From 92e6966461f2a6020869de2759ec0a850e452eca Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Thu, 1 Jun 2023 07:21:52 +0400 Subject: [PATCH 01/25] Created using Colaboratory --- cohen_functions_c01.ipynb | 369 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 369 insertions(+) create mode 100644 cohen_functions_c01.ipynb diff --git a/cohen_functions_c01.ipynb b/cohen_functions_c01.ipynb new file mode 100644 index 0000000..18ae324 --- /dev/null +++ b/cohen_functions_c01.ipynb @@ -0,0 +1,369 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyMdyEFJiOITu5442SOV+dqo", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "zDKIELk8SFO4" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt\n", + "from decimal import getcontext, Decimal" + ] + }, + { + "cell_type": "code", + "source": [ + "xDomain = [-2, 2]\n", + "\n", + "#Dealing with floats and Decimals\n", + "df_test = np.arange(Decimal('-2.0'), Decimal('2.0'), Decimal('0.1'))\n", + "df_test" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "ohGazC54UR8N", + "outputId": "665a50ab-f4ff-4638-f723-6e3ec6767e1a" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([Decimal('-2.0'), Decimal('-1.9'), Decimal('-1.8'), Decimal('-1.7'),\n", + " Decimal('-1.6'), Decimal('-1.5'), Decimal('-1.4'), Decimal('-1.3'),\n", + " Decimal('-1.2'), Decimal('-1.1'), Decimal('-1.0'), Decimal('-0.9'),\n", + " Decimal('-0.8'), Decimal('-0.7'), Decimal('-0.6'), Decimal('-0.5'),\n", + " Decimal('-0.4'), Decimal('-0.3'), Decimal('-0.2'), Decimal('-0.1'),\n", + " Decimal('0.0'), Decimal('0.1'), Decimal('0.2'), Decimal('0.3'),\n", + " Decimal('0.4'), Decimal('0.5'), Decimal('0.6'), Decimal('0.7'),\n", + " Decimal('0.8'), Decimal('0.9'), Decimal('1.0'), Decimal('1.1'),\n", + " Decimal('1.2'), Decimal('1.3'), Decimal('1.4'), Decimal('1.5'),\n", + " Decimal('1.6'), Decimal('1.7'), Decimal('1.8'), Decimal('1.9')],\n", + " dtype=object)" + ] + }, + "metadata": {}, + "execution_count": 11 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Option 1\n", + "resolution = .1\n", + "x = np.arange(xDomain[0], xDomain[1]+resolution, resolution)\n", + "np.set_printoptions(suppress=False)\n", + "x" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "2kjHqC0Jkqyp", + "outputId": "391f9128-072d-46e5-dca7-e4bc9dfcf59f" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-2.00000000e+00, -1.90000000e+00, -1.80000000e+00, -1.70000000e+00,\n", + " -1.60000000e+00, -1.50000000e+00, -1.40000000e+00, -1.30000000e+00,\n", + " -1.20000000e+00, -1.10000000e+00, -1.00000000e+00, -9.00000000e-01,\n", + " -8.00000000e-01, -7.00000000e-01, -6.00000000e-01, -5.00000000e-01,\n", + " -4.00000000e-01, -3.00000000e-01, -2.00000000e-01, -1.00000000e-01,\n", + " 1.77635684e-15, 1.00000000e-01, 2.00000000e-01, 3.00000000e-01,\n", + " 4.00000000e-01, 5.00000000e-01, 6.00000000e-01, 7.00000000e-01,\n", + " 8.00000000e-01, 9.00000000e-01, 1.00000000e+00, 1.10000000e+00,\n", + " 1.20000000e+00, 1.30000000e+00, 1.40000000e+00, 1.50000000e+00,\n", + " 1.60000000e+00, 1.70000000e+00, 1.80000000e+00, 1.90000000e+00,\n", + " 2.00000000e+00])" + ] + }, + "metadata": {}, + "execution_count": 12 + } + ] + }, + { + "cell_type": "code", + "source": [ + "np.set_printoptions(suppress=True)\n", + "x" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "abAf_H5bjlOs", + "outputId": "a4ddc94d-de1d-4203-b143-b632b38d95d4" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-2. , -1.9, -1.8, -1.7, -1.6, -1.5, -1.4, -1.3, -1.2, -1.1, -1. ,\n", + " -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0. , 0.1,\n", + " 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. , 1.1, 1.2,\n", + " 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2. ])" + ] + }, + "metadata": {}, + "execution_count": 25 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Option 2\n", + "x2 = np.linspace(xDomain[0], xDomain[1], 41)\n", + "# ODD number above : 41 will gurentee a true 0\n", + "x2" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "fCoahddMk-Md", + "outputId": "70dbc6af-cf84-4d95-b2c8-89dcc91246fa" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-2. , -1.9, -1.8, -1.7, -1.6, -1.5, -1.4, -1.3, -1.2, -1.1, -1. ,\n", + " -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0. , 0.1,\n", + " 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. , 1.1, 1.2,\n", + " 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2. ])" + ] + }, + "metadata": {}, + "execution_count": 23 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Function - in form of math function and not as python function\n", + "y = x**2 + 3*x**3 - x**4\n", + "y" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "n12q7dMWmk8J", + "outputId": "b4e76ae0-e5ee-49de-9a5c-782ce3833e71" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-36. , -29.9991, -24.7536, -20.2011, -16.2816, -12.9375,\n", + " -10.1136, -7.7571, -5.8176, -4.2471, -3. , -2.0331,\n", + " -1.3056, -0.7791, -0.4176, -0.1875, -0.0576, 0.0009,\n", + " 0.0144, 0.0069, 0. , 0.0129, 0.0624, 0.1629,\n", + " 0.3264, 0.5625, 0.8784, 1.2789, 1.7664, 2.3409,\n", + " 3. , 3.7389, 4.5504, 5.4249, 6.3504, 7.3125,\n", + " 8.2944, 9.2769, 10.2384, 11.1549, 12. ])" + ] + }, + "metadata": {}, + "execution_count": 28 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# plot\n", + "plt.plot(x, y, label='$y=x^2+3x^3-x^4$')\n", + "plt.grid()\n", + "plt.legend()\n", + "plt.xlim(xDomain[0], xDomain[1])\n", + "plt.xlabel('x')\n", + "plt.ylabel('y=f(x)')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "k97NGhiyndnH", + "outputId": "f3ea34d8-a08c-4a09-db5b-afc22bb8a5aa" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# symbolic variable\n", + "s_beta = sym.var('beta')\n", + "s_beta\n", + "# xN or n_ or -> numpy variable\n", + "# xS or s_ or -> sympy variable\n", + "\n", + "# function\n", + "s_y = s_beta**2 + 3*s_beta**3 - s_beta**4\n", + "s_y" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 39 + }, + "id": "I1dUouVSsEWe", + "outputId": "5827a255-1704-4b2a-9625-99daaec4479a" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "-beta**4 + 3*beta**3 + beta**2" + ], + "text/latex": "$\\displaystyle - \\beta^{4} + 3 \\beta^{3} + \\beta^{2}$" + }, + "metadata": {}, + "execution_count": 40 + } + ] + }, + { + "cell_type": "code", + "source": [ + "sym.plot(s_y,(s_beta, xDomain[0], xDomain[1]), xlabel='x', ylabel=None, title=f'$f(\\\\beta)={sym.latex(s_y)}$')" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 505 + }, + "id": "D--gTBYYtY6U", + "outputId": "9cab6d9c-f78f-45d7-b09d-c3d4a370ab7e" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "execution_count": 55 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# converting sympy objects into functions that we can query and use in numpy and matplotlib \n", + "fx = sym.lambdify(s_beta, s_y)\n", + "fx(2)\n", + "\n", + "l_y = fx(x)\n", + "plt.plot(x, l_y)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 448 + }, + "id": "zPTIcmNiv2jo", + "outputId": "a60b25ce-b92e-482b-e9f9-bd97d761340a" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 58 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From e6289c661b678caea82e5ca804b1105799c405b4 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Thu, 1 Jun 2023 07:28:04 +0400 Subject: [PATCH 02/25] functions exercise 1,2, and 3 --- practice/functions/functions_c01.ipynb | 369 +++++++++++++++++++++++++ 1 file changed, 369 insertions(+) create mode 100644 practice/functions/functions_c01.ipynb diff --git a/practice/functions/functions_c01.ipynb b/practice/functions/functions_c01.ipynb new file mode 100644 index 0000000..5922851 --- /dev/null +++ b/practice/functions/functions_c01.ipynb @@ -0,0 +1,369 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyMdyEFJiOITu5442SOV+dqo", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "zDKIELk8SFO4" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt\n", + "from decimal import getcontext, Decimal" + ] + }, + { + "cell_type": "code", + "source": [ + "xDomain = [-2, 2]\n", + "\n", + "#Dealing with floats and Decimals\n", + "df_test = np.arange(Decimal('-2.0'), Decimal('2.0'), Decimal('0.1'))\n", + "df_test" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "ohGazC54UR8N", + "outputId": "665a50ab-f4ff-4638-f723-6e3ec6767e1a" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([Decimal('-2.0'), Decimal('-1.9'), Decimal('-1.8'), Decimal('-1.7'),\n", + " Decimal('-1.6'), Decimal('-1.5'), Decimal('-1.4'), Decimal('-1.3'),\n", + " Decimal('-1.2'), Decimal('-1.1'), Decimal('-1.0'), Decimal('-0.9'),\n", + " Decimal('-0.8'), Decimal('-0.7'), Decimal('-0.6'), Decimal('-0.5'),\n", + " Decimal('-0.4'), Decimal('-0.3'), Decimal('-0.2'), Decimal('-0.1'),\n", + " Decimal('0.0'), Decimal('0.1'), Decimal('0.2'), Decimal('0.3'),\n", + " Decimal('0.4'), Decimal('0.5'), Decimal('0.6'), Decimal('0.7'),\n", + " Decimal('0.8'), Decimal('0.9'), Decimal('1.0'), Decimal('1.1'),\n", + " Decimal('1.2'), Decimal('1.3'), Decimal('1.4'), Decimal('1.5'),\n", + " Decimal('1.6'), Decimal('1.7'), Decimal('1.8'), Decimal('1.9')],\n", + " dtype=object)" + ] + }, + "metadata": {}, + "execution_count": 11 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Option 1\n", + "resolution = .1\n", + "x = np.arange(xDomain[0], xDomain[1]+resolution, resolution)\n", + "np.set_printoptions(suppress=False)\n", + "x" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "2kjHqC0Jkqyp", + "outputId": "391f9128-072d-46e5-dca7-e4bc9dfcf59f" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-2.00000000e+00, -1.90000000e+00, -1.80000000e+00, -1.70000000e+00,\n", + " -1.60000000e+00, -1.50000000e+00, -1.40000000e+00, -1.30000000e+00,\n", + " -1.20000000e+00, -1.10000000e+00, -1.00000000e+00, -9.00000000e-01,\n", + " -8.00000000e-01, -7.00000000e-01, -6.00000000e-01, -5.00000000e-01,\n", + " -4.00000000e-01, -3.00000000e-01, -2.00000000e-01, -1.00000000e-01,\n", + " 1.77635684e-15, 1.00000000e-01, 2.00000000e-01, 3.00000000e-01,\n", + " 4.00000000e-01, 5.00000000e-01, 6.00000000e-01, 7.00000000e-01,\n", + " 8.00000000e-01, 9.00000000e-01, 1.00000000e+00, 1.10000000e+00,\n", + " 1.20000000e+00, 1.30000000e+00, 1.40000000e+00, 1.50000000e+00,\n", + " 1.60000000e+00, 1.70000000e+00, 1.80000000e+00, 1.90000000e+00,\n", + " 2.00000000e+00])" + ] + }, + "metadata": {}, + "execution_count": 12 + } + ] + }, + { + "cell_type": "code", + "source": [ + "np.set_printoptions(suppress=True)\n", + "x" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "abAf_H5bjlOs", + "outputId": "a4ddc94d-de1d-4203-b143-b632b38d95d4" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-2. , -1.9, -1.8, -1.7, -1.6, -1.5, -1.4, -1.3, -1.2, -1.1, -1. ,\n", + " -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0. , 0.1,\n", + " 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. , 1.1, 1.2,\n", + " 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2. ])" + ] + }, + "metadata": {}, + "execution_count": 25 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Option 2\n", + "x2 = np.linspace(xDomain[0], xDomain[1], 41)\n", + "# ODD number above : 41 will gurentee a true 0\n", + "x2" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "fCoahddMk-Md", + "outputId": "70dbc6af-cf84-4d95-b2c8-89dcc91246fa" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-2. , -1.9, -1.8, -1.7, -1.6, -1.5, -1.4, -1.3, -1.2, -1.1, -1. ,\n", + " -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0. , 0.1,\n", + " 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. , 1.1, 1.2,\n", + " 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2. ])" + ] + }, + "metadata": {}, + "execution_count": 23 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Function - in form of math function and not as python function\n", + "y = x**2 + 3*x**3 - x**4\n", + "y" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "n12q7dMWmk8J", + "outputId": "b4e76ae0-e5ee-49de-9a5c-782ce3833e71" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-36. , -29.9991, -24.7536, -20.2011, -16.2816, -12.9375,\n", + " -10.1136, -7.7571, -5.8176, -4.2471, -3. , -2.0331,\n", + " -1.3056, -0.7791, -0.4176, -0.1875, -0.0576, 0.0009,\n", + " 0.0144, 0.0069, 0. , 0.0129, 0.0624, 0.1629,\n", + " 0.3264, 0.5625, 0.8784, 1.2789, 1.7664, 2.3409,\n", + " 3. , 3.7389, 4.5504, 5.4249, 6.3504, 7.3125,\n", + " 8.2944, 9.2769, 10.2384, 11.1549, 12. ])" + ] + }, + "metadata": {}, + "execution_count": 28 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# plot\n", + "plt.plot(x, y, label='$y=x^2+3x^3-x^4$')\n", + "plt.grid()\n", + "plt.legend()\n", + "plt.xlim(xDomain[0], xDomain[1])\n", + "plt.xlabel('x')\n", + "plt.ylabel('y=f(x)')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "k97NGhiyndnH", + "outputId": "f3ea34d8-a08c-4a09-db5b-afc22bb8a5aa" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# symbolic variable\n", + "s_beta = sym.var('beta')\n", + "s_beta\n", + "# xN or n_ or -> numpy variable\n", + "# xS or s_ or -> sympy variable\n", + "\n", + "# function\n", + "s_y = s_beta**2 + 3*s_beta**3 - s_beta**4\n", + "s_y" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 39 + }, + "id": "I1dUouVSsEWe", + "outputId": "5827a255-1704-4b2a-9625-99daaec4479a" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "-beta**4 + 3*beta**3 + beta**2" + ], + "text/latex": "$\\displaystyle - \\beta^{4} + 3 \\beta^{3} + \\beta^{2}$" + }, + "metadata": {}, + "execution_count": 40 + } + ] + }, + { + "cell_type": "code", + "source": [ + "sym.plot(s_y,(s_beta, xDomain[0], xDomain[1]), xlabel='x', ylabel=None, title=f'$f(\\\\beta)={sym.latex(s_y)}$')" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 505 + }, + "id": "D--gTBYYtY6U", + "outputId": "9cab6d9c-f78f-45d7-b09d-c3d4a370ab7e" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "execution_count": 55 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# converting sympy objects into functions that we can query and use in numpy and matplotlib \n", + "fx = sym.lambdify(s_beta, s_y)\n", + "fx(2)\n", + "\n", + "l_y = fx(x)\n", + "plt.plot(x, l_y)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 448 + }, + "id": "zPTIcmNiv2jo", + "outputId": "a60b25ce-b92e-482b-e9f9-bd97d761340a" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 58 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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+ }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From af951cd920c2e779a22ea0c38c4e1b59ed411a07 Mon Sep 17 00:00:00 2001 From: Hammad Date: Thu, 1 Jun 2023 07:32:12 +0400 Subject: [PATCH 03/25] practice folder setup --- .gitignore | 1 + cohen_functions_c01.ipynb | 369 -------------------------------------- 2 files changed, 1 insertion(+), 369 deletions(-) create mode 100644 .gitignore delete mode 100644 cohen_functions_c01.ipynb diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..62c8935 --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +.idea/ \ No newline at end of file diff --git a/cohen_functions_c01.ipynb b/cohen_functions_c01.ipynb deleted file mode 100644 index 18ae324..0000000 --- a/cohen_functions_c01.ipynb +++ /dev/null @@ -1,369 +0,0 @@ -{ - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "provenance": [], - "authorship_tag": "ABX9TyMdyEFJiOITu5442SOV+dqo", - "include_colab_link": true - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - }, - "language_info": { - "name": "python" - } - }, - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "id": "view-in-github", - "colab_type": "text" - }, - "source": [ - "\"Open" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "id": "zDKIELk8SFO4" - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import sympy as sym\n", - "import matplotlib.pyplot as plt\n", - "from decimal import getcontext, Decimal" - ] - }, - { - "cell_type": "code", - "source": [ - "xDomain = [-2, 2]\n", - "\n", - "#Dealing with floats and Decimals\n", - "df_test = np.arange(Decimal('-2.0'), Decimal('2.0'), Decimal('0.1'))\n", - "df_test" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "ohGazC54UR8N", - "outputId": "665a50ab-f4ff-4638-f723-6e3ec6767e1a" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - 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"np.set_printoptions(suppress=False)\n", - "x" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "2kjHqC0Jkqyp", - "outputId": "391f9128-072d-46e5-dca7-e4bc9dfcf59f" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "array([-2.00000000e+00, -1.90000000e+00, -1.80000000e+00, -1.70000000e+00,\n", - " -1.60000000e+00, -1.50000000e+00, -1.40000000e+00, -1.30000000e+00,\n", - " -1.20000000e+00, -1.10000000e+00, -1.00000000e+00, -9.00000000e-01,\n", - " -8.00000000e-01, -7.00000000e-01, -6.00000000e-01, -5.00000000e-01,\n", - " -4.00000000e-01, -3.00000000e-01, -2.00000000e-01, -1.00000000e-01,\n", - " 1.77635684e-15, 1.00000000e-01, 2.00000000e-01, 3.00000000e-01,\n", - " 4.00000000e-01, 5.00000000e-01, 6.00000000e-01, 7.00000000e-01,\n", - " 8.00000000e-01, 9.00000000e-01, 1.00000000e+00, 1.10000000e+00,\n", - " 1.20000000e+00, 1.30000000e+00, 1.40000000e+00, 1.50000000e+00,\n", - " 1.60000000e+00, 1.70000000e+00, 1.80000000e+00, 1.90000000e+00,\n", - " 2.00000000e+00])" - ] - }, - "metadata": {}, - "execution_count": 12 - } - ] - }, - { - "cell_type": "code", - "source": [ - "np.set_printoptions(suppress=True)\n", - "x" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "abAf_H5bjlOs", - "outputId": "a4ddc94d-de1d-4203-b143-b632b38d95d4" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "array([-2. , -1.9, -1.8, -1.7, -1.6, -1.5, -1.4, -1.3, -1.2, -1.1, -1. ,\n", - " -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0. , 0.1,\n", - " 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. , 1.1, 1.2,\n", - " 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2. ])" - ] - }, - "metadata": {}, - "execution_count": 25 - } - ] - }, - { - "cell_type": "code", - "source": [ - "# Option 2\n", - "x2 = np.linspace(xDomain[0], xDomain[1], 41)\n", - "# ODD number above : 41 will gurentee a true 0\n", - "x2" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "fCoahddMk-Md", - "outputId": "70dbc6af-cf84-4d95-b2c8-89dcc91246fa" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "array([-2. , -1.9, -1.8, -1.7, -1.6, -1.5, -1.4, -1.3, -1.2, -1.1, -1. ,\n", - " -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0. , 0.1,\n", - " 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. , 1.1, 1.2,\n", - " 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2. ])" - ] - }, - "metadata": {}, - "execution_count": 23 - } - ] - }, - { - "cell_type": "code", - "source": [ - "# Function - in form of math function and not as python function\n", - "y = x**2 + 3*x**3 - x**4\n", - "y" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "n12q7dMWmk8J", - "outputId": "b4e76ae0-e5ee-49de-9a5c-782ce3833e71" - }, - "execution_count": null, - "outputs": [ - { - "output_type": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "# symbolic variable\n", - "s_beta = sym.var('beta')\n", - "s_beta\n", - "# xN or n_ or -> numpy variable\n", - "# xS or s_ or -> sympy variable\n", - "\n", - "# function\n", - "s_y = s_beta**2 + 3*s_beta**3 - s_beta**4\n", - "s_y" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 39 - }, - "id": "I1dUouVSsEWe", - "outputId": "5827a255-1704-4b2a-9625-99daaec4479a" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "-beta**4 + 3*beta**3 + beta**2" - ], - "text/latex": "$\\displaystyle - \\beta^{4} + 3 \\beta^{3} + \\beta^{2}$" - }, - "metadata": {}, - "execution_count": 40 - } - ] - }, - { - "cell_type": "code", - "source": [ - "sym.plot(s_y,(s_beta, xDomain[0], xDomain[1]), xlabel='x', ylabel=None, title=f'$f(\\\\beta)={sym.latex(s_y)}$')" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 505 - }, - "id": "D--gTBYYtY6U", - "outputId": "9cab6d9c-f78f-45d7-b09d-c3d4a370ab7e" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - }, - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "" - ] - }, - "metadata": {}, - "execution_count": 55 - } - ] - }, - { - "cell_type": "code", - "source": [ - "# converting sympy objects into functions that we can query and use in numpy and matplotlib \n", - "fx = sym.lambdify(s_beta, s_y)\n", - "fx(2)\n", - "\n", - "l_y = fx(x)\n", - "plt.plot(x, l_y)" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 448 - }, - "id": "zPTIcmNiv2jo", - "outputId": "a60b25ce-b92e-482b-e9f9-bd97d761340a" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "[]" - ] - }, - "metadata": {}, - "execution_count": 58 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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- }, - "metadata": {} - } - ] - } - ] -} \ No newline at end of file From f4574e9a919100c6143b6795e17d0b80908cb9aa Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Fri, 2 Jun 2023 02:58:45 +0400 Subject: [PATCH 04/25] exercise 1 - random polynomials in numpy --- polynomials_c01.ipynb | 129 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 129 insertions(+) create mode 100644 polynomials_c01.ipynb diff --git a/polynomials_c01.ipynb b/polynomials_c01.ipynb new file mode 100644 index 0000000..33c5317 --- /dev/null +++ b/polynomials_c01.ipynb @@ -0,0 +1,129 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyMG1NjgFUpilYohgv7YBGLc", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "BMoeJ9D7WOAf" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "np.set_printoptions(suppress=True)" + ], + "metadata": { + "id": "S3FTKG10Wai2" + }, + "execution_count": 2, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "xDomain = [-6, 6]\n", + "resolution = .5\n", + "n_coefs = np.random.randn(4)\n", + "x = np.arange(xDomain[0], xDomain[1]+resolution, resolution)\n", + "y = np.zeros(len(x))\n", + "fname = '$y = '\n", + "for i,c in enumerate(n_coefs):\n", + " y += c*x**i\n", + " fname += '+ '[int(c<0)] + f'{c:.2f}x^{i}'\n", + "y, n_coefs" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "bGNnY49VXA2c", + "outputId": "10e4596e-955e-4d31-eb47-a8d010955bfa" + }, + "execution_count": 32, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(array([ 69.82772365, 52.57972036, 38.46030961, 27.15368498,\n", + " 18.34404005, 11.71556841, 6.95246364, 3.73891931,\n", + " 1.75912902, 0.69728634, 0.23758486, 0.06421815,\n", + " -0.13862019, -0.68673659, -1.89593746, -4.08202922,\n", + " -7.5608183 , -12.6481111 , -19.65971405, -28.91143356,\n", + " -40.71907605, -55.39844794, -73.26535564, -94.63560558,\n", + " -119.82500417]),\n", + " array([-0.13862019, -0.64568593, -0.69055611, -0.42107522]))" + ] + }, + "metadata": {}, + "execution_count": 32 + } + ] + }, + { + "cell_type": "code", + "source": [ + "plt.plot(x, y)\n", + "plt.title(fname + '$')\n", + "plt.grid()\n", + "plt.xlim(xDomain[0], xDomain[1])\n", + "plt.xlabel('x')\n", + "plt.ylabel('y=f(x)')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 476 + }, + "id": "5Bk3aY44Xyy0", + "outputId": "4442fc6d-e9ae-4b16-ba99-e5f8ca1b6c65" + }, + "execution_count": 33, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From a3b3f90de6e4ddded6cfabb6fbed65bfd3abc538 Mon Sep 17 00:00:00 2001 From: Hammad Date: Fri, 2 Jun 2023 03:01:13 +0400 Subject: [PATCH 05/25] practice/functions base path added to polynomials_c01.ipynb --- polynomials_c01.ipynb => practice/functions/polynomials_c01.ipynb | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename polynomials_c01.ipynb => practice/functions/polynomials_c01.ipynb (100%) diff --git a/polynomials_c01.ipynb b/practice/functions/polynomials_c01.ipynb similarity index 100% rename from polynomials_c01.ipynb rename to practice/functions/polynomials_c01.ipynb From 8a7441eb665f6fa88097b2aad8e00ad469be0220 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Mon, 5 Jun 2023 00:24:51 +0400 Subject: [PATCH 06/25] code challenge 01 polynomials completed --- practice/functions/polynomials_c01.ipynb | 124 +++++++++++++++++++---- 1 file changed, 102 insertions(+), 22 deletions(-) diff --git a/practice/functions/polynomials_c01.ipynb b/practice/functions/polynomials_c01.ipynb index 33c5317..7095e65 100644 --- a/practice/functions/polynomials_c01.ipynb +++ b/practice/functions/polynomials_c01.ipynb @@ -4,7 +4,7 @@ "metadata": { "colab": { "provenance": [], - "authorship_tag": "ABX9TyMG1NjgFUpilYohgv7YBGLc", + "authorship_tag": "ABX9TyOn6gvcN5BGFAy2ztZhbudb", "include_colab_link": true }, "kernelspec": { @@ -23,7 +23,7 @@ "colab_type": "text" }, "source": [ - "\"Open" + "\"Open" ] }, { @@ -47,7 +47,7 @@ "metadata": { "id": "S3FTKG10Wai2" }, - "execution_count": 2, + "execution_count": 7, "outputs": [] }, { @@ -56,46 +56,46 @@ "xDomain = [-6, 6]\n", "resolution = .5\n", "n_coefs = np.random.randn(4)\n", - "x = np.arange(xDomain[0], xDomain[1]+resolution, resolution)\n", - "y = np.zeros(len(x))\n", + "n_x = np.arange(xDomain[0], xDomain[1]+resolution, resolution)\n", + "n_y = np.zeros(len(x))\n", "fname = '$y = '\n", "for i,c in enumerate(n_coefs):\n", - " y += c*x**i\n", + " n_y += c*n_x**i\n", " fname += '+ '[int(c<0)] + f'{c:.2f}x^{i}'\n", - "y, n_coefs" + "n_y, n_coefs" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "bGNnY49VXA2c", - "outputId": "10e4596e-955e-4d31-eb47-a8d010955bfa" + "outputId": "120bc66e-b667-4316-f9e1-54a769d46647" }, - "execution_count": 32, + "execution_count": 8, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ - "(array([ 69.82772365, 52.57972036, 38.46030961, 27.15368498,\n", - " 18.34404005, 11.71556841, 6.95246364, 3.73891931,\n", - " 1.75912902, 0.69728634, 0.23758486, 0.06421815,\n", - " -0.13862019, -0.68673659, -1.89593746, -4.08202922,\n", - " -7.5608183 , -12.6481111 , -19.65971405, -28.91143356,\n", - " -40.71907605, -55.39844794, -73.26535564, -94.63560558,\n", - " -119.82500417]),\n", - " array([-0.13862019, -0.64568593, -0.69055611, -0.42107522]))" + "(array([ 112.43582432, 85.22762935, 62.66471028, 44.31922304,\n", + " 29.76332358, 18.56916785, 10.3089118 , 4.55471136,\n", + " 0.87872248, -1.14689888, -1.94999679, -1.9584153 ,\n", + " -1.59999846, -1.30259033, -1.49403496, -2.60217641,\n", + " -5.05485873, -9.27992598, -15.7052222 , -24.75859146,\n", + " -36.86787781, -52.46092531, -71.965578 , -95.80967994,\n", + " -124.42107519]),\n", + " array([-1.59999846, 0.79843965, -0.12201742, -0.57045874]))" ] }, "metadata": {}, - "execution_count": 32 + "execution_count": 8 } ] }, { "cell_type": "code", "source": [ - "plt.plot(x, y)\n", + "plt.plot(n_x, n_y)\n", "plt.title(fname + '$')\n", "plt.grid()\n", "plt.xlim(xDomain[0], xDomain[1])\n", @@ -109,9 +109,9 @@ "height": 476 }, "id": "5Bk3aY44Xyy0", - "outputId": "4442fc6d-e9ae-4b16-ba99-e5f8ca1b6c65" + "outputId": "906ec374-2172-41a8-ade0-35150630f4f1" }, - "execution_count": 33, + "execution_count": 10, "outputs": [ { "output_type": "display_data", @@ -119,11 +119,91 @@ "text/plain": [ "
" ], - "image/png": 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\n" + "image/png": 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\n" }, "metadata": {} } ] + }, + { + "cell_type": "code", + "source": [ + "from sympy import symbols\n", + "s_x = symbols('x')" + ], + "metadata": { + "id": "fqzwNqGGpy5G" + }, + "execution_count": 21, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "nume = s_x**2 - 2*s_x\n", + "deno = s_x**2 - 4\n", + "s_f = nume / deno\n", + "s_f" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 55 + }, + "id": "R21GXg2zp5Gw", + "outputId": "b8c1d567-82b8-409d-8183-ebca4a969121" + }, + "execution_count": 26, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(x**2 - 2*x)/(x**2 - 4)" + ], + "text/latex": "$\\displaystyle \\frac{x^{2} - 2 x}{x^{2} - 4}$" + }, + "metadata": {}, + "execution_count": 26 + } + ] + }, + { + "cell_type": "code", + "source": [ + "sym.plot(s_f, (s_x, -3, 3), ylim=[-10, 10], title=f'$y= {sym.latex(s_f)}$')" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 504 + }, + "id": "R9U4MlM0EATs", + "outputId": "5477bc67-5480-4af4-a741-fa2297677af6" + }, + "execution_count": 29, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "execution_count": 29 + } + ] } ] } \ No newline at end of file From 0bc3996ea870a78c683aa45fa929d39423ceae6a Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Fri, 9 Jun 2023 17:04:34 +0400 Subject: [PATCH 07/25] exercise completed --- practice/functions/polynomials_c02.ipynb | 140 +++++++++++++++++++++++ 1 file changed, 140 insertions(+) create mode 100644 practice/functions/polynomials_c02.ipynb diff --git a/practice/functions/polynomials_c02.ipynb b/practice/functions/polynomials_c02.ipynb new file mode 100644 index 0000000..e3b5399 --- /dev/null +++ b/practice/functions/polynomials_c02.ipynb @@ -0,0 +1,140 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyOt23NQQtqQe+e4ZiN4fDUy", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "PPNtQEUeih4-" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "order = 10\n", + "x = np.linspace(-2*np.pi, 2*np.pi, 100)\n", + "y = np.zeros(len(x))\n", + "x, y" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "AcxI5_zUiqWu", + "outputId": "fb9fb4eb-b058-4c6a-c066-a755b4a7d0ad" + }, + "execution_count": 2, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(array([-6.28318531, -6.15625227, -6.02931923, -5.9023862 , -5.77545316,\n", + " -5.64852012, -5.52158709, -5.39465405, -5.26772102, -5.14078798,\n", + " -5.01385494, -4.88692191, -4.75998887, -4.63305583, -4.5061228 ,\n", + " -4.37918976, -4.25225672, -4.12532369, -3.99839065, -3.87145761,\n", + " -3.74452458, -3.61759154, -3.4906585 , -3.36372547, -3.23679243,\n", + " -3.10985939, -2.98292636, -2.85599332, -2.72906028, -2.60212725,\n", + " -2.47519421, -2.34826118, -2.22132814, -2.0943951 , -1.96746207,\n", + " -1.84052903, -1.71359599, -1.58666296, -1.45972992, -1.33279688,\n", + " -1.20586385, -1.07893081, -0.95199777, -0.82506474, -0.6981317 ,\n", + " -0.57119866, -0.44426563, -0.31733259, -0.19039955, -0.06346652,\n", + " 0.06346652, 0.19039955, 0.31733259, 0.44426563, 0.57119866,\n", + " 0.6981317 , 0.82506474, 0.95199777, 1.07893081, 1.20586385,\n", + " 1.33279688, 1.45972992, 1.58666296, 1.71359599, 1.84052903,\n", + " 1.96746207, 2.0943951 , 2.22132814, 2.34826118, 2.47519421,\n", + " 2.60212725, 2.72906028, 2.85599332, 2.98292636, 3.10985939,\n", + " 3.23679243, 3.36372547, 3.4906585 , 3.61759154, 3.74452458,\n", + " 3.87145761, 3.99839065, 4.12532369, 4.25225672, 4.37918976,\n", + " 4.5061228 , 4.63305583, 4.75998887, 4.88692191, 5.01385494,\n", + " 5.14078798, 5.26772102, 5.39465405, 5.52158709, 5.64852012,\n", + " 5.77545316, 5.9023862 , 6.02931923, 6.15625227, 6.28318531]),\n", + " array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n", + " 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n", + " 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n", + " 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n", + " 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n", + " 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]))" + ] + }, + "metadata": {}, + "execution_count": 2 + } + ] + }, + { + "cell_type": "code", + "source": [ + "for n in range(1, order+1):\n", + " # creat this term\n", + " sign = (-1)**(n+1)\n", + " nume = x**(2*n-1)\n", + " deno = np.math.factorial(2*n -1)\n", + " thisterm = sign * (nume / deno)\n", + "\n", + " # plot it\n", + " plt.plot(x, thisterm, '--')\n", + " y+= thisterm\n", + "\n", + "plt.plot(x, y, 'k', linewidth=3, label=f'Sum over {order} terms')\n", + "plt.plot(x[::5], np.sin(x[::5]), 'bo', markerfacecolor='w', linewidth=3, label='sin(x)')\n", + "plt.ylim([-5, 5])\n", + "plt.xlim(x[[0, -1]])\n", + "plt.legend()\n", + "plt.show()\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "id": "Rcj53FpljdYK", + "outputId": "ef22fa52-6211-4cd0-a6e7-940b8c99b81d" + }, + "execution_count": 3, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From 03845bde156c233cdfcac6bc991cdc8af26782c9 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Fri, 9 Jun 2023 17:30:18 +0400 Subject: [PATCH 08/25] exp function estimate for certain number of n --- .../functions/exp_and_log_funcs_cc_e1.ipynb | 80 +++++++++++++++++++ 1 file changed, 80 insertions(+) create mode 100644 practice/functions/exp_and_log_funcs_cc_e1.ipynb diff --git a/practice/functions/exp_and_log_funcs_cc_e1.ipynb b/practice/functions/exp_and_log_funcs_cc_e1.ipynb new file mode 100644 index 0000000..c51c5ad --- /dev/null +++ b/practice/functions/exp_and_log_funcs_cc_e1.ipynb @@ -0,0 +1,80 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyMyoobNUrOIDXvTrsnCMB9o", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "id": "uK6I8b0yQtoR" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "n = [1, 2, 5, 10]\n", + "\n", + "for i in n:\n", + " # estimate\n", + " e = (1 + (1/i))**i\n", + " \n", + " # np.exp(1) is also an estimate but it is going to be much more accurate than\n", + " # our calculated e hence we will use it\n", + " print(f'n: {i:2.0f}, est.e: {e:.5f}, diff to e: {(np.exp(1) - e):.7f}')\n", + "\n", + "\n", + "\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "CUNwkWtWRjMm", + "outputId": "484934ce-9a36-46b5-98a2-0d3369b17dcd" + }, + "execution_count": 11, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "n: 1, est.e: 2.00000, diff to e: 0.7182818\n", + "n: 2, est.e: 2.25000, diff to e: 0.4682818\n", + "n: 5, est.e: 2.48832, diff to e: 0.2299618\n", + "n: 10, est.e: 2.59374, diff to e: 0.1245394\n" + ] + } + ] + } + ] +} \ No newline at end of file From ea851123e7699f48dbf6041631067fd2871ec323 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Sat, 10 Jun 2023 12:39:46 +0400 Subject: [PATCH 09/25] exo_and_log_funcs_cc_e2 completed --- .../functions/exo_and_log_funcs_cc_e2.ipynb | 122 ++++++++++++++++++ 1 file changed, 122 insertions(+) create mode 100644 practice/functions/exo_and_log_funcs_cc_e2.ipynb diff --git a/practice/functions/exo_and_log_funcs_cc_e2.ipynb b/practice/functions/exo_and_log_funcs_cc_e2.ipynb new file mode 100644 index 0000000..0ff198a --- /dev/null +++ b/practice/functions/exo_and_log_funcs_cc_e2.ipynb @@ -0,0 +1,122 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyOlRea0LQmBDvrZOk94nqk6", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "id": "u9aSHthBWgQF" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "n = [1, 2, 5, 10]\n", + "\n", + "for i in n:\n", + " # estimate\n", + " e = (1 + (1/i))**i\n", + " \n", + " # np.exp(1) is also an estimate but it is going to be much more accurate than\n", + " # our calculated e hence we will use it\n", + " print(f'n: {i:2.0f}, est.e: {e:.5f}, diff to e: {(np.exp(1) - e):.7f}')" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "d_nacGShWpYv", + "outputId": "28276bb7-73dc-4c73-b9c4-ca19b95351e4" + }, + "execution_count": 6, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "n: 1, est.e: 2.00000, diff to e: 0.7182818\n", + "n: 2, est.e: 2.25000, diff to e: 0.4682818\n", + "n: 5, est.e: 2.48832, diff to e: 0.2299618\n", + "n: 10, est.e: 2.59374, diff to e: 0.1245394\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "n = np.arange(1, 1001)\n", + "\n", + "# numpy arr is different from simple list(used above)\n", + "# on numpy arr (vector n)\n", + "# element wise algebric operations (divison, power) can be perfomed\n", + "# \n", + "e_diffs = np.exp(1) - (1 + 1/n)**n\n", + "plt.plot(n, e_diffs)\n", + "\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "fiJvz_rUam0B", + "outputId": "f5a85185-56f3-4e12-a74f-dc1b04fbbf18" + }, + "execution_count": 7, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 7 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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eTGGkq6tLjY2NKi0t7duB06nS0lLV19cPu929996r7OxsffOb3xx9pWMgHEYknk8DAIApSbE0PnDggAKBgLxeb9R6r9er9957b8httmzZokcffVTbtm0b8XE6OzvV2dkZ+ez3+2Mpc8ScfVlEQUtyOYZvCwAAxsaYXk3T3t6um2++WY888oiysrJGvF1NTY0yMjIir7y8vDGpz9FvZCTAuRoAAIyIaWQkKytLLpdLLS0tUetbWlqUk5MzqP3//u//aufOnfryl78cWRcMBnsPnJSkpqYmzZo1a9B21dXVqqqqinz2+/1jEkiiR0YIIwAAmBBTGHG73SosLFRdXV3k8txgMKi6ujpVVlYOaj979my9/fbbUeu+973vqb29XT/+8Y+HDRgej0cejyeW0kYles7ImB8OAAAMIaYwIklVVVVavHixioqKtGDBAq1evVodHR2qqKiQJC1atEi5ubmqqalRSkqK5s6dG7V9ZmamJA1ab0L/MMLICAAAZsQcRsrLy9Xa2qrly5fL5/OpoKBAGzdujExqbW5ultM5Pm7s6uA0DQAAxjmscXBNq9/vV0ZGhtra2pSenh63/Xb1BHXB9/4gSXpzxTXKSE2O274BALC7kf79Hh9DGGOk/wTWcZDJAAA4I9k8jPSfM2KwEAAAbMzWYYQ5IwAAmGfzMOKInKohjAAAYIatw4jUd6qGLAIAgBmEkciTe0kjAACYYPsw4oicpjFbBwAAdmX7MBIZGSGNAABgBGEkNDLCWRoAAMwgjDBnBAAAo2wfRhxc2gsAgFG2DyNOZ3hkxHAhAADYFGEkcp8R0ggAACYQRri0FwAAo2wfRhxMYAUAwCjbhxGeTQMAgFmEEZ5NAwCAUYQRTtMAAGAUYSTUAz3MYAUAwAjbhxEXz6YBAMAowkhoBmuAMAIAgBGEEcIIAABGEUZCk0YCTGAFAMAIwggTWAEAMIowEhoZYQIrAABmEEZCd2BlZAQAADNsH0aSGBkBAMAo24cRbnoGAIBZtg8jkZERrqYBAMAI24cRZ+g+Iz0BwggAACbYPowkhW96xsgIAABG2D6MhJ/ayx1YAQAww/ZhJInbwQMAYJTtwwjPpgEAwCzbhxEnYQQAAKNsH0Y4TQMAgFmjCiNr1qxRfn6+UlJSVFxcrIaGhmHbPvXUUyoqKlJmZqYmTJiggoIC/frXvx51wfEWmcDK1TQAABgRcxhZv369qqqqtGLFCm3dulXz5s1TWVmZ9u/fP2T7KVOm6K677lJ9fb3eeustVVRUqKKiQs8///wpFx8PjIwAAGBWzGFk1apVWrJkiSoqKjRnzhzV1tYqLS1Na9euHbL91Vdfra985Su66KKLNGvWLC1btkyXXHKJtmzZcsrFxwNzRgAAMCumMNLV1aXGxkaVlpb27cDpVGlpqerr60+6vWVZqqurU1NTkz772c/GXu0YCI+M8GwaAADMSIql8YEDBxQIBOT1eqPWe71evffee8Nu19bWptzcXHV2dsrlculnP/uZPv/5zw/bvrOzU52dnZHPfr8/ljJjEr60l6f2AgBgRkxhZLQmTZqkbdu26ciRI6qrq1NVVZXOPfdcXX311UO2r6mp0T333JOI0vruM8IEVgAAjIgpjGRlZcnlcqmlpSVqfUtLi3Jycobdzul06rzzzpMkFRQU6N1331VNTc2wYaS6ulpVVVWRz36/X3l5ebGUOmLc9AwAALNimjPidrtVWFiourq6yLpgMKi6ujqVlJSMeD/BYDDqNMxAHo9H6enpUa+xQhgBAMCsmE/TVFVVafHixSoqKtKCBQu0evVqdXR0qKKiQpK0aNEi5ebmqqamRlLvKZeioiLNmjVLnZ2d2rBhg37961/roYceiu8vGSUXD8oDAMComMNIeXm5WltbtXz5cvl8PhUUFGjjxo2RSa3Nzc1yOvsGXDo6OnTbbbfp448/VmpqqmbPnq3HHntM5eXl8fsVp4CREQAAzHJY1uk/c9Pv9ysjI0NtbW1xP2Xzk7r3tWrTDt24YIZqvnpxXPcNAICdjfTvt+2fTcOlvQAAmEUY4aZnAAAYZfswEr4Da/D0P1sFAMAZyfZhJPzUXkZGAAAww/ZhJMkVvpomaLgSAADsiTASugy5O8DICAAAJhBGQiMjPQFGRgAAMMH2YSTZxZwRAABMIoy4erugq4eREQAATLB9GAnPGWFkBAAAM2wfRpKZMwIAgFG2DyNJLq6mAQDAJNuHkfDISDcjIwAAGEEYcTFnBAAAk2wfRsLPpmFkBAAAM2wfRiIjI8wZAQDACMJIZAIrIyMAAJhg+zCSxARWAACMsn0YSeamZwAAGGX7MNL3oDzCCAAAJhBGwqdpgkFZFoEEAIBEs30YcYcmsFqWFOBUDQAACWf7MBK+HbzEvBEAAEwgjIRueiZxRQ0AACbYPowk9x8ZYRIrAAAJZ/sw4nI6FB4cYWQEAIDEs30YkfrmjXQRRgAASDjCiCRPUiiM9BBGAABINMKI+oURRkYAAEg4wogkT5JLEiMjAACYQBiR5A6NjHQSRgAASDjCiPruwsrICAAAiUcYkeRJDo+MBAxXAgCA/RBGxMgIAAAmEUbUf2SEMAIAQKIRRtQ3MkIYAQAg8UYVRtasWaP8/HylpKSouLhYDQ0Nw7Z95JFHdOWVV2ry5MmaPHmySktLT9jeBK6mAQDAnJjDyPr161VVVaUVK1Zo69atmjdvnsrKyrR///4h22/evFk33nijXnzxRdXX1ysvL0/XXHON9uzZc8rFxwv3GQEAwJyYw8iqVau0ZMkSVVRUaM6cOaqtrVVaWprWrl07ZPvHH39ct912mwoKCjR79mz953/+p4LBoOrq6k65+Hhxczt4AACMiSmMdHV1qbGxUaWlpX07cDpVWlqq+vr6Ee3j6NGj6u7u1pQpU4Zt09nZKb/fH/UaS54kLu0FAMCUmMLIgQMHFAgE5PV6o9Z7vV75fL4R7eOOO+7Q9OnTowLNQDU1NcrIyIi88vLyYikzZoyMAABgTkKvplm5cqXWrVunp59+WikpKcO2q66uVltbW+S1e/fuMa0rPGeECawAACReUiyNs7Ky5HK51NLSErW+paVFOTk5J9z2wQcf1MqVK/WnP/1Jl1xyyQnbejweeTyeWEo7JSmh+4wc6+Y0DQAAiRbTyIjb7VZhYWHU5NPwZNSSkpJht/vhD3+o73//+9q4caOKiopGX+0YSXP3jowc6yKMAACQaDGNjEhSVVWVFi9erKKiIi1YsECrV69WR0eHKioqJEmLFi1Sbm6uampqJEk/+MEPtHz5cj3xxBPKz8+PzC2ZOHGiJk6cGMefMnqp7t5uONrVY7gSAADsJ+YwUl5ertbWVi1fvlw+n08FBQXauHFjZFJrc3OznM6+AZeHHnpIXV1d+ru/+7uo/axYsUL/9m//dmrVx0lacu/IyFFGRgAASLiYw4gkVVZWqrKycsjvNm/eHPV5586dozlEQnGaBgAAc3g2jaQ0T/g0DWEEAIBEI4yob2SEOSMAACQeYURSKnNGAAAwhjAi5owAAGASYURSWvjS3u6ALMsyXA0AAPZCGJGUGhoZCQQtdQW4JTwAAIlEGFHfaRqJUzUAACQaYURSssspt6u3KzoIIwAAJBRhJCQ1MomVy3sBAEgkwkhI371GGBkBACCRCCMhqYQRAACMIIyEcK8RAADMIIyEpCXzfBoAAEwgjISkeXpHRjqYwAoAQEIRRkI4TQMAgBmEkZDU0GkaRkYAAEgswkhIempvGPEfI4wAAJBIhJGQzFS3JKntWLfhSgAAsBfCSEhmWrIkqe1Yl+FKAACwF8JISEZqbxg5fJSREQAAEokwEpIRGRkhjAAAkEiEkZBMRkYAADCCMBISPk3jZ2QEAICEIoyEZKb1Xk3T3tmj7kDQcDUAANgHYSQkPSUp8p7REQAAEocwEpLkcmqSpzeQMIkVAIDEIYz0E76i5jBhBACAhCGM9JPJ5b0AACQcYaSf8C3hDx/lLqwAACQKYaSfqRN7w8iBdsIIAACJQhjpx5ueIklq8R83XAkAAPZBGOkne5JHkrS/vdNwJQAA2AdhpJ9sRkYAAEg4wkg/3tDISCsjIwAAJAxhpB9GRgAASDzCSD/hOSMdXQEd6ewxXA0AAPYwqjCyZs0a5efnKyUlRcXFxWpoaBi27TvvvKOvfe1rys/Pl8Ph0OrVq0db65ib4EnSxNAt4fczOgIAQELEHEbWr1+vqqoqrVixQlu3btW8efNUVlam/fv3D9n+6NGjOvfcc7Vy5Url5OSccsFjLTu9d3Skxc+8EQAAEiHmMLJq1SotWbJEFRUVmjNnjmpra5WWlqa1a9cO2f7SSy/VAw88oBtuuEEej+eUCx5ruZmpkqTdh44argQAAHuIKYx0dXWpsbFRpaWlfTtwOlVaWqr6+vq4FdXZ2Sm/3x/1SpQZU9IkSc2fEEYAAEiEmMLIgQMHFAgE5PV6o9Z7vV75fL64FVVTU6OMjIzIKy8vL277PpmZU3vDyK6DhBEAABLhtLyaprq6Wm1tbZHX7t27E3bsGVMmSJKaP+lI2DEBALCzpFgaZ2VlyeVyqaWlJWp9S0tLXCenejweY/NLGBkBACCxYhoZcbvdKiwsVF1dXWRdMBhUXV2dSkpK4l6cCeE5I4ePdqvtWLfhagAAOPPFfJqmqqpKjzzyiH71q1/p3Xff1a233qqOjg5VVFRIkhYtWqTq6upI+66uLm3btk3btm1TV1eX9uzZo23btumDDz6I36+IowmeJJ0VuvnZRwc4VQMAwFiL6TSNJJWXl6u1tVXLly+Xz+dTQUGBNm7cGJnU2tzcLKezL+Ps3btX8+fPj3x+8MEH9eCDD+qqq67S5s2bT/0XjIELvZPU2t6pJp9fBXmZpssBAOCMFnMYkaTKykpVVlYO+d3AgJGfny/LskZzGGNm50zSlg8O6N197aZLAQDgjHdaXk1j2uxp6ZKk93yJu78JAAB2RRgZwuycSZKkJl/7uBvVAQBgvCGMDOG87IlyOR06dLRbe9t4YB4AAGOJMDKElGSX5oRO1WzddchwNQAAnNkII8MonDlZktRIGAEAYEwRRobx6VAY2dpMGAEAYCwRRoYRHhl5Z69f/uPciRUAgLFCGBlGbmaqzs2aoEDQ0ssffGK6HAAAzliEkRP47AVnSZJe2tFquBIAAM5chJETuOrC3jDy4nv7FQxyvxEAAMYCYeQESs6dqkkpSfL5j6th50HT5QAAcEYijJxASrJLX5w7TZL07LY9hqsBAODMRBg5iesKpkuSNrztU2dPwHA1AACceQgjJ1F87lR50z1qO9atjdt9pssBAOCMQxg5CZfToZuKZ0qSfv7Shzw4DwCAOCOMjMBNl81UarJLf93n1/9wzxEAAOKKMDICkye4VX5pniTpR5uaGB0BACCOCCMjdNvVs5TmdumN5sP63Zt7TZcDAMAZgzAyQtnpKbrt6lmSpPs3vKu2ozyvBgCAeCCMxOCWK8/VOVkT1OLv1N3PbjddDgAAZwTCSAxSkl36v+UFcjkd+t2be/XEq82mSwIAYNwjjMSoIC9T/3zNBZKk5c9u15b3DxiuCACA8Y0wMgq3XjVL1xVMV0/Q0i3/7zX9zwcEEgAARoswMgoOh0M/+Nol+j8XnqXj3UF945evcXdWAABGiTAySinJLtXeXKjSi7LV2RPUtx5r1I/+2KSeQNB0aQAAjCuEkVPgSXLpoZsKVXFFviTppy98oK899LKafO1mCwMAYBwhjJyiZJdTK778Ka0uL9CklCS9+XGbvvTTv+i+3/9Vhzq6TJcHAMBpz2GNg3ub+/1+ZWRkqK2tTenp6abLGVaL/7juenq7/vRuiyRpkidJFVfk66aSmcqelGK4OgAAEmukf78JI3FmWZY272jVDzc26d19fklSssuhL10yXV8vOlvF50yVy+kwXCUAAGOPMGJYMGjpD9t9Wvs/H6lx16HI+pz0FH3pkmm65lM5mj8jU8kuzpQBAM5MhJHTyJu7D+s3Dc3a8PY++Y/3RNZP8iTpivOydOUFWSqaOUXnZ0+Uk1ETAMAZgjByGursCeilplb9/u19+vOOVh0a8LC9SZ4kFczI1PwZk3VRziTNnpauGVPSOK0DABiXCCOnuUDQ0vY9bdrc1KpXPvxE23Yf1rHuwKB2qckuXeCdqAu8k5SfNUEzpqRp5tQ0zZwyQRlpyQYqBwBgZAgj40xPIKj3fO3a2nxIb33cpiZfu3a0tKuzZ/ibqGWkJitvSqpy0lPkTU/RtIzeZU5GinLSU5SdnqL0lCQ5HIysAAASb6R/v5MSWBNOIMnl1NzcDM3NzYisCwQt7fykQ02+dr3fckS7Dnao+ZOj2nXwqFrbO9V2rFtte7q1fY9/+P06HZo8wa0paW5NmdD7mjwhOfJ58gS3JqUkaVJKctRyojuJ+SsAgIQgjJzGXE6HZp01UbPOmihdHP1dR2ePmg8e1Z5Dx+TzH1eL/7h8bcej3vuP96gnaKm1vVOt7Z0xH3+iJykUUPpCygR3klKSXUpz977C71PdLqUmu5TmTlKq26nU5CSlhtqkJve28yQ75XY55UlyMloDAIgYVRhZs2aNHnjgAfl8Ps2bN08//elPtWDBgmHbP/nkk7r77ru1c+dOnX/++frBD36gL37xi6MuGtIET5Iumpaui6YNP+x1vDugQ0e7dLCj73Woo0sHj3b3Lju6dOhol9qP96j9eHdo2aOu0PN1jnT26Ehnj/a1xb9+t8spd1JvMIleuqI+u11OeZJdoWXv52SXQ0kup5Kdvcskl0PJzt5l//XJLoeSQuuj3zuV5AwtQ+sH7tPldPS+HA45nVKS0ymnQ4QoABgDMYeR9evXq6qqSrW1tSouLtbq1atVVlampqYmZWdnD2r/8ssv68Ybb1RNTY2+9KUv6YknntD111+vrVu3au7cuXH5ERhaSrJL0zJSNS0jNabtOnsCkWDSF1K65T/eo+PdAR3t6n31vu/p9z4Q9f5YV0DHQm2Od0fPfekKBNUVCOpI7AM2RjkdGhBUHEoKfXY6HH3fDfg+/F2kff+Q43TI1X+//fflcMjhcMjpkJyhbaI+OxxyRN4r9Ln/9+H2oXXOGNv3379zZO2dzn7bSpJDcqivrcMhOaTeZahN37J3O4W/V6h9v/05QjsduC7cVgr9ziH2EXnf75jO0Ir+650D9ucY+Bv61Q/g1MU8gbW4uFiXXnqp/uM//kOSFAwGlZeXp3/8x3/UnXfeOah9eXm5Ojo69Nxzz0XWXXbZZSooKFBtbe2IjmmHCaxnOsuyegNIT++rc9AyEPnc2e9zVyCozu6+ZWdPQD1BS92BoHoClnqCQXUHLPUEguoO9i57AtaA96FlIKie0Pru0LbR63vbnv5TunE6GRhuHAMDS78AFAk+4fYDtg3vT3L0e69+IWxASIps0xeKwsEr3LZ/jeG2kdaOwfsY7lgaYvuTHUuDflff7x3qWINrGrDfIY41XF0nOpaG7JfB++2/7uR9NeC/w6A3w9Stfu8H9sWAWgZuNdR+HEMcL3rf/Y8X/R/3m585R3lT0hRPYzKBtaurS42Njaquro6sczqdKi0tVX19/ZDb1NfXq6qqKmpdWVmZnnnmmWGP09nZqc7Ovv+X2e8ffoImxgeHwyFPkkueJJfpUk4qELT6XpYV9Tk44HPAshQMWuo54fdSTzAY+k4KBIO9y37bBoc5Vu9LClqWLKv3zr59n/veBy2FPg9o32+dFaolpvZD7T/Y1z4wqH3090HLkqXe73qXA97LCq0bvD4YWq9wG/XVFG6rgev7tVXUfvr2HW99x+u/cxItxp/rCqbHPYyMVExh5MCBAwoEAvJ6vVHrvV6v3nvvvSG38fl8Q7b3+XzDHqempkb33HNPLKUBcRM+VYIz18BQMygYDQhAliQrOPT6YGjFwP2EA5mGWq/BQat/O0mDtu2/Lup79TtOqK7w+752fdtHHWuItuFjyRq4j5MfSwNq7d823O/D1dW3zxMfq//vH+mxBtZ1smOFG568r/qONbC28H4Hrxvcrn/boQJz//2faD9DHW/gbxq4rn87b7q5B7qellfTVFdXR42m+P1+5eXlGawIwJnE4eidpxM9aA3AlJjCSFZWllwul1paWqLWt7S0KCcnZ8htcnJyYmovSR6PRx6PJ5bSAADAOBXTI2PdbrcKCwtVV1cXWRcMBlVXV6eSkpIhtykpKYlqL0mbNm0atj0AALCXmE/TVFVVafHixSoqKtKCBQu0evVqdXR0qKKiQpK0aNEi5ebmqqamRpK0bNkyXXXVVfrRj36ka6+9VuvWrdPrr7+uhx9+OL6/BAAAjEsxh5Hy8nK1trZq+fLl8vl8Kigo0MaNGyOTVJubm+V09g24XH755XriiSf0ve99T9/97nd1/vnn65lnnuEeIwAAQNIo7jNiAvcZAQBg/Bnp3++Y5owAAADEG2EEAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGn5VN7Bwrfl83v9xuuBAAAjFT47/bJ7q86LsJIe3u7JCkvL89wJQAAIFbt7e3KyMgY9vtxcTv4YDCovXv3atKkSXI4HHHbr9/vV15ennbv3s1t5scQ/ZwY9HPi0NeJQT8nxlj2s2VZam9v1/Tp06OeWzfQuBgZcTqdOvvss8ds/+np6fwfegLQz4lBPycOfZ0Y9HNijFU/n2hEJIwJrAAAwCjCCAAAMMrWYcTj8WjFihXyeDymSzmj0c+JQT8nDn2dGPRzYpwO/TwuJrACAIAzl61HRgAAgHmEEQAAYBRhBAAAGEUYAQAARtk2jKxZs0b5+flKSUlRcXGxGhoaTJc0rtTU1OjSSy/VpEmTlJ2dreuvv15NTU1RbY4fP66lS5dq6tSpmjhxor72ta+ppaUlqk1zc7OuvfZapaWlKTs7W9/5znfU09OTyJ8yrqxcuVIOh0O33357ZB39HB979uzRTTfdpKlTpyo1NVUXX3yxXn/99cj3lmVp+fLlmjZtmlJTU1VaWqr3338/ah8HDx7UwoULlZ6erszMTH3zm9/UkSNHEv1TTmuBQEB33323zjnnHKWmpmrWrFn6/ve/H/XsEvo6dn/+85/15S9/WdOnT5fD4dAzzzwT9X28+vStt97SlVdeqZSUFOXl5emHP/xhfH6AZUPr1q2z3G63tXbtWuudd96xlixZYmVmZlotLS2mSxs3ysrKrF/84hfW9u3brW3btllf/OIXrRkzZlhHjhyJtPnWt75l5eXlWXV1ddbrr79uXXbZZdbll18e+b6np8eaO3euVVpaar3xxhvWhg0brKysLKu6utrETzrtNTQ0WPn5+dYll1xiLVu2LLKefj51Bw8etGbOnGn9/d//vfXqq69aH374ofX8889bH3zwQaTNypUrrYyMDOuZZ56x3nzzTetv//ZvrXPOOcc6duxYpM3f/M3fWPPmzbNeeeUV6y9/+Yt13nnnWTfeeKOJn3Tauu+++6ypU6dazz33nPXRRx9ZTz75pDVx4kTrxz/+caQNfR27DRs2WHfddZf11FNPWZKsp59+Our7ePRpW1ub5fV6rYULF1rbt2+3fvOb31ipqanWz3/+81Ou35ZhZMGCBdbSpUsjnwOBgDV9+nSrpqbGYFXj2/79+y1J1ksvvWRZlmUdPnzYSk5Otp588slIm3fffdeSZNXX11uW1fs/HqfTafl8vkibhx56yEpPT7c6OzsT+wNOc+3t7db5559vbdq0ybrqqqsiYYR+jo877rjD+sxnPjPs98Fg0MrJybEeeOCByLrDhw9bHo/H+s1vfmNZlmX99a9/tSRZr732WqTNH/7wB8vhcFh79uwZu+LHmWuvvdb6xje+EbXuq1/9qrVw4ULLsujreBgYRuLVpz/72c+syZMnR/27cccdd1gXXnjhKddsu9M0XV1damxsVGlpaWSd0+lUaWmp6uvrDVY2vrW1tUmSpkyZIklqbGxUd3d3VD/Pnj1bM2bMiPRzfX29Lr74Ynm93kibsrIy+f1+vfPOOwms/vS3dOlSXXvttVH9KdHP8fK73/1ORUVF+vrXv67s7GzNnz9fjzzySOT7jz76SD6fL6qfMzIyVFxcHNXPmZmZKioqirQpLS2V0+nUq6++mrgfc5q7/PLLVVdXpx07dkiS3nzzTW3ZskVf+MIXJNHXYyFefVpfX6/PfvazcrvdkTZlZWVqamrSoUOHTqnGcfGgvHg6cOCAAoFA1D/MkuT1evXee+8Zqmp8CwaDuv3223XFFVdo7ty5kiSfzye3263MzMyotl6vVz6fL9JmqP8O4e/Qa926ddq6datee+21Qd/Rz/Hx4Ycf6qGHHlJVVZW++93v6rXXXtM//dM/ye12a/HixZF+Gqof+/dzdnZ21PdJSUmaMmUK/dzPnXfeKb/fr9mzZ8vlcikQCOi+++7TwoULJYm+HgPx6lOfz6dzzjln0D7C302ePHnUNdoujCD+li5dqu3bt2vLli2mSznj7N69W8uWLdOmTZuUkpJiupwzVjAYVFFRke6//35J0vz587V9+3bV1tZq8eLFhqs7s/zXf/2XHn/8cT3xxBP61Kc+pW3btun222/X9OnT6Wsbs91pmqysLLlcrkFXG7S0tCgnJ8dQVeNXZWWlnnvuOb344os6++yzI+tzcnLU1dWlw4cPR7Xv3885OTlD/ncIf4fe0zD79+/Xpz/9aSUlJSkpKUkvvfSSfvKTnygpKUler5d+joNp06Zpzpw5UesuuugiNTc3S+rrpxP9u5GTk6P9+/dHfd/T06ODBw/Sz/185zvf0Z133qkbbrhBF198sW6++WZ9+9vfVk1NjST6eizEq0/H8t8S24URt9utwsJC1dXVRdYFg0HV1dWppKTEYGXji2VZqqys1NNPP60XXnhh0NBdYWGhkpOTo/q5qalJzc3NkX4uKSnR22+/HfU/gE2bNik9PX3QHwa7+tznPqe3335b27Zti7yKioq0cOHCyHv6+dRdccUVgy5N37Fjh2bOnClJOuecc5STkxPVz36/X6+++mpUPx8+fFiNjY2RNi+88IKCwaCKi4sT8CvGh6NHj8rpjP7T43K5FAwGJdHXYyFefVpSUqI///nP6u7ujrTZtGmTLrzwwlM6RSPJvpf2ejwe65e//KX117/+1fqHf/gHKzMzM+pqA5zYrbfeamVkZFibN2+29u3bF3kdPXo00uZb3/qWNWPGDOuFF16wXn/9daukpMQqKSmJfB++5PSaa66xtm3bZm3cuNE666yzuOT0JPpfTWNZ9HM8NDQ0WElJSdZ9991nvf/++9bjjz9upaWlWY899likzcqVK63MzEzr2Weftd566y3ruuuuG/LSyPnz51uvvvqqtWXLFuv888+39eWmQ1m8eLGVm5sbubT3qaeesrKysqx//dd/jbShr2PX3t5uvfHGG9Ybb7xhSbJWrVplvfHGG9auXbssy4pPnx4+fNjyer3WzTffbG3fvt1at26dlZaWxqW9p+KnP/2pNWPGDMvtdlsLFiywXnnlFdMljSuShnz94he/iLQ5duyYddttt1mTJ0+20tLSrK985SvWvn37ovazc+dO6wtf+IKVmppqZWVlWf/8z/9sdXd3J/jXjC8Dwwj9HB///d//bc2dO9fyeDzW7NmzrYcffjjq+2AwaN19992W1+u1PB6P9bnPfc5qamqKavPJJ59YN954ozVx4kQrPT3dqqiosNrb2xP5M057fr/fWrZsmTVjxgwrJSXFOvfcc6277ror6nJR+jp2L7744pD/Ji9evNiyrPj16Ztvvml95jOfsTwej5Wbm2utXLkyLvU7LKvfbe8AAAASzHZzRgAAwOmFMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMCo/w8HCWdfoBL3RwAAAABJRU5ErkJggg==\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From 8a5a147f7fe42181db35c45f92b8208db7d670cd Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Sat, 10 Jun 2023 14:23:58 +0400 Subject: [PATCH 10/25] exp_and_log_funcs_cc_e3 --- .../functions/exp_and_log_funcs_cc_e3.ipynb | 97 +++++++++++++++++++ 1 file changed, 97 insertions(+) create mode 100644 practice/functions/exp_and_log_funcs_cc_e3.ipynb diff --git a/practice/functions/exp_and_log_funcs_cc_e3.ipynb b/practice/functions/exp_and_log_funcs_cc_e3.ipynb new file mode 100644 index 0000000..7189920 --- /dev/null +++ b/practice/functions/exp_and_log_funcs_cc_e3.ipynb @@ -0,0 +1,97 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyPl7C/hIi/LdgA2YAM+Ykaj", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "bOl03zxWdqzA" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "x_domain = [-2, 2]\n", + "x = np.linspace(x_domain[0], x_domain[1], 53)\n", + "x\n", + "\n", + "# functions\n", + "y1 = np.exp(x)\n", + "y2 = np.exp(x**2)\n", + "y3 = np.exp((-x)**2)\n", + "y4 = np.exp(-(x**2))\n", + "y5 = np.exp(x)**2\n", + "\n", + "# and plot\n", + "plt.figure(figsize=(8,6))\n", + "plt.plot(x, y1, linewidth=2, label='$y=e^x$')\n", + "plt.plot(x, y2, linewidth=2, label='$y=e^{x^2}$')\n", + "plt.plot(x, y3, '--', linewidth=2, label='$y=e^{(-x)^2}$')\n", + "plt.plot(x, y4, linewidth=2, label='$y=e^{-(x^2)}$')\n", + "plt.plot(x, y5, linewidth=2, label='$y={(e^x)}^2$')\n", + "\n", + "plt.xlim([x[0], x[-1]])\n", + "plt.ylim([-1, 10])\n", + "\n", + "plt.xlabel('x')\n", + "plt.ylabel('y=f(x)')\n", + "\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 547 + }, + "id": "RMRACZ_Ewwih", + "outputId": "3aa1829e-dab5-43a4-acf8-0f71ba993dbe" + }, + "execution_count": 2, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From 16c97a3b03b716d7cbd41789259aad494a13e82b Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Sat, 10 Jun 2023 14:25:27 +0400 Subject: [PATCH 11/25] exp_and_log_funcs_cc_e3 - data --- .../functions/exp_and_log_funcs_cc_e3.ipynb | 46 ++++++++++++++++--- 1 file changed, 40 insertions(+), 6 deletions(-) diff --git a/practice/functions/exp_and_log_funcs_cc_e3.ipynb b/practice/functions/exp_and_log_funcs_cc_e3.ipynb index 7189920..edc0063 100644 --- a/practice/functions/exp_and_log_funcs_cc_e3.ipynb +++ b/practice/functions/exp_and_log_funcs_cc_e3.ipynb @@ -4,7 +4,7 @@ "metadata": { "colab": { "provenance": [], - "authorship_tag": "ABX9TyPl7C/hIi/LdgA2YAM+Ykaj", + "authorship_tag": "ABX9TyP4gDpmtE4vF/Ycce3VWgcn", "include_colab_link": true }, "kernelspec": { @@ -44,8 +44,42 @@ "source": [ "x_domain = [-2, 2]\n", "x = np.linspace(x_domain[0], x_domain[1], 53)\n", - "x\n", - "\n", + "x" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "RMRACZ_Ewwih", + "outputId": "88ea6766-d1be-47ec-e91f-24b993a943db" + }, + "execution_count": 4, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-2. , -1.92307692, -1.84615385, -1.76923077, -1.69230769,\n", + " -1.61538462, -1.53846154, -1.46153846, -1.38461538, -1.30769231,\n", + " -1.23076923, -1.15384615, -1.07692308, -1. , -0.92307692,\n", + " -0.84615385, -0.76923077, -0.69230769, -0.61538462, -0.53846154,\n", + " -0.46153846, -0.38461538, -0.30769231, -0.23076923, -0.15384615,\n", + " -0.07692308, 0. , 0.07692308, 0.15384615, 0.23076923,\n", + " 0.30769231, 0.38461538, 0.46153846, 0.53846154, 0.61538462,\n", + " 0.69230769, 0.76923077, 0.84615385, 0.92307692, 1. ,\n", + " 1.07692308, 1.15384615, 1.23076923, 1.30769231, 1.38461538,\n", + " 1.46153846, 1.53846154, 1.61538462, 1.69230769, 1.76923077,\n", + " 1.84615385, 1.92307692, 2. ])" + ] + }, + "metadata": {}, + "execution_count": 4 + } + ] + }, + { + "cell_type": "code", + "source": [ "# functions\n", "y1 = np.exp(x)\n", "y2 = np.exp(x**2)\n", @@ -76,10 +110,10 @@ "base_uri": "https://localhost:8080/", "height": 547 }, - "id": "RMRACZ_Ewwih", - "outputId": "3aa1829e-dab5-43a4-acf8-0f71ba993dbe" + "id": "ISsWAGXg1ecV", + "outputId": "45954224-28f9-4a8f-9eed-12cc886b4f92" }, - "execution_count": 2, + "execution_count": 5, "outputs": [ { "output_type": "display_data", From ec58bdf704531507ac821886881587c80ff2e9a8 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Sun, 11 Jun 2023 07:30:26 +0400 Subject: [PATCH 12/25] exp_and_log_funcs: exercises --- practice/functions/exp_and_log_funcs_cc.ipynb | 300 ++++++++++++++++++ 1 file changed, 300 insertions(+) create mode 100644 practice/functions/exp_and_log_funcs_cc.ipynb diff --git a/practice/functions/exp_and_log_funcs_cc.ipynb b/practice/functions/exp_and_log_funcs_cc.ipynb new file mode 100644 index 0000000..5c96bf3 --- /dev/null +++ b/practice/functions/exp_and_log_funcs_cc.ipynb @@ -0,0 +1,300 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyNzyYbt37pGrCSHBpmm9ceY", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "bOl03zxWdqzA" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 1: estimate\n", + "e1_n = [1, 2, 5, 10]\n", + "\n", + "for i in e1_n:\n", + " # estimate\n", + " e = (1 + (1/i))**i\n", + " \n", + " # np.exp(1) is also an estimate but it is going to be much more accurate than\n", + " # our calculated e hence we will use it\n", + " print(f'e1_n: {i:2.0f}, est.e: {e:.5f}, diff to e: {(np.exp(1) - e):.7f}')\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "oayIPOkKd-ky", + "outputId": "d74cc608-ae3b-4a4b-e1db-e2ff6472ce7b" + }, + "execution_count": 2, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "e1_n: 1, est.e: 2.00000, diff to e: 0.7182818\n", + "e1_n: 2, est.e: 2.25000, diff to e: 0.4682818\n", + "e1_n: 5, est.e: 2.48832, diff to e: 0.2299618\n", + "e1_n: 10, est.e: 2.59374, diff to e: 0.1245394\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 2: Visualize e's approach\n", + "e2_n = np.arange(1, 1001)\n", + "\n", + "# numpy arr is different from simple list(used above)\n", + "# on numpy arr (vector n)\n", + "# element wise algebric operations (divison, power) can be perfomed\n", + "# \n", + "e_diffs = np.exp(1) - (1 + 1/e2_n)**e2_n\n", + "plt.plot(e2_n, e_diffs)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "75nSkLKGeqtO", + "outputId": "2a12e6fc-3913-4135-90df-1b7f9e410990" + }, + "execution_count": 3, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 3 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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eTGGkq6tLjY2NKi0t7duB06nS0lLV19cPu929996r7OxsffOb3xx9pWMgHEYknk8DAIApSbE0PnDggAKBgLxeb9R6r9er9957b8httmzZokcffVTbtm0b8XE6OzvV2dkZ+ez3+2Mpc8ScfVlEQUtyOYZvCwAAxsaYXk3T3t6um2++WY888oiysrJGvF1NTY0yMjIir7y8vDGpz9FvZCTAuRoAAIyIaWQkKytLLpdLLS0tUetbWlqUk5MzqP3//u//aufOnfryl78cWRcMBnsPnJSkpqYmzZo1a9B21dXVqqqqinz2+/1jEkiiR0YIIwAAmBBTGHG73SosLFRdXV3k8txgMKi6ujpVVlYOaj979my9/fbbUeu+973vqb29XT/+8Y+HDRgej0cejyeW0kYles7ImB8OAAAMIaYwIklVVVVavHixioqKtGDBAq1evVodHR2qqKiQJC1atEi5ubmqqalRSkqK5s6dG7V9ZmamJA1ab0L/MMLICAAAZsQcRsrLy9Xa2qrly5fL5/OpoKBAGzdujExqbW5ultM5Pm7s6uA0DQAAxjmscXBNq9/vV0ZGhtra2pSenh63/Xb1BHXB9/4gSXpzxTXKSE2O274BALC7kf79Hh9DGGOk/wTWcZDJAAA4I9k8jPSfM2KwEAAAbMzWYYQ5IwAAmGfzMOKInKohjAAAYIatw4jUd6qGLAIAgBmEkciTe0kjAACYYPsw4oicpjFbBwAAdmX7MBIZGSGNAABgBGEkNDLCWRoAAMwgjDBnBAAAo2wfRhxc2gsAgFG2DyNOZ3hkxHAhAADYFGEkcp8R0ggAACYQRri0FwAAo2wfRhxMYAUAwCjbhxGeTQMAgFmEEZ5NAwCAUYQRTtMAAGAUYSTUAz3MYAUAwAjbhxEXz6YBAMAowkhoBmuAMAIAgBGEEcIIAABGEUZCk0YCTGAFAMAIwggTWAEAMIowEhoZYQIrAABmEEZCd2BlZAQAADNsH0aSGBkBAMAo24cRbnoGAIBZtg8jkZERrqYBAMAI24cRZ+g+Iz0BwggAACbYPowkhW96xsgIAABG2D6MhJ/ayx1YAQAww/ZhJInbwQMAYJTtwwjPpgEAwCzbhxEnYQQAAKNsH0Y4TQMAgFmjCiNr1qxRfn6+UlJSVFxcrIaGhmHbPvXUUyoqKlJmZqYmTJiggoIC/frXvx51wfEWmcDK1TQAABgRcxhZv369qqqqtGLFCm3dulXz5s1TWVmZ9u/fP2T7KVOm6K677lJ9fb3eeustVVRUqKKiQs8///wpFx8PjIwAAGBWzGFk1apVWrJkiSoqKjRnzhzV1tYqLS1Na9euHbL91Vdfra985Su66KKLNGvWLC1btkyXXHKJtmzZcsrFxwNzRgAAMCumMNLV1aXGxkaVlpb27cDpVGlpqerr60+6vWVZqqurU1NTkz772c/GXu0YCI+M8GwaAADMSIql8YEDBxQIBOT1eqPWe71evffee8Nu19bWptzcXHV2dsrlculnP/uZPv/5zw/bvrOzU52dnZHPfr8/ljJjEr60l6f2AgBgRkxhZLQmTZqkbdu26ciRI6qrq1NVVZXOPfdcXX311UO2r6mp0T333JOI0vruM8IEVgAAjIgpjGRlZcnlcqmlpSVqfUtLi3Jycobdzul06rzzzpMkFRQU6N1331VNTc2wYaS6ulpVVVWRz36/X3l5ebGUOmLc9AwAALNimjPidrtVWFiourq6yLpgMKi6ujqVlJSMeD/BYDDqNMxAHo9H6enpUa+xQhgBAMCsmE/TVFVVafHixSoqKtKCBQu0evVqdXR0qKKiQpK0aNEi5ebmqqamRlLvKZeioiLNmjVLnZ2d2rBhg37961/roYceiu8vGSUXD8oDAMComMNIeXm5WltbtXz5cvl8PhUUFGjjxo2RSa3Nzc1yOvsGXDo6OnTbbbfp448/VmpqqmbPnq3HHntM5eXl8fsVp4CREQAAzHJY1uk/c9Pv9ysjI0NtbW1xP2Xzk7r3tWrTDt24YIZqvnpxXPcNAICdjfTvt+2fTcOlvQAAmEUY4aZnAAAYZfswEr4Da/D0P1sFAMAZyfZhJPzUXkZGAAAww/ZhJMkVvpomaLgSAADsiTASugy5O8DICAAAJhBGQiMjPQFGRgAAMMH2YSTZxZwRAABMIoy4erugq4eREQAATLB9GAnPGWFkBAAAM2wfRpKZMwIAgFG2DyNJLq6mAQDAJNuHkfDISDcjIwAAGEEYcTFnBAAAk2wfRsLPpmFkBAAAM2wfRiIjI8wZAQDACMJIZAIrIyMAAJhg+zCSxARWAACMsn0YSeamZwAAGGX7MNL3oDzCCAAAJhBGwqdpgkFZFoEEAIBEs30YcYcmsFqWFOBUDQAACWf7MBK+HbzEvBEAAEwgjIRueiZxRQ0AACbYPowk9x8ZYRIrAAAJZ/sw4nI6FB4cYWQEAIDEs30YkfrmjXQRRgAASDjCiCRPUiiM9BBGAABINMKI+oURRkYAAEg4wogkT5JLEiMjAACYQBiR5A6NjHQSRgAASDjCiPruwsrICAAAiUcYkeRJDo+MBAxXAgCA/RBGxMgIAAAmEUbUf2SEMAIAQKIRRtQ3MkIYAQAg8UYVRtasWaP8/HylpKSouLhYDQ0Nw7Z95JFHdOWVV2ry5MmaPHmySktLT9jeBK6mAQDAnJjDyPr161VVVaUVK1Zo69atmjdvnsrKyrR///4h22/evFk33nijXnzxRdXX1ysvL0/XXHON9uzZc8rFxwv3GQEAwJyYw8iqVau0ZMkSVVRUaM6cOaqtrVVaWprWrl07ZPvHH39ct912mwoKCjR79mz953/+p4LBoOrq6k65+Hhxczt4AACMiSmMdHV1qbGxUaWlpX07cDpVWlqq+vr6Ee3j6NGj6u7u1pQpU4Zt09nZKb/fH/UaS54kLu0FAMCUmMLIgQMHFAgE5PV6o9Z7vV75fL4R7eOOO+7Q9OnTowLNQDU1NcrIyIi88vLyYikzZoyMAABgTkKvplm5cqXWrVunp59+WikpKcO2q66uVltbW+S1e/fuMa0rPGeECawAACReUiyNs7Ky5HK51NLSErW+paVFOTk5J9z2wQcf1MqVK/WnP/1Jl1xyyQnbejweeTyeWEo7JSmh+4wc6+Y0DQAAiRbTyIjb7VZhYWHU5NPwZNSSkpJht/vhD3+o73//+9q4caOKiopGX+0YSXP3jowc6yKMAACQaDGNjEhSVVWVFi9erKKiIi1YsECrV69WR0eHKioqJEmLFi1Sbm6uampqJEk/+MEPtHz5cj3xxBPKz8+PzC2ZOHGiJk6cGMefMnqp7t5uONrVY7gSAADsJ+YwUl5ertbWVi1fvlw+n08FBQXauHFjZFJrc3OznM6+AZeHHnpIXV1d+ru/+7uo/axYsUL/9m//dmrVx0lacu/IyFFGRgAASLiYw4gkVVZWqrKycsjvNm/eHPV5586dozlEQnGaBgAAc3g2jaQ0T/g0DWEEAIBEI4yob2SEOSMAACQeYURSKnNGAAAwhjAi5owAAGASYURSWvjS3u6ALMsyXA0AAPZCGJGUGhoZCQQtdQW4JTwAAIlEGFHfaRqJUzUAACQaYURSssspt6u3KzoIIwAAJBRhJCQ1MomVy3sBAEgkwkhI371GGBkBACCRCCMhqYQRAACMIIyEcK8RAADMIIyEpCXzfBoAAEwgjISkeXpHRjqYwAoAQEIRRkI4TQMAgBmEkZDU0GkaRkYAAEgswkhIempvGPEfI4wAAJBIhJGQzFS3JKntWLfhSgAAsBfCSEhmWrIkqe1Yl+FKAACwF8JISEZqbxg5fJSREQAAEokwEpIRGRkhjAAAkEiEkZBMRkYAADCCMBISPk3jZ2QEAICEIoyEZKb1Xk3T3tmj7kDQcDUAANgHYSQkPSUp8p7REQAAEocwEpLkcmqSpzeQMIkVAIDEIYz0E76i5jBhBACAhCGM9JPJ5b0AACQcYaSf8C3hDx/lLqwAACQKYaSfqRN7w8iBdsIIAACJQhjpx5ueIklq8R83XAkAAPZBGOkne5JHkrS/vdNwJQAA2AdhpJ9sRkYAAEg4wkg/3tDISCsjIwAAJAxhpB9GRgAASDzCSD/hOSMdXQEd6ewxXA0AAPYwqjCyZs0a5efnKyUlRcXFxWpoaBi27TvvvKOvfe1rys/Pl8Ph0OrVq0db65ib4EnSxNAt4fczOgIAQELEHEbWr1+vqqoqrVixQlu3btW8efNUVlam/fv3D9n+6NGjOvfcc7Vy5Url5OSccsFjLTu9d3Skxc+8EQAAEiHmMLJq1SotWbJEFRUVmjNnjmpra5WWlqa1a9cO2f7SSy/VAw88oBtuuEEej+eUCx5ruZmpkqTdh44argQAAHuIKYx0dXWpsbFRpaWlfTtwOlVaWqr6+vq4FdXZ2Sm/3x/1SpQZU9IkSc2fEEYAAEiEmMLIgQMHFAgE5PV6o9Z7vV75fL64FVVTU6OMjIzIKy8vL277PpmZU3vDyK6DhBEAABLhtLyaprq6Wm1tbZHX7t27E3bsGVMmSJKaP+lI2DEBALCzpFgaZ2VlyeVyqaWlJWp9S0tLXCenejweY/NLGBkBACCxYhoZcbvdKiwsVF1dXWRdMBhUXV2dSkpK4l6cCeE5I4ePdqvtWLfhagAAOPPFfJqmqqpKjzzyiH71q1/p3Xff1a233qqOjg5VVFRIkhYtWqTq6upI+66uLm3btk3btm1TV1eX9uzZo23btumDDz6I36+IowmeJJ0VuvnZRwc4VQMAwFiL6TSNJJWXl6u1tVXLly+Xz+dTQUGBNm7cGJnU2tzcLKezL+Ps3btX8+fPj3x+8MEH9eCDD+qqq67S5s2bT/0XjIELvZPU2t6pJp9fBXmZpssBAOCMFnMYkaTKykpVVlYO+d3AgJGfny/LskZzGGNm50zSlg8O6N197aZLAQDgjHdaXk1j2uxp6ZKk93yJu78JAAB2RRgZwuycSZKkJl/7uBvVAQBgvCGMDOG87IlyOR06dLRbe9t4YB4AAGOJMDKElGSX5oRO1WzddchwNQAAnNkII8MonDlZktRIGAEAYEwRRobx6VAY2dpMGAEAYCwRRoYRHhl5Z69f/uPciRUAgLFCGBlGbmaqzs2aoEDQ0ssffGK6HAAAzliEkRP47AVnSZJe2tFquBIAAM5chJETuOrC3jDy4nv7FQxyvxEAAMYCYeQESs6dqkkpSfL5j6th50HT5QAAcEYijJxASrJLX5w7TZL07LY9hqsBAODMRBg5iesKpkuSNrztU2dPwHA1AACceQgjJ1F87lR50z1qO9atjdt9pssBAOCMQxg5CZfToZuKZ0qSfv7Shzw4DwCAOCOMjMBNl81UarJLf93n1/9wzxEAAOKKMDICkye4VX5pniTpR5uaGB0BACCOCCMjdNvVs5TmdumN5sP63Zt7TZcDAMAZgzAyQtnpKbrt6lmSpPs3vKu2ozyvBgCAeCCMxOCWK8/VOVkT1OLv1N3PbjddDgAAZwTCSAxSkl36v+UFcjkd+t2be/XEq82mSwIAYNwjjMSoIC9T/3zNBZKk5c9u15b3DxiuCACA8Y0wMgq3XjVL1xVMV0/Q0i3/7zX9zwcEEgAARoswMgoOh0M/+Nol+j8XnqXj3UF945evcXdWAABGiTAySinJLtXeXKjSi7LV2RPUtx5r1I/+2KSeQNB0aQAAjCuEkVPgSXLpoZsKVXFFviTppy98oK899LKafO1mCwMAYBwhjJyiZJdTK778Ka0uL9CklCS9+XGbvvTTv+i+3/9Vhzq6TJcHAMBpz2GNg3ub+/1+ZWRkqK2tTenp6abLGVaL/7juenq7/vRuiyRpkidJFVfk66aSmcqelGK4OgAAEmukf78JI3FmWZY272jVDzc26d19fklSssuhL10yXV8vOlvF50yVy+kwXCUAAGOPMGJYMGjpD9t9Wvs/H6lx16HI+pz0FH3pkmm65lM5mj8jU8kuzpQBAM5MhJHTyJu7D+s3Dc3a8PY++Y/3RNZP8iTpivOydOUFWSqaOUXnZ0+Uk1ETAMAZgjByGursCeilplb9/u19+vOOVh0a8LC9SZ4kFczI1PwZk3VRziTNnpauGVPSOK0DABiXCCOnuUDQ0vY9bdrc1KpXPvxE23Yf1rHuwKB2qckuXeCdqAu8k5SfNUEzpqRp5tQ0zZwyQRlpyQYqBwBgZAgj40xPIKj3fO3a2nxIb33cpiZfu3a0tKuzZ/ibqGWkJitvSqpy0lPkTU/RtIzeZU5GinLSU5SdnqL0lCQ5HIysAAASb6R/v5MSWBNOIMnl1NzcDM3NzYisCwQt7fykQ02+dr3fckS7Dnao+ZOj2nXwqFrbO9V2rFtte7q1fY9/+P06HZo8wa0paW5NmdD7mjwhOfJ58gS3JqUkaVJKctRyojuJ+SsAgIQgjJzGXE6HZp01UbPOmihdHP1dR2ePmg8e1Z5Dx+TzH1eL/7h8bcej3vuP96gnaKm1vVOt7Z0xH3+iJykUUPpCygR3klKSXUpz977C71PdLqUmu5TmTlKq26nU5CSlhtqkJve28yQ75XY55UlyMloDAIgYVRhZs2aNHnjgAfl8Ps2bN08//elPtWDBgmHbP/nkk7r77ru1c+dOnX/++frBD36gL37xi6MuGtIET5Iumpaui6YNP+x1vDugQ0e7dLCj73Woo0sHj3b3Lju6dOhol9qP96j9eHdo2aOu0PN1jnT26Ehnj/a1xb9+t8spd1JvMIleuqI+u11OeZJdoWXv52SXQ0kup5Kdvcskl0PJzt5l//XJLoeSQuuj3zuV5AwtQ+sH7tPldPS+HA45nVKS0ymnQ4QoABgDMYeR9evXq6qqSrW1tSouLtbq1atVVlampqYmZWdnD2r/8ssv68Ybb1RNTY2+9KUv6YknntD111+vrVu3au7cuXH5ERhaSrJL0zJSNS0jNabtOnsCkWDSF1K65T/eo+PdAR3t6n31vu/p9z4Q9f5YV0DHQm2Od0fPfekKBNUVCOpI7AM2RjkdGhBUHEoKfXY6HH3fDfg+/F2kff+Q43TI1X+//fflcMjhcMjpkJyhbaI+OxxyRN4r9Ln/9+H2oXXOGNv3379zZO2dzn7bSpJDcqivrcMhOaTeZahN37J3O4W/V6h9v/05QjsduC7cVgr9ziH2EXnf75jO0Ir+650D9ucY+Bv61Q/g1MU8gbW4uFiXXnqp/uM//kOSFAwGlZeXp3/8x3/UnXfeOah9eXm5Ojo69Nxzz0XWXXbZZSooKFBtbe2IjmmHCaxnOsuyegNIT++rc9AyEPnc2e9zVyCozu6+ZWdPQD1BS92BoHoClnqCQXUHLPUEguoO9i57AtaA96FlIKie0Pru0LbR63vbnv5TunE6GRhuHAMDS78AFAk+4fYDtg3vT3L0e69+IWxASIps0xeKwsEr3LZ/jeG2kdaOwfsY7lgaYvuTHUuDflff7x3qWINrGrDfIY41XF0nOpaG7JfB++2/7uR9NeC/w6A3w9Stfu8H9sWAWgZuNdR+HEMcL3rf/Y8X/R/3m585R3lT0hRPYzKBtaurS42Njaquro6sczqdKi0tVX19/ZDb1NfXq6qqKmpdWVmZnnnmmWGP09nZqc7Ovv+X2e8ffoImxgeHwyFPkkueJJfpUk4qELT6XpYV9Tk44HPAshQMWuo54fdSTzAY+k4KBIO9y37bBoc5Vu9LClqWLKv3zr59n/veBy2FPg9o32+dFaolpvZD7T/Y1z4wqH3090HLkqXe73qXA97LCq0bvD4YWq9wG/XVFG6rgev7tVXUfvr2HW99x+u/cxItxp/rCqbHPYyMVExh5MCBAwoEAvJ6vVHrvV6v3nvvvSG38fl8Q7b3+XzDHqempkb33HNPLKUBcRM+VYIz18BQMygYDQhAliQrOPT6YGjFwP2EA5mGWq/BQat/O0mDtu2/Lup79TtOqK7w+752fdtHHWuItuFjyRq4j5MfSwNq7d823O/D1dW3zxMfq//vH+mxBtZ1smOFG568r/qONbC28H4Hrxvcrn/boQJz//2faD9DHW/gbxq4rn87b7q5B7qellfTVFdXR42m+P1+5eXlGawIwJnE4eidpxM9aA3AlJjCSFZWllwul1paWqLWt7S0KCcnZ8htcnJyYmovSR6PRx6PJ5bSAADAOBXTI2PdbrcKCwtVV1cXWRcMBlVXV6eSkpIhtykpKYlqL0mbNm0atj0AALCXmE/TVFVVafHixSoqKtKCBQu0evVqdXR0qKKiQpK0aNEi5ebmqqamRpK0bNkyXXXVVfrRj36ka6+9VuvWrdPrr7+uhx9+OL6/BAAAjEsxh5Hy8nK1trZq+fLl8vl8Kigo0MaNGyOTVJubm+V09g24XH755XriiSf0ve99T9/97nd1/vnn65lnnuEeIwAAQNIo7jNiAvcZAQBg/Bnp3++Y5owAAADEG2EEAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGn5VN7Bwrfl83v9xuuBAAAjFT47/bJ7q86LsJIe3u7JCkvL89wJQAAIFbt7e3KyMgY9vtxcTv4YDCovXv3atKkSXI4HHHbr9/vV15ennbv3s1t5scQ/ZwY9HPi0NeJQT8nxlj2s2VZam9v1/Tp06OeWzfQuBgZcTqdOvvss8ds/+np6fwfegLQz4lBPycOfZ0Y9HNijFU/n2hEJIwJrAAAwCjCCAAAMMrWYcTj8WjFihXyeDymSzmj0c+JQT8nDn2dGPRzYpwO/TwuJrACAIAzl61HRgAAgHmEEQAAYBRhBAAAGEUYAQAARtk2jKxZs0b5+flKSUlRcXGxGhoaTJc0rtTU1OjSSy/VpEmTlJ2dreuvv15NTU1RbY4fP66lS5dq6tSpmjhxor72ta+ppaUlqk1zc7OuvfZapaWlKTs7W9/5znfU09OTyJ8yrqxcuVIOh0O33357ZB39HB979uzRTTfdpKlTpyo1NVUXX3yxXn/99cj3lmVp+fLlmjZtmlJTU1VaWqr3338/ah8HDx7UwoULlZ6erszMTH3zm9/UkSNHEv1TTmuBQEB33323zjnnHKWmpmrWrFn6/ve/H/XsEvo6dn/+85/15S9/WdOnT5fD4dAzzzwT9X28+vStt97SlVdeqZSUFOXl5emHP/xhfH6AZUPr1q2z3G63tXbtWuudd96xlixZYmVmZlotLS2mSxs3ysrKrF/84hfW9u3brW3btllf/OIXrRkzZlhHjhyJtPnWt75l5eXlWXV1ddbrr79uXXbZZdbll18e+b6np8eaO3euVVpaar3xxhvWhg0brKysLKu6utrETzrtNTQ0WPn5+dYll1xiLVu2LLKefj51Bw8etGbOnGn9/d//vfXqq69aH374ofX8889bH3zwQaTNypUrrYyMDOuZZ56x3nzzTetv//ZvrXPOOcc6duxYpM3f/M3fWPPmzbNeeeUV6y9/+Yt13nnnWTfeeKOJn3Tauu+++6ypU6dazz33nPXRRx9ZTz75pDVx4kTrxz/+caQNfR27DRs2WHfddZf11FNPWZKsp59+Our7ePRpW1ub5fV6rYULF1rbt2+3fvOb31ipqanWz3/+81Ou35ZhZMGCBdbSpUsjnwOBgDV9+nSrpqbGYFXj2/79+y1J1ksvvWRZlmUdPnzYSk5Otp588slIm3fffdeSZNXX11uW1fs/HqfTafl8vkibhx56yEpPT7c6OzsT+wNOc+3t7db5559vbdq0ybrqqqsiYYR+jo877rjD+sxnPjPs98Fg0MrJybEeeOCByLrDhw9bHo/H+s1vfmNZlmX99a9/tSRZr732WqTNH/7wB8vhcFh79uwZu+LHmWuvvdb6xje+EbXuq1/9qrVw4ULLsujreBgYRuLVpz/72c+syZMnR/27cccdd1gXXnjhKddsu9M0XV1damxsVGlpaWSd0+lUaWmp6uvrDVY2vrW1tUmSpkyZIklqbGxUd3d3VD/Pnj1bM2bMiPRzfX29Lr74Ynm93kibsrIy+f1+vfPOOwms/vS3dOlSXXvttVH9KdHP8fK73/1ORUVF+vrXv67s7GzNnz9fjzzySOT7jz76SD6fL6qfMzIyVFxcHNXPmZmZKioqirQpLS2V0+nUq6++mrgfc5q7/PLLVVdXpx07dkiS3nzzTW3ZskVf+MIXJNHXYyFefVpfX6/PfvazcrvdkTZlZWVqamrSoUOHTqnGcfGgvHg6cOCAAoFA1D/MkuT1evXee+8Zqmp8CwaDuv3223XFFVdo7ty5kiSfzye3263MzMyotl6vVz6fL9JmqP8O4e/Qa926ddq6datee+21Qd/Rz/Hx4Ycf6qGHHlJVVZW++93v6rXXXtM//dM/ye12a/HixZF+Gqof+/dzdnZ21PdJSUmaMmUK/dzPnXfeKb/fr9mzZ8vlcikQCOi+++7TwoULJYm+HgPx6lOfz6dzzjln0D7C302ePHnUNdoujCD+li5dqu3bt2vLli2mSznj7N69W8uWLdOmTZuUkpJiupwzVjAYVFFRke6//35J0vz587V9+3bV1tZq8eLFhqs7s/zXf/2XHn/8cT3xxBP61Kc+pW3btun222/X9OnT6Wsbs91pmqysLLlcrkFXG7S0tCgnJ8dQVeNXZWWlnnvuOb344os6++yzI+tzcnLU1dWlw4cPR7Xv3885OTlD/ncIf4fe0zD79+/Xpz/9aSUlJSkpKUkvvfSSfvKTnygpKUler5d+joNp06Zpzpw5UesuuugiNTc3S+rrpxP9u5GTk6P9+/dHfd/T06ODBw/Sz/185zvf0Z133qkbbrhBF198sW6++WZ9+9vfVk1NjST6eizEq0/H8t8S24URt9utwsJC1dXVRdYFg0HV1dWppKTEYGXji2VZqqys1NNPP60XXnhh0NBdYWGhkpOTo/q5qalJzc3NkX4uKSnR22+/HfU/gE2bNik9PX3QHwa7+tznPqe3335b27Zti7yKioq0cOHCyHv6+dRdccUVgy5N37Fjh2bOnClJOuecc5STkxPVz36/X6+++mpUPx8+fFiNjY2RNi+88IKCwaCKi4sT8CvGh6NHj8rpjP7T43K5FAwGJdHXYyFefVpSUqI///nP6u7ujrTZtGmTLrzwwlM6RSPJvpf2ejwe65e//KX117/+1fqHf/gHKzMzM+pqA5zYrbfeamVkZFibN2+29u3bF3kdPXo00uZb3/qWNWPGDOuFF16wXn/9daukpMQqKSmJfB++5PSaa66xtm3bZm3cuNE666yzuOT0JPpfTWNZ9HM8NDQ0WElJSdZ9991nvf/++9bjjz9upaWlWY899likzcqVK63MzEzr2Weftd566y3ruuuuG/LSyPnz51uvvvqqtWXLFuv888+39eWmQ1m8eLGVm5sbubT3qaeesrKysqx//dd/jbShr2PX3t5uvfHGG9Ybb7xhSbJWrVplvfHGG9auXbssy4pPnx4+fNjyer3WzTffbG3fvt1at26dlZaWxqW9p+KnP/2pNWPGDMvtdlsLFiywXnnlFdMljSuShnz94he/iLQ5duyYddttt1mTJ0+20tLSrK985SvWvn37ovazc+dO6wtf+IKVmppqZWVlWf/8z/9sdXd3J/jXjC8Dwwj9HB///d//bc2dO9fyeDzW7NmzrYcffjjq+2AwaN19992W1+u1PB6P9bnPfc5qamqKavPJJ59YN954ozVx4kQrPT3dqqiosNrb2xP5M057fr/fWrZsmTVjxgwrJSXFOvfcc6277ror6nJR+jp2L7744pD/Ji9evNiyrPj16Ztvvml95jOfsTwej5Wbm2utXLkyLvU7LKvfbe8AAAASzHZzRgAAwOmFMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMCo/w8HCWdfoBL3RwAAAABJRU5ErkJggg==\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 3: Exploring e in numpy\n", + "x_domain = [-2, 2]\n", + "x = np.linspace(x_domain[0], x_domain[1], 53)\n", + "x" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "RMRACZ_Ewwih", + "outputId": "58a19514-3eed-46fb-d39b-c17ec2102edc" + }, + "execution_count": 4, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-2. , -1.92307692, -1.84615385, -1.76923077, -1.69230769,\n", + " -1.61538462, -1.53846154, -1.46153846, -1.38461538, -1.30769231,\n", + " -1.23076923, -1.15384615, -1.07692308, -1. , -0.92307692,\n", + " -0.84615385, -0.76923077, -0.69230769, -0.61538462, -0.53846154,\n", + " -0.46153846, -0.38461538, -0.30769231, -0.23076923, -0.15384615,\n", + " -0.07692308, 0. , 0.07692308, 0.15384615, 0.23076923,\n", + " 0.30769231, 0.38461538, 0.46153846, 0.53846154, 0.61538462,\n", + " 0.69230769, 0.76923077, 0.84615385, 0.92307692, 1. ,\n", + " 1.07692308, 1.15384615, 1.23076923, 1.30769231, 1.38461538,\n", + " 1.46153846, 1.53846154, 1.61538462, 1.69230769, 1.76923077,\n", + " 1.84615385, 1.92307692, 2. ])" + ] + }, + "metadata": {}, + "execution_count": 4 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# functions\n", + "y1 = np.exp(x)\n", + "y2 = np.exp(x**2)\n", + "y3 = np.exp((-x)**2)\n", + "y4 = np.exp(-(x**2))\n", + "y5 = np.exp(x)**2\n", + "\n", + "# and plot\n", + "plt.figure(figsize=(8,6))\n", + "plt.plot(x, y1, linewidth=2, label='$y=e^x$')\n", + "plt.plot(x, y2, linewidth=2, label='$y=e^{x^2}$')\n", + "plt.plot(x, y3, '--', linewidth=2, label='$y=e^{(-x)^2}$')\n", + "plt.plot(x, y4, linewidth=2, label='$y=e^{-(x^2)}$')\n", + "plt.plot(x, y5, linewidth=2, label='$y={(e^x)}^2$')\n", + "\n", + "plt.xlim([x[0], x[-1]])\n", + "plt.ylim([-1, 10])\n", + "\n", + "plt.xlabel('x')\n", + "plt.ylabel('y=f(x)')\n", + "\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 547 + }, + "id": "ISsWAGXg1ecV", + "outputId": "732fbc58-6597-48aa-d147-390151a6d8b5" + }, + "execution_count": 5, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 4: Exploring e in sympy\n", + "s_beta = sym.var('beta')\n", + "\n", + "s_y = sym.exp(s_beta) - sym.log(s_beta) - np.exp(1)\n", + "s_y\n", + "\n", + "sym.plot(s_y, (s_beta, x_domain[0], x_domain[1]), title=f'$f(\\\\beta) = {sym.latex(s_y)}$', ylabel='$y=f(\\\\beta)$', xlabel='$\\\\beta$');" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 484 + }, + "id": "s7yvoSLKQbuq", + "outputId": "69d1fc4c-6984-4957-c59e-392367320a87" + }, + "execution_count": 6, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 5: exp and log\n", + "e5_ds = np.linspace(-4, 4, 30)\n", + "plt.plot(e5_ds, np.exp(e5_ds), linewidth=2, label='exp(x)')\n", + "\n", + "plt.plot(e5_ds, np.log(np.exp(e5_ds)), linewidth=2, label='log(exp(x))')\n", + "plt.plot(e5_ds, np.exp(np.log(e5_ds)), 'o', linewidth=2, label='exp(log(x))')\n", + "\n", + "\n", + "# log with fine grained dataset\n", + "e5_ds_for_log = np.linspace(.001, 4, 30)\n", + "plt.plot(e5_ds_for_log, np.log(e5_ds_for_log), linewidth=2, label='log(x)')\n", + "\n", + "\n", + "\n", + "plt.legend()\n", + "# plt.axis('square')\n", + "plt.xlim([-4, 4])\n", + "plt.ylim([-4, 4])\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 490 + }, + "id": "9vHDIu9JHm-r", + "outputId": "d20e0716-3f9d-4950-b310-4169d7e39906" + }, + "execution_count": 7, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + ":6: RuntimeWarning: invalid value encountered in log\n", + " plt.plot(e5_ds, np.exp(np.log(e5_ds)), 'o', linewidth=2, label='exp(log(x))')\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From 3fd41d1528cc4d2612540b1adae51472cc89e790 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Sun, 11 Jun 2023 07:31:15 +0400 Subject: [PATCH 13/25] Delete exo_and_log_funcs_cc_e2.ipynb --- .../functions/exo_and_log_funcs_cc_e2.ipynb | 122 ------------------ 1 file changed, 122 deletions(-) delete mode 100644 practice/functions/exo_and_log_funcs_cc_e2.ipynb diff --git a/practice/functions/exo_and_log_funcs_cc_e2.ipynb b/practice/functions/exo_and_log_funcs_cc_e2.ipynb deleted file mode 100644 index 0ff198a..0000000 --- a/practice/functions/exo_and_log_funcs_cc_e2.ipynb +++ /dev/null @@ -1,122 +0,0 @@ -{ - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "provenance": [], - "authorship_tag": "ABX9TyOlRea0LQmBDvrZOk94nqk6", - "include_colab_link": true - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - }, - "language_info": { - "name": "python" - } - }, - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "id": "view-in-github", - "colab_type": "text" - }, - "source": [ - "\"Open" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "id": "u9aSHthBWgQF" - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import sympy as sym\n", - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "code", - "source": [ - "n = [1, 2, 5, 10]\n", - "\n", - "for i in n:\n", - " # estimate\n", - " e = (1 + (1/i))**i\n", - " \n", - " # np.exp(1) is also an estimate but it is going to be much more accurate than\n", - " # our calculated e hence we will use it\n", - " print(f'n: {i:2.0f}, est.e: {e:.5f}, diff to e: {(np.exp(1) - e):.7f}')" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "d_nacGShWpYv", - "outputId": "28276bb7-73dc-4c73-b9c4-ca19b95351e4" - }, - "execution_count": 6, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "n: 1, est.e: 2.00000, diff to e: 0.7182818\n", - "n: 2, est.e: 2.25000, diff to e: 0.4682818\n", - "n: 5, est.e: 2.48832, diff to e: 0.2299618\n", - "n: 10, est.e: 2.59374, diff to e: 0.1245394\n" - ] - } - ] - }, - { - "cell_type": "code", - "source": [ - "n = np.arange(1, 1001)\n", - "\n", - "# numpy arr is different from simple list(used above)\n", - "# on numpy arr (vector n)\n", - "# element wise algebric operations (divison, power) can be perfomed\n", - "# \n", - "e_diffs = np.exp(1) - (1 + 1/n)**n\n", - "plt.plot(n, e_diffs)\n", - "\n" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 447 - }, - "id": "fiJvz_rUam0B", - "outputId": "f5a85185-56f3-4e12-a74f-dc1b04fbbf18" - }, - "execution_count": 7, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "[]" - ] - }, - "metadata": {}, - "execution_count": 7 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - } - ] -} \ No newline at end of file From f09ea8a7b90dbdf6b96581fe44428a2ff8896cea Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Sun, 11 Jun 2023 07:31:27 +0400 Subject: [PATCH 14/25] Delete exp_and_log_funcs_cc_e1.ipynb --- .../functions/exp_and_log_funcs_cc_e1.ipynb | 80 ------------------- 1 file changed, 80 deletions(-) delete mode 100644 practice/functions/exp_and_log_funcs_cc_e1.ipynb diff --git a/practice/functions/exp_and_log_funcs_cc_e1.ipynb b/practice/functions/exp_and_log_funcs_cc_e1.ipynb deleted file mode 100644 index c51c5ad..0000000 --- a/practice/functions/exp_and_log_funcs_cc_e1.ipynb +++ /dev/null @@ -1,80 +0,0 @@ -{ - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "provenance": [], - "authorship_tag": "ABX9TyMyoobNUrOIDXvTrsnCMB9o", - "include_colab_link": true - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - }, - "language_info": { - "name": "python" - } - }, - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "id": "view-in-github", - "colab_type": "text" - }, - "source": [ - "\"Open" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "id": "uK6I8b0yQtoR" - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import sympy as sym\n", - "import matplotlib as plt" - ] - }, - { - "cell_type": "code", - "source": [ - "n = [1, 2, 5, 10]\n", - "\n", - "for i in n:\n", - " # estimate\n", - " e = (1 + (1/i))**i\n", - " \n", - " # np.exp(1) is also an estimate but it is going to be much more accurate than\n", - " # our calculated e hence we will use it\n", - " print(f'n: {i:2.0f}, est.e: {e:.5f}, diff to e: {(np.exp(1) - e):.7f}')\n", - "\n", - "\n", - "\n" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "CUNwkWtWRjMm", - "outputId": "484934ce-9a36-46b5-98a2-0d3369b17dcd" - }, - "execution_count": 11, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "n: 1, est.e: 2.00000, diff to e: 0.7182818\n", - "n: 2, est.e: 2.25000, diff to e: 0.4682818\n", - "n: 5, est.e: 2.48832, diff to e: 0.2299618\n", - "n: 10, est.e: 2.59374, diff to e: 0.1245394\n" - ] - } - ] - } - ] -} \ No newline at end of file From c6b860995a24dd451b9365ad304168f81c78cc01 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Sun, 11 Jun 2023 07:31:36 +0400 Subject: [PATCH 15/25] Delete exp_and_log_funcs_cc_e3.ipynb --- .../functions/exp_and_log_funcs_cc_e3.ipynb | 131 ------------------ 1 file changed, 131 deletions(-) delete mode 100644 practice/functions/exp_and_log_funcs_cc_e3.ipynb diff --git a/practice/functions/exp_and_log_funcs_cc_e3.ipynb b/practice/functions/exp_and_log_funcs_cc_e3.ipynb deleted file mode 100644 index edc0063..0000000 --- a/practice/functions/exp_and_log_funcs_cc_e3.ipynb +++ /dev/null @@ -1,131 +0,0 @@ -{ - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "provenance": [], - "authorship_tag": "ABX9TyP4gDpmtE4vF/Ycce3VWgcn", - "include_colab_link": true - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - }, - "language_info": { - "name": "python" - } - }, - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "id": "view-in-github", - "colab_type": "text" - }, - "source": [ - "\"Open" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "id": "bOl03zxWdqzA" - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import sympy as sym\n", - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "code", - "source": [ - "x_domain = [-2, 2]\n", - "x = np.linspace(x_domain[0], x_domain[1], 53)\n", - "x" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "RMRACZ_Ewwih", - "outputId": "88ea6766-d1be-47ec-e91f-24b993a943db" - }, - "execution_count": 4, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "array([-2. , -1.92307692, -1.84615385, -1.76923077, -1.69230769,\n", - " -1.61538462, -1.53846154, -1.46153846, -1.38461538, -1.30769231,\n", - " -1.23076923, -1.15384615, -1.07692308, -1. , -0.92307692,\n", - " -0.84615385, -0.76923077, -0.69230769, -0.61538462, -0.53846154,\n", - " -0.46153846, -0.38461538, -0.30769231, -0.23076923, -0.15384615,\n", - " -0.07692308, 0. , 0.07692308, 0.15384615, 0.23076923,\n", - " 0.30769231, 0.38461538, 0.46153846, 0.53846154, 0.61538462,\n", - " 0.69230769, 0.76923077, 0.84615385, 0.92307692, 1. ,\n", - " 1.07692308, 1.15384615, 1.23076923, 1.30769231, 1.38461538,\n", - " 1.46153846, 1.53846154, 1.61538462, 1.69230769, 1.76923077,\n", - " 1.84615385, 1.92307692, 2. ])" - ] - }, - "metadata": {}, - "execution_count": 4 - } - ] - }, - { - "cell_type": "code", - "source": [ - "# functions\n", - "y1 = np.exp(x)\n", - "y2 = np.exp(x**2)\n", - "y3 = np.exp((-x)**2)\n", - "y4 = np.exp(-(x**2))\n", - "y5 = np.exp(x)**2\n", - "\n", - "# and plot\n", - "plt.figure(figsize=(8,6))\n", - "plt.plot(x, y1, linewidth=2, label='$y=e^x$')\n", - "plt.plot(x, y2, linewidth=2, label='$y=e^{x^2}$')\n", - "plt.plot(x, y3, '--', linewidth=2, label='$y=e^{(-x)^2}$')\n", - "plt.plot(x, y4, linewidth=2, label='$y=e^{-(x^2)}$')\n", - "plt.plot(x, y5, linewidth=2, label='$y={(e^x)}^2$')\n", - "\n", - "plt.xlim([x[0], x[-1]])\n", - "plt.ylim([-1, 10])\n", - "\n", - "plt.xlabel('x')\n", - "plt.ylabel('y=f(x)')\n", - "\n", - "plt.legend()\n", - "plt.grid()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 547 - }, - "id": "ISsWAGXg1ecV", - "outputId": "45954224-28f9-4a8f-9eed-12cc886b4f92" - }, - "execution_count": 5, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - } - ] -} \ No newline at end of file From 195949e3f4d1e63e86ba4700e56a1a85db01bdd2 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Sun, 11 Jun 2023 14:47:03 +0400 Subject: [PATCH 16/25] power_and_log_cc --- practice/functions/power_and_log_cc.ipynb | 648 ++++++++++++++++++++++ 1 file changed, 648 insertions(+) create mode 100644 practice/functions/power_and_log_cc.ipynb diff --git a/practice/functions/power_and_log_cc.ipynb b/practice/functions/power_and_log_cc.ipynb new file mode 100644 index 0000000..c89f3af --- /dev/null +++ b/practice/functions/power_and_log_cc.ipynb @@ -0,0 +1,648 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyMf7OUKipiUTmunaREgfjsw", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "id": "0xmK9O81pYaT" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from IPython.display import display, Math\n", + "from sympy.abc import x,a,b" + ] + }, + { + "cell_type": "code", + "source": [ + "# compute the terms individually\n", + "e1_xa = x**a\n", + "e1_xb = x**b\n", + "\n", + "e1_xab = e1_xa*e1_xb\n", + "\n", + "display(e1_xab)\n", + "display(sym.simplify(e1_xab))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 60 + }, + "id": "QcGM9tmppsQ5", + "outputId": "92c720c8-8b49-4b14-f011-38c57705cd81" + }, + "execution_count": 2, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "x**a*x**b" + ], + "text/latex": "$\\displaystyle x^{a} x^{b}$" + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "x**(a + b)" + ], + "text/latex": "$\\displaystyle x^{a + b}$" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "e1_n1 = 3.4\n", + "e1_n2 = 7.3\n", + "e1_xa.subs(a, e1_n1)*e1_xb.subs(b, e1_n2)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 38 + }, + "id": "PSx1ukD6G-4U", + "outputId": "479c849e-76b1-4d04-af5e-619960a786c5" + }, + "execution_count": 3, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "x**10.7" + ], + "text/latex": "$\\displaystyle x^{10.7}$" + }, + "metadata": {}, + "execution_count": 3 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 2: Subtracting powers\n", + "e2_xa = x**a\n", + "e2_xb = x**b\n", + "\n", + "e2_xab = e2_xa/e2_xb\n", + "\n", + "display(e2_xab)\n", + "display(sym.simplify(e2_xab))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 60 + }, + "id": "KbIDFKnXIVQy", + "outputId": "a255672b-e3bf-4633-aec1-c88098c8817a" + }, + "execution_count": 5, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "x**a/x**b" + ], + "text/latex": "$\\displaystyle x^{a} x^{- b}$" + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "x**(a - b)" + ], + "text/latex": "$\\displaystyle x^{a - b}$" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "e2_n = 4\n", + "e2_xa.subs(a, e2_n)/e2_xb.subs(b, e2_n)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 37 + }, + "id": "yWrckhDE40hm", + "outputId": "1a3573a8-e7a9-4c05-9861-0cbcf7fe03e0" + }, + "execution_count": 8, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "1" + ], + "text/latex": "$\\displaystyle 1$" + }, + "metadata": {}, + "execution_count": 8 + } + ] + }, + { + "cell_type": "code", + "source": [ + "0**0 # 1 OR = 0/0 = NaN ----> by convention 1" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "yLFMADNZ5cx1", + "outputId": "66074252-05ae-4c4d-d275-60cf2d7ff872" + }, + "execution_count": 10, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "1" + ] + }, + "metadata": {}, + "execution_count": 10 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 3: Powers upon powers\n", + "e3_xa = x**a\n", + "display((e3_xa)**b)\n", + "display(sym.simplify((e3_xa)**b))\n", + "display(sym.powsimp((e3_xa)**b))\n", + "# sympy will only simplify equations when they are true in their general case" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 86 + }, + "id": "MEKIJG_-5sg4", + "outputId": "83e7a00c-4e41-4127-9bc7-a34bd4ce28d1" + }, + "execution_count": 15, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "(x**a)**b" + ], + "text/latex": "$\\displaystyle \\left(x^{a}\\right)^{b}$" + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "(x**a)**b" + ], + "text/latex": "$\\displaystyle \\left(x^{a}\\right)^{b}$" + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "(x**a)**b" + ], + "text/latex": "$\\displaystyle \\left(x^{a}\\right)^{b}$" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# simplifications from slides\n", + "e3_n1 = 3\n", + "e3_n2 = 7\n", + "display((x**e3_n1)**e3_n2)\n", + "display(x**(e3_n1*e3_n2))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 60 + }, + "id": "viZQagJX6dqE", + "outputId": "8caf4c39-a1c1-41b2-ed40-69a81553b85c" + }, + "execution_count": 19, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "x**21" + ], + "text/latex": "$\\displaystyle x^{21}$" + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "x**21" + ], + "text/latex": "$\\displaystyle x^{21}$" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "e3_n1 = 4.1\n", + "e3_n2 = -.3\n", + "display((x**e3_n1)**e3_n2)\n", + "display(x**(e3_n1*e3_n2))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 63 + }, + "id": "_F2xD_FF7mUv", + "outputId": "e47cecdf-66e8-45ed-980b-e8103f14f856" + }, + "execution_count": 21, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "(x**4.1)**(-0.3)" + ], + "text/latex": "$\\displaystyle \\left(x^{4.1}\\right)^{-0.3}$" + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "x**(-1.23)" + ], + "text/latex": "$\\displaystyle x^{-1.23}$" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# x replaced with -2\n", + "e3_n1 = 4.1\n", + "e3_n2 = -.3\n", + "y = -2\n", + "display((y**e3_n1)**e3_n2)\n", + "display(y**(e3_n1*e3_n2))\n", + "# result is complex nums." + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 52 + }, + "id": "y02QIXUE72jU", + "outputId": "27e90fbc-424d-4920-e73b-26c973d78052" + }, + "execution_count": 24, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "(0.4244254339688208-0.040120015770397914j)" + ] + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "(-0.3197854353341568+0.28192878535754856j)" + ] + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# constraints for sympy\n", + "y, c, d = sym.symbols('y, c, d', positive=True)\n", + "# because the power upon power only works for positive real numbers\n", + "\n", + "display((y**c)**d)\n", + "display(y**(c*d))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 60 + }, + "id": "P_DxgTmk8SJP", + "outputId": "517f2fdd-2d4d-46fe-e5ec-e3127462a5c6" + }, + "execution_count": 28, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "y**(c*d)" + ], + "text/latex": "$\\displaystyle y^{c d}$" + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "y**(c*d)" + ], + "text/latex": "$\\displaystyle y^{c d}$" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 4: the power of log\n", + "# with numpy\n", + "\n", + "# simple numbers\n", + "m = np.random.rand()\n", + "n = np.random.rand()\n", + "\n", + "np.log(m*n) == np.log(m) + np.log(n)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "60YXAOsJ9llQ", + "outputId": "c62f5b86-98a7-485c-94f0-d262e4775ccb" + }, + "execution_count": 39, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "True" + ] + }, + "metadata": {}, + "execution_count": 39 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# vector - arr of nums\n", + "# rand provides uniformly distributed random number between 0 and 1;\n", + "# all positive as b/w 0 and 1\n", + "\n", + "# randn provides normally distributed random numbers \n", + "# some will be negative\n", + "# and we cannot take log of negative numbers\n", + "\n", + "m = np.random.rand(100)\n", + "n = np.random.rand(100)\n", + "v = np.log(m*n) - ( np.log(m) + np.log(n))\n", + "plt.plot(v, 's-')" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 462 + }, + "id": "CcZfH00mBGG7", + "outputId": "c36d136c-24ed-4b4a-99ad-cacbf7f44344" + }, + "execution_count": 42, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 42 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# randn provides normally distributed random numbers \n", + "# i.e. some will be negative\n", + "# and we cannot take log of negative numbers\n", + "# so we will see some misisng data points\n", + "\n", + "m = np.random.randn(100)\n", + "n = np.random.randn(100)\n", + "v = np.log(m*n) - ( np.log(m) + np.log(n))\n", + "plt.plot(v, 's-')" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 497 + }, + "id": "QvNpiG3jCTbo", + "outputId": "e045eac1-3d40-42b9-9014-5480d1dfab74" + }, + "execution_count": 45, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + ":8: RuntimeWarning: invalid value encountered in log\n", + " v = np.log(m*n) - ( np.log(m) + np.log(n))\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 45 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# fix negatives in normally distributed random numbers by taking square of every\n", + "m = np.random.randn(100) ** 2\n", + "n = np.random.randn(100) ** 2\n", + "v = np.log(m**n) - (n * np.log(m))\n", + "plt.plot(v, 's-')" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 462 + }, + "id": "Kukm9a5yChy-", + "outputId": "aaec5f2f-5ffc-42fc-d4ef-6f89d3ba05d0" + }, + "execution_count": 50, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 50 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "v = np.log(m/n) - ( np.log(m) - np.log(n))\n", + "plt.plot(v, 's-')" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 462 + }, + "id": "ms9ycd5BCtAI", + "outputId": "f3672dcf-2b77-4fc1-e5d5-e0e637e38506" + }, + "execution_count": 51, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 51 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From aa817333c87bbd89ea7ebb8710c55869fbc48ba8 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Mon, 12 Jun 2023 20:38:02 +0400 Subject: [PATCH 17/25] trigonometry_cc --- practice/functions/trigonometry_cc.ipynb | 248 +++++++++++++++++++++++ 1 file changed, 248 insertions(+) create mode 100644 practice/functions/trigonometry_cc.ipynb diff --git a/practice/functions/trigonometry_cc.ipynb b/practice/functions/trigonometry_cc.ipynb new file mode 100644 index 0000000..625cb1a --- /dev/null +++ b/practice/functions/trigonometry_cc.ipynb @@ -0,0 +1,248 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyPonXIYZ3ZRaT4DFJifnmFr", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "0xmK9O81pYaT" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 1: Fun with trig\n", + "xx = np.linspace(-np.pi, 2*np.pi, 1234)\n", + "xx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "UeD2E05daaLM", + "outputId": "d6ea6ffe-9ddf-437e-f9e7-44b6fe4d6335" + }, + "execution_count": 2, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-3.14159265, -3.13394888, -3.1263051 , ..., 6.26789775,\n", + " 6.27554153, 6.28318531])" + ] + }, + "metadata": {}, + "execution_count": 2 + } + ] + }, + { + "cell_type": "code", + "source": [ + "f = [0]*3\n", + "f[0] = np.sin(xx), 'sin(x)'\n", + "f[1] = np.sin(xx)**2, 'sin(x)**2'\n", + "f[2] = np.sin(xx**2), 'sin(x**2)'\n", + "\n", + "for y,label in f:\n", + " plt.plot(xx, y, label=label)\n", + "\n", + "plt.legend()\n", + "plt.xlabel('Angle (rad.)')\n", + "plt.ylabel('y = f(x)')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "gQQ_XAVsapX_", + "outputId": "77186ed0-2cf9-47ad-a95c-3e68238f269d" + }, + "execution_count": 3, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 2: More fun with trig\n", + "xx = np.linspace(-np.pi, 2*np.pi, 1234)\n", + "xx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "IOBKZcMXa4-b", + "outputId": "9ddf9313-ba9a-4518-f188-7e2127c3285d" + }, + "execution_count": 4, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-3.14159265, -3.13394888, -3.1263051 , ..., 6.26789775,\n", + " 6.27554153, 6.28318531])" + ] + }, + "metadata": {}, + "execution_count": 4 + } + ] + }, + { + "cell_type": "code", + "source": [ + "f = [0]*3\n", + "f[0] = np.sin(np.cos(xx)), 'sin(cos(θ))'\n", + "f[1] = np.cos(np.sin(xx)), 'cos(sin(θ))'\n", + "f[2] = np.cos(xx), 'cos(θ)'\n", + "\n", + "for y,label in f:\n", + " plt.plot(xx, y, label=label)\n", + "\n", + "plt.legend()\n", + "plt.xlabel('Angle (rad.)')\n", + "plt.ylabel('y = f(x)')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "M8WotxVVYGga", + "outputId": "0b5986e8-0599-481b-c0ce-405ce8e663a4" + }, + "execution_count": 9, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 3: resolution and tan\n", + "for p in range(2, 5):\n", + " dataset = np.linspace(0, 2*np.pi, 10**p)\n", + " plt.plot(dataset, np.tan(dataset), label=f'{10**p} pnts')\n", + "\n", + "plt.legend()\n", + "plt.xlabel('Angle (rad.)')\n", + "plt.ylabel('y = f(x)')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "i1uA7vQFaB1d", + "outputId": "933b7a77-27f7-45f4-d0ed-0a9ed84b5539" + }, + "execution_count": 24, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 3: resolution and tan --- zoomed in\n", + "for p in range(2, 5):\n", + " dataset = np.linspace(0, 2*np.pi, 10**p)\n", + " plt.plot(dataset, np.tan(dataset), label=f'{10**p} pnts')\n", + "\n", + "plt.xlim([1.55, 1.6])\n", + "plt.legend()\n", + "plt.xlabel('Angle (rad.)')\n", + "plt.ylabel('y = f(x)')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "lqqlEQqSc86q", + "outputId": "fa0abef7-ff00-4d37-86dd-4730ee225d06" + }, + "execution_count": 28, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From 5468d5f345f8014d31543dcd8cc1735b9a662286 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Mon, 12 Jun 2023 22:36:10 +0400 Subject: [PATCH 18/25] piecewise_functions --- .../functions/piecewise_functions_cc.ipynb | 393 ++++++++++++++++++ 1 file changed, 393 insertions(+) create mode 100644 practice/functions/piecewise_functions_cc.ipynb diff --git a/practice/functions/piecewise_functions_cc.ipynb b/practice/functions/piecewise_functions_cc.ipynb new file mode 100644 index 0000000..54a0410 --- /dev/null +++ b/practice/functions/piecewise_functions_cc.ipynb @@ -0,0 +1,393 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyP6Y6UtfKiRHkrA5XrpVZdS", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "0xmK9O81pYaT" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 1: piecewise function in numpy\n", + "xx = np.linspace(-3, 5, 100)\n", + "\n", + "piece1 = 0 * (xx < 0)\n", + "piece1" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "UeD2E05daaLM", + "outputId": "4b025425-c8b4-478e-c959-3edd5a160f71" + }, + "execution_count": 4, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n", + " 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])" + ] + }, + "metadata": {}, + "execution_count": 4 + } + ] + }, + { + "cell_type": "code", + "source": [ + "piece2 = -2 * xx * ((xx >= 0) & (xx<3))\n", + "piece2" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "Bo9vXRJKiaYh", + "outputId": "7917ef3b-02cc-4851-9735-b551712c52d1" + }, + "execution_count": 5, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([ 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , 0. , 0. ,\n", + " 0. , 0. , 0. , -0.14141414, -0.3030303 ,\n", + " -0.46464646, -0.62626263, -0.78787879, -0.94949495, -1.11111111,\n", + " -1.27272727, -1.43434343, -1.5959596 , -1.75757576, -1.91919192,\n", + " -2.08080808, -2.24242424, -2.4040404 , -2.56565657, -2.72727273,\n", + " -2.88888889, -3.05050505, -3.21212121, -3.37373737, -3.53535354,\n", + " -3.6969697 , -3.85858586, -4.02020202, -4.18181818, -4.34343434,\n", + " -4.50505051, -4.66666667, -4.82828283, -4.98989899, -5.15151515,\n", + " -5.31313131, -5.47474747, -5.63636364, -5.7979798 , -5.95959596,\n", + " -0. , -0. , -0. , -0. , -0. ,\n", + " -0. , -0. , -0. , -0. , -0. ,\n", + " -0. , -0. , -0. , -0. , -0. ,\n", + " -0. , -0. , -0. , -0. , -0. ,\n", + " -0. , -0. , -0. , -0. , -0. ])" + ] + }, + "metadata": {}, + "execution_count": 5 + } + ] + }, + { + "cell_type": "code", + "source": [ + "piece3 = xx**3/10 * (xx >= 3)\n", + "piece3" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "JVG5CBDnicBp", + "outputId": "27406abe-918b-46d7-e3a8-09d644453fe4" + }, + "execution_count": 7, + "outputs": [ + { + "output_type": "execute_result", + "data": { + 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 2: draw separate lines\n", + "plt.plot(xx[xx<0], np.zeros(len(xx[xx<0])), label='Piece 1')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "id": "k5ae5IgLjEVz", + "outputId": "e201c089-c02c-4dd9-a87f-dbf32bf19b2c" + }, + "execution_count": 14, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# OR using np.sum(xx < 0)\n", + "plt.plot(xx[xx<0], np.zeros(np.sum(xx < 0)), label='Piece 1')\n", + "plt.plot(xx[(xx >= 0) & (xx < 3)], -2 * xx[(xx >= 0) & (xx < 3)], label='Piece 2')\n", + "plt.plot(xx[xx >= 3], xx[xx >= 3]**3/10, label='Piece 3')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "id": "K3wQEsvd18yO", + "outputId": "89504263-3cab-45e3-9e88-173a5f3a6648" + }, + "execution_count": 18, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 3: piecewise function in sympy\n", + "from sympy.abc import x\n", + "piece1 = 0\n", + "piece2 = -2*x\n", + "piece3 = x**3/10\n", + "fx = sym.Piecewise(\n", + " (piece1, (x < 0)),\n", + " (piece2, (x >= 0) & (x < 3)),\n", + " (piece3, (x >= 3))\n", + ")\n", + "fx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 90 + }, + "id": "Yk87JQkK3oE3", + "outputId": "b52c03d4-cc7a-4c62-8c72-303cab9cfcff" + }, + "execution_count": 19, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "Piecewise((0, x < 0), (-2*x, x < 3), (x**3/10, True))" + ], + "text/latex": "$\\displaystyle \\begin{cases} 0 & \\text{for}\\: x < 0 \\\\- 2 x & \\text{for}\\: x < 3 \\\\\\frac{x^{3}}{10} & \\text{otherwise} \\end{cases}$" + }, + "metadata": {}, + "execution_count": 19 + } + ] + }, + { + "cell_type": "code", + "source": [ + "sym.plot(\n", + " fx,\n", + " (x, xx[0], xx[-1]),\n", + " title='Piecewise function',\n", + " xlabel='x',\n", + " ylabel='y'\n", + ")" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 503 + }, + "id": "IUg8FmFo4Xen", + "outputId": "871c6231-abd6-4753-d7c8-a8e61af2f60a" + }, + "execution_count": 22, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "execution_count": 22 + } + ] + } + ] +} \ No newline at end of file From e10c9a46a53c478092541d0234604c49e4d37136 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Mon, 12 Jun 2023 23:35:19 +0400 Subject: [PATCH 19/25] piecewise_functions_cc_02 --- .../functions/piecewise_functions_cc_02.ipynb | 406 ++++++++++++++++++ 1 file changed, 406 insertions(+) create mode 100644 practice/functions/piecewise_functions_cc_02.ipynb diff --git a/practice/functions/piecewise_functions_cc_02.ipynb b/practice/functions/piecewise_functions_cc_02.ipynb new file mode 100644 index 0000000..5c3ebd4 --- /dev/null +++ b/practice/functions/piecewise_functions_cc_02.ipynb @@ -0,0 +1,406 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyPOd8qGMLKuUx4c/+l0aa+8", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "id": "XCTLkkoL6Pw6" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 4: Evaluate the function at or near a point" + ], + "metadata": { + "id": "fnKC37EM_WCt" + }, + "execution_count": 68, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# with numpy\n", + "xx = np.linspace(-3, 5, 100) # rought approximation\n", + "\n", + "# increase resolution for better approximation\n", + "#xx = np.linspace(-3, 5, 1000) # better approximation\n", + "#xx = np.linspace(-3, 5, 10000) # even better approximation\n", + "piece1 = 0 * (xx < 0)\n", + "piece2 = -2 * xx * ((xx >= 0) & (xx<3))\n", + "piece3 = xx**3/10 * (xx >= 3)\n", + "y = piece1 + piece2 + piece3\n", + "xx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "xBuGCl2PAO9u", + "outputId": "33d1c749-2656-4e8c-9919-5ae8acf696fe" + }, + "execution_count": 69, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-3. , -2.91919192, -2.83838384, -2.75757576, -2.67676768,\n", + " -2.5959596 , -2.51515152, -2.43434343, -2.35353535, -2.27272727,\n", + " -2.19191919, -2.11111111, -2.03030303, -1.94949495, -1.86868687,\n", + " -1.78787879, -1.70707071, -1.62626263, -1.54545455, -1.46464646,\n", + " -1.38383838, -1.3030303 , -1.22222222, -1.14141414, -1.06060606,\n", + " -0.97979798, -0.8989899 , -0.81818182, -0.73737374, -0.65656566,\n", + " -0.57575758, -0.49494949, -0.41414141, -0.33333333, -0.25252525,\n", + " -0.17171717, -0.09090909, -0.01010101, 0.07070707, 0.15151515,\n", + " 0.23232323, 0.31313131, 0.39393939, 0.47474747, 0.55555556,\n", + " 0.63636364, 0.71717172, 0.7979798 , 0.87878788, 0.95959596,\n", + " 1.04040404, 1.12121212, 1.2020202 , 1.28282828, 1.36363636,\n", + " 1.44444444, 1.52525253, 1.60606061, 1.68686869, 1.76767677,\n", + " 1.84848485, 1.92929293, 2.01010101, 2.09090909, 2.17171717,\n", + " 2.25252525, 2.33333333, 2.41414141, 2.49494949, 2.57575758,\n", + " 2.65656566, 2.73737374, 2.81818182, 2.8989899 , 2.97979798,\n", + " 3.06060606, 3.14141414, 3.22222222, 3.3030303 , 3.38383838,\n", + " 3.46464646, 3.54545455, 3.62626263, 3.70707071, 3.78787879,\n", + " 3.86868687, 3.94949495, 4.03030303, 4.11111111, 4.19191919,\n", + " 4.27272727, 4.35353535, 4.43434343, 4.51515152, 4.5959596 ,\n", + " 4.67676768, 4.75757576, 4.83838384, 4.91919192, 5. ])" + ] + }, + "metadata": {}, + "execution_count": 69 + } + ] + }, + { + "cell_type": "code", + "source": [ + "xloc = .5\n", + "shifted_vector_xx = xx - xloc\n", + "# shift the value, and in new values required value is closet to 0\n", + "shifted_vector_xx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "Z0tY6AkxBTvs", + "outputId": "d7206b40-f45e-479c-9fda-2eb409215844" + }, + "execution_count": 70, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-3.5 , -3.41919192, -3.33838384, -3.25757576, -3.17676768,\n", + " -3.0959596 , -3.01515152, -2.93434343, -2.85353535, -2.77272727,\n", + " -2.69191919, -2.61111111, -2.53030303, -2.44949495, -2.36868687,\n", + " -2.28787879, -2.20707071, -2.12626263, -2.04545455, -1.96464646,\n", + " -1.88383838, -1.8030303 , -1.72222222, -1.64141414, -1.56060606,\n", + " -1.47979798, -1.3989899 , -1.31818182, -1.23737374, -1.15656566,\n", + " -1.07575758, -0.99494949, -0.91414141, -0.83333333, -0.75252525,\n", + " -0.67171717, -0.59090909, -0.51010101, -0.42929293, -0.34848485,\n", + " -0.26767677, -0.18686869, -0.10606061, -0.02525253, 0.05555556,\n", + " 0.13636364, 0.21717172, 0.2979798 , 0.37878788, 0.45959596,\n", + " 0.54040404, 0.62121212, 0.7020202 , 0.78282828, 0.86363636,\n", + " 0.94444444, 1.02525253, 1.10606061, 1.18686869, 1.26767677,\n", + " 1.34848485, 1.42929293, 1.51010101, 1.59090909, 1.67171717,\n", + " 1.75252525, 1.83333333, 1.91414141, 1.99494949, 2.07575758,\n", + " 2.15656566, 2.23737374, 2.31818182, 2.3989899 , 2.47979798,\n", + " 2.56060606, 2.64141414, 2.72222222, 2.8030303 , 2.88383838,\n", + " 2.96464646, 3.04545455, 3.12626263, 3.20707071, 3.28787879,\n", + " 3.36868687, 3.44949495, 3.53030303, 3.61111111, 3.69191919,\n", + " 3.77272727, 3.85353535, 3.93434343, 4.01515152, 4.0959596 ,\n", + " 4.17676768, 4.25757576, 4.33838384, 4.41919192, 4.5 ])" + ] + }, + "metadata": {}, + "execution_count": 70 + } + ] + }, + { + "cell_type": "code", + "source": [ + "plt.plot(shifted_vector_xx)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "275lz5OFBpN-", + "outputId": "e6ad3c43-d465-4a1f-ae30-050f25d26475" + }, + "execution_count": 71, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 71 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# approach, take the abs value and look for minimum\n", + "plt.plot(np.abs(shifted_vector_xx))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "CRacYLXgCeQT", + "outputId": "8136661b-0a1d-43ee-f912-87bf72c952ae" + }, + "execution_count": 72, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 72 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# another approach, square the values, which has same effect\n", + "plt.plot(shifted_vector_xx**2)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "tFysUcWJCpJ2", + "outputId": "7a2203f9-8697-4a87-fc7c-31015bf3efd1" + }, + "execution_count": 73, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 73 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# minimum of the function shifted_vector_xx**2 corresponds to the point in,\n", + "# x-axis that is close to the .5\n", + "xidx = np.argmin(shifted_vector_xx**2)\n", + "xidx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "7VhoA3jzDAwW", + "outputId": "1f2f8f23-c78f-4d71-a88f-935100f417a9" + }, + "execution_count": 74, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "43" + ] + }, + "metadata": {}, + "execution_count": 74 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# possible closet number, in vector xx, to the desired number .5\n", + "xx[xidx]" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "h6Jw6o5OEJf0", + "outputId": "bf6a33f9-4a78-465e-ee5d-4658d27de764" + }, + "execution_count": 75, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "0.4747474747474749" + ] + }, + "metadata": {}, + "execution_count": 75 + } + ] + }, + { + "cell_type": "code", + "source": [ + "y[xidx]" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "VLt6Vc2MEr8B", + "outputId": "2cb0cbcf-0365-40d0-96e1-ee996cc3d756" + }, + "execution_count": 76, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "-0.9494949494949498" + ] + }, + "metadata": {}, + "execution_count": 76 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# with sympy\n", + "from sympy.abc import x\n", + "piece1 = 0\n", + "piece2 = -2*x\n", + "piece3 = x**3/10\n", + "fx = sym.Piecewise(\n", + " (piece1, (x < 0)),\n", + " (piece2, (x >= 0) & (x < 3)),\n", + " (piece3, (x >= 3))\n", + ")\n", + "fx.subs(x, xloc)\n", + "# is giving direct and complete answer" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 37 + }, + "id": "uS45AaAmAJHP", + "outputId": "591667a1-ec31-4376-8e84-38ec5e647c53" + }, + "execution_count": 77, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "-1.00000000000000" + ], + "text/latex": "$\\displaystyle -1.0$" + }, + "metadata": {}, + "execution_count": 77 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Difference: why its diffcult to locate specific point in numpy than sympy\n", + "\n", + "# sympy is encoding the piecewise fucntion as symbolic expression\n", + "# whereas\n", + "# numpy is storing computed numbers " + ], + "metadata": { + "id": "DfGCeGroFzPJ" + }, + "execution_count": 78, + "outputs": [] + } + ] +} \ No newline at end of file From 72dba44639f6ddf147e7eda9a5e038ce3cd749c5 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Tue, 13 Jun 2023 00:40:23 +0400 Subject: [PATCH 20/25] discontinuities_cc_e01 --- .../functions/discontinuities_cc_e01.ipynb | 322 ++++++++++++++++++ 1 file changed, 322 insertions(+) create mode 100644 practice/functions/discontinuities_cc_e01.ipynb diff --git a/practice/functions/discontinuities_cc_e01.ipynb b/practice/functions/discontinuities_cc_e01.ipynb new file mode 100644 index 0000000..5f8c999 --- /dev/null +++ b/practice/functions/discontinuities_cc_e01.ipynb @@ -0,0 +1,322 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyP94AzYeFJKqwWUbmqXQ9iw", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "id": "oDsQY96sQfSi" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "xx = np.arange(-1, 2)\n", + "# default skip value is 1\n", + "xx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "tKogb0UmQwJ4", + "outputId": "2d44473d-593d-47df-cd54-14a8d7a0467b" + }, + "execution_count": 22, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-1, 0, 1])" + ] + }, + "metadata": {}, + "execution_count": 22 + } + ] + }, + { + "cell_type": "code", + "source": [ + "resolution = .1\n", + "xx = np.arange(-1, 2, resolution)\n", + "xx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "vJpnU4cJRA8e", + "outputId": "fc74f062-2bd8-4a48-8ea5-c54927d702b4" + }, + "execution_count": 23, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-1.00000000e+00, -9.00000000e-01, -8.00000000e-01, -7.00000000e-01,\n", + " -6.00000000e-01, -5.00000000e-01, -4.00000000e-01, -3.00000000e-01,\n", + " -2.00000000e-01, -1.00000000e-01, -2.22044605e-16, 1.00000000e-01,\n", + " 2.00000000e-01, 3.00000000e-01, 4.00000000e-01, 5.00000000e-01,\n", + " 6.00000000e-01, 7.00000000e-01, 8.00000000e-01, 9.00000000e-01,\n", + " 1.00000000e+00, 1.10000000e+00, 1.20000000e+00, 1.30000000e+00,\n", + " 1.40000000e+00, 1.50000000e+00, 1.60000000e+00, 1.70000000e+00,\n", + " 1.80000000e+00, 1.90000000e+00])" + ] + }, + "metadata": {}, + "execution_count": 23 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# list of function pieces\n", + "\n", + "# acrosss all values of xx\n", + "y = [0] * 3\n", + "y[0] = np.sin(xx * np.pi)\n", + "y[1] = 1.5 * np.ones(len(xx))\n", + "y[2] = -(xx - 2)**2\n", + "y" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "6DpULA-GRMGC", + "outputId": "98e4a63c-30c7-49a8-b42f-729f62e0e392" + }, + "execution_count": 24, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[array([-1.22464680e-16, -3.09016994e-01, -5.87785252e-01, -8.09016994e-01,\n", + " -9.51056516e-01, -1.00000000e+00, -9.51056516e-01, -8.09016994e-01,\n", + " -5.87785252e-01, -3.09016994e-01, -6.97573700e-16, 3.09016994e-01,\n", + " 5.87785252e-01, 8.09016994e-01, 9.51056516e-01, 1.00000000e+00,\n", + " 9.51056516e-01, 8.09016994e-01, 5.87785252e-01, 3.09016994e-01,\n", + " 1.45473231e-15, -3.09016994e-01, -5.87785252e-01, -8.09016994e-01,\n", + " -9.51056516e-01, -1.00000000e+00, -9.51056516e-01, -8.09016994e-01,\n", + " -5.87785252e-01, -3.09016994e-01]),\n", + " array([1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5,\n", + " 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5,\n", + " 1.5, 1.5, 1.5, 1.5]),\n", + " array([-9. , -8.41, -7.84, -7.29, -6.76, -6.25, -5.76, -5.29, -4.84,\n", + " -4.41, -4. , -3.61, -3.24, -2.89, -2.56, -2.25, -1.96, -1.69,\n", + " -1.44, -1.21, -1. , -0.81, -0.64, -0.49, -0.36, -0.25, -0.16,\n", + " -0.09, -0.04, -0.01])]" + ] + }, + "metadata": {}, + "execution_count": 24 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# list domains\n", + "x_domains = [0] * 3\n", + "x_domains[0] = xx < 0\n", + "x_domains[1] = np.abs(xx) < resolution/2\n", + "x_domains[2] = xx > 0\n", + "x_domains" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "Gdzj5SARRVOr", + "outputId": "3ff77eb3-5432-48b8-eab2-ca584a516b30" + }, + "execution_count": 25, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[array([ True, True, True, True, True, True, True, True, True,\n", + " True, True, False, False, False, False, False, False, False,\n", + " False, False, False, False, False, False, False, False, False,\n", + " False, False, False]),\n", + " array([False, False, False, False, False, False, False, False, False,\n", + " False, True, False, False, False, False, False, False, False,\n", + " False, False, False, False, False, False, False, False, False,\n", + " False, False, False]),\n", + " array([False, False, False, False, False, False, False, False, False,\n", + " False, False, True, True, True, True, True, True, True,\n", + " True, True, True, True, True, True, True, True, True,\n", + " True, True, True])]" + ] + }, + "metadata": {}, + "execution_count": 25 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# use absolute value to overcome precision problem\n", + "# one point that is as closet as possible to 0 smaller than our grid spacing \n", + "# i.e. smaller than our resolution\n", + "np.abs(xx) < resolution/2" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "36r0GTxPScF-", + "outputId": "4c8763dd-3434-4bbc-e959-0b056cff0e96" + }, + "execution_count": 26, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([False, False, False, False, False, False, False, False, False,\n", + " False, True, False, False, False, False, False, False, False,\n", + " False, False, False, False, False, False, False, False, False,\n", + " False, False, False])" + ] + }, + "metadata": {}, + "execution_count": 26 + } + ] + }, + { + "cell_type": "code", + "source": [ + "for i in range(len(y)):\n", + " plt.plot(xx, y[i])\n", + "\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 435 + }, + "id": "4x6r1Xe8SkOo", + "outputId": "447073bf-90de-432a-d528-059534e79a54" + }, + "execution_count": 27, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "for i in range(len(y)):\n", + " plt.plot(xx[x_domains[i]], y[i][x_domains[i]])\n", + "\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "id": "bT8djXLCVGHt", + "outputId": "9d79995e-318c-46dd-9959-8e7a2919faee" + }, + "execution_count": 28, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "marker = '-o-'\n", + "for i in range(len(y)):\n", + " plt.plot(\n", + " xx[x_domains[i]],\n", + " y[i][x_domains[i]],\n", + " marker[i]\n", + " )\n", + "\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "id": "ama8GjhzU-kk", + "outputId": "43331efa-5c4f-4309-d41a-c60978b52720" + }, + "execution_count": 29, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From 9febc493b73e5b5b6ac8c83eddb132276509344e Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Tue, 13 Jun 2023 00:53:20 +0400 Subject: [PATCH 21/25] discontinuities_cc_e02 --- practice/functions/discontinuities_cc.ipynb | 527 ++++++++++++++++++++ 1 file changed, 527 insertions(+) create mode 100644 practice/functions/discontinuities_cc.ipynb diff --git a/practice/functions/discontinuities_cc.ipynb b/practice/functions/discontinuities_cc.ipynb new file mode 100644 index 0000000..d17647b --- /dev/null +++ b/practice/functions/discontinuities_cc.ipynb @@ -0,0 +1,527 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyMn1qrQU2qaMGXXksD7w/Il", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "id": "oDsQY96sQfSi" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 1: Jump discontinuity in numpy\n", + "xx = np.arange(-1, 2)\n", + "# default skip value is 1\n", + "xx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "tKogb0UmQwJ4", + "outputId": "a1a07d6a-552e-48cb-c6b7-9e2a04f25011" + }, + "execution_count": 37, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-1, 0, 1])" + ] + }, + "metadata": {}, + "execution_count": 37 + } + ] + }, + { + "cell_type": "code", + "source": [ + "resolution = .1\n", + "xx = np.arange(-1, 2, resolution)\n", + "xx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "vJpnU4cJRA8e", + "outputId": "fc74f062-2bd8-4a48-8ea5-c54927d702b4" + }, + "execution_count": 23, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-1.00000000e+00, -9.00000000e-01, -8.00000000e-01, -7.00000000e-01,\n", + " -6.00000000e-01, -5.00000000e-01, -4.00000000e-01, -3.00000000e-01,\n", + " -2.00000000e-01, -1.00000000e-01, -2.22044605e-16, 1.00000000e-01,\n", + " 2.00000000e-01, 3.00000000e-01, 4.00000000e-01, 5.00000000e-01,\n", + " 6.00000000e-01, 7.00000000e-01, 8.00000000e-01, 9.00000000e-01,\n", + " 1.00000000e+00, 1.10000000e+00, 1.20000000e+00, 1.30000000e+00,\n", + " 1.40000000e+00, 1.50000000e+00, 1.60000000e+00, 1.70000000e+00,\n", + " 1.80000000e+00, 1.90000000e+00])" + ] + }, + "metadata": {}, + "execution_count": 23 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# list of function pieces\n", + "\n", + "# acrosss all values of xx\n", + "y = [0] * 3\n", + "y[0] = np.sin(xx * np.pi)\n", + "y[1] = 1.5 * np.ones(len(xx))\n", + "y[2] = -(xx - 2)**2\n", + "y" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "6DpULA-GRMGC", + "outputId": "98e4a63c-30c7-49a8-b42f-729f62e0e392" + }, + "execution_count": 24, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[array([-1.22464680e-16, -3.09016994e-01, -5.87785252e-01, -8.09016994e-01,\n", + " -9.51056516e-01, -1.00000000e+00, -9.51056516e-01, -8.09016994e-01,\n", + " -5.87785252e-01, -3.09016994e-01, -6.97573700e-16, 3.09016994e-01,\n", + " 5.87785252e-01, 8.09016994e-01, 9.51056516e-01, 1.00000000e+00,\n", + " 9.51056516e-01, 8.09016994e-01, 5.87785252e-01, 3.09016994e-01,\n", + " 1.45473231e-15, -3.09016994e-01, -5.87785252e-01, -8.09016994e-01,\n", + " -9.51056516e-01, -1.00000000e+00, -9.51056516e-01, -8.09016994e-01,\n", + " -5.87785252e-01, -3.09016994e-01]),\n", + " array([1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5,\n", + " 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5,\n", + " 1.5, 1.5, 1.5, 1.5]),\n", + " array([-9. , -8.41, -7.84, -7.29, -6.76, -6.25, -5.76, -5.29, -4.84,\n", + " -4.41, -4. , -3.61, -3.24, -2.89, -2.56, -2.25, -1.96, -1.69,\n", + " -1.44, -1.21, -1. , -0.81, -0.64, -0.49, -0.36, -0.25, -0.16,\n", + " -0.09, -0.04, -0.01])]" + ] + }, + "metadata": {}, + "execution_count": 24 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# list domains\n", + "x_domains = [0] * 3\n", + "x_domains[0] = xx < 0\n", + "x_domains[1] = np.abs(xx) < resolution/2\n", + "x_domains[2] = xx > 0\n", + "x_domains" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "Gdzj5SARRVOr", + "outputId": "3ff77eb3-5432-48b8-eab2-ca584a516b30" + }, + "execution_count": 25, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[array([ True, True, True, True, True, True, True, True, True,\n", + " True, True, False, False, False, False, False, False, False,\n", + " False, False, False, False, False, False, False, False, False,\n", + " False, False, False]),\n", + " array([False, False, False, False, False, False, False, False, False,\n", + " False, True, False, False, False, False, False, False, False,\n", + " False, False, False, False, False, False, False, False, False,\n", + " False, False, False]),\n", + " array([False, False, False, False, False, False, False, False, False,\n", + " False, False, True, True, True, True, True, True, True,\n", + " True, True, True, True, True, True, True, True, True,\n", + " True, True, True])]" + ] + }, + "metadata": {}, + "execution_count": 25 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# use absolute value to overcome precision problem\n", + "# one point that is as closet as possible to 0 smaller than our grid spacing \n", + "# i.e. smaller than our resolution\n", + "np.abs(xx) < resolution/2" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "36r0GTxPScF-", + "outputId": "4c8763dd-3434-4bbc-e959-0b056cff0e96" + }, + "execution_count": 26, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([False, False, False, False, False, False, False, False, False,\n", + " False, True, False, False, False, False, False, False, False,\n", + " False, False, False, False, False, False, False, False, False,\n", + " False, False, False])" + ] + }, + "metadata": {}, + "execution_count": 26 + } + ] + }, + { + "cell_type": "code", + "source": [ + "for i in range(len(y)):\n", + " plt.plot(xx, y[i])\n", + "\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 435 + }, + "id": "4x6r1Xe8SkOo", + "outputId": "447073bf-90de-432a-d528-059534e79a54" + }, + "execution_count": 27, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "for i in range(len(y)):\n", + " plt.plot(xx[x_domains[i]], y[i][x_domains[i]])\n", + "\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "id": "bT8djXLCVGHt", + "outputId": "9d79995e-318c-46dd-9959-8e7a2919faee" + }, + "execution_count": 28, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "marker = '-o-'\n", + "for i in range(len(y)):\n", + " plt.plot(\n", + " xx[x_domains[i]],\n", + " y[i][x_domains[i]],\n", + " marker[i]\n", + " )\n", + "\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "id": "ama8GjhzU-kk", + "outputId": "0479b98a-8c05-4fd8-aef5-0ba92ff972c1" + }, + "execution_count": 30, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 3: Jump discontinuity in sympy\n", + "from sympy.abc import x\n", + "\n", + "fx = sym.Piecewise(\n", + " (sym.sin(x * sym.pi), x < 0),\n", + " (1.5, sym.Eq(x, 0)),\n", + " (-(x-2)**2, x > 0)\n", + ")\n", + "fx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 90 + }, + "id": "ZfbK1CqlYF5n", + "outputId": "d1c06f71-be5c-47cc-d865-4bb1ff5bd9b2" + }, + "execution_count": 31, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "Piecewise((sin(pi*x), x < 0), (1.5, Eq(x, 0)), (-(x - 2)**2, x > 0))" + ], + "text/latex": "$\\displaystyle \\begin{cases} \\sin{\\left(\\pi x \\right)} & \\text{for}\\: x < 0 \\\\1.5 & \\text{for}\\: x = 0 \\\\- \\left(x - 2\\right)^{2} & \\text{for}\\: x > 0 \\end{cases}$" + }, + "metadata": {}, + "execution_count": 31 + } + ] + }, + { + "cell_type": "code", + "source": [ + "sym.plot(fx)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 504 + }, + "id": "G5c9hXvSYG-y", + "outputId": "d1da4cb4-df51-4801-fb4a-1938578a23f1" + }, + "execution_count": 32, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "execution_count": 32 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# domain correction\n", + "sym.plot(fx, (x, xx[0], xx[-1]))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 504 + }, + "id": "9urFqaNxYIr2", + "outputId": "61af8ef1-7c4a-43db-d1b6-9ad25eb19de1" + }, + "execution_count": 33, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "execution_count": 33 + } + ] + }, + { + "cell_type": "code", + "source": [ + "x" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 38 + }, + "id": "KUz6LsoNYM-t", + "outputId": "e60e5d46-ae5b-45e3-e028-420a200e5aad" + }, + "execution_count": 34, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "x" + ], + "text/latex": "$\\displaystyle x$" + }, + "metadata": {}, + "execution_count": 34 + } + ] + }, + { + "cell_type": "code", + "source": [ + "fx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 90 + }, + "id": "mepkf0ulYQLC", + "outputId": "05449562-f750-4a9c-a925-422f8582545d" + }, + "execution_count": 35, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "Piecewise((sin(pi*x), x < 0), (1.5, Eq(x, 0)), (-(x - 2)**2, x > 0))" + ], + "text/latex": "$\\displaystyle \\begin{cases} \\sin{\\left(\\pi x \\right)} & \\text{for}\\: x < 0 \\\\1.5 & \\text{for}\\: x = 0 \\\\- \\left(x - 2\\right)^{2} & \\text{for}\\: x > 0 \\end{cases}$" + }, + "metadata": {}, + "execution_count": 35 + } + ] + }, + { + "cell_type": "code", + "source": [ + "fx.subs(x, 0)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 37 + }, + "id": "GgiWWUZsYRCm", + "outputId": "8c2496c1-0ca9-411b-a8be-3e96486e3420" + }, + "execution_count": 36, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "1.50000000000000" + ], + "text/latex": "$\\displaystyle 1.5$" + }, + "metadata": {}, + "execution_count": 36 + } + ] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "IOgX2x-bYR4Y" + }, + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file From fa01edd56fb5d09e9c360a40979bd08c6ff71f73 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Tue, 13 Jun 2023 01:19:19 +0400 Subject: [PATCH 22/25] discontinuities_cc_e03 --- practice/functions/discontinuities_cc.ipynb | 136 +++++++++++++------- 1 file changed, 86 insertions(+), 50 deletions(-) diff --git a/practice/functions/discontinuities_cc.ipynb b/practice/functions/discontinuities_cc.ipynb index d17647b..0e7fe65 100644 --- a/practice/functions/discontinuities_cc.ipynb +++ b/practice/functions/discontinuities_cc.ipynb @@ -4,7 +4,7 @@ "metadata": { "colab": { "provenance": [], - "authorship_tag": "ABX9TyMn1qrQU2qaMGXXksD7w/Il", + "authorship_tag": "ABX9TyPiAeSFnUhaT4xnzUqMjfIu", "include_colab_link": true }, "kernelspec": { @@ -28,7 +28,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 61, "metadata": { "id": "oDsQY96sQfSi" }, @@ -52,9 +52,9 @@ "base_uri": "https://localhost:8080/" }, "id": "tKogb0UmQwJ4", - "outputId": "a1a07d6a-552e-48cb-c6b7-9e2a04f25011" + "outputId": "021ccc6a-290c-41e7-dc76-8eb746da0948" }, - "execution_count": 37, + "execution_count": 62, "outputs": [ { "output_type": "execute_result", @@ -64,7 +64,7 @@ ] }, "metadata": {}, - "execution_count": 37 + "execution_count": 62 } ] }, @@ -80,9 +80,9 @@ "base_uri": "https://localhost:8080/" }, "id": "vJpnU4cJRA8e", - "outputId": "fc74f062-2bd8-4a48-8ea5-c54927d702b4" + "outputId": "cb29455f-145b-4771-acaf-4dd3a2586520" }, - "execution_count": 23, + "execution_count": 63, "outputs": [ { "output_type": "execute_result", @@ -99,7 +99,7 @@ ] }, "metadata": {}, - "execution_count": 23 + "execution_count": 63 } ] }, @@ -120,9 +120,9 @@ "base_uri": "https://localhost:8080/" }, "id": "6DpULA-GRMGC", - "outputId": "98e4a63c-30c7-49a8-b42f-729f62e0e392" + "outputId": "7c3451cb-2913-4f1e-d12c-cfe2b9e62c36" }, - "execution_count": 24, + "execution_count": 64, "outputs": [ { "output_type": "execute_result", @@ -146,7 +146,7 @@ ] }, "metadata": {}, - "execution_count": 24 + "execution_count": 64 } ] }, @@ -165,9 +165,9 @@ "base_uri": "https://localhost:8080/" }, "id": "Gdzj5SARRVOr", - "outputId": "3ff77eb3-5432-48b8-eab2-ca584a516b30" + "outputId": "71bd0d2e-bea5-482b-bbb9-5c118c40539d" }, - "execution_count": 25, + "execution_count": 65, "outputs": [ { "output_type": "execute_result", @@ -188,7 +188,7 @@ ] }, "metadata": {}, - "execution_count": 25 + "execution_count": 65 } ] }, @@ -205,9 +205,9 @@ "base_uri": "https://localhost:8080/" }, "id": "36r0GTxPScF-", - "outputId": "4c8763dd-3434-4bbc-e959-0b056cff0e96" + "outputId": "11789846-5260-478a-a2be-53d8fe8721da" }, - "execution_count": 26, + "execution_count": 66, "outputs": [ { "output_type": "execute_result", @@ -220,7 +220,7 @@ ] }, "metadata": {}, - "execution_count": 26 + "execution_count": 66 } ] }, @@ -238,9 +238,9 @@ "height": 435 }, "id": "4x6r1Xe8SkOo", - "outputId": "447073bf-90de-432a-d528-059534e79a54" + "outputId": "2dc786af-158a-45de-c6c1-2b047efc81bd" }, - "execution_count": 27, + "execution_count": 67, "outputs": [ { "output_type": "display_data", @@ -268,9 +268,9 @@ "height": 430 }, "id": "bT8djXLCVGHt", - "outputId": "9d79995e-318c-46dd-9959-8e7a2919faee" + "outputId": "fee6f9b3-efe2-4712-cbf0-656b525baec9" }, - "execution_count": 28, + "execution_count": 68, "outputs": [ { "output_type": "display_data", @@ -303,9 +303,9 @@ "height": 430 }, "id": "ama8GjhzU-kk", - "outputId": "0479b98a-8c05-4fd8-aef5-0ba92ff972c1" + "outputId": "84dcebb5-738f-4bfb-fbe5-f1483ef8ebc0" }, - "execution_count": 30, + "execution_count": 69, "outputs": [ { "output_type": "display_data", @@ -322,7 +322,7 @@ { "cell_type": "code", "source": [ - "# Exercise 3: Jump discontinuity in sympy\n", + "# Exercise 2: Jump discontinuity in sympy\n", "from sympy.abc import x\n", "\n", "fx = sym.Piecewise(\n", @@ -338,9 +338,9 @@ "height": 90 }, "id": "ZfbK1CqlYF5n", - "outputId": "d1c06f71-be5c-47cc-d865-4bb1ff5bd9b2" + "outputId": "b602fd92-1603-4293-9cb8-dd740c2640ef" }, - "execution_count": 31, + "execution_count": 70, "outputs": [ { "output_type": "execute_result", @@ -351,7 +351,7 @@ "text/latex": "$\\displaystyle \\begin{cases} \\sin{\\left(\\pi x \\right)} & \\text{for}\\: x < 0 \\\\1.5 & \\text{for}\\: x = 0 \\\\- \\left(x - 2\\right)^{2} & \\text{for}\\: x > 0 \\end{cases}$" }, "metadata": {}, - "execution_count": 31 + "execution_count": 70 } ] }, @@ -366,9 +366,9 @@ "height": 504 }, "id": "G5c9hXvSYG-y", - "outputId": "d1da4cb4-df51-4801-fb4a-1938578a23f1" + "outputId": "9bb6a530-4dbc-4352-8681-f3d216ce740a" }, - "execution_count": 32, + "execution_count": 71, "outputs": [ { "output_type": "display_data", @@ -376,7 +376,7 @@ "text/plain": [ "
" ], - "image/png": 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\n" + "image/png": 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\n" }, "metadata": {} }, @@ -384,11 +384,11 @@ "output_type": "execute_result", "data": { "text/plain": [ - "" + "" ] }, "metadata": {}, - "execution_count": 32 + "execution_count": 71 } ] }, @@ -404,9 +404,9 @@ "height": 504 }, "id": "9urFqaNxYIr2", - "outputId": "61af8ef1-7c4a-43db-d1b6-9ad25eb19de1" + "outputId": "7a539895-fe9d-470d-a947-64e397f56867" }, - "execution_count": 33, + "execution_count": 72, "outputs": [ { "output_type": "display_data", @@ -414,7 +414,7 @@ "text/plain": [ "
" ], - "image/png": 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\n" 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\n" }, "metadata": {} }, @@ -422,11 +422,11 @@ "output_type": "execute_result", "data": { "text/plain": [ - "" + "" ] }, "metadata": {}, - "execution_count": 33 + "execution_count": 72 } ] }, @@ -441,9 +441,9 @@ "height": 38 }, "id": "KUz6LsoNYM-t", - "outputId": "e60e5d46-ae5b-45e3-e028-420a200e5aad" + "outputId": "5ffa8762-1012-42a8-886e-88ab155aa569" }, - "execution_count": 34, + "execution_count": 73, "outputs": [ { "output_type": "execute_result", @@ -454,7 +454,7 @@ "text/latex": "$\\displaystyle x$" }, "metadata": {}, - "execution_count": 34 + "execution_count": 73 } ] }, @@ -469,9 +469,9 @@ "height": 90 }, "id": "mepkf0ulYQLC", - "outputId": "05449562-f750-4a9c-a925-422f8582545d" + "outputId": "f46221f3-045b-4842-94d7-152d41c352b4" }, - "execution_count": 35, + "execution_count": 74, "outputs": [ { "output_type": "execute_result", @@ -482,7 +482,7 @@ "text/latex": "$\\displaystyle \\begin{cases} \\sin{\\left(\\pi x \\right)} & \\text{for}\\: x < 0 \\\\1.5 & \\text{for}\\: x = 0 \\\\- \\left(x - 2\\right)^{2} & \\text{for}\\: x > 0 \\end{cases}$" }, "metadata": {}, - "execution_count": 35 + "execution_count": 74 } ] }, @@ -497,9 +497,9 @@ "height": 37 }, "id": "GgiWWUZsYRCm", - "outputId": "8c2496c1-0ca9-411b-a8be-3e96486e3420" + "outputId": "1d29273e-f3c1-47d8-ec5e-046d64abac2b" }, - "execution_count": 36, + "execution_count": 75, "outputs": [ { "output_type": "execute_result", @@ -510,18 +510,54 @@ "text/latex": "$\\displaystyle 1.5$" }, "metadata": {}, - "execution_count": 36 + "execution_count": 75 } ] }, { "cell_type": "code", - "source": [], + "source": [ + "# Exercise 3: removeable discontinuity\n", + "y = np.sin(xx*np.pi) + xx**2\n", + "\n", + "# (xx - 0) centring x-axis variable to the numerical value we are looking for\n", + "# take the absolute value, then we are looking for the minimum of shifted function above\n", + "# and then aregmin returns the index, at which that minimum occurs\n", + "# we can omit 0, but keeping for elaboration of general form of technique\n", + "y[np.argmin(np.abs(xx - 0))] = np.pi\n", + "plt.plot(xx, y, 'o')" + ], "metadata": { - "id": "IOgX2x-bYR4Y" + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "IOgX2x-bYR4Y", + "outputId": "5e419f99-5ff8-42a9-fb37-6561ad7e469b" }, - "execution_count": null, - "outputs": [] + "execution_count": 76, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 76 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] } ] } \ No newline at end of file From 6f2e2d53da3e825b5d2a0a97f2a17bdb2713e976 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Tue, 13 Jun 2023 21:37:32 +0400 Subject: [PATCH 23/25] discontinuities_cc - 5 exercises completed --- practice/functions/discontinuities_cc.ipynb | 671 ++++++++++++++++++-- 1 file changed, 618 insertions(+), 53 deletions(-) diff --git a/practice/functions/discontinuities_cc.ipynb b/practice/functions/discontinuities_cc.ipynb index 0e7fe65..dccfb17 100644 --- a/practice/functions/discontinuities_cc.ipynb +++ b/practice/functions/discontinuities_cc.ipynb @@ -4,7 +4,7 @@ "metadata": { "colab": { "provenance": [], - "authorship_tag": "ABX9TyPiAeSFnUhaT4xnzUqMjfIu", + "authorship_tag": "ABX9TyON747V5ticpJHnprUvAZY8", "include_colab_link": true }, "kernelspec": { @@ -28,7 +28,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 37, "metadata": { "id": "oDsQY96sQfSi" }, @@ -52,9 +52,9 @@ "base_uri": "https://localhost:8080/" }, "id": "tKogb0UmQwJ4", - "outputId": "021ccc6a-290c-41e7-dc76-8eb746da0948" + "outputId": "c7c75e0d-3a12-48e3-9fb9-7cd778a93dc2" }, - "execution_count": 62, + "execution_count": 38, "outputs": [ { "output_type": "execute_result", @@ -64,7 +64,7 @@ ] }, "metadata": {}, - "execution_count": 62 + "execution_count": 38 } ] }, @@ -80,9 +80,9 @@ "base_uri": "https://localhost:8080/" }, "id": "vJpnU4cJRA8e", - "outputId": "cb29455f-145b-4771-acaf-4dd3a2586520" + "outputId": "7ac64008-051c-4874-87d7-6994c394ea01" }, - "execution_count": 63, + "execution_count": 39, "outputs": [ { "output_type": "execute_result", @@ -99,7 +99,7 @@ ] }, "metadata": {}, - "execution_count": 63 + "execution_count": 39 } ] }, @@ -120,9 +120,9 @@ "base_uri": "https://localhost:8080/" }, "id": "6DpULA-GRMGC", - "outputId": "7c3451cb-2913-4f1e-d12c-cfe2b9e62c36" + "outputId": "d462fee3-684d-42d6-cf0b-82121898235f" }, - "execution_count": 64, + "execution_count": 40, "outputs": [ { "output_type": "execute_result", @@ -146,7 +146,7 @@ ] }, "metadata": {}, - "execution_count": 64 + "execution_count": 40 } ] }, @@ -158,19 +158,25 @@ "x_domains[0] = xx < 0\n", "x_domains[1] = np.abs(xx) < resolution/2\n", "x_domains[2] = xx > 0\n", - "x_domains" + "display(x_domains)\n", + "display(y)\n", + "display(len(y))\n", + "display(range(len(y)))\n", + "for i in range(len(y)):\n", + " display(i)" ], "metadata": { "colab": { - "base_uri": "https://localhost:8080/" + "base_uri": "https://localhost:8080/", + "height": 573 }, "id": "Gdzj5SARRVOr", - "outputId": "71bd0d2e-bea5-482b-bbb9-5c118c40539d" + "outputId": "4b7badbf-407e-4592-f2d3-133d8be863d6" }, - "execution_count": 65, + "execution_count": 41, "outputs": [ { - "output_type": "execute_result", + "output_type": "display_data", "data": { "text/plain": [ "[array([ True, True, True, True, True, True, True, True, True,\n", @@ -187,8 +193,75 @@ " True, True, True])]" ] }, - "metadata": {}, - "execution_count": 65 + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "[array([-1.22464680e-16, -3.09016994e-01, -5.87785252e-01, -8.09016994e-01,\n", + " -9.51056516e-01, -1.00000000e+00, -9.51056516e-01, -8.09016994e-01,\n", + " -5.87785252e-01, -3.09016994e-01, -6.97573700e-16, 3.09016994e-01,\n", + " 5.87785252e-01, 8.09016994e-01, 9.51056516e-01, 1.00000000e+00,\n", + " 9.51056516e-01, 8.09016994e-01, 5.87785252e-01, 3.09016994e-01,\n", + " 1.45473231e-15, -3.09016994e-01, -5.87785252e-01, -8.09016994e-01,\n", + " -9.51056516e-01, -1.00000000e+00, -9.51056516e-01, -8.09016994e-01,\n", + " -5.87785252e-01, -3.09016994e-01]),\n", + " array([1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5,\n", + " 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5,\n", + " 1.5, 1.5, 1.5, 1.5]),\n", + " array([-9. , -8.41, -7.84, -7.29, -6.76, -6.25, -5.76, -5.29, -4.84,\n", + " -4.41, -4. , -3.61, -3.24, -2.89, -2.56, -2.25, -1.96, -1.69,\n", + " -1.44, -1.21, -1. , -0.81, -0.64, -0.49, -0.36, -0.25, -0.16,\n", + " -0.09, -0.04, -0.01])]" + ] + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "3" + ] + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "range(0, 3)" + ] + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "0" + ] + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "1" + ] + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "2" + ] + }, + "metadata": {} } ] }, @@ -205,9 +278,9 @@ "base_uri": "https://localhost:8080/" }, "id": "36r0GTxPScF-", - "outputId": "11789846-5260-478a-a2be-53d8fe8721da" + "outputId": "07931b97-9ef0-4692-b3d1-51d5cac78fd4" }, - "execution_count": 66, + "execution_count": 42, "outputs": [ { "output_type": "execute_result", @@ -220,7 +293,7 @@ ] }, "metadata": {}, - "execution_count": 66 + "execution_count": 42 } ] }, @@ -238,9 +311,9 @@ "height": 435 }, "id": "4x6r1Xe8SkOo", - "outputId": "2dc786af-158a-45de-c6c1-2b047efc81bd" + "outputId": "ae725d98-9e6c-4319-b778-ccb113e31193" }, - "execution_count": 67, + "execution_count": 43, "outputs": [ { "output_type": "display_data", @@ -268,9 +341,9 @@ "height": 430 }, "id": "bT8djXLCVGHt", - "outputId": "fee6f9b3-efe2-4712-cbf0-656b525baec9" + "outputId": "c506ade9-56a6-4d39-b1e1-ba03e7cd2e80" }, - "execution_count": 68, + "execution_count": 44, "outputs": [ { "output_type": "display_data", @@ -303,9 +376,9 @@ "height": 430 }, "id": "ama8GjhzU-kk", - "outputId": "84dcebb5-738f-4bfb-fbe5-f1483ef8ebc0" + "outputId": "4449bb89-b4d9-49b8-9ead-d07b86a706e8" }, - "execution_count": 69, + "execution_count": 45, "outputs": [ { "output_type": "display_data", @@ -338,9 +411,9 @@ "height": 90 }, "id": "ZfbK1CqlYF5n", - "outputId": "b602fd92-1603-4293-9cb8-dd740c2640ef" + "outputId": "8e4554f1-61cf-4903-fa1f-c7582cc1aada" }, - "execution_count": 70, + "execution_count": 46, "outputs": [ { "output_type": "execute_result", @@ -351,7 +424,7 @@ "text/latex": "$\\displaystyle \\begin{cases} \\sin{\\left(\\pi x \\right)} & \\text{for}\\: x < 0 \\\\1.5 & \\text{for}\\: x = 0 \\\\- \\left(x - 2\\right)^{2} & \\text{for}\\: x > 0 \\end{cases}$" }, "metadata": {}, - "execution_count": 70 + "execution_count": 46 } ] }, @@ -366,9 +439,9 @@ "height": 504 }, "id": "G5c9hXvSYG-y", - "outputId": "9bb6a530-4dbc-4352-8681-f3d216ce740a" + "outputId": "2ce60453-3dbb-4e96-b688-de4b97169043" }, - "execution_count": 71, + "execution_count": 47, "outputs": [ { "output_type": "display_data", @@ -376,7 +449,7 @@ "text/plain": [ "
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HsrB6/yVcLa+d/Pnu3kH42+Te8GvDvXQNOZpRjDd+SDEXski/dnh+dBfc3TsYri5O2LhxIx5//HGsWbMGgwcPxgcffIBNmzYhNTUVAQEBSLpSgk/2pmNvWiGA2s/uzft64d6+ISiq0GPAX7+XpNiZTAKHLxXhm+PZ+PmMGpXXXW0luoMKo7oHYFT3AER3ULX5SQ7Xbyfu7TxwMluDXSlq7DijRmZxpXk5d4UT7u0bgmmxYYjuoJL8/wVLs+Z/sKXC9+RG1vyesNg1YMfpPLz90zlkl1QBqC1oI6MCMLpHIHp38EKItxtcnZ1QVl2DjKsV+P1KCXamqM1TOgC1U3IsvadXq1zTtTXfk9JKPd784Sy+vbb3Dqi9usPdvYMRE+6DboEe8HJzgdEkkK+txplcLfamFuCXs/kou/ZXvZ+HAi+N7YZHB4VJdqm2m70nRpPA5t+zsGpPOnJKaz87D6UzxvQIwMjuAegV4oUglRtcnGQorazBpcIKHLtcjB1n1DiXV1sqZDJgUp8Q/HViD6uZDLlObmkV3t2ZVu+z6x/mjTE9AjE40hfh7d3hZKiGf1AIfj97ERmlRhy4UIhdKfnmSZRDfd2wYHx3TIwOtqp/pI0mgS1J2VixM81cPn3cXTC+dxDu7OKH47u/x39W/QNqdR6iY+7AnFeWokwZgJ9T1OYhZSe5DI8OCsULY7oiwLP2sysq16H/tWKXmZmJ0NBQi7+WSr0BW5Ky8dnBy8i4WmG+P6K9Ox4Y0BH39+8g6VyFQMPfKUIInM3TYucZNbafysOl6/L3CvHCY7HheGBAB5u+DndjrOHfH2vD9+RG1vyeWGWx0+l0WLZsGRYtWgSlUrq9CTVGE7Yl5+LTfenmYbBbkcuACdHBeGZEZ/QKab29WJZ4T9LUZfh0Xzp+PJ3X5DPtOvq44ck7I/HIoFC0k3h4prH3RG8w4ZukbPxzX7q5nN+Ki5MME6KD8ezILuga2DbHCTbXmRwNPtp9AXtSC8yXlruVLgEemHVXJB6K6dimQ+a3q1xnwPqDGfjySCZyNdW3fgJqhw7v798Bc4Z3RqRf/bPoiyv06PfaNmR98DDU6nwEBt56QuPmKtBWY/2hy9hwJNN8JRlPV2dM6hOCh2I6YECYj9WU6aZ8pwhReyWRL49mYsdptflKIn4eSjxxZwT+dEc4VG7Wdym8lrCWf3+sCd+TG1nze2KVxc7aCCGQkqvFj6fzkHS5BOfytOY9VwAQ6KVEdAdvDOvmh/heQS2azFUKmsoa7Dyrxr60ApzN1eJy0f+GYVxd5IgK9MTACF/c3TsIA8J8bGpeLJNJ4ERWKXaczkNSZgnS1GXm4TC5DAhWuaF/mDeGdPbD3b2DLDLFhyUVlunw0+k8JF4sQnJWKQrKqs3XofVQOqNroAfiOrXH6B6BDV7CzVoZjCb8ln4VB85fReKlIlwpqjB/dk5yGTp41352d3Xxw7heQQ0WjOuLXUlJKby9W/+wgavlOqzedxFfHL5iHioP83U3F2mp/whqDSUVenyTlI31hy7X2xv++JBwzB7W2e4KHpGtYrFrBiEE9EYTqvW1c5q15Ng5a2QwmlB97R+ndgonmyoDtyKEgM5ggq7GBA9XZ8mGkS3FYDShQmeE0kUOpbPc7j67cp0BAoC7S9P/vyup0KPvtWJXXFIKn1YsdqWVeqw5cAmfH7psLp39w7wxZ1hnjO0ZaHfbF1A7kvHDyVys2X/JfCk8L1dnPD2iM2YOiXDYs2mJrAWLHRHZtdJKPfosri12RcUl8PXxbvE6jSaBTb9nYcXPqSiprB1y7dtRhZfGdsPwbv52VagbIoTArrP5+MeuNPMxjv6eSrw6oTsm95P+hCMiR8U/rYjIrsnQugUjOasUS7adwans2ulwugV64JX47hjdI8ChyoxMJkN8ryCM6RGI70/m4L2E88gqrsJLG0/im6RsvDU5+objHYnI8iQZQ3z77bcxZMgQuLu7w9vb+6bLZGZmYuLEiXB3d0dAQABefvllGAyGmy5bp7i4GI899hi8vLzg7e2NWbNmoby83AKvwPL27dsHmUx209uxY8cafN6IESNuWP7pp59uw+SWFRERccPrW758eaPPqa6uxty5c9G+fXt4eHjgwQcfRH5+fhsltqzLly9j1qxZiIyMhJubGzp37oylS5dCr9c3+jx73E4++eQTREREwNXVFbGxsTh69OgNy1w/PLF582Z0794drq6uiI6Oxk8//dTo+ovKdVjwzSlM/uQgTmVr4KmsvVbxj88PxZiejU8a3daWLVuGQYMGwdPTEwEBAZg8eTLS0tIafc769etv2CZcXW99vLCTXIb7+3fE7nkj8HJ8FJTOchxML0L8Bwfw0e4L0BmMt1xHW3n99ddveI3du3dv9Dm3u53Ympt9p8pkMsydO/emyzd3O7FmBw4cwD333IOQkBDIZDJs3bq13uNCCCxZsgTBwcFwc3PDmDFjcOHChVuutynfSZYgSbHT6/WYMmUKnnnmmZs+bjQaMXHiROj1ehw6dAiff/451q9fjyVLljS63sceewwpKSlISEjA9u3bceDAAcyePdsSL8HihgwZgry8vHq3P//5z4iMjMTAgQMbfe5TTz1V73krVqxoo9Rt480336z3+p577rlGl3/ppZfwww8/YPPmzdi/fz9yc3PxwAMPtFFay0pNTYXJZMKaNWuQkpKC999/H6tXr8arr756y+fa03ayceNGzJs3D0uXLsXx48fRt29fxMfHo6CgANfvsKs78OTQoUOYOnUqZs2ahRMnTmDy5MmYPHkyzpw5c8O6TSaBLxIvY+S7+7Dx9ywAwIMDOmLP/xuBJ++KtMozjPfv34+5c+fi8OHDSEhIQE1NDcaNG4eKisbP7vfy8qq3TVy5cqXJv1PhLMfckV2w66VhGNrVD3qDCe8lnMeED3/F4UtFLX1JraZXr171XuNvv/3W4LK3s53YqmPHjtV7PxISEgAAU6ZMafA5LdlOrFFFRQX69u2LTz755KaPr1ixAh999BFWr16NI0eOoF27doiPj0d1dcNn7Tf6nWRpQkLr1q0TKpXqhvt/+uknIZfLhVqtNt/36aefCi8vL6HT6W66rrNnzwoA4tixY+b7duzYIWQymcjJyWn17G1Nr9cLf39/8eabbza63PDhw8ULL7zQNqEkEB4eLt5///0mL19aWipcXFzE5s2bzfedO3dOABCJiYkWSCi9FStWiMjIyEaXsbftZPDgwWLu3Lnmn41GowgJCRHLli0Tmiq9CH1xkwAgCotKhBBCPPzww2LixIn11hEbGyvmzJlT77680iox7V+JInzBdhG+YLuY8OEB8fvlIou/ntZWUFAgAIj9+/c3uExD38fNYTKZxLbkHBHztwTze/f/NiWLovKbf3+3laVLl4q+ffs2efmmbif25IUXXhCdO3cWJpPppo+35nZijQCI7777zvyzyWQSQUFBYuXKleb7SktLhVKpFF999VWD62nsO8nSrO9PTQCJiYmIjo5GYGCg+b74+HhotVqkpKQ0+Bxvb+96e7PGjBkDuVyOI0eOWDyzpX3//fcoKirCE088cctlN2zYAD8/P/Tu3RuLFi1CZWXlLZ9jS5YvX4727dujf//+WLlyZaND9ElJSaipqcGYMWPM93Xv3h1hYWFITExsi7htTqPRwNfX95bL2ct2otfrkZSUVO8zlsvlGDNmzA2fsbg2GJuYmFhveaD2O+b65X86nYf4Dw7gYHoRXF3keOPeXvj+2bsQE37r99baaDS1xwPearsoLy9HeHg4QkNDcd999zX4fXsrMpkM9/YNwe75w/FYbBgAYHNSNkb/Yx+2n8pt1jpby4ULFxASEoJOnTrhscceQ2ZmZoPLNmU7sSd6vR7//e9/8eSTTzZ6aEFrbSe2ICMjA2q1ut52oFKpEBsb2+B2cDvfSZZglSdPqNXqeqUOgPlntVrd4HMCAupPPOrs7AxfX98Gn2NL/vOf/yA+Pv6Wl0OaNm0awsPDERISglOnTmHBggVIS0vDt99+20ZJLev555/HgAED4Ovri0OHDmHRokXIy8vDe++9d9Pl1Wo1FArFDcdyBgYG2sV28Ufp6elYtWoV3n333UaXs6ft5OrVqzAajTf9zkhNTb3pqRMNfceo1WqUVdfg9e/PYsvxbABAn44qvP9IP3T297DUS7Aok8mEF198EXfeeSd69+7d4HJRUVH47LPP0KdPH2g0Grz77rsYMmQIUlJSmn0ZNpWbC96+PxoPDOiIxd+dRqq6DM9+eQJHLhXjtUk9oHRu26tXxMbGYv369YiKikJeXh7eeOMNDB06FGfOnIGn542Tkje2ndijrVu3orS0FDNnzmxwGUtsJ9as7rO+ne3gVt9JltZqxW7hwoX4+9//3ugy586du+WBqvauOe9TdnY2du7ciU2bNt1y/dcfUxgdHY3g4GCMHj0aFy9eROfOnZsf3IJu5z2ZN2+e+b4+ffpAoVBgzpw5WLZsmdXN/t0SzdlOcnJyMH78eEyZMgVPPfVUo8+1xe2kua7f83CryZ3kAV1w94e/IrukCnIZ8JcRXfDCmK5WeRxdU82dOxdnzpxp9FgyAIiLi0NcXJz55yFDhqBHjx5Ys2YN/va3v7UoQ0y4D3547i588Mt5fLK3diLnk9ml+GTagDa9tNrdd99t/u8+ffogNjYW4eHh2LRpE2bNmtVmOazVf/7zH9x9990ICQlpcBlLbifUOlqt2M2fP7/Rlg8AnTp1atK6goKCbjh7pO4sxqCgoAaf88eDEg0GA4qLixt8jhSa8z6tW7cO7du3x7333nvbvy82NhZA7Z4ca/0HuyXbTmxsLAwGAy5fvoyoqKgbHg8KCoJer0dpaWm9vXb5+flWtV380e2+J7m5uRg5ciSGDBmCtWvX3vbvs4XtpCF+fn5wcnK64Uznxj7joKCgessbTQI7c5yhnLAQ2SVV6Ojjhvcf6YdBEbY37Hq9Z5991nwi2e3uTXFxcUH//v2Rnp7eKllcnOR4Ob47Bkb44qWNyTiVrcHEj37FPx7uh7E9A2+9Agvw9vZGt27dGnyNf9xOAOv/7miuK1eu4JdffrntvfatvZ1Ym7rPOj8/H8HBweb78/Pz0a9fv5s+pznfSa2p1Yqdv78//P39W2VdcXFxePvtt1FQUGAeXk1ISICXlxd69uzZ4HNKS0uRlJSEmJgYAMCePXtgMpnM/2hZg9t9n4QQWLduHWbMmAEXl9u/ZE9ycjIA1NsgrU1Ltp3k5GTI5fIbhuHrxMTEwMXFBbt378aDDz4IAEhLS0NmZma9vzqtze28Jzk5ORg5ciRiYmKwbt06yOW3v3fJFraThigUCsTExGD37t2YPHkygNrhx927d+PZZ5+96VBsXFwcdu/ejRdffBGayhq8sPEETho7ADLggQEd8Ma9veDparuXyBJC4LnnnsN3332Hffv2ITIy8rbXYTQacfr0aUyYMKFVs42MCsCPzw/Fs18ex4nMUjz1f79jzrBO+H/xUW2+Z7S8vBwXL17E9OnTb/r49dtJnYSEBKv+7miudevWISAgABMnTryt51lqO7EWkZGRCAoKwu7du81FTqvV4siRIw3O7HGr7ySLs/jpGTdx5coVceLECfHGG28IDw8PceLECXHixAlRVlYmhBDCYDCI3r17i3Hjxonk5GTx888/C39/f7Fo0SLzOo4cOSKioqJEdna2+b7x48eL/v37iyNHjojffvtNdO3aVUydOrXNX19r+uWXXwQAce7cuRsey87OFlFRUeLIkSNCCCHS09PFm2++KX7//XeRkZEhtm3bJjp16iSGDRvW1rEt4tChQ+L9998XycnJ4uLFi+K///2v8Pf3FzNmzDAv88f3RAghnn76aREWFib27Nkjfv/9dxEXFyfi4uKkeAmtLjs7W3Tp0kWMHj1aZGdni7y8PPPt+mXsfTv5+uuvhVKpFOvXrxdnz54Vs2fPFt7e3kKtVosKXY35rFh1YbEQQoiDBw8KZ2dnsWj5RyLurZ0ifMF2ETpvi/joe/s4U/qZZ54RKpVK7Nu3r942UVlZaV5m+vTpYuHCheaf33jjDbFz505x8eJFkZSUJB599FHh6uoqUlJSLJJRV2MUb3yfYj5r9qFPD4q80iqL/K468+fPF/v27RMZGRni4MGDYsyYMcLPz08UFBQIIW58T+q2k3fffVecO3dOLF26VLi4uIjTp09bNGdbMxqNIiwsTCxYsOCGx6TeTtpCWVmZuYcAEO+99544ceKEuHLlihBCiOXLlwtvb2+xbds2cerUKXHfffeJyMhIUVX1v+111KhRYtWqVeafG/tOsjRJit3jjz8uUDtXaL3b3r17zctcvnxZ3H333cLNzU34+fmJ+fPni5qaGvPje/fuFQBERkaG+b6ioiIxdepU4eHhIby8vMQTTzxhLou2aurUqWLIkCE3fSwjI6Pe+5aZmSmGDRsmfH19hVKpFF26dBEvv/yy0Gg0bZjYcpKSkkRsbKxQqVTC1dVV9OjRQ7zzzjuiurravMwf3xMhhKiqqhJ/+ctfhI+Pj3B3dxf3339/veJjy9atW3fT/5eu/5vNUbaTVatWibCwMKFQKMTgwYPF4cOHhRCiXrHLK/zfVCVL1m4R4fO+EeELtouI574Qqzdulyp6q2tom1i3bp15meHDh4vHH3/c/POLL75ofv8CAwPFhAkTxPHjxy2e9adTuaL3kp9F+ILtYsCbu8Sv5wst9rseeeQRERwcLBQKhejQoYN45JFHRHp6uvnxP74nQgixadMm0a1bN6FQKESvXr3Ejz/+aLF8Utm5c6cAINLS0m54zFq2E0uq6xN/vNW9bpPJJP7617+KwMBAoVQqxejRo294r8LDw8XSpUvr3dfQd5Kl8VqxRGTXqvRGRC34FlkfPIy8wiIE+Prgg90X8NHu2pnj7+jki0+mDUB7D/s5+cbWXL5agWc2HMe5PC3kMuBvk3vjsdhwqWMR2STbPdWLiKgJrp+OS1djwvNfnzCXuifujMAXs2JZ6iQW4dcO3/1lCB6K6QiTABZ/dwbv7UoD9zsQ3T6rnMeOiMgSntlwHGev1sBZLsOyB6IxZWCo1JHoGlcXJ6x8qA86eLvhw90X8NGedORrdXj7/t5wtuHpZojaGv9vISKHcSZHA0+lMz5/cjBLnRWSyWR4aWw3vHN/NOQyYOPvWZjzRRKq9EapoxHZDBY7IrJr1w/FBnopsfmZONzZxU+6QHRL02LDsPpPMVA6y7E7tQDT/n0YxRV6qWMR2QQWOyKya0pnJ8RfmwD3yz/fge5BXhInoqYY1ysIXz4VC293F5zILMVDnx5CVrFtXs+YqC3xrFgisntarRYqlQoajQZeXix2tiS9oAyPf3YMOaVV8PdUYv0Tg9ArRCV1LCKrxT12RERktboEeOLbvwxB9yBPFJbp8Miaw0i6UiJ1LCKrxWJHRERWLdDLFZuejkNspC/KdQbM/OwoTmWXSh2LyCqx2BERkdXzcnXBuicGYXCkL8p0Bkz/z1GczdVKHYvI6rDYERGRTXBXOOOzmYMwIMwbmqoa/Ok/R3Ahv0zqWERWhcWOiIhshofSGeufHIw+HVUortBj2r+P4FJhudSxiKwGix0R2a2vvvoKbm5uUKvV5vueeOIJ9OnTBxqNRsJk1BJeri74vycHo0ewFwrLdJj2ryPILOJUKEQApzshIjsmhEC/fv1wxx13YO3atViwYAE2bNiAw4cPo0OHDlLHoxYqKtfh0bWHcaGgHB283bBxzh3o6OMudSwiSbHYEZFd2759Ox588EHo9Xp4e3vjt99+Q69evaSORa2koKwaj645jEtXKxDe3h0bZ8chSOUqdSwiybDYEZHd69u3L06dOoUff/wREyZMkDoOtTK1phoPr0lEZnElOvm3w8bZcfD3VEodi0gSPMaOiOzazz//jPPnzwMAAgICJE5DlhCkcsWXT8Wig7cbLhVWYNbnx1ClN0odi0gSLHZEZLeOHz+Ohx9+GB9//DEA4K233pI4EVlKRx93bPhzLHzcXXAqW4N5m5JhMnFAihwPix0R2aXLly9j4sSJePXVVzFlyhQAwLZt23D8+HGJk5GlRPi1w9oZA6FwkmPHGTVW7kqTOhJRm+MxdkRkd4qLizFkyBCMGDECq1evhlarhUqlwtixYyGXy/Hzzz9LHZEs6LsT2Xhp40kAwIqH+uDhgaESJyJqOyx2RGT36oqdRqOBl5eX1HGoDby3Kw0f7UmHs1yGL2bFIq5ze6kjEbUJDsUSEZHdeWlsN0zqEwyDSeDp/ybx6hTkMFjsiIjI7shkMrw7pS/6X7uu7JPrj6GkQi91LCKLY7EjIiK75OrihLXTB6KDtxsuF1Vizn+ToDeYpI5FZFEsdkREZLf8PZVY98QgeCqdcTSjGIu+PQ0eWk72jMWOiIjsWrdAT3z82AA4yWXYcjwb/9x3UepIRBbDYkdERHZveDd/vH5PTwDAyp1p+Ol0nsSJiCyDxY6IiBzC9LgIPHFnBADgpY3JSMnVSBuIyAJY7IiIyGG8NrEnRkT5Q2cwYe6G4yirrpE6ElGrYrEjIiKH4SSX4YNH+pnPlF24hSdTkH1hsSMiIofi7a7Aqmn94SyX4cfTefji8BWpIxG1GhY7IiJyOAPCfLBoQg8AwFvbz+F0No+3I/vAYkdERA7pyTsjEN8rEHqjCX/5MgmaKh5vR7aPxY6IiBySTCbDiof6ItTXDVnFVXjlm5M83o5sHosdERE5LJWbCz6ZNgAKJzl2puTjs4OXpY5E1CIsdkRE5ND6dPTGa5Nqj7db9tM5nMgskTgRUfOx2BERkcObfkc4JkYHw2ASePbLEyit1EsdiahZWOyIiMjhyWQyLH8wGhHt3ZFTWoX5m07CZOLxdmR7WOyISDJvv/02hgwZAnd3d3h7e990mczMTEycOBHu7u4ICAjAyy+/DIPB0LZBySF4urrgk8cGQOEsx+7UAnx2MEPqSES3jcWOiCSj1+sxZcoUPPPMMzd93Gg0YuLEidDr9Th06BA+//xzrF+/HkuWLGnjpOQoeoWosPSengCAFTvTkF5QJnEiotsjEzy3m4gktn79erz44osoLS2td/+OHTswadIk5ObmIjAwEACwevVqLFiwAIWFhVAoFE1av1arhUqlgkajgZeXV2vHJzsjhMAT649hX1oh+nZUYcszQ+DsxP0gZBu4pRKR1UpMTER0dLS51AFAfHw8tFotUlJSJExG9kwmk+HvD/aBl6szTmZrsHr/RakjETUZix0RWS21Wl2v1AEw/6xWqxt8nk6ng1arrXcjuh2BXq54877eAIAPd19ASi4vOUa2gcWOiFrVwoULIZPJGr2lpqZaNMOyZcugUqnMt9DQUIv+PrJP9/ULwfheQagxCszfdBI6g1HqSES35Cx1ACKyL/Pnz8fMmTMbXaZTp05NWldQUBCOHj1a7778/HzzYw1ZtGgR5s2bZ/5Zq9Wy3NFtk8lkeOv+3jh2uRip6jJ8tPsCXo7vLnUsokax2BFRq/L394e/v3+rrCsuLg5vv/02CgoKEBAQAABISEiAl5cXevbs2eDzlEollEplq2Qgx+bnocTb9/fG0/89jk/3XcSYHoHoH+YjdSyiBnEologkk5mZieTkZGRmZsJoNCI5ORnJyckoLy8HAIwbNw49e/bE9OnTcfLkSezcuROvvfYa5s6dy+JGbWZ872BM7hcCkwDmbzqJKj2HZMl6cboTIpLMzJkz8fnnn99w/969ezFixAgAwJUrV/DMM89g3759aNeuHR5//HEsX74czs5NH3DgdCfUUprKGoz7YD/ytTo8eWckltzT8B5jIimx2BGR3WOxo9awN60AT6w7BgD46qk7ENe5vcSJiG7EoVgiIqImGBkVgKmDa0/CefmbkyjX8dJ2ZH1Y7IiIiJpo8cSe6OjjhuySKrzz0zmp4xDdgMWOiIioiTyUzljxUB8AwJdHMrH/fKHEiYjqY7EjIiK6DUM6+2HmkAgAwCvfnISmskbaQETXYbEjIiK6TQvGd0ekXzvka3VYsdOyV1Ihuh0sdkRERLfJTeGEd+6PBgB8eTQTJzJLJE5EVIvFjoiIqBniOrfHAwM6QAhg8XdnYDCapI5ExGJHRETUXK9O6AGVmwvO5mnxeeIVqeMQsdgRERE1l5+HEgvv7g4AeG9XGtSaaokTkaNjsSMiImqBRwaGYkCYNyr0Rry5PUXqOOTgWOyIiIhaQC6X4a3J0XCSy/DTaTX2phVIHYkcGIsdERFRC/UM8cKTd0YAAJZsO4PqGqO0gchhsdgRERG1ghfHdEOwyhVZxVX4eE+61HHIQbHYERERtYJ2SmcsvacXAGDNgYtILyiTOBE5IhY7IiKiVhLfKxCjuwegxijw2tYzEEJIHYkcDIsdERFRK5HJZHj93l5wdZHj8KVifHciR+pI5GBY7IiIiFpRqK87nh/dFQDw9o/nUFqplzgRORIWOyIiolb257s6oWuAB4oq9Pj7z2lSxyEHwmJHRETUyhTOcrw1uTcA4OtjmTidrZE4ETkKFjsiIiILiO3UHvf1C4EQwN+2n+WJFNQmWOyIiIgsZMH47nB1kePo5WL8fEYtdRxyACx2REREFhLi7YbZQzsBAN7ZcQ46A69IQZbFYkdERGRBc4Z3RqCXElnFVVh38LLUccjOsdgRERFZUDulM16O7w4A+HhPOgrLdBInInvGYkdERGRhD/TvgOgOKpTrDHgv4bzUcciOsdgRERFZmFwuw18n9QQAbDyWiXN5WokTkb1isSMiImoDgyN9MTE6GCYBvPUjpz8hy2CxIyIiaiML7+4OhZMcB9OLsPtcgdRxyA6x2BEREbWRUF93zBoaCQB4+6dz0BtMEicie8NiR0RE1Ib+MqIz/DwUyLhagS8OX5E6DtkZFjsiIqI25OnqgvnjogAAH/5yHiUVeokTkT1hsSMiImpjDw8MRfcgT2irDfjgF05/Qq2HxY6IiKiNOcllWHJt+pMNRzJxpahC4kRkL1jsiIiIJDCkix+GdfOHwSTwPictplbCYkdERCSRV+Jrj7XbdjIXqWpOWkwtx2JHREQkkd4dVJgYHQwhgHd3cq8dtRyLHRERkYReGtsNchnwy7l8JF0pkToO2TgWOyIiIgl1CfDAQzEdAQArd6byUmPUIix2REREEnthTDconOQ4fKkYv6VflToO2TAWOyIiIol18HbDY3eEAQBW7kzjXjtqNhY7IiIiKzB3ZBe4K5xwKluDnSlqqeOQjWKxIyIisgJ+Hkr8+a5IAMC7u87DaOJeO7p9LHZERERW4s/DOsHb3QXpBeX49ni21HHIBrHYERERWQkvVxc8M7wzAOCDXy5AZzBKnIhsDYsdERGRFXl8SAQCvZTIKa3CV0cypY5DNobFjoiIyIq4ujjhuVFdAQAf701Hhc4gcSKyJSx2REREVuaRQaEI83XH1XI91h+6LHUcsiEsdkRERFbGxUmOeWO7AQBW77+I0kq9xInIVrDYERERWaF7+4age5AnyqoNWL3/ktRxyEaw2BEREVkhuVyG/zcuCgCw/lAGCrTVEiciW8BiR0REZKVG9wjAgDBvVNeYsOYA99rRrbHYERERWSmZTIYXxtQea7fhyBVcLddJnIisHYsdEUnm8uXLmDVrFiIjI+Hm5obOnTtj6dKl0OvrHyh+6tQpDB06FK6urggNDcWKFSskSkzU9oZ19UPfjipU15jw718zpI5DVo7Fjogkk5qaCpPJhDVr1iAlJQXvv/8+Vq9ejVdffdW8jFarxbhx4xAeHo6kpCSsXLkSr7/+OtauXSthcqK2I5PJ8Oy1ee2+SLyMkgqeIUsNkwkheJVhIrIaK1euxKeffopLl2qPJ/r000+xePFiqNVqKBQKAMDChQuxdetWpKamNmmdWq0WKpUKGo0GXl5eFstOZClCCEz46Decy9Pi+dFdzVOhEP0R99gRkVXRaDTw9fU1/5yYmIhhw4aZSx0AxMfHIy0tDSUlJVJEJGpzMpkMz43qAgBYdzAD2uoaiRORtWKxIyKrkZ6ejlWrVmHOnDnm+9RqNQIDA+stV/ezWq2+6Xp0Oh20Wm29G5GtG98rCF0DPFBWbcD/8WoU1AAWOyJqdQsXLoRMJmv09sdh1JycHIwfPx5TpkzBU0891aLfv2zZMqhUKvMtNDS0ResjsgZyuQzPXttr95/fMngNWbopHmNHRK2usLAQRUVFjS7TqVMn8/Bqbm4uRowYgTvuuAPr16+HXP6/vzlnzJgBrVaLrVu3mu/bu3cvRo0aheLiYvj4+Nywbp1OB53uf9NCaLVahIaG8hg7snkGowlj3tuPy0WVeHVCd8we1lnqSGRlnKUOQET2x9/fH/7+/k1aNicnByNHjkRMTAzWrVtXr9QBQFxcHBYvXoyamhq4uLgAABISEhAVFXXTUgcASqUSSqWyZS+CyAo5O8nxl5Fd8Mo3p7D2QAZmxEXA1cVJ6lhkRTgUS0SSycnJwYgRIxAWFoZ3330XhYWFUKvV9Y6dmzZtGhQKBWbNmoWUlBRs3LgRH374IebNmydhciLp3N+/Azr6uOFquQ5fHc2UOg5ZGRY7IpJMQkIC0tPTsXv3bnTs2BHBwcHmWx2VSoVdu3YhIyMDMTExmD9/PpYsWYLZs2dLmJxIOi5OcjwzonYIds3+S9AZjBInImvCY+yIyO5xHjuyNzqDEcNX7INaW423JvfGn+4IlzoSWQnusSMiIrIxSmcnzBneCQDw6b6LqDGaJE5E1oLFjoiIyAZNHRwGPw8lckqr8N2JHKnjkJVgsSMiIrJBri5OmD0sEgDwz73pMHCvHYHFjoiIyGY9FhsOH3cXXC6qxPZTeVLHISvAYkdERGSj2imd8eehtcfafbw3HSYTz4d0dCx2RERENmx6XDi8XJ2RXlCOXWfzpY5DEmOxIyIismFeri6YHlc73cm/f70kcRqSGosdERGRjXs8LgIKJzl+v1KC45klUschCbHYERER2bgAL1fc1y8EAPfaOToWOyIiIjtQdxLFz2fUyCyqlDgNSYXFjoiIyA5EBXlieDd/mATw2cEMqeOQRFjsiIiI7MRT1/babTyWhdJKvcRpSAosdkRERHbizi7t0T3IE1U1Rmw4kil1HJIAix0REZGdkMlkmD2sdq/d54cuQ2cwSpyI2hqLHRERkR2Z1CcEgV5KFJTp8H1yrtRxqI2x2BEREdkRhbMcM4dEAgD+/WsGhOBlxhwJix0REZGdmRYbhnYKJ6Tll+HAhatSx6E2xGJHRERkZ1RuLnh4UCgATljsaFjsiIiI7NCTd0ZCLgN+vXAV5/K0UsehNsJiR0REZIdCfd1xd3QwAOBf3GvnMFjsiIiI7FTdhMU/nMyFWlMtcRpqCyx2REREdqpfqDcGR/iixiiw/tBlqeNQG2CxIyIismN/Hlo79cmXR66gXGeQOA1ZGosdERGRHRvTIxCRfu2grTZg07EsqeOQhbHYERER2TG5XIZZd9XutfvsYAYMRpPEiciSWOyIiIjs3IMDOsLH3QXZJVXYmZIvdRyyIBY7IiIiO+emcML0uAgAwNpfL/EyY3aMxY6IiMgBzIgLh8JZjpNZpfj9SonUcchCWOyIiIgcgJ+HEg8O6AAAWHuAExbbKxY7IiIiBzHrrtoJi385l49LheUSpyFLYLEjIiJyEF0CPDCqewCEAP7zW4bUccgCWOyIiIgcyJ+vTX3y3YkcaKtrJE5DrY3FjoiIyIHEdW6PrgEeqNQbsSUpW+o41MpY7IiIiByITCbD9LhwAMAXh69w6hM7w2JHRETkYO7v3wHtFE64VFiBg+lFUsehVsRiR0RE5GA8XV3wwICOAID/S7wsbRhqVSx2REREDqhuOPaXc/nIKa2SOA21FhY7IiIiB9Qt0BN3dPKFSQBfHrkidRxqJSx2REREDmrGtevHfn00CzqDUdow1CpY7IiIiBzU2J6BCPRSoqhCjx2n1VLHoVbAYkdEROSgXJzkmDa49lg7nkRhH1jsiIiIHNjU2FC4OMlwPLMUZ3I0UsehFmKxIyIicmABnq4Y3zsYAPBFIk+isHUsdkRERA5uxrWpT7adzIGmktePtWUsdkRERA5uYLgPugd5orrGhM1JWVLHoRZgsSMiInJwMpnMPPXJF4evwGTi9WNtFYsdERERYXL/EHi6OuNKUSUOXCiUOg41E4sdERERwV3hjIdiaq8fy5MobBeLHREREQEApt9RexLFnrQCZBVXSpyGmoPFjoiIiAAAnfw9MLSrH4QA/svrx9okFjsiIiIyq9trt+lYFqpreP1YW8NiR0RERGajewSig7cbSiprsP1UntRx6Dax2BGRpO69916EhYXB1dUVwcHBmD59OnJzc+stc+rUKQwdOhSurq4IDQ3FihUrJEpLZP+c5DJMiw0DAHzB68faHBY7IpLUyJEjsWnTJqSlpWHLli24ePEiHnroIfPjWq0W48aNQ3h4OJKSkrBy5Uq8/vrrWLt2rYSpiezbo4NCoXCS42S2BiezSqWOQ7dBJoTgLIREZDW+//57TJ48GTqdDi4uLvj000+xePFiqNVqKBQKAMDChQuxdetWpKamNmmdWq0WKpUKGo0GXl5eloxPZDde2piM707k4NFBoVj+YB+p41ATcY8dEQEAampqkJWVhbS0NBQXF0uSobi4GBs2bMCQIUPg4uICAEhMTMSwYcPMpQ4A4uPjkZaWhpKSEklyEjmCRweFAgC+P5mLcp1B4jTUVCx2RA6srKwMn376KYYPHw4vLy9ERESgR48e8Pf3R3h4OJ566ikcO3bM4jkWLFiAdu3aoX379sjMzMS2bdvMj6nVagQGBtZbvu5ntVp90/XpdDpotdp6NyK6PYMjfdHJvx0q9Ub8cDL31k8gq8BiR+Sg3nvvPURERGDdunUYM2YMtm7diuTkZJw/fx6JiYlYunQpDAYDxo0bh/Hjx+PChQtNXvfChQshk8kavV0/jPryyy/jxIkT2LVrF5ycnDBjxgy05CiRZcuWQaVSmW+hoaHNXheRo5LJZOa9dl8fzZQ4DTUVj7EjclBTp07Fa6+9hl69ejW6nE6nw7p166BQKPDkk082ad2FhYUoKipqdJlOnTrVG16tk52djdDQUBw6dAhxcXGYMWMGtFottm7dal5m7969GDVqFIqLi+Hj43PTzDqdzvyzVqtFaGgoj7Ejuk1F5TrcsWw3aowCPz0/FD1D+P+PtXOWOgARSeOrr74y/3dZWRk8PT1vupxSqcTTTz99W+v29/eHv79/s3KZTCYAMBezuLg4LF68GDU1Nebj7hISEhAVFXXTUleXWalUNuv3E9H/tPdQYlzPIPx4Og8bj2Xijft6Sx2JboFDsUSEoUOHNni8miUdOXIEH3/8MZKTk3HlyhXs2bMHU6dORefOnREXFwcAmDZtGhQKBWbNmoWUlBRs3LgRH374IebNm9fmeYkc0aODa4djvzuRwytR2AAWOyJC//79ERsbe8P0IcnJyZgwYYLFfq+7uzu+/fZbjB49GlFRUZg1axb69OmD/fv3m/e4qVQq7Nq1CxkZGYiJicH8+fOxZMkSzJ4922K5iOh/7uzsh1BfN2irDfjpNK9EYe14jB0RAQCWLl2KTz75BFu3bkVAQABee+01bNmyBRMmTMAPP/wgdbwW4Tx2RC3z8Z4LeHfXeQyO8MWmp+OkjkON4DF2RAQAeOONN6BUKjF27FgYjUaMHj0aiYmJGDx4sNTRiEhiD8WE4r2E8zh6uRjpBeXoEuAhdSRqAIdiiQj5+fl44YUX8NZbb6Fnz55wcXHBzJkzWeqICAAQpHLFqO4BAICNxzj1iTVjsSMiREZG4sCBA9i8eTOSkpKwZcsWzJ49GytXrpQ6GhFZiUcHhQEAthzPgc7AkyisFYsdEeGzzz7DiRMnMHHiRADA+PHjsXfvXrz//vuYO3euxOmIyBqMiPJHoJcSxRV6JJzNlzoONYDFjojw6KOP3nDfgAEDcOjQIezZs0eCRERkbZyd5Hh4YO3UJxuPZUmchhrCYkdEDYqIiMChQ4ekjkFEVuLhgaGQyYBfL1xFVnGl1HHoJljsiBxUZmbTDoCuu7pDTk6OJeMQkQ0I9XXHXV38AHCvnbVisSNyUIMGDcKcOXNw7NixBpfRaDT417/+hd69e2PLli1tmI6IrNXUwbUnUWxOyoLBaJI4Df0R57EjclATJ06Eh4cHxo4dC1dXV8TExCAkJASurq4oKSnB2bNnkZKSggEDBmDFihUWvQIFEdmOMT0C0b6dAvlaHfamFWJsz0CpI9F1eOUJIgelUCiQlZUFT09P+Pv7Y+rUqSgqKkJVVRX8/PzQv39/xMfHo3dv27/oN688QdS6lv10DmsOXMLo7gH4z8xBUseh63CPHZGDCgkJQXJyMuLj41FVVYV33nkHAQEBUsciIhvwyKBQrDlwCXvTCpCnqUKwyk3qSHQNj7EjclDz58/HPffcg6FDh0Imk2HDhg04duwYqqqqpI5GRFauk78HBkf6wiSAzb9nSx2HrsNiR+SgnnvuOfz+++8YP348hBD45JNPEBcXBy8vL/To0QOPPvooli9fjh07dkgdlYis0NTBtXPafZOUDR7VZT14jB0RoWvXrkhMTES7du1w6tQpJCcnm29nzpxBWVmZ1BFbhMfYEbW+Sr0Bg9/ejXKdAZvmxGFwpK/UkQgsdkR0C0IIyGQyqWO0CIsdkWUs+OYUNv6ehYcHdsSKh/pKHYfAoVgiugVbL3VEZDkPDewIAPjxVB4q9QaJ0xDAYkdERETNNDDcB+Ht3VGhN+LnM2qp4xBY7IiIiKiZZDIZHhpQu9fumySeHWsNWOyIiIio2R6I6QiZDDh0sQjZJZVSx3F4LHZERETUbB283TCkc3sAwLfHcyROQyx2RERE1CIPXhuO3XKcc9pJjcWOiIiIWmR87yC0UzjhSlElfr9SInUch8ZiR0RERC3irnDGxD7BAIBveIkxSbHYERERUYs9FFN7ibEfT3NOOymx2BEREVGLDYrwQZivO8p1BuxM4Zx2UmGxIyIiohaTyWR4KIZz2kmNxY6IiIhaxQMDOgDgnHZSYrEjIiKiVtHRxx1DOreHEMB3nNNOEix2RERE1GrMw7Gc004SLHZERETUajinnbRY7IiIiKjVuCucMSGac9pJhcWOiIiIWlXdcCzntGt7LHZERETUqgZF+HJOO4mw2BEREVGrkstluL9/7dQnW0/kSpzGsbDYERERUaubfK3Y/ZZ+FVfLdRKncRwsdkRERNTqIv3aoW9HFYwmge0nudeurbDYERERkUXc1+/acGwyi11bYbEjIiIii7inbwic5DIkZ5Ui42qF1HEcAosdERERWYS/pxJ3dvEDAGxL5iXG2gKLHREREVnM5H4hAIBtybm8xFgbYLEjIiIiixnXKwiuLnJkXK3AqWyN1HHsHosdERERWYyH0hnjegYBAL47weFYS2OxIyIiIoua3L92OHb7qVwYjCaJ09g3FjsiIiKyqKFd/eHbToGr5XocvFgkdRy7xmJHREREFuXiJMfE6GAAwDYOx1oUix0RERFZXN0lxnamqFGpN0icxn6x2BEREZHFDQjzRpivOyr0RiSczZc6jt1isSMiIiKLk8lkuO+6Oe3IMljsiIiIqE3UXTv2wPlCFFfoJU5jn1jsiIiIqE10CfBA7w5eMJgEfjzFvXaWwGJHREREbWbytb12nKzYMljsiIiIqM3c2zcEchlwPLMUmUWVUsexOyx2RGQVdDod+vXrB5lMhuTk5HqPnTp1CkOHDoWrqytCQ0OxYsUKaUISUYsFeLliSGc/AMC2ZO61a20sdkRkFV555RWEhITccL9Wq8W4ceMQHh6OpKQkrFy5Eq+//jrWrl0rQUoiag11Z8duTc6BEELiNPaFxY6IJLdjxw7s2rUL77777g2PbdiwAXq9Hp999hl69eqFRx99FM8//zzee+89CZISUWsY3zsISmc5LhZWICVXK3Ucu8JiR0SSys/Px1NPPYUvvvgC7u7uNzyemJiIYcOGQaFQmO+Lj49HWloaSkpKbrpOnU4HrVZb70ZE1sPT1QVjegYC4EkUrY3FjogkI4TAzJkz8fTTT2PgwIE3XUatViMwMLDefXU/q9Xqmz5n2bJlUKlU5ltoaGjrBieiFqs7O/aHk7kwmjgc21pY7Iio1S1cuBAymazRW2pqKlatWoWysjIsWrSoVX//okWLoNFozLesrKxWXT8Rtdzwbv7wdndBQZkOiReLpI5jN5ylDkBE9mf+/PmYOXNmo8t06tQJe/bsQWJiIpRKZb3HBg4ciMceewyff/45goKCkJ9f/7qSdT8HBQXddN1KpfKGdRKRdVE4yzEhOhhfHsnEDydzcVdXP6kj2QUWOyJqdf7+/vD397/lch999BHeeust88+5ubmIj4/Hxo0bERsbCwCIi4vD4sWLUVNTAxcXFwBAQkICoqKi4OPjY5kXQERtYlKf2mL3c4oab93fGy5OHEhsKb6DRCSZsLAw9O7d23zr1q0bAKBz587o2LEjAGDatGlQKBSYNWsWUlJSsHHjRnz44YeYN2+elNGJqBXERraHn4cSmqoa/JZ+Veo4doHFjoismkqlwq5du5CRkYGYmBjMnz8fS5YswezZs6WORkQt5CSXYUJ07SEV20/mSZzGPsgEZwYkIjun1WqhUqmg0Wjg5eUldRwius7RjGI8vCYRnq7O+P21MVA6O0kdyaZxjx0RERFJZmC4DwK9lCirNuDX8xyObSkWOyIiIpKMXC7DhOhgAMCPpzkc21IsdkRERCSpSX1qi13C2XxU1xglTmPbWOyIiIhIUv1DfRCickW5zoD95wuljmPTWOyIiIhIUtcPx24/xeHYlmCxIyIiIslN6hsCANh9Lh9Veg7HNheLHREREUmub0cVOvq4oVJvxN60Aqnj2CwWOyIiIpKcTCbDxGsnUfzI4dhmY7EjIiIiq3BPn2vDsan5qNAZJE5jm1jsiIiIyCr0CvFCeHt3VNeYsCeVw7HNwWJHREREVkEmk5nntNt+KlfiNLaJxY6IiIisxsTo2uHYvWmFKOdw7G1jsSMiIiKr0SPYE53820FvMOGXs/lSx7E5LHZERERkNWQyGSZxsuJmY7EjIiIiq1I3WfGB84XQVNVInMa2sNgRERGRVekW6ImuAR7QGzkce7tY7IiIiMjqTLo2px3Pjr09LHZERERkdequQvHrhasordRLnMZ2sNgRERGR1ekS4IHuQZ4wmAR2pXA4tqlY7IiIiMgq3XPtJIofOBzbZCx2REREZJUmXpv25NDFIhRXcDi2KVjsiIiIyCpF+LVD7w5eMJoEfj6jljqOTWCxIyIiIqtVd4kxnh3bNCx2REREZLUmXTs79vAlDsc2BYsdERERWa1QX3f07uAFkwASznI49lZY7IiIiMiqje8VBAA8zq4JWOyIiIjIqo3vXVvsfku/Cm01rx3bGBY7IiIismpdAjzRJcADNUaBvakFUsexaix2REREZPXqhmN3nOZwbGNY7IiIiMjq1Q3H7jtfgCq9UeI01ovFjoiIiKxerxAvdPRxQ3WNCfvPF0odx2qx2BEREZHVk8lk150dmydxGuvFYkdEREQ24e7o2mK3+1wB9AaTxGmsE4sdERER2YT+oT4I8FSiTGfAwYtXpY5jlVjsiIiIyCbI5TLEXxuO3cnJim+KxY6IiIhsRt3ZsbvO5sNoEhKnsT4sdkRERGQzBkf6wtvdBcUVehzNKJY6jtVhsSMiIiKb4eIkx9gegQCAnSkcjv0jFjsiIiKyKXXDsT+fUcPE4dh6WOyIiIjIptzZxQ/tFE5Qa6txMrtU6jhWhcWOiIiIbIqrixNGXRuO/ZnDsfWw2BEREZHN+d9VKNQQgsOxdVjsiIiIyOaMiPKH0lmOK0WVSFWXSR3HarDYERERkc1pp3TGsG7+AIAdnKzYjMWOiIiIbNJ4XoXiBix2REREZJPG9AiEs1yGtPwyXCoslzqOVWCxIyIiIpukcndBXOf2AHh2bB0WOyIiIrJZd/cOBsDh2DosdkRERGSzxvYMhEwGnMzWIKe0Suo4kmOxIyIiIpvl76nEoHBfALVz2jk6FjsiIiKyafHXrh2bcJbFjsWOiIiIbNrYa5cXO3a5BKWVeonTSIvFjogkFRERAZlMVu+2fPnyesucOnUKQ4cOhaurK0JDQ7FixQqJ0hKRNQpr746oQE8YTQJ70wqkjiMpFjsiktybb76JvLw88+25554zP6bVajFu3DiEh4cjKSkJK1euxOuvv461a9dKmJiIrM3YnrV77RLO5kucRFrOUgcgIvL09ERQUNBNH9uwYQP0ej0+++wzKBQK9OrVC8nJyXjvvfcwe/bsNk5KRNZqbM9AfLw3HfvTCqEzGKF0dpI6kiS4x46IJLd8+XK0b98e/fv3x8qVK2EwGMyPJSYmYtiwYVAoFOb74uPjkZaWhpKSkpuuT6fTQavV1rsRkX2L7qBCgKcSFXojEi8WSR1HMix2RCSp559/Hl9//TX27t2LOXPm4J133sErr7xiflytViMwMLDec+p+VqtvfgbcsmXLoFKpzLfQ0FDLvQAisgpyuQxjrg3H/nLOcYdjWeyIqNUtXLjwhhMi/nhLTU0FAMybNw8jRoxAnz598PTTT+Mf//gHVq1aBZ1O1+zfv2jRImg0GvMtKyurtV4aEVmxurNjfzlbACGExGmkwWPsiKjVzZ8/HzNnzmx0mU6dOt30/tjYWBgMBly+fBlRUVEICgpCfn79v77rfm7ouDylUgmlUnn7wYnIpsV1bg93hRPU2mqcztGgT0dvqSO1ORY7Imp1/v7+8Pf3b9Zzk5OTIZfLERAQAACIi4vD4sWLUVNTAxcXFwBAQkICoqKi4OPj02qZicj2ubo4YXg3f+w4o8YvZ/MdsthxKJaIJJOYmIgPPvgAJ0+exKVLl7Bhwwa89NJL+NOf/mQubdOmTYNCocCsWbOQkpKCjRs34sMPP8S8efMkTk9E1mjMteHYXQ467Qn32BGRZJRKJb7++mu8/vrr0Ol0iIyMxEsvvVSvtKlUKuzatQtz585FTEwM/Pz8sGTJEk51QkQ3Nap7AOQyIFVdhqziSoT6uksdqU3JhKMeXUhEDkOr1UKlUkGj0cDLy0vqOERkYQ+vScTRjGIsvacnnrgzUuo4bYpDsURERGRXxjnwtCcsdkRERGRX6o6zO3KpGJqqGonTtC0WOyIiIrIrEX7t0DXAAwaTwL60AqnjtCkWOyIiIrI7Y68NxyY42NmxLHZERERkd+ouL7Y/rRB6g0niNG2HxY6IiIjsTr+O3vDzUKJMZ8CRjCKp47QZFjsiIiKyO3K5DGN61F7BxpGGY1nsiIiIyC7VHWf3y9l8OMq0vSx2REREZJfu7OIHNxcn5GqqkZKrlTpOm2CxIyIiIrvk6uKEoV39ADjOcCyLHREREdmtsQ52FQoWOyIiIrJbo7oHQC4DUnK1yCmtkjqOxbHYERERkd1q76FETLgPAGC3A+y1Y7EjIiIiu1Z37VhHOM6OxY6IiIjsWt1xdocvFUFbXSNxGstisSMiIiK71snfA53926HGKLA/rVDqOBbFYkdERER2r+7asfY+HMtiR0RERHZv3LVitzetADVGk8RpLIfFjoiIiOxev1Af+HkoUFZtwNGMYqnjWAyLHREREdk9J7kMI6ICAAB7UgskTmM5LHZERETkEEZ1ry12e1nsiIiIiGzbXV394CyX4dLVCly+WiF1HItgsSMiIiKH4OXqgkERvgDsdziWxY6IiIgchnk4No3FjoiIiMimjbxW7I5cKkaFziBxmtbHYkdEREQOo7N/O4T5ukNvNOG39KtSx2l1LHZERETkMGQymV2fHctiR0RERA5l5HXH2QkhJE7TuljsiIiIyKHERvrCzcUJ+VodUnK1UsdpVSx2RERE5FBcXZxwZxc/APY3HMtiR0RERA5ndI/a4djdLHZEREREtm3ktevGnswuRVG5TuI0rYfFjoiIiBxOkMoVPYO9IASwL61Q6jithsWOiIiIHFLdtCd77OgqFCx2RERE5JDqpj05cL4QNUaTxGlaB4sdEREROaR+od7wbadAWbUBSVdKpI7TKljsiIiIyCE5yWUY3s0fgP1Me8JiR0RERA6rbjh2D4sdERERkW0b3tUfTnIZLhSUI6u4Uuo4LcZiR0RERA5L5e6CmDAfALXXjrV1LHZERETk0OxpOJbFjoiIiBxa3Xx2iReLUKU3SpymZVjsiIiIyKF1C/RAB2836AwmHLp4Veo4LcJiR0RERA5NJpNhZPfaaU922/hwLIsdEREROby64di9qQUQQkicpvlY7IiIiMjhxXXyg9JZjjxNNVLVZVLHaTYWOyIiInJ4bgonDOncHoBtnx3LYkdEREQEYFSPQAC2fXkxFjsiIiIi/O84u+OZJSip0EucpnlY7IiIiIgAdPB2Q1SgJ0wCOHChUOo4zcJiR0RERHTNiKjaaU/2n2exIyIiIrJpw7vVFrsD56/CZLK9aU9Y7IhIUj/++CNiY2Ph5uYGHx8fTJ48ud7jmZmZmDhxItzd3REQEICXX34ZBoNBmrBEZPdiInzgrnDC1XIdzuZppY5z25ylDkBEjmvLli146qmn8M4772DUqFEwGAw4c+aM+XGj0YiJEyciKCgIhw4dQl5eHmbMmAEXFxe88847EiYnInuldK6d9uSXcwXYf74QvTuopI50W2TClqdXJiKbZTAYEBERgTfeeAOzZs266TI7duzApEmTkJubi8DA2mkIVq9ejQULFqCwsBAKhaJJv0ur1UKlUkGj0cDLy6vVXgMR2acvEi/jr9tSMDjSF5vmxEkd57ZwKJaIJHH8+HHk5ORALpejf//+CA4Oxt13311vj11iYiKio6PNpQ4A4uPjodVqkZKS0uC6dTodtFptvRsRUVMN73Zt2pMrJdBW10ic5vaw2BGRJC5dugQAeP311/Haa69h+/bt8PHxwYgRI1BcXAwAUKvV9UodAPPParW6wXUvW7YMKpXKfAsNDbXQqyAiexTW3h2Rfu1gMAkcSi+SOs5tYbEjola1cOFCyGSyRm+pqakwmUwAgMWLF+PBBx9ETEwM1q1bB5lMhs2bN7cow6JFi6DRaMy3rKys1nhpRORA6s6OtbVpT3jyBBG1qvnz52PmzJmNLtOpUyfk5eUBAHr27Gm+X6lUolOnTsjMzAQABAUF4ejRo/Wem5+fb36sIUqlEkqlsjnxiYgA1Ba79Ycu48D5QgghIJPJpI7UJCx2RNSq/P394e/vf8vlYmJioFQqkZaWhrvuugsAUFNTg8uXLyM8PBwAEBcXh7fffhsFBQUICKg95iUhIQFeXl71CiERUWuL7eQLhbMcOaVVuFhYji4BnlJHahIOxRKRJLy8vPD0009j6dKl2LVrF9LS0vDMM88AAKZMmQIAGDduHHr27Inp06fj5MmT2LlzJ1577TXMnTuXe+SIyKLcFc6IjfQFAOw/f1XiNE3HYkdEklm5ciUeffRRTJ8+HYMGDcKVK1ewZ88e+Pj4AACcnJywfft2ODk5IS4uDn/6058wY8YMvPnmmxInJyJHYIvH2XEeOyKye5zHjoia40J+Gca+fwBKZzlOLh0HVxcnqSPdEvfYEREREd1ElwAPhKhcoTOYcPiSbUx7wmJHREREdBMymQzDo2xrOJbFjoiIiKgBtnacHYsdERERUQOGdPGDk1yGS4UVyCqulDrOLbHYERERETXAy9UFA8K8AdjGXjsWOyIiIqJG2NJwLIsdERERUSOGd6u98s2h9KvQG0wSp2kcix0RERFRI3qFeKF9OwUq9EYkXSmROk6jWOyIiIiIGiGXyzDMRoZjWeyIiIiIbsFWjrNjsSMiIiK6haFd/SCTAefytMjXVksdp0EsdkRERES30N5DiegOKgDAASvea8diR0RERNQEtjAcy2JHRERE1AR1xe7XC1dhNAmJ09wcix0RERFRE/QL9YanqzM0VTU4mV0qdZybYrEjIiIiagJnJzmGdvUDAOxPs87hWBY7IiIioiay9uPsWOyIiIiImqhuouJT2aUoqdBLnOZGLHZERERETRSsckNUoCdMAvgt/arUcW7gLHUAIiIiIlsyZWBH5JRWobO/h9RRbiATQljn+bpERK1Eq9VCpVJBo9HAy8tL6jhERBbDoVgiIiIiO8FiR0RERGQnWOyIiIiI7ASLHREREZGdYLEjIiIishMsdkRERER2gsWOiIiIyE6w2BERERHZCRY7IiIiIjvBYkdERERkJ1jsiIiIiOwEix0RERGRnWCxIyIiIrITLHZEREREdoLFjoiIiMhOsNgRERER2QkWOyIiIiI7wWJHREREZCdY7IiIiIjshEwIIaQOQURkSUIIlJWVwdPTEzKZTOo4REQWw2JHREREZCc4FEtERERkJ1jsiIiIiOwEix0RERGRnWCxIyIiIrITLHZEREREdoLFjoiIiMhOsNgRERER2Yn/D3FznRm4XlNrAAAAAElFTkSuQmCC\n" + "image/png": 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mZwvKMPvrY+aTG0J8XTFzcCQm9u3YrHJ+JPMK/rnzPLadri3j7tdKz9RWnPHaVuoK2b9+vQR9jQkyGXBP306YOSTyujPFG9pXrlbX4MsDmVjx60Xz4s+jYwLw2p09EOwt/eXNDqfXFrIL167Y0cXfA38Z1hm39wyCi7MCa9aswSOPPIJPPvkEAwcOxPvvv4+vv/4aZ86cgb+/P5IuFuOzPZfMP7sALxXenNgTo2ICcKVcj97z1yPr/ftxKSMT4e1Y7IQQ2HehGKsPZGDb6ULoa367Ykf3IC8Mi9ZgeLQ/+oa2/2XYfr+fuLl74HiOFjtOF2Lb6QLz8jtA7fqFE3oF4Z5+ndAv1Nvu5+VZ8x9sqfAzuZ41fyYsdo3YeaYQr/2YivTi2gLj6qzAyO7+GBbtj9iOXujk4wYnuQxXq2tw6XI5DqWXYNupAhzJLDW/xvBoDV4eH4Mu/q0/IaMtP5N8bRXe+OkUfjqRZz5q0C3QE7f3DEL/MB909veAt5sz9DUmFOiqkZqrxe6zRdh2qgC6a4so+3ko8fzoaDw4wHInZNxIQ5+J0STw7ZFsvLMlDQW62gLjrlRgbGwQhnT1Q49gLwSpXeGkkEFbYcDFy+U4nF6CTan5OJlTe1UMmQyY0CsYL93ezequ6Zp9pQJLN6dh/bWznoHacj2qewAGRvgizNcNCmMVNIHBSD51ARdKjfjlbBG2nipApaF2oeeO3q5YcEcMEi1w8kdrVNcYsXp/JpbtOIcr1xZ89nZzxrjYINzWxQ/J29fj02XvID8/Hz3j4vH4iwtRqtRg08l8cyGUy4AHBoRg7rju5jX3Siv06PVy+xa7sioDvjuSg/8kpZuzAbVrTE7s2xF39g5u1WLNbaGp3ylnC8rw3ZEcrDuag3zdb1fw6R7khRmDIzChV7DVLILe1qzh74+14WdyPWv+TKyy2FVXV2PRokWYN28eVCrproFaXWPE90dysGpfer1/wTZFIZdhVHd/zBwSibgw37bLYoHP5GxBGT7ccR6bTuY3ee3P3wvr4IapCeGYPDAEbkppLzXc1GdSoa/BmkNZ+GJ/Rr0/rE1xksswsW9HPDmsMzpbyZVJGpOSVYrluy5g2+kC1PxxslQjIjXueGJIZ0zs29Gq/yjrqgz4z750fHkwCzmllc16jptSgbv7dsRjt0Vc97P7fbHLyctHcGCAJWIDAErK9fhszyV8vu+3SwO6KxW4N64THhgQgpggL6s54tWc3ylGk8D+i8X49kg2Np7IN//jIMBLhWmDIvBQfOhNLVptC6zl74814WdyPWv+TKyy2FkbIQSOZpVi55lC7D1/GRcvl5svISWTAcFqV3QP8sTgKA3Gxga22bpm7UVbYcDPJ/Ow9/xlHM0sRZ62st61TLsFeiEuzAejYwIwMNzXptbFEkLgwKUS7DxTiKSLxbhUVG7+gyuXAR19XNEjSI3BXf0wLjYIvjY2YbywrAobT+Rj34XLOJalRWFZlfln56lyQpcADwzq3AEjuwegb4htDaMZTQK/nivC7rNFOHCxBOnF5ai4dnk5hVyGMF83xHZUY1i0BqNiAuDVyHC7tsKAni+vQ9b796Oo+Ar8fL3bPGuhrgr/+vUivtifaS4/kRp3PJIQjnv6NW8qgLUrrdBj9YFMfL4vHYVlvx0Nn35bBP48JLLRz5+I2heLXQtV6GtgEoBSIbfqox8tYTIJlFXVQOUsh8pJblNloDmuVtfAJARcnRXtPq/J0mqMJpRXG6F0ksPF2b5+dkIIXK2ugUwmg4uTvNnzHrWVBvR8yTLFTldlwMe7LuCzPZdQfW3+XGxHL/x1eBTGxATY1D+CmktfY8IPx3Lx718vmkcyvN2c8ZdhnTE1IdyiJ30Q0Y2x2BGRXft9sSssLoHGt/WXEDQYTfjqYCbe23YOJeV6ALVzHZ8eEYVh0Rq7KtSNEUJgc2o+3t5yFucLa8/YDvBS4blRXXF/f+nm3hI5OmknSRERWVhbd6xfzhbh1R9TcfHa3M1IjTteGtcdI7v7O0ShqyOTyTA2NgijYwLx3ZFsvL/tHHJKKzH3uxP48lAW3rgrFj07cWF7ovYmyTjUm2++iUGDBsHNzQ3e3t4NbpOZmYnx48fDzc0N/v7+eOGFF1BTU9PgtnVKSkrw8MMPw8vLC97e3pg+fTquXr1qgXdgebt27YJMJmvwdujQoUafN2zYsOu2f+KJJ9oxuWWFh4df9/4WL17c5HOqqqowa9YsdOjQAR4eHrj33ntRUFDQToktKz09HdOnT0dERARcXV3RuXNnLFy4EHq9vsnn2eN+8tFHHyE8PBwuLi6Ij4/HwYMHAQC/r1q/H59Yu3YtunXrBhcXF/Ts2RM///xzk69fWqHH7K+PYepnB3GxqBy+7kr87a4e2PzsEIyKaXrR6Pa2aNEiDBgwAJ6envD398fEiRORlpbW5HNWrVp13T7h4nLj+cIKuQyT+odgx/8Nxfzx3eGhcsKxrFLc+dEevLLuJLTX5iNbg1dfffW699itW7cmn3Oz+4mtaeh3qkwmw6xZsxrcvqX7iTX75ZdfcMcddyA4uPba2OvWrav3uBACCxYsQFBQEFxdXTFq1CicO3fuhq/b2O8kS5Ok2On1ekyaNAlPPvlkg48bjUaMHz8eer0e+/btw+eff45Vq1ZhwYIFTb7uww8/jNTUVGzduhUbNmzAL7/8gpkzZ1riLVjcoEGDkJeXV+/25z//GREREejfv3+Tz50xY0a95y1ZsqSdUreP119/vd77e+qpp5rc/rnnnsOPP/6ItWvXYvfu3cjNzcU999zTTmkt68yZMzCZTPjkk0+QmpqK9957D8uXL8dLL710w+fa036yZs0aPP/881i4cCGOHDmC3r17IzExEYWFhQ1uv2/fPkyePBnTp0/H0aNHMXHiREycOBEnT55scPuNJ/Iw6t1f8O2RbMhkwKO3hmPXC8MwJSHcKudp7t69G7NmzcL+/fuxdetWGAwGjBkzBuXlTZ8h7uXlVW+fyMjIaPb3VDkp8OfBkdg+eyju6hMMIYD/7s/AiHd2YX1KTmvfUpvp0aNHvfe4Z8+eRre92f3EFh06dKje57F161YAwKRJkxp9Tmv2E2tUXl6O3r1746OPPmrw8SVLluAf//gHli9fjgMHDsDd3R2JiYmoqqpqcHvg5n8ntSkhoZUrVwq1Wn3d/T///LOQy+UiPz/ffN/HH38svLy8RHV1dYOvderUKQFAHDp0yHzfxo0bhUwmEzk5OW2evb3p9Xqh0WjE66+/3uR2Q4cOFc8880z7hJJAWFiYeO+995q9fWlpqXB2dhZr164133f69GkBQCQlJVkgofSWLFkiIiIimtzG3vaTgQMHilmzZpm/NhqNIjg4WCxatEiUVRlEyLNfCwCi4HKJEEKI+++/X4wfP77ea8THx4vHH3+83n0FukrxxH8Pi7A5G0TYnA1i5Du7xOH0Esu/oTZWWFgoAIjdu3c3uk1jv49bat/5y2LUO7vMn93TXx4R2kp9m71+SyxcuFD07t272ds3dz+xJ88884zo3LmzMJlMDT7e1vuJtQEgvv/+e/PXJpNJBAYGiqVLl5rvKy0tFSqVSnz55ZeNvk5Tv5Mszfr+qQkgKSkJPXv2REDAb+tNJSYmQqfTITU1tdHneHt71zuaNWrUKMjlchw4cMDimS3thx9+QHFxMR599NEbbrt69Wr4+fkhNjYW8+bNQ0VFRTskbD+LFy9Ghw4d0LdvXyxdurTJIfrk5GQYDAaMGjXKfF+3bt0QGhqKpKSk9ojb7rRaLXx9b7yGor3sJ3q9HsnJyfV+xnK5HKNGjWr0Z5yUlFRve6D2d0zd9kIIfJOcjdHv/oKNJ/PhJJfhqRFd8NPTtyEurPUnX7Q3rbb2aiw32i+uXr2KsLAwhISE4K677mr0921zJHTugJ+fGYznR3eFQi7D+pRc3P7BrzicXtLi12wL586dQ3BwMCIjI/Hwww8jMzOz0W1vtJ/YG71ejy+++AKPPfZYk1ML2nI/sXaXLl1Cfn5+vf1ArVYjPj6+0f2gJb+T2pJVnjyRn59fr9QBMH+dn5/f6HP8/f3r3efk5ARfX99Gn2NLPv30UyQmJqJTp6YvYP7QQw8hLCwMwcHBOH78OObMmYO0tDR899137ZTUsp5++mn069cPvr6+2LdvH+bNm4e8vDy8++67DW6fn58PpVJ53VzOgIAAu9gv/uj8+fNYtmwZ3n777Sa3s6f95PLlyzAajQ3+zjhz5kyDc+wa+x2Tn5+PknI9/m/tMey4dp3nHsFeWHJfrxZdV9kamEwmPPvss7j11lsRGxvb6HbR0dH47LPP0KtXL2i1Wrz99tsYNGgQUlNTb/h7pzHOCjmeHhmF26L88MxXR5FVUon7P0nCUyOi8NSILu1+qb74+HisWrUK0dHRyMvLw2uvvYbBgwfj5MmT8PS8/lrQTe0n9mjdunUoLS3FtGnTGt3GEvuJNav7Wd/MfnCj30mW1mbFbu7cufj73//e5DanT5++4URVe9eSzyk7OxubN2/G119/fcPX//2cwp49eyIoKAgjR47EhQsX0Llz55YHt6Cb+Uyef/558329evWCUqnE448/jkWLFlnd6t+t0ZL9JCcnB2PHjsWkSZMwY8aMJp9ri/tJS/3+wINA06s7yTWdMf4fvyJPWwWlkxzPjorCjMGRVjmPrrlmzZqFkydPNjmXDAASEhKQkJBg/nrQoEHo3r07PvnkE/ztb39rVYZ+oT74+enBWLg+Fd8dzcEH289hz/nLeP+BPgjxbb9Lq40bN87837169UJ8fDzCwsLw9ddfY/r06e2Ww1p9+umnGDduHIKDgxvdxpL7CbWNNit2s2fPbrLlA0BkZGSzXiswMPC6s0fqzmIMDGz4+paBgYHXTUqsqalBSUlJo8+RQks+p5UrV6JDhw648847b/r7xcfHA6g9kmOtf7Bbs+/Ex8ejpqYG6enpiI6Ovu7xwMBA6PV6lJaW1jtqV1BQYFX7xR/d7GeSm5uL4cOHY9CgQVixYsVNfz9b2E8a4+fnB4VCcd2Zzk39jAMDA+ttL4TAjhxAdftc5GmrEOnnjo8e7ofuQdZ1Dcib9de//tV8ItnNHk1xdnZG3759cf78+TbJ4unijHcf6IOh0RrM//4kkjOu4PYPfsXfJsZiYt+ObfI9bpa3tze6du3a6Hv8434CWP/vjpbKyMjAtm3bbvqofVvvJ9am7mddUFCAoKAg8/0FBQXo06dPg89pye+kttRmxU6j0UCj0bTJayUkJODNN99EYWGheXh169at8PLyQkxMTKPPKS0tRXJyMuLi4gAAO3bsgMlkMv/RsgY3+zkJIbBy5UpMnToVzs43f8melJQUAKi3Q1qb1uw7KSkpkMvl1w3D14mLi4OzszO2b9+Oe++9FwCQlpaGzMzMev/qtDY385nk5ORg+PDhiIuLw8qVKyGX3/zRJVvYTxqjVCoRFxeH7du3Y+LEiQBqhx+3b9+Ov/71r5D9bjC2big2ISEB27dvx7PPPgtdlQEvrj2Ow8YwQA6M7xWExff0tOnLgAkh8NRTT+H777/Hrl27EBERcdOvYTQaceLECdx+++1tmu2uPh3RL9QHz61JweGMK3h2TQp2phXizbt7wkPVvrODrl69igsXLmDKlCkNPv77/aTO1q1brfp3R0utXLkS/v7+GD9+/E09z1L7ibWIiIhAYGAgtm/fbi5yOp0OBw4caHRljxv9TrI4i5+e0YCMjAxx9OhR8dprrwkPDw9x9OhRcfToUVFWViaEEKKmpkbExsaKMWPGiJSUFLFp0yah0WjEvHnzzK9x4MABER0dLbKzs833jR07VvTt21ccOHBA7NmzR0RFRYnJkye3+/trS9u2bRMAxOnTp697LDs7W0RHR4sDBw4IIYQ4f/68eP3118Xhw4fFpUuXxPr160VkZKQYMmRIe8e2iH379on33ntPpKSkiAsXLogvvvhCaDQaMXXqVPM2f/xMhBDiiSeeEKGhoWLHjh3i8OHDIiEhQSQkJEjxFtpcdna26NKlixg5cqTIzs4WeXl55tvvt7H3/eSrr74SKpVKrFq1Spw6dUrMnDlTeHt7i/z8fFFRXWM+Kza3sFgIIcTevXuFk5OTmLN4mbjljU0ibM4GEfp/34tF3+xr9GxAW/Lkk08KtVotdu3aVW+fqKioMG8zZcoUMXfuXPPXr732mti8ebO4cOGCSE5OFg8++KBwcXERqampFsloqDGK97eeFZHzfhJhczaIxPd2i5wrFTd+YivMnj1b7Nq1S1y6dEns3btXjBo1Svj5+YnCwkIhxPWfSd1+8vbbb4vTp0+LhQsXCmdnZ3HixAmL5mxvRqNRhIaGijlz5lz3mNT7SXsoKysz9xAA4t133xVHjx4VGRkZQgghFi9eLLy9vcX69evF8ePHxV133SUiIiJEZWWl+TVGjBghli1bZv66qd9JliZJsXvkkUcEgOtuO3fuNG+Tnp4uxo0bJ1xdXYWfn5+YPXu2MBgM5sd37twpAIhLly6Z7ysuLhaTJ08WHh4ewsvLSzz66KPmsmirJk+eLAYNGtTgY5cuXar3uWVmZoohQ4YIX19foVKpRJcuXcQLL7wgtFptOya2nOTkZBEfHy/UarVwcXER3bt3F2+99Zaoqqoyb/PHz0QIISorK8Vf/vIX4ePjI9zc3MTdd99dr/jYspUrVzb4/9Lv/83mKPvJsmXLRGhoqFAqlWLgwIFi//79QgghKvW/Fbuca8VOCCFeWv6tCPu/70XYnA0i/Kn/iI++3CBV9DbX2D6xcuVK8zZDhw4VjzzyiPnrZ5991vz5BQQEiNtvv10cOXLE4lkPpxeL/m9sFWFzNoj+b2wVx7KuWOx7PfDAAyIoKEgolUrRsWNH8cADD4jz58+bH//jZyKEEF9//bXo2rWrUCqVokePHuKnn36yWD6pbN68WQAQaWlp1z1mLfuJJdX1iT/e6t63yWQSr7zyiggICBAqlUqMHDnyus8qLCxMLFy4sN59jf1OsjReK5aI7FqVwYiuL36HrPfvR05hMYL8fPDB9nN4f1vtyvHDozV474E+8HZTSpzUceWUVmL6qkM4k18GF2c5PniwLxJ72N88NqL2YLunehER3aRqgxHPfJViLnUzBkfg348MYKmTWEdvV6x9IgFDu2pQZTDhiS+SseKXC+BxB6Kbx2JHRHbt98udTP/8EH44lgsnuQyL7umJl8fHQCG3nmu8OjJPF2d8+kh/TLklDEIAb/18Bi99fxIGo0nqaEQ2hcWOiBzG+cJyeLk44T+PDcTkgaFSx6E/cFLI8fpdPbBgQgxkMuDLg5l4dOUhaCsNUkcjshksdkRk136/3ImniwLf/WUQBnXxkzARNUUmk+Gx2yLwryn94aZUYM/5y7jv433IKrHNS94RtTcWOyKya0onOcb2qL20z/pZt6GL//WXjiLrMyomAF8/noAALxXOFV7FpOVJuHS5XOpYRFaPZ8USkd3T6XRQq9XQarXw8rLtq0k4mnxtFaZ8egDnCq/C31OFL2fegs4aD6ljEVktHrEjIiKrFah2wZczb0F0gCcKy6rx4Ir9OF9YJnUsIqvFYkdERFbNz0OF/82IR7dATxSVVePBFQdwroDljqghLHZERGT1Onio8L8ZtyAmyAuXr9YeuUvLZ7kj+iMWOyIisgm+7kr8b0Y8egR7obhcj8n/2o/TeTqpYxFZFRY7IiKyGd5uSvzvz7egZ0c1Ssr1eOhf+5Gaq5U6FpHVYLEjIrv15ZdfwtXVFfn5+eb7Hn30UfTq1QtaLcuArVK7OeOLP8ejdyc1rlQY8PC/D+BkDn+eRACXOyEiOyaEQJ8+fXDLLbdgxYoVmDNnDlavXo39+/ejY8eOUsejVtJVGTD104NIySqFt5szvn1yEJdCIYfHYkdEdm3Dhg249957odfr4e3tjT179qBHjx5Sx6I2UlZlwJ/+fQDHsrUI8XXFd0/eCo2nSupYRJLhUCwR2bUJEyagW7duAIDVq1ez1NkZTxdnfDptAEJ93ZBVUonHVh1CeXWN1LGIJMNiR0R2bdOmTTh79iwAwN/fX+I0ZAl+Hip8/thA+Lg540SOFn/93xHUGE1SxyKSBIsdEdmtI0eO4P7778eHH34IAHjjjTckTkSWEuHnjk+nDYDKSY6daUV4Zf1JcKYROSIWOyKyS+np6Rg/fjxeeuklTJo0CQCwfv16HDlyROJkZCn9Qn2wbHJfyGXAlwez8NHO81JHImp3PHmCiOxOSUkJBg0ahGHDhmH58uXQ6XRQq9UYPXo05HI5Nm3aJHVEsqD/JKVjwfpUAMDbk3rjvrhOEiciaj8sdkRk9+qKnVarhZeXl9RxqB0s2ngan+y+CCe5DCsfHYDBURqpIxG1Cw7FEhGR3ZmT2A139g5GjUngyS+O4FQuLz1GjoHFjoiI7I5cLsPSSb1wS6QvrlbX4NFVB5FTWil1LCKLY7EjIiK7pHJS4JMp/dE1wAMFumpM++wgtBUGqWMRWRSLHRER2S21qzNWPToQAV4qnCu8imfWHIXJxKnlZL9Y7IiIyK4Fe7vis2tr3O1KK8IH289JHYnIYljsiIjI7vUIVuOtu3sCAD7Yfg47zhRInIjIMljsiIjIIdwb1wlTbgkDADz7VQoyisslTkTU9ljsiIjIYbwyIQb9Qr2hq6rB4/9NRqXeKHUkojbFYkdERA5D6STHPx+Og5+HEmfyy/DS9yd4TVmyKyx2RETkUALVLvjwoX5QyGX4/mgO/pOUIXUkojbDYkdERA7nlsgOmDeuGwDgbxtOITmjROJERG2DxY6IiBzS9NsiML5XkPmyY4VlVVJHImo1FjsiInJIMpkMS+7thSh/DxSWVeOvq4/CYDRJHYuoVVjsiIjIYbmrnLB8Shw8VE44mF6Cf3DxYrJxLHZEROTQOms8sPje2sWLP9p5HofSOd+ObBeLHRERObwJvYJxT7+OMAnguTUpKKsySB2JqEVY7IiIiAC8dmcPdPJxRfaVSiz8IVXqOEQtwmJHRJJ58803MWjQILi5ucHb27vBbTIzMzF+/Hi4ubnB398fL7zwAmpqato3KDkETxdnvPdAH8hlwHdHcrDheK7UkYhuGosdEUlGr9dj0qRJePLJJxt83Gg0Yvz48dDr9di3bx8+//xzrFq1CgsWLGjnpOQoBoT74i/DugAAXv7+JPK0lRInIro5MsFrqRCRxFatWoVnn30WpaWl9e7fuHEjJkyYgNzcXAQEBAAAli9fjjlz5qCoqAhKpbJZr6/T6aBWq6HVauHl5dXW8cnOGIwm3PvxPhzP1mJQ5w74Yno85HKZ1LGImoVH7IjIaiUlJaFnz57mUgcAiYmJ0Ol0SE3lHCiyDGeFHO8/0Aeuzgrsu1CMT/dckjoSUbOx2BGR1crPz69X6gCYv87Pz2/0edXV1dDpdPVuRDcjUuOBVybEAACWbk7DqVzuQ2QbWOyIqE3NnTsXMpmsyduZM2csmmHRokVQq9XmW0hIiEW/H9mnyQNDMKq7P/RGE55dcxRVBqPUkYhuiMWOiNrU7Nmzcfr06SZvkZGRzXqtwMBAFBQU1Luv7uvAwMBGnzdv3jxotVrzLSsrq+VviByWTCbD4nt7wc9DibMFV/H3TZb9BwlRW3CSOgAR2ReNRgONRtMmr5WQkIA333wThYWF8Pf3BwBs3boVXl5eiImJafR5KpUKKpWqTTKQY/PzUGHpfb3x6KpDWLk3HcOj/TGka9vs30SWwCN2RCSZzMxMpKSkIDMzE0ajESkpKUhJScHVq1cBAGPGjEFMTAymTJmCY8eOYfPmzZg/fz5mzZrF4kbtZng3f0y5JQwAMHvtMZSU6yVORNQ4LndCRJKZNm0aPv/88+vu37lzJ4YNGwYAyMjIwJNPPoldu3bB3d0djzzyCBYvXgwnp+YPOHC5E2qtSr0RE5b9igtF5RjbIxDLp8RJHYmoQSx2RGT3WOyoLZzM0WLiR3tRYxJY/qc4jI1tfJ4nkVQ4FEtERNQMsR3VeHxo7Yk/C384CV2VQeJERNdjsSMiImqmp0ZEIbyDGwp01Vi6KU3qOETXYbEjIiJqJhdnBd66uycA4IsDGUjOKJE4EVF9LHZEREQ3YVAXP9wX1wlCAPO+OwF9jUnqSERmLHZEREQ36eXbu6ODe+3CxSt+uSB1HCIzFjsiIqKb5OOuxII7ahfJ/seO87hYdFXiRES1WOyIiIha4M7ewRjSVQN9jQnzvjsBrh5G1oDFjoiIqAVkMhnenBgLF2c5DlwqwdrD2VJHImKxIyIiaqkQXzc8P7orAODNn0+jqKxa4kTk6FjsiIiIWuGxWyPQI9gL2koD/rbhlNRxyMGx2BEREbWCk0KOxff0glwG/HAsFzvTCqWORA6MxY6IiKiVenZS47FbIwAA878/iQp9jcSJyFGx2BEREbWB50Z3RUdvV+SUVuK9rWeljkMOisWOiIioDbirnPDG3bEAgE/3XMLJHK3EicgRsdgRERG1keHR/rizdzBMApj73XEYTVzbjtoXix0REVEbemVCDDxdnHAyR4e1h7OkjkMOhsWOiIioDWk8VXh2VO3adm9vSYOuyiBxInIkLHZERERtbGpCGCI17rh8VY8Pd5yXOg45EBY7IiKiNuaskOOVCTEAgJV7L+HS5XKJE5GjYLEjIiKygOHR/hgerYHBKPDmT7wiBbUPFjsiIiILmT8hBk5yGbadLsTus0VSxyEHwGJHRERkIZ01HnhkUDgA4G8bTsFgNEkbiOweix0REZEFPT0yCr7uSpwvvIrV+zOkjkN2jsWOiIjIgtSuzpg9pnb5k/e2ncOVcr3EiciesdgRERFZ2IMDQtEt0BPaSgPe28bryJLlsNgRERFZmEIuw8I7egAAvtifgTP5OokTkb1isSMiImoHCZ07YFxsIEyi9kQKIXgdWWp7LHZERETt5KXbu0PpJMfe88XYeqpA6jhkh1jsiIiI2kmIrxtmDI4AALzx02lU1xglTkT2hsWOiIioHf1lWBf4e6qQWVKBz/akSx2H7AyLHRERUTtyVzlh7rhuAICPdp5HCZc/oTbEYkdERNTOJvbpiNiOXrhaXYN/7jwvdRyyIyx2RERE7Uwul+HFxNqjdv9JykBOaaXEichesNgRERFJYHCUHxIiO0BvNOH9rVy0mNoGix0REZEEZDIZXhwbDQD49kg2zhWUSZyI7AGLHRERkUT6hvogsUcATAJ4e0ua1HHIDrDYERERSej/xkRDLgM2pxbgaOYVqeOQjWOxIyIiklBUgCfu7dcJAPD3TWd4qTFqFRY7IiIiiT07uiuUCjn2XyzBL+cuSx2HbBiLHRERkcQ6ertiSkIYAGDJpjMwmXjUjlqGxY6IiMgKzBreBR4qJ6Tm6vDTiTyp45CNYrEjIiKyAr7uSswcEgkAeGdLGgxGk8SJyBax2BEREVmJ6bdFoIO7EunFFfj6cJbUccgGsdgRERFZCXeVE54a0QUA8MG2c6jUGyVORLaGxY6IiMiKTI4PRScfVxSWVWPlvktSxyEbw2JHRERkRVROCjw/uisAYPmuC9BWGCRORLaExY6IiMjK3NWnI6IDPKGrqsHHuy9IHYdsCIsdERGRlVHIZfi/xGgAwOf70lF8tVriRGQrWOyIiIis0Kju/ujZUY1KgxH/3sO5dtQ8LHZERERWSCaT4emRUQCA/+xLx5VyvcSJyBaw2BEREVmpUd39ERPkhXK9Ef/ec1HqOGQDWOyIiIis1O+P2n2+LwOlFTxqR01jsSMiyaSnp2P69OmIiIiAq6srOnfujIULF0Kvr//H6/jx4xg8eDBcXFwQEhKCJUuWSJSYqP2NiQlAt0BPXK2uwWeca0c3wGJHRJI5c+YMTCYTPvnkE6SmpuK9997D8uXL8dJLL5m30el0GDNmDMLCwpCcnIylS5fi1VdfxYoVKyRMTtR+5HIZnrl21G7l3nSua0dNkgkhhNQhiIjqLF26FB9//DEuXqydT/Txxx/j5ZdfRn5+PpRKJQBg7ty5WLduHc6cOdOs19TpdFCr1dBqtfDy8rJYdiJLMZkExn3wK9IKyvDMyCg8d20BY6I/4hE7IrIqWq0Wvr6+5q+TkpIwZMgQc6kDgMTERKSlpeHKlStSRCRqd3K5DE+NrL2G7Gd7L0FXxaN21DAWOyKyGufPn8eyZcvw+OOPm+/Lz89HQEBAve3qvs7Pz2/wdaqrq6HT6erdiGzd7bFBiPL3QFlVDVbtTZc6DlkpFjsianNz586FTCZr8vbHYdScnByMHTsWkyZNwowZM1r1/RctWgS1Wm2+hYSEtOr1iKxB7VG72rl2n+65hDIetaMGcI4dEbW5oqIiFBcXN7lNZGSkeXg1NzcXw4YNwy233IJVq1ZBLv/t35xTp06FTqfDunXrzPft3LkTI0aMQElJCXx8fK577erqalRX/3YJJp1Oh5CQEM6xI5tnNAmMeW83LhSV44XEaMwa3kXqSGRlnKQOQET2R6PRQKPRNGvbnJwcDB8+HHFxcVi5cmW9UgcACQkJePnll2EwGODs7AwA2Lp1K6KjoxssdQCgUqmgUqla9yaIrJBCLsNTI6Lw7JoU/OvXi3hkUDg8VPxTTr/hUCwRSSYnJwfDhg1DaGgo3n77bRQVFSE/P7/e3LmHHnoISqUS06dPR2pqKtasWYMPPvgAzz//vITJiaRzR+9gRPq5o7TCgP8kpUsdh6wMix0RSWbr1q04f/48tm/fjk6dOiEoKMh8q6NWq7FlyxZcunQJcXFxmD17NhYsWICZM2dKmJxIOgq5DH8dUTsE++9fL6G8ukbiRGRNOMeOiOwe17Eje1NjNGHUu7uRXlyBeeO64fGhnaWORFaCR+yIiIhsjJNCbj5xYsUvF1GpN0qciKwFix0REZENurtvR4T4uqK4XI9vkrOkjkNWgsWOiIjIBjkp5JgxOBIA8K9fL6HGaJI4EVkDFjsiIiIbNSkuBD5uzsgsqcDGkw1fiYUcC4sdERGRjXJVKvDIoHAAwCe/XADPhyQWOyIiIhv2SEI4XJ0VOJmjw74LTV/xhewfix0REZEN83FX4oEBtddDXr77gsRpSGosdkRERDZu+m0RUMhl+PXcZZzM0UodhyTEYkdERGTjQnzdML5n7RVbVvxyUeI0JCUWOyIiIjvw+NDapU9+OpGHrJIKidOQVFjsiIiI7ECPYDUGR/nBaBL4dM8lqeOQRFjsiIiI7MQT164Z+9WhTJSU6yVOQ1JgsSMiIrITgzp3QGxHL1QZTPhPUrrUcUgCLHZERER2QiaTmY/afb4vHZV6o8SJqL2x2BEREdmRsT0CEerrhisVBqxNzpI6DrUzFjsiIiI74qSQY8bgCAC1S5/UGE0SJ6L2xGJHRERkZ+6LC4GvuxLZVyrx88l8qeNQO2KxIyIisjOuSgWmDQoHAHyy+wKEENIGonbDYkdERGSHptwSBldnBVJzddh7vljqONROWOyIiIjskI+7Eg8MCAEALN99QeI01F5Y7IiIiOzU9NsioJDLsOf8ZZzM0Uodh9oBix0REZGdCvF1w4ReQQCAlXvTpQ1D7YLFjoiIyI49emvt0ic/HstFUVm1xGnI0ljsiIiI7FifEG/0CfGG3mjClwczpY5DFsZiR0REZOcevTUcAPDf/RnQ13DBYnvGYkdERGTnxsUGwd9ThaKyamw8mSd1HLIgFjsiIiI7p3SS40+3hAHgSRT2jsWOiIjIATwUHwqlQo6UrFIczbwidRyyEBY7IiIiB+DnocIdvYMBAKv2pUsbhiyGxY6IiMhB1J1E8dPxPBToqqQNQxbBYkdEROQgYjuqMSDcBzUmgdX7M6SOQxbAYkdERORApg2qXbB49YFMVBmMEqehtsZiR0RE5EASewQgSO2C4nI9Nhzn0if2hsWOiIjIgTgp5JiSULf0ySUIISRORG2JxY6IiMjBTB4QCpWTHKm5OhzO4NIn9oTFjoiIyMH4uCtxd9+OAIBVXLDYrrDYEREROaBp15Y+2ZSaj9zSSmnDUJthsSMiInJA3QK9kBDZAUaTwH+59IndYLEjIiJyUHVH7b48mIlKPZc+sQcsdkRERA5qVPcAdPJxRWmFAetTcqSOQ22AxY6IiMhBKeQyPJIQDgBYuTedS5/YARY7IiIiB3Z//xC4OiuQVlCGpIvFUsehVmKxIyIicmBqN2fcG1e79MlKLn1i81jsiIiIHNy0QeEAgO2nC7j0iY1jsSMiInJwXfw9MTDCFyYBrDmUJXUcagUWOyIiIsLD8aEAaotdjdEkcRpqKRY7IiIiwtjYQPi6K5Gvq8LOtCKp41ALsdgRERERVE4K3BfXCQCw+gCvRGGrWOyIiIgIADB5YO1w7O6zRcgqqZA4DbUEix0REREBACL83HFrlw4QPInCZrHYERERkdlDA8MAAGsOZ8HAkyhsDosdERERmY2OCYCfhwpFZdXYdqpA6jh0k1jsiEhSd955J0JDQ+Hi4oKgoCBMmTIFubm59bY5fvw4Bg8eDBcXF4SEhGDJkiUSpSWyf0onOe7vX3sSxf8OZkqchm4Wix0RSWr48OH4+uuvkZaWhm+//RYXLlzAfffdZ35cp9NhzJgxCAsLQ3JyMpYuXYpXX30VK1askDA1kX2bPDAUMhnw67nLyCgulzoO3QSZEEJIHYKIqM4PP/yAiRMnorq6Gs7Ozvj444/x8ssvIz8/H0qlEgAwd+5crFu3DmfOnGnWa+p0OqjVami1Wnh5eVkyPpHdeOSzg9h9tghPDO2MueO6SR2HmolH7IgIAGAwGJCVlYW0tDSUlJRIkqGkpASrV6/GoEGD4OzsDABISkrCkCFDzKUOABITE5GWloYrV65IkpPIETx07UoUaw9nQV/DkyhsBYsdkQMrKyvDxx9/jKFDh8LLywvh4eHo3r07NBoNwsLCMGPGDBw6dMjiOebMmQN3d3d06NABmZmZWL9+vfmx/Px8BAQE1Nu+7uv8/PwGX6+6uho6na7ejYhuzshu/gjwUqG4XI/NqQ3/v0bWh8WOyEG9++67CA8Px8qVKzFq1CisW7cOKSkpOHv2LJKSkrBw4ULU1NRgzJgxGDt2LM6dO9fs1547dy5kMlmTt98Po77wwgs4evQotmzZAoVCgalTp6I1s0QWLVoEtVptvoWEhLT4tYgclZNCjgcG1B61+98BnkRhKzjHjshBTZ48GfPnz0ePHj2a3K66uhorV66EUqnEY4891qzXLioqQnFxcZPbREZG1hterZOdnY2QkBDs27cPCQkJmDp1KnQ6HdatW2feZufOnRgxYgRKSkrg4+PTYObq6mrz1zqdDiEhIZxjR3STcksrcdvfd8AkgO2zh6KzxkPqSHQDTlIHICJpfPnll+b/Lisrg6enZ4PbqVQqPPHEEzf12hqNBhqNpkW5TKbauTx1xSwhIQEvv/wyDAaDed7d1q1bER0d3WCpq8usUqla9P2J6DfB3q4YHu2P7WcK8eWBTMyfECN1JLoBDsUSEQYPHtzofDVLOnDgAD788EOkpKQgIyMDO3bswOTJk9G5c2ckJCQAAB566CEolUpMnz4dqampWLNmDT744AM8//zz7Z6XyBE9fEvtcOw3R7JRZTBKnIZuhMWOiNC3b1/Ex8dft3xISkoKbr/9dot9Xzc3N3z33XcYOXIkoqOjMX36dPTq1Qu7d+82H3FTq9XYsmULLl26hLi4OMyePRsLFizAzJkzLZaLiH4ztKs/Onq7orTCgE0neRKFteMcOyICACxcuBAfffQR1q1bB39/f8yfPx/ffvstbr/9dvz4449Sx2sVrmNH1Dr/2H4O7249i4Hhvvj6iQSp41ATOMeOiAAAr732GlQqFUaPHg2j0YiRI0ciKSkJAwcOlDoaEUnsgQEh+GD7ORxML8HZgjJ0DWh4Ti5Jj0OxRISCggI888wzeOONNxATEwNnZ2dMmzaNpY6IAAABXi4Y1d0fAJc+sXYsdkSEiIgI/PLLL1i7di2Sk5Px7bffYubMmVi6dKnU0YjISjwUHwYA+I4nUVg1FjsiwmeffYajR49i/PjxAICxY8di586deO+99zBr1iyJ0xGRNRjcxQ8hvq7QVdVgw/E8qeNQI1jsiAgPPvjgdff169cP+/btw44dOyRIRETWRi6XYfLA2qVPVh/IkDgNNYbFjogaFR4ejn379kkdg4isxKS4EDjJZTiaWYpzBWVSx6EGsNgROajMzOZNgK67ukNOTo4l4xCRDdB4qjC8W+1JFGuTsyVOQw1hsSNyUAMGDMDjjz+OQ4cONbqNVqvFv/71L8TGxuLbb79tx3REZK3u7x8CAPjuSA4MRpPEaeiPuI4dkYMaP348PDw8MHr0aLi4uCAuLg7BwcFwcXHBlStXcOrUKaSmpqJfv35YsmSJRa9AQUS2Y1i0Bn4eSly+Wo1daUUYHRMgdST6HV55gshBKZVKZGVlwdPTExqNBpMnT0ZxcTEqKyvh5+eHvn37IjExEbGxsVJHbTVeeYKobb3182ms+OUixsQEYMXU/lLHod/hETsiBxUcHIyUlBQkJiaisrISb731Fvz9/aWORUQ2YFJcJ6z45SJ2nCnE5avV8PNQSR2JruEcOyIHNXv2bNxxxx0YPHgwZDIZVq9ejUOHDqGyslLqaERk5aICPNEnxBs1JoF1R3lilTVhsSNyUE899RQOHz6MsWPHQgiBjz76CAkJCfDy8kL37t3x4IMPYvHixdi4caPUUYnICk3q3wkA8PXhLHBWl/XgHDsiQlRUFJKSkuDu7o7jx48jJSXFfDt58iTKymx7vSrOsSNqe7oqAwa8sQ3VNSasn3Ureod4Sx2JwGJHRDcghIBMJpM6Rquw2BFZxrNfHcW6lFw8HB+KN+/uKXUcAodiiegGbL3UEZHl1K1p98OxXFQZjBKnIYDFjoiIiFrolsgO6OTjirKqGmxOzZc6DoHFjoiIiFpILpfhvrjakyjWHuYlxqwBix0RERG12H1xnSCTAXsvXEb2lQqp4zg8FjsiIiJqsU4+bhjUuQOEAL5N5pp2UmOxIyIiolapO4libXIWTCYutiElFjsiIiJqlcQegfB0cUL2lUrsv1QsdRyHxmJHREREreLirMCdvYMB8CQKqbHYERERUatNujYcu/FkHnRVBonTOC4WOyIiImq13p3U6BrggSqDCRuO5Ukdx2Gx2BEREVGryWQyTIqrPWr3TXKWxGkcF4sdERERtYm7+gZDLgOOZJYi/XK51HEcEosdERERtQl/TxcMjtIAAL47yjXtpMBiR0RERG3mnn4dAQDrjuZACK5p195Y7IiIiKjNjIkJhLtSgcySCiRnXJE6jsNhsSMiIqI246pUYFzPIADAt0c4HNveWOyIiIioTd3Tt3Y49qfjuagyGCVO41hY7IiIiKhN3RLZAcFqF+iqarDzTKHUcRwKix0RERG1KblchruuHbXjcGz7YrEjIiKiNlc3HLsrrRAl5XqJ0zgOFjsiIiJqc1EBnojt6IUak8CG47lSx3EYLHZERERkEff07QQA+I7Dse2GxY6IiIgs4s4+wVDIZUjJKsWFoqtSx3EILHZERERkEX4eKgyJ8gNQeyUKsjwWOyIiIrKYe/rVDsd+fzQHJhMvMWZpLHZERERkMaNjAuCpckL2lUocSi+ROo7dY7EjIiIii3FxVmBcz0AAtUftyLJY7IiIiMii7r52duxPJ/J4iTELY7EjIiIii4qP8EVHb1eUVdVg2+kCqePYNRY7IiIisii5XIa7+gQDAH5I4WLFlsRiR0RERBZ3V5+6S4wVQVtpkDiN/WKxIyIiIouLDvREdIAn9EYTNp/MlzqO3WKxIyIionZxZ91w7DEOx1oKix0RERG1izt61Ra7fRcuo7CsSuI09onFjoiIiNpFaAc39AnxhkkAPx3PkzqOXWKxIyIionZzF4djLYrFjoiIiNrN+F5BkMuAo5mlyCqpkDqO3WGxIyKrUF1djT59+kAmkyElJaXeY8ePH8fgwYPh4uKCkJAQLFmyRJqQRNRq/p4uSOjcAQCP2lkCix0RWYUXX3wRwcHB192v0+kwZswYhIWFITk5GUuXLsWrr76KFStWSJCSiNrCnb25WLGlsNgRkeQ2btyILVu24O23377usdWrV0Ov1+Ozzz5Djx498OCDD+Lpp5/Gu+++K0FSImoLY3sEwVkhQ1pBGdLyy6SOY1dY7IhIUgUFBZgxYwb++9//ws3N7brHk5KSMGTIECiVSvN9iYmJSEtLw5UrVxp8zerqauh0uno3IrIeajdnDIv2BwD8cCxH4jT2hcWOiCQjhMC0adPwxBNPoH///g1uk5+fj4CAgHr31X2dn9/w6vWLFi2CWq0230JCQto2OBG1Wt1w7I/H8iCEkDiN/WCxI6I2N3fuXMhksiZvZ86cwbJly1BWVoZ58+a16fefN28etFqt+ZaVldWmr09ErTeqewDclApkllQgJatU6jh2w0nqAERkf2bPno1p06Y1uU1kZCR27NiBpKQkqFSqeo/1798fDz/8MD7//HMEBgaioKCg3uN1XwcGBjb42iqV6rrXJCLr4qpUYHRMANan5GJ9Si76hvpIHckusNgRUZvTaDTQaDQ33O4f//gH3njjDfPXubm5SExMxJo1axAfHw8ASEhIwMsvvwyDwQBnZ2cAwNatWxEdHQ0fH/4hILJld/YOxvqUXPx0Ig+vTIiBQi6TOpLN41AsEUkmNDQUsbGx5lvXrl0BAJ07d0anTp0AAA899BCUSiWmT5+O1NRUrFmzBh988AGef/55KaMTURsYHKWBt5szisqqsf9isdRx7AKLHRFZNbVajS1btuDSpUuIi4vD7NmzsWDBAsycOVPqaETUSkonOcbFBgHgmnZtRSZ4KgoR2TmdTge1Wg2tVgsvLy+p4xDR7yRdKMbkf+2Hp4sTDs8fBZWTQupINo1H7IiIiEgyAyN8EeClQllVDXanFUkdx+ax2BEREZFkFHIZJvS6dokxXju21VjsiIiISFJ39aktdttOF6C8ukbiNLaNxY6IiIgk1bOjGuEd3FBlMGHb6YIbP4EaxWJHREREkpLJZOZLjK3n2bGtwmJHREREkrvz2nDsL2eLUFqhlziN7WKxIyIiIsl18fdEt0BP1JgEtqRyOLalWOyIiIjIKozvWbtY8U8n8iROYrtY7IiIiMgq3N6rttjtPX+Zw7EtxGJHREREVqGzxoPDsa3EYkdERERWg8OxrcNiR0RERFaDw7Gtw2JHREREVqPecOwpDsfeLBY7IiIisiq3XxuO/ZnDsTeNxY6IiIisSl2x23OOw7E3i8WOiIiIrEoXfw7HthSLHREREVkdDse2DIsdERERWZ26Yrf3/GVoKwwSp7EdLHZERERkdeqGYw1GgS2n8qWOYzNY7IiIiMgq3c7Fim8aix0RERFZJQ7H3jwWOyIiIrJKXfw9EB3A4dibwWJHREREVotnx94cFjsiIiKyWuN7BQIA9nA4tllY7IiIiMhqdfH35HDsTWCxIyIiIqvG4djmY7EjIiIiq1ZvOLaSw7FNYbEjIiIiq9bF3xNdAzxgMAps5bVjm8RiR0RERFZvfM9gAByOvREWOyIiIrJ6t/e8Nhx77jLKqjgc2xgWOyIiIrJ6UQGeiNS4Q280YWdakdRxrBaLHREREdmEsT1qj9ptPsllTxrDYkdEREQ2IfFasduZVogqg1HiNNaJxY6IiIhsQq9OagSpXVChN2LPuctSx7FKLHZERERkE2Qymfmo3eZUDsc2hMWOiIiIbEZdsdt2ugA1RpPEaawPix0RERHZjAHhPvBxc8aVCgMOppdIHcfqsNgRERGRzXBSyDE6JgAAsCWVV6H4IxY7IiIisim/n2cnhJA4jXVhsSMiIiKbcmsXP7grFcjTVuF4tlbqOFaFxY6IiIhsiouzAsO6+QMANvHs2HpY7IiIiMjm/P4qFByO/Q2LHREREdmcYdEaKBVyXLxcjvOFV6WOYzVY7IiIiMjmeLo447YoPwBcrPj3WOyIiIjIJiX2qF32hPPsfsNiR0RERDZpVPcAyGXAyRwdsq9USB3HKrDYERERkU3q4KHCgHBfAMBmLlYMgMWOiIiIbNjY2N8WKyYWOyIiIrJhY64te3IovQSXr1ZLnEZ6LHZERERkszp6u6JXJzWEALad4nAsix0RERHZtLprx/LsWBY7IiIisnF1xW7f+WLoqgwSp5EWix0RSSo8PBwymazebfHixfW2OX78OAYPHgwXFxeEhIRgyZIlEqUlImvUxd8DnTXu0BtN2HmmUOo4kmKxIyLJvf7668jLyzPfnnrqKfNjOp0OY8aMQVhYGJKTk7F06VK8+uqrWLFihYSJicja1J0du8XBlz1xkjoAEZGnpycCAwMbfGz16tXQ6/X47LPPoFQq0aNHD6SkpODdd9/FzJkz2zkpEVmrxB6B+GjnBexMK0SVwQgXZ4XUkSTBI3ZEJLnFixejQ4cO6Nu3L5YuXYqamhrzY0lJSRgyZAiUSqX5vsTERKSlpeHKlSsNvl51dTV0Ol29GxHZt54d1QhWu6BCb8Sec5eljiMZFjsiktTTTz+Nr776Cjt37sTjjz+Ot956Cy+++KL58fz8fAQEBNR7Tt3X+fkNnwG3aNEiqNVq8y0kJMRyb4CIrIJMJjOvaefIZ8ey2BFRm5s7d+51J0T88XbmzBkAwPPPP49hw4ahV69eeOKJJ/DOO+9g2bJlqK5u+UKj8+bNg1arNd+ysrLa6q0RkRWrm2e37XQBaowmidNIg3PsiKjNzZ49G9OmTWtym8jIyAbvj4+PR01NDdLT0xEdHY3AwEAUFNSfDF33dWPz8lQqFVQq1c0HJyKb1j/MB95uziitMOBIZikGRvhKHandsdgRUZvTaDTQaDQtem5KSgrkcjn8/f0BAAkJCXj55ZdhMBjg7OwMANi6dSuio6Ph4+PTZpmJyPY5KeQYEe2P747mYNvpAocsdhyKJSLJJCUl4f3338exY8dw8eJFrF69Gs899xz+9Kc/mUvbQw89BKVSienTpyM1NRVr1qzBBx98gOeff17i9ERkjUbF1M7BddTLi/GIHRFJRqVS4auvvsKrr76K6upqRERE4LnnnqtX2tRqNbZs2YJZs2YhLi4Ofn5+WLBgAZc6IaIGDY7yg7NChouXy3Gh6Co6azykjtSuZEIIIXUIIiJL0ul0UKvV0Gq18PLykjoOEVnYlE8P4Ndzl/HS7d0wc0hnqeO0Kw7FEhERkV0ZbR6OdbzLi7HYERERkV0Z2b222B3OKEFJuV7iNO2LxY6IiIjsSkdvV3QP8oJJADvPONZROxY7IiIisjuju9cumbT9jGOdHctiR0RERHanbtmT3WlFqK4xSpym/bDYERERkd2JDVYjwEuFcr0R+y+WSB2n3bDYERERkd2Ry2UY0c3xFitmsSMiIiK7NDrm2jy70wVwlGV7WeyIiIjILg3q7AdXZwVytVU4laeTOk67YLEjIiIiu+TirMBtUX4AHGexYhY7IiIislujry1WvO20Y8yzY7EjIiIiuzW8mz9kMuBEjhb52iqp41gcix0RERHZLY2nCn1DvAE4xmLFLHZERERk1+quHesIy56w2BEREZFdG33tKhR7LxSjQl8jcRrLYrEjIiIiuxbl74FQXzfoa0z49dxlqeNYFIsdERER2TWZTIZRDjIcy2JHREREdm9U99qrUOw4UwijyX6vQsFiR0RERHZvQIQvPF2cUFyuR0pWqdRxLIbFjoiIiOyes0KO4dG1R+3sebFiFjsiIiJyCKNi7H+eHYsdEREROYShXTVwkstwrvAqMorLpY5jESx2RERE5BDUrs4YGOELANh2ulDiNJbBYkdEREQOw96XPWGxIyIiIodRV+wOppdAW2GQOE3bY7EjIiIihxHawQ1dAzxgNAnsOmt/w7EsdkRERORQhnerXfZkV1qRxEnaHosdEREROZQR0XXFzv6uQsFiR0RERA6lX5gPPF2ccKXCgGPZpVLHaVMsdkRERORQnBVyDOmqAQDsPGNf8+xY7IiIiMjh1A3H7mCxIyIiIrJtQ6M1kMmA1FwdCnRVUsdpMyx2RERE5HD8PFTo1ckbQO1JFPaCxY6IiIgckj0Ox7LYERERkUMa3q32BIo95y6jusYocZq2wWJHREREDik2WA0/DxXK9UYcTr8idZw2wWJHREREDkkul2F4dO1RO3sZjmWxIyIiIodVd3kxe1nPjsWOiIiIHNZtUX5wkstw8XI50i+XSx2n1VjsiIiIyGF5uThjQLgvAGCnHSx7wmJHREREDq3u7Fh7mGfHYkdEREQObcS1eXYHLpagQl8jcZrWYbEjIiIih9ZZ44EQX1fojSbsPV8sdZxWYbEjIiIihyaTyTDcTq5CwWJHREREDq9u2ZNdaYUQQkicpuVY7IiIiMjhJUR2gIuzHHnaKpzJL5M6Toux2BEREZHDc3FWYFBnPwC2PRzLYkdEREQE+7gKBYsdEREREWC+buyRzCsordBLnKZlWOyIiIiIAHTycUPXAA+YBLD7bJHUcVqExY6IiIjomt/OjmWxIyIiIrJpw7rWFrtfzxXBZLK9ZU9Y7IhIUj/99BPi4+Ph6uoKHx8fTJw4sd7jmZmZGD9+PNzc3ODv748XXngBNTW2fckfIrJecWE+cFcqcPmqHqfydFLHuWlOUgcgIsf17bffYsaMGXjrrbcwYsQI1NTU4OTJk+bHjUYjxo8fj8DAQOzbtw95eXmYOnUqnJ2d8dZbb0mYnIjsldJJjkFd/LD1VAF2ny1CbEe11JFuikzY8vLKRGSzampqEB4ejtdeew3Tp09vcJuNGzdiwoQJyM3NRUBAAABg+fLlmDNnDoqKiqBUKpv1vXQ6HdRqNbRaLby8vNrsPRCRffpifwbmrzuJgeG++PqJBKnj3BQOxRKRJI4cOYKcnBzI5XL07dsXQUFBGDduXL0jdklJSejZs6e51AFAYmIidDodUlNTG33t6upq6HS6ejciouYa2rV22ZPkzCvQVRkkTnNzWOyISBIXL14EALz66quYP38+NmzYAB8fHwwbNgwlJSUAgPz8/HqlDoD56/z8/EZfe9GiRVCr1eZbSEiIhd4FEdmjEF83RPq5w2gS2Hf+stRxbgqLHRG1qblz50ImkzV5O3PmDEwmEwDg5Zdfxr333ou4uDisXLkSMpkMa9eubVWGefPmQavVmm9ZWVlt8daIyIEMuXbUztbWs+PJE0TUpmbPno1p06Y1uU1kZCTy8vIAADExMeb7VSoVIiMjkZmZCQAIDAzEwYMH6z23oKDA/FhjVCoVVCpVS+ITEQEAhkZrsGpfOnanFUEIAZlMJnWkZmGxI6I2pdFooNFobrhdXFwcVCoV0tLScNtttwEADAYD0tPTERYWBgBISEjAm2++icLCQvj7164ttXXrVnh5edUrhEREbe2WiA5QOsmRq63C+cKriArwlDpSs3Aologk4eXlhSeeeAILFy7Eli1bkJaWhieffBIAMGnSJADAmDFjEBMTgylTpuDYsWPYvHkz5s+fj1mzZvGIHBFZlKtSgfgIXwC2NRzLYkdEklm6dCkefPBBTJkyBQMGDEBGRgZ27NgBHx8fAIBCocCGDRugUCiQkJCAP/3pT5g6dSpef/11iZMTkSMYaoPz7LiOHRHZPa5jR0Qtcb6wDKPe/QVKJzmOLRgDV6VC6kg3xCN2RERERA3orPFAR29X6GtM2H+pWOo4zcJiR0RERNQAmUz227InabYxHMtiR0RERNSIunl2v9jIPDsWOyIiIqJGDOrSAQq5DBcvlyOzuELqODfEYkdERETUCC8XZ8SF1p6pv/uc9R+1Y7EjIiIiasLQaNuZZ8diR0RERNSEunl2+y5chr7GJHGaprHYERERETUhJsgLfh5KVOiNOJxRInWcJrHYERERETVBLpdhSFTd2bGXJU7TNBY7IiIiohswz7Oz8mVPWOyIiIiIbuC2Ln6QyYDTeToU6KqkjtMoFjsiIiKiG+jgoUKvjmoA1r1YMYsdERERUTPUnR1rzcOxLHZEREREzVB33dhfz12G0SQkTtMwFjsiIiKiZugT4g1PFydoKw04ll0qdZwGsdgRERERNYOTQo7BUX4ArPcqFCx2RERERM1k7fPsWOyIiIiImqlunt2x7FJcKddLnOZ6LHZEREREzRSkdkV0gCeEAPact76rUDhJHYCIiIjIlkzq3wk5pZXorPGQOsp1ZEII6zxfl4iojeh0OqjVami1Wnh5eUkdh4jIYjgUS0RERGQnWOyIiIiI7ASLHREREZGdYLEjIiIishMsdkRERER2gsWOiIiIyE6w2BERERHZCRY7IiIiIjvBYkdERERkJ1jsiIiIiOwEix0RERGRnWCxIyIiIrITLHZEREREdoLFjoiIiMhOsNgRERER2QkWOyIiIiI7wWJHREREZCdY7IiIiIjsBIsdERERkZ2QCSGE1CGIiCxJCIGysjJ4enpCJpNJHYeIyGJY7IiIiIjsBIdiiYiIiOwEix0RERGRnWCxIyIiIrITLHZEREREdoLFjoiIiMhOsNgRERER2QkWOyIiIiI78f+AxrPmxVhcNQAAAABJRU5ErkJggg==\n" }, "metadata": {} }, @@ -384,11 +457,11 @@ "output_type": "execute_result", "data": { "text/plain": [ - "" + "" ] }, "metadata": {}, - "execution_count": 71 + "execution_count": 47 } ] }, @@ -404,9 +477,9 @@ "height": 504 }, "id": "9urFqaNxYIr2", - "outputId": "7a539895-fe9d-470d-a947-64e397f56867" + "outputId": "2a48e749-dbf2-4db0-dcab-4982773cd284" }, - "execution_count": 72, + "execution_count": 48, "outputs": [ { "output_type": "display_data", @@ -414,7 +487,7 @@ "text/plain": [ "
" ], - "image/png": 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\n" + "image/png": 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Ep0P3M76fkpJywec5ODiYlJSUS95ezi8gIABXV9d/9Vy6u7vTsmVL4uPjSyOinOZCr3sfHx+NzpmgXbt25y0iJ7JymbZ2P1+t3s/RDCsAFT1c6d+uFoM6hhPq713WUe3SI488UjTZ8GKj+yXxnl9qhS4wMJDAwMBS+dm1a9fGK34RFaNuIjE1m0+XJDC4fTBr164tdqass7jU5z4qKoqTJ0+yceNGWrduDcCiRYuw2WxFJe1SxMTEAIVD9vJ/X6/eT2xyBn7e7gSm/8XChTb69OkDFA7DL1y4kEceeeS8+0ZFRbFw4UIef/zxotvmz59/xsiRXJyHhwetW7dm4cKFl/zcn62goICtW7dy/fXXl2JSgcLX/dlLNeh1b56YmJgz3tf3H89i8oq9zNhwkFN5BQAE+3hx31Xh9G9Xy+kvvfUPwzB49NFHmTVrFkuWLKF27doX3adE3vOvcNJGidq/f7+xefNm48UXXzQqVapkbN682di8ebORkZFRtE2DBg2MmTNnFn39+uuvGwEtrzHCRs8z6o6dZ0Tfdo9Ru3Zt49SpU2Y8BIcVHR1ttGzZ0li7dq2xYsUKo169esaAAQOKvn/w4EGjQYMGxtq1aw3DMIz4+HjjpZdeMjZs2GDs3bvX+Pnnn42IiAijS5cuZj0Eu5SSdspo/MLvRtjoeca0NfuN7777zvD09DSmTp1q7Nixwxg6dKjh5+dnJCcnG4ZhGB2Hv3PGLNeVK1cabm5uxttvv23s3LnTGDdunOHu7m5s3brV5EfmeC723N9zzz3GmDFjirZ/8cUXjT/++MNISEgwNm7caPTv39/w8vIytm/fbtZDcFgZGRlF7+eA8e677xqbN2829u/fbxiGYYwZM8a45557irbfs2eP4e3tbTz11FPGzp07jY8//thwdXU1fv/9d7MegsO63Of+vffeM2bPnm3s3r3b2Lp1qzFixAjDxcXFWLBggbFxf6rx4Ncbzpitet37y4xZmw4aufkFZj1Eu/XQQw8Zvr6+xpIlS4zDhw8XfWRnZxdtc/b7Tkm859tFobv33nsN4JyPxYsXF20DGFOmTCn62mazGc8997xR8+7XjbDR84yGwz4yYmNjyz68gzt+/LgxYMAAo1KlSoaPj49x3333nVGk9+7de8b/i8TERKNLly6Gv7+/4enpadStW9d46qmnjLS0NJMegX16bPomI2z0POOmj1YYBQWFU/MnTJhg1KpVy/Dw8DDatWtnrFmzpmj7pveMO6PQGYZh/PDDD0b9+vUNDw8Po3HjxsYvv/xixkMpF4p77rt27Wrce++9RV8//vjjRdsGBQUZ119/vbFp0yYTUju+f5bCOPvjn+f73nvvNbp27XrOPi1atDA8PDyMiIiIM9735dJd7nP/xhtvGHXq1DG8vLwMf39/o1u3bsYXM+cbd09aU1TiwkbPMwZ9udZYufuo0yw5ciXO97yf3WHOft8xjH//nm/5+84d1t5jWfR6bxm5BTY+uasV1zfVYT8x1+qE4wz4Yg0WC8wZ3ommNX0vus8r83bw+cLtHHi/H2lpafj4+JRBUhGRc8UcOMl783exdNdRANxcLNzSsgZDu0RQL8jxF/4trxxu2ZKz1Q6oyLBudfhw4W5emruDLvUDqeTp8A9LHFRegY0Xfi6cCHFX+1qXVOZEROzBloOFRW5xXGGRc3Wx0LdVDR7pXo9aVTXRwd6Vi+bzcLc6zN6cRGJqNh8u3M0z1zc0O5I4qS9X7GX3kUyqVvTgqWsvb0keEREzbD2YxvsLdrEwtnDVA9e/R+QevbouYVWdc/04R1QuCp2Xuysv3tSY+6auZ/KKvfRtVZMGwRoWlrJ1OO0UHyzcDcCY6yLx9daMLxGxXwlHM3nz91j+2F64XIaLBfq0rMFjV9cj3EkXAnZk5aLQAXSPrEavxkH8sT2F52Zv5YcHo5zmsiJiH16et4Ps3ALahFWhb6vLu6KAXqoiUlaOZlj5YOEupq87QIHNwMUCN7coHJGLCKxkdjy5QuWm0AG8cGNjlu06xvp9J/hpUxK3tdZleqRsLNt1lF+3JuNigZduboKLrgghInYmOzefycv3MnFpAlm5hevI9WxYjdHRkZrsUA6Uq0JXw68Cj/Woxxu/xzL+151c0zBIh72k1FnzCxg3p/Di7fd2DKdRdc1QFRH7UWAz+HHjAd6dv4uU9MIrOzSr6cvY6xoSVaeqyemkpJSrQgcwuFNtftp0kPgjmbz1Zyyv9GlqdiQp5z5dksDeY1kEVvbkiWvqmx1HRKTI2j3HGTdnO7HJGQCE+lfgqV6R3NA0REcSyplyV+g83Fx4+eYmDPhiDdPWJnJ761Cah/qZHUvKqfgjmXyyOAGAF25ohI+XRoRFxHzJaTm89utO5vx1CADfCu48enVd7okKw9PN1eR0UhpczA5QGqLqVOWWljUwDHhu9jYKbA69drLYKcMweHbWVnILbHRrEMgNzbSotYiYy5pfwKdLErj6nSXM+esQFkvhmphLnuzGA50jVObKsXI3QvePsddHsmBnCluT0pi6ah+DO1384rgil2PGxoOs3ZuKl3vhqLBmVYuImZbEHeHFuTvYeywLgNZhVXjxpsY0qaEFzp1BuRyhA6hW2Ysx1xUu7Pr2H3EcSM02OZGUJ8czrbz2604AnuhZn1B/raIuIuY4kJrNA19tYNCU9ew9lkVAJU/e7decH4dFqcw5kXJb6AAGtK1Fu3B/TuUV8NzsbTj4ZWvFjrz6y05OZufRMMSH+zX6a3emT59OhQoVOHz4cNFt9913H82aNSMtLc3EZCIlJ7/AxsSlCVzz3lIW7EzBzcXCkM61WfxkV25tVVNHDZxMuS50Li4WXru1KR6uLizddbTo5FCRf2PF7mPM3JyExQLjb22Ku2u5/jVySP3796d+/fq89tprAIwbN44FCxbw22+/4eurEQtxfFsPpnHTRyt5/bdYcvJsREVU5ffHO/Ns70ZU1uQsp1Ruz6H7R91qlXj06rq8M38XL87dQed6gfhX9DA7ljionLwCnp29FYCBHcJooRnUdslisfDqq69y2223ERwczIQJE1i+fDk1atQwO5rIv5Kdm8+7f+7iy5V7sRng5+3Os9c35LbWGpFzdk4xtPBg1zo0CKpMalYur/yyw+w44sAmLNrN/uPZBPt48WSvBmbHkWLccMMNNGrUiJdeeolZs2bRuHFjsyOJ/CtL4o5wzbvLmLSisMzd1Lw6C0Z25fY2oSpz4hyFzsPNhfF9m2KxwMxNSSzbddTsSOKAdqVk8NnSPQD856bGOqxh537//XdiY2MpKCggKCjI7DgiV+x4ppUR321m0JT1JJ08RQ2/Cky5ry0fDmhJQCVPs+OJnXCKQgfQqlYV7o0KB+DZ2VvJzs03N5A4FJvNYOzMreTbDHo2DKJXYxUEe7Zp0yb69evH5MmT6dGjB88//7zZkUSuyJ/bk+n1/jJ+jjmEiwXuv6o2fz7Rhe4NqpkdTexMuT+H7nRP9mrAn9uTOZB6ivcX7OaZ6xuaHUkcxPT1iWzcf4KKHq68dHNjHd6wY/v27aN3794888wzDBgwgIiICKKioti0aROtWrUyO57IJUk7lceLc7czc1MSAPWDKvHWbc115SO5IKcZoQOo5OnGK7c0AWDS8j1sPajlC+TiktNyeP23WABGXduA6n4VTE4kF5Kamkp0dDQ333wzY8aMAaB9+/Zcd911PPPMMyanE7k0K3YfI/r9ZczclISLBYZ1rcPcRzupzEmxnGqEDuDqyCBubF6duX8dYvRPW/j5kau07IRckGEYPDNrKxk5+TSv6cu9HcPNjiTF8Pf3JzY29pzbf/nlFxPSiFye7Nx8Xv8tlq9X7wcgrKo37/ZrTuswf5OTiSNwyibzwg2N8K3gzo7D6UxesdfsOGLHZm5KYlHsETxcXXjr9ua4uuhQq4iUvI37U7n+g+VFZe6eDmH8NqKzypxcMqcsdIGVPXm2d+H5c+/N38W+v697J3K6lPQcXpy7HYARPetRP6iyyYlEpLzJzbfx+m+x3D5xNfv+XhLp6/vb8XKfJnh7ON1BNPkXnLLQAdzeuiYd61TFmm/j2dlbdVkwOYNhGDwzcyvpOfk0reHLg10izI4kIuXMvmNZ9P10FROXJmAz4NaWNfjjiS50qR9odjRxQE5b6CwWC6/d0hRPNxdWxh9nxoaDZkcSOzI7JomFsUdwd7Xw9u3NcdN5liJSgn6OSaL3h8vZmpSGn7c7E+9uxbt3tMC3gta3lCvj1H+lwgMq8sQ19QF4ad4ODqRmm5xI7MGR9Bz+M6fwiiIjetSjQbAOtYpIycjOzeepGX8x4rsYsnILaBfuz28jOhPdJMTsaOLgnLrQAQzpHEHrsCpkWvN5csZf2Gw69OrMDMPgye83kXYqj/wje3iub3sGDx5MZmZmsft169YNi8VyxsewYcPKKLWIOIKdh9O5ccIKZmw8iMUCj/Wox7dD2hPiq6WQ5N9z+kLn6mLh3X7N8fZwZe3eVM16dXI/xxxiWcIJsOXzXv9WzJs7h2XLljF06NCL7jtkyBAOHz5c9PHmm2+WQWIRsXeGYfDN6n3c/PFKEo5mEeTjybcPdGDkNfV1OoeUGL2SgLCqFXn+hkYAvPVHHLHJ6SYnEjMcycjhuVlbAOjf1Jfbr72KTp06MWHCBL777jsOHTpU7P7e3t4EBwcXffj4+FzyfevKEyLlU1p2Hg/9dxPP/7yd3Hwb3RsE8utjnYmqU9XsaFLOqND9rX/bUHpEViO3wMYT3/+FNb/A7EhShgzD4NlZ28jMtVFwdB8v39ml6Hs9e/bExcWFtWvXFvszpk2bRkBAAE2aNGHs2LFkZ+ucTBFntnH/Ca7/cDm/b0/G3dXCc70b8uWgtlSt5Gl2NCmHtMjN3ywWC+P7NiX6/eXsPJzO+wt2Mzo60uxYUkbm/HWI+TtSsGDgtWUG7q7Di77n5uaGv78/ycnJF9z/zjvvJCwsjOrVq7NlyxZGjx5NXFwcM2fOvOA+VqsVq9Va9LmIlA+GYfDfNft5ad4O8goMwqp6M2FAS5rV9DM7mpRjGqE7TbXKXrx2S1MAJi5NYP2+VJMTSUkZM2bMOZMW/vlwq1yVR6YsA6CVZwou6Ycv++cPHTqUXr160bRpU+666y6+/vprZs2aRUJCwgX3GT9+PL6+vvj6+vLhhx9e8WMTEfuRk1fAUz9u4fmft5NXYHB902DmPdpJZU5KnQrdWaKbBHNb65oYBoz8IYZMa77ZkaQEjBo1ip07d57zsX3HDm54ZQauFXxoFFKZ6FoWjhw5csa++fn5pKamEhwcfMn31759ewDi4+MvuM3YsWNJS0sjLS2Nxx577MoemIjYjaSTp7h94mp+3HgQFwuMvS6Sj+9sRWUvrS0npU+HXM9j3I2NWJ1wnAOpp3h57g7euK2Z2ZHkXwoMDCQw8NzV1z9bmkDM4VNUcHflwwGtyDseyMmTJ9m4cSOtW7cGYNGiRdhstqKSdiliYmIACAm58NpSnp6eeHp6Fn0uIo5rVfwxHpm+mdSsXKp4uzNhQCs61QswO5Y4EY3QnUdlL3fe6dcciwW+33CA+TtSzI4kpWDLwZO89UccUFji61arRMOGDYmOjmbIkCGsW7eOlStX8sgjj9C/f3+qV68OQFJSEpGRkaxbtw6AhIQEXn75ZTZu3Mi+ffuYM2cOAwcOpEuXLjRrpn8MiJRnhmHwxbI93D15LalZuTSu7sOcRzqpzEmZU6G7gA4RVRnSufD6nWNnbuFYpk5aL0+yrPk8Nn0z+TaD65oEc0fb0KLvTZs2jcjISHr06MH1119Pp06d+Pzzz4u+n5eXR1xcXNEsVg8PDxYsWMC1115LZGQko0aNom/fvsydO7fMH5eIlJ3s3Hwe+y6GV3/dWXgt1lY1+OmhjoT6e5sdTZyQDrkWY+Q19Vkad5S4lAzGztzK5/e01nph5cR/5mxn3/FsQny9GH9r0zP+v/r7+/Ptt99ecN/w8HAM4/9XFAkNDWXp0qWlmldE7Mv+41k8+M1GYpMzcHOx8MKNjbinQ5j+RohpNEJXDC93V967owXurhbm70hhxsaDZkeSEjD3r0NFl955/44W+Hl7mB1JRBzI4rgj3DhhBbHJGQRW9mT60A4MjApXmRNTqdBdRKPqPoy8pgEAL87ZzoFULRbryA6kZvPMrK0APNK9Lu0jtFq7iFwawzD4eHE8909dT3pOPq1q+THv0U60Dfc3O5qICt2lGNolgrbhVcjKLeCx7zaTm28zO5JcgfwCG098H0PG32/EI3rUMzuSiDiInLwCnvg+hrf+iMMw4K72tfhuaBRBPl5mRxMBVOguiauLhXf7tcDHy43NiSd55ZcdZkeSKzBhUTwb9p+gsqcbH/RvqYtii8glOZ5p5e5Ja5kdcwg3Fwuv3dKUV29pioeb3kPEfujVeIlC/b15v38LAL5evZ+Zm3Q+nSNZvy+VCYt2A/DKLU00C01ELsnulAz6fLKy8B+DXm58dX877mxfy+xYIudQobsMV0cG8djfh+membWVHYfSTU4klyItO4/Hv4spWlbg5hY1zI4kIg5g+e6j3PrpKg6knqKWvzezHr6Kq+pqfTmxTyp0l2lEj3p0rR9ITp6Nh6ZtJO1UntmRpBgFNoNHv9tM0slThFX15qWbm5gdSUQcwH/X7GfQlPVk5OTTNrwKs4dfRd1qlcyOJXJBKnSXydXFwvt3tKCGXwX2H89m1A8x2GzGxXcUU7z9ZxzLdh3Fy92FT+9qTSVPLb0oIhdWYDN4ae4Onpu9jQKbwa2tavDfB9rjX1HLG4l9U6G7AlUqejDx7tZ4uLmwYOcRPlly4Quwi3l+2XKYT5ckAPDmbc1pVN3H5EQiYs+yc/MZ+vUGvly5F4CnejXgndub4+nmanIykYtTobtCTWv68srfh+/emb+LZbuOmpxIThebnM6TM/4CCpedual5dZMTiYg9O55pZcAXa1kYewRPNxc+vrMVw7vX1WLB4jBU6P6Ffm1DGdAuFMOAx77brEWH7URadh4PfrORU3kFdKobwNO9GpgdSUTs2IHUbG6buJq/DpzEz9udb4d0oHezELNjiVwWFbp/adyNjWlaw5eT2Xk8PG0TOXkFZkdyav9Mgth/PJuaVSowYYDWmxORC9uWlMatn65i77EsavhV4MdhHWkdVsXsWCKXTX/p/iUvd1c+vbsVft7ubE1K48W5282O5NROnwTx+T1tqKITmUXkAlbGH6P/52s4mmElMrgyMx/uqJms4rBU6EpAzSrefNi/JRYLTF93gO/XJ5odySmdPgnijb7NNAlCRC5ozl+HGDRlHZnWfDpE+PPDMF3GSxybCl0J6VI/kFHX1Afg+Z+3s3F/qsmJnEtccgZP/Vg4CWJI59paPFhELmjS8j08Nn0zeQUGvZuF8NX97fDxcjc7lsi/okJXgh7uVpeeDYPIzbdx35T1xCVnmB3JKRxJz+GBr9eTnVvAVXWrMjo60uxIl03z6ERKn81m8NqvO3nll50ADOoYzoT+LbUsiZQLKnQlyMXFwocDWtCqlh/pOfkM/HKtZr6WsrTsPAZ+ua7o0jwfDWilSRAico7cfBsjf4jh82V7ABhzXSTjbmyEi4v+OSXlg/7ylTBvDze+HNSW+kGVSEm3cs/ktRzLtJodq1zKzs3n/q/WE5ucQWBlT/47uL0mQYjIOU7lFjD0mw3MjjmEm4uFd/s1Z1jXOlpjTsoVFbpS4Oftwdf3t6eGXwX2Hc/m3i/XkZGja76WpNx8G8P+u4mN+0/g4+XGN4PbUauqt9mxRMTOZOTkce+UdSyJO0oFd1cm3duGW1vVNDuWSIlToSslwb5efDO4HVUrerD9UDpDvt6gNepKSIHNYOQPMSzbVfgGPeW+tkQGa0ariJzpRFYud01ay7q9qVT2LPyHX7cG1cyOJVIqVOhKUURgJb66vx2VPN1YsyeVEd9tJr/AZnYsh2YYBi/8vI15Ww7j7mph4j2taR3mb3YsEbEzR9JzuOPz1Ww5mIZ/RQ+mD+1Am3C9V0j5pUJXyprU8OXzga3xcHXhj+0pPDtrG4ZhmB3LYb39ZxzT1iZiscB7d7Sga/1AsyOJiJ05eCKbfp+tZldKJkE+nnw/tANNaviaHUukVKnQlYGOdQL4cEBLXCzw/YYDvPF7nNmRHNIXy/bw8eLChYNf7dOUG5pVNzmRiNibPUczuX3iavYdzybUvwIzHuxIvaDKZscSKXUqdGUkukkwr93SFICJSxP44u+p83JpfthwgFd/LVw76qleDbizfS2TE4mIvdlxKJ1+n63mcFoOdQIrMuPBjposJU5Dha4M9W9Xq2jR21d/3cmPGw+anMgx/L4tmTE/bQFgaJcIHu5Wx+REImJvYg6cpP/nqzmWmUujEB9+eDCKYF9dykuchwpdGRvWNYIhnWsD8PSPfzFjwwGTE9m3BTtSeGz6ZmwG9GtTk7HXRWrtKBE5w6bEE9wzaS3pOfm0DqvC9KEdqFrJ0+xYImVKha6MWSwWnrm+If3bhmIz4KkftzBpuQ6/ns+PGw/y4H83kltg47q/D1mrzInI6TYlnmDg5HVkWPNpV9ufr+9vh28FXZdVnI8KnQksFguv3dKUBzoVjtS98stO3v4jTrNfTzNp+R6enPEXBTaDvq1qMmFAS13SS0TOsHF/YZnLtObTIcKfqfe1paKnm9mxREyhv5AmcXGx8GzvhjzVqwEAHy2O57nZ2yiwOXepMwyDN3+PLbp49pDOtXnrtmYqcyJyho37Uxk4eS2Z1nyiIqry5aC2eHuozInz0qvfRBaLheHd6+JbwZ3nf97GtLWJpGbl8k6/5k75xpRXYOP52dv4bn3heYWjoyMZ1jVCh1lF5Awb9qVy75fryMotKCpzFTxczY4lYirnaw126O4OYfhWcGfkDzH8ti2Z/cez+Xxga2pWcZ7p9scyrTw8bRPr9qbiYoFXb2nKgHZamkREzrR+XyqD/i5zHetUZfK9KnMioEOuduPG5tWZ9kAHqlb0YMfhdG7+aCXr9qaaHatMbEtK46YJK1i3N5VKnm58fk8blTkROcf600bmrqqrMidyOhU6O9Kutj9zHu1EoxAfjmflctekNXy7NtHsWKXq55gkbpu4ikNpOdQOqMjs4R3p2SjI7FgiYmfW7S0sc9m5BXSqG8CkgSpzIqdTobMzNfwq8ONDUfRuFkJegcEzs7byxPcxpOfkmR2tROXkFfCfOdsZ8V0MOXk2ujUIZPbwq6hbTZfoEZEzrdubyqApp5W5e9uozImcRYXODnl7uPHRgJY81asBLhaYtTmJ6z9YzoZ95eMQ7PZDadw4YQVTV+0DYFjXOky+t63WjhKRc2xKPMF9f5e5zvUKy5yXu8qcyNlU6OzUPzNgZwyLomaVChw8cYp+n63m3T/jyM23mR3vihTYDD5flkCfj1ey+0gmAZU8mXJfW8ZcF4mri2ayisiZth9KO2MCxBcDVeZELkSFzs61DvPntxGdubVlDWwGfLgonhsmON5o3c7D6fT9dBWv/RpLXoHBNY2C+OPxznRvUM3saCJih3anZHDP5HVFl/NSmRMpnpYtcQCVvdx5944WdIusxn/mbGdXSia3TVzNHW1CGdWrPtUq2+8FqNOy8/hg4W6+Wr2PAptBJU83nuvdkDvahmp9ORE5r33Hsrhr0lpSs3JpWsOXKboChMhF6TfEgdzUvDqd6wbw+m+xfL/hAN9vOMC8LYd4uHtdBnUMt6s3vJy8Ar5dm8iERbs5kV04oeO6JsH856bGBPnYbwEVEXMlnTzFXZPWciTDSoOgynx9fzt8vHR+rcjF2E8DkEtSpaIHb9zWjNvb1OTleTv462Aab/0Rx+QVe3mwSwR3tq9FZRPf/E7lFjBj4wE+XhxPSroVgPpBlXiudyO61A80LZfd02ClCEfSc7jrizUknTxFREBFvnmgHVUqepgdS8Qh6Bw6B9Um3J9ZD1/FB/1bEF7Vm9SsXMb/FkvH8Yt4Zd4O9h7LKtM8SSdP8dYfsUS9vpAXft5OSrqV6r5ejL+1Kb8+1tmhytyrr75Kx44d8fb2xs/P75L2MQyDF154gZCQECpUqEDPnj3ZvXt36QYVKUdSs3K5a9Ja9h3PpoZfBf77QHu7Pp1ExN5ohM6BubhYuLlFDXo3DWHW5iQmLk0g4WgWk1bsZdKKvbQL9+fWVjW4plEQVSt5lvj9p53KY8GOFGbHJLEi/hiGUXh7LX9vhnSuTb+2oXi6Od5JzLm5udx+++1ERUUxefLkS9rnzTff5MMPP+Srr76idu3aPP/88/Tq1YsdO3bg5aU/SiLFSTuVxz2T17L7SCZBPp5MH9KB6n4VzI4l4lAshvHPn2FxdDabwdLdR/l61T6W7jqK7e//sy4WaB1WhU51A2kf4U+zmr54e1x+l8/JK2D7oTTW7T3Bsl1H2bA/lbyC/798oiKqcm/HMK5pFFwuliGZOnUqjz/+OCdPnix2O8MwqF69OqNGjeLJJ58EIC0tjaCgIKZOnUr//v0vel/jf9vJp39u48D7/UhLS8PHx6ckHoKI3cvOzefuSWvZlHiSqhU9+P7BKOpWq2R2LBGHoxG6csTFxUL3BtXo3qAayWk5zNx8kF+3HmZbUjrr951g/b4TALi6WAiv6k3dapUIq1qRapU98a3gTkVPN9xcLOTbDHLyCjiZnUdKeg4HT5xi95EM9hzNIt92Zv+vH1SJ65uGcEvLGoRVrWjGwzbd3r17SU5OpmfPnkW3+fr60r59e1avXn1JhU7EGeUV2Hjov5vYlHgS3wrufDO4vcqcyBVSoSungn29eLhbXR7uVpcDqdks332MlfHH2Lj/BMnpOSQczSLh6OWfZxdQyYOWtarQqW4AnesFEBGoN9/k5GQAgoLOvAZtUFBQ0ffOx2q1YrUWThzJteaWXkARO2SzGTw14y+W7jqKl7sLXw5qS6PqGpkWuVIqdE4g1N+bO9vX4s72tQBISc8hLjmD+COZHDxxiqOZVtJP5ZGdm0++zcDdxQVPdxd8KrgTWMmTUH9vIgIqUj+4MtV9vRxy/bgxY8bwxhtvFLvNzp07iYyMLKNEMH78eF588UUA/LoOonLL68vsvkXMZBgGL/+yg9kxh3BzsfDp3a1pHVbF7FgiDk2FzgkF+XgR5OPlUDNP/61Ro0YxaNCgYreJiIi4op8dHBwMQEpKCiEhIUW3p6Sk0KJFiwvuN3bsWEaOHAnAe4v2Mnnpriu6fxFH88mSBKas3AfA27c31xVjREqACp04hcDAQAIDS6fA1q5dm+DgYBYuXFhU4NLT01m7di0PPfTQBffz9PTE07Nw9rGHp9baEucwfV0ib/0RB8ALNzSiT8saJicSKR+0Dp3IWRITE4mJiSExMZGCggJiYmKIiYkhMzOzaJvIyEhmzZoFgMVi4fHHH+eVV15hzpw5bN26lYEDB1K9enX69Olj0qMQsT+/bzvMs7O2AjC8ex3u71Tb5EQi5YdG6ETO8sILL/DVV18Vfd2yZUsAFi9eTLdu3QCIi4sjLS2taJunn36arKwshg4dysmTJ+nUqRO///671qAT+duqhGM8Nj0GmwH924by5LUNzI4kUq5oHToRO6B16KQ825aURv/P15BpzadX4yA+vrMVbq46QCRSkvQbJSIipWbvsSzu/XIdmdZ8OkT480H/lipzIqVAv1UiIlIqjmVauffLdRzPyqVxdR++GNgGL3fHuxygiCNQoRMRkRKXnZvP4K82kJiaTah/Babe147KXu5mxxIpt1ToRESkRBXYDB6bHsNfB07i5+3O1PvaEVjZ0+xYIuWaCp2IiJQYwzB4ce52FuxMwcPNhUkD21BHlwgUKXUqdCIiUmI+X7aHr1fvx2KB9+9oQZtwf7MjiTgFFToRESkRc/46xPjfYgF49vqGXN805CJ7iEhJUaETEZF/bc2e4zz5w18A3HdVOA90vrJrI4vIlVGhExGRfyX+SAZDv95AboGN6MbBPNe7kdmRRJyOCp2IiFyxoxlW7v1yPek5+bSq5cf7/Vvg6mIxO5aI01GhExGRK5KTV8DQbzaQdPIU4VW9mXRvWy0cLGISFToREblshmHw1I9b2Jx4Et8K7ky5rx3+FT3MjiXitFToROyABR2iEsfywcLdzP3rEG4uFibe3ZraARXNjiTi1FToRETksvwck8T7C3YD8OotTYiqU9XkRCKiQiciIpdsU+IJnvpxCwBDu0RwR9taJicSEVChExGRS3TwRHbh8iT5Nno2DGJ0dKTZkUTkbyp0IiJyURk5eQyeuoFjmbk0DPHhAy1PImJXVOhERKRYBTaDx6ZvJi4lg8DKnky+tw0VPd3MjiUip1GhExGRYr36y04Wxx3F082FSQPbUN2vgtmRROQsKnQiInJB/12zny9X7gXg3X4taB7qZ24gETkvFToRETmvVfHHGDdnOwBPXluf3s1CTE4kIheiQiciIuc4kJrNw99uosBm0KdFdYZ3r2t2JBEphgqdiIicIcuaz5CvN3AyO49mNX15vW8zLBbNaBWxZyp0IiJSxDAMnpzxF7HJGQRU8uSze1rj5e5qdiwRuQgVOhERKfLRonh+25aMu6uFz+5pRYivZrSKOAIVOhERAWD+jhTemb8LgFf6NKF1mL/JiUTkUqnQiYgIu1MyeOL7GAAGRoXpGq0iDkaFTkTEyaVl5zHk6w1kWvNpX9uf529oZHYkEblMKnQiIk4sv8DGI9M3se94NjX8KvDJXa1wd9WfBhFHo99aEREn9tafcSzffYwK7q58PrA1VSt5mh1JRK6ACp2IiJP6bethPlu6B4C3bm9G4+q+JicSkSulQici4oTij2Ty5Iy/ABjSuTY3NKtuciIR+TdU6EREnEymNZ9h/91IVm4BHSL8GR0daXYkEfmXVOhERJyIYRg8/eNfxB/JJNjHiwkDWuGmSRAiDk+/xSIiTmTS8r38urXwShAf39WKwMqaBCFSHqjQiYg4idUJx3n991gAXrihEa3DqpicSERKigqdiB2wWMxOIOXd4bRTPPLtJgpsBre2qsHdHcLMjiQiJUiFTkSknLPmF/DwtE0cz8qlYYgPr/ZpikX/ihApV1ToRETKuVfm7WRz4kl8vNyYeHcrKni4mh1JREqYCp2ISDn208aDfLNmPwAf9G9JWNWKJicSkdKgQidylldffZWOHTvi7e2Nn5/fJe0zaNAgLBbLGR/R0dGlG1TkInYeTueZWVsBGNGjHt0jq5mcSERKi5vZAUTsTW5uLrfffjtRUVFMnjz5kveLjo5mypQpRV97emo5CDFPpjWf4dM2Yc230bV+ICN61DM7koiUIhU6kbO8+OKLAEydOvWy9vP09CQ4OLgUEolcHsMweGbmVvYcyyLE14v37miBi4smQYiUZzrkKlJClixZQrVq1WjQoAEPPfQQx48fNzuSOKlv1yUy569DuLpYmDCgJf4VPcyOJCKlTCN0IiUgOjqaW2+9ldq1a5OQkMAzzzzDddddx+rVq3F1Pf+MQqvVitVqBSD37/+K/FvbktJ4ce4OAJ7u1YA24f4mJxKRsqAROnEKY8aMOWfSwtkfsbGxV/zz+/fvz0033UTTpk3p06cP8+bNY/369SxZsuSC+4wfPx5fX198fX159933rvi+Rf6RkZPHI99uIjffRo/IagzpHGF2JBEpIxqhE6cwatQoBg0aVOw2EREl98cvIiKCgIAA4uPj6dGjx3m3GTt2LCNHjgTgg8V7+WLJrhK7f3E+hmEw5qet7DueTQ2/CrzTr7nOmxNxIip04hQCAwMJDAwss/s7ePAgx48fJyQk5ILbeHp6Fs2E9dCMWPmXvlmzn1+2HsbNxcKEO1vi563z5kSciQ65ipwlMTGRmJgYEhMTKSgoICYmhpiYGDIzM4u2iYyMZNasWQBkZmby1FNPsWbNGvbt28fChQu5+eabqVu3Lr169TLrYYgT2XowjVfm7QRgzHWRtKpVxeREIlLWNEIncpYXXniBr776qujrli1bArB48WK6desGQFxcHGlpaQC4urqyZcsWvvrqK06ePEn16tW59tprefnll7UWnZS69Jw8hn+7idwCG9c2CmJwp9pmRxIRE6jQiZxl6tSpF12DzjCMos8rVKjAH3/8UcqpRM5lGAZPz9hCYmo2NatU4K3bmmOx6Lw5EWekQ64iIg5q6qp9/L49GXdXCx/f2Qpfb3ezI4mISVToREQc0NaDabz2a+F5c89e35DmoX7mBhIRU6nQiYg4mExrPo9O30RegUF042Du7RhudiQRMZkKnYiIg3nh523sO55NdV8v3ujbTOfNiYgKnYiII5m1+SAzNyXhYoEPBrTUeXMiAqjQiYg4jH3Hsnhu1jYARvSoT1tdp1VE/qZCJyLiAHLzbTz23WaycgtoV9ufR66ua3YkEbEjKnQiIg7g7T/j2HIwDT9vdz7o3wJXXadVRE6jQiciYueW7jrK58v2APBG32aE+FYwOZGI2BsVOhE7oLEWuZAjGTmM+iEGgHs6hNGrcbC5gUTELqnQiYjYKZvNYNQPf3EsM5fI4Mo827uh2ZFExE6p0ImI2KlJK/awfPcxvNxdmDCgJV7urmZHEhE7pUInImKHtiWl8dYfcQC8cENj6gVVNjmRiNgzFToRETtzKreAEd9tJq/AoFfjIAa0CzU7kojYORU6ERE789qvO0k4mkW1yp68fqsu7SUiF6dCJyJiRxbFpvDNmv0AvNOvOVUqepicSEQcgQqdiIidOJZp5ekftwBw/1W16Vwv0OREIuIoVOhEROyAYRiM/nFL0RIlT0c3MDuSiDgQFToRETswbW0iC2OP4OHmwvv9W2iJEhG5LCp0IiImiz+SySu/7ABgdHQkkcE+JicSEUejQiciYqLcfBuPf7+ZnDwbneoGcF/HcLMjiYgDUqETETHRBwt3sS0pHT9vd97p1xwXFy1RIiKXT4VORMQkG/ef4NMlCQCMv6UpQT5eJicSEUelQiciYoLs3HxG/RCDzYBbW9XguqYhZkcSEQemQiciYoLxv8ay73g2Ib5ejLuxsdlxRMTBqdCJiJSxZbuOFl0N4q3bmuNbwd3kRCLi6FToRETKUFp2XtHVIAZ1DKdTvQCTE4lIeaBCJyJShsbN2UZyeg4RARUZHR1pdhwRKSdU6EREysgvWw4zO+YQLhZ4p19zKnjoahAiUjJU6EREysCR9Byem70VgOHd69KyVhWTE4lIeaJCJyJSygzDYMzMrZzIzqNxdR8evbqe2ZFEpJxRoRMRKWU/bDjAotgjeLi68G6/Fni46a1XREqW3lVERErRgdRsXpq7A4Ane9WnQXBlkxOJSHmkQiciUkpsNoOnf9xCVm4BbcOrMLhThNmRRKSccjM7gEhx8vLySE5OJjs7m8DAQPz9/c2OVCosuh57uTRtXSKr9xzHy92Ft29vjquL/keLSOnQCJ3YnYyMDD799FO6du2Kj48P4eHhNGzYkMDAQMLCwhgyZAjr1683O6ZIsQ6kZjP+150AjI6OJKxqRZMTiUh5pkInduXdd98lPDycKVOm0LNnT2bPnk1MTAy7du1i9erVjBs3jvz8fK699lqio6PZvXu32ZFFzmEYBqN/2kJ2bgHtwv25Nyrc7EgiUs7pkKvYlfXr17Ns2TIaNz7/xcrbtWvH/fffz8SJE5kyZQrLly+nXj0tASH25dt1iaxKKDzU+sZtzXDRoVYRKWUqdGJXpk+fXvR5RkYGlSuff0agp6cnw4YNK6tYIpfsQGo2r/1SeKj1qV6R1A7QoVYRKX065Cp2q3PnziQnJ5sdQ+SSFS4g/P9Zrfd1DDc7kog4CRU6sVstW7akffv2xMbGnnF7TEwM119/vUmpRC5s+roDrIw/jqebC2/e1lyHWkWkzKjQid2aMmUKgwYNolOnTqxYsYJdu3bRr18/Wrdujatr6VzUfN++fQwePJjatWtToUIF6tSpw7hx48jNzS12v5ycHIYPH07VqlWpVKkSffv2JSUlpVQyin06eCKbV38pXED4qV4NdKhVRMqUzqETu/biiy/i6enJNddcQ0FBAT169GD16tW0a9euVO4vNjYWm83GZ599Rt26ddm2bRtDhgwhKyuLt99++4L7PfHEE/zyyy/MmDEDX19fHnnkEW699VZWrlxZKjnFvhiGwdiZW8nKLaB1WBXuu6q22ZFExMmo0IndSklJ4bXXXuOLL76gUaNGxMbGMmjQoFIrcwDR0dFER0cXfR0REUFcXByffvrpBQtdWloakydP5ttvv+Xqq68GCkcXGzZsyJo1a+jQoUOp5RX78N36AyzffQxPNxfeuq2ZFhAWkTKnQ65it2rXrs2yZcuYMWMGGzdu5KeffmLo0KG89dZbZZojLS2t2CtUbNy4kby8PHr27Fl0W2RkJLVq1WL16tUX3M9qtZKenk56ejpWa/GHdMV+JZ08xatFs1obEBFYyeREIuKMVOjEbn355Zds3ryZ3r17A4WjZ4sXL+a9995j+PDhZZIhPj6eCRMm8OCDD15wm+TkZDw8PPDz8zvj9qCgoGJn6Y4fPx5fX198fX15p5jDuWK/DMNgzE9byLTm06qWnw61iohpVOjEbvXv3/+c21q1asWqVatYtGjRZf2sMWPGYLFYiv04ezZtUlIS0dHR3H777QwZMuRfPZbzGTt2LGlpaaSlpTHqySdL/OdL6Zux4SDLdx/Dw82Ft3StVhExkc6hE4cTHh7OqlWrLmufUaNGMWjQoGK3iYiIKPr80KFDdO/enY4dO/L5558Xu19wcDC5ubmcPHnyjFG6lJQUgoODL7ifp6cnnp6ef3/ucfEHIXblSHoOr/w9q3XUNfWpo0OtImIiFTqxK4mJidSqVeui21WpUgUoHEWrUaPGRbcPDAwkMDDwkjIkJSXRvXt3WrduzZQpU3BxKX4gu3Xr1ri7u7Nw4UL69u0LQFxcHImJiURFRV3SfYrj+c/c7aTn5NO0hi+DO+lQq4iYS4dcxa60bduWBx98kPXr119wm7S0NL744guaNGnCTz/9VKL3n5SURLdu3ahVqxZvv/02R48eJTk5+Yxz4ZKSkoiMjGTdunUA+Pr6MnjwYEaOHMnixYvZuHEj9913H1FRUZrhWk79sT2ZX7cm4+pi4fW+TXFz1VupiJhLI3RiV3r37k2lSpW45ppr8PLyonXr1lSvXh0vLy9OnDjBjh072L59O61ateLNN98s8StGzJ8/n/j4eOLj46lZs+YZ3zMMA4C8vDzi4uLIzs4u+t57772Hi4sLffv2xWq10qtXLz755JMSzSb2IT0njxd+3gbA0C4RNK7ua3IiERGwGP/8lRKxAx4eHhw4cIDKlSsTGBjIgAEDOH78OKdOnSIgIICWLVvSq1cvmjRpYnbUEvXWH7FM+H0rB97vR1paGj4+PmZHkgt4dtZWpq1NJLyqN78/3gUv99K5aomIyOXQCJ3YlerVqxMTE0OvXr04deoUr732GtWqVTM7lggA6/amMm1tIgDjb22mMicidkMnfohdGTVqFDfeeCOdO3fGYrEwbdo01q9fz6lTp8yOJk4uJ6+AMT9tAWBAu1Ci6lQ1OZGIyP+p0IldefTRR9mwYQPR0dEYhsHHH39MVFQUPj4+NGzYkP79+/P666/z22+/mR1VnMxHi+LZcyyLwMqejLmuodlxRETOoEOuYneaNWtGs2bNmDp1KqtXr6ZixYps2bKFmJgYYmJi+Pnnn3n11VfJyMgwO6o4iZ2H05m4NAGAl29ujG8Fd5MTiYicSYVO7Nbu3buLPm/fvj3t27cv+lpzeaSsFNgKL++VbzPo1TiI6CYhZkcSETmHDrmKQ7JYdIklKRtTV+3jr4NpVPZy46Wby9fsahEpP1ToROyABRVUe3QgNZu3/4gD4JnrGxLk42VyIhGR81OhExE5D8MweHb2Nk7lFdC+tj93tAk1O5KIyAWp0ImInMfsmCSW7TqKh5sL429tiouLRlFFxH6p0ImInOV4ppWX5u4AYESPekQEVjI5kYhI8VToRETO8tK8HZzIzqNhiA9Du0SYHUdE5KJU6ERETrNs11F+jjmEiwXe6NsUd1e9TYqI/dM7lYjI33LyCnj+520A3NsxnGY1/cwNJCJyiVToRET+9sniePYfzybIx5OR19Q3O46IyCVToRMRAeKPZPLp35f3+s+Njanspct7iYjjUKETEadnGAbPzd5KXoHB1ZHViG4SbHYkEZHLokInIk5v5qYk1uxJxcvdhRdvaqxLy4mIw1GhExGndiIrl1d/3QnAiB71CfX3NjmRiMjlU6ETEaf2xu+xpGblUj+oEg90rm12HBGRK6JCJyJOa/2+VL5bfwCAV2/RmnMi4rj07iUiTik338azs7YCcEebUNqG+5ucSETkyqnQiYhTmrxiL7tSMvGv6MGY6yLNjiMi8q+o0ImI0zmQms0HC3cB8Mz1DalS0cPkRCIi/44KnYg4FcMweOHnbeTk2Whf25++rWqYHUlE5F9ToRMRp/L7tmQWxx3F3dXCq7c01ZpzIlIuqNCJiNPIsubz0rwdADzYpQ51q1UyOZGISMlQoRMRpzFhUTyH03KoWaUCj1xd1+w4IiIlRoVORJxC/JFMJq/YA8C4Gxvj5e5qciIRkZKjQici5Z5hGPxnznbyCgyujqxGz4bVzI4kIlKiVOhEpNz7dWsyK+KP4eHmwrgbG2kihIiUOyp0InZA/aL0ZFnzeeWXwokQw7rWIaxqRZMTiYiUPBU6ESnXTp8I8XC3OmbHEREpFSp0IlJuxR/JZNLywokQ/9FECBEpx1ToRKRc+mciRL7t74kQjYLMjiQiUmpU6ESkXDp7IoSISHmmQici5U6WNZ+X/74ixEOaCCEiTkCFTkTKnQmL4klOzyHUvwIPaSKEiDgBFToRKVfij2QUTYQYd4MmQoiIc1ChE5FywzAMxv09EaKHJkKIiBNRoRORcuPXrcmsjD/+90SIxmbHEREpMyp0IqfZt28fgwcPpnbt2lSoUIE6deowbtw4cnNzi92vW7duWCyWMz6GDRtWRqkFzp0IUauqt8mJRETKjpvZAUTsSWxsLDabjc8++4y6deuybds2hgwZQlZWFm+//Xax+w4ZMoSXXnqp6GtvbxWKsvTRYk2EEBHnpUIncpro6Giio6OLvo6IiCAuLo5PP/30ooXO29ub4ODg0o4o57HvWBaTl+8F4AVNhBARJ6RDriIXkZaWhr+//0W3mzZtGgEBATRp0oSxY8eSnZ1d7PZWq5X09HTS09OxWq0lFdcpvfLLDnILbHSuF0DPhtXMjiMiUuY0QidSjPj4eCZMmHDR0bk777yTsLAwqlevzpYtWxg9ejRxcXHMnDnzgvuMHz+eF198EQDfznfj0/qmEs3uLJbuOsqCnUdwc7Ew7sZGWCwWsyOJiJQ5i2EYhtkhRErbmDFjeOONN4rdZufOnURGRhZ9nZSURNeuXenWrRuTJk26rPtbtGgRPXr0ID4+njp1zn8+l9VqLRqZ+2jpPiYuiuPA+/1IS0vDx8fnsu7PWeUV2Ih+fxkJR7MY3Kk2z9+gS3yJiHPSCJ04hVGjRjFo0KBit4mIiCj6/NChQ3Tv3p2OHTvy+eefX/b9tW/fHqDYQufp6Ymnp2fR53L5vlq1j4SjWVSt6MFjPeqZHUdExDQqdOIUAgMDCQwMvKRtk5KS6N69O61bt2bKlCm4uFz+qaYxMTEAhISEXPa+cmmOZlj5YMFuAJ6OboBvBXeTE4mImEeTIkROk5SURLdu3ahVqxZvv/02R48eJTk5meTk5DO2iYyMZN26dQAkJCTw8ssvs3HjRvbt28ecOXMYOHAgXbp0oVmzZmY9lHLv7T/iyLDm07SGL7e3DjU7joiIqTRCJ3Ka+fPnEx8fT3x8PDVr1jzje/+cbpqXl0dcXFzRLFYPDw8WLFjA+++/T1ZWFqGhofTt25fnnnuuzPM7iy0HT/LDxgMA/OemRri4aCKEiDg3FTqR0wwaNOii59qFh4dz+lyi0NBQli5dWsrJ5B+GYfCfOdsxDLilZQ1ah118SRkRkfJOh1xFxKHMjkliU+JJvD1cGXNd5MV3EBFxAip0IuIwMq35jP81FoDh3esS5ONlciIREfugQiciDuPTJfEcybASVtWbwZ1qmx1HRMRuqNCJ2AGd0n9xB1Kz+eLv67U+c31DXa9VROQ0KnQi4hBe/z2W3HwbHetU5dpGQWbHERGxKyp0ImL31u9L5Zcth3GxwPM36HqtIiJnU6ETEbtmsxm8NHcHAHe0rUXDEF3nVkTkbCp0ImLXZm5OYmtSGpU83Rh1bX2z44iI2CUVOhGxW1nWfN78vXCZkkevrktAJU+TE4mI2CcVOhGxWxOXJnAkw0otf28GXRVudhwREbulQicidungiWw+X7YHKFymxNNNy5SIiFyICp2I2KU3fo/Dmm+jQ4Q/vRprmRIRkeKo0ImI3dm4P5W5fx3ComVKREQuiQqdiNiVM5YpaRNK4+q+JicSEbF/KnQiYldmxyTx18F/lilpYHYcERGHoEInInbjVG4Bb/0RB8DD3esQWFnLlIiIXAoVOhGxG5NX7OFwWg41/Cpw/1W1zY4jIuIwVOhExC4cycjh0yUJADwd3QAvdy1TIiJyqVToRMQuvL9gN1m5BTSr6cuNzaqbHUdExKGo0ImI6XalZPDdukQAnuvdCBcXLVMiInI5VOhExHTjf92JzYBejYNoV9vf7DgiIg5HhU5ETLVi9zEWxx3FzcXC6OhIs+OIiDgkFToRMU2BzeCVXwoXEb67QxgRgZVMTiQi4phU6ETEND9tOkhscgaVvdx4rEc9s+OIiDgsFToRMUV2bj5v/72I8KNX18W/oofJiUREHJcKnYiY4vNleziSYaVmlQoMjAo3O46IiENToRORMnckPYfPlu4BYHR0pBYRFhH5l1ToROyBxbnWXXvnz12cyiugRagfNzQLMTuOiIjDU6ETkTIVl5zBjI0HAHiud0MsTlZmRURKgwqdiJSpN36PxWZAdONg2oRrEWERkZKgQiciZWZ1wnEWxR7B1cXC09ENzI4jIlJuqNCJSJkwDIPXf9sJwIB2oVpEWESkBKnQiUiZ+GXrYf46mIa3hysjetQ3O46ISLmiQicipS4338abvxcuIjy0SwSBlT1NTiQiUr6o0IlIqft27X4SU7MJqOTJkM4RZscRESl3VOhEpFRl5OTx4aJ4AB7vWY+Knm4mJxIRKX9U6ESkVH22dA+pWblEBFTkjrahZscRESmXVOhEpNSkpOcwaUXhJb6ejo7E3VVvOSIipUHvriJSat6bv4ucPButw6rQq3GQ2XFERMotFToRKRW7UzL4YUPhJb7GXhepS3yJiJQiFTqRs9x0003UqlULLy8vQkJCuOeeezh06FCx++Tk5DB8+HCqVq1KpUqV6Nu3LykpKWWU2D79c4mvaxsF6RJfIiKlTIVO5Czdu3fnhx9+IC4ujp9++omEhARuu+22Yvd54oknmDt3LjNmzGDp0qUcOnSIW2+9tYwS25/1+1JZsPOfS3xFmh1HRKTc0/oBImd54oknij4PCwtjzJgx9OnTh7y8PNzd3c/ZPi0tjcmTJ/Ptt99y9dVXAzBlyhQaNmzImjVr6NChQ5lltweGYfDGb7EA9GtTk7rVdIkvEZHSphE6kWKkpqYybdo0OnbseN4yB7Bx40by8vLo2bNn0W2RkZHUqlWL1atXX/BnW61W0tPTSU9Px2q1lnh2syyOO8KG/SfwdHPRJb5ERMqICp3IeYwePZqKFStStWpVEhMT+fnnny+4bXJyMh4eHvj5+Z1xe1BQEMnJyRfcb/z48fj6+uLr68sbb7xeUtFNVWAzii7xNeiqcIJ9vUxOJCLiHFToxCmMGTMGi8VS7EdsbGzR9k899RSbN2/mzz//xNXVlYEDB2IYRolmGjt2LGlpaaSlpTF69JgS/dlmmfNXErHJGfh4ufFQ1zpmxxERcRo6h06cwqhRoxg0aFCx20RE/P8aowEBAQQEBFC/fn0aNmxIaGgoa9asISoq6pz9goODyc3N5eTJk2eM0qWkpBAcHHzB+/P09MTT07Poc0dnzS/gnT93ATCsWx38vD1MTiQi4jxU6MQpBAYGEhgYeEX72mw2gAue59a6dWvc3d1ZuHAhffv2BSAuLo7ExMTzFsDyavraRA6eOEW1yp7c17G22XFERJyKCp3IadauXcv69evp1KkTVapUISEhgeeff546deoUlbOkpCR69OjB119/Tbt27fD19WXw4MGMHDkSf39/fHx8ePTRR4mKinKaGa6Z1nwmLIoH4LEe9ajg4WpyIhER56JCJ3Iab29vZs6cybhx48jKyiIkJITo6Giee+65osOieXl5xMXFkZ2dXbTfe++9h4uLC3379sVqtdKrVy8++eQTsx5GmZu8fC/Hs3IJr+rNHW1DzY4jIuJ0LEZJn+ktIpft3fm7eP/Xvzjwfj/S0tLw8fExO9IlO55ppcubi8nKLWDCgJbc2Ly62ZFERJyOZrmK2AFHvsrpx4sTyMotoEkNH3o3DTE7joiIU1KhE5ErdvBENv9dsx+Ap3tF4uLiyNVURMRxqdCJyBV7b/5ucgtsdKxTlc71AsyOIyLitFToROSK7ErJYObmgwA8HR2JxaLRORERs6jQicgVeefPOAwDohsH0yLUz+w4IiJOTYVORC7bXwdO8sf2FCwWGHVtfbPjiIg4PRU6Eblsb/8ZB8AtLWpQL6iyyWlERESFTkQuy9o9x1m++xhuLhYe76nRORERe6BCJyKXzDCMotG5O9qGUquqt8mJREQEVOhE5DIs3XWU9ftO4OnmwqNX1zM7joiI/E2FTkQuyemjcwOjwgj29TI5kYiI/EOFTkQuye/bktmWlE5FD1ce6lbX7DgiInIaFToRuagCm8E783cBMLhTbfwrepicSERETqdCJyIXNXtzEvFHMvGt4M4DXSLMjiMiImdRoRORYuXm23h/YeHo3LCudfDxcjc5kYiInE2FTkSK9cOGAxxIPUVAJU/u7RhmdhwRETkPFToRuaCcvAImLNoNwKNX18Xbw83kRCIicj4qdCJyQd+s3k9KupUafhXo3y7U7DgiInIBKnQicl6Z1nw+XZoAwIie9fB0czU5kYiIXIgKnYic19SVe0nNyiUioCK3tqxhdhwRESmGCp2InCM9J4/Pl+0BCkfn3Fz1ViEiYs/0Li0i5/hyxV7Sc/KpV60SNzSrbnYcERG5CBU6ETlDWnYek5fvBeDxnvVxdbGYnEhERC5GhU5EzjBpxR4yrPlEBlfmuibBZscREZFLoEInYgcsdjIIdiIrly9X/H90zkWjcyIiDkGFTkSKfL58D1m5BTSu7kOvxkFmxxERkUukQiciABzLtPLVqn0APNGzPhZ7GTYUEZGLUqETEQA+W5pAdm4BzWr60qNhNbPjiIjIZVChExGOpOfw9er9ADxxjUbnREQcjQqdiPDp0gSs+TZa1vKjW/1As+OIiMhlUqETcXLJaTlMW5sIwEiNzomIOCQVOhEn98mSeHLzbbQNr0KnugFmxxERkSugQifixJJOnuK7dQcAnTsnIuLIVOhEnNjHi+PJLbARFVGVjnU0Oici4qhU6ESc1IHUbH5Y///RORERcVwqdCJO6qNF8eTbDDrXC6BdbX+z44iIyL+gQifihPYfz+LHTQeBwmu2ioiIY1OhE3FCExbFU2Az6Fo/kNZhVcyOIyIi/5IKnYiT2X88i1mbkwB4vGc9k9OIiEhJUKETcTIfLy4cnetSP5CWtTQ6JyJSHqjQiZzlpptuolatWnh5eRESEsI999zDoUOHit2nW7duWCyWMz6GDRtWRokv3YHUbGZuKhydG9FDo3MiIuWFCp3IWbp3784PP/xAXFwcP/30EwkJCdx2220X3W/IkCEcPny46OPNN98sg7SX5+PF/5/ZqnPnRETKDzezA4jYmyeeeKLo87CwMMaMGUOfPn3Iy8vD3d39gvt5e3sTHBxcFhGvyIHUbH7cWDizVaNzIiLli0boRIqRmprKtGnT6NixY7FlDmDatGkEBATQpEkTxo4dS3Z2drHbW61W0tPTSU9Px2q1lmTs8/pkSQL5NoOr6lalTbjWnRMRKU9U6ETOY/To0VSsWJGqVauSmJjIzz//XOz2d955J//9739ZvHgxY8eO5ZtvvuHuu+8udp/x48fj6+uLr68v48ePL8n450g6eYofNxZeFWJED607JyJS3lgMwzDMDiFS2saMGcMbb7xR7DY7d+4kMjISgGPHjpGamsr+/ft58cUX8fX1Zd68eZd88fpFixbRo0cP4uPjqVOnznm3sVqtRSNzny7fz8cLYjnwfj/S0tLw8fG5jEd3cc/O2sq0tYlERVRl+tAOJfqzRUTEfDqHTpzCqFGjGDRoULHbREREFH0eEBBAQEAA9evXp2HDhoSGhrJmzRqioqIu6f7at28PUGyh8/T0xNPTs+jz0nLo5Cl+2PD36JzWnRMRKZdU6MQpBAYGEhgYeEX72mw2gMs6zy0mJgaAkJCQK7rPkvTpkgTyCgza1/anQ0RVs+OIiEgp0Dl0IqdZu3YtH330ETExMezfv59FixYxYMAA6tSpUzQ6l5SURGRkJOvWrQMgISGBl19+mY0bN7Jv3z7mzJnDwIED6dKlC82aNbuk+7VwaYdyL9fhtFN8v16jcyIi5Z0KnchpvL29mTlzJj169KBBgwYMHjyYZs2asXTp0qLDonl5ecTFxRXNYvXw8GDBggVce+21REZGMmrUKPr27cvcuXPNfCgATFySQG6BjXbh/kRpdE5EpNzSIVeR0zRt2pRFixYVu014eDinzyUKDQ1l6dKlpR3tsqWk5zD9tNG5S53QISIijkcjdCLl1KdLEsjNt9EmrAod62h0TkSkPFOhEymHjmTkMH1dIqDRORERZ6BCJ1IOTVq+F2u+jVa1/OhUN8DsOCIiUspU6ETKmdSsXP67Zj8Aj/bQ6JyIiDNQoRMpZ6as3Et2bgFNavjQrf6Vrb0nIiKORYVOpBxJO5XH1JX7AHiku0bnRESchQqdSDnyzep9ZFjzqR9UiWsbBZkdR0REyogKnUg5kWXNZ/KKvQAM714XFxeNzomIOAsVOpFyYtra/ZzIzqN2QEVuaFbd7DgiIlKGVOhEyoGcvAI+X1Y4OvdQtzq4anRORMSpqNCJlAPfrz/AsUwrNfwqcEvLGmbHERGRMqZCJ+LgcvNtTFyaAMCwbnVwd9WvtYiIs9E7v4iDm7npIIfTcqhW2ZPbW9c0O46IiJhAhU7EgeUX2PhkSeHo3NAuEXi5u5qcSEREzKBCJ+LA5m45RGJqNv4VPbizfS2z44iIiElU6EQclM1m8NGieAAGd6qNt4ebyYlERMQsKnQiDur37ckkHM3Cx8uNgVFhZscRERETqdCJOCDDMJjw9+jcoKtqU9nL3eREIiJiJhU6EQe0KPYIOw+nU9HDlfs6hpsdR0RETKZCJ+JgTh+duzsqjCoVPUxOJCIiZlOhE3EwqxKOE3PgJJ5uLjzQKcLsOCIiYgdU6ETsgOUyLr36yZLC0bn+bUMJrOxZSolERMSRqNCJOJC/DpxkZfxx3FwsDOmi0TkRESmkQifiQP4ZnbupRXVqVvE2OY2IiNgLFToRBxF/JIM/tqcA8FDXOianERERe6JCJ+IgJi7dA8C1jYKoF1TZ5DQiImJPVOhEHEDSyVPM3pwEwEPdNDonIiJnUqETcQBfLNtDvs0gKqIqLWtVMTuOiIjYGRU6ETt3PNPKd+sTAXi4u0bnRETkXCp0InZu6qp95OTZaFrDl051A8yOIyIidkiFTsSOZeTk8dWqfQA83K0OlstZgVhERJyGCp2IHZu+LpH0nHwiAivSq3Gw2XFERMROqdCJ2ClrfgGTlu8FYFjXOri4aHRORETOT4VOxE79tDGJIxlWQny96NOihtlxRETEjqnQidih/AIbny1LAOCBzhF4uOlXVURELkx/JUTs0K/bktl/PJsq3u4MaBdqdhwREbFzKnQidsYwDD5dUjg6N6hjbbw93ExOJCIi9k6FTsTOLI8/xs7D6VT0cOXejmFmxxEREQegQidiZyYvK5zZemf7Wvh5e5icRkREHIEKnYid2Zh4Ag9XFx7oHGF2FBERcRAqdCIXYLVaadGiBRaLhZiYmGK3zcnJYfjw4VStWpVKlSrRt29fUlJSrvi+b21VgyAfryveX0REnIsKncgFPP3001SvXv2Stn3iiSeYO3cuM2bMYOnSpRw6dIhbb731iu7XxQIPdq1zRfuKiIhzUqETOY/ffvuNP//8k7fffvui26alpTF58mTeffddrr76alq3bs2UKVNYtWoVa9asuez7vqZhELUDKl5JbBERcVIqdCJnSUlJYciQIXzzzTd4e3tfdPuNGzeSl5dHz549i26LjIykVq1arF69+pLu8+CJ7KLPB3euffmhRUTEqanQiZzGMAwGDRrEsGHDaNOmzSXtk5ycjIeHB35+fmfcHhQURHJy8gX3s1qtpKenk56eTkCF//8qNqrue0XZRUTEeanQiVMYM2YMFoul2I/Y2FgmTJhARkYGY8eOLfVM48ePx9fXF19fX8b2jeLkim9L/T5FRKR8shiGYZgdQqS0HT16lOPHjxe7TUREBP369WPu3LlYLJai2wsKCnB1deWuu+7iq6++Ome/RYsW0aNHD06cOHHGKF1YWBiPP/44TzzxxHnvz2q1YrVai75OT08nNDSUtLQ0fHx8LvMRioiIM1OhEzlNYmIi6enpRV8fOnSIXr168eOPP9K+fXtq1qx5zj5paWkEBgYyffp0+vbtC0BcXByRkZGsXr2aDh06XNJ9p6en4+vrq0InIiKXTReJFDlNrVq1zvi6UqVKANSpU6eozCUlJdGjRw++/vpr2rVrh6+vL4MHD2bkyJH4+/vj4+PDo48+SlRU1CWXORERkX9DhU7kMuXl5REXF0d29v9npr733nu4uLjQt29frFYrvXr14pNPPjExpYiIOBMdchWxEzrkKiIiV0qzXEVEREQcnAqdiIiIiINToRMRERFxcCp0IiIiIg5OhU5ERETEwanQiYiIiDg4FToRERERB6dCJyIiIuLgVOhEREREHJwKnYiIiIiDU6ETERERcXAqdCIiIiIOToVORERExMGp0ImIiIg4OBU6EREREQdnMQzDMDuEiIBhGGRkZFC5cmUsFovZcURExIGo0ImIiIg4OB1yFREREXFwKnQiIiIiDk6FTkRERMTBqdCJiIiIODgVOhEREREHp0InIiIi4uBU6EREREQc3P8AM8w+X+zF5G4AAAAASUVORK5CYII=\n" }, "metadata": {} }, @@ -422,11 +495,11 @@ "output_type": "execute_result", "data": { "text/plain": [ - "" + "" ] }, "metadata": {}, - "execution_count": 72 + "execution_count": 48 } ] }, @@ -441,9 +514,9 @@ "height": 38 }, "id": "KUz6LsoNYM-t", - "outputId": "5ffa8762-1012-42a8-886e-88ab155aa569" + "outputId": "82744428-c1b7-4162-ad7f-a6a55311d822" }, - "execution_count": 73, + "execution_count": 49, "outputs": [ { "output_type": "execute_result", @@ -454,7 +527,7 @@ "text/latex": "$\\displaystyle x$" }, "metadata": {}, - "execution_count": 73 + "execution_count": 49 } ] }, @@ -469,9 +542,9 @@ "height": 90 }, "id": "mepkf0ulYQLC", - "outputId": "f46221f3-045b-4842-94d7-152d41c352b4" + "outputId": "d6530503-d49e-4422-b8c0-cb03b43b91c3" }, - "execution_count": 74, + "execution_count": 50, "outputs": [ { "output_type": "execute_result", @@ -482,7 +555,7 @@ "text/latex": "$\\displaystyle \\begin{cases} \\sin{\\left(\\pi x \\right)} & \\text{for}\\: x < 0 \\\\1.5 & \\text{for}\\: x = 0 \\\\- \\left(x - 2\\right)^{2} & \\text{for}\\: x > 0 \\end{cases}$" }, "metadata": {}, - "execution_count": 74 + "execution_count": 50 } ] }, @@ -497,9 +570,9 @@ "height": 37 }, "id": "GgiWWUZsYRCm", - "outputId": "1d29273e-f3c1-47d8-ec5e-046d64abac2b" + "outputId": "5f9027ff-ea4d-4f02-d653-19a16bfca977" }, - "execution_count": 75, + "execution_count": 51, "outputs": [ { "output_type": "execute_result", @@ -510,7 +583,7 @@ "text/latex": "$\\displaystyle 1.5$" }, "metadata": {}, - "execution_count": 75 + "execution_count": 51 } ] }, @@ -533,19 +606,19 @@ "height": 447 }, "id": "IOgX2x-bYR4Y", - "outputId": "5e419f99-5ff8-42a9-fb37-6561ad7e469b" + "outputId": "0ac55d45-de0e-4418-d140-462c722a8382" }, - "execution_count": 76, + "execution_count": 52, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ - "[]" + "[]" ] }, "metadata": {}, - "execution_count": 76 + "execution_count": 52 }, { "output_type": "display_data", @@ -558,6 +631,498 @@ "metadata": {} } ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 4: infinite discontinuity\n", + "\n", + "resolution = .1\n", + "xx = np.arange(-2, 2, resolution)\n", + "y = 3/( 1 - xx**2)\n", + "xx, y" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "g1GO3xdNfETD", + "outputId": "1709db51-3a77-428a-81d7-43e0b08f2169" + }, + "execution_count": 53, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(array([-2.00000000e+00, -1.90000000e+00, -1.80000000e+00, -1.70000000e+00,\n", + " -1.60000000e+00, -1.50000000e+00, -1.40000000e+00, -1.30000000e+00,\n", + " -1.20000000e+00, -1.10000000e+00, -1.00000000e+00, -9.00000000e-01,\n", + " -8.00000000e-01, -7.00000000e-01, -6.00000000e-01, -5.00000000e-01,\n", + " -4.00000000e-01, -3.00000000e-01, -2.00000000e-01, -1.00000000e-01,\n", + " 1.77635684e-15, 1.00000000e-01, 2.00000000e-01, 3.00000000e-01,\n", + " 4.00000000e-01, 5.00000000e-01, 6.00000000e-01, 7.00000000e-01,\n", + " 8.00000000e-01, 9.00000000e-01, 1.00000000e+00, 1.10000000e+00,\n", + " 1.20000000e+00, 1.30000000e+00, 1.40000000e+00, 1.50000000e+00,\n", + " 1.60000000e+00, 1.70000000e+00, 1.80000000e+00, 1.90000000e+00]),\n", + " array([-1.00000000e+00, -1.14942529e+00, -1.33928571e+00, -1.58730159e+00,\n", + " -1.92307692e+00, -2.40000000e+00, -3.12500000e+00, -4.34782609e+00,\n", + " -6.81818182e+00, -1.42857143e+01, 1.68884986e+15, 1.57894737e+01,\n", + " 8.33333333e+00, 5.88235294e+00, 4.68750000e+00, 4.00000000e+00,\n", + " 3.57142857e+00, 3.29670330e+00, 3.12500000e+00, 3.03030303e+00,\n", + " 3.00000000e+00, 3.03030303e+00, 3.12500000e+00, 3.29670330e+00,\n", + " 3.57142857e+00, 4.00000000e+00, 4.68750000e+00, 5.88235294e+00,\n", + " 8.33333333e+00, 1.57894737e+01, -5.62949953e+14, -1.42857143e+01,\n", + " -6.81818182e+00, -4.34782609e+00, -3.12500000e+00, -2.40000000e+00,\n", + " -1.92307692e+00, -1.58730159e+00, -1.33928571e+00, -1.14942529e+00]))" + ] + }, + "metadata": {}, + "execution_count": 53 + } + ] + }, + { + "cell_type": "code", + "source": [ + "plt.plot(xx, y)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 462 + }, + "id": "AoywMl3Dfwx-", + "outputId": "618527e9-d232-4c3f-a9f9-0b96c61988ae" + }, + "execution_count": 54, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 54 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# lets try with linspace\n", + "xx = np.linspace(-2, 2, 1000)\n", + "y = 3/( 1 - xx**2)\n", + "# xx, y\n", + "plt.plot(xx, y, 'k')" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "MJGo0Tfgf4jG", + "outputId": "8d779fa6-b7e3-42d3-e32c-4f4283a505f5" + }, + "execution_count": 55, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 55 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "plt.ylim([-20, 20])\n", + "plt.plot(xx, y, 'k')" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "f8DDR7fekfTg", + "outputId": "f83b7f7a-01cb-4ac9-fa4e-32bc784b5105" + }, + "execution_count": 56, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 56 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# impliment same in sympy\n", + "sfx = 3 / (1 - x**2)\n", + "sfx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 52 + }, + "id": "QMiq5ztXmhdX", + "outputId": "976c4d44-67dc-45f9-a6c4-f45a23734b55" + }, + "execution_count": 57, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "3/(1 - x**2)" + ], + "text/latex": "$\\displaystyle \\frac{3}{1 - x^{2}}$" + }, + "metadata": {}, + "execution_count": 57 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# use sympy's ability to identify singularities and continuous domains\n", + "sym.calculus.util.continuous_domain(sfx, x, sym.Interval(-2, 2))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 37 + }, + "id": "swoTFaQkmtXa", + "outputId": "2f49ab95-5d23-4623-cd80-4ffbbef57af4" + }, + "execution_count": 58, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "Union(Interval.Ropen(-2, -1), Interval.open(-1, 1), Interval.Lopen(1, 2))" + ], + "text/latex": "$\\displaystyle \\left[-2, -1\\right) \\cup \\left(-1, 1\\right) \\cup \\left(1, 2\\right]$" + }, + "metadata": {}, + "execution_count": 58 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# singlarities OR infinite discontinuities\n", + "sym.singularities(sfx, x)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 37 + }, + "id": "sM3td1cdnaWF", + "outputId": "86297421-32d2-48f3-d30e-5ee5e94c8cb3" + }, + "execution_count": 59, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "{-1, 1}" + ], + "text/latex": "$\\displaystyle \\left\\{-1, 1\\right\\}$" + }, + "metadata": {}, + "execution_count": 59 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 5: Oscillating discontinuity\n", + "xx = np.linspace(-1, 2, 123)\n", + "fx = np.sin(1 / (xx - 1))\n", + "plt.plot(xx, fx)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "28TpLnX_nqXI", + "outputId": "75240e24-ea09-490e-8708-fdfb39d8012c" + }, + "execution_count": 60, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 60 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "xx = np.linspace(-10, 20, 123)\n", + "# not a sin wave when xx is in denominator\n", + "fx = np.sin(1 / (xx - 1))\n", + "plt.plot(xx, fx)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "BXdbx1F7ziIR", + "outputId": "4d51c686-2959-4747-85fb-66ebae921460" + }, + "execution_count": 61, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 61 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "xx = np.linspace(-10, 20, 123)\n", + "# we get sin wave when x is in numenator\n", + "fx = np.sin((xx - 1))\n", + "plt.plot(xx, fx)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "ks6Fz83Rz0AW", + "outputId": "d036d82b-9e1b-4261-e7a9-7ed7deb9c6fd" + }, + "execution_count": 62, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 62 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "xx = np.linspace(.95, 1.05, 1230)\n", + "# we get sin wave when x is in numenator\n", + "fx = np.sin(1 / (xx - 1))\n", + "plt.plot(xx, fx)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "2z6622ul0K-W", + "outputId": "365ef7cd-dcc0-49aa-84f2-edf45066eb48" + }, + "execution_count": 63, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": {}, + "execution_count": 63 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# implement same in sympy\n", + "sfx = sym.sin(1 / (x - 1))\n", + "# if domain not speicfied, sympy's default in this case is -10, 10\n", + "sym.plot(sfx)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 504 + }, + "id": "ho-w66KH0hH7", + "outputId": "ca8dd23f-7d79-484d-8939-2987109598db" + }, + "execution_count": 64, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "execution_count": 64 + } + ] + }, + { + "cell_type": "code", + "source": [ + "sfx = sym.sin(1 / (x - 1))\n", + "sym.plot(sfx, (x, -1, 2))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 504 + }, + "id": "aYGTPm7205dA", + "outputId": "05399306-bd52-4fde-be16-bb1b1a027a77" + }, + "execution_count": 65, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "execution_count": 65 + } + ] } ] } \ No newline at end of file From b79e5adfd97378a1ea24122b036d80e1c6ec8438 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Tue, 13 Jun 2023 21:38:04 +0400 Subject: [PATCH 24/25] Delete discontinuities_cc_e01.ipynb --- .../functions/discontinuities_cc_e01.ipynb | 322 ------------------ 1 file changed, 322 deletions(-) delete mode 100644 practice/functions/discontinuities_cc_e01.ipynb diff --git a/practice/functions/discontinuities_cc_e01.ipynb b/practice/functions/discontinuities_cc_e01.ipynb deleted file mode 100644 index 5f8c999..0000000 --- a/practice/functions/discontinuities_cc_e01.ipynb +++ /dev/null @@ -1,322 +0,0 @@ -{ - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "provenance": [], - "authorship_tag": "ABX9TyP94AzYeFJKqwWUbmqXQ9iw", - "include_colab_link": true - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - }, - "language_info": { - "name": "python" - } - }, - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "id": "view-in-github", - "colab_type": "text" - }, - "source": [ - "\"Open" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "id": "oDsQY96sQfSi" - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import sympy as sym\n", - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "code", - "source": [ - "xx = np.arange(-1, 2)\n", - "# default skip value is 1\n", - "xx" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "tKogb0UmQwJ4", - "outputId": "2d44473d-593d-47df-cd54-14a8d7a0467b" - }, - "execution_count": 22, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "array([-1, 0, 1])" - ] - }, - "metadata": {}, - "execution_count": 22 - } - ] - }, - { - "cell_type": "code", - "source": [ - "resolution = .1\n", - "xx = np.arange(-1, 2, resolution)\n", - "xx" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "vJpnU4cJRA8e", - "outputId": "fc74f062-2bd8-4a48-8ea5-c54927d702b4" - }, - "execution_count": 23, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "array([-1.00000000e+00, -9.00000000e-01, -8.00000000e-01, -7.00000000e-01,\n", - " -6.00000000e-01, -5.00000000e-01, -4.00000000e-01, -3.00000000e-01,\n", - " -2.00000000e-01, -1.00000000e-01, -2.22044605e-16, 1.00000000e-01,\n", - " 2.00000000e-01, 3.00000000e-01, 4.00000000e-01, 5.00000000e-01,\n", - " 6.00000000e-01, 7.00000000e-01, 8.00000000e-01, 9.00000000e-01,\n", - " 1.00000000e+00, 1.10000000e+00, 1.20000000e+00, 1.30000000e+00,\n", - " 1.40000000e+00, 1.50000000e+00, 1.60000000e+00, 1.70000000e+00,\n", - " 1.80000000e+00, 1.90000000e+00])" - ] - }, - "metadata": {}, - "execution_count": 23 - } - ] - }, - { - "cell_type": "code", - "source": [ - "# list of function pieces\n", - "\n", - "# acrosss all values of xx\n", - "y = [0] * 3\n", - "y[0] = np.sin(xx * np.pi)\n", - "y[1] = 1.5 * np.ones(len(xx))\n", - "y[2] = -(xx - 2)**2\n", - "y" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "6DpULA-GRMGC", - "outputId": "98e4a63c-30c7-49a8-b42f-729f62e0e392" - }, - "execution_count": 24, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "[array([-1.22464680e-16, -3.09016994e-01, -5.87785252e-01, -8.09016994e-01,\n", - " -9.51056516e-01, -1.00000000e+00, -9.51056516e-01, -8.09016994e-01,\n", - " -5.87785252e-01, -3.09016994e-01, -6.97573700e-16, 3.09016994e-01,\n", - " 5.87785252e-01, 8.09016994e-01, 9.51056516e-01, 1.00000000e+00,\n", - " 9.51056516e-01, 8.09016994e-01, 5.87785252e-01, 3.09016994e-01,\n", - " 1.45473231e-15, -3.09016994e-01, -5.87785252e-01, -8.09016994e-01,\n", - " -9.51056516e-01, -1.00000000e+00, -9.51056516e-01, -8.09016994e-01,\n", - " -5.87785252e-01, -3.09016994e-01]),\n", - " array([1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5,\n", - " 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5,\n", - " 1.5, 1.5, 1.5, 1.5]),\n", - " array([-9. , -8.41, -7.84, -7.29, -6.76, -6.25, -5.76, -5.29, -4.84,\n", - " -4.41, -4. , -3.61, -3.24, -2.89, -2.56, -2.25, -1.96, -1.69,\n", - " -1.44, -1.21, -1. , -0.81, -0.64, -0.49, -0.36, -0.25, -0.16,\n", - " -0.09, -0.04, -0.01])]" - ] - }, - "metadata": {}, - "execution_count": 24 - } - ] - }, - { - "cell_type": "code", - "source": [ - "# list domains\n", - "x_domains = [0] * 3\n", - "x_domains[0] = xx < 0\n", - "x_domains[1] = np.abs(xx) < resolution/2\n", - "x_domains[2] = xx > 0\n", - "x_domains" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "Gdzj5SARRVOr", - "outputId": "3ff77eb3-5432-48b8-eab2-ca584a516b30" - }, - "execution_count": 25, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "[array([ True, True, True, True, True, True, True, True, True,\n", - " True, True, False, False, False, False, False, False, False,\n", - " False, False, False, False, False, False, False, False, False,\n", - " False, False, False]),\n", - " array([False, False, False, False, False, False, False, False, False,\n", - " False, True, False, False, False, False, False, False, False,\n", - " False, False, False, False, False, False, False, False, False,\n", - " False, False, False]),\n", - " array([False, False, False, False, False, False, False, False, False,\n", - " False, False, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True])]" - ] - }, - "metadata": {}, - "execution_count": 25 - } - ] - }, - { - "cell_type": "code", - "source": [ - "# use absolute value to overcome precision problem\n", - "# one point that is as closet as possible to 0 smaller than our grid spacing \n", - "# i.e. smaller than our resolution\n", - "np.abs(xx) < resolution/2" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "36r0GTxPScF-", - "outputId": "4c8763dd-3434-4bbc-e959-0b056cff0e96" - }, - "execution_count": 26, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "array([False, False, False, False, False, False, False, False, False,\n", - " False, True, False, False, False, False, False, False, False,\n", - " False, False, False, False, False, False, False, False, False,\n", - " False, False, False])" - ] - }, - "metadata": {}, - "execution_count": 26 - } - ] - }, - { - "cell_type": "code", - "source": [ - "for i in range(len(y)):\n", - " plt.plot(xx, y[i])\n", - "\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 435 - }, - "id": "4x6r1Xe8SkOo", - "outputId": "447073bf-90de-432a-d528-059534e79a54" - }, - "execution_count": 27, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "for i in range(len(y)):\n", - " plt.plot(xx[x_domains[i]], y[i][x_domains[i]])\n", - "\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "bT8djXLCVGHt", - "outputId": "9d79995e-318c-46dd-9959-8e7a2919faee" - }, - "execution_count": 28, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "marker = '-o-'\n", - "for i in range(len(y)):\n", - " plt.plot(\n", - " xx[x_domains[i]],\n", - " y[i][x_domains[i]],\n", - " marker[i]\n", - " )\n", - "\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "ama8GjhzU-kk", - "outputId": "43331efa-5c4f-4309-d41a-c60978b52720" - }, - "execution_count": 29, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - } - ] -} \ No newline at end of file From e954a9a19309e96aff4ddd69f23482c8b458bec9 Mon Sep 17 00:00:00 2001 From: Hammad <42832718+HammadArshd@users.noreply.github.com> Date: Wed, 14 Jun 2023 01:17:19 +0400 Subject: [PATCH 25/25] composite_and_inverse_functions - 4 exercises solved --- .../composite_and_inverse_functions.ipynb | 653 ++++++++++++++++++ 1 file changed, 653 insertions(+) create mode 100644 practice/functions/composite_and_inverse_functions.ipynb diff --git a/practice/functions/composite_and_inverse_functions.ipynb b/practice/functions/composite_and_inverse_functions.ipynb new file mode 100644 index 0000000..43f5017 --- /dev/null +++ b/practice/functions/composite_and_inverse_functions.ipynb @@ -0,0 +1,653 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyMJLzqvpY440nWLQLQvxiCG", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": 117, + "metadata": { + "id": "AqWyWwq5SgjT" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy as sym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 1a: Composite functions in numpy" + ], + "metadata": { + "id": "tMLi8SfqVtEV" + }, + "execution_count": 118, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "def fx(x):\n", + " return 2 * x**2 - 4\n", + "\n", + "def gx(x):\n", + " return 7*np.abs(x) + 3" + ], + "metadata": { + "id": "a_cwV6y2S_x6" + }, + "execution_count": 119, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "def fgx(xx):\n", + " return fx(gx(xx))\n", + "\n", + "def gfx(xx):\n", + " return gx(fx(xx))" + ], + "metadata": { + "id": "4R-W77N-UJD2" + }, + "execution_count": 120, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "xx = np.linspace(-5, 5, 200)\n", + "xx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "m6gSx0GSTig_", + "outputId": "6532b755-0101-4a64-d437-88de1de562d3" + }, + "execution_count": 121, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([-5. , -4.94974874, -4.89949749, -4.84924623, -4.79899497,\n", + " -4.74874372, -4.69849246, -4.64824121, -4.59798995, -4.54773869,\n", + " -4.49748744, -4.44723618, -4.39698492, -4.34673367, -4.29648241,\n", + " -4.24623116, -4.1959799 , -4.14572864, -4.09547739, -4.04522613,\n", + " -3.99497487, -3.94472362, -3.89447236, -3.84422111, -3.79396985,\n", + " -3.74371859, -3.69346734, -3.64321608, -3.59296482, -3.54271357,\n", + " -3.49246231, -3.44221106, -3.3919598 , -3.34170854, -3.29145729,\n", + " -3.24120603, -3.19095477, -3.14070352, -3.09045226, -3.04020101,\n", + " -2.98994975, -2.93969849, -2.88944724, -2.83919598, -2.78894472,\n", + " -2.73869347, -2.68844221, -2.63819095, -2.5879397 , -2.53768844,\n", + " -2.48743719, -2.43718593, -2.38693467, -2.33668342, -2.28643216,\n", + " -2.2361809 , -2.18592965, -2.13567839, -2.08542714, -2.03517588,\n", + " -1.98492462, -1.93467337, -1.88442211, -1.83417085, -1.7839196 ,\n", + " -1.73366834, -1.68341709, -1.63316583, -1.58291457, -1.53266332,\n", + " -1.48241206, -1.4321608 , -1.38190955, -1.33165829, -1.28140704,\n", + " -1.23115578, -1.18090452, -1.13065327, -1.08040201, -1.03015075,\n", + " -0.9798995 , -0.92964824, -0.87939698, -0.82914573, -0.77889447,\n", + " -0.72864322, -0.67839196, -0.6281407 , -0.57788945, -0.52763819,\n", + " -0.47738693, -0.42713568, -0.37688442, -0.32663317, -0.27638191,\n", + " -0.22613065, -0.1758794 , -0.12562814, -0.07537688, -0.02512563,\n", + " 0.02512563, 0.07537688, 0.12562814, 0.1758794 , 0.22613065,\n", + " 0.27638191, 0.32663317, 0.37688442, 0.42713568, 0.47738693,\n", + " 0.52763819, 0.57788945, 0.6281407 , 0.67839196, 0.72864322,\n", + " 0.77889447, 0.82914573, 0.87939698, 0.92964824, 0.9798995 ,\n", + " 1.03015075, 1.08040201, 1.13065327, 1.18090452, 1.23115578,\n", + " 1.28140704, 1.33165829, 1.38190955, 1.4321608 , 1.48241206,\n", + " 1.53266332, 1.58291457, 1.63316583, 1.68341709, 1.73366834,\n", + " 1.7839196 , 1.83417085, 1.88442211, 1.93467337, 1.98492462,\n", + " 2.03517588, 2.08542714, 2.13567839, 2.18592965, 2.2361809 ,\n", + " 2.28643216, 2.33668342, 2.38693467, 2.43718593, 2.48743719,\n", + " 2.53768844, 2.5879397 , 2.63819095, 2.68844221, 2.73869347,\n", + " 2.78894472, 2.83919598, 2.88944724, 2.93969849, 2.98994975,\n", + " 3.04020101, 3.09045226, 3.14070352, 3.19095477, 3.24120603,\n", + " 3.29145729, 3.34170854, 3.3919598 , 3.44221106, 3.49246231,\n", + " 3.54271357, 3.59296482, 3.64321608, 3.69346734, 3.74371859,\n", + " 3.79396985, 3.84422111, 3.89447236, 3.94472362, 3.99497487,\n", + " 4.04522613, 4.09547739, 4.14572864, 4.1959799 , 4.24623116,\n", + " 4.29648241, 4.34673367, 4.39698492, 4.44723618, 4.49748744,\n", + " 4.54773869, 4.59798995, 4.64824121, 4.69849246, 4.74874372,\n", + " 4.79899497, 4.84924623, 4.89949749, 4.94974874, 5. ])" + ] + }, + "metadata": {}, + "execution_count": 121 + } + ] + }, + { + "cell_type": "code", + "source": [ + "plt.plot(xx, fx(xx), label='f(x)')\n", + "plt.plot(xx, gx(xx), label='g(x)')\n", + "plt.plot(xx, fgx(xx), label='f(g(x))')\n", + "plt.plot(xx, gfx(xx), '.', label='g(f(x))')\n", + "plt.ylim([-5, 50])\n", + "plt.legend()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 435 + }, + "id": "TNyWRJEWTrDU", + "outputId": "c293c101-04b1-4228-cffe-08c88ae79f28" + }, + "execution_count": 122, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 1b: Composite functions in numpy" + ], + "metadata": { + "id": "iN5HB4K4TzYn" + }, + "execution_count": 123, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "def fx(x):\n", + " return np.sin(x)\n", + "\n", + "def gx(x):\n", + " return np.log(x)\n", + "\n", + "def hx(x):\n", + " return 2*x**2 + 5" + ], + "metadata": { + "id": "7IU4vK6sV3JT" + }, + "execution_count": 124, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "def fghx(x):\n", + " return fx(gx(hx(x)))" + ], + "metadata": { + "id": "gCAk9QjOWAnc" + }, + "execution_count": 125, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "xx = np.linspace(-100*np.pi, 100*np.pi, 1001)\n", + "plt.plot(xx, fghx(xx), label='f(g(h(x)))')\n", + "plt.legend()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "id": "xSqf9wKCWhGM", + "outputId": "86d25e17-8e7b-4fdf-a63d-52372176f55f" + }, + "execution_count": 126, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 2: Inverse function in numpy" + ], + "metadata": { + "id": "-kxVHUw9Wwb7" + }, + "execution_count": 127, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "def f(x):\n", + " return np.log(2*x)\n", + "\n", + "def g(x):\n", + " return np.exp(x) / 2" + ], + "metadata": { + "id": "7nVwgAzYaUoR" + }, + "execution_count": 128, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "xx = np.linspace(.01, 5, 54)\n", + "plt.plot(xx, f(xx), label='f(x)')\n", + "plt.plot(xx, g(xx), label='g(x)')\n", + "plt.plot(xx, f(g(xx)), label='f(g(x))')\n", + "plt.plot(xx, g(f(xx)), '.', label='g(f(x))')\n", + "# plt.xlim([1, 5])\n", + "plt.ylim([-5, 10])\n", + "plt.legend()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 435 + }, + "id": "SLRmVsNFaqvU", + "outputId": "039b9dbd-689e-4611-d62f-c26bc4b3835e" + }, + "execution_count": 129, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 3: Composite functions in sympy" + ], + "metadata": { + "id": "6-NjRrgXgM97" + }, + "execution_count": 130, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "sx = sym.symbols('x')\n", + "fx = sym.sin(sx)\n", + "gx = sym.log(sx)\n", + "hx = 2*sx**2 + 5\n", + "fx, gx, hx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "nozxz9ligRgn", + "outputId": "7af6d0db-3784-421f-d840-ebe6e755b28d" + }, + "execution_count": 131, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(sin(x), log(x), 2*x**2 + 5)" + ] + }, + "metadata": {}, + "execution_count": 131 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# use of .subs\n", + "fx.subs(sx, 0)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 37 + }, + "id": "nYO2T5Jcg2Aa", + "outputId": "fb67fcb2-854d-4346-84fb-43f35c3ed616" + }, + "execution_count": 132, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "0" + ], + "text/latex": "$\\displaystyle 0$" + }, + "metadata": {}, + "execution_count": 132 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# original fx\n", + "fx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 38 + }, + "id": "719CLE63hGmM", + "outputId": "888eaea0-6a15-4537-d419-0af755ac4f27" + }, + "execution_count": 133, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "sin(x)" + ], + "text/latex": "$\\displaystyle \\sin{\\left(x \\right)}$" + }, + "metadata": {}, + "execution_count": 133 + } + ] + }, + { + "cell_type": "code", + "source": [ + "fghx = fx.subs(sx, gx.subs(sx, hx))\n", + "fghx" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 38 + }, + "id": "jyodso4ihILP", + "outputId": "49c77b83-173f-45b0-f1e7-587fcbed33d1" + }, + "execution_count": 134, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "sin(log(2*x**2 + 5))" + ], + "text/latex": "$\\displaystyle \\sin{\\left(\\log{\\left(2 x^{2} + 5 \\right)} \\right)}$" + }, + "metadata": {}, + "execution_count": 134 + } + ] + }, + { + "cell_type": "code", + "source": [ + "sym.plot(\n", + " fghx,\n", + " (sx, -100, 100),\n", + " title=f'$y = {sym.latex(fghx)}$'\n", + ")" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 504 + }, + "id": "72ENo-KWhTfT", + "outputId": "841a1b8c-95a6-433d-c074-6524312e7676" + }, + "execution_count": 135, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "execution_count": 135 + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Exercise 4: Inverting functions in sympy" + ], + "metadata": { + "id": "QeVWJJvMiVTt" + }, + "execution_count": 136, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "sy = sym.symbols('y')\n", + "\n", + "fx = 2*sx + 3\n", + "gx = 2*sx + sym.sin(sx)\n", + "\n", + "display(fx)\n", + "display(gx)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 60 + }, + "id": "9FF9uhphi4ec", + "outputId": "c1d1bacf-8494-4057-9f9b-eb6f931aa973" + }, + "execution_count": 137, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "2*x + 3" + ], + "text/latex": "$\\displaystyle 2 x + 3$" + }, + "metadata": {} + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "2*x + sin(x)" + ], + "text/latex": "$\\displaystyle 2 x + \\sin{\\left(x \\right)}$" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Solve for inverse\n", + "invfx = sym.solve(sy - fx, sx)[0]\n", + "# invgx = sym.solve(sy - gx, sx)[0] # non invertible function\n", + "display(invfx)\n", + "# display(invgx)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "id": "uMF6ZcuEjiSP", + "outputId": "3c29dede-3015-4036-b3c2-9174febe07ce" + }, + "execution_count": 138, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "y/2 - 3/2" + ], + "text/latex": "$\\displaystyle \\frac{y}{2} - \\frac{3}{2}$" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "fx.subs(sx, 4)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 37 + }, + "id": "2kMBQAsul6JL", + "outputId": "08b6a671-7c6e-4545-804b-c968acb6f102" + }, + "execution_count": 139, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "11" + ], + "text/latex": "$\\displaystyle 11$" + }, + "metadata": {}, + "execution_count": 139 + } + ] + }, + { + "cell_type": "code", + "source": [ + "invfx.subs(sy, (fx.subs(sx, 4)))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 37 + }, + "id": "Gt6PZk3pl8zt", + "outputId": "f6c2b4fe-799f-43c3-e85f-2c27831bbb93" + }, + "execution_count": 140, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "4" + ], + "text/latex": "$\\displaystyle 4$" + }, + "metadata": {}, + "execution_count": 140 + } + ] + }, + { + "cell_type": "code", + "source": [ + "fx.subs(sx, invfx.subs(sy, 4))" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 37 + }, + "id": "A3r94itsmDPD", + "outputId": "e40476f2-cfba-4c5e-9a99-d20feabb79ed" + }, + "execution_count": 141, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "4" + ], + "text/latex": "$\\displaystyle 4$" + }, + "metadata": {}, + "execution_count": 141 + } + ] + } + ] +} \ No newline at end of file