Matrix.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array([\n",
    "    [0, 0, 1],\n",
    "    [0, 1, 0],\n",
    "    [1, 0, 0],\n",
    "    [1 ,1, 0],\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 3)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = np.array([\n",
    "    [1],\n",
    "    [2],\n",
    "    [3],\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 1)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3],\n",
       "       [2],\n",
       "       [1],\n",
       "       [3]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(X, W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 3],\n",
       "       [0, 2, 0],\n",
       "       [1, 0, 0],\n",
       "       [1, 2, 0]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X * W.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3],\n",
       "       [2],\n",
       "       [1],\n",
       "       [3]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X @ W # np.dot(X, W) # X.dot(W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 1],\n",
       "       [0, 1, 0],\n",
       "       [1, 0, 0],\n",
       "       [1, 1, 0]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 1, 0],\n",
       "       [1, 2, 0],\n",
       "       [0, 0, 1]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.T @ X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "# load the data\n",
    "X = []\n",
    "Y = []\n",
    "for line in open('data_2d.csv'):\n",
    "    x1, x2, y = line.split(',')\n",
    "    X.append([float(x1), float(x2), 1]) # add the bias term\n",
    "    Y.append(float(y))\n",
    "\n",
    "\n",
    "\n",
    "# let's turn X and Y into numpy arrays since that will be useful later\n",
    "X = np.array(X)\n",
    "Y = np.array(Y)\n",
    "\n",
    "\n",
    "\n",
    "# let's plot the data to see what it looks like\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.scatter(X[:,0], X[:,1], Y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.linalg.solve( (X.T @ X), (X.T @ Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.01666793, 2.96985048, 1.46191241])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "Yhat = X @ w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 3)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "def r2(Y, Yhat):\n",
    "    d1 = ((Y - Yhat) ** 2.0).sum()\n",
    "    d2 = ((Y - Y.mean()) ** 2.0).sum()\n",
    "\n",
    "    return ( 1 - ( d1 / d2 ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the r-squared is: 0.9991412296366858\n"
     ]
    }
   ],
   "source": [
    "print(\"the r-squared is:\", r2(Y, Yhat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load the data\n",
    "X = []\n",
    "Y = []\n",
    "for line in open('data_poly.csv'):\n",
    "    x, y = line.split(',')\n",
    "    x = float(x)\n",
    "    X.append([1, x, x*x]) # add the bias term x0 = 1\n",
    "    # our model is therefore y_hat = w0 + w1 * x + w2 * x**2\n",
    "    Y.append(float(y))\n",
    "\n",
    "# let's turn X and Y into numpy arrays since that will be useful later\n",
    "X = np.array(X)\n",
    "Y = np.array(Y)\n",
    "\n",
    "# let's plot the data to see what it looks like\n",
    "plt.scatter(X[:,1], Y)\n",
    "plt.title(\"The data we're trying to fit\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.linalg.solve( (X.T @ X), (X.T @ Y))\n",
    "Yhat = X @ w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,1], Y)\n",
    "plt.plot(sorted(X[:,1]), sorted(Yhat))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9991412296366858"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2(Y, Yhat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([\n",
    "    [1, 12, 11, 41],\n",
    "    [2, 13, 12, 42],\n",
    "    [3, 14, 13, 43],\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "B = np.array([\n",
    "    [1.5, 12.5, 11.5, 41.5],\n",
    "    [2.5, 13.5, 12.5, 42.5],\n",
    "    [3.5, 14.5, 13.5, 43.5],\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.5000e+00, 1.5000e+02, 1.2650e+02, 1.7015e+03],\n",
       "       [5.0000e+00, 1.7550e+02, 1.5000e+02, 1.7850e+03],\n",
       "       [1.0500e+01, 2.0300e+02, 1.7550e+02, 1.8705e+03]])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6354.5"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(A * B).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  17. ,   83. ,   77. ,  257. ],\n",
       "       [  99.5,  528.5,  489.5, 1659.5],\n",
       "       [  92. ,  488. ,  452. , 1532. ],\n",
       "       [ 317. , 1703. , 1577. , 5357. ]])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.T @ B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*** No CODEPAGE record, no encoding_override: will use 'ascii'\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "df = pd.read_excel('mlr02.xls')\n",
    "X = df.values\n",
    "\n",
    "# using age to predict systolic blood pressure\n",
    "plt.scatter(X[:,1], X[:,0])\n",
    "plt.show()\n",
    "# looks pretty linear!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['ones'] = 1\n",
    "# df['ten'] = 10\n",
    "\n",
    "Y = df['X1']\n",
    "X = df[['X2', 'X3', 'ones']]\n",
    "\n",
    "X2only = df[['X2', 'ones']]\n",
    "X3only = df[['X3', 'ones']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r2 for x2 only: 0.9578407208147356\n",
      "r2 for x3 only: 0.9419952085293065\n",
      "r2 for both: 0.9768471041502091\n"
     ]
    }
   ],
   "source": [
    "def get_r2(X, Y):\n",
    "    w = np.linalg.solve( X.T @ X, X.T @ Y )\n",
    "    Yhat = X @ w\n",
    "\n",
    "    # determine how good the model is by computing the r-squared\n",
    "    d1 = Y - Yhat\n",
    "    d2 = Y - Y.mean()\n",
    "    r2 = 1 - d1.dot(d1) / d2.dot(d2)\n",
    "    return r2\n",
    "\n",
    "print(\"r2 for x2 only:\", get_r2(X2only, Y))\n",
    "print(\"r2 for x3 only:\", get_r2(X3only, Y))\n",
    "print(\"r2 for both:\", get_r2(X, Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}