534 lines
193 KiB
Plaintext
534 lines
193 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "view-in-github",
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"colab_type": "text"
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},
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"source": [
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"<a href=\"https://colab.research.google.com/github/udlbook/udlbook/blob/main/Notebooks/Chap01/1_1_BackgroundMathematics.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "s5zzKSOusPOB"
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},
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"source": [
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"\n",
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"# **Notebook 1.1 -- Background Mathematics**\n",
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"\n",
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"The purpose of this Python notebook is to make sure you can use CoLab and to familiarize yourself with some of the background mathematical concepts that you are going to need to understand deep learning. <br><br> It's not meant to be difficult and it may be that you know some or all of this information already.<br><br> Math is *NOT* a spectator sport. You won't learn it by just listening to lectures or reading books. It really helps to interact with it and explore yourself. <br><br> Work through the cells below, running each cell in turn. In various places you will see the words **\"TO DO\"**. Follow the instructions at these places and write code to complete the functions. There are also questions interspersed in the text.\n",
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"\n",
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"Contact me at udlbookmail@gmail.com if you find any mistakes or have any suggestions."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"id": "aUAjBbqzivMY"
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},
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"outputs": [],
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"source": [
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"# Imports math library\n",
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"import numpy as np\n",
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"# Imports plotting library\n",
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "WV2Dl6owme2d"
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},
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"source": [
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"**Linear functions**<br> We will be using the term *linear equation* to mean a weighted sum of inputs plus an offset. If there is just one input $x$, then this is a straight line:\n",
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"\n",
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"\\begin{equation}y=\\beta+\\omega x,\\end{equation} <br>\n",
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"\n",
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"where $\\beta$ is the y-intercept of the linear and $\\omega$ is the slope of the line. When there are two inputs $x_{1}$ and $x_{2}$, then this becomes:\n",
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"\n",
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"\\begin{equation}y=\\beta+\\omega_1 x_1 + \\omega_2 x_2.\\end{equation} <br><br>\n",
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"\n",
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"Any other functions are by definition **non-linear**.\n",
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"\n",
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"id": "WeFK4AvTotd8"
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},
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"outputs": [],
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"source": [
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"# Define a linear function with just one input, x\n",
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"def linear_function_1D(x,beta,omega):\n",
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" # TODO -- replace the code lin below with formula for 1D linear equation\n",
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" y = x\n",
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"\n",
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" return y"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 473
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},
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"id": "eimhJ8_jpmEp",
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"outputId": "41fc3d1e-8917-4fda-e89d-7c2568d9eed9"
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},
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"outputs": [
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{
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"<function matplotlib.pyplot.show(close=None, block=None)>"
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]
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},
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"metadata": {},
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"execution_count": 3
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},
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{
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"output_type": "display_data",
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"data": {
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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],
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"image/png": 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4YJg5M5qnTYO//CVsHkmS9pNlR9/u3HOhV69o7tYNiorC5pEkaT9YdrRvhg2Do46Cf/8bCgpCp5EkaZ9ZdrRvateO1lmxWHSW1rPPhk4kSdI+sexo351zDuTnR/M118D69UHjSJK0Lyw72j9DhsCxx8LHH0OfPqHTSJL0rSw72j8HHQQPPggZGTBrFjz9dOhEkiR9I8uO9t+ZZ+46SLl7d/jii7B5JEn6BpYdHZi774bjj4c1a6B379BpJEnaK8uODkytWrvWWb/5DTz5ZOhEkiTtkWVHB+6MM3bdEf266+Czz8LmkSRpDyw7Kp8774RWrWDdOrjxxtBpJEn6GsuOyicrK1pnZWbCb38LTzwROpEkSbux7Kj8TjsN+vWL5h494NNPw+aRJOk/WHZUMQYMgBNPjIpOXl7oNJIk7WTZUcX4ap1VrRr87nfw+OOhE0mSBFh2VJFOPRVuuy2ab7gB1q4Nm0eSJCw7qmi33w4nnwyffx4dvxOPh04kSUpzlh1VrBo1ontmVasGs2dHZ2hJkhSQZUcV7+STYeDAaM7Lg08+CZtHkpTWLDuqHP36RcfwrF8P11/vOkuSFIxlR5WjevXo7Kzq1eGpp+Dhh0MnkiSlqYQvO6tXr+aqq66iXr161KpVixNPPJHXX389dCztixNPjG4nAdGtJD7+OGgcSVJ6Suiys379etq1a0f16tV59tlneeuttxg9ejR169YNHU376tZboW1b2LABund3nSVJqnKxeDxx33369evHK6+8wt/+9rcD/hnFxcXk5ORQVFREdnZ2BabTPnvrLTjlFNi+HWbOhC5dQieSJCW4inz/TuhPdp566inatm3L5ZdfTv369TnllFOYPn36N76mpKSE4uLi3R4KrFUruPvuaO7dG/7977B5JElpJaHLzvvvv8/kyZM55phjeO655+jRowe9evVi1qxZe31NYWEhOTk5Ox9NmzatwsTaq5tugjPOgOJiuPZa11mSpCqT0GusGjVq0LZtW1599dWdz/Xq1YtFixbx2muv7fE1JSUllJSU7Py6uLiYpk2busZKBMuXQ5s2UFICM2ZAt26hE0mSElTarLEaNWpEq1atdnvuO9/5Dh999NFeX5OVlUV2dvZuDyWI44+HoUOjuU8f+IbfoyRJFSWhy067du1YsWLFbs+tXLmS5s2bB0qkcsvPh7POgo0b4ZprXGdJkipdQpedPn36MH/+fIYNG8a7777LI488wrRp08jLywsdTQcqMzM6I6tmTZgzB77lgHNJksorocvOaaedxuzZs3n00Udp3bo1gwcPZuzYsXTq1Cl0NJXHscdCYWE033QTfPhh0DiSpNSW0AcoVwSvs5OgysrgBz+Av/0NfvjD6FOejITu3pKkKpQ2BygrhWVkwAMPQK1a8PzzMGVK6ESSpBRl2VE4Rx8NI0ZE8y23wPvvh80jSUpJlh2FlZcH554LW7ZA167RekuSpApk2VFYX62zateGefNg4sTQiSRJKcayo/COPBLuuSea+/aFd98Nm0eSlFIsO0oM110XnZW1dSvk5rrOkiRVGMuOEkNGBtx/Pxx8MLz8MowbFzqRJClFWHaUOFq0gNGjo7l/f1i5MmgcSVJqsOwosVx7LfzoR7BtG3TpAqWloRNJkpKcZUeJJRaDGTOgTh147TW4997QiSRJSc6yo8TTrNmuknPHHbB8edg8kqSkZtlRYuraFX78Yygpgc6d4csvQyeSJCUpy44SUywG06dDTg4sXLjrwGVJkvaTZUeJq0kTuO++aB44EP75z7B5JElJybKjxParX8Ell8D27dHZWa6zJEn7ybKjxBaLwbRpcMgh8PrrMHJk6ESSpCRj2VHia9wYxo+P5jvvhGXLgsaRJCUXy46SQ6dOcOmlsGNHdHbWjh2hE0mSkoRlR8khFoMpU+DQQ+Hvf4fCwtCJJElJwrKj5NGwIUyYEM2DB8PSpUHjSJKSg2VHyeWKK+CnP43OyurSJTpLS5Kkb2DZUXKJxWDyZDjsMHjjDRg6NHQiSVKCs+wo+dSvD5MmRfPQobBkSdg8kqSEZtlRcrr88uhRWhqdnVVSEjqRJClBWXaUvCZOhMMPhzffjA5YliRpDyw7Sl6HHx4dvwMwfDgsWhQ2jyQpIVl2lNx+9jO48spondWlC2zbFjqRJCnB7HfZ6dy5My+99FJlZJEOzPjx0KABvPVWdDsJSZL+w36XnaKiItq3b88xxxzDsGHDWL16dWXkkvZdvXowdWo033MPLFgQNo8kKaHsd9l58sknWb16NT169OCxxx6jRYsWXHTRRfz+979nh/crUiiXXgpXXQVlZdE6a+vW0IkkSQnigI7ZOfzwwykoKOCNN95gwYIFHH300Vx99dU0btyYPn368M4771R0Tunb3XcfNGoEy5fDwIGh00iSEkS5DlD+5JNPmDNnDnPmzCEzM5OLL76YZcuW0apVK+69996Kyijtm0MPhWnTonn0aHj11bB5JEkJYb/Lzo4dO3jiiSf4yU9+QvPmzfnd735Hfn4+H3/8MbNmzeKvf/0rjz/+OHfffXdl5JW+2U9+El1kMB6P1llbtoROJEkKrNr+vqBRo0aUlZVx5ZVXsnDhQtq0afO1P3PeeedxyCGHVEA86QCMHQtz5sA778Add8CYMaETSZICisXj8fj+vOChhx7i8ssvp2bNmpWVqUIVFxeTk5NDUVER2dnZoeOoqjz7LFx8cXTj0Hnz4JxzQieSJO2Hinz/3u811tVXX500RUdp7KKLoFu3aJ2VmwubN4dOJEkKxCsoK3WNHg1NmsB770H//qHTSJICsewodeXkwP33R/P48dE6S5KUdiw7Sm0XXADdu0dzbi5s2hQ2jySpyll2lPpGjYLmzeGDD6Bv39BpJElVzLKj1Fenzq511qRJMHdu2DySpCpl2VF6OP986NEjmrt1g40bw+aRJFUZy47Sx8iR0KIF/OtfcMstodNIkqqIZUfp4+CDYebMaJ46Ff7yl7B5JElVwrKj9PKDH8CNN0bzNddAUVHQOJKkymfZUfopLISjjoJVq+Cmm0KnkSRVMsuO0k/t2tE6KxaLztL6859DJ5IkVSLLjtLTOedA797RfM01sGFD0DiSpMpj2VH6GjoUjjkGVq+GPn1Cp5EkVRLLjtLXQQftWmc9+CA880zoRJKkSmDZUXpr1w4KCqK5e3dYvz5sHklShbPsSIMHw3HHwSef7DqOR5KUMiw7Uq1a0RorIwMeegj+8IfQiSRJFciyIwF873u7biFx3XXw+edh80iSKoxlR/rKnXdCq1awdu2uqyxLkpKeZUf6Ss2a0TorMxMefRT+7/9CJ5IkVQDLjvSfTjsN+vaN5uuvh08/DZtHklRulh3pvw0cCK1bR0WnZ8/QaSRJ5WTZkf5bVtauddbjj8Pvfhc6kSSpHCw70p5897tw223RfMMNsG5d2DySpANm2ZH25o474KST4LPPosITj4dOJEk6AJYdaW9q1IBZs6BaNXjiCXjssdCJJEkHwLIjfZM2bWDAgGjOy4M1a4LGkSTtv6QqO8OHDycWi5Gfnx86itJJ//5wyinwxRfR6eiusyQpqSRN2Vm0aBFTp07lpJNOCh1F6aZ69ejsrOrVo/tmPfJI6ESSpP2QFGVn06ZNdOrUienTp1O3bt3QcZSOTjoJBg2K5htvhI8/DptHkrTPkqLs5OXlcckll9C+fftv/bMlJSUUFxfv9pAqRN++0Snp69dHNwt1nSVJSSHhy85vf/tblixZQmFh4T79+cLCQnJycnY+mjZtWskJlTaqVYvOzqpRA555Bn7969CJJEn7IKHLzqpVq+jduzcPP/wwNWvW3KfX9O/fn6Kiop2PVatWVXJKpZUTToC77orm3r1h9eqweSRJ3yoWjyfuZ/FPPvkkl112GZmZmTufKy0tJRaLkZGRQUlJyW7f25Pi4mJycnIoKioiOzu7siMrHXz5JbRrBwsXwkUXwR//CLFY6FSSlFIq8v07oT/ZOf/881m2bBlLly7d+Wjbti2dOnVi6dKl31p0pEpRrVp0dlZWFjz7LMycGTqRJOkbVAsd4JvUqVOH1q1b7/Zc7dq1qVev3teel6rUd74DQ4bALbdAnz7Qvj00axY6lSRpDxL6kx0pofXpA2eeCcXFcM01np0lSQkqoY/ZqQges6NKtWJFdEuJbdtg2jS49trQiSQpJaTNMTtSwjvuOBg2LJoLCuBf/wqbR5L0NZYdqbx69YKzz4ZNm6BrVygrC51IkvQfLDtSeWVmRmdk1aoFzz8PU6eGTiRJ+g+WHakiHH00DB8ezbfcAh98EDaPJGkny45UUXr2hO9/HzZvdp0lSQnEsiNVlIyMaJ1Vuza8+CJMmhQ6kSQJy45UsY48EkaOjOa+feHdd8PmkSRZdqQKd/31cN55sGWL6yxJSgCWHamiZWTAAw/AwQfD3/4G48eHTiRJac2yI1WGFi1g1Kho7t8fVq4MGkeS0pllR6os3btHNwjduhVyc6G0NHQiSUpLlh2pssRicP/9UKcOvPoqjB0bOpEkpSXLjlSZmjWDMWOi+Y47YPnysHkkKQ1ZdqTK1q0bXHhhdGf0Ll1cZ0lSFbPsSJUtFoMZMyAnBxYsgNGjQyeSpLRi2ZGqQpMmu47ZGTAA3noraBxJSieWHamqdO4Ml1wC27dH85dfhk4kSWnBsiNVlVgMpk6FQw6B11+He+4JnUiS0oJlR6pKRxwB48ZF86BBsGxZ2DySlAYsO1JVu+oq+J//gR07orOzduwInUiSUpplR6pqsRhMmQJ168KSJTB8eOhEkpTSLDtSCI0awYQJ0Tx4MLzxRtg8kpTCLDtSKFdeCZddtmudtX176ESSlJIsO1IosRhMngz16sHSpTBsWOhEkpSSLDtSSA0awKRJ0Tx0aHQMjySpQll2pNB+8Qv4+c+jiwy6zpKkCmfZkRLBpElw+OHRdXcGDw6dRpJSimVHSgSHHx4dvwNQWBhdYVmSVCEsO1Ki+NnP4IoroLQ0undWSUnoRJKUEiw7UiIZPx7q14/uin7nnaHTSFJKsOxIieSww6KrKwOMHAkLF4bNI0kpwLIjJZrLLoNOnaCsLFpnbdsWOpEkJTXLjpSIxo2Dhg1h+XIYODB0GklKapYdKREdeihMmxbNo0bBq6+GzSNJScyyIyWqDh3gV7+CeBxyc2Hr1tCJJCkpWXakRDZ2LDRuDCtXwh13hE4jSUnJsiMlsrp1Yfr0aL73Xnj55bB5JCkJWXakRHfxxdC166511ubNoRNJUlKx7EjJYMwYaNIE3n0XbrstdBpJSiqWHSkZ5OTAjBnRPG4czJsXNo8kJRHLjpQsLrwQrr02mrt2hU2bwuaRpCRh2ZGSyahR0KwZvP8+9OsXOo0kJQXLjpRMsrPh/vujeeJEeP75sHkkKQlYdqRk0749XH99NHfrBhs3hs0jSQnOsiMlo5EjoUUL+PBDuPXW0GkkKaFZdqRkVKcOPPBANE+ZAnPmhM0jSQnMsiMlq/POg549o7lbNyguDptHkhKUZUdKZsOHw5FHwqpVcNNNodNIUkKy7EjJrHZtmDkzmmfMgOeeC5tHkhKQZUdKdt//PvTuHc3dusGGDUHjSFKisexIqWDYMDj6aFi9GgoKQqeRpIRi2ZFSwUEHwYMPQiwWrbX++MfQiSQpYVh2pFTRrh306RPN3bvD+vVh80hSgrDsSKlkyBA49lj4+GPIzw+dRpISgmVHSiW1asGsWZCRAb/+NTz1VOhEkhScZUdKNd/7Htx8czRfdx18/nnYPJIUmGVHSkV33QXf+Q6sWQO9eoVOI0lBWXakVFSzZnR2VkYGPPIIzJ4dOpEkBWPZkVLV6adD377RfP318NlnYfNIUiCWHSmVDRoEJ5wA69btummoJKUZy46UyrKyorOzMjPhscfg978PnUiSqpxlR0p13/0u9O8fzT16RJ/ySFIasexI6WDAADjppOi4nRtugHg8dCJJqjIJXXYKCws57bTTqFOnDvXr16djx46sWLEidCwp+dSoEZ2dVa0aPPEEPP546ESSVGUSuuzMmzePvLw85s+fz5w5c9ixYwcXXHABmzdvDh1NSj6nnAJ33BHNN9wQXYNHktJALB5Pns+zP/30U+rXr8+8efP4/ve/v0+vKS4uJicnh6KiIrKzsys5oZTgduyITklfuhQ6doT/+7/oTumSlGAq8v07oT/Z+W9FRUUAHHrooXv9MyUlJRQXF+/2kPT/Va8erbOqV4cnn4RHHw2dSJIqXdKUnbKyMvLz82nXrh2tW7fe658rLCwkJydn56Np06ZVmFJKAiefDAMHRnPPnvDJJ2HzSFIlS5o1Vo8ePXj22Wd5+eWXadKkyV7/XElJCSUlJTu/Li4upmnTpq6xpP+0YweceSYsXgwdOsAf/uA6S1JCSbs1Vs+ePXnmmWd44YUXvrHoAGRlZZGdnb3bQ9J/+WqdVaMGPP00PPRQ6ESSVGkSuuzE43F69uzJ7Nmzef7552nZsmXoSFLqaN0a7rwzmnv3htWrg8aRpMqS0GUnLy+P3/zmNzzyyCPUqVOHNWvWsGbNGrZu3Ro6mpQabrkFTjsNNmyA7t292KCklJTQx+zE9nIMwcyZM+nSpcs+/QxPPZe+xVtvwamnQkkJPPAA5OaGTiRJ6XPMTjwe3+NjX4uOpH3QqhUMHhzN+fmwalXQOJJU0RK67EiqIgUF8L3vQXExXHut6yxJKcWyIwkyM6Ozs2rWhOeeg/vvD51IkiqMZUdS5LjjYOjQaC4ogH/9K2weSaoglh1Ju/TuDe3awcaN0K2b6yxJKcGyI2mXzEyYORNq1YK5c2Hq1NCJJKncLDuSdnfMMVBYGM033wwffBA2jySVk2VH0tfdeCOccw5s3hyts8rKQieSpANm2ZH0dRkZ0TrroIPghRdg8uTQiSTpgFl2JO3ZUUfByJHRfOut8N57YfNI0gGy7Ejaux494Ac/gC1boGtX11mSkpJlR9LeZWRE98uqXRteegkmTAidSJL2m2VH0jdr2RJGjYrmfv3gnXfC5pGk/WTZkfTtrrsO2reHrVuju6KXloZOJEn7zLIj6dvFYjBjBtSpA6+8AvfdFzqRJO0zy46kfdO8OYweHc233w4rVoTNI0n7yLIjad9dcw1ccAFs2wZdurjOkpQULDuS9t1X66zsbJg/H8aMCZ1Ikr6VZUfS/mnaFO69N5oHDIC33w6bR5K+hWVH0v7LzYWLLoKSkmid9eWXoRNJ0l5ZdiTtv1gMpk+HnBxYuHDXdXgkKQFZdiQdmCOOgHHjonnQIHjzzbB5JGkvLDuSDtzVV0OHDrB9e7TO2rEjdCJJ+hrLjqQDF4vB1KlQty4sXgwjRoROJElfY9mRVD6NGsH48dF8993wj3+EzSNJ/8WyI6n8/vd/oWPHaI3VubPrLEkJxbIjqfxiMZgyBerVg6VLYdiw0IkkaSfLjqSK0aABTJgQzUOGRKVHkhKAZUdSxfnlL+FnP4suMti5c3SWliQFZtmRVHFiMZg0CQ47LDpQeciQ0IkkybIjqYLVrx8VHoiO3Vm8OGweSWnPsiOp4l1+ebTSKi2N1lklJaETSUpjlh1JlWPChOhTnn/+E+66K3QaSWnMsiOpchx2WHQ6OkRXVl60KGweSWnLsiOp8lx2WXTBwbKyaJ21bVvoRJLSkGVHUuUaNw4aNoS3347uji5JVcyyI6ly1asX3SwUYNQomD8/bB5JaceyI6ny/c//wNVXR+usLl1g69bQiSSlEcuOpKpx333RHdJXrIABA0KnkZRGLDuSqkbdujB9ejSPGQOvvBI2j6S0YdmRVHUuuQRycyEej9ZZW7aETiQpDVh2JFWtMWPgiCPg3XfhtttCp5GUBiw7kqrWIYfAjBnRPG4cvPRS0DiSUp9lR1LV+/GP4ZpronVWbi5s3hw6kaQUZtmRFMbo0dC0Kbz/PvTrFzqNpBRm2ZEURnY23H9/NE+YAC+8EDaPpJRl2ZEUzo9+BNddF81du8KmTWHzSEpJlh1JYd1zDzRvDh9+CLfeGjqNpBRk2ZEUVp068MAD0Tx5Mvz1r2HzSEo5lh1J4f3wh5CXF83dukFxcdg8klKKZUdSYhg+HFq2hI8+gptvDp1GUgqx7EhKDAcfDDNnRvP06fCXv4TNIyllWHYkJY5zz4VevaK5WzcoKgqbR1JKsOxISizDhsHRR8O//w0FBaHTSEoBlh1JiaV27WidFYtFZ2n96U+hE0lKcpYdSYnn7LMhPz+ar70W1q8PGkdScrPsSEpMQ4bAscfCxx9Dnz6h00hKYpYdSYnpoIPgwQchIwNmzYKnnw6dSFKSsuxISlxnngk33RTN3bvDF1+EzSMpKVl2JCW2u++G44+HNWt2nZYuSfvBsiMpsdWsuWud9fDD8OSToRNJSjKWHUmJ74wzdt0R/brr4LPPwuaRlFQsO5KSw513wgknwLp1cOONodNISiKWHUnJISsrWmdlZsJvfwtPPBE6kaQkkRRlZ+LEibRo0YKaNWtyxhlnsHDhwtCRJIXQti306xfNPXrAp5+GzSMpKSR82XnssccoKChg0KBBLFmyhJNPPpkLL7yQdevWhY4mKYQBA+DEE6Oik5cXOo2kJJDwZWfMmDFce+215Obm0qpVK6ZMmcJBBx3EAw88EDqapBC+WmdVqwa/+x08/njoRJISXLXQAb7J9u3bWbx4Mf3799/5XEZGBu3bt+e1117b42tKSkooKSnZ+XVRUREAxcXFlRtWUtU5+mi4+WYYPhyuvx5OPRXq1w+dSlIF+up9Ox6Pl/tnJXTZ+eyzzygtLaVBgwa7Pd+gQQOWL1++x9cUFhZy1113fe35pk2bVkpGSYGtXw/HHBM6haRK8vnnn5OTk1Oun5HQZedA9O/fn4KCgp1fb9iwgebNm/PRRx+V+1+Wyqe4uJimTZuyatUqsrOzQ8dJa/4uEou/j8Th7yJxFBUV0axZMw499NBy/6yELjuHHXYYmZmZrF27drfn165dS8OGDff4mqysLLKysr72fE5Ojv/FTRDZ2dn+LhKEv4vE4u8jcfi7SBwZGeU/vDihD1CuUaMG3/3ud5k7d+7O58rKypg7dy5nnnlmwGSSJClZJPQnOwAFBQV07tyZtm3bcvrppzN27Fg2b95Mbm5u6GiSJCkJJHzZ+eUvf8mnn37KwIEDWbNmDW3atOHPf/7z1w5a3pusrCwGDRq0x9WWqpa/i8Th7yKx+PtIHP4uEkdF/i5i8Yo4p0uSJClBJfQxO5IkSeVl2ZEkSSnNsiNJklKaZUeSJKW0lC47EydOpEWLFtSsWZMzzjiDhQsXho6UlgoLCznttNOoU6cO9evXp2PHjqxYsSJ0LAHDhw8nFouRn58fOkpaWr16NVdddRX16tWjVq1anHjiibz++uuhY6Wd0tJSBgwYQMuWLalVqxZHHXUUgwcPrpB7MunbvfTSS3To0IHGjRsTi8V48sknd/t+PB5n4MCBNGrUiFq1atG+fXveeeed/fo7UrbsPPbYYxQUFDBo0CCWLFnCySefzIUXXsi6detCR0s78+bNIy8vj/nz5zNnzhx27NjBBRdcwObNm0NHS2uLFi1i6tSpnHTSSaGjpKX169fTrl07qlevzrPPPstbb73F6NGjqVu3buhoaWfEiBFMnjyZCRMm8PbbbzNixAhGjhzJ+PHjQ0dLC5s3b+bkk09m4sSJe/z+yJEjGTduHFOmTGHBggXUrl2bCy+8kG3btu37XxJPUaeffno8Ly9v59elpaXxxo0bxwsLCwOmUjwej69bty4OxOfNmxc6StrauHFj/JhjjonPmTMnfu6558Z79+4dOlLa6du3b/zss88OHUPxePySSy6Jd+3adbfnfvrTn8Y7deoUKFH6AuKzZ8/e+XVZWVm8YcOG8XvuuWfncxs2bIhnZWXFH3300X3+uSn5yc727dtZvHgx7du33/lcRkYG7du357XXXguYTBDd3A2okJu76cDk5eVxySWX7Pa/EVWtp556irZt23L55ZdTv359TjnlFKZPnx46Vlo666yzmDt3LitXrgTgjTfe4OWXX+aiiy4KnEwffPABa9as2e3/q3JycjjjjDP26/084a+gfCA+++wzSktLv3aV5QYNGrB8+fJAqQTRvc3y8/Np164drVu3Dh0nLf32t79lyZIlLFq0KHSUtPb+++8zefJkCgoKuO2221i0aBG9evWiRo0adO7cOXS8tNKvXz+Ki4s5/vjjyczMpLS0lKFDh9KpU6fQ0dLemjVrAPb4fv7V9/ZFSpYdJa68vDzefPNNXn755dBR0tKqVavo3bs3c+bMoWbNmqHjpLWysjLatm3LsGHDADjllFN48803mTJlimWnij3++OM8/PDDPPLII5xwwgksXbqU/Px8Gjdu7O8iRaTkGuuwww4jMzOTtWvX7vb82rVradiwYaBU6tmzJ8888wwvvPACTZo0CR0nLS1evJh169Zx6qmnUq1aNapVq8a8efMYN24c1apVo7S0NHTEtNGoUSNatWq123Pf+c53+OijjwIlSl+33HIL/fr144orruDEE0/k6quvpk+fPhQWFoaOlva+es8u7/t5SpadGjVq8N3vfpe5c+fufK6srIy5c+dy5plnBkyWnuLxOD179mT27Nk8//zztGzZMnSktHX++eezbNkyli5duvPRtm1bOnXqxNKlS8nMzAwdMW20a9fua5dgWLlyJc2bNw+UKH1t2bKFjIzd3w4zMzMpKysLlEhfadmyJQ0bNtzt/by4uJgFCxbs1/t5yq6xCgoK6Ny5M23btuX0009n7NixbN68mdzc3NDR0k5eXh6PPPIIf/jDH6hTp87OPWtOTg61atUKnC691KlT52vHStWuXZt69ep5DFUV69OnD2eddRbDhg3jF7/4BQsXLmTatGlMmzYtdLS006FDB4YOHUqzZs044YQT+Pvf/86YMWPo2rVr6GhpYdOmTbz77rs7v/7ggw9YunQphx56KM2aNSM/P58hQ4ZwzDHH0LJlSwYMGEDjxo3p2LHjvv8lFXjGWMIZP358vFmzZvEaNWrETz/99Pj8+fNDR0pLwB4fM2fODB1N8binngf09NNPx1u3bh3PysqKH3/88fFp06aFjpSWiouL47179443a9YsXrNmzfiRRx4Zv/322+MlJSWho6WFF154YY/vEZ07d47H49Hp5wMGDIg3aNAgnpWVFT///PPjK1as2K+/IxaPe4lISZKUulLymB1JkqSvWHYkSVJKs+xIkqSUZtmRJEkpzbIjSZJSmmVHkiSlNMuOJElKaZYdSZKU0iw7kiQppVl2JElSSrPsSEoqn376KQ0bNmTYsGE7n3v11VepUaPGbndGlqSveG8sSUnnT3/6Ex07duTVV1/luOOOo02bNlx66aWMGTMmdDRJCciyIykp5eXl8de//pW2bduybNkyFi1aRFZWVuhYkhKQZUdSUtq6dSutW7dm1apVLF68mBNPPDF0JEkJymN2JCWl9957j48//piysjI+/PDD0HEkJTA/2ZGUdLZv387pp59OmzZtOO644xg7dizLli2jfv36oaNJSkCWHUlJ55ZbbuH3v/89b7zxBgcffDDnnnsuOTk5PPPMM6GjSUpArrEkJZUXX3yRsWPH8tBDD5GdnU1GRgYPPfQQf/vb35g8eXLoeJISkJ/sSJKklOYnO5IkKaVZdiRJUkqz7EiSpJRm2ZEkSSnNsiNJklKaZUeSJKU0y44kSUpplh1JkpTSLDuSJCmlWXYkSVJKs+xIkqSUZtmRJEkp7f8BPrnbyMDz8g4AAAAASUVORK5CYII=\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
],
|
|
"source": [
|
|
"# Plot the 1D linear function\n",
|
|
"\n",
|
|
"# Define an array of x values from 0 to 10 with increments of 0.1\n",
|
|
"# https://numpy.org/doc/stable/reference/generated/numpy.arange.html\n",
|
|
"x = np.arange(0.0,10.0, 0.01)\n",
|
|
"# Compute y using the function you filled in above\n",
|
|
"beta = 0.0; omega = 1.0\n",
|
|
"\n",
|
|
"y = linear_function_1D(x,beta,omega)\n",
|
|
"\n",
|
|
"# Plot this function\n",
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(x,y,'r-')\n",
|
|
"ax.set_ylim([0,10]);ax.set_xlim([0,10])\n",
|
|
"ax.set_xlabel('x'); ax.set_ylabel('y')\n",
|
|
"plt.show\n",
|
|
"\n",
|
|
"# TODO -- experiment with changing the values of beta and omega\n",
|
|
"# to understand what they do. Try to make a line\n",
|
|
"# that crosses the y-axis at y=10 and the x-axis at x=5"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"id": "AedfvD9dxShZ"
|
|
},
|
|
"source": [
|
|
"Now let's investigate a 2D linear function"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"id": "57Gvkk-Ir_7b"
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Code to draw 2D function -- read it so you know what is going on, but you don't have to change it\n",
|
|
"def draw_2D_function(x1_mesh, x2_mesh, y):\n",
|
|
" fig, ax = plt.subplots()\n",
|
|
" fig.set_size_inches(7,7)\n",
|
|
" pos = ax.contourf(x1_mesh, x2_mesh, y, levels=256 ,cmap = 'hot', vmin=-10,vmax=10.0)\n",
|
|
" fig.colorbar(pos, ax=ax)\n",
|
|
" ax.set_xlabel('x1');ax.set_ylabel('x2')\n",
|
|
" levels = np.arange(-10,10,1.0)\n",
|
|
" ax.contour(x1_mesh, x2_mesh, y, levels, cmap='winter')\n",
|
|
" plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"metadata": {
|
|
"id": "YxeNhrXMzkZR"
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Define a linear function with two inputs, x1 and x2\n",
|
|
"def linear_function_2D(x1,x2,beta,omega1,omega2):\n",
|
|
" # TODO -- replace the code line below with formula for 2D linear equation\n",
|
|
" y = x1\n",
|
|
"\n",
|
|
" return y"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 619
|
|
},
|
|
"id": "rn_UBRDBysmR",
|
|
"outputId": "fd139263-f48b-49df-cd53-2c05ee6ffad0"
|
|
},
|
|
"outputs": [
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 700x700 with 2 Axes>"
|
|
],
|
|
"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
],
|
|
"source": [
|
|
"# Plot the 2D function\n",
|
|
"\n",
|
|
"# Make 2D array of x and y points\n",
|
|
"x1 = np.arange(0.0, 10.0, 0.1)\n",
|
|
"x2 = np.arange(0.0, 10.0, 0.1)\n",
|
|
"x1,x2 = np.meshgrid(x1,x2) # https://www.geeksforgeeks.org/numpy-meshgrid-function/\n",
|
|
"\n",
|
|
"# Compute the 2D function for given values of omega1, omega2\n",
|
|
"beta = 0.0; omega1 = 1.0; omega2 = -0.5\n",
|
|
"y = linear_function_2D(x1,x2,beta, omega1, omega2)\n",
|
|
"\n",
|
|
"# Draw the function.\n",
|
|
"# Color represents y value (brighter = higher value)\n",
|
|
"# Black = -10 or less, White = +10 or more\n",
|
|
"# 0 = mid orange\n",
|
|
"# Lines are conoturs where value is equal\n",
|
|
"draw_2D_function(x1,x2,y)\n",
|
|
"\n",
|
|
"# TODO\n",
|
|
"# Predict what this plot will look like if you set omega_1 to zero\n",
|
|
"# Change the code and see if you are right.\n",
|
|
"\n",
|
|
"# TODO\n",
|
|
"# Predict what this plot will look like if you set omega_2 to zero\n",
|
|
"# Change the code and see if you are right.\n",
|
|
"\n",
|
|
"# TODO\n",
|
|
"# Predict what this plot will look like if you set beta to -5\n",
|
|
"# Change the code and see if you are correct\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"id": "i8tLwpls476R"
|
|
},
|
|
"source": [
|
|
"Often we will want to compute many linear functions at the same time. For example, we might have three inputs, $x_1$, $x_2$, and $x_3$ and want to compute two linear functions giving $y_1$ and $y_2$. Of course, we could do this by just running each equation separately,<br><br>\n",
|
|
"\n",
|
|
"\\begin{eqnarray}y_1 &=& \\beta_1 + \\omega_{11} x_1 + \\omega_{12} x_2 + \\omega_{13} x_3\\\\\n",
|
|
"y_2 &=& \\beta_2 + \\omega_{21} x_1 + \\omega_{22} x_2 + \\omega_{23} x_3.\n",
|
|
"\\end{eqnarray}<br>\n",
|
|
"\n",
|
|
"However, we can write it more compactly with vectors and matrices:\n",
|
|
"\n",
|
|
"\\begin{equation}\n",
|
|
"\\begin{bmatrix} y_1\\\\ y_2 \\end{bmatrix} = \\begin{bmatrix}\\beta_{1}\\\\\\beta_{2}\\end{bmatrix}+ \\begin{bmatrix}\\omega_{11}&\\omega_{12}&\\omega_{13}\\\\\\omega_{21}&\\omega_{22}&\\omega_{23}\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\x_{2}\\\\x_{3}\\end{bmatrix},\n",
|
|
"\\end{equation}<br>\n",
|
|
"or\n",
|
|
"\n",
|
|
"\\begin{equation}\n",
|
|
"\\mathbf{y} = \\boldsymbol\\beta +\\boldsymbol\\Omega\\mathbf{x}.\n",
|
|
"\\end{equation}\n",
|
|
"\n",
|
|
"for short. Here, lowercase bold symbols are used for vectors. Upper case bold symbols are used for matrices.\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"id": "MjHXMavh9IUz"
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Define a linear function with three inputs, x1, x2, and x_3\n",
|
|
"def linear_function_3D(x1,x2,x3,beta,omega1,omega2,omega3):\n",
|
|
" # TODO -- replace the code below with formula for a single 3D linear equation\n",
|
|
" y = x1\n",
|
|
"\n",
|
|
" return y"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"id": "fGzVJQ6N-mHJ"
|
|
},
|
|
"source": [
|
|
"Let's compute two linear equations, using both the individual equations and the vector / matrix form and check they give the same result"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/"
|
|
},
|
|
"id": "Swd_bFIE9p2n",
|
|
"outputId": "46425c0f-aacd-4db8-c3cd-d23e30f1a191"
|
|
},
|
|
"outputs": [
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Individual equations\n",
|
|
"y1 = -4.500\n",
|
|
"y2 = 2.900\n",
|
|
"Matrix/vector form\n",
|
|
"y1= -4.500\n",
|
|
"y2 = 2.900\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Define the parameters\n",
|
|
"beta1 = 0.5; beta2 = 0.2\n",
|
|
"omega11 = -1.0 ; omega12 = 0.4; omega13 = -0.3\n",
|
|
"omega21 = 0.1 ; omega22 = 0.1; omega23 = 1.2\n",
|
|
"\n",
|
|
"# Define the inputs\n",
|
|
"x1 = 4 ; x2 =-1; x3 = 2\n",
|
|
"\n",
|
|
"# Compute using the individual equations\n",
|
|
"y1 = linear_function_3D(x1,x2,x3,beta1,omega11,omega12,omega13)\n",
|
|
"y2 = linear_function_3D(x1,x2,x3,beta2,omega21,omega22,omega23)\n",
|
|
"print(\"Individual equations\")\n",
|
|
"print('y1 = %3.3f\\ny2 = %3.3f'%((y1,y2)))\n",
|
|
"\n",
|
|
"# Define vectors and matrices\n",
|
|
"beta_vec = np.array([[beta1],[beta2]])\n",
|
|
"omega_mat = np.array([[omega11,omega12,omega13],[omega21,omega22,omega23]])\n",
|
|
"x_vec = np.array([[x1], [x2], [x3]])\n",
|
|
"\n",
|
|
"# Compute with vector/matrix form\n",
|
|
"y_vec = beta_vec+np.matmul(omega_mat, x_vec)\n",
|
|
"print(\"Matrix/vector form\")\n",
|
|
"print('y1= %3.3f\\ny2 = %3.3f'%((y_vec[0],y_vec[1])))\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"id": "3LGRoTMLU8ZU"
|
|
},
|
|
"source": [
|
|
"# Questions\n",
|
|
"\n",
|
|
"1. A single linear equation with three inputs (i.e. **linear_function_3D()**) associates a value y with each point in a 3D space ($x_1$,$x_2$,$x_3$). Is it possible to visualize this? What value is at position (0,0,0)?\n",
|
|
"\n",
|
|
"2. Write code to compute three linear equations with two inputs ($x_1$, $x_2$) using both the individual equations and the matrix form (you can make up any values for the inputs $\\beta_{i}$ and the slopes $\\omega_{ij}$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"id": "7Y5zdKtKZAB2"
|
|
},
|
|
"source": [
|
|
"# Special functions\n",
|
|
"\n",
|
|
"Throughout the book, we'll be using some special functions (see Appendix B.1.3). The most important of these are the logarithm and exponential functions. Let's investigate their properties.\n",
|
|
"\n",
|
|
"We'll start with the exponential function $y=\\mbox{exp}[x]=e^x$ which maps the real line $[-\\infty,+\\infty]$ to non-negative numbers $[0,+\\infty]$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 473
|
|
},
|
|
"id": "c_GkjiY9IWCu",
|
|
"outputId": "240f5196-b914-42f9-9c6e-7a18ab367af0"
|
|
},
|
|
"outputs": [
|
|
{
|
|
"output_type": "execute_result",
|
|
"data": {
|
|
"text/plain": [
|
|
"<function matplotlib.pyplot.show(close=None, block=None)>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"execution_count": 10
|
|
},
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
],
|
|
"source": [
|
|
"# Draw the exponential function\n",
|
|
"\n",
|
|
"# Define an array of x values from -5 to 5 with increments of 0.1\n",
|
|
"x = np.arange(-5.0,5.0, 0.01)\n",
|
|
"y = np.exp(x) ;\n",
|
|
"\n",
|
|
"# Plot this function\n",
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(x,y,'r-')\n",
|
|
"ax.set_ylim([0,100]);ax.set_xlim([-5,5])\n",
|
|
"ax.set_xlabel('x'); ax.set_ylabel('exp[x]')\n",
|
|
"plt.show"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"id": "XyrT8257IWCu"
|
|
},
|
|
"source": [
|
|
"# Questions\n",
|
|
"\n",
|
|
"1. What is $\\mbox{exp}[0]$? \n",
|
|
"2. What is $\\mbox{exp}[1]$?\n",
|
|
"3. What is $\\mbox{exp}[-\\infty]$?\n",
|
|
"4. What is $\\mbox{exp}[+\\infty]$?\n",
|
|
"5. A function is convex if we can draw a straight line between any two points on the\n",
|
|
"function, and this line always lies above the function. Similarly, a function is concave\n",
|
|
"if a straight line between any two points always lies below the function. Is the exponential function convex or concave or neither?\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"id": "R6A4e5IxIWCu"
|
|
},
|
|
"source": [
|
|
"Now let's consider the logarithm function $y=\\log[x]$. Throughout the book we always use natural (base $e$) logarithms. The log funcction maps non-negative numbers $[0,\\infty]$ to real numbers $[-\\infty,\\infty]$. It is the inverse of the exponential function. So when we compute $\\log[x]$ we are really asking \"What is the number $y$ so that $e^y=x$?\""
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 467
|
|
},
|
|
"id": "fOR7v2iXIWCu",
|
|
"outputId": "b128197d-6fcf-43e8-9833-8fee7d70be17"
|
|
},
|
|
"outputs": [
|
|
{
|
|
"output_type": "execute_result",
|
|
"data": {
|
|
"text/plain": [
|
|
"<function matplotlib.pyplot.show(close=None, block=None)>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"execution_count": 11
|
|
},
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
],
|
|
"source": [
|
|
"# Draw the logarithm function\n",
|
|
"\n",
|
|
"# Define an array of x values from -5 to 5 with increments of 0.1\n",
|
|
"x = np.arange(0.01,5.0, 0.01)\n",
|
|
"y = np.log(x) ;\n",
|
|
"\n",
|
|
"# Plot this function\n",
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(x,y,'r-')\n",
|
|
"ax.set_ylim([-5,5]);ax.set_xlim([0,5])\n",
|
|
"ax.set_xlabel('x'); ax.set_ylabel('$\\log[x]$')\n",
|
|
"plt.show"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"id": "yYWrL5AXIWCv"
|
|
},
|
|
"source": [
|
|
"# Questions\n",
|
|
"\n",
|
|
"1. What is $\\mbox{log}[0]$? \n",
|
|
"2. What is $\\mbox{log}[1]$?\n",
|
|
"3. What is $\\mbox{log}[e]$?\n",
|
|
"4. What is $\\mbox{log}[\\exp[3]]$?\n",
|
|
"5. What is $\\mbox{exp}[\\log[4]]$?\n",
|
|
"6. What is $\\mbox{log}[-1]$?\n",
|
|
"7. Is the logarithm function concave or convex?\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"source": [],
|
|
"metadata": {
|
|
"id": "XG0CKLiPJI7I"
|
|
},
|
|
"execution_count": null,
|
|
"outputs": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"colab": {
|
|
"provenance": [],
|
|
"include_colab_link": true
|
|
},
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.9.10"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 0
|
|
} |