From bb00033bc984d480566613e1b3dd131690a6b84a Mon Sep 17 00:00:00 2001 From: LIU Date: Mon, 1 Mar 2021 20:21:51 +0800 Subject: [PATCH 1/5] exception handling tutorial added --- README.md | 2 + .../ex6_exception_handling-checkpoint.ipynb | 430 ++++++++++++++++++ tutorials/__pycache__/GP_DRT.cpython-38.pyc | Bin 0 -> 6742 bytes tutorials/ex6_exception_handling.ipynb | 430 ++++++++++++++++++ 4 files changed, 862 insertions(+) create mode 100644 tutorials/.ipynb_checkpoints/ex6_exception_handling-checkpoint.ipynb create mode 100644 tutorials/__pycache__/GP_DRT.cpython-38.pyc create mode 100644 tutorials/ex6_exception_handling.ipynb diff --git a/README.md b/README.md index c23bee8..0145468 100644 --- a/README.md +++ b/README.md @@ -37,6 +37,8 @@ The frequency range is from 1E-4 Hz to 1E4 Hz with 10 ppd. * **ex5_inductance_plus_ZARC.ipynb**: this notebook adds an inductance to the model used in ex1_single_ZARC.ipynb +* **ex6_exception_handling.ipynb**: in this notebook, we show how to resolve the error raised by `np.linalg.cholesky()` + # Citation ``` diff --git a/tutorials/.ipynb_checkpoints/ex6_exception_handling-checkpoint.ipynb b/tutorials/.ipynb_checkpoints/ex6_exception_handling-checkpoint.ipynb new file mode 100644 index 0000000..d2a890f --- /dev/null +++ b/tutorials/.ipynb_checkpoints/ex6_exception_handling-checkpoint.ipynb @@ -0,0 +1,430 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gaussian Process Distribution of Relaxation Times" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## In this tutorial, we will try to handle the exception that may be encountered while doing the Cholesky decomposition for $\\mathbf K_{\\rm im}^{\\rm full}$ https://doi.org/10.1016/j.electacta.2019.135316" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This tutorial is based on that `ex1_simple_ZARC.ipynb` and we will handle the exception during in the `np.linalg.cholesky(K_im_full)`." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from math import sin, cos, pi\n", + "import GP_DRT\n", + "from scipy.optimize import minimize\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1) Define parameters of the ZARC circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# define the frequency range\n", + "N_freqs = 81\n", + "freq_vec = np.logspace(-4., 4., num=N_freqs, endpoint=True)\n", + "xi_vec = np.log(freq_vec)\n", + "tau = 1/freq_vec\n", + "\n", + "# define the frequency range used for prediction\n", + "# note: we could have used other values\n", + "freq_vec_star = np.logspace(-4., 4., num=81, endpoint=True)\n", + "xi_vec_star = np.log(freq_vec_star)\n", + "\n", + "# parameters for ZARC model, the impedance and analytical DRT are calculated as the above equations\n", + "R_inf = 10\n", + "R_ct = 50\n", + "phi = 0.8\n", + "tau_0 = 1.\n", + "\n", + "C = tau_0**phi/R_ct\n", + "Z_exact = R_inf+1./(1./R_ct+C*(1j*2.*pi*freq_vec)**phi)\n", + "gamma_fct = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau/tau_0))-cos((1.-phi)*pi))\n", + "\n", + "# we will use a finer mesh for plotting the results\n", + "freq_vec_plot = np.logspace(-4., 4., num=10*(N_freqs-1), endpoint=True)\n", + "tau_plot = 1/freq_vec_plot\n", + "# for plotting only\n", + "gamma_fct_plot = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau_plot/tau_0))-cos((1.-phi)*pi))\n", + "\n", + "# we will add noise to the impedance computed analytically\n", + "rng = np.random.seed(214975)\n", + "sigma_n_exp = 1.\n", + "Z_exp = Z_exact + sigma_n_exp*(np.random.normal(0, 1, N_freqs)+1j*np.random.normal(0, 1, N_freqs))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2) Show the synthetic impedance in the Nyquist plot" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "\n", + "# Nyquist plot of the impedance\n", + "plt.plot(np.real(Z_exact), -np.imag(Z_exact), linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.plot(np.real(Z_exp), -np.imag(Z_exp), \"o\", markersize=10, color=\"red\", label=\"synth exp\")\n", + "plt.plot(np.real(Z_exp[20:60:10]), -np.imag(Z_exp[20:60:10]), 's', markersize=10, color=\"black\")\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.axis('scaled')\n", + "\n", + "plt.xticks(range(10, 70, 10))\n", + "plt.yticks(range(0, 60, 10))\n", + "plt.gca().set_aspect('equal', adjustable='box')\n", + "plt.xlabel(r'$Z_{\\rm re}/\\Omega$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "# label the frequency points\n", + "plt.annotate(r'$10^{-2}$', xy=(np.real(Z_exp[20]), -np.imag(Z_exp[20])), \n", + " xytext=(np.real(Z_exp[20])-2, 10-np.imag(Z_exp[20])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10^{-1}$', xy=(np.real(Z_exp[30]), -np.imag(Z_exp[30])), \n", + " xytext=(np.real(Z_exp[30])-2, 6-np.imag(Z_exp[30])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$1$', xy=(np.real(Z_exp[40]), -np.imag(Z_exp[40])), \n", + " xytext=(np.real(Z_exp[40]), 10-np.imag(Z_exp[40])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10$', xy=(np.real(Z_exp[50]), -np.imag(Z_exp[50])), \n", + " xytext=(np.real(Z_exp[50])-1, 10-np.imag(Z_exp[50])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3) Compute the optimal hyperparameters" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigma_n, sigma_f, ell\n", + "1.0000290 5.0000028 0.0079106\n", + "1.0000582 5.0000205 0.0135268\n", + "1.0001011 5.0000654 0.0218110\n", + "1.0001540 5.0001736 0.0342186\n", + "1.0001779 5.0004275 0.0527574\n", + "1.0000006 5.0010074 0.0802152\n", + "0.9989934 5.0022977 0.1203504\n", + "0.9950320 5.0050874 0.1780736\n", + "0.9810932 5.0109940 0.2604866\n", + "0.9323377 5.0238470 0.3836633\n", + "0.8036473 5.0473572 0.5451553\n", + "0.8278384 5.0853525 0.7852677\n", + "0.8287949 5.1293254 1.2514261\n", + "0.8303948 5.1721020 1.2189826\n", + "0.8304461 5.2594414 1.2326420\n", + "0.8305238 5.3960799 1.2534148\n", + "0.8305327 5.4070244 1.2546809\n", + "0.8305262 5.4070989 1.2546864\n", + "0.8305267 5.4070910 1.2546867\n", + "Optimization terminated successfully.\n", + " Current function value: 53.657989\n", + " Iterations: 19\n", + " Function evaluations: 20\n", + " Gradient evaluations: 87\n", + " Hessian evaluations: 0\n" + ] + } + ], + "source": [ + "# initialize the parameters for the minimization of the NMLL, see (31) in the manuscript\n", + "sigma_n = 1.0\n", + "sigma_f = 5.0\n", + "ell = 0.001\n", + "\n", + "theta_0 = np.array([sigma_n, sigma_f, ell])\n", + "seq_theta = np.copy(theta_0)\n", + "def print_results(theta):\n", + " global seq_theta\n", + " seq_theta = np.vstack((seq_theta, theta))\n", + " print('{0:.7f} {1:.7f} {2:.7f}'.format(theta[0], theta[1], theta[2]))\n", + "\n", + "print('sigma_n, sigma_f, ell')\n", + "\n", + "# minimize the NMLL L(\\theta) w.r.t sigma_n, sigma_f, ell using the Newton-CG method as implemented in scipy\n", + "# Here we will show one solution to handle the exception that may be raised in np.linalg.cholesky(K_im_full) \n", + "# due to the non-positive definite K_im_full\n", + "# Once the message of \"numpy.linalg.LinAlgError: Matrix is not positive definite\" appears, we modify the theta_0\n", + "# to ensure that the K_im_full becomes positive definite\n", + "\n", + "# the flag to denote whether the K_im_full can be successfully decomposed\n", + "ch_flag = True\n", + "while ch_flag:\n", + " try:\n", + " res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='Newton-CG', \n", + " jac=GP_DRT.grad_NMLL_fct, callback=print_results, options={'disp': True})\n", + " ch_flag = False\n", + " except np.linalg.LinAlgError as err:\n", + " if 'positive definite' in str(err):\n", + " theta_0 = np.abs([sigma_n, sigma_f, ell]) + np.random.random()*np.ones((3))\n", + " \n", + "# collect the optimized parameters\n", + "sigma_n, sigma_f, ell = res.x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4) Core of the GP-DRT" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4a) Compute matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "K = GP_DRT.matrix_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L_im_K = GP_DRT.matrix_L_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L2_im_K = GP_DRT.matrix_L2_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "Sigma = (sigma_n**2)*np.eye(N_freqs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4b) Factorize the matrices and solve the linear equations" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", + "K_im_full = L2_im_K + Sigma\n", + "\n", + "# Cholesky factorization, L is a lower-triangular matrix\n", + "L = np.linalg.cholesky(K_im_full)\n", + "\n", + "# solve for alpha\n", + "alpha = np.linalg.solve(L, Z_exp.imag)\n", + "alpha = np.linalg.solve(L.T, alpha)\n", + "\n", + "# estimate the gamma of eq (21a)\n", + "gamma_fct_est = np.dot(L_im_K, alpha)\n", + "\n", + "# covariance matrix\n", + "inv_L = np.linalg.inv(L)\n", + "inv_K_im_full = np.dot(inv_L.T, inv_L)\n", + "\n", + "# estimate the sigma of gamma for eq (21b)\n", + "cov_gamma_fct_est = K - np.dot(L_im_K, np.dot(inv_K_im_full, L_im_K.T))\n", + "sigma_gamma_fct_est = np.sqrt(np.diag(cov_gamma_fct_est))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4c) Plot the obtained DRT against the analytical DRT" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the DRT and its confidence region\n", + "plt.semilogx(freq_vec_plot, gamma_fct_plot, linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.semilogx(freq_vec, gamma_fct_est, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec, gamma_fct_est-3*sigma_gamma_fct_est, gamma_fct_est+3*sigma_gamma_fct_est, color=\"0.4\", alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E4,-5,25])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$\\gamma/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4d) Predict the $\\gamma$ and the imaginary part of the GP-DRT impedance" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# initialize the imaginary part of impedance vector\n", + "Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "gamma_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_gamma_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "# calculate the imaginary part of impedance at each $\\xi$ point for the plot\n", + "for index, val in enumerate(xi_vec_star):\n", + " xi_star = np.array([val])\n", + "\n", + " # compute matrices shown in eq (23), xi_star corresponds to a new point\n", + " k_star = GP_DRT.matrix_K(xi_vec, xi_star, sigma_f, ell)\n", + " L_im_k_star_up = GP_DRT.matrix_L_im_K(xi_star, xi_vec, sigma_f, ell)\n", + " L2_im_k_star = GP_DRT.matrix_L2_im_K(xi_vec, xi_star, sigma_f, ell)\n", + " k_star_star = GP_DRT.matrix_K(xi_star, xi_star, sigma_f, ell)\n", + " L_im_k_star_star = GP_DRT.matrix_L_im_K(xi_star, xi_star, sigma_f, ell)\n", + " L2_im_k_star_star = GP_DRT.matrix_L2_im_K(xi_star, xi_star, sigma_f, ell)\n", + "\n", + " # compute Z_im_star mean and standard deviation using eq (26)\n", + " Z_im_vec_star[index] = np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_Z_im_vec_star[index] = L2_im_k_star_star-np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, L2_im_k_star))\n", + " \n", + " # compute gamma_star mean and standard deviation using eq (29)\n", + " gamma_vec_star[index] = np.dot(L_im_k_star_up, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_gamma_vec_star[index] = k_star_star-np.dot(L_im_k_star_up, np.dot(inv_K_im_full, L_im_k_star_up.T))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4e) Plot the imaginary part of the GP-DRT impedance together with the exact one and the synthetic experiment" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.semilogx(freq_vec_star, -np.imag(Z_exact), \":\", linewidth=4, color=\"blue\", label=\"exact\")\n", + "plt.semilogx(freq_vec, -Z_exp.imag, \"o\", markersize=10, color=\"black\", label=\"synth exp\")\n", + "plt.semilogx(freq_vec_star, -Z_im_vec_star, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec_star, -Z_im_vec_star-3*np.sqrt(abs(Sigma_Z_im_vec_star)), -Z_im_vec_star+3*np.sqrt(abs(Sigma_Z_im_vec_star)), alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E4,-5,25])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + 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+ }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This tutorial is based on that `ex1_simple_ZARC.ipynb` and we will handle the exception during in the `np.linalg.cholesky(K_im_full)`." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from math import sin, cos, pi\n", + "import GP_DRT\n", + "from scipy.optimize import minimize\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1) Define parameters of the ZARC circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# define the frequency range\n", + "N_freqs = 81\n", + "freq_vec = np.logspace(-4., 4., num=N_freqs, endpoint=True)\n", + "xi_vec = np.log(freq_vec)\n", + "tau = 1/freq_vec\n", + "\n", + "# define the frequency range used for prediction\n", + "# note: we could have used other values\n", + "freq_vec_star = np.logspace(-4., 4., num=81, endpoint=True)\n", + "xi_vec_star = np.log(freq_vec_star)\n", + "\n", + "# parameters for ZARC model, the impedance and analytical DRT are calculated as the above equations\n", + "R_inf = 10\n", + "R_ct = 50\n", + "phi = 0.8\n", + "tau_0 = 1.\n", + "\n", + "C = tau_0**phi/R_ct\n", + "Z_exact = R_inf+1./(1./R_ct+C*(1j*2.*pi*freq_vec)**phi)\n", + "gamma_fct = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau/tau_0))-cos((1.-phi)*pi))\n", + "\n", + "# we will use a finer mesh for plotting the results\n", + "freq_vec_plot = np.logspace(-4., 4., num=10*(N_freqs-1), endpoint=True)\n", + "tau_plot = 1/freq_vec_plot\n", + "# for plotting only\n", + "gamma_fct_plot = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau_plot/tau_0))-cos((1.-phi)*pi))\n", + "\n", + "# we will add noise to the impedance computed analytically\n", + "rng = np.random.seed(214975)\n", + "sigma_n_exp = 1.\n", + "Z_exp = Z_exact + sigma_n_exp*(np.random.normal(0, 1, N_freqs)+1j*np.random.normal(0, 1, N_freqs))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2) Show the synthetic impedance in the Nyquist plot" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "\n", + "# Nyquist plot of the impedance\n", + "plt.plot(np.real(Z_exact), -np.imag(Z_exact), linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.plot(np.real(Z_exp), -np.imag(Z_exp), \"o\", markersize=10, color=\"red\", label=\"synth exp\")\n", + "plt.plot(np.real(Z_exp[20:60:10]), -np.imag(Z_exp[20:60:10]), 's', markersize=10, color=\"black\")\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.axis('scaled')\n", + "\n", + "plt.xticks(range(10, 70, 10))\n", + "plt.yticks(range(0, 60, 10))\n", + "plt.gca().set_aspect('equal', adjustable='box')\n", + "plt.xlabel(r'$Z_{\\rm re}/\\Omega$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "# label the frequency points\n", + "plt.annotate(r'$10^{-2}$', xy=(np.real(Z_exp[20]), -np.imag(Z_exp[20])), \n", + " xytext=(np.real(Z_exp[20])-2, 10-np.imag(Z_exp[20])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10^{-1}$', xy=(np.real(Z_exp[30]), -np.imag(Z_exp[30])), \n", + " xytext=(np.real(Z_exp[30])-2, 6-np.imag(Z_exp[30])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$1$', xy=(np.real(Z_exp[40]), -np.imag(Z_exp[40])), \n", + " xytext=(np.real(Z_exp[40]), 10-np.imag(Z_exp[40])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10$', xy=(np.real(Z_exp[50]), -np.imag(Z_exp[50])), \n", + " xytext=(np.real(Z_exp[50])-1, 10-np.imag(Z_exp[50])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3) Compute the optimal hyperparameters" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigma_n, sigma_f, ell\n", + "1.0000290 5.0000028 0.0079106\n", + "1.0000582 5.0000205 0.0135268\n", + "1.0001011 5.0000654 0.0218110\n", + "1.0001540 5.0001736 0.0342186\n", + "1.0001779 5.0004275 0.0527574\n", + "1.0000006 5.0010074 0.0802152\n", + "0.9989934 5.0022977 0.1203504\n", + "0.9950320 5.0050874 0.1780736\n", + "0.9810932 5.0109940 0.2604866\n", + "0.9323377 5.0238470 0.3836633\n", + "0.8036473 5.0473572 0.5451553\n", + "0.8278384 5.0853525 0.7852677\n", + "0.8287949 5.1293254 1.2514261\n", + "0.8303948 5.1721020 1.2189826\n", + "0.8304461 5.2594414 1.2326420\n", + "0.8305238 5.3960799 1.2534148\n", + "0.8305327 5.4070244 1.2546809\n", + "0.8305262 5.4070989 1.2546864\n", + "0.8305267 5.4070910 1.2546867\n", + "Optimization terminated successfully.\n", + " Current function value: 53.657989\n", + " Iterations: 19\n", + " Function evaluations: 20\n", + " Gradient evaluations: 87\n", + " Hessian evaluations: 0\n" + ] + } + ], + "source": [ + "# initialize the parameters for the minimization of the NMLL, see (31) in the manuscript\n", + "sigma_n = 1.0\n", + "sigma_f = 5.0\n", + "ell = 0.001\n", + "\n", + "theta_0 = np.array([sigma_n, sigma_f, ell])\n", + "seq_theta = np.copy(theta_0)\n", + "def print_results(theta):\n", + " global seq_theta\n", + " seq_theta = np.vstack((seq_theta, theta))\n", + " print('{0:.7f} {1:.7f} {2:.7f}'.format(theta[0], theta[1], theta[2]))\n", + "\n", + "print('sigma_n, sigma_f, ell')\n", + "\n", + "# minimize the NMLL L(\\theta) w.r.t sigma_n, sigma_f, ell using the Newton-CG method as implemented in scipy\n", + "# Here we will show one solution to handle the exception that may be raised in np.linalg.cholesky(K_im_full) \n", + "# due to the non-positive definite K_im_full\n", + "# Once the message of \"numpy.linalg.LinAlgError: Matrix is not positive definite\" appears, we modify the theta_0\n", + "# to ensure that the K_im_full becomes positive definite\n", + "\n", + "# the flag to denote whether the K_im_full can be successfully decomposed\n", + "ch_flag = True\n", + "while ch_flag:\n", + " try:\n", + " res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='Newton-CG', \n", + " jac=GP_DRT.grad_NMLL_fct, callback=print_results, options={'disp': True})\n", + " ch_flag = False\n", + " except np.linalg.LinAlgError as err:\n", + " if 'positive definite' in str(err):\n", + " theta_0 = np.abs([sigma_n, sigma_f, ell]) + np.random.random()*np.ones((3))\n", + " \n", + "# collect the optimized parameters\n", + "sigma_n, sigma_f, ell = res.x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4) Core of the GP-DRT" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4a) Compute matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "K = GP_DRT.matrix_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L_im_K = GP_DRT.matrix_L_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L2_im_K = GP_DRT.matrix_L2_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "Sigma = (sigma_n**2)*np.eye(N_freqs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4b) Factorize the matrices and solve the linear equations" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", + "K_im_full = L2_im_K + Sigma\n", + "\n", + "# Cholesky factorization, L is a lower-triangular matrix\n", + "L = np.linalg.cholesky(K_im_full)\n", + "\n", + "# solve for alpha\n", + "alpha = np.linalg.solve(L, Z_exp.imag)\n", + "alpha = np.linalg.solve(L.T, alpha)\n", + "\n", + "# estimate the gamma of eq (21a)\n", + "gamma_fct_est = np.dot(L_im_K, alpha)\n", + "\n", + "# covariance matrix\n", + "inv_L = np.linalg.inv(L)\n", + "inv_K_im_full = np.dot(inv_L.T, inv_L)\n", + "\n", + "# estimate the sigma of gamma for eq (21b)\n", + "cov_gamma_fct_est = K - np.dot(L_im_K, np.dot(inv_K_im_full, L_im_K.T))\n", + "sigma_gamma_fct_est = np.sqrt(np.diag(cov_gamma_fct_est))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4c) Plot the obtained DRT against the analytical DRT" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the DRT and its confidence region\n", + "plt.semilogx(freq_vec_plot, gamma_fct_plot, linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.semilogx(freq_vec, gamma_fct_est, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec, gamma_fct_est-3*sigma_gamma_fct_est, gamma_fct_est+3*sigma_gamma_fct_est, color=\"0.4\", alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E4,-5,25])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$\\gamma/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4d) Predict the $\\gamma$ and the imaginary part of the GP-DRT impedance" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# initialize the imaginary part of impedance vector\n", + "Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "gamma_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_gamma_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "# calculate the imaginary part of impedance at each $\\xi$ point for the plot\n", + "for index, val in enumerate(xi_vec_star):\n", + " xi_star = np.array([val])\n", + "\n", + " # compute matrices shown in eq (23), xi_star corresponds to a new point\n", + " k_star = GP_DRT.matrix_K(xi_vec, xi_star, sigma_f, ell)\n", + " L_im_k_star_up = GP_DRT.matrix_L_im_K(xi_star, xi_vec, sigma_f, ell)\n", + " L2_im_k_star = GP_DRT.matrix_L2_im_K(xi_vec, xi_star, sigma_f, ell)\n", + " k_star_star = GP_DRT.matrix_K(xi_star, xi_star, sigma_f, ell)\n", + " L_im_k_star_star = GP_DRT.matrix_L_im_K(xi_star, xi_star, sigma_f, ell)\n", + " L2_im_k_star_star = GP_DRT.matrix_L2_im_K(xi_star, xi_star, sigma_f, ell)\n", + "\n", + " # compute Z_im_star mean and standard deviation using eq (26)\n", + " Z_im_vec_star[index] = np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_Z_im_vec_star[index] = L2_im_k_star_star-np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, L2_im_k_star))\n", + " \n", + " # compute gamma_star mean and standard deviation using eq (29)\n", + " gamma_vec_star[index] = np.dot(L_im_k_star_up, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_gamma_vec_star[index] = k_star_star-np.dot(L_im_k_star_up, np.dot(inv_K_im_full, L_im_k_star_up.T))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4e) Plot the imaginary part of the GP-DRT impedance together with the exact one and the synthetic experiment" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.semilogx(freq_vec_star, -np.imag(Z_exact), \":\", linewidth=4, color=\"blue\", label=\"exact\")\n", + "plt.semilogx(freq_vec, -Z_exp.imag, \"o\", markersize=10, color=\"black\", label=\"synth exp\")\n", + "plt.semilogx(freq_vec_star, -Z_im_vec_star, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec_star, -Z_im_vec_star-3*np.sqrt(abs(Sigma_Z_im_vec_star)), -Z_im_vec_star+3*np.sqrt(abs(Sigma_Z_im_vec_star)), alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E4,-5,25])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + } + ], + "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": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 6b608efcfefb94bb3b64ef72d9a35e405f1d6eaa Mon Sep 17 00:00:00 2001 From: LIU Date: Fri, 6 Aug 2021 10:23:30 +0800 Subject: [PATCH 2/5] fixed the error in cholesky decomposition --- .../ex1_single_ZARC-checkpoint.ipynb | 515 ++++++++++++++++++ .../ex2_double_ZARC-checkpoint.ipynb | 429 +++++++++++++++ .../ex3_truncated_ZARC-checkpoint.ipynb | 410 ++++++++++++++ .../ex4_experiment-checkpoint.ipynb | 446 +++++++++++++++ .../ex5_inductance_plus_ZARC-checkpoint.ipynb | 452 +++++++++++++++ tutorials/GP_DRT.py | 79 ++- tutorials/__pycache__/GP_DRT.cpython-38.pyc | Bin 6742 -> 7571 bytes tutorials/ex1_single_ZARC.ipynb | 30 +- tutorials/ex2_double_ZARC.ipynb | 32 +- tutorials/ex3_truncated_ZARC.ipynb | 34 +- tutorials/ex4_experiment.ipynb | 21 +- tutorials/ex5_inductance_plus_ZARC.ipynb | 12 +- tutorials/ex6_exception_handling.ipynb | 42 +- 13 files changed, 2428 insertions(+), 74 deletions(-) create mode 100644 tutorials/.ipynb_checkpoints/ex1_single_ZARC-checkpoint.ipynb create mode 100644 tutorials/.ipynb_checkpoints/ex2_double_ZARC-checkpoint.ipynb create mode 100644 tutorials/.ipynb_checkpoints/ex3_truncated_ZARC-checkpoint.ipynb create mode 100644 tutorials/.ipynb_checkpoints/ex4_experiment-checkpoint.ipynb create mode 100644 tutorials/.ipynb_checkpoints/ex5_inductance_plus_ZARC-checkpoint.ipynb diff --git a/tutorials/.ipynb_checkpoints/ex1_single_ZARC-checkpoint.ipynb b/tutorials/.ipynb_checkpoints/ex1_single_ZARC-checkpoint.ipynb new file mode 100644 index 0000000..eb88848 --- /dev/null +++ b/tutorials/.ipynb_checkpoints/ex1_single_ZARC-checkpoint.ipynb @@ -0,0 +1,515 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gaussian Process Distribution of Relaxation Times" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## In this tutorial we will reproduce Figure 7 of the article https://doi.org/10.1016/j.electacta.2019.135316\n", + "\n", + "GP-DRT is our newly developed approach that can be used to obtain both the mean and covariance of the DRT from EIS data by assuming that the DRT is a Gaussian process (GP). The GP-DRP can predict the DRT and the imaginary part of the impedance at frequencies that were not previously measured.\n", + "\n", + "To obtain the DRT from the impedance we take that $\\gamma(\\xi)$ is a GP where $f$ is the frequency and $\\xi=\\log f$. Under the DRT model and considering that GPs are closed linear transformations, it follows that $Z^{\\rm DRT}_{\\rm im}\\left(\\xi\\right)$ is also a GP.\n", + "\n", + "In other words, we can write\n", + "\n", + "$$\\begin{pmatrix}\n", + "\\gamma(\\xi) \\\\\n", + "Z^{\\rm DRT}_{\\rm im}\\left(\\xi\\right)\n", + "\\end{pmatrix}\\sim \\mathcal{GP}\\left(\\mathbf 0, \\begin{pmatrix}\n", + "k(\\xi, \\xi^\\prime) & \\mathcal L^{\\rm im}_{\\xi^\\prime} \\left(k(\\xi, \\xi^\\prime)\\right)\\\\\n", + "\\mathcal L^{\\rm im}_{\\xi} k(\\xi, \\xi^\\prime) & \\mathcal L^{\\rm im}_{\\xi^\\prime}\\left(\\mathcal L^{\\rm im}_{\\xi} \\left(k(\\xi, \\xi^\\prime)\\right)\\right)\n", + "\\end{pmatrix}\\right)$$\n", + "\n", + "where\n", + "\n", + "$$\\mathcal L^{\\rm im}_\\xi \\left(\\cdot\\right) = -\\displaystyle \\int_{-\\infty}^\\infty \\frac{2\\pi \\displaystyle e^{\\xi-\\hat \\xi}}{1+\\left(2\\pi \\displaystyle e^{\\xi-\\hat \\xi}\\right)^2} \\left(\\cdot\\right) d \\hat \\xi$$\n", + "\n", + "is a linear functional. The latter functional, maps the DRT to the imaginary part of the impedance.\n", + "\n", + "Assuming $N$ observations, we can set $\\left(\\mathbf Z^{\\rm exp}_{\\rm im}\\right)_n = Z^{\\rm exp}_{\\rm im}(\\xi_n)$ with $\\xi_n =\\log f_n$ and $n =1, 2, \\ldots N $. The corresponding multivariate Gaussian random variable can be written as \n", + "\n", + "$$\\begin{pmatrix}\n", + "\\boldsymbol{\\gamma} \\\\\n", + "\\mathbf Z^{\\rm exp}_{\\rm im}\n", + "\\end{pmatrix}\\sim \\mathcal{N}\\left(\\mathbf 0, \\begin{pmatrix}\n", + "\\mathbf K & \\mathcal L_{\\rm im} \\mathbf K\\\\\n", + "\\mathcal L_{\\rm im}^\\sharp \\mathbf K & \\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I\n", + "\\end{pmatrix}\\right)$$\n", + "\n", + "where \n", + "\n", + "$$\\begin{align}\n", + "(\\mathbf K)_{nm} &= k(\\xi_n, \\xi_m)\\\\\n", + "(\\mathcal L_{\\rm im} \\mathbf K)_{nm} &= \\left. \\mathcal L^{\\rm im}_{\\xi^\\prime} \\left(k(\\xi, \\xi^\\prime)\\right) \\right |_{\\xi_n, \\xi_m}\\\\\n", + "(\\mathcal L_{\\rm im}^\\sharp \\mathbf K)_{nm} &= \\left.\\mathcal L^{\\rm im}_{\\xi} \\left(k(\\xi, \\xi^\\prime)\\right) \\right|_{\\xi_n, \\xi_m}\\\\\n", + "(\\mathcal L^2_{\\rm im} \\mathbf K)_{nm} &= \\left.\\mathcal L^{\\rm im}_{\\xi^\\prime}\\left(\\mathcal L^{\\rm im}_{\\xi} \\left(k(\\xi, \\xi^\\prime)\\right)\\right) \\right|_{\\xi_n, \\xi_m}\n", + "\\end{align}$$\n", + "\n", + "and $\\mathcal L_{\\rm im} \\mathbf K^\\top = \\mathcal L_{\\rm im}^\\sharp \\mathbf K$.\n", + "\n", + "To obtain the DRT from impedance, the distribution of $\\mathbf{\\gamma}$ conditioned on $\\mathbf Z^{\\rm exp}_{\\rm im}$ can be written as\n", + "\n", + "$$\\boldsymbol{\\gamma}|\\mathbf Z^{\\rm exp}_{\\rm im}\\sim \\mathcal N\\left( \\mathbf \\mu_{\\gamma|Z^{\\rm exp}_{\\rm im}}, \\mathbf\\Sigma_{\\gamma| Z^{\\rm exp}_{\\rm im}}\\right)$$\n", + "\n", + "with\n", + "\n", + "$$\\begin{align}\n", + "\\mathbf \\mu_{\\gamma|Z^{\\rm exp}_{\\rm im}} &= \\mathcal L_{\\rm im} \\mathbf K \\left(\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I \\right)^{-1} \\mathbf Z^{\\rm exp}_{\\rm im} \\\\\n", + "\\mathbf \\Sigma_{\\gamma| Z^{\\rm exp}_{\\rm im}} &= \\mathbf K- \\mathcal L_{\\rm im} \\mathbf K \\left(\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I \\right)^{-1}\\mathcal L_{\\rm im} \\mathbf K^\\top\n", + "\\end{align}$$\n", + "\n", + "The above formulas depend on 1) the kernel, $k(\\xi, \\xi^\\prime)$; 2) the noise level, $\\sigma_n$; and 3) the experimental data, $\\mathbf Z^{\\rm exp}_{\\rm im}$ (at the log-frequencies $\\mathbf \\xi$). " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from math import sin, cos, pi\n", + "import GP_DRT\n", + "from scipy.optimize import minimize\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1) Define parameters of the ZARC circuit which will be used for the synthetic experiment generation\n", + "\n", + "The impedance of a ZARC can be written as\n", + "$$\n", + "Z^{\\rm exact}(f) = R_\\infty + \\displaystyle \\frac{1}{\\displaystyle \\frac{1}{R_{\\rm ct}}+C \\left(i 2\\pi f\\right)^\\phi}\n", + "$$\n", + "\n", + "where $\\displaystyle C = \\frac{\\tau_0^\\phi}{R_{\\rm ct}}$.\n", + "\n", + "The corresponding DRT is given by\n", + "\n", + "$$\n", + "\\gamma(\\log \\tau) = \\displaystyle \\frac{\\displaystyle R_{\\rm ct}}{\\displaystyle 2\\pi} \\displaystyle \\frac{\\displaystyle \\sin\\left((1-\\phi)\\pi\\right)}{\\displaystyle \\cosh(\\phi \\log(\\tau/\\tau_0))-\\cos(\\pi(1-\\phi))}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# define the frequency range\n", + "N_freqs = 81\n", + "freq_vec = np.logspace(-4., 4., num=N_freqs, endpoint=True)\n", + "xi_vec = np.log(freq_vec)\n", + "tau = 1/freq_vec\n", + "\n", + "# define the frequency range used for prediction\n", + "# note: we could have used other values\n", + "freq_vec_star = np.logspace(-4., 4., num=81, endpoint=True)\n", + "xi_vec_star = np.log(freq_vec_star)\n", + "\n", + "# parameters for ZARC model, the impedance and analytical DRT are calculated as the above equations\n", + "R_inf = 10\n", + "R_ct = 50\n", + "phi = 0.8\n", + "tau_0 = 1.\n", + "\n", + "C = tau_0**phi/R_ct\n", + "Z_exact = R_inf+1./(1./R_ct+C*(1j*2.*pi*freq_vec)**phi)\n", + "gamma_fct = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau/tau_0))-cos((1.-phi)*pi))\n", + "\n", + "# we will use a finer mesh for plotting the results\n", + "freq_vec_plot = np.logspace(-4., 4., num=10*(N_freqs-1), endpoint=True)\n", + "tau_plot = 1/freq_vec_plot\n", + "# for plotting only\n", + "gamma_fct_plot = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau_plot/tau_0))-cos((1.-phi)*pi))\n", + "\n", + "# we will add noise to the impedance computed analytically\n", + "rng = np.random.seed(214975)\n", + "sigma_n_exp = 1.\n", + "Z_exp = Z_exact + sigma_n_exp*(np.random.normal(0, 1, N_freqs)+1j*np.random.normal(0, 1, N_freqs))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2) Show the synthetic impedance in the Nyquist plot - this is similar to Figure 7 (a)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "\n", + "# Nyquist plot of the impedance\n", + "plt.plot(np.real(Z_exact), -np.imag(Z_exact), linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.plot(np.real(Z_exp), -np.imag(Z_exp), \"o\", markersize=10, color=\"red\", label=\"synth exp\")\n", + "plt.plot(np.real(Z_exp[20:60:10]), -np.imag(Z_exp[20:60:10]), 's', markersize=10, color=\"black\")\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.axis('scaled')\n", + "\n", + "plt.xticks(range(10, 70, 10))\n", + "plt.yticks(range(0, 60, 10))\n", + "plt.gca().set_aspect('equal', adjustable='box')\n", + "plt.xlabel(r'$Z_{\\rm re}/\\Omega$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "# label the frequency points\n", + "plt.annotate(r'$10^{-2}$', xy=(np.real(Z_exp[20]), -np.imag(Z_exp[20])), \n", + " xytext=(np.real(Z_exp[20])-2, 10-np.imag(Z_exp[20])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10^{-1}$', xy=(np.real(Z_exp[30]), -np.imag(Z_exp[30])), \n", + " xytext=(np.real(Z_exp[30])-2, 6-np.imag(Z_exp[30])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$1$', xy=(np.real(Z_exp[40]), -np.imag(Z_exp[40])), \n", + " xytext=(np.real(Z_exp[40]), 10-np.imag(Z_exp[40])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10$', xy=(np.real(Z_exp[50]), -np.imag(Z_exp[50])), \n", + " xytext=(np.real(Z_exp[50])-1, 10-np.imag(Z_exp[50])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3) Obtain the optimal hyperparameters of the GP-DRT model by minimizing the negative marginal log-likelihood (NMLL)\n", + "\n", + "We constrain the kernel to be a squared exponential, _i.e._,\n", + "\n", + "$$\n", + "k(\\xi, \\xi^\\prime) = \\sigma_f^2 \\exp\\left(-\\frac{1}{2 \\ell^2}\\left(\\xi-\\xi^\\prime\\right)^2 \\right)\n", + "$$\n", + "\n", + "and optimize its two parameters, $\\sigma_f$ and $\\ell$ as well as the noise level $\\sigma_n$. Therefore, the vector of GP-DRT hyperparameters is $\\boldsymbol \\theta = \\begin{pmatrix} \\sigma_n, \\sigma_f, \\ell \\end{pmatrix}^\\top$.\n", + "\n", + "Following the article, we can write that\n", + "\n", + "$$\n", + "\\log p(\\mathbf Z^{\\rm exp}_{\\rm im}|\\boldsymbol \\xi, \\boldsymbol \\theta)= - \\frac{1}{2} {\\mathbf Z^{\\rm exp}_{\\rm im}}^\\top \\left(\\mathcal L^2_{\\rm im} \\mathbf K +\\sigma_n^2\\mathbf I \\right)^{-1} \\mathbf Z^{\\rm exp}_{\\rm im} -\\frac{1}{2} \\log \\left| \\mathcal L^2_{\\rm im} \\mathbf K+\\sigma_n^2\\mathbf I \\right| - \\frac{N}{2} \\log 2\\pi\n", + "$$\n", + "\n", + "We will call $L(\\boldsymbol \\theta)$ the negative (and shifted) MLL (NMLL):\n", + "$$\n", + "L(\\boldsymbol \\theta) = - \\log p(\\mathbf Z^{\\rm exp}_{\\rm im}|\\boldsymbol \\xi, \\boldsymbol \\theta) - \\frac{N}{2} \\log 2\\pi\n", + "$$\n", + "\n", + "the experimental evidence is maximized for\n", + "\n", + "$$\n", + "\\boldsymbol \\theta = \\arg \\min_{\\boldsymbol \\theta^\\prime}L(\\boldsymbol \\theta^\\prime)\n", + "$$\n", + "\n", + "The above minimization problem is solved using the `optimize` function given in `scipy`" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigma_n, sigma_f, ell\n", + "0.8903599 5.0014151 1.0120875\n", + "0.8136354 5.0035337 1.0291912\n", + "0.8291863 5.0357867 1.2588673\n", + "0.8303934 5.0832372 1.2117784\n", + "0.8304464 5.2060761 1.2283664\n", + "0.8305219 5.3874435 1.2524151\n", + "0.8305286 5.4068909 1.2546651\n", + "0.8305276 5.4070863 1.2546870\n", + "0.8305265 5.4070865 1.2546866\n", + "Optimization terminated successfully.\n", + " Current function value: 53.657989\n", + " Iterations: 9\n", + " Function evaluations: 11\n", + " Gradient evaluations: 54\n", + " Hessian evaluations: 0\n" + ] + } + ], + "source": [ + "# initialize the parameters for the minimization of the NMLL, see (31) in the manuscript\n", + "sigma_n = sigma_n_exp\n", + "sigma_f = 5.\n", + "ell = 1.\n", + "\n", + "theta_0 = np.array([sigma_n, sigma_f, ell])\n", + "seq_theta = np.copy(theta_0)\n", + "def print_results(theta):\n", + " global seq_theta\n", + " seq_theta = np.vstack((seq_theta, theta))\n", + " print('{0:.7f} {1:.7f} {2:.7f}'.format(theta[0], theta[1], theta[2]))\n", + "\n", + "print('sigma_n, sigma_f, ell')\n", + "\n", + "# minimize the NMLL L(\\theta) w.r.t sigma_n, sigma_f, ell using the Newton-CG method as implemented in scipy\n", + "res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='Newton-CG', \\\n", + " jac=GP_DRT.grad_NMLL_fct, callback=print_results, options={'disp': True})\n", + "\n", + "# collect the optimized parameters\n", + "sigma_n, sigma_f, ell = res.x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4) Core of the GP-DRT" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4a) Compute matrices\n", + "Once we have identified the optimized parameters we can compute $\\mathbf K$, $\\mathcal L_{\\rm im} \\mathbf K$, and $\\mathcal L^2_{\\rm im} \\mathbf K$, which are given in equation (18) in the article" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "K = GP_DRT.matrix_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L_im_K = GP_DRT.matrix_L_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L2_im_K = GP_DRT.matrix_L2_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "Sigma = (sigma_n**2)*np.eye(N_freqs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4b) Factorize the matrices and solve the linear equations\n", + "We are computing\n", + "$$\n", + "\\boldsymbol{\\gamma}|\\mathbf Z^{\\rm exp}_{\\rm im}\\sim \\mathcal N\\left( \\boldsymbol \\mu_{\\gamma|Z^{\\rm exp}_{\\rm im}}, \\boldsymbol \\Sigma_{\\gamma| Z^{\\rm exp}_{\\rm im}}\\right)\n", + "$$\n", + "\n", + "using \n", + "$$\n", + "\\begin{align}\n", + "\\boldsymbol \\mu_{\\gamma|Z^{\\rm exp}_{\\rm im}} &= \\mathcal L_{\\rm im} \\mathbf K\\left(\\mathcal L^2_{\\rm im} \\mathbf K+\\sigma_n^2\\mathbf I\\right)^{-1}\\mathbf Z^{\\rm exp}_{\\rm im} \\\\\n", + "\\boldsymbol \\Sigma_{\\gamma| Z^{\\rm exp}_{\\rm im}} &= \\mathbf K-\\mathcal L_{\\rm im} \\mathbf K\\left(\\mathcal L^2_{\\rm im} \\mathbf K+\\sigma_n^2\\mathbf I\\right)^{-1}\\mathcal L_{\\rm im} \\mathbf K^\\top\n", + "\\end{align}\n", + "$$\n", + "\n", + "The key step is to do Cholesky factorization of $\\mathcal L^2_{\\rm im} \\mathbf K+\\sigma_n^2\\mathbf I$, _i.e._, K_im_full" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", + "K_im_full = L2_im_K + Sigma\n", + "\n", + "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", + "if not GP_DRT.is_PD(K_im_full):\n", + " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", + "\n", + "# Cholesky factorization, L is a lower-triangular matrix\n", + "L = np.linalg.cholesky(K_im_full)\n", + "\n", + "# solve for alpha\n", + "alpha = np.linalg.solve(L, Z_exp.imag)\n", + "alpha = np.linalg.solve(L.T, alpha)\n", + "\n", + "# estimate the gamma of eq (21a)\n", + "gamma_fct_est = np.dot(L_im_K, alpha)\n", + "\n", + "# covariance matrix\n", + "inv_L = np.linalg.inv(L)\n", + "inv_K_im_full = np.dot(inv_L.T, inv_L)\n", + "\n", + "# estimate the sigma of gamma for eq (21b)\n", + "cov_gamma_fct_est = K - np.dot(L_im_K, np.dot(inv_K_im_full, L_im_K.T))\n", + "sigma_gamma_fct_est = np.sqrt(np.diag(cov_gamma_fct_est))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4c) Plot the obtained DRT against the analytical DRT" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the DRT and its confidence region\n", + "plt.semilogx(freq_vec_plot, gamma_fct_plot, linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.semilogx(freq_vec, gamma_fct_est, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec, gamma_fct_est-3*sigma_gamma_fct_est, gamma_fct_est+3*sigma_gamma_fct_est, color=\"0.4\", alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E4,-5,25])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$\\gamma/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4d) Predict the $\\gamma$ and the imaginary part of the GP-DRT impedance\n", + "\n", + "#### This part is explained in Section 2.3.3 of the main article" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# initialize the imaginary part of impedance vector\n", + "Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "gamma_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_gamma_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "# calculate the imaginary part of impedance at each $\\xi$ point for the plot\n", + "for index, val in enumerate(xi_vec_star):\n", + " xi_star = np.array([val])\n", + "\n", + " # compute matrices shown in eq (23), xi_star corresponds to a new point\n", + " k_star = GP_DRT.matrix_K(xi_vec, xi_star, sigma_f, ell)\n", + " L_im_k_star_up = GP_DRT.matrix_L_im_K(xi_star, xi_vec, sigma_f, ell)\n", + " L2_im_k_star = GP_DRT.matrix_L2_im_K(xi_vec, xi_star, sigma_f, ell)\n", + " k_star_star = GP_DRT.matrix_K(xi_star, xi_star, sigma_f, ell)\n", + " L_im_k_star_star = GP_DRT.matrix_L_im_K(xi_star, xi_star, sigma_f, ell)\n", + " L2_im_k_star_star = GP_DRT.matrix_L2_im_K(xi_star, xi_star, sigma_f, ell)\n", + "\n", + " # compute Z_im_star mean and standard deviation using eq (26)\n", + " Z_im_vec_star[index] = np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_Z_im_vec_star[index] = L2_im_k_star_star-np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, L2_im_k_star))\n", + " \n", + " # compute gamma_star mean and standard deviation using eq (29)\n", + " gamma_vec_star[index] = np.dot(L_im_k_star_up, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_gamma_vec_star[index] = k_star_star-np.dot(L_im_k_star_up, np.dot(inv_K_im_full, L_im_k_star_up.T))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4e) Plot the imaginary part of the GP-DRT impedance together with the exact one and the synthetic experiment" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.semilogx(freq_vec_star, -np.imag(Z_exact), \":\", linewidth=4, color=\"blue\", label=\"exact\")\n", + "plt.semilogx(freq_vec, -Z_exp.imag, \"o\", markersize=10, color=\"black\", label=\"synth exp\")\n", + "plt.semilogx(freq_vec_star, -Z_im_vec_star, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec_star, -Z_im_vec_star-3*np.sqrt(abs(Sigma_Z_im_vec_star)), -Z_im_vec_star+3*np.sqrt(abs(Sigma_Z_im_vec_star)), alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E4,-5,25])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + } + ], + "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": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tutorials/.ipynb_checkpoints/ex2_double_ZARC-checkpoint.ipynb b/tutorials/.ipynb_checkpoints/ex2_double_ZARC-checkpoint.ipynb new file mode 100644 index 0000000..6c91663 --- /dev/null +++ b/tutorials/.ipynb_checkpoints/ex2_double_ZARC-checkpoint.ipynb @@ -0,0 +1,429 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gaussian Process Distribution of Relaxation Times. \n", + "## In this tutorial we will reproduce Figure 9 of the article https://doi.org/10.1016/j.electacta.2019.135316Reproduce\n", + "\n", + "This tutorial shows how the GP-DRT model can manage overlapping timescales, where the impedance was generated using two ZARC elements in series. " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from math import sin, cos, pi\n", + "import GP_DRT\n", + "from scipy.optimize import minimize\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1) Define parameters for the synthetic impedance based on two ZARCs in series. \n", + "\n", + "The impedance has the format of \n", + "\n", + "$$\n", + "Z^{\\rm exact}(f) = 2R_\\infty + \\displaystyle \\frac{1}{\\displaystyle \\frac{1}{R_{\\rm ct}}+C_1 \\left(i 2\\pi f\\right)^{\\phi}} + \\displaystyle \\frac{1}{\\displaystyle\\frac{1}{R_{\\rm ct}}+C_2 \\left(i 2\\pi f\\right)^{\\phi}}\n", + "$$ \n", + "where $\\displaystyle C_1 = \\frac{\\tau_1^\\phi}{R_{\\rm ct}}$ and $\\displaystyle C_2 = \\frac{\\tau_2^\\phi}{R_{\\rm ct}}$\n", + "\n", + "In this tutorial, $\\tau_1=0.1$ and $\\tau_2=10$\n", + "\n", + "The analytical DRT is calculated as \n", + "\n", + "$$\n", + "\\gamma(\\log \\tau) = \\displaystyle \\frac{\\displaystyle R_{\\rm ct}}{\\displaystyle 2\\pi} \\sin\\left((1-\\phi)\\pi\\right) \\displaystyle \\left(\\frac{1 }{\\displaystyle \\cosh(\\phi \\log(\\tau/\\tau_1))-\\cos(\\pi(1-\\phi))} + \\displaystyle \\frac{1}{\\displaystyle \\cosh(\\phi \\log(\\tau/\\tau_2))-\\cos(\\pi(1-\\phi))}\\right)\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# define the frequency range\n", + "N_freqs = 81\n", + "freq_vec = np.logspace(-4., 4., num=N_freqs, endpoint=True)\n", + "xi_vec = np.log(freq_vec)\n", + "tau = 1/freq_vec\n", + "\n", + "# define the frequency range used for prediction\n", + "freq_vec_star = np.logspace(-4., 4., num=81, endpoint=True)\n", + "xi_vec_star = np.log(freq_vec_star)\n", + "\n", + "# parameters for two ZARCs in series, the impedance, and the analytical DRT are calculated as the above equations\n", + "R_inf = 10\n", + "R_ct = 50\n", + "phi = 0.8\n", + "tau_1 = 0.1\n", + "tau_2 = 10\n", + "\n", + "C_1 = tau_1**phi/R_ct\n", + "C_2 = tau_2**phi/R_ct\n", + "\n", + "Z_exact = 2*R_inf + 1./(1./R_ct+C_1*(1j*2.*pi*freq_vec)**phi) + 1./(1./R_ct+C_2*(1j*2.*pi*freq_vec)**phi)\n", + "gamma_fct = (R_ct)/(2.*pi)*sin((1.-phi)*pi)*(1/(np.cosh(phi*np.log(tau/tau_1))-cos((1.-phi)*pi)) +\\\n", + " 1/(np.cosh(phi*np.log(tau/tau_2))-cos((1.-phi)*pi)))\n", + "\n", + "# used for plotting only\n", + "freq_vec_plot = np.logspace(-4., 4., num=10*(N_freqs-1), endpoint=True)\n", + "tau_plot = 1/freq_vec_plot\n", + "gamma_fct_plot = (R_ct)/(2.*pi)*sin((1.-phi)*pi)*(1/(np.cosh(phi*np.log(tau_plot/tau_1))-cos((1.-phi)*pi)) +\\\n", + " 1/(np.cosh(phi*np.log(tau_plot/tau_2))-cos((1.-phi)*pi)))\n", + "# adding random noise to the synthetic data\n", + "rng = np.random.seed(214975)\n", + "sigma_n_exp = 0.1\n", + "Z_exp = Z_exact + sigma_n_exp*(np.random.normal(0, 1, N_freqs)+1j*np.random.normal(0, 1, N_freqs))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2) show the synthetic impedance in the Nyquist plot. Note: this is similar to Figure 9 (a)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "\n", + "# Nyquist plot of the impedance\n", + "fig, ax = plt.subplots()\n", + "plt.plot(np.real(Z_exact), -np.imag(Z_exact), linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.plot(np.real(Z_exp), -np.imag(Z_exp), \"o\", markersize=10, color=\"red\", label=\"synth exp\")\n", + "plt.plot(np.real(Z_exp[10:70:10]), -np.imag(Z_exp[10:70:10]), 's', markersize=10, color=\"black\")\n", + "\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.axis('scaled')\n", + "\n", + "plt.xticks(range(10, 150, 10))\n", + "plt.yticks(range(0, 60, 10))\n", + "plt.gca().set_aspect('equal', adjustable='box')\n", + "plt.xlabel(r'$Z_{\\rm re}/\\Omega$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "\n", + "# label points with frequency\n", + "plt.annotate(r'$10^{-3}$', xy=(np.real(Z_exp[10]), -np.imag(Z_exp[10])), \n", + " xytext=(np.real(Z_exp[10])+10, 5-np.imag(Z_exp[10])), \n", + " arrowprops=dict(arrowstyle=\"-\", connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10^{-2}$', xy=(np.real(Z_exp[20]), -np.imag(Z_exp[20])), \n", + " xytext=(np.real(Z_exp[20])+10, 5-np.imag(Z_exp[20])), \n", + " arrowprops=dict(arrowstyle=\"-\", connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10^{-1}$', xy=(np.real(Z_exp[30]), -np.imag(Z_exp[30])), \n", + " xytext=(np.real(Z_exp[30])-5, 10-np.imag(Z_exp[30])), \n", + " arrowprops=dict(arrowstyle=\"-\", connectionstyle=\"arc\"))\n", + "plt.annotate(r'$1$', xy=(np.real(Z_exp[40]), -np.imag(Z_exp[40])), \n", + " xytext=(np.real(Z_exp[40])-5, 10-np.imag(Z_exp[40])), \n", + " arrowprops=dict(arrowstyle=\"-\", connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10$', xy=(np.real(Z_exp[50]), -np.imag(Z_exp[50])), \n", + " xytext=(np.real(Z_exp[50])-5, 10-np.imag(Z_exp[50])), \n", + " arrowprops=dict(arrowstyle=\"-\", connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10^2$', xy=(np.real(Z_exp[60]), -np.imag(Z_exp[60])), \n", + " xytext=(np.real(Z_exp[60])-5, 10-np.imag(Z_exp[60])), \n", + " arrowprops=dict(arrowstyle=\"-\", connectionstyle=\"arc\"))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3) Compute the optimal hyperparameters" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigma_n, sigma_f, ell\n", + "0.0811204 5.0008041 0.9965226\n", + "0.0867785 5.0011230 0.9948113\n", + "0.0859594 5.0061593 0.9701405\n", + "0.0844965 5.0183275 0.9169197\n", + "0.0824855 5.0565844 0.7970074\n", + "0.0833165 5.0568936 0.7969524\n", + "0.0831371 5.2802597 0.7983940\n", + "0.0828131 5.7792052 0.8033088\n", + "0.0823995 6.8379559 0.8215798\n", + "0.0824148 7.5411947 0.8457864\n", + "0.0824349 7.7843276 0.8555132\n", + "0.0824372 7.8069559 0.8563856\n", + "0.0824366 7.8069559 0.8563856\n", + "Optimization terminated successfully.\n", + " Current function value: -86.240579\n", + " Iterations: 13\n", + " Function evaluations: 17\n", + " Gradient evaluations: 70\n", + " Hessian evaluations: 0\n" + ] + } + ], + "source": [ + "# initialize the parameters for the minimization of the NMLL, see (31) in the manuscript\n", + "sigma_n = sigma_n_exp\n", + "sigma_f = 5.\n", + "ell = 1.\n", + "\n", + "theta_0 = np.array([sigma_n, sigma_f, ell])\n", + "seq_theta = np.copy(theta_0)\n", + "def print_results(theta):\n", + " global seq_theta\n", + " seq_theta = np.vstack((seq_theta, theta))\n", + " print('{0:.7f} {1:.7f} {2:.7f}'.format(theta[0], theta[1], theta[2]))\n", + "\n", + "print('sigma_n, sigma_f, ell')\n", + "# minimize the NMLL L(\\theta) w.r.t sigma_n, sigma_f, ell using the Newton-CG method as implemented in scipy\n", + "res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='Newton-CG', \\\n", + " jac=GP_DRT.grad_NMLL_fct, callback=print_results, options={'disp': True})\n", + "\n", + "# collect the optimized parameters\n", + "sigma_n, sigma_f, ell = res.x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4) Core of the GP-DRT" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4a) Compute matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# calculate the matrices shown in eq (18)\n", + "K = GP_DRT.matrix_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L_im_K = GP_DRT.matrix_L_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L2_im_K = GP_DRT.matrix_L2_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "Sigma = (sigma_n**2)*np.eye(N_freqs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4b) Factorize the matrices and solve the linear equations" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", + "K_im_full = L2_im_K + Sigma\n", + "\n", + "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", + "if not GP_DRT.is_PD(K_im_full):\n", + " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", + "\n", + "# Cholesky factorization\n", + "L = np.linalg.cholesky(K_im_full)\n", + "\n", + "# solve for alpha\n", + "alpha = np.linalg.solve(L, Z_exp.imag)\n", + "alpha = np.linalg.solve(L.T, alpha)\n", + "\n", + "# estimate the gamma of eq (21a)\n", + "gamma_fct_est = np.dot(L_im_K, alpha)\n", + "\n", + "# covariance matrix\n", + "inv_L = np.linalg.inv(L)\n", + "inv_K_im_full = np.dot(inv_L.T, inv_L)\n", + "\n", + "# estimate the sigma of gamma for eq (21b)\n", + "cov_gamma_fct_est = K - np.dot(L_im_K, np.dot(inv_K_im_full, L_im_K.T))\n", + "sigma_gamma_fct_est = np.sqrt(np.diag(cov_gamma_fct_est))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4c) Plot the obtained DRT against the analytical DRT" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the DRT and its confidence region\n", + "plt.semilogx(freq_vec_plot, gamma_fct_plot, linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.semilogx(freq_vec, gamma_fct_est, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec, gamma_fct_est-3*sigma_gamma_fct_est, gamma_fct_est+3*sigma_gamma_fct_est, color=\"0.4\", alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E4,-5,30])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$\\gamma/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4d) Predict the $\\gamma$ and the imaginary part of the GP-DRT impedance" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# initialize the imaginary part of impedance vector\n", + "Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "gamma_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_gamma_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "# calculate the imaginary part of impedance at each $\\xi$ point for the plot\n", + "for index, val in enumerate(xi_vec_star):\n", + " xi_star = np.array([val])\n", + "\n", + " # compute matrices shown in eq (23), xi_star corresponds to a new point\n", + " k_star = GP_DRT.matrix_K(xi_vec, xi_star, sigma_f, ell)\n", + " L_im_k_star_up = GP_DRT.matrix_L_im_K(xi_star, xi_vec, sigma_f, ell)\n", + " L2_im_k_star = GP_DRT.matrix_L2_im_K(xi_vec, xi_star, sigma_f, ell)\n", + " k_star_star = GP_DRT.matrix_K(xi_star, xi_star, sigma_f, ell)\n", + " L_im_k_star_star = GP_DRT.matrix_L_im_K(xi_star, xi_star, sigma_f, ell)\n", + " L2_im_k_star_star = GP_DRT.matrix_L2_im_K(xi_star, xi_star, sigma_f, ell)\n", + "\n", + " # compute Z_im_star mean and standard deviation using eq (26)\n", + " Z_im_vec_star[index] = np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_Z_im_vec_star[index] = L2_im_k_star_star-np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, L2_im_k_star))\n", + " \n", + " # compute gamma_star mean and standard deviation using eq (29)\n", + " gamma_vec_star[index] = np.dot(L_im_k_star_up, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_gamma_vec_star[index] = k_star_star-np.dot(L_im_k_star_up, np.dot(inv_K_im_full, L_im_k_star_up.T))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4e) Plot the imaginary part of the GP-DRT impedance together with the synthetic experiment" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.semilogx(freq_vec, -Z_exp.imag, \"o\", markersize=10, color=\"black\", label=\"synth exp\")\n", + "plt.semilogx(freq_vec_star, -Z_im_vec_star, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec_star, -Z_im_vec_star-3*np.sqrt(abs(Sigma_Z_im_vec_star)), -Z_im_vec_star+3*np.sqrt(abs(Sigma_Z_im_vec_star)), alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E4,-5,30])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + } + ], + "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": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tutorials/.ipynb_checkpoints/ex3_truncated_ZARC-checkpoint.ipynb b/tutorials/.ipynb_checkpoints/ex3_truncated_ZARC-checkpoint.ipynb new file mode 100644 index 0000000..859de87 --- /dev/null +++ b/tutorials/.ipynb_checkpoints/ex3_truncated_ZARC-checkpoint.ipynb @@ -0,0 +1,410 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gaussian Process Distribution of Relaxation Times. \n", + "## In this tutorial we will reproduce Figure 8 of the article https://doi.org/10.1016/j.electacta.2019.135316\n", + "\n", + "The impedance used in this tutorial is similar to that `ex1_simple_ZARC.ipynb` except that at lower frequencies ($f < 10^{-3}~{\\rm Hz}$) the EIS data is not available. We how the GP-DRT model can predict the impedance value at those frequencies." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from math import sin, cos, pi\n", + "import GP_DRT\n", + "from scipy.optimize import minimize\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1) Define parameters of the ZARC circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# define the frequency range\n", + "N_freqs = 71\n", + "freq_vec = np.logspace(-3., 4., num=N_freqs, endpoint=True)\n", + "xi_vec = np.log(freq_vec)\n", + "tau = 1/freq_vec\n", + "\n", + "# define the frequency range used for prediction\n", + "freq_vec_star = np.logspace(-4., 4., num=81, endpoint=True)\n", + "xi_vec_star = np.log(freq_vec_star)\n", + "\n", + "# parameters for ZARC model\n", + "R_inf = 10\n", + "R_ct = 50\n", + "phi = 0.8\n", + "tau_0 = 1.\n", + "\n", + "C = tau_0**phi/R_ct\n", + "Z_exact = R_inf+1./(1./R_ct+C*(1j*2.*pi*freq_vec)**phi)\n", + "gamma_fct = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau/tau_0))-cos((1.-phi)*pi))\n", + "\n", + "# used for plotting only\n", + "freq_vec_plot = np.logspace(-4., 4., num=10*(N_freqs-1), endpoint=True)\n", + "tau_plot = 1/freq_vec_plot\n", + "# for plotting only\n", + "gamma_fct_plot = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau_plot/tau_0))-cos((1.-phi)*pi))\n", + "\n", + "# adding random noise to the impedance\n", + "rng = np.random.seed(214974)\n", + "sigma_n_exp = 0.1\n", + "Z_exp = Z_exact + sigma_n_exp*(np.random.normal(0, 1, N_freqs)+1j*np.random.normal(0, 1, N_freqs))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2) show the synthetic impedance in a Nyquist plot. \n", + "### Note: this part is similar to Figure 8 (a)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "\n", + "# Nyquist plot of impedance together with labeled frequency points\n", + "fig, ax = plt.subplots()\n", + "plt.plot(np.real(Z_exact), -np.imag(Z_exact), linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.plot(np.real(Z_exp), -np.imag(Z_exp), \"o\", markersize=10, color=\"red\", label=\"synth exp\")\n", + "plt.annotate(r'$10^{-3}$', xy=(np.real(Z_exp[0]), -np.imag(Z_exp[0])), \n", + " xytext=(np.real(Z_exp[0])-15, -np.imag(Z_exp[0])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10^{-2}$', xy=(np.real(Z_exp[10]), -np.imag(Z_exp[10])), \n", + " xytext=(np.real(Z_exp[10])-2, 10-np.imag(Z_exp[10])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10^{-1}$', xy=(np.real(Z_exp[20]), -np.imag(Z_exp[20])), \n", + " xytext=(np.real(Z_exp[20])-2, 6-np.imag(Z_exp[20])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$1$', xy=(np.real(Z_exp[30]), -np.imag(Z_exp[30])), \n", + " xytext=(np.real(Z_exp[30]), 10-np.imag(Z_exp[30])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10$', xy=(np.real(Z_exp[40]), -np.imag(Z_exp[40])), \n", + " xytext=(np.real(Z_exp[40])-1, 10-np.imag(Z_exp[40])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.axis('scaled')\n", + "\n", + "plt.xticks(range(10, 70, 10))\n", + "plt.yticks(range(0, 60, 10))\n", + "plt.gca().set_aspect('equal', adjustable='box')\n", + "plt.xlabel(r'$Z_{\\rm re}/\\Omega$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3) Compute the optimal hyperparameters" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigma_n, sigma_f, ell\n", + "0.1050094 5.0001097 0.9994337\n", + "0.1048101 5.0107903 0.9481658\n", + "0.1047302 5.0306224 0.8953992\n", + "0.1047554 5.2374445 0.9106782\n", + "0.1047695 5.6761672 0.9283906\n", + "0.1047295 5.6761793 0.9283937\n", + "0.1047294 5.6884928 0.9290939\n", + "0.1047294 5.7147866 0.9305899\n", + "0.1047292 5.7762536 0.9340913\n", + "0.1047301 5.8021615 0.9355663\n", + "0.1047302 5.8024810 0.9355922\n", + "0.1047297 5.8024810 0.9355922\n", + "Optimization terminated successfully.\n", + " Current function value: -68.171912\n", + " Iterations: 12\n", + " Function evaluations: 16\n", + " Gradient evaluations: 80\n", + " Hessian evaluations: 0\n" + ] + } + ], + "source": [ + "# initialize the parameter for global 3D optimization to maximize the marginal log-likelihood as shown in eq (31)\n", + "sigma_n = sigma_n_exp\n", + "sigma_f = 5.\n", + "ell = 1.\n", + "\n", + "theta_0 = np.array([sigma_n, sigma_f, ell])\n", + "seq_theta = np.copy(theta_0)\n", + "def print_results(theta):\n", + " global seq_theta\n", + " seq_theta = np.vstack((seq_theta, theta))\n", + " print('{0:.7f} {1:.7f} {2:.7f}'.format(theta[0], theta[1], theta[2]))\n", + " \n", + "print('sigma_n, sigma_f, ell')\n", + "\n", + "# minimize the NMLL L(\\theta) w.r.t sigma_n, sigma_f, ell using the Newton-CG method as implemented in scipy\n", + "res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='Newton-CG', \\\n", + " jac=GP_DRT.grad_NMLL_fct, callback=print_results, options={'disp': True})\n", + "\n", + "# collect the optimized parameters\n", + "sigma_n, sigma_f, ell = res.x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4) Core of the GP-DRT" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4a) Compute matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# calculate the matrices shown in eq (18)\n", + "K = GP_DRT.matrix_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L_im_K = GP_DRT.matrix_L_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L2_im_K = GP_DRT.matrix_L2_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "Sigma = (sigma_n**2)*np.eye(N_freqs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4b) Factorize the matrices and solve the linear equations" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", + "K_im_full = L2_im_K + Sigma\n", + "\n", + "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", + "if not GP_DRT.is_PD(K_im_full):\n", + " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", + "\n", + "# Cholesky factorization, L is a lower-triangular matrix\n", + "L = np.linalg.cholesky(K_im_full)\n", + "\n", + "# solve for alpha\n", + "alpha = np.linalg.solve(L, Z_exp.imag)\n", + "alpha = np.linalg.solve(L.T, alpha)\n", + "\n", + "# estimate the gamma of eq (21a)\n", + "gamma_fct_est = np.dot(L_im_K, alpha)\n", + "\n", + "# covariance matrix\n", + "inv_L = np.linalg.inv(L)\n", + "inv_K_im_full = np.dot(inv_L.T, inv_L)\n", + "\n", + "# estimate the sigma of gamma for eq (21b)\n", + "cov_gamma_fct_est = K - np.dot(L_im_K, np.dot(inv_K_im_full, L_im_K.T))\n", + "sigma_gamma_fct_est = np.sqrt(np.diag(cov_gamma_fct_est))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4c) Predict the imaginary part of the GP-DRT and impedance" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# initialize the imaginary part of impedance vector\n", + "Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "gamma_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_gamma_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "# calculate the imaginary part of impedance at each $\\xi$ point for the plot\n", + "for index, val in enumerate(xi_vec_star):\n", + " xi_star = np.array([val])\n", + "\n", + " # compute matrices shown in eq (23), xi_star corresponds to a new point\n", + " k_star = GP_DRT.matrix_K(xi_vec, xi_star, sigma_f, ell)\n", + " L_im_k_star_up = GP_DRT.matrix_L_im_K(xi_star, xi_vec, sigma_f, ell)\n", + " L2_im_k_star = GP_DRT.matrix_L2_im_K(xi_vec, xi_star, sigma_f, ell)\n", + " k_star_star = GP_DRT.matrix_K(xi_star, xi_star, sigma_f, ell)\n", + " L_im_k_star_star = GP_DRT.matrix_L_im_K(xi_star, xi_star, sigma_f, ell)\n", + " L2_im_k_star_star = GP_DRT.matrix_L2_im_K(xi_star, xi_star, sigma_f, ell)\n", + "\n", + " # compute Z_im_star mean and standard deviation using eq (26)\n", + " Z_im_vec_star[index] = np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_Z_im_vec_star[index] = L2_im_k_star_star - np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, L2_im_k_star))\n", + " \n", + " # compute gamma_star mean and standard deviation using eq (29)\n", + " gamma_vec_star[index] = np.dot(L_im_k_star_up, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_gamma_vec_star[index] = k_star_star - np.dot(L_im_k_star_up, np.dot(inv_K_im_full, L_im_k_star_up.T))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4d) Plot the obtained GP-DRT against the analytical DRT\n", + "#### Note: the predicted credible interval broadens at low frequencies" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the DRT and its confidence region\n", + "plt.semilogx(freq_vec_plot, gamma_fct_plot, linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.semilogx(freq_vec_star, gamma_vec_star, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.semilogx([1E-3, 1E-3], [-5, 25], ':', linewidth=3, color=\"black\")\n", + "plt.fill_between(freq_vec_star, gamma_vec_star-3*np.sqrt(abs(Sigma_gamma_vec_star)), gamma_vec_star+3*np.sqrt(abs(Sigma_gamma_vec_star)), color=\"0.4\", alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E4,-5,25])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$\\gamma/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4e) Plot the imaginary part of the GP-DRT impedance together with the exact one and the synthetic experiment\n", + "#### Note: the predicted credible interval broadens at low frequencies" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.semilogx(freq_vec, -Z_exp.imag, \"o\", markersize=10, color=\"black\", label=\"synth exp\")\n", + "plt.semilogx(freq_vec_star, -Z_im_vec_star, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.semilogx([1E-3, 1E-3], [-5, 25], ':', linewidth=3, color=\"black\")\n", + "plt.fill_between(freq_vec_star, -Z_im_vec_star-3*np.sqrt(abs(Sigma_Z_im_vec_star)), -Z_im_vec_star+3*np.sqrt(abs(Sigma_Z_im_vec_star)), alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E4,-5,25])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + } + ], + "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": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tutorials/.ipynb_checkpoints/ex4_experiment-checkpoint.ipynb b/tutorials/.ipynb_checkpoints/ex4_experiment-checkpoint.ipynb new file mode 100644 index 0000000..877b734 --- /dev/null +++ b/tutorials/.ipynb_checkpoints/ex4_experiment-checkpoint.ipynb @@ -0,0 +1,446 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gaussian Process Distribution of Relaxation Times. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## In this tutorial we will show use the GP-DRT method to analyze actual experimental data\n", + "\n", + "The impedance data in the csv file named `EIS_experiment.csv`. The file has three columns. The first column is the frequency, the second one the real part of the impedance. The third column is the imaginary part of impedance. To use this tutorial for your own data, we recommend the frequencies go are sorted ascendingly." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from math import sin, cos, pi\n", + "import GP_DRT\n", + "from scipy.optimize import minimize\n", + "import pandas as pd\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1) Read in the impedance data from the csv file\n", + "### IMPORTANT: frequencies should be sorted ascendingly (low to high)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "Z_data = pd.read_csv('EIS_experiment.csv')\n", + "freq_vec, Z_exp = Z_data['freq'].values, Z_data['Z_real'].values+1j*Z_data['Z_imag'].values\n", + "\n", + "# define the frequency range\n", + "N_freqs = len(freq_vec)\n", + "xi_vec = np.log(freq_vec)\n", + "tau = 1/freq_vec\n", + "\n", + "# define the frequency range used for prediction, we choose a wider range to better display the DRT\n", + "freq_vec_star = np.logspace(-4., 6., num=101, endpoint=True)\n", + "xi_vec_star = np.log(freq_vec_star)\n", + "\n", + "# finer mesh for plotting only\n", + "freq_vec_plot = np.logspace(-4., 6., num=1001, endpoint=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2) Show the impedance spectrum as a Nyquist plot" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "\n", + "# Nyquist plot of the EIS spectrum\n", + "plt.plot(np.real(Z_exp), -np.imag(Z_exp), \"o\", markersize=10, fillstyle='none', color=\"red\", label=\"experiment\")\n", + "plt.plot(np.real(Z_exp[40:80:10]), -np.imag(Z_exp[40:80:10]), 'o', markersize=10, color=\"black\")\n", + "\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.axis('scaled')\n", + "\n", + "# this depends on the data used - if you wish to use your own data you may need to modify this\n", + "plt.xlim(1.42, 1.52)\n", + "plt.ylim(-0.001, 0.051)\n", + "plt.xticks(np.arange(1.42, 1.521, 0.02))\n", + "plt.yticks(np.arange(0.00, 0.051, 0.01))\n", + "plt.gca().set_aspect('equal', adjustable='box')\n", + "plt.xlabel(r'$Z_{\\rm re}/\\Omega$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "\n", + "# label the frequencies - if you wish to use your own data you may need to modify this\n", + "label_index = range(40,80,10)\n", + "move = [[-0.005, 0.008], [-0.005, 0.008], [-0.005, 0.008], [-0.005, 0.01]]\n", + "for k, ind in enumerate(label_index):\n", + " power = int(np.log10(freq_vec[ind]))\n", + " num = freq_vec[ind]/(10**(power))\n", + " plt.annotate(r'${0:.1f}\\times 10^{1}$'.format(num, power), xy=(np.real(Z_exp[ind]), -np.imag(Z_exp[ind])), \n", + " xytext=(np.real(Z_exp[ind])+move[k][0], move[k][1]-np.imag(Z_exp[ind])), \n", + " arrowprops=dict(arrowstyle=\"-\", connectionstyle=\"arc\"))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3) Compute the optimal hyperparameters\n", + "### Note: the intial parameters may adjusting" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigma_n, sigma_f, ell\n", + "0.0003150 0.0063000 1.8000000\n", + "0.0002850 0.0066000 1.8000000\n", + "0.0002850 0.0066000 1.8000000\n", + "0.0002850 0.0066000 1.8000000\n", + "0.0003050 0.0065000 1.7666667\n", + "0.0003050 0.0065000 1.7666667\n", + "0.0002972 0.0066778 1.7722222\n", + "0.0002945 0.0065796 1.8231481\n", + "0.0002920 0.0065929 1.7936728\n", + "0.0002920 0.0065929 1.7936728\n", + "0.0002963 0.0066274 1.7858325\n", + "0.0002953 0.0065863 1.8050762\n", + "0.0002972 0.0065803 1.7881838\n", + "0.0002941 0.0065954 1.7933518\n", + "0.0002947 0.0065473 1.8052421\n", + "0.0002954 0.0065624 1.7861090\n", + "0.0002954 0.0065624 1.7861090\n", + "0.0002966 0.0065272 1.7952438\n", + "0.0002966 0.0065272 1.7952438\n", + "0.0002954 0.0064920 1.7963716\n", + "0.0002966 0.0064797 1.7815173\n", + "0.0002966 0.0064797 1.7815173\n", + "0.0002959 0.0063540 1.7833807\n", + "0.0002949 0.0064469 1.7782003\n", + "0.0002949 0.0064469 1.7782003\n", + "0.0002949 0.0064469 1.7782003\n", + "0.0002957 0.0063636 1.7714437\n", + "0.0002952 0.0063418 1.7738371\n", + "0.0002956 0.0063690 1.7789372\n", + "0.0002952 0.0064025 1.7764698\n", + "0.0002955 0.0063673 1.7739292\n", + "0.0002953 0.0063607 1.7751413\n", + "0.0002953 0.0063607 1.7751413\n", + "0.0002953 0.0063847 1.7759231\n", + "0.0002954 0.0063701 1.7749851\n", + "0.0002954 0.0063701 1.7749851\n", + "0.0002953 0.0063679 1.7749955\n", + "0.0002954 0.0063760 1.7761313\n", + "0.0002954 0.0063780 1.7756469\n", + "0.0002954 0.0063780 1.7756469\n", + "0.0002953 0.0063726 1.7754937\n", + "0.0002953 0.0063726 1.7754937\n", + "0.0002953 0.0063768 1.7758893\n", + "0.0002953 0.0063766 1.7756545\n", + "0.0002953 0.0063758 1.7756412\n", + "0.0002953 0.0063745 1.7756110\n", + "0.0002953 0.0063745 1.7756110\n", + "0.0002953 0.0063745 1.7756110\n", + "0.0002953 0.0063745 1.7756110\n", + "0.0002953 0.0063745 1.7756110\n", + "Optimization terminated successfully.\n", + " Current function value: -577.496686\n", + " Iterations: 51\n", + " Function evaluations: 97\n", + "0.0002953 0.0063745 1.7756110\n", + "0.0002953 0.0063749 1.7756110\n", + "0.0002953 0.0063751 1.7756659\n", + "0.0002953 0.0063749 1.7756443\n", + "0.0002953 0.0063749 1.7756443\n", + "Warning: Desired error not necessarily achieved due to precision loss.\n", + " Current function value: -577.496686\n", + " Iterations: 5\n", + " Function evaluations: 74\n", + " Gradient evaluations: 62\n" + ] + } + ], + "source": [ + "# initial parameters parameter to maximize the marginal log-likelihood as shown in eq (31)\n", + "sigma_n = 3.0E-4\n", + "sigma_f = 6.0E-3\n", + "ell = 2.0\n", + "\n", + "theta_0 = np.array([sigma_n, sigma_f, ell])\n", + "seq_theta = np.copy(theta_0)\n", + "def print_results(theta):\n", + " global seq_theta\n", + " seq_theta = np.vstack((seq_theta, theta))\n", + " print('{0:.7f} {1:.7f} {2:.7f}'.format(theta[0], theta[1], theta[2]))\n", + " \n", + "print('sigma_n, sigma_f, ell')\n", + "\n", + "# minimize the NMLL $L(\\theta)$ w.r.t sigma_n, sigma_f, ell using the BFGS method as implemented in scipy\n", + "res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='Nelder-Mead', \\\n", + " callback=print_results, options={'disp': True})\n", + "\n", + "theta_0 = res.x\n", + "res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='BFGS', \\\n", + " jac=GP_DRT.grad_NMLL_fct, callback=print_results, options={'disp': True})\n", + "\n", + "# collect the optimized parameters\n", + "sigma_n, sigma_f, ell = res.x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4) Core of the GP-DRT" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4a) Compute matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# calculate the matrices shown in eq (18)\n", + "K = GP_DRT.matrix_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L_im_K = GP_DRT.matrix_L_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L2_im_K = GP_DRT.matrix_L2_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "Sigma = (sigma_n**2)*np.eye(N_freqs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4b) Factorize the matrices and solve the linear equations" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", + "K_im_full = L2_im_K + Sigma\n", + "\n", + "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", + "if not GP_DRT.is_PD(K_im_full):\n", + " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", + "\n", + "# Cholesky factorization, L is a lower-triangular matrix\n", + "L = np.linalg.cholesky(K_im_full)\n", + "\n", + "# solve for alpha\n", + "alpha = np.linalg.solve(L, Z_exp.imag)\n", + "alpha = np.linalg.solve(L.T, alpha)\n", + "\n", + "# estimate the gamma of eq (21a)\n", + "gamma_fct_est = np.dot(L_im_K, alpha)\n", + "\n", + "# covariance matrix\n", + "inv_L = np.linalg.inv(L)\n", + "inv_K_im_full = np.dot(inv_L.T, inv_L)\n", + "\n", + "# estimate the sigma of gamma for eq (21b)\n", + "cov_gamma_fct_est = K - np.dot(L_im_K, np.dot(inv_K_im_full, L_im_K.T))\n", + "sigma_gamma_fct_est = np.sqrt(np.diag(cov_gamma_fct_est))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4c) Predict the imaginary part of the GP-DRT and impedance" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# initialize the imaginary part of impedance vector\n", + "Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "gamma_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_gamma_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "# calculate the imaginary part of impedance at each $\\xi$ point for the plot\n", + "for index, val in enumerate(xi_vec_star):\n", + " xi_star = np.array([val])\n", + "\n", + " # compute matrices shown in eq (18), xi_star corresponds to a new point\n", + " k_star = GP_DRT.matrix_K(xi_vec, xi_star, sigma_f, ell)\n", + " L_im_k_star_up = GP_DRT.matrix_L_im_K(xi_star, xi_vec, sigma_f, ell)\n", + " L2_im_k_star = GP_DRT.matrix_L2_im_K(xi_vec, xi_star, sigma_f, ell)\n", + " k_star_star = GP_DRT.matrix_K(xi_star, xi_star, sigma_f, ell)\n", + " L_im_k_star_star = GP_DRT.matrix_L_im_K(xi_star, xi_star, sigma_f, ell)\n", + " L2_im_k_star_star = GP_DRT.matrix_L2_im_K(xi_star, xi_star, sigma_f, ell)\n", + "\n", + " # compute Z_im_star mean and standard deviation using eq (26)\n", + " Z_im_vec_star[index] = np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_Z_im_vec_star[index] = L2_im_k_star_star - np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, L2_im_k_star))\n", + " \n", + " # compute gamma_star mean and standard deviation using eq (29)\n", + " gamma_vec_star[index] = np.dot(L_im_k_star_up, np.dot(inv_K_im_full, Z_exp.imag))\n", + " Sigma_gamma_vec_star[index] = k_star_star - np.dot(L_im_k_star_up, np.dot(inv_K_im_full, L_im_k_star_up.T))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4d) Plot the obtained GP-DRT" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the DRT and its confidence region\n", + "plt.semilogx(freq_vec_star, gamma_vec_star, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec_star, gamma_vec_star-3*np.sqrt(abs(Sigma_gamma_vec_star)), gamma_vec_star+3*np.sqrt(abs(Sigma_gamma_vec_star)), color=\"0.4\", alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E6,-0.01,0.025])\n", + "plt.yticks(np.arange(-0.01, 0.025, 0.01))\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$\\gamma/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4e) Plot the imaginary part of the GP-DRT impedance together with the experimental one" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.semilogx(freq_vec, -Z_exp.imag, \"o\", markersize=10, color=\"black\", label=\"synth exp\")\n", + "plt.semilogx(freq_vec_star, -Z_im_vec_star, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec_star, -Z_im_vec_star-3*np.sqrt(abs(Sigma_Z_im_vec_star)), -Z_im_vec_star+\\\n", + " 3*np.sqrt(abs(Sigma_Z_im_vec_star)), alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-3,1E5,-0.01,0.03])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + } + ], + "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": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tutorials/.ipynb_checkpoints/ex5_inductance_plus_ZARC-checkpoint.ipynb b/tutorials/.ipynb_checkpoints/ex5_inductance_plus_ZARC-checkpoint.ipynb new file mode 100644 index 0000000..e957f64 --- /dev/null +++ b/tutorials/.ipynb_checkpoints/ex5_inductance_plus_ZARC-checkpoint.ipynb @@ -0,0 +1,452 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gaussian Process Distribution of Relaxation Times. \n", + "## In this tutorial we will reproduce Figure 10 of the article https://doi.org/10.1016/j.electacta.2019.135316\n", + "\n", + "This tutorial shows how the GP-DRT model can recover DRT from the impedance including an inductance at high frequency.\n", + "\n", + "The impedance is similar to that `ex1_simple_ZARC_model.ipynb`, except for the presence of an inductor with $L_{0}=500~\\mu\\rm {H}$. The DRT is identical" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from math import sin, cos, pi\n", + "import GP_DRT\n", + "from scipy.optimize import minimize\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1) Define parameters of the ZARC circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# define the frequency range\n", + "N_freqs = 81\n", + "freq_vec = np.logspace(-4., 4., num=N_freqs, endpoint=True)\n", + "xi_vec = np.log(freq_vec)\n", + "tau = 1/freq_vec\n", + "\n", + "# define the frequency range used for prediction\n", + "freq_vec_star = np.logspace(-4., 4., num=81, endpoint=True)\n", + "xi_vec_star = np.log(freq_vec_star)\n", + "\n", + "# parameters for ZARC model\n", + "R_inf = 10\n", + "R_ct = 50\n", + "phi = 0.8\n", + "tau_0 = 1.\n", + "L_0 = 5E-4\n", + "\n", + "C = tau_0**phi/R_ct\n", + "Z_exact = R_inf + 1j*(2*pi*freq_vec)*L_0 + 1./(1./R_ct+C*(1j*2.*pi*freq_vec)**phi)\n", + "gamma_fct = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau/tau_0))-cos((1.-phi)*pi))\n", + "\n", + "# used for plotting only\n", + "freq_vec_plot = np.logspace(-4., 4., num=10*(N_freqs-1), endpoint=True)\n", + "tau_plot = 1/freq_vec_plot\n", + "# for plotting only\n", + "gamma_fct_plot = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau_plot/tau_0))-cos((1.-phi)*pi))\n", + "\n", + "# adding random noise to the impedance\n", + "rng = np.random.seed(214974)\n", + "sigma_n_exp = 0.5\n", + "Z_exp = Z_exact + sigma_n_exp*(np.random.normal(0, 1, N_freqs)+1j*np.random.normal(0, 1, N_freqs))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2) show the synthetic impedance in a Nyquist plot. \n", + "### Note: this is similar to Figure 10 (a)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "\n", + "# Nyquist plot of impedance together with labeled frequency points\n", + "fig, ax = plt.subplots()\n", + "plt.plot(np.real(Z_exact), -np.imag(Z_exact), linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.plot(np.real(Z_exp), -np.imag(Z_exp), \"o\", markersize=10, color=\"red\", label=\"synth exp\")\n", + "plt.annotate(r'$10^{-4}$', xy=(np.real(Z_exp[0]), -np.imag(Z_exp[0])), \n", + " xytext=(np.real(Z_exp[0])-15, -np.imag(Z_exp[0])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10^{-1}$', xy=(np.real(Z_exp[20]), -np.imag(Z_exp[20])), \n", + " xytext=(np.real(Z_exp[20])-5, 10-np.imag(Z_exp[20])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$1$', xy=(np.real(Z_exp[30]), -np.imag(Z_exp[30])), \n", + " xytext=(np.real(Z_exp[30]), 8-np.imag(Z_exp[30])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10$', xy=(np.real(Z_exp[40]), -np.imag(Z_exp[40])), \n", + " xytext=(np.real(Z_exp[40]), 8-np.imag(Z_exp[40])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$10^2$', xy=(np.real(Z_exp[60]), -np.imag(Z_exp[60])), \n", + " xytext=(np.real(Z_exp[60])+5, -np.imag(Z_exp[60])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "plt.annotate(r'$5\\times 10^3$', xy=(np.real(Z_exp[77]), -np.imag(Z_exp[77])), \n", + " xytext=(np.real(Z_exp[77])+5, -np.imag(Z_exp[77])), \n", + " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", + "\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.axis('scaled')\n", + "\n", + "plt.xticks(range(10, 70, 10))\n", + "plt.yticks(range(-30, 40, 10))\n", + "plt.gca().set_aspect('equal', adjustable='box')\n", + "plt.xlabel(r'$Z_{\\rm re}/\\Omega$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3) Compute the optimal hyperparameters" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigma_n, sigma_f, ell, sigma_L\n", + "0.4999994 5.6000000 0.9000003 0.0007129\n", + "0.4783180 5.5996571 0.9093610 0.0007138\n", + "0.4784722 5.5971341 0.9761654 0.0007134\n", + "0.4786302 5.5398552 1.1156550 0.0007052\n", + "0.4806697 5.5553961 1.4395532 0.0006567\n", + "0.4814963 5.7338434 1.3170056 0.0006469\n", + "0.4811801 5.7848347 1.3435225 0.0006199\n", + "0.4810202 5.8622583 1.3707405 0.0005578\n", + "0.4810493 5.8534375 1.3638917 0.0005450\n", + "0.4811226 5.8227503 1.3537372 0.0005396\n", + "0.4811214 5.8165253 1.3536523 0.0005392\n", + "0.4811196 5.8137873 1.3537183 0.0005394\n", + "0.4811197 5.8138615 1.3537392 0.0005393\n", + "0.4811196 5.8138589 1.3537368 0.0005393\n", + "Optimization terminated successfully.\n", + " Current function value: 19.343917\n", + " Iterations: 14\n", + " Function evaluations: 23\n", + " Gradient evaluations: 23\n" + ] + } + ], + "source": [ + "# initialize the parameters to minimize the negative marginal log-likelihood, see eq (31)\n", + "sigma_n = sigma_n_exp\n", + "sigma_f = 5.6\n", + "ell = 0.9\n", + "sigma_L = 3E-4\n", + "\n", + "theta_0 = np.array([sigma_n, sigma_f, ell, sigma_L])\n", + "seq_theta = np.copy(theta_0)\n", + "def print_results(theta):\n", + " global seq_theta\n", + " seq_theta = np.vstack((seq_theta, theta))\n", + " print('{0:.7f} {1:.7f} {2:.7f} {3:.7f}'.format(theta[0], theta[1], theta[2], theta[3]))\n", + " \n", + "print('sigma_n, sigma_f, ell, sigma_L')\n", + "\n", + "# minimize the NMLL L(\\theta) w.r.t sigma_n, sigma_f, ell using the BFGS method as implemented in scipy\n", + "res = minimize(GP_DRT.NMLL_fct_L, theta_0, args=(Z_exp, xi_vec), method='BFGS', \\\n", + " jac=GP_DRT.grad_NMLL_fct_L, callback=print_results, options={'disp': True})\n", + "\n", + "# collect the optimized parameters\n", + "sigma_n, sigma_f, ell, sigma_L = res.x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4) Core of the GP-DRT" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4a) Compute matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# calculate the matrices shown in eq (38)\n", + "K = GP_DRT.matrix_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L_im_K = GP_DRT.matrix_L_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "L2_im_K = GP_DRT.matrix_L2_im_K(xi_vec, xi_vec, sigma_f, ell)\n", + "h_L = GP_DRT.compute_h_L(xi_vec)\n", + "Sigma = (sigma_n**2)*np.eye(N_freqs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4b) Factorize the matrices and solve the linear equations" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# the matrix in (38), $\\mathcal L^2_{\\rm im}\\mathbf K+\\sigma_n^2\\mathbf I+\\sigma_n^2 \\mathbf{h} \\mathbf{h}^\\top$ \n", + "# whose inverse is needed\n", + "K_im_full = L2_im_K + Sigma + (sigma_L**2)*np.outer(h_L, h_L)\n", + "\n", + "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", + "if not GP_DRT.is_PD(K_im_full):\n", + " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", + "\n", + "# Cholesky factorization, L is a lower-triangular matrix\n", + "L = np.linalg.cholesky(K_im_full)\n", + "\n", + "# solve for alpha\n", + "alpha = np.linalg.solve(L, Z_exp.imag)\n", + "alpha = np.linalg.solve(L.T, alpha)\n", + "\n", + "# covariance matrix\n", + "inv_L = np.linalg.inv(L)\n", + "inv_K_im_full = np.dot(inv_L.T, inv_L)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4c) Predict the imaginary part of the GP-DRT and impedance" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# initialize the imaginary part of impedance vector\n", + "Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_Z_im_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "gamma_vec_star = np.empty_like(xi_vec_star)\n", + "Sigma_gamma_vec_star = np.empty_like(xi_vec_star)\n", + "\n", + "# calculate the imaginary part of impedance at each $\\xi$ point for the plot\n", + "for index, val in enumerate(xi_vec_star):\n", + " xi_star = np.array([val])\n", + "\n", + " # compute matrices shown in eq (40), xi_star corresponds to a new point\n", + " k_star = GP_DRT.matrix_K(xi_vec, xi_star, sigma_f, ell)\n", + " L_im_k_star_up = GP_DRT.matrix_L_im_K(xi_star, xi_vec, sigma_f, ell)\n", + " L2_im_k_star_up = GP_DRT.matrix_L2_im_K(xi_vec, xi_star, sigma_f, ell)\n", + " k_star_star = GP_DRT.matrix_K(xi_star, xi_star, sigma_f, ell)\n", + " L_im_k_star_star = GP_DRT.matrix_L_im_K(xi_star, xi_star, sigma_f, ell)\n", + " L2_im_k_star_star = GP_DRT.matrix_L2_im_K(xi_star, xi_star, sigma_f, ell)\n", + "\n", + " # assemble the matrix for equation (41)\n", + " L2_im_k_star_up = L2_im_k_star_up.T + (sigma_L**2)*(GP_DRT.compute_h_L(xi_star))*h_L.T\n", + " L2_im_k_star_star = L2_im_k_star_star + (sigma_L**2)*(GP_DRT.compute_h_L(xi_star)**2)\n", + " \n", + " # compute Z_im_star mean and standard deviation following eq (26)\n", + " Z_im_vec_star[index] = np.dot(L2_im_k_star_up, np.dot(inv_K_im_full,Z_exp.imag))\n", + " Sigma_Z_im_vec_star[index] = L2_im_k_star_star-np.dot(L2_im_k_star_up, np.dot(inv_K_im_full, L2_im_k_star_up.T))\n", + " \n", + " # compute gamma_star mean and standard deviation following eq (47)\n", + " gamma_vec_star[index] = np.dot(L_im_k_star_up, np.dot(inv_K_im_full,Z_exp.imag))\n", + " Sigma_gamma_vec_star[index] = k_star_star-np.dot(L_im_k_star_up, np.dot(inv_K_im_full, L_im_k_star_up.T))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4d) Plot the obtained GP-DRT against the analytical DRT" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the DRT and its confidence region\n", + "plt.semilogx(freq_vec_plot, gamma_fct_plot, linewidth=4, color=\"black\", label=\"exact\")\n", + "plt.semilogx(freq_vec_star, gamma_vec_star, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec_star, gamma_vec_star-3*np.sqrt(abs(Sigma_gamma_vec_star)), gamma_vec_star+3*np.sqrt(abs(Sigma_gamma_vec_star)), color=\"0.4\", alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1E4,-5,25])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$\\gamma/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4e) Plot the imaginary part of the GP-DRT impedance together with the exact one and the synthetic experiment" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.semilogx(freq_vec, -Z_exp.imag, \"o\", markersize=10, color=\"black\", label=\"synth exp\")\n", + "plt.semilogx(freq_vec_star, -Z_im_vec_star, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", + "plt.fill_between(freq_vec_star, -Z_im_vec_star-3*np.sqrt(abs(Sigma_Z_im_vec_star)), -Z_im_vec_star+3*np.sqrt(abs(Sigma_Z_im_vec_star)), alpha=0.3)\n", + "plt.rc('text', usetex=True)\n", + "plt.rc('font', family='serif', size=15)\n", + "plt.rc('xtick', labelsize=15)\n", + "plt.rc('ytick', labelsize=15)\n", + "plt.axis([1E-4,1.3E4,-33,33])\n", + "plt.legend(frameon=False, fontsize = 15)\n", + "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", + "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 4f) Estimate the inductance $L_{0}$" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "estimated L_0 = 0.000537 H\n", + "relative error = 7.44 %\n" + ] + } + ], + "source": [ + "# the inductance is predicted using equation (44a) \n", + "K_im_full_reg = L2_im_K + Sigma\n", + "\n", + "# covariance matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$\n", + "L = np.linalg.cholesky(K_im_full_reg)\n", + "inv_L = np.linalg.inv(L)\n", + "inv_K_im_full_reg = np.dot(inv_L.T, inv_L)\n", + "\n", + "# the numerator and denominator of the equation (44a)\n", + "num_L_0 = np.dot(np.dot(inv_K_im_full_reg, Z_exp.imag), h_L)\n", + "den_L_0 = (sigma_L**-2) + np.dot(h_L.T, np.dot(inv_K_im_full_reg, h_L))\n", + "\n", + "L_0_est = num_L_0/den_L_0\n", + "print('estimated L_0 = {0:.6f} H'.format(L_0_est[0][0]))\n", + "print('relative error = {0:.2f} %'.format((L_0_est[0][0]-L_0)/L_0*100.))" + ] + } + ], + "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": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tutorials/GP_DRT.py b/tutorials/GP_DRT.py index ec9454e..fc0773d 100644 --- a/tutorials/GP_DRT.py +++ b/tutorials/GP_DRT.py @@ -20,7 +20,50 @@ from math import log from scipy import integrate import numpy as np +from numpy import linalg as la +# is a matrix positive definite? +# if input matrix is positive-definite (<=> Cholesky decomposable), then true is returned +# otherwise return false + +def is_PD(A): + + try: + np.linalg.cholesky(A) + return True + except np.linalg.LinAlgError: + return False + +# Find the nearest positive-definite matrix +def nearest_PD(A): + + # based on + # N.J. Higham (1988) https://doi.org/10.1016/0024-3795(88)90223-6 + # and + # https://www.mathworks.com/matlabcentral/fileexchange/42885-nearestspd + + B = (A + A.T)/2 + _, Sigma_mat, V = la.svd(B) + + H = np.dot(V.T, np.dot(np.diag(Sigma_mat), V)) + + A_nPD = (B + H) / 2 + A_symm = (A_nPD + A_nPD.T) / 2 + + k = 1 + I = np.eye(A_symm.shape[0]) + + while not is_PD(A_symm): + eps = np.spacing(la.norm(A_symm)) + + # MATLAB's 'chol' accepts matrices with eigenvalue = 0, numpy does not not. + # So where the matlab implementation uses 'eps(mineig)', we use the above definition. + + min_eig = min(0, np.min(np.real(np.linalg.eigvals(A_symm)))) + A_symm += I * (-min_eig * k**2 + eps) + k += 1 + + return A_symm # Define squared exponential kernel, $\sigma_f^2 \exp\left(-\frac{1}{2 \ell^2}\left(\xi-\xi^\prime\right)^2 \right)$ def kernel(xi, xi_prime, sigma_f, ell): @@ -89,8 +132,9 @@ def matrix_K(xi_n_vec, xi_m_vec, sigma_f, ell): # assemble the matrix of eq (18b), added the term of $\frac{1}{\sigma_f^2}$ and factor $2\pi$ before $e^{\Delta\xi_{mn}-\chi}$ def matrix_L_im_K(xi_n_vec, xi_m_vec, sigma_f, ell): + if np.array_equal(xi_n_vec, xi_m_vec): - # considering the case that $\xi_n$ and $\xi_m$ are identical, i.e., the matrice are symmetry square + # considering the case that $\xi_n$ and $\xi_m$ are identical, i.e., the matrix is square symmetrix xi_vec = xi_n_vec N_freqs = xi_vec.size L_im_K = np.zeros([N_freqs, N_freqs]) @@ -98,6 +142,7 @@ def matrix_L_im_K(xi_n_vec, xi_m_vec, sigma_f, ell): delta_xi = log(2*pi) integral, tol = integrate.quad(integrand_L_im, -np.inf, np.inf, epsabs=1E-12, epsrel=1E-12, args=(delta_xi, sigma_f, ell)) np.fill_diagonal(L_im_K, -(sigma_f**2)*(integral)) + for n in range(1, N_freqs): delta_xi = xi_vec[n]-xi_vec[0] + log(2*pi) integral, tol = integrate.quad(integrand_L_im, -np.inf, np.inf, epsabs=1E-12, epsrel=1E-12, args=(delta_xi, sigma_f, ell)) @@ -113,16 +158,19 @@ def matrix_L_im_K(xi_n_vec, xi_m_vec, sigma_f, ell): for n in range(0, N_n_freqs): for m in range(0, N_m_freqs): + delta_xi = xi_m_vec[m] - xi_n_vec[n] + log(2*pi) integral, tol = integrate.quad(integrand_L_im, -np.inf, np.inf, epsabs=1E-12, epsrel=1E-12, args=(delta_xi, sigma_f, ell)) L_im_K[n,m] = -(sigma_f**2)*(integral) + return L_im_K # assemble the matrix of eq (18d), added the term of $\frac{1}{\sigma_f^2}$ and factor $2\pi$ before $e^{\Delta\xi_{mn}-\chi}$ def matrix_L2_im_K(xi_n_vec, xi_m_vec, sigma_f, ell): + if np.array_equal(xi_n_vec, xi_m_vec): - # considering the case that $\xi_n$ and $\xi_m$ are identical, i.e., the matrice are symmetry square + # considering the case that $\xi_n$ and $\xi_m$ are identical, i.e., the matrix is square symmetric xi_vec = xi_n_vec N_freqs = xi_vec.size L2_im_K = np.zeros([N_freqs, N_freqs]) @@ -169,6 +217,12 @@ def NMLL_fct(theta, Z_exp, xi_vec): L2_im_K = matrix_L2_im_K(xi_vec, xi_vec, sigma_f, ell) # $\mathcal L^2_{\rm im} \mathbf K$ K_im_full = L2_im_K + Sigma # $\mathbf K_{\rm im}^{\rm full} = \mathcal L^2_{\rm im} \mathbf K + \sigma_n^2 \mathbf I$ + + # begin FC - added + if not is_PD(K_im_full): + K_im_full = nearest_PD(K_im_full) + # end FC - added + L = np.linalg.cholesky(K_im_full) # Cholesky decomposition to get the inverse of $\mathbf K_{\rm im}^{\rm full}$ # solve for alpha @@ -193,7 +247,14 @@ def NMLL_fct_L(theta, Z_exp, xi_vec): Sigma = (sigma_n**2)*np.eye(N_freqs) h_L = compute_h_L(xi_vec) - K_im_full = L2_im_K + Sigma + (sigma_L**2)*np.outer(h_L, h_L) + K_im_full = L2_im_K + Sigma + (sigma_L**2)*np.outer(h_L, h_L) + K_im_full = 0.5*(K_im_full+K_im_full.T) + + # begin FC - added + if not is_PD(K_im_full): + K_im_full = nearest_PD(K_im_full) + # end FC - added + L = np.linalg.cholesky(K_im_full) # solve for alpha @@ -210,9 +271,9 @@ def der_ell_matrix_L2_im_K(xi_vec, sigma_f, ell): xi = xi_vec[n] xi_prime = xi_vec[0] integral, tol = integrate.quad(integrand_der_ell_L2_im, -np.inf, np.inf, epsabs=1E-12, epsrel=1E-12, args=(xi, xi_prime, sigma_f, ell)) - np.fill_diagonal(der_ell_L2_im_K[n:, :], exp(xi_prime-xi)*(sigma_f**2)/(ell**3)*integral) np.fill_diagonal(der_ell_L2_im_K[:, n:], exp(xi_prime-xi)*(sigma_f**2)/(ell**3)*integral) + return der_ell_L2_im_K # gradient of the negative marginal log-likelihhod (NMLL) $L(\bm \theta)$ @@ -227,6 +288,12 @@ def grad_NMLL_fct(theta, Z_exp, xi_vec): L2_im_K = matrix_L2_im_K(xi_vec, xi_vec, sigma_f, ell) # $\mathcal L^2_{\rm im} \mathbf K$ K_im_full = L2_im_K + Sigma # $\mathbf K_{\rm im}^{\rm full} = \mathcal L^2_{\rm im} \mathbf K + \sigma_n^2 \mathbf I$ + + # begin FC - added + if not is_PD(K_im_full): + K_im_full = nearest_PD(K_im_full) + # end FC - added + L = np.linalg.cholesky(K_im_full) # Cholesky decomposition to get the inverse of $\mathbf K_{\rm im}^{\rm full}$ # solve for alpha @@ -269,6 +336,10 @@ def grad_NMLL_fct_L(theta, Z_exp, xi_vec): K_im_full = L2_im_K + Sigma + (sigma_L**2)*np.outer(h_L, h_L) + # begin FC - added + if not is_PD(K_im_full): + K_im_full = nearest_PD(K_im_full) + 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\n", + "image/png": 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\n", 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" ] @@ -246,18 +246,18 @@ "sigma_n, sigma_f, ell\n", "0.8903599 5.0014151 1.0120875\n", "0.8136354 5.0035337 1.0291912\n", - "0.8291863 5.0357867 1.2588672\n", - "0.8303934 5.0832373 1.2117783\n", - "0.8304465 5.2060767 1.2283657\n", - "0.8305252 5.3874453 1.2524159\n", - "0.8305232 5.4068912 1.2546643\n", - "0.8305268 5.4070896 1.2546863\n", - "0.8305264 5.4070895 1.2546870\n", + "0.8291863 5.0357867 1.2588673\n", + "0.8303934 5.0832372 1.2117784\n", + "0.8304464 5.2060761 1.2283664\n", + "0.8305219 5.3874435 1.2524151\n", + "0.8305286 5.4068909 1.2546651\n", + "0.8305276 5.4070863 1.2546870\n", + "0.8305265 5.4070865 1.2546866\n", "Optimization terminated successfully.\n", " Current function value: 53.657989\n", " Iterations: 9\n", " Function evaluations: 11\n", - " Gradient evaluations: 50\n", + " Gradient evaluations: 54\n", " Hessian evaluations: 0\n" ] } @@ -335,13 +335,17 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", "K_im_full = L2_im_K + Sigma\n", "\n", + "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", + "if not GP_DRT.is_PD(K_im_full):\n", + " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", + "\n", "# Cholesky factorization, L is a lower-triangular matrix\n", "L = np.linalg.cholesky(K_im_full)\n", "\n", @@ -375,7 +379,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -459,7 +463,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -503,7 +507,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.9" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/tutorials/ex2_double_ZARC.ipynb b/tutorials/ex2_double_ZARC.ipynb index 022c5dc..6c91663 100644 --- a/tutorials/ex2_double_ZARC.ipynb +++ b/tutorials/ex2_double_ZARC.ipynb @@ -101,7 +101,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -175,21 +175,21 @@ "0.0811204 5.0008041 0.9965226\n", "0.0867785 5.0011230 0.9948113\n", "0.0859594 5.0061593 0.9701405\n", - "0.0844965 5.0183275 0.9169196\n", + "0.0844965 5.0183275 0.9169197\n", "0.0824855 5.0565844 0.7970074\n", - "0.0833165 5.0568936 0.7969525\n", - "0.0831366 5.2802597 0.7983940\n", - "0.0828135 5.7792060 0.8033087\n", - "0.0823987 6.8380146 0.8215793\n", - "0.0824158 7.5411797 0.8457629\n", - "0.0824354 7.7840680 0.8554877\n", - "0.0824365 7.8073390 0.8564169\n", - "0.0824369 7.8073402 0.8564052\n", + "0.0833165 5.0568936 0.7969524\n", + "0.0831371 5.2802597 0.7983940\n", + "0.0828131 5.7792052 0.8033088\n", + "0.0823995 6.8379559 0.8215798\n", + "0.0824148 7.5411947 0.8457864\n", + "0.0824349 7.7843276 0.8555132\n", + "0.0824372 7.8069559 0.8563856\n", + "0.0824366 7.8069559 0.8563856\n", "Optimization terminated successfully.\n", " Current function value: -86.240579\n", " Iterations: 13\n", " Function evaluations: 17\n", - " Gradient evaluations: 76\n", + " Gradient evaluations: 70\n", " Hessian evaluations: 0\n" ] } @@ -259,6 +259,10 @@ "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", "K_im_full = L2_im_K + Sigma\n", "\n", + "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", + "if not GP_DRT.is_PD(K_im_full):\n", + " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", + "\n", "# Cholesky factorization\n", "L = np.linalg.cholesky(K_im_full)\n", "\n", @@ -292,7 +296,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -374,7 +378,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -417,7 +421,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.9" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/tutorials/ex3_truncated_ZARC.ipynb b/tutorials/ex3_truncated_ZARC.ipynb index b603791..859de87 100644 --- a/tutorials/ex3_truncated_ZARC.ipynb +++ b/tutorials/ex3_truncated_ZARC.ipynb @@ -84,7 +84,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -151,17 +151,21 @@ "sigma_n, sigma_f, ell\n", "0.1050094 5.0001097 0.9994337\n", "0.1048101 5.0107903 0.9481658\n", - "0.1047303 5.0306223 0.8953994\n", - "0.1047554 5.2374446 0.9106751\n", - "0.1047344 5.6762154 0.9283942\n", - "0.1047286 5.7954129 0.9351723\n", - "0.1047278 5.8023412 0.9355591\n", - "0.1047296 5.8023412 0.9355592\n", + "0.1047302 5.0306224 0.8953992\n", + "0.1047554 5.2374445 0.9106782\n", + "0.1047695 5.6761672 0.9283906\n", + "0.1047295 5.6761793 0.9283937\n", + "0.1047294 5.6884928 0.9290939\n", + "0.1047294 5.7147866 0.9305899\n", + "0.1047292 5.7762536 0.9340913\n", + "0.1047301 5.8021615 0.9355663\n", + "0.1047302 5.8024810 0.9355922\n", + "0.1047297 5.8024810 0.9355922\n", "Optimization terminated successfully.\n", " Current function value: -68.171912\n", - " Iterations: 8\n", - " Function evaluations: 9\n", - " Gradient evaluations: 41\n", + " Iterations: 12\n", + " Function evaluations: 16\n", + " Gradient evaluations: 80\n", " Hessian evaluations: 0\n" ] } @@ -232,6 +236,10 @@ "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", "K_im_full = L2_im_K + Sigma\n", "\n", + "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", + "if not GP_DRT.is_PD(K_im_full):\n", + " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", + "\n", "# Cholesky factorization, L is a lower-triangular matrix\n", "L = np.linalg.cholesky(K_im_full)\n", "\n", @@ -307,7 +315,7 @@ "outputs": [ { "data": { - "image/png": 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1Ue/1xpR56+un1LVx7bXX4gTOACtCZUprvIcPw7XxozoZKAsnIzQ1NfHoo4+OuY6ltrY20rqYqrFmo03m+eefn3AdTTS73Z4VASYjB/nno+3bt0duIvtdePttKqMeOwHXqlXk5+dP+txly5ZhsVg4Fn/g6FGZSZYkGzduZNOmTWzeHL/Oe/xB9/gutdlobW2NWSA50fvU1tayb98+gJguvGTUa7akBSNEggUCAQJvvRVTdjI/H20ykZeXN+nzrVYrFRUVHG1vJ3qfU8uZM3i93gm72MTMNTU10dzczKOPPhpZye9wOHjmmWfYv38/cHWFPRD5Gb8OZTzxz12/fn3MSv7obrTwuZs2bYq0hsLvs2PHDrZs2cLOnTsj40d2u52dO3fy/PPP43A42LJlCytWrEj7eK6aD9+IGhoadPgXRIhkczqd7L39du6M+sD4ZU0N1Tt3Trlb4/3vfz+1f/wjz0WVdb///ZhffpmioqLEVliIcSilWrTWM15II11kQiSYy+Vi8blzMWWXli2jpKRkyq9RW1vL0bgya3u7JL0UWUW6yDLEd7/73cj9L33pS2msiZgt58gIS+P6wQfXrJlWssoVK1bwYlyZ9cIFLvf1IamPRLaQAJMhvvzlL0fuS4DJbi67nUq/P/L4CpC7cuWUxl/CVqxYwRBwjqvbLSu/H8+RI7B6dSKrK0TSSBeZEAnmP3w45vFxoGrJkmltGFZTUwMwqpuMo6NKhMhY0oLJEH/7t3+b7iqIBNBaEzhyJKbsGHDDypXx2SkmVF1dHXnun0WVm9va8Hq946aaESKTzIsA43K5OHbsGIFAIFKWk5ODyWQiJyeHnJwcLBYLFosFs9k8rQ+CRIkegxHZy+12o44fjyk7l5/PxmmuwK+oqCA3N5ejcQkurWfP4nK5JMCIrDAvAozH44msxA0Hj0AgELmFaa0xGo0UFhZSXl5OaWmprDkQ0+J2u7G0t8eUdS9YQEFBwbRex2AwsHTpUo62tcWUW8+exeV2U1hYOM4zhcgc8yLAKKWwWq1TOjcQCOByuThx4gRwdY8Om82GwSBDVmJibrcbW2dnTNmVqqop//5Fq66u5p34AHP+PL0DAyxcuHBW9RQiFeQTM47BYMBisWCz2SguLsbhcPDuu+9y8OBBhoeH0109keGGL1ygKOr3xAMY6upm1KW1fPly+oFLUWUGrxdPXBecEJlqXrRgZkopRX5+Pvn5+QwPD7N//35qa2uprKzEaDRO/gLT8I//+I9j3hfZxXfoUMzjU8DyuroZvdby5cuB4EyyxdEHjh6F++6b0WsKkUoSYKYoPz8fv99PW1sbXV1drFmzZkqJC6fqn/7pnyL3JcBksWOxKSqPAatnuG4lOsDcFVVuOnmSQCAgXbYi48lv6DQYjUZKSkrwer0cOHCAkZGRyZ8k5g2v1ztqgP8YUDfLFkx8VmVrezveuK0AhMhE0oKZAavVysjICAcPHuTGG2+c1grt8Xz9619PQM1EOrlcrlEB5jjw31atmtHrjbfY0nruHG63W7ZPFhlPAswMWa1WhoeHeffdd1m3bt20VmmPRbrFsp/b7cZy5kxM2YXCwhlPKV68eDE5OTkcjWutWM+epd/lAsmqLDKcdJHNQn5+Pj6fj0OHDuGJWxAn5p/h3l7yL1+OKXOFVuTPhNFoZNmyZXQDPdHlbjeeU6dm/LpCpIoEmFkqKCjA4/GMyhQg5h/vkSMYovZXagfKQt1cMxU90B/NHzdbTYhMJAEmAQoKCujr6+Ny3LdXMc/ErU85xtUAMVPjBRhJeimygYzBJEhRURGnTp3CZrPNaDwmOkW/5CXLPoFAANPp0zFlx7k6UD9T480kyzl1Cq11WvLmCTFVEmASxGQyoZSira2NtWvXTvsP/3vf+17kvgSY7ON2u7GOMUX5/hUrZvW647VgrGfP4vV6JVeeyGjSRZZABQUFdHV10dPTM/nJYk5xu91Y47ZJTmYXmfXsWdwu16xeW4hkkxZMAimlKCwsjHSVTSf/1He+850k1kwkm3tkhMLz52PKjnF1X5eZCgeYiwR3xgxPTDaNjOA5fx6uvXZWry9EMmVcgFFK1QNPAtu01s1R5U8AC4DngVLgbq31lvTUcny5ubk4nU7OnDnDqmkssJNtkrOb68QJjFFT1XsAb1ERxcXFs3rd8FoYr9fLKWB91DHf8eMSYERGy6guMqXURoLBo3acUxqBV4FHgadTVa/pKioq4uLFizidznRXRaTIWLtYLlu2bNavG14LA3A67ljg5MlZv74QyZRRAUZr3RxqtfSNcdihtS4J3TZrrR0prt6UKaUwGo1cuHAh3VURKRK/i2Uixl/Cwq8TH2CQxZYiw2VUgJkKpVS9Umq8Fk7GKCgo4MKFC7jd7nRXRSSZz+fDHJci5hiwYpYzyMLGCzDG9nZ01MJOITJNVgUYpdQmwA7UK6Wa0l2fiRgMBpRSdMbtbjiexsbGyE1kl/FmkCU7wORduCBZlUVGy7hB/vForbdHPdyplGpSSu2OnggQTSnVSHDMhvLy8lRUcZSCggLOnz9PZWXlpDPKnnnmmcj97du3T3CmyDRul4vCs2djyo4Dj9cmpqE9UYBxud2yFkZkrKxpwYRml0VrBe4e73yt9XatdYPWumG2M3lmymg04vf76e7uTsv7i9TwXLhAzuBg5PEIcA6oTXCA6QSiN+02DQ/juXgxIe8hRDJkRQsmFFxeBUqiim1AW1oqNA35+fmcPXuW8vLyCbdZ3rZtWwprJRLJc/hwzOMTgCZxg/zR6WZOA+uijvlPnIAZ7pgpRLJlRYDRWrcqpR6JK64FXkhHfaYjJyeHoaEhent7KSsrG/c8GXvJXvrEiZjHJwmuX0nERnQQuxYmPsD4jh+Hj3wkIe8jRKJlVBdZaIbYE0ADsCV0P8yulHpCKdWolNoGZPRU5WhWq5X29nZJ5z8Haa0xxiW5PEniuscgOGEknBFg1FTl06NKhMgYGdWC0Vq3Ehxb2TrBsaxjNpvp7+9naGiIItmFcE7xer1Y4maQnSRxM8jCamtrOX36NPErX8JTlSWrsshEGdWCmctMJpPsFzMHud1u8jo6YspOkNgWDEBdXR0wugVj6ejA5/Ml9L2ESJSMasHMZVarlUuXLlFTUzPmYP+nP/3pyP2f/exnqayamAX3yAilcRkbTpG6AJPX0YHb7Z5WYlUhUkUCTIqEpywPDAxQWlo66vjPf/7zyH0JMNnDc/o0hqjFjpcBB8kLMBcBJxCePpAzOMhQVxcUFCT0/YRIBOkiSyGz2cxFWbcwp/jiti4Op59MVoDRjJ6b7z0Wv9+lEJlBWjAplJeXR29vLx6PZ9Tq65/+9KdpqpWYjbGmKOfl5VFRUZHQ96mpqUEphdaa08B1Ucf8J07A/fcn9P2ESAQJMCkUnunT19c36gMoegxGZIdAIIDJbo8pC09RTvSsLovFwtKlSzl37tyocRgtWZVFhpIushSzWCySxn+O8Hg8WON2sUzGDLKw8Qb6TZJVWWQoCTApZrFYGBwcZGRkJN1VEbPkdrvJiwswJ4HVSUrdMl6AMctUZZGhJMCkgcFgoLe3N93VELPkdjgwR61tChAcgE91gMmTfYdEhpIxmDSwWq10dHRQVVWFwRCM8X/+538eOf7yyy+nq2piGjzHjqGiuqbOAm5g1apVSXm/cIA5H3ofc6g81+FgqLtbpiqLjCMBJg1ycnIYHh6OSR3zm9/8Js21EtPlj5seHJ6inOwAEyC4696aqGPe48chKuuyEJlAusjSxGAw0N/fn+5qiNkYY4pyUVFR0ja4i548EN9N5pO1MCIDSQsmTfLy8ujs7GTZsmUopXjppZfSXSUxDV6vF3PcLpYnCLZekpV4Mj8/n8rKSi5evChZlUVWmHaAUUrdCKC1PjDGsU8AbWMdE7HC3WROpxOr1RozBiMy31hJLk+SvO6xsNWrV48ZYIxnzkhWZZFxptxFppT6slLKD7QALUopv1LqB0qpwvA5WusXg6cqfxLqOic5HI50V0HMgMvlGnOKcrIDzJo1wZGXsWaSeTyepL63ENM1pQCjlPpX4PPAV4F7QrcngTrAoZR6Onyu1vodQL5GTYHFYqGrqyvd1RAz4LxwgdyBgchjF8HZXcmaohw2XoCxyFRlkYEm7SJTSt0EoLWuizv0KrBVKVUMfFIp9QKwC9iR8FrOUWazGYfDgdvtxmw2T/4EkTHchw/HPD5NcHZXqlowZwEvEE7Sb+7r40pvL8iGdiKDTGUM5i6t9efHO6i1HgCeAZ4JBZsGYEuC6jenKaVQSjEwMMAnP/nJSPkf/vCH9FVKTMlYSS4BVq5cmdT3veaaawDwA+1A9Lt5jx2Tqcoio0wlwJyZ6ouFgs2roZuYgtzcXC5fvszrr7+e7qqIKfJ6veSeif2zOAEsXryYwsLCsZ+UIJWVlRQWFjI4OMgpYgOM//hx+PCHk/r+QkzHVMZgJIteEoVT+IvsMd4MsrVr1yb9vZVSkW6yk/EHJauyyDCyDibNwnt8/PrXv46s6heZzeVyjcqifBK4+brrxn5Cgq1Zs4Y//elPxIeTnPZ2AoFAJP2QEOk2lQBzi1KqWWt9ZbITlVIfBEqAT2qtH5x17eaJnJwcVq9enfQZSCIxhgcHKYnbcuEk8LkUBpjwe0bLO38ej8eDxWJJST2EmMxUvupsA3ZEr3eJppT6oFLqX5VSzwN9obUwmxJZybkuLy+P7u5uAoFAuqsipsDZ1obR5Yo87gd6gOvSHGCs58/LVGWRUSZtwWitzyilXgTalVLNwD5gAVALbAT6gEe11r9Pak3nMKPRiN/vj0l+KTLXeEkuUzEGA1cDzHmC62/C7ZWcK1fwdHZCcXFK6iHEZKbUWau13g48CKwAthKchrwC+KrWemU4uCilapRSX2EaM89EkCS/zA4+n4/cuLxfx4Fly5al7MtBTU0Nubm5aEYvuPQePZqSOggxFVMeDdRaN2utG7TWhtCtQWv9TNxpNq31t8dYlDllSql6pdQOpdTGuHKbUuoJpdSm0M/6mb5HJmpsbORDH/oQ69evT3dVxARcLhf5cVOUj5C67jEAk8kUaS3FD/THt66ESKeEziILpYmZsaigMtam5jsIdsXZQ+fuVkpt1lo7ZvOemeL48ePproKYApfLhTUui/JRUhtgANatW8eBAwdGjcMoyaosMsiELRil1LdCM8NSItRKaiY4rhNdDxtQGw4uIXaCY0BCpMzI8DD57e0xZaluwUAwwMDogf7c9nb8fsk1KzLDZC2YbcCjSqmtBAf3t6UpFX8D4IgrcwB3AztTXZlk+NnPfobb7ZYpphlu+MwZcq5cnbE/TDAvWKoDzI033giM7iILZ1XOy8tLaX2EGMuEAUZrfYZgBuVw0svPK6XWA80Eg0170msYZCOuVQP0MnZXWlZau3YtWmsGBgbw+XyYTLIGNhMFDh2KeXwMUAZDJEdYqozXgsk7f55Bp1MCjMgI0xnkf0dr/Xmt9c0EA8xWpdQrSqmHlVKpmD5TOp2TlVKNSqn9Sqn9A1Fp1TNZeLOowcHBNNdEjGWsGWRHgbq6upR/oJeWlrJkyRK6gOjfFpPTiTcuy4AQ6TKjnBJa61e11p/UWn+I4DqznaFg8/HEVi/CQbAVE20Bo1s10XXcHprp1lCcResCjEYjfX3j/rNEGrlcrjHHX9I182+8VoxMVRaZYtZJi7TWL2qt7wE+CSxQSu1SSj2f4MkB+xndgrEBuxP4HhkhLy+Prq4utJYco5lmvBlkmRZgZKqyyBQJy4qntR7QWj8TCjZfBdaHuqh+qJS6cZav7QD2K6Wix1waCHbVzQkf+chH+MhHPsLHP/5xvF4vIyMj6a6SiDPeDLL6+vQsyRpvoN/Q1pbyuggxlqSMJIcmB3wb+HZocsB/UUo9OVkCzNDiyY2ENi1TStVrrbeGDm8GGpVSdoKD+4/MlTUwAOfOnYvcV0rhcDjIz89PY41EvOH2dnKixvNGCG76ddNNN6WlPuO1YCznzuHxeMjNzU19pYSIkvSpSqHFl1NagKm1bgVaCaajiT/mGKt8LjKbzVy+fJmqqqp0V0VEGWsGWfXy5dhstrTUp66ujsLCQk7GTQrJ6+jA6XRKgBFpN6MAo5T6uNb6PxNdmfns17/+deS+2WxmYGBAvoVmEI/HQ07chl5HudqKSAeDwUBDQwPvvPZaTHnehQtcHhoimya3iLlpprPI/lMp9YhS6stKqeUJrtO8VF1dHbmFpytfuTLpFjwiRUZGRiiIG+A/AjQ0NKSnQiHvec97cADdUWUGr5eREyfSVCMhrprxIH9oQP87BAfzv5zEKcrzUk5ODt3d3ZOfKFJicHBwzBlkt956a3oqFLJhwwZg9EC/98iR1FdGiDiJmEXWTDA9/y1KqdOhKcoPS8tmdvLy8ujp6ZG8Uhmiv78fa1wW5WNKccstt6SpRkHhABM/0G84fVp+d0TazTjAKKU+HtrF8i6gWWv9Va11XWim2KsEWzb/Gpqm/HSKVvvPGQaDgUAgIN1kGSAQCDBy9iy5UTPInEDuqlUUFo650WvKVFRUsGzZstEpYy5cwBW166YQ6TDTQf5vAZ8A1mutR30ChqYpnwFeDJ1fPNZ54qq77747cn/37uD6UZPJxOXLlykpKUlXtQTgdDqxxK0tOQasT3PrJWzDhg2ciprmDsHtk10ul0x1F2k10xZMI9A01aChtc6OZGBp1N3dHbmF5eXlcfnyZenqSLORkZFRCyyPEhxgzwQbNmwY3YLp6GBoaCgt9REibDZjMJLLJMmMRqN0k2WAgYGBUQP8R4D3vve96alQnA0bNozaOtnS2cmVnp601EeIsJkutPwqwdxjzyawLvParl27xiw3Go309PRIN1ka9ff3Uxi34+gZiyXle8CMZ/369fhyc+nweFgSKlOBAN4TJ9D19ZFp70Kk2kzXwWwHmpVSTye4PvNWWVlZ5BbNarXS1dVFIBBIU83mt3BeuPy4FozxhhswGo1pqlWsvLw8brnlljF3t/R4PGmpkxAwu3Uw3wa2y/qX5DIajfh8PtkjJk1GRkbIcTgocDojZU6g9q670lepMdx5552jAoy1vV1mkom0mtU6GK31GUkZk3wmk4ke6U9Pi6GhIfLi1r8cB+7IsADzwQ9+kHfjygpOn2Z4eDgt9RECEpiuXySP1Wqls7NTusnSoL+/H+87sblaT5pMaUvRP573vOc9HIvbZtty8qS0fEVaSYDJELfddlvkFi/cTSbTTlNLa83AwABq//6Y8r7KyoxbX2KxWDDGbRtQcPEig5cvp6lGQkiAyRgjIyOR21gMBoN0k6WYy+XC5/NRZrfHlPsaGsjJyUlTrcbX8MEPEl1Tg9aoo0dlHZVIGwkwWSI/P5+LFy/i8/nSXZV5Y3h4GH93N9VRA+V+oPoTn8jIqb933HEHB+PK8k+floF+kTZJ33BMTM2bb7454fFwN9nly5eprKxMUa3mt4GBAfpfeSWm7JjJxNoMSRET7/bbb+efc3L4mNcbKfPu34/T6cy4Lj0xP0gLJkPk5+dHbuMpKCjg7NmzMtifIv39/ei33oopO19VRVFRZuZtzc/Px716dUxZzrFjMtAv0kYCTBbJycnB7XbLWEwKhCdVLIpLcumpr8dsNqepVpNbGDd9enF3N1cGJBWgSA8JMFnGarXS3t4urZgku3LlCu12OzfEjV/Y7rkHi8WSplpN7pYHHyS6vVIcCHDpT39Ca0kdKFJPAkyWMZvNjIyMMCDfSpOqs7MT+yuvEJ0BbtBoxLh2Lbm5uWmr12SWVldzOi8vpuzi734nA/0iLSTAZIgbb7wxcpuMxWKhPS59vEgcr9cb3E30jTdiyi8tXUpBUVFGziALs1gsOKqrY8q8+/bJFxKRFhJgslBeXh4Oh0PS+CdJf38/XV1dLL14MaY8cMstad/BcjJmsxnzzTfHlC3o6OD06fiE/kIknwSYLJWbm8u5c+ekbz0JOjs7ef3114nfTsy7fj0FBQVpqdNUWSwWLBs2xJRdD/zqV7+SBZci5STAZIgDBw5EblORn59Pd3c3HR0dya3YPON2u+nr6+ON3/2O6+OOXbnmmowe4Ifgein/2rVETwFZCbzxyiuSakiknASYLKWUori4mNOnT3Pp0qV0V2fO6O3txW63Y2trI3q3l+ElS/AVF2d8gAEoXLyY4YqKyGMDwOHDHI/bNE2IZMu6AKOUekIp1aSUqldKbVRKNaW7TuliNBopLi7m+PHjXJakhglx6dIlXnvttVHdY6516zCZTBk9gyysqKgI16pVMWU3AD//+c/TUyExb2VdgAlpBF4FHgXm9a6aRqORwsJCjh49Sl9fX7qrk9VGRkZwOBzs2rVrVIAZWLMGm82W0TPIwqxWK0N1dTFlNwC//OUvcUZtnCZEsmVjgHForUtCt81aa0e6K5QIw8PDkdt05eTkkJ+fz7vvvsuZM2fkQ2SGent7+dOf/sTly5fZEHesf/VqSkpKxnxeprFYLAzX1saUrQPOnTvHrl270lMpMS9lbbJLpVQ9wWBjn/TkLPDe9743cn+qA/3RcnNzMRqNdHR0cPbsWcrKyliyZAmFhYVZ8a073bTWXLhwgZdeeollwOKoYwGLhaGamqxJGGk2m3GO0UUG8Mwzz/DAAw+kvlJiXsrGFgxKqU2AHagfbwxGKdWolNqvlNo/XxaZGY1GioqKsNls9Pf309raSktLC52dnXijMuyK0a5cucLJkyfZu3fvqO6xkbVrwWTCarWmpW7TpZQid+VKfFFTqouB5cArr7xCZ2dnuqom5pmsCzBa6+1a651aa4fWeiewSSm1cZzzGrTWDcXFxWmo6fRYrdbIbbaUUhQUFFBSUkIgEODEiRO89dZbnDhxQvZoH4PX6+XEiRP89re/BeB9cccHr7sOq9WakZuMjaeouHjMbjKfz8f3v//99FRKzDtZF2BCXWPRWoG701GXRNqzZ0/klkhmsxmbzUZhYSHd3d3s37+f8+fPS7LMEK01bW1tdHd389vf/hYD8PG4c/pXr8Zms6WhdjNXWFjI0IoVMWU3hn7+4Ac/GHfnVCESKasCTCi4vBpXbAPaRp8tohkMBgoLCyksLKStrY0DBw5Iawbo6uri0qVL/OY3v2F4eJjbgaqo4/68PHrXr8+6AGOxWBhauTKm7IOhn319fTz77LOpr5SYd7IqwGitW4FH4oprgRfSUJ2sZDQaKSkpwe12s3//fjo6OuZtupnh4WFOnDiBwWDgpz/9KQCfijvnyp13ErBYsmb8JSwvL4/++tjG/m1AeKu073znOzIuJ5IuqwJMiD202LJRKbUNmDNTlVPJarVSWFjIqVOnaG9vn3dBxufzcfToUXJzc9m5cyeDg4PkAJvjzuv70IcwGAzkxaXAz3RGoxFDTQ3OmppImQkIb0d27tw5nnvuuXRUTcwjWTdNOdSKaU13PRIteiV+WVlZSt7TaDRis9lob2/H5/OxYsUKDIZs/M4xdU6nk56eHjo6OiLf4P/jP/4DgHuA0qhzfTYbvevXU1RQkJXXpbi4mP5bbiHvzJlI2YeAX4buP/XUU3z605+e8fRrr9eLy+XC6XQyODhISUkJNpstK6+VSI6sCzBz1T333BO5P5N1MDNlMBgoKSnhwoUL+P1+Vq5cidFonPyJGSIQCDA4OMiVK1cIBAJorSM3pRQGgyFy6+7uZmBgAKVUZMZeU1NTZNuDT8e9tmPjRlx+P4tLS0e/cRYoLCykt6GByuefj5TdG3W8s7OT7373uzz11FPTet3+/n5Onz4dM1HAaDRy/vx5zGYzS5cupaysLCvS6ojkkgAjUEphs9no7OzE7/dzzTXXZHSQCQQCDAwMcPnyZbq7u/H7/SilIrdo0QHHbDZTXFwcOefMmTO88EJw+M4KxC8/dNx7L1rrjE/RP578/HzabriBgNmMwe0GYBlwDRBOe7l161YeeeQRFi9ePN7LRHg8Hux2O5cuXcJqtY458cHr9WK322lra6Ouro6qqqrRLyTmDQkwGWLRokVpff9wkOnp6eHw4cOsXbs2I9d9DA0NcfLkSa5cuUJOTg5Wq3VGwVBrzdatWyN7pPw5EN1R5CkvZ/imm+DKlaxZwR/PYrEQMJsZamig6M03I+Ufs1h4OrSF8vDwMI8//jg7d+4c93UCgQDd3d2cOnUKrTUlJSXjZofIycmhuLgYv9/PiRMn8Hg8VFdXS7fZPCX/6xli9+7dkVu6hIPMwMAAhw4dwuPxpK0u8Xw+H3a7nf379+N2uykpKaGgoGDGLa1f//rXvPXWW5HHo7rHPvQhfIEAubm5WdvVk5ubi8lkYuA9sbkJ/jKutfLiiy/y8ssvj/kag4ODHDx4kKNHj2KxWCia4pbR4dmK7e3tnD59WtZdzVMSYMQoxcXFjIyM8O677+IOda2kU39/f2SBaHFx8aynDF++fJnvfOc7kcclwL1xH5qOe++NBLJspZSisLCQvrgtlOsuXKD+mmtiyj7/+c9z7ty5yMQHt9vNqVOnaGlpweVyUVpaOu0WbXh879KlSxw7dgyfzze7f5DIOhJgxJgKCwtxu90cOHCA/v7+tExj9vv92O12Dhw4gMFgSMgMJb/fz9e//vWY3R0fNJnIifr3uZYvx3nNNXi93qxbYBmvuLiYK4sX44lqtRg8Hr730Y/GtP4uXrzIQw89xJtvvsmePXt4++236ezsxGazzSqgh1vFvb29HDlyRLZtnmckwIhxhQe3Dx48yKFDh1K65e7w8DDvvPMO58+fx2azYTabE/K6zz77bEzXmBX4x6KimHMcf/ZnEGrRZOsAf1h+fj4BrbkSla0bYO25czz00EMxZa+//jrNzc1YLBYKCgqm3B02FcXFxTgcDk6ePCndZfOIDPJniLNnz0buV1dXp7EmsSwWSzDtyNAQ+/fvp6KiIjLIG/7wCQQCeDwe3G53pEutsLAQq9WKxWLBbDZPuXvF4/HQ1dVFW1tbJI9aorz11lv88Ic/jCn76YIFlPf2xpT1h2aPAVm3wDJeuP6Dt93GwqiB/MI9e3jshRfYu3cvx44di5R/+9vfZtWqVaxbty7hdSkuLqarqwuTyURdXZ1sIzEPSIDJENF7dKRyHcxU5efnY7Va6enpoaura9RxpRRGoxGj0YjWmt7e3shaFK01RUVFlJWVUVRURH5+/qiurqGhIS5evMilS5dQSlFUVJTQqdKnT5/mK1/5SkxX38P5+Xw0Lrj0fvSjeKqrcbtcCa9DOlgsFgAGb74ZbTKhQuMglvZ2Crq7+da3vsWnPvWpyJoWj8fDf//v/52f/OQnVFZWJrQu4e6yjo4OTCYTy5cvlyAzx0mAEVMWHjSeLq01brebtra2SNAxGo2RBZAQXGFvMpkoKipK+JTWrq4uvvjFL8Z08dUB348bdHbV1HBxy5bgfZcro1qSMxXeUtvl8zG8bh0FLS2RY4V79lC9eTNf+9rXePLJJyPlfX19fPGLX+Tf/u3fKE3wItNwkDlz5gwmk4mlS5cm9PVFZpExmAyxbNmyyG2uUUphsVgoLi7GZrNRVFREXl4eZrMZk8kUmdJaWFiY8OBy+fJlHnnkkZhNtnKB35eVkRs1Qy6Qm8vZpiYCeXmRVk6iP1zTZdGiRbjdbgZvuy2mvOSllyAQ4N577+Xhhx+OOWa32/n85z8fyXIwEeVykXv+PGqKW3WHJ2ycPn2as2fPzrs8ePOJtGAyxEsvvZTuKqRMuAWTbBcvXuSxxx7j3LlzACwgmC35S8XFLI3K/QZw8StfwRXaZtjlclFSUpK161/i2Ww2AoEAV26/ncX/+39HyvMPHaLkpZfo/+hH+cIXvkB7ezvNzc2R4ydPnuThhx/m+9//fsxC4NyODop//3ssJ06Qd/w4lvZ2lN9PwGym/9576f0v/wVn3DToeOE8eHa7Hb/fT01NjXSXzUFqPnx7WL16tQ6nBBFzj2FwEOuxY5i6u8np6cHU28vwmTO0/OlPkUkHNoK70o0VMhwbN3L229+OzBxzOBysWbMmZUlHky0QCPDmm2+Sn5/Pir/9W4pffz1yzFdSwvFf/Qp/cTFut5u/+Zu/Ye/evTHPr6ys5Ic//CHLKyoof+YZFj33HIZJ1rQM33ADPZ/5DI577olc1/Hq5nA4WLJkybxItpptlFItWuuGGT9fAozISlpjPXiQBS++iG3XrkiurelyV1Zy8he/IBCaqqy15sqVK9x6660ZmSpnpo4dO0Z/fz8lDgerP/7xmOvVs2kTF/7hH4DgWNgXv/hFWqLGagDuz8/nx1Yrtu7uab2v4557OPfNb6InaA1qrXE4HJSXl7NixYqMbTlqrQkEAjE3v98fSbIa/glEEq2GJ77k5ORgMmVPh5HH42FgYICysrJZBZjs+RcLAeDzseCXv2TBCy+Qd+rUjF9GK8Xg+95Hx9//fSS4QPADduHChXMquAAsXLiQy5cv46mqouvhh1n8/e9Hji148UX6HngA5/XXk5eXx7/8y7/wla98hTfeeINFQBPwueFhmGAHVH9BAcYx1knZdu3C6HDQ/r3vERhnTVF44L+7u5ve3l7q6uooKyubdWvG7XbjcrnweDyRbQWcTid+vz8SGMILP8Pdc+Gf0V+8w+dFl4VnR4Z/jif69XJycigoKKCgoCAyjT8vLy9jWm1+v5+BgQEuXbpET09PQjakkxZMhjh69Gjk/tq1a9NYk8xlOXWKpV//OtaoazVdrupq+j/yEfrvvx9vefmo4/39/Vx//fUsWLBgNlXNOC6Xi7179wbXMHk8rNq8GUvU2quRNWs49ZOfQGhszDcywsFHHuETR45QPMbrOUtK6P/c5xhZuxbn6tUErFaK/vhHFv7iFxTGdbEBOFevxv797+NbuHDCenq9XgYHB7HZbNTV1U151qLX62VkZIShoSEcDgcDAwMxH5BKqciEEoPBMGH27bHGgsLPmQ2/34/X68Xr9UYCm8FgoKioiNLSUoqKirBarSn9chO+3l1dXfT09BAIBCJJZAcGBrjjjjuki2wyqQwwhuFhcs+fJ6enB0IrllUggDYY8FRW4q6uhjF+gW688cbI/UxcB5NWXi/lP/oRZc88M27f/1ngbaATuAR0AT6Dgfvvv58NGzYA4F6+HOfateOOCQQCAYaGhrj11luzqjtjqvbt2wcEk2AWvPUWKx57LOZ4OEWOe/lybL/7HZb29lGvEQD+Ffia0cjHP/c5Pve5z43KNm1ua2P5l7406vnuJUuw/+AHeKYwU3JkZASXy4XFYsFms1FcXExBQQFKKXw+X+Q2ODhIf38/rlB2aKUUOTk5mM3mrFjDFL1IOfxZbLVaWbhwYcxi5US1crTWuFwuBgYG6Onpoa+vD601JpOJvLy8mGvmcDgkwExFUgKM1uSeO0f+wYPkHzyIpa0tGFjiFu7FC5hMuGtrcdXVMVRfz8A99+AvKpIAMw7LyZMs+4d/IO/kyVHH/ErxO6ORf/H52EXwwy+sqqqKpqYmrrvuuim/19DQEAsXLmT16tWzr3gGOnv2LOfOnaMo1CVY/cQT2HbtmvLzDwONwFtRZQsWLOALX/gCDzzwQExQNvb3U/PXf03+oUMxr+EpL+f0c8/hncL+MxDMou3xeMbN7G0ymaaVKSLTaa3xer243e6YfY6KioooKiqioKAAs9mMxWIhJydn0laV3+/H6XRGgkp3d3dk4ktubi55eXnjvoYEmClKSIDRGnN7O4V791Lw9tvkHzyIqb9/1nUL5OYy8MEPcvvRowSsVlCKn//857N+3awXCLDw5z9n8T//M4YxPlxeMpv5gtvNhTGeet999/HVr3512otC+/v7WbduXVZnUJ7IwMAABw4ciKTfMXV1cc3HPoYxamfKsfgLCmh76CEeP3aMXa+9NuY5VVVVPPTQQzzwwAOR7AEGp5PqL385Zi8aCLaUTv/oR/jnyDqjZAu3csJda9HjPrm5uZjNZsxmMwaDIWbiQXgMKsxoNEYC01RIgJmimQYYo8NB4d69FL71FgV795I7RoqURHJXVdH5hS/g+PCHJ5zaOdeZenpY+tRTFO3ZM+rYZaV4TGv+c4znLV68mK997WvcFregcCr8fj/Dw8PcdtttWdG1MhN+v589e/ZQUFAQ6XIp2LOHqm9/G8uZM6PO10rR99GP0vn44/hCwWD37t1861vfoneclnpJSQkPPPAAH/vYx4KZELxelv7TP1H6m9/EnDeydi1tzzxDIEs3c8sE4Zlr4UkL4fGj8M1gMMyqZScBZoqmHGC8XvIPH6bgrbco3LMH65EjqGleH20y4Vm8GE9lJdpkAoMBrRQGtxuL3U7OFKZ5Dt94Ixe2bMG5Zs203jvraY1t1y4qv/UtcsZoHf4U+GugL648Pz+fv/zLv+Qv/uIvZpyccmBggKqqKlasWDGj52eLw4cPMzg4OCoFv+HKFfLa2rCcPInl9GnQmr5PfGLM38Hh4WGee+45fvzjH8d8Q463fv167r33Xj74gQ9wU1MTtqhFnACDt9zCmX/5lwmnMIv0kQAzReMGGL8fy6lTFOzfT+Hbb5Pf0jJpd0HM061WRq6/nuF16xi5/nrcNTV4KipgggFio8MRfM+WFkpefhnzhbE6ea5+e7z013+Nf4522USzvvMOld/9LvmHD4865gAeBeL/B81mM5/4xCd4+OGHZ5XWxel0YjAYuOmmm+ZMX/54Ojs7OXHiREKyVHd1dbF9+3ZeeumlCae0KqXYcOON/HtfH6uiZq4BDNx5J2e3bkXP8euejSTATFE4wBhGRsg7doz8AwfIb20l/+DBMefujydgNjNcX8/ge97D0IYNOFeujEzrnJFAgPyWFkp/9Stsr7wy5gwp76JFnPvmNxkKzYSaS3wuF45XXqHsZz/j+hMnxjznj8BfAOeiymw2Gw8++CAPPvjgrPOF+f1+rly5wvr162eUyDPbOJ1O3n777YSOM3V3d/PTn/6UnTt3TrhnUAHwKnBLXPnAbbdx9nvfQ4fGbkRmkAAzReuKi/XeRYuwnDmDmuZmR85Vqxi87TYGb72V4RtvRCdo46t4B377Wxa88AIFBw9yR9wxrRSXP/c5Oh97bMwpzhlDawzDwxicTjAa0UYj2mAArXF2dXH51Cm6Tp7EdeQItSdPsmFggPHCgxf4H8D/5OrssA0bNvCRj3yEu+66KzKQPLvqavr7+1m5ciVLliyZ9etlA601b7/9NiaTKeGtNafTye7du/nP//zPcWdCLiD4pSG+421/QQHb7ruPJWvWUFtbS01NzbwI+JlMAswUNSil90/xXO/ChQxu2MDQhg0M3norvqgkf8kUPU3ZuXz5mGsQhq+/nnNPP40nAz4MTV1dFP3xjxTu3UvuxYuYensx9vVhTMDq318CW4BTwHXXXccdd9zBvffeS1VV1axfO1p4Qd/atWszZjV1KnR0dHD69OmkzpY7c+YMzc3NvPrqqxw/fjzmWBXwe2BV3HPeBu4FwqNvZWVl1NbWsnTpUiorK2NupaWlkhwzyeZlgFFK2QhOx7cDtUCz1rp1oudMFGB8xcUM33QTQzffzOCGDbhXrEjLDK6YdTD79lGxbRtlzz47apKBv6CAc9/4BlfuvDOp9QnPqgqvjHY4HATa2lj15pusPnmSZX3xQ+2z9yfgqbw8RhoauP322/nABz5A+Rir7RPB6XQSCARoaGjI2NxXyeL3+2lpaUFrPauWoNfrxePx4PP50FpjNBqxWq2jZuFduHCB3//+9+zdu5fW1lacTiflwC7ghrjXPEbwj/uNSd7bbDZTWlrKggULWLhwYeR++FZUVERhYWHwZ0EBxV4ved3d5HR3o1wuDB4Pyu2OTIHXBkNwQk7oi0bk705rlM8XPNfpxBD+OTKCwenEGG6x+/0ovz94rt9PIC8Pf0EB/sJC/AUFeMvKcFdXB2/Ll4+bNieTzNcAsxt4VGttj3q8WWvtGO850QHGFVrNPXzTTQzddBPu2lrIgG+vf/VXfxW5/+yzz6K1Ju/tt6n52tfIHWPmmf0Tn+DYZz+Lj6uL0cJbFofvR/8M52SKfjwyMsLw8HDkNjQ0FEm3ET07aAXwd8BDJD55XZ9StC5aRMeGDZgffJDVa9YkbZqwz+djeHiYQCBAYWEhK1eujCw6nG8GBgZobW2NbH89VVprhoeH8Xq95OXlUVxcHNnfp7e3l4sXL6K1xmq1jhm4vV4vR44cYd++fbS3tvJPf/oT60NpU6L9O/AEcHnUkYktANYDNwMNwFpgKZBpG197ysoYueGG4AShG2/Eec01GTPRweB0UvTaaxS89BIL9+6dPwEm1Hpp0VqviCrbBuzWWu8c73nVZrP+2OrVHM/PZyj04RXOfBr+98c/js6OOt45Ez1nKq8Rnr/u9/vx+Xwxj8O5ihYAzwJXN1S+6v8BDxJMj5IMdcDXgM8AU/3IHwGuhM43EgxIKlQ2nJODNy8PbbMxsmYN6sMfJvd975vdRIko8au+oz84w+kwKisrKSsrG5XeZD46fvw4PT0908r3NTg4yMKFC6mrqxtzSrjX66W7u5vz58/jcrkoLi6eMICpoSGWPPYYpXEr/iE4e/CfCY7Z7CP4OxTNSrAFtCHqVjulf0nmcQL7c3N5MzeXt/LyOGyxEAjlTTMajTHrW6JzqE2lbCrn5mhNw5Ur3N3dzft7e7GG01wFP2/nTYDZCDRprddHlTUBNq31oxM8L3v+keP4G+DbQPx3nMvA5wmOWyRKMfAU8PgY7xcWAPYCvwFeJ5j/y2OzUbR4MeXl5VRUVFBVVUV1dTXLly+nsrIyKfm9/H4/Q0NDBAIB8vLyKCgowGazRfIqhRecKaUyKnNtJnC73ezbt4+8vLwJ/2/CWxgYjUZWrVrFwoULp5Si5OTJk3R2dk7aSlIuF0uefprSX/963HMCwDmrlUG/nyKPhwVak/mdTDM3COwh2FX4R4Ldx1PbL3TqqgiOed0LbATGasvPtwCziWD32N1RZU8AN2utN8ed20iwOxeCreasdyvBtSBjDfGPtwhxOozAI8A3gPFy3l4sLOT39fW0r1tHblUVpaWllJeXU15ejjlJM+zGEg4sANXV1SxevHjejaUkwsWLFzl58uS4A/4jIyO43W6qqqpYvnz5tGaeBQIB7HY758+fx2azTRrc81tbqfqf/5O806en9W+YikGCCVE7CLaE3IAr9FMT3Ds+3OrWoRuhnz6CLfMRgh/yI8BQ6DWHgGHAEzrPRzAYFhD8olYMlBBsWa0O3VYw/he38XiBI8Ch0O1dgoPQnaF6TKQIqCDYI1EP3BT6uXwK7zsfA8yTcS2YMQNM3POy5x8ZJbxZUfhmMpkoV4ptQ0N8YIzZWt0mE9+tqWFPeTlmiyWSp2isn7m5ueTn55Ofn0+BxcK1hw5x/W9+Q1FHx5h1cdXU0PXIIzg+9KGEdWnNhNaawcHgn9Ty5cspLy+XwDILgUCAd955hytXrkR+N0wmE16vl6GhoWmnzY+nteb8+fO0tbVRXFw8+fia18vCX/yCih/+cFqLniPvZzLhrKvDuXZtcCuBtWtxL1mCLz+f4ZERBgcHuXLlSiRbczgRZHivmOiy8H2v14vP54uk2h/rNtbx6P1mouUA64Dbom5Lp/0vvcpJMNAMcTUwQjDIVRDsSpyuDuBnwJZ5FmA2AtvixmAm7SKrqqrSW7ZsiTTTo/eDiH88lXNm8pyxysL7UxiNRvbu3RvZq+KOO+6IdO+Mye+n7Ec/onzbtjEXZ7pqa+n+zGfov+++CRevKbeb0l//mkXPPYf54sUxz/EsXsylxx9Pe2CBq2MA5eXl1NXVSWBJEJfLRV9fX8yHb25uLnV1dSxYsCAh3YqXLl3i+PHjUwsygLGvj+LXXsN66BDWQ4ew2O2jZlRqkwlPRQUj117LyHXXMXL99cHB8gxbsBkeb41ORBn+GQgECPj95F64QMk771B64AClBw9icThSXs/hwkLar7uOEw0NdNTWMjQywt///d/PqwBjA85orUuiyiYd5M+GDcdmkq7fcuIEy556irxxVsH7bDYc99yDe+lSvIsX4ykvx+RwYD10iPyDB7EePoxxnF0K/RYLl//qr+j+7Gcz4g82PM6yatUqysrKZA1EEoW/dSd6Nl9HR0ekO266QcswNITl1CkwGPCVlOArKQlO9Z2LvwdaYz57lvx33glmHHnnHczj9CzM6m2MRkauv54r730vg+97H87Vq2Nm1CZimnJW7aqktXYopfYrpWrD05QJzkbcks56pYtr9WpO/eQnlP3bv1H+7LOouNaMyeFg4TQDqzYY6L/vPi49/ji+srJEVndGwtu4lpaWsnr16oSs4BcTS9Y08SVLluDz+Thz5sy0p0cHCgoYuemmpNQr4yiFe/ly3MuX0/exjwHB/XUsp0+Td+oUllOnsNjtmLq7yentxRDa32U8AbMZ78KF+BYtwrlyJc5rrsF5zTW46uqSlpkkLKsCTMhmoFEpFV5o+chEa2Cyxfvf//4ZPU/n5ND12GMM3HUXZc8+i625GTVGv+9kAjk59D3wAN3/9b/iWTqbHuHECfeFr1y5ksrKSpkBNgdUV1fj9Xrp6OiYdpCZz/wlJQzffDPDN98ceyCUnsk0RqDRubl4FyxIa0svq7rIZiobusgSJaezk4W/+AWlL76IaXCy+SXgKymh78//nO6/+IuMaLHA1WmxFouFNWvWSE6qOSYQCHDixAm6urqw2WwSZDLUvOsiE5PzVlRw6b/9N7oaGyl8803M58+Tc+kSuZ2d5HR2onNygoOiN9zA8A03BPdHz6A/cI/Hw9DQEFVVVdTW1iZl7YxIL4PBwKpVqwgEAnR3d0uQmcPkr3eOClitDNx99+QnZgitNUNDQyiluOGGG1iwYEG6qySSyGg0siaUFqizs1OCzBwlAUaknUw/np/CLRmj0UhHR8eUFmOK7CIBJkP8n//zfyL3P/zhD6exJqkTHmsxGAysXbtWph/PQwaDgbq6OoxGI2fPnqWwsDCjdxWNzy8YnXswfByCOb7C69rCa9/mIwkwGeLv/u7vIvfnQ4CJTkFSXV0trZZ5TClFTU0N+fn5nDp1ipGREQoLC2fVmtFaR7YT8Pv9MUFAKcVMJzeFA4fJZMJgMGAymTCZTKOSR4ZX87vd7siqfoPBgNYapVQkq8Zcb7FJgBEpFZ56XFRUxHXXXSczxAQQ/GAuLy+npKSEc+fO0dHRgdlsJi8vb0rf/sMf5r6otWBWq5WysjKsVitms5mcnBxyc3NjEqCGX3uigBM+bzYtkXD9wulnInsshbIW5+TkYLFYkrYGKV0kwGSIP/uzP0t3FZImOuNxcXExK1asSFgKEjG3hFPUlJeXY7fbcUSlTMnJyUEpFUmzEh0ULBYLixYtori4mPz8/Eg27UyRk5NDTk4OBaGNxpYuXUogEMDpdDI8PExvby+9vb34/X6UUpjNZsxmc1q61sKbDQamub38WGQdjJiV+H1toveygatdCrIPi5gJv98f2RgvHGzik7ZardaMHreZqkAgwPDwMAMDA3R3dzM4OIjWGoPBgMViiQTYZPD5fDidTvx+PyaTiYqKinDAlnUwIj3CGWjDf+D5+flYLJbILTc3N9ItIa0VMRNGo5HCwkIKCwupqKhId3WSymAwRP6tS5YsiWS0djgc9PT0MDAwEDk3PA4UTpY71e678BdCn88XuUEwaJeXl7Nw4UKKi4sT9vcqAUZMm8/nY3BwkIKCAtavXz9vtx0WIplycnIoKSmhpKSEmpoa/H5/5EtdeHvz6G3So4UnMsSPMUV3v4Vfu6CgAIvFkpTWkQQYMS1DQ0P4/X5WrVpFRUWFtEyESBGj0UhBQQEFBQUsWrQo5lh4TCr6Z1j0liHRM95SQQJMhti58+puA5s2bUpjTcbn8XgwGAysX79eshoLkUHCX/QyaWIDSIDJGN/85jcj9zMxwIRTudxwww0SXIQQUyL9G2JKBgcHWbx4seQIE0JMmbRgMsTHP/7xdFdhXF6vF6UUtbW16a6KECKLSIDJEE899VS6qzAmrTWDg4Ncd911ks5FCDEt0kUmJjQ0NERZWRkLFy5Md1WEEFlGAowYVzglR11d3bzNBiuEmDkJMGJcQ0NDLF26FLPZnO6qCCGykIzBZIj/+I//iNx/6KGH0liToPCCrcrKynRXRQiRpSTAZIjvfe97kfuZEGCGh4dZsmSJtF6EEDMmXWRilEAggN/vl9aLEGJWpAWTIT772c+muwoRw8PDLF68mLy8vHRXRQiRxSTAZIgvfelL6a4CEFz34vP5qKqqSndVhBBZTrrIRIzwuhfZGEwIMVtZ1YJRSj0BLACeB0qBu7XWW9Jbq7kj3HpZtmxZuqsihJgDsirAhDSGbs3AI2muy5wyPDzMwoULI/uGCyHEbGRbgHForUvSXYlk+OEPfxi5/9hjj6X8/bXWeL1eampqUv7eQoi5KdsCDABKqXqCwcae7rokyrZt2yL30xFghoaGqKiokLEXIUTCZN0gv1JqE2AH6pVSTemuz1wQCATw+XxUV1enuypCiDlEaa3TXYcZU0q1AY9qrZvHOBYeqwG4DjicyrrNcQuBnnRXYo6Qa5lYcj0Ta7XWunCmT05rgAkFgfWTnNYU7gpTStVrrVujnr8DsE82k0wptV9r3TDrCgtArmciybVMLLmeiTXb65nWMRit9fapnhsad3kViB7ktwFtCa6WEEKIBMiaMZhQyyV+WnIt8EIaqiOEEGIS2TaLzB5abOkg2LW2WWvtmMLzptxSElMi1zNx5FomllzPxJrV9czqQf5EU0pt01o/mu56ZDOllA3YSCjTArBlLk0nT4WomZIbtdZb012fbCW/i8kz1c/KrOkiSzal1EZABgdn75NAbWh8bTcgqXymIfR7WBrqEm4OtdjFzMjvYhJM57My6wKMUqpeKbUj9I+MLrcppZ5QSm0K/ayfxmvaCH5j7EtwdTNeoq+n1np71LfuFczzSRgzuL53E/xdhGBX8N0prG5Gm+61lN/Fic3kb3+6n5VZNQYTdSFqxzi8g+CamPCU5t1KqamO0TRorZuVUgmqaXZI4vUMq53PyUhncn0JzowM6yPYvTPvJeB3dV7/LsabxfWc1mdlVgWY8IJKpVRM9AxF1dq4/lU7wf7XnaH1NmO93nal1MaxFmrOB8m4nlGv8YTWenPCK51FZnh9HVwNMqXMw1b1WGb6uxo6Z97/LsabyfVUSjmm+1mZVQFmAg0E/zCjOQh2L+ycZL1NX2hQFaB2PgecKLO5nuFB6u2h+3I9R5vo+u7g6rfKWoJjB2J8E/6uyu/itE10PbdN97My68ZgxmFj9De9XqbQvaC1btVa7ww9lO6IIBszvJ6h/tom4NVQKp+xmuDznY1xrm/oD9YW6sKol1lkk7IxzrWU38UZsTH+7+a0PyvnSgsGZhkcQhdu56Qnzh8zup6h2U8rElyXuWjc6xsVVOTb9tSMeS3ld3HGJvzbn85n5VxpwTiIHRyF4M6X0n89Mw7keiaTA7m+ieJArmUiOUjg9ZwrAWY/o6OuDem/nim5nskl1zdx5FomVkKv55wIMKHpc/uVUtF9rA1IF8OMyPVMLrm+iSPXMrESfT2zKlVMaNBuI/AkwUi7O9xfHZpe10hwSl0t0Byd2l+MJtczueT6Jo5cy8RK1fXMqgAjhBAie8yJLjIhhBCZRwKMEEKIpJAAI4QQIikkwAghhEgKCTBCCCGSQgKMEEKIpJAAI0SKKaVqlVJN6a6HEMkmAUaIWQoHDKVUY1Q684k8SlTqjdBzW5RSWim1LXqHwdBr7g4d2zHeXjxCZCJZaCnELCmlWoDNBAPHRq31+snOjz8nFDiatNYlY5xfD7QAJdPcUVSItJpL6fqFSLnQh3+t1toe2nNkwqSAofP3p6RyQqSZBBghZudBQokAJ9vpM+RRYFtSayREhpAxGCFmZyPTS2XeIIkYxXwhLRghZkAp9QTB3RLrgbuVUuuBbRMFj9DgfULSyIe62l4FniaY9RaCmW+bkLEakSEkwAgxA1rrraEP+Uat9eYpPu1RYMsEx22hwBVvrG1/S4FHovZIRym1G9giwUVkCgkwQsxcA1dbD1Nh01pPdL4jvCdHtHAgi38tolpDoVlopWM9X4h0kQAjxMytB6Y0nhJaH7Mjge/dHG6phHYfbArVR4iMIYP8QsxcA7Bviuc+CryQqDeO6wbbQbBrbDqtKSGSTgKMEDNXzxQG7UNb0MYHhYQIj9lET5EOdakJkXbSRSbEDIQ/xKc45fiTJGHtS6hr7EmiusZCZaWJfi8hZkJaMELMzHQG+DdHz/ZKoLG6xjYBfUl4LyGmTVowQszMlAb4Qy0KxyTnNBFcsGlTSm0Ddmitm0PHGgnmOQN4Rin1vNZ6Z6i8FugLTSAoDdWpkbGnNQuRcpLsUogZCCW4fHqylklojKQ1HDCEmE8kwAgxRaGWgkNr3ayU0lprNYXnjMqcLMR8IWMwQkzdM0B9KOXLpAsaJXOymO9kDEaIqQuneblbaz1RypewB5HMyWIeky4yIZJEKbVjGnnKhJhzJMAIIYRIChmDEUIIkRQSYIQQQiSFBBghhBBJIQFGCCFEUkiAEUIIkRQSYIQQQiTF/w8inv8xurNheAAAAABJRU5ErkJggg==\n", 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5mptT6tq48cYbcQHdhObpAyit8R05AjcmjurkoDycjLB9+3a2bt2adB2L3W6fsvssmd27d0+7Dj/60Y+mXEcTy+Fw5EWAyclB/oVo165d0UPkvwuvvkptzH0X4F69GpvNdt3HLl++HIvFwtGEcn3smMwky5CNGzeyadMmNm9OXOc9+aB7YpfabHR2dsYtkJzqdRobGzlw4ABAXBdeJuo1W9KCESLNgsEgwVdeiSs7abOhTSaKioqu+3ir1UpNTQ1Hu7uJ3ee0yOHA5/NN2cUmZm779u20t7ezdevWuJX8u3fvjn6QOxyO6EyuyJqZxHUok4mszo88tqWlJW4lf2w3WuTaTZs2RVfhR15n9+7dbNu2jba2tuj4UWS8aPfu3TidTnbs2EFjY2N0xX+2qIXwjai1tVV3dHRkuxpigXC5XOy/5x7eEfOB8dOGBurb2lLu1njb295G4+9/z7djyvrf9jbML7xAaWlpeissxCSUUge11jNeSCNdZEKkmdvtZsm5c3Fll5Yvp7y8POXnaGxsnNBFZu3ulqSXIq9IF1mO+MpXvhK9/ZnPfCaLNRGz5RofZ1lCP/jI2rXTSla5cuVKfpJQZr1wgcuDg0jqI5EvJMDkiL/5m7+J3pYAk9/cDge1gUD0/lWgcNWqlMZfIlauXMkocI5r2y2rQADvm2/CmjXprK4QGSNdZEKkWeDIkbj7x4G6pUuntWFYQ0MDAMcSTxxN7DgTIndJCyZH/PVf/3W2qyDSQGtN8M0348qOAbesWpWYnWJK9fX1ABwF3h1Tbu7qwufzTZpqRohcsiACjNvt5tixYwSDwWiZyWSioKAgelgsFiwWC2azeVofBOkSOwYj8pfH40EdPx5Xds5mY+M0V+DX1NRQWFjI0YQEl9azZ3G73RJgRF5YEAHG6/XidDrjAkcwGIweEVprjEYjxcXF1NTUUFFRIWsOxLR4PB4s3d1xZf2LFlFcXDyt5zEYDCxbtoyjXV1x5dazZ3F7PJSUlEzySCFyx4IIMEoprFZrStcGg0E8Hg8nTpwAoLKykiVLlmC32zEYZMhKTM3j8WDv7Y0ru1pXl/LvX6z6+npeSwww588zMDxMZWXlrOopxFyQT8wEBoMBi8WC3W6nrKyM4eFhXn/9dQ4fPszY2Fi2qydy3NiFC5TG/J54AUNT04y6tFasWMEQcCmmzODz4U3oghMiVy2IFsxMKaWw2WzYbDbGxsbo6OigsbGR2tpajEbj9Z9gGv7xH/8x6W2RX/xvvBF3/xSwoqlpRs+1YsUKIDTQvyT2xNGj8OCDM3pOIeaSBJgU2Ww2AoEAXV1d9PX1sXbt2pQSF6bqn/7pn6K3JcDksWPxE4uPAWtmuG4lEmCOAe+KKTedPEkwGJQuW5Hz5Dd0GoxGI+Xl5fh8Pg4dOsT4+Pj1HyQWDJ/PN2GA/xjQlIYWTCxrdze+hK0AhMhF0oKZAavVyvj4OIcPH+bWW2+d1grtyXz+859PQ81ENrnd7gkB5jjwn1evntHzRRZbTggw587h8Xhk+2SR8yTAzJDVamVsbIzXX3+d9evXT2uVdjLSLZb/PB4PljNn4soulJTMeErxkiVLKCgo4GhCa8V69ixDbjdIVmWR46SLbBZsNht+v5833ngDb8KCOLHwjA0MYLt8Oa7MHV6RPxNGo5Hly5fTD1yJLfd48J46NePnFWKuSICZpeLiYrxe74RMAWLh8b35JoaY/ZW6gapwN9dMTTYOE0iYrSZELpIAkwbFxcUMDg5yOeHbq1hgEtanHONagJipyQKMJL0U+UDGYNKktLSUU6dOYbfbZzQeE5uiX/KS5Z9gMIjp9Om4suNcG6ifqdipyrEKTp1Ca52VvHlCpEoCTJqYTCaUUnR1dbFu3bpp/+F/9atfjd6WAJN/PB4P1iRTlB9auXJWzzvpVOWzZ/H5fJIrT+Q06SJLo+LiYvr6+rhy5cr1LxbzisfjwZqwTXImu8isZ8/icbtn9dxCZJq0YNJIKUVJSUm0q2w6+ae+/OUvZ7BmItM84+OUnD8fV3aMa/u6zFQkwFwktDNmZGKyaXwc7/nzcOONs3p+ITIp5wKMUqoR2A7s1Fq3x5Q/CSwCfgRUAJu11luzU8vJFRYW4nK5OHPmDKunscBOtknOb+4TJzDGTFW/AvhKSykrK5vV80bWwvh8Pk4BLTHn/MePS4AROS2nusiUUhuBxvCRzBbgRWArsG2u6jVdpaWlXLx4EZfLle2qiDmSbBfL5cuXz/p5I2thAE4nnAuePDnr5xcik3IqwGit28OtlsEkp51a6/LwsVlr7Zzj6qVMKYXRaOTChQvZroqYI4m7WKZj/CUi8jyJAQZZbClyXE4FmFQopZrD3Wg5rbi4mAsXLuDxeLJdFZFhfr8fc0KKmGPAylnOIIuYLMCYurvRMQs7hcg1eRVglFKbAAfQrJTanu36TMVgMKCUojdhd8PJbNmyJXqI/DLZDLJMBxjLhQuSVVnktJwb5J+M1npXzN02pdR2pdTe2IkAsZRSWwiN2VBdXT0XVZyguLiY8+fPU1tbe90ZZc8++2z09q5du6a4UuQaj9tNydmzcWXHgU83pqehPVmAKbpwAbfHI2thRM7KmxaMUqo5oagTuG+y67XWu7TWrVrr1tnO5Jkpo9FIIBCgv78/K68v5ob3wgUKRkai98eBc0BjmgNMLxC7abdpbAzvxYtpeQ0hMiEvWjDh4PIiUB5TbAe6slKhabDZbJw9e5bq6uopt1neuXPnHNZKpJP3yJG4+ycATfoG+WPTzZwG1secC5w4ATPcMVOITMuLAKO17lRKJU5LbgR+nI36TEdBQQGjo6MMDAxQVVU16XUy9pK/9IkTcfdPElq/ko6N6CB+LUxigPEfPw7vfW9aXkeIdMupABNuqWwEWoFtSqnGmLGXjvBiSyewktBCS2dWKjpNVquV7u5uKisrZR/1eUZrjTEhyeVJ0tc9BqEJI/X19Zw+fXriVOXTE0qEyBk5FWC01p2ExlZ2THEu75jNZoaGhhgdHaVUdiGcV3w+H5aEGWQnSd8MsojGxkZOnz5N4soXY3iqsmRVFrlIvk7PEZPJJPvFzEMej4einp64shOktwUD0NTUBCSZqtzTg9/vT+trCZEuOdWCmc+sViuXLl2ioaEh6WD/Rz7ykejt73//+3NZNTELnvFxKhIyNpxi7gJMUU8PHo9nWolVhZgrEmDmSGTK8vDwMBUVFRPO/+AHP4jelgCTP7ynT2OIWex4mdAgYaYCzEXABUSmDxSMjDDa1wfFxWl9PSHSQbrI5pDZbOairFuYV/wJWxdH0k9mKsBoJs7N9x1L3O9SiNwgLZg5VFRUxMDAAF6vd8Lq6+9973tZqpWYjWRTlIuKiqipqUnr6zQ0NKCUQmvNaeCmmHOBEyfgoYfS+npCpIMEmDkUmekzODg44QModgxG5IdgMIjJ4Ygri0xRTvesLovFwrJlyzh37tyEcRgtWZVFjpIusjlmsVgkjf884fV6sSbsYpmJGWQRkw30S1ZlkaskwMwxi8XCyMgI4+Pj2a6KmCWPx0NRQoA5CazJUOqWyQKMWaYqixwlASYLDAYDAwMD2a6GmCWP04k5Zm1TkNAA/FwHmCLZd0jkKBmDyQKr1UpPTw91dXXR1DF/+qd/Gj3/wgsvZKtqYhq8x46hYrqmzgIeYPXq1Rl5vUiAOR9+HXO4vNDpZLS/X6Yqi5wjASYLCgoKGBsbi0sd84tf/CLLtRLTFUiYHhyZopzpABMktOve2phzvuPHISbrshC5QLrIssRgMDA0NJTtaojZSDJFubS0NGMb3MVOHkjsJvPLWhiRg6QFkyVFRUX09vayfPlylFI8//zz2a6SmAafz4c5YRfLE4RaL5lKPGmz2aitreXixYuSVVnkhWkHGKXUrQBa60NJzn0Q6Ep2TsSLdJO5XC6sVmvcGIzIfcmSXJ4kc91jEWvWrEkaYIxnzkhWZZFzUu4iU0r9jVIqABwEDiqlAkqpryulSiLXaK1/ErpUBTJQ13nJ6XRmuwpiBtxud9IpypkOMGvXhkZeks0k83q9GX1tIaYrpQCjlPqfwCeAvwXuDx9PAU2AUyn1TORarfVrgHyNSoHFYqGvry/b1RAz4LpwgcLh4eh9N6HZXZmaohwxWYCxyFRlkYOu20WmlLoNQGvdlHDqRWCHUqoM+JBSag+hLYx3p72W85TZbMbpdOLxeDCbzdd/gMgZniNH4u6fJjS7a65aMGcBHxBJ0m8eHOTqwADIhnYih6QyBvMurfUnJjuptR4GngWeDQebVmBbmuo3rymlUEoxPDzMhz70oWj57373u+xVSqQkWZJLgFWrVmX0dW+44QYAAkA3EPtqfpmqLHJMKgHmTKpPFg42L4YPkYLCwkIuX77MSy+9lO2qiBT5fD4Kz8T/WZwAlixZQklJSfIHpUltbS0lJSWMjIxwioQAc+wYPPBARl9fiOlIZQxGsuhlUFFREYODg9muhpiGyWaQrVu3LuOvrZSKdpOdTDwnWZVFjpF1MFmmlCIYDPLzn/88uqpf5Da32z0hi/JJ4Pabbkr+gDRbu3Ytf/zjH0kMJ6buboLBYDT9kBDZlkqAuUMp1a61vnq9C5VS7wTKgQ9prR+Zde0WiIKCAtasWZPxGUgiPcZGRihP2HLhJPDxOQwwkdeMVXT+PF6vF4vFMif1EOJ6UvmqsxPYHbveJZZS6p1Kqf+plPo1MBheC7MpnZWc74qKiujv7ycYDGa7KiIFrq4ujG539P4QcAW4KcsBxnr+vExVFjnlui0YrfUZpdRPgG6lVDtwAFgENAIbgUFgq9b6Nxmt6TxmNBoJBAJxyS9F7posyeVcjMHAtQBzntD6m0h7peDqVby9vVBWNif1EOJ6Uuqs1VrvAh4BVgI7CE1DXgn8rdZ6VSS4KKVWKKUeZxozz0SIJL/MD36/n8KEvF/HgeXLl8/Zl4OGhgYKCwvRTFxw6Tt6dE7qIEQqUh4N1Fq3a61btdaG8NGqtX424bJyrfWzSRZlpkwp1aiU2q2U2phQbldKPamU2hT+t3mmr5GLtmzZwrvf/W5aWlqyXRUxBbfbjS1hivKbzF33GIDJZIq2lhIH+hNbV0JkU1pnkYXTxMxYTFBJtqn5bkJdcY7wtXuVUpu11s7ZvGauOH78eLarIFLgdruxJmRRPsrcBhiA9evXc+jQoYlTlSWrssghU7ZglFJfDM8MmxPhVlI7oXGd2HrYgcZIcAlzEBoDEmLOjI+NYevujiub6xYMhAIMTBzoL+zuJhCQXLMiN1yvBbMT2KqU2kFocH9nllLxtwLOhDIncB/QNteVyYTvf//7eDwemWKa48bOnKHg6rUZ+2OE8oLNdYC59dZbgYldZJGsykVFRXNaHyGSmTLAaK3PEMqgHEl6+QmlVAvQTijYdGe8hiF2Elo1wADJu9Ly0rp169BaMzw8jN/vx2SSNbC5KPjGG3H3jwHKYIjmCJsrk7Vgis6fZ8TlkgAjcsJ0Bvlf01p/Qmt9O6EAs0Mp9Wul1GNKqbmYPlMxnYuVUluUUh1KqY7hmLTquSyyWdTIyEiWayKSSTaD7CjQ1NQ05x/oFRUVLF26lD4g9rfF5HLhS8gyIES2zCinhNb6Ra31h7TW7ya0zqwtHGw+kN7qRTkJtWJiLWJiqya2jrvCM91ay/JoXYDRaJTcZDnK7XYnHX/J1sy/yVoxMlVZ5IpZJy3SWv9Ea30/8CFgkVJqj1LqR2meHNDBxBaMHdibxtfICUVFRfT19aG15BjNNZPNIMu1ACNTlUWuSFtWPK31cHgNzP2Exm1awl1U31BK3TrL53YCHUqp2DGXVkJddfPCe9/7Xt773vfygQ98AJ/Px/j4eLarJBJMNoOsuTk7S7ImG+g3dHXNeV2ESCYjI8nhyQFfAr4Unhzwn5RST10vAWZ48eRGwpuWKaUaw1kEADYDW5RSDkKtmcfnyxoYgHPnzkVvK6VwOp3YbLYs1kgkGuvupiBmPG+c0KZft912W1bqM1kLxnLuHF6vl8LCwrmvlBAxMj5VKbz4MqUFmFrrTqCTUDqaxHPOZOXzkdls5vLly9TV1WW7KiJGshlk9StWYLfbs1KfpqYmSkpKOJkwKaSopweXyyUBRmTdjAKMUuoDWuv/SHdlFrKf//zn0dtms5nh4WH5FppDvF4vBQkbeh3lWisiGwwGA62trbz229/GlRdduMDl0VHyaXKLmJ9mOovsP5RSjyul/kYptSLNdVqQ6uvro0dkuvLVq9fdgkfMkfHxcYoTBvjfBFpbW7NTobA777wTJ9AfU2bw+Rg/cSJLNRLimhkP8ocH9L9MaDD/sQxOUV6QCgoK6O/vv/6FYk6MjIwknUF21113ZadCYRs2bAAmDvT73nxz7isjRIJ0zCJrJ7QW5o6YWWOPzXbm2EJXVFTElStXJK9UjhgaGsKakEX5mFLccccdWapRSCTAJA70G06flt8dkXUzHuQPt1geAX4EtId3soycawA2KqX+DigjNHD/TCrbLosQg8FAMBjk6tWrlJeXZ7s6C1owGGT87FkKY2aQuYDC1aspKUm60eucqampYfny5ZyMmYUIoXEYt9stMxFFVs10kP+LwAeBlmRBIzxN+dnwgVKqTILL1O67777o7b17Q+tHTSYTly9flgCTZS6XC0vC2pJjQEuWWy8RGzZs4FRCgLGePy8BRmTdTLvItgDbUw0aWuv8SAaWRf39/dEjoqioiMuXL0tXR5aNj49PWGB5lNAAey7YsGHDxKSXPT2Mjo5mpT5CRMxmDEZymWSY0WiMdpOJ7BkeHp4wwP8m8Ja3vCU7FUqwYcOGCVsnW3p7uXrlSlbqI0TETMdg/pZQ7rHn0liXBW3Pnj1Jy41GI1euXJFusiwaGhqiJGHH0TMWy5zvATOZlpYW/IWF9Hi9LA2XqWAQ34kT6Obm6LR3IebaTNfB7ALalVLPpLk+C1ZVVVX0iGW1Wunr6yMYDGapZgtbJC+cLaEFY7zlFoxGY5ZqFa+oqIg77rgj6e6WXq83K3USAma3DuZLwC5Z/5JZRqMRv98ve8Rkyfj4OAVOJ8UuV7TMBTS+613Zq1QS73jHOyYEGGt3N263Oyv1EQJmuQ5Ga31GUsZknslk4or0p2fF6OgoRQnrX44D9+ZYgHnnO9/J6wllxadPMzY2lpX6CAFpTNcvMsdqtdLb2yvdZFkwNDSE77X4XK0nTaaspeifzJ133smxhG22LSdPSstXZJUEmBxx9913R49EkW4ymXY6t7TWDA8Pozo64soHa2tzbn2JxWLBmLBtQPHFi4xcvpylGgkhASZnjI+PR49kDAaDdJPNMbfbjd/vp8rhiCv3t7ZSUFCQpVpNrvWd7yS2pgatUUePyjoqkTUSYPKEzWbj4sWL+P3+bFdlwRgbGyPQ3099zEB5AKj/4Adzcurvvffey+GEMtvp0zLQL7Im4xuOidS8/PLLU56PdJNdvnyZ2traOarVwjY8PMzQr38dV3bMZGJdjqSISXTPPffwLwUFvN/ni5b5OjpwuVw516UnFgZpweQIm80WPSZTXFzM2bNnZbB/jgwNDaFfeSWu7HxdHaWlpVmq0dRsNhueNWviygqOHZOBfpE1EmDySEFBAR6PR8Zi5kBkUsXihCSX3uZmzGZzlmp1fZUJ06eX9PdzdVhSAYrskACTZ6xWK93d3dKKybCrV6/S7XBwS8L4hf3++7FYLFmq1fXd8cgjxLZXyoJBLv3xj2gtqQPF3JMAk2fMZjNjY2MMy7fSjOrt7cXx618TmwFuxGjEuG4dhYWFWavX9Syrr+d0UVFc2cVf/UoG+kVWSIDJEbfeemv0uB6LxUJ3Qvp4kT4+ny+0m+gf/hBXfmnZMopLS3NyBlmExWLBWV8fV+Y7cEC+kIiskACTh6xWK06nU9L4Z8jQ0BB9fX0su3gxrjx4xx1Z38HyesxmM+bbb48rW9TTw+nTiQn9hcg8CTB5qrCwkPPnz0vfegb09vby0ksvkbidmK+lheLi4qzUKVUWiwXLhg1xZTcDP/vZz2TBpZhzEmByxKFDh6JHKmw2G5cvX6anpyezFVtgPB4Pg4OD/OFXv+LmhHNXb7ghpwf4IbReKrBuHbFTQFYBf/j1ryXVkJhzEmDylFKKsrIyTp8+zaVLl7JdnXljYGAAh8OBvauL2N1expYuxV9WlvMBBqBkyRLGamqi9w0AR45wPGHTNCEyLe8CjFLqSaXUdqVUs1Jqo1JqZ7brlC1Go5GysjKOHz/OZUlqmBaXLl3it7/97YTuMff69ZhMppyeQRZRWlqKe/XquLJbgB/84AfZqZBYsPIuwIRtAV4EtgLbslyXrDIajZSUlHD06FEGBwezXZ28Nj4+jtPpZM+ePRMCzPDatdjt9pyeQRZhtVoZbWqKK7sF+OlPf4orZuM0ITItHwOMU2tdHj42a62d2a5QOoyNjUWP6SooKMBms/H6669z5swZ+RCZoYGBAf74xz9y+fJlNiScG1qzhvLy8qSPyzUWi4Wxxsa4svXAuXPn2LNnT3YqJRakvE12qZRqJhRsHNe9OA+85S1vid5OdaA/VmFhIUajkZ6eHs6ePUtVVRVLly6lpKQkL751Z5vWmgsXLvD888+zHFgScy5osTDa0JA3CSPNZjOuJF1kAM8++ywPP/zw3FdKLEj52IJBKbUJcADNSqntk1yzRSnVoZTqWCiLzIxGI6WlpdjtdoaGhujs7OTgwYP09vbii8mwKya6evUqJ0+eZP/+/RO6x8bXrQOTCavVmpW6TZdSisJVq/DHTKkuA1YAv/71r+nt7c1W1cQCk3cBRmu9S2vdprV2aq3bgE1KqY2TXNeqtW4tKyvLQk2nx2q1Ro/ZUkpRXFxMeXk5wWCQEydO8Morr3DixAnZoz0Jn8/HiRMn+OUvfwnAWxPOj9x0E1arNSc3GZtMaVlZ0m4yv9/P1772texUSiw4eRdgwl1jsTqB+7JRl3Tat29f9Egns9mM3W6npKSE/v5+Ojo6OH/+vCTLDNNa09XVRX9/P7/85S8xAB9IuGZozRrsdnsWajdzJSUljK5cGVd2a/jfr3/965PunCpEOuVVgAkHlxcTiu1A18SrRSyDwUBJSQklJSV0dXVx6NAhac0AfX19XLp0iV/84heMjY1xD1AXcz5QVMRAS0veBRiLxcLoqlVxZe8M/zs4OMhzzz0395USC05eBRitdScTpyU3Aj/OQnXyktFopLy8HI/HQ0dHBz09PQs23czY2BgnTpzAYDDwve99D4APJ1xz9R3vIGix5M34S0RRURFDzfGN/buByFZpX/7yl2VcTmRcXgWYsI7wYsst4QH+eTNVeS5ZrVZKSko4deoU3d3dCy7I+P1+jh49SmFhIW1tbYyMjFAAbE64bvDd78ZgMFCUkAI/1xmNRgwNDbgaGqJlJiCyHdm5c+f49re/nY2qiQUk76Yph1sxndmuR7rFrsSvqqqak9c0Go3Y7Xa6u7vx+/2sXLkSgyEfv3OkzuVyceXKFXp6eqLf4P/93/8dgPuBiphr/XY7Ay0tlBYX5+X7UlZWxtAdd1B05ky07N3AT8O3n376aT7ykY/MePq1z+fD7XbjcrkYGRmhvLwcu92el++VyIy8CzDz1f333x+9PZN1MDNlMBgoLy/nwoULBAIBVq1ahdFovP4Dc0QwGGR0dJTh4WGCwSBa6+ihlMJgMESP/v5+hoeHUUpFZ+xt3749uu3BRxKe27lxI+5AgCUVFRNfOA+UlJQw0NpK7Y9+FC17IOZ8b28vX/nKV3j66aen9bxDQ0N0dXXFjeEZjUbOnz+P2Wxm2bJlVFVV5UVaHZFZEmAESinsdju9vb0EAgFuuOGGnA4ywWCQ4eFhLl++TH9/fzQNvcFgmLCoNDbgmM1mysrKotecOXOGH/84NHxnBRKXHzofeACtdc6n6J+MzWaj65ZbCJrNGDweAJYDNwCRtJc7duzg8ccfZ8mSJZM9TZTX68XhcHDp0iWsVmvSiQ8+nw+Hw0FXVxdNTU3U1dVNfCKxYEiAyRGLFy/O6utHgsyVK1c4cuQI69aty8l1H6Ojo5w8eZKrV69SUFCA1WqdUTDUWrNjx45ocPpTILajyFtdzdhtt8HVq3mzgj+RxWIhaDYz2tpK6csvR8vfb7HwTHgL5bGxMT796U/T1tY26fMEg0H6+/s5deoUWmvKy8snzQ5RUFBAWVkZgUCAEydO4PV6qa+vl26zBUr+13PE3r17o0e2RILM8PAwb7zxBl6vN2t1SeT3+3E4HHR0dODxeCgvL6e4uHjGLa2f//znvPLKK9H7E7rH3v1u/MEghYWFedvVU1hYiMlkYvjO+NwEf57QWvnJT37CCy+8kPQ5RkZGOHz4MEePHsVisVCa4pbRkdmK3d3dnD59WtZdLVASYMQEZWVljI+P8/rrr+MJd61k09DQUHSBaFlZ2aynDF++fJkvf/nL0fvlwAMJH5rOBx6IBrJ8pZSipKSEwYQtlJsuXKD5hhviyj7xiU9w7ty56MQHj8fDqVOnOHjwIG63m4qKimm3aCPje5cuXeLYsWP4/f7Z/UAi70iAEUmVlJTg8Xg4dOgQQ0NDWZnGHAgEcDgcHDp0CIPBkJYZSoFAgM9//vNxuzs+YjJREPPzuVeswHXDDfh8vrxbYJmorKyMq0uW4I1ptRi8Xr76vvfFtf4uXrzIo48+yssvv8y+fft49dVX6e3txW63zyqgR1rFAwMDvPnmm7Jt8wIjAUZMKjK4ffjwYd5444053XJ3bGyM1157jfPnz2O32zGbzWl53ueeey6ua8wK/GNpadw1zj/5Ewi3aPJ1gD/CZrMR1JqrMdm6AdadO8ejjz4aV/bSSy/R3t6OxWKhuLg45e6wVJSVleF0Ojl58qR0ly0gMsifI86ePRu9XV9fn8WaxLNYLKG0I6OjdHR0UFNTEx3kjXz4BINBvF4vHo8n2qVWWlpKUVERFosFs9mccveK1+ulr6+Prq6uaB61dHnllVf4xje+EVf2vUWLqB4YiCsbCs8eA/JugWWiSP1H7r6bypiB/JJ9+3jixz9m//79HDt2LFr+pS99idWrV7N+/fq016WsrIy+vj5MJhNNTU2yjcQCIAEmR8Tu0TGX62BSZbPZsFqtXLlyhb6+vgnnlVIYjUaMRiNaawYGBqJrUbTWlJaWUlVVRWlpKTabbUJX1+joKBcvXuTSpUsopSgtLU3rVOnTp0/z2c9+Nq6r7zGbjfclBJeB970Pb309Hrc77XXIBovFAsDI7bejTSZUeBzE0t1NcX8/X/ziF/nwhz8cTX7p9Xr5L//lv/Dd736X2tratNYl0l3W09ODyWRixYoVEmTmOQkwImWRQePp0lrj8Xjo6uqKBh2j0RhdAAmhFfaR/WzSPaW1r6+PT33qU3FdfE3A1xIGnd0NDVzcFkp153a7c6olOVORLbXdfj9j69dTfPBg9FzJvn3Ub97M5z73OZ566qlo+eDgIJ/61Kf45je/SUWaF5lGgsyZM2cwmUwsW7Ysrc8vcouMweSI5cuXR4/5RimFxWKhrKwMu90e7T4zm82YTKbolNZMBJfLly/z+OOPx22yVQj8pqqKwpgZcsHCQs5u306wqCjaykn3h2u2LF68GI/Hw8jdd8eVlz//PASDPPDAAzz22GNx5xwOB5/4xCeiWQ6mojweCs+fR6W4VXdkwsbp06c5e/bsgsuDt5BICyZHPP/889muwpyJtGAy7eLFizzxxBOcO3cOgEWEsiV/pqyMZTG53wAufvazuMPbDLtcLsrLy/N2/Usiu91OMBjk6j33sOR//I9oue2NNyh//nmG3vc+PvnJT9Ld3U17e3v0/MmTJ3nsscf42te+FrcQuPDCBUp/8xuKjh+n6PhxLN3dqECAoNnM0AMPMPCf/hOuhGnQiSJ58BwOB4FAgIaGBukum4fUQvj2sGbNGh1JCSLmH8PICNZjxzD191Nw5QqmgQHGzpzh4B//GJ10YCe0K12ykOHcuJGzX/pSdOaY0+lk7dq1c5Z0NNOCwSAvv/wyNpuNlX/915S99FL0nL+8nOM/+xmBsjI8Hg9/9Vd/xf79++MeX1tbyze+8Q1W1NRQ/c1vsvh//S8M11nTMnbLLVz56Edx3n9/9H2drG5Op5OlS5cuiGSr+UYpdVBr3Trjx0uAEXlJa6yHD7PoJz/BvmdPNNfWdHlqazn5wx8SDE9V1lpz9epV7rrrrpxMlTNTx44dY2hoiHKnkzUf+EDc+3Vl0yYu/MM/AKHW26c+9SkOxozVADxks/EdqxV7f/+0Xtd5//2c+8IX0FO0BrXWOJ1OqqurWblyZc62HLXWBIPBuCMQCESTrEb+BaKJViMTXwoKCjCZ8qfDyOfz4XQ6qaqqmlWAyZ+fWAgAv59FP/0pi378Y4pOnZrx02ilGHnrW+n5+7+PBhcIfcBWVlbOq+ACUFlZyeXLl/HW1dH32GMs+drXoucW/eQnDD78MK6bb6aoqIh//dd/5bOf/Sx/+MMfWAx8Efh/x8Zgih1QA8XFGJOsk7Lv2YPR6aT7q18lOMmaosjAf39/PwMDAzQ1NVFVVTXr1ozH48HtduP1eqPbCrhcLgKBQDQwRBZ+RrrnIv/GfvGOXBdbFpkdGfl3MrHPV1BQQHFxMcXFxZSUlGC1WikqKsqZVlsgEGB4eJje3l76+/vTsiGdtGByxNGjR6O3161bl8Wa5C7LqVMs+/znsca8V9Plrq9n6L3vZeihh/BVV08473Q6ufnmm+fNAH+E2+1m//79oTVMXi+rN2/GErP2anztWk5997sQHhvzj49z+PHH+eCbb1KW5Plc5eUMffzjjK9bh2vNGoJWK6W//z2VP/whJQldbACuNWtwfO1r+Csrp6ynz+djZGQEu91OU1NTyrMWfT4f4+PjjI6O4nQ6GR4ejvuAVEpFJ5REsm7HruWKiASNRMkydU9XIBDA5/Ph8/nw+/3RVk5paSkVFRWUlpZitVrn9MtN5P2OZCYPBoPRJLLDw8Pce++90kV2PXMZYAxjYxSeP0/BlSsQXrGsgkG0wYC3thZPfT0k+QW69dZbo7dzcR1MVvl8VH/rW1Q9++ykff9ngVeBXuAS0Af4DQYeeughNmzYAIBnxQpc69ZNOiYQ2VvmrrvuyqvujFQdOHAACCXBLH7lFVY+8UTc+UiKHM+KFdh/9Sss3d0TniMI/E/gc0YjH/j4x/n4xz8+Idu0uauLFZ/5zITHe5YuxfH1r+NNYabk+Pg4brcbi8WC3W6nrKyM4uJilFL4/f7oMTIywtDQEO5wdmilFAUFBZjN5rxYwxS7SDnyWWy1WqmsrIy2ciwWS9paOVpr3G43w8PDXLlyhcHBQbTWmEwmioqK4t4zp9MpASYVGQkwWlN47hy2w4exHT6MpasrFFgSFu4lCppMeBobcTc1MdrczPD99xMoLZUAMwnLyZMs/4d/oOjkyQnnAkrxK6ORf/X72UPowy+irq6O7du3c9NNN6X8WqOjo1RWVrJmzZrZVzwHnT17lnPnzlEa7hKsf/JJ7Hv2pPz4I8AW4JWYskWLFvHJT36Shx9+OC4oG4eGaPjLv8T2xhtxz+Gtrub0t7+NL4X9ZyCURdvr9U6a2dtkMk0rU0Su01rj8/nweDwEAoFoK6u0tJTS0lKKi4sxm81YLBYKCgqu26oKBAK4XK5oUOnv749OfCksLKSoqGjS55AAk6K0BBitMXd3U7J/P8Wvvort8GFMQ0OzrluwsJDhd76Te44eJWi1glL84Ac/mPXz5r1gkMof/IAl//IvGJJ8uDxvNvNJj4cLSR764IMP8rd/+7fTXhQ6NDTE+vXr8zqD8lSGh4c5dOhQNP2Oqa+PG97/fozhVfyTCRQX0/Xoo3z62DH2/Pa3Sa+pq6vj0Ucf5eGHH45mDzC4XNT/zd/E7UUDoZbS6W99i8A864bMlEgrx+fzRYNO5HO7sLAQs9mM2WzGYDDETTyIjEFFGI3GaGBKhQSYFM00wBidTkr276fklVco3r+fwiQpUtLJU1dH7yc/ifM975lyaud8Z7pyhWVPP03pvn0Tzl1Wiie05j+SPG7JkiV87nOf4+6EBYWpCAQCjI2Ncffdd+dF18pMBAIB9u3bR3FxcbTLpXjfPuq+9CUsZ85MuF4rxeD73kfvpz+NPxwM9u7dyxe/+EUGJmmpl5eX8/DDD/P+978/lAnB52PZP/0TFb/4Rdx14+vW0fXsswTzdDO3XBCZuRaZtBAZP4ocBoNhVi07CTApSjnA+HzYjhyh+JVXKNm3D+ubb6Km+f5okwnvkiV4a2vRJlMoUCiF8nqxOBwUpDDNc+zWW7mwbRuutWun9dp5T2vse/ZQ+8UvUpCkdfg94C+BwYRym83Gn//5n/Nnf/ZnM05OOTw8TF1dHStXrpzR4/PFkSNHGBkZmZCC33D1KkVdXVhOnsRy+jRozeAHP5j0d3BsbIxvf/vbfOc734n7hpyopaWFBx54gHe+/e3ctn079phFnAAjd9zBmX/91ymnMIvskQCTokkDTCCA5dQpijs6KHn1VWwHD163uyDu4VYr4zffzNj69YzffDOehga8NTUwxQCx0ekMvebBg5Q//zzmixeTXhf59njpL/+SwDztsollfe01ar/yFWxHjkw45wS2Aon/g2azmQ9+8IM89thjs5r15XK5MBgM3HbbbfOmL38yfX19HD9+PC1Zqvv6+ti1axfPP//8lFNalVJsuPVW/m1wkNUxM9cAht/xDs7u2IGe5+97PpIAk6JIgDGMj1N07Bi2Q4ewdXZiO3w46dz9yQTNZsaamxm5805GN2zAtWpVdFrnjASDFHd0UPGzn1G2Z0/SGVK+xYs594UvMBqeCTWf+N1unL/+NVXf/z43nziR9JrfA38GnIsps9vtPPLIIzzyyCOznk4cCAS4evUqLS0tM0rkmW9cLhevvvpqWseZ+vv7+d73vkdbW9uUewYVAy8CdySUD999N2e/+lV0eOxG5AYJMClaX1am9y9ejOXMGdQ0NztyrV7NyN13M3LXXYzdeis6TRtfJTr0i1+w6Mc/pvj117k34ZxWissf/zi9TzyRdIpzztAaw9gYBpcLbTSCyYQ2GEBrxnt76T91ir6TJ3G/+SaNJ0+yYXiYycKDD/ivwH/j2uywDRs28N73vpd3vetd0YHk2VVXMzQ0xKpVq1i6dOmsny8faK159dVXMZlMaW+tuVwu9u7dy3/8x39MOhNyEaEvDYkdbx3Fxex88EGWrl1LY2MjDQ0NCyLg5zIJMClqVUp3pHitr7KSkQ0bGN2wgZG77sIfk+Qvk2KnKbtWrEi6BmHs5ps598wzeHPgw9DU10fp739Pyf79FF68iGlgAOPgIMY0rP79KbANOAXcdNNN3HvvvTzwwAPU1dXN+rljjYyMUF5eztq1a3NmNfVc6Onp4fTp0xmdLXfmzBna29t58cUXOX78eNy5OuA3wOqEx7wKPABERt+qqqpobGxk2bJl1NbWxh0VFRWSHDPDFmSAUUrZCU3HdwCNQLvWunOqx0wVYPxlZYzddhujt9/OyIYNeFauzMoMrrh1MAcOULNzJ1XPPTdhkkGguJhz//zPXH3HOzJan8isqsjKaKfTSbCri9Uvv8yakydZPpg41D57fwSeLipivLWVe+65h7e//e1UJ1ltnw4ul4tgMEhra2vO5r7KlEAgwMGDB9Faz6ol6PP58Hq9+P1+tNYYjUasVuuEWXgXLlzgN7/5Dfv376ezsxOXy0U1sAe4JeE5jxH64/7DdV7bbDZTUVHBokWLqKysjN6OHKWlpZSUlIT+LS6mzOejqL+fgv5+lNuNwetFeTzRKfDaYAClQi1vCP3dRfKK+f2ha10uDJF/x8cxuFwYwy12AgFUIBC6NhAgWFREoLiYQEkJgeJifFVVeOrrQ8eKFZOmzcklCzXA7AW2aq0dMfc3a62dkz0mNsC4w6u5x267jdHbbsPT2Ag58O31L/7iL6K3n3vuObTWFL36Kg2f+xyFSWaeOT74QY597GP4ubYYLbJlceR27L+RnEyx98fHxxkbG4seo6Oj0XQbsbODVgJ/BzxK+pPXDSpF5+LF9GzYgPmRR1izdm3Gpgn7/X7GxsYIBoOUlJSwatWq6KLDhWZ4eJjOzs7o9tep0lozNjaGz+ejqKiIsrKy6P4+AwMDXLx4Ea01Vqs1aeD2+Xy8+eabHDhwgO7OTv7pj3+kJZwPLNa/AU8ClyecmdoioAW4HWgF1gHLgFzb+NpbVcX4LbeEJgjdeiuuG27ImYkOBpeL0t/+luLnn6dy//6FE2DCrZeDWuuVMWU7gb1a67bJHldvNuv3r1nDcZuN0fCHVyTzaeTnT7wfmx11smumekwqzxGZvx4IBPD7/XH3I0n4FgHPAdc2VL7m/wKPEEqPkglNwOeAjwKpfuSPA1fD1xsJBSQVLhsrKMBXVIS22xlfuxb1nvdQ+Na3zm6iRIzEVd+xH5yRdBi1tbVUVVVNSG+yEB0/fpwrV65MK9/XyMgIlZWVNDU1JZ0S7vP56O/v5/z587jdbsrKyqYMYGp0lKVPPEFFwop/CM0e/BdCYzYHCP0OxbISagFtiDkaU/pJco8L6CgsZF9hIa8UFfGGxUIwnDfNaDTGrW+JzaGWSlkq1xZoTevVq9zX38/bBgawRtJchT5vF0yA2Qhs11q3xJRtB+xa661TPC5/fshJ/BXwJSDxO85l4BOExi3SxU4osHw6yetFBIH9wC+Alwjl//La7ZQuWUJ1dTU1NTXU1dVRX1/PihUrqK2tzUh+r0AgwOjoKMFgkKKiIoqLi7Hb7dG8SpEFZ0qpnMpcmws8Hg8HDhygqKhoyv+byBYGRqOR1atXU1lZmVKKkpMnT9Lb23vdVpJyu1n6zDNU/Pznk14TBM5ZrYwEApR6vSzSmtzvZJq5UWAfoa7C3xMan0ptv9DU1REa83oA2Agka8svtACziVD32H0xZU8Ct2utNydcu4VQdy6EWs157y5Ca0GSDfFPtghxOoyE3rD/CkyW8/ZiSQm/aW6me/16CuvqqKiooLq6murqaswZmmGXTCSwKKVYvnw5S5YsWXBjKelw8eJFTp48OemA//j4OB6Ph7q6OlasWDGtmWfBYBCHw8H58+ex2+3XDe62zk7q/tt/o+j06Wn9DKkYIZQQtYdQS8gdPjyAJrR3fKTVHflE1OEjQKhlPk7oQ36cUAAYCf87Bngh1F1NKBgWA2Xho5xQy2pN+FjJ5F/cJuMD3gTeCB+vExqE7g3XYyqlQA2hHolm4LbwvytSeN2FGGCeSmjBJA0wCY/Lnx8yRmSzoshhMpmoVoqdo6O8PclsrX6Tia80NLCvuhqzxRLNU5Ts38LCQmw2GzabjRKLhXWvv87Nv/wlpT09Sevibmig7/HHcb773Wnr0poJrTUjI6E/qRUrVlBdXS2BZRaCwSCvvfYaV69ejf5umEwmfD4fo6Oj006bn0hrzfnz5+nq6qKsrOz642s+H5U//CE13/jGtBY9R1/PZMLV1IRr3brQVgLr1uFZuhS/zcbY+DgjIyNcvXo1mq05kggysldMbFnkdiS9fiTVfrIj2fnY/WZiFQDrgbtjjmXT/kmvcREKNKNcC44QCnI1hLoSp6sH+D6wbYEFmI3AzoQxmOt2kdXV1elt27ZFm+mx+0Ek3k/lmpk8JllZZH8Ko9HI/v37o3tV3HvvvdHunaQCAaq+9S2qd+5MujjT3dhI/0c/ytCDD065eE15PFT8/Ocs/va3J80o4F2yhEuf/nTWAwtcGwOoqanJ6Z0P843b7WZwcDDuw7ewsJCmpiYWLVqUlm7FS5cucfz48dSCDGAcHKTst7/F+sYbWN94A4vDMWFGpTaZ8NbUMH7jjYzfdBPjN98cGizPsQWbkfHW2ESUkX+DwSDBQIDCCxcof+01Kg4douLwYSxO55zXc6ykhO6bbuJEays9jY2Mjo/z93//9wsqwNiBM1rr8piy6w7y58OGYzNJ1285cYLlTz9N0SSr4P12O87778ezbBm+mhp8NTUYnU5sr7+O9fXXsR45gnGSXQoDFguX/+Iv6P/Yx3LiD3Z0dBStNatWraKqqkrWQGRQ5Ft3umfz9fT0RLvjphu0DKOjWE6dAoMBf3k5/vLy0FTf+fh7oDXms2exvfZaKOPIa69hnqRnYVYvYzQyfvPNXH3LWxh561txrVkTN6M2HdOU82pXJa21UynVoZRqjExTJjQbcVs265Ut7jVrOPXd71L1zW9S/dxzqITWjMnppHKagVUbDAw9+CCXPv1p/FVV6azujES2ca2oqGDNmjVpWcEvppapaeJLly7F7/dz5syZaU+PDhYXM37bbRmpV85RCs+KFXhWrGDw/e8HQvvrWE6fpujUKSynTmFxODD191MwMIAhvL/LZIJmM77KSvyLF+NatQrXDTfguuEG3E1NGctMEpFXASZsM7BFKeUAKoDHp1oDky/e9ra3zehxuqCAvieeYPhd76Lqueewt7ejkvT7Xk+woIDBhx+m///5f/Aum02PcPpE+sJXrVpFbW2tzACbB+rr6/H5fPT09Ew7yCxkgfJyxm6/nbHbb48/EU7PZEoSaHRhIb5Fi7La0surLrKZyocusnQp6O2l8oc/pOInP8E0cr35JeAvL2fwT/+U/j/7s5xoscC1abEWi4W1a9dKTqp5JhgMcuLECfr6+rDb7RJkctSC6yIT1+erqeHSf/7P9G3ZQsnLL2M+f56CS5co7O2loLcXXVAQGhS95RbGbrkltD96Dv2Be71eRkdHqauro7GxMSNrZ0R2GQwGVq9eTTAYpL+/X4LMPCZ/vfNU0Gpl+L77rn9hjtBaR9e13HLLLSxatCjbVRIZZDQaWRtOC9Tb2ytBZp6SACOyLjL9uLq6mqamJpl+vEBEWjJGo5Genp6UFmOK/CIBJkf87//9v6O33/Oe92SxJnMnMtZiMBhYt26dTD9egAwGA01NTRiNRs6ePUtJSUlO7yqamF8wNvdg5DyEcnxF1rVF1r4tRBJgcsTf/d3fRW8vhAATm4Kkvr5eWi0LmFKKhoYGbDYbp06dYnx8nJKSklm1ZrTW0e0EAoFAXBBQSjHTyU2RwGEymTAYDJhMJkwm04TkkZHV/B6PJ7qq32AwoLVGKRXNqjHfW2wSYMScikw9Li0t5aabbpIZYgIIfTBXV1dTUVHB2bNn6enpwWw2U1RUlNK3/8iHuT9mLZjNZqOqqgqr1YrZbKagoIDCwsK4BKiJGbcnq1vsY2YiUr9I+pnoHkvhrMUFBQVYLJaMrUHKFgkwOeJP/uRPsl2FjInNeFxWVsbKlSvTloJEzC8FBQU0NTVRXV2Nw+HAGZMypaCgAKVUNM1KbECwWCwsXryYsrIybDZbNJt2rigoKKCgoIDi8EZjy5YtIxgM4nK5GB8f58qVKwwMDBAIBFBKYTabMZvNWelai2w2GJzm9vLJyDoYMSuJ+9rE7mUD17oUZB8WMROBQCC6MV4k2CQmbbVarTk9bpOqYDDI2NgYw8PD9Pf3MzIygtYag8GAxWKJBthM8Pv9uFwuAoEAJpOJmpqaSMCWdTAiOyIZaCN/4DabDYvFEj0KCwuj3RLSWhEzYTQaKSkpoaSkhJqammxXJ6MMBkP0Z126dGk0o7XT6eTKlSsMDw9Hr42MA0WS5abafRf5Quj3+6MHhIJ2dXU1lZWVlJWVpe3vVQKMmDa/38/o6Cg2m42WlpYFu+2wEJlUUFBAeXk55eXlNDQ0EAgEol/qItubx26THisykSESdGJnt0W63yLPXVxcjMViyUjrSAKMmJbR0VECgQCrVq2ipqZGWiZCzBGj0UhxcTHFxcUsXrw47lxkTCr234jYLUNiZ7zNBQkwOaKt7dpuA5s2bcpiTSbn9XoxGAy0tLRIVmMhckjki14uTWwACTA54wtf+EL0di4GmEgql1tuuUWCixAiJdK/IVIyMjLCkiVLJEeYECJl0oLJER/4wAeyXYVJ+Xw+lFI0NjZmuypCiDwiASZHPP3009muQlJaa0ZGRrjpppsknYsQYlqki0xMaWxsjKqqKiorK7NdFSFEnpEAIyYVWZXf1NS0YLPBCiFmTgKMmNTo6CjLli3DbDZnuypCiDwkYzA54t///d+jtx999NEs1iQksmCrtrY221URQuQpCTA54qtf/Wr0di4EmNHRUZYuXSqtFyHEjEkXmZggGAwSCASk9SKEmBVpweSIj33sY9muQtTY2Bi1tbUUFRVluypCiDwmASZHfOYzn8l2FYDQuhe/309dXV22qyKEyHPSRSbijI6OysZgQoi0yKsWjFLqSWAR8COgAtistd6a3VrNH1prfD4fy5cvz3ZVhBDzQF4FmLAt4aMdeDzLdZlXxsbGWLx4cXTfcCGEmI18CzBOrXV5tiuRCd/4xjeit5944ok5f/1I66WhoWHOX1sIMT/lW4ABQCnVTCjYOLJdl3TZuXNn9HY2Aszo6Cg1NTUy9iKESJu8G+RXSm0CHECzUmp7tuszHwSDQfx+P/X19dmuihBiHlFa62zXYcaUUl3AVq11e5JzkbEagJuAI3NZt3muEriS7UrME/Jeppe8n+m1RmtdMtMHZzXAhINAy3Uu2x7pClNKNWutO2MevxtwaK23Xed1OrTWrbOusADk/UwneS/TS97P9Jrt+5nVMRit9a5Urw2Pu7wIxA7y24GuNFdLCCFEGuTNGEy45ZLYUmkEfpyF6gghhLiOfJtF1hFebOkEVhJaaOlM4XEpt5RESuT9TB95L9NL3s/0mtX7mdeD/OmmlNopmQFmRyllB1oJdV/eDuycT9PJ50LMTMnW6XQji3jyu5g5qX5W5k0XWaYppTYS+mUUs/MhoFlr3UZofGzKCRgiXvj3sCLcJRxpsYuZkd/FDJjOZ2XeBRilVKNSanf4h4wttyulnlRKbQr/2zyN57QT+sY4mObq5rx0v59a611a6x3huytZ4JMwZvD+3kfodxFCXcH3zWF1c9p030v5XZzaTP72p/tZmVdjMDFvRGOS07sJrYmJTGneq5RKdYymVWvdrpRKU03zQwbfz4hmrfWC/YCcyftLqDsnYpBQUtcFLw2/qwv6dzHRLN7PaX1W5lWAiSyoVErFRc9wVG1M6F91ABuBtvB6m2TPt0sptTHZQs2FIBPvZ8xzPAlsTned88kM318n14JMBQuwVZ3MTH9Xw9cs+N/FRDN5P5VSzul+VuZVgJlCK6E/zFhOQt0LbdcZKB0MD6oCNC7kgBNjNu9nZJB6l9baKe9nUlO9v7u59q2yEdg7Z7XKT1P+rsrv4rRN9X7unO5nZd6NwUzCzsRvegOk0L2gte4MDwKSyvULhJ0Zvp/h/trtwItKqYMkb4IvdHYmeX/Df7D2cBdGc8wYgkjOziTvpfwuzoidyX83p/1ZOV9aMDDL4BB+49que+HCMaP3Mzz7aWWa6zIfTfr+xgQV+badmqTvpfwuztiUf/vT+aycLy0YJ/GDoxDa+VL6r2fGibyfmeRE3t90cSLvZTo5SeP7OV8CTAcTo64d6b+eKXk/M0ve3/SR9zK90vp+zosAE54+16GUiu1jbUW6GGZE3s/Mkvc3feS9TK90v595lSomPGi3EXiKUKTdHZnRFJ5et4XQlLoKoCM2tb+YSN7PzJL3N33kvUyvuXo/8yrACCGEyB/zootMCCFE7pEAI4QQIiMkwAghhMgICTBCCCEyQgKMEEKIjJAAI4QQIiMkwAgxx8IbPW3Pdj2EyDQJMELMUiRgKKW2xKQzn8pWYlJvhB97UCmllVI7E3YQ3BLe8EmHdx9M5fmFyAmy0FKIWQqngt9MKHBs1Fq3XO/6xGvCm7ht11qXJ7m+GTgIlE9zR1Ehsmo+pesXYs6F921p1Fo7lFJdXCcpYDhYdMxJ5YTIMgkwQszOZsKJAK+302fYVmBnRmskRI6QMRghZmcj00tl3iqJGMVCIS0YIWZAKfUkod0SG4H7lFItwM6pgke4Oy0taeTDXW0vAs8QynpLuC7bkbEakSMkwAgxA1rrHeEP+S1a680pPmwrsG2K8/Zw4EqUbNvfCuDxmD3SUUrtBbZJcBG5QgKMEDPXyrXWQyrsWuuprndqrXckFkYCWeJzEdMaCs9Cq0j2eCGyRQKMEDPXAqQ0nhJev7I7ja/dHmmphHcf3B6ujxA5Qwb5hZi5VuBAitduBX6crhdO6AbbTahrbDqtKSEyTgKMEDPXTAotmPAWtIlBIS0iYzaxU6RjMwEIkU3SRSbEDIS7pSC1RZMfIgNrX8J1eIqYrrFwWUW6X0uImZAWjBAz00xoUN6ZwrWbY2d7pVGyrrFNwGAGXkuIaZMWjBAzcx8prGkJtyic17nmSeARQtOUtwM/iqynCc8Oi0yDflYp9SOtdVu4vBEYDE8gqCDUktlC8mnNQsw5SXYpxAyEE1zuvF56mHDw6NRap2WBpRD5RAKMECkKtxScWut2pZQmhRXzyTInC7FQyBiMEKl7FmgOp3zZkUJwkczJYkGTMRghUhdJ83Kf1nqqlC8RjyCZk8UCJl1kQmSIUmr3NPKUCTHvSIARQgiRETIGI4QQIiMkwAghhMgICTBCCCEyQgKMEEKIjJAAI4QQIiMkwAghhMiI/x89HAsaRXPzIQAAAABJRU5ErkJggg==\n", 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" ] @@ -350,7 +358,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -394,7 +402,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.9" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/tutorials/ex4_experiment.ipynb b/tutorials/ex4_experiment.ipynb index 48411f1..877b734 100644 --- a/tutorials/ex4_experiment.ipynb +++ b/tutorials/ex4_experiment.ipynb @@ -75,7 +75,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -194,13 +194,14 @@ " Function evaluations: 97\n", "0.0002953 0.0063745 1.7756110\n", "0.0002953 0.0063749 1.7756110\n", - "0.0002953 0.0063751 1.7756660\n", + "0.0002953 0.0063751 1.7756659\n", + "0.0002953 0.0063749 1.7756443\n", "0.0002953 0.0063749 1.7756443\n", "Warning: Desired error not necessarily achieved due to precision loss.\n", " Current function value: -577.496686\n", - " Iterations: 4\n", - " Function evaluations: 37\n", - " Gradient evaluations: 25\n" + " Iterations: 5\n", + " Function evaluations: 74\n", + " Gradient evaluations: 62\n" ] } ], @@ -274,6 +275,10 @@ "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", "K_im_full = L2_im_K + Sigma\n", "\n", + "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", + "if not GP_DRT.is_PD(K_im_full):\n", + " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", + "\n", "# Cholesky factorization, L is a lower-triangular matrix\n", "L = np.linalg.cholesky(K_im_full)\n", "\n", @@ -348,7 +353,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -389,7 +394,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -433,7 +438,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.9" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/tutorials/ex5_inductance_plus_ZARC.ipynb b/tutorials/ex5_inductance_plus_ZARC.ipynb index 2a4d432..e957f64 100644 --- a/tutorials/ex5_inductance_plus_ZARC.ipynb +++ b/tutorials/ex5_inductance_plus_ZARC.ipynb @@ -87,7 +87,7 @@ "outputs": [ { "data": { - "image/png": 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UWsdx7SpmTjBzgJkD27Zt655EFYFJ46h2hjS1FiSE2ds0imvQr1W/Aaso7B13APm8KIUWMbHeQcxiGtXWQ2+wMh6djCUtulE9WRgMKjMtx8ZwYWwMa82OO3MGuP9+UQotkkW1pWAAcNdcrxPY02Wdcumlku487NjiGmh1FeOXXIImlTkVX/sapl9+WWYf3MLMpvYR2GcgAgAWeyqI3bHolIkJ4MMfVj8YjzQzFdqHXBR7nf7zP8dr73hHF6Upx1NKQQckBaFveCLyM3NMbw4DiBBRAWrofk/PYxQcZDxWIT6D0eTSSx0PL6fX1rD8gx+oh04PhpKeUgrMnAOQAxCrsc2stb6nOMh4LDExoRbxGYwmu3cDjzziaNdpAMvMKhS6B9bksPgUBgM3jkXxGYw2e/c63nUaan6dH3+8a+LYEaXQSZwW95yYkLTnUWdmBvjABxztugnKpH+jzaYzThGl0A+cNhkRhpu/+RvHqfPTAJYvuaS78mhcKwUiehcRvavOtjvqbRsJLlxwtl+7PR+F4WBmBvjSl1RqfBOmASw7tCzaxbFSIKI/IqJVAEsAloholYgeJqJS9Q9mflLtSr2rCDFArG3a5GxHKZgiWOzcCXzjG0CTfqJbiQZLKRDRZwB8FMDHAdyql30ArgNgEtF+a19m/ic4iN4dNvjQIaydOSO5DIJ73vc+4KtfrRkKvQoVDn05M16NRHrSSKapUiCi/wwAzHwdMz/AzEf0EmPmW6EiCQtEdJCIfp+ILuuqxINIPo8Lt93mLPNR4hKEWlSGQhOV5UZcDsA8fx7cg0YyTiyFHcz80XobmfkkMz/KzLugCp30PpKwz5z7+Mcxdt5BRb7xcYlLEOpjhULncqBNm0BAKRR6GsBrUL1A7MlS3cCJUvix05NpBXGEmR9oQyZvcfgwLkqlnMWxb9okcQlCc2pExlqxCiV0slQ3cKIURrstdT3yeWD3bvAHPuDcgeK2e7EwmtSIjL0cNVJ+v/a1rlgLngpzHhgOHwZuvx04e9adR1UqKAlOqBGk9OsAfrHWvr/5m8Df/31Hh6ROLIWbiGjSycmI6H06VuGJNuUaXPJ54Lbb3NdNlFkHwSk1Hh4GgF+qte+//mvHHY9OlEIcQNIej2BHK4LPaEVwQscqhDom4aDxyU8CzRqH1kJmHQSn7N7tbv/Tp1XI9O/8TkeGE8QOKgoTUQTAfgAZAM9C+T18UGnMJ6BKq/9f2/6rzOzI99ZvAoEAZ7NZ5wdcdFFrEYmHDomTUXBGPg9cd13rx3/gAyqEusmQgoiWmDlQud5R8BIzJwDcCWAGKj15Ub//ODO/zVIIRPRWIvpjuJix8BxuFQKR0uCiEEaa+fl55zu7SJaqyaFDwDvf2fKQwnGYMzNndLHTMb0EmPnRit0MHeDUhpobUKy6i27ZtAn4sz/riAimaSKVSiGRSCAcDqNQKDQ/SOg7mUwGrqxRwFWyVE3Onm3Yo7IRHc2S1CHOw8fhw8Av/iLwmc+4O67DhVcPHjyIQqGASCSCubk5RKPRjpxXUORyOYTDYWQymbL1pmkiFoshlUohFoshl8s5PqdpmvD5fJiaclxsXGElS23e7O44Ow16VDaEmesuAP4HgPc12sfry+zsLDfkyBHmsTFmVZXf+XL99cxHjzY89dLSEodCIU6n02Xri8UiR6NRTiaTHI1GeWlpqerYhYUFjkajjWUXHJNOpzmdTrPf76/6fwSDQc7n82Wfi8Wi4/Nax7TE0aPuf3v2ZXKy7qkBZLnGPdEsTiEOYJ6IYlAOxjgz/7N71eNRDh8Gfv3XgbWmxbjL2bhRjesaWAjW06jWECAcDiMej8PnU10i5ubmkEwmYRhGaZ9CoSCWQgcJBlWb0sonummaKBQKpf8FAPh8PmQyGYRCISQSiZrni0QiyGQypfO2zMwMcMklwBtvtHZ8C4VZGioFZv4xVGaklRj1USKahZqFiDPzT9xL6RGseAS3CgEAvvzlpkOGVn+EABCLxZBMJt3LJbgmm82WKWMAMAwD6XQaoVAIkUik7rFTU1NIpVQr00Kh0LqSuPtuIJFQLe/d0sLww42j8Z+Y+aPMvB1KKcSI6Bs6M9JRcJOn+MM/bC0eAWhrpqHRjxAAUqlU6YdYOfYVOo9pmlWKe3p6GidONO8z5Pf7S4rcyf512btXWZ+t8PM/7/qQlhyNrJKedjHzrwIoAkhpBXF7K+cbOPJ5Zf73gUY/wlwuh8XFRezYsQMzMzMy+9Aj2rqhAYRCIRSLxdaHElbruVZo4TfSdu4DqwjGJ3UdhV1E9H+gFEWcbQFNvUC3pI9AtaH3AciwKgvvjgcf7KxgLqn3I/T7/ch3ucCGUI5hGDBNs2zd8vKy+9mEdtm5E/jt3wb+7u/cHXf6tPKNubBeOzYlyet1FW6F8kPM6q5Nj/SwbmMSQIqZU6yaxES1onDHgQOtS9Bm0tPA/AgFAEAgEKhS0qZpYm5urqPX+frXv46nnnoKzz33HF577TVr9q+c3/u91k7+oQ+5ilfoSpakdlA+AOAB7aD8LSLax8x3duN6QMlKsLeNA5TFEATgzvZy07/Bzvi4agEH4PXXX8fRo0dx9OhRvPjii4hEIrjEQTXeXv0IBWcYhoFAIFDm/M1msx2f+fnmN7+J73//+3jxxRfx0ksv4fTp07jyyitx1VVX4eqrr8ZVV12Fq773PVwN4Cq9XA3A0SPo/HlVe+GrX3UkS9dTp1kFNPUiqCkA1X3ajglgDm6VwsRE03Bmhkr6OKqXvPX+u9/F0Te9CW+88Qauu+46zMzM4IYbbqit+WvQqx+hUE4ulytFHkajUeRyOSwsLAAAkskkEokEfD4fCoUCHn300SpncLt8+tOfLvt85swZvPTSS6XlxRdfxEsPP4x/BvASgBf1sgFKQbwZwMMArq93Aav2goNAOkcJUV6AiEJQiVlztnULALYzc7jecTUTohwkPf01gE9BVa4tLR/7GGZuuw3XXXcdrrjiClCD/g7Wj3D//v0IBAKYm5sr/QhN0yz7EQaDQfj9/sZfgDD8jI2pkCQNA3gdSjm8AuDdABpOQN53X1nbuXoJUV1XCkT0R8z86eZ7tn2dEIB9zDxrW1dTKeiszwgAXHPNNbPHjh2rPFnT69mLaq6vHA4FKwwok5OtD22t40+eLH1sK0vSKUR0DxGdIKJlvZwA0Cu714SqRWFnGjWqWDFzglVCV2Dbtm3lGx06ZAgjWMde6C9u6yxU4jC6seNt45h5ipmn9TIF1S+iF2Shys3bMQCkXZ2l1enIJs08BKFt9u511E2qLg5nxjqtFGpFSvSkNBurVvRZIvLZVgegoi+d0850pMQQCN1kZgaIx1s71kU5wE4rhTwR3W71m9TxCb10m4cBhIgopP0J92hl4ZxWO/sStZamKghu+MhHgP37m+9XiYtygB11NOr2cgGUj+NnmXm6YxfpMFWzD+04cyocOYLQNfbvB/7kT5rvNzamirWkUlVRjT1xNAJIawferdYC7eX3DO04c1q1MgTBLfv2AZ/9bGNf1sUXA/feq9rR9SPMWVOssc5bA+1QG4Wopa+D0Es+8hHghz9U8QeTk8oqmJxUn48eVV2kHnrIdeWvTkc0zhBRGKpdPaBm7UIAfrXD1+keqZTSvm5z16Wvg9APrP6TtqCkdum0pTAP4CSArXoxoGIFvMOBA60Vsxgfl74OwlDQaUthkZmP2FcQkbcqgbTqF2AGfvQj6SgteJ5OV3M+UmN1LT/D4NKqX+DcuZZLagvCINGWUiCi91V8/v2K5R6o4q/eYfdu5R9ohVZLagvCANGupRCrKKDyUaz7E7zpU9i7tz2l8MUvdlYeQegxTX0KRLQM1fvhXyq31Qh8uIcrGsJ4zqdg1cNrtW2XxCoIHseJpbAVQI6Ibmu2Y6VCqLdu4Nm5U9XabwWJVRA8jhOlkACwD6o4697KjUR0GRH9MRHt13kPw1Hu/e673Q8jJFZBGAKcKAXWRVB3QdVcfLhi40lWTWX3QXWiLhLRU12Qtbe04lsYG5NYBcHzuGkGk4JKdvotInqqlkXAzA8AuBeqLqK3sXwLmzfjgoNKTIIwLDhRCqXCJbqHQgDA26BqF1xbuTMzJ6CiGr3Pzp3Ac8/h2zfcgHNYL8FWl7U1mZIUPI8TpWAvWgJdQt0P4BiUA/KXahyTrbHOm8zM4MC7342zcFB+TaYkhSHAiVLwV1oE2o9glU6vNTNhdki+gWGL0x1lSlLwOE6UAkH1iqzlQ5iHmplIVcxMtNd8b1DI54E9e/Dw3/6t8yKtMiUpeBwnCVEzUOnPjxHR/wOQYObXrY3MHCOiAoCDRDTDzHu6JGtvOXxY5TKsrGBTkx4QJWRKUhgCmioFWws46CayU1A9KOz7pIgoACBDRDPw+vAhn1cK4fRpd8e5qIMnCIOKq9RpZj6JOjMLzJzTiiEN4OfbF62PPPhg0w5RZUxMqCWVktRpwfN0OnW6AGAWwJOdPG/POXDAuVKYnAQiEdd18ARhUOl4g1ldUn1Xp8/bU5zOIIyNSfVmYejoeIeoocDpDILMNAhDSEeUAhG10J2i5Wv5iShJRMGK9QYRLViNYIio9TbNTgqtyEyDMKR0ylIINt+lfbQimEJFlKUmCSDFzCmdwBUlIqOlC+3d27w3pMw0CENKp5RCTzKGmDnDzBlUBEfpm9+nHZ0WBbSqrH70o7pt5RnAhQ0bZKZBGFo6pRQ613uuNQKojo0w0Uq2phWjcO5czc0EqL6R11/v+tSC4AWGxdFooDq0ehnVrekBAEQUIaIsEWWPHz9evtFBjAJJNqQwxAyLUgDqKIBaMHNC97wMbNu2rXyjgxiF8dVVyYYUhpaOxym4gYgiUMFOjYhW+ApqYUJZC3am0UpiltMYBcmGFIaUvioFXZClE2RRbSkYUCHX7rj0Umet6MfHlf9BnI3CkDEUwwcdRZklIvtUZQCA+/LyTpvBXLgA3HijyqYUhCHCU0pBBy4tQN3wi/q9RRhAyApegupBYbq+iNOCrcwqi1JaxQlDRl+HD27RNSJzAGI1tpm11rvGKtgaCgFnztSNVyhhtYrrYCtwQegnngpe6hm6YCs2ONCZUpdRGDI6pRTCHTrP4DAzo/wGThjCmYhMJoNMJoP5+XmYptlvcYQe0hGloKszDR8jmi2Zy+WQTCYRDKoo8UzGW+1AhfbwlKOx53QxWzIWi2FxcRG5XA6ZTAaLi4stCtmcXC6HcDhcdXObpolYLIZUKoVYLIZcLgcA8Pv9iMfjME0TJ06cKCkHYTTwlKOx5+zdC3zhC40jHNvIlkwkEkgkEggGg3j00UdbFLIxliIoFKrjv8LhMOLxOHw+NZM7NzeHZDIJwzAAANlsFtu3b++KXMLgIpZCI/RMxLnxcZyv3DYxAWze3HK2pGEYKBaLKBaLZTdiPRqN6xttCwaDCAaDmJoqj+0yTROFQqGkEADA5/OVWROWhbB/f8/KZQgDgCiFZuzcif/+G78BqxfeKoDzmzZ1rC5jLper+RSv5ODBg0gkqgNAw+EwTpxwH82dzWarFJFhGEin04jFYqVrGYYhjsYRQ5SCQ8j+yqz6RrZJKpWCz+dDLpdr6lOIRCIwTbNMMYTDYUSj0bKnvVNM06yyHqanp3HixAlEIpGS1bC0tIRoNOr6/IKHYeaRXmZnZ7khhw7x2fFxPqdUwfoyMcG8eTPzoUONj3eIz+fjdDrddL9oNMrxeJxDoRDn83nH5w8Gg2XnTyaT7Pf7q84dCoWcCy14GgBZrnFPiKXQCF1wZePqKi6q3Lay0laYs+Xpt/D7/Uinm+dvLSwsIB6PY/v27S1ZCBa1hgXLy8tV1oMwesjsQyOcNIVZWcHqgw/i+Cc/iZdffhmvvPJK2evLL7+M3/3d38Wv/dqvlQ7J5XLYsWMHisViaZ1pmphx4LAMh8NIJpOIx+NIpVIIhUIt/WmBQKDKF2GaJubm3BerEoYLUQqNqFNw5RUAEQAvAHh5ZQWvPfIItqZSuPLKK3HFFVeUXq+77jrcfPPNuOmmm8qO9/v9VVOQhUIBu3Y1bpcxPz9f8iFEo9GSH6IVxWAYBgKBQNkMRDabFf+BAOJmCT9DTiAQ4Gw2W3vj2FjNhKhzAL4FVcXlSgBvIsKES8ejFbRkGAaWlpYwPz8Pv79+VfpYLIZQKFQ1ZFhcXMSdd95Z91jrOvv370cgEMDc3BwWFlRyqeW49Pl8KBQKCAaDDWUQhgsiWmLmQNV6UQoNlMLkpLOCK5OT0ilK8Bz1lII4GhshTWGEEUSUQiOcFFyRpjDCkCFKoRFdDHMWhEFFlEIzdu7EJz74wa6FOQvCoCFKwQGvbtmCP4AqD70BwP/+zGdU+TWxEIQhRJSCIAhliFJoRj6Pu7/3PZhQQwcTwE1f+IJUcBaGFlEKjTh8GLjxRrz33/8dl0F9WZcBeNu3vy09H4ShxVNhzkTkx3p7+e0A4qxa01vt6CNQLeh9ADKsSsK3htV9+vTpqi9pfHV1PRnquefEtyAMFZ5SCgCCzBwDSkrgx0S0Q9/8SQDzrPtOElGaiMLcSkMYwHEylPR8EIYNzwwftJWwz/qsb/YsgKBWED4ub0RbwLpV4R4H3ael54MwjHhGKWhroLK/hA/K9xfQr3ZMAK3nAUv3aWFE8YxSAADLfwAAupnsFICDUCEElYUKl1Hdido5I9rzQRA8pRQqiAPYYfMZOFYARBQhoiwRZY8fP157J0mGEkaUvjoaiSgCYLbJbtEKXwF0V+lF2+yCCWUt2JlGtfUAAGDmBIAEoFKna161yz0fBGFQ6atS0DenK4goBNt0o3ZAZlFtKRgAmhc9rIet+/SFM2ewwVZ3YnV8HOMbN0oylFAikUggEon0W4yO4KnhAxEFAZg2heADELBmIvRniwCA9pog6u7T33zb20rJUCcB/Pt73yvJUEIJ0zSHqjeGZ+IU9A2f1u/tm6zhRxhAhIis4KV7Wo5RsDMzg8dvugm3/uhHpVWPf/jDePsIWAgV33PfGPTqYIuLi46K7noFzygF7Veo+yvVCiDWM4GEgaRQKJSa7Dz77LPYt28fDMNAKpXC/v37YZomlpaWcOLECczMzCASiWBxcbHUlKdQKODEiROlJjhWF61CoVAqrW8YBqampuD3+5HJZFAoFFAoFGAYBnw+n/cb8tZqBjFKS9NmMMy8e/duBlBaHn/88abHDAP2v7mfixt8Pl/pfT6f52AwWPpcLBbZ5/NxsVjkYrHI8Xi86tilpSVmVs1yIpFI2bZiscjMzEtLS2WNdKLRKEejUVdyDgKo0wzGM5aCIDQjkUiUVaP2+XywF+U1DAPRaBThcBjhcLjKMbi0tFSyDKwK14Bq72cYRmmb3+/HkSNHuvvH9BFRCkJdeMDH8pXk83mYplnWOTuZTJbtEwqFEI/H657D8g+YpllqllMoFKo6ZzXrEu5lRCkIQ8P27duRy+UajumtZr7z8/MIBoOlPhqmaWJ2drZkLeRyOTzxxBMAgOuvv770vh7Ly8sA0FbXrkHBU1OSgtCIUCiEEydOlE0PplKp0nvTNJHNZhEMBhGPxxEOr6fSZLPZsiGCNXQoFAq45pprytZVntfn8w3VlKQoBWGoSCaT2L9/P1KpFFKpVMnHEIvF8Na3vhV5XTFramoKuVwO4XC4ZF0EAgEkEglkMhn4/X4EAoHS+yNHjiAajVadF1hXRolEYiiGFdIhqlGHKM1dd92FAwcOlD4//vjjuEtyHgSPIx2iWiGfB/bsQeKJJ0r1GR8CcOl//Ed/5RKELiKOxnocPqzKra2sYJNOiroMwD0A6BOfAN7xDglzFoYSsRRqYavPWJkleRGAifPn1Xap6CwMIaIUauGmPqMgDBmiFGoh9RmFEUaUQi2kPqMwwohSqIXUZxRGGFEKtZD6jMIII0qhFnv3OlMKUp9RGEJEKdTCqs+4eXOVcjgPYOWii6Q+44iTyWQwOzuLxcXFfovScUQp1EPXZ0QkgtMTE6X6jAkAX/uLv5DApUboSFBMTgJjY+p1zx5Px3UkEuU1hoPBIObn5/skTXcRpdCImRngoYcwf+ed2ABVHvoPAPzs536uv3INMrpTNx57DDh1CmBWr4895tlO3cNWmLUZohSEztEgEhQrK+uduj1mMQzjEKERohSEzjEAkaBW6nMqlSqZ96lUCjMzM5ibmys98cPhMGZnZ5HL5Ur+gVgsVkqNnp+fR6FQKBVmTafTpXNXUnlMIwqFQuk6i4uLJXlSqRRmZ2dLVZ8KhQKIqEyOmZkZzM/PI5FIOL5eS9Qq3DhKixRu7SBbtjCrAUPjZXKyK5ePRqOlwqvWZ4tkMsmhUKj0OZ1OlwqxMjPH4/GyYqzxeJwXFhZK56lVmLXRMfVop7BsNBot+xus/VsFdQq3iqUgdI4+R4L6fD7cc889SCQSME2zrDBrKBRCJpMpPZlN06wqiGKVZgNUERYnfgQ3x7gpLHvw4MGaHafs17NKylc6QdvFU0qBiPxEFNJLVPeUtLYZRLSgty3odnJCL+lzJGgoFMK+ffuQTCaxdevWKl/Arl27SgrDfnNZVBZntQq3NsLNMfbCstZSq7CsG3w+X6maVKfwlFIAcARAgZlTzLwIIGq7+ZMAUnpbTG8z+iXoSNLnSNBMJoNQKIR0Oo1isYhsNls25l5cXEQ8Hi+VWHODvTBrq2zfvh2Ams60L3aswrLRaNSRv6BQKHS8O5XXlMIOXu8jaeh1pn7v4/Lu1AUAHm/V4zH6HAmaTqdLN5JhGFU3nM/ng2EYjiyAyuM6MSXZTmFZC7uisBySnW5s6ymlwOut5wFgF5RlUIBqJmtW7G4CmOuNZAKAhpGgmJhQ67sYCTozM1Myy1OpFLZv3141TJifn8euXbvK1uVyOSSTydJxuVwO8XgcuVyuVLK9sjBrs2Pq0WphWTvWNffv3490uvXG6nWp5X0c5AWqeWwEQNK2LgQgXbHfgn2feovMPnSBo0eZ77tPzTKMjanX++5T6/tMMpnstwgtE41Gm85uuAHD0jaOlWWQICIQUZKZLRtrqtFxdogoAqVYSjX9hQ6iI0Hx0EP9lgSAsg7C4TB8Pp9rX8Io0leloG/O2Sa7RbncVwAAYOYEES3qGYgcVBSynWkANQePzJyASmNAIBAY7Rr3I0A4HEahUIBpmp7t3pTJZPDEE0/ANE3Mzc11tbN1X5WCvjkdoWcZksxsH5AWAMxA3eCVloIBoGMDLh+A/wZgN4DJu+8G7rtPedv37pVsyQHH863hof6GpaWlnlzLS45GE0ClBycA5UswAWSJyFexrTomtQVufPFFPAdV3v0yAAR4PslHEOrhqQ5RRBSEemgDatixZFkbeloyAmU9+ABkuHy2oiZNO0Tl8zh3ww3YuLpaf5/Nm1WatVgMgoeo1yHKU45GZq775NfWQqzjF33wQYyvrTXex0ryGRDHmiC0g5eGD/3hwAFsaGZNSbl3YYgQpdAMKfcujBiiFJoh5d6FEUOUQjOk3LswYohSaIaUexdGDFEKzehzko8g9BpRCk6wlXsvK1seiaj1Uu5dGCI8FbzUDZoGLwnCkFIveEksBUEQyhClIAhCGSM/fCCi4wCOOdz9cgCvdVEcpwyCHIMgAyBytCPDtcy8rXLlyCsFNxBRttYYbBTlGAQZRI7uyCDDB0EQyhClIAhCGaIU3NHZVjytMwhyDIIMgMhhpyMyiE9BEIQyxFIQBKEMT1Ve6hW6SOw+AHF7tadWS761KYdVdXS7XZ5eyaJlsErgbQewzKotX8+/D5tMQQAGM6d6KYeuHD4N4AmoQsFzrNoX9vO3UQAw1W5ZwjJqNYMY5UV/0UEASwCCFdvSUO3p7J+NLsqyYHtvACgC8PdSFvs19WfutQwV8hgA8gAivf6/QDUYKuolab9GL78LAFZlc+vzUif/JzJ8qICZM6yexmU9I3rdr9JmrVhymQCyAII9lmXQ+nfugq1Kd4/lMJl5q17C+n/S898GgEcB2Ftq72DmXKfkEKXgnJ72q9Q3YmWHUZ++Zs9k4QHq36mHDZXFe/shh79GO4GeyKBvfD8zFyw5LOXUKTlEKTjHQHXHqWW4aFfnFi73Z/j0tQ72WhYi8uluXnO83qav1zIYUGZwZbewXssRgnr6+oko2gcZAgAKNjl8RBTvpByiFNzRNQXggDiUmWj2WhZmLrByZKWJKGnb1MvvI8jasViDnsjBzAlmTjGzqWUJaeulZzJA3fiWA9HUDw6fVhIdkUOUgnNMuOhX2Um013vRZsr3RRatGPxanp7JoP0r9TzovZbDTg7KNO+ZDFDWgWl7OFjrOiaHTEk6J4su96ushX4CZGzOPn+vZOl3/04bUwACRGR9DgKY0p8P9kIO/V0cAbC14jp59Pa3UUD1jQ8ohdAZObo5feTlRX+RzaYkl9DdKcmgXQYoszHSK1n09aIV64oAQv34PmzXSaLxlGRX5LD+btvnvHWdXn4X+u/3V1yr3pSkazkkzLkCW1DIPijNm+Y+BOtox2K+xqZZXp9+6kXATsf7d7YpzwLU/6YAYD8zp3ocyBWEeirPQgWT2adre/XbMKC+gzyU1ZbmDga1iVIQBKEMcTQKglCGKAVBEMoQpSAIQhmiFARBKEOUgiAIZYhSEAShDFEKwkCik7CizfcUOo2EOQuOqAimykEFx9hj6iPQ9QY6dMl51AjP1XLMA3jWtrpnVZ9GAVEKglNCUMogzBXpyzrKEAB2dPB6QdalzmzXiUDVmCgVOLFtixMRmHm+gzKMJDJ8EJyyHSp1u1IhhABEoW7UjjypbUlf9nVB23XMymO0MgjaFJTQIqIUhKboePpnazyd/VDJOYtcv9ZBK8xD1Y+wE4WuIdDguLjeT2gDUQqCE6ZQ0WhEj+2PAEhYCWMdJFDD6vCj3I9QC3t6udAi4lMQmlJjyGBAOQGznR7D16nDaDHdyWsJtRFLQWgFqyRbZWHZTlBr6AAoK8BXY70dP1BVbFZwiSgFwRW6SGgAqoir2YVLGJWWiSaO5qXK5zAYPR09jdRTEByjPftR6EIvtvVGJxSEnskodTuqsT0PYJ5tVa7tMkBVhdraJWU1MoilIDiiydRjpEOXmYequdhoe70hyy4AMVEI7SNKQWiKg6nHth2AVvepRje1thDqlTCfqwx2ElpDlILQkGZTj3pI8ax+HySiPBFF9JK0rV8golCDfIZdqO1grOzItN/Wa8HabsAWEm3rgSC0gPgUhLrom20JQIGZq1qP6bDjOGzjeKtbETPPawvDhCpwOqe3L0DlSFTGPaRrXcO2fcFWQDdkt1i0ksgys2nFKMgMROtInILQiEehpgFzttZkU1C9BAL6tTLK0IROnNJVpxegGtLaA4pm7RfRVoD9HLWYt1kZKb1Y+KG6V0FflyC0jCgFoS683jfSLfbsyWkoS8N6ctd6godQZ+hgk2WmwbYYgE5HVY4s4lMQus0T0EFFFjXCkO+sNc0o9AexFISOocf2QaiGpyYzZ/QQIqqHETnoIYftmKqMSKG/iKNR6CvaT/CEOAYHBxk+CP3GJwphsBBLQRCEMsRSEAShDFEKgiCUIUpBEIQyRCkIglCGKAVBEMoQpSAIQhn/H6rJCsUU3logAAAAAElFTkSuQmCC\n", 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\n", 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" ] @@ -246,6 +246,10 @@ "# whose inverse is needed\n", "K_im_full = L2_im_K + Sigma + (sigma_L**2)*np.outer(h_L, h_L)\n", "\n", + "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", + "if not GP_DRT.is_PD(K_im_full):\n", + " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", + "\n", "# Cholesky factorization, L is a lower-triangular matrix\n", "L = np.linalg.cholesky(K_im_full)\n", "\n", @@ -317,7 +321,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -358,7 +362,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -440,7 +444,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.9" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/tutorials/ex6_exception_handling.ipynb b/tutorials/ex6_exception_handling.ipynb index d2a890f..ede6fdb 100644 --- a/tutorials/ex6_exception_handling.ipynb +++ b/tutorials/ex6_exception_handling.ipynb @@ -149,7 +149,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -207,16 +207,18 @@ "# to ensure that the K_im_full becomes positive definite\n", "\n", "# the flag to denote whether the K_im_full can be successfully decomposed\n", - "ch_flag = True\n", - "while ch_flag:\n", - " try:\n", - " res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='Newton-CG', \n", - " jac=GP_DRT.grad_NMLL_fct, callback=print_results, options={'disp': True})\n", - " ch_flag = False\n", - " except np.linalg.LinAlgError as err:\n", - " if 'positive definite' in str(err):\n", - " theta_0 = np.abs([sigma_n, sigma_f, ell]) + np.random.random()*np.ones((3))\n", - " \n", + "# ch_flag = True\n", + "# while ch_flag:\n", + "# try:\n", + "# res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='Newton-CG', \n", + "# jac=GP_DRT.grad_NMLL_fct, callback=print_results, options={'disp': True})\n", + "# ch_flag = False\n", + "# except np.linalg.LinAlgError as err:\n", + "# if 'positive definite' in str(err):\n", + "# theta_0 = np.abs([sigma_n, sigma_f, ell]) + np.random.random()*np.ones((3))\n", + "\n", + "res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='Newton-CG', \n", + " jac=GP_DRT.grad_NMLL_fct, callback=print_results, options={'disp': True}) \n", "# collect the optimized parameters\n", "sigma_n, sigma_f, ell = res.x" ] @@ -237,7 +239,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -256,13 +258,17 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", "K_im_full = L2_im_K + Sigma\n", "\n", + "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", + "if not GP_DRT.is_PD(K_im_full):\n", + " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", + "\n", "# Cholesky factorization, L is a lower-triangular matrix\n", "L = np.linalg.cholesky(K_im_full)\n", "\n", @@ -291,12 +297,12 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { - "image/png": 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J/qGhIcRiMSgUCmg0GoyPj6OmpiZ3vwQhWUB9MIRkWXd3t2S7srISarUaAKC7cgUNf/ZnUITD075G1dGjeFRUQwmHw8LiZTqdDg6HgzIsk4JHAYaQLLt48aJkO9k8ph4eRsNTT0Epq524b7sNAZsNXCVtUPjHYBDihrVkP4xCoUA0GoVH9jqEFBoKMIRk2blz5yTbtbW1ULjdaHjqKWhETWcAMPg//gd6f/hDXPrP/8Tln/8csURNBwAssRh+IjpX3A+jUCgKasY2IelQgCEkiyKRSEoTWW1tLWp/8APoZfvHH3kEY5//vLAdWLcOw6LJmQDwYQBfSvycrMEA8eHKo7JgRUihoQBDSBa53W4MDw9L9q02m1H2/POSfc7mZgx8+cspC2ONfe5z8MiWuP02gHWQBhi1Wo1AIAC/35/V8hOSTRRgCMmisbGxlJrFPVeuQBEKCduh2lr0feMbgFKZ+gJKJfq+/nVES0qEXQYA34W0iQwAOOeU/JIUNAowhGRJLBbD6OgoRkZGhH0aAFveeENy3tinPw2u1U75OuFlyzAgW5v9fgDo65Ps02q1wsgyQgoRBRhCssTr9SIUCklqMA8D0ImyIkcNBtg//vEZX8vx4IOYXLdO2FYAuG9oSJIiRqfTwW6303BlUrAowBCSJW63O+UL/2lZM5j94x9HzGSa+cUYg/OTn5Ts+pNoFHZRjUWhUCAWi9FwZVKwKMAQkiWjo6OSTMd3ANgiCjacMYx/+tMZv57z/vsREA0CaAAQfeUVyTmMMcm6MYQUEgowhGRBJBKB2+2W9In8mewc1113IbR8ecavGTOb8bpsmeVlv/2tZNtgMEj6fAgpJBRgCMmCZDNVcojyagAPys4Z/8xnZv26x2+6SbK99swZKEUjx9RqNfx+PwKBwKxfm5BcowBDSBY4HA4oFAphrsr/gPSPy7dxI7yNjbN+Xdf27RCvCK+ORmH5zW9SzvN6vbN+bUJyjQIMIVkwNjYGnU6HoaEhqAB8Vn78s59NmVSZidply/D/ZPvKfvlLybZSqYTD4Zj1axOSaxRgCJmnYDAIv98PjUaDoaEh3AHAKjoesVjguu++Ob12bW0tfgogJtpnuHABOlFCTZ1OR8sok4JEAYaQeUr2v3DOMTw8jE/IjrvvuANclMRyNurq6tAP4GXZfnHqmWTamJAoWwAhhaDgAgxjzMYYa2WMNcv272OMHWCMNTLGmhljhxaqjISITUxMQKVSwW63IxQM4mOy4667757za5eWlsJgMEiyKgOA9cUXgUhEso/mw5BCU1ABJhFUbIlHOnsAvAJgL4D9U5xDSN5wzjE+Pg6dTofBwUE0ARAPRI7q9Zi89dY5vz5jDLW1tXgBgDg5v8rlguHMGWFbqVTC5XLN+X0IyYWCCjCc83bOeTukf0tJTs65NfFo4Zw781w8QlIEAgGEw2GoVCr09/enNI9Nvv/94DrdvN6jrq4OIQC/le03v/mm8DPlJSOFqKACTCYSTWRT1XAIyStxNuN0AcZ1113zfo/kipjywcmmt94SftZoNPD5fAjPsBQzIflUVAGGMbYbQA+ARsbYgYUuDyHj4+PQaDTxjYsXsUF0LKpQwH377VM+l3MOp9MJl8sFp9MJp9OJycnJlCBRW1sLAHhJ9nzD+fNQyUaPUT8MKSRFE2A454c5522ccyfnvA3AbvlAADHG2B7GWAdjrGNsbCyPJSVLRSwWg91uhy7RBLZRNHQYAAbWrUPMbJ7y+W63GxUVFdi5cye2bduGjRs3ora2FpOTk5KEmckazBiADtlriGsxjDFaH4YUlKIJMIwx+TToLgD3TnV+IiA1cc6bKmX5nAjJBp/Ph1gsBoUi/md0m2yhMccdd0z5XI/HA5PJhPXr10Ov16O0tBRVVVVYvXo11qxZIwkUyQADpGkmE/XD0HwYUmiKIsAkgssrst0WAN2pZxOSH263Gyw5O7+/H9tlTVuxB+XZyOK8Xi/UajVuuukmqFSqlOPLli1DaWmp0Nw1bYA5dgxI1HY0Gg08Hg8isuHLhCyUoggwnPMupA5LtgE4sgDFIQRAfP5Lsv+FvfCC5FiHWg1FmszJgUAAnHNs3rz5vb4bGYVCgfXr1yMSiSASicBqtQrNcCcAiJPCqFwuGM6di5eBMXDOKS8ZKRgFFWASI8T2AWgCsJ8xtkd0uCMx2XJPooOfhiqTBROLxeB0OqFNLH1s/f3vJcePVVWlPIdzDr/fj82bN0Ov10/7+gaDAevXrxeaypK1mChSZ/WbREsyUz8MKSQFFWA4512c84OJuS73cs4Ppzl2mHO+P1GrIWRBiPtfFJOTqLt8WXL8/Pr1Kc/x+/0oLy+HeZqOf7Hq6mpUVVXB4/EII8mA6Ycra7Va6ochBaOgAgwhxULc/2Ls6ICSc+HYBQCKDRtSnhMMBrF8FguOMcawZs0aRKNRSYBJGa587hyU9vjcZK1WC5fLJRmFRshCoQBDyByI+19Mx49Ljr2MeEe9WDAYhMFgQGlp6azeR6vVoqqqCtXV1cK+YQC9FouwzTiPd/YDQtCjfhhSCCjAEDJL8v4XoyzAtAMpNRWfz4eVK1cKQ5pno7a2VjKSDAB+L+vDkc+HoQmXpBBQgCFklsT9L+qREeh6e4VjEQC/hzTARCIRqNVqzHU+ltlsxqpVqyT7ng8GJdumt94CYvFVY9RqNez2dOn8CMkvCjCEzJKk/0VWe3kbQFinQ1lZmbDP6/VixYoVUCqVc3o/hUKBnTt3vjfnBsCv7XZESkqEbbXDAf2lSwDizWpOpxOxWCzltQjJJwowhMySuP9lquaxZDCIxWLgnEv6UOZi+fLlqBINfQ4DGLnpJsk5JZ2dAOKp+6PRKAKBwLzek5D5ogBDyCxI+l84T+ngl/e/eL1e1NbWCv01c6XX61Oaya7K+mVKuqQj96mjnyw0CjCEzIK4/0Xb3Q21aA2WSQDHAaxcuVLYF4lEUjro52qDbOhzh8Eg2TZ2dQGJ4dIqlQpOpzMr70vIXFGAIWQWxP0v8trL7xHv5K+vrwcAhEIhGAwGGI3GrLz3TbImsRPBIKKifhiV0wltTw+AeD8MdfSThUYBhpBZmKn/BXgvwAQCAckEyflaL8sOcO3GDXi3bZPsMyaaydRqNfx+P0KhUNben5DZogBDSIYk/S/hMIwd0tVZ5AEmFovBarVm7f3XrFkj2e7r64N3xw7JvmRHPxCfD0P9MGQhUYAhJEPi/hfD2bNQ+nzCsWEA5xBPUllRUYFIJAKNRoMSURPWfNlsNslQ5eHhYdhvvllyTomoH4YxhsnJyay9PyGzRQGGkAyJsxSnGz0GxGsvjDH4fD7U1NRIAsJ86XQ6rFixQrLvksmEmGiEmmZ0FJqBAQCU+JIsvFkHGMbYNsbYtimOfXKqY4QUu4mJiWnTwwDS5jHxZMtsWbt2rWT7+tAQvFu2SPYlm8m0Wm3K8suE5FPGAYYx9jRjLAqgE0AnYyzKGPshY8yUPIdz/h/xUxl9osmiEovF4HA4oNVqofB6UXLmjOR4crnV+vp6RKNRKJVKmEym1BeaJ3mA6evrg7dRupp4sqM/uQCZT9SUR0g+ZRRgGGP/BOAJAH8J4L7E4xkAawA4GWPfTJ7LOT8FIHvtAoQUAK/XC845FAoFSrq6wETLEl8E0J/4ub6+Hj6fD9XV1XNKbDkTeYC5du1aakc/TbgkBSJ1QXAZxth2AOCcr5EdegXAQcZYKYBPMcZeRnwJ49asl5KQBSZf/0XsVdHPyRpMRUVFTsqxadMmyXZPTw+8mzeDq1RC0NPeuAHVyAgi1dXQaDSw2+2oqanJSXkImU4mt1j3cM6fmOog59zFOf8R5/w+xINLE4D92SogIYVA0v8iCzCviX5evnw5FApFxqtWzla6ABPT6eCT7TeeOgUg3g/jcDjARQuiEZIvmQSY3plPiUsEm1c45/8wjzIRUlCi0ShcLle8/8Xjgf7iRcnx3yf+rayshEqlQnl5+ZwzJ89kxYoVkswAHo8HY2NjU86HUSqViEQilPiSLIhMAgzd+pAlzev1IhaLgTGGktOnwUSjss4DGEv8bLPZEA6HJVmPs40xlpKTrKenBx5ZRz/1w5BCQPNgCJnBdP0vvxP9vHr1agCY9bLIsyVvJuvt7YV32zZw0ZwbfXc3lA4HgHgtxuVy5bRMhKSTSYC5hTGWUYMyY+zuxFyYZ+dZLkIKxvj4uND/UjJNgFm5ciVKS0uhVqtzWh55gOnu7kbMZIJflqusJNEPo9PpaMIlWRCZBJhDAFrF813EEkHlnxhjLwGwJ+bC7M5mIQlZKNFoFG63W+h/MVy4IDn+e9HPK1asmPOyyLOxceNGyXZ3dzcAwLt9u2R/yenTACjxJVk4Mw5T5pz3Msb+A8A1xlg7gJMAygHYADQDsAPYyzl/dZqXIaQoeTwecM6n7H8ZFZ27cuXKnI0eE0vXRAYA3m3bUPnv/y7sTwaYJK/XK2SCJiQfZgwwAMA5P8wY6wHwLQAtid1dAP6Sc/6j5HmMsVUA7sUsRp4RUsgk/S+iTMWAtPZSVVWF0tLSrCa3nEpDQwO0Wi2CwSAAwOl0wuFwQC1L3a+/cAEsGATXaoXEl9nM7kzITDLu5Oect3POmzjnisSjSRxcEqyJOTHySZkZY4zZGGOtjLFm2X4LY2wfY2x34t/GqV6DkGzJtP9l1apVKCsry8nsfTmlUpkykuzixYsIV1cjJFp/RhEOQ3/+PABKfEkWRlb/GhJpYuYsEVRsiYdcK4A2znkb5/wggAOMMct83o+Q6UQiEUxOTgr5xwyJL+skcQ2mvr4+Z7P309kiS3B5PlE279atkv0l77wDIB5g3G43Jb4keTVtgGGMfYsxdne+CpOoJbUj3q8jLocFgI1z3iPa3YN4HxAhOZHMP5au/+W6wYAR0bmrVq3KSXLLqWyVBZIrV64AQMoKl8l+mGQzH82HIfk0Uw3mEID7GGMdjLH/u4Cp+JsAOGX7nIj39xCSEy6Xa8r5L3+Qnbt+/Xro9fo8lSw1wFy9ehUA4JMFGMM770gWIPN4PHkpHyHADAGGc97LOf9LznkTgMMAnmCMnWSMfTPRoZ8vFshqNQAmAGR/wQ1CEkZHR4WgIe9/+bUoBb5SqcQtt9yS1cXFZiIPMNevX0cgEIB/zRpEDQZhv9rhgKavL/6zWg27Xf5nREjuzKaT/xTn/AnO+U7E11c6yBh7iTH2WKYTMedpVsGEMbYnUfPqGBsbm/kJhIgEg0FhWK/C55u2/2XlypWoq6vLa/kqKysl7xkOh3Hp0iVApYJv82bJueJ+GKfTiVgslteykqVrTp38iYSWn+KcfwiAA0BbItg8lN3iCZyI12LEypFaqxGX8XBipFtTPia/kcVFvJa9vP9l1GrFsOjctWvXShJQ5ou8FnPp0iUAaTr6E/0wSqUS0WgUfr8/L+UjZN6jyDjn/5FI1f8pAOWMsZcZY89meXBAB1JrMBYAR7P4HoQIxsfHhZQvxpMnJce6ZJ35mzZtEoYy59M2WX/LVP0w8gmXtMIlyZesDVOWrQvzlwB2ZGtwAOfcCaCDMSYevtyE95ZCJyRrYrEYxsfHodPpAAAlsgDz28QEx6SdO3fmrWxi8hpMd3c3otFofAEyUX+QrqcHSrcbAPXDkPzKyaywxOCAfxANDngkkwSYjLFGxtg+JBYtY4ztER1uAbA7MdFyD4DHE4GHkKzy+XyIRqNQKpVQTE6m9L+0yvr0du3alc/iCeQ1mCtXriAQCCBmMiGwRjrX2SDqh6EAQ/Ilo1Qx85GYfJnRBEzOeRfiKWgOpjnmTLefkGxzOp3CiLCSU6fARJ3irro6DA4OCts1NTVYvnx53ssIxPt+TCaT0F/kdrvR29uLm2++Gd5t26BPzI0B4h39k7ffDpVKBY/Hg0AgINTQCMmVOdVgctiZT8iCGx0dfW95ZFnz2AXZ2vYbN27MeXr+qSgUipTmuYuJ1TZ9U3T0J1E/DMmHuY4i+0/G2OOMsafzPB+GkJwKh8NCehggNcC8Jpvrcsstt+StbOnI3//ChQuIxWIpM/r1Z88C4TCA+Ggyp9OZpxKSpWzOfTCJDv1vI96Z/xjVashiMDk5KaSHUbpc0CeG/iYdGRmRbH/gAx/IZ/FSyANMsh8mtGwZwqLcaMpAAPrLlwHEFyAbHx/PaznJ0pSNTv52xOfC3CIaNfbYAqaVScETqTIImcnExARUqnjXZElnJ5jos+NZvRqn+/uFbYVCgdtvvz3vZRS79dZbJduXLl2KN38xNuV8mOQCZEHZaDhCsm3OAYYx9lBiZNg9ANqTKWU4518C8AqAnYyxI4kJmN/M02z/tPx+P+VgIjPinGNsbExIDyNvHutesUKyvXbtWpSWluatfOnU1dVh2bJlwnYwGHxvhcsZ5sNQ4kuSa3Pt5P8WgAOIDxX+T865S3w8MUz5R6LZ/t/inLuzUN45icViuHbt2kK9PSkSPp8P4XBYqMHIA8ybstUgF2r+i9xU/TBpJ1wmamRKpZKGK5Ocm2sNZg+AA5kGDXkAWgijo6NwuxcsxpEi4HK99zFV2u3QJ2bGAwBXKPBLh0Ny/m233Za3sk1HHmAuX76MUCgE34YNiImGIqvHxqAZGAAA6PV6jI+PU/Mxyan59MEU1SdTo9Ggt7eX/qDIlMbGxt4bPSbLnuxfvx7HLlyQ7LvjjjvyVrbpyAcadHV1IRAIAGo1vPLEl6fiU9JUKhWCwWD8PEJyZK4B5i8Rzz1WNAwGAxwOh+QulZCkUCgEp9MpTD6UN4/1rV4t6cczm80pyxYvlJ07d0omTQ4PD2N4OJ6O07t9u+TcZIBJor5JkktznQdzGEA7Y+ybWS5PTul0OvT09FAthqRIzgsRFhiTBZg3ZJMpd+3aBYUiJ5mWZk2r1eJ973ufZN/p06fBOZ+2o1+tVmNiYiIPJSRL1XzmwfwDgMPFNP9Fr9fD5XLBIWtLJ2R4eFhoHlONjkInGhTClUr8x+io5Pw777wzj6Wb2Qc/+EHJ9vnz5xEOh+HbsgVcFAh1PT1QJj7/Op0OExMTdMNFcmZet2CJ0WL/ma3C5IPBYEB3dzctukQEoVAIDofjveYxWf+Ld9MmvJFIFpl033335a18mZAHmHfeeQfBYBAxoxH+deskx5ILkCmVSkQiEUobQ3KmMOr4eaTT6eD1emkmMxHM1DzWZ7NJ+ipKS0tTMhkvtPe9733C8GogvoRypv0w4sXVCMmmJRdgAKCkpAQ9PT2IilYpJEuXuHkMnMP01luS439QSZOOF1L/S1JJSUnKvJyuri4AaSZcigKMRqOhfhiSM4X1V5InGo0GwWBQuMMjS5e8eUzb3Q2NKN9YVKfDEVF6fgC466678lrGTN17772S7ZMnT8YXIJMnvjx/HiwxPFmn08Fut1OTMcmJJRlgAMBoNKKnpwfhRIZZsjTJm8fMstqLu7ERbyVqAkkf+tCH8lK22frwhz8s2e7o6IDP50OkuhpBUToZRSQCw7lz8Z8Vivisf+qHITmwZAOMSqUC5xz9ouSFZOmRNI8BML35puT4mbo6SVLImpoabNmyJW/lm42dO3fCYrEI206nE+cSgSSlH0YUNBljlOWC5MSSDTBAvBbT19cHv9+/0EUhC0DePKbw+yVfvADwnOyz0dzcLNR2Co1KpUJzc7Nk34kTJwBMn/hSo9HQoBeSE0s6wCiVSiiVSly/fn2hi0IWgLx5rKSjAwpRk2lw+XK0yTIQf+QjH8lX8eZE3kx2/Pjx+IRLeQ3mnXeAxCAXnU4Hh8OBSCSSt3KSpWFJBxggXosZHh6moZpLUErzmKz/ZfDmm9GfSA4JxGe+P/DAA3kr31zI+4fOnz+PgYEBBBsaEBEtLaD0eKBLJPNkjIFzTs1kJOuWfIBhjEGr1eLKlSs0kmYJCQQCsNvtkhxeZln/S7ssPcyOHTtgNi/YskYZWb58OXbs2CFsc87x6quvAgrFtMOV1Wo1xsbG8lVMskQs+QADxGf3u91uGra8hIyMjEChUAjNY5r+fmj7+oTjMZUKhxNLDCcVevNY0kMPSbM3/eEPfwAw/XwYvV6P0dFRuskiWUUBJsFkMuHq1auUvnwJiEajuHHjBkpKSoR98uYx+6ZN6Lh0SdhmjOHhhx/OWxnn45Of/KRk+9SpU3C5XCn9MMaODskCZLFYjJqKSVZRgElQqVRQKBTo7u6m5H+L3MTEBCKRiCS1ijzAvGUySba3bNkCm82Wl/LN1/r167Fp0yZhOxqN4pVXXoH/ppsQTSwHDQDqiQloE8srA/E5MTSrn2QTBRgRo9GI0dFRGrK5iHHO0dfXB4PBIOxj4TCMieG8ST8dGpJs33///VAqlXkpYzbIm8l+85vfgKvV8DY2SvabRL+3wWDA8PAwNZORrKEAI8IYg9FoxJUrV2iG/yLldrvh8Xgko8cMp09DKZrJHrBY8FxPj7DNGENLS0teyzlfjzzyiGS7o6MDIyMj8Nx6q2S/OLCqVKr4Uss0q59kSdEFGMbYPsbYAcZYI2OsmTF2KJuvr9FoEIlEKKX/IjUwMAC1bHSYPD3MyfJyyfbWrVuxZs2anJctm2666SY0imornHO8+OKL8Nxyi+Q8Y0cHIJr/olAoaL0kkjVFF2AS9gB4BcBeAPuz/eJmsxlDQ0PoE40qIsXP7/djdHRU0rkPAKbEKKukn4mSXQLAAw88kPKcYvDoo49Ktv/rv/4LvrVrERGlk1F6PNBfvChs6/V6DMmaBwmZq2IMME7OuTXxaOGcO7P9BowxWCwW9Pb20tDlRWR4eBhKpVKS6kXb0wO9qKM7plDgOdHaLwaDAX/0R39UVP0vSY888ohkIENPTw/OnDsHT1OT5DxxP4xGo4HP56P0SSQrijHAAAASTWQ5G9ajUChgNptx4cIF2O32eb8e5xzBYBButxtjY2Po7e3F1atXMTY2Bq/XS81xORaJRDAwMJBSE7EcPSrZ7iwthfh/++6778aKFSvyUMLsq6qqSsk88Oyzz6b2wxw/LtlmjFEzGckK1cynFB7G2G4A7QCaGWN7OecpzWSMsT2IN6Whurp6Tu+jUqlgNBpx9uxZNDY2wmg0zvo1wuEwxsfHcePGDfj9fiEtR/JOemBgQLijLisrw6pVq+b0PmR6/f39iEajKTWR0pdflmwfln2x3n///TDJhiwXky996Ut44YUXhO2XXnoJN1pasFx0Tsnp02ChELhGAyCem2xkZAR1dXV5Li1ZbIquBsM5P8w5b+OcOznnbQB2M8aapziviXPeJE5hPlsajQYajQZdXV3Cl1QGZYTb7cbly5dx7NgxXE7MCLdYLCgtLYXFYoHJZILRaBT2mUwmuN1udHR04PLlyzThM4u8Xi+uXbuWEijkzWNRxvCc6PjGjRtx8803F2X/S9J9990nGaAQiUTwbydOICS66VIEgzC8846wrdVq4Xa76TNI5q3oAgxjrFG2qwvAvenOzRa9Xo+SkhJ0d3fj5MmTmJiYSDsZMxAIYGBgACdOnEBXVxdGR0dhMplgsVgkw2LTUSgUKCkpgcViwejoKE6cOIEbN27Qss7zFIvFcOXKFWg0mpTai7x57DXGIJ5m+KlPfQplZWUFtzzybCgUCjz11FOSfc8eOQKXrB/GePKk8DNjDIwxyk1G5q2omsgSweUVAFbRbguA7rRPyCKVSgWLxYJgMIh3330XZrMZarUanHNwzhGNRuHxeMAYg16vh9VqnflF02CMwWQyIRqNoru7GxMTE9iwYYMkKSPJ3NjYGBwOB8rKylKOyZvHfiHqB6uoqMAHPvCBtM8rNp///Ofx1a9+FV6vFwAwPj6O3zEG8cwe0/HjGHnySWG7pKQEfX19qKurK8oBDqQwFNWtGee8C6nDkm0AjuSrDFqtFmVlZYhGo/D7/QgEAgiFQojFYigtLUVpaSk0ibbs+VAqlbBarfB6vejo6KBO1zkIhUK4cuVK2j4UefNYBMAvRccffvhhqNVqlIpS3Bcri8WCJ554QrLvm7LMBYZz56BIBCAgfkMVDoeFNXMImYuiCjAJHYnJlnsYYwcA5GSo8ky0Wi10Oh10Oh20Wi00Gk1OVjo0Go3QarU4ffo0bty4QaPNZuHatWvgnKdMrARSm8deBYTmMaPRiJaWFqhUKuhFubuK2V/8xV9ImmlPjY5iTDShlEUiKat56nQ6mgtG5qXoAgznvItzfjDRib8/UatZ1DQaDUpLS3H16lWcO3cOoVBooYtU8CYmJjAwMDDlCDB585i4CvzZz34WKpUKlZWVRd3/IlZbW4svfvGLkn2/EtVYAKTkY9Pr9fEszLLzCMnU4vjrWQKUSiXKysrgcrnQ1dVFadWnMTExgTNnzsBoNKatVU7XPGY0GvHpT38akUgE5bKUMcVu//79kubbX8lGiZlk82GAeFMZzewnc1VUnfwkvm5NIBBAZ2cn1q9fj5qampw0zWUiFAohEAggGAwiFAoJ/yZrWEqlEgqFAgqFAgaDAXq9XmhSTNdslQ3j4+M4e/YsjEbjlO8xXfPYF77wBZhMJrhcrqKe/5LOypUrsXfvXvzgBz8AALwGIIb37jL1ly9DPTSEcG2t8ByDwYDBwUHU19fn7P9sqYnFYohGo1CpVAv2t5svFGCKkE6ng0qlwsWLF2G322Gz2XLeVxAKheD1euHxeOBwODA5OYlIJCJMHGWMQaFQCEEFgDDCjnOOkZERydBunU6HyspKWK3WaYPBbIyMjODChQvTvx7nsLz0kmRXsnmstrYWn/3sZxEKhWA0GrMyWKPQfOUrX8HPfvYzuN1uOAC8BeADouOlv/sdxv/4j4VtpVIJzjnGx8dRKwo8ZGaxWAx+vx9utxtOpxN+vx/BYBDhcFj4m0nedInnxC2WZlmAAkzRUqlUsFqtcDqdOH78OFatWoXly5dLck/NRyAQEILJxMQEAoGAMD9Cq9VCr9fPa/hqOBzG4OAg+vr6hKHZ1dXVKC0tRUlJyazu7ILBIEZGRtDd3Q2z2TztNSg5dQo6USp+cfPY//yf/xNarRYulwsNDQ1z+8UKXHV1NR577DF897vfBRD/3cUBxvzaa5IAA8RrMTdu3FjQ2nKxiEajcLlcGB0dFRa2AyDMw0r+7SRvzCKRCLxeL1wuF/r6+qBSqVBTU4PKykqYTKaiv94UYIpYcv2aaDSK69evY3BwEA0NDbBYLLOq0STvtHw+H+x2O+x2u9DMpVKpoNVq5zyvZypqtVqoZXDOEQqFhNVE1Wo1KisrYbFYhKY1+V0d5xyTk5MYGhrC8PAwGGMoLS2dMehV/Pznku1fI948tnPnTtx3330A4tdjPtkfCt1jjz2G3/zmN7hw4QJ+CeDbomPGzk4onU5ERb+/RqOB3W6fcj7RUheLxeB2uzEyMoLR0VFEo1Go1eoZb8IYY5K/AyAeoAYHB3Hjxg2YzWbYbLai/ixSgFkElEolLBYLQqGQkJZGr9ejpqZGqHIrFAqhBpLsL0k2eblcLkSjUeHLXafTSVZ8zLVkrSg5jDYSiWB0dBSDg4PC8WStJlnOSCSCUCgElUoFs9mcUbOCemgIpa++Ktn3fcSb6/7qr/5KeH2lUlnU6WFmUlFRgb/4i7/A3r170R2N4gyAzYljLBqF+fXX4XjwQclzSkpKcPnyZTQ1NWWtljxX4v//SCQiNM0mH/koXywWg8fjwdjYGIaHhxEOh4XchfNp4lIqlTCbzQDiy0ucOnUKFRUVaGhoKMochRRgFpFk3jQg3mdy7do14ViyzVe8rVQqoVarYTAYCmq2dvIPNYlzLqwwmgySOp1u1kGg4sgRMNE8ojOId3T/2Ze+hJUrVwKINw1WVFQsqnZwOaPRiDVr1uDRRx/FP//zP+OXeC/AAPFmMnmA0Wq1cDqduHHjRt6bD6PRKCYnJzExMSE01yY/z+J+veS2Wq2G0WgU8v3p9fp5N+kC8WZdj8cDp9OJoaEhhEIh4WYkF1/+yf6ZZI7C2tpaNDQ0FFXfIAWYRUocbIodY2zevwvz+2F+9lnJvv8F4JZbbsFnP/tZYV84HEZFRcW83qvQ6XQ6qNVqPPbYYzh27Bh+eeEC/kp03PjGG2B+P7ismdVsNuPatWuoqKjI+Qg7zjlcLheGhoYwPj4u1Cz1ej3MZvO0fRPJLBsul0syMVmv1wuJZZPXQKPRCE1UyZuXWCyGcDgsjIr0+/0YHx+H2+0GAGFUZD5quclmcM45RkdHMTY2hrVr16Kqqqoo+mcowJAlIfzTn0InWmveDuBFiwU/+8Y3Uu5sF9vwZDnGGCoqKjA2NoYDBw7gjx95BH0+H1YmjqtCIYR+/Wuod++WPE+hUECn0+Hy5cvYvn17Tmp5sVgMTqcTvb29mJycFGojs3mvZFOZOH9fslltYmIiZUQjgJTakHhfsgm3tLR0wb7UGWMwm80Ih8M4f/48RkZGsGbNmrw2Zc8FS5cVeLHZsGED//nPf15QzUAkf0aGh7Hiox/FRtHa8wcBmH74Q9x2223CvlAoBM45bpGtW78YjY+P49y5c7BYLHjppZeg278f/110vM1oROWvfpW2g9lut2Pt2rVYvnx5yrG54pxjYmICPT098Pl80Ol0iyZNTy54PB6Ew2HYbDYsW7YsZ99tjLFOznnTzGemt3gbmglBfG7MTz73OUlwiQIIPf64JLgA8f6XuS5OV2zEfQYf+tCHEJatfHmnx4MvPf542mSXpaWl6O7uztqyym63G6dPn8bZs2fBOYfVaqXgMgOj0Qiz2Yze3t6CToZLAYYsWsPDw3j88cfxx7J1TU4uX46PilLTJy324cliyUStycETd//N32BSNFy2AkDVlSvYu3dvypLhSqUSGo0Gp0+fnlfKIr/fjwsXLqCzsxOBQABWq5WWpZiF5OhRADh9+jTOnz9fcHnjKMCQRenixYv43Oc+h7K+PvyR7Jj1a19LaUuPRqNQKBRFORR0rioqKoRVKxUaDYL3Stft+ziAS5cu4U/+5E8kIxKB+ORLhUKBzs5OjIyMzOp9/X4/Ll++jOPHj2NiYgJWq7Xg+xIKmU6ng9Vqhd1ux8mTJ3H+/Hl4PJ55v26i+2RenU4UYMii097eji984QuYGBvDIUg/5L61axHYuTPlOT6fD1VVVUuqn85qtUpWTJ1slq48/onEv/39/Xj00Ufx1ltvSY4nU5ycP38evb29My4l4fP5cPnyZZw4cQIjIyPCiK5iGA1V6JLZMCwWixBozp49i4mJCaGWmqlAIID+/n6cOHECWq3WPJ9y0SgysmgEg0F897vfxbOJ4chPAJB31w//6Z8Cab7QotEoqqqqcl/IApKsrSVHSk3u2oWYTgdFolZTD+BOAL8D4HK58OSTT+K//bf/hieffFKYzKhWq2GxWHD9+nWMjY3BYrHAbDbDYDBArVbD6/VK0g3NZmIsmb1koOGcw+12Y2Iinsa1tLQUVVVVKCkpESajqlQqxGIxYeJ1IBDAxMQE7Ha7MDWAMTav/ygKMGRROHPmDL7+9a/jypUrAIBqAN+UneNsbsbkBz+Y8txk81hyBvVSodFoUFJSgnA4DI1GA67Xw/3BD8IiWivnScQDTNI///M/4+TJk/jrv/5rrFmzBkB8+LLVakU4HMbY2BiGhoYkw35VKhWNCsuzZPYLIH4DEQwGcfXqVWFbfm7yJkOj0cBisYAxNuuaTzoUYEhRc7vd+Kd/+if84he/kDTRfAeARXRe1GDA4Je/nPY1lmLzWFJlZSWuX78uTGQdb2mRBJiHGMNyAP2iL6UzZ87gkUcewec//3l88YtfFAKHPK8WKQzJzBcLMYCC6qmkKAWDQfzrv/4rHnzwQfz85z+XBJd7AHxGdv7wk08iPMUQ5KXYPJZUWloquaP1NjUhYLMJ20rO8fxHP4rKykrJ8yKRCH784x/jwQcfRGtra1budsniQwGGFBWPx4N//dd/xcc+9jF85zvfgcvlkhw3A/iZLIWHf/16jD/ySNrXW6rNY0nifhgAAGMY/9SnJOdsPnYMR/7t33DnnXemPH98fBzf+MY38NBDD+HIkSNZmxtDFgcKMKQoXL16Fd/5znfw4Q9/GN/5zncwPDyccs6mmhpcWbkSy0RzAThj6P/qV4EpMuwu5eYxAEKnezAYFPY5PvpRREXDhtXj41h16hS+973v4dvf/nbaXG03btzA3//93+P+++/HD37wA/T19eWl/KSwUR8MmbtwGPpLl6Dr7YWmvx+a/n5ob9yA0uMBZwxQKsEVCnCNBsEVKxBctQrBhgYEEv9ihi/1sbExvPrqq3jhhRdw7ty5Kc8rKSnBUw8/jK+9/jpKEp38SRO7d8O3efMUz1zazWNJFRUV6O3tFdroY0YjHB/9KCqOHHnvnCNH4PrQh9Dc3Ixbb70VP/3pT/Fv//ZvwjyaJKfTiZ/85Cf4yU9+gu3bt+PBBx/EXXfdlfX1hIpONAqVywWl3Q6VwwGoVAjV1SFcWQks4hF1lIuMZC4Wg/7cORg7OmDs6EDJqVNQihJIzkbUaISnqQmeW2/F5C23IGizIcY5uru78Yc//AG/+93vcObMmWlfQ6vVYvfu3fjSQw+hcd8+6Lu7Jce9W7ei5//+X8SmmMQXjUbh9Xpx2223LenPhtvtxqlTpyRZDLRXr2KDLNnlpdZWBNauFbZHR0dx6NAhPP/888LKjekoFAps27YNd955J26//XasWrVqcc994Rza7u73/k7eeQeq8XGwNN+1MbUa4dpaBOvr4brjDriamyWLvS2kcDiM22+/vcfv96+e62tQgCHTYqEQjCdOoPS112D+3e+gToyrz7YxrRa/5RzPhUJoBzBdAhKr1YqHH34Yj3zsY7C9/TaqfvxjaAcGJOd4duxA7//6X4hNk1J9cnISlZWVWL9+fXZ+iSIVjUbx1ltvpWQtXv3FL8LY2Slsj7e0YOArX0l5/ujoKH7xi1/gyJEjGc0gr6iowI4dO9DU1ITt27ejoaGh+P82w2GYTpyA5eWXYfrDH6CeY24wrlLBfdttcN5/P1x33QW+gKlzKMBkqKACDOdQDw6i5OxZqMbGoHI6oXQ6oXI6AcYQNZniD7MZEas13qTU0JDXuxqFxwPzm2/C/NprML/+OpR5zm8UBnACQFficQpAH4D3b9+Oj9xxBz6wdSsq33wT5W1t8esmM3nrrej9x39MWc9Ezul0YsuWLdR8A+DChQtwOBySNU5KX34Zq/btE7ajej0uvPQSolMMiPB6vXj55Zfxwgsv4NSpUxm/t06nw/r167Fp0yZs2LABa9asQX19feGn7YlEYOzshOWll1D66qtpP4vzEa6sxPDevbB//ONT9iHmEgWYDC10gFGNjsL8+uswdnaipKsLmjQd1DMJW60I2mzwb9gA36ZN8G/ciGB9/Yz9GBnhHLrubpR0dMTLefw4FNM0eUjKVV4O35Yt8C9fjgmLBf1aLfojEYyPjWFkcBAjQ0PwDgygdnISGwFsANCIeDLFXHB/4AO49p3vgCeWX54KNY9JTUxM4OzZs9Jkn+EwNj3wANSiZKFT1WLkrl+/jhdffBGvvfaasIz3bFVWVqK+vh6rVq2Cra4O24JBrIzFUBUKwTI5Ce3oKBCLCTdlMZMJEasVgVWrEFizBuHa2rRZG+YlFkPJ6dOw/Pa3KG1vh1qWCHQ6kcRNY9RqBQuFoBkYgEo2CjKdQH09hv/7f4fr7ruz//tMY0kGGMaYBcAeAD0AbADaOedd0z1nQQJMLAbTsWMob2uD+Q9/ABPlfMqWqF6PwNq1CKxejcCaNQisWYNQXR0iFRWITXH3zsJhaAYGoL1+Hdrr12F4912UdHZmXKUPaDQ4W1eHUxYL3tJq0eXzYXhkBOPj4zPmohLKAGAL4vNV7gFwB4D5rg3IFQrYP/EJDOzfD57B6pdutxvLly/P+/K/hSocDuPYsWMpq0VW/fjHqP3f/1ty7tX/9//g3b4949ceGBjA73//e7z++us4ffp0xkOZrQA+AuBjAD4MYLb1mbBOB299Pfzr1iG8eTMCGzcisHbtrJud1ENDMB0/DuPbb8N44kRGQSVqNMK7fXu8n7GpCYF168DTTEJVTE5C298P0+uvw/rii9DJkoqKebdsQf/XvoZAIoNCri3VAHMUwF7OeY9ou4Vz7pzqOfkMMAq/H+XPPovy1taUfoF8Cmm18JSUIKJQQBGNQhGJQBmNwuj3QznL//NhAM8D+CWAVwGEsljOyspKbN2wAZ+sqsKdPh9WXbgw7R+ZXMRkgv0Tn8D4ww8jvGxZRs/hnMPpdOLWW2+l9CUi7777Lnw+n+SasGAQ61taoBUNOw7YbLj8i19kFMjlwuGwkKK/o6MD58+fT1nLpAnAMwD+CNkf5hoBMKBSYVCnw6jBgDGzGWGdDgqNBkq1Gkq1GmXhMKq9XlS63ahwOlGaWCp5JiGTCeO3347xe+6Bp6kJKp0OKpUq8+8dzqG/dAnWF15A+X/8BxSioeNJMZUKo489htEvfjFtwMqmJRdgErWXTs75atG+QwCOcs7bpnqe0Wjk2xN3XMnfNxaLgXOe0XYm56g4xyedTvx/djuqZqitBAB0aTS4qFRiHMA4gNFYDLFYDObEo5Rz1APYBGAdgHx39V0B8BziQeU4gMzqJlNTqVRYuXIlVq1ahfXr12Pjxo3YuHFjygxxAFAPD0N//jz0Fy9Cf+kS9BcvQunxIKbXC4+I1QrX3XfD8eCDU44Sm4rH44HVasWmTZvm+VstLiMjI7h48WLKmjglJ09izeOPS/YNP/EERp54Yt7vyTnHyMgILpw/j+irr+KDb76JnQW6eFY6LsT/Rp4FcBTxACbHGBMCjVKpBGMMCoUCCoUCjLG0+5Zxjj9zu/EprxfpwtMlrRZ/s3w5zpeUgDGW8hC/91z3c85x8uTJJRVgmgEc4JzvEO07AMDCOd87zfNy+ku2APgGgLXTnHMWwC8QTxx4ErOrBSgANADYCmAH4n0YOwCkfjXPnRvA6wBeA/AigAtzeA2r1YqamhpUV1ejpqYGdXV1WLVqFVatWoW6ujohA+9Cczgc2L59O0pLSxe6KAUlGAzi7bffTrv2/PK//VuUP/ecsB1Tq3H52WcRFKWVmSvDO++g7nvfQ8np09OeN67R4LhWi+5QCFeDQfQDCAIoRTzvnBXASgA3A7gJ0lx02TQJ4L8QDyovJcqQKxsAfAvxZkK5KIBvA/jrHJZBp9MtqQCzG/HmsXtF+/YB2Mk5b5Gduwfxvhog/n2cdRsA/BDAXVMcDwA4AuAQgLemOGc+liH+x5R8bARQC6AGwHSNFwMALicelwC8gfhoLXm9y2AwoKSkBFarVXhYLBbJv1arFdXV1aiuroZ2ho71QhAMBsEYQ1NT0+KeizFHXV1dCIfDKYkRlS4X1n/iE5L+B8/27ej+8Y/nPNBEMzCA2u9/X5JcUy5gs8F1991w3Xkn/Js2CZMS/X4/RkZGMDo6CofDAYfDAbvdLvzssNuhHR9HvcuFdT4fbg6H0Yh4p+1shQEcA9CeeJxE+ppKLj0E4P8g/rctdwHAFxBvaci2pRhgnpHVYNIGGNnzsvpL6gF8BcCXkf6L3A/g+wD+AUDmY0xSJavUyYe4mi3eVigU0Gq10Gg00Gq10Go0KFcqUc05dGo1mFYLhU4HptUiZjKBGY3QaDQwGAwwGo1CIBE/kisWLjYOhwObNm1a8rP3pzI4OIgrV66kXTra8tJLqN+/X7LPffvtuP73f4+YyZTxeyjtdlT99Keo+Pd/h2KKJJmeHTsw8sUvwrNrV1ZGTkWjUfh8PvjHxoBr16C8fh3q/n7oR0aAQACxSAQ8HAaPRuFRKDBkMGBAq0WfWo0+pRLeaBSBQADhcBjhcBiRSCTjR6aDX2ZiBfA9AI+m+/0QzyD+N4h//2TLUgswzQAOyfpgZmwiW758OX/66aeFzrZkO2fyDla8nW6feLvuzBnc8tOfwiRb5x0AYgoFrt19Ny60tCBQXp7yuvLHVAFD3FZLsicSicDv92PXrl00NHkKPp8PJ0+eTBtgwDka/vRPYX7jDcnuQEMDev/xHxGqr5/2tVV2Oyp/9jOUHzkC5RQjydzvfz9GHnsMvlmMUit0sVgMkUgE0WgUsURfK+cc0WgUnHNhn/hYun3J86tPncLOH/0IJWlGs3nKynDyk59E986dQKIfRdxvPJufI5EIvvrVry6pAGMB0Ms5t4r2zdjJn41RZEqHA3Xf/jbKfv3rtMcnd+3CwP79CK5aNef3ILnlcrlQX1+P+hm+CJeyRMcuFApF2rVd1MPDWPu5z0nmxgDx0Xz9X/saJt//fsmgC+b3o+Tdd2H+3e9Q/txzwmqZcr6NGzH4538Ob5rlrEkqxeQk6r77XUm/mJh361YMfPnL8N9885zfI+L34wN33bV0AgyQdphyJ4B7cjZMmXNYXnwRy7797XiSOplwZSUGnn4arvvuy+skKDI7yaHJ73vf+xZk4aVi0tfXh2vXrk05CEI1MoKGP/9zGNIkIOWMIVhfj8C6dVCNjcFw5sy0k3ZDVVUY/tM/heMjH1nUSR9zxfjWW1jx9a9POXnbfdttsD/0ENx33JHxsGbdxYsoe+EFWH7zG5j9/iUXYCx4b6JlGYCOXE201F67hmXf+hZMb7+dcowrFBh/+GEMP/UUYoWe0oJQ3rFZmJycRGdn57QpdFgggOV/93dT1uhnEq6owOijj2Ji9+4ZU/qQ6Sk8HlQfPoyKn/98ymAetlrhePBB+LZuRXDlSgRXrIhPOI1EoB4ZgWZwEIYLF2D91a+gF2Ve0C+lPpi5mm2AUfj9qPrRj1D5L/+S9j/Mv24dbnzta/OqfpL8Sfa97Ny5syhGui20WCyGt99+G1qtdvqh5Zyj8l/+BbXf/z5Yhh3Z4cpKjH7hC5h46KEFTeS4GGmuX0fdd7+L0t//PqPzI1YrlC7XtP938w0whTExoVDEYihtb0fd974HzdBQ6mGNBiNPPIHRz30OoLXHi8bk5CTWr19PwSVDCoUCK1asQG9v7/RzhRjD2KOPwrttGyp+8Qvoz5+H7vr1lNOCK1bEU6bs3AnXPffMmCeOzE2ovh7Xvv99GI8dQ+0PfgDD+fPTnp+uyT/bKMAAAOcwvfEGav7P/4Hh4sW0p0zecgv6v/KVGUfKkMLi8/lgNptRXV290EUpKpWVleju7gbnfMbRjL6tW9G3dSsAQOH1Qnf5MnQ9PYgZDPBu345wTbrZGyRXPLt24cquXdBfvIiy556D9de/hjKDZRSSuEKByV27MPbAA8Df/d28yrK0m8hiMRjffhs1hw6h5J130j43XFmJwaefhpM68YtOLBaDy+VCU1NT4ad+L0DJPGF07Yob8/tR+tprKDl9Gtq+Pmj6+qAZGhIWQAuXlyNUW4twbS28W7bA+eEPI1JZmZVcZEuyBqMaG0PZCy+g7LnnoO3vT3sOVyox9pnPYGTv3mkXrSKFa3JyEitXrqQvyDlatmwZRkdHF7oYZJ64Xg/nAw/A+cADwj4WDEJltyNitea0L2zJBBj9xYswd3XB9PbbML399rTp85333YfhL30pvm48KUrBYBBqtRorVqxY6KIULbPZDIPBgFAoBM0cMieTwsW12vh6OTm2JAJMyZUr2PiZz8x4nuuDH8Twk08isGFDHkpFciUUCsHn82Hbtm1pJwuSzDDGsGLFCly+fJkCDJmTJRFgphuGF9No4LrnHoz/8R/Dt2VLHktFciEYDCIQCGDbtm3p052QWamoqMDVq1cRjUYpvQ6ZtSURYNLxr14N+0MPwfGRj+R1vfvFKBKJIBQKIRwOC6OOpho8klz/QqPRZP2uOBAIIBQKYevWrZSKP0vUajVqa2sxNDQEs9m80MUpSpxzhMNhSS6yWCwGlUoFlUoFtVq9KBPLAksowETMZnh37IBn5054du6MLztKo8LmLBwOw+fzgXMOjUYDi8UCs9mMkpIS6HS6lLvdSCQi1C48Ho+QVj0ZcHQ63byas3w+H8LhMLZt20ZfhFlWW1uL/ikGw5BUsVhMuNkB4jdVRqMROp0OWq0WarUaKpUKPp8PXq8XXq8XkcSEbp1OB51Ot2gS3S6JAONbtQrvtrZCSe3x85JMeR6NRqHValFfX4/y8nKUJFbVm45arU5ZnjgUCgnBZmxsDB6PB4wxaDQa6HS6Ge/qOOfwer0IhUIoLS3F5s2bacRYDiTXBPL5fDDMcvXQpSIajcLv9yMSiUChUKCsrAxlZWUwmUzQ6/UzNi+GQiE4nU4MDw/DbreDMYaSkpKi70NcEgEmptVSIr15CAaD8Pv9UCgUqK2tRXV1NYxG47zvsjQajfCHaLPZEAgE4HK5MD4+DofDIayjkVzaIJlGXLxUdXV1NZYtWwaTybRo7voKUUNDA7q6ujIK/PmSbHISLzec7/f3+/0Ih8NQKpWoqqpCVVUVzGbzrPurNBqN8PxgMIiJiQlcv34dXq8XRqOxYFaDna3iLDXJuWg0Cq/Xi2g0CqPRiPXr16O8vDxnd1SMMej1euj1etTU1CAWiwlNaj6fDx6PBwqFAiqVChqNBiqVCmazOaVWRHLDbDZj5cqV6O/vX5D+rVAoBH9iDZlk/17ysxCNRoU+DrHkkgMajSZrAxSSee2i0SgUCsW8gspUtFot6urqUF1djaGhIfT29oJzDqPRWHQDLSjAEEE0sWpfKBSCSqXCsmXLUFVVlVETWLYpFAoh4EyX1Zfkz4oVKzAyMoJgMJiXvG7J4eZAfPnuhoYGlJaWQqPRQK1Wp3zZxmIxRKNR4cbE6/XC7XbD7XYLfRyMMaEPRKVSTVvrSS4UllzFEog39VZXV6OioiKrQSUdpVKJ5cuXo6qqCgMDA7h+/Tq0Wm1RNVNSgFnCkn88oVAInHMolUqUl5ejuroapaWlRXe3RHJLrVZj3bp1ePfdd6HRaHJ20xEIBOD3+6HX67Fu3TpYLJaMaqrJZjK1Wg2j0YiKigoA8RpPsgbk9XoxOTkpdLBHo1HJ7yEeBalQKGAwGFBWVgar1Qqz2bwgHfAajQYNDQ2orKzExYsX4XQ6YTKZiuLvkwLMIpRcXjW5TGuyrRqAZAixRqOB0WjEihUrUFpaCoPBUDDt66QwlZeXo6amBhMTEzCZTFl9bb/fD7/fD5PJhJtvvhllZWVZ+TwyxqDVaqHVaiVzo5LLAkciEcmSwQCEZthC6tczGo3Yvn07+vv70dvbC51OV/BNxBRgihznHMFgEMFgUPgDSf5B6fV6YWikuFkh+cdWDHdApPDYbDZMTEwgHA5npU8uHA7D4/HAaDQKE2Tz8cWebC4rppFaSqUS9fX1KCsrw4ULF+B0OlFaWlpQgVCMAkwR4pwL8z4YYzCbzairqxM6vdVqdcF+4Ejx02q1WLt2Lc6fPw+j0TjnCbPRaBSTk5PQaDTYuHEjKisrqQadIZPJhMbGRvT29qK/vx8mk6kgAyUFmCKSHC4MAFVVVaipqcl5RyMh6VRXV0OtVuPcuXOIRCKz6niORqPwJNYnsdlsqK2tLdphuAtJpVJh7dq1sFqtuHjxIgKBQNabLeeL/lcLXLK2EgqFhOHCZWVllHyQLLiysjI0Njbi3LlzcLvdM2ZQSAYWxhjq6+tRW1tLn+MsqKioQFNTEy5fvoyJiQmYzeaCCdiFUQqSIhaLCSkkysvLsXLlSpjNZmr6IgWlpKQE27dvx6VLlzA+Pi5Mik328QWDQWGUokKhQENDA2pqagqyOaeY6XQ6bN68GSMjI7hy5YqQnmahvy8owBSYcDgMr9cLxhjq6upQW1uLElrwjBQwtVqNTZs2wePxwOfzweVywe12w+PxwGKxCDdHNEoxtxhjqKmpgcViwdWrVzE2NoaSkpK8zFmaCgWYAsA5h9/vFyawrV69GlVVVdR8QIqGQqGA2WyG2WxGTU0NgPfmlJD80ul0uOmmmzA+Po7e3l7Y7XYYDAboZrFyZSwWE5LZzgcFmAWUrK0AgNVqxbp162C1WukujywKFFwWDmMMlZWVKC8vh9PpRG9vLxwOh7BUhlarTfn/SaZnCgaDUCgUqKmpQSgUcs+nHBRg8kyc5l6n02H16tWoqKiY1d0FIYRkIpnZ2Wq1wuVywel0wuFwwO12p9ROlEolzGYzVq9eDavVmkwwO/Xa8hmgAJMHycSRsVhs1mnuCSFkvhhjsFgssFgsWLVqFWKxGPx+P2KxmDDZNBfTHYoqwDDG9gEoB/AsgDIALZzzvQtbqqklcyotdOJIQggRUygUeRk8VFQBJmFP4tEO4PEFLkta4XAYbrcbpaWl2LRpE8rLy2kyJCFkySm2AOPknBds7nbOuTBDefPmzaioqKDaCiFkySq2AAMAYIw1Ih5seha6LEmRSARutxsVFRVYt27dgo49J4SQQlB042EZY7sB9ABoZIwdWOjyAPHgMjk5iQ0bNuDmm2+m4EIIIQDYfCfSLCTGWDeAvZzz9jTHkn01ALBVq9VeB5CLX5YpFAp1KBRyR6PRYA5evxBVABhf6EIsEnQts4uuZ3at55zPOYPmggaYRBDYMcNpB5JNYYyxRs55l+j5rQB6OOf7Z3ifDs5507wLTADQ9cwmupbZRdczu+Z7PRe0D4ZzfjjTcxP9Lq8AEHfyWwB0Z7lYhBBCsqBo+mASNRd5TcUG4MgCFIcQQsgMim0UWUdisqUTwGrEJ1o6M3hexjUlkhG6ntlD1zK76Hpm17yuZ1F38mcbY+xQIWcGKAaMMQuAJsSbL3cCOFRIw8mLgWikZNNsmpGJFH0WcyfT78qiaSLLNcZYM+IfRjI/nwLQyDlvQ7x/bNoBGEQq8TksSzQJJ2vsZG7os5gDs/muLLoAwxizMcZaE7+keL+FMbaPMbY78W/jLF7Tgvgdoz3LxS142b6enPPDnPODic3VWOKDMOZwfe9F/LMIxJuC781jcQvabK8lfRanN5e//dl+VxZVH4zoQtjSHG5FfE5MckjzUcZYpn00TZzz9qWW1iWH1zOpkXO+ZL8g53J9EW/OSbIjntR1ycvCZ3VJfxbl5nE9Z/VdWVQBJjmhkjEmiZ6JqGqTta/2AGgG0JaYb5Pu9Q4zxprTTdRcCnJxPUWvsQ9AS7bLXEzmeH2deC/IlGEJ1qrTmetnNXHOkv8sys3lejLGnLP9riyqADONJsT/MMWciDcvtM3QUWpPdKoCgG0pBxyR+VzPZCf1Yc65k65nWtNd31a8d1dpA3A0b6UqTtN+VumzOGvTXc9Ds/2uLLo+mClYkHqnN4EMmhc4512JTkBkcv4SYcEcr2eivfYAgFcYY51IXwVf6iyY4vom/mAtiSaMRlEfAknPgimuJX0W58SCqT+bs/6uXCw1GGCewSFx4dpmPHHpmNP1TIx+Wp3lsixGU15fUVChu+3MpL2W9Fmcs2n/9mfzXblYajBOSDtHgfjKl9R+PTdO0PXMJSfo+maLE3Qts8mJLF7PxRJgOpAadS2g9uu5ouuZW3R9s4euZXZl9XouigCTGD7XwRgTt7E2gZoY5oSuZ27R9c0eupbZle3rWVSpYhKdds0AnkE80rYmRzQlhtftQXxIXRmADnFqf5KKrmdu0fXNHrqW2ZWv61lUAYYQQkjxWBRNZIQQQgoPBRhCCCE5QQGGEEJITlCAIYQQkhMUYAghhOQEBRhCCCE5QQGGkDxLLPR0YKHLQUiuUYAhZJ6SAYMxtkeUznw6eyFKvZF4bidjjDPGDslWENyTWPCJJ1YfzOT1CSkINNGSkHlKpIJvQTxwNHPOd8x0vvycxCJuBzjn1jTnNwLoBGCd5YqihCyoxZSun5C8S6zbYuOc9zDGujFDUsBEsOjIS+EIWWAUYAiZnxYkEgHOtNJnwl4Ah3JaIkIKBPXBEDI/zZhdKvMmSsRIlgqqwRAyB4yxfYivlmgDcC9jbAeAQ9MFj0RzWlbSyCea2l4B8E3Es94iUZYDoL4aUiAowBAyB5zzg4kv+T2c85YMn7YXwP5pjlsSgUsu3bK/ZQAeF62RDsbYUQD7KbiQQkEBhpC5a8J7tYdMWDjn053v5JwflO9MBjL5a0FUG0qMQitL93xCFgoFGELmbgeAjPpTEvNXWrP43u3Jmkpi9cEDifIQUjCok5+QuWsCcDLDc/cCOJKtN5Y1g7Ui3jQ2m9oUITlHAYaQuWtEBjWYxBK08qCQFck+G/EQaXEmAEIWEjWRETIHiWYpILNJk59CDua+JMrwDERNY4l9Zdl+L0LmgmowhMxNI+Kd8s4Mzm0Rj/bKonRNY7sB2HPwXoTMGtVgCJmbe5HBnJZEjcI5wzn7ADyM+DDlAwCeTc6nSYwOSw6D/hFj7FnOeVtivw2APTGAoAzxmswepB/WTEjeUbJLQuYgkeDy0EzpYRLBo4tznpUJloQUEwowhGQoUVNwcs7bGWMcGcyYT5c5mZClgvpgCMncjwA0JlK+HMwguFDmZLKkUR8MIZlLpnm5l3M+XcqXpIdBmZPJEkZNZITkCGOsdRZ5yghZdCjAEEIIyQnqgyGEEJITFGAIIYTkBAUYQgghOUEBhhBCSE5QgCGEEJITFGAIIYTkxP8PZn5GRJY7fsoAAAAASUVORK5CYII=\n", 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\n", 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" ] @@ -332,7 +338,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 16, "metadata": {}, "outputs": [], "source": [ @@ -373,12 +379,12 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 17, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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FtWvXmo6jqdSon8YLGGDIc6LRKL7+9QxEAgCcz/gSAb78ZeDVV4HVVSPgtJm4RC4yNTWFeDyOmZmZQ881upnXNql1I5fLVQ2QbHaeSCSCmzdvAkDdVSrtLJcT2AdDnnT//dNQ3QTwLIAXAdzGiRNB/PqvN+7A71Q+n8df/qUxY8Dt27cRCAQOJQ489dRTuHjxItOYPSKZTCKbzWJ2drZqJH86nS7fyAuFQjmTq1Tjsdp0VhqdX3ptLBarGslfWdMp7RuPx8uj8EvnSafTWFhYQCaTKfcflfqL0uk0isUiFhcXEYlEyiP+3cR1U8WISARAEkBKVbMVj18C8ACAawDGAMyoav1k9hqcKmYw5fPAn/wJ8MILwNmzwJ/+qf3nqLcEQD1+vx9+vx+ZTAbT09P2F4SoD7qdKsZVAUZESl8PkgAW6gSYUp0yC+CcqhatHJcBZrAVi8B77wE/+ZP2Hjefz2N8fBx7e3uWXxMIBLhmDA2MbgOMq/pgVDVrBpV6DYtFVT1pbjNWgwsNvnDY/uACdDZjANeMIbrHVQHGChGZMJvRiBzVyYwBXDOG6B5PBRgRiQMoAJgQkc6H0RJZ0OnaL1wzhsjgmQCjqsuqmlHVoqpmAMQr+mwOEZGEiKyLyPqbb77Zw5KSU957z9h6JRgM9vR1RIPGMwFGRGqHvOYAnG60vxmQJlV18sEHH3S2cNQTX/868P73AwsLwL//u/PnszJjQC27ZhAgGgSeCDBmcLlR83AYQL73paF+ee65PN58cw6LiyE88ogPx46FMDc3h3zembeBlRkDanHNGKJ7PBFgVDUHoHbxhAiAl/pQHOqDr351FbncOIAVALsAFD/60S5WVlYwPj6O1dVV28/ZbI2YWlwzhuiwtgOMiHxURD7a4LnHGz1n8dgT5niXSQALIlK54MK6iFwy+1aSMAZaFjs9F3lHPp/H5z4XB7AHoDqra39/H3t7e4jH447UZOqtERMMBvHoo48iGAxWrRmzubnJQZZEFSwPtBSR34UxALJSCsaAyN2K/R6DsY7ziG2l7BIHWnrb3NwcVlZWWo6kTyQSVeu4EFF3ejKSX0S+CmAKRkApzR0dMx/7OIBFVb1csf9dVXVN8xsDjLeFQqGerf9CRPd0G2BaTnZp1kigqh+seeoGgEURuR/AEyLy9zD6RNKdFoaoHqvjStww/uTdd4EjRwCfa75eEfWPlY/Bx1X16UZPquotVX1eVf8XjOAyicMd8kQdszqupJ/jT/75n4HPfQ543/sAc0JcoqFnJcBYXrvPDDY3VPWLXZSJqEovV7DsxB/+IfDhDwPPPQfs7ABXruQxNzdXTgoIhZxNpyZyq5Z9MCLya6rq6RXI2QfjTT/+MfBf/wW8917rWY37OYvxP/4j8HM/V/ppFUAco6P7uHPnXlICp/MnLxqo2ZSJKv3N3wA//dPAZz8bxe/8Tv3xKG4Yf/KzPwt86EOAMe7XSKeuDC6A8+nURG5kJcB8TERCVg4mIr9gjoW51mW5iPDCC4Aq8J3vAM88M41Pfap6PIpbxp+IAJ/5DPD+91/ByEjz2Zc5nT8NEytNZB8A8FUA8crxLhXP/wKAJwB8AMaYmFdE5IDjYKgbb7wBPPywEWBKXnkF+MhH+lWi5lSB++9nOjUNFsfTlFX1NRH5BoDXRSQL4CaMpYsjMMbBbAOYVdWXOy0EUa3//E/gox8Fvv994+dYzL3BBTBqMV5KpybqhZYBBjBmJhaRAoAvAJgxH84B+LyqPl/aT0QehjHDseXMM6J6Tp0CcjkjwLzwgvGzW+XzeVy5cgVWZ8XgdP40LCwFGMBYzhjGGJdmTpoB5/kW+xFZ8thjwJe+1O9SNLa6uop4PG555UtO50/DxHKAsUJVv2/n8YjcLJ/PIx6PN02frsXp/GmYNM0iE5EvmJ34RI7L5701QPHKlStt1Vz6nU5N1GtNs8jMDLJZGJ35NwGkVPWV3hTNPswic7/KpqbKm7abByhanYQTAObn53HhwgUGF/KUnsymbJ7oMRjBJgYgCyPYvN7piXuJAcbd8nl3j9RvxOfzWezY9+G99w7Q5uKYRH3Xs5H8qvp9VX1aVU/BCDCLIvJ3IvIZqwMxieqx0tTkxgGKVrPBfL4APv1p7zT9EdnFcg2m4QFEHodRs1EYtRrXzVvGGow7ldJ7v/KVr1ja320DFK0shObzjcDnE4iIZ5r+iEr6PheZqn7DnKr/CQAPiMjfi8g1JgdQM6urqxgfH8fKyorl17z99tuu+uZ/8eLFlrM83717gDt37hwKQpybjIaBbZNd1qwL83kAMRFZF5GviMhH7ToPeV9leq/VLKySlZUVjI+PY3V11aHSWReNRpHJNJ6Ec2RkBCMjzWdMcmPTH5FdHJlNWVVfU9UvmlWrZQCf5ASYVNJOem8tt33zn56exuZm/Uk4jx49ioODg6av39/fx4svvtij0hL1Vtd9MF7APhh3aSe9txG/349EIoGlpSWbSmU/q1lmPp+vZSAi6oe+98EQtcuOyR698M3fC0s9EznJ8QAjIr/r9DnIW+y6obp9VmK3L/VM5DRbA4yInBORbRF5y9y2ASTtPAd5n5UbrxVu/+ZvJcuMc5PRILO7BhNW1TFVfcDcxgA8bfM5yOOs3Hhb8cI3/1KWmd8fAOC+pZ6JnGZ3gMnWeayt7DERiYhIWkSmah4Pi8glEYmb/050VVLqm9KN99ix+jfeo0eP4siRI02P4ZVv/tPT0/judzchkgAQAuDDffeF8Nu/3f+lnomcZneA2RGRXxORj5Y2tNFEZgaViLnVSgPIqGpGVRcBJEUkbEehqfemp6dx5swmgHs33pERI7331VdfxTe/+c2G40u89s3/Yx+L4vLlJTz//C3cvn2AH//4Fr761SXPlJ+oU7amKYvIF3BvGeWSmKo+0OZx1gAkzUXOYAaSDVWNVuyTArCmqplWx2Oasvu8+y7w/vcD2xXvlBdeAH7rt+79nM/n8eyzz+LFF1/E7du3EQwGcfbsWc5KTNQj3aYp27rgGIC8qn6+8gFzrrJuTQIo1jxWhLE8c8sAQ+4jAvzRHwFf/jLw6qvAyZPAJz9ZvU80GsXS0pKrx7oQUWN2B5hCncfsGG4dRnWtCADeQv2mNPKAo0eBp58GZmeB734XeOMN4NixfpeKiOxkd4D5gIh8BcCG+bMAiAP43zYce6ydncXoVU0AwEMPPWTD6ckJIsDP/3y/S0FETrC7k/9pALcAnDS3MIC2+l8aKJrHqvQADtdqylR1WVUnVXXywQcftKEI1C2vLYnstEIBsLhSAZEn2R1gzqnq582JLr+oql8EcM6G467jcA0mDGDNhmNTD1ROz7+7uwtVxe7urqtmR+4FVWBlJY+HHppDNBrC3JwPweBwB1oaXLYGGFX9fp2Hd2w4bhHAuohU9rlMov64G3KZZtPzu212ZKd95zurmJ0dx3/8xwqAXQCKd94ZvkBLw6GrAFO7qJi5fHLldg5Aqo3jTYjIJRjBY8HsRymZARA3B1omYNSWit2Un3rDq0si260UaO/e3QMw3IGWhkNX42BEZB3AZ1T1lYqfa0fuP9lNHrUdOA6mv6xOz++2JZHtZmWJZS8sQ0DDo9txMC0DjIi8BeAXVPWfLBTmsdpmsnqP9RoDTH9xXRQDAy15TS/WgzkJICci/7fVjvUCSb+DC/Uf10UxWF1ewO3LEBBZZSXALAO4DOAbInKx9kkRuV9Efk9EnjHnIQvZXkryNK6LYmCgpWFjJcCoObnkEwC+KCJ/WvPkLTMl+TKAKIwJL7/jQFnJo7guioGBloaN5Swyc1LJSQCfFJHv1KupmONezsOYI4wIwL3p+QdlduROMdDSsLESYMoDHFU1ByPI/A8Y41J+unZnVV2GMZqfhkirUfrT09PY3NxEIpGo2ieRGJ51UVoF2iNHAnjooQwqJg0n8jZVbboBuFnnsfthjKJ/C8BH6jz/962O28stFospOef69esaCATU7/crgPLm9/s1EAjo9evX+11EV9na2tL5+XkNhULq8/n02LGQnjgxr8CWAqpzc/0uIZEBwLp2ce+1kqZ8ACCiqv+vznMpAJ8BEFfVb1Y8/pKqPmFD/LMF05Sdk8/nMT4+jr29vYb7BAIBbG5uDnwTWKeuXgUqu12OHTNml/6Jn+hfmYiA3qQpC4BMgz6XWRgZZpmaDLOGk1DSYLEySn9vbw8f+tCHON9WA08+Cbzvffd+fu89YwkDIq+zEmCiAF4CsCIiv1sbaNTIMHsSdTLMaPBdvXq1ZYABjKlQlpc531Y9fj/wuc8BPh/wG78B/Ou/Ap/4RL9LRdS9tqaKEZH7AZxU1dfrPDcBY/LJmwCKqvqkXYXsFpvInGN1lH4lNpkd9vbbwA9/CDzySL9LQnRPL5rIytQY8/J6g+dKGWYfhLHIGA2BTgYFDsPElu0KhaqDC9fOoUFg93T9BQAxAN+w87jkXlYGD9ba39/Hiy++6FCJvI9r59CgsHvBMahq0U0ZZOQsK4MH6+F8W9VKNZZgMIhf/MVf5No5NBBsDzA0XJoNHmyG823dU1ljeeedd1ruzyZG8gpbAoyIPGPHccibKkfpWwkynG/rnmarfTbCJkbyCrtqMFM2HYc8KhqNYmlpCf/yL/+CQCDQdF/Ot3WPlXFE9bCJkbzArgAjNh2HPKJellMkMocf/ACc2LINVscR1WITI3mBXQGm83WXyXMaZTm99toKfvVXx/Hcc8A//MNwT2xpVSc1ETYxkle0NdCy4UFEbqrqKRvK4wgOtLSPlbnHgAAuXNjEH/8xaymtWF1GuRIHqlKv9HSgJZG1PoN9vPMOs5ysaGcckYjREv3uu+/iscce48BLcj3WYKgtVr9xh0Ih3LrFZYFasVYjNIhI1bQ8fr8ffr8fmUyGzY7kCNZgqKes9hkwy8maVouQHT16FEeOHAGAQ3O+ceAluR0DDLXFavYSs5ysa7ba5+OPP467d+82fT0HXpJbMcBQW6z0GTDLqX2lcUS3bt3CwcEBbt26haWlJXz7299u2efFgZfkVgww1BYrc49xIKV92CRJXua5gZYicklEkiIyISJT5rLN1CPRaBSf/WwGfj8HUvYCmyTJy+wKMDM2HceqBIAbAGYBLPT43EPthz8Enn9+Gvv7mwiFEjh+nAMpncQmSfIyW9KUe0lEEqq63M5rmKZsD1Xg8ceBb37z3mPBIPDGG8DJk/0r1yCzksbMgZfklKFNUzabyCL9LsewyOfz+M3fnMO3vhWC8bYJAZjD/HyewcVBrdKY2SRJbubJACMicQAFABMikmywT0JE1kVk/c033+xtAQdMae6xv/qrFajuwph6bhfACr70Ja6w6LRmacxskiQ381wTWS0RyQOYVdVso33YRNY5NtEQDa+hayITkYmah3IATvejLMPAytxjHOjnDv/2b8DnP2/0lRG5gacCjBlcbtQ8HAbAeTIcYmW9Eg7067+XXgJiMSCZBJ57rt+lITJ4KsCoag6H05IjAF7qQ3EG3htvcKCfFzz7LPDkk0DpT/B7vwd873v9LRMR4LEAY1o3B1smzA7+GVUt9rtQg2ZzM4/HHps7NMFiIxzo1z+/8ivA/fff+/nOHSCT6V95iEpG+12Adpm1mFy/yzHI/vZvV/GJT8Rx9661pXw50K/38vk8rly5gqtXr+L27ds4ejQI4Cn4/Rfx3HNRPP10v0tI5M0aDDkon88jHo/j7t09ANYDDOce6516S1a/++4ufL4VjIyM4+GHVyFi/C3n5uaqUpu5SBn1EgPMEKi90QSDQTz66KMIBoOHbjxXrlyBqvXAwoF+vVX6ArC3t3co+eLu3X386EfG+jAvvPDCoSC0u7uLlZUVjI9z7BL1hufHwVgxzONgVldXEY/Hsb+/3zQbrLQ6ovFt+F1Lx56fn8eFCxcYXHpobm4OKysrTf+Wo6NGy/edO3ca7sOxS2TF0I2DocMaNYW8/PLLDb/t1iqtjmg1uPh8PiwtLfEG1WNW0sbv3LnTNLgAHLtEvcEajMc1qqH4/f7ySogHBwe2nzcUCuHWrVu2H5ea8/l8ljP7WuHfkFphDWaINWuP39/fx8HBgSPBhVlj/WNnOjjHLpHTGGA8zMo0Lk5g1lj/WFkfxqq7d+92nVXGTDVqhk1kHhYKhbC7u9uz85USATKZDGfw7RMrk4+2o5u/abPmWb5PBgObyDzGzm98vWzi4PTw7tBsfZhOlJI74vF4W+/BVs2znRyTBpCqDvwWi8XUDa5fv66BQED9fr/CWFRFAajf79dAIKDXr19v63gnTpyoOo5Tm8/nc+iKUKe2trZ0fn7etr+x3+/X+fl5y+c/f/78ofdxt8d0s62tLT1//ryeOHFCRURPnDih58+f162trX4XzVEA1rWLe2/fb/692NwQYLa2tjQQCDT9QAYCgbbesFY+5KVNRDq++YRCIQevDHWjm79r7XbffSF9911r57X65WYQ3jt2fzH0km4DDJvIesTquip/8Ad/YLkJ7eLFi203k4hIeSR/aUBeM8wYczc7s8ree+9t/NRPzeHb327drDUss2yzKbBL3UQnr2xuqMG005zVzjelRt+uGm2VtSQnalXUW+3UYq1tUq7xNmsGGpYajNebArtt2gObyLwRYOxoymh0sy+1x1u50dR+GIa5+j8IrHxJGBkZ0dHR0Y7ec6X3be3NaVhuvF4OpHZ8thlgPBJg7OiQb/WB7fTDUApQoVBIfT6fhkIhnZ+fZ83FI1rdSP7sz/6sZRBq5z1o9Zhurf22c+O1+sXQbYkwdrVOMMB4JMDY1ZTR7JuSVz8M1L1WXxLabUpttVUGmXa+Ifc7G6vdG69XazB21TAZYDwSYKy8sa1sItLwA+rVDwP1hp2pzaOj/nIAqwxswWBQH330UT1+/Pih96ddzbHdBKl2b7xebQq0617AANNhgKn3Jv3Upz6lZ86ccezbVaMPWLv9M6Oj9T+gv/RLv+TJDwP1ll3jp2pvTs0CyNGjR/XIkSNNj2elyabbINXujderiTB2tWYwwHQQYNppLrC7s7vyG19lB6odH/ijR4/qsWPHPPdhoN6yq7m28uZkVw3d7/c3/FJnx82+kxuvFxNhWIPpcYAp1ViOHz/e0Rvf7huzXR/I2jf8L//yL3vuw0C9Zdd7r/LmZGe6dKP3qh3NVcOSCMM+mB5uH/zgB7vu4LS7acn+8Qv3Phhe+zBQ73Xb6V/7eXBi2qLSl7rSl8N2XtuoFuTVPpV2MYush5vP57PlDR8MBm3LgHFqHjFmiJFV3TTX1t6c7JyypvJG36hGbuW19WpBXu1TaaRZwgPHwfRos/PN3+yP1U7igBMfSIAZYtQ5KwGn0c2pVxOvtrvVCxZe6lPpNoB00ppReU4AqgwwLX7JHryRjxw5oseOHbOcOOBEGQahak/u0c7N6fz584eyG92y+f3+Q1/0jh8/rh/+8Ic1GAy6phm5NpgcO3ZMR0dHD83C0Gkt04p6QUsZYPofYNywealqT4PFStNTO1/CehV43FJjsXsgbOn3q/3C2axG1OhvqMMUYACEAVwCEDf/nbDwmr6/mYflg0LDq50mG8AdQQYwvpjduHGj6/7VTgeAOpFRWtoqm8wb/X1GR0d1ZGRER0ZG6h5DhyzArAGI1Pwcbv6azvs7nOorqf0A1v7c7A9eud133319r9oTlVhtVvvzP99Sv9+Zm2r7mzEZaL3P4bFjAZ2dva6plOrXvqb6ve/V/72vX7+ux44FGg6Cbvblz6mMUuBe0k83QUy7uF+LGjdpTxCRMIANVY1WPJYCsKaqmUavmxTR9R6Uj4hokAgAVZVOX++1BccmARRrHisCON3zkhARUVNeCzBhANs1j70FYKx2RxFJiMi6iLDyQkTUB14LMECdYFKPqi6r6qSqTjpdICIiOsxrAaYIoxZT6QEcrtVUi8UAI6PB0uYTgQCObff5/TgeCGD1+vW2ysWNWz+20IkTlt7X94dC5dfkt7ZwPBBouv/xQAD5ra2uzlO5WTmnE59bq+Xu1VZ7/7rP78foyAhGR0baPla3vBZg1nG4BhOGkUlmm2AwaMtx7rvvPjz11FM4c+YMQqEQfD4fQqEQEokENjc3MT09bct5iJx0+/bttve7cuUK9vf3m+6/v7+PZ599tqvzVIpGo8hkMggEAvD7/S2P4/f7MTIygpGREUvn3d/fx97eHuLxOF5++WXMzc0hFAphd3fX0us7MTo6ipGREQQCAYgYt/zSvyV+vx9Hjx7FkSNHAAC1iVv7+/s4ODjAwcGBY+VsqJsUtH5sOJymvIEWacrtLjhmR9ogBz3SoOhkBuJevaaeeqnSTz31lJ45c+ZQ+vSNGzfaTt8dGamf1uzEVpvi3SgN/MyZMy3L02G5D7Sb+3U3L+7HhuqBlglYGGjZboDpZlQyBz3SoOlkBuJO1l3p10zHToyit2NrZ+Jaq8E5GAxWBahG09GU7mMA/k2HKcB0snWyZLJTE8kReU0nMxB3Uhvp50zHdi4nbdfWzsS13axg2ew+Bs6mbOGXBDqe+oEBhKj9GYg7rY30e6Zju2aFPnbsmK3r7dhV7nZnW2eAsRhgevkmJRpE7Xzh6qY20s8vdnYuJ136PTo5Xrs1NaeaFxlg2ggwnf7xiKh9/a6NdMKJ5aTbOWan18ap5sVuA4zX0pRtUZseSUT2m56exubmJhKJhGfS9JulOltNa/b7/Th79qylY1amHndzbVqVOxAIIJPJIBqNNjiCQ7qJTl7ZYENbJBENj0bNdFbSmvvZ9Gf3OdBlDcZTsyl3ysywqOLz+foz8IiIPG11dRXxeBz7+/tVg0n9fj/8fj8ymYwra2edEJEN7WK6raFsIgPsG61PRMPFi01//TKUNRi/349EIoGlpaV+FYmIyPVYg+mA3+/HhQsX+l0MIqKBNtrvAvRSZRtpz7MpiIiGzNDUYNhGSkTUW0NRg4nFYlhf58KWRES9NDQ1GCIi6i0GGCIicgQDDBEROYIBhoiIHMEAQ0REjmCAISIiRzDAEBGRIxhgiIjIEQwwRETkCAYYIiJyBAMMERE5ggGGiIgcwQBDRESO8NRsyiJyCcADAK4BGAMwo6qz/S0VERHV46kAY0qYWxbAuT6XhYiIGvBagCmq6sl+F4KIiFrzZB+MiEyISKTf5SAiosY8F2BEJA6gAGBCRJL9Lg8REdUnqtrvMnRMRPIAZlU1W+e5Ul8NADwK4NVelm3A/QSA/+53IQYEr6W9eD3t9T9V9USnL+5rgDGDQKzFbklVLZj7T6hqruL1aQAFVV1ocZ51VZ3susAEgNfTTryW9uL1tFe317Ovnfyqumx1XxGZAHADQGUnfxhA3uZiERGRDTzTB2PWXGprKhEAL/WhOERE1ILX0pTXzcGWRQBRGAMtixZeZ7mmRJbwetqH19JevJ726up6erqT324ikuLMAN0RkTCASRjNl6cApEp9aGRNRabkZDvNyFSN70XnWL1XeqaJzGkiMgXjzUjdeQLAhKpmYPSPNU3AoGrm+3DMbBIu1dipM3wvOqCde6XnAoyIREQkbf6SlY+HReSSiMTNfyfaOGYYxjfGbZuL63p2X09VXVbVRfPHKIY8CaOD63saxnsRMJqCT/ewuK7W7rXke7G5Tj777d4rPdUHU3Eh6o3iT8MYE1NKaV4TEat9NJOqmhURm0rqDQ5ez5IJVR3aG2Qn1xdGc07JNoxJXYeeDe/VoX4v1urierZ1r/RUgCkNqBSRquhpRtVITftqAcAUgIw53qbe8ZZFZKreQM1h4MT1rDjGJQAzdpfZSzq8vkXcCzJjGMJadT2dvlfNfYb+vVirk+spIsV275WeCjBNTML4YFYqwmheyLToKN02O1UBIDLMAadCN9ez1Em9rKpFXs+6ml3fNO59q4wAWOtZqbyp6XuV78W2NbueqXbvlZ7rg2kgjMPf9N6CheYFVc2ZnYCwsv+QCKPD62m21yYB3BCRDdSvgg+7MBpcX/MDGzabMCYq+hCovjAaXEu+FzsSRuP3Ztv3ykGpwQBdBgfzwmVa7jg8OrqeZvZT1OayDKKG17ciqPDbtjV1ryXfix1r+tlv5145KDWYIqo7RwFj5Uu2X3emCF5PJxXB62uXIngt7VSEjddzUALMOg5H3TDYft0pXk9n8frah9fSXrZez4EIMGb63HrNImSTYBNDR3g9ncXrax9eS3vZfT09NVWM2Wk3BeAyjEibLmU0mel1CRgpdWMA1iun9qfDeD2dxetrH15Le/XqenoqwBARkXcMRBMZERG5DwMMERE5ggGGiIgcwQBDRESOYIAhIiJHMMAQEZEjGGCIesxc6CnZ73IQOY0BhqhLpYAhIomK6cybmUXF1BvmazdEREUkVbOCYMJc8EnN1QetHJ/IFTjQkqhL5lTwMzACx5SqxlrtX7uPuYhbUlVP1tl/AsAGgJNtrihK1FeDNF0/Uc+Z67ZEVLUgInm0mBTQDBbrPSkcUZ8xwBB1ZwbmRICtVvo0zQJIOVoiIpdgHwxRd6bQ3lTmk5yIkYYFazBEHRCRSzBWS4wAOC0iMQCpZsHDbE6zZRp5s6ntBoBnYMx6C7MsSbCvhlyCAYaoA6q6aN7kE6o6Y/FlswAWmjwfNgNXrXrL/o4BOFexRjpEZA3AAoMLuQUDDFHnJnGv9mBFWFWb7V9U1cXaB0uBrPZYqKgNmVloY/VeT9QvDDBEnYsBsNSfYo5fSdt47myppmKuPpg0y0PkGuzkJ+rcJICbFvedBfCSXSeuaQZLw2gaa6c2ReQ4Bhiizk3AQg3GXIK2NijYotRnU5kiXTkTAFE/sYmMqANmsxRgbdDkE3Bg7ItZhsuoaBozHxuz+1xEnWANhqgzEzA65YsW9p2pzPayUb2msTiAbQfORdQ21mCIOnMaFsa0mDWKYot9LgF4EkaachLAtdJ4GjM7rJQG/byIXFPVjPl4BMC2mUAwBqMmk0D9tGainuNkl0QdMCe4TLWaHsYMHjlVtWWAJZGXMMAQWWTWFIqqmhURhYUR8/VmTiYaFuyDIbLueQAT5pQvixaCC2dOpqHGPhgi60rTvJxW1WZTvpQ8Cc6cTEOMTWREDhGRdBvzlBENHAYYIiJyBPtgiIjIEQwwRETkCAYYIiJyBAMMERE5ggGGiIgcwQBDRESO+P8YJcIfBssclgAAAABJRU5ErkJggg==\n", 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" ] From 9784e75dde9ea822b98173345564f5a960c52ff2 Mon Sep 17 00:00:00 2001 From: LIU Date: Fri, 6 Aug 2021 10:36:31 +0800 Subject: [PATCH 3/5] fixed the error in cholesky decomposition --- tutorials/ex6_exception_handling.ipynb | 436 ------------------------- 1 file changed, 436 deletions(-) delete mode 100644 tutorials/ex6_exception_handling.ipynb diff --git a/tutorials/ex6_exception_handling.ipynb b/tutorials/ex6_exception_handling.ipynb deleted file mode 100644 index ede6fdb..0000000 --- a/tutorials/ex6_exception_handling.ipynb +++ /dev/null @@ -1,436 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Gaussian Process Distribution of Relaxation Times" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## In this tutorial, we will try to handle the exception that may be encountered while doing the Cholesky decomposition for $\\mathbf K_{\\rm im}^{\\rm full}$ https://doi.org/10.1016/j.electacta.2019.135316" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This tutorial is based on that `ex1_simple_ZARC.ipynb` and we will handle the exception during in the `np.linalg.cholesky(K_im_full)`." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from math import sin, cos, pi\n", - "import GP_DRT\n", - "from scipy.optimize import minimize\n", - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 1) Define parameters of the ZARC circuit" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# define the frequency range\n", - "N_freqs = 81\n", - "freq_vec = np.logspace(-4., 4., num=N_freqs, endpoint=True)\n", - "xi_vec = np.log(freq_vec)\n", - "tau = 1/freq_vec\n", - "\n", - "# define the frequency range used for prediction\n", - "# note: we could have used other values\n", - "freq_vec_star = np.logspace(-4., 4., num=81, endpoint=True)\n", - "xi_vec_star = np.log(freq_vec_star)\n", - "\n", - "# parameters for ZARC model, the impedance and analytical DRT are calculated as the above equations\n", - "R_inf = 10\n", - "R_ct = 50\n", - "phi = 0.8\n", - "tau_0 = 1.\n", - "\n", - "C = tau_0**phi/R_ct\n", - "Z_exact = R_inf+1./(1./R_ct+C*(1j*2.*pi*freq_vec)**phi)\n", - "gamma_fct = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau/tau_0))-cos((1.-phi)*pi))\n", - "\n", - "# we will use a finer mesh for plotting the results\n", - "freq_vec_plot = np.logspace(-4., 4., num=10*(N_freqs-1), endpoint=True)\n", - "tau_plot = 1/freq_vec_plot\n", - "# for plotting only\n", - "gamma_fct_plot = (R_ct)/(2.*pi)*sin((1.-phi)*pi)/(np.cosh(phi*np.log(tau_plot/tau_0))-cos((1.-phi)*pi))\n", - "\n", - "# we will add noise to the impedance computed analytically\n", - "rng = np.random.seed(214975)\n", - "sigma_n_exp = 1.\n", - "Z_exp = Z_exact + sigma_n_exp*(np.random.normal(0, 1, N_freqs)+1j*np.random.normal(0, 1, N_freqs))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 2) Show the synthetic impedance in the Nyquist plot" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.rc('text', usetex=True)\n", - "plt.rc('font', family='serif', size=15)\n", - "plt.rc('xtick', labelsize=15)\n", - "plt.rc('ytick', labelsize=15)\n", - "\n", - "# Nyquist plot of the impedance\n", - "plt.plot(np.real(Z_exact), -np.imag(Z_exact), linewidth=4, color=\"black\", label=\"exact\")\n", - "plt.plot(np.real(Z_exp), -np.imag(Z_exp), \"o\", markersize=10, color=\"red\", label=\"synth exp\")\n", - "plt.plot(np.real(Z_exp[20:60:10]), -np.imag(Z_exp[20:60:10]), 's', markersize=10, color=\"black\")\n", - "plt.legend(frameon=False, fontsize = 15)\n", - "plt.axis('scaled')\n", - "\n", - "plt.xticks(range(10, 70, 10))\n", - "plt.yticks(range(0, 60, 10))\n", - "plt.gca().set_aspect('equal', adjustable='box')\n", - "plt.xlabel(r'$Z_{\\rm re}/\\Omega$', fontsize = 20)\n", - "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", - "# label the frequency points\n", - "plt.annotate(r'$10^{-2}$', xy=(np.real(Z_exp[20]), -np.imag(Z_exp[20])), \n", - " xytext=(np.real(Z_exp[20])-2, 10-np.imag(Z_exp[20])), \n", - " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", - "plt.annotate(r'$10^{-1}$', xy=(np.real(Z_exp[30]), -np.imag(Z_exp[30])), \n", - " xytext=(np.real(Z_exp[30])-2, 6-np.imag(Z_exp[30])), \n", - " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", - "plt.annotate(r'$1$', xy=(np.real(Z_exp[40]), -np.imag(Z_exp[40])), \n", - " xytext=(np.real(Z_exp[40]), 10-np.imag(Z_exp[40])), \n", - " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", - "plt.annotate(r'$10$', xy=(np.real(Z_exp[50]), -np.imag(Z_exp[50])), \n", - " xytext=(np.real(Z_exp[50])-1, 10-np.imag(Z_exp[50])), \n", - " arrowprops=dict(arrowstyle=\"-\",connectionstyle=\"arc\"))\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 3) Compute the optimal hyperparameters" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "sigma_n, sigma_f, ell\n", - "1.0000290 5.0000028 0.0079106\n", - "1.0000582 5.0000205 0.0135268\n", - "1.0001011 5.0000654 0.0218110\n", - "1.0001540 5.0001736 0.0342186\n", - "1.0001779 5.0004275 0.0527574\n", - "1.0000006 5.0010074 0.0802152\n", - "0.9989934 5.0022977 0.1203504\n", - "0.9950320 5.0050874 0.1780736\n", - "0.9810932 5.0109940 0.2604866\n", - "0.9323377 5.0238470 0.3836633\n", - "0.8036473 5.0473572 0.5451553\n", - "0.8278384 5.0853525 0.7852677\n", - "0.8287949 5.1293254 1.2514261\n", - "0.8303948 5.1721020 1.2189826\n", - "0.8304461 5.2594414 1.2326420\n", - "0.8305238 5.3960799 1.2534148\n", - "0.8305327 5.4070244 1.2546809\n", - "0.8305262 5.4070989 1.2546864\n", - "0.8305267 5.4070910 1.2546867\n", - "Optimization terminated successfully.\n", - " Current function value: 53.657989\n", - " Iterations: 19\n", - " Function evaluations: 20\n", - " Gradient evaluations: 87\n", - " Hessian evaluations: 0\n" - ] - } - ], - "source": [ - "# initialize the parameters for the minimization of the NMLL, see (31) in the manuscript\n", - "sigma_n = 1.0\n", - "sigma_f = 5.0\n", - "ell = 0.001\n", - "\n", - "theta_0 = np.array([sigma_n, sigma_f, ell])\n", - "seq_theta = np.copy(theta_0)\n", - "def print_results(theta):\n", - " global seq_theta\n", - " seq_theta = np.vstack((seq_theta, theta))\n", - " print('{0:.7f} {1:.7f} {2:.7f}'.format(theta[0], theta[1], theta[2]))\n", - "\n", - "print('sigma_n, sigma_f, ell')\n", - "\n", - "# minimize the NMLL L(\\theta) w.r.t sigma_n, sigma_f, ell using the Newton-CG method as implemented in scipy\n", - "# Here we will show one solution to handle the exception that may be raised in np.linalg.cholesky(K_im_full) \n", - "# due to the non-positive definite K_im_full\n", - "# Once the message of \"numpy.linalg.LinAlgError: Matrix is not positive definite\" appears, we modify the theta_0\n", - "# to ensure that the K_im_full becomes positive definite\n", - "\n", - "# the flag to denote whether the K_im_full can be successfully decomposed\n", - "# ch_flag = True\n", - "# while ch_flag:\n", - "# try:\n", - "# res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='Newton-CG', \n", - "# jac=GP_DRT.grad_NMLL_fct, callback=print_results, options={'disp': True})\n", - "# ch_flag = False\n", - "# except np.linalg.LinAlgError as err:\n", - "# if 'positive definite' in str(err):\n", - "# theta_0 = np.abs([sigma_n, sigma_f, ell]) + np.random.random()*np.ones((3))\n", - "\n", - "res = minimize(GP_DRT.NMLL_fct, theta_0, args=(Z_exp, xi_vec), method='Newton-CG', \n", - " jac=GP_DRT.grad_NMLL_fct, callback=print_results, options={'disp': True}) \n", - "# collect the optimized parameters\n", - "sigma_n, sigma_f, ell = res.x" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 4) Core of the GP-DRT" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 4a) Compute matrices" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "K = GP_DRT.matrix_K(xi_vec, xi_vec, sigma_f, ell)\n", - "L_im_K = GP_DRT.matrix_L_im_K(xi_vec, xi_vec, sigma_f, ell)\n", - "L2_im_K = GP_DRT.matrix_L2_im_K(xi_vec, xi_vec, sigma_f, ell)\n", - "Sigma = (sigma_n**2)*np.eye(N_freqs)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 4b) Factorize the matrices and solve the linear equations" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [], - "source": [ - "# the matrix $\\mathcal L^2_{\\rm im} \\mathbf K + \\sigma_n^2 \\mathbf I$ whose inverse is needed\n", - "K_im_full = L2_im_K + Sigma\n", - "\n", - "# check if the K_im_full is positive definite, otherwise, a nearest one would replace the K_im_full\n", - "if not GP_DRT.is_PD(K_im_full):\n", - " K_im_full = GP_DRT.nearest_PD(K_im_full)\n", - "\n", - "# Cholesky factorization, L is a lower-triangular matrix\n", - "L = np.linalg.cholesky(K_im_full)\n", - "\n", - "# solve for alpha\n", - "alpha = np.linalg.solve(L, Z_exp.imag)\n", - "alpha = np.linalg.solve(L.T, alpha)\n", - "\n", - "# estimate the gamma of eq (21a)\n", - "gamma_fct_est = np.dot(L_im_K, alpha)\n", - "\n", - "# covariance matrix\n", - "inv_L = np.linalg.inv(L)\n", - "inv_K_im_full = np.dot(inv_L.T, inv_L)\n", - "\n", - "# estimate the sigma of gamma for eq (21b)\n", - "cov_gamma_fct_est = K - np.dot(L_im_K, np.dot(inv_K_im_full, L_im_K.T))\n", - "sigma_gamma_fct_est = np.sqrt(np.diag(cov_gamma_fct_est))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 4c) Plot the obtained DRT against the analytical DRT" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# plot the DRT and its confidence region\n", - "plt.semilogx(freq_vec_plot, gamma_fct_plot, linewidth=4, color=\"black\", label=\"exact\")\n", - "plt.semilogx(freq_vec, gamma_fct_est, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", - "plt.fill_between(freq_vec, gamma_fct_est-3*sigma_gamma_fct_est, gamma_fct_est+3*sigma_gamma_fct_est, color=\"0.4\", alpha=0.3)\n", - "plt.rc('text', usetex=True)\n", - "plt.rc('font', family='serif', size=15)\n", - "plt.rc('xtick', labelsize=15)\n", - "plt.rc('ytick', labelsize=15)\n", - "plt.axis([1E-4,1E4,-5,25])\n", - "plt.legend(frameon=False, fontsize = 15)\n", - "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", - "plt.ylabel(r'$\\gamma/\\Omega$', fontsize = 20)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 4d) Predict the $\\gamma$ and the imaginary part of the GP-DRT impedance" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [], - "source": [ - "# initialize the imaginary part of impedance vector\n", - "Z_im_vec_star = np.empty_like(xi_vec_star)\n", - "Sigma_Z_im_vec_star = np.empty_like(xi_vec_star)\n", - "\n", - "gamma_vec_star = np.empty_like(xi_vec_star)\n", - "Sigma_gamma_vec_star = np.empty_like(xi_vec_star)\n", - "\n", - "# calculate the imaginary part of impedance at each $\\xi$ point for the plot\n", - "for index, val in enumerate(xi_vec_star):\n", - " xi_star = np.array([val])\n", - "\n", - " # compute matrices shown in eq (23), xi_star corresponds to a new point\n", - " k_star = GP_DRT.matrix_K(xi_vec, xi_star, sigma_f, ell)\n", - " L_im_k_star_up = GP_DRT.matrix_L_im_K(xi_star, xi_vec, sigma_f, ell)\n", - " L2_im_k_star = GP_DRT.matrix_L2_im_K(xi_vec, xi_star, sigma_f, ell)\n", - " k_star_star = GP_DRT.matrix_K(xi_star, xi_star, sigma_f, ell)\n", - " L_im_k_star_star = GP_DRT.matrix_L_im_K(xi_star, xi_star, sigma_f, ell)\n", - " L2_im_k_star_star = GP_DRT.matrix_L2_im_K(xi_star, xi_star, sigma_f, ell)\n", - "\n", - " # compute Z_im_star mean and standard deviation using eq (26)\n", - " Z_im_vec_star[index] = np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, Z_exp.imag))\n", - " Sigma_Z_im_vec_star[index] = L2_im_k_star_star-np.dot(L2_im_k_star.T, np.dot(inv_K_im_full, L2_im_k_star))\n", - " \n", - " # compute gamma_star mean and standard deviation using eq (29)\n", - " gamma_vec_star[index] = np.dot(L_im_k_star_up, np.dot(inv_K_im_full, Z_exp.imag))\n", - " Sigma_gamma_vec_star[index] = k_star_star-np.dot(L_im_k_star_up, np.dot(inv_K_im_full, L_im_k_star_up.T))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 4e) Plot the imaginary part of the GP-DRT impedance together with the exact one and the synthetic experiment" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.semilogx(freq_vec_star, -np.imag(Z_exact), \":\", linewidth=4, color=\"blue\", label=\"exact\")\n", - "plt.semilogx(freq_vec, -Z_exp.imag, \"o\", markersize=10, color=\"black\", label=\"synth exp\")\n", - "plt.semilogx(freq_vec_star, -Z_im_vec_star, linewidth=4, color=\"red\", label=\"GP-DRT\")\n", - "plt.fill_between(freq_vec_star, -Z_im_vec_star-3*np.sqrt(abs(Sigma_Z_im_vec_star)), -Z_im_vec_star+3*np.sqrt(abs(Sigma_Z_im_vec_star)), alpha=0.3)\n", - "plt.rc('text', usetex=True)\n", - "plt.rc('font', family='serif', size=15)\n", - "plt.rc('xtick', labelsize=15)\n", - "plt.rc('ytick', labelsize=15)\n", - "plt.axis([1E-4,1E4,-5,25])\n", - "plt.legend(frameon=False, fontsize = 15)\n", - "plt.xlabel(r'$f/{\\rm Hz}$', fontsize = 20)\n", - "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n", - "plt.show()" - ] - } - ], - "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": "3.8.5" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} From ae1bcea57f5c1c232c523f4664f8bd3338f5e8da Mon Sep 17 00:00:00 2001 From: LIU Date: Fri, 6 Aug 2021 12:11:08 +0800 Subject: [PATCH 4/5] update README --- README.md | 2 -- 1 file changed, 2 deletions(-) diff --git a/README.md b/README.md index 0145468..c23bee8 100644 --- a/README.md +++ b/README.md @@ -37,8 +37,6 @@ The frequency range is from 1E-4 Hz to 1E4 Hz with 10 ppd. * **ex5_inductance_plus_ZARC.ipynb**: this notebook adds an inductance to the model used in ex1_single_ZARC.ipynb -* **ex6_exception_handling.ipynb**: in this notebook, we show how to resolve the error raised by `np.linalg.cholesky()` - # Citation ``` From 3eeb0ab12db77151311f8eb25fb8f14bfbd98cc3 Mon Sep 17 00:00:00 2001 From: ciuccislab <57649983+ciuccislab@users.noreply.github.com> Date: Mon, 13 Sep 2021 12:36:22 +0800 Subject: [PATCH 5/5] Add files via upload --- docs/main.pdf | Bin 3642008 -> 3673341 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/docs/main.pdf b/docs/main.pdf index 170f109a25a4964f171bc4e16b820fa9aa8cc669..f179cec95bd9d53b93cc81d8b4372da5869f1f05 100644 GIT binary patch delta 182765 zcmcG0by!y0w=Ufw-O}CN-QCjNozn2p()A%AjYvpJ2uOFAAPthzA|(h2URnFF+3xc@ z&pr2#`#d_IZ>~AVJKph*G3Q#7^+86_XUN-EYmiCOl7^hTJiq_*8nUsm$=^55_l@U$ z<9^?`+&7l@&GY-l;=Tb!?e0GTqseMwtp9}3x*xH;{F17P{mBUw3Hx|rJ|fs>$! z!KN^X$-Q`%|1_1oH!!)baQ`FC6S-Y-He6DE#~6fVUv={?OuIiG83Ybsv<*eFIE* zxGeJ@LI<+y_&%Upt$}w8~|y6YItxDumTbX$O`BU@q0OvpzJeKJLv>_WeP}GmHFyGrt5#6`{)R&w6 zZ=t{i$RuDi7&LG*6yE=`!e^nBxc*t;^7rsS{dwJg0(b#JJuVGE2QUM)68}F99~U2B z18fpNeE(^a0E3|aTv(caI|GCSApT_tkg~a-_aG6FtjDe8;j-NQ9N+uK^>0)l1fcu( zawYw1$v?^uz&!>G-hozP_-BNY_h>-yfX$;Jzzoa}Bm4hWn}6l=9`v8-{A;;;-(Lpg zdkpd+zQ+{(dnd-aw|d-j{@TM{!ASfO2H*?`6G-XfA_P2v*Z&m;kQqQtAk0TP00hu| zO!EUp>3br;Likq-fT{md4#0Tab$Hmpapny5x98d_Tynh0r{`Lq|(O+eA^DjpK z%j*5V6z>B;)%*AWO&-Gl`Cn zT7d3@cL3^-o7Q6{9}@*A1n~K@FxdYh^_Z9kSO5gD0vf;z@CiKnFVm$v_ zgaCwrbUnaJ{iVu-D8ST*F`xs${9&T@w;wB(`;WjN5Yl6<0$qTs^WPgbA3Hc1iaLFg zffpX^2#@{8{-Jsg^jLC06pwcqKt7-WZ~;nxY>vPU7cc@Mbh}6UPYDCefhivJ;0$<$ zKQ?vwd#lHA0sF^@9>oBzfe+wi_5ZnSHSVneXkaEl{y|9T`?3G09Re(lprrOscwlD& zR03j^yhnV12Z#gZ1ZV`10Fv@=&Y1|xf2aa>#M>K#J0PS%P2WCEs415Bv0e8a(3XcT? 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