWa3DX0CO3B3UPubutTt9jyRUWsWl4KaPUJdz3QlbCIdlif4GiA3f+EAy9qF+ju90C334ElH0rXQE0a+MSCXxLojFCxDSq2ahd4nVF72SqgoUC78CPANw58oqF6LzjqTjynb5yWBIxBYKsEWzkc/gIy3v11m5AhkPIAuGzaelullkhs+cccasOGDQwcOJCkpKQjdQy9hRC7pJT93fnPpigdRfsuU2kldqedn7J+4rb+t3k6lJNyuSSV5TZ2btGa0V40KYLJ02LRGzxUdCQl1GdDXSbovLS7eekCe612h7/nae3i3/UOsFXB3v+Dvc/+ur9PrLaddGjvDWYIHgShqeByaBfu4EFgTgCfGC1h1KZpiaXrHRA6AoIHaE8iQg/GQO3u/2RxWvK0fQP7gc9JG7idYNmyZce8b0FzVUU5r5wXiWFj/kYaHA1kVrW/Sbp+WVXGim+Lqa2xA4IZf+7adk1RXU4oWgG5n4G9Rrv4O+qgcjs0lp16P3MCTFgBURdp7+uy4PDX4N8dwkeBV6h27IY87enCPxl0buhvIQSY47RXCwwePJht27aRkJBw/KqjzVVP1S9HUc4n50VimLdLm3zuxr43ejiSX9ntLr6Yl8falWXo9BAYZOTBv6cQHtlKRUeOeu2uvno/1Bz49YULfOO1YpuilWDJ1crsfaIBHei9IHYyhA6DgB7aXb+jQTumKRAM/hDQ89c6AdCKjHo9fOz5dXotgRzP5QCnFYxNU4xWH4DGUnBYwFmv/TQGQpemG/iDb0J9jraPs0H7GdgT+vxNW7/uJm29ywbORu1n5AQY9pa2fmESWItgSi779+8/0tP5eEd6PreoX46idHbnRWL4PuN7AK7peY2HI9FUltt475VMsjMsmEwCb189Dz2Rcvb1CfY6KF0HpWuhapdWeVvX7OlI6LSK2oCeIAzahbRyGwT1h0EvQJcpWkJoCZddKz46khjKNkL1Pq08316lrRN6GPKytn7z/VC4THsicdRqF/aAnnDlfm39phlavURzwYN/TQyZ/4OqPaD30YqWTqjo1mlFVboQ0Jm0V0DKr6sTbwVXI+i9OHDgwEk/0nFFSaftl6Mo54NOnxisDis5VTlE+0UT7BPs6XAA+GROLgWHrfj66dHpBA/+/SySgssOh7+C9Le0pCAd2gU5oAeEDIWkOyCwt3YR9u9++gu/lFoLo4Z8rZy/oVCrTBY6SH8bsj/S6gGspdrFX+cFNzRoRTnpb0HWB00HEmAK0iqKjzDHQehwMAZoTwkG/6ankyYDn9eeFPS+YPDVWhAZ/X9df+nm0zc/HTX/9P9OA545+mtCQsCptjqnns+K0tl0+sSw/NByJJJxieM8GoeUErtNYvLS0WdgIGl7ajGZ9Nz3WDeiYlrY3NNeC+UboWSNdidtyQO/7tDrEa34JHyUdvd8wsld2gW/9pBWqVyfDT0e0oqG9r8EOx/XimCa63I1eIdpCUgYtcpir3DwDgevMLQBcwUM+Bf0e0orjjL6a8mkud5nGAYr/ILTr1eDAypKm+v0iWFLwRYEgpmj22wQ1xM0WJx8+HY29XUOYuN9WL2ijKRkM3c/1JXAoGaT6kgJFVu09viWw2ApgMYSrULYUX9s887I8TD0LYi54teLsaNeaxZavQ+iLgafKMj+BDbeqRXhHCW0C79pAIQM0pKEbxethZBvrPbT1PR01eMB7XUqvl1a+59LURQP6/SJYVXOKobGDqV/pGeaqB/Oruf15zKoq9WabmYerGfU+FCunx6H0dh0Qa/PgZzPIGuudlFHgHeE1uzTO1KrHzD4aUU04SMhZJhWLKMzaJW3O/+m1S3UZXJ0hsoxX0LcNRDYC7rfqxUn+XcHcxKY438tWoocr73OwOlysqtoF6uzVhPhF8E1fa7By3Dm4i8pJXuK9/DFni8orismPjCe+KB4QnxD8DH64Gv0RdeU2OxOOxWWCkrqSyipK6G4vpicyhwsNgtxQXHEB8cT6x9LhF8EUf5R9Ajrwdb8rXy550uqrFU4XU4anY2UW8qpaazBYrMQ4B2A0+VkaJehvH11h5x0UFHaXKdODHWNdazLXccdA+7wyPnXrizlk7mHkS6Ijfdh/GUR9BsciJ+/Aepz4dDnWlPR8k3aDqEjYOjbkHCDVlZ/hK0KyjZoxUhpr2jb9/0n9Lgf9CatU1jwIEi6HQL7aHUL/t0BKDJEUhl3NylhKeibmoxKKcmpzKbR0YjJYMKkM1FlraK0vpSKhgoaHY3YnDbqbHUU1hZSUF3ArqJdVFp/nU/phdUvcPcw7bj7S/ZTUFOA0+XEJV1H9+0a0pUNhzewr2QfOqHDS++F1WFFtnB65S4BXYgPiiezIpP0ivRj1umFHpd0nfJYkeZIbhhyA7W2WpYcWILZeJIiNkVRTqpTJ4Z5u+YhkYT6hrb5uYsKGvjsgzykCyZeEcHVN8WiwwmZc2H9/6BsvbZh8CAY8H8Qf/3RizkNhVBdqN3t2+vgyzCQTkBoF/7Yq7SLP4BfV7JGL+P79O/ZdHATfl7lRJgPIJGsy1nHwbKDAJiNZvpG9sXuspNWmka9vb5FnyPYJxiBOCYpAFQ3VvOfNf857b4bDm+gZ3hPLoi/gApLBb4mX7wNWn1KkHcQvx/6eyx2Cz8c+oGSuhJMehMBXgEEegcSHxTPtX21UXDX566ntrGWBnsDxXXFFNUWUVpfSvfQ7qR2SSUuIA5fky8mvQmj3ohJbzqaBAH+dfG/WvRZFUXRdOrE8PGejwH4Q+of2uycpcWN1NXYefe/Wej1cOf9SQwaFgwF38H2R7WioqB+MOBZiJ+mJQN7HRT/CGmvQtEPULMfoi6BCcvB6MfmpL/yr33rOVxfSX/TAAY4+uFM30bWxi9JK0sjqzILgHDfcBqdjdTb6nFJF4NjBjPzwpnsK9nHov2L2Jh37IyTsybOwuxl5odDP7AuZx1mk5kArwD8vfzx9/Ln+UufJ9QcyprsNewp3oPZaMbX6IvZZMbH6EN8UDx1tjoabA1IJAadAYlEL/R0CexCuDm8RTPLjYwfedr1F8SfoYJaUZRW1akTw5aCLfib/OkW0q1NzrdpXQXz383B5ZQEh5p49OmexAZkwk83QeFyrQXRmK+1fgPWYq1yGODnq6BkldZWP2IsdL0TV+QE9hXv4b3N7/HtgW8J8g4iJiCWnYU7WZOttfuP9o+mT0QfBkYP5Ot9X1NqKcWgMxBuDifMHMazlzxLclgyu4p20TO8JyE+IQR6BxLsE0ygdyBJwUkY9Uau7n31aT/XmMQxjEkc4+Z/PUVR2otOmxg25mnDYFzW7TK3n6vB4uTd/2aStrcWgPgEHffdWYp/8Vuw7h2t7f6gFyHiQshfCLuehNo0aiZlkt9QS2nIVLIMIzlodZJdcpi89MUU1r2L0+XEpDdxbZ9r+XLvl9Q01hDlF0VKWAqxAbHcPfRuekX0oqqhirtS7yLCL4Jgn+CjlblH9I/qT/8oNT6coigt02kTw5FhMO5Nvdet59m+qZI5r2fjdEq8jI1clPQ+F3f9EONmu9bhLPleiJwIO2fC9kdA6NjqO4xXrCPZMHsCTnliR1ud0BHiE8LkXpO5Z9g9+Jn8uHfEvcQGxGLSm07YPsgniCAf946v5HS5KKpqIL+8HokkyOxFoK8Jg06HRKITgmA/L3THFR1JKSmuauBAQRVmLwNDuoWfsE1RpYU1BwrZn1fF8OQIxveNwWQ4+dhKUkqq6m0UVNbj520kNsSMQX/yyYusNgcHC6vZn1eJwym5ZWzHmtJVUTyl0yaG3SW76RfRj6t6uG/QzH27avjgzSxcLheXJ7/P5T3mo0/5Hfi/otUTRFyIPXYy29IXsqDIyF7HEAoa6ml0apPWdQ3uyiNjHiHUN5S12WvpH9WfAdEDCDOHnXCupOCkFsUkpaS0xkpJdQM+JgNmbwNBvia8TYaj63NK69iSUYpEEubvjb+PiUOF1ezMKSejqAYfkx5/HxMmg456q4O6RjtVdY04XKdvTeRj0pMUEUBMiC91DXaqLDYKKy1UW37tPBcd7Mvk1AT8fUykFVSx73AlGcU1AASbvVh3oIj3Vx7gwj7ReBsNSCmx2ByU1Vgpq7FSWGXB0ug4ejyDThAX5kf3qECSYwKJDPThQH4VO7LKSCuoxiW1mHvFBqnEoCgt1CkTQ1l9GWtz1vK3MX9rUeXnb2Wpd/DVR9lsXFtFtF8GM4bNJGzA9RA2F3I/o+LA27xZbWa9WEOefRZ1Nm1+AUEDAd4BpMYO5bZBtzEyYSRmkxm704W3qxveRj166Y2l0UFGcQ0HC6oormpArxPodQKzt5HwAG/CArxptDsprmqgpLqBmgbb0QtxTmktdVbHCTGH+HkRHexLWY2V4uqGk36upAh/LkiJxO50Udtgo9HhIjbEF7O3kWA/L7qEmokNMaPX6aiqb6TaYsPZNC+1wyk5XFZHRnENO7LLCfAxEWw2cUFKJMkxgfSICaKgop6Fm7N5Z4U2TpKvyUByTCC/n9iTMb2iiQzyYWdOOQs3ZbNs+2GkBJ0AL6OesAAfwgO86RMfTJcQM9HBZmobbGSX1pFVUsPmjBJW7MoDQCcEPWIDmTayK73jgukVG0yA74lPWoqinFynTAz/Wf8fXLjoE9Gn1Y+dvr+Wt15Ip7ERugbv4r5rVtE44FtWrJrBsvVz2WDzpcgZC4Be1HN9v+sZmzSWpOAkuod2P1r+75KSjKIaVu7ex4+784+5q27O10u7a3Y4JXan64T1Rr2OQLMJPy8j/j5GLuwTQ1JEANHBvlhtDuobHZTXWimstFBYaSEpMoAbR3dneHIE3iY95TVWqiw24sP8CDK7d1Kg5OhALuwTQ3ZJLUJAXJjfCcVKAxPDGJh44hMTAGvXwoGdYAnRXoMGQX+t57WUktLqBorTsujqp8Ns1IPBAKHe4GM8+fEURTmpTpkYvtz/JQBXplzZasd0uSTffJLPyiXFgCA6ahWZvT5lUoYvOdumNG2lDf7WLaQbN/S/gZsH3IKP8ddxkKrqG1l/sJitGWXsyimn2mLDoBOMSIlkfN8YhBCU1VqxNDpIivCnR0wQwX6/XqytdidlNQ2U1ljxMuqJCvIhyHxiuf5vYQ43En/We59EeTls3gwxMdCtG5hP7FiWGOF/kh2bkRIcDjA2XdALCuCRR+CTT47dzmSCK66AyZMRO3YQ8c03ROTmnng8gwEGD4aNG09cpyjKCTpdYmh0NJJRkUFcQBx+Jr9WOaaUkhee3Etutg0hnFQkvs6yoHVQJRkUnsINY/5CqG8o4X7hDO8ynAP5dcxfnc41y34kOtiX+DA/6hvt7MmtwCUhzN+bod3DGZAYyvDkSAJbWMzhbdTTJdSPLqHn+LmkhMZGsFh+fQUFQWUl7N8PWVng5aVtV12tvQYOhD59oKYGZs+GQ4cgJwe8vSEsDCZPhu3bYeFCpMOBS6fDqdPjMpqQRhPeEaGIqCga0NGYX4hLSqTDicvhRAIRof7g5UVVSQX1DTYkIA0GpNGEaGwkrroYnnqKEi9/6j7+DOl0gtWK3LQHwy/bSawqhEsvJX/UROq37Tj6/4bLhZetkcTL3N86TVE6i06XGD7c+SESyVUp517pLJ0O7Flf8e3nReRmj0aaSljb7VnqvAsIMnpx+8BbuW7gdCqrfcgtqyMj08LCn7ex93AlIX5eTBmWSFlNAzmldeh1ghtHd2d0z2i6RvqfW92Hy/XrRfzLL5FFRUg/P3QREdRHRlO0eRdWnRGr3UmjzY61wcbg7hEEBfuTkZ7P+sJ6bHoTNoMRm0H7OX3VAsKrStnQYxiLhl+JXW/FoTfg0Pvg0Pnzr3vuJ7S2gkXDJvHpmOtwRV2MY6wBp16HS+j48Nm7CPDzZs49T/NJ5IATQv72x5cwCcn/olJZdMmFx6zTOx0s/fFF8PfnvRE3sCLq2CJAP2s9X14eA6NH887rS1h73ZPHrI9orGXePaMgLo43/ruYrb2uPWZ9gr2G2Y9PPft/b0U5z3S6xDB762wA/nzBn8/+IE4b9Xs/Yt48G4cro6hqGI1f0i98FfA63kbJrAuf4KaB09meVc5zX6RxsKAaAL1OEBPsy32X9ubywfGnbHJ5Oja7g7xftlGdX0x1cTnVFTXUVtUyyuwgacQA0iusvP1LLvVevtR7m6n3GUFDTx9mzX+GoZnb2ZEyjFk3/f2E4/7n/b8SdHg/2WOmMG/iXRidDoxOByaXA6N0cl2MgfDh/bEbI7Bk1mFwOTBJF2ajAYPJiPjgA3BaiSy0MEQfij4mGr2XCb1OoHM4MKz5Gfr3ZWBeNYbcCm25EAgh0OlA97cVoNcxNqecuJJadE3rj/y78dRqAC4/XMGgSgtCCIQAgcBo0EFPrTPgdVePZFytFQHaNmiV08SFA3DbdaOY3Ky+RgjwMRm0JxtFUVpESNmyAc08KTU1VW7ZsuWM2zlcDkL/XyhxAXHsuW/Pbz+RlJD7OduWLuCDjX/Ebg9B4qK412dkGUqI109COv3x8zZi0OsormogItCHm8d0Z0jXcEL9vbWL3EkPLRFCYGl08POa3ZTmFlGWW0R5vY1yDFxfupeJoYKM3Ye4b8yME/Z/9MuXuHjnj2RFJPDmpHvws1sxBwfgmxCHb1Q4E1K7Et+9C+X7D3FgRzreZcV4O+x4u+x4+XoTPqgvXoMG4PTWZl47VZznIyHEVillaluft6Xfa0U5W2f73e5UTwyrsldR01jDrPGzfvvOVXspXX0Pz6+eSEPhP3DhQOIgM2ELMJwIuw/xYYH0jQ/B0qi19rluRFcuGxR3zJOB0+Vi48ESDmfkk5eRR2GVhQKHgcuqDnH7/ddij47jv+sLEC4XwfV6wmotRNZWYt66DnJ2ETNiJE9k/kCQcBKgkwT6GPHrnojhuccg6kWSjEZeMBohIUGrBzhOaN8ejOrb45Qf87c/wyiKcr7pVInhtY2v4WPw4fLul7d8JymxH3yDxev+wQdZlxNTOBmQSKGjML6CgNCuDEqM4OphSfTuEny0bqC+0U5GUQ2Lf9rDob2ZdCnN4+bDmxHp6Tx30aM0mrwJqa0huqKQweUFdD+wAV77GwEmEx/6BBKqd2G4ZwbceAn4+IB5GqSk4GMyoUYlUhTFkzpNYnC4HCxJX0KQdxA+Rp8W7dNQX8if500hL/1CTNZZRFcPA6A21MLV07owbkBfQv29jw7DIIQAp5O/vfUD2yrsyKYkEVpTS+DunbDnR3QpKbyydT4RlmrM/fvABQNg0EUgb4PduxG7dxPZrRvceaeWEBRFUdqZTpMYPt79MU7pbFHfBSkli7a+weuf76J73hskoMeld1ITaMW7m4tZtwzC7G1k8748tq3fw65qF3qHnY82vo/Yvp2BPS+kj95ISv5BujeUE9yvF1xyMXz+Mvj7c8rBK4YMadXPrCiK4g6dJjG8vul1AGaOOv3czodK9vOXz/+I964HSK7TxvmvCq8lZpCJsV2jmDIwls8/XcWCQq1SPqSmhkFZu+iXvQdXZQb6Sy9l2tCh4OcHl7+odeRSFEXpRDpFYnC4HGwr2kaITwg9w3uefKPq/TjTXufDNRbCdzyPwaXHZbQz9Pog6htdrD9QxB9Wz8f3q/mkBkTj16UHQ9K3keCoRVx5JTx0K1x2mdaZS1EUpRPrFIlhUdoiHC4Hk5InnXT98k3/j29X/0Bl/n34l3XB4NKhj7BSF1nJp9vKMNkbGZq+FdZ+D5Mn0+e66+iTlgbjn9DG49GdfFhnRVGUzqhTJIZlh5ZhNpp5buJzxywvqSvhwbkPw96bCa6ZSBACQ3Q1d19g4MkdJfQ4sJ/bdvzIyLRN+PbrDf/6O0yfru18lfuG61YURWnPOnxisDvtfLX/K6b0nEJMwK/l/bNXv8uyr8xElf4ZgcClc2ELLeD11c8gXtzMR0GhmMND4KGHYNpnqohIURSlSYdPDK9vep3yhnJGdtEmlLdarTw5703KN1xAtNULiaQyuI6Y+vVcs/wbsBTDq69ivv12CAz0cPSKoijtT4dPDEfGRprWZxr/+2ou/7+9M4+vqyr3/vfZ+4w5yUlyMpMmbdImHaG0tEAtvUUGPzhAuYAyqCgyKSoKCCJ6FeFV8YrgywX1VqkVeRHlIrYUQV6lINRW2wItHdI2adqmTdOmaeaTnHHdP9ZJmtOmNm2Tkyas7+ezP2fPa62dlf3b63nWetYrq7LwH5iLJ+Qg7IxQ0vkKdyz9LRVFmfCVG+CWW4zPwGAwGP4FQyYMIrII+BiwXyk1LbEvAPwOGAfsAD6hlGo+0TTaQm1sadrChXI53/piFY7IGeQBlrRx0+b/IpDRQcmnroJfrdHdSw2GE0RELgH+LzqqyC+VUg8ddvxO4CYgCjQCn1NK7Ux5Rg2GQWAoWwyLgceBp/rsuxf4q1LqIRG5N7H99RNN4Id/+wG3tN2B1XAdAAqF27mFH0/ejfXkM/3GEjIYjhcRsYEngIuB3cBqEVmqlNrU57R3gFlKqaCIfAH4T+Dq1OfWYDh5hsymopT6G3DwsN0LgF8n1n8NXH6i9w8e2EvHs/OxGz6JIHR52/l4y3/x6FenYH39HiMKhsHkbKBaKbVdKRUGnkXX5V6UUsuVUsHE5ipgTIrzaDAMGqk2thcopfYm1huAgqOdKCK3iMgaEVnT2Nh4xPGVb+0lGMsiZsVoLX6N7+T8jtwzs1i/+i3aGvYecb6Kx1HqyDmTDYYBUAzU9dnendh3NG4EXu7vwLHqtcFwKjBszmellBKRo04GoZRaCCwEHbf+8OOFs92sfu8hSpoP8mCwhLxAJsW2DfW1xH/+IzqcLkJxhRUJ47JtnCiU24M9bQbWnPlYOXlDWDrD+xUR+RQwC5jf3/Fj1WuD4VQg1cKwbtYFeAAAHQ9JREFUT0SKlFJ7RaQI2H+iN5paPJVXvvoYWc4Crr4+wu69G/E1/ZZ5zvW4Yu3k+dI4Z0whFTkBnJaeSUxC3ai1K4ms+Tut0RhpLhc2oDxeHHn5WIXFSHYO1jnnIWKhDh5AdQXB6UJ86eByg8NxctNyGkYie4CSPttjEvuSEJGLgG8C85VSoRTlzWAYdFItDEuBzwAPJX6XnMzNCjP0dI9Lfu/ilVen863/LuLveWHmlkWZfl4Tt/3nenYvf5ED1cuoLCygLJDJOJ+HsjFj8Ks4E7P9TAhkkRmLIl2dqF21xJXi4Ov/n5DtIKe7E0c8lpyo24PjrvsRp5PosudQ1VsgGoE0H5Luh8xsHAuuRjU3EfvzEtSB/RAMakEpLUNKy7DPPg+A+Pq1qGCn7j5r2YhlQYYfGV+JWDbx6iqIhEEsfY4I+HxIdi643ai9eyAe08cT02iS5kOyAgA6bdDX9SxuD5LmQ8ViqI52xLZBBAUQ7EAFg1gZfpQ3DWyHzpP0uQfSrzCqYAe43IjDeTJ/0lOV1UCFiJShBeEa4Lq+J4jIDOC/gUuUUif8wWMwnAoM2dSeIvJb4HwgF9gHfAf4I/B7oBTYie6ueriD+ggGOgXi9h1xbvh2I3Z6CGJCW5MDvx/CXeuoWvkw8WiQmz9/Jw9980qam1t48MEH+dnPfkooFGJyXoB/G1fC1LwcSrP85PnSaA520xYK4XHaTM7LZWyWH4dlgcOJjBtPZEcNjmgEhX534nRCVgBJS0ftrOl5EmAJxBP+Dbcb69z5qJaDqM3rIRxOLoRl63MDOdDRduTxHrxpEIloUepLVgCrcir4fMTf/OuRx/MKEKdLi8qJ+FzyC7FKy6FkHPE/PqsLHldAoh653EheAcqXDtu3ajFRKrEABUVIQRFEIqhtm/Tzse3exZp9HpKZRXzvHtR7b+v9lqUFMBZHKqcg/ixUUyNqZzU4XXpRCuJxrNlzEV86qq6WeFVielelsM4+D3tOv9adAU1/KCIfAX6C7q66SCn1PRF5AFijlFoqIn8BTgd6HFy7lFKX/at7mqk9DUPNiU7tOarmfAZobo1z6z2dvLctTE5xGFdGhFgUwge9TKqw+PL1acyc7GXLzhC3/3gflWMUp/kPku09iN/dRnFRgLy8PNrb23n88cd58cUXaW1tBcBl28wbW8w1Z03nkonj2binnkWr1/HytlquOn0yd583mwlZfmKZ2bSOncDzVTXkja9gXFkZRXl55O/ejqx8HYKdkJEJ/kwtAsFOCHVDZhbk5mMF8lAH9qF274KuTkjPBL8f8fogIwMJ5KH27kZVbdAtCki0JtL1yzca0ffrD9uBlIyFohJobIBwCBUOI243eH1I0Rj9Ym5vRW1cp8+J9Wk1ebx6O9JHsFwuyC9KtEi8SCyqWyvt+rlhWeD26F+nS18fDul79BWVoSQ7B+ft9/V7yMz5bBitGGE4jF/8Ar70JcjKj1BxThuOnE4sG/Kzbc6Z6iXb46IzFua9mjDVu8O9H/SP3VXAtPFudu2LUN8YZWyBEA7uIxwO093dzZo1a1iyZAmvvvoqXV1dSWmKwNhMPzta2o6ar+uuvpoHH3yAhsYD3HvvveTk5FBaWkppaSnBYJCuri7i8Tif+9znyMvLIzMzEysxUjsUCrF//34aGxspLy8nMyMdtWcX4kmDnFzEPmQZVOEQau8eVH0dhLqRvEKkoBACedo8NEBUNIKqroKuIFJaDoFciEVRO2pQ27chhachU6cnpd17bSQC4W5ISz+qX0YpBW0tWkhamrUpLSsbPGmothZoOahbRlkBvT/NB7YDbAtamlEN9agD+3RLxZcOvgzE49EC5nLpcy0LbLvfPOq/mxEGw+jECEM/rF0Ljz8OK1bAjt0xcsd1UX56F97cbmJKEW53UJGXwU1Xe0nPjrJ5R5hL56Xj81osXtbCU3/SL/h0rzC2yMnYIidfvCobr9viYGs34e4OYtEQwWCQuro6tm/fzt69e8nMzCQQCNDW1saGDRvYsmULmzdvZu/eI7vR9kePEMTjcUQEl8tFLBYjGo32nuPxeCgtLWXGjBmEw2Fqamqora3F5/ORk5NDIBCgtLSUWbNmUVBQwNatW9m0aRN+v58LL7yQ888/n8LCwuN+pn2Jx+O9eR3JGGEwjFaMMByDhgZ4/nn41a/gnXfj5E8IUjq9A19OmGhI6N6fztdvzuDKy/RXZWdXnO17wmzfE2F7fYRdDRH2HojyzIOnYVnCw0838crKTvIDNkW5DopyHBTnO7n2Q34AWjtieN0WLqf0yUMDb7zxBl1dXeTn55OXl0drayu1tbXU1tZSVFTE3LlzKSoq4jvf+Q5PPvlk78u3sLAQv9/PRRddxPz583n22Wd5/vnnjyjnvHnzyMvLY9OmTVRVVR1x3Ov1JrV0RATbtnuXmTNn4nK5qKuro76+HpfLhcfjwe1243Q6mT9/PsFgkJUrV7Jjxw6Ki4uZN28e5eXlOBwObrvtNpxOJytWrODNN9/E4XAQCATIysrC6XRy5ZVX4vP5qKqqYsuWLdi2TVdXF5s2bWLnzp3cdNNNzJkzh7q6Ovbt25eUN9u2mTRpEiJCU1MTnZ2dvfsty+pNC6Crq4uOjg4yMzN7jx+t1WKEwTBaMcJwHGzcCH/8IyxbBhu3hyib2U5gbBCxtKkpw+2k/YCT82a5WPAhN2MK7CNeKqs3dbGhJkT9gSj1jVEaDkbxui2e/q4O/X33Y/tZW9VNZrpFTqZNbqZNRYmLGxdkAfB2VTcIZGdYZPps/OkWDjs5jZ07d1JVVcXcuXNJ7yfWU2trKy+++CLl5eVMmzaNzs5O/H4/Pp+PlpYWVqxYwbp16zh48CBFRUV4vV4uvvhimpubee6551i+fDmdnZ10dXURCoUIh8Pk5eWRm5tLJBKhpqaGcDhMOBwmGo2ilMK2bQoKCsjJyaGqqopwOEzfOpSenk5HR8dRn312djYiQigUorOzs99zpkyZgs/nY/Xq1UccKyoqory8nH379lFdXZ10zO1289hjj7F8+XJeeOEFQqFDPUaXLFnCpZde2q84GGEwjFaMMJwgGzbAddfB1u1RLvtUkJziMDsbIgSjESxbnyNxi/J8L5++3EvlWBe2BbYtZGckf4VGY6r35f7Wu0Fq6yMcaIlxoDVGU2uMwhyb+2/WA+tueKCenQ3RpLx84Awv/+fz+vgPn2oiHFVkeC0y0ix8aRbji53MnuIFoGpHCLdL8Hks0jwWXrdg26kfX9HV1cXChQtZtGgROTk5TJo0iYqKCnw+H06nk2g0Sn19PfX19bS3t/d+wbe2tnLw4EG6u7spKyvjzDPPpKSkhIaGBhYvXsyqVavw+XwEAgH8fj8ZGRmkp6czZswYamtrqaqqoq2tjUgkkmRiAygsLGTy5MkA1NTUUFdXx/jx49m2bVu/ZTDCYBitGGE4Cbq74b774NFHD+0TS3HOvAj+ghBN3SF8+V3YzuRnVVni4p7rA5QXu447zV37IjS1xGjtiNHaEaelI05+wObDc3TL4O7H9tPQFKU9GKejK048DhefncY3PqsnFLrkK3WEI8n5uXx+OrdfHSAWV9z6/QY8bsHjEtwuC49bmDfdy/ln+QiF4/z21TbcLgu3U3AllspSF+OKnIQjis07Qnq/Q3Amlsx0LULxuCIaA4cNljU0YhSLxbBte8DndnR00NraSjQapaysLEmwW1pa2LVrF2eccUa/1xthMIxWTrRuj/j5GAYDjwceeQS+8Q3YvVv7I1asEH7+cxdNb7g4/fQM5lco5l4UwuuP8o37dLfYcFcbNz7YQJHbzyXzPMyfaxPItMlIO7ZDtrTASWnB0QeD/ej2/N51pRRdIdXbc0opxXdvyaWrO05ntyLYHacrpJgwRt8vFoOiPAfdIUV3OE5rZ5RQWDGxVAtYZ7fqdaz35ebLsxhX5KSxJcodjx45Ruv2q7O5fH4GtfURbv5+A6A7/DhswWnDHdcFuGCWjy07QzzwZBMOG2xLen9vvSKLMys9bN4RYtHSVj10wRLdaciC6z+SSXmxi821IZa+2YFtaeGxRKfziYv8FOY42LwjxN/eDiYdE4HL5xeTlWFTtSPE21u6sUQS4/IsLp037Zh/E4PBoDHC0Ie8PL0AfPjDuhXxm9/AU0/Bo48Ij/zYg8cDaWngcEBjyEdmRQsNxW0sfq2Nxa/pa73iYmqplwUXpnHuDMdJm3hEhDSPJG2fM9V71PNdTuHBW48eCyrgt/nL4yWEo4pwRBGKKMJhRXpC0HIybR6+PZ9wRBGOKiKJZUqZjlibnWFz02WZRGLafBaNKiIxKM7T1cnrtpha5iKaOB5XEIspnA5dhlgMukJxYnG9Px6HmIJQWLeAmttjvLOlm1gc4kofVwoumZNOYQ7s2BvhD6+36zFt6tDYwQtm+cjKsHmvJsQvl7Qmlfmis314TcBdg2FAGFPSAGlogCVLoLpaR7hoa4NVq/S2NzPClOkxPrYghj83yu+WdeHL1QPAYmELd9zFWWc4yM+HSExRlONg9hQPlaWuI0wxDU1R6vZFmFLmxucd+V1BU0VPPRYRYjGlRSeuR1vHFXjdclSzlzElGUYrxpQ0xBQWwq23Hrl/xw548UUnP/uZk+/eBdnZMGdOJkU5UUJ2NwcJ0RoN825tiLQGIRoR2oIxfrWsFZdtcVqukzGFNj6vsHF7iN37tSPV6YAzKz2cN93L/Jlp+H0Ds7e/X+nrU7BtQbsnTLBDg+FEMC2GQUIpWL4cnn4a/vEP2LxZ78vKgksvhQ98QJugtm+HN96Ksbu5G0dmN56MKG5fjIKiOJPLXZQGPKQ5nbRFu1m9uYs9jVGcDjhnqpc5Z3gZV+ikpMCJbUFrZ5z2YJxIVJtbLAsqSly9Jhudr0Nf0n2JxRWWHLn//YhpMRhGK6bFMMyIwAUX6AW0qen11+EPf4ClS7WvogfLsrnuOh833OCjuRnWrIH/+A8tHHfeqXtHiXiprMxi2qwIGcWdbNzeyVvruvpNuy/pXmHu9DQmjXWxqTbEu1tDtHTEKM5zUlroIBaDnQ0R6g9EKcpxMG9GGvPO9FJZ4hqW7q4Gg+HUw7QYUkAkAvv2QSgEnZ3amf3Tn+push6P/lUKvF5tikpP16YrgJ079XW79yj2Hohy3/0R9jRGKSyEsSUWleUW5WVCWhoEuxV/X9/FivVBOrsUWekW0ys95Gfb7GnUvgtLoLTQSXG+k+q6cK+T1+0Uxo9xMmGMi9wsm4DfJttvk5VukZVhk+238LhGp8/DtBgMoxXTYjiFcTphTJ8ZgB9+GO65BxYuhNZWLQhOp15vaoJt2+Ctt3Rvm8JCuPhi+OMLwqxZTooynGz6J6x8CXoiW8ycqeNCAWxdm8Ynzw5QVBrl3JkO3O5/3Qpo64yxelM3VTvDbNsVZvnaIO3B/sNx+7xCbqaNz2thWz12fC1qAHlZOjxIwG/THozT2hnHacO5p3uZWu7GPsz5G40p2oNxMn3WcY2HaGmPsX1PhDH5DvIDpgobDIONaTGcojQ1wZ/+BC+9BH/+M7S0JB+fN09Hj7USc/hccYV+Qefl6WtBi01lJXzmM3D33Xrfli1QVqYDjx6NcERxsC1Gc3uM1vY4zR0xmlsPjeAOditicaWjcfeZbqKxJcr+gzEdSRvdEygaU0SiOvTH2CInXd2Kzu44bZ16AchMt5g50cOkcS7qG6Ns3RVmf3OMgoDNmHwn6V6htTNOS3ucXQ0RGlt0GHARmD3Zw4c/kM6Mie4kB31Le4xtdWGqd0fYtiuMw4b7bsjtt7ymxWAYrZiRz6OYaBRWrtQtiY4OaGzUYcX37YPLL4dJk7RwhEIwaxZMmAD79+uYUBs3wvnna99FRwdkZOi5byZMgMmT9bJgAZxzzuDkNRJVtHXGyUjTAQSD3XH+ubGLN9d1caA5htcjpLktMhMmKp9X2LYrzNtbQjS1xkjzCBUlLgpzHOxrirKnMUpnd5ysDG3WKsxxUFnqouw0JxtqQry8spMDCaEoyrE5Lc+ZJB4ARbkOzpjg5uvX5/SbZyMMhtGKEYb3GR0derT2ww9rk1J2tt7f2Kh/Z8+Ge+/VwtETGTsYhBde0D2mNm3Sv9XV2tn9pS/p1sSFF2qhmTjx0O/s2YfuP1QopWhui5OVcXxmpVhcsX5bqNcUVn8gSkmBgwljXFSUuKgodR1zJLoRBsNoxfgY3mekp8O3vw3f+tah6ZiV0i2El17S4cWvvBKmT4frr9ei0Nysnd1jx2pTVFkZFBXpUdygBeSCC7RAPP207lkFOhLtggW6G+7DD2vzVGUlVFTo35ycxHTQJ4GIEMg8/rEatiXMmOhhxkTPyWXAYDD0YoRhhNN3nhwRmDZNL1/7GjzzDHz3u3DXXfq416unkO47U6cInHaado4XF2vR+PjH4YMfhPZ22LpV3w/gwAFYt04LRd+ApmvXagf4G2/osRwTJmjRmDABAoGTFw2DwZBajDCMUmwbPv1pHVK8qQkyM8Ht1i/0+nrdDXbHDj3grrYW9uzRpqWXX9amJZcLzj5bC0VxMUydCh/7mBaKSERfu3Wr9ntUVuo0V66EBx441EsJ9AC/2lr9+9pr+rrychg/Xt93FEwAZzCMOowwjHJsG/IPBWrF4YDSUr3Mm3fk+aGQ7ir78svadPT3v2vRCIf1tR/8oBaMnBzdA+oTn9BmLdA+jTvu0GJTXa2XnTu1KAEsXpw80M/lgilT4O23davi1Vf1OI+yMr30XGcwGFKLEQZDEm63dkBfeOGhfUppc9Hzz+uR3H/5y6FWgdMJ114LN94I69frczZsgH//dx1b6qyzDt1n0SK4/36oqdHiUVOjB/f1mJp+8AM9WryH7GyYP187zEH/Ohy6FTN2rBEOg2GoML2SDMdNPK67x9bVwZNP6hd+zyydU6Zos9OyZbq31KRJcOaZev/kydrsNGGCDv9xOM3N2uzUY96qrdXi8L3v6eMVFboV0kNmpm6xLFyot3/xC/D7dWuopEQ71gcy14/plWQYrZheSYaUYVnaqRwIwGOPaQf3K6/AjBlaCEALx9NPa5PUqlXw7LPJ9ygv162JmTO1KSoe162PSy/V+/rjrbe0aarHP7Jz5yH/hlJw++26BdKDbet9jzwy6I/AYBjVmBaDISV0dBxyVm/bpns3rV2rWwV9sSzt5L7+ev3SLy7WrYaB9Gxqa9NiUVenl127tPhcccW/vs60GAyjFdNiMJzSpKfrlsDhrYG2Nu3wtm3dHXbxYm2eWrr00DkFBXDVVXD11Vos6uv1qO+KCt27qQe/H04/XS8Gg+HEMcJgGFb8/kPrgQB8//vaQb12rZ5/e/du3TPqySfhiSeOvH7iRPjoR7XgTJyoxcLvP9TC6O7WTu62NpgzJyVFMhhGPEYYDKccLlfyS/yOO/Rgu5de0q2K007TXWXffVc7uR9/XHen7Xt9bq5uhezerf0PEydCVVXqy2IwjESMMBhGBBkZcM01yfvmzYMvf1mbompqdCiP6motHk1NWizGj9etiB6nuMFgODZGGAwjHrdbd4edMmW4c2IwjA5MQAKDwWAwJGGEwWAwGAxJGGEwGAwGQxJGGAwGg8GQxLAIg4hcIiJbRKRaRO4djjwYDAaDoX9SLgwiYgNPAB8GpgDXiojpT2I4pTnWx4yIuEXkd4nj/xCRcanPpcEwOAxHi+FsoFoptV0pFQaeBRYMQz4MhgExwI+ZG4FmpdQE4FHgh6nNpcEweAyHMBQDdX22dyf2JSEit4jIGhFZ09gzw73BMDwM5GNmAfDrxPr/ABeKmElNDSOTU3aAm1JqIbAQQEQaRWTnUU7NBQ6kLGOpZ7SXD4a/jGOPcby/j5lzjnaOUioqIq1ADoeVS0RuAW5JbIZEZMOJZvokGa5nPpx/6/djmSeeyEXDIQx7gJI+22MS+46KUirvaMdEZM1whExOFaO9fPD+KGMPh33wDFu5hyttU+bUp30i1w2HKWk1UCEiZSLiAq4Blh7jGoNhOBnIx0zvOSLiADKBppTkzmAYZFIuDEqpKPAl4M/AZuD3SqmNqc6HwXAcDORjZinwmcT6VcBraiTMgmUw9MOw+BiUUn8C/jRIt1s4SPc5VRnt5YNTvIwJn0HPx4wNLFJKbRSRB4A1SqmlwJPAb0SkGjiIFo9jMZzlHq60TZlHQNojYmpPg8FgMKQOExLDYDAYDEkYYTAYDAZDEiNWGEZ7vCURKRGR5SKySUQ2ishXhjtPQ4GI2CLyjogsG+68DBXDGU5jAGnfmahj60XkryJyrDEdg5Jun/OuFBElIoPSnXMg6YrIJ/r8Xz0zGOkOJG0RKU38T7+TeN4fGaR0F4nI/qONiRHNY4l8rReRmce8qVJqxC1oB2ANUA64gHXAlOHO1yCXsQiYmVjPALaOtjImynYn8AywbLjzMkTlO2ZdBW4Dfp5Yvwb4XQrT/iCQllj/wmCkPdD/z0S9/huwCpiVovJWAO8A2Ynt/BQ+64XAFxLrU4Adg5T2vwEzgQ1HOf4R4GVAgHOBfxzrniO1xTDq4y0ppfYqpd5OrLeju/YeETpkJCMiY4CPAr8c7rwMIcMZTuOYaSulliulgonNVegxGkOeboIH0TGlugchzYGmezPwhFKqGUAptT+FaSvAn1jPBOoHI2Gl1N/QPeGOxgLgKaVZBWSJSNG/uudIFYYBxVsaLSRMCzOAfwxvTgadnwD3APHhzsgQMpC6mhROA+gJp5GKtPtyI/rLcsjTTZgzSpRSLw1CegNOF6gEKkVkhYisEpFLUpj2/cCnRGQ3urv+lwcp7WNx3O/LkSoM7xtEJB14HviqUqptuPMzWIjIx4D9Sqm1w50XA4jIp4BZwI9SkJYFPALcNdRp9YMDbU46H7gW+IWIZKUo7WuBxUqpMWjzzm8Sz+KU45TM1AA47nhLIxERcaJF4f8ppf4w3PkZZOYCl4nIDnSz+wIReXp4szQkDGc4jQH9n4jIRcA3gcuUUqEUpJsBTANeT/z9zwWWDoIDeiDl3Q0sVUpFlFK1aN9dxUmmO9C0bwR+D6CUWgl40AH2hprjf18OhvMj1Qta9bcDZRxy9Ewd7nwNchkFeAr4yXDnJQVlPZ/R63w+Zl0Fvkiy8/n3KUx7BtppWpHKMh92/usMjvN5IOW9BPh1Yj0XbWLJSVHaLwOfTaxPRvsYZJCe+TiO7nz+KMnO538e836DVRlSvaCbYlsTlfqbw52fISjfeWhn1Xrg3cTykeHO1xCVddQKQ6J8R9RV4AH0FzroL8fngGrgn0B5CtP+C7CvTx1bmop0Dzt3UIRhgOUVtBlrE/AecE0Kn/UUYEVCNN4FPjRI6f4W2AtE0C2iG4HPA5/vU+YnEvl6byDP2oTEMBgMBkMSI9XHYDAYDIYhwgiDwWAwGJIwwmAwGAyGJIwwGAwGgyEJIwwGg8FgSMIIwwhBRLJE5LbE+mki8j/DnSeDYTAwdfvUw3RXHSEk4iUtU0pNG+asGAyDiqnbpx7DMuez4YR4CBgvIu8C24DJSqlpIvJZ4HLAhx7a/zB65OWngRB6UNxBERmPHuSSBwSBm5VSVakvhsFwBKZun2IYU9LI4V6gRil1JnD3YcemAVcAs4HvAUGl1AxgJXB94pyFwJeVUmcBXwN+mpJcGwzHxtTtUwzTYhgdLFd6zoZ2EWkFXkzsfw84IxGh9QPAc33C/LtTn02D4bgxdXsYMMIwOugbETPeZzuO/htbQEvii8xgGEmYuj0MGFPSyKEdHa74uFF6HodaEfk49M4BO30wM2cwnASmbp9iGGEYISilmoAViQm/T2QylU8CN4rIOmAjo2wqVMPIxdTtUw/TXdVgMBgMSZgWg8FgMBiSMMJgMBgMhiSMMBgMBoMhCSMMBoPBYEjCCIPBYDAYkjDCYDAYDIYkjDAYDAaDIYn/Bcy/d71E5F0dAAAAAElFTkSuQmCC", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the fit using median values of parameters\n", + "\n", + "post1 = df[df.columns[7:]][0:iend].to_numpy()\n", + "est = np.median(post1, axis=0)\n", + "\n", + "# fill mu_h\n", + "# mu_h = mu # if mu is fixed\n", + "mu_h = est[0:num_species]\n", + "est = est[num_species:]\n", + "\n", + "# fill M_h\n", + "M_h = np.zeros([num_species, num_species])\n", + "# np.fill_diagonal(M_h, M.diagonal() ) # if Md fixed\n", + "np.fill_diagonal(M_h, -est[0:num_species])\n", + "est = est[num_species:]\n", + "\n", + "count = 0\n", + "# print(\"est:\", est)\n", + "for i in range(num_species):\n", + " for j in range(num_species):\n", + " if i != j:\n", + " # M_h[i,j] = est[2*num_species + count]\n", + " # M_h[i,j] = est[num_species + count]\n", + " M_h[i, j] = est[count]\n", + " count = count + 1\n", + "\n", + "# print(mu_h)\n", + "# print(M_h)\n", + "\n", + "# make the plot and comparison\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h)\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(\n", + " times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)\n", + "\n", + "# this does the stem plots with orange crosses the actual parameters\n", + "compare_params(mu=(mu, mu_h), M=(M, M_h))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[]\n", + "[]\n", + "[]\n", + "[]\n", + "[]\n", + "(20, 94)\n", + "[False True True True True True True False False True False False\n", + " True True False False False False False True False False False False\n", + " False False False False False False False False False False True False\n", + " False False False False False False True False False False True False\n", + " False False False False False False False False False False False False\n", + " False True False False False False False False False False False False\n", + " False False False False True True False False False False False False\n", + " False False False False False False False False False False]\n", + "[ 1 2 3 4 5 6 9 12 13 19 34 42 46 61 76 77]\n", + "(20, 16)\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/examples-sde-maria.ipynb b/examples/examples-sde-maria.ipynb new file mode 100644 index 00000000..cadcb084 --- /dev/null +++ b/examples/examples-sde-maria.ipynb @@ -0,0 +1,787 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "53eb7b1a-08b4-4878-bb14-bc1073082119", + "metadata": { + "tags": [] + }, + "source": [ + "# Full Bayesian inference using linear approximation of dynamics" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "593af750-956c-4d93-b8ab-8e830d57d5c2", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "from scipy.integrate import odeint\n", + "\n", + "from numpy import random\n", + "\n", + "from gMLV import *\n", + "\n", + "def set_all_seeds(seed):\n", + " np.random.seed(seed)\n", + " random.seed(seed)\n", + "\n", + "# some plotting functions\n", + "\n", + "cols = [\"red\", \"green\", \"blue\", \"royalblue\",\"orange\", \"black\", \"salmon\", \"forestgreen\", \"steelblue\", \"slateblue\",\"gold\", \"palegreen\"]\n", + "\n", + "def plot_gMLV(yobs, sobs, timepoints):\n", + " #fig, axs = plt.subplots(1, 2, layout='constrained')\n", + " fig, axs = plt.subplots(1, 2)\n", + " for species_idx in range(yobs.shape[1]):\n", + " axs[0].plot(timepoints, yobs[:, species_idx], color=cols[species_idx])\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]')\n", + " if sobs.shape[1] > 0:\n", + " for metabolite_idx in range(sobs.shape[1]):\n", + " axs[1].plot(timepoints, sobs[:, metabolite_idx], color=cols[metabolite_idx])\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]');\n", + "\n", + "def plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, timepoints):\n", + " # plot the fit\n", + " #fig, axs = plt.subplots(1, 2, layout='constrained')\n", + " fig, axs = plt.subplots(1, 2) \n", + " for species_idx in range(yobs.shape[1]):\n", + " axs[0].plot(timepoints, yobs[:, species_idx], color=cols[species_idx])\n", + " axs[0].plot(timepoints, yobs_h[:, species_idx], '--', color=cols[species_idx])\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]');\n", + "\n", + " for metabolite_idx in range(sobs.shape[1]):\n", + " axs[1].plot(timepoints, sobs[:, metabolite_idx], color=cols[metabolite_idx])\n", + " axs[1].plot(timepoints, sobs_h[:, metabolite_idx], '--', color=cols[metabolite_idx])\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]');\n", + "\n", + "def compare_params(mu=None, M=None, alpha=None, e=None):\n", + " # each argument is a tuple of true and predicted values\n", + " if mu is not None:\n", + " print(\"mu_hat/mu:\")\n", + " print(np.array(mu[1]))\n", + " print(np.array(mu[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0,len(mu[0]), dtype=\"int32\"), np.array(mu[1]), markerfmt=\"D\")\n", + " ax.stem(np.arange(0,len(mu[0]), dtype=\"int32\"), np.array(mu[0]), markerfmt=\"X\")\n", + " ax.set_xlabel('i')\n", + " ax.set_ylabel('mu[i]');\n", + "\n", + " if M is not None:\n", + " print(\"\\nM_hat/M:\")\n", + " print(np.round(np.array(M[1]), decimals=2))\n", + " print(\"\\n\",np.array(M[0]))\n", + "\n", + " #fig, ax = plt.subplots()\n", + " #ax.stem(np.arange(0, M[0].shape[0] ** 2), np.array(M[1]).flatten(), markerfmt=\"D\")\n", + " #ax.stem(np.arange(0, M[0].shape[0] ** 2), np.array(M[0]).flatten(), markerfmt=\"X\")\n", + " #ax.set_ylabel('M[i,j]');\n", + "\n", + " fig, ax = plt.subplots()\n", + " Ns = M[0].shape[0]\n", + " ax.stem(np.arange(0, Ns), np.array(M[1]).diagonal(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, Ns), np.array(M[0]).diagonal(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]');\n", + " \n", + " fig, ax = plt.subplots()\n", + " Ns = M[0].shape[0]\n", + " \n", + " count = 0\n", + " Mij = np.zeros([Ns*Ns - Ns])\n", + " Mij_h = np.zeros([Ns*Ns - Ns])\n", + " for i in range(Ns):\n", + " for j in range(Ns):\n", + " if i != j:\n", + " Mij[count] = np.array(M[0])[i,j]\n", + " Mij_h[count] = np.array(M[1])[i,j]\n", + " count = count + 1\n", + " \n", + " ax.stem(np.arange(0, Ns*Ns - Ns), Mij.flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, Ns*Ns - Ns), Mij_h.flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]');\n", + " \n", + " if alpha is not None:\n", + " print(\"\\na_hat/a:\")\n", + " print(np.round(np.array(alpha[1]), decimals=2))\n", + " print(\"\\n\",np.array(alpha[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, alpha[0].shape[0] * alpha[0].shape[1]), np.array(alpha[1]).flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, alpha[0].shape[0] * alpha[0].shape[1]), np.array(alpha[0]).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('a[i,j]');\n", + "\n", + " if e is not None:\n", + " print(\"\\ne_hat/e:\")\n", + " print(np.round(np.array(e[1]), decimals=2))\n", + " print(\"\\n\",np.array(e[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, e[0].shape[0]), np.array(e[1]).flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, e[0].shape[0]), np.array(e[0]).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('e[i]');\n", + "\n", + "def print_params(mu=None, M=None, e=None):\n", + " # each argument is a tuple of true and predicted values\n", + " if mu is not None:\n", + " print(\"mu_hat:\")\n", + " print(np.array(mu))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0,len(mu), dtype=\"int32\"), np.array(mu), markerfmt=\"X\")\n", + " ax.set_xlabel('i')\n", + " ax.set_ylabel('mu[i]');\n", + "\n", + " if M is not None:\n", + " print(\"\\nM_hat:\")\n", + " print(np.round(np.array(M), decimals=2))\n", + "\n", + " fig, ax = plt.subplots()\n", + " Ns = M.shape[0]\n", + " ax.stem(np.arange(0, Ns), np.array(M).diagonal(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]');\n", + " \n", + " fig, ax = plt.subplots()\n", + " Ns = M.shape[0]\n", + " \n", + " count = 0\n", + " Mij_h = np.zeros([Ns*Ns - Ns])\n", + " for i in range(Ns):\n", + " for j in range(Ns):\n", + " if i != j:\n", + " Mij_h[count] = np.array(M)[i,j]\n", + " count = count + 1\n", + " \n", + " ax.stem(np.arange(0, Ns*Ns - Ns), Mij_h.flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,i]');\n", + " \n", + " if e is not None:\n", + " print(\"\\ne_hat:\")\n", + " print(np.round(np.array(e), decimals=2))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, e.shape[0]), np.array(e).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('e[i]');\n", + "\n", + "\n", + "# some MCMC analysis functions\n", + "\n", + "def make_trace_plot(var,istart,iend):\n", + " plt.figure()\n", + " post = df[var][istart:iend]\n", + " plt.plot(range(0,(iend-istart)),post)\n", + " #print(var, np.median(post))\n", + " return\n", + " \n", + "def make_hist_plot(var,istart,iend):\n", + " plt.figure()\n", + " post = df[var][istart:iend]\n", + " plt.hist(post)\n", + " print(var, np.median(post))\n", + " return\n", + " \n", + "def get_Rhat(N,p1,p2):\n", + " M = 2\n", + " mean1 = np.mean(p1,axis=0) \n", + " mean2 = np.mean(p2,axis=0) \n", + " var1 = np.var(p1,axis=0) \n", + " var2 = np.var(p2,axis=0)\n", + " \n", + " meanM = (1/M)*(mean1 + mean2)\n", + " \n", + " B = (N/(M-1)) * (mean1-meanM)*(mean1-meanM) + (mean2-meanM)*(mean2-meanM)\n", + " W = (1/M)*(var1 + var2)\n", + " \n", + " Vhat = ((N-1)/N)*W + ((M+1)/(M*N))*B\n", + " \n", + " Rhat = Vhat/W\n", + " \n", + " return Rhat\n", + "\n", + "def get_horseshoe_tau(p0,D,sigma,n):\n", + " return p0*sigma/( np.sqrt(n)*(D-p0) )\n", + "\n", + "# extract gLV vectors and matrix from posterior sample\n", + "def extract_gLV_pars(est, num_species, e=False):\n", + "\n", + " # fill mu_h\n", + " #mu_h = mu # if mu is fixed\n", + " mu_h = est[0:num_species]\n", + " est = est[num_species:]\n", + "\n", + " # fill M_h\n", + " M_h = np.zeros([num_species,num_species])\n", + " #np.fill_diagonal(M_h, M.diagonal() ) # if Md fixed\n", + " np.fill_diagonal(M_h, -est[0:num_species])\n", + " est = est[num_species:]\n", + "\n", + " count = 0\n", + " #print(\"est:\", est)\n", + " for i in range(num_species):\n", + " for j in range(num_species):\n", + " if i != j:\n", + " #M_h[i,j] = est[2*num_species + count]\n", + " #M_h[i,j] = est[num_species + count]\n", + " M_h[i,j] = est[count]\n", + " count = count + 1\n", + "\n", + " #print(mu_h)\n", + " #print(M_h)\n", + " \n", + " if e==False:\n", + " return mu_h, M_h\n", + " else:\n", + " est = est[num_species*(num_species-1):]\n", + " E_h = np.reshape(est[0:num_species],(num_species,1))\n", + "\n", + " return mu_h, M_h, E_h\n", + "\n", + "def get_signal_matrix(npert, tp):\n", + " # calculate signal matrix\n", + " u = np.zeros([npert,len(times)])\n", + " for i in range(npert):\n", + " ui = (times >= tp[i][0]) & (times <= tp[i][1]) \n", + " u[i,:] = ui\n", + "\n", + " # remove last column of signal matrix\n", + " u = u[:,:(u.shape[1]-1)]\n", + " print('signal matrix:\\n', u)\n", + " return u\n", + " \n", + "def visualise_chains():\n", + " print(\"mu:\",mu)\n", + " for i in range(num_species):\n", + " make_trace_plot(\"mu.\"+str(i+1),istart,iend)\n", + " make_hist_plot(\"mu.\"+str(i+1),istart,iend)\n", + "\n", + " print(\"Md:\",M.diagonal())\n", + " for i in range(num_species):\n", + " make_trace_plot(\"Md.\"+str(i+1),istart,iend)\n", + " make_hist_plot(\"Md.\"+str(i+1),istart,iend)\n", + "\n", + " for i in range( num_species*(num_species - 1)):\n", + " make_trace_plot(\"M.\"+str(i+1),istart,iend)\n", + " make_hist_plot(\"M.\"+str(i+1),istart,iend)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "b828f96e-f573-4fca-a14f-3e05402267b3", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + " \n", + "set_all_seeds(1234)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "1b6d7776-a94f-41e5-b359-6c0377423869", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'sigma')" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Prior visualisation\n", + "# mu\n", + "x_mu = np.random.lognormal(0.01,0.5,size=10000)\n", + "plt.figure()\n", + "plt.hist(x_mu);\n", + "plt.title('mu') \n", + "\n", + "# Md\n", + "x_Md = np.random.normal(0.1,0.05,size=10000)\n", + "plt.figure()\n", + "plt.hist(x_Md);\n", + "plt.title('M[i,i]') \n", + " \n", + "# Shrinkage, M\n", + "tau0 = 0.001;\n", + "x_M = np.zeros([1000])\n", + "for i in range(1000):\n", + " tau = np.random.standard_cauchy(size=1)\n", + " lam = np.random.standard_cauchy(size=1)\n", + " x_M[i] = np.random.normal(0,np.abs(lam)*np.abs(tau),size=1)\n", + "#print(x_M)\n", + "plt.figure()\n", + "plt.hist(x_M, range=(-5,5));\n", + "plt.title('M[i,j]'); \n", + "\n", + "# sigma\n", + "x_sig = np.random.lognormal(0.01,0.5,size=10000)\n", + "plt.figure()\n", + "plt.hist(x_sig);\n", + "plt.title('sigma') " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a5b5d5aa-8732-47d7-b0ca-ef03dbb75d24", + "metadata": {}, + "outputs": [], + "source": [ + "def gLV_sde(y, mu, M, e=None):\n", + " if e==None:\n", + " return mu + M @ y\n", + " else:\n", + " return mu + M @ y\n", + "\n", + "def sample_trajectories(nsample, times, num_species, mu_h, M_h, sigma_w):\n", + "\n", + " traj = np.zeros([nsample, len(times),num_species])\n", + " for g in range(nsample):\n", + " traj[g, 0,:] = yobs[0,:]\n", + " for i in range(1,len(times)):\n", + " dt = times[i]-times[i-1]\n", + " f_x = gLV_sde(traj[g, i-1,:], mu_h, M_h)\n", + " \n", + " for j in range(num_species):\n", + " traj[g,i,j] = traj[g,i-1,j] + f_x[j]*dt + np.random.normal(0, scale=np.sqrt(dt)*sigma_w)\n", + "\n", + " return traj\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "76c0b50c", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "## M40 (no perturbations)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "0aafdf7b-e681-463e-b9c4-736f9311f7fe", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Error handling request\n", + "Traceback (most recent call last):\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/aiohttp/web_protocol.py\", line 435, in _handle_request\n", + " resp = await request_handler(request)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/aiohttp/web_app.py\", line 504, in _handle\n", + " resp = await handler(request)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/httpstan/views.py\", line 253, in handle_show_params\n", + " services_module = httpstan.models.import_services_extension_module(model_name)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/httpstan/models.py\", line 90, in import_services_extension_module\n", + " module: ModuleType = importlib.util.module_from_spec(spec) # type: ignore\n", + " File \"\", line 556, in module_from_spec\n", + " File \"\", line 1101, in create_module\n", + " File \"\", line 219, in _call_with_frames_removed\n", + "ImportError: /home/sandy/.cache/httpstan/4.7.2/models/ldclfmcb/stan_services_model_ldclfmcb.cpython-38-x86_64-linux-gnu.so: undefined symbol: _ZNSt19basic_ostringstreamIcSt11char_traitsIcESaIcEEC1Ev\n", + "Error handling request\n", + "Traceback (most recent call last):\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/aiohttp/web_protocol.py\", line 435, in _handle_request\n", + " resp = await request_handler(request)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/aiohttp/web_app.py\", line 504, in _handle\n", + " resp = await handler(request)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/httpstan/views.py\", line 83, in handle_create_model\n", + " httpstan.models.import_services_extension_module(model_name)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/httpstan/models.py\", line 90, in import_services_extension_module\n", + " module: ModuleType = importlib.util.module_from_spec(spec) # type: ignore\n", + " File \"\", line 556, in module_from_spec\n", + " File \"\", line 1101, in create_module\n", + " File \"\", line 219, in _call_with_frames_removed\n", + "ImportError: /home/sandy/.cache/httpstan/4.7.2/models/ldclfmcb/stan_services_model_ldclfmcb.cpython-38-x86_64-linux-gnu.so: undefined symbol: _ZNSt19basic_ostringstreamIcSt11char_traitsIcESaIcEEC1Ev\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "times:\n", + " [30 31 33 35 37 38 39 40 42]\n", + "data:\n", + " [[ 913 487 328 150 10]\n", + " [ 901 476 354 119 28]\n", + " [ 438 1117 229 162 39]\n", + " [ 718 672 366 109 1]\n", + " [ 614 83 352 297 53]\n", + " [ 80 475 71 52 1]\n", + " [ 138 136 34 51 28]\n", + " [ 376 185 189 273 166]\n", + " [ 935 399 363 309 85]]\n" + ] + }, + { + "ename": "ValueError", + "evalue": "The JSON document has an improper structure: missing or superfluous commas, braces, missing keys, etc.", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "Input \u001b[0;32mIn [10]\u001b[0m, in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 28\u001b[0m gLV_code\u001b[38;5;241m=\u001b[39mf\u001b[38;5;241m.\u001b[39mread()\n\u001b[1;32m 30\u001b[0m obs_data_lin \u001b[38;5;241m=\u001b[39m {\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mN\u001b[39m\u001b[38;5;124m\"\u001b[39m: num_species,\n\u001b[1;32m 31\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mT\u001b[39m\u001b[38;5;124m\"\u001b[39m: \u001b[38;5;28mlen\u001b[39m(times), \n\u001b[1;32m 32\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mx\u001b[39m\u001b[38;5;124m\"\u001b[39m: np\u001b[38;5;241m.\u001b[39mlog(yobs),\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 36\u001b[0m \u001b[38;5;66;03m#\"sigma\": 10,\u001b[39;00m\n\u001b[1;32m 37\u001b[0m } \n\u001b[0;32m---> 39\u001b[0m posterior \u001b[38;5;241m=\u001b[39m \u001b[43mstan\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbuild\u001b[49m\u001b[43m(\u001b[49m\u001b[43mgLV_code\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdata\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mobs_data_lin\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrandom_seed\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m 41\u001b[0m sample_kwargs \u001b[38;5;241m=\u001b[39m {\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mnum_samples\u001b[39m\u001b[38;5;124m\"\u001b[39m: \u001b[38;5;241m1000\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mnum_chains\u001b[39m\u001b[38;5;124m\"\u001b[39m: \u001b[38;5;241m2\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mnum_warmup\u001b[39m\u001b[38;5;124m\"\u001b[39m: \u001b[38;5;241m5000\u001b[39m }\n\u001b[1;32m 42\u001b[0m \u001b[38;5;66;03m#fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\u001b[39;00m\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/stan/model.py:517\u001b[0m, in \u001b[0;36mbuild\u001b[0;34m(program_code, data, random_seed)\u001b[0m\n\u001b[1;32m 514\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m Model(model_name, program_code, data, param_names, constrained_param_names, dims, random_seed)\n\u001b[1;32m 516\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 517\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43masyncio\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mgo\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 518\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mKeyboardInterrupt\u001b[39;00m:\n\u001b[1;32m 519\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/nest_asyncio.py:35\u001b[0m, in \u001b[0;36m_patch_asyncio..run\u001b[0;34m(main, debug)\u001b[0m\n\u001b[1;32m 33\u001b[0m task \u001b[38;5;241m=\u001b[39m asyncio\u001b[38;5;241m.\u001b[39mensure_future(main)\n\u001b[1;32m 34\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m---> 35\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mloop\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_until_complete\u001b[49m\u001b[43m(\u001b[49m\u001b[43mtask\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 36\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m 37\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m task\u001b[38;5;241m.\u001b[39mdone():\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/nest_asyncio.py:89\u001b[0m, in \u001b[0;36m_patch_loop..run_until_complete\u001b[0;34m(self, future)\u001b[0m\n\u001b[1;32m 86\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m f\u001b[38;5;241m.\u001b[39mdone():\n\u001b[1;32m 87\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mRuntimeError\u001b[39;00m(\n\u001b[1;32m 88\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mEvent loop stopped before Future completed.\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m---> 89\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mf\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mresult\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m/usr/lib/python3.8/asyncio/futures.py:175\u001b[0m, in \u001b[0;36mFuture.result\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 173\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m__log_traceback \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m\n\u001b[1;32m 174\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_exception \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m--> 175\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_exception\n\u001b[1;32m 176\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_result\n", + "File \u001b[0;32m/usr/lib/python3.8/asyncio/tasks.py:280\u001b[0m, in \u001b[0;36mTask.__step\u001b[0;34m(***failed resolving arguments***)\u001b[0m\n\u001b[1;32m 276\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m 277\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m exc \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 278\u001b[0m \u001b[38;5;66;03m# We use the `send` method directly, because coroutines\u001b[39;00m\n\u001b[1;32m 279\u001b[0m \u001b[38;5;66;03m# don't have `__iter__` and `__next__` methods.\u001b[39;00m\n\u001b[0;32m--> 280\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[43mcoro\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msend\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43;01mNone\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[1;32m 281\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 282\u001b[0m result \u001b[38;5;241m=\u001b[39m coro\u001b[38;5;241m.\u001b[39mthrow(exc)\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/stan/model.py:484\u001b[0m, in \u001b[0;36mbuild..go\u001b[0;34m()\u001b[0m\n\u001b[1;32m 481\u001b[0m resp \u001b[38;5;241m=\u001b[39m task\u001b[38;5;241m.\u001b[39mresult()\n\u001b[1;32m 483\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m resp\u001b[38;5;241m.\u001b[39mstatus \u001b[38;5;241m!=\u001b[39m \u001b[38;5;241m201\u001b[39m:\n\u001b[0;32m--> 484\u001b[0m match \u001b[38;5;241m=\u001b[39m re\u001b[38;5;241m.\u001b[39msearch(\u001b[38;5;124mr\u001b[39m\u001b[38;5;124m\"\"\"\u001b[39m\u001b[38;5;124mValueError\u001b[39m\u001b[38;5;124m\\\u001b[39m\u001b[38;5;124m([\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m](.*)[\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m]\u001b[39m\u001b[38;5;124m\\\u001b[39m\u001b[38;5;124m)\u001b[39m\u001b[38;5;124m\"\"\"\u001b[39m, \u001b[43mresp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mjson\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mmessage\u001b[39m\u001b[38;5;124m\"\u001b[39m])\n\u001b[1;32m 485\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m match: \u001b[38;5;66;03m# unknown error, should not happen\u001b[39;00m\n\u001b[1;32m 486\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mRuntimeError\u001b[39;00m(resp\u001b[38;5;241m.\u001b[39mjson()[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mmessage\u001b[39m\u001b[38;5;124m\"\u001b[39m])\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/stan/common.py:24\u001b[0m, in \u001b[0;36mHTTPResponse.json\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 23\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mjson\u001b[39m(\u001b[38;5;28mself\u001b[39m) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m \u001b[38;5;28mdict\u001b[39m:\n\u001b[0;32m---> 24\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43msimdjson\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mloads\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcontent\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/simdjson/__init__.py:61\u001b[0m, in \u001b[0;36mloads\u001b[0;34m(s, cls, object_hook, parse_float, parse_int, parse_constant, object_pairs_hook, **kwargs)\u001b[0m\n\u001b[1;32m 58\u001b[0m s \u001b[38;5;241m=\u001b[39m s\u001b[38;5;241m.\u001b[39mencode(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mutf-8\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 60\u001b[0m parser \u001b[38;5;241m=\u001b[39m Parser()\n\u001b[0;32m---> 61\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mparser\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparse\u001b[49m\u001b[43m(\u001b[49m\u001b[43ms\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n", + "\u001b[0;31mValueError\u001b[0m: The JSON document has an improper structure: missing or superfluous commas, braces, missing keys, etc." + ] + } + ], + "source": [ + "# Read in data\n", + "num_species=5\n", + "\n", + "data = pd.read_csv(\"data/data-top5-M40.csv\")\n", + "times = data.iloc[:,0].to_numpy()\n", + "print(\"times:\\n\",times)\n", + "yobs = data.drop(columns=['timepoint', 'subjectID']).to_numpy()\n", + "#yobs = yobs.astype(float)\n", + "\n", + "ymiss = yobs == 0\n", + "ymiss = ymiss.astype(int)\n", + "\n", + "#yobs[yobs == 0] = np.nan\n", + "yobs[yobs == 0] = 1\n", + "\n", + "#print(yobs)\n", + "#print(ymiss)\n", + "#print(np.log(yobs))\n", + "\n", + "#print(data)\n", + "print(\"data:\\n\",yobs)\n", + "\n", + "import nest_asyncio\n", + "nest_asyncio.apply()\n", + "import stan\n", + "\n", + "f = open(\"model_sde_nopert.txt\", \"r\")\n", + "gLV_code=f.read()\n", + "\n", + "obs_data_lin = {\"N\": num_species,\n", + " \"T\": len(times), \n", + " \"x\": np.log(yobs),\n", + " \"times\": times,\n", + " \"xmiss\": ymiss,\n", + " \"tau0\": 0.01,\n", + " #\"sigma\": 10,\n", + " } \n", + "\n", + "posterior = stan.build(gLV_code, data=obs_data_lin, random_seed=1)\n", + "\n", + "sample_kwargs = {\"num_samples\": 1000, \"num_chains\": 2, \"num_warmup\": 5000 }\n", + "#fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\n", + "fit = posterior.sample(**sample_kwargs);\n", + "\n", + "#print(fit)\n", + "\n", + "df = fit.to_frame()\n", + "print(df.describe().T)\n", + "#print(df.head())\n", + "\n", + "post1 = df[df.columns[7:]][0:500].to_numpy()\n", + "post2 = df[df.columns[7:]][500:1000].to_numpy()\n", + "Rhat = get_Rhat(500, post1, post2)\n", + "print(\"Rhat:\", Rhat)\n", + "istart = 0\n", + "iend = 2000\n", + "\n", + "# plot the fit using median values of parameters\n", + "post1 = df[df.columns[7:]][0:iend].to_numpy()\n", + "est = np.median(post1,axis=0)\n", + " \n", + "mu_h, M_h = extract_gLV_pars(est, num_species)\n", + " \n", + "print_params(mu=mu_h, M=M_h)\n", + "\n", + "# plot trajectories corresponding to posterior median\n", + "sigma_w = np.median(df[\"sigma\"].to_numpy())\n", + "nsample = 10\n", + "traj = sample_trajectories(nsample, times, num_species, mu_h, M_h, sigma_w)\n", + " \n", + "#yobs_h = traj[0,:,:]\n", + "yobs_h = np.median(traj, axis=0)\n", + "\n", + "## PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)" + ] + }, + { + "cell_type": "markdown", + "id": "a01843f5-57b4-4ef0-a475-599426d7d8cb", + "metadata": {}, + "source": [ + "## Q160 (no perturbations)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "4a100659-d183-4cf3-9f06-efeee463bc0a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Error handling request\n", + "Traceback (most recent call last):\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/aiohttp/web_protocol.py\", line 435, in _handle_request\n", + " resp = await request_handler(request)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/aiohttp/web_app.py\", line 504, in _handle\n", + " resp = await handler(request)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/httpstan/views.py\", line 253, in handle_show_params\n", + " services_module = httpstan.models.import_services_extension_module(model_name)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/httpstan/models.py\", line 90, in import_services_extension_module\n", + " module: ModuleType = importlib.util.module_from_spec(spec) # type: ignore\n", + " File \"\", line 556, in module_from_spec\n", + " File \"\", line 1101, in create_module\n", + " File \"\", line 219, in _call_with_frames_removed\n", + "ImportError: /home/sandy/.cache/httpstan/4.7.2/models/ldclfmcb/stan_services_model_ldclfmcb.cpython-38-x86_64-linux-gnu.so: undefined symbol: _ZNSt19basic_ostringstreamIcSt11char_traitsIcESaIcEEC1Ev\n", + "Error handling request\n", + "Traceback (most recent call last):\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/aiohttp/web_protocol.py\", line 435, in _handle_request\n", + " resp = await request_handler(request)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/aiohttp/web_app.py\", line 504, in _handle\n", + " resp = await handler(request)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/httpstan/views.py\", line 83, in handle_create_model\n", + " httpstan.models.import_services_extension_module(model_name)\n", + " File \"/home/sandy/.local/lib/python3.8/site-packages/httpstan/models.py\", line 90, in import_services_extension_module\n", + " module: ModuleType = importlib.util.module_from_spec(spec) # type: ignore\n", + " File \"\", line 556, in module_from_spec\n", + " File \"\", line 1101, in create_module\n", + " File \"\", line 219, in _call_with_frames_removed\n", + "ImportError: /home/sandy/.cache/httpstan/4.7.2/models/ldclfmcb/stan_services_model_ldclfmcb.cpython-38-x86_64-linux-gnu.so: undefined symbol: _ZNSt19basic_ostringstreamIcSt11char_traitsIcESaIcEEC1Ev\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "times:\n", + " [ 7 10 13 15 16 17 20 21]\n", + "data:\n", + " [[1266 734 270 300 120]\n", + " [ 730 58 1002 26 79]\n", + " [ 905 964 282 147 1]\n", + " [ 460 189 114 304 1]\n", + " [ 698 733 82 71 11]\n", + " [1026 666 119 313 136]\n", + " [ 328 451 870 644 87]\n", + " [1124 1499 526 186 104]]\n" + ] + }, + { + "ename": "ValueError", + "evalue": "The JSON document has an improper structure: missing or superfluous commas, braces, missing keys, etc.", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "Input \u001b[0;32mIn [8]\u001b[0m, in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 28\u001b[0m gLV_code\u001b[38;5;241m=\u001b[39mf\u001b[38;5;241m.\u001b[39mread()\n\u001b[1;32m 30\u001b[0m obs_data_lin \u001b[38;5;241m=\u001b[39m {\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mN\u001b[39m\u001b[38;5;124m\"\u001b[39m: \u001b[38;5;241m5\u001b[39m,\n\u001b[1;32m 31\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mT\u001b[39m\u001b[38;5;124m\"\u001b[39m: \u001b[38;5;28mlen\u001b[39m(times), \n\u001b[1;32m 32\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mx\u001b[39m\u001b[38;5;124m\"\u001b[39m: np\u001b[38;5;241m.\u001b[39mlog(yobs),\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 36\u001b[0m \u001b[38;5;66;03m#\"sigma\": 10,\u001b[39;00m\n\u001b[1;32m 37\u001b[0m } \n\u001b[0;32m---> 39\u001b[0m posterior \u001b[38;5;241m=\u001b[39m \u001b[43mstan\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbuild\u001b[49m\u001b[43m(\u001b[49m\u001b[43mgLV_code\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdata\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mobs_data_lin\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrandom_seed\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m 41\u001b[0m sample_kwargs \u001b[38;5;241m=\u001b[39m {\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mnum_samples\u001b[39m\u001b[38;5;124m\"\u001b[39m: \u001b[38;5;241m1000\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mnum_chains\u001b[39m\u001b[38;5;124m\"\u001b[39m: \u001b[38;5;241m2\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mnum_warmup\u001b[39m\u001b[38;5;124m\"\u001b[39m: \u001b[38;5;241m5000\u001b[39m }\n\u001b[1;32m 42\u001b[0m \u001b[38;5;66;03m#fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\u001b[39;00m\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/stan/model.py:517\u001b[0m, in \u001b[0;36mbuild\u001b[0;34m(program_code, data, random_seed)\u001b[0m\n\u001b[1;32m 514\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m Model(model_name, program_code, data, param_names, constrained_param_names, dims, random_seed)\n\u001b[1;32m 516\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 517\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43masyncio\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mgo\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 518\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mKeyboardInterrupt\u001b[39;00m:\n\u001b[1;32m 519\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/nest_asyncio.py:35\u001b[0m, in \u001b[0;36m_patch_asyncio..run\u001b[0;34m(main, debug)\u001b[0m\n\u001b[1;32m 33\u001b[0m task \u001b[38;5;241m=\u001b[39m asyncio\u001b[38;5;241m.\u001b[39mensure_future(main)\n\u001b[1;32m 34\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m---> 35\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mloop\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_until_complete\u001b[49m\u001b[43m(\u001b[49m\u001b[43mtask\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 36\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m 37\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m task\u001b[38;5;241m.\u001b[39mdone():\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/nest_asyncio.py:89\u001b[0m, in \u001b[0;36m_patch_loop..run_until_complete\u001b[0;34m(self, future)\u001b[0m\n\u001b[1;32m 86\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m f\u001b[38;5;241m.\u001b[39mdone():\n\u001b[1;32m 87\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mRuntimeError\u001b[39;00m(\n\u001b[1;32m 88\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mEvent loop stopped before Future completed.\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m---> 89\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mf\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mresult\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m/usr/lib/python3.8/asyncio/futures.py:175\u001b[0m, in \u001b[0;36mFuture.result\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 173\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m__log_traceback \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m\n\u001b[1;32m 174\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_exception \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m--> 175\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_exception\n\u001b[1;32m 176\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_result\n", + "File \u001b[0;32m/usr/lib/python3.8/asyncio/tasks.py:280\u001b[0m, in \u001b[0;36mTask.__step\u001b[0;34m(***failed resolving arguments***)\u001b[0m\n\u001b[1;32m 276\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m 277\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m exc \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 278\u001b[0m \u001b[38;5;66;03m# We use the `send` method directly, because coroutines\u001b[39;00m\n\u001b[1;32m 279\u001b[0m \u001b[38;5;66;03m# don't have `__iter__` and `__next__` methods.\u001b[39;00m\n\u001b[0;32m--> 280\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[43mcoro\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msend\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43;01mNone\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[1;32m 281\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 282\u001b[0m result \u001b[38;5;241m=\u001b[39m coro\u001b[38;5;241m.\u001b[39mthrow(exc)\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/stan/model.py:484\u001b[0m, in \u001b[0;36mbuild..go\u001b[0;34m()\u001b[0m\n\u001b[1;32m 481\u001b[0m resp \u001b[38;5;241m=\u001b[39m task\u001b[38;5;241m.\u001b[39mresult()\n\u001b[1;32m 483\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m resp\u001b[38;5;241m.\u001b[39mstatus \u001b[38;5;241m!=\u001b[39m \u001b[38;5;241m201\u001b[39m:\n\u001b[0;32m--> 484\u001b[0m match \u001b[38;5;241m=\u001b[39m re\u001b[38;5;241m.\u001b[39msearch(\u001b[38;5;124mr\u001b[39m\u001b[38;5;124m\"\"\"\u001b[39m\u001b[38;5;124mValueError\u001b[39m\u001b[38;5;124m\\\u001b[39m\u001b[38;5;124m([\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m](.*)[\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m]\u001b[39m\u001b[38;5;124m\\\u001b[39m\u001b[38;5;124m)\u001b[39m\u001b[38;5;124m\"\"\"\u001b[39m, \u001b[43mresp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mjson\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mmessage\u001b[39m\u001b[38;5;124m\"\u001b[39m])\n\u001b[1;32m 485\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m match: \u001b[38;5;66;03m# unknown error, should not happen\u001b[39;00m\n\u001b[1;32m 486\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mRuntimeError\u001b[39;00m(resp\u001b[38;5;241m.\u001b[39mjson()[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mmessage\u001b[39m\u001b[38;5;124m\"\u001b[39m])\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/stan/common.py:24\u001b[0m, in \u001b[0;36mHTTPResponse.json\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 23\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mjson\u001b[39m(\u001b[38;5;28mself\u001b[39m) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m \u001b[38;5;28mdict\u001b[39m:\n\u001b[0;32m---> 24\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43msimdjson\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mloads\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcontent\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/.local/lib/python3.8/site-packages/simdjson/__init__.py:61\u001b[0m, in \u001b[0;36mloads\u001b[0;34m(s, cls, object_hook, parse_float, parse_int, parse_constant, object_pairs_hook, **kwargs)\u001b[0m\n\u001b[1;32m 58\u001b[0m s \u001b[38;5;241m=\u001b[39m s\u001b[38;5;241m.\u001b[39mencode(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mutf-8\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 60\u001b[0m parser \u001b[38;5;241m=\u001b[39m Parser()\n\u001b[0;32m---> 61\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mparser\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparse\u001b[49m\u001b[43m(\u001b[49m\u001b[43ms\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n", + "\u001b[0;31mValueError\u001b[0m: The JSON document has an improper structure: missing or superfluous commas, braces, missing keys, etc." + ] + } + ], + "source": [ + "# Read in data\n", + "num_species=5\n", + "\n", + "data = pd.read_csv(\"data/data-top5-Q160.csv\")\n", + "times = data.iloc[:,0].to_numpy()\n", + "print(\"times:\\n\",times)\n", + "yobs = data.drop(columns=['timepoint', 'subjectID']).to_numpy()\n", + "#yobs = yobs.astype(float)\n", + "\n", + "ymiss = yobs == 0\n", + "ymiss = ymiss.astype(int)\n", + "\n", + "#yobs[yobs == 0] = np.nan\n", + "yobs[yobs == 0] = 1\n", + "\n", + "#print(yobs)\n", + "#print(ymiss)\n", + "#print(np.log(yobs))\n", + "\n", + "#print(data)\n", + "print(\"data:\\n\",yobs)\n", + "\n", + "import nest_asyncio\n", + "nest_asyncio.apply()\n", + "import stan\n", + "\n", + "f = open(\"model_sde_nopert.txt\", \"r\")\n", + "gLV_code=f.read()\n", + "\n", + "obs_data_lin = {\"N\": 5,\n", + " \"T\": len(times), \n", + " \"x\": np.log(yobs),\n", + " \"times\": times,\n", + " \"xmiss\": ymiss,\n", + " \"tau0\": 0.01,\n", + " #\"sigma\": 10,\n", + " } \n", + "\n", + "posterior = stan.build(gLV_code, data=obs_data_lin, random_seed=1)\n", + "\n", + "sample_kwargs = {\"num_samples\": 1000, \"num_chains\": 2, \"num_warmup\": 5000 }\n", + "#fit = posterior.sample(num_chains=2, num_samples=500, num_warmup=10000, adapt={'delta':0.99})\n", + "fit = posterior.sample(**sample_kwargs);\n", + "\n", + "#print(fit)\n", + "\n", + "df = fit.to_frame()\n", + "print(df.describe().T)\n", + "#print(df.head())\n", + "\n", + "post1 = df[df.columns[7:]][0:500].to_numpy()\n", + "post2 = df[df.columns[7:]][500:1000].to_numpy()\n", + "Rhat = get_Rhat(500, post1, post2)\n", + "print(\"Rhat:\", Rhat)\n", + "istart = 0\n", + "iend = 2000\n", + "\n", + "# plot the fit using median values of parameters\n", + "post1 = df[df.columns[7:]][0:iend].to_numpy()\n", + "est = np.median(post1,axis=0)\n", + " \n", + "mu_h, M_h = extract_gLV_pars(est, num_species)\n", + " \n", + "print_params(mu=mu_h, M=M_h)\n", + "\n", + "# plot trajectories corresponding to posterior median\n", + "sigma_w = np.median(df[\"sigma\"].to_numpy())\n", + "nsample = 10\n", + "traj = sample_trajectories(nsample, times, num_species, mu_h, M_h, sigma_w)\n", + " \n", + "yobs_h = traj[0,:,:]\n", + "#yobs_h = np.median(traj, axis=0)\n", + "\n", + "## PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7f47e299-3d6f-4d1d-b36c-a832e499d095", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/examples-simulated.ipynb b/examples/examples-simulated.ipynb new file mode 100644 index 00000000..cb88e9c1 --- /dev/null +++ b/examples/examples-simulated.ipynb @@ -0,0 +1,1314 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "import random\n", + "import pandas as pd\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import sklearn.linear_model\n", + "from scipy.integrate import odeint\n", + "\n", + "from numpy import linalg as la\n", + "\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.linear_model import Ridge\n", + "from sklearn.linear_model import Lasso\n", + "from sklearn.linear_model import ElasticNet, ElasticNetCV\n", + "from sklearn.model_selection import RepeatedKFold\n", + "from sklearn.model_selection import cross_val_score\n", + "from sklearn.model_selection import KFold\n", + "from sklearn.model_selection import GridSearchCV\n", + "\n", + "from gMLV import *" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "def set_all_seeds(seed):\n", + " np.random.seed(seed)\n", + " random.seed(seed)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "# some plotting functions\n", + "\n", + "cols = [\"red\", \"green\", \"blue\", \"royalblue\",\"orange\", \"black\"]\n", + "\n", + "def plot_gMLV(yobs, sobs, timepoints):\n", + " #fig, axs = plt.subplots(1, 2, layout='constrained')\n", + " fig, axs = plt.subplots(1, 2)\n", + " for species_idx in range(yobs.shape[1]):\n", + " axs[0].plot(timepoints, yobs[:, species_idx], color=cols[species_idx])\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]')\n", + " if sobs.shape[1] > 0:\n", + " for metabolite_idx in range(sobs.shape[1]):\n", + " axs[1].plot(timepoints, sobs[:, metabolite_idx], color=cols[metabolite_idx])\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]');\n", + "\n", + "def plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, timepoints):\n", + " # plot the fit\n", + " #fig, axs = plt.subplots(1, 2, layout='constrained')\n", + " fig, axs = plt.subplots(1, 2)\n", + " \n", + " for species_idx in range(yobs.shape[1]):\n", + " axs[0].plot(timepoints, yobs[:, species_idx], color=cols[species_idx])\n", + " axs[0].plot(timepoints, yobs_h[:, species_idx], '--', color=cols[species_idx])\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]');\n", + "\n", + " for metabolite_idx in range(sobs.shape[1]):\n", + " axs[1].plot(timepoints, sobs[:, metabolite_idx], color=cols[metabolite_idx])\n", + " axs[1].plot(timepoints, sobs_h[:, metabolite_idx], '--', color=cols[metabolite_idx])\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]');\n", + "\n", + "def compare_params(mu=None, M=None, alpha=None, e=None):\n", + " # each argument is a tuple of true and predicted values\n", + " if mu is not None:\n", + " print(\"mu_hat/mu:\")\n", + " print(np.array(mu[1]))\n", + " print(np.array(mu[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0,len(mu[0]), dtype=\"int32\"), np.array(mu[1]), markerfmt=\"D\")\n", + " ax.stem(np.arange(0,len(mu[0]), dtype=\"int32\"), np.array(mu[0]), markerfmt=\"X\")\n", + " ax.set_xlabel('i')\n", + " ax.set_ylabel('mu[i]');\n", + "\n", + " if M is not None:\n", + " print(\"\\nM_hat/M:\")\n", + " print(np.round(np.array(M[1]), decimals=2))\n", + " print(\"\\n\",np.array(M[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, M[0].shape[0] ** 2), np.array(M[1]).flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, M[0].shape[0] ** 2), np.array(M[0]).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('M[i,j]');\n", + "\n", + " if alpha is not None:\n", + " print(\"\\na_hat/a:\")\n", + " print(np.round(np.array(alpha[1]), decimals=2))\n", + " print(\"\\n\",np.array(alpha[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, alpha[0].shape[0] * alpha[0].shape[1]), np.array(alpha[1]).flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, alpha[0].shape[0] * alpha[0].shape[1]), np.array(alpha[0]).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('a[i,j]');\n", + "\n", + " if e is not None:\n", + " print(\"\\ne_hat/e:\")\n", + " print(np.round(np.array(e[1]), decimals=2))\n", + " print(\"\\n\",np.array(e[0]))\n", + "\n", + " fig, ax = plt.subplots()\n", + " ax.stem(np.arange(0, e[0].shape[0]), np.array(e[1]).flatten(), markerfmt=\"D\")\n", + " ax.stem(np.arange(0, e[0].shape[0]), np.array(e[0]).flatten(), markerfmt=\"X\")\n", + " ax.set_ylabel('e[i]');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "## Simulate some time course data and perform ridge regression as in Stein et al. 2013\n", + "I have coded up the Stein model and ridge regression without the perturbation term (Ridge1) and with a single perturbation (Ridge 2).
\n", + "Ridge regression is designed to cause shrinkage to prevent overfitting. It isn't supposed to be used for variable\n", + "selection. We should use Lasso for this, however I think we need to constrain parameters." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "# Five species, single time course" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of species: 5\n", + "specific growth rates: [1.27853844 0.55683415 2.06752757 0.86387608 0.70448068]\n", + "interaction matrix: \n", + "[[-0.05 0. -0.025 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0.02 0. 0. 0. -0.2 ]]\n", + "metabolite production: \n", + "None\n", + "perturbation matrix: \n", + "[]\n", + "minimum found: a0/a1/error: 0.06951927961775606 0.0003359818286283781 0.10405332708602122\n", + "unconstrained error : 0.10508759597523323\n", + "mu_hat/mu:\n", + "[ 3.49527384 1.37524268 3.77460614 0.2759617 12.15587567]\n", + "[1.27853844 0.55683415 2.06752757 0.86387608 0.70448068]\n", + "\n", + "M_hat/M:\n", + "[[-0.29 -0.12 0.07 0.08 -0.05]\n", + " [-0.15 -0.18 0.09 0.1 0.01]\n", + " [ 0.24 0.11 -0.47 -0.07 -0.13]\n", + " [ 0.09 0.06 -0.04 -0.05 -0.01]\n", + " [-0.12 -0.08 -0.5 0.05 -0.68]]\n", + "\n", + " [[-0.05 0. -0.025 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0.02 0. 0. 0. -0.2 ]]\n" + ] + }, + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# In this example n >> p and it it is basically same as standard regression\n", + "# We have to be careful as most of these gLV models are very weakly identifiable\n", + "\n", + "set_all_seeds(1234)\n", + "\n", + "## SETUP MODEL\n", + "# establish size of model\n", + "num_species = 5\n", + "num_metabolites = 0\n", + "\n", + "# construct interaction matrix\n", + "#TODO do this programmatically\n", + "M = np.zeros((num_species, num_species))\n", + "np.fill_diagonal(M, [-0.05, -0.1, -0.15, -0.01, -0.2])\n", + "M[0, 2] = -0.025\n", + "M[1, 3] = 0.05\n", + "M[4, 0] = 0.02\n", + "\n", + "# construct growth rates matrix\n", + "mu = np.random.lognormal(0.01, 0.5, num_species)\n", + "\n", + "# instantiate simulator\n", + "simulator = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M,\n", + " mu=mu)\n", + "simulator.print()\n", + "\n", + "## PRODUCE SIMULATED RESULTS\n", + "# initial conditions\n", + "init_species = 10 * np.ones(num_species)\n", + "init_metabolites = 10 * np.ones(num_metabolites)\n", + "\n", + "times = np.arange(0, 5, 0.1)\n", + "yobs, sobs, sy0, mu, M, _ = simulator.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# add some gaussian noise\n", + "yobs = yobs + np.random.normal(loc=0, scale=0.1, size=yobs.shape)\n", + "sobs = sobs + np.random.normal(loc=0, scale=0.1, size=sobs.shape)\n", + "\n", + "# plot simulation\n", + "# plot_gMLV(yobs, sobs, times)\n", + "\n", + "## PERFORM REGRESSION\n", + "# linearise\n", + "X, F = linearize_time_course_16S(yobs, times)\n", + "# print(f\"n: {num_species * F.shape[0]}, p: {num_species + num_species ** 2}\")\n", + "\n", + "# get the best lambda/alpha values on a grid via cross validation\n", + "a0, a1 = fit_alpha_Ridge1(X, F, num_species=num_species, n_a0=20, n_a1=20)\n", + "\n", + "# do final fit\n", + "mu_h, M_h = do_final_fit_Ridge1(X, F, num_species, a0, a1)\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h)\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "## PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)\n", + "\n", + "# this does the stem plots with orange crosses the actual parameters\n", + "compare_params(mu=(mu,mu_h), M=(M, M_h))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "# Five species, lower number of time points, multiple time course" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of species: 5\n", + "specific growth rates: [1.27853844 0.55683415 2.06752757 0.86387608 0.70448068]\n", + "interaction matrix: \n", + "[[-0.05 0. -0.025 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0.02 0. 0. 0. -0.2 ]]\n", + "metabolite production: \n", + "None\n", + "perturbation matrix: \n", + "[]\n", + "X: (12, 6)\n", + "F: (12, 5)\n", + "n: 60, p: 30\n", + "minimum found: a0/a1/error: 1.2742749857031335 3.792690190732254e-05 0.04085166635824657\n", + "unconstrained error : 0.07450427435032814\n", + "mu_hat/mu:\n", + "[0.41552428 0.88691095 0.40526676 0.6406298 0.15583877]\n", + "[1.27853844 0.55683415 2.06752757 0.86387608 0.70448068]\n", + "\n", + "M_hat/M:\n", + "[[-0.02 -0. 0. 0. -0.01]\n", + " [-0.02 -0.03 0. 0.01 0. ]\n", + " [-0. -0.01 -0.03 0. -0. ]\n", + " [ 0. 0. -0.01 -0.01 0.01]\n", + " [ 0. -0. -0.01 0. -0.04]]\n", + "\n", + " [[-0.05 0. -0.025 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0.02 0. 0. 0. -0.2 ]]\n", + "examining mu_i\n", + "0 -0.122 - 0.223 \n", + "1 -0.125 - 0.821 \n", + "2 -0.815 - 0.537 \n", + "3 0.029 - 0.609 *\n", + "4 -0.858 - -0.023 *\n", + "\n", + "examining Mij\n", + "1 (0, 0) -0.001 - 0.0 \n", + "2 (0, 1) -0.003 - 0.0 \n", + "3 (0, 2) -0.004 - 0.001 \n", + "4 (0, 3) -0.001 - 0.002 \n", + "5 (0, 4) -0.002 - 0.0 \n", + "6 (1, 0) -0.001 - 0.0 \n", + "7 (1, 1) -0.007 - 0.0 \n", + "8 (1, 2) -0.009 - 0.001 \n", + "9 (1, 3) -0.006 - 0.004 \n", + "10 (1, 4) -0.004 - 0.001 \n", + "11 (2, 0) -0.002 - 0.001 \n", + "12 (2, 1) -0.01 - 0.003 \n", + "13 (2, 2) -0.023 - 0.0 \n", + "14 (2, 3) -0.001 - 0.013 \n", + "15 (2, 4) -0.012 - 0.0 \n", + "16 (3, 0) 0.0 - 0.0 *\n", + "17 (3, 1) -0.003 - 0.001 \n", + "18 (3, 2) 0.0 - 0.004 *\n", + "19 (3, 3) -0.006 - 0.0 \n", + "20 (3, 4) 0.0 - 0.002 *\n", + "21 (4, 0) -0.002 - 0.0 \n", + "22 (4, 1) -0.006 - 0.004 \n", + "23 (4, 2) -0.02 - -0.0 *\n", + "24 (4, 3) -0.0 - 0.014 \n", + "25 (4, 4) -0.01 - -0.0 *\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": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "set_all_seeds(1234)\n", + "\n", + "## SETUP MODEL\n", + "# establish size of model\n", + "num_species = 5\n", + "num_metabolites = 0\n", + "\n", + "# construct interaction matrix\n", + "#TODO do this programmatically\n", + "M = np.zeros((num_species, num_species))\n", + "np.fill_diagonal(M, [-0.05, -0.1, -0.15, -0.01, -0.2])\n", + "M[0, 2] = -0.025\n", + "M[1, 3] = 0.05\n", + "M[4, 0] = 0.02\n", + "\n", + "# construct growth rates matrix\n", + "mu = np.random.lognormal(0.01, 0.5, num_species)\n", + "\n", + "# instantiate simulator\n", + "simulator = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M,\n", + " mu=mu)\n", + "simulator.print()\n", + "\n", + "## PRODUCE SIMULATED RESULTS\n", + "# data structures for results\n", + "ryobs = []\n", + "rsobs = []\n", + "ry0 = []\n", + "rs0 = []\n", + "X = np.array([], dtype=np.double).reshape(0, num_species+1)\n", + "F = np.array([], dtype=np.double).reshape(0, num_species)\n", + "\n", + "num_timecourses = 3\n", + "times = np.arange(0,5,1)\n", + "for timecourse_idx in range(num_timecourses):\n", + " # initial conditions\n", + " init_species = np.random.uniform(low=10, high=50, size=num_species)\n", + " init_metabolites = np.random.uniform(low=10, high=50, size=num_metabolites)\n", + "\n", + " yobs, sobs, sy0, mu, M, _ = simulator.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + " # add some gaussian noise\n", + " yobs = yobs + np.random.normal(loc=0, scale=0.1, size=yobs.shape)\n", + " sobs = sobs + np.random.normal(loc=0, scale=0.1, size=sobs.shape)\n", + "\n", + " # append results\n", + " ryobs.append(yobs)\n", + " rsobs.append(sobs)\n", + " ry0.append(init_species)\n", + " rs0.append(init_metabolites)\n", + " Xs, Fs = linearize_time_course_16S(yobs,times)\n", + " X = np.vstack([X, Xs])\n", + " F = np.vstack([F, Fs])\n", + "\n", + "print(f\"X: {X.shape}\")\n", + "print(f\"F: {F.shape}\")\n", + "print(f\"n: {num_species*F.shape[0]}, p: {num_species + num_species**2}\")\n", + "\n", + "## PERFORM REGRESSION\n", + "# get the best lambda/alpha values on a grid via cross validation\n", + "a0, a1 = fit_alpha_Ridge1(X, F, num_species=num_species, n_a0=20, n_a1=20)\n", + "\n", + "# do final fit\n", + "mu_h, M_h = do_final_fit_Ridge1(X, F, num_species, a0=a0, a1=a1)\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h)\n", + "\n", + "## PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "for timecourse_idx in range(num_timecourses):\n", + " yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times, sy0=np.hstack((ry0[timecourse_idx], rs0[timecourse_idx])))\n", + " plot_fit_gMLV(ryobs[timecourse_idx], yobs_h, rsobs[timecourse_idx], sobs_h, times)\n", + "\n", + "# this does the stem plots with orange crosses the actual parameters\n", + "compare_params(mu=(mu,mu_h), M=(M, M_h))\n", + "\n", + "## ANALYSE RESULTS\n", + "# do some bootstrapping to help with interpretation of parameters\n", + "# starred parameters are considered different to zero\n", + "do_bootstrapping(X, F, num_species, a0, a1, len(times), nboots=100)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "# Five species, single time course including a perturbation" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of species: 5\n", + "specific growth rates: [1.27853844 0.55683415 2.06752757 0.86387608 0.70448068]\n", + "interaction matrix: \n", + "[[-0.05 0. -0.025 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0.02 0. 0. 0. -0.2 ]]\n", + "metabolite production: \n", + "None\n", + "perturbation matrix: \n", + "[ 0 -1 0 -1 0]\n", + "perturbation:\n", + " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0\n", + " 0 0 0 0 0 0 0 0 0 0 0 0 0]\n", + "n: 245, p: 30\n", + "minimum found: a0/a1/a2/error: 1e-05 0.0001 1000.0 0.1047716423552287\n", + "unconstrained error : 0.10856113205421243\n", + "mu_hat/mu:\n", + "[ 4.37361183 1.77020527 4.61846116 0.22002797 15.49733173]\n", + "[1.27853844 0.55683415 2.06752757 0.86387608 0.70448068]\n", + "\n", + "M_hat/M:\n", + "[[-0.34 -0.15 0.07 0.1 -0.07]\n", + " [-0.18 -0.2 0.1 0.12 -0. ]\n", + " [ 0.27 0.12 -0.55 -0.08 -0.18]\n", + " [ 0.1 0.07 -0.05 -0.05 -0.02]\n", + " [-0.19 -0.12 -0.63 0.08 -0.81]]\n", + "\n", + " [[-0.05 0. -0.025 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0.02 0. 0. 0. -0.2 ]]\n", + "\n", + "e_hat/e:\n", + "[[-0.]\n", + " [-0.]\n", + " [-0.]\n", + " [ 0.]\n", + " [ 0.]]\n", + "\n", + " [ 0 -1 0 -1 0]\n" + ] + }, + { + "data": { + "image/png": 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\n", 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\n", 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "set_all_seeds(1234)\n", + "\n", + "## SETUP MODEL\n", + "# establish size of model\n", + "num_species = 5\n", + "num_metabolites = 0\n", + "\n", + "# construct interaction matrix\n", + "#TODO do this programmatically\n", + "M = np.zeros((num_species, num_species))\n", + "np.fill_diagonal(M, [-0.05, -0.1, -0.15, -0.01, -0.2])\n", + "M[0, 2] = -0.025\n", + "M[1, 3] = 0.05\n", + "M[4, 0] = 0.02\n", + "\n", + "# construct growth rates matrix\n", + "mu = np.random.lognormal(0.01, 0.5, num_species)\n", + "\n", + "# construct perturbation matrix\n", + "epsilon = np.array([0, -1, 0 , -1, 0])\n", + "\n", + "# instantiate simulator\n", + "simulator = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M,\n", + " mu=mu,\n", + " epsilon=epsilon)\n", + "simulator.print()\n", + "\n", + "## PRODUCE SIMULATED RESULTS\n", + "# initial conditions\n", + "init_species = 10 * np.ones(num_species)\n", + "init_metabolites = 10 * np.ones(num_metabolites)\n", + "\n", + "# perturbation\n", + "tp = 2\n", + "\n", + "times = np.arange(0, 5, 0.1)\n", + "yobs, sobs, sy0, mu, M, _ = simulator.simulate(times=times, \n", + " sy0=np.hstack((init_species, init_metabolites)),\n", + " tp=tp)\n", + "\n", + "\n", + "# add some gaussian noise\n", + "yobs = yobs + np.random.normal(loc=0, scale=0.1, size=yobs.shape)\n", + "sobs = sobs + np.random.normal(loc=0, scale=0.1, size=sobs.shape)\n", + "\n", + "# plot simulation\n", + "# plot_gMLV(yobs, sobs, times)\n", + "\n", + "## PERFORM REGRESSION\n", + "# time dependent perturbation\n", + "u = (times >= 2) & (times < 3) \n", + "u = u.astype(int)\n", + "print('perturbation:\\n', u)\n", + "\n", + "# linearise\n", + "X, F = linearize_time_course_16S_u(yobs, times, u)\n", + "print(f\"n: {num_species * F.shape[0]}, p: {num_species + num_species ** 2}\")\n", + "\n", + "# get the best lambda/alpha values on a grid via cross validation\n", + "a0, a1, a2 = fit_alpha_Ridge2(X, F, num_species=num_species, num_pert=1, n_a0=10, n_a1=10, n_a2=10)\n", + "\n", + "# do final fit\n", + "mu_h, M_h, e_h = do_final_fit_Ridge2(X, F, num_species=num_species, num_pert=1, a0=a0, a1=a1, a2=a2)\n", + "\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h,\n", + " epsilon=e_h)\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times,\n", + " sy0=np.hstack((init_species, init_metabolites)),\n", + " tp=tp)\n", + "\n", + "## PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)\n", + "\n", + "# this does the stem plots with orange crosses the actual parameters\n", + "compare_params(mu=(mu,mu_h), M=(M, M_h), e=(np.array([0, -1, 0 , -1, 0]), e_h))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "## Simulate some time course data and metabolites\n", + "This model assumes metabolite production is associated with abundance: dS/dt = alpha X
\n", + "Note that this model needs rethinking as it cannot handle negative productivities
\n", + "In this simple example we don't need to infer the time course. We just linearize and estimate the elements of alpha with Lasso
\n", + "Number of metabolites is 6 here" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of species: 5\n", + "specific growth rates: [1.27853844 0.55683415 2.06752757 0.86387608 0.70448068]\n", + "interaction matrix: \n", + "[[-0.05 0. 0. 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0. 0. 0. 0. -0.2 ]]\n", + "metabolite production: \n", + "[[ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 1. ]\n", + " [ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. -0.5 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. ]]\n", + "perturbation matrix: \n", + "[]\n", + "minimum found: a0/a1/error: 0.016237767391887217 8.858667904100832e-06 0.12034285709957337\n", + "unconstrained error : 0.1222818215867086\n", + "minimum found: a/error: 0.6158482110660264 1.232535377243475\n", + "min + se rule: a/error: 1.2742749857031335 1.2447335692907107\n" + ] + }, + { + "data": { + "image/png": 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nWjRmnZElYVcx8rre5Lj+Se+IS2ic58PMV5+jx3UjKW53BWOmxRHTYQo5xaVYjzzBK+FHOLLsD9oOuJyud9zGl9u/ZObembgb3BEIvFy8+LjLBHb+Mof4LRuxehlY3SQVnc2NRmleROUIDCE+uNzeExt23Pcn0eKH/wg6mEV6mDs7/IPQ2ST99iQQ196Nm35eS6lFh90ueWnhvdz9+kYK2nUgzpxPq3ue4ZF/C7i8mS/jfn4ZvZsrTebMYfwHtxC6uYSeN95M7xG3VnYdqASnKJWxFxWR9s4EcmfNwvvqqwl75210Li41cuxaTHC5Ukrf8p8FkHPs9wr2HQOMAYiKiupy5MiRCs9hLyoiafwzFC5Zwl+Ne9DiyfvJ+eMb0tNScJeCEiHxLrLR+WgyQZdfzqftS8jYtR2rwY5r2D14EU6jP6bTOXsXCX4m0nw8oXzgqVUnMdgFZqOdAxGF5JsshOWF4ZftSmRpER13HWbeQBfmdSwDmyfdw9vTKqA5/+38kwe+TsVo8+S/zpEc9szCqvMhJtEDL72OEa+/T3SjcEotNmbGJTB73lIuPfQb7pYS5t1i5Mqoy+n28DdkhZpoPfUX3F/5lPxVq7m+/7Pc6bYL1wPrCRozmG2zZtM4152Be5NpvuQfDH5+zN8cz6RfPmR4vxt49Op+ABzeuomfJ76Ga6kVsCBdXXA3eGAzCBY0P4Bv+GjWbo+iZ/YGuuXF4W/J4rZZKzDqjQBsmTOTZT//gAtQcn07zDHe2LFjl3bSitM4mn+UpMIkPHJh6IYIPIqstPY08VqXw/Rx6UTjPXqysrKY1T0bs3cG3npvRm9uh620jLs++IyR32wi1bKZUu8veN7nLnbPy8U/K4mo/i05ELeSVn0HMPiBxzlccIQP4iaSWJDEsz53sXHaz0hpp+cNN9Nm4GCu+mEymda9NIssJK3wMMXWEoJzJSP/s9N7p6TQU8fiq0LY3zMS7/gyolcW8V9sGVFdRpCe1oFtB5MI05cw5KpCkmdMpsWRcPD1YUrz+xB6PZdtXMCdu/7CddKn5Hf25/YFt3N/0qXoEwq4e+LnuJo8Kvw/Wtn15dBalIpSHxStXUfKCy9gSU4m4L77CHricYSuft+ellJKIcRZP71KKaegFT+na9euFW5nKyxi/22jse/bwZQOw7FdeyPjruiMfWA31s7+hV0rljJg1B3MzQtmyacTuXrh3yzSjcfcYjceROJX2JT7FnxMbMo+fIYOpfvNN0GTJmQlHWXztq3MXT8Na5CRVn16cWNEF+Jz4/lm+zTK7AV42I08WGTl1r8skNiTa59/ga7tY7Dl5zP89RWU5mfy7kgr26LieaDDA9zb7l5yEhP4+cWnWP3FB0S+8g6uBgOdS/eTn/Y3Rg8veq0/zJ7tnmzf8h2DC6Dl668R6NeckrvvouDvv3lRd4DXzK2513UnpbM3EprtRuOUTAzXX4XBz4+ckiJeWj8eW+s9fJW2kpK1d/BwlzF8nf8Hv/c/SO+krrS2ubEjbzdhvt4YU4oZFBdMo4EGdloK6FK4DX9vL3qsPMicz5+kf/878PUKwmvqdLqnpLGsRSCu87azsWcR6aE2dEJHkHsQzf2aM8C1G/pl23HzMDGwdSyW76fx6JU38bLlNy7r3ZPwOSUM2m3EK7s5ZZ6p5BYkMmzc82xMKmZnUjyjM77l6rV2XCzf0A6w6AzYj2zC7Y5R7Fi5jJT9ewhp0RprSiuik/WsLvqKQA9vevqE0rR3f+btzubIkbZ8csvtDG0fjjktlYxPPiF/9lyE0RX/+26n5dgx9Cjv8bDbbHy1Zwwtjkh+LQ1lkG05d6euR1jLsH8CXq6NyDcZaHswgTsyfmbQuy8iZ/3L+sj2TFxnJSjzI/SY+FkMxhhm5/6zJLdzUS045aIlrVbS33uP7B+mYmwcRfjbb2Pq3LnGz1NfuyjNpVZ+efRXrIY8Pgttwt/jLiXA0/WM7falFXDfqzP4YukHbB92Fz2fe4BwHxPWvfuJv+56gh5/nMD7x56xn8Vmx6g/9YPE0r0JjJ37OZe1t9M36CpynvuKQQkbj/3BCBcXkJJGX3xOUcdmFJoLaeLb5Pj++9etZv7Et2jZux+lRYUc3rKRyNZtufK+R8geez+W0hJK/T0wpeXT7J/FCIP2Gf/wzbdgzcjg96c/Zv4fSxiavhAB9Nl7mG+ebcOkEd9z3ayxJJk3MzBkNIv2b0TvvRV3gzsl1hLMWZey4LZ3aBrsxY+7fmTChgnobYK7Enti25mMzs2EsFu5440POHDTcLxyT0xlsAuYMEJHSN8raP2PmfzUVG566W1Cm7UAIHHXDua+9zou7iZGvvQW3j6+xI+4EXt+PgtfH8yUI9O5LLcVUauLaZyRS5K/F67WMhrdcRNL9/ky8M+3ickoQzewD2HX3IB7p87sTS/kyH1jaJyfQuE9d5FQnMeRnTsQ0gpS0iw9h2ZZhejsdrwGD+aOsKG4GvUseLQP9qJi4q+/HktKCn4jRxIwdgzG4OAz/n23Ll7AP19/hquXD2UFeTTr1hOftj34+s/1eOv/wySNuCf6csvODZR6uuBSZqPs2694YUMyiaZX8bdeTRfvUUQHePDIZc3OOudUteAU5TT2sjKSn3qKgsX/4HfrrQQ/9SQ6d3dnh3Wh5qOtsfgONbDWotFVTxP/9WzNHcr9mPAQFbdqW4R48cnzN2LMWkKX7ctp5DseIQSpU6ag8/DA75abKz6+/szjdWscijW3N1H2GD7/JxW3K0Zza8e7ITUFW04Otrw8vAdfialbNzyAYNOpb6zNe1xCz+tvYu3sGRhcXbns7rF0vGIIQqdD/+STJN7/AC4J4PfYo8eTG4D/3XeR9OhjjPpvOo27dGPxv025LGEzBf26sbosjqGzh5FuTqWV8W4mDX6CCezhy3VLad1xA/uOBNPJ93qaBmvl2m5rfRtCCKbvmc4tN71B4op1LJ/2NX1vHY1/4xg6/vEP+9b8xZ6kLRxI2UG6v44xI16kT0Qfirrn8POLTzF7wqvc/Pp7ZCYc4c+P3sUnKIQbXngN70Dt74344H0O3ziS4TMT6fvyVBqtOcyiPydxJMgXIXQ0S0om4vlJROkEhe6StJdG0/+Wp4//vW1Dgsn4bArbH3ucjl99i8ngQhurmZymzdjTpAtfBoTz5Ss34TbrJzI/+YSAnqGMfvJWhBCkvfUWlsREGk/9AVPXs39ua9NvEBvm/4aLu4n+jz9DVNv2AAS2687Nv6aD71LoDDJIx63/mvntEsGMXWPwD/DH1eLCnFHj8XfzP+vxq0K14JSLjq2wkMSHHqZ43TpCnn8e/ztud+j5HDSKcjrQHwgE0tCWpZoLzASigCPASCnlmRPCTnO266vYbGXvW5eQa+3Onpwb8AlyZ+jDHfAOrPiDQO6cuaQ89xyNp01FHxjIoauHEHDvvQQ/Oe68/rbBk1awN00rXv3r/b3o0vj83uSk3c6O5f/QqHV7fENCTzwuJUfvvIviTZtovmwphqCgE8/ZbCSVf+DBakXqdNgQjL3yOYIuWc6h4jWQcT1Lxz5PkJcrRWVWBn6wnCKzlYJSK9/d1Y0BLc9sxRxjKSvF6Fq1+ZPZyYlMf2k8eoOB4txcQps157pnXsbdy/uU7bK+/570dybgd8vN5P76G4b27YmLCaVp914khnuz+5PH8CqRFI2+kWeveLXCc01bsY+Utydow/3vu4PBN1xGcm4J/d//l2vahzNhWEtWDLgKN0sp3Zctonj1apIee4yA+8cS/Pjj5/xbbFYrOr3+jNbXsgMH+HjD99zZpReXRHbDJ62IFD9YdHQxS44uYUCjAdzf4f4qvV5qkImilLPm5JBw732U7t1L+Ntv4XPNNQ4/p6O6KGtKZddX0Y+34pq9l7QrF/PXl9vx9HNj1P8qXs7RXlLC/kv74dmvH8LNlfzf/6DZkn8wBAaeVzzPzd7G9PUJ3NMnhv8NbX3ef09lrBkZmBMSztoVbSsspGjVagpXrsAW3Yy33Nrx184EdC4ZvHj5IEb3iTm+7fytyTw6fTPRASaWPtkfna7myrYl79vNrDdeJKpNe4Y+9gzGCooLSLudhDFjKfrvP4yNGhE9cwYGvxNTHyes/Zj9Ofv5/IqJxwe0VGTamsMEebkxuO2JDwNvLdjNVysP8djA5iycuZiJKz/FZ8gQilauxBgVRfTPPyGMZz9mbVJdlIqCltyO3j0ac3w8kZ9MrlMTt+sqD/8ISFhJRKwfnQc3Zs3sgxTnmzF5nznCVOfujs+115I7YwYS8LtxxHknN4AbOkeSX2rlqStqvhyaISjolJbb6fSennhfeQXeV14BwOfAn9vC2Xgkhzt6NT5l22vah7HlaC49m/jXaHIDCG/Rivu/mIaLu/vZ7z3pdIS//RbpH04i4J7RpyQ3gGd6Plqlc93eK/qMxx7o15Tp644y6Z/9NGnRBr9Gt5D7008Id3fC351QZ5LbuagEp1wUrDk5HL3rbsyHDxP52ad49u7t7JDqB68QKMsDSwnhzXwBSDmYS9NOFXfH+d54Izk//gh6Pf6j76nWKbtG+9M1+sLuvdSkIe3DGNI+7IzHhRC8dE3NtjBP5moynXMbQ1AQ4W+9WePn9vNw4f7+TXnv7708OKAZwbHdsMTH43PD9bjGxJz7AHWESnBKg2fNztZabocP0+jzz/C45BJnh1R/eIZo3wtSCWrUGL1BR8rBvLMmOLfYFnhdPghDaBgukRG1GKhS08Zc2oQWIV4MbBmMTieI+vabc+9Ux6gEpzRoZYfiSbj/fqxpaSq5VYdn+X2ZwjT0/jEER3uRcqDydbsiJ9fMOmOKcxn1Oi5vHeLsMC5I/Z7NqiiVKFq7jsOjRmEvLKTxD9+r5FYdXidacABhzXzJPFqApQ6vVq0ox6gEpzRIefPnc/TeezEEBRE9cwbuHTs6O6T66XgLLh2AsKY+2O2S9Ph8JwalKFXjsAQnhIgVQmw56StfCPF4TS/poSiny/97EcnPPoepSxeip/+MS2Sks0Oqv0wBoDNAodaCC23iA2gDTRSlrnNYgpNS7pVSdpRSdgS6AMXAHOBZYImUsjmwpPx3RakRRWvXkvzUU7i3b0+jzz9D7+197p2Us9PpwCMYCtIAcPMw4h/uQcrByu/DKUpdUFtdlAOBg1LKI8C1wA/lj/8ADK+lGJQGrmT7DhIffAiX6GgaffE5uioMs1aqwCvkeAsOtG7K1IN52O11v0iEcnGrrQQ3Cphe/nOIlDKl/OdUoMJhOkKIMUKIOCFEXEZGRm3EqNRjltRUEsaORe/nR6Ovv0bv6+vskBoOz5DjLTjQBpqYS21kJxc5MShFOTeHJzghhAswDJh1+nNSqxNW4cdAKeUUKWVXKWXXoEoqDyiKtNlIfupp7KWlNPpqCsaQs9cEVKrB88wWHEDKgVwnBaQoVVMbLbirgE1SymMfAdPKl/Kg/Ht6LcSgNGCZn31OcVwcYS+/hGuTJufeQTk/XqFQlAk2q/ZrgBsePi7qPpxS59VGgruZE92TcGJJD6iBJT2Ui1vRuvVkfv45Ptdei8+11zo7nIbJMwSQUKTdKhBCENbMV42kVOo8hyY4IYQHcDkw+6SH3wEuF0LsBwaV/64o582alUXy00/j0rgxoS/9z9nhNFxex+bCndRN2cyHwuwyDm1W98eVusuhCU5KWSSlDJBS5p30WJaUcqCUsrmUclBV1qtSlNPZCotIGDMWW34+ERM/QOdRvSXtlSo4Ntn7pIEmLXuGERztzcKvdrB/Q9pZdlQU51KVTJR6R5rNJD36CKV79hDx4UTcWrVydkgNm2f5oJ2TWnAu7gaufawjYU19WPTtTnavTnZScIpydirBKfWKtNtJfvY5ilavIez11/EaMMDZITV8x1cUOLWl5uJuYOgjHWjUyp+lU/ewdUmCE4JTlLNTCU6pVzImfUT+ggUEP/Ukvtdf5+xwLg4GF3D3P6UFd4zRRc+QB9rTpFMQ/83az5q5B9Fm/yiK86kEp9QbhStXkjVlCr43jsD/nuotpqlUk1foGS24Y/RGHVfe15bWfcPZtPAIy6btwW6z13KAinImtR6cUi9Y0tJJfuZZXJs3J+SFFxBCODuki4tnCBSefTCJTifof0ssJi8X4hYcxsXNQJ+RzWsxQEU5k2rBKXWetNlIHj8ee0kJER9OROfm5uyQLj5eoZUmONDmx/UY1oRmXYLZtyEVqWpVKk6mEpxS52V++SXF69YR+uKLuDZr5uxwLk7HWnBVuL/WpGMQJQUW0g6rNeMU51IJTqnTCleuJHPyJ3gPuwYfNajEeTxDwGaGkpxzbtqotT9CJzi8PbMWAlOUs1MJTqmzzEeOkPTkU7jGxhL26qvqvpszeR2bKnDmSMrTuXkYCWvqw+HtWQ4OSlEqpxKcUifZi4pIfPgRhBBEfjIZnbu7s0OqN4QQjwkhdgghdgohHq+Rg3qeWa6rMtHtAslKLKQgu7RGTq8o1aESnFLnSClJfuFFyg4eJHziB7hERjo7pHpDCNEWuA/oDnQAhgohLvzGpdeZ5boqE90+AIAjO1QrTnEeleCUOidn6lQKFi4keNwTePbu7exw6ptWwDopZbGU0gosB66/4KMeq2ZyjpGUx/iGmPAOclf34RSnUglOqVNKtmwh7b338Rw4UE3mrp4dQF8hRIAQwgRcDTS64KO6eoKLZ5UTnBCC6HYBJO7JwWK2XfDpFaU6VIJT6gxrTg6JT4zDGBpK+NtvqUEl1SCl3A1MABYBC4EtwBkZRggxRggRJ4SIy8io4pI3niFVGmRyTHS7QGwWO0l7zj3yUlEcQSU4pU6QdjvJzzyDLTOTiEmT0Ht7OzukektK+Y2UsouU8lIgB9hXwTZTpJRdpZRdg4KCqnbgc1QzOV14c1+Mrnrit2diLrWSn1VCXkZxlfdXlAulSnUpdULOtGkUrVhJ6Msv4d62jbPDqdeEEMFSynQhRBTa/beeNXJgrxBI2VblzfUGHVGt/dm1MpldK08spzPkofZEtwuskZAUpTIqwSlOZ05IIH3SR3j264fvqFHODqch+E0IEQBYgIeklLk1clSvcNj3t1bNpIrdx92uicEnxISruwE3TyMbFx5hzZyDRLUJQKdTXdCKY6kEpziVlJKU/72E0OkIffUVdd+tBkgp+zrkwN5hYCmG0jxw963SLgHhnvQa7nn8d6OrnkVf72Tf+lRa9gxzSJiKcoy6B6c4Vd5vv1G8di3BTz+NMTTU2eEolfEqT0gFKdU+RLPOwQQ39mLd/ENYLWp0peJYKsEpTmNJSydtwruYunXDd+SNzg5HORfvcO17fnLl21VC6AS9rmtKYXYZO5Yn1VBgilIxleAUp5BSkvrKK0izmbDXX0Po1H/FOq8GWnAAkS39adTan7i/DlNWYq2BwBSlYg59VxFC+AohfhVC7BFC7BZC9BJC+AshFgsh9pd/93NkDErdlPfbbxQuW0bwuCdwiY52djhKVRxLcPkXluAAeg1vSlmRlZUz9iGrsASPolSHoz82fwQslFK2RKuLtxt4FlgipWwOLCn/XbmImBMSSHvrbUw9e+J3++3ODkepKqMbmAKgoPpdlMcERXnRbWgMe9emsv6P+BoITlHO5LAEJ4TwAS4FvgGQUprLhytfC/xQvtkPwHBHxaDUPdJmI/nZ50CnI/ytN1XXZH3jFV4jLTiAbkOiaXlJGHF/HmbXqgtPmopyOkdOE4gBMoDvhBAdgI3AY0CIlPLYFZIKhDgwBqWOyfr2W0o2biR8wjsYw8OdHY5yvrzDaqQFB1q9yv63xlKcW8a/P+3Fxc1A085BaqqIUmMc+fHZAHQGPpdSdgKKOK07Umqd7xV2wFerVp5Sp5Vs2ULGx5PxuvxyvIcNc3Y4SnV4hV3QKMrT6fU6rhzTlsBIT/7+agcz39rA3nWp2Kz2GjuHcvFyZIJLBBKllOvKf/8VLeGlCSHCAMq/p1e0c7Vq5Sl11vFCysHBhL3xuvqUXl95h0NRBljNNXZIFzcD1z/VmQG3tcRmsfPPd7v45fX1WNUqBMoFcliCk1KmAglCiNjyhwYCu4D5wJ3lj90JzHNUDErdIO12kp8erxVS/ugj9D4+zg5Jqa5jIymruLJ3VRlc9LTuE87NL/dgwO0tyU0r5vB2tViqcmEcfYf/EeAnIcQ2oCPwFvAOcLkQYj8wqPx3pQHL/OILiv77j5AXXlCFlOu745O9a2agyemEELTsFYaHryt719VsElUuPg6tRSml3AJ0reCpgY48r1J3lGzbRubkT/Aedg2+N410djjKhTo+2dtxox51OkGLbiFsXZJASaEZd08Xh51LadjUGG3FYaTdTuqbb6IPDCD0pZfVfbeGwMEtuGNa9AjFbpcciKvwFr2iVIlKcIrD5P/xB6VbtxE87kn0nh7ODkepCe5+YHBzaAsOIDDSk4AID/atV92USvWpBKc4hL2oiPT3P8CtXTt8rlVTAhoMIcqnCji2BQfQonsoqYfy1SrgSrWpBKc4RObXX2NNTyfk+edUtZKGxjv8ggsuV0WL7iEgYN/6NIefS2mY1IKnSo0zJyaR/c23eF9zDaZOnZwdjlLTvMIgaaPDT+Pp50ZECz/2rk2l61XRlBRaKMguJS+9mJy0YnLTijF5udB9WBNc3dVbmXIm9b9CqVFSStLefBP0eoKfHOfscBRH8A6D3ckgpdZl6UCxPUJYOnUPXz66/JTqJkKAV4AbBdllxG/NZNDo1oQ383VoLEr9oxKcUqMKFi/WlsEZP16t0N1QeYWDrQxKcsDk79BTNesaQsaRAvRGHV4Bbnj6ueET7I5vkAm9UUfqoTwWf7uTuR9sotMVjelyVWNc3Kr2tnZkRxZxC+K5/J42eAe4O/TvaGiS9uUgJUTG1u3VzlSCU2qMrbCQtDfexLVlS/zvUMvgNFjex9aFS3Z4gjO66Ln05tizPh/axIebXuzOfzP3s+nvI+xcmUSHgY1o1z8SNw/jWfeL35rBwq92YLdKdq5Iptd1TR0RfoMk7ZJ/vtuF1WLnzrcvwWDUOzuks1J3/5UakzHpI6wZGYS99irCoD47NVhe5XPhamGgSVW4uBm47I5WjHimK2HNfFn/ezxTX1jNoS0VF2k/uCmdhV/uIDDCk8iWfuxZk4LdVv+LO0sp2R+XRsbRAoeeJ3l/LoU5ZZQWWmpkAJDVbGPZT3tIOZB74cGdRiU4pUaUbN9Ozk8/4XfLLbi3b+/scBRHOrkFV4eExHgz5MH23PRid/xCTCz6eidJ+3JO2Wb36mT+/nonwdFeDHu8E+0HRFKcb+bIjlPrXtrtEru9/qw0brPZ+fenvSz6eie/vhPHxoWHHRb/vvWpGFz1+IV5sG1pwgWvyH5wcwa7Vibz++StpMbn1VCUGpXglAsmLRZS/vcShqAggh5/zNnhKI7mGQqIOtOCO11gpCfXPNIR70A3Fny2jczEAixlNpb8sIulU/cQ0cKXax7tiKu7gcZtAzD5uLBr1Ym/xWazM3fiJma+uZ7i/AtfNcFmtbN27kFSD9Xsm/cxZcUW/pi8lV3/JdP5yiiadA5i7dxDzPtwMwXZpTV6LpvFzsHNGTTpGEinyxuRlVRE0t4THyJKiyxs+DOeksKqv267Vyfj5e+Gu5eRPyZvJSNBa4FKuyTlYB67/qv+BynVj6RcsKzvvqdszx4iJn+M3svL2eEojmZwAY+gOteCO5mbp5FrHu3I7Pc28vvHW3H1MJKTWkTXIdF0GxKDTqeN/tTpdbTsGcbmxUcpyi3Dw9eVuD8Pk3IgD51BMP+jzVz7RKcLqoe5bVkiGxceYdOio3S/JobOVzY+fv4LVZRXxrxJW8hLL+ayO1rR6pIwpJQ0bhPAil/28euEOEY80xUvf7cqH1NKedayekd2ZlFWbKVF91AiWviyZs5Bti5NJLKlPxazjQWfbSPlYB75WaUMvKPVOc+Vl1FC0t5cegxrQoseIcx5fxPzP9pC087BHN6aQVGeGaObnhY9Qqp1r0+14JQLYj58mMxPPtEWMb38cmeHo9QW77A624I7xsvfjWse6YjNaqe00MywRzvS45omZySXVpeEIe2SPWtTSD6Qy8a/DtOyVyhDH+5AbnoJ8z/aQmmRBdBaYyUFVW+dFOebifsznkat/WnaOYh18w7x+8db2B+XxpZ/jvLfzP0s/nYnC7/czh+fbuXvr3ZQmFO1VldpkYX5H22hILuUax7tSKtLtK7jYysy3DC+C9YyG39+uhVzifX4fhlHC5g3afMZ3bcAa+ce5JfX12MutZ7xHGjdk+5eRhq19MNg1NPm0ggOb88kO6WIv6fsIOVQHuHNfdmzJqVK9wL3rEkBAS17heId4M61T3RCpxfsXZNCSIwPg+5uzZ1v9672QBbVglOqTdrtpPzvJYSrKyH/e9HZ4SjlhBBPAPcCEtgO3C2lrNm+Kq9wyEus0UM6gn+4Bze/3AO9QXfWUZW+ISbCm/uy679kdq5IxivAjb43tcDFzcDV97fjz8+3Mf1Vbd3m4gIzSGjUyo+ew5sS3Ni70vOvm3cQq9nOpTe1wCfYnUat/Fn5yz4S92jJxeCiw+TtgsFFj96gIye1iPzMEq57qnOlb+qW8sSVm17M0Ic7VDhcPyDCk8Fj2/HH5K0s/GoHQx5qz66Vyfz3637sVklOajE3v9QdV5P2uiTvz2XjwiMAbPzryBkjS80lVg5vy6J1n3B0eq1t1PbSCDYtPMKc9zdRWmSh/62xNOsSzI8vreW/WfsZPq7TWVuDdrtkz5oUolr74+mntTB9g03c+mpPhBAYXS98dKZKcEq15f72G8UbNhD6+msYg4OdHY4CCCEigEeB1lLKEiHETGAU8H2Nnsg7DBLX1+ghHcXDx/Wc27TuE84/3+1C6ATXP9X5+Fy6qDYBDHmwPTuWJ+HuacSj/I14+7JEZr0dR7MuwbToEYp3oBvege4YXU68KWccLWDX6hQ6DGyEb4hJO0/vcBq3DaCkwIynnxuuJsMpCeDQ5gz++nI7y6fv47LbWyKEICe1iKVTd5OfWUpEC18iYv04tDmDtPh8rhzTlkYtzz5Vo1Erf/rdGsuyaXv4+ZV15GeUENUmgA6XRfLHp9tYOWM/g+5ujdVsY+m03XgFuBES7c2Wf47SslcofqEniqQf3JyBzWrXSqid9No27xbC3rWp9Li2CW36RgDQfWgMK37ZR/yWTJp0CkLaJQc2pWMptdHqkjCETpC4O5vCnDJ6j2h+SsxVncdYFSrBKdVizcoi/b33MXXvju+IEc4ORzmVAXAXQlgAE1DzN8u8wqE4CyylYKz6/Z26qmmnIDYv9iS2RyihTU5dcT6qdQBRrQNOeazDwEZsWXyULUsSOLDxxJI+PkHuRLUNILptAHF/Hcbd00i3q6NP2dfDx/WsSbdJpyC6Xh1N3ILDBDXywuCiY+WMfeiNOqJa+ZO0P5f95UsIDbi9JU07nfuDZeve4eRnlrDp76P0HN6Ezlc0RugEXa9qzIY/D9OkYxCph/LISy9h2OMdCQj35OjOLFbO3M81j3RACIGUkn3rU/EOcick5tRWa58bm9OsczCN2514jdr0DWf78iRWzT4AAtb/Hk9WUiEABzalM/DOVuxenYKrh4GY9oHn/BuqSyU4pVrSP5iIvaSE0FfUOm91iZQySQjxPnAUKAEWSSkX1fiJjq8LlwQB9X+StMFFz00vdKvy/2VXdwM9hjWh0+VRZKcWUZBZSl5GCWnxeez+L5nty7Tu2/63xh7vAqyq7kNjyEwoYOWMfQBExPox6K7WePq5IqUkN60Ym9VOYGTVB3T1vLYpna88tcpLl6ujObw9i6XTdmMusdK6T/jx1mD3a5rw36z9xG/JxMPXlTVzD5C0N5fu18Sc8Rq5eRiJPi1J6fQ6+oxoxu+Tt/LXF9vxDnLn8tGtMZdY+e/XA8x4Yz1lJVba9o1Ab3TcUBCV4JTzVrx5M3mzZxNw7z24Nmni7HCUkwgh/IBrgRggF5glhLhNSvnjaduNAcYAREVFnf+JAsu7lTL3N4gEB1Trg5qLu4HQGB9CY060+qxmG4l7cyjIKqVV7/Dzj0MnGDS6Df98u5Ow5r50GhSFKB8YI4Q4pdvwvGI9retPr9cx8K5WzHxrAyYfVy65odnx59r1j2DXqmQWf78La5kNdy8jfUY2p22/iCqfL6pNAL2ua4qryUDLS8LQl9+3C2/ux6Jvd1JSaKFV77Bq/S1VJS50kl5t6Nq1q4yLi3N2GAogbTYO3zgSa2YmTf9agM5DLWR6LkKIjVLKrrV0rhuBwVLKe8p/vwPoKaV88Gz7VOv6Ks2Dd6Jg0CvQ54kLiFhxtpSDebh5GM5InCkH8/jnu53E9gil4+VRNXpvzGaxk5dZgn/Yhb9/VHZ9qRaccl5yZ82idNcuwj94XyW3uuko0FMIYULrohwI1PynQzcf7T5c+p4aP7RSu8Ka+pz18dvfuMQh59QbdTWS3M5FzYNTqsyak0PGh5Mwde+O99VXOzscpQJSynXAr8AmtCkCOmCKQ04W3BIyVIJT6i6V4JQqy/zkU2wFBYS8+IIaWFKHSSlfllK2lFK2lVLeLqUsc8iJglpB5j6w1/9CxUrD5NAEJ4Q4LITYLoTYIoSIK3/MXwixWAixv/x73V5QSAGg7OBBcn75Bd+bRuLWooWzw1HqgqBYsBRD3lFnR6IoFaqNFtwAKWXHk24CPgsskVI2B5aU/67UcWnvvovOZCLokUecHYpSVwSX1xpU9+GUOsoZXZTXAj+U//wDMNwJMSjnofC/VRQtX0Hg/fdj8HfsApdKPRJY3pLP2O3cOBTlLByd4CSwSAixsXzeDUCIlPJYldZUIKTiXZW6QFqtpE94B2OjRvjdfpuzw1HqEndfbSRlxl5nR6IoFXL0NIE+5ZUVgoHFQohT+jKklFIIUeFEvAueiKrUiNxff6Ns/wEiPvoInUv1lwxRGqigWEhXLTilbnJogpNSJpV/TxdCzAG6A2lCiDApZYoQIgxIP8u+Uygf3ty1a9e6Pxu9AbIVFpExeTLuXbrgdYVaCscRhBDbqrBZhpRyoMODqY7gVrDxe20kpU4NylbqFoclOCGEB6CTUhaU/3wF8BowH7gTeKf8+zxHxaBcmKxvvsaWlUXI55+paQGOowcqm1Qo0K6ZuunkkZR+0c6ORlFO4cgWXAgwp/yN0QD8LKVcKITYAMwUQtwDHAFGOjAGpZosqalkf/c93ldfjXv79s4OpyEbK6U8UtkGQoizltlyuqCTRlKqBKfUMQ5LcFLKQ0CHCh7PQisfpNRhGR99DDYbQeNUnUFHklL+d+xnIYQ7ECWl3Hu2beqcoFjte8YeiB3s3FgU5TSq01w5Q+mePeTNnYvf7bfjEhnp7HAuCkKIYcAWYGH57x2FEHW3a/IYd1/wClMlu5Q6SSU45RTSbiftrbfRe3sTOHbMuXdQasrLaIOwcgGklFvQlryp+4JaqpGUSp2kEpxyiuzvf6B4/XqCxo1D71NxlXHFISxSyrzTHqsfo4eDWqqalEqdVOk9OCHEuCoco0hK+WUNxaM4UemuXaR/+CGegwbiO/JGZ4dzsdkphLgF0AshmgOPAqudHFPVBLdUIymVOulcLbinAU/Aq5KvJx0ZoFI77CUlJD31NAY/P8Jef11NC6h9jwBtgDLgZyAPeMypEVVVUEvtu6pootQx5xpFOU1K+VplG5TPcVPqubR3JmCOjyfq228w+KkFHpxgiJTyBeCFYw+Ur849y3khVdGxBJe+G1pc6dxYFOUklbbgpJTjz3WAqmyj1G3FmzaRO2MG/qPvxqNXL2eHc7F6roqP1T3uvuAZqlpwSp1TpXlwQojHgO+AAuBroBPwrJRykQNjU2qBlJL09z/AEBRE0MMPOzuci44Q4iq0SiYRQoiPT3rKG7A6J6pqCG6pVhVQ6pyqjqIcLaXMRyu35QfcjlZqS6nnCpcto2TTJgIffhidu7uzw7kYJQNxQCmw8aSv+UD96e8LagkZaiSlUrdUtZLJsREHV6Pdl9sp1CiEek/abKRPnIhLdDS+N1zv7HAuSlLKrcBWIcRPUsr602I7XVBLsBRBXgL4NXZ2NIoCVD3BbRRCLEKbePqcEMILUB/V6rm8ufMwHzhIxMcfIQyOXjlJqYgQYqaUciSwuaKlo6SU9aMQ6MkjKVWCU+qIqr6r3QN0BA5JKYuFEAHA3Q6LSnE4e2kpGZMn49ahPV6Xq6VwnOjYVIChTo3iQh2vSbkbWlzh3FgUpVxVE5wEWqNdhK8BHoCbo4JSHC972jSsqamET5ig5rw50bHV7c+1okCdZ/IHzxA1klKpU6qa4D5D65K8DC3BFQC/Ad0cFJfiQNasLLK++BLPyy7Do0d3Z4dzURNCFHBqSS5R/rtAW/Te2ymBVUdQS1V0WalTqprgekgpOwshNgNIKXOEEC4OjEtxoIzJk7GXlRH81FPODqX+kRKOrIakOMg9CjlHwGaGO6tX+F9K6VXDETpPUEvY8pP2GqleAaUOqGqCswgh9JR/0hRCBKEGmdRLpfv2kTtzFn633oprk/pRrL5OkBIOLIEV70LCOu0xN1/wjQL/mBp5UxdCdAD6lv+6Qkq57YIOWNuCW4K5EPISwbeRs6NRlConuI+BOUCwEOJNYATwosOiUhwm/d330Hl6EvjgA84OpX6wWWH3fFg9GZI3gXckXP0+tLtRq+BRQ8qLKdwHzC5/6CchxBQp5eTzPE4sMOOkh5oAL0kpJ9VIoJU5PpJyj0pwSp1QpQQnpfxJCLERbSVuAQyXUqqyBfVM4cqVFP33H8HPPqPqTZ6LuQg2/gDrPte6Iv1i4JqPocPNYHBI7/w9aLcCigCEEBOANcB5Jbjy1cA7lh9DDyShfTh1vJMTXHM1MldxvnMtl+MtpcwXQvgD6cD0k57zl1JmOzpApWZIq5W0CRMwRkXhf8stzg6n7rKUQNy3sHIiFGdCVC+48m2IvQp0ekeeWQC2k363caLAQnUNBA7W2ghNkz94BEO6Gmii1A3nasH9jDY1YCMVj/Rq4qC4lBqW++uv2qTuyR8jXNT4oDPYbbB5Gvz7DhSkQEw/GPACRPWorQi+A9YJIeagXV/XAt9c4DFHcdKH0loRFKtGUip1RqUJTko5tPy7Go1Qj9kKC8n4eDLuXbvgNWiQs8Ope46sgb/GQ+o2aNQDrv8KYvqee78aJKWcKIT4F+iD9uHxbinl5uoer3yU8zDOsiKBEGIMMAYgKiqquqc5U3Ar2DJdjaRU6oSqriZwHbBUSplX/rsv0F9KOddxoSk1JevLKdiyswn58ks1qfsYSwkc+Ae2/gJ7/tAGj4z4Ftpc7+w35pPnwV2Iq4BNUsq0ip6UUk4BpgB07dr1jBJh1RYUC+YCyE8Cn8gaO6yiVEdVVxN4+VhyA5BS5gIvV2VHIYReCLFZCPFH+e8xQoh1QogDQogZaj6dY1mSksj+4Qe8h12De7u2zg7H+XITYPYYeK8ZzLhNm9N26Xh4eD20vcFpyU0I8RLwA9pqHYHAd0KICxmpfDO13T0JENRK+67uwyl1QFWnCVSUCKu672PAbrT1rQAmAB9KKX8RQnyBNnrs8yoeSzlP6RM/BCEIfuIJZ4fiXFLCtpmw4Cntflu7EdDmOojuC/o6UWj6VqCDlLIUQAjxDrAFeON8DySE8AAuB8bWZIBVcspIStUdrjhXVVtwcUKIiUKIpuVfE9EGnlRKCBEJDEFbJJXyJXYuA34t3+QHYPh5R61USXFcHPl//on/6LsxhoU5OxznKc6GWXfBnDEQ3BoeWAXDPoamA+pKcgNtXbiT67u6og3xP29SyiIpZcDJvS61xiMAPILU4qdKnVDVq/sR4H9oE0glsBh4qAr7TQLGA8fKEQUAuSete5UIRFS0o8Nugl8kpNVK6muvYwgPI3DMGGeH4zxH18Gvo6EwDQa+DL0fc/Rw//MihJiMdk3lATuFEIvLf78cWO/M2KotuDWk7nB2FIpS5YneRcCzQgiPYxNRz0UIMRRIl1JuFEL0P9/AHHYT/CKR8/N0yvbtI+Ljjy7Olbrtdlj9ESx5Xauqcc8iiOjs7KgqElf+fSOnTsj+t/ZDqSFhHWDdF2CzgN7o7GiUi1hVR1FegtbN6AlEldfMGyulfLCS3XoDw4QQV6N1vXgDHwG+QghDeSsukmp2wyhnZ83IIOPjj/Ho3fviXOst9yjMfwQO/Quth2vdkW4+zo6qQlLKH5wdQ40L66AVoM7YA6HtnB2NchGr6j24D4ErgSwAKeVW4NLKdpBSPieljJRSRqNNOF0qpbwVWIZWyxLgTmBeNeJWKpH+/gfYy8oIefGFi2tagN0O67+Cz3pBYhwMnQQ3fl9nk9vJhBDNhRC/CiF2CSEOHftydlzVEtZR+56y1alhKEpVExxSyoTTHrJVuOG5PQOME0IcQLsnd6HVGpSTFG/aRN68eQTcfTeuMRfR/PycI/DDNdooyUbd4cE10PVuZ89pOx/foY0mtgIDgKnAj06NqLr8m4CLp0pwitNVdZBJQnk3pRRCGDkx9L9KpJT/Un5PQUp5CFCrbDrA8YEloaEE3l/7I8SdQkrYNgP+LF/bbtgn0Om2+pTYjnGXUi4RQojy2pGvlBc4f8nZgZ03nU7rmlQJTnGyqia4+9Hun0WgDWf+m6qNolRqUc4vMyjbs4eISR+iM5mcHY7jFWfDn+Ng5xyIugSu+wL8Gjs7quoqE0LogP1CiIfR7k17Ojmm6gvrAJumaXMO69CoVeXiUtVRlJloE1GVOsqalUXGxx9j6tUTryuvdHY4jrd/Mcx7WKv4XweH/1fDY4AJeBR4Ha2b8g6nRnQhwjqA5QvIOghBLZwdjXKRqtI9OCFEEyHE70KIDCFEuhBinhBCrSRQh6RPnIi9uJjQF19s2ANLygrh98fhpxHg7gf3LYW+4+p7cgOIllIWSikTpZR3SylvAOrvBNCwDtp31U2pOFFVB5n8DMwEwoBwYBbOqHOnVKhk61byfpuN/5134Nq0qbPDcZysg/D1QNj4PVzyKIz598Qbaf1XUdX/ClcCqBcCW4DeFVK2ODsS5SJW1XtwJinltJN+/1EI8bQjAlLOj5SStLfeRh8USOADlU1LrOcO/KNVJBE6uH2OVmarARBCXAVcDUQIIT4+6SlvtBGV9ZPeCCFttCWIFMVJqtqC+0sI8awQIloI0VgIMR5YIITwL1/tW3GSgr/+omTrVoIffxy9p4ezw6l5UsLqyfDTjdqSNvctazDJrVwyWjWTUrRqJse+5qPNPa2/wjpoXZRSFSJSnKOqLbiR5d9PH3s+CrWyt9PYy8pI/2AirrGx+Awf7uxwap7Nos1r2/g9tL4Whn8OLg0riZcXTdgqhPgZ7XqMklLudXJYNSOsA2z8DnKPgF+0s6NRLkJVHUV5Ec0Yrj9yfvwRS1ISUd9+g9DX+0EWpyrN01YAOLgU+j4JA17U5lc1XIOB9wEXIEYI0RF4TUo5zKlRXYiTB5qoBKc4QVVHUd4ohPAq//lFIcRsIUQnx4amVMaanU3m51/g2a8fHpdc4uxwalZuAnw7GOJXaBO3B77U0JMbwCtoBRByAaSUW4D6/cEyuDUIPaSo+3CKc1T1XeN/UsoCIUQfYBBaea0vHBeWci6Zn3yKvaSE4PENbKxP4kb46jLIS4LbfoPOtzs7otpiqWD9tvp988roBsGt1FQBxWmqmuCO1Z0cAkyRUv6J1pWiOEHZoXhyZszAd+SNDWtawM658P3V4GKCexdDk/7Ojqg27RRC3ALoywsvTwZWOzuoCxbWAZI3a4WwFaWWVTXBJQkhvgRuQhs96Xoe+yo1LP3999G5uRH08MPODqVm5KfA/Edh1p3aG+K9SyAo1tlR1bZHgDZAGdoc03zgcWcGVCNi+mnVZhI3ODsS5SJ0PqMoBwPvSylzhRBhQAPrG6sfitatp3DpUoLGjcMQEODscC5MWQGs+ghWfwJ2K/R8SLvfZnRzdmS1TkpZDLxQ/tVwxF6lTfjeNReiejg7GuUiU2mCE0JsklJ2Lr/4Zh97XEqZAqScvI1jw1QApN1O+rvvYggPw/+Oen5vqqwQvh+i3Z9pewNc9j/wr99jKi6EEKIr8DwQzUnXpZSyvbNiqhFu3tBsIOyaB1e8eTEMFlLqkHO14FoJISobAiWAur+aZAOR/8cflO7cSfh776Jzq8etHLsNfrsHUrfDqOnQ8mpnR1QX/ITWK7IdaFg3rFoPh70LtG5K1YpTatG5ElzLKhyjugufKufBXlxM+oeTcGvTBu8hQ5wdTvVJCX89A/sWwtXvq+R2QoaUcr6zg3AI1U2pOEmlCa584UWlDsiY/AnWlBQiPngfUZ+7edZ8Ahu+gl4PQ/f7nB1NXfKyEOJrYAnaQBMApJSzz75LPXGsm3LnXNVNqdSqqg4yUZyodNcusqdOxXfkSEyd6+ntTrsNFr+kJbhWw+Dy150dUV1zN1qPiZETXZSSk+5912uqm1JxApXg6jhps5Hy0svo/fwIfnKcs8OpnpJc7Z7bgX+g+xi48i31Kf5M3aSUDXduxLFuyp1zVIJTao16l6njcn76idIdOwh57ln0PvVwPE9+Mnw9CA79C0MnwdXvaUupKKdbLYRoXRMHEkL4CiF+FULsEULsFkL0qonjXpCTR1OqSd9KLVEtuDrMkpJCxqSP8OjbF++r6+FgjOJsmHYdFKTCHfMguo+zI6rLegJbhBDxaPfgBCCrOU3gI2ChlHKEEMIFMNVgnNV3rJsyeRNEdnV2NMpFwGEJTgjhBqwAXMvP86uU8mUhRAzwCxCAtu7V7VJKs6PiqK+klKS89DJSSkJffgkhhLNDOj9lhdoabtnxWk1JldzOZXBNHEQI4QNcCtwFUH5t1Y3rq9lA7fuhf1WCU2qFI7soy4DLpJQdgI7AYCFET2AC8KGUshmQA9zjwBjqrby58yhauZLgceNwiYx0djjnx1oGM27TPqmP+BZi+jo7ojpLCLEJtBHLFX2dvE0VxQAZwHdCiM1CiK+FEGcsoieEGCOEiBNCxGVkZNTI33JOHoEQ3AYOr6yd8ykXPYclOKkpLP/VWP4lgcuAX8sf/wEY7qgY6itLWjppb7+Ne5cu+N16i7PDOT92O8y5Hw4tg2GTodVQZ0dU17USQmyr5Gs7EHgexzMAnYHPpZSdgCLg2dM3klJOkVJ2lVJ2DQoKqpm/pCpi+sLRddqHIEVxMIfegxNC6NG6IZsBnwIHgVwppbV8k0QgwpEx1DdSSlJffRVZVkb4m2/UrzlvUsLfz8PO2TDoVeh0m7Mjqg9quphCIpAopVxX/vuvVJDgnCa6L6z7AhLjILq3s6NRGjiHJjgppQ3oKITwBeZQtYsZ0LpQgDEAUVFRDomvLspfsIDCpUsJHj8el+hoZ4dzflZNgnWfQ88Hofdjzo6mXqjpYgpSylQhRIIQIlZKuRcYCOyqyXNckOjegNC6KVWCUxysVpoHUspcYBnQC/AVQhxLrJFA0ln2cU4XihNZc3JIe+NN3Nq3x//OO5wdzvmJ+xb+eUUrnHzFm1DfBsU0LI8AP5XXke0IvOXccE7i7gdh7SFe3YdTHM9hCU4IEVTeckMI4Q5cDuxGS3Qjyje7E5jnqBjqm/R3JmArKCDs9dcRer2zw6ma0nyYPRb+eAKaDoThn6tJ3E4mpdxS/uGwvZRyuJQyx9kxnSK6LySuB0uJsyNRGjhHvhOFAcvKP0VuABZLKf8AngHGCSEOoE0V+MaBMdQbhatWkTdvHgH33oNbbAtnh1M1iRvhy76wfSb0fw5umQkGV2dHpdR1Mf3AZoaEdefeVlEugMPuwUkptwGdKnj8ENDdUeetj+wlJaS+/Aou0dEEPvCAs8Opmv3/wC83g2cI3LUAGju/WIZSTzTuBUKvdVM26e/saJQGTFUyqQMyJn+CJTGRxtOmonOtBy2gg8vgl1sgqKVWocTk7+yIlPrE1QvCO0H8CmdHojRw6maJkxVv2kz2999rKwV06+bscM7t0HKYPgoCm6vkplRfzKVaIYCywnNvqyjVpBKcE9mLi0l+9lmMYWEEjx/v7HDO7eg6Lbn5xajkplyYmL5gt8LRtc6ORGnAVIJzovT338eSkEDY22+h9zyjmlLdkrEXfh4JXmFw53yt7JKiVFejntryOfsXOTsSpQFTCc5JCletIufn6fjfcQce3ev4mJv8ZPjxBtC7wO2zwTPY2REp9Z2LCWIHw47fwGZxdjRKA6USnBPY8vNJeeFFXJo0IeiJx50dTuVKcuHHEVCSA7f9Cn7Rzo5IaSjaj4LiTDi41NmRKA2USnBOkPbmW1gzMgif8A46Nzdnh3N2NgvMvAMy98FN0yCsg7MjUhqSZoPA3R+2zXB2JEoDpaYJ1LKCf/4hb948Ah98APd27ZwdztlJqVUniV+uVSdpepmzI3I6m12SnFvCkaxi0vJLySk2k1NsxmaHZ6+qcplV5RiDC7S9Hjb/qFXEcfN2dkRKA6MSXC2yZmeT8vIruLZqReD99zs7nMqt/hg2T4O+T0FH5y3ZY7NL4jOLyC+14KLXYdTrkEiKzTZKzDZKLTZ0QqDXCYSAlLxS4jOLiM8oIjW/lLwSC7nFZsxWO0FergR7uxHi7UZ0gIkmQR5EB3iQll/KpqO5bDqSQ2JOCRabHbPVjtUucTPqcDPqMep1pOaXYrbaT4lPrxOEerupBFdd7UfBhq9h93y1+oRS41SCqyVSSlJfeRV7fj7h336LcHFxdkhnt2s+LH4Z2lwPA144793NVjtJuSUUllopKLNQXGajyGylxGyjyGyjuMxKkdlGUZkVvU4Q6edOpJ8Jfw8X0gtKScktJTGnmF0p+exMzqfYfD6rxYBRL4jyNxHu604jfxO+7kYMekFmoZm0/FK2JuTy57Zk7PLEPi56HW0jvOnbPBBXo5ZIDTpBmdVOidmG2WYnxNuNmEAtKYb5uOHn4YKXqwGdThWWrrbIruDfBLb+ohKcUuNUgqsl+X/8QcGiRQQ9Oa7u1pqUEtZ+Bov+p73xDP+swsLJRWVWtiflsSMpjzKrHYNOYNDrSMktYXNC7vHHK+Oi12Fy1WO22itMYJ6uBmJDvRjZtRFtwr0J9HTFYtNaVQDuLnpMRj1uRj0SsNntWG2SEG83Iv3cMegrv71stto5ml1EfGYxAZ4utAn3xtVQTwpcNyRCQPub4N93IC8RfOrZ6vVKnaYSXC2wJCeT+trruHfsSMDo0c4Op2LmYvj9Udg+C1oOpXTop6w+mM/iXfvZnVKAlBKJltziM4tOaf0c42rQ0TbCh9t6NqZVmDc+7kY8XQ14uOoxuRgwuejLvwy4GLQEJKUkt9hCYk4J2cVmQrxdCfNxx9vNgHDgkjsuBh3Ngr1oFuzlsHMoVdR+JPz7trYQard7tbmWqmi3UgNUgnMwabeT/NzzYLMR/u6EOrUMTnaRmb2pBRxNPMKla8cQUnKAuX6jmZk7gm3vrqXYbMPT1UCHRj4Y9ToEEOrtxtD24XRs5Ev7SB+83IxY7XYsVonJVbtXdT6EEPh5uODnUYe7bBXH8m8CUZfA6snaF0Bwa7htNniHOTc2pV5TCc7BsqdOpXjdOsLeeB0XJ69MnlNkZl18NqsPZvLfgUwOZRThTRHTXd7AV6TwrNsL7KAnHgiu6xTB5a1D6NU04Jxddy7oQOUn5UKM+kmrTVmQCnlJsOojmHk73PWnas0p1aYSnAOV7ttHxsQP8bzsMnxuuKHWziulJDW/lIPpRRzMKGRbYh6bj+ZwKLMIAJOLnu4x/tzaMYARux/BOzsZbv6Fd5sPqrUYFeUUJn9tXtwxQbEw605Y8DQM+9h5cSn1mkpwDmIvKyP56fHovLwIe/01h95PMlvtxB3OZsPhHOKOZLP5aC6FZdbjzwd4uNApyo8RXSPp2tifjo18cZFm+PlGyNoGN34PKrkpdUmb4ZAyDv6bCOEdoWsdvXet1GkqwTlI+gcfULZ3L42+/AJDQIBDzpGUW8L0dUf5ZUMCmYVlCAEtQ725rlMELUK9aBrkQdMgT4K9XE9NsJYSbT23+BVw3ZfQephD4lOUC3LZi5C6HRaMh4guqpKOct5UgnOAwuXLyZk6Db87bsezX78aPXaZ1caS3en8ujGRf/emI4HLYoO5qVsjejYNwNvNWPkBzMXaStyHlsOwT6DDqBqNT1FqjE4PN3wFk7vA4pe0JZoU5TyoBFfDrJmZJD//Aq6xsQQ/+WSNHFNKyZaEXOZsTmL+1mRyiy2EervxQP+m3Nw9ikg/U9UOZC6G6TdB/EptjpsTK5QoSpW4+2nVdP5+TltJvukAZ0ek1CMqwdUgabOR/Myz2AsLifjhe3SuFzb6Kz2/lOnrE5i7JYn4zCJcDDquaB3CjV0b0adZIPrzqaBRkAYzboOkOLjuC9VyU+qPrqO1AgRLXoUm/bXJ4YpSBSrB1aCMDz+kaNUqQl97Fddmzap9nAPphXy14hBzNidhsdvpGRPAA/2aMrhd6Lm7ICuSshWm3wLFWdqAktbXVjs2Ral1Rjfo/xzMe1CrWan+/ypVpBJcDcn7/Xeyvv4G35tH4Tdy5HnvX1hmZeGOVOZsTmTVgSxcDTpGdovk3j5NiA68gNW+d82HOWO1rp7RC7URaYpS33QYpRUAX/I6xA4BvXrrUs7NYf9LhBCNgKlACCCBKVLKj4QQ/sAMIBo4DIyUUuY4Ko7aULJ9OykvvIipWzdCn3++yvuVWmws35fBH9tSWLwrlVKLnSh/E+Mub8GtPaII8LzACa77FsGsuyCiM9z0E3iFXNjxFMVZdHoY+JI2+nfzVDVtQKkSR34MsgJPSik3CSG8gI1CiMXAXcASKeU7QohngWeBZxwYh0NZMzJIfOhhDEFBRHw0CWE8dxdiTpGZd/7aw4LtKRSUWfEzGbmhcyTXd46gc5RfzcyZS96iJbeQNnD7HHBVNRcvFkKIw0ABYAOsUsquzo2ohsReDY37wKKXtPUJ1eryyjk4LMFJKVOAlPKfC4QQu4EI4Fqgf/lmPwD/Uk8TnLRaSXpiHLb8fKJn/ILB3/+c++xIyuP+HzeSnl/G8E7hDG0fTq+mAeddw7FSuUfh55FadYhbZqrkdnEaIKXMdHYQNUoIuO5z+Lw3zB6rlfFSXZVKJWrwXfXshBDRQCdgHRBSnvwAUtG6MOuljEmTKI6LI+zVV3CLjT3n9jPjErj+89XY7ZKZ9/fi3REduLRFUM0mt4JU+OlGsJTCrbNUsVqlYfGNgiETIWGtVuVEUSrh8AQnhPAEfgMel1Lmn/yclFKi3Z+raL8xQog4IURcRkaGo8M8bwVLlmiDSm66CZ9rKx/VVVBq4cmZWxn/6za6Rfvx+yN96NjIt+aDOroOvuynteBG/QjBrWr+HEp9IIFFQoiNQogxFW1Q16+vSrW/EdrdqK0hlxjn7GiUOsyhCU4IYURLbj9JKWeXP5wmhAgrfz4MSK9oXynlFCllVyll16CgIEeGed7MR46Q/OxzuLVpQ8jzz1W67cYjOVz98UrmbE7k0cua8cPd3S988MjppIQN38D3Q8DoDvf+AzGX1uw5lPqkj5SyM3AV8JAQ4oz/DHX5+qqSq98H73CY+yDYK19cV7l4OSzBCW2kxDfAbinlyX0J84E7y3++E6hX9XesWVkcHTMGodMR8dFHZ53MnZxbwqu/72Tkl2uQEmaO7cW4K2LPudL0eSvN16YB/DlOmwQ7Zpk2sES5aEkpk8q/pwNzgO7OjcgB3H1h0CuQuRcOLHZ2NEod5cg7tL2B24HtQogt5Y89D7wDzBRC3AMcAc5/0piT2AoLSbhvDNa0dKK++xaXyIgzttmXVsAXyw8yf0syEhjROZIXhraq3gTtc0lYD7/dC3kJ0P95uPQpbTi1ctESQngAuvKBXR7AFcBrTg7LMVpfq9WoXPMJtLjS2dEodZAjR1H+B5xtvPtAR53XUexmM4kPP0Lp3r00+uxTTJ06nfJ8al4pHyzay6+bEnEz6Lm9V2Pu6RNT9TqR50NKWDVJm/TqEwF3L4SoHjV/HqU+CgHmlE81MQA/SykXOjckB9EbocdYLcmlbIOw9s6OSKlj1BjbKpBSkvLiixSvXUv4hHdOWSGgqMzKl8sPMmXlIex2uLdPDA/2b4afh4OWuLZZYcGTsPF7aHMdXPMRuPk45lxKvSOlPARcPOvKdL4T/p2g1aq87gtnR6PUMSrBVUHenLnkz/+dwEcePj5i0m6XzN6cxLsL95BeUMY1HcIZf2Usjfwd0GI7xlwEs+6G/X9Dn3FaZQdVeFa5mLn7QqfbIO5bGPiymhajnEIluHMwHz5M6htvYOrWjcD77wdgd0o+43/dxvakPDo28uWL27vQOcrPsYHkJsDM27XCyUM+gG73OvZ8ilJf9Lwf1k+BDV9pH/oUpZxKcJWQZjNJTz6FMBoJf3cCQq9n2Z50Hv55EyZXA5Nu6siwDuHozmfZmurY97c2UtJm1WpKtrzasedTlPrEvwm0HKK14jrcAoHVX8lDaVhqpZJJfZU+6SNKd+4k7PXXMIaF8cPqw9zzwwaiAz34/eE+DO8U4djkZrPAP69qZbe8I2HscpXcFKUi/Z7RBl990QfWf6X9rFz0VAuuAtJsJu2dCeT8/DO+N90Elw7gudnbmL4+gUGtQvhoVEc8XB380h36FxaM1+b5dLkLBr+jTeJWFOVMYe3hwTUw72FY8BTs/Qtu+Fqrx6pctFSCO40lLZ2kxx+nZPNm/EffzcYrbuGVD5aTWVjG/f2a8vSVsee3kvb5KkiFv56BXXO1auk3z4DYwY47n6I0FN7hcNtvsOFrWPgs/Ps2XP2es6NSnEgluJOU7t7N0TFjsBcV4/32BF7ID+OfX7bSJtybr+/sSvtIX8cGUJiuldvKS4IBL8Ilj2irGSuKUjVCQPf7IHkzbJoG/Z4FjwBnR6U4iboHV65k506O3HU3wmCkaOKX3LDbgxX7M3nh6lbMe6i345NbSQ5Mux7yk+GOedDvaZXcFKW6LnkUrCXayErloqUSHFCyfQdH7x6NzsOD1Y+8zshF6bgadcx+4BLuu7RJzdePPF1ZIfw0UrvfNuonVZVEUS5UcEtocRWs+xLMxefevjgb1nwGOUccH5tSay76LsqS7ds5OvoehJcXU657ilnrc7mqbSgTRrR3TP3IY0rz4ehaOLwC9i6E7INw4w/aSsWKoly43o/Bd4Nh84/Qo8JVg8oT2yflibBQ+5B5zUe1G6fiMBd1givdt4+j996H3dOLFy59iK0pkheHtOKePjEIR1UIKcmB/ybBui/AWgp6F4jsBoNehlbXOOacinIxiuoJkd1hzWToOvrM1b93/w5zHtASW5vh2r3v+BVOCVVxjIs2wZmPHuXoPfdg1hl4uNNoio3e/HxHJ3o0cdAN6dJ82PgdrJwIpXnQfiR0vEW7AF0cWN7rHKSU5JvzSS1KJa047fh3gzAQ6hFKiEcIPi4+mO1mzDYzNmkj1COUCM8IXPXnXtfOYrdQZi3Dw+hxxocGq91KkaUIi92C1W5FSomvmy/uhoqnQ9ilnUO5h0grTsPLxQsfVx88jZ4YdAaEEAgEeWV5ZJVmkVWShYvehSY+TQj1CEUndEgpKbIUkV2ajVFnxGQ0YTKYju8PkFSYxOrk1axJXsOB3AM09m5MC78WNPdtfjw2d4M7IaYQfFxVDdA6TQjo8zj8cgts/Rk633HiubVfaCMtI7rAsMkQ0lrrovz7Oa1qkG8jp4Wt1JyLMsFZUlM5cvdoiorKeKznWEJaxPDpLZ0J9q7hQR12GxxcBlunU7bnD5KElYCoS/Ee9CoirD2ZJZmsSVjC6uTVZBRnYMeOXdpxM7gR4x1DjE8MIaYQjhYc5UDuAQ7mHqTIUoTVbsVit2DUGfF19cXX1RcPFw9sdhs2aUNKSYB7AGEeYYR6hFJqLSW1OJWUwhSyS7MpsZZQbC2m0FxIenE6pbbSU8LWCR12WfkikgJBkCkIV70rNrsNq7Ril3Zk+QRbm7RRbCnGbDcDYNQZCTYFE+QeRJmtjIySDLJLsys8j8lgIsA9AD83P/xd/fFz8yOtOI3tGdspsBSc9z+Du8GdALcAskqzKLGWnHW7k//uEFMIrQJakZCfwMrEldik7Yztg9yDaOrblGa+zXi629PohLqlXee0uApC2sH8R7QC5V1HQ/purVsydog2V+7YB8xjiwQfXql9+FTqPSHrwYz/rl27yri4mlmavuzgQeLH3k9JehZPXzKWAdf0ZfzglhgvYCBJdmk2R/KPkFCQQGJBIjZpw1SSj8fOuWQVpRFn8mCbqwtmtDdPd4M7/m7+JBUmAeDv5k9j78bohA6d0FFoLuRw/uFT3oz93fxp6tsUHxcfDDoDBp0Bi91CblkueWV5FFmK0As9Bp32mSWjJIO8srzj++uEjiD3IPzd/I+3XDyMHgSbggn1CD3+PcQUQqB7IFJK0orTSCtOo8BcgIvOBRe9tkJCSlEKiYWJJBUkYZXW4+cViOMtKZ3QYTKa8DB44Kp3Jbssm4ziDDKKM3DRuxBkCiLIPQgfVx9cdC4Y9cbjr2VWSRZZpVnklOYc//J186VDUAc6BHWgkVcjCi2F5JXlUWAu0BIrEru04+3iTYB7AAHuAZRaSzmYe5D4vHiySrIINAUS7B6Mv7s/VruVYksxxdZirHYtOdulnQD3AHqF9SLG50Q3dZmtjMN5hykwF1BiLaHIWkRyYTIHcw9yIPcAJdYS5g+ff9b/H0KIjVLKrtX+D+ZgNXl91UmlebBlulbKK3Ov9lj3MVrxhJPXT7Tb4f3m0GwQXP+lc2JVzltl19dF1YIrXLGCI4+Po8AumNB3LE89MIzBbc9dfVxKSWZJJpklmce70zJKMtiQuoF1Kes4nH/4+Lba2zvYkeACOhdfWvq3ZFRoN2L9Y8kpzSG1KJXMkkxuaH4DvSN609K/5Rmf/o8lmNSiVBp5NSLA/fy7TostxaQWpeJmcCPIFIRRd36DZiK9Ion0ijzv89YlXUK6XPAxXPWuxPrHnvX5+vAh8aLm5qMVZO4xFo6sgqJMbbHU0++z63QQ01e7Dyflqc/brGfew1PqvIviX0xKSca335H5/gfEe4cyfdgjTBx7OTGBHhVuX2AuYHP6ZuJS49iVvYt92fvIKcs5YzuTwUSXkC5c3/x6mroGEpW0hYjtczBkHaS03QiKBjyHu1cYHsaKz1MZIQShHqGEeoSe977H4zOaaOLbpNr7K1XjsAFJSs0SAqL7VL5NzKWwcw5kHTxRtHnNp1pN2C53aiMzfer3h76LSYNPcLbCIg6Ofw7b0sWsCm9H6oPP8O3wjrgatK6JzJJMViau1LrcCpOIz4tnT/Ye7NKOUWck1i+Wy6Iuo7lfc8I8wjDqjBh0BrxdvGnh3wJj+h5YPkGrfWe3aoNGbn4T99irUJUjFaWeiSlfzDj+Xy3BFWdrC6p6BmtdnHHfaffnrpqgasPWAw06wZXt38+e+x/GkJzA9A5D6fPC49zXPgKAUmsp03ZN46vtX1FiLUEndIR5hBHpFcl97e6je2h32ge1x81wloEneUkw71HYOr28C+QB6HibNsFUUZT6yb+JtnJH/AptzcVVk6AsH0b/Ba5e2hSfuG8gtJ1WEkyp0xpsgstZvpLEhx+hUOfCr8Of5ImnRuFhKmVD6gb25exj6s6pJBclMzBqIA90eIAmvk0qv0dlLoLEOEjcoH0/tEzrp7/kEeg7DtwdvOCpoiiOJ4TWTblvIeQlahPA298EIW2054dO1EZZ7vlDJbh6oEEmuLiFqzA89QhJJn82PPIQ4bGHuWvJNWSUZBzfJtYvlm96f0P3sO5nP5ClFA4shh2/adVGjo1qDGgOHW7WEptvlIP/GkVRalXMpdq8uV/v0ab6DHj+1OdbDoHVk7WiDeqDbZ3WoBJcYZmVz6Yu5dLJz1PsbmTmQ4Fssr+Cfo+eSyMvpVtoN5r6NKWJbxNCTCGnDg6w2yBzHyRthOQtWjXytB1atRFTgNbvHnsVRHZV/6kVpSE7Nh8uYS30uB/8Gp/6fMuh8N+HsH+xVrBBqbMcluCEEN8CQ4F0KWXb8sf8gRlANHAYGCmlPHN4YjXsTM5j/DezeHr+Jwi9mTdu1mH0KuLx5o9zbbNrCXQPPLFxaR4cXQMZeyBjL6TugJQtWskeABdPCOuo9cE3vUy78ayGCCvKxcEnAgKaQX4K9H3qzOfDO4NXmFbqSyW4Os2R79rfA58AU0967FlgiZTyHSHEs+W/P3MhJ5FSMmP1fjZOeZ6Xt+7EaIPFT/XlzQG30NU3FmErg8JsyDqs9Z3vX6wVOT5WmcLoAcGttBZaRBftP29AM21OjKIoF6er3wObBTyDznxOp4PYq2HrL2ApUaMp6zCHJTgp5QohRPRpD18L9C//+QfgXy4gwZWYrawcdwWR61PokA9HG0O79vmMj58B8TMq3im0nTaXpfElENQSvCNUMlMU5VTnWtWj5RBtNOWh5RA7uHZiUs5bbfe7hUgpU8p/TgVCzrahEGIMMAYgKqrigRxlRTmkZwzBNXQP1iH7uaJDG4TJT+tidPHQPlkZ3MHgqv0c3hm8z125RFHqOyGEHogDkqSUQ50dT4MT3RdcfWDP7yrB1WFOu7EkpZRCiLPWOJJSTgGmgFYrr6JtPDz8sbdrS3piJyLaRcGwpqBTVSUUBXgM2A14OzuQBsngAi2uKC/wYDu1puXpUrfDH09Ap9u1aihKrantvrk0IUQYQPn39As5mNFFz23PXU7bSyPYvOgof3+9E6v5zKrvinIxEUJEAkOAr50dS4PWcggUZ0HCurNvc3ApfHuVNir790dh0YtaQlRqRW0nuPnAsY8wdwLzLvSAOr2OS29uwSU3NOPg5nTmTdpMaaHlQg+rKPXZJGA8UPmaR8qFaTYI9K6w7C1tZPbptvwMP92ozZV9dLO2gsHqyTDjdq1whOJwDktwQojpwBogVgiRKIS4B3gHuFwIsR8YVP57TZyLTpdHMfi+tmQcLeS39zaSn3X2db8UpaESQhybmrPxHNuNEULECSHiMjIyKttUORtXLxjygTbl6OvLtQLNABn7YNbdMPcBaNxbK/PlG6WNzLzqXdj3F/z+uOPjs9vAanb8eeqwBrceXPL+XBZ8vg29Ucc1j3QgMNLLwdEpSuVqcz04IcTbwO2AFXBDuwc3W0p529n2afDrwTla/AqYWb5aeEw/2D1fG9zW8wHo94x2v+5kC8bDxu/gqX2OLRox9yFI3gRjVzboebyVXV8Nbnx8eHNfrnuyM0IIfnt3I/98t4vD2zOxWVVvjdLwSSmfk1JGSimjgVHA0sqSm1IDYi6F+5aCRzDs+xt6PQSPb4OB/zszuQF0vBlsZm1ZHkcpzobtMyF9F+yc7bjz1HENMq0HRHgy4pkurPs9nvgtGexdl4qryUDbfhF0HBSFm8f5LfypKIpSKf8mcP9KbeK3u2/l24Z1hKBW2kTxrqMdE8+2mVoS9QqDFe9D2xsqH+nZQDW4Ftwxnn5uDLyjFXe/24chD7YnMtaPjX8dYdoLq1n/+yHKitVAFKVhk1L+q+bA1SKD67mTG2grFnQYpY2+PHbfDrSBKuu+hLLCC4tDStg0FcI7wZVvQeZe2HXB4/nqpQab4I7RG3REtw9k8Nh2jPpfdyJb+bPhz8N8/+wqlv24h4yjBc4OUVGUi037kSB0WisOtKQ0eyz8NR5+uVlbyaS6kjdB+k5t3l3rayEwFla8B/aL7zZNg+yiPJuACE+uGtuOjIQCtv+byL51qez6L5mACE+CG3sREOlJcJQXoU18EGrCuKIojuIdDk36w7ZfoP9zsGayNrqy1TVaEedf74aRU0F/2u0Uuw1yDoPeBXwbVXzsTVO1QS7tRmjdkpc+BbPvg71/ase/iFxUCe6YoEZeXHZ7Ky65vhl716ZyeHsmh7dnsnu1VkXMP9yDzlc2pnnXYHT6Bt/IVRTFGTrcrCWe/yZqc+laDdOS2oavYcFT2jSDrqNPWr5rJ2QdAFuZ1vq7bTY0HXDqMc1FsP03aDMc3Hy0x9pcD/++A/+8qhWaL0jVJqj7RkFYe+2eYFjHikda5iVpqys4i5Ral241NbhpAtUlpaQ430zC7mw2LzpKdnIR3oFuNOsaQlhTH8Ka+uBqUoNTlPNXm9MEqkNNE3AScxG830Jbpsu/CYz590RSWvkBLHntxLZe4RDaFoJitS7HNZ9CYaq2j1/0ie02/wTzHoS7/9IKyh+z/Vf47R6tZecVAu7+kH0ISnO15zvcDNd9cWp8O+fCrDthwIvQ7+ka//OrZNNUbWTqdV9o8w4rUNn1dVG24CoihMDDx5WWPcOI7R5K/LZMti5JYMuio2yySxAQGOlJo1b+NGrtT0i0VuLPbpNIKXHzMJ66gKqiKEplXDy0bsStv8CNP5xIbgB9n4TQ9lqXZHhH8Ao9dd/Gl8BXA+CXW+GeRdqx0vdoiS+gGUT1OnX7diO07km9y4kWkZSQlwDLJ8CW6XDZi+ATeWKftZ9rLcVlb2jTHXo/dn5/n5RaabLAFtWrwVmYru0f0lZb1qwaVIKrgNAJmnQMoknHICxlNtIO55NyIJfEPTlsXZLA5kVHz9jHzcNIUJQnQVHeBEZ64hdmwjfEhMF48Q3NVRSliq56V5sM7h1+5nPNLz/7fgFN4YZv4acRWtUUodPu4Rnc4dpPKu7WM7ie+rsQWjflpeO1ll/cd9rcPdAKRCeshUGvQspWWPwSGNygx9iq/237/oY1n2g/p2zR/tbT7ylW5q9ntGkXQydVe0kzleDOweiqJzLWj8hYP7oNicFcaiV5fy5ZSYXo9Dr0BoG0Q3ZyIelHC9jyz1HsNq3bVwjwC/MgsqUfjVr5E97MF4OrHiFQrT1FUbSkU1Fyq4rmg2DgS7DkVa3Lsf9z0O0+8Ag4v+P4NYbYq2Dj99BvvBbThm+0hNb5Dq1r0GbWRnhu+Rk8g8EjSFtPM/ZqCGx25jHtdlj6OvjFQOthsOojyNyv3WM0+Z87pn1/axPUB7wAQS3O7+85iUpw58nFzUB0u0Ci2wVW+LzNYic3vZjslCKyU4pIi89n58pkti1NPGU7oRO4mgy4expx8zSi0+uwWWxYLXZ0OoFXgBveAe54B7kTGOlJQIQnRlfVGlQU5SR9ntC6K0Pbg4up+sfpfh/sXaDdd4sdrE0UbzviRDIa8Z3WVZm2EwrTIHUHbPkJFv9P64JsO0LrVj02UGXnbEjbAdd/De1vhODWMP8R+OZyuOvPM7tcT1ZWCH8+qSXQ3o9X/29CJbgapzfqCIjQEtIxVouNlIN5pB/Ox26T2O0SaZOUFVspKTRTUmDBbrNjcNHj5umCzWonK6mI+G2Z2K3lg4AE+AabMLjosFnsWM123DyNhMZ4E9LEB/8wD6xmG+YyG5ZSG3a7HWnXBs94B7gTHO11SndpWYmV/MwS9AYdBhcdBqMeKSV2m8RmtSOEwGDUoTfqkFJSUmChpMCMudSGydsFL3833L3UfUdFcSohIKrnhR8npj8ENIf1U7SBJ5Yi6H7viecNLnD5a6fuk5ugrYe35w/49y2tG3LEd9rUhGVvQnAbrYIKaBPbfaPgxxEw9VotyXlU0EjIPaqN9sxLgNGLKi51dh5UgqsFBqOeRi39adSyCk3zk0i7pDC3jMyEAjISCslKLMRus6M36jEYdRTmlrFnbSrblyed81h6g47gaC/cPIxkJRWSn3kBE0lPOqanvyte/m7aV4Ab3oHueAe64+KuJy+9hJzUIgqySnE1GTB5u2LydsFqsVGUa6YotwxLmQ29QaA36nE1GQhr5qN15bpoybgwp5TUQ/nojTpCor0xeWv/4e12SV56MbnpJeh0J5KxzWrHXGrDUmpFCIGblxF3TxfcPIy4uOkxuurVHEdFOZ1Op7Xi/hoPOfEQ0UWrhFIZ30bQY4z2tW4K/PW0dk+wxWBthObNv5x676zxJXDLL9oSQtOGwx3ztWLT2YfgyGrYNgMOr9S27TMOonpc8J+lElwdJnTiePKI6RBU4TZ2uyQnpYi89BKMrnqM5W/iOr04/kaenVxEyoFckg/kkZtWTHBjb1r3Ccc32ITdLrGabVjNdoROoNML9HqBBKxmOzaLHQSYvFxw9zJidDNQnFdGQXYpBVmlFOZoPx/ZkUVxfsVLc7h5GDGXWo/fmzz5caObHptVO4+51Ia0S/QGHUFRXhTmaMc/2bGWY3ZyEVZL9SozGFx06HQChEAIMHm74BtiwifYhE4nyEouJDupiKL8MvzDPAiO0ooAlBRayE0rJjetGKvZjsFFh96gw83TyNCHOlQrFkWpMzrcrE1NKM6CK948v317jNHKlM25X0tSkd20RHe6mEth1E8w/Wb4oq/WUizJ0Z7zi9HuubW/SbsvWANUgqvndDpxRpfo6XyDTTTpWHGCrElWs42C7FLyMkowl1jxCTbhF2LCxd2AlJKyIitFeWUYXPR4+LqcMcLUUmYjeX8uCXuyST2YR1hTH0Kb+hAS44PNaictPp+0+HxKiyy06RtBYCNPfENNIMFqsWM12zAYdbi4GzC66pF2jncBlxZZsJTaMJdZsZTZoLz7VtolRXlmctOLObozGyklfqEmQpv6YPJxITupkINbMti1KgUEeAe44RtiwsXNgNViP96dqyj1nps3dL5Tu3/W5rrz37/9SHD1hoXPagnybNdFs0Fw00+wapI2/y+yK0R0hZA2FzSpuyJqoreilLPbJUh5RvUaKSXFeWZcPQzVmvahJnor9YbNqlVKcanevDNnUBO9FaUKdDoBnPkJUgiBh6/rmTsoSkOjNzSoxVFVoUVFURSlQVIJTlEURWmQVIJTFEVRGiSV4BRFUZQGySkJTggxWAixVwhxQAjxrDNiUBRFURq2Wk9wQgg98ClwFdAauFkI0bq241AURVEaNme04LoDB6SUh6SUZuAX4FonxKEoiqI0YM5IcBFAwkm/J5Y/piiKoig1ps4OMhFCjBFCxAkh4jIyMpwdjqIoilLPOGPKehLQ6KTfI8sfO4WUcgowBUAIkSGEOFLJMQOBzJoMsh5Sr4GmLr4ONVM51kE2btyYqa6vc1KvgaYuvg5nvb5qvRalEMIA7AMGoiW2DcAtUsqdF3DMuLpc6682qNdAo16HmqdeU/UaHFPfXodab8FJKa1CiIeBvwE98O2FJDdFURRFqYhTqmpKKRcAC5xxbkVRFOXiUGcHmZynKc4OoA5Qr4FGvQ41T72m6jU4pl69DvViPThFURRFOV8NpQWnKIqiKKeo1wlO1bQEIUQjIcQyIcQuIcROIcRjzo7JWYQQeiHEZiHEH86OpSFQ15e6vk5WH6+vepvgVE3L46zAk1LK1kBP4KGL9HUAeAzY7ewgGgJ1fR2nrq8T6t31VW8THKqmJQBSyhQp5abynwvQ/gNedKXPhBCRwBDga2fH0kCo6wt1fR1TX6+v+pzgVE3L0wghooFOwDonh+IMk4DxgN3JcTQU6vo6jbq+6t/1VZ8TnHISIYQn8BvwuJQy39nx1CYhxFAgXUq50dmxKA2Tur7q5/VVnxNclWpaXgyEEEa0i+8nKeVsZ8fjBL2BYUKIw2hdaZcJIX50bkj1nrq+yqnrq/5eX/V2HpwjalrWR0IIAfwAZEspH3dyOE4nhOgPPCWlHOrkUOo1dX1p1PV1qvp2fdXbFpyU0gocq2m5G5h5sV185XoDt6N9qtpS/nW1s4NS6jd1fR2nrq96rN624BRFURSlMvW2BacoiqIolVEJTlEURWmQVIJTFEVRGiSV4BRFUZQGSSU4RVEUpUFSCa6BEkL4CiEeLP85XAjxq7NjUpSGQl1f9YOaJtBAldfN+0NK2dbZsShKQ6Our/rB4OwAFId5B2gqhNgC7AdaSSnbCiHuAoYDHkBz4H3ABW0yaxlwtZQyWwjRFG25lCCgGLhPSrmntv8IRamj1PVVD6guyobrWeCglLIj8PRpz7UFrge6AW8CxVLKTsAa4I7ybaYAj0gpuwBPAZ/VRtCKUk+o66seUC24i9Oy8rWtCoQQecDv5Y9vB9qXV06/BJilleIDwLX2w1SUekldX3WESnAXp7KTfraf9Lsd7f+EDsgt/3SqKMr5UddXHaG6KBuuAsCrOjuWr3cVL4S4EbSK6kKIDjUZnKLUc+r6qgdUgmugpJRZwCohxA7gvWoc4lbgHiHEVmAncG1Nxqco9Zm6vuoHNU1AURRFaZBUC05RFEVpkFSCUxRFURokleAURVGUBkklOEVRFKVBUglOURRFaZBUglMURVEaJJXgFEVRlAZJJThFURSlQfo/G0en1oHBU88AAAAASUVORK5CYII=\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mu_hat/mu:\n", + "[ 2.33074275 1.17918873 5.94054837 0.66579005 18.7667204 ]\n", + "[1.27853844 0.55683415 2.06752757 0.86387608 0.70448068]\n", + "\n", + "M_hat/M:\n", + "[[-0.13 -0.1 0.03 0.06 -0.03]\n", + " [-0.12 -0.26 0.1 0.15 0.02]\n", + " [ 0.14 0.16 -0.54 -0.11 -0.2 ]\n", + " [ 0.07 0.1 -0.06 -0.07 -0.03]\n", + " [-0.19 -0.22 -0.84 0.14 -0.91]]\n", + "\n", + " [[-0.05 0. 0. 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0. 0. 0. 0. -0.2 ]]\n", + "\n", + "a_hat/a:\n", + "[[-0. -0. 0. 0. -0. ]\n", + " [-0.12 -0. -0.36 -0. 0.44]\n", + " [-0. -0. -0. 0. -0. ]\n", + " [ 0. -0. 0. 0. -0. ]\n", + " [-0.1 0. -0.04 -0. 0. ]\n", + " [-0. -0. 0. -0. 0. ]]\n", + "\n", + " [[ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 1. ]\n", + " [ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. -0.5 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. ]]\n" + ] + }, + { + "data": { + "image/png": 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XFxdXX/2XdVNUqNqZbSvepGaNN4mMfIGXX36NV17J2+XzUteXCRMwGID0DDsf/hjHxBkJdGzuSaVyLrz9XRx//KP92wsrbsVMBRE5lvv+OFAhrx3zW2/xh7+aUjtwK0EeMbi6BeEb2BCr1ZNju35h/retWLPqC1w9gvGt0BT/Ci3x9KuHq0dF3Lx7MaPV7Uyq3R2f4Ib4BDfAxd2PzNRjpMbt4uCa5/lo6c2MyTxIdnYiLh4VcPOOwOoWiN2WhZu7L9W7fM/E+TWwYUFQKAQLAgp2uYdRu/NHBPtdi6tHBdw8K6MsLqQn7wbJwrN9S2ruWUCDuu7YMpJJT4zExT0AV8/K2MXCgWQr/oEDGNjtHty9K2F198bF1Rc39/JkZRync+vVbN36FW6eIbi4+YFN9JIt2LOEuzNXM/XthnRrdjvefnUARWrcLpJObCDx+HrW/NSJcWOakZS4S9uMkJlyHHtOGh5+4dSsWZ/HHnuMFo2G4ukTQU52MsnRm8lOT8GOlQe67mRUxDyi0oKxiRWbWMnOTic1fhug6Hf3ImAtAcG9sVjdSEvZR47dhh1Flt3KqFEPUrVqVcoFNwHR4ghgsdgRdxfKHWvCA3feT3LyPtKS92HBhouyn36MePLJn7n++qZkZsbg4VUFv8DGuLsH4+YRgl+5Hri5x3Po0D9k44pyAeUCKLDlQFaClUrlXiQtYS9p8SchR7QNtmxs2Sl4kMKelf6sWPAlVhevXHEDrPrhwTczgzX/KSIjn8PFvRxffvkFiYmJhbsiinroxBGLGaI0OJL1O9Nl0AuHpcv9kTLu51h55APtrDDhtzjJKcSQ5PngICcTIJxzhygTztsen5928rq+UtNtMnDML7Lu0zYiUxD7GL1fdna2vPzyyxIRESE//vijyFNPybgOr0mPUfvkkFe41GGn3Oo/V6RhQ3nmtl+l56g98u6kY7J9f4bExsbKsmXL5L2nXpFgNUSqBY2T0aNT5eef9XxdsFeqgIiHl00a9tLznmNbvitxC1ZKjs0uCck5Mvy1o9J1dJRUiEgXq1Xk9ddFcnJEtmzZIt7e3tK6dWvJyMgQu90ukyZNEn9/f6kQGi7t794s1ZukSrlwPQy2YJWe+9q2X88LTb//a0kAqeTlJREREQJIRKtn5M2v9HxRekyK9PJYrO0jTV54NFmSkkQeGJ4qkCntQh+UJk1uEbhLqld/QHx8GgsoefmuEXIQxNvFRWrV7yGdRh2UkU+lyLqtmXL4RJbc88ZRaX3bHLFYqgu4iI/PbAkO1g46TZqIDBggctddG8TPL1jCwsLkzS/W6rnLV9MFRDp02CbgKa7W62R02x8loMKbAsj06dNFliyRSEsVadjupHS8L+r0kG2P+3ZL73t3yuh7nxZAatasKXcPGSJfRkTIIC9//d1rt5TH31mrHXZyh4jl559FROREbLa8+12sdH0gUno9HCUTZ8RLStqZocTs7GypXq2atFJK0kDGhoSIj6vrWcPBlQSQ2te9Ke92/UBOrNwivR88IC9eP0kkMFD6V1sngS6JElOplhyuWLHQ15fTxetKLkCD4UrIyTkT2zbkpSMy798UGfTCYenxUKQsWH0RD7lCUowCtwsIzX0fCuzKTzt5Xl9ZybL36xD5dXx5kWddRaYgsuWNC8MCtm6V/UG1pfPoSJn2yA+Sue+QZGeL7InKlM6jI+WHOQl5tH+hB2HKrMUyjgfl3t5R8u/4f+WtLh+cvil3uT9Sej4cJT0eipS1O9LlyJEz3v6nmD59ugAyaNCg096DHTt2lD179snw147KwOeOyNAXjsttzx6WnJwz3+PB947J4BcOS85Lr8gfuTdhZbFKmzvWSNsOOZKaKtKnxg4BkXdv/U9uVz8J6NAHEHmSd8W+c5eIiHz8seQ6SqZK48Z6vivA21s8PT1l+8590vmew+fMD3YaFSnBVdOkf/94adSouXh5ecl///132ra///5b/P39pUqVKrJ3715Jz7TJXa8ekVvGHJbHnswREKlRQ7vrhzW6S6xuvuJXoaNM/OiQ7Oh7r3S8da90Hh0pj38QLUvWpUp0fLbELt8g9942R7qN3CdPP/eZ9OzeU3xdPXPFR0m1Fg9J19F7pesDkfLG1ydFatfWamu3S2q6Te546Yh0f1A7YOXldPX5558LIBXKlRNA+vfvL9M++EDe9PISf3W9lPPoIS81HyudR0dK15GHpOv9kbJuzkHZ0ehWUdjkxcqTtBvna6/lGYoiYgTOYLiAzCy7vPiF7iF88lOspGfaJPJ4ltz9+lHZcaBwwbR5UYwC9x7nOpm8m5928ry+7HYZO85FZAqSM6WuyLLbRH60isRfJGJ77Vp58K3DMvSVI6fjA1/9Mlr6PhYlyan5CI4+RWKidut74gmRatXEVruOrFgTL9MXJ8k3s+Llk59iZePuS7vIv/DCCwKIl5eXjB8//nRw9qrNaadF5bu/zhXdv9frXt37P8TIxnd+lGFuPlKl4TB54OlIAZFqYVkCIhPaTNIHjBkjK2kj3VvGyVjfN8Xes9c57X3yiUitWiJHjthl3Lhx4uLicjpgPiYhR76bniYPjEmVtr2SpXn7dDkVZnjs2DEJDw+XkJAQ2bNnj8yYMUPc3d2lbt26EhkZebr9vYcypcdDkfL8Zydl+XK7/LU8WSrU6q8dZ6wu0rL/Yv1d7zsg1w47JG+Nv9DPPmXGX/LE9VOk8+hI6TVyt3QadVBuG/GnjLv1NdlRqYVk7j0o387WXp2rqnYW+fVXERF557sY6Xp/pGzac+m/Q3p6ukREREiTJk1k8eLFZzasWyfPur9/OlqiajN9johr4gV0zKSHx+kog8tiBM5gOIuUNJs89pEehpy+OEk27Uk/fVMujJfk5XCEwAFTgWNANnAYGIGur7gIHSawEAjKT1t5Xl8pKVLrEYvc8QFi/9FFZGYdkajf8vyec1dpN/aNu9Ml6niWdLk/UibOiC/4D9aokRY5pURWrCjw4TabTb7++mvZdypmIRe73S6PfXhcuj0QKbHn9TpybHZ59cto6faAFsCuow9K9/v2yvGAqnJLQ91z+8zjMZHjx/UBycnay9HfX99G//zzkjalXiqQ6zx27twpwcHBEhoaKhaLRdq0aSMxMTEX7DdtoQ4G/3hqrPR4KFLuf3OvtGvXXt577z1Z/NUuqd46Tup0jJH7R+YdyZ057jP5uMPr8n7Ht2TnF3/olVFRIu7uIsOGSWZGjtw19B8ZOHyNpKZmn34Q+OqP+Hx9l6ysrIsmRDgye7081+wv+fmbVDlyRCTqeJbs3GWXN94QadFCd9ryixE4gyGXhOQcGfnWMen2QKTM/zdZvpkVr+djinBI8nwc1YMrquVS11e3L9qJ31hfObT7e5FpASJ/NtYbon4T+fceEVv26X3TM23S7/EoeWNStLz3fYz0fDhKYhMLFjMoIiL33qtvTY89VvBjL0NswqVTq6Wk2eTv9any3vcxMn3mEZEBAyQdd9lIYz32eDZTp2o7a9a8ZFaSwrBy5Urx8vKSvn37XjygXPTD2NPjT0jn0ZEy+MUjkpB87m/96qNxMqBb/KVC5TSffiry23kPLk8+qR8wXnlFtlZoLl1GH5Q3JkXLjU8eklFvH5PsnKJ/ECwsl7q+TLkcw1VDYoqNJ8ed5NCJHF69txyrt2Uwa3kKfa71plMLL2ebVyKpV7U5a+K3UrnWEMg+BhufhvQTkLQD9n0FWQlw7RSwuuHhZqFHa29mL09BBPq28yHIz1rwkw4bBomJ8MYbRf59gvytBPnnbZO3p4XrmnlxXbPc/4frf8Xjl19osnIlPPDAuTsPHKiTQ3fqBJaidUhv27Ytx44dw9fXF6Uu7sFrsSieuTOYr2YmMLCbH/4+536vlz4KzN/J7r//wnVjxsDEifDKKzSoXZv+HX2Y8XcqHm6K5+4KLi1exUbgDFcHiSk2nvjkJIdP5vDKvcHM/zeNpevTGNzTjxE3+Od5E7naCfUJJTEzkYT0BAJC2uuVMSugwXNg9YT1j8M/KdBhOrh40bedDzOWpmCxwMDufoU7abt2eikp3HqrXs5HKfjoI4ed1s/v8r9fkL+Vp+8MLvqTBwfDM8/A88/Dc88x4sZAok7Y6H2tN1UquBb9+RyEEThDmSchWffcDp/MYezoENxdFcs2pjHq5gBu61bIm/BVQkWfigAM/m0wf90+AyzuEL0CqtwMdR8DVz9YfS8s6QldFlA9zIP2TTwpH2ilYrC5vZRqnnoKGjaEfv3wslh47+HyzraowJj/QEOZJupENs99Fk1Mgo03RpWjRV0PACa/UolK5cy//+UI9Q0FYH/8frC6Q3AriF5+ZocaI8DFF+LWaPEDXhsZ4gxTDUWNqyvccIOzrbgiTCYTQ5llw64MHnz3OGnpdsaOLscPc5L4Z4OusmzELX+E+miBO5KcW9g0pD3ErYecs6pVV7sNmr2nh+wStkHKweI31GC4CEbgDGWSBatTeXr8SYL9rbz7UHm+npnItv2Zzjar1HGqB5eSlUJSZhKEtAPJgdj/LtxZ7LBiICxop4XOYHAyDhM4pVQdpdTGs5YkpdSjSqkgpdQCpdSe3Nd8uvoYDPnjnw1pvPNdLI1quvPOg+X5cGocew9l8cp95c54xxnyRTmvcliUvk0ciD8AIdfqDWcPU55CWaDdVC10CzvouTqDwYk4TOBEZJeINBWRpkALIA2Ygc6wsEhEaqGDUsc4ygbD1cf6XRmM/SaGuuFuvHxPOcZ+E8ueqCxevqcc7RobcSsoFmUhxCuExuUbE+ARAG6B4N8gb/EKaAQ9VoJ7OVjcDQ79XpzmGgznUFxDlF2BfSISCdwITM5dPxnoX0w2GMo4uyIzefGLaCqXd+XN+0Pw87bQoLobz99djnZNjLgVlir+VajkV4lqAdX0ipD2ELMS7LaLH+ATAd1XQEBj2PO5zshkMDiB4hK429GphSCfJT3yW87DYACIjs/h2U+j8fexMHZ0OdIzBaUU990USKfmRtyuhIo+FTmceJijyUf1ipD2kJ0EiZeYZ/MIga6LocMv2vkkO0kPXRoMxYjDBU4p5QbcAPxy/rbcNCsXfbwTkYki0lJEWoaEGLdjQ97Y7MLYb2LJyBbevD+Er2cmcv+7x0lOMzfUoiDUJ5QdMTsYNXuUXhGSG4R9sXm4s3Hx1nFytixY3BNWDgGbcfQxFB/F0YPrDawXkRO5n0/kVhsm9/VkMdhgKMN8/1cim/dm8sjAQGYtS2HRmjQGdPbF18s4CRcFoT6h2MTGgYQDeoV3OHhWurzAncLiCpVvhMipsLg7ZMY6zFaD4WyK4w4wiDPDkwAzgWG574cBfxSDDYYyysbdGfwwJ4kerb05GWdjxtIUbu3qy6AeJkNJUXEqVOBA/AGdoV0pPUyZXy9JpaDBGLh2qg4vmNcaEnc40GKDQeNQgVNKeQPdgd/OWv020F0ptQfolvvZYCgw8ck2xn4TS1h5F1rW8+Cb2Yn0aO3NyJsCTG7JIuRUsHdqdiqx6bm9r5D2kBYFh2bkv6Hw26HrEshJhlVDjfOJweE4NJ2DiKSia1SdvS4W7VVpMBSatAw7z34aTUqanbfur0BYeRfu6ufP4J5+WCxG3IqSUz04gIMJBynnVQ6qD4ODP8DyW6HtD1q88kNIW+i5BmwZumdnzwFl1e8NhiLGTFIYSh3ZOcLLE2PYeziL0QMCqBTigqe7haF9/EtNGY/SxOmEyw0HE+Ybple6+kGXBdrhZOVg2PdN/hv0rgp+tXUPbvU9sGoY5KQ7wHLD1Y4ROEOpwm4X3v4ulnU7MxjZP4Dv5yQx9hvjtOBITglcnXJ1zunN4eoHneZAxe6w+m7Y+UnBG/epAQe/hwXtITWqiCw2GDRG4AylikmzElmyNo3h/fxZsCaV9Ew7I27wd7ZZZRo3qxvBnsFsj97OlhNbzt3o4gUdZ+ryOesfhY3P5X9uTSlo9CJ0nAUpe2Fuczg6t8jtN1y9GIEzlBr+25bOj/OS6H2tF3sPZ7H/cDYv3F2O6mFuzjatzBPqG8rcvXN5euHTF260ukO7aVDzPtj+lh52tOfkv/GwfnpezrOSHu7MSiw6ww1XNaZmiKFUEJOQw9uTY4mo5Er5QBfmrExi9IAA2jT0dLZpVwWhPqEcSTqi68JdDIsVrvkCPCrA1tf18GWLAlS79qsNPf7V2VHc/HUvMDMWPMoVzRcwXJWYHpyhxGOzC29+G0tGlvDiiHL0bOPD3df7c0sXX2ebdtUQ6quDvffF7SMzJ49sJEpB49eg6m1wcErBU3O5eEHwNfr97vHwZz04MvvKDDdc1RiBM5R4fpybxMbdmQy/3p+qFVyoGOzCkN7+JtatGAn1CSU1KxWb2Ngdu/vSO1e+CTKjL14zLr9U7A6eYfD39bD2YR1WYDAUECNwhhLNf9vS+fbPRK5r5slvS5IZPy3e2SZdlVT0qYhNdPWAbdGXKWZaqaeObbuS3pd/Pej5L9R5RPfm5jTXlcQNhgJgBM5QYjlyMps3JsUQUcmFpFQ7cUk2erbxdrZZVyWnspmM6zWOrhGXydPgFqgznVzp8KLVA1p8DJ3nQU4KZBvnE0PBMAJnKJGkZ9h5aWIMFouiXrg7G3dn8uigIOqGuzvbtBKPUuoRpdRWpdQ2pdSjRdHmqfi3uuXqEuKdj+oeYf0gYROkHiqCk/eA6/dAhc76867xELvmyts1lHmMwBlKHCLCuz/EEXksmxuv8+HPFanc0MGH3m19nG1aiUcp1RC4F2gFNAH6KaVqXmm7p3pwq4+s5tuN317+gEr99OvRP6/01Bpr7oNNTirseA/mt4H1T+jPBkMeGIEzlDimL0nm7/Vp3HNjAM3qeNC2kSf33xLobLNKC/WA1SKSJiI5wN/AzVfa6Kke3NKDS7ln5j15e1Kewq+OzlJS1F6QLt7QZzPUuBd2fgh/NoDDf5jEzYaLYgTOUKLYfiCTCb8lcG0jDwZ296VpbQ/Gjg7BzdV4TOaTrUAHpVSwUsoL6ANUudJGfdx88HHzwc3qhk1s7IrddekDlNLDlCcWQU7alZ7+XNwCoNUX0O0fcPGB5bdB+pGiPYehTGAEzlBiSEyx8dpXMZQPtOLjZWXyn8apoKCIyA7gHWA+MBfYCNjO308pdZ9Saq1Sam10dHS+2g71CcWeG9u27eRlPClBC5wtA04szq/5BaN8B+i9QZfg8aqs1+2dCFnG09agMQJnKBHY7cJbk2OJT7bRs60P81enYjejToVCRL4WkRYich0QD1wQuCYiE0WkpYi0DAnJh9MIOlQgNTsVq7JePlQAIOQ63cM6MguyUyA1EpL3FfDbXAaLK4Rcq98nbof/RsHMmjrxsy2raM9lKHUYgTOUCH5bmsx/2zIY1MOPnxYk0bimO8P6mCTKhUEpVT73tSp6/u3Homg31DeUEyknqBVcK38CZ3WD0J66V/WLL/wRDrNqwpG/isKcC/Gvr3t0Qc114ufZtWHfpILlxTSUKUwuSoPTORqTw6SZibSq787Kzem4uSieHx6M1dR2KyzTlVLBQDbwgIgkFEWjYb5hzN49my2jtlDRt2L+Dmr0KvjW1vNm7sGw7S3Y+IwWPou1KMw6l8Am0Hk+HF8Am16AjWN06jCL8cC9GjECZ3AqIsIHU2KxWKBnWx/enhzLK/eGEBJo/jULi4h0cES7Yb5hpGWnEeQVhJerV/4OCmgATd8889nFF1YM1Lkqqw91hJnawSW0h073lXoQXH3AboOlvaByf6h+N7iYJN1XA2aI0uBU5qxMZcOuTEbeFEDnFt788Fol2jYyN5+SSJifrub93+H/eHrB0+yN21vwRqreAkEtYfOLjs8vqRT4ROj3mSd1zNzaB+GParDpRUg76tjzG5yOETiD04hJyOHz3+KpH+FGgK8ergoJMD23kkqYrxa4g4kHeW/le6w+vLrgjSgLNH0H0qJg92dFbOEl8AyF7iug61Io1wa2jdVCF7eu+GwwFDtG4AxOQUT4aGo8WdmCxQJvfhNLXOIF3uyGEsSpHpxC4WJxyZ+jycWo2AUq9tAiU5zFTZWCCh11BfLrd0OD5yCgqd62azzseB/STxSfPQaH41CBU0oFKKV+VUrtVErtUEq1VUoFKaUWKKX25L6aFBVXIXNWprJqSzqtGniwdV8W998SQJC/A5wODEVGJd9KAJxIPUGtoHx6UuZF07chKw7WPeycLCS+NaHxq2ccXU4sgQ1Pwe+VYHFP2P8dZCcXv12GIsXRPbhPgLkiUhedF28HMAZYJCK1gEW5nw1XEUdjcvj013jqVnPlv20ZXNvYk37tjZdbScfDxYNyXuU4knSEBuUb5C/YOy+CmkGjV+DAd7DllaIysfBc9xv03Q71x0Dybvh3mBZfyK0uHudc+wyFwmECp5TyB64DvgYQkaxcd+Ubgcm5u00G+jvKBkPJw2YX3pkci0JIzRB8vSw8eUeQKV5aSgjzDeNI8hEahDQgKTOJrCsJpm74ElQfDltfg31fF52RhcW/HjQZCzfsh+7Loc5jen3iVvgtBOa3g61v6Hm7glYrNzgFR87oRwDRwDdKqSbAOuARoIKIHMvd5zhQwYE2GEoY0xYms2VfJs8M1aIW4GM57WBiKPmE+WmBm37bdF7u+PKVPZgoBa0mQPpR+G8kuPpBlVv0emeiFIS0O/PZNQAaPA9H52jvz80v6pp3nedDcEvtnWlxB4txkCppOPIv4gI0Bx4SkdVKqU84bzhSREQpddEBeKXUfcB9AFWrVnWgmYbiYvuBTL6ZlUD7Jh70aO1tem2lkDDfMNYeXYur1bVoGrS4QvtfYGEnnTQ5sBnUfVwHZ1vdiuYcV4p3FWj8ml4yTsKx+XrOzreW3r7jQ9jxDgS31ktQC51NxTvc+WJ9lePIObjDwGEROeVL/Cta8E4opUIBcl9PXuzgwuTKM5RcTiVSDvK3cOhEDovXFnGGeUOxEOYbxsnUk2TZsnh4zsO8uvTVK2/U1VcPCbb6UsfGrboT5jSGnPQrb7uo8SgPEUOgzdfglptKrnwHPdSanahr1S2/RZfxkVyv4ANTYPencHwRpB02w5vFiMN6cCJyXCl1SClVR0R2AV2B7bnLMODt3Nc/HGWDoWRgtwtvfqsTKbdp6MnyTemUDzTDkqWRU6ECx5KPsSt2FydTT/Jyp5evvGEXT6h5D9QYAfu/gdUj4OhsqHrrlbftaCp00gtogU7YquP8Tg1ZHvgWji88s7/VC0K7w3W/689RvwAKvKroqggeFcxwZxHh6F/xIWCKUsoN2A8MR/capymlRgCRwG0OtsHgZKbMTWLN9gxu6uTDjKUpDOzmS6OaHs42y1AITgV7H0k+QovQFry38j0ycjLwcCmiv6dSEDEMNr8EB74vHQJ3NlYPPS8X3PLMus7z9Txj0i7toZm0S8/hnWLDU7rSwmmUHqJt/5P+uOZBUFZwLwfuQeAWpB1iApvq7enHdNUGF28dSG84jUMFTkQ2Ai0vsqmrI89rKDnsOJjJt38m0qm5J8s3plOtogvDrw9wtlmGQnKqB3ckSQtcjj2HLSe2cE3YNUV3EosVwgfDzo8gIwY8yhVd285AKfAK00vFLhdu77VOD12mHdKv6cfPpBgDOLlUb8tOOrOuxr3QeqIe7pwRBuS6Mrh4a7Gr/SA0fEEXm/27H1g9cxcPvVTur+v1ZSfpOUSrO1jc9JyoxRVC2kNAI7396Fzdo1SnFisENNTfJzsZErbodcqS+2oF72o6wXZOKqQdyd1mASz693Avr3vttgzISgBU7nyl0vu5+mk7bFm6vUIm5jb9YIPDsNuF/02LJ9DXQst6nvyzMZ1X7qtgqnOXYs7uwfWv2x+AdcfWFa3AAYQP0fNZUdOg9v1F23ZJwz1YL4FNLr6971b9as/WYpAVp0UKtMBd8znkJOuaeznJkJMCfnXOHGPPgewTYEvXgmLLAP8GentWPGy9yDxq84+1wKVG6eTY59P6a6hxNyRugwXtLtzefprufUevhCU9LtzeaQ5U6gVH/4JlAy7c3n259mSNnKp7qnn9NpfBCJzBYSxak8aOg1k8MzSInm18aFbHg9By5l+uNBPkGYSHiwdHko5Qzb8a7aq0w80R3o6BjfUN9uAPZV/g8ovFFTxC9HJ6nQvUGpn3MW7+0P2fvLd7V4NBtlwhzDrz6pKbeMG3JvTdptdLjq7KIDngU0Nv96sLnebmOtTY9avYILiV3h7QEK6dooVYcrcjej1or9lrPs91vJHcrDZ28M7twQa11I49hcTcbQwOIT3DzsTfE6hZxZUq5fW/mRG30o9S6nSwt1KK5Xcvd9zJwofo2nHJ+8C3huPOc7WjLHqI0up+4Tarhy4kmxduAVCpZ97bPUP1cHNe+ERArVF5bw9okPe2fGBmJA0OYeqCJGITbVQIdOHRj04Sk2CqKpcVTgV7n0JEEEfkkwwfDChdO85gKARG4AxFzvHYHH5ekETzOu6s2JzOzZ19KWfK4JQZwnzDOJKkBW5Z5DKC3w1m7dG1RX8ir8pQobP2phS7DrKOXQMHf4TNL8Py22HtI8VbkcBQqjB3HUORIiKMnxaPRcGR6BzCQly4q5+/s80yFCFhvmEcTjqMiFDFvwrxGfGOcTQBPUy5+m742QvsmWfWKwt4VdPxZkf+gLY/QPn2RX9+Q6nGCJyhSFm2MZ1VW9JpUsudTXsy+fDR8ni4mYGCskSYXxiZtkzi0uOo5l+NIM8g1h11UOHQagN1cmOrh3aI8KqiU2T51tRzRtGrYNUQWNQR6j2ta7y5+uav7aNzYOvr0G6qbtuQf078Ddh1D7sEYwTOUGSkptsZPy2eGpVduaa+BzUqu9G0tgnoLmucHSoQ7BVMi9AWrD3mgCFKABcvuOZ/eW8PaQu9N8K6R2H727B3AtR5FOo8dG4w9fkcngnLb9Ueg3u+gKZvFbHhZRix64cKWwb0P3QmZKEEYh6tDUXGpFkJxCXZeHxwEIN7+vPgraaWbVnk7GBvgBahLdh6cisZORnOMcjVV+eG7LEaQjrAlpfh92pwOI8sgFHTdexVQBOo0BX2f6tjxUo7IhD5M8Std+x5Tv6jA9IzY/R86JWSk66rSUSvuPK2zsMInKFI2Hkwk9//TqFxTXei423ONsfgQM7uwQH0qdWHJ9o+4TyBO0W5VtDxD+i9ScdnLR+YO5R2Fvu+0YHLwddAlwVQ52HIOK4Djs/GbtNLacGerUVixe0wrzVse8tx9h+cojOm+NeHXR9feUX2Q9Nh70RY0gtiVl9+/wJgBM5wxeTYhA9+jMPf28L2A5ksXpvqbJMMDiTUNxSFOt2D61CtA293e5sAjwDnGnaKwMbQeQ74VId/boD4TTpl1L/DtcNK+U7QeZ4Ogq7UR8dq7fvqzPH2bFjUGeY2056bV4otCzY9r+cLHUFWAiztA/u+hPrPQJUBsOk5WNwVUg8V7blsmRD1K1S+Ceo+qdN0nVhyli3xsOV1nWItv+yfpOdAPcprkYvfqNeLXWdC2fvVJQ+/FEbgDFfMtIVJ7DucTaCfFTdXxUO3BTnbJIMDcbO6Ud67/DmxcOnZ6eyO3e1Eq87DPViLmKufvmnOawX7J+sq4p3nnXFEsbjo5M5H/4K0o3rd1tcheplOiry4W8Fu1hdj93jY9iYs7KBfi7JnlX5Mp8o6+Te0+Qaavq2dZtp8q51z5rfW6bYKwqV6ZEfnQHYChN8B4YPAPUT34iA37+X1sOUl2Ph0/s6Vsl8LZI17oeti/XdZ3B3+Gw2/V9Hfbf3jer6vEBiBM1wRh09mM/nPRGpVceXA0WxG3hRIsL8phVPWOT/Ye+jvQ+n1Qy8nWnQRvKtoMbNn6vmiLvOh8asXJu6tfrdOIXVgMpxcDtvGQvW7oNNfkLwHlnSHzDi9ry0LMqLzb0P6Cdj6GlTsoauVb3oelvSEyGk6yfG6x2DlEFh2Cyztp4dV0w7nr+3MOFjcQ1ci6DxP2ww6aXH1YdBjpe65/t3v3ETNceu1iJw/fAvavr8a67yWF+PgFC1qFbtp55Jao+HIbEjcoZ12oldC+Y56XjM/c4H7vwVy7fWupkXO4qr/FsGtdfjHFTiyGC9KQ6Gx24UPpsTh6gLHYnJoVNOdPtd6O9usqx6l1GPAPegU81uA4SJSpBNkYb5hRCWe6Rm0rdyWX7f/yrHkY4T6hhblqa4M//o6l6LVI2+vSr9a+qa890vthekdDi3G6d5Eh9/1MOefuSmjMk4AAhW7a8/LoBaXPv/m3Iz+Lcfr8IbQ7rD2ITixSG+3eun6by5e2sbEHZByQOePvNRN/ZRwJe/WQnwxd/2ARtBhOizpDctuhU6z9Xdc/5j2Hk3coRM5uwXo/U8u0z1M0CJ/vmdpdhIcmQU17z1Tr67WaNj+lu6dZsZCqwm61M+sWrrn1XVJ3lXN7TZd+y+0pw7qBx3+0W+XjnN0ufJ7iRE4Q6GZsyqVTXsyeXxwIJ7uFmpUdsNiMZUCnIlSKgx4GKgvIulKqWnA7cC3RXmeMN8wVh0+M6fUrorOKL/i0ApuqX9LUZ7qyvHMh+DWuEdXEldWncn+1BBmpZ7QcRbs+Uz3XE7diHePh7kt9c08fIie7/OJ0EJ1irj1sO9rqPsY+NXOPc8IqNRXC6VXFS26ZwvAoRmw7GZYc7/O2K+UHir9d7gWvgqdoEIX7ZgRuxra/wIVL1F9rGI3aPUFrL4HZteDlH0Q2hvqPAJ/94W1D8O132lPxtUjtLgHt4KdH+ge4amqBACHftO94fA7zvptK0K1QXDgO2gyFmrep9c3ehXWPgCHf4cqN+n5tKhfdHmdGndrATu+UPdWm394rs35jWPMB0bgDIUiPtnGhN/iaVLTjb7tfFB5PaUZnIEL4KmUyga8gKNFfYIwvzBi0mJOFzttFtoMDxcPVkSVQIHLD1UGwI73IeJOKNfm3G2hPfRyNnUe1SKw80Nd0ucUPjWhUm8tYtve0EVKG7547rGeFfVyUTtu0vtvfR0Cm+uaaWsf1r250B56ri0ytxBq66+gys2X/241Rmhx3P42NHkL6j+tBabBC7pUTpWbIGaVHo7tshD8G8Kxufq8nedqkRWBAz/oKgLBrc9tv8XHujROpb5n1tW8D/Z8qou5onToRsJmvS3qF2g7WTuXuAVB2A2X/w6FxAicoVB8+XsC6ZlCQoqd+atT6dnGx9kmGQAROaKUeh+IAtKB+SIyv6jPU9lP92QOJx2mZlBN3KxuXFPpGlYcKvpYpmLBxRN6b8h7OO183Pyh8WtQ78kzw4op+yDmX+2RuXu83q/VxDNDgPml0SsQtwHWPaQ/V+gCbb/TBUZFdI/OnlmwGmlN3oD6Y8D1rOu04fN6yHH1CMhO1I4ep3qDjV6D9Y/qHphnGGwao51BGr124W/kFqiLp56NxQWafQhLe8Gym7QwXjtFn2f947nzfIlQc9TFqxgUEUbgDAVm2/5M5q5KpUF1N7btzzJOJSUIpVQgcCMQASQAvyilhojID+ftdx9wH0DVqlULfJ46wXroamfMTmoG1QTgjS5vOKY2XHFRmFEIVz8o11ovp8hJ12KQekA7sBTYDgtc+4N2Pil/HdR7Ircadq6N/nUL3iacK26gnTnafgdzm4NHKDR778y22g9ooV51p57vcw+BFp/oObf8Uqmn9up0C4Tqw/X5QM93rhisHX9qFOL3KQBG4AwFwmYXxv0cR4CPhV2RWXS9xouW9TydbZbhDN2AAyISDaCU+g24FjhH4ERkIjARoGXLlgWO1K0fomuEbTu5jX619dP7ddWuuxK7yw4unhDW58racPOHTrOKxp5LEdBAO4K4B+tznsLioh1GVg6BukO1yBZmbqz+Mxeu868PPVfrEAH/eoW3PR8YgTMUiD+Xp7DnUDbhoa5k24TRA0w6rhJGFNBGKeWFHqLsChR5okh/D3/CfMPYFr3tnPUzd83Ex82HLhFdivqUBkcRcm3e62/c75hzWt0dLm5g4uAMBSAxxcakWTrm7eCxbO65IYAgPzM8WZIQkdXAr8B6dIiAhdyeWlHToHwDtkdvP2fdmIVj+GDVB444ncFQYEwPzpBvJv+ZSEqanY8eK09WtlCzSimebynDiMjLwMuOPk+DkAZMWDcBu9ix5M4RtavSjuk7pp+zzmBwFg79D1RKHVRKbVFKbVRKrc1dF6SUWqCU2pP7asa4SgGRx7KZuSyFrtd4EVHJjTrV3LGamLermvoh9UnLTiMyIfL0unZV2xGfEc/OmJ1OtMxg0BTHI1ZnEWkqIi1zP48BFolILWBR7mdDCeeL3+Jxc4Ul69JYuj7N2eYYSgANQnR2j7Pn4a6toudzVkSV0nABQ5nCGWMINwKTc99PBvo7wQZDAVizPZ3V2zLw87Li622hZd2SW+DQUHzUC9FOAttOnhG4WkG1CPEKYcPxDc4yy2A4jaPn4ASYr5QSYEKua3IFETmWu/04UMHBNhiuAJtN+Hx6Av4+Fk7G23h2WDA+XmZuxQABHgGE+YaxPeaMo4lSivUj15+uGWcwOBNHC1z73MwK5YEFSqlzBuZFRHLF7wKuNBDVUDT8tTKFg8ey8XRXNK7pTrdWXpc/yHDVUD+k/jk9ODiT5cRgcDYOfRQXkSO5ryeBGUAr4IRSKhQg9/WiFQVFZKKItBSRliEhIY4005AHaRl2vp2dSLWKLigFj9weaHJOFjFKqc35WBY52868aBDSgB0xO7CL/fS6tOw0Rvwxgmnbpl3iSIPB8TisB6eU8gYsIpKc+74H8BowExgGvJ37+oejbDBcGT8tSCI+2c4bo0OoUsEVH08zNOkArMCl0l4o9DVTIjnbkzIiMAIATxdP5u6bS2p2Krc1uM3JFhquZhw5RFkBmJH7xO8C/Cgic5VSa4BpSqkRQCRgroASSHR8DtMWJNGkljt1q7mZnpvjGCkikZfaQSl1f3EZU1AalD/jSXlK4JRSdInowry98xAR879jcBoOeyQXkf0i0iR3aSAiY3PXx4pIVxGpJSLdRCTOUTYYCs+kWYnk2GHTnkw27M50tjllFhFZfuq9UspTKVXnUvuUNE7lpDw/o0nXiK5Ep0Wz9eRWZ5hlMAAmVZfhIuw7nMW8f1NxsUCzOu40q+24chYGjVLqBmAjMDf3c1OlVIkdmjxFgEcAlXwrXZCT8lQuysUHFjvDLIMBMAJnOA+7Xfj0l3hcXcBmh4duCzJDTMXDy2gnrAQAEdmILnlT4mkQ0uACT8qq/lXpVr0bLhaTDdDgPMx/n+Ecfl2czMY9ekjytm6+hIe6Otmiq4ZsEUk872GiwGVsnEH9kPp8uf7LC/JPLrhzgROtMhguI3BKqcfz0UaqiEwoInsMTmTPoSy++iOB+hFuZOcIQ/v4X/4gQ1GxTSk1GLAqpWoBDwMrnWxTvmgQ0uACT8pT2MVOli0LDxeT/cZQ/FxuiPIpwAfwvcTyhCMNNBQPGVl2xk6Kwd/HytjRIXwxpiJeHmYEuxh5CGgAZAI/AonAI061KJ/k5WiSmpVK6AehfPzvx06wymC4/BDl9yLy2qV2yI1xM5RyPv81gagTOfTv6IO3p8XMuxU/fUXkeeD5UyuUUrcCvzjPpPxxdqhA39p9T6/3dvOmgncFFh1YxJj2Jqe6ofi55CO6iDx9uQbys4+hZLN1XyazlqdQo7IrM5elcOhEtrNNuhp5Np/rShwBHgGE+oRe0IMDHS6wPGo56dnpTrDMcLWTrzEopdQjSik/pflaKbVeKdXD0cYZHI+IMPF3nUx5/5Fs+l/nQ0QlU8i0uFBK9VZKjQfClFLjzlq+BXKcbF6+aVC+wQWhAgC9a/UmIyeDpQeXFr9Rhque/E6y3C0iSeh0W4HAnehUW4ZSzsot6Wzdl4m3h4UAHwt39QtwtklXG0eBtUAGsO6sZSbQ04l2FYj65eqzI/rcnJQA11W7Di9XL/7a85eTLDNczeQ3TODUhEwf9LzcNmUmaUo9Nrvw1R+JBPpaOBqTw1N3BplSOMWMiGwCNimlpohIqemxnU+D8g1IzU4lKjGK8IDw0+s9XDz4sMeHp2vHGQzFSX4Fbp1Saj468PRZpZQvYL/MMYYSzvzVqUQey+bu6/05FpNDz9bGX6i4UUpNE5HbgA0XKx0lIo2dYFaBOduT8myBAxjZcqQTLDIY8i9wI4CmwH4RSVNKBQPDHWaVweFkZtn5dlYi9cLduKOXn/GadB6nQgH6OdWKK+SUwG07uY0+tS4sjvDv4X+x2W20q9quuE0zXMXkV+AEqI++CF8DvAETuVmK+W1pCtEJNuqGu5GaIfh4GoFzBqeq21+uokBJJ8gziIo+Fc+p7n029866l/Le5Vk0tMSWtjOUQfI74fIZ0BYYlPs5GfjUIRYZHE58so0f5iTg521h4+5MbLZSkRGqTKKUSlZKJZ21JJ/96mz7CkKDkAYXDRUA6FOzD/9E/kNSZqn6SoZSTn4FrrWIPID29EJE4gHjS15K+XZ2IhlZkJRq5+4b/PH3sTrbpFKDiPBP5D+8t+I9HvjzAfpM6UO377pdSXu+IuJ31uJ79msRmu5w6ofUZ3v0dkQufGDqW7svOfYcFu5f6ATLDFcr+R2izFZKWclN/qqUCsE4mZRKDhzNYvayFDzcFWEhLvRr7+Nsk0oFIsK8ffN4/Z/XWXlIp4j0d/fH08WTNlXaFElhT6VUE6BD7sd/RGTzlVldvDQIaUBKVgqHkg5R1b/qOdvaVm6Lv7s/f+35i5vr3ewkCw1XG/ntwY0DZgDllVJjgeXAmw6zyuAwvvgtARcXSM8UHh4YhNVi5t4uRY49h2nbptH6q9b0ntKbQ4mH+LTPp/xx+x8kZyVzMu0ko1uOLgpxewSYApTPXaYopR4qRDt1lFIbz1qSlFKPXpFx+eRsR5PzcbW60qNGD/6O/Ls4TDEYgHz24ERkilJqHdAVHRPXX0R2ONQyQ5Hz37Z01mzPYHBPXwJ9rTSsYQqZ5kVqVipfrv+ST1Z/wsGEg0QERDCsyTC6Ve/GkMZDyMjJ4IUOL3B3s7upFlCtKE45Aj0VkAqglHoHWAWML0gjIrIL7fFM7qjLEfTDqcM5O1Sgd63eF2z/pNcnBHoGFocpBgNw+XI5fiKSpJQKAk4CU8/aFiQicY420FA02GzC578lUCnEhWF9A3B1MT23i5Genc4Xa7/greVvEZ0WTZvKbWhfpT3z989n8qbJxGfEM6TxEDxcPHi186tFeWoF2M76bONMgoXC0hXYV1wemsFewVTwrnDRlF0Aob6hxWGGwXCay/XgfkSHBqzj3OKLKvdzdQfZZShi/lyRQuSxbGpXdSUtw24cS87DZrcxacMkXvn7FY4mH6VrRFdaVmrJ52s/59/D/9KrZi+euvYpOod3dpQJ3wCrlVIz0NfXjcDXV9jm7Zz1UFocnHI0yYvvNn3HjJ0zmDGwWDqVhqucSwqciPTLfY241H6Gkk1qup1vZiXg5gIZmYK3p0nHdTbLo5bz8JyH2XB8A9dUuoYJ/SbQr3Y//trzFwcSDjCm3RiahTZzqA0i8qFSainQHv3wOFxENhS2PaWUG3ADeVQkUErdB9wHULVq1YvtUigahDRg8qbJeTrdJGUm8fvO39kRvcOk7zI4nPxWE7hJKeV/1ucApVR/h1llKFJ+nJdEYqqQlQMPDQzCxWqGJ9Oz05mxYwY3/XwTHb7pwMnUk/Sv05/t0dtZEbUCgD61+vDzLT87XNzOQ533Wlh6A+tF5MTFNorIRBFpKSItQ0JCrvBUZ6gfUp/krGQOJx2+6Pab6t4EwG87fiuycxoMeZHfR/mXRSTx1AcRSQBezs+BSimrUmqDUmp27ucIpdRqpdRepdTPuU+aBgdxPDaHXxYlYbHAdc08aVH36k5AE5UYxZ0z7qT8++W5edrN/HPwH7pGdCUtO43fd/3O9XWuZ1jTYcVul1LqJWAyulpHOeAbpdQLV9DkIIp5eBLOLX56McL8wmhbuS3Td0wvTrMMVyn5FbiL7ZffGLpHgLM9Lt8BPhKRmkA82nvM4CC++iMBux1crYrRA65eDzYR4YfNP9Do80bM2DGDQQ0HseDOBfSr049FBxbRunJrNozcwNQBU6lbrq4zTLwDuEZEXhGRl4E26LJUBUYp5Q10B4q9m3S2J2VeDKg3gA3HN7A/fn9xmWW4SsmvSK1VSn3ImfRcD6AdTy6JUqoy0BcYCzyeW2KnCzA4d5fJwCvA5wWw2ZBPNu/NYPHaNG7t5kvLuh5UCMrvn7tsEZcex6jZo/hl+y+0q9KOR9o8QsvQlkQERlDVvyrDmw6nU3gnZ5t5FJ3fNSP3szvaxb/A5IYaBBeRXQWinFc5ynuXv2gs3Clurnczyw8tJyMnI899DIaiIL93vIeAF4Gf0RPgC9Aidzk+Bp4GfHM/BwMJZ9W9OgyEXexAR02CXy3YbMInU+MICbQwvJ8/Hm5Xp2PJykMruf3X2zmecpxn2z9LVGIUt/1yG/c2v5eJ10+kdnBtagfXdpp9udW8BUgEtimlFuR+7g785zTDroBG5Rux6cSmPLdHBEYYL0pDsZDfQO9UYIxSyvtUIOrlUEr1A06KyDqlVKeCGiYiE4GJAC1btjTZgAvIH/+kcOBYDhWCrOTYLr9/WcMudt5b8R7PL36eqv5VebDVg/zvv/+Racvk+Q7P82z7izoXOoO1ua/rODcge2nxm1I0NA9tzierPyHblo2r1TXP/Q4mHMTf3d8EfxscRr4ETil1LfAV4ANUzc2ZN1JE7r/EYe2AG5RSfdBDL37AJ0CAUsoltxdXmUIOwxjyJi7Rxtcz47EoqB7mis9VFhYQmRDJPbPuYeH+hdxa/1ZqBtXkreVv0btmbz7p9Qm1gms528TTiMhkZ9tQ1DQPbU6WLYvt0dtpUrHJRfc5EH+A6uOqM773eB5s9WAxW2i4Wsjvne8joCcQCyAim4DrLnWAiDwrIpVFJBwdcLpYRO4AlgC35O42DPijEHYbLsHE3xPIyAKrBR64NcjZ5hQbdrHz2ZrPaPh5Q1YdWsUbnd/g51t+5qlrn2LGwBn8OfjPEiVuZ6OUqqWU+lUptV0ptf/U4my7CkPz0OYArD+2Ps99IgIjaFS+ET9u+bG4zDJcheT70V5EDp23qrADX8+gHU72oufkrjRbg+Estu7LZP7qVERgcC9/KpW7OhxLDiYcpMvkLjzw1wPUCa5DgEfAaVf0QM9A+tftX9Krln+DdrbKAToD3wE/ONWiQlIzqCY+bj6XFDiAIY2HsOrwKvbF7SsmywxXG/kVuEO5w5SilHJVSj3Jua7/l0RElp6VFWW/iLQSkZoicquIZBbCbsNFsNmET36Ow80VKgRZub277+UPKuWICN9v+p7Gnzdm3dF1dKzWkXXH1uHj5sP/+vyvpIva2XiKyCJAiUikiLyC9kAudViUhaYVm7L++KUFblDDQSiU6cUZHEZ+BW4U2msyDO3O3JT8eVEaipGZy1LYdzibp+4M5v2Hy+Nexj0n49LjuH367Qz9fSh1guvg5+HHsqhlPNn2STaM3MC1Va51tokFIVMpZQH2KKUeVErdhJ7zLpU0r9icTcc3YbPnPdBTxb8KncI78fO2n4vRMsPVRH69KGPQgaiGEkp8so1JM+NpUtONLi28SlPPpVDM2TOHETNHEJ0WzVtd3+KR1o8w9PehPN7mcdpWaets8wrDI4AX8DDwOnqYcqhTLboCmoc2Z9x/49gTt+eSgfOf9vmUcl7litEyw9VEfnNRVldKzVJKRSulTiql/lBKmUoCJYivfk8gLQOOxtjKdFhASlYKo2aPos+PffBy9aJt5baMajkKT1dPfrn1l9IqbgDhIpIiIodFZLiIDABKbQBofhxNAOqF1CPEu+hyYRoMZ5PfMawfgWlAKFAJ+AUn5LkzXJwdBzKZsyoVAfq08ymztd72xu2l9VetmbBuAj1r9ORo8lF2xuxkb9xeZ5tWFFwsMK/EBOsVlLrl6uJudb+swAEs2r+I/j/1J9uWXQyWGa4m8uti5yUi35/1+Qel1FOOMMhQMESE//0Sh8UC5QOtDOrh52yTHMK8vfO4ffrtAHSs1pF5++bRrXo3vr/peyr6VHSydYVHKdUb6AOEKaXGnbXJD+1RWSpxtbrSuEJjNhy/fMWflKwU/tj1Bwv3L7xoJXCDobDktwc3Ryk1RikVrpSqppR6GvhLKRWUW+3b4CSWrktjx8Fs7HZ4+LYg3FzLVu9NRPhg5Qf0+bEPVfyq0Dm8M8ujlvN217eZN2ReqRa3XI6is5lkoLOZnFpmomNPSy3NQ5uz/th6RC6diKh3rd4EeQbx/ebvL7mfwVBQ8tuDuy33deR562/HVPZ2GlnZwsTf4/H2UDSp7UGbRp7ONqlIybZl8+BfDzJx/URuqnsT39/0PUmZSTx57ZOlzUMyT3KTJmxSSv2Ivh6risguJ5tVJDQPbc6EdRM4mHCQiMC8aya7Wd0Y1HAQX63/irj0OII8zTOzoWjIVw9ORCIusRhxcxK/LU3mRJydl+8txwt3OyV5vMNIzEik39R+TFw/kUblG5GYkYiHiwehvqFlRtzOoxewEZgLoJRqqpSa6VSLrpD8OpoA3Nv8XjJtmXy/yfTiDEVHfr0ob1VK+ea+f0Ep9ZtSqljLHBvOJSHZxnd/JtC0thst63mWqWoBUYlRtP+mPYv2L6KafzW2nNxCh2odnG2Wo3kFaAUkAIjIRiDvbk8poGH5hliVNV/zcE0qNmF40+GE+V20uIjBUCjyO0T5ooj8opRqD3QD3gO+AFo7zDLDJfl6ls43mZAsiEiZiXv778h/3DD1BlKyUvB28yY+I55Zg2bRr3Y/Z5vmaLJFJPG8v2OprqLh4eJBg/IN8tWDA5h04yQHW2S42sjvY/+pyKq+wEQR+RNwc4xJhssRdSKbP5frqkUPDwwsM+L26/Zf6fhtR7xcvQj0DKSyX2XW3LvmahA30LXgBgPW3MTL44GVzjbqSmke2py1R9diF3u+9k/KTGLxgcUOtspwtZBfgTuilJoADER7T7oX4FhDEfPx1DgArmvmSdPaHk625so5mnyU+2bdx62/3Eqzis1Yfc9qFt65kH9H/OvUYqTFzENAAyATHWOaBDzqTIOKgq4RXYlOi+bfw//ma//nFj1H3x/7Ep8e72DLDFcD+RWp24B5QE8RSQCCABMH5wQ27Epn4+5M3Fzh4YGl29ssOTOZFxe/SM1xNflmwzeE+YbRpGITQrxDqFOuDr7uZT9Z9ClEJE1EnheRa0SkZe77DGfbdaXcUOcG3K3u/LLtl3ztP6LZCDJyMpiyZYqDLTNcDVxS4JRS6+H0xfebiOzJ/XxMROafvY/B8djtwue/JeDprhh5UwBBflZnm1RoUrJS6DS5E28se4POEZ2p5FuJmLQYOlQt884kF0Up1TLXeWu9UmrzqcXZdl0pfu5+9KzZk193/JqvYcpmoc1oWaklE9ZNuGz8nMFwOS7Xg6t39sV2kWULYDKlFhOL1qSx91A2jw0K4qZOpTdjic1uY9D0QWw8vpHXO7/OykMrybBlsPSupQxuNNjZ5jmLKcC3wADg+rOWUs+t9W/lcNLhfA9Tjmwxkq0nt/JP5D8OtsxQ1rmcF2XeacDPUIZT+5Yc0jPtjJsWR5UKLnRp6eVscwqNiPDI3EeYvXs273V/jzf+eYMwvzBmD5p9yWDgq4BoESnVcW95cfYwZX5iGO9odAfPLnqWBfsX0DG8YzFYaCirXFLgRCSyuAwxXJr3f4glNV1oVd8Ni6X0ek1+uOpDPl3zKU+0fYInr32SaypdQ5OKTQjwCHC2ac7mZaXUV8AitKMJACLym/NMKhpODVP+sv0XPuj5ARZ16YEjT1dPtt+/3VQZMFwxxhOyFLDjYCZL1qXj6a548o7S6Vhis9t4cv6TPLngScL9w097R3YM72jETTMcXUi4F2eGJ8tMfMSt9W/lSPKRfA9TnhK3tOw0R5plKOPkN9Db4CRsduHlCTEAPHlHEJ4epe+ZJCEjgUHTBzF371yq+lflYOJBjiUfc7ZZJY1rRKSOs41wFKeGKadtm5bvVGtfrf+KZxY+w76H95mHIEOhKH13y6uMybMTiEm0US/cjc4tvZ1tToE5knSENl+1YcG+BYT7h3M46TBfXv8lL3d62dmmlTRWKqXqF0VDSqkApdSvSqmdSqkdSimnV4E97U25PX/elAAtK7UkLj2OL9d96WDrDGUVI3AlmJNxOfy6OJkq5V149b7S56wamxZLjx96cCTpCJV8K3E89TgzBs7gnub3ONu0kkgbYKNSatcpD+UrCBP4BJgrInWBJsCOIrPyCjg1TLnmyJp87d+0YlM6hXdi/H/jTTFUQ6Fw2BClUsoD+Adwzz3PryLyslIqAvgJCEbXvbpTRLIcZUdpRUT4YEosoHj7wfKUCyhdo8kpWSn0/bEv++L2MXfIXDYc20CrsFa0q9rO2aaVVHoVRSNKKX/gOuAugNxrq0RcXz1r6PJ2iw4sonXl/KWxfazNY9z4041M2zaNOxrf4UjzDGUQR/bgMoEuItKE3MlzpVQb4B3gIxGpCcQDIxxoQ6llxtJk1uzIpFdbb0LLlS5xy8zJ5Oafb+a/I//xSqdX6BTeicfaPmbE7SKclUwh8mLL2fvkkwggGvhGKbVBKfWVUuqCsW2l1H1KqbVKqbXR0dFF8l0uR4h3CI3KN2LJwSX5PqZf7X40CGnAuyvfNYHfhgLjMIETTUruR9fcRYAuwK+56ycD/R1lQ2klJiGHL35LQAHXt/dxtjkFwi52hv0+jAX7F+BqdWXGzhnmxnRpijqZggvQHPhcRJoBqcCY83cSkYm5KcFahoQUnzt+5/DOrIhaQWZO5uV3BizKwqQbJ/H7wN/LTFJxQ/Hh0K6BUsqKHoasCXwK7AMSRCQnd5fDgCkAdRYiwksTY8ixwc2dfIgIKz1FG0SEx+c9zs/bfsaiLDQIacCsQbPMjenSFHUyhcPAYRFZnfv5Vy4icM6ic0Rnxv03jtVHVnNdtevydUyrsFYOtspQVnGok4mI2ESkKVAZXcwxPxcz4JwhlJLA3H9T2Xkwi0A/CyNvDnS2OQXi3RXv8snqTwBoX6U9S4Ytobx3eSdbVbLJa2jyvOVwAdo7DhxSSp0KOegKbHeI8YWgY7WOKBRLDuR/mBLgZOpJ+kzpw+87f3eMYYYySbF4UeZWIFgCtAUClFKneo6VgSN5HOOUIRRnkphiY/w0XSbklXvK4epSeno+E9ZOYMyiMVTxq0Lvmr2ZO2Qu/h7+zjbrauUhYEquF2ZT4E3nmnOGQM9AmoU2K9A8HECQZxB74vbw2t+vmSFvQ75xmMAppUKUUgG57z2B7mh35SXALbm7DQP+cJQNpY3PpyeQlSW8cHcwjWqWjjpvSZlJ3PnbnYz6cxQ9a/Rk2/3b+P323/F09XS2aVctIrIx9+GwsYj0F5ESVVytc3hnVh1eRXp2er6PcbG48Fz759hwfAN/7vnTgdYZyhKO7MGFAktynyLXAAtEZDbwDPC4UmovOlTgawfaUGpYtSWN+atTGdTTjy6lJKD7vyP/0fSLpvyw5QdCvEKYcvMUfN19cbOWnnlDQ/HTJaILWbYsVh4qWMHyIY2HEBEQwYtLXsx3sLjh6saRXpSbRaRZ7lNkQxF5LXf9fhFpJSI1ReRWEcmfO1UZJiPLzpvfxKIU9Lm2dHhNzt07l/aT2nMy9SQAgxoOItCzdM0ZGpxDh6odsCprgYcpXa2ujO0ylo3HNzJ1y1QHWWcoS5SuAKsyygdT4kjNENo28igVMW8L9y/kxqk34uPmQ3xGPM+2f5axXcYab0lDvvB196VlpZYsPrC4wMcObDiQmLQYrq9TJkrlGRyMSdXlZDbsymDRmjQ83BTP3lXy03EtPrCY66dej7+HP/EZ8bzR+Q3e7PqmETdDgegS0YU1R9eQkpVy+Z3PwqIsPNT6IfzcS2/BX0PxYQTOiaRn2nl5og6BeHZYMD6eJfvPsfLQSq6fej01AmuweNhivr7ha56/7nlnm2UohXQO70yOPYflUcsLdfyqQ6vo8E0H4tNLlP+MoYRRsu+oZZwJv8WTki60aehBh2Ylu0r3jugd9J3SF08XT+YNmUfD8g25u9ndzjbLUEppV7Ud7lZ3/trzV6GO93bzZkXUCt5a/lYRW2YoSxiBcxJrd6Qzc1kqt3Tx5Y1RJTvO70jSEXr80IPU7FTiM+LZG7fX2SYZSjlerl5cX+d6ftr6U6EqBTSu0JihTYbyyepP2B272wEWGsoCRuCcQEqanVe/jKFCkJURN/hjsZTc+auEjAR6fN+Do8lHsYudH2/+kY7hHZ1tlqEMcGfjO4lOi2b+vvmFOv7tbm/j4eLBQ3MeMsHfhotiBM4JvP51DKkZQu2qbri7ldw/QbYtmxun3siOmB1YlIVfbv2FgQ0HOtssQxmhV81eBHsG88OWHwp1fEWfirzR+Q3m75vPvH3zitg6Q1mg5PuklzEW/ZfCmh0Z+HgqxgwNdrY5eSIijP5zNP9E/YOvmy9TB0ylb+2+zjar+BCBrCy92O3g7w82G6xYATt3wrFjEBsLcXFQvjx8+KGzLS51uFndGNhgIJM2TiIpM6lQnpGjrxlNOa9ydK/e3QEWGko7RuCKkYRkG+9NiQPgtZEheHqU3N7bm8ve5OsNX/N8h+cZ034MPm5OCkC32WDPHkhIADc3cHGBtDSIjtbiEh+v92nUCJSCBQtg0yY4elRvS0uDjAywWqFiRcjOhszMM21ZLFq8OneGVatg7Vq9/WxcXaFKFThy5MJtAKGhRuAKyZ1N7uSztZ8xfft0hjcbXuDjXSwuDGo0CNB1CN1d3IvaREMpxghcMSEivPJlNFnZ0Odab5rWLrm5Jieum8gLS16gecXmvNb5NSyqgEKclQWRkZCUpJeUFL2kpkJyshammBi9ZGeDnx/ccANUqAAzZ8KyZXpbbKw+3n4FaZmsVvD1hWHD4MQJ+OcfLXznC9WWLdCiBTRrpgXRzU0vdrsWuLAwqFRJ2xsYqEWtXDktjq1MOZfC0jqsNTWDavL95u8LJXCn+Pvg3wz8dSDzhsyjScUmRWihoTRjBK6YWLQmjc17s2jfxJNHbg9ytjkXRUR4cfGLjF0+Fquy8n6P9y8ubikpsG6dXjIytAC4usKhQ7B0qRaL7AJ6xn3//bmfLRbw8oLKlfUQ4Asv6PX//afP4+8PAQH61dNTC1NODnh4aDE6td5qvfj5srJg3z7dOyxfXh/vbp7+ixulFEMaDeHVv1/lUOIhqvhXKVQ7Dcs3BOCuP+5i9T2rTT5UA2AErlg4HpvNxz/FUj/CjZfvLYe1BHpNpmWnMfDXgczePRtXiysLBv5Jx+1p8NZ9sHmzHgYE3fs6cEDPUZ2Ph4cWpFPi5uoKQUG6p/Phh1CvHuzYoYWxQgW9PjBQi5DVqochK1XSw4H+/nrI8XxuvLFovrCbm7anXr2iac9QaIY0HsIrf7/CuNXjuP+a+6nkW6nAQ43BXsFM6DeB/j/3581lb/JKp1ccY6yhVGEEzsHY7cLT46NJy4ARN/qXLHGLiYGtW4ne8i9dT77HFmsc3nYryxdUpekb/XQv55T4NGigh+Xc3WH/ft27Cg+HiAi9/t57dS8oKQlOntTrLiZSVapAjx5O+bqGkkmNoBp0qNqB91e9z/ur3gd0j2zekHlU8q2U73ZurHsjQxoPYeyysdxQ5waahzZ3lMmGUoIROAfz5R8JHD6ZQ3ioK01rOXneLTZWz0EtWqSdMXbvJsEDegyDveXg4Z1+jN4fTN01+/T+/v7QsCHUrQv33ANt2ui5q7Q03fO6GMHBejEYCsDvt//OmiNrOJp8lENJh3h3xbsMmDaApcOWFqg390mvT1i0fxG/7/zdCJzBCJwj2R2Vyc8LknGxwnsPhxRfQmIR7fG3c6de1q6FlSv1fBPo+S0gxQ06DIcd5eBPj+H0/GmSHopcuRLq17+4ULm7m7kqQ5ET5BlEz5o9T3+uH1KfW3+5lYfmPMTE6ycWqJ2NozZS3ru8I8w0lDKMwDmIrGw9NAnw9J3BBPs78KfOyoLly88s//6rvRVPYbVCSAi89Ra0aweffEJG5Yp0qDCbrVmRVA+IoPvDX53Zt0MHx9lqMOSDW+rfwrPtn+Wt5W/RIrQFI1uOzPexp8Rty4ktRKdF0yWii6PMNJRwjMA5iAkz4klKtdO2kSfdWjmoQndUFEycCF99pV3glYLGjfX8V0qK7sn5+EDHjtCnD9x/PwDpbVpy7aRr2Xg8ksp+lVkxYmXBQwEMBgfzeufX2Xh8Iw/NeYhWYa1oFtos38eKCPfNvo89sXvYOGojlf0qO9BSQ0nF3NUcwL9b05mxNIWbOvnw2n1FXOMtMxN+/RX69dNOHmPHam/FkBCdXWPjRhgzBl57TQcux8fD7NmnxS0tO41rvryGjcc3EhEQwcaRG6noU7FobTQYigCrxcqUm6fg7+HP0wufLtCxSim+vfFbMnIyGDx9MDn2HAdZaSjJGIErYqLjc3j1y2iqVHBh5E2BWK1FMO8mAqtXw4MPajf6W2+FxYu1sIEejuzR44zr/vDhOm6sTRudrSOXtOw0rp96Pduit1GvXD02jdpEsJdxCDGUXAI9A3m+w/Ms3L+QhfsXFujYOuXqMKHfBJZFLePFxS86yEJDScYIXBFiswuPfHiCzGzoc60Pbq5XKG7HjumeWO3aWqwmToTu3WH8eB3EPGwYzJ2r3fJ/+EGnosqrqeRjdPq2E0sPLuWbG75h/cj1+Lr7Xpl9BkMxMKrlKKr6V+XZRc8WuGrAHY3v4L7m9/H2ircLXbXAUHoxc3BFyOtfxXA81kbDGu4M7F7wxLGn2bkT3n8fvvtOB017587h3X67XicC992ng5Xzwbqj6+g0uROpWalMunESdzW9q/C2GQzFjIeLB692epXhfwzntx2/MaD+gAIdP77PeOqWq0vn8M4OstBQUjE9uCLi10VJ/LMxHT9vC+89VIgCpsnJMHkydOums2t8++2ZHIz168MXX+ieG2hnknyK27Rt02j9VWtSslK4veHtDG0ytOC2GQxO5s7Gd1I/pD7PL36+wPNpblY3Hmv7GK5WV6JTozmectxBVhpKGg7rwSmlqgDfARUAASaKyCdKqSDgZyAcOAjcJiLxjrKjONh5MJPPf0vAYoHxT1bIf423jAw9xPjzz/D77/pzRIQelkxI0J6Qo0dD06aFsuu3Hb8x8Fddv+2Zds/wVte3ii8Wz2AoQqwWK292eZP+P/fn6/VfFyhs4BQ2u40u33XBy9WLxUMX4+3mIO9mQ4nBkUOUOcATIrJeKeULrFNKLQDuAhaJyNtKqTHAGOAZB9rhUOISbbw4IYaQQAtPDA6mSgXXyx8UGwvPPAO//KJTW3l76x5ZRgZMmKDn2a6Q9cfWnxa3j3t+zCNtHrniNg2lA6XUQSAZsAE5ItLSuRYVDTfUuYGO1Try1IKn6FGjBxGBEQU63mqx8kbnN7h52s3c+sut/HH7H7ha83G9GkotDhuiFJFjIrI+930ysAMIA24EJufuNhno7ygbHI3NJjw9/iTJqTbGjirPNfU9L3/Q+vXQsqWeS6tbVycjTk3V76dN03XJrpDIhEj6/tiXCt4V+P6m7424XZ10FpGmZUXcQLv+T+4/GaUUd864s1Cu/zfWvZHP+37OnL1zGDFzBHa5glJMhhJPsczBKaXCgWbAaqCCiBzL3XQcPYRZKnn3+1j2H82mQQ13alTOx5zYN99A27Y6HdbixbooZ9Om+v2//2r3f5cr61T/tfsvmnzRhLSsNOYNmceQxkOuqD2DoSRRLaAan/f9nBWHVvDWsrcK1cZ9Le7j9c6v8/3m7/lg5QdFbKGhJOFwL0qllA8wHXhURJLOngMSEVFKXdTvVyl1H3AfQNWqVR1tZoGZuyqFBf+l4eWueGnEZYK5k5LggQe0K7+fn871WLkybNigS8YUEWOXjeWFxS+gUEwdMJUG5RsUWduGUoUA83OvrQkickEyx5J+fV2KwY0G8+eeP3n171fpUaMHrSu3LnAbz3d4Hl83X/MAWMZxaA9OKeWKFrcpIvJb7uoTSqnQ3O2hwMmLHSsiE0WkpYi0DAkphFeiA4k8msX7U+JQCt5/pDz+PnkU1QQtZjVranEDnUrrFEUkbna7nQE/D+CFxS/gbnVnybAlDGw4sEjaNpRK2otIc6A38IBS6rrzdyjJ11d++LTPp4T5hTH8j+GFGmZUSvFIm0cI9gomMyeTKZunFDjGzlDycZjAKd1V+xrYISIfnrVpJjAs9/0w4A9H2eAI4pNtPPTBCex2eOi2QOqG55FZ/9AhHavWrh1ER0ONGvDXX7pcTeWiy4uXlJlEkwlN+G3nb1T0qcj+h/fTMbxjkbVvKH2IyJHc15PADKCVcy0qegI8Ani769vsiNnBnD1zrqitL9d/yZAZQ3h56ctG5MoYjuzBtQPuBLoopTbmLn2At4HuSqk9QLfcz6WC1HQ7Y/53kqxs4bZuvvTveJFMINu2wZAhUL06fP21zhf5v//Brl3Qu/fFq1QXklWHVtH0i6ZsO7mNjtU6EvVoFJX88l8g0lD2UEp553oto5TyBnoAW51rlWO4pf4tVParzIf/fnj5nS/B/dfczz3N7uH1f17nmYXPGJErQzhsDk5ElgN53c27Ouq8jiIrW3hq/An2Hs5m7OgQ2jQ8z2PyyBF47jntHamULhD6/PNQrVqR2yIiPDb3Mcb9N45qAdVYfvdyrq1ybZGfx1AqqQDMyJ3rdgF+FJG5zjXJMbhaXXm41cM8vfBpNh7fSNOKTQvVjkVZmHD9BNxd3Hlv5XucSD3BV9d/ZUIIygAmk0k+EBFemhjNzoPZtG3kea64paTASy/pHtt33+l1ffvCK684RNxy7Dl0+64bn/z3CR4uHiy8c6ERN8NpRGS/iDTJXRqIyFhn2+RI7m1xL96u3nz070dX1I5FWRjfezyvd36dWbtmEZUYVUQWGpyJEbh8MG1hEv9ty8DbQ/H4oCC90m7XqbVq1YLXX9dFR6tVgzlzYNYsnfW/iElIT6DW+FosPriYyn6V2fvQXmoE1Sjy8xgMpYUAjwDubnY3U7dM5Wjy0StqSynFC9e9wK4Hd1EjqAYiQkxaTBFZanAGRuAuw86DmUz8PRGrBT5+ogJB/lbYvBlatYK77tKi1rcvvPwy7NgBvXo5xI6oxCjCPwnnYMJBOoV3Yv/D+818m8EAPNL6EXLsOXz636dF0l6It/Yq/WDVBzT6vBGrD68uknYNxY8RuEuQlW3nyU9OIgIvDA+mRpib9oRs2xa2bIG33tJhALNm6SFJz3xkMikEf+7+k2YTmpFpy+SxNo+xZNgSMz9gMORSI6gG/ev254t1X7A7dneRtdurZi88XTzp+G1Hvtv0XZG1ayg+jMBdgkmzEknL1B6THVt4w7hxupJ2RobOHVmnDlgsReoZeTZpWWm0/bot/ab2o4pfFTaP2syHPa/MY8xgKIu81PElRISmXzTlszWfFYknZMPyDVlz7xqurXItw34fxshZI0nPTi8Caw3FhRG4i5CZZefFCdFMW5jM9e19GNXVomuxPfKIrsXWubMOB7jpJofZ8O2Gbwl+L5h/D/9Lg5AGrBqxilrBtRx2PoOhNNO0YlO2jN7CddWu44G/HqD3lN7EpsVecbvBXsHMGzKPMe3GMGnjJDYe33jlxhqKDSNw5xEdn80dLx1lxaZ0urT04mGXxbo+288/617bhAmwYAE4KL3R0aSjNJ/QnOEzh5Nly2JMuzFsvX8rnq6OGf40GMoKYX5hzLljDp/2+ZRFBxbxytJXiqRdV6srb3V7i10P7qJtlbaAjkE18XIlHyNwZ7H3UBbDXj1GXJKd1rUsPP/zHVgH3goVK8KKFbBnj85O4qAhyRMpJ2g7qS0bjm+gVlAt9j60l7e6FS6hrMFwNaKU4v5r7mdI4yF8veHrIvWCrB5YHYA1R9Zw7aRr6Te13xV7bhocixG4XHZHZfHg+yfIyIL2ldN4c2xT1Pz5EBICq1bBtdc6rNdmFztz9syh5w89iUmL4X+9/8euB3cVuN6VwWDQPHXtU6TnpBeZZ+XZtKjUgk96fcLiA4tp+FlDvt/0venNlVCMwAG7IjN57KPjZGUL13oc4uUXG6JiY3WM2+LF4J5HvskiYOPxjbT9ui19fuzD9ujt/D7wdx5o9YCpvG0wXAH1Q+pzfe3rGf/feNKy0y67f2xaLB//+zEHEw5edl+LsvBw64fZOHIjdcvVZejvQ+n/c38jciWQq17gdh7M5MlxJ/H3UjwVM5lXP74Oq90G99+vQwEaNnTIeaMSo7hh6g00n9CcdUfXnS5x073GlVfzNhgM8HS7p4lNj2XShkl57hOXHsfzi54n/JNwHpv3WIFqzNUpV4fldy/ni75f0KdmH5RS2MVOalZqUZhvKAKuaoHbfySTRz86iYey8dHMQfSe/grW5s1g7lz49FOH9Nzi0+N5av5ThH8czqzds1BK0SqsFdNvm86A+gOK/HwGw9VKuyrtaFu5LR+s+uCi1b9n7JhB+MfhvLX8LfrU6kPbym1ZfHBxgc5hURZGthzJyJYjAZi6ZSq1xtfi243fmmrhJQCHFzwtqRw+mcWD750gKxuabf+DCid2w5IlcN0FpbOKhMSMRJ5b9Bw/bvmRxMxE2lRuw9DGQxnadCherl4OOWd+EIH4eF3d5/DhM4uLC1SpopeAAB36l56u969WTVf8EdEZy04tIuDvD66uet+EBJ3BLD0dvL21b0758toZNSVFVxFKSYHsbL2IaIdVf39ITobExDN2KqXPER8Px47pNtzddf1YV1ewWnVIoohuNypKf65TR38Ha27JPrtdb1dKx+X7+em2LBa9REXB/Pl62bYNatfWJfwaNtTl+7y99VK5MgQGOuMvZsgvSimeafcM/X/uz+SNkxnRfMTpbeNWj+PRuY/SKqwVX93wFQ3LN+Tjfz/msXmPEZUYRVX/ws231wquRVX/qgz/YzjjVo/jjS5v0LtmbzPl4CSuSoE7EZvNyLeOk5EFXXb/zpjFj8OEL4pc3Gx2G/P3zee9le+xZM8qSKhG0xrN+GbYRzQNbcKJEzD9J30zPXoUcnL0DdjHR0//eXvrG/DBg7BvH0RG6u0uLpCZqcXBw0Pf6F1c9PGhoVChgm7jv//0zT8rC9LStNBUrQq+vvomv2ePPub8qQOLRZ+nMAQGasFITdX2nU/jxtrWvXt1ofOL4eOjv1PslYcxFRpPT/177dwJM2defB+l9G81aJBOS2q5qsdDSibX17meJhWacM+se5i4fiKjWoxi68mtfPjvh9xY50Z+HPDj6QfMLhFdAFhyYAnDmg67VLN50iqsFStHrOSnrT/x/OLn6ftjX+5sfCff3WQyoTiDq07g9h7K4uH3j5GRreizfSpPbHobtXIFtGlT6Dajo2H3bi1C+/eDzQZJ9iNM/ncWiSf84fhnEF8D7K5sBNq/qHsDkZH6+FMPdyK6Z1C+vK6LmnaRufE6daBpU32OX3/Vx546XqkzPafDh8/tAYEWjcRELSDly2sB8vHRgufrq8V0+HCdTnPvXvjkEy1U2dlaKN3cdIy7CKxdqyMn7HbdO7Ja9fkjInRbp3poHh762JQUbZerqz5PRIQWaW9vLXguuf+J1app4du1Swt7crJefHx0zdg77oD69fX5N27Uv9Gp3qPdrkvuVa6sqxdt3gzHj8OJE7oNX1+44Qb93dev198xM1P/lna7Fqj+/aF7dz39umWLbjcrS4utxQI336zb+uUX2L4dYmK0k60Rt5KJRVn4+66/mbxpMl+s/YK7Z94NwIPXPMjHvT7GarGe3rdh+YaEeIWw6MCiQgvcqXMObjSYW+rfwjcbvqGSr84Zm5SZxJIDS7i+zvVYlPmHKQ5UafD8admypaxdu/aK21m9LZ3XvzhOdlYO/bZN4SEW6tySfn6XPE5E3yiPH9c3u+xsPUw2aZK+0cacE2ojKIsg9gv/gV1coGVLaN1at7V1q74Zh4frYTlfX62z3bqdKVaQkqJv7GFhuldRvrweMhTRN2aXSzyipKTooUcvL13cwNWkr3QIIpcOjVRKrRORlsVnUcEoquurpCMi/BP5D9Fp0QyoN+Ciw4YDfx3IiqgVHHrs0Dnbc+w5uFiurD/wv//+x0NzHqJeuXo80fYJBjUa5NTpibLCpa6vq6IHJyJMmhHHjwuTqRG9k9cOfkDF23rCk8suemdKTITly3Xlm5Urde8s9SKOUaeG8ry9ISgkkzSvHSSE/Yrt2rHcXvduGiU9QcsaNahdw/30/E1+h+ItFt2bygulLi1uoHs99erl73yGwmOmV0oHSik6hne85D5dwrswbds09sTtoXZwbQA+WvURzy56lnub38vT7Z6min+VQp1/VMtRBHkG8e6Kd7ln1j08teApRjQbwdvd3j6nJ2koOsq8wKVl2Hnxw0g2HLbinx7PxyFz8frhz9MeksePayHbtQvWrdOvR45o4VLqzPyUj4/uadWpA6NG6V5UQKCNP49+w/trX+VQ0mEA/Nz9+KjH19zd/G7nfGGDwVBoulbvCsCi/YuoHVybuPQ4Xv37VSr4VOCLdV8wYd0E7mp6F5/0+qTA6fNcLC4MbjSYQQ0HsSxqGeP/G8/mk5tPi9uSA0toXbm16dUVIWVa4A4czeKptw8Sl+2OX2Y8Hx77AK/fJoK7O+np8Oyz8NlnesjxbJ56Ss/lKKWHARs21I4boHuDmbZMYtJiuGfmPczbNw+FonnF5rza+VX61e5X/F/UYDAUCTUCa1DFrwqLDy5m9DWjeWf5OyRlJrFs+DL83P14Z8U7fL72c5pUaMIDrR4o1DmUUlxX7Tquq3YdNrsN0Gn6un/fHW83b26qexO3N7ydrhFdTVmsK6TMCtzqDYm8MDEWm/Kgdsxm3ml1kLgXf+CVd7WzxMSJZ5w8GjXSjgWdOkG7dhAUdG5bdrHzz8HlfLHuC+bvm4+fux/HUo5ht9vpX6c/n/X9jFDf0GL/jgaDoWhRStEloguzd8/mUOIhxv03jiGNh9CoQiMAPuv7GUsOLuH3Xb8XWuDO5lTvLcQ7hIVDFzJ502Rm7JjB5E2TCfYM5scBP9KjRo8rPs/VSpkUuJ2/r+aVvwKwomgV+Q/bbf2p+FI/Mp4+s0+TJjqW+9pr845nysjJYOAvA5m/fz4ZORmn17tZ3RjWZBjPtn+WagHVHPxtDAZDcdIloguTN01m0PRB2Ow2Xuv82jnb+9fpz/ur3ic+PZ5Az6IJhrQoC53CO9EpvBNf9P2Cefvm8dPWn6gZVBOAX7f/ynebvqNnjZ70qNGDmkE1TWxdPihbApeczKIHPmWctReu9ixiN4bw5ua7AD3l1qED3HgjDBig3dHP/v84mnSUX7b/wl97/mJn7E4qeldk88nNZORk4GZ1o2tEV+5pdg89a/Yssn9qg8FQ8jgVD7fi0AoebvUw4QHh52zvX7c/b694m7/2/MUdje8o8vO7u7hzQ50buKHODafXJWcmsy16G7N2zwIgPCCczuGdmdBvghnGvAQOEzil1CSgH3BSRBrmrgsCfgbCgYPAbSISXxTns63bwPtP/MO8eoOw5SjW/BJKWIgrnTvDsGEwePAZN/nDiYdZenAPu2N389uO3/gn6p9zemhWZaWKXxXub3k/PWv2pEtElyt2ETYYDKWDyn6VqR1cmyNJR3j+uucv2H5N2DVU8q3EjJ0zHCJwF2N4s+EMbzacvXF7mbd3HgsPLGRX7K7T4nbvzHuJTY+lTeU2XFPpGpqFNiPAI6BYbCvJOPKu/S3wP+DsEP4xwCIReVspNSb38zNXdBYRDoydyMgdHcmpfxN2O+yYX47vv8uibacYDiVFsfjAYu6ZvZP/jv7HgfgDZNoyTx/ubnXHy9WL5hWb0zWiK7c0uIWG5RuaQEyD4Srmf73/R5Yti/Le5S/YZlEWbqxzI99t+o707PRiLUZcM6gmNVvVvGD+z9vNmyUHlzBj54zT6wY2GMhPt/wEwPx986nqX5UagTWuqh6fQwO9lVLhwOyzenC7gE4ickwpFQosFZE6l2snr0BUSUvjurt/wyu4FdniQUqcle2JP5Ha/CVwu3iJjACPAJpUaMJdTe+iS0QXKvtVNmJmcCgm0LvsMX/ffHr+0JNZg2aVKM/p6NRo1h9bz/pj6wn1DeWupneRbcvG5y0fsmxZWJWV6oHVqVOuDoMbDmZQo0GICNujt1PVvyq+7r7O/goFpiQFelcQkWO5748DFfLaUSl1H3AfQNU8Co3Gp1r4/LoPqOp9gB5/vs22Rs/i7+VJNc9wOlbtSKMKjbAoC+k56VT1q0qbKm1Op80xGMoySikrsBY4IiIl5w5cRugU3gl/d39m7JhRogQuxDuEnjV70rNmz9PrLMrCqhGr2HpyK7tidrErdhe7Y3efrkZ+POU4DT/XZcECPAKo7FeZMN8wHrjmAa6vcz2JGYnM2TuHCt4VCPEOIdgzmGCvYNysbk75jgXBaRNLIiJKqTy7jyIyEZgI+gnzYvsEBdrJDvDGj0T+veUZ6LMRfEwVbIMBeATYAVw6D52hULhZ3ehbuy8zd8/EZrddMhPJpuObGPXnKEY0G8E9ze8pRis1VouV5qHNaR7a/KLbfdx8mDpgKlGJURxKPERUUhTHko+RnpMOwO7Y3QyaPuiC46bcPIXBjQaz/th6Hpv3GH7ufvi7++Pn7oevmy93N7ubOuXqEJUYxbLIZXi5euHp6omniyeerp7UD6mPj5sPqVmppGSl4O7ijpvVDTerG1ZlLRIv0eIWuBNKqdCzhihPXlFrLl5UuH0prBgEh36FvxpB703gW6NIjDUYSiNKqcpAX2As8LiTzSmz9K/Tnx+3/MjKQyvpUK3DRfdZsG8BA6YNID0nnX8P/8uumF0lLjWXr7svtze8Pc/tjSo0YuvorZxMPUlMWgyx6bHEpMXQpEITQFdNUSiOJB1he+Z2EjMSSclKoXuN7tQpV4fVh1czZMaQC9pdefdK2lZpy7Rt004nwT6bLaO30LD8lRWcLm6BmwkMA97Off3jilu0uED7abDuEdg9Hv5sAP12gk/4FTdtMJRSPgaeBkrfhEopolfNXrhb3Xl56cvMGDgDfw//c7ZP3jiZe2bdQ71y9Zg1aBbvr3yf91e9z564PUy5eQrebt5OsrxgeLh40KB8AxrQ4KLbrwm7hqV3Lb1g/Sn/jj61+rD7wd2kZqeSlp1GRk4G6dnp1AvRiXLbVmnLZ30+I8uWRZYti0xbJtm2bCp45zmDlX9ExCELMBU4BmQDh4ERQDCwCNgDLASC8tNWixYtJF9sfVPkR6vIrDoiKQdF7Lb8HWcwOBBgrTjoOjt/QYfmfJb7vhPayeti+92HnqNbW7VqVcf/CGWUr9d/LS6vuUi9/9WTPbF7RERkR/QOGfjLQOEVpOvkrpKQnnB6/3H/jhPLqxa5Y/odDrctx5YjmTmZDj+Ps7nU9VX2yuWcXAZ/3wAWK7gGQvMPIayfSflucBrF6UWplHoLuBPIATzQc3C/iciFY0S5GC/KK2PJgSXc8sstAHSN6Mr0HdPxdPHk0TaP8lLHly5wxnh4zsNMWDeB408cd2jSiLv/uJs1R9ewYeSGMh3He6nrq+z5x5fvAN2XgShI2Qf/3ACz68PR+c62zGBwOCLyrIhUFpFw4HZg8aXEzXDldI7ozH/3/EcF7wrM3j2bx9s8zoFHDvBGlzcu6mk4rMkwsmxZTNs2zWE2xabFMmXLFLae3MrPW3922HlKOmVP4AACGkKfDRAxFKyekLwTlvaEmbUgM87Z1hkMhjJGjaAabBi5gaNPHOW9Hu8R4h2S577NQ5vTIKQB323+Ls99rpQpW6aQZcuikm8lxi4be7pqwdVG2RQ4AK/K0PZbuCUBOkyHgCaQshdmRsCml2Hrm5By0MlGGgyOQ0SWiomBKzbcXdzzlR5LKcXQJkNZeWgle+P2nl6fmJHI+NXjSclKuSI7RISv1n9Fy0ot+ajnR+yI2cH0HdOvqM3SStkVuFNY3aDKzTpGrs9mqNgNtr0Gm5/XYjf3Gtg3yfTsDAZDsXFHozuwKAvfbdK9OBHhzhl38vDch7nxpxvPyY1bUNYeXcuWk1sY0WwEA+oNoF65erz+z+vYxV5U5pcayr7AnU1AI92b670Bqt4GygXi1sLqETC9HGx4CqJXgC3L2ZYaDIYyTJhfGN2qd+P7zd9jFzvvr3yfWbtncXO9m1l8YDEDfx1Iti37guNsdht7YvcQlRiVZ9tfrf8KTxdPBjUchNVi5fkOz7P15Fb+2HnlUVmljbLnRVkQsuJh32SImgoJW8GWm7/SLRisHlD1VqjYHcq3B1eTEMJQOEwuSsPFmLJ5CkNmDGFsl7G8tOQl+tftzy+3/sJnaz7jwTkPMrjRYEa1GMW6Y+tYe3Qtm09sZnfsbjJtmViUhXlD5tGterdz2kzNSiX0g1BuqncTk/tPBiDHnkP9T+tjURb61urLsZRjxKTFEB4QTrOKzWge2pwWlVpc1NPycNJhKvtVLpbf42KIyGUzmlzq+rq6Be5sRCDjOBxbAJueg/QjZ220QIXO0HWh/pgVD64BJvTAkC+MwBkuRmpWKhU/qEhKVgo1g2qy9t61p4PF31r2Fs8tfu70vmG+YTSp2IT65epTL6QeH676kGMpx1h771oiAs+kJ/x247cM/2M4/9z1zznZVX7a+hODpg/C08WTUN9Qgj2D2Ru3l/gMXa1saJOhpwXxFL9u/5Vbf7mV1zu/zgvXveDInyJPvl7/NX/u+ZPJ/SfnmQjaCFxBETscmQU73oPoVUDu2HVgM92jO/A9iA0Cm4B/A/BvqAXQt3rx2WgoNRiBM+TFyFkj+W7zd6wasYqmFZues23OnjnYxEaL0BaE+oaes21v3F6u+fIaqvpXZeXdK/F282Z79HZu//V2Mm2Z7Hxg5wU9n8ycTNysbqfXiwhRiVG89vdrTN40mQOPHKCKf5XT+7ef1J5Vh1dhFzvvdnuXp9o9VaDvJiI8teAp6parW6gcnCdSTlD307o0rtCYJcOW5Fn1xQjclZCTCrH/6QDyE4v1HJ3kXLifxR3KX6dF8OQyCKgPwW3Avx54R4BnRTBlea5KjMAZ8iIzJ5OYtBjC/MIKfOzcvXPpM6UPfWr1waIszNo9C08XTybdOOmSuSXP52DCQap/Up3nOjzHG13eAHSC6KYTmvJOt3dYf2w9P2/7mXG9xvFQ64fy3e7s3bO5fur1AIxqMYpxvccVqBbd7b/ezoydM9g0ahN1y9XNcz8jcEVJdgqc/BsStoDFFVCQfhRSI3VgecKWiwtgxFBoOV4fv+l58K4KXmHgWUkvvrXA1aQOLIsYgTM4ireXv82zi54l2DOYh1o9xAOtHqCcV7kCt3PjTzey6tAqDj12CHcXd0bNHsXkTZM58vgRfN18GfjrQGbsnEGL0BZU8KlAee/yNAhpwA11bqB2cO0L2rOLnWYTmpGalcqAegN4d+W7dArvxK+3/kqwV/Bl7flz95/0m9qP1zq9xosdX7zkvkbgihNbJiTvgfjNELNSL3mJ3tn41Qc3f8iMhdQocPUBt0DwqKh7gPUe10OiGSchcYfe5hYArv5aGE3vsMRiBM7gKESElYdW0iy0GV6uXoVuZ8G+BfT4oQff3/Q919e+nrAPw7itwW1MunESAFm2LF5c/CKbT27mZOpJTqSc4Eiy9lOoW64ugxoO4rkOz512VJm6ZSqDfxt8uqTO95u+555Z9xAeEM7SYUsvGHI9m5SsFBp81gAfNx82jNxw2bpzRuCcjS1DD23GrgF7thY7eyakHYW0I5B5AqxeWuBsWZC0E3KS9XGc9ffxra2PS4087wQK2nyrywQdnQtR08DqDhYPPXTqUR5afAje1SB+I8St08dkJ2vvULcACL5Gh01kxYMtXWeAcfEDVy+w2yAzWotrdpIebvWqqts1jjaXxQicoaRjFzv1P61PgEcAdzS6g4fnPszae9fSolKLPI+JSoxi5q6Z/L7zdxYdWMQNdW7g51t+xqqs1P+sPp4unmwctfH03NmyyGX0ntKbagHVWDps6UWzvUQmRPLsomeZunUqK+5ewbVVrr2s7UbgSitih7TDELcB4tfrnmB2CkiW9vrMPAkp+8Gej7g95QblWumA9qTtRWSgyhVCH53Q2jtcD9dmxuoeaHYyZCWALVXPT3pU1CKZfkwLeHaiFnQXL/CtqT1TPSuBTw1w9QZl1W0l79Hrgltpgbdl6tOnRmmxd/HSomv1gIwYfV5bCmDVIuxRAbwq6Z6uxSO3t6tyxVk5XKSNwBlKA+NXj+fhuQ9Tzqsc1QOrs/qe1fk+9n///Y+H5jxE5/DO9KvdjyfmP8HM22dyfZ3rz9lvyYEl9PmxD3XL1WXR0EUEegSyN24vy6KW8cPmH1hycAkAz7Z/lje7vpmvcxuBK8vYbVqwkvdqoXH11a8WVy0QAInbtONL9DItOL61taB4VNS9texEPQxqdTsjGvYs7WBjSwfJhpr3axE5Ph+OLYScJC22tnS9r6ufDrO4KErX7bNfGLiqN1v18dlJ2jv1Uljc8ifoBcHFFyp20fOguz89r+es9O9V+wHIjIFtb55lY64whrSD7v/k2bwROENpICkzibAPw0jJSmFy/8kMbTK0QMdP2TyFYb8PwyY22lRuw8q7V140hm3e3nnc8NMNVPCuQGp2KnHpOotUjcAaDGsyjDub3El4QHi+z3up66vs1lC4WrBYdYaWgEZ57+NbEyrfWDTnq9gFmuaxLSc919lmP2QnaMHwral7eRZ3yIrT84cA7kGARYunsoJ/fS2o+7+FE0t14L1nefCtC4FN9feLXQ2H/9C9Oq/K4FVF99DcAiG4pT5/9DItgBY3LUTZybk9xNq613h8oV4ndkByxUrpB4Sjc7U97uXAPQRcvPXQbPoRWPew3s/VT5/P4p471Jyje44GQynHz92Pe5vfy8/bfua2BrcV+Pg7Gt+Bv4c/j859lA96fJBngHbPmj2ZMXAG76x4h1pBtWgd1prWlVvTqHyjywZ1FxTTgzMYTmG3AaJ7m2cjoodV3YMKJWamB2coLeTYc8jMySw11cbB9OAMhvxhsV58vVJ6Ds9gKOO4WFxwcSs7smB8yw0Gg8FQJjECZzAYDIYyiRE4g8FgMJRJjMAZDAaDoUziFIFTSvVSSu1SSu1VSo1xhg0Gg8FgKNsUu8AppazAp0BvoD4wSClVv7jtMBgMBkPZxhk9uFbAXhHZLyJZwE9AEUUhGwwGg8GgcYbAhQGHzvp8OHedwWAwGAxFRol1MlFK3aeUWquUWhsdHe1scwwGg8FQynBGyPoRoMpZnyvnrjsHEZkITARQSkUrpc6vEXM25YCYojSyFGJ+A01J/B2qOduAS7Fu3boYc31dFvMbaEri75Dn9VXsuSiVUi7AbqArWtjWAINFZNsVtLm2JOf6Kw7Mb6Axv0PRY35T8xucorT9DsXegxORHKXUg8A8wApMuhJxMxgMBoPhYjglq6aI/AX85YxzGwwGg+HqoMQ6mRSQic42oARgfgON+R2KHvObmt/gFKXqdygV9eAMBoPBYCgoZaUHZzAYDAbDOZRqgTM5LUEpVUUptUQptV0ptU0p9YizbXIWSimrUmqDUmq2s20pC5jry1xfZ1Mar69SK3Amp+VpcoAnRKQ+0AZ44Cr9HQAeAXY424iygLm+TmOurzOUuuur1AocJqclACJyTETW575PRv8DXnWpz5RSlYG+wFfOtqWMYK4vzPV1itJ6fZVmgTM5Lc9DKRUONANWO9kUZ/Ax8DRgd7IdZQVzfZ2Hub5K3/VVmgXOcBZK/b+9e2eNKorCMPwu8VKoYGNjGyyEwQtiYxqxDEFFsBJFEBtBSBHBPyAIWlvYCdp4a7S3EishoqIgorVgUAOBgGRZnKNEi6AhmZ29531gYO6sgflYZx/Y68Q24CEwlZnfS9czTBExCXzOzBela1GbzFed+aq5wf3TTMtREBGb6MJ3NzMfla6ngHHgWER8ojuVdjQi7pQtqXrmq2e+6s1Xtfvg1mKmZY0iIoDbwGxmThUup7iIOAJMZ+Zk4VKqZr465utPteWr2hVcZv4Afs20fAvcG7Xw9caBM3RHVTP9baJ0Uaqb+frNfFWs2hWcJEnLqXYFJ0nScmxwkqQm2eAkSU2ywUmSmmSDkyQ1yQbXqIjYEREX+/u7IuJB6ZqkVpivOrhNoFH93LwnmTkoXYvUGvNVh42lC9CauQaMRcQM8B7Yk5mDiDgHnAC2AruBG8Bmus2sC8BEZs5GxBjd5VJ2AvPAhcx8N+wfIa1T5qsCnqJs1xXgQ2buBy7/9doAOAkcAq4C85l5AHgOnO3fcwu4lJkHgWng5jCKliphvirgCm40Pe2vbTUXEd+Ax/3zr4C9/eT0w8D9bhQfAFuGX6ZUJfO1TtjgRtPCkvuLSx4v0v0nNgBf+6NTSf/HfK0TnqJs1xywfSUf7K939TEiTkE3UT0i9q1mcVLlzFcFbHCNyswvwLOIeA1cX8FXnAbOR8RL4A1wfDXrk2pmvurgNgFJUpNcwUmSmmSDkyQ1yQYnSWqSDU6S1CQbnCSpSTY4SVKTbHCSpCbZ4CRJTfoJ03lM701IvBIAAAAASUVORK5CYII=\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Simulate some microbiota and metabolites\n", + "set_all_seeds(1234)\n", + "\n", + "# SETUP MODEL\n", + "# establish size of model\n", + "num_species = 5\n", + "num_metabolites = 6\n", + "\n", + "# construct interaction matrix\n", + "#TODO do this programmatically\n", + "M = np.zeros((num_species, num_species))\n", + "np.fill_diagonal(M, [-0.05, -0.1, -0.15, -0.01, -0.2])\n", + "# M[0,2] = -0.025\n", + "M[1, 3] = 0.05\n", + "# M[4,0] = 0.02\n", + "\n", + "# construct growth rates matrix\n", + "mu = np.random.lognormal(0.01, 0.5, num_species)\n", + "\n", + "# construct metabolite production matrix\n", + "alpha = np.zeros((num_metabolites, num_species))\n", + "alpha[1, 4] = 1\n", + "alpha[4, 2] = -0.5\n", + "\n", + "# instantiate simulator\n", + "simulator = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M,\n", + " mu=mu,\n", + " beta=alpha)\n", + "simulator.print()\n", + "\n", + "## PRODUCE SIMULATED RESULTS\n", + "# initial conditions\n", + "init_species = 10 * np.ones(num_species)\n", + "init_metabolites = 10 * np.ones(num_metabolites)\n", + "\n", + "times = np.arange(0, 5, 0.1)\n", + "yobs, sobs, sy0, _, _, _ = simulator.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# add some gaussian noise\n", + "yobs = yobs + np.random.normal(loc=0, scale=0.1, size=yobs.shape)\n", + "sobs = sobs + np.random.normal(loc=0, scale=0.1, size=sobs.shape)\n", + "\n", + "# plot simulation\n", + "plot_gMLV(yobs, sobs, times)\n", + "\n", + "## PERFORM REGRESSION\n", + "## fit growth first\n", + "# linearise\n", + "X, F = linearize_time_course_16S(yobs, times)\n", + "# print(f\"n: {num_species * F.shape[0]}, p: {num_species + num_species ** 2}\")\n", + "\n", + "# get the best lambda/alpha values on a grid via cross validation\n", + "a0, a1 = fit_alpha_Ridge1(X, F, num_species=num_species, n_a0=20, n_a1=20)\n", + "\n", + "# do final fit\n", + "mu_h, M_h = do_final_fit_Ridge1(X, F, num_species, a0, a1)\n", + "\n", + "## fit metabolite production\n", + "# Linearize this problem\n", + "G, S = linearise_time_course_metabolites(sobs, yobs, times)\n", + "\n", + "# get the best lambda/alpha value on a grid via cross validation\n", + "a_min, a_se = fit_alpha_lasso(G, S, n_a=20)\n", + "model = Lasso(fit_intercept=False, max_iter=10000, alpha=a_min)\n", + "\n", + "# perform final fit\n", + "model.fit(G, S)\n", + "alpha_h = model.coef_\n", + "\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h,\n", + " beta=alpha_h)\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "## PLOT RESULTS\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)\n", + "\n", + "compare_params(mu=(mu,mu_h), M=(M, M_h), alpha=(alpha, alpha_h))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "## SIMULATE SOME DATA" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of species: 5\n", + "specific growth rates: [1.27853844 0.55683415 2.06752757 0.86387608 0.70448068]\n", + "interaction matrix: \n", + "[[-0.05 0. -0.025 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0.02 0. 0. 0. -0.2 ]]\n", + "metabolite production: \n", + "[[ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 1. ]\n", + " [ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. -0.5 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. ]]\n", + "perturbation matrix: \n", + "[]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Simulate some microbiota and metabolites\n", + "set_all_seeds(1234)\n", + "\n", + "# SETUP MODEL\n", + "# establish size of model\n", + "num_species = 5\n", + "num_metabolites = 6\n", + "\n", + "# construct interaction matrix\n", + "#TODO do this programmatically\n", + "M = np.zeros((num_species, num_species))\n", + "np.fill_diagonal(M, [-0.05, -0.1, -0.15, -0.01, -0.2])\n", + "M[0,2] = -0.025\n", + "M[1, 3] = 0.05\n", + "M[4,0] = 0.02\n", + "\n", + "# construct growth rates matrix\n", + "mu = np.random.lognormal(0.01, 0.5, num_species)\n", + "\n", + "# construct metabolite production matrix\n", + "rho = np.zeros((num_metabolites, num_species))\n", + "rho[1, 4] = 1\n", + "rho[4, 2] = -0.5\n", + "\n", + "# instantiate simulator\n", + "simulator = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M,\n", + " mu=mu,\n", + " beta=rho)\n", + "simulator.print()\n", + "\n", + "## PRODUCE SIMULATED RESULTS\n", + "# initial conditions\n", + "init_species = 10 * np.ones(num_species)\n", + "init_metabolites = 10 * np.ones(num_metabolites)\n", + "\n", + "times = np.arange(0, 5, 0.1)\n", + "yobs, sobs, sy0, _, _, _ = simulator.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# add some gaussian noise\n", + "yobs = yobs + np.random.normal(loc=0, scale=0.1, size=yobs.shape)\n", + "sobs = sobs + np.random.normal(loc=0, scale=0.1, size=sobs.shape)\n", + "\n", + "# plot simulation\n", + "plot_gMLV(yobs, sobs, times)" + ] + }, + { + "cell_type": "markdown", + "id": "faa84f27", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "## FIT WITH MULTI-PENALTY LASSO" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "58bae043", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum found: a/error: [7.74263683e-05 2.78255940e-07] 0.10996301478040563\n" + ] + }, + { + "data": { + "image/png": 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\n", 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# F = dlnX/dt\n", + "DlnX = np.diff(np.log(yobs), axis=0)\n", + "Dt = np.tile(np.diff(times), (num_species, 1))\n", + "F = np.divide(DlnX, np.transpose(Dt))\n", + "\n", + "# X matrix: stacked observed counts\n", + "mX = np.vstack([np.transpose(yobs), np.ones(len(times))])\n", + "tX = np.transpose(mX[:, :-1])\n", + "\n", + "alphas = fit_alpha_MPLasso(tX, F, 10)\n", + "\n", + "alpha = np.append(np.ones(num_species)*alphas[0], alphas[1])\n", + "model = MultiPenaltyLasso(alpha=alpha)\n", + "model.fit(tX, F)\n", + "\n", + "mu_h = [model.coef_[i][-1] for i in range(0, num_species)]\n", + "M_h = [model.coef_[i][0:num_species].tolist() for i in range(0, num_species)]\n", + "\n", + "# this does the stem plots with orange crosses the actual parameters\n", + "compare_params(mu=(mu, mu_h), M=(M, M_h))\n", + "\n", + "# get prediction\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h,\n", + " beta=rho)\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# plot comparison of simulated and predicted timeseries\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "## MARIA'S DATA" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum found: a0/a1/a2/error: 100.0 1e-06 1.0 0.006848013080354236\n", + "unconstrained error : nan\n" + ] + }, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "# import data\n", + "F = pd.read_csv('data/F.csv', delimiter = ',', header=None, index_col=None)\n", + "Y = pd.read_csv('data/Y.csv', delimiter = ',', header=None, index_col=None)\n", + "\n", + "num_species = F.shape[0]\n", + "num_pert = Y.shape[0] - (num_species + 1)\n", + "\n", + "# get the best lambda/alpha values on a grid via cross validation\n", + "a0, a1, a2 = fit_alpha_Ridge2(Y.T, F.T, num_species=num_species, num_pert=num_pert, n_a0=20, n_a1=20, n_a2=20)\n", + "\n", + "# do final fit\n", + "mu_h, M_h, e_h = do_final_fit_Ridge2(Y.T, F.T, num_species, num_pert, a0, a1, a2)\n", + "\n", + "# predictor = gMLV_sim(num_species=num_species,\n", + "# num_metabolites=num_metabolites,\n", + "# M=M_h,\n", + "# mu=mu_h,\n", + "# epsilon=e_h)\n", + "# yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times,\n", + "# sy0=np.hstack((init_species, init_metabolites)),\n", + "# tp=tp)\n", + "#\n", + "# ## PLOT RESULTS\n", + "# # plot comparison of simulated and predicted timeseries\n", + "# plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/model_nopert.txt b/examples/model_nopert.txt new file mode 100644 index 00000000..dc193bf8 --- /dev/null +++ b/examples/model_nopert.txt @@ -0,0 +1,74 @@ +functions { + vector lotka_volterra_N_red(real[] x, int N, vector mu, vector Md, vector M) { + // Model: F = dlnX/dt = mu + M x + + vector[N] dydt; + + int countM = 1; + + for(i in 1:N){ + dydt[i] = mu[i] - Md[i]*x[i]; + + for(j in 1:N){ + if ( i != j ){ + dydt[i] += M[countM]*x[j]; + countM += 1; + //print("loop iteration: ", i, j, countM); + } + } + } + + return dydt; + } + +} + +data { + int N; + int T; + + array[T,N] real y; + array[T,N] real x; + + real tau0; + real sigma; +} + +parameters { + vector[N] mu; + vector[N] Md; + vector[N*N - N] M; + + vector[N*N - N] lambda; + real tau; + + //real sigma; +} + +model { + + // mu + target += lognormal_lpdf(mu | 0.01, 0.5); + + // Md + target += normal_lpdf(Md | 0.1, 0.05); + + // Mij: Horsehoe prior + target += cauchy_lpdf(tau | 0, tau0); + + for(i in 1:(N*(N-1))){ + target += normal_lpdf(M[i] | 0, lambda[i]*tau); + target += cauchy_lpdf(lambda[i] | 0, 1); + } + // + + // sigma + //target += lognormal_lpdf(sigma | 0.01, 0.5); + + for (t in 1:T) { + vector[N] y_hat = lotka_volterra_N_red(x[t,:], N, mu, Md, M); + for (s in 1:N){ + target += normal_lpdf(y[t,s] | y_hat[s], sigma); + } + } +} \ No newline at end of file diff --git a/examples/model_pert.txt b/examples/model_pert.txt new file mode 100644 index 00000000..e9ac2628 --- /dev/null +++ b/examples/model_pert.txt @@ -0,0 +1,85 @@ + +functions { + vector lotka_volterra_N_red(real[] x, int N, vector mu, vector Md, vector M, vector E, real u) { + // Model: F = dlnX/dt = mu + M x + E u + + vector[N] F; + + int countM = 1; + + for(i in 1:N){ + F[i] = mu[i] - Md[i]*x[i]; + + // off diagonal interaction terms + for(j in 1:N){ + if ( i != j ){ + F[i] += M[countM]*x[j]; + countM += 1; + //print("loop iteration: ", i, j, countM); + } + } + + // epsilon terms + F[i] += E[i]*u; + } + + return F; + } + +} + +data { + int N; + int T; + int Np; + + array[T,N] real y; + array[T,N] real x; + array[T,Np] real u; + + real sigma; + real tau0; +} + +parameters { + vector[N] mu; + vector[N] Md; + vector[N*N - N] M; + vector[N] E; + + vector[N*N - N] lambda; + real tau; + + //real sigma; +} + +model { + + // mu + target += lognormal_lpdf(mu | 0.01, 0.5); + + // Md + target += normal_lpdf(Md | 0.1, 0.05); + + // Mij: Horsehoe prior + target += cauchy_lpdf(tau | 0, tau0); + + for(i in 1:(N*(N-1))){ + target += normal_lpdf(M[i] | 0, lambda[i]*tau); + target += cauchy_lpdf(lambda[i] | 0, 1); + } + // + + // sigma + //target += lognormal_lpdf(sigma | 0.01, 0.5); + + // epsilon + target += normal_lpdf(E | 0, 0.5); + + for (t in 1:T) { + vector[N] y_hat = lotka_volterra_N_red(x[t,:], N, mu, Md, M, E, u[t,1] ); + for (s in 1:N){ + target += normal_lpdf(y[t,s] | y_hat[s], sigma); + } + } +} diff --git a/examples/model_sde_nopert.txt b/examples/model_sde_nopert.txt new file mode 100644 index 00000000..6d0ea422 --- /dev/null +++ b/examples/model_sde_nopert.txt @@ -0,0 +1,86 @@ +functions { + vector gLV_sde(real[] x, int N, vector mu, vector Md, vector M) { + // Model: f(x) = mu + M x + + vector[N] f; + + int countM = 1; + + for(i in 1:N){ + f[i] = mu[i] - Md[i]*x[i]; + + for(j in 1:N){ + if ( i != j ){ + f[i] += M[countM]*x[j]; + countM += 1; + //print("loop iteration: ", i, j, countM); + } + } + } + + return f; + } + +} + +data { + int N; + int T; + + array[T,N] real x; + array[T] real times; + array[T,N] int xmiss; + + real tau0; + //real sigma; +} + +parameters { + vector[N] mu; + vector[N] Md; + vector[N*N - N] M; + + vector[N*N - N] lambda; + real tau; + + real sigma; + + //real d0; + //real d1; +} + +model { + + // mu + target += lognormal_lpdf(mu | 0.01, 0.5); + + // Md + target += normal_lpdf(Md | 0.1, 0.05); + + // Mij: Horsehoe prior + target += cauchy_lpdf(tau | 0, tau0); + + for(i in 1:(N*(N-1))){ + target += normal_lpdf(M[i] | 0, lambda[i]*tau); + target += cauchy_lpdf(lambda[i] | 0, 1); + } + + // Negative binomial observation error + //target += neg_binomial_lpmf(x[i] | x[i], d0/x[i] + d1) + + // sigma + target += lognormal_lpdf(sigma | 0.01, 0.5); + + // SDE likelihood + // log xi(t+1) ~ N( log xi(t) + f(x)dt, ) + + for (t in 1:(T-1)) { + vector[N] f_x = gLV_sde(x[t,:], N, mu, Md, M); + real dt = times[t+1] - times[t]; + + for (s in 1:N){ + target += normal_lpdf(x[t+1,s] | x[t,s] + f_x[s]*dt, sqrt(dt)*sigma); + } + } + // tmp +} \ No newline at end of file diff --git a/examples/multi-omics-v2.ipynb b/examples/multi-omics-v2.ipynb new file mode 100644 index 00000000..839448d0 --- /dev/null +++ b/examples/multi-omics-v2.ipynb @@ -0,0 +1,651 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "f07fa1f2-187e-4ce0-af95-31d6120977fe", + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.integrate import odeint\n", + "\n", + "from numpy import linalg as la\n", + "\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.linear_model import Ridge\n", + "from sklearn.linear_model import Lasso\n", + "from sklearn.linear_model import ElasticNet\n", + "from sklearn.model_selection import RepeatedKFold\n", + "from sklearn.model_selection import cross_val_score\n", + "from sklearn.model_selection import KFold\n", + "from sklearn.model_selection import GridSearchCV\n", + "\n", + "from gMLV import *\n", + "\n", + "import seaborn as sns" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "f24a82c9-f85e-49db-979d-f23fae68f172", + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "# some plotting functions\n", + "def plot_gMLV(yobs, sobs, timepoints):\n", + " fig, axs = plt.subplots(1, 2, layout='constrained')\n", + " axs[0].plot(timepoints, yobs)\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]')\n", + " if sobs.shape[1] > 0:\n", + " axs[1].plot(timepoints, sobs)\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]');\n", + "\n", + "def plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, timepoints):\n", + " # plot the fit\n", + " cols = [\"red\", \"green\", \"blue\", \"royalblue\",\"black\"]\n", + " fig, axs = plt.subplots(1, 2, layout='constrained')\n", + "\n", + " for species_idx in range(yobs.shape[1]):\n", + " axs[0].plot(timepoints, yobs[:, species_idx], color=cols[species_idx])\n", + " axs[0].plot(timepoints, yobs_h[:, species_idx], '--', color=cols[species_idx])\n", + " axs[0].set_xlabel('time')\n", + " axs[0].set_ylabel('[species]');\n", + "\n", + " for metabolite_idx in range(sobs.shape[1]):\n", + " axs[1].plot(timepoints, sobs[:, metabolite_idx], color=cols[metabolite_idx])\n", + " axs[1].plot(timepoints, sobs_h[:, metabolite_idx], '--', color=cols[metabolite_idx])\n", + " axs[1].set_xlabel('time')\n", + " axs[1].set_ylabel('[metabolite]');\n", + "\n", + "def compare_params(mu_h, mu, M_h, M):\n", + " print(\"\\nINFERRED PARAMS:\")\n", + " print(\"mu_hat/mu:\")\n", + " print(np.array(mu_h))\n", + " print(np.array(mu))\n", + " print(\"\\nM_hat/M:\")\n", + " print(np.round(np.array(M_h),decimals=2))\n", + " print(\"\\n\",np.array(M) )\n", + "\n", + " # plot the params\n", + " fig, axs = plt.subplots(1, 2, layout='constrained', figsize=(6.4*2,4.8))\n", + " axs[0].stem(np.arange(0,len(mu), dtype=\"int32\"), np.array(mu_h), markerfmt=\"D\")\n", + " axs[0].stem(np.arange(0,len(mu), dtype=\"int32\"), np.array(mu), markerfmt=\"X\")\n", + " axs[0].set_xlabel('i')\n", + " axs[0].set_ylabel('mu[i]');\n", + "\n", + " axs[1].stem(np.arange(0, M.shape[0] ** 2), np.array(M_h).flatten(), markerfmt=\"D\")\n", + " axs[1].stem(np.arange(0, M.shape[0] ** 2), np.array(M).flatten(), markerfmt=\"X\")\n", + " axs[1].set_ylabel('M[i,j]');" + ] + }, + { + "cell_type": "markdown", + "id": "27f9ef3f-7097-401a-80ab-fe8e92ff7eba", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "## Simulate some time course data and perform ridge regression as in Stein et al. 2013\n", + "I have coded up the Stein model and ridge regression without the perturbation term. We can include this at a later date\n", + "if needed.
\n", + "Ridge regression is designed to cause shrinkage to prevent overfitting. It isn't supposed to be used for variable\n", + "selection. We should use Lasso for this, however I think we need to constrain parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "17afad1f-293b-4f8b-bc99-f9dd3fed4ac1", + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "MODEL SPEC:\n", + "number of species: 5\n", + "specific growth rates: [0.83618329 2.05255299 0.72018307 2.08618352 0.51406958]\n", + "interaction matrix: \n", + "[[-0.05 0. -0.025 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0.02 0. 0. 0. -0.2 ]]\n", + "metabolite production: \n", + "None\n", + "minimum found: a0/a1/error: 0.29763514416313175 0.0003359818286283781 0.1352507468429699\n", + "unconstrained error : 0.1369748704349958\n", + "\n", + "INFERRED PARAMS:\n", + "mu_hat/mu:\n", + "[ 1.86604021 1.98232841 1.71145119 2.10085546 -1.17641472]\n", + "[0.83618329 2.05255299 0.72018307 2.08618352 0.51406958]\n", + "\n", + "M_hat/M:\n", + "[[-0.15 0.02 -0.01 -0.01 -0.03]\n", + " [ 0.02 -0.08 -0.03 0.04 -0. ]\n", + " [ 0. 0.02 -0.51 -0.01 0.25]\n", + " [-0. 0.03 -0. -0.03 -0.02]\n", + " [ 0.11 -0.01 0.35 0.01 -0.47]]\n", + "\n", + " [[-0.05 0. -0.025 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0.02 0. 0. 0. -0.2 ]]\n" + ] + }, + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Single time course. In this example n >> p and it it is basically same as standard regression\n", + "# We have to be careful as most of these gLV models are very weakly identifiable\n", + "# SETUP MODEL\n", + "num_species = 5\n", + "init_species = 10 * np.ones(num_species)\n", + "num_metabolites = 0\n", + "init_metabolites = 10 * np.ones(num_metabolites)\n", + "\n", + "M = np.zeros((num_species, num_species))\n", + "np.fill_diagonal(M, [-0.05, -0.1, -0.15, -0.01, -0.2])\n", + "M[0, 2] = -0.025\n", + "M[1, 3] = 0.05\n", + "M[4, 0] = 0.02\n", + "\n", + "mu = np.random.lognormal(0.01, 0.5, num_species)\n", + "\n", + "simulator = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M,\n", + " mu=mu)\n", + "\n", + "simulator.print()\n", + "\n", + "# produce simulated results\n", + "times = np.arange(0, 5, 0.1)\n", + "yobs, sobs, sy0, mu, M, _ = simulator.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# add some gaussian noise\n", + "yobs = yobs + np.random.normal(loc=0, scale=0.1, size=yobs.shape)\n", + "sobs = sobs + np.random.normal(loc=0, scale=0.1, size=sobs.shape)\n", + "\n", + "# plot simulation\n", + "# plot_gMLV(yobs, sobs, times)\n", + "\n", + "# linearise\n", + "X, F = linearize_time_course_16S(yobs, times)\n", + "# print(f\"n: {num_species * F.shape[0]}, p: {num_species + num_species ** 2}\")\n", + "\n", + "# get the best lambda/alpha values on a grid via cross validation\n", + "a0, a1 = fit_alpha_cRidge(X, F, nsp=num_species, n_a0=20, n_a1=20)\n", + "\n", + "# do final fit\n", + "mu_h, M_h = do_final_fit_cRidge(X, F, num_species, a0, a1)\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h)\n", + "yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "plot_fit_gMLV(yobs, yobs_h, sobs, sobs_h, times)\n", + "\n", + "# this does the stem plots with orange crosses the actual parameters\n", + "compare_params(mu_h, mu, M_h, M)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "2828116e-9999-40e3-93de-58e8b42c4584", + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "MODEL SPEC:\n", + "number of species: 5\n", + "specific growth rates: [1.23422619 1.41635198 0.57281213 1.04207098 0.78834736]\n", + "interaction matrix: \n", + "[[-0.05 0. -0.025 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0.02 0. 0. 0. -0.2 ]]\n", + "metabolite production: \n", + "None\n", + "X: (12, 6)\n", + "F: (12, 5)\n", + "n: 60, p: 30\n", + "minimum found: a0/a1/error: 2.06913808111479 4.281332398719396e-06 0.0376019203273467\n", + "unconstrained error : 0.1708818872751557\n", + "\n", + "INFERRED PARAMS:\n", + "mu_hat/mu:\n", + "[ 0.31547741 0.83521454 -0.37972915 0.62811993 -0.22246654]\n", + "[1.23422619 1.41635198 0.57281213 1.04207098 0.78834736]\n", + "\n", + "M_hat/M:\n", + "[[-0.01 -0. -0.01 0. 0. ]\n", + " [-0. -0.03 0. 0.01 -0.01]\n", + " [ 0. -0.01 -0.03 0.01 0. ]\n", + " [ 0.01 0. 0. -0.01 -0. ]\n", + " [ 0.02 -0.02 -0.01 0.01 -0.03]]\n", + "\n", + " [[-0.05 0. -0.025 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0.02 0. 0. 0. -0.2 ]]\n", + "examining mu_i\n", + "0 -0.495 - 0.066 \n", + "1 0.521 - 0.755 *\n", + "2 -1.813 - -0.198 *\n", + "3 0.515 - 0.825 *\n", + "4 -0.425 - -0.062 *\n", + "\n", + "examining Mij\n", + "1 (0, 0) -0.004 - 0.0 \n", + "2 (0, 1) -0.0 - 0.003 \n", + "3 (0, 2) -0.009 - -0.0 *\n", + "4 (0, 3) -0.0 - 0.004 \n", + "5 (0, 4) -0.001 - -0.0 *\n", + "6 (1, 0) 0.0 - 0.003 *\n", + "7 (1, 1) -0.005 - 0.0 \n", + "8 (1, 2) 0.0 - 0.006 *\n", + "9 (1, 3) -0.006 - 0.0 \n", + "10 (1, 4) 0.0 - 0.001 *\n", + "11 (2, 0) -0.01 - 0.006 \n", + "12 (2, 1) -0.0 - 0.009 \n", + "13 (2, 2) -0.028 - 0.005 \n", + "14 (2, 3) -0.0 - 0.014 \n", + "15 (2, 4) -0.002 - 0.001 \n", + "16 (3, 0) 0.0 - 0.002 *\n", + "17 (3, 1) -0.004 - 0.0 \n", + "18 (3, 2) 0.0 - 0.004 *\n", + "19 (3, 3) -0.006 - 0.0 \n", + "20 (3, 4) 0.0 - 0.0 *\n", + "21 (4, 0) -0.002 - 0.001 \n", + "22 (4, 1) -0.0 - 0.002 \n", + "23 (4, 2) -0.006 - 0.001 \n", + "24 (4, 3) -0.0 - 0.003 \n", + "25 (4, 4) -0.001 - 0.0 \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": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Lower number of time points, multiple time course\n", + "# SETUP MODEL\n", + "num_species = 5\n", + "num_metabolites = 0\n", + "\n", + "M = np.zeros((num_species, num_species))\n", + "np.fill_diagonal(M, [-0.05, -0.1, -0.15, -0.01, -0.2])\n", + "M[0, 2] = -0.025\n", + "M[1, 3] = 0.05\n", + "M[4, 0] = 0.02\n", + "\n", + "mu = np.random.lognormal(0.01, 0.5, num_species)\n", + "\n", + "simulator = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M,\n", + " mu=mu)\n", + "\n", + "simulator.print()\n", + "\n", + "# produce simulated results\n", + "ryobs = []\n", + "rsobs = []\n", + "ry0 = []\n", + "rs0 = []\n", + "X = np.array([], dtype=np.double).reshape(0, num_species+1)\n", + "F = np.array([], dtype=np.double).reshape(0, num_species)\n", + "\n", + "num_timecourses = 3\n", + "times = np.arange(0,5,1)\n", + "for timecourse_idx in range(num_timecourses):\n", + " init_species = np.random.uniform(low=10, high=50, size=num_species)\n", + " init_metabolites = np.random.uniform(low=10, high=50, size=num_metabolites)\n", + "\n", + " yobs, sobs, sy0, mu, M, _ = simulator.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + " # add some gaussian noise\n", + " yobs = yobs + np.random.normal(loc=0, scale=0.1, size=yobs.shape)\n", + " sobs = sobs + np.random.normal(loc=0, scale=0.1, size=sobs.shape)\n", + "\n", + " ryobs.append(yobs)\n", + " rsobs.append(sobs)\n", + " ry0.append(init_species)\n", + " rs0.append(init_metabolites)\n", + "\n", + " Xs, Fs = linearize_time_course_16S(yobs,times)\n", + " X = np.vstack([X, Xs])\n", + " F = np.vstack([F, Fs])\n", + "\n", + "print(f\"X: {X.shape}\")\n", + "print(f\"F: {F.shape}\")\n", + "print(f\"n: {num_species*F.shape[0]}, p: {num_species + num_species**2}\")\n", + "\n", + "## get the best lambda/alpha values on a grid via cross validation\n", + "a0, a1 = fit_alpha_cRidge(X, F, nsp=num_species, n_a0=20, n_a1=20)\n", + "\n", + "# do final fit\n", + "mu_h, M_h = do_final_fit_cRidge(X, F, num_species, a0=a0, a1=a1)\n", + "predictor = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M_h,\n", + " mu=mu_h)\n", + "\n", + "for timecourse_idx in range(num_timecourses):\n", + " yobs_h, sobs_h, _, _, _, _ = predictor.simulate(times=times, sy0=np.hstack((ry0[timecourse_idx], rs0[timecourse_idx])))\n", + " plot_fit_gMLV(ryobs[timecourse_idx], yobs_h, rsobs[timecourse_idx], sobs_h, times)\n", + "\n", + "compare_params(mu_h, mu, M_h, M)\n", + "\n", + "# do some bootstrapping to help with interpretation of parameters\n", + "# starred parameters are considered different to zero\n", + "do_bootstrapping(X, F, num_species, a0, a1, len(times), nboots=100)\n" + ] + }, + { + "cell_type": "markdown", + "id": "70fc81c1-b7ce-482f-a6a0-a645bc1ec2aa", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "## Simulate some time course data and metabolites\n", + "This model assumes metabolite production is associated with abundance: dS/dt = alpha X
\n", + "Note that this model needs rethinking as it cannot handle negative productivities
\n", + "In this simple example we don't need to infer the time course. We just linearize and estimate the elements of alpha with Lasso
\n", + "Number of metabolites is 6 here" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "df873518-15bf-48ea-8a59-8f6c6671bda5", + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "MODEL SPEC:\n", + "number of species: 5\n", + "specific growth rates: [0.8407952 2.00305621 1.37998189 1.37693195 1.86572983]\n", + "interaction matrix: \n", + "[[-0.05 0. 0. 0. 0. ]\n", + " [ 0. -0.1 0. 0.05 0. ]\n", + " [ 0. 0. -0.15 0. 0. ]\n", + " [ 0. 0. 0. -0.01 0. ]\n", + " [ 0. 0. 0. 0. -0.2 ]]\n", + "metabolite production: \n", + "[[ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 1. ]\n", + " [ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. -0.5 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. ]]\n", + "minimum found: a/error: 0.8858667904100825 1.4909478950544621\n", + "min + se rule: a/error: 1.2742749857031335 1.4946762796634585\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "inferred params:\n", + "A_hat/A:\n", + "[[ 0. -0. 0. -0. 0. ]\n", + " [ 0.19 0. 0. -0. 0.72]\n", + " [-0. 0. -0. 0. -0. ]\n", + " [ 0. -0. 0. -0. 0. ]\n", + " [-0.21 -0. -0.21 0.01 -0. ]\n", + " [ 0. 0. -0. 0. -0. ]]\n", + "\n", + " [[ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 1. ]\n", + " [ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. ]\n", + " [ 0. 0. -0.5 0. 0. ]\n", + " [ 0. 0. 0. 0. 0. ]]\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Simulate some microbiota and metabolites\n", + "# SETUP MODEL\n", + "num_species = 5\n", + "num_metabolites = 6\n", + "\n", + "M = np.zeros((num_species, num_species))\n", + "np.fill_diagonal(M, [-0.05, -0.1, -0.15, -0.01, -0.2])\n", + "# M[0,2] = -0.025\n", + "M[1, 3] = 0.05\n", + "# M[4,0] = 0.02\n", + "\n", + "mu = np.random.lognormal(0.01, 0.5, num_species)\n", + "\n", + "alpha = np.zeros((num_metabolites, num_species))\n", + "alpha[1, 4] = 1\n", + "alpha[4, 2] = -0.5\n", + "\n", + "simulator = gMLV_sim(num_species=num_species,\n", + " num_metabolites=num_metabolites,\n", + " M=M,\n", + " mu=mu,\n", + " beta=alpha)\n", + "\n", + "simulator.print()\n", + "\n", + "# produce simulated results\n", + "times = np.arange(0, 5, 0.1)\n", + "init_species = 10 * np.ones(num_species)\n", + "init_metabolites = 10 * np.ones(num_metabolites)\n", + "yobs, sobs, sy0, _, _, _ = simulator.simulate(times=times, sy0=np.hstack((init_species, init_metabolites)))\n", + "\n", + "# add some gaussian noise\n", + "yobs = yobs + np.random.normal(loc=0, scale=0.1, size=yobs.shape)\n", + "sobs = sobs + np.random.normal(loc=0, scale=0.1, size=sobs.shape)\n", + "\n", + "# Linearize this problem\n", + "X, S = linearise_time_course_metabolites(sobs, yobs, times)\n", + "\n", + "# get the best lambda/alpha value on a grid via cross validation\n", + "a_min, a_se = fit_alpha_lasso(X, S, n_a=20)\n", + "model = Lasso(fit_intercept=False, max_iter=10000, alpha=a_min)\n", + "\n", + "# just fit based on plot\n", + "#gMLV_ML.plot_alpha_lasso(X, S, n_a=20)\n", + "#model = Lasso(fit_intercept=False, max_iter=10000, alpha=2)\n", + "\n", + "model.fit(X, S)\n", + "alpha_h = model.coef_\n", + "#print(\"alpha_h:\",alpha_h.shape)\n", + "\n", + "print(\"\\ninferred params:\")\n", + "print(\"A_hat/A:\")\n", + "print(np.round(np.array(alpha_h),decimals=2))\n", + "print(\"\\n\",np.array(alpha) )\n", + "\n", + "# plot the params\n", + "# You can see Lasso does a pretty good job at picking out the metabolite, microbiota interactions\n", + "plt.figure()\n", + "plt.stem( np.arange(0, num_metabolites * num_species), np.array(alpha_h).flatten(), markerfmt=\"D\" )\n", + "plt.stem( np.arange(0, num_metabolites * num_species), np.array(alpha).flatten(), markerfmt=\"X\" )\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "ed29a4de-868c-4108-b30d-14902dd4f903", + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}