{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is previous post with my multivariable gradient descent implementation: https://nbviewer.jupyter.org/github/lion137/blog/blob/master/gradient_descent_multi.ipynb, but it has a bug and also lacked input features, so I rebuilt it and also updated the old version. This is a code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import time\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# helping functions\n",
    "def split_input_and_to_float(xs):\n",
    "    def helper(ys):\n",
    "        l = list(map(int, ys))\n",
    "        l = list(map(float, ys))\n",
    "        return l\n",
    "    l1 = list(map(helper, xs))\n",
    "    return l1\n",
    "\n",
    "def split(x):\n",
    "    \"\"\"simple split string\"\"\"\n",
    "    return x.split(',')\n",
    "\n",
    "def Sum(X, y, theta, ind):\n",
    "    \"compute sum under the sigma in g d algorithm\"\n",
    "    i = 0\n",
    "    s = 0\n",
    "    while i < len(X):\n",
    "        s += (theta * X[i,:].transpose() - y[0, i]) * X[i, ind]\n",
    "        i += 1\n",
    "    return float(s)\n",
    "\n",
    "def J_m(A, y, theta):\n",
    "    \"\"\"computes cost function \"\"\"\n",
    "    n = len(A)\n",
    "    return (1 / (2 * n)) * float(sum([x * x for x in A * theta.transpose() - y.transpose()]))\n",
    "\n",
    "def scaling(X):\n",
    "    \"\"\"mean normalzation\"\"\"\n",
    "    l = []\n",
    "    for k in range(X.shape[1]):\n",
    "        x = X[:,k]\n",
    "        def f(e):\n",
    "            tmp0 = sum(x) / len(x)\n",
    "            tmp1 = max(x) - min(x)\n",
    "            return (e - tmp0) / tmp1\n",
    "        m =  list(map(float, (list(map(f, x[:, 0])))))\n",
    "        l.append(m)\n",
    "    return np.matrix(l).transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time in secs:  0.02801966667175293\n",
      "[[17 31]] 0.0 0.625 8\n"
     ]
    },
    {
     "data": {
      "image/png": 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69/dl4cEHQycRERFJHklREho3hn794IEH/NwJIiIiUnlJURIAhg6FlSth+vTQSURERJJD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\nt86XC03sJBIdGklIQLm5uWR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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb6a538748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n",
      "Wall time: 2.51 ms\n",
      "[[ 17.5]\n",
      " [ 33. ]]\n"
     ]
    }
   ],
   "source": [
    "# gradient descent\n",
    "l_iin = [] # debbuging data arrays\n",
    "l_cost = []\n",
    "f = open('data1.txt', 'r') # reading from file added\n",
    "f1 = list(map(str.rstrip, f.readlines()))\n",
    "f2 = f1[0].split(',')\n",
    "f3 = list(map(split, f1))\n",
    "f4 = split_input_and_to_float(f3)\n",
    "X = np.matrix([0] * len(f4[0]))\n",
    "for elem in f4:\n",
    "       X = np.vstack([X, elem])\n",
    "X = X[1: , :]\n",
    "y = X[:,X.shape[1] - 1].transpose()\n",
    "X = X[:,:X.shape[1] - 1]\n",
    "X = scaling(X)\n",
    "X = np.c_[[1] * len(X), X]\n",
    "theta = np.matrix([0] * X.shape[1])\n",
    "tmp = np.matrix([0] * X.shape[1])\n",
    "m = X.shape[0]\n",
    "cnt = 0\n",
    "alfa = 1.64\n",
    "precision = 0.001\n",
    "delta = precision + 1\n",
    "t_start = time.time()\n",
    "while delta > precision:\n",
    "    beg = J_m(X, y, theta)\n",
    "    for i in range(X.shape[1]):\n",
    "        tmp[0,i] = theta[0,i] - (alfa / m) * (Sum(X, y, theta, i))\n",
    "    theta = tmp\n",
    "    end = J_m(X, y, theta)\n",
    "    delta = abs(end - beg)\n",
    "    l_iin.append(cnt)\n",
    "    l_cost.append(J_m(X, y, theta))\n",
    "    cnt += 1\n",
    "t_end = time.time()\n",
    "print(\"time in secs: \", t_end - t_start)\n",
    "print(theta, delta, end, cnt)\n",
    "\n",
    "\n",
    "plt.plot(l_iin, l_cost, color=\"blue\", linewidth=1, label=\"alfa=1.64\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.show()  \n",
    "\n",
    "%time theta = ((X.transpose() * X).getI()) * X.transpose() * y.transpose()\n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There  is also added analytically method for minimizing cost function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "theta = ((X.transpose() * X).getI()) * X.transpose() * y.transpose()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is Octave's:    \n",
    "pinv(X' *  X) * X' y    \n",
    "Doesnt work for singular matrixes though, but is great for testing purposes and after checking lots of datasets, algorithm seems to be OK. There are still, differences beetwen both methods, so I'm going, obviously, to work this out and publish results here!"
   ]
  }
 ],
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  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
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