week_3_answer_file.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Week 3 lab answers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q-3) Plot the function and identify region where it is concave and convex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import libraries\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# 500 linearly spaced numbers\n",
    "x = np.linspace(-2,2,500)\n",
    "\n",
    "# Define cost function, \n",
    "def f(x):\n",
    "    return (x**4 + x**3 - x**2 - 5)\n",
    "\n",
    "# setting the axes at the centre\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.spines['left'].set_position('zero')\n",
    "ax.spines['bottom'].set_position('zero')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# plot the function, you can use latex expression for the labels\n",
    "plt.plot(x,f(x), 'r', label=\"$y= x^5 + x^3 - x^2 -5$\")\n",
    "plt.legend(loc='upper left')\n",
    "# show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Global Minimum (using default Nelder-mead method)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Start Point x0 = -2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: -6.096735\n",
      "         Iterations: 20\n",
      "         Function evaluations: 40\n",
      "       message: Optimization terminated successfully.\n",
      "       success: True\n",
      "        status: 0\n",
      "           fun: -6.096734558075643\n",
      "             x: [-1.175e+00]\n",
      "           nit: 20\n",
      "          nfev: 40\n",
      " final_simplex: (array([[-1.175e+00],\n",
      "                       [-1.175e+00]]), array([-6.097e+00, -6.097e+00]))\n"
     ]
    }
   ],
   "source": [
    "# import optimize from scipy\n",
    "from scipy import optimize\n",
    "\n",
    "# The default (Nelder Mead)\n",
    "print(optimize.minimize(f, x0=-2, method='nelder-mead',\n",
    "               options={'xatol': 1e-5, 'disp': True}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local Minimum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Start point x0 = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: -5.071234\n",
      "         Iterations: 35\n",
      "         Function evaluations: 71\n",
      "       message: Optimization terminated successfully.\n",
      "       success: True\n",
      "        status: 0\n",
      "           fun: -5.071234191924322\n",
      "             x: [ 4.254e-01]\n",
      "           nit: 35\n",
      "          nfev: 71\n",
      " final_simplex: (array([[ 4.254e-01],\n",
      "                       [ 4.254e-01]]), array([-5.071e+00, -5.071e+00]))\n"
     ]
    }
   ],
   "source": [
    "from scipy import optimize\n",
    "\n",
    "# The default (Nelder Mead)\n",
    "print(optimize.minimize(f, x0=0, method='nelder-mead',\n",
    "               options={'xatol': 1e-8, 'disp': True}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q-4) The approximation of $f(x) = e^{-x} \\approx 1- x + \\frac{x^2}{2} - \\frac{x^3}{3!}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import libraries\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# 500 linearly spaced numbers\n",
    "x = np.linspace(-1,1,500)\n",
    "\n",
    "# Define cost function, \n",
    "def f_ori(x):\n",
    "    return np.exp(-x)\n",
    "def f_linear(x):\n",
    "    return 1- x\n",
    "def f_quadratic(x):\n",
    "    return 1 - x + (x ** 2) / 2\n",
    "# setting the axes at the centre\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.spines['left'].set_position('zero')\n",
    "ax.spines['bottom'].set_position('zero')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# plot the function, you can use latex expression for the labels\n",
    "plt.plot(x,f_ori(x), 'r', label=\"$f(x) = e^{-x}$\")\n",
    "plt.plot(x,f_linear(x), 'y', label=\"$f(x) = 1- x$\")\n",
    "plt.plot(x,f_quadratic(x), 'b', label=\"$f(x) = 1- x + x^2/2$\")\n",
    "plt.legend(loc='upper right')\n",
    "# show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q-5) $f(x) = -x^3 + 4x^2 - 3x + 5$\n",
    "##        subject to: $-2 \\le x \\le 2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import libraries\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# 500 linearly spaced numbers\n",
    "x = np.linspace(-2,2,500)\n",
    "\n",
    "# the function, \n",
    "def f(x):\n",
    "    return (-x**3 + 4*x**2 - 3*x + 5)\n",
    "\n",
    "# setting the axes at the centre\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.spines['left'].set_position('zero')\n",
    "ax.spines['bottom'].set_position('zero')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# plot the function\n",
    "plt.plot(x,f(x), 'r', label='$y= -x^3 + 4x^2 - 3x + 5$')\n",
    "plt.legend(loc='upper right')\n",
    "# show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2) Use Nelder-Mead"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 4.368870\n",
      "         Iterations: 36\n",
      "         Function evaluations: 73\n",
      "       message: Optimization terminated successfully.\n",
      "       success: True\n",
      "        status: 0\n",
      "           fun: 4.368869690559101\n",
      "             x: [ 4.514e-01]\n",
      "           nit: 36\n",
      "          nfev: 73\n",
      " final_simplex: (array([[ 4.514e-01],\n",
      "                       [ 4.514e-01]]), array([ 4.369e+00,  4.369e+00]))\n"
     ]
    }
   ],
   "source": [
    "# The default (Nelder Mead)\n",
    "from scipy import optimize\n",
    "# Define the bounds for the variables\n",
    "bounds = [(-2, 2)]\n",
    "print(optimize.minimize(g, x0=0, method='nelder-mead', bounds=bounds,\n",
    "               options={'xatol': 1e-8, 'disp': True}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3) Develop Bisection algorithm from scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    a            b\n",
      "-2.0000       2.0000\n",
      "--------------------------------\n",
      "0.0000       2.0000\n",
      "--------------------------------\n",
      "0.0000       1.0000\n",
      "--------------------------------\n",
      "0.0000       0.5000\n",
      "--------------------------------\n",
      "0.2500       0.5000\n",
      "--------------------------------\n",
      "0.3750       0.5000\n",
      "--------------------------------\n",
      "0.4375       0.5000\n",
      "--------------------------------\n",
      "0.4375       0.4688\n",
      "--------------------------------\n",
      "0.4375       0.4531\n",
      "--------------------------------\n",
      "0.4453       0.4531\n",
      "--------------------------------\n",
      "0.4492       0.4531\n",
      "--------------------------------\n",
      "0.4512       0.4531\n",
      "--------------------------------\n",
      "0.4512       0.4521\n",
      "--------------------------------\n",
      "0.4512       0.4517\n",
      "--------------------------------\n",
      "0.4514       0.4517\n",
      "--------------------------------\n",
      "0.4514       0.4515\n",
      "x* = 0.4514    Minimum = 4.3689\n",
      "Number of function calls =  60\n"
     ]
    }
   ],
   "source": [
    "# Import libraries\n",
    "import numpy as np\n",
    "\n",
    "# the function, \n",
    "def f(x):\n",
    "    return (-x**3 + 4*x**2 - 3*x + 5)\n",
    "\n",
    "# set initial value of a and b\n",
    "a = -2\n",
    "b = 2\n",
    "\n",
    "# set the tolerance \n",
    "epsilon = 0.0001\n",
    "delta_x = 0.01\n",
    "\n",
    "print('    a            b')\n",
    "\n",
    "for i in range(100):\n",
    "    print(\"%.4f\" % a,\"     \",\"%.4f\" % b) # print the values of a and b at each step\n",
    "    alpha = (a+b)/2\n",
    "    derivative = (f(a + delta_x) - f(a - delta_x)) / (2 * delta_x)\n",
    "    derivative_alpha = (f(alpha + delta_x) - f(alpha - delta_x)) / (2 * delta_x)\n",
    "    if derivative * derivative_alpha < 0:\n",
    "        b = alpha\n",
    "    else:\n",
    "        a = alpha\n",
    "        \n",
    "    if abs(a - b) < epsilon:\n",
    "        break\n",
    "    \n",
    "    print('--------------------------------')\n",
    "# print the final results\n",
    "print(\"x* = %.4f\" %a, \"  \", \"Minimum = %.4f\" % f(a))\n",
    "print('Number of function calls = ', 4*i)\n",
    "        \n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
   "name": "python3"
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    "name": "ipython",
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   "file_extension": ".py",
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