From 3aeab77fa95c2ce23748e97391ad6efb676f6bbe Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 8 Oct 2017 19:57:32 +0530 Subject: [PATCH 1/9] Initial Commit --- examples/lagrange_interpolation_test.ipynb | 144 +++++++++++++++++++++ 1 file changed, 144 insertions(+) create mode 100644 examples/lagrange_interpolation_test.ipynb diff --git a/examples/lagrange_interpolation_test.ipynb b/examples/lagrange_interpolation_test.ipynb new file mode 100644 index 0000000..ecf0a11 --- /dev/null +++ b/examples/lagrange_interpolation_test.ipynb @@ -0,0 +1,144 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "import os\n", + "import sys\n", + "sys.path.insert(0, os.path.abspath('../'))\n", + "\n", + "import numpy as np\n", + "\n", + "from dg_maxwell import lagrange\n", + "from dg_maxwell import isoparam" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def test_function(x):\n", + " return np.sin(2 * np.pi * x)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0. 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1. ]\n" + ] + } + ], + "source": [ + "M = 8\n", + "x_nodes = np.linspace(0, 1, 9)\n", + "print(x_nodes)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "x_nodes = np.array([[0. , 0.125],\n", + " [0.125, 0.25],\n", + " [0.25 , 0.375],\n", + " [0.375, 0.5],\n", + " [0.5 , 0.625],\n", + " [0.625, 0.75],\n", + " [0.75 , 0.875],\n", + " [0.875, 1.]])" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# for N in np.arange(3, 24):\n", + "N = 8\n", + "xi_LGL = np.array(lagrange.LGL_points(int(N)))\n", + "x_LGL = []\n", + "y = []\n", + "\n", + "for node in x_nodes:\n", + " x_LGL.append(isoparam.isoparam_1D(node, xi_LGL))\n", + " y.append(test_function(x_LGL[-1]))\n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 6.58335179e-15 5.03462325e-02 1.59652832e-01 3.05541879e-01\n", + " 4.57241238e-01 5.85145281e-01 6.70609883e-01 7.07106781e-01]\n", + "[ 0.70710678 0.74181021 0.81092848 0.88934271 0.95217864 0.98717322\n", + " 0.99873182 1. ]\n", + "[ 1. 0.99873182 0.98717322 0.95217864 0.88934271 0.81092848\n", + " 0.74181021 0.70710678]\n", + "[ 7.07106781e-01 6.70609883e-01 5.85145281e-01 4.57241238e-01\n", + " 3.05541879e-01 1.59652832e-01 5.03462325e-02 1.01064310e-15]\n", + "[ -6.09478426e-15 -5.03462325e-02 -1.59652832e-01 -3.05541879e-01\n", + " -4.57241238e-01 -5.85145281e-01 -6.70609883e-01 -7.07106781e-01]\n", + "[-0.70710678 -0.74181021 -0.81092848 -0.88934271 -0.95217864 -0.98717322\n", + " -0.99873182 -1. ]\n", + "[-1. -0.99873182 -0.98717322 -0.95217864 -0.88934271 -0.81092848\n", + " -0.74181021 -0.70710678]\n", + "[ -7.07106781e-01 -6.70609883e-01 -5.85145281e-01 -4.57241238e-01\n", + " -3.05541879e-01 -1.59652832e-01 -5.03462325e-02 -2.02128620e-15]\n" + ] + } + ], + "source": [ + "for element in y:\n", + " print(element)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From a334ad426c4a5c58e9fd74dd82fab1447ac19cbb Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 8 Oct 2017 20:36:29 +0530 Subject: [PATCH 2/9] Temporary commit --- examples/lagrange_interpolation_test.ipynb | 30 +++++++++++++++------- 1 file changed, 21 insertions(+), 9 deletions(-) diff --git a/examples/lagrange_interpolation_test.ipynb b/examples/lagrange_interpolation_test.ipynb index ecf0a11..0aa4377 100644 --- a/examples/lagrange_interpolation_test.ipynb +++ b/examples/lagrange_interpolation_test.ipynb @@ -28,7 +28,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -41,13 +41,13 @@ ], "source": [ "M = 8\n", - "x_nodes = np.linspace(0, 1, 9)\n", + "x_nodes = np.linspace(0, 1, M + 1)\n", "print(x_nodes)" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -63,20 +63,32 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 34, "metadata": {}, "outputs": [], "source": [ + "xi_check = np.linspace(-1, 1, 10)\n", + "\n", "# for N in np.arange(3, 24):\n", - "N = 8\n", - "xi_LGL = np.array(lagrange.LGL_points(int(N)))\n", - "x_LGL = []\n", - "y = []\n", + "N = 8\n", + "xi_LGL = np.array(lagrange.LGL_points(int(N)))\n", + "x_LGL = []\n", + "y = []\n", + "x_check = []\n", + "\n", + "lagrange_basis, temp = lagrange.lagrange_polynomials(xi_LGL)\n", + "error = 0.\n", + "y_interop = 0.\n", "\n", "for node in x_nodes:\n", " x_LGL.append(isoparam.isoparam_1D(node, xi_LGL))\n", + " x_check.append(isoparam.isoparam_1D(node, xi_check))\n", " y.append(test_function(x_LGL[-1]))\n", - " \n" + " \n", + " for i in np.arange(len(y[-1])):\n", + " y_interop += lagrange_basis[i] * y[-1][i]\n", + " y_test = y_interop(xi_check)\n", + " " ] }, { From 553502a06188a7df01a9e353cb0670f1b4ed49fe Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 8 Oct 2017 21:32:50 +0530 Subject: [PATCH 3/9] Lagrange interpolation test code completed --- examples/lagrange_interpolation_test.ipynb | 144 ++++++++++++--------- 1 file changed, 84 insertions(+), 60 deletions(-) diff --git a/examples/lagrange_interpolation_test.ipynb b/examples/lagrange_interpolation_test.ipynb index 0aa4377..c6dadbd 100644 --- a/examples/lagrange_interpolation_test.ipynb +++ b/examples/lagrange_interpolation_test.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -11,43 +11,67 @@ "sys.path.insert(0, os.path.abspath('../'))\n", "\n", "import numpy as np\n", + "from matplotlib import pyplot as plt\n", "\n", "from dg_maxwell import lagrange\n", - "from dg_maxwell import isoparam" + "from dg_maxwell import isoparam\n", + "\n", + "plt.rcParams['figure.figsize'] = 12, 7.5\n", + "plt.rcParams['lines.linewidth'] = 1.5\n", + "plt.rcParams['font.family'] = 'serif'\n", + "plt.rcParams['font.weight'] = 'bold'\n", + "plt.rcParams['font.size'] = 20 \n", + "plt.rcParams['font.sans-serif'] = 'serif'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['axes.linewidth'] = 1.5\n", + "plt.rcParams['axes.titlesize'] = 'medium'\n", + "plt.rcParams['axes.labelsize'] = 'medium'\n", + "\n", + "plt.rcParams['xtick.major.size'] = 8\n", + "plt.rcParams['xtick.minor.size'] = 4\n", + "plt.rcParams['xtick.major.pad'] = 8\n", + "plt.rcParams['xtick.minor.pad'] = 8\n", + "plt.rcParams['xtick.color'] = 'k'\n", + "plt.rcParams['xtick.labelsize'] = 'medium'\n", + "plt.rcParams['xtick.direction'] = 'in' \n", + "\n", + "plt.rcParams['ytick.major.size'] = 8\n", + "plt.rcParams['ytick.minor.size'] = 4\n", + "plt.rcParams['ytick.major.pad'] = 8\n", + "plt.rcParams['ytick.minor.pad'] = 8\n", + "plt.rcParams['ytick.color'] = 'k'\n", + "plt.rcParams['ytick.labelsize'] = 'medium'\n", + "plt.rcParams['ytick.direction'] = 'in'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['text.latex.unicode'] = True\n" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def test_function(x):\n", + " '''\n", + " The test wave function.\n", + " '''\n", " return np.sin(2 * np.pi * x)" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 3, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 0. 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1. ]\n" - ] - } - ], + "outputs": [], "source": [ - "M = 8\n", - "x_nodes = np.linspace(0, 1, M + 1)\n", - "print(x_nodes)" + "M = 8 # Number of elements\n", + "x_nodes = np.linspace(0, 1, M + 1) # x nodes dividing the elements" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -63,65 +87,65 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ - "xi_check = np.linspace(-1, 1, 10)\n", + "# The test points at which the analytical and interpolated wave functions\n", + "# will be compared.\n", + "xi_check = np.linspace(-.9, .9, 10)\n", + "L1_norm = [] # Stores the L1 norm of the interpolated wave function\n", "\n", - "# for N in np.arange(3, 24):\n", - "N = 8\n", - "xi_LGL = np.array(lagrange.LGL_points(int(N)))\n", - "x_LGL = []\n", - "y = []\n", - "x_check = []\n", - "\n", - "lagrange_basis, temp = lagrange.lagrange_polynomials(xi_LGL)\n", - "error = 0.\n", - "y_interop = 0.\n", + "for N in np.arange(3, 31):\n", + " xi_LGL = np.array(lagrange.LGL_points(int(N)))\n", + " x_LGL = [] # x_nodes calculated at the LGL points for an element\n", + " x_check = [] # x coordinates at which the analytical and interpolated functions are compared\n", + " \n", + " # Test function calculated at the LGL points, to be used for finding the lagrange interpolation.\n", + " test_func_LGL = []\n", "\n", - "for node in x_nodes:\n", - " x_LGL.append(isoparam.isoparam_1D(node, xi_LGL))\n", - " x_check.append(isoparam.isoparam_1D(node, xi_check))\n", - " y.append(test_function(x_LGL[-1]))\n", + " lagrange_basis, temp = lagrange.lagrange_polynomials(xi_LGL)\n", + " test_func_intepol_poly = 0. # Stores the Lagrange interpolation function for an element.\n", " \n", - " for i in np.arange(len(y[-1])):\n", - " y_interop += lagrange_basis[i] * y[-1][i]\n", - " y_test = y_interop(xi_check)\n", - " " + " # Stores the value of the inerpolated function at the xi_check points for each elements.\n", + " test_function_interpol = []\n", + " \n", + " # This loop loops over all the elements and finds the interpolation function using\n", + " # Lagrange basis polynomials and test_func_LGL. It then uses the interpolation function\n", + " # to calculate the value of the polynomial at the xi_check points for each element.\n", + " for node in x_nodes:\n", + " test_func_intepol_poly = 0.\n", + " x_LGL.append(isoparam.isoparam_1D(node, xi_LGL))\n", + " x_check.extend(isoparam.isoparam_1D(node, xi_check))\n", + " test_func_LGL.append(test_function(x_LGL[-1]))\n", + "\n", + " for i in np.arange(len(test_func_LGL[-1])):\n", + " test_func_intepol_poly += lagrange_basis[i] * test_func_LGL[-1][i]\n", + " test_function_interpol.extend(test_func_intepol_poly(xi_check))\n", + "\n", + " L1_norm.append(np.sum(np.array(test_function_interpol) - test_function(np.array(x_check))))" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 8, "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 6.58335179e-15 5.03462325e-02 1.59652832e-01 3.05541879e-01\n", - " 4.57241238e-01 5.85145281e-01 6.70609883e-01 7.07106781e-01]\n", - "[ 0.70710678 0.74181021 0.81092848 0.88934271 0.95217864 0.98717322\n", - " 0.99873182 1. ]\n", - "[ 1. 0.99873182 0.98717322 0.95217864 0.88934271 0.81092848\n", - " 0.74181021 0.70710678]\n", - "[ 7.07106781e-01 6.70609883e-01 5.85145281e-01 4.57241238e-01\n", - " 3.05541879e-01 1.59652832e-01 5.03462325e-02 1.01064310e-15]\n", - "[ -6.09478426e-15 -5.03462325e-02 -1.59652832e-01 -3.05541879e-01\n", - " -4.57241238e-01 -5.85145281e-01 -6.70609883e-01 -7.07106781e-01]\n", - "[-0.70710678 -0.74181021 -0.81092848 -0.88934271 -0.95217864 -0.98717322\n", - " -0.99873182 -1. ]\n", - "[-1. -0.99873182 -0.98717322 -0.95217864 -0.88934271 -0.81092848\n", - " -0.74181021 -0.70710678]\n", - "[ -7.07106781e-01 -6.70609883e-01 -5.85145281e-01 -4.57241238e-01\n", - " -3.05541879e-01 -1.59652832e-01 -5.03462325e-02 -2.02128620e-15]\n" - ] + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "for element in y:\n", - " print(element)" + "plt.title(r'$L_1$ norm vs $N_{LGL}$')\n", + "plt.plot(L1_norm, 'o')\n", + "plt.show()" ] }, { From c42b1736cc3d1cc4a4abfb358de0f8f74e8f2cb3 Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 8 Oct 2017 21:34:29 +0530 Subject: [PATCH 4/9] L1 norm graph now plotting in semilogy --- examples/lagrange_interpolation_test.ipynb | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/examples/lagrange_interpolation_test.ipynb b/examples/lagrange_interpolation_test.ipynb index c6dadbd..cc1a17c 100644 --- a/examples/lagrange_interpolation_test.ipynb +++ b/examples/lagrange_interpolation_test.ipynb @@ -128,14 +128,14 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 12, "metadata": {}, "outputs": [ { "data": { - "image/png": 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VtVFV13rXAQAA81j7IJ7kapIzvYsAAIB5rHUQr6rNCOEAAKyhtQ7iSbaS3Opd\nBAAAzGttg3hVbSX5Ze86AADgUXyjdwGPYaO1tltVj/Tge/fu5fz58/uu397ezvb29qPWBgAAB1rL\nIF5VF1trNx9nG2fPns2dO3cWVBEAAMxn7VpTqmojyW7vOgAA4HF0GxEfZjyZ1f3W2l74/klr7foy\nagIAgKPSJYgPIfzqHA95P8mbVXUuyQfLqQoAAI5OlyDeWttJcukRHno+ydNV9fLYsnNJNqvqapL3\nH7d3HAAAjsJanaw5rSWlql5L8kJr7UqHkgAA4JGs3cmaU/x17wIAAGBeaxvEq2qzqq4l2U5ysaqu\nDT3kAACw8taqNWXc0Gd+ebgBAMBaWdsRcQAAWGeCOAAAdCCIAwBAB4I4AAB0IIgDAEAHgjgAAHQg\niAMAQAeCOAAAdCCIAwBAB4I4AAB0IIgDAEAHgjgAAHQgiAMAQAeCOAAAdCCIAwBAB4I4AAB0IIgD\nAEAHgjgAAHQgiAMAQAeCOAAAdCCIAwBAB4I4AAB0IIgDAEAHgjgAAHQgiAMAQAeCOAAAdCCIAwBA\nB4I4AAB0IIgDAEAHgjgAAHQgiAMAQAeCOAAAdCCIAwBAB4I4AAB0IIgDAEAHgjgAAHQgiAMAQAeC\nOAAAdCCIAwBAB4I4AAB0IIgDAEAHgjgAAHQgiAMAQAeCOAAAdCCIAwBAB4I4AAB0IIgDAEAHgjgA\nAHQgiAMAQAff6F0AAAAn268/+ixvvftx/rj7IN/ZOJVXX3wmP3ruqd5lLZ0gDgBAN7/+6LO8/s7v\n8+DPf0mSfLb7IK+/8/skOfZhfO1aU6pqo6peq6rN4fvNqrpaVVu9awMAYD5vvfvxlyF8z4M//yVv\nvftxp4qOztoF8SRnklxN8kmSz5N8mOT91trtrlUBADC3P+4+mGv5cbKOQTxJLiQ5neTp1trp1trN\n3gUBADC/72ycmmv5cbKuQTyttd3W2k7vOgAAeHSvvvhMTn3zya8tO/XNJ/Pqi890qujoOFkTAIBu\n9k7INGvK+tisqovD92eS3J+3PeXevXs5f/78vuu3t7ezvb39GCUCADCLHz331IkI3pPWMYjfT5Lx\n4F1VN6oq84Txs2fP5s6dO0soDwAADrd2PeJDb/j1icXXMppJBQAA1kK3EfGq2pzj7vdba7sHrN/J\nqF1l45D7AQDASugSxIcQPs8I9vtJ3hwe+1pr7c2J9feHr5tJ7j5+hQAAsFxdgvgw7eCleR+3F+Cr\n6ubE1IXea4QEAAAHpklEQVRnhq+mMwQAYC2sVY/4EL4vT5k/fCvJXW0py3H9+mRLPuvGPlx/9uF6\ns//Wn324/lZxH65VEB/cH+8vr6qNJJeTvNKvpONtFf/jMh/7cP3Zh+vN/lt/9uH6W8V9uHbTF7bW\nblbVxWEe8b9OspHkkqtsAgCwTtYuiCeZa75wAABYRevYmgIAAGtPEAcAgA4EcQAA6KBaa71rOHJV\n9f99+9vffurZZ5/tXcpa+PDDD/P888/3LoPHYB+uP/twvdl/688+XH899uHvfve7fPHFF5+11v7z\ntPUnNYh/lORvkvxb71rWxNkk93oXwWOxD9effbje7L/1Zx+uvx778HtJ/ndr7blpK09kEAcAgN70\niAMAQAeCOAAAdCCIAwBAB4I4AAB0IIgDAEAHgjgAAHQgiAMAQAff6F0Aq6mqNpJsJ7mZ5H6SM0ku\nJ7nVWrvdszb2V1UXk+xO20dVdS7J+SQ7STaT7NiXq2W//ed4XA/D/ttM8vTw9Vpr7ebEfRyHK+yw\nfehYXH1VtZXkQpI/ZbQfP2ytXZ+4z8ochy7ow1RVtZnkk7FFu0lemfyjwuoYXnxuJLk0Jcjt/UG5\nMLbsRpIrrbWdo62UaWbYf47HFTYEuJ3W2t3h540kHya5uhcCHIerbY596FhcUcPraMZfQ6vqwyRv\nt9beHH5eqeNQawoHuZDkdJKnW2unvdCspqrarKprGb2rv7/P3S4nuTax7FqSq8usjcPNuP8Sx+Oq\n29wLcEnSWtvN6PgaP+4ch6ttln2YOBZX2eUpy25PLF+p41AQ50CttV0jNauttbbTWrs8+dHbhItJ\n7k4s+2BYTkcz7r+9+zoeV9Awcvry8HXc7WH95vCz43BFzbEPkzgWV9yFKct2x75fqeNQEIdjbvjD\n8tBo6zDa89AfGGA+w7G0Odymchyutln2IauvtXaptXZlYvHFJG8nq3kcOlmTg2wOPXPJ6ISU+z6C\nW0tnkq9eaKbYzOiEFVab43GFtdZOT1m8ldHJtzt7f+Adh6vrsH04tsyxuCaqajvJ3b3+8Kzg30NB\nnP3cT5KJs8VvVFW84KydyY9aWT+Ox/V0Ockbw/eOw/U0vg8Tx+JaGN4oXUhGo+Rjq1buONSawlRD\n/9tkz6qTiqADx+P6GUbi7o+NxLFmpu1Dx+J6aK3dbK1dTnKlqj4cpitcSYI489jJ6CO5lXtHyeHs\nt2PH8biihjaUy+PTo42ts7/WwEH7cArH4ooaWlCuJXlvfPkq7StBnKmq6rUpi/dObnAyy3rZ63c7\nM75w7IVIX+qKczyunatJfjixzHG4XqbtQ8fierqdZGOYY3zljkNBnIcMIwFXp5w9vPcf1x+MNTKM\nCOzk4d64M3n4JCRWjONxvQxzwl+ZPBnMcbg+9tuHjsXVNlyT4fMD2lA2VvE4FMR5yPAf8fKU/5Bb\nGZ19vN/Zxqyu2xldznfcuWE5K8zxuD6GnuKr4/uqqrbGgpvjcMUdtA8diytvI6OQPbl/9o6/vbnD\nV+o4FMTZz/3xd/3DxzaXk7zSryRmcCbTzwq/kuTSxLLLw3JWx377z/G44sams9uoqnPDbSvJpbHg\n5jhcYTPuQ8fiihquivr2lFVXkry5qsdhtdZ6PC9rYHhR2kzy1xmFg6s+Pl09wx+C1zPaVxczGg24\nneTWxBRb55K8nOT94b53W2tG4jqbY/85HlfUsA8/32f1Tmvt6bH7Og5X0Jz70LG4woZPNZ5O8qfh\n64eTM92s0nEoiAMAQAdaUwAAoANBHAAAOhDEAQCgA0Ec4Jirqteq6lZVtar6ZMr6jbH1n1fVjR51\nApw0TtYEOAGGWQJez2hmlueHqb4m73MjySvmQwY4GkbEAU6GrXw11/Hlfe7zvhAOcHQEcYATYgjZ\n15NsT64b5lEWwgGOkCAOcLJcS7686MW4rbjUOsCREsQBjrmhP/xu8uVloHfycHvKpqsDAhwtQRzg\n+Duf5IOxn68lOVdVm53qASCCOMBJsDFxEub14euVRH84QC+COMAJM4Tym0l+Miw6n336w6tqe5hf\n/EZVXdxvm8P9Xhu+blfVxaraqqqtR9kewElgHnGAY2xoPznXWrs5sXwrya0klzLqD39zn8dvJPm8\ntVYHbP9qkjfG5yYfln8y+bjDtgdwkhgRBzjeps6G0lq7nVE7yn5zih/4+OTLUH0ryZXJCwQNJ35e\nn/Iws7MADARxgONtsj983PWMgvFBXs4obE9zI8m1A2ZbuTrn9gBOFEEc4JgaRqxfOOAu14avB41Q\nTx3BHra9lVGv+VT7BHQj4gADQRzgGKqqG0k+TXJxODFyY/I+e+0jk20lY9vYHO53d2L5RkYneD4U\ntoeTNK9NOxnzkO0BnDiCOMAx1Fq71Fo73Vqr4fup7SmttYN6xPcbvd7K6KJA07Z3M8NUiJMniB6y\nPYATRxAHYD+XMtHPXVWvJbk7jITfnDLqvZHk4uTjDtveIosGWBemLwTga4YwvZ3RyZZvJvkkyUaS\nC0nSWrswdt+rSf6U0Sj4/eHrRr4K63NtD+AkEcQBAKADrSkAANCBIA4AAB0I4gAA0IEgDgAAHQji\nAADQgSAOAAAdCOIAANCBIA4AAB0I4gAA0IEgDgAAHfwfzf7zQjyjwEIAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -144,7 +144,9 @@ ], "source": [ "plt.title(r'$L_1$ norm vs $N_{LGL}$')\n", - "plt.plot(L1_norm, 'o')\n", + "plt.xlabel(r'$N_{LGL}$')\n", + "plt.ylabel(r'$L_1$ norm of error')\n", + "plt.plot(np.arange(3, 31), L1_norm, 'o')\n", "plt.show()" ] }, From 8c6eb7462744d9c121ace8945ab4b595b4e8bc85 Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 8 Oct 2017 23:29:58 +0530 Subject: [PATCH 5/9] find_li_norm function added. It finds the l1 norm of an error function from -1, 1 --- examples/lagrange_interpolation_test.ipynb | 57 ++++++++++++++++------ 1 file changed, 42 insertions(+), 15 deletions(-) diff --git a/examples/lagrange_interpolation_test.ipynb b/examples/lagrange_interpolation_test.ipynb index cc1a17c..bb4ddc2 100644 --- a/examples/lagrange_interpolation_test.ipynb +++ b/examples/lagrange_interpolation_test.ipynb @@ -10,11 +10,13 @@ "import sys\n", "sys.path.insert(0, os.path.abspath('../'))\n", "\n", + "from scipy import integrate\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "from dg_maxwell import lagrange\n", "from dg_maxwell import isoparam\n", + "from dg_maxwell import wave_equation\n", "\n", "plt.rcParams['figure.figsize'] = 12, 7.5\n", "plt.rcParams['lines.linewidth'] = 1.5\n", @@ -51,6 +53,24 @@ "execution_count": 2, "metadata": {}, "outputs": [], + "source": [ + "def find_L1_norm(epsilon, dx_dxi, x):\n", + " '''\n", + " '''\n", + " lagrange_basis, temp = lagrange.lagrange_polynomials(x)\n", + " \n", + " epsilon_interpol = 0.\n", + " for i in np.arange(x.shape[0]):\n", + " epsilon_interpol += lagrange_basis[i] * epsilon[i]\n", + " \n", + " return integrate.quad(epsilon_interpol * dx_dxi, -1, 1)[0]\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], "source": [ "def test_function(x):\n", " '''\n", @@ -61,7 +81,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -71,7 +91,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -82,60 +102,66 @@ " [0.5 , 0.625],\n", " [0.625, 0.75],\n", " [0.75 , 0.875],\n", - " [0.875, 1.]])" + " [0.875, 1.]])\n", + "\n", + "dx_dxi = (x_nodes[0][1] - x_nodes[0][0]) / 2" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# The test points at which the analytical and interpolated wave functions\n", "# will be compared.\n", - "xi_check = np.linspace(-.9, .9, 10)\n", + "xi_check = np.linspace(-.9, .9, 8)\n", "L1_norm = [] # Stores the L1 norm of the interpolated wave function\n", "\n", "for N in np.arange(3, 31):\n", + "# N = 8\n", " xi_LGL = np.array(lagrange.LGL_points(int(N)))\n", " x_LGL = [] # x_nodes calculated at the LGL points for an element\n", " x_check = [] # x coordinates at which the analytical and interpolated functions are compared\n", - " \n", + "\n", " # Test function calculated at the LGL points, to be used for finding the lagrange interpolation.\n", " test_func_LGL = []\n", "\n", " lagrange_basis, temp = lagrange.lagrange_polynomials(xi_LGL)\n", " test_func_intepol_poly = 0. # Stores the Lagrange interpolation function for an element.\n", - " \n", + "\n", " # Stores the value of the inerpolated function at the xi_check points for each elements.\n", " test_function_interpol = []\n", - " \n", + "\n", + " L1_norm.append(0.)\n", + " L1 = 0.\n", " # This loop loops over all the elements and finds the interpolation function using\n", " # Lagrange basis polynomials and test_func_LGL. It then uses the interpolation function\n", " # to calculate the value of the polynomial at the xi_check points for each element.\n", " for node in x_nodes:\n", " test_func_intepol_poly = 0.\n", " x_LGL.append(isoparam.isoparam_1D(node, xi_LGL))\n", - " x_check.extend(isoparam.isoparam_1D(node, xi_check))\n", + " x_check.append(isoparam.isoparam_1D(node, xi_check))\n", " test_func_LGL.append(test_function(x_LGL[-1]))\n", "\n", " for i in np.arange(len(test_func_LGL[-1])):\n", " test_func_intepol_poly += lagrange_basis[i] * test_func_LGL[-1][i]\n", - " test_function_interpol.extend(test_func_intepol_poly(xi_check))\n", + " test_function_interpol.append(test_func_intepol_poly(xi_check))\n", "\n", - " L1_norm.append(np.sum(np.array(test_function_interpol) - test_function(np.array(x_check))))" + " L1_norm[-1] += find_L1_norm(np.abs(test_function_interpol[-1] - test_function(x_check[-1])),\n", + " dx_dxi, xi_check)" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 8, "metadata": {}, "outputs": [ { "data": { - "image/png": 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FtYPENROH6p4ZeZKk7676QLsqI+NNvqYWtxauLNa+oyc0KjtFy26ZrIS46H8M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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -146,7 +172,8 @@ "plt.title(r'$L_1$ norm vs $N_{LGL}$')\n", "plt.xlabel(r'$N_{LGL}$')\n", "plt.ylabel(r'$L_1$ norm of error')\n", - "plt.plot(np.arange(3, 31), L1_norm, 'o')\n", + "plt.semilogy(np.arange(3, 31), L1_norm, 'o-')\n", + "# plt.savefig('lagrange_interpolation_test.png')\n", "plt.show()" ] }, From d4eed7efd26430d29d6ad040b651d299dae83d7f Mon Sep 17 00:00:00 2001 From: AAT Date: Mon, 9 Oct 2017 01:46:29 +0530 Subject: [PATCH 6/9] volume_integral_error_analysis.ipynb added. --- dg_maxwell/params.py | 6 +- examples/lagrange_interpolation_test.ipynb | 105 +++++++++-- examples/volume_integral_error_analysis.ipynb | 175 ++++++++++++++++++ 3 files changed, 269 insertions(+), 17 deletions(-) create mode 100644 examples/volume_integral_error_analysis.ipynb diff --git a/dg_maxwell/params.py b/dg_maxwell/params.py index ec3dea1..6fd2104 100644 --- a/dg_maxwell/params.py +++ b/dg_maxwell/params.py @@ -10,13 +10,13 @@ from dg_maxwell import isoparam # The domain of the function. -x_nodes = af.np_to_af_array(np.array([-1., 1.])) +x_nodes = af.np_to_af_array(np.array([0, 1.])) # The number of LGL points into which an element is split. N_LGL = 8 # Number of elements the domain is to be divided into. -N_Elements = 10 +N_Elements = 8 # The scheme to be used for integration. Values are either # 'gauss_quadrature' or 'lobatto_quadrature' @@ -109,7 +109,7 @@ int(total_time / delta_t)) # Initializing the amplitudes. Change u_init to required initial conditions. -u_init = np.e ** (-(element_LGL) ** 2 / 0.4 ** 2) +u_init = af.sin(2 * np.pi * element_LGL) u = af.constant(0, N_LGL, N_Elements, time.shape[0],\ dtype = af.Dtype.f64) u[:, :, 0] = u_init diff --git a/examples/lagrange_interpolation_test.ipynb b/examples/lagrange_interpolation_test.ipynb index bb4ddc2..db1927a 100644 --- a/examples/lagrange_interpolation_test.ipynb +++ b/examples/lagrange_interpolation_test.ipynb @@ -50,7 +50,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 109, "metadata": {}, "outputs": [], "source": [ @@ -63,12 +63,34 @@ " for i in np.arange(x.shape[0]):\n", " epsilon_interpol += lagrange_basis[i] * epsilon[i]\n", " \n", - " return integrate.quad(epsilon_interpol * dx_dxi, -1, 1)[0]\n" + " return integrate.quad(epsilon_interpol * dx_dxi, -1, 1)[0]\n", + "\n", + "\n", + "def integrate_quad(function, order, scheme = 'gauss_legendre'):\n", + " '''\n", + " '''\n", + " if scheme == 'gauss_legendre':\n", + " nodes = np.array(lagrange.gauss_nodes(order))\n", + " weights = np.array(lagrange.gaussian_weights(order))\n", + "\n", + " elif scheme == 'gauss_lobatto':\n", + " nodes = np.array(lagrange.LGL_points(order))\n", + " weights = np.array(lagrange.lobatto_weights(order))\n", + " \n", + " else:\n", + " return\n", + "\n", + " integral = 0.\n", + "\n", + " for node, weight in zip(nodes, weights):\n", + " integral += weight * function(node)\n", + " \n", + " return integral" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 60, "metadata": {}, "outputs": [], "source": [ @@ -76,12 +98,23 @@ " '''\n", " The test wave function.\n", " '''\n", - " return np.sin(2 * np.pi * x)" + " return np.sin(2 * np.pi * x)\n", + "\n", + "def int_sin2pix_dLdxi(x_nodes, xi_LGL, lagrange_basis_order):\n", + " '''\n", + " '''\n", + " L_i, temp = lagrange.lagrange_polynomials(xi_LGL)\n", + " \n", + " def sin2pix_dLdxi(xi):\n", + " x = (((x_nodes[1] - x_nodes[0]) * xi + (x_nodes[1] + x_nodes[0]))) / 2\n", + " return np.sin(2 * np.pi * x) * L_i[lagrange_basis_order].deriv()(xi)\n", + " \n", + " return integrate.quad(sin2pix_dLdxi, -1, 1)[0]\n" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 42, "metadata": {}, "outputs": [], "source": [ @@ -91,7 +124,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 43, "metadata": {}, "outputs": [], "source": [ @@ -109,7 +142,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 19, "metadata": {}, "outputs": [], "source": [ @@ -154,14 +187,58 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 127, + "metadata": {}, + "outputs": [], + "source": [ + "# The test points at which the analytical and interpolated wave functions\n", + "# will be compared.\n", + "xi_check = np.linspace(-.9, .9, 8)\n", + "error = [] # Stores the error of the interpolated wave function\n", + "\n", + "for N in np.arange(3, 31):\n", + "# N = 8\n", + " xi_LGL = np.array(lagrange.LGL_points(int(N)))\n", + " x_LGL = [] # x_nodes calculated at the LGL points for an element\n", + " x_check = [] # x coordinates at which the analytical and interpolated functions are compared\n", + "\n", + " # Test function calculated at the LGL points, to be used for finding the lagrange interpolation.\n", + " test_func_LGL = []\n", + "\n", + " lagrange_basis, temp = lagrange.lagrange_polynomials(xi_LGL)\n", + " test_func_intepol_poly = 0. # Stores the Lagrange interpolation function for an element.\n", + "\n", + " # Stores the value of the inerpolated function at the xi_check points for each elements.\n", + " test_function_interpol = []\n", + "\n", + " error.append(0.)\n", + " # This loop loops over all the elements and finds the interpolation function using\n", + " # Lagrange basis polynomials and test_func_LGL. It then uses the interpolation function\n", + " # to calculate the value of the polynomial at the xi_check points for each element.\n", + " for node in x_nodes:\n", + " test_func_intepol_poly = 0.\n", + " x_LGL.append(isoparam.isoparam_1D(node, xi_LGL))\n", + " x_check.append(isoparam.isoparam_1D(node, xi_check))\n", + " test_func_LGL.append(test_function(x_LGL[-1]))\n", + "\n", + " for i in np.arange(len(test_func_LGL[-1])):\n", + " test_func_intepol_poly += lagrange_basis[i] * test_func_LGL[-1][i]\n", + " \n", + " error[-1] += abs(integrate_quad(test_func_intepol_poly * lagrange_basis[0].deriv(), 9)\n", + " - int_sin2pix_dLdxi(node, xi_LGL, 0))\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 128, "metadata": {}, "outputs": [ { "data": { - "image/png": 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FtYPENROH6p4ZeZKk7676QLsqI+NNvqYWtxauLNa+oyc0KjtFy26ZrIS46H8M\nj/6fEOhl910+RpL0+w8OaE/VcYfTAAAAAOHD7bb67qoPdPBYo/IHpeqHXxsf9LW+95VxujA/Sw1N\nrZr/zBbVNTaHMGnoWWv1L7/brk27q5WeFK/H75gS8YtZBoqiAeih8cMydOnZg+S20vK3WKsBAAAA\n8Hn8nTL9ZWelEuNd+vnNRUpNCn7jw/g4l/735iLl9E9W6eEG/cOLH8gdxotDPv5OmV54f69cRvrZ\nzed3a7pIpKNoAELgvssLJEmr3t+nymONDqcBAAAAnLd1z1Et9e6ysHhOoc7J7d/jaw5MS9KyW4uU\nGOfSn3cc0rI3w/ONvtc/rdS//+kTSdI/XX2Orhg72OFEfYuiAQiBC/KyNHnUADW1uvX4O2VOxwEA\nAAAcVXu8WX/93Fa1uK2+OiFXN08bGbJrnz9ygJZ87VxJ0o///Kne/OxwyK4dCrsq63T/c541KW6c\nMkJ3e9eWiCUUDUAIGGP07Ss8oxpWbihX7fHwni8GAAAA9BZrrR54+QPtr/EsgPjwdeeFfJeFm6aN\n1E3TRsha6f7nt2pvdXislXa0oUl3P/W+6k62aNroLP3w2vFRv8NERygagBC5YuxgjctJV0NTq558\nr0zrS6r0yrb9Wl9SpdYwnjsGAAAAhNLT68v1fx8fUkKc0f/eVKT05IReuc8PrjlXE0dkqvZEsxY8\ns0Unmlp75T6Bam51a+GzW1RedVzDB/TzTPGIj81HbmMtD0CRxhiTKqlekurr65WamupwIvj8/oMD\nuv/5rTJGavuvVm5GshbPKdTs8bnOhQMAAAB62fb9tbruF++pqdWtxXMKdefFvTtt4EDNCc35n3dU\n1dCk684fpv+8YaIjIwistfr+77bruY17lJoYp9/cd7HG5kTX4o8NDQ1KS0vzfZlmrW3wd25s1itA\nL4nz/jetfX93sLZRC1cWa832ir4PBQAAAPSBusZm/fVzxWpqdWtW4RB986LRvX7PoZn99D83n684\nl9Fvtu7X0+vLe/2eHXnqvd16buMeGSP97Kbzo65k6C6KBiBEWt1WP/rjJx0e8/UOS1bvYBoFAAAA\noo61Vv/02+3aXXVcwzL76T/mTuizkQUXFQzUg18ZJ0n64R92aPPu6j65r89bnx3Wv/5hhyTpe7PH\n6apzhvTp/cMRRQMQIpvKqlVR639rSyuporZRm8r69j98AAAAQG97YfNerf7ggOJcRj+76XxlpiT2\n6f3vnpF8rjUlAAAgAElEQVSnOROHqsVtdd+zxTrUR1vOlxyu17efK5bbStcXDdf8S/P75L7hjqIB\nCJHKusD+YxboeQAAAEAk+PRgnRb//mNJ0j9+eawmjxrQ5xmMMVp6/XkaOyRdh+tOauHKLWpqcffq\nPWuON+mep95XXWOLJo8aoH+/LjZ3mOgIRQMQIoPTk0N6HgAAABDujje16NvPFetki1uXnT1I8y9x\n7h39lMR4Lb9tstKT41W8p0Y/9E5n6A3NrW59+7lilR1p0LDMflp+22Qlxcf12v0iDUUDECLT8rKU\nm5Esfx2mkWf3iWl5WX0ZCwAAAOg1i1/5WLsq6zWkf5J+csNEuVzOvqM/emCq/vsbkyRJz2wo16r3\n9/bKfX74hx16d1eVUhLj9OjtUzQwLalX7hOpKBqAEIlzGS2eUyhJfsuGxXMKFefwf3wBAACAUPhN\n8T6t2rJPLiP99zfOV3aYPGxfOW6I/nbmWZKk7/9uu7bvrw3p9Z/ZUH5qd4uf3jhJhUP7h/T60YCi\nAQih2eNztezWIuVknD49ol9CnJbdWqTZ43MdSgYAAACETsnhev3z77ZLkv525tm6MD/b4USnu//K\ns3TVuMFqanFrwTNbVN3QFJLrvrfriH7QZj2KL5+bE5LrRhuKBiDEZo/P1TuLrtTz9154qkltaXVr\n8iimTAAAACDyNTa36tvPFut4U6suKsjWt68Y43SkM7hcRj+5cZJGZ6dof80J/c3zxWpp7dnikGVH\nGrTw2WK1uq2unTRU911eEKK00YeiAegFcS6j6QXZ+tuZZ+v8kZlqdls9s6Hc6VgAAABAj/3ojzu0\n82CdBqYl6r9unBS2U4Mz+iVo+W1T1C8hTu/uqtKP//xZ0NeqPdGsu5/arNoTzZo0IlMPXz+BHSY6\nQdEA9LK7Z+RJklZuKFdjc6vDaQAAAIDg/eHDA1q5YY+M8axPMLh/eO+oNjYnXY/MnSBJ+uWbJXr1\no4puX6Ol1a2/eX6rSg83KDcjWStun6zkBHaY6AxFQx8zxuQbY5YaYx7wfp7rdCb0rtnn5mhYZj9V\nNzTpd1v3Ox0HAAAACEp5VYMefPkjSdJ9lxfokrMGOZwoMHMmDtW9l3je/Pvuqg/0+aG6bn3/v/3p\nE7312WH1S/DsMMF29V2jaOhDxpiZkpZLesha+4j3z0uNMZnOJkNvio9z6ZsXjZYkPf5Omay1zgYC\nAAAAuulkS6v++rmtqjvZoimjBujvZp7tdKRuWTR7nC7Mz1JDU6sWPLNFxxqbA/q+5zft0ZPv7pYk\n/eSGiRo/LKMXU0YPioa+tUrSImttjffrfEmsEBgDbpw2QqmJcfq8sl5vfX7E6TgAAABAtyx99VN9\ntL9WmSkJ+tlN5ys+LrIeJePjXPrfm4uUm5Gs0iMN+ocXP5Db3fkbgBtKq/Qv3p01/n7W2frKeewg\nF6jI+u2IYMaYBySVWmuLfa9Za9dZawe0KR4QpfonJ+iGqSMkSY+9XepwGgAAACBwa3cc0hPvlkmS\nfjx3ooZm9nM4UXAGpiVp2a2TlRjn0todh/SLN3b5PXdP1XEtXLlFLW6rOROH6m+uDL+dNcIZRUPf\nWSCJJ8wYdudFeXIZ6e3Pj+jTg92bFwYAAAA4YX/NCX131QeSpHtm5Glm4RCHE/XMpBGZ+uG150qS\n/nPtZ3rj08ozzqlr9OwwcfR4syYMz9B/zGWHie6iaOg7+ZJKjTHzvR8PeEc5IEaMzE7Rl8/NkSQ9\n8U6Zw2kAAACAzjW3unX/81tVe6JZE0dk6oHZ45yOFBI3Th2pm6aNlLXSd369TWWHG7S+pEqvbNuv\nd3cd0d88V6zPK+s1pH+SHr19CjtMBCHe6QCxoM1ij/mSlltrS72vP2CMWWWtnedcOvSlu2fk6dXt\nB/Xbbfv1j7PHamBaktORAAAAgA79ZO1n2lJ+VOnJ8frfm85XYnz0vE/9g2sKtaPimD7YW6NZP31T\nLe3Wa4h3GT16+xQNCfPtO8NV9PymtOPdOnJmAOdles/1bTm53BgzP8RxTi346CsZvFZImmuMKQrx\n/RCmJo8aoIkjMtXU4tbKDeVOxwEAAAAkSa1ue+pd/fUlVXp9Z6WWvVEiSXrk+gkakZXicMLQSoqP\n0zemDpekM0oG32sHak70dayoEXUjGrwP7Q9KmitpcxfnZkraImle20UavaXDcmvtglBkstaWeuf0\nbG73eo339ZmSijv4VkQZY4zunpGn+5/fqmfWl+tblxUwFAsAAACOWrO9QktW71BFbeOp11zeJQlu\nnz4qKndbaHVb/ew1/4tBGklLVu/QrMIcxblYn6G7oqZo8I5CmCfPA/taeYqGrqyS9FLbkkGSrLWL\njDFHvdMa1rW5R6ak17oR6yFr7UsBnFfQjWsiwn1lfI6GZiTrQG2jfr/twKndKAAAAIC+tmZ7hRau\nLFb79/R9b/JPGTWgzzP1hU1l1acVK+1ZSRW1jdpUVq3pBdl9FyxKRE3RYK1dIc9UBAUyFcEYky/P\nSAJ/oxZelLRU0uQ296hp+3U3FUvy9xtaEuQ1EYES4ly646LReujVnXrsnVLNmzKcVWwBAADQ51rd\nVktW7zijZGjroVd36qsThkbdu/qVdf5LhmDOw+mido2GAMyVzlgzoa0SSUVtFnLsqeWSTitAvGWH\nJAUy6gFR5BvTRiolMU6fHarXO7uOOB0HAAAAMaird/WlL97VjzaD0wNb5DHQ83C6WC4aZkmq6eS4\nr4CYEoqbeUdc5LcbbbFU0opOyg5EqYx+CbphimfKxGNvs9UlAAAA+l4sv6s/LS9LuRnJ8jdOw0jK\nzUjWtLwsP2egM7FcNGRJ6qya85UQ+Z2c012TJS3wLTYpaXOoFpxE5Lnz4tEyRnrzs8P6/FCd03EA\nAAAQY2L5Xf04l9HiOYWSdEbZ4Pt68ZzCqJsy0leiZo2GIHQ1JcJXQoRq6oRvjYeQFgvHjh1Ta2tr\nl+clJSUpKSkplLdGD43KTtWXCofo/z4+pCfeLdND101wOhIAAABiyLS8LGWlJqq6oanD40ZSThS/\nqz97fK6W3Vp0xo4bORnJWjynULPHR99uG30llouGLH0xPaIzYb3E6NChQwM6b/HixfrBD37Qu2HQ\nbXfPyNf/fXxIvyner+9+aayy0yiDAAAA0De2lB9V/cmWDo/Fyrv6s8fnalZhjjaVVauyrlGD0z3F\nSjT/zH0hlouGkI1UcNKBAweUmpra5XmMZghPU0cP0IThGfpwX62e3bhH9191ltORAAAAEAM2767W\nN5/cpKYWt87JTdfRhiYdPHby1PFYelc/zmXYwjLEYrloqFFgZUNVbwfpif79+wdUNCA8GWN094w8\nfefX2/T0+nItuCxfSfFxTscCAABAFHt/d7W++cQmHW9q1SVnDdSjt09RQpyLd/URMrG8GGRXe7T4\nJiJ1tjMF0GNXn5ernP7JOlJ/Ur/fdsDpOAAAAIhiW8qrdccTm9TQ1KoZYzwlQ3JC3Kl39b82aZim\nF2RTMqBHYrloKFbnO0r4Rjuw9SR6VUKcS9+8eLQk6fF3ymStdTYQAAAAotKW8qO644nNamhq1cVj\nsk+VDECoxXLRsLaL4/mSZK1d1wdZEONumjpS/RLitPNgnd4rCevZOgAAAIhAxXuO6o4nNqn+ZIsu\nKsjWY7dPVb9ESgb0jlguGtZJkjGmyM/xqb5zgN6WkZKgG6YMlyQ99jaDaAAAABA6W/cc1R2Pe0qG\n6fnZevwOSgb0rpgtGqy1pfIUCQv8nDJX0tK+S4RYd+fFeTJGev3Tw9pVWe90HAAAAESBbXtrdPvj\nm1R3skUX5GXp8W9OoWRAr4vWoiGr3Wd/5kma2X5UgzFmlaQVTJtAXxo9MFUzzxkiSXri3TKH0wAA\nACDSfbC3Rrc9vlF1J1s0LS9LT945VSmJsbzxIPpK1BQNxpi5xpi1xpgSfbH+wnJjTIn39bntv8da\nWyNpsqQFxpilxpgHjDHLJa211vob6QD0mrtn5EmSXt6yT9UNTQ6nAQAAQKT6cF+Nbn18o+oaWzRt\ndJae/CYlA/pOUL9pxpj+1tpjoQ7TE9balyS9FMT31cj/9AmgT12Ql6Xxw/pr+/5jem5juf76yrOc\njgQAAIAIs31/rW59zFMyTB09QE/eOVWpSZQM6DvdHtFgjPmlpKPGmCt7IQ8Q04wxp0Y1PLW+XCdb\nWh1OBAAAgEiyfX+tbnlso441tmjKqAF68s5plAzoc8FOnXhU0vuhDALA46vnDdWQ/kk6XHdSf/ig\nwuk4AAAAiBC+kqH2RLMmjxqgX901TWmUDHBAMEVDibX2W4FMnWDUA9B9ifEu3XHRaEnSY++UyVrr\nbCAAAACEvY8P1OrWxz0lQ9HITP3qzqmUDHBMMEVDsTHmngDPXRTE9YGYd/O0keqXEKdPKo5pfWmV\n03EAAAAQxnYcOKZbHtuomuPNOn9kpp66a5rSkxOcjoUY1u2iwVr7mqQyY8xDxph7jDGTjDGjO/qQ\nNCXUgYFYkJmSqLmTh0uSHn+brS4BAADQsU8qjumWxzao5nizJo6gZEB46PZYGmOMW5KVZLwv+RvX\nbTo5BqALd148Ws9sKNdrOytVerhe+YPSnI4EAACAMLLzoGckw9HjzZo4PENP3zVN/SkZEAaCmbRT\nKmmdpFVdnDdA0vIgrg9AUv6gNM08Z7DWfVKpJ94t04+uPc/pSAAAAAgTnx6s082PblR1Q5MmDM/Q\n03dfoIx+lAwID8EUDTWSHrbW7u7qRGPM/CCuD8Drrhl5WvdJpV7ask//MGusBqQmOh0JAAAADvvs\nUJ1ufnSDqhuadN6wDD1zFyUDwkswi0FeFUjJ4DUviOsD8Jqen63C3P5qbHbruU17nI4DAAAQ9Vrd\nVutLqvTKtv1aX1KlVnd4zQb/3FsyVDU0afyw/lp59wXKSKFkQHjp9ogGa21tb5wL4EzGGN1zSZ7+\n/sUP9NR7u3XvJflKjA+mHwQAAEBX1myv0JLVO1RR23jqtdyMZC2eU6jZ43MdTOaxq7JONz26UUfq\nm3TuUEoGhK8ePbEYY6707j7xf8aYzcaYXxhjrghVOADSX00YqsHpSaqsO6k/fnTA6TgAAABRac32\nCi1cWXxaySBJB2sbtXBlsdZsr3Aomceuynp9Y8VGHak/qcLc/nr2nguUmcK0WoSnoIoGY0x/Y8yL\n8iwKuUjSVEmTJX1L0jpjzBpjTP/QxQRiV2K8S3dcNFqS9NjbZbI2vIbvAQAARLpWt9WS1Ts63DLP\n99qS1Tscm0ZRcrheNz26QUfqT+ocSgZEgGBHNLwkz+4TBdZal7U2y/vZJenLkuokvRaqkECsu3na\nSCUnuPTxgWPaWFbtdBwAAICosqms+oyRDG1ZSRW1jdrkwP8PKz1cr5tWbNDhupMal5OuZ++5gAXC\nEfa6vUaDMeYeScuttS93dNxau06eUQ3XG2O+a639cU9DArFuQGqiri8armc37tFjb5fpwvxspyMB\nAABEjco6/yVDW4te/lCTRmRqdHaKRmanalR2ikZlpWhQepKMMT3O0eq22lRWrcq6Rg1OT9ag9CTd\n8tgGVXpLhufuvVBZlAyIAMFsbznAWvtYVydZa182xjwcxPUBdOCuGXl6duMevbbzkMqONChvYKrT\nkQAAAKLC4PTkgM7bU31ce6qPn/F6v4Q4jcpO0cisFM/n7FSN8v55WGY/xcd1PZC8o4UoXUZyW2ns\nEM9IBkoGRIpgioaabpxbFcT1AXSgYFCarhw3WH/ZWakn3y3Tv35tvNORAAAAosK0vCzlZCTroJ/p\nE0ZSdlqilsw5V3trTqi86rj2VDdo95Hjqqg9oRPNrdp5sE47D9ad8b3xLqNhA/qdKiFGZXlHQmSn\namRWivolxp1aiLL9ChC+JSHuviRP2WlJof2hgV4UTNHQnRVQWLUOCKF7ZuTpLzsrter9ffr7WWez\nCBAAAEAIxLmMrh6foyfe3X3GMd+EiB9dO77DLS6bWtzad/S4yquPa0/Vce2uatCeKu/X1cfV1OJW\nedVxlVcd19ufn3nvQWmJqjnR3OmD00/Xfqbri4YrztXz6RlAXwimaBhjjOlvrT3W2UnGmNGSxgQT\nCkDHphdka1xOunYerNPzm/Zq4eUFTkcCAACIeFX1J/XbrfslSWlJ8ao/2XLqWE5GshbPKeywZJA8\nO4TlD0pT/qC0M4653VaH6hq1+4hnBER51emFRF1jiw7XN3WZz7cQ5fQC1ulCZAimaHhI0mvGmLnW\n2vKOTjDGTJK0StKsnoQDcDpjjO65JF/fXfWBnnpvt+65JE8JAcz5AwAAgH9LVu/Q0ePNGpeTrt/e\nd7G27a05tSDjtLysoEcSuFxGuRn9lJvR74ySwFqrmuPNemZDuX6y9rMurxXogpVAOOh20WCtrTXG\nPCipzBizRdL7+mLdhkxJMyXlS7rBWrs7VEEBeMyZmKuHX92pg8ca9aePKvS1ScOcjgQAABCx1u04\npN9/cEAuIz0yd4L6Jcb1ycgBY4wGpCZq6uisgM4PdMFKIBwE9VaodwvLMZJ2S1ogaZH3Y4GkMklj\n/G1/CaBnkuLjdMf0UZKkx94uk7UshQIAABCMY43N+v7vPpIk3XtpviYMz+zzDNPyspSbkSx/YyaM\npNwMz8gKIFIEPebaWltqrZ1nrXVJKpA02VrrstZ+yVpbFrqIANq75cJRSop36aP9tdq8+6jTcQAA\nACLSQ3/aqUPHTmp0dor+bubZjmSIcxktnlMoSWeUDb6vF88pZCFIRJSgigZjTP+2X1try6y1W0MT\nCUBXslITdV3RcEnSY2+XOpwGAAAg8rxXckTPb9ojSXr4+glKTohzLMvs8bladmuRcjJOnx6Rk5Gs\nZbcW+V2IEghX3V6jwRjzS0n3GmNmWWv/0guZAATg7hmj9fymPVr7ySHtPtKg0QNTnY4EAAAQEU40\ntep7L3umTNxywUhdmO/8bg6zx+dqVmGONpVVh2QhSsBJwU6deFSeRSABOGTM4HRdPnaQrJV+9d5u\np+MAAABEjJ+s/VR7qo8rNyNZ3/vKOKfjnBLnMppekK2vTRqm6QXZlAyIWMEUDSXW2m9Za491daIx\n5sogrg8gQPfMyJckvfj+XtWeaHY4DQAAQPjbtrdGj7/jWVLu374+XunJCQ4nAqJPMEVDsTHmngDP\nXRTE9QEE6OIx2RqXk67jTa36tXeOIQAAADrW1OLWopc+lNtK104aqivHDXE6EhCVul00WGtfk1Rm\njHnIGHOPMWaSMWZ0Rx+SpoQ6MIAvGGN014w8SZ7pE82tbocTAQAAhK9fvLFLnx6qU3Zqov7fnHOd\njgNErWAWg3RLsvpitxXr79ROjgEIkWsmDtUja3aqorZRr24/qGsmDnU6EgAAQNj59GCdfv76LknS\nD645V1mpiQ4nAqJXt4sGSaWS1kla1cV5AyQtD+L6ALohOSFOt104Wj9d95kee7tUcybkyhgWDgIA\nAPBpdVs98PKHam61mnnOEP3VBLaLBHpTMEVDjaSHrbW7uzrRGDM/iOsD6KZbLhypn7+xSx/uq9X7\n5Uc1dXSW05EAAADCxpPvlumDvTVKT4rXj64dz5syQC8LZjHIqwIpGbzmBXF9AN00MC1J150/TJL0\n+NtlDqcBAAAIH+VVDfrxnz+VJH3/q+coJyPZ4URA9AtmMchaY0z/QM/tfiQAwfAtCrnm44N6Zet+\nvbJtv9aXVKnVzVIpAAAgNllr9b2XP1Jjs1vT87N149QRTkcCYkIwi0H+UtK9xphZ1tq/9EImAEE4\ne0i6CnP7a0fFMX3nhW2nXs/NSNbiOYWaPZ65iAAAILa8sHmv1pdWKTnBpYevP48pE0AfCWbqhCQ9\nKun9UAYB0DNrtldoR8WxM14/WNuohSuLtWZ7hQOpAAAAnHGwtlH/9sdPJEnf/dJYjcpOdTgREDuC\nKRpKrLXfstae+UTTjjHmyiCuD6CbWt1WS1bv6PCYb+LEktU7mEYBAABigrVW//y7j1R3skUTR2Tq\nzovznI4ExJRgioZiY8w9AZ67KIjrA+imTWXVqqht9HvcSqqobdSmsuq+CwUAAOCQP3xYoXWfVCoh\nzuiR6ycozsWUCaAvdXuNBmvta8aYq4wxD0kqkWcKRY2f06f0JByAwFTW+S8ZgjkPAAAgUlU3NOkH\nv/9YkvTtK8ZobE66w4mA2BPMYpBued4g9dWC/sZim06OAQihwemBbdMU6HkAAACR6l9Xf6yqhiaN\nHZKu+y4f43QcICZ1u2iQVCppnaRVXZw3QNLyIK4PoJum5WUpNyNZB2sbO2z3jKScjGRNy8vq62gA\nAAB95i87D+l32w7IZaSlcycoMT7Yte8B9EQwRUONpIettbu7OtEYMz+I6wPopjiX0eI5hVq4stjv\nUKLFcwqZnwgAAKJWXWOzvv/b7ZKku2fkadKITIcTAbErmIrvqkBKBq95QVwfQBBmj8/VsluLlJNx\n+vQII+m/vjFJs8fnOhMMAACgDzz86k5V1DZqVHaK/n7WWKfjADEtmMUga31/NsZcJylfUo219jHv\na3mSMqy129qeC6D3zR6fq1mFOdpUVq1Dxxr10Kuf6NCxkzre1Op0NAAAgF6zobRKz27cI0l66Lrz\n1C8xzuFEQGwLatKSMeZKY0y1pJckPSJplu+YtbZMUoEx5ruhiQigO+JcRtMLsnXt+cN0z4x8SdIz\n68tlLWuzAgCA6NPY3KrvvfyhJOmmaSN1UcFAhxMB6HbRYIw5X9IKSQ9JKrDWuuRZHPIUa+3Lkl7z\njngA4JB5U4YrKd6lHRXHVLznqNNxAAAAQu6n6z7T7qrjyumfrAevHud0HAAKbkTDfEmzrLX/4R29\nIHWw9py1dqsklrgHHJSZkqhrJg6VJD29vtzhNAAAAKH14b4aPfpWqSTpR9eOV//kBIcTAZCCKxpK\n2xQMXWGpV8Bht08fLUn600cVOlx30tkwAAAAIdLU4tYDL30ot5WumThUMwuHOB0JgFcwRUN3xl8X\nBHF9ACF03vAMTRqRqeZWqxff3+t0HAAAgJBY/maJdh6sU1ZqohbPKXQ6DoA2gikaxhhj+rd7zbQ/\nyRgzqaPXAfS92y4cJUl6dkO5WlrdDqcBAADomc8P1el//rJLkrR4TqGy05IcTgSgrWCKhhfkWehx\nYpvXTlujwRhzlaTXJD3cg2wAQuSrE3KVlZqoA7WNem1npdNxAAAAgtbqtnrg5Q/V1OrWVeMGn1qP\nCkD46HbR4F3k8VFJW40xnxtjXpA0zxjzkDFmmTFms6Q/S5pvrd0d2rgAgpGcEKcbpoyQJK3cwKKQ\nAAAgcj313m5t3VOj9KR4/ejr42UMg6iBcBPMiAZZa1dImiJpt6R5kmZJWiRpgTxrOIzxbnEJIEzc\ncsFIGSO9/fkRlR6udzoOAABAt+2tPq7/+L9PJUkPXn2OcjP6OZwIQEeCKhokyVpbbK2dZa11SZos\nqcBa67LWfqkbu1IA6CMjslJ05djBkqRnGNUAAAAijLVWD/7mI51obtWF+Vn6xtQRTkcC4EfQRUNb\n1tqtlAtA+LttumdRyJe27NPxphaH0wAAAARu1fv79M6uI0qKd+nh6ybI5WLKBBCuQlI0AIgMl541\nSKOyU1TX2KJXth1wOg4AAEBADh1r1A//uEOS9A9fOlujB6Y6nAhAZygagBjichndeoFnVMPT68tl\nre3iOwAAAJxlrdW//G676hpbNHF4hu66OM/pSAC6QNEAxJh5U4YrKd6lTyqOaUv5UafjAAAAdOpP\nHx3Un3ccUrzLaOncCYqP4xEGCHf8WwrEmMyURH1tkme/aRaFBAAA4ajVbbW+pErPbSzXg7/5UJJ0\n3xVjNC6nv8PJAAQi3ukAAPre7dNH68X39+lPH1Xon79aqEHpSU5HAgAAkCSt2V6hJat3qKK28dRr\n8S6jswazLgMQKRjRAMSg8cMyNGlEpppbrV7YvMfpOAAAAJI8JcPClcWnlQyS1OK2uv/5bVqzvcKh\nZAC6o8OiwRiTZ4x5yBjD2CQgSt3u3ery2Y171NLqdjgNAACIda1uqyWrd6izpaqXrN6hVjeLWQPh\nzt+IhkXejxvaHzDGXNmriQD0iavPy1VWaqIqahv12s5Kp+MAAIAYt6ms+oyRDG1ZSRW1jdpUVt13\noQAExV/RUCKpwFr7WAfHFgV6cWPMdUGlAtDrkhPidMOUEZKkZ9azKCQAAHDWgZrjAZ1XWee/jAAQ\nHvwVDQXW2jI/x0w3rr+gm3kA9KFbLhgpY6R3dh1RyeF6p+MAAIAY9cHeGv1k7WcBnTs4PbmX0wDo\nKX+7TrxkjPlc0sOStkiqaXNsgDFmorouHLIkTel5RAC9ZURWiq4aN1jrPqnUyg3lWjznXKcjAQCA\nGHKypVU/e+1z/fLNUrW6rVxG8rcEg5GUk5GsaXlZfZoRQPd1WDRYa9cZYx6UtEJSpnTGmizFAVzb\ndPB9AMLMbdNHa90nlXppyz7945fHKiWRXW/x/9m78/ioq3v/4+8zWSErCYSEsG9KCIsJoNjFDRQX\npLXgitrbRYq9v9v21qv1bpTe3lprb9vb64a1t1WxLkCrF620gNqqRRMSEJAdwh4IJGSFbDPn98dM\nkCXrZCbfzMzr+XjMIzczZ77fN94+snzyOZ8DAEDwbTpUqQeWfaydx7xdlbMnDdLnx/TXg8s3STr3\nF4mWv3Aump2jKFdXGqwBOKHN3yistcvl7WxIkTTS97SRt/jw9U5c20ha3e2EAILqc6P7a3h6X+0r\nP6XXNhzRnZcOdToSAAAIY+d3MfRPjNUPv5CrWblZkqSk+GgtXrn1nMGQmSnxWjQ758waAL2bsbZr\nTQfGmD9ba68N9Fp0njEmQVKtJNXW1iohIcHhRAh1z763Vz98c5suzkzSW9/6nIzhLwUAACDwNh+q\n0gPLPtaOYzWSpJsmZukHc3KVlhB7zjq3x6qgpEJlNfXKSPJul6CTAXBWXV2dEhMTWz5NtNbWtbXW\nn0XIHVcAACAASURBVELDNdbatd3Ih26i0IBAqzrVpEsfWaP6Jo+Wf2O6pgxn7yMAAAicxmaP/uft\nXXry3T1ye6zSE7xdDNdPoEMBCBVdKTS0depEmygyAOEnpW+M5kzKliQ9z1GXAAAggLYcrtLNj7+v\n/3l7t9weqxsnZunP3/k8RQYgjHVr6psx5mpJMyXlyXvKRKGkZdbadwKQDUAPunv6ML2y/qDe2lKq\n4zU5GpAU53QkAAAQwhqbPXr87V16wtfFkObrYriBAgMQ9vwqNBhjkiU9K2mu76lKeU+nyJe0wBiz\nWtKt1trqgKQME8aYkZIWSCqXlC6p3Fr7E2dTAV652Sm6ZGiqNhyo1CuFB/T3V49xOhIAAAhRWw57\nZzFsP+qdxXDjhCz9YM54pSfyhwwgEnR564TPckl7JY2y1rqstWm+jy5J10mqkcQWi7MYY1IlLbDW\nPmSt/Ym19iFJxcaYJU5nA1rcM32YJOnFjw6o2e1xOA0AAAg1jc0e/Wz1Tn3hiQ+0/WiN0hJi9cSd\neXrirjyKDEAE8WcY5NcknbTWruhg3ZckjbDW/rQb+cKGMeZRSUustXvPe77IWpvfxWsxDBJBUd/k\n1uU/flsVdY16en6+ZuVmOh0JAACEiE+OVOmBZZu0rdTb1HzDhEz9YE6u+lNgAMJCUIdBSurXUZFB\nknxr+vtx/XA1UtKMVp6v6OkgQFviY6J029QhkqQXPtznbBgAABASGps9+vnqnZrz+AfaVlqtfn1j\n9Pidl+jJu/IpMgARyp9CQ2UX1pb7cf1wVShpiTGmZa6FjDF56tp/TyDo7rp0qFxG+mB3uXaX1Tod\nBwAA9GJbj1RrzhMf6L/X7lKzx+r63Eyt/scrdNPEQU5HA+AgfwoNXdlr0bV9GWHMN/SxWNIyY8wy\nY8wMSbdZa+c5HA04x+B+fXX1xQMlSUs/5KhLAABwoSa3R79Ys1M3P/7+mS6GX95xiZ68K48uBgB+\nFRpG+06daJcxZrik0X5cP2z5ZjGskfe0jtWSXnE2EdC6u31DIVcUHVJdQ7PDaQAAQG+y9Ui15jz+\ngX6xxtvFcN34gfrzd67QzZMGyRjjdDwAvYA/x1s+ImmtMWautbbVP3caYyZLWiZpZnfCdYdv+OJq\na+2aDtalSnrY92m5pFGSiqy1zwQp0zLfY4mkImPMgmDcC+iOz43ur+HpfbWv/JRe33hEd1461OlI\nAACgB7k9VgUlFSqrqVdGUrymjUiTx1o9+c4e/c/b3gJDat8Y/WBOrmZPzKLAAOAcXS40WGurjDEP\nSyoxxhRJWq9P5wykyjvwcKSkW621+wIVtLN8cw8elrdroLCDtamSiiTNs9YWn/X8o8aYJdbaBQHM\n9aikPS1FBWPMGvkKDsaY9WffH3Cay2U0/7Jh+uGb2/T8un26Y9oQfoAAACBCrNpSqsUrt6q0qv7M\nc/0TY9UnJkoHT56WJF03fqB++IUJGpDENgkAF/Kno0HW2jXGmNGSHpV0/i/jayRda60t6W64rjDG\n3CdpnrxzEFbLW2joyDJJy8//Jd9a+5Ax5qQxZtnZHRG+wsTaLsR6xFq73Pd/z7XWjjrrHnsl5fuK\nNbf5cgO9xrz8Ifrpn3do+9Eard9/UlOHpzkdCQAABNmqLaVauLT4gkFrJ2obJUl9Y6P0yC0T2CYB\noF1+FRqkM78oz5MkY8wISanW2g2BCuZHnmcktXQL5HW03hjTctxkW10Lr8pbSMk/6x6VZ3/eWb57\n7W3j5UckTe3qNYFgS+kbozmTsvXK+oN6Yd1+Cg0AAIQ5t8dq8cqt7U5zT4qP1k0TKTIAaJ8/wyAv\nYK0tcbLI4Ke50pmCSWv2SMrzdTF0i+8eI9t4OU0dbPEAnNIyFPKtLaU6XtPgcBoAABBMBSUV52yX\naM2x6gYVlFT0UCIAoSoghYYQNVOfzpZoTUsBYkqA7rfEN6fhDF+nw8yztlcAvUpudoryhqaqyW31\ncsEBp+MAAIAgKqtpv8jQ1XUAIpffWyfCQJqk9sqxLUWItjoRusRa+xNjzFxjzJKzrl1urZ3XnetW\nV1fL7XZ3uC4uLk5xcQzrQdfdPX2Yig9U6ncFB7TwylGKjork+iQAAOErPSG2U+sykuKDnARAqIvk\nQkNHWyJaihDd3jrRwte5ENDuhUGDBnVq3aJFi/T9738/kLdGhLhhQpZ++MY2lVbVa822Ms3KzXQ6\nEgAACLCq0016+i972l1jJGWmeI+6BID2RHKhIU1tD2g8W3qwg3THkSNHlJCQ0OE6uhngr7joKN02\ndYiefHePXvhwH4UGAADCzIHyU/rKc4XaXVar2CiXGt0eGemcoZAtox8Xzc5RlItBkADaF8mFhoB1\nKjgpOTm5U4UGoDvuvHSonv7LHn2wu1y7y2o1OiPR6UgAACAA1u+r0H0vFKmirlGZyfF69t4pOnTy\nlBav3HrOYMjMlHgtmp2jWblZDqYFECoiudBQqc4VG8qDHQTo7Qb366urLx6oNduOaemH+/X9m8c7\nHQkAAHTTaxsO68Hlm9To9ig3O1nP3jNVmSnxys1O0cycTBWUVKispl4ZSd7tEnQyAOisSJ7q1tG5\nPC2bz9o7mQKIGPf4jrpcUXRIdQ3NDqcBAAD+stbqZ6t36tuvbFSj26Nrcwbq1QXTlZny6ZDHKJfR\n9FHpmjM5W9NHpVNkANAlQS00GGNuCeb1u6lY7Z8o0dLt0Jk5DkDY++zo/hrRP0E1Dc16beNhp+MA\nAAA/1De59Q8vb9Qv1+6SJC24YqSenp+vvrGR3OgMINCC3dHwcJCv3x2rO3h9pCRZa9f0QBag13O5\njO66dKgk6YV1+2Wt7eAdAACgNzlR26A7f/WhVn58RNEuox/fMkEPXz9OLroVAASYX6VLY0yypPvk\nPZGhvTkHef5cv4eskSRjTJ61triV16e2rAHgNS9/iH765x3afrRG6/ef1NThHG8FAEAo2HmsRl/5\nbaEOnTyt5PhoPT0/X5eP7u90LABhqsuFBmPMJZKKfJ+G7PwCa+1eY8waSQt8j/PNlTSzZ1MBvVtK\n3xh9YXK2Xi48qOfX7afQAABACPjLzuP6+xeLVdPQrGHpffW/X56qUQM4QQpA8PizdeJhSfOstS5r\nbVp7D0klAc7bWWnnfWzLPEkzjDHndF4YY5ZJeoZtE8CF7vYNhVy1pVRlNfUdrAYAAE56Yd0+feW3\nhappaNa0EWl67f7PUGQAEHT+FBr2WmtXdHLtcj+u7xdjzFxjzGpjzB59On9hiTFmj+/5uee/x1pb\nKSlf0gJjzKPGmAeNMUskrbbWttblAES88YNSlDc0VU1uq1cKDjodBwAAtMLtsfr+/32if3v9E7k9\nVl/KG6wXvjpN/RJinY4GIAL4M6PhRGcXWmu/58f1/WKtXS4/Chu+YgNFBaAL7pk+XMUHNup3BQe0\n8MpRio6K5JNyAQDoXWobmvUPL23Q29vLJEn/dN1Fuv/KUTKGoY8AeoY/vx10+iuUMWayH9cH0Mtd\nPyFT6QmxKq2q15ptx5yOAwAAfA5Xntbcp/6mt7eXKS7apSfuzNM3rxpNkQFAj/Kn0PCMMeaffCdP\ndORRP64PoJeLi47SbVOHSJKeX7ff4TQAAECSNh6s1JzHP9D2ozXqnxinVxZM140Ts5yOBSACdXnr\nhLW2yhjzjKRfGWMqJO1R66dPpEqa0c18AHqpuy4bpqf/skd/21Ou3WU1Gp2R5HQkAAAi1h83l+o7\nr2xUQ7NHF2cm6ddfnqrs1D5OxwIQofw53nKEvMdbpnZiue1yIgAhITu1j64ZN1Crtx7T0g8P6Ps3\nj3c6EgAAEcdaqyff3aPH/rRDknT1xRn65R2XKDHOn1FsABAY/mydWCLpEUmjJPXzHXN5wUPeoyWd\nOt4SQA+4x3fU5YqiQ6praHY4DQAAkaWh2a0Hlm06U2T4u88M16/umUKRAYDj/D3e8jFrbYm1tqqt\nRb7THIr9jwagt/vMqP4a0T9BNQ3Nem3jYafjAAAQMU7WNeruZwu0oviQolxG//GFXC2aPV5RLoY+\nAnCeP4WG9Z1daK291Y/rAwgRLpfR/Mu8XQ0vrNsva9ktBQBAsO05XqsvPvmBCvZVKCkuWv/75am6\n2/f9GAB6A38KDf06u7CTJ1MACGFz8wcrPsal7UdrVLjvpNNxAAAIG26P1bo95Xp942Gt21Mut8fq\nb3tO6ItPfKB95ac0uF8frbj/cl0xdoDTUQHgHP5s4FpujHnAWvvTTqxdJuk6P+4BIESk9InRFyZn\n6+XCg3p+3T5NG5HmdCQAAELeqi2lWrxyq0qr6s88l9InRjX1TfJYKW9oqp65Z4r6J8Y5mBIAWudP\nocFK2mCMeUVSgaQNkipaWZcmaUo3sgEIEXdPH6aXCw9q1ZajKqupV0ZSvNORAAAIWau2lGrh0uIL\njm+rOt0kSZoyrJ+Wfu1SxcdE9Xw4AOgEfwoNe+UtNhhJ83zPtbYx27TxPIAwM35QivKH9VPR/pN6\nbNUOfXZMf2UkxWvaiDSGUgEA0AVuj9XilVvb/SH6cOVpxUT5swMaAHqGv4WG5ZJe6WBdeifWAAgT\nkwanqGj/SS0rOqRlRYckSVkp8Vo0O0ezcrMcTgcAQO/X2OzR6xsPn7NdojWlVfUqKKnQ9FHpPZQM\nALrGn0JDpaQfWWurO1pojCny4/oAQsyqLaX6zQf7Lnj+aFW9Fi4t1lPz8yg2AABCkttjVVBScWZr\nYCC69U41NmtPWZ12H6/RrmO12l1Wq93Ha7W//JTcns41BJfVtF+MAAAn+VNouKYzRQafeR0vARDK\n2mvxbNljtXjlVs3MyWQbBQAgpLQ2kLEr3Xon6xq1+7ivkHDW43Dl6TbfEx/jUn2Tp8NrMw8JQG/W\n5UKDtbbKGJPcmWKDtbbKv1gAQkVBSUW7LZ5WtHgCAEJPWwMZz+/Ws9bqWHWDr4hQo12+YsKe47U6\nUdvY5vXTE2I1OiPxgseAxDh97ifv6GhVfZtD0DJT4jnlCUCv1uVCgzHmaUlfN8bMtNa+HYRMAEJI\nZ1s3afEEAISKjrr1JOk7r3ysp97do73H61TT0NzmtbJT+2hURqJGD0jUmIG+gsKARPVLiG3zPYtm\n52jh0uILJqubs16nSxBAb+bP1glJ+pWk9YEMAiA0dbZ1kxZPAECo6KhbT5JON7n18SFv826Uy2hY\nel+NHvBpZ8KYjCSNHJCghLiu/7g9KzdLT83Pu2DbRiZDlgGECH8KDXustY91ZqEx5mq6HoDwNm1E\nmrJS4mnxBACEjc524f3dZ4brjmlDNTw9QbHRgT1uclZulmbmZAZ8ECUA9AR/viIWG2O+1sm1D/lx\nfQAhJMpltGh2jqRPWzrPR4snACCUdLYL79qcTI0dmBTwIkOLKJfR9FHpmjM5W9NHpfO9FEDI6PJX\nRWvtWkklxphHjDFfM8ZMNsYMb+0haUqgAwPofVpaPDNTLvzB7AdzxtPiCQAIKVOG9VN8O8UDI+/p\nE3TrAUDr/BkG6dGnp9ZJarVbWr7XO3cQMICQd36L56/fL9GmQ1Ud7nEFAKC3+e+1u1Tf3PoRkwxk\nBICO+TOjYa+kNZKWdbCun6QlflwfQIhqafGUpNgolxa+WKxlRYf0nZljFRMVnLZSAAAC6bUNh/X4\nO7slSfdOH6Y/bz3GQEYA6CJ/Cg2Vkn5srd3X0UJjzH1+XB9AGLhm3ED1T4zV8ZoGvbO9TNeOz3Q6\nEgAA7Sraf1IPrtgkSfrGFaP0vesv1r/PHs9ARgDoIn/+xHhNZ4oMPvP8uD6AMBAb7dKX8gdLkl4u\nPOhwGgAA2nfo5CkteGG9Gps9ujZnoB687iJJDGQEAH/4MwyyKhhrAYSf26cOlSS9u6NMpVWnHU4D\nAEDrahua9dXfrteJ2kaNy0rWz2+bLBcFBQDwW7c2TRtjrvadPvEnY0yhMeZJY8xVgQoHILSN6J+g\nS0ekyWOlVwsPOR0HAIALuD1W33ppg3Ycq9GApDj9+t4pSojzZ3cxAKCFX4UGY0yyMeZVeYdCPiRp\nqqR8Sd+QtMYYs8oYkxy4mABC1R3TvF0Nr64/KLeHg2gAAL3Lj9/aprXbyxQX7dKv7pmiQal9nI4E\nACHP346G5fKePjHKWuuy1qb5ProkXSepRtLaQIUEELpm5WYqpU+MDlee1nu7jjsdBwCAM14pPKBf\nvVciSXps3iRNHpLqcCIACA9dLjQYY74maYm19nvW2pLzX7fWrrHWzpP0Y2PMA4EICSB0xcdE6YuX\nZEuSXi5gKCQAoHdYt6dc//KHLZKkb10zRjdPGuRwIgAIH/50NPSz1q7oaJFvTX8/rg8gzLRsn1iz\n7ZiO1zQ4nAYAEOn2najTwheL1Oyxumlilr49Y4zTkQAgrPhTaKjswtpyP64PIMxclJmkS4amqtlj\ntbyIoZAAAOdUnW7SV58rVOWpJk0anKKfzpskYzhhAgACyZ9CQ1emuTH5DYAk6Q7fUZevFB6QtXxp\nAAD0vGa3R3//u2LtOV6nrJR4/eqeKYqPiXI6FgCEHX8KDaM7c6KEMWa4pNF+XB9AGLppUpYS46K1\nr/yU1u2l2QkA0PN+8MZWvbfrhPrEROlX90xRRnK805EAICz5U2h4RNJaY8ywthYYYyZLWi3px/4G\nAxBe+sZG6+bJ3kFbrxQyFBIA0LOeX7dPz6/bL0n6+W2TlZud4mwgAAhj0V19g7W2yhjzsKQSY0yR\npPX6dG5DqqQZkkZKutVauy9QQQGEvjumDtXvPjqgt7Yc1eJTjUrtG+t0JABABPjrzuNavHKrJOnB\nWRdpVm6mw4kAILz509Ega+0aebdF7JO0QNJDvscCSSWSRnfmZAoAkSU3O1k5WclqbPbo98WHnY4D\nAIgAu8tq9c3fFcvtsbolL1sLrxjldCQACHt+FRokyVq711o7z1rrkjRKUr611mWtvdZaWxK4iADC\nhTFGd0wbIkl6maGQAIAgO1nXqK8+V6ia+mZNGdZPj9wygRMmAKAH+F1oOJu1tsRau+H8532zGgDg\njDmXZCs+xqWdx2pVfKArp+UCANB5jc0efWNpkfaXn9Lgfn205O58xUVzwgQA9ISAFBra8WiQrw8g\nxCTHx+jGCd6hkC8XHHA4DQAgHFlr9W+vbdFHJRVKjIvWr++dqvTEOKdjAUDE6PIwyBbGmKvlHfrY\nlpbBkABwjjumDdGK4kN6Y1Op/n12jpLiY5yOBAAII8++V6JX1h+Uy0j/c8cluigzyelIABBRulxo\nMMakSCpS+0WGFmzABnCB/GH9NDojUbvLavX6xiOaf1mbp+UCANAla7cd04/e2iZJ+pcbc3TVxRkO\nJwKAyOPP1olfSVoi7wDIfr4BkBc8JKXJewIFAJzDGKPbp346FBIAgEDYVlqtf3hpg6yV7pg2VF/5\nzHCnIwFARPKn0LDXWvuYbwBkVVuLrLWVkor9jwYgnN2SN1ixUS5tOVytLYfb/FICAECnHK9p0Nee\nW6+6Rremj0zXD+aM54QJAHCIP4WG3Z1daK291Y/rA4gAaQmxui43UxJdDQCA7qlvcmvBC+t1uPK0\nRvRP0FPz8xQTFeyZ5wCAtvjzFbhfZxcaY5L9uD6ACHGHb/vE6xuO6FRjs8NpAAChyFqr763YpOID\nlUqOj9az905Rat9Yp2MBQETzp9Cw3BjzQCfXLvPj+gAixGUj0zU0ra9qGpr15qZSp+MAAELQE+/s\n1msbjyjKZfTkXfkaNSDR6UgAEPH8Od7SStpgjHlFUoGkDZIqWlmXJmlKN7IBCHMul9FtU4fosT/t\n0MuFBzVvyhCnIwEAWuH2WBWUVKispl4ZSfGaNiJNUS7n5x+8tblUP/3zTknS4pvH67Nj+jucCAAg\n+Vdo2CtvscFImud7rrVjLE0bzwPAGfPyB+tnq3eqaP9J7TxWo7EDOescAHqTVVtKtXjlVpVW1Z95\nLislXotm52hWbpZjuTYfqtJ3Xt0oSfry5cM5KhkAehG/Tp2Q9Jik/LMeU1p5XCupMjAxAYSrjOR4\nXeM74/zlgoMOpwEAnG3VllItXFp8TpFBko5W1Wvh0mKt2uLMtrejVfX62vOFqm/y6PNjB+hfbxzn\nSA4AQOv8KTRUSvqRtXZDB481kooCnBdAGLpj2lBJ0u83HFJ9k9vhNAAAybtdYvHKra22p7Y8t3jl\nVrk9PdvAerrRra8/v17Hqhs0JiNRj995iaI5YQIAehV/tk5cY62t7uTaeR0vARDpPj92gAalxOtI\nVb3+9MlRzZmc7XQkAIh4BSUVF3QynM1KKq2q1y1PfaAJ2Ska3K+vBvfrc+ZjekKsjOn+HIez50MM\nSIzTCx/u0+bDVUpLiNWv752q5PiYbt8DABBYXS40WGurgrEWQOSKchnNmzJE/712l14uOEihAQB6\ngbKatosMZ/v4YJU+Pnjhj3zxMa6zig99/CpEtDYfQpKiXNLT8/M1NL1v5/9BAIAe409HAwAE3K1T\nh+iXb+/Sur3l2neiTsP7JzgdCQAiWkZSfKfWff1zIxQXHaVDJ0/p0MnTOnTytI7V1Ku+yaPdZbXa\nXVbb6vs6KkQUllTo/heLW9264fZIFXUN3fjXAQCCiUIDgF4hO7WPrhg7QO/uOK6XCw/qe9df7HQk\nAIho00akKSslvs3tE0ZSZkq8vnf9uAuOumxodqu0st5XeDh13sfOFSLaY+SdDzEzJ7NXHLMJADgX\nhQYAvcbtU4fq3R3HtbzokL577VjFMNwLABwT5TJaNDtH31hafMFrLb/aL5qd0+ov+nHRURreP6HN\n7rSOChFHq9vfttEyH6KgpELTR6V39Z8GAAgyCg0Aeo1rxmWof2KcTtQ2aO22Ms3KzXQ6EgBEtMH9\nWp+BkJkSr0WzczQrN8uv63ZUiFhRdFDfXbapw+t0do4EAKBnUWgA0GvERLk0N3+wnv7LHr1ceIBC\nAwA47Pl1+yRJsydm6c5Lh6mspl4ZSfGaNiItqFsWBqV2bshjZ+dIAAB6Fn3JAHqV26cOkST9Zedx\nHa487XAaAIhcJ+sa9frGI5Kkey8frumj0jVncramj0oP+lyElvkQbd3FSMpK8RY8AAC9D4UGAL3K\n8P4Jmj4yXdZKrxYedDoOAESsZUUH1dDs0bisZOUP69ej926ZDyHpgmJDR/MhAADOo9AAoNe5fZq3\nq2HZ+oNye1o72AwAEEwej9XSDw9Iku6dPkzG9Pwv9LNys/TU/Dxlppy7PSIzJV5Pzc/zez4EACD4\nmNEAoNe5bnymUvvG6EhVvf6687iuujjD6UgAEFH+svO4DlScUnJ8tOZMznYsx6zcLM3MyVRBSUWP\nzYcAAHQfHQ0Aep34mCjdcslgSdJLBQccTgMAkadlCOS8KUPUJzbK0SxRLtOj8yEAAN3Xo4UGY8wD\nPXk/AKHrDt/2ibXby1TWwXnqAIDA2V9ep3d3Hpckzb9smMNpAAChqKc7Gqb28P0AhKgxA5OUP6yf\n3B6rZUWHnI4DABFj6Yf7Za30+bEDNKJ/gtNxAAAhyO8ZDcaYH0vqypS2VElz/b0fgMhz+9QhKtp/\nUq+uP6iFV4ySi3ZZAAiq041uvbreW9y9dzrdDAAA/3RnGOSrktZIKpdU1Yn1qd24F4AIdOPELP1g\n5VbtLz+lD/eW6/LR/Z2OBABhbeXHR1R1ukmD+/XRlRcxiBcA4B+/Cw3W2mJjzAxJ86y1D3fmPcaY\nV/29H4DI0zc2WjdPHqQXPzqglwoPUmgAgCCy1uq5dfskeWczMHQRAOCvbs1osNYWSxrVhbfs7c79\nAESeO6YNlST9actRVdQ1OpwGAMJX8YFKfXKkWrHRLt06ZYjTcQAAISwQwyAf6sLaRwJwPwARJDc7\nRbnZyWp0e/T7YoZCAkCwvLBunyRp9sRBSkuIdTQLACC0dbvQYK0t6cLazsxyAIBz3D7V29XwcuFB\nWduVGbQAgM44UdugP24+Kkm693KGQAIAuicgx1saY64OxHVCnTEmzxjzaBuvjTTGLDHGPGiMuc8Y\nc19P5wNC1ZzJg9QnJkq7y2pVtP+k03EAIOy8UnhQjW6PJg1J1cTBzO8GAHRPQAoNkvoZY141xjxl\njJkcoGuGFGNMnqS1bbyWKmm1pIestT+x1j4jKZ9iA9A5SfExumliliTppYKDDqcBgPDS7PZo6Yf7\nJUn3XEY3AwCg+wJSaLDWrrDW3irpGUnPGmN2GWN+ZIwZHojr92a+ToVlkm6TVNHGsoclrbHWVp71\n3KO+B4BOuN03FPLNzd6j1wAAgbFmW5lKq+qVlhCrG31FXQAAuiNQHQ2SJGvtBmvtFElvS/qepN2B\nvH5vZK3da62dZ619SFJlG8vmSio6/32SUn2dEAA6kDc0VWMHJqq+yaP/23jY6TgAEDZe+HCfJOm2\nqUMUHxPlbBgAQFhotdBgjOnW6RDW2gXybiPgAGavkWr9aM9KSTN6OAsQkowxZ4ZCvlTAUEgACITd\nZbX6YHe5XEa669KhTscBAISJtjoa5gbg2l059jJs+eYztKVCUnpPZQFC3RcvyVZslEtbS6u15XC1\n03EAIOS1zGa4+uKBGtyvr8NpAADhoq1Cw8juXthaWyw6GiQprYPXGe0MdFK/hFjNys2UJL1UeMDh\nNAAQ2mobmrW86JAk6Z7pDIEEAAROW4UGY4z5YgCu39p2gW4xxjxqjOlwu4ExJtW39lHfkZJLOOUB\nCH23TxsiSfq/jUdU19DscBoACF1/2HBYtQ3NGtE/QZ8d3d/pOACAMNLeMMjlxhi3MabQGPOIMeZq\nP64fsAPvjTF5vtMdHlQHXQC+7QpFkl6x1rYcKblA0ihjzJJAZeqi1jKnqe0BkgBaMX1kuoan91Vt\nQ7Pe3FTqdBwACEnWWr2wbp8k6e7LhsnlogkVABA47RUajO+RL+8v96sDUHjoMmPMfcaY1fIeH7m6\nk29bJmm5b/vGGb6TIW49vyPC1/1Q1IVHV2ZYtBx52doWilRJ5V24FhDxjDG6rWUoJNsnAMAvGXlu\nDwAAIABJREFUH5VUaOexWvWJidKX8gc7HQcAEGai23j+pLU23RgzQlKepJnyno4wUt7CQ56kB40x\nklQsaY2k1dbatwMd0Fr7jKRnJG9XQ0frjTEjfVkXtLHkVUmPyvvvaLlH5dmfB5K1ttIYs1dtd2Gs\nCcZ9gXA2N3+w/uvPO7ThQKV2HK3RRZlJTkcCgJDywjrvEMgvXJKtlD4xDqcBAISbtjoaSiTJWlti\nrV1hrf2GtXa0pH6S5kn6lW9NWx0PPzLG3KIADJX0w1xf9rbmQ+yRlNfBaRCBtlzSqLOfaCmanN91\nAaBjA5LiNGPcQEnSSwV0NQBAVxytqteqT45KYggkACA42io0XNPak9baqk4WHh6Sd/uCEycqzFT7\ncw9aChBTgnDvVLX+b35E0ozzihsL5P1vB8APLUMh/7DhsOqb3A6nAYDQ8buCA3J7rKYO76dxWclO\nxwEAhKFWt05Ya6s682bfuhW+h4wxKfJuW5gp70wFJ757penTuQitaSlCBKTbwlc8eNh3vZGS7jPG\npEkqtNb+RDqzfWKmpIeNMXvk7W4ostYuD0QGIBJ9bswAZaf20eHK01q15ai+cEm205EAoNdrbPac\n6QS7Z/pwZ8MAAMJWWzMa/HJe4eEbxhgn/szYURdFSxEiIN0WvvkOD3Vi3d7OrOuq6upqud0d/2eO\ni4tTXFxcoG8POCbKZXTrlCH6+ZqdeqngAIUGAOiEP31yVMdrGjQgKU7Xjc90Og4AIEy1d+pEIJQE\n+fqt6eyRkenBDtITBg0apJSUlA4fjzzyiNNRgYCbN2WwXMY7PX3v8Vqn4wBAr9cyBPKOaUMVGx3s\nHwMBAJEqoB0NrVgS5Ou3xom5EI45cuSIEhISOlxHNwPC0aDUPrpi7AC9s+O4Xll/UA9fP87pSADQ\na20rrVbBvgpFuYzunDbU6TgAgDAW1EKDtfaxYF6/DZXqXLGhPNhBekJycnKnCg1AuLp92lC9s+O4\nVhQd0ndnXsRf6ACgDc/7uhmuGz9QmSnxDqcBAISzcPyJvL1BkJJ3a4XUue0VAHq5qy/O0ICkOJ2o\nbdTabcecjgMAvVLV6Sa9tuGwJIZAAgCCLxwLDcVq/0SJlm6Hve2sARAiYqJcmpc/WJL3yLZ1e8r1\n+sbDWrenXG6PdTgdAPQOK4oO6XSTW2MHJurSEWkdvwEAgG4I9owGJ6yWNLed10dKkrV2Tc/EARBs\nt00doiff3aP3dp3Qe7tOnHk+KyVei2bnaFZuloPpAMBZHo/VCx96t03cPX24jDEOJwIAhLtw7GhY\nI0nGmLw2Xp/asgZAeNhWWt3q80er6rVwabFWbSnt4UQA0Hu8v/uESk7UKTEuWl/kKGAAQA8Iu0KD\ntXavvIWEBW0smSvp0Z5LBCCY3B6rxSu3tvpay8aJxSu3so0CQMRqGQL5pbxsJcaFYzMrAKC3CbVC\nQ9p5H9syT9KM87sajDHLJD3DtgkgfBSUVKi0qr7N162k0qp6FZR0NCcWAMLPoZOn9PZ276DcuxkC\nCQDoIb2+rG2MmStvd8JIfTrkcYkx5iF5BzousdYuP/s91tpKY0y+pEeNMZXyHmU5StJqa+0zPZce\nQLCV1bRdZPBnHQCEkxc/OiCPlT4zOl2jMxKdjgMAiBC9vtDgKyIs73Dhhe+rVNvbJwCEiYykzp0F\n39l1ABAu6pvcernggCTp7suGOxsGABBRQm3rBACcY9qINGWlxKutGepG3tMnpnGcG4AI8+amUp08\n1aRBKfGaMS7D6TgAgAhCoQFASItyGS2anSNJFxQbWj5fNDtHUS6OcwMQWZ73HWl512XDFB3Fj3wA\ngJ7Ddx0AIW9Wbpaemp+nzJRzt0cMTI7TU/PzNCs3y6FkAOCMTYcq9fHBSsVGuXTb1CFOxwEARJhe\nP6MBADpjVm6WZuZkqqCkXN96eaPKahr04HUXU2QAEJFajrS8YUKm+ifGOZwGABBp6GgAEDaiXEbT\nR/XX7b6/3v1xS6nDiQCg51XUNer/Pj4iiSMtAQDOoNAAIOzcNGmQJOkvO4+r6nSTw2kAoGe9uv6g\nGps9Gj8oWXlDU52OAwCIQBQaAISdsQOTNHZgoprcVqu3HnM6DgD0GLfHaqlvCOS904fLGAbhAgB6\nHoUGAGHpxgneroY3Nh1xOAkA9Jx3d5Tp0MnTSukTo9m+7i4AAHoahQYAYemmSd4hkO/vOqGTdY0O\npwGAntEyBPLWKYPVJzbK4TQAgEhFoQFAWBo1IFHjspLV7LH689ajTscBgKArOVGnv+w8LmOk+ZcN\nczoOACCCUWgAELZumujtanhjE6dPAAh/LbMZrhg7QMPSExxOAwCIZBQaAIStlkLD3/aUq7y2weE0\nABA8pxvdWrb+oCTvEEgAAJxEoQFA2BqWnqAJ2Slye6ze2sL2CQDh6/WNh1Vd36yhaX11xdgBTscB\nAEQ4Cg0AwlpLV8ObbJ8AEKastXrONwRy/mVD5XJxpCUAwFkUGgCEtRsmeAsNH5WUq6ym3uE0AEKZ\n22O1bk+5Xt94WOv2lMvtsU5HkiQV7T+pbaXViot26dYpQ5yOAwCAop0OAADBNCStryYPSdXGg5V6\na/NR3Xv5cKcjAQhBq7aUavHKrSqt+rRgmZUSr0WzczQrN8vBZJ8eaXnzpEFK7RvraBYAACQ6GgBE\nALZPAOiOVVtKtXBp8TlFBkk6WlWvhUuLtWqLc19bjtc06C3f/SmkAgB6CwoNAMJey/aJwv0VOlrF\n9gkAnef2WC1euVWtbZJoeW7xyq2ObaN4ueCAmtxWlwxNVW52iiMZAAA4H4UGAGFvUGofTRnWT9ZK\nb26mqwFA5xWUVFzQyXA2K6m0ql4FJRU9F8qn2e3Rix8dkCTdM31Yj98fAIC2UGgAEBE+3T5xxOEk\nAEJJZ4fIvrbhsMprG4Kc5lyrtx7T0ep6pSfEnuncAgCgN6DQACAiXD8hS8ZIxQcqdbjytNNxAISA\n041uvb/rRKfWvrL+oKb9aK3uevZD/e6jAz1SdGgZAnnb1CGKi44K+v0AAOgsCg0AIsLA5HhNG54m\nia4GAO3zeKxe23BYV//Xu1pWdKjD9Unx0codlCy3x+qD3eX65z9s1rQfrdX8Zz8KWtFh17Eardtb\nLpeR7rqMbRMAgN6F4y0BRIybJg3SRyUVemNTqe77/Cin4wDohdbvq9B/vLlNHx+slCRlp/bRdeMH\n6jcf7JOkc4ZCGt/Hx+ZO1KzcLB0oP6U3N5fqj5tLtflwld7ffULv7z6hf3t9i6aPTNcNE7J03fiB\nSk+M63bOFz70djPMGDdQ2al9un09AAACyVjrzJRk+M8YkyCpVpJqa2uVkJDgcCIgNByvadClP1oj\nj5X++k9XaWh6X6cjAeglDlac0o9XbT9zDG5CbJTuv2q0vvrZEYqPidKqLaVavHLrOYMhs1LitWh2\njmblXjgf4fyiQ4sol+l20aGmvkmX/Wit6hrdWvrVS/XZMf39+BcDANA1dXV1SkxMbPk00Vpb19Za\nCg0hiEID4L+7nv1QH+wu14OzLtL9V452Og4Ah9XUN+nJd/fo1++XqLHZI2Ok26YM0T9eO1YZSfHn\nrHV7rApKKlRWU6+MpHhNG5GmKJdp48qfClTRoeX+K4oPaXnRIY3o31dvf/dKGdNxBgAAuotCQ5ij\n0AD476WCA3r495uVk5WsP37rc07HAeAQt8fqlcKD+tnqHTpR2yhJunxUuv71xhzlDEoO2n33l9fp\nj5uP6s3NR7TlcPWZ5zsqOrTWUZEcH62f+LZtAAAQbBQawhyFBsB/J+saNeU/18jtsXr7u1do5IDE\njt8EIKy8t+u4/vPNbdp+tEaSNKJ/gv75hnGaMS6jR7sDOio63DgxS9eNz1RBSbkWLi3W+T+xtSR9\nan4exQYAQNBRaAhzFBqA7rnnfwv0153H9d2ZY/X/rhnjdBwAPWR3Wa1+9Mdtent7mSQppU+MvnXN\nGM2/bJhio509iGt/ed2Z7RVnFx1cRop2udTo9rT6PiMpMyVe7z90dae2cQAA4C8KDWGOQgPQPa+u\nP6gHl2/SRQOT9KfvfN7pOACC7GRdo36xZqeWfnRAbo9VtMto/mXD9O0ZY5TaN9bpeBdoq+jQnpe+\nfpmmj0oPcjIAQCTrSqGB4y0BRJzrcjL1L1GbteNYjXYdq9GYgUlORwIQBI3NHj2/bp9+uXaXquub\nJUkzxmXo4RvGaVQv3jY1LD1B9185WvdfOVq/fn+v/uONbR2+p6ymvsM1AAD0FAoNACJOSt8YfW7M\nAL29vUxvbCrVd2ZSaADCibVWq7ce0yNvbVfJCe8fWy7OTNK/3ZSjz4wOraMgc7JSOrXu/BMyAABw\nEoUGABHppolZvkLDEX17xhiOhwPCxCdHqvTDN7Zp3d5ySVL/xDg9cO1YzZsyJCRnGEwbkaaslHgd\nraq/YBik9OmMhmkj0no6GgAAbaLQACAizcwZqNhol/Ycr9P2ozUalxW84+wABI7bY1VQUqGymnpl\nJHl/wY5yGZVV1+unf96hZUWHZK0UG+3S1z47QvdfNVqJcaH7406Uy2jR7BwtXFosI51TbGgpmyya\nnROSRRQAQPgK3e+8ANANSfExumLsAK3eekxvbiql0ACEgFVbSrV45VaVVn06jyAzOU7ThqdpzfYy\nnWp0S5JmTxqkh2ZdpMH9+joVNaBm5Wbpqfl5F/7bU+K1aHYOR1sCAHodTp0IQZw6AQTG6xsP61sv\nb9Tw9L5654Er2T4B9GKrtpRq4dLiVrcPtJg8JFX/dlOO8of167FcPamtbg4AAHoCp04AQCfMGDdQ\ncdEu7Ss/pU+OVCs3u3ND1wD0LLfHavHKre0WGVL7xmj5N6YrOsrVY7l6WpTLcIQlACAkhO93YwDo\nQEJctK6+OEOS9MamUofTAGhLQUnFOVsGWlN5qkmF+072UCIAANAeCg0AItpNEwdJkt7YdERsJQN6\np7Ka9osMXV0HAACCi0IDgIh29cUZ6hsbpUMnT+vjQ1VOxwHQioyk+ICuAwAAwUWhAUBE6xMbpWvG\nDZQkvbnpiMNpALQmf1g/xUW3/SOLkZSV4h2OCAAAnEehAUDEu3GC92i4NzeVyuNh+wTQ2zy6arsa\nmj2tvtZy5sKi2TmcwAAAQC9BoQFAxLvyogFKjIvWkap6bTjIMDmgN3nxo/369fslkqSvf26EslLO\n3R6RmRKvp+bnaVZulhPxAABAKzjeEkDEi4+J0sycgfrDhsN6Y1Op8ofRfg30Bu/vOqF/f/0TSdID\n147V3189Rt+7fpwKSipUVlOvjCTvdgk6GQAA6F3oaAAAfbp94o+b2T4B9Aa7y2q18MUiuT1WX7wk\nW9+8arQkKcplNH1UuuZMztb0UekUGQAA6IUoNACApM+N7a+k+Ggdq25Q4b4Kp+MAEe1kXaO++lyh\nauqblT+sn378pQkyhoICAAChgkIDAEiKi47SdeMzJUlvbCp1OA0QuRqbPVqwtEj7y09pcL8+WnJ3\nvuKio5yOBQAAuoBCAwD43DjRu33irS2lcrN9Auhx1lr962ubVVBSocS4aP3vl6eqf2Kc07EAAEAX\nUWgAAJ/Pju6v1L4xOlHbqI/2ljsdB4g4z/x1r15df0guIz1+5yUaOzDJ6UgAAMAPFBoAwCcmyqVZ\nvu0TK9k+AfSoP31yVD9etV2StGj2eF15UYbDiQAAgL8oNADAWVq2T6zaUqpmt8fhNEBk2HK4St9+\neaOsle6ZPkz3Xj7c6UgAAKAbKDQAwFmmj0xXekKsTp5q0t/2sH0CCLZj1fX62nPrdbrJrc+N6a9/\nvynH6UgAAKCbKDQAwFmio1yaldty+sQRh9MA4e10o1tfe269jlbXa0xGop64K0/RUfxoAgBAqOO7\nOQCc56aJgyRJf/rkmBqb2T4BBIPHY/WPr27U5sNVSkuI1a/vnark+BinYwEAgACg0AAA55k2Ik0D\nkuJUdbpJH+w+4XQcICz91+odemvLUcVGubTk7nwNTe/rdCQAABAgFBoA4DxRLqMbcltOn2D7BBBo\nvy8+pCfe2SNJeuSWCZo6PM3hRAAAIJAoNABAK26a5N0+sfqTY6pvcjucBggfhfsq9L0VmyVJ37xq\nlL6UP9jhRAAAINAoNABAK/KH9lNmcrxqGpr13i62TwCBcKD8lBa8UKRGt0fX52bquzMvcjoSAAAI\nAgoNANAKl8vohglZkjh9AgiE6vomfeW5QlXUNWpCdop+dutkuVzG6VgAACAIKDQAQBtumuQtNKzZ\nyvYJoDua3R5988Vi7S6rVWZyvJ69d4r6xEY5HQsAAAQJhQYAaMMlQ1KVndpHdY1uvbujzOk4QMj6\nwRtb9d6uE+oTE6Vn752igcnxTkcCAABBRKEBANpgjNGNE71dDSs3lTqcBghNz/1tn55ft1/GSL+4\nfbJys1OcjgQAAIKMQgMAtOMmX6Hh7W1lOtXY7HAaILS8u6NMi1d+Ikl6aNbFum58psOJAABAT6DQ\nAADtmJCdoqFpfXW6ya23t7N9Auisncdq9P9+t0EeK83LH6wFnx/pdCQAANBDKDQAQDvO3j7xxsds\nnwA6o7y2QV/5baFqGpo1bUSa/vOLE2QMJ0wAABApKDQAQAdatk+8s6NMtQ1snwDaU9/k1n0vFOnQ\nydMalt5XS+bnKzaaHzcAAIgkfOcHgA7kZCVrZP8ENTR7tHbbMafjAL2WtVYP/36zivafVHJ8tH59\n71T1S4h1OhYAAOhhFBoAoAPnnD7B9gmgTU+8s1t/2HBYUS6jp+bna3RGotORAACAAyg0AEAn3DRx\nkCTprzuPq+p0k8NpgN7nzU2l+umfd0qS/mNOrj4zur/DiQAAgFMoNABAJ1yUmaQxGYlqdHu0eivb\nJ4CzfXywUt9dtlGS9NXPjtCdlw51OBEAAHAShQYA6KSW7RNvbjricBLAWW6P1bo95Xp942G98fER\nffW5QtU3eXT1xRn65xvGOR0PAAA4LNrpAOHEGJMn6TZr7UOtvDZD0kxJqZJGSlpmrX2mhyMC6Iab\nJg7SL9bs0nu7TqjyVKNS+zLkDpFn1ZZSLV65VaVV9ec8n50ar1/ecYmiXBxjCQBApKOjIUB8RYa1\n7byWZ619yFq7QNI8SY8aY5b0ZEYA3TM6I1EXZyap2WP1p0+OOh0H6HGrtpRq4dLiC4oMknS4sl7v\n7zruQCoAANDbUGjoJmPMSGPMMkm3SapoY9kCa+1PWj6x1lZKekjSfcaYkT0QE0CA3OTbPvHGJk6f\nQGRxe6wWr9wq28brRtLilVvl9rS1AgAARAoKDd1krd1rrZ3n2y5R2cayW40xD5733HrfxxnBSwcg\n0FpOn/jbnnKV1zY4nAboOQUlFa12MrSwkkqr6lVQ0lbNHQAARAoKDT2jQlK60yEAdN/w/gnKzU6W\n22O1iu0TiCBlNW0XGfxZBwAAwheFhh5grR3VyoDIli0T689fD6B3u3GCt6vhTbZPIIIkxnVufnRG\nUnyQkwAAgN6OQoNzFkhaY60tdjoIgK5pmdPw4d5yHa9h+wTC35HK03r0re3trjGSslLiNW1EWs+E\nAgAAvVbIFRqMMY/6jorsaF2qb+2jxpgHjTFLjDH39UTGjhhj5srb0TDP6SwAum5IWl9NGpIqj5Xe\n2kJXA8Lb1iPV+uKTH2hnWa2S471dDecfYNny+aLZORxvCQAAQqfQYIzJ853u8KCk1A7WpkoqkvSK\n70jJn/iOlRzl9JGSvmyPSprpO30CQAia3XL6xMcUGhC+/rrzuG5dsk7Hqhs0dmCi3vr25/X0/Dxl\nppy7PSIzJV5Pzc/TrNwsh5ICAIDepHMbLh3k60KYJ6lY0mpJczvxtmWSlp+/LcFa+5Ax5qQxZpm1\nds1Z90iVtLYLsR6x1i7vwvrzs8201u718/0AeoEbJmTph29uU+H+Ch2tqr/gFy8g1L1aeFAP/2Gz\n3B6r6SPT9fTd+UrpE6Ps1D6amZOpgpIKldXUKyPJu12CTgYAANCi1xcarLXPSHpG8nY1dLTeGDNS\n3iMjF7Sx5FV5Owryz7pH5dmfB4uvm+Khs4sMxpg85jQAoWdQah/lD+unov0n9cfNpfrKZ0c4HQkI\nCGutfr5ml365dpck6YuXZOvRL01UbPSnTZBRLqPpozhMCQAAtC5ktk50wVxJaqdjYI+kPF8XQ4/x\ndWYsO7uo4CuKjGz7XQB6s5ahkG9sOuJwEiAwGps9emDZpjNFhr+/arR+duukc4oMAAAAHQnHnxxm\nSmpv9kFLAWJKEO6dqlbmR/iGV86Tt8DxYMtD0pKz8gAIMTdMyJIxUvGBSh2uPO10HKBbquub9JXf\nFmpF8SFFuYweuWWCHrjuIhnDlggAANA1vX7rhB/SJFW083pLESIgnQS+zoiHfdcbKek+Y0yapEJr\n7U98y5bJW4C44LQMtk0AoWtgcrymDk9TQUmF/ripVF//PA1KCE2lVaf1d78p1PajNeobG6Un7srT\nVRdlOB0LAACEqHAsNHS0JaKlCBGQrRO++Q4PdbCmXyDu1Zrq6mq53e4O18XFxSkuLi5YMYCINXti\nlgpKKvTGpiMUGhCSth6p1ld+W6ij1fUakBSn33x5qnKzU5yOBQAAQlg4bp1IU/tbJ1qExRSrQYMG\nKSUlpcPHI4884nRUICzNys2Sy0gfH6rSwYpTTscBuuS9Xd7jK49W12tMRqL+cP/lFBkAAEC3RWJH\nQ1g5cuSIEhISOlxHNwMQHAOS4nTZyHT9bU+5nnxnty4blc5xfwgJr64/qH/+/WY1e6wuG5mmJfOn\nKKVvjNOxAABAGAjHQkOlOldsKA92kJ6QnJzcqUIDgOAZnp6gv+0p10uFB/VS4UFJUlZKvBbNztGs\n3CyH0wHnstbqF2t26b99J0vMmTxIP5k7UXHRUQ4nAwAA4SIct060NwhS8m6tkDq3vQIA2rVqS6le\nKjhwwfNHq+q1cGmxVm0pdSAV0Lomt0f/tHzTmSLDN68apZ/fOpkiAwAACKhwLDQUq/0TJVq6HThW\nEkC3uD1Wi1dulW3ltZbnFq/cKrentRVAz6rxHV+5vMh7fOWPvjhB/3TdxXKxxQcAAARYOBYaVnfw\n+khJstau6YEsAMJYQUmFSqvq23zdSiqtqldBSUeNVkBwlVad1ryn1+m9XSfUNzZKz94zRXdeOtTp\nWAAAIEyF44yGNZJkjMmz1ha38vrUljUA0B1lNW0XGfxZBwTDttJq/d1vPj2+8n/vnaoJgzlZAgAA\nBE/YdTRYa/fKW0hY0MaSuZIe7blEAMJVRlJ8QNcBgfb+rhO69Wnv8ZWjMxL1+4WXU2QAAABBF2qF\nhrTzPrZlnqQZxpi8s580xiyT9AzbJgAEwrQRacpKiVdbO9yNvKdPTBvR0ZcsIPCWrT+oL/+mQDUN\nzbp0RJpWfONyDUnr63QsAAAQAYy1vXtImTFmrrzdCSN17pDHvb7HEmvt8lbelypv50KlvEdZjpJU\nZK19Juihg8wYkyCpVpJqa2s53hJw0KotpVq41LtL6/yvpkbSU/PzOOIyTLk9VgUlFSqrqVdGkreg\nFNULBitaa/XLtbv18zU7JUk3Txqkx+ZxfCUAAOieuro6JSYmtnyaaK2ta2ttry804EIUGoDeZdWW\nUi1eufWCwZDfmTFW35oxxqFUCKbW/n+elRKvRbNzHC0sNbk9+uffb9ayokOSpIVXjtI/XXsRJ0sA\nAIBuo9AQ5ig0AL3P2X/dfuPjUq3edkyXj0rX775+mdPREGAtXSytdbBIPdPF0lo3xanGZt3/YrHe\n23VCLiP9YE6u5l82LKg5AABA5OhKoSEcT50AgB4X5TKaPipdkpQ/rJ/e2VGmv+0pV9H+CuUPY0ZD\nuHB7rBav3HpBkUHybp0xkhav3KqZOZlB20bRWjdFRlKcYqKMDlfWq09MlB6/8xJdM25gUO4PAADQ\nEQoNABBgg/v11S152Xp1/SE9/vZu/ebvpjkdCQFSUFJxwRaZs1lJpVX1enD5xxo/KEUpfWKU3CdG\nKb5Hcp9opfSJUZ+YKBnT9UJEW90UZTUNkqSk+Gi9+LVLNXFwapevDQAAECgUGgAgCO6/crSWFx3S\nOzuOa8vhKuVmc6RgOCirabvIcLYVxYe1ovhwm6/HRBklx8ecKUR8WoyIPvP8+UWKxLhoLfq/T1rt\npmjRJyZK4wfxvzUAAOAsCg0AEATD+yfo5kmD9NrGI3r87d16+u58pyMhADKS4ju17ppxGeoTE6Wq\n002qPt2k6vpmVZ1uUtXpJrk9Vk1uq/K6RpXXNQY0X1lNgwpKKs5s4wEAAHAChQYACJJvXjVar208\nolWfHNXOYzUaOzDJ6Ujopmkj0pQcH63q+uZWXzeSMlPi9czdU1qd0WCt1alG95miQ7XvY9VZxYjq\ns56vrv/09Yq6RjW5Ox7g3NmuCwAAgGCh0AAAQTJmYJKuz83UW1uO6vG3d+uXd1zidCR00x83l7Zb\nZJCkRbNz2hwEaYxRQly0EuKiNSi1T5fuvW5Pue741Ycdruts1wUAAECwuJwOAADh7JtXjZYkvbHp\niPYer3U4DbrjvV3H9Y+vbpQkXTF2gDJTzv2FPjMlPqhHW04bkaaslHi1NULSSMpK8R51CQAA4CQ6\nGgAgiHKzU3T1xRl6e3uZnnp3jx6bN8npSPDDxwcrteCFIjW5rW6cmKVf3u7tTikoqVBZTb0ykry/\n4AfrSEvp/7d378FRnWeex3+PJEBIAl1wAPkKAo8NY+xEXOyEjK9il2TWMxuXSHZmGXvsZGFwnNqq\nqRqIa6bWcVV2PHKmMrObSRwY23ESX2YsyknWya4nwnbIzeEi2ZM4OL5IGAPGgBESSEIIpHf/OKdx\nS/RNrdN9uo++nypV3073eVx+6z3dD8/7vN4WqvfdulgbHu+QSaOaQmZSTQEAAJAvVDQAQI7dc7NX\n1fC9lw9qf/dAyNFgvDqP9unOx3ZpYGhYKxfO0lc/fY1KS0ylJaaPLpilP/7wRfroglmqsR6FAAAa\npUlEQVR5+YG/+qp6PbS2Me/VFAAAAONhzqVvLIXCYmaVkvokqa+vT5WVlSFHBCCdtQ/v0M/fel9r\nr7tUX/7PS8IOBxk6fGJQt33jlzrYc0pLLqrWU+uuU9W08IsBh0dcXqspAAAA+vv7VVVVFXtY5Zzr\nT3YsFQ0AkAexqoandx3Qe73sClAMegfO6PZHdupgzynNv6BS37pzeUEkGSSFUk0BAACQKRINAJAH\n186v0/J5tRoaHtGWn3aFHQ7SODU0rM9+e5deP3xSs2dM03fuWqELqqaFHRYAAEBRINEAAHlgZrrn\n5sslSU/u3Kf3+06HHBGSOTs8onue7NDufcc1o7xM375rhS6pqwg7LAAAgKJBogEA8uT6yy/QNRdX\na/DMiB75+d6ww0ECzjnd+8xv9PzvjmhaWYkeuWO5FtXPDDssAACAokKiAQDyJL6q4Tu/fFs9A0Mh\nR4SxWp57Xa3tB1RaYvqnP23Uivl1YYcEAABQdEg0AEAe3XLlbF05d4b6h4b12C/fDjscxHn4Z136\n5vZOSdIDn1qiVYvnhBwRAABAcSLRAAB5VFJi53agePTne3Vy8EzIEUGSnuk4oC//6DVJ0sbVV+jT\nyy8JOSIAAIDiRaIBAPLsE1fVa8GHKnVi8Ky++6t9YYcz6b34uyPauPXXkqTPfny+NtywIOSIAAAA\nihuJBgDIs9IS0+dv8qoaHv7ZXg0MnQ05osmrfd9xbXiiXWdHnD71kYv0159cJDMLOywAAICiRqIB\nAELwR9dcqEvqpqu7f0hP7dwfdjiT0puHT+qux3Zp8MyIbvi9D+nB5qtVUkKSAQAAYKJINABACMpK\nS3T3jV5Vw5afdmrwzHDIEU0u7/ac0u2P7lTvqTP68CU1emhto6aUckkEAAAIAt+qACAktzVepPrq\nch0+cVqt7QfCDmfSON4/pD97ZIcO9Q5q4ewqfevPl6tialnYYQEAAEQGiQYACMm0slL9hd948Js/\n6dSZ4ZGQI4q+gaGzuvOxXeo82q/66nJ9564Vqq2cGnZYAAAAkUKiAQBC9Jnll+iCqmk62HNK33v5\nYNjhRNqZ4RFteLxDr+zvUU3FFH3nrhW6sGZ62GEBAABEDokGAAhR+ZRSrbt+viTpGy++peERF3JE\n0TQy4vRXrf+u7W8cVfmUEj1yx3JdPmdG2GEBAABEEokGAAjZf732MtVUTNHbxwb0w1+/G3Y4keOc\n05d/9Jq+/8q7KisxPbR2qZZeVht2WAAAAJFFogEAQlY5rUyfXelVNXz9xbc0QlVDoB7a3qlHf7FX\nkvSVNVfrpitmhxwRAABAtJFoAIACcMfKeZpRXqY3Dvfpx3veCzucyHh61349+NzrkqS/+cNF+tRH\nLg45IgAAgOgj0QAABWBm+RT9+cfmSZK+9sJbco6qholq23NYX3zm15Kk9Tc06HN/0BByRAAAAJMD\niQYAKBB3rpyviqml+u27J/ST14+GHU5R27m3W/c82aERJ61ZerG+uPrKsEMCAACYNEg0AECBqKuc\nqrXXXSZJ+t8vvElVQ5ZeO3RCn/32Lp0+O6KmRbP1wG1LZGZhhwUAADBpkGgAgALyuT+Yr2llJXr5\nnR691Hks7HCKzv7uAd3x6E6dHDyrZZfV6mt/0qiyUi51AAAA+cS3LwAoILNnlOtPVlwqyatqQGrD\nI04vdR7TD145qOdePaQ/e2SHjpw8rSvmzNAjdyzX9KmlYYcIAAAw6ZSFHQAAYLR11zfoiR379Kuu\nbu16u1vL59WFHVJBeu7VQ7r/2T061Ds46vm6iqn69l0rVF0xJaTIAAAAJjcqGgCgwFxYM13NS71t\nGP/phbdCjqYwPffqIW14vOO8JIMkdQ8M6ZX9x0OICgAAABKJBgAoSBtuWKjSEtP2N47q1wd6wg6n\noAyPON3/7B4la5Vpku5/do+GR2imCQAAEAYSDQBQgC6dVaE//vCFkqhqGGvn3u6ElQwxTtKh3kHt\n3Nudv6AAAABwDokGAChQd9+4UGbSj/cc1muHToQdTsFo35fZsogjJ5MnIwAAAJA7JBoAoEAtnF2l\nTy6plyR9/UWqGo6cHNRftf67/v7Hr2d0/OwZ5TmOCAAAAImQaACAAnbPTQslST/6zSF1Hu0LOZpw\nDJ4Z1tdffEs3feUnam0/IEkqn5L88mWS6qvLtWI+u3UAAACEgUQDABSwRfUz1bRojpyTvvFiZ9jh\n5JVzTv/vN4e06h+26yv/9rr6h4Z1zSU1eubuj+kfP/NhmbykQrzY4/tuXazSkrGvAgAAIB9INABA\ngfvCzV5Vw/dfOaj93QMhR5Mfv323V/9ly6+04YkO7e8+pTkzp+mrn75G39vwMTVeWqvVV9XrobWN\nmls9ennE3OpyPbS2Uauvqg8pcgAAAJhzbP9VbMysUlKfJPX19amysjLkiADk2u2P7tRP3ziqP732\nUv3tp5aEHU7OHD15Wl9te13/smu/nJOmlZVo/fUN+osbF6hiatl5xw+POO3c260jJwc1e4a3XIJK\nBgAAgOD19/erqqoq9rDKOdef7FgSDUWIRAMw+ex6u1trvvmSppaWaPvGG1VfPT3skAJ1+uywHvvF\n2/raC2+p7/RZSdJ/urpeX/zElbq4tiLk6AAAADCeRMP5/zwEACg4y+fV6dr5ddqxt1ubt3fpS3/0\n+2GHFAjnnNr2HNb//L+vad8xb1nIkouq9T9uXazl82jmCAAAUIzo0QAAReILN18uSXpq5zs6evJ0\nyNFM3O/eO6G1j+zQuu+2a9+xAX1oxjR9pflq/eDzK0kyAAAAFDEqGgCgSKxcOEsfubRGL7/To4d/\n3qV7P7Eo7JCycqzvtL7a9oae2vmORpw0taxEn/v4fN1900JVTeOyBAAAUOyoaACAImFm53agePyl\nfTrePxRyROMzdHZED/+sSzf+/U/0xA4vyfCJq+bq+b+8QRtXX0mSAQAAICL4VgcAReSmK2Zrcf1M\n7Tl0Qt/6xV795X+4IuyQ0nLO6cXXj+jLP3xNXe97PYMW1c/Ufbcu1nUNs0KODgAAAEGjogEAikh8\nVcO3fvm2TgyeCTmi1N48fFK3P7pTdz22W13v9+uCqqn6u9uW6Idf+DhJBgAAgIiiogEAisx//P25\nunx2ld480qfvvrRPn79pYWixDI847dzbrSMnBzV7RrlWzK9TaYmpZ2BI/9D2hh7f8Y6GR5ymlJru\nWjlf99y8UDPKp4QWLwAAAHKPRAMAFJmSEtM9Ny/Uf/+XV/Twz7p058p5qpia/+n8uVcP6f5n9+hQ\n7+C55+bOLNf1v3eB/u23h9V7yqu2WLV4jv76k4s074LKvMcIAACA/GPpBAAUoT9cUq95syp0fOCM\nntzxTt7P/9yrh7Th8Y5RSQZJeu/EoJ7efUC9p87oyrkz9MTnrtU/376MJAMAAMAkQqIBAIpQWWmJ\n7r7RWzLxze2d2v7GEf3glYN6qfOYhkdcTs89POJ03//5rVKdpXr6FP3g8yu1cuEFOY0FAAAAhcec\ny+0XUgTPzCol9UlSX1+fKiv5l0JgMho6O6Lr/vZ5dQ+M3uayvrpc9926WKuvqs/6s08OntHBnlM6\n0H3Kuz0+oAPHvft73+/XycGzaT/jqf92nT66gIaPAAAAUdDf36+qqqrYwyrnXH+yY+nRAABF6oXf\nHT4vySBJ7/UOasPjHXpobWPSZEPvqTM6cHxAB4+f0gH/72DPwLn7sf4KE3Hk5GD6gwAAABA5JBoA\noAgNjzjd/+yehK85SSbpb77/qkZGnN7tHTyXQDhwfEAHe05lVJFQUzFFF9dO18U1Fbqodrp3v7ZC\nx/pO64vP/Cbt+2fPKB/nfxUAAACigEQDABShnXu7z2vEGM9Jer9vSHc/+XLSY2ZVTtXFtdP9JEKF\nd7/Gu39R7XRVTUt8iRgecfpfz7+p93oHE/ZpMElzq72tLgEAADD5kGgAgCKU6bKEy2ZVaMlF1R8k\nEmqn65La6bqwZnrWW2KWlpjuu3WxNjzeIZNGJRvMv73v1sUqLbEE7wYAAEDUkWgAgCKU6bKEv7vt\n6pw0ZFx9Vb0eWtuo+5/dM6qyYm4AjSgBAABQ3Eg0AEARWjG/TvXV5aEuX1h9Vb1WLZ6rnXu7deTk\noGbP8M5HJQMAAMDkRqIBAIpQoSxfKC0xtrAEAADAKCVhBwAAyE5s+cLc6tHLKOZWl6fc2hIAAADI\nJXMuUdEtCpmZVUrqk6S+vj5VVlaGHBGAMA2POJYvAAAAIKf6+/tVVVUVe1jlnOtPdixLJwCgyLF8\nAQAAAIWEpRMAAAAAACAwJBoAAAAAAEBgSDQAAAAAAIDAkGgAAAAAAACBIdEAAAAAAAACQ6IhQGbW\naGYtGR7blut4AAAAAADINxINATGzRknPZ3jsOklNuY0IAAAAAID8Kws7gGJnZg2SWiR1SerO4Pga\nSWtyHRcAAAAAAGGgomGCnHNdzrk1zrlNknoyeMs6SZtzHBYKwOnTp/WlL31Jp0+fDjsUTAKMN+Qb\nYw75xHhDvjHmkE9RHG/mnAs7hsgws3ZJ2/ykQ6LXGyQ1+g9bnXOW5XkqJfVJUl9fnyorK7P5GOTY\niRMnVF1drd7eXs2cOTPscBBxjDfkG2MO+cR4Q74x5pBPxTLe+vv7VVVVFXtY5ZzrT3YsFQ351eyc\n2xp2EAAAAAAA5AqJhjwxsyZJJBkAAAAAAJFWdM0g/e0j25xz29IcVyPpXv/hMUkLJLU757bkOMRk\nGtPFDAAAAABAsSuaRIO/feS9kpol7UpzbI2kdklrnHMdcc+3mNlm59z6nAZ7fjzrJIWV4AAAAAAA\nIG8KPtHg/0hfI6lDUpu8REM6rZK2xicZJMk5t8nMjptZa3x1gZ+YeH4cYT2Qaa8F/7PlnMtkRwoA\nA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JAAAApKxgyGrjtn1R15f3tj1x4LgkqTAvWysXztC1i2fqivLJyskKJKxOAEB0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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -169,11 +246,11 @@ } ], "source": [ - "plt.title(r'$L_1$ norm vs $N_{LGL}$')\n", + "plt.title(r'Error for $\\int sin(2 \\pi x) \\frac{d L_0}{d\\xi} d\\xi$ vs $N_{LGL}$')\n", "plt.xlabel(r'$N_{LGL}$')\n", - "plt.ylabel(r'$L_1$ norm of error')\n", - "plt.semilogy(np.arange(3, 31), L1_norm, 'o-')\n", - "# plt.savefig('lagrange_interpolation_test.png')\n", + "plt.ylabel(r'Error')\n", + "plt.semilogy(np.arange(3, 31), error, '-o')\n", + "plt.savefig('error_int_fxi_dLi_dxi.png')\n", "plt.show()" ] }, diff --git a/examples/volume_integral_error_analysis.ipynb b/examples/volume_integral_error_analysis.ipynb new file mode 100644 index 0000000..d6da802 --- /dev/null +++ b/examples/volume_integral_error_analysis.ipynb @@ -0,0 +1,175 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import os\n", + "import sys\n", + "sys.path.insert(0, os.path.abspath('../'))\n", + "\n", + "from scipy import integrate\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "\n", + "from dg_maxwell import lagrange\n", + "from dg_maxwell import isoparam\n", + "from dg_maxwell import wave_equation\n", + "from dg_maxwell import params\n", + "\n", + "plt.rcParams['figure.figsize'] = 12, 7.5\n", + "plt.rcParams['lines.linewidth'] = 1.5\n", + "plt.rcParams['font.family'] = 'serif'\n", + "plt.rcParams['font.weight'] = 'bold'\n", + "plt.rcParams['font.size'] = 20 \n", + "plt.rcParams['font.sans-serif'] = 'serif'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['axes.linewidth'] = 1.5\n", + "plt.rcParams['axes.titlesize'] = 'medium'\n", + "plt.rcParams['axes.labelsize'] = 'medium'\n", + "\n", + "plt.rcParams['xtick.major.size'] = 8\n", + "plt.rcParams['xtick.minor.size'] = 4\n", + "plt.rcParams['xtick.major.pad'] = 8\n", + "plt.rcParams['xtick.minor.pad'] = 8\n", + "plt.rcParams['xtick.color'] = 'k'\n", + "plt.rcParams['xtick.labelsize'] = 'medium'\n", + "plt.rcParams['xtick.direction'] = 'in' \n", + "\n", + "plt.rcParams['ytick.major.size'] = 8\n", + "plt.rcParams['ytick.minor.size'] = 4\n", + "plt.rcParams['ytick.major.pad'] = 8\n", + "plt.rcParams['ytick.minor.pad'] = 8\n", + "plt.rcParams['ytick.color'] = 'k'\n", + "plt.rcParams['ytick.labelsize'] = 'medium'\n", + "plt.rcParams['ytick.direction'] = 'in'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['text.latex.unicode'] = True" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def find_L1_norm(epsilon, dx_dxi, x):\n", + " '''\n", + " '''\n", + " lagrange_basis, temp = lagrange.lagrange_polynomials(x)\n", + " \n", + " epsilon_interpol = 0.\n", + " for i in np.arange(x.shape[0]):\n", + " epsilon_interpol += lagrange_basis[i] * epsilon[i]\n", + " \n", + " return integrate.quad(epsilon_interpol * dx_dxi, -1, 1)[0]\n", + "\n", + "\n", + "def integrate_quad(function, order, scheme = 'gauss_legendre'):\n", + " '''\n", + " '''\n", + " if scheme == 'gauss_legendre':\n", + " nodes = np.array(lagrange.gauss_nodes(order))\n", + " weights = np.array(lagrange.gaussian_weights(order))\n", + "\n", + " elif scheme == 'gauss_lobatto':\n", + " nodes = np.array(lagrange.LGL_points(order))\n", + " weights = np.array(lagrange.lobatto_weights(order))\n", + " \n", + " else:\n", + " return\n", + "\n", + " integral = 0.\n", + "\n", + " for node, weight in zip(nodes, weights):\n", + " integral += weight * function(node)\n", + " \n", + " return integral" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def test_function(x):\n", + " '''\n", + " The test wave function.\n", + " '''\n", + " return np.sin(2 * np.pi * x)\n", + "\n", + "def int_sin2pix_dLdxi(x_nodes, xi_LGL, lagrange_basis_order):\n", + " '''\n", + " '''\n", + " L_i, temp = lagrange.lagrange_polynomials(xi_LGL)\n", + " \n", + " def sin2pix_dLdxi(xi):\n", + " x = (((x_nodes[1] - x_nodes[0]) * xi + (x_nodes[1] + x_nodes[0]))) / 2\n", + " return np.sin(2 * np.pi * x) * L_i[lagrange_basis_order].deriv()(xi)\n", + " \n", + " return integrate.quad(sin2pix_dLdxi, -1, 1)[0]\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "arrayfire.Array()\n", + "Type: double\n", + "\n", + "[8 8 1 1]\n", + " -0.0140 -0.7170 -1.0000 -0.6972 0.0140 0.7170 1.0000 0.6972 \n", + " -0.0826 -0.0555 0.0042 0.0614 0.0826 0.0555 -0.0042 -0.0614 \n", + " -0.1322 -0.0784 0.0214 0.1086 0.1322 0.0784 -0.0214 -0.1086 \n", + " -0.1542 -0.0741 0.0495 0.1440 0.1542 0.0741 -0.0495 -0.1440 \n", + " -0.1440 -0.0495 0.0741 0.1542 0.1440 0.0495 -0.0741 -0.1542 \n", + " -0.1086 -0.0214 0.0784 0.1322 0.1086 0.0214 -0.0784 -0.1322 \n", + " -0.0614 -0.0042 0.0555 0.0826 0.0614 0.0042 -0.0555 -0.0826 \n", + " 0.6972 1.0000 0.7170 0.0140 -0.6972 -1.0000 -0.7170 -0.0140 \n", + "\n", + "\n" + ] + } + ], + "source": [ + "print(wave_equation.volume_integral_flux(params.u_init))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From f457b526d6bea796a3596e70d27c71834324940c Mon Sep 17 00:00:00 2001 From: AAT Date: Mon, 9 Oct 2017 03:07:25 +0530 Subject: [PATCH 7/9] examples/volume_integral_error_analysis.ipynb modified --- dg_maxwell/wave_equation.py | 3 +- examples/volume_integral_error_analysis.ipynb | 335 +++++++++++++++++- 2 files changed, 334 insertions(+), 4 deletions(-) diff --git a/dg_maxwell/wave_equation.py b/dg_maxwell/wave_equation.py index 88a9bbd..b8c070f 100644 --- a/dg_maxwell/wave_equation.py +++ b/dg_maxwell/wave_equation.py @@ -236,7 +236,7 @@ def volume_integral_flux(u_n, t_n): if(params.volume_integral_scheme == 'lobatto_quadrature'\ and params.N_quad == params.N_LGL): - + print('option1') # Flux using u_n, reordered to 1 X N_LGL X N_Elements array. F_u_n = af.reorder(flux_x(u_n), 2, 0, 1) @@ -265,6 +265,7 @@ def volume_integral_flux(u_n, t_n): else: + print('option3') # Obtaining the u_n in polynomial form using the value at LGL points. analytical_form_flux = flux_x(lagrange.\ wave_equation_lagrange(u_n)) diff --git a/examples/volume_integral_error_analysis.ipynb b/examples/volume_integral_error_analysis.ipynb index d6da802..f588165 100644 --- a/examples/volume_integral_error_analysis.ipynb +++ b/examples/volume_integral_error_analysis.ipynb @@ -13,11 +13,14 @@ "from scipy import integrate\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", + "import arrayfire as af\n", + "af.set_backend('cpu')\n", "\n", "from dg_maxwell import lagrange\n", "from dg_maxwell import isoparam\n", "from dg_maxwell import wave_equation\n", "from dg_maxwell import params\n", + "from dg_maxwell import utils\n", "\n", "plt.rcParams['figure.figsize'] = 12, 7.5\n", "plt.rcParams['lines.linewidth'] = 1.5\n", @@ -110,12 +113,221 @@ " x = (((x_nodes[1] - x_nodes[0]) * xi + (x_nodes[1] + x_nodes[0]))) / 2\n", " return np.sin(2 * np.pi * x) * L_i[lagrange_basis_order].deriv()(xi)\n", " \n", - " return integrate.quad(sin2pix_dLdxi, -1, 1)[0]\n" + " return integrate.quad(sin2pix_dLdxi, -1, 1)[0]\n", + "\n", + "def int_exp_dLdxi(x_nodes, xi_LGL, lagrange_basis_order):\n", + " '''\n", + " '''\n", + " L_i, temp = lagrange.lagrange_polynomials(xi_LGL)\n", + " \n", + " def exp_dLdxi(xi):\n", + " x = (((x_nodes[1] - x_nodes[0]) * xi + (x_nodes[1] + x_nodes[0]))) / 2\n", + " return np.e ** (-x ** 2 / 0.4 ** 2) * L_i[lagrange_basis_order].deriv()(xi)\n", + " \n", + " return integrate.quad(exp_dLdxi, -1, 1)[0]\n" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def change_parameters(N_LGL = 8, N_Elements = 8, wave = 'sin'):\n", + " '''\n", + " '''\n", + " # The domain of the function.\n", + " params.x_nodes = af.np_to_af_array(np.array([0, 1.]))\n", + "\n", + " # The number of LGL points into which an element is split.\n", + " params.N_LGL = N_LGL\n", + "\n", + " # Number of elements the domain is to be divided into.\n", + " params.N_Elements = N_Elements\n", + "\n", + " # The number quadrature points to be used for integration.\n", + " params.N_quad = N_LGL\n", + "\n", + " # Array containing the LGL points in xi space.\n", + " params.xi_LGL = lagrange.LGL_points(params.N_LGL)\n", + "\n", + " # N_Gauss number of Gauss nodes.\n", + " params.gauss_points = af.np_to_af_array(lagrange.gauss_nodes\\\n", + " (params.N_quad))\n", + "\n", + " # The Gaussian weights.\n", + " params.gauss_weights = lagrange.gaussian_weights(params.N_quad)\n", + "\n", + " # The lobatto nodes to be used for integration.\n", + " params.lobatto_quadrature_nodes = lagrange.LGL_points(params.N_quad)\n", + "\n", + " # The lobatto weights to be used for integration.\n", + " params.lobatto_weights_quadrature = lagrange.lobatto_weights\\\n", + " (params.N_quad)\n", + "\n", + " # A list of the Lagrange polynomials in poly1d form.\n", + " params.lagrange_product = lagrange.product_lagrange_poly(params.xi_LGL)\n", + "\n", + " # An array containing the coefficients of the lagrange basis polynomials.\n", + " params.lagrange_coeffs = af.np_to_af_array(\\\n", + " lagrange.lagrange_polynomials(params.xi_LGL)[1])\n", + "\n", + " # Refer corresponding functions.\n", + " params.lagrange_basis_value = lagrange.lagrange_function_value\\\n", + " (params.lagrange_coeffs)\n", + "\n", + " # A list of the Lagrange polynomials in poly1d form.\n", + " params.lagrange_poly1d_list = lagrange.lagrange_polynomials(params.xi_LGL)[0]\n", + "\n", + "\n", + " # list containing the poly1d forms of the differential of Lagrange\n", + " # basis polynomials.\n", + " params.differential_lagrange_polynomial = lagrange.differential_lagrange_poly1d()\n", + "\n", + "\n", + " # While evaluating the volume integral using N_LGL\n", + " # lobatto quadrature points, The integration can be vectorized\n", + " # and in this case the coefficients of the differential of the\n", + " # Lagrange polynomials is required\n", + " params.volume_integrand_N_LGL = np.zeros(([params.N_LGL, params.N_LGL - 1]))\n", + "\n", + " for i in range(params.N_LGL):\n", + " params.volume_integrand_N_LGL[i] = (params.differential_lagrange_polynomial[i]).c\n", + "\n", + " params.volume_integrand_N_LGL= af.np_to_af_array(params.volume_integrand_N_LGL)\n", + "\n", + " # Obtaining an array consisting of the LGL points mapped onto the elements.\n", + "\n", + " params.element_size = af.sum((params.x_nodes[1] - params.x_nodes[0])\\\n", + " / params.N_Elements)\n", + " params.elements_xi_LGL = af.constant(0, params.N_Elements, params.N_LGL)\n", + " params.elements = utils.linspace(af.sum(params.x_nodes[0]),\n", + " af.sum(params.x_nodes[1] - params.element_size),\\\n", + " params.N_Elements)\n", + "\n", + " params.np_element_array = np.concatenate((af.transpose(params.elements),\n", + " af.transpose(params.elements +\\\n", + " params.element_size)))\n", + "\n", + " params.element_mesh_nodes = utils.linspace(af.sum(params.x_nodes[0]),\n", + " af.sum(params.x_nodes[1]),\\\n", + " params.N_Elements + 1)\n", + "\n", + " params.element_array = af.transpose(af.np_to_af_array\\\n", + " (params.np_element_array))\n", + " params.element_LGL = wave_equation.mapping_xi_to_x(af.transpose\\\n", + " (params.element_array), params.xi_LGL)\n", + "\n", + " # The minimum distance between 2 mapped LGL points.\n", + " params.delta_x = af.min((params.element_LGL - af.shift(params.element_LGL, 1, 0))[1:, :])\n", + "\n", + " # dx_dxi for elements of equal size.\n", + " params. dx_dxi = af.mean(wave_equation.dx_dxi_numerical((params.element_mesh_nodes[0 : 2]),\\\n", + " params.xi_LGL))\n", + "\n", + "\n", + " # The value of time-step.\n", + " params.delta_t = params.delta_x / (4 * params.c)\n", + "\n", + " # Array of timesteps seperated by delta_t.\n", + " params.time = utils.linspace(0, int(params.total_time / params.delta_t) * params.delta_t,\n", + " int(params.total_time / params.delta_t))\n", + "\n", + " if (wave =='sin'):\n", + " params.u_init = af.sin(2 * np.pi * params.element_LGL)\n", + " \n", + " if (wave =='gaussian'):\n", + " params.u_init = np.e ** (-(params.element_LGL) ** 2 / 0.4 ** 2)\n", + " \n", + " params.u = af.constant(0, params.N_LGL, params.N_Elements, params.time.shape[0],\\\n", + " dtype = af.Dtype.f64)\n", + " params.u[:, :, 0] = params.u_init\n", + " \n", + " return\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3\n", + "option1\n", + "4\n", + "option1\n", + "5\n", + "option1\n", + "6\n", + "option1\n", + "7\n", + "option1\n", + "8\n", + "option1\n", + "9\n", + "option1\n", + "10\n", + "option1\n", + "11\n", + "option1\n", + "12\n", + "option1\n", + "13\n", + "option1\n" + ] + } + ], + "source": [ + "p = 0\n", + "error = []\n", + "\n", + "for N_LGL in np.arange(3, 14):\n", + " print(N_LGL)\n", + " change_parameters(int(N_LGL), wave = 'gaussian')\n", + " volume_integral_flux = wave_equation.volume_integral_flux(params.u_init, 0)\n", + " volume_integral_flux_analytical = np.zeros([params.N_LGL, params.N_Elements])\n", + "\n", + " for p in np.arange(N_LGL):\n", + " for element_idx, element in enumerate(params.element_array):\n", + " volume_integral_flux_analytical[p][element_idx] = int_exp_dLdxi(np.array(element)[0],\n", + " params.xi_LGL, p)\n", + "\n", + " volume_integral_flux_analytical = af.np_to_af_array(volume_integral_flux_analytical)\n", + "\n", + " error.append(np.array(af.sum(af.abs(volume_integral_flux_analytical - volume_integral_flux), 1))[p])" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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RNACIO1ePGqClt+aof8aZyyMGZKTo2jHebS2L/lGhB35bprr64I0j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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.semilogy(np.arange(3, 14), error, '-o')\n", + "plt.title(r'Error for $\\int e^{\\frac{-x^2}{0.4^2}} \\frac{d L_0}{d\\xi} d\\xi$ vs $N_{LGL}$')\n", + "plt.xlabel(r'$N_{LGL}$')\n", + "plt.ylabel(r'Error')\n", + "plt.savefig('error_int_fxi_dLi_dxi.png')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 45, "metadata": {}, "outputs": [ { @@ -140,7 +352,124 @@ } ], "source": [ - "print(wave_equation.volume_integral_flux(params.u_init))" + "N_LGL = 8\n", + "volume_integral_flux_analytical = np.zeros([params.N_LGL, params.N_Elements])\n", + "\n", + "for p in np.arange(N_LGL):\n", + " for element_idx, element in enumerate(params.element_array):\n", + " volume_integral_flux_analytical[p][element_idx] = int_sin2pix_dLdxi(np.array(element)[0],\n", + " params.xi_LGL, p)\n", + "\n", + "volume_integral_flux_analytical = af.np_to_af_array(volume_integral_flux_analytical)\n", + "print(volume_integral_flux_analytical)\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "arrayfire.Array()\n", + "Type: double\n", + "\n", + "[1 2 1 1]\n", + " 0.0000 0.1250 \n", + "\n", + "arrayfire.Array()\n", + "Type: double\n", + "\n", + "[1 2 1 1]\n", + " 0.1250 0.2500 \n", + "\n", + "arrayfire.Array()\n", + "Type: double\n", + "\n", + "[1 2 1 1]\n", + " 0.2500 0.3750 \n", + "\n", + "arrayfire.Array()\n", + "Type: double\n", + "\n", + "[1 2 1 1]\n", + " 0.3750 0.5000 \n", + "\n", + "arrayfire.Array()\n", + "Type: double\n", + "\n", + "[1 2 1 1]\n", + " 0.5000 0.6250 \n", + "\n", + "arrayfire.Array()\n", + "Type: double\n", + "\n", + "[1 2 1 1]\n", + " 0.6250 0.7500 \n", + "\n", + "arrayfire.Array()\n", + "Type: double\n", + "\n", + "[1 2 1 1]\n", + " 0.7500 0.8750 \n", + "\n", + "arrayfire.Array()\n", + "Type: double\n", + "\n", + "[1 2 1 1]\n", + " 0.8750 1.0000 \n", + "\n" + ] + } + ], + "source": [ + "for element in params.element_array:\n", + " print(element)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.01402496723026015" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "analytical_integral = 0.\n", + "p = 0\n", + "\n", + "\n", + "int_sin2pix_dLdxi(np.array(params.element_array[0])[0],\n", + " params.xi_LGL, p)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0. 0.125]\n" + ] + } + ], + "source": [ + "print(np.array(params.element_array[0])[0])" ] }, { From cc4996162b49bfea686f75df5f58882ce7396704 Mon Sep 17 00:00:00 2001 From: AAT Date: Mon, 9 Oct 2017 13:02:43 +0530 Subject: [PATCH 8/9] Minor modifications. --- examples/volume_integral_error_analysis.ipynb | 73 ++++++++++--------- 1 file changed, 40 insertions(+), 33 deletions(-) diff --git a/examples/volume_integral_error_analysis.ipynb b/examples/volume_integral_error_analysis.ipynb index f588165..03845ae 100644 --- a/examples/volume_integral_error_analysis.ipynb +++ b/examples/volume_integral_error_analysis.ipynb @@ -133,7 +133,7 @@ "metadata": {}, "outputs": [], "source": [ - "def change_parameters(N_LGL = 8, N_Elements = 8, wave = 'sin'):\n", + "def change_parameters(N_LGL = 8, N_Elements = 8, N_quad = 8, wave = 'sin'):\n", " '''\n", " '''\n", " # The domain of the function.\n", @@ -146,7 +146,7 @@ " params.N_Elements = N_Elements\n", "\n", " # The number quadrature points to be used for integration.\n", - " params.N_quad = N_LGL\n", + " params.N_quad = N_quad\n", "\n", " # Array containing the LGL points in xi space.\n", " params.xi_LGL = lagrange.LGL_points(params.N_LGL)\n", @@ -248,45 +248,51 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", "option1\n", - "4\n", - "option1\n", - "5\n", - "option1\n", - "6\n", - "option1\n", - "7\n", - "option1\n", - "8\n", - "option1\n", - "9\n", - "option1\n", - "10\n", - "option1\n", - "11\n", - "option1\n", - "12\n", - "option1\n", - "13\n", - "option1\n" + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n", + "option3\n" ] } ], "source": [ "p = 0\n", "error = []\n", + "N_LGL = 8\n", "\n", - "for N_LGL in np.arange(3, 14):\n", - " print(N_LGL)\n", - " change_parameters(int(N_LGL), wave = 'gaussian')\n", + "for N_quad in np.arange(3, 31):\n", + " change_parameters(int(N_LGL), N_quad = int(N_quad), wave = 'gaussian')\n", " volume_integral_flux = wave_equation.volume_integral_flux(params.u_init, 0)\n", " volume_integral_flux_analytical = np.zeros([params.N_LGL, params.N_Elements])\n", "\n", @@ -302,14 +308,14 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 17, "metadata": {}, "outputs": [ { "data": { - "image/png": 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RNACIO1ePGqClt+aof8aZyyMGZKTo2jHebS2L/lGhB35bprr64I0j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79fKxc3LOycyiLgkAAAAAoCLoRED5Wb+yUbNmVOrs+St6u+981OUAAAAAAHyE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\n5yTtHL0ygrX2IWNMuzHmueCRDP7Q4ScTKOsRa+3F5Rv9yzteHOHgDzw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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -317,9 +323,10 @@ } ], "source": [ - "plt.semilogy(np.arange(3, 14), error, '-o')\n", - "plt.title(r'Error for $\\int e^{\\frac{-x^2}{0.4^2}} \\frac{d L_0}{d\\xi} d\\xi$ vs $N_{LGL}$')\n", - "plt.xlabel(r'$N_{LGL}$')\n", + "plt.semilogy(np.arange(3, 31), error, '-o')\n", + "plt.title(r'Error for $\\int e^{\\frac{-x^2}{0.4^2}} \\frac{d L_0}{d\\xi} d\\xi$ vs $N_{quad}$')\n", + "# plt.title(r'Error for $\\int \\sin(2 \\pi x) \\frac{d L_0}{d\\xi} d\\xi$ vs $N_{quad}$')\n", + "plt.xlabel(r'$N_{quad}$')\n", "plt.ylabel(r'Error')\n", "plt.savefig('error_int_fxi_dLi_dxi.png')\n", "plt.show()" From 0638c18b25dbf65d879fff2413756b4d5763baf0 Mon Sep 17 00:00:00 2001 From: AAT Date: Mon, 9 Oct 2017 14:43:50 +0530 Subject: [PATCH 9/9] Minor changes --- examples/volume_integral_error_analysis.ipynb | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/examples/volume_integral_error_analysis.ipynb b/examples/volume_integral_error_analysis.ipynb index 03845ae..d14020c 100644 --- a/examples/volume_integral_error_analysis.ipynb +++ b/examples/volume_integral_error_analysis.ipynb @@ -248,7 +248,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 36, "metadata": {}, "outputs": [ { @@ -290,6 +290,7 @@ "p = 0\n", "error = []\n", "N_LGL = 8\n", + "N_quad = 8\n", "\n", "for N_quad in np.arange(3, 31):\n", " change_parameters(int(N_LGL), N_quad = int(N_quad), wave = 'gaussian')\n", @@ -299,7 +300,7 @@ " for p in np.arange(N_LGL):\n", " for element_idx, element in enumerate(params.element_array):\n", " volume_integral_flux_analytical[p][element_idx] = int_exp_dLdxi(np.array(element)[0],\n", - " params.xi_LGL, p)\n", + " params.xi_LGL, p)\n", "\n", " volume_integral_flux_analytical = af.np_to_af_array(volume_integral_flux_analytical)\n", "\n", @@ -308,14 +309,14 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 37, "metadata": {}, "outputs": [ { "data": { - "image/png": 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79fKxc3LOycyiLgkAAAAAoCLoRED5Wb+yUbNmVOrs+St6u+981OUAAAAAAHyE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\n5yTtHL0ygrX2IWNMuzHmueCRDP7Q4ScTKOsRa+3F5Rv9yzteHOHgDzw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my9/0HG5gJHk7geS907lN3BDPr6dJc1/DvixmRsTuOBLPfw2OuHPskTcLo0nez868vhBB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\n1iwoiF6RABBnCBGAJFQ2I1u5GSlq9w7ocEO7rp2b53RJAABEVFV9i77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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -324,7 +325,8 @@ ], "source": [ "plt.semilogy(np.arange(3, 31), error, '-o')\n", - "plt.title(r'Error for $\\int e^{\\frac{-x^2}{0.4^2}} \\frac{d L_0}{d\\xi} d\\xi$ vs $N_{quad}$')\n", + "plt.title(r'Error for $\\int e^{\\frac{-x^2}{0.4^2}} \\frac{d L_0}{d\\xi} d\\xi$ vs $N_{quad}(N_{LGL} = 8)$')\n", + "# plt.title(r'Error for $\\int e^{\\frac{-x^2}{0.4^2}} \\frac{d L_0}{d\\xi} d\\xi$ vs $N_{LGL} (N_{quad} = 8)$')\n", "# plt.title(r'Error for $\\int \\sin(2 \\pi x) \\frac{d L_0}{d\\xi} d\\xi$ vs $N_{quad}$')\n", "plt.xlabel(r'$N_{quad}$')\n", "plt.ylabel(r'Error')\n",