week4_lab.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 251,
   "id": "12d95d03-52af-49c3-9d28-e309d8986d7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import bisect, newton, minimize\n",
    "import matplotlib.pyplot as plt\n",
    "import sympy as sp\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60385e7e-348c-4103-b877-5f4f765034d7",
   "metadata": {},
   "source": [
    "### Question 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "id": "f5211f69-00b0-4a56-8000-78ec164cbe6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0, 2 , 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "id": "46b5fcad-dbf4-44f8-9cde-4f083a9050fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_func(x_val):\n",
    "    return x_val**4 + x_val**3 - x_val**2 - 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "id": "36ae8377-4b97-45a0-94dd-3cda0ee6aa66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, cost_func(x))\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.title(\"$f(x)= x^4 + x^3 - x^2 - 5$\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fee3acd3-83ad-44cc-9176-4d3bd1097a41",
   "metadata": {},
   "source": [
    "### Using the Bisection algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "id": "8db9754e-780a-4cc6-b4a9-45742d2cb507",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4259134167095908"
      ]
     },
     "execution_count": 257,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bisect(cost_func, 0, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "564b20fd-ea44-48d0-b4da-f9796233ab93",
   "metadata": {},
   "source": [
    "### Using the Newton algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "id": "d465f568-92cf-499d-abbd-e904677734fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4259134167081748"
      ]
     },
     "execution_count": 259,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "newton(cost_func, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7e3ab74-50cd-4db2-be42-929b6a1f1ec6",
   "metadata": {},
   "source": [
    "### Question 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d85b6f5d-4f3c-4a11-ac49-7586ca9eb9dd",
   "metadata": {},
   "source": [
    "### Bisection Algorithm from Scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "id": "b6e389d4-9233-4ffd-8832-8181c9405136",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bisec_opt(a, b):\n",
    "    minimum = 0.0001\n",
    "    while b - a > minimum:\n",
    "        alpha = (a + b) / 2\n",
    "        y_alpha = cost_func(alpha)\n",
    "        if y_alpha > 0:\n",
    "            b = alpha\n",
    "        elif y_alpha < 0:\n",
    "            a = alpha\n",
    "        else:\n",
    "            return alpha\n",
    "    # Return the mean of the two\n",
    "    return (a + b) / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "id": "2071fb5d-78d3-414c-9273-4031096dd3c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4259185791015625"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bound_a = -1\n",
    "bound_b = 2\n",
    "bisec_opt(bound_a, bound_b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3975732f-28c6-4ad0-9aa9-12f0fb6aa44b",
   "metadata": {},
   "source": [
    "### Question 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5125a939-2705-4167-9ada-85a6a3f3b045",
   "metadata": {},
   "source": [
    "### Newton-Raphson algorithm from Scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "id": "f093fc4d-a5f3-4fa4-aa8f-d15cb6384fb8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_value(function, x):\n",
    "    return function(x)\n",
    "\n",
    "def newton_raphson(function, i):\n",
    "    minimum = 0.0001\n",
    "    f_prime = sp.diff(function, x)\n",
    "    i_next = 0\n",
    "    while True:\n",
    "        y_val = get_value(lambda x_val: function.subs(x, x_val), i)\n",
    "        f_prime_val = get_value(lambda x_val: f_prime.subs(x, x_val), i)\n",
    "        i_next = i - (y_val / f_prime_val)\n",
    "        if abs(i - i_next) < minimum:\n",
    "            break\n",
    "        else:\n",
    "            i = i_next\n",
    "    \n",
    "    return float(i_next)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "id": "a88ce7da-55bb-4dae-92f7-f72f747654e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.425913416709838"
      ]
     },
     "execution_count": 267,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sp.symbols('x')\n",
    "# cost_function = -x ** 3 + 4 * x ** 2 - 3 * x + 5 Struggles with complex function like this\n",
    "cost_function = x**4 + x**3 + - x**2 - 5\n",
    "guess_point = 2\n",
    "newton_raphson(cost_function, guess_point)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d6b451f-0961-4edf-9639-2cce9b1d5d9f",
   "metadata": {},
   "source": [
    "### Question 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "id": "cea320ff-395a-43a3-8b99-fe16ce2b86bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-2, 2 , 50)\n",
    "\n",
    "def cost_func(x_val):\n",
    "    return -x_val**3 + 4*x_val**2 - 3*x_val + 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "id": "434777f3-609b-451c-bca4-5e65c86ea524",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, cost_func(x))\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.title(\"$f(x)= -x^3 + 4x^2 - 3x + 5$\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32ca55d2-fcea-47b7-85de-f8463630eeba",
   "metadata": {},
   "source": [
    "### Using Scipy Optimize function 'minimize'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "id": "d522ba82-8b80-4cff-866b-234246757b3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4514172516938504"
      ]
     },
     "execution_count": 288,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minimize(cost_func, 2).x[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d72a9fa-e33a-45b5-9236-553606940c0b",
   "metadata": {},
   "source": [
    "### Golden Section algorithm from Scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "id": "bcfbb456-3b8a-489a-9e7a-9bba43934e5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def golden_section(a, b):\n",
    "    minimum = 0.0001\n",
    "    # Calculate the golden ratio\n",
    "    golden_ratio = (math.sqrt(5) - 1) / 2\n",
    "    while b - a > minimum:\n",
    "        c = golden_ratio * (b - a)\n",
    "        x1 = a + c\n",
    "        x2 = b - c\n",
    "        if cost_func(x1) > cost_func(x2):\n",
    "            b = x1\n",
    "        elif cost_func(x1) < cost_func(x2):\n",
    "            a = x2\n",
    "        else:\n",
    "            return x1\n",
    "    # Return the mean of the two\n",
    "    return (a + b) / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "id": "c59017ee-6a8a-46a0-8ba9-a428de3d2cc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.45143801695435315"
      ]
     },
     "execution_count": 286,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bound_a = -1\n",
    "bound_b = 2\n",
    "golden_section(bound_a, bound_b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c68b77a0-5538-485e-83bf-a3039d3528ab",
   "metadata": {},
   "source": [
    "### Bisection Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "id": "a2337968-064c-41fe-9505-ebce1f335101",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bisec_opt(a, b):\n",
    "    minimum = 0.0001\n",
    "    delta = 0.01\n",
    "    while b - a > minimum:\n",
    "        print(f\"current a: {a}------- current b: {b}\")\n",
    "        alpha = (a + b) / 2\n",
    "        alpha_gradient = (cost_func(alpha + delta) - cost_func(alpha - delta)) / 2 * delta\n",
    "        a_gradient = (cost_func(a + delta) - cost_func(a - delta)) / 2 * delta\n",
    "        print(f\"alpha_gradient: {alpha_gradient}------- a_gradient: {a_gradient}\")\n",
    "        if alpha_gradient * a_gradient < 0:\n",
    "            b = alpha\n",
    "        elif alpha_gradient * a_gradient > 0:\n",
    "            a = alpha\n",
    "        else:\n",
    "            return alpha\n",
    "    # Return the mean of the two\n",
    "    return (a + b) / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "id": "95447284-4d0b-4fd1-8450-de92776dcfa7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "current a: -1------- current b: 2\n",
      "alpha_gradient: 2.498999999999807e-05------- a_gradient: -0.0014000099999999982\n",
      "current a: -1------- current b: 0.5\n",
      "alpha_gradient: -0.0005187600000000004------- a_gradient: -0.0014000099999999982\n",
      "current a: -0.25------- current b: 0.5\n",
      "alpha_gradient: -0.00020469749999999732------- a_gradient: -0.0005187600000000004\n",
      "current a: 0.125------- current b: 0.5\n",
      "alpha_gradient: -7.93068749999959e-05------- a_gradient: -0.00020469749999999732\n",
      "current a: 0.3125------- current b: 0.5\n",
      "alpha_gradient: -2.4521718749999088e-05------- a_gradient: -7.93068749999959e-05\n",
      "current a: 0.40625------- current b: 0.5\n",
      "alpha_gradient: 8.933203125005562e-07------- a_gradient: -2.4521718749999088e-05\n",
      "current a: 0.40625------- current b: 0.453125\n",
      "alpha_gradient: -1.164940429687622e-05------- a_gradient: -2.4521718749999088e-05\n",
      "current a: 0.4296875------- current b: 0.453125\n",
      "alpha_gradient: -5.336843261720681e-06------- a_gradient: -1.164940429687622e-05\n",
      "current a: 0.44140625------- current b: 0.453125\n",
      "alpha_gradient: -2.2114617919921643e-06------- a_gradient: -5.336843261720681e-06\n",
      "current a: 0.447265625------- current b: 0.453125\n",
      "alpha_gradient: -6.564958190891091e-07------- a_gradient: -2.2114617919921643e-06\n",
      "current a: 0.4501953125------- current b: 0.453125\n",
      "alpha_gradient: 1.19055976868232e-07------- a_gradient: -6.564958190891091e-07\n",
      "current a: 0.4501953125------- current b: 0.45166015625\n",
      "alpha_gradient: -2.685589885720319e-07------- a_gradient: -6.564958190891091e-07\n",
      "current a: 0.450927734375------- current b: 0.45166015625\n",
      "alpha_gradient: -7.471127271507782e-08------- a_gradient: -2.685589885720319e-07\n",
      "current a: 0.4512939453125------- current b: 0.45166015625\n",
      "alpha_gradient: 2.2182410361892836e-08------- a_gradient: -7.471127271507782e-08\n",
      "current a: 0.4512939453125------- current b: 0.45147705078125\n",
      "alpha_gradient: -2.626191661025956e-08------- a_gradient: -7.471127271507782e-08\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.4514312744140625"
      ]
     },
     "execution_count": 301,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bound_a = -1\n",
    "bound_b = 2\n",
    "bisec_opt(bound_a, bound_b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2fd9618-9869-44ce-b541-c8294f21be68",
   "metadata": {},
   "source": [
    "### Newton-Raphson algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "id": "036370c2-d823-4909-9e9e-77030752acc3",
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/3m/7yx097tn2wz5t7h3fbj4dj_00000gn/T/ipykernel_91483/2935050387.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mcost_function\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m3\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mguess_point\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mnewton_raphson\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcost_function\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mguess_point\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/var/folders/3m/7yx097tn2wz5t7h3fbj4dj_00000gn/T/ipykernel_91483/3191294736.py\u001b[0m in \u001b[0;36mnewton_raphson\u001b[0;34m(function, i)\u001b[0m\n\u001b[1;32m      9\u001b[0m         \u001b[0my_val\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mx_val\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_val\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0mf_prime_val\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mx_val\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mf_prime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_val\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m         \u001b[0mi_next\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0my_val\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mf_prime_val\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mi_next\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0mminimum\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m             \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/sympy/core/decorators.py\u001b[0m in \u001b[0;36m__sympifyit_wrapper\u001b[0;34m(a, b)\u001b[0m\n\u001b[1;32m     63\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'_op_priority'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     64\u001b[0m                     \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msympify\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstrict\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 65\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     66\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mSympifyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     67\u001b[0m                 \u001b[0;32mreturn\u001b[0m \u001b[0mretval\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/sympy/core/numbers.py\u001b[0m in \u001b[0;36m__truediv__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m   1479\u001b[0m                     \u001b[0;32mreturn\u001b[0m \u001b[0mRational\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0migcd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1480\u001b[0m             \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRational\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1481\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mRational\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0migcd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0migcd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1482\u001b[0m             \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mFloat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1483\u001b[0m                 \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/sympy/core/cache.py\u001b[0m in \u001b[0;36mwrapper\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     70\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     71\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 72\u001b[0;31m                 \u001b[0mretval\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     73\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mTypeError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     74\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstartswith\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'unhashable type:'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/sympy/core/numbers.py\u001b[0m in \u001b[0;36m__new__\u001b[0;34m(cls, p, q, gcd)\u001b[0m\n\u001b[1;32m   1375\u001b[0m             \u001b[0mgcd\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0migcd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mq\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1376\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mgcd\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1377\u001b[0;31m             \u001b[0mp\u001b[0m \u001b[0;34m//=\u001b[0m \u001b[0mgcd\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1378\u001b[0m             \u001b[0mq\u001b[0m \u001b[0;34m//=\u001b[0m \u001b[0mgcd\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1379\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mq\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "x = sp.symbols('x')\n",
    "cost_function = -x**3 + 4*x**2 - 3*x + 5\n",
    "guess_point = 2\n",
    "newton_raphson(cost_function, guess_point)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a8eed488-7b73-4884-ade0-e272e5ef6638",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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