Scipy.optimize.curve_fit/Curve_fit_from_scipy_optimize.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scipy.optimize.curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# lets generate a stimulated data, where we have X and y\n",
    "np.random.seed(1)\n",
    "X = np.random.randint(1,20,25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6, 12, 13,  9, 10, 12,  6, 16,  1, 17,  2, 13,  8, 14,  7, 19,  6,\n",
       "       19, 12, 11, 15, 19,  5, 10, 18])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# in this case, y is linearly related to X, therefore, we expect the linear function to perform the best\n",
    "np.random.seed(2)\n",
    "y = -1 + X*3.5 + 10*np.random.randn(25)\n",
    "# here the intercept is -1, slope is 3.5 and some randon noise is added"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Distribution of data')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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86hjv1CT1Bpt61DHzh4fqDicwkzs1eY5AOnzu8atjDve688lzBKPjEyT7zxFs2DLahmqlwWXwq2MO905NniOQWsOmHnXU4Vx37jkCqTXc41ffaHQuYCbnCCQZ/JqBDVtGWbJ6E6euvJklqzd1vG3dsWmk1rCpR03phc5Xjk0jtYbBr6b0ym3+emVsGi8rVT8z+NUUT6zu1wtHP9LhsI1fTfHE6n5eVqp+Z/CrKZ5Y3W/Qjn66fdJenWdTj5riidX9WjH0RK+w2aqaDH41rVdOrHbbiqWLDghL6N+jn145aa/OMvilGRqko59Ba7ZScwx+aRYG5ehnkJqt1DxP7koV5kn7anKPX6qwQWq2UvPaFvwRcRLwaeC5wJPA2sz8s4g4DrgeWAg8ALwhM7/frjrUOvZWHUyD0myl5rWzqWcv8P7MfAFwNvCbEXEGsBK4LTNPB24rn6vHeRMUaXC0Lfgzc1dm3lU+/gFwL7AAuABYVy62DljWrhq03+F20rG3qjQ4OtLGHxELgcXAHcBzMnMXFF8OEfHsBq+5GLgY4OSTT+5EmQOrFZ10vOxPGhxtv6onIo4C/h54T2Y+3uzrMnNtZo5k5si8efPaV2AFtGJv3bF6pMHR1uCPiLkUoX9tZq4vJ++OiBPK+ScAD7ezBrVmb93L/qTB0bbgj4gArgTuzcwrambdBCwvHy8HbmxXDSq0Ym/9cG+ULql3tLONfwnwFmBrRNxdTvsQsBq4ISIuAh4EXt/GGkTrxpbxsj9pMLQt+DPzX4BoMPucdr2vDmYnHUm17LlbEe6tt5ad2dTPDH41zbArOIa9+p2DtKkp9tzdz85s6ncGv5pi2O1nZzb1O4NfTTHs9rMzm/qdwa+mGHb72ZlN/c7gV1MMu/3szKZ+51U9aop9AQ7k5bHqZwa/mmbYSYPBph5JqhiDX5IqxqaeadhTVdIgMvgbsFu+pEFlU08D9lSVNKgM/gbsqSppUBn8DdhTVdKgMvgbsKeqpEHlyd0G7KkqaVAZ/NOwp6qkQWRTjyRVjMEvSRVj8EtSxRj8klQxBr8kVYzBL0kVY/BLUsUY/JJUMQa/JFWMwS9JFWPwS1LFGPySVDEGvyRVjMEvSRVj8EtSxRj8klQxBr8kVYzBL0kV05Xgj4jzImJbRGyPiJXdqEGSqqrjwR8Rc4C/As4HzgB+JSLO6HQdklRV3djjPwvYnpn3Z+aPgeuAC7pQhyRVUjeCfwHwUM3zHeW0A0TExRGxOSI2j42Ndaw4SRp03Qj+qDMtD5qQuTYzRzJzZN68eR0oS5KqoRvBvwM4qeb5icDOLtQhSZXUjeD/D+D0iDg1Io4ELgRu6kIdklRJR3T6DTNzb0S8C9gIzAGuysxvdLoOSaqqjgc/QGbeAtzSjfeWpKqz564kVYzBL0kVY/BLUsUY/JJUMQa/JFWMwS9JFWPwS1LFGPySVDEGvyRVjMEvSRXTlSEbOmHDllHWbNzGzvEJ5g8PsWLpIpYtPmjYf0mqnIEM/g1bRlm1fisTe/YBMDo+war1WwEMf0mVN5BNPWs2bnsq9CdN7NnHmo3bulSRJPWOgQz+neMTM5ouSVUykME/f3hoRtMlqUoGMvhXLF3E0Nw5B0wbmjuHFUsXdakiSeodA3lyd/IErlf1SNLBBjL4oQh/g16SDjaQTT2SpMYMfkmqGINfkirG4JekijH4JaliIjO7XcMhRcQY8J1u13EIxwOPdLuIJlhna1ln6/VLrf1Q5ymZOW/qxL4I/n4QEZszc6TbdRyKdbaWdbZev9TaL3XWY1OPJFWMwS9JFWPwt87abhfQJOtsLetsvX6ptV/qPIht/JJUMe7xS1LFGPySVDEGf5Mi4qSI+HJE3BsR34iI366zzMsj4rGIuLv8ubQbtZa1PBARW8s6NteZHxHx5xGxPSK+FhFndqHGRTXb6u6IeDwi3jNlma5s04i4KiIejoiv10w7LiJujYj7yt/HNnjt8nKZ+yJieRfqXBMR3yz/Xf8hIoYbvHbaz0iHar0sIkZr/n1f1eC150XEtvLzurILdV5fU+MDEXF3g9d2dJvOWmb608QPcAJwZvn4aOC/gDOmLPNy4PPdrrWs5QHg+Gnmvwr4AhDA2cAdXa53DvBdig4nXd+mwEuBM4Gv10z7OLCyfLwS+Fid1x0H3F/+PrZ8fGyH63wlcET5+GP16mzmM9KhWi8DPtDEZ+NbwGnAkcA9U//vtbvOKfP/GLi0F7bpbH/c429SZu7KzLvKxz8A7gX6ecD/C4BPZ+GrwHBEnNDFes4BvpWZPdFDOzO/Ajw6ZfIFwLry8TpgWZ2XLgVuzcxHM/P7wK3AeZ2sMzO/lJl7y6dfBU5s1/vPRINt2oyzgO2ZeX9m/hi4juLfoi2mqzMiAngD8Jl2vX8nGPyzEBELgcXAHXVmvzgi7omIL0TE/+hoYQdK4EsRcWdEXFxn/gLgoZrnO+juF9mFNP7P1Cvb9DmZuQuKHQHg2XWW6bXt+naKI7t6DvUZ6ZR3lc1SVzVoPuulbfoSYHdm3tdgfq9s02kZ/DMUEUcBfw+8JzMfnzL7LoqmihcBfwFs6HR9NZZk5pnA+cBvRsRLp8yPOq/pyrW9EXEk8Frgs3Vm99I2bUYvbddLgL3AtQ0WOdRnpBM+ATwP+FlgF0UzylQ9s02BX2H6vf1e2KaHZPDPQETMpQj9azNz/dT5mfl4Zv6wfHwLMDciju9wmZO17Cx/Pwz8A8Xhcq0dwEk1z08EdnamuoOcD9yVmbunzuilbQrsnmwOK38/XGeZntiu5UnlVwNvyrLxeaomPiNtl5m7M3NfZj4J/N8GNfTKNj0CeB1wfaNlemGbNsPgb1LZtnclcG9mXtFgmeeWyxERZ1Fs3+91rsqn6nhGRBw9+ZjiZN/Xpyx2E/Cr5dU9ZwOPTTZjdEHDvahe2aalm4DJq3SWAzfWWWYj8MqIOLZstnhlOa1jIuI84IPAazPzRw2WaeYz0nZTziv97wY1/AdwekScWh4dXkjxb9Fp5wLfzMwd9Wb2yjZtSrfPLvfLD/DzFIeXXwPuLn9eBbwTeGe5zLuAb1BcdfBV4Oe6VOtpZQ33lPVcUk6vrTWAv6K4WmIrMNKlWp9OEeTH1Ezr+jal+CLaBeyh2OO8CHgWcBtwX/n7uHLZEeBTNa99O7C9/HlbF+rcTtEmPvk5/WS57Hzgluk+I12o9Zry8/c1ijA/YWqt5fNXUVxJ961211qvznL61ZOfy5plu7pNZ/vjkA2SVDE29UhSxRj8klQxBr8kVYzBL0kVY/BLUsUY/NIMRTFS67cj4rjy+bHl81O6XZvUDINfmqHMfIhiqIHV5aTVwNrskQHmpEPxOn5pFsrhO+4ErgJ+DVicxciRUs87otsFSP0oM/dExArgi8ArDX31E5t6pNk7n6Jr/wu7XYg0Ewa/NAsR8bPAL1Lcvey9Xb6JjTQjBr80Q+VooZ+guCfDg8Aa4I+6W5XUPINfmrlfAx7MzFvL538N/FREvKyLNUlN86oeSaoY9/glqWIMfkmqGINfkirG4JekijH4JaliDH5JqhiDX5Iq5v8D9xsukhqZcDUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# lets visualize the data we have\n",
    "plt.scatter(X,y)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Distribution of data')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this callable function is the first parameter to the function curve_fit.\n",
    "# the parameters are given such that func(x,*params) - y is minimized\n",
    "def func(x,a,b):\n",
    "    return a + x*b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the first return value is an array of all the values of the coefficients, which were given as an input to the above function.\n",
    "popt,pcov = curve_fit(func,X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.69098784  3.2476999 ]\n"
     ]
    }
   ],
   "source": [
    "# these are the values returned by the function curve fit, we can see that the intercept -0.69 is close to the choosen \n",
    "# value of -1, whlie estimated slope is 3.247 is close to the true value of 3.5.\n",
    "print(popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[24.45764497 -1.80404084]\n",
      " [-1.80404084  0.16107507]]\n",
      "Std dev of estimates are  [4.94546711 0.40134159]\n"
     ]
    }
   ],
   "source": [
    "# this gives the correlation between the estimators\n",
    "print(pcov)\n",
    "# if one needs to find the std dev , then\n",
    "print('Std dev of estimates are ',np.sqrt(np.diag(pcov)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "# lets now generate some test values, and see how it is predicting for the \n",
    "X_test = np.random.randint(0,25,30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root Mean squred error  is - 9.356681126734257\n"
     ]
    }
   ],
   "source": [
    "# as a measure of fit, we will calculate the root mean squared error for test_data\n",
    "# since it is a stimulated data we can calculate y_test\n",
    "np.random.seed(2)\n",
    "y_test = -1 + X_test*3.5 + 10*np.random.randn(30)\n",
    "RMSE = np.sqrt(np.sum((y_test - func(X_test,*popt))**2) / len(X_test))\n",
    "print('Root Mean squred error  is -',RMSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Linear fit')"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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,y)\n",
    "sns.lineplot(X_test,func(X_test,popt[0],popt[1]),color = 'red')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Linear fit')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## We can use any function to fit the data, just change the first paramter to curve fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quadratic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[14.06155054  0.14239792]\n",
      "Root Mean squred error  is - 13.488919462878902\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Quad fit')"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# just change the func used for optimization\n",
    "def func(x,a,b):\n",
    "    return a + b*x**2\n",
    "\n",
    "popt,pcov = curve_fit(func,X,y)\n",
    "\n",
    "print(popt)\n",
    "\n",
    "X_test = np.random.randint(0,25,50)\n",
    "\n",
    "np.random.seed(2)\n",
    "y_test = -1 + X_test*3.5 + 10*np.random.randn(50)\n",
    "RMSE = np.sqrt(np.sum((y_test - func(X_test,*popt))**2) / len(X_test))\n",
    "print('Root Mean squred error  is -',RMSE)\n",
    "\n",
    "plt.scatter(X,y)\n",
    "sns.lineplot(X_test,func(X_test,popt[0],popt[1]),color = 'red')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Quad fit')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cubic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.04551542e+01  2.43375808e-01 -5.16003922e-03]\n",
      "Root Mean squred error  is - 10.756198331477277\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Cubic')"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "def func(x,a,b,c):\n",
    "    return a + b*x**2 + c*x**3\n",
    "\n",
    "popt,pcov = curve_fit(func,X,y)\n",
    "\n",
    "print(popt)\n",
    "\n",
    "X_test = np.random.randint(0,25,50)\n",
    "\n",
    "np.random.seed(2)\n",
    "y_test = -1 + X_test*3.5 + 10*np.random.randn(50)\n",
    "RMSE = np.sqrt(np.sum((y_test - func(X_test,*popt))**2) / len(X_test))\n",
    "print('Root Mean squred error  is -',RMSE)\n",
    "\n",
    "plt.scatter(X,y)\n",
    "sns.lineplot(X_test,func(X_test,popt[0],popt[1],popt[2]),color = 'red')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Cubic')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-15.48702599  22.77687623]\n",
      "Root Mean squred error  is - inf\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Lenovo\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'LOG')"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "def func(x,a,b):\n",
    "    return a + b* np.log(x)\n",
    "\n",
    "popt,pcov = curve_fit(func,X,y)\n",
    "\n",
    "print(popt)\n",
    "\n",
    "X_test = np.random.randint(0,25,50)\n",
    "\n",
    "np.random.seed(2)\n",
    "y_test = -1 + X_test*3.5 + 10*np.random.randn(50)\n",
    "RMSE = np.sqrt(np.sum((y_test - func(X_test,*popt))**2) / len(X_test))\n",
    "print('Root Mean squred error  is -',RMSE)\n",
    "\n",
    "plt.scatter(X,y)\n",
    "sns.lineplot(X_test,func(X_test,popt[0],popt[1]),color = 'red')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('LOG')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exponential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.00097224e+01 2.21584085e-07]\n",
      "Root Mean squred error  is - 453.8158813913978\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Exponential')"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "def func(x,a,b):\n",
    "    return a + b*(np.exp(x))\n",
    "\n",
    "popt,pcov = curve_fit(func,X,y)\n",
    "\n",
    "print(popt)\n",
    "\n",
    "X_test = np.random.randint(0,25,50)\n",
    "\n",
    "np.random.seed(2)\n",
    "y_test = -1 + X_test*3.5 + 10*np.random.randn(50)\n",
    "RMSE = np.sqrt(np.sum((y_test - func(X_test,*popt))**2) / len(X_test))\n",
    "print('Root Mean squred error  is -',RMSE)\n",
    "\n",
    "plt.scatter(X,y)\n",
    "sns.lineplot(X_test,func(X_test,popt[0],popt[1]),color = 'red')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Exponential')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "# gen function\n",
    "\n",
    "# def func(X,*params)\n",
    "#     -------- \n",
    "\n",
    "def curve_fit_test(func,X,y):\n",
    "    popt,pcov = curve_fit(func,X,y)\n",
    "\n",
    "    print('Coefficients are ',popt)\n",
    "\n",
    "    X_test = np.random.randint(0,25,50)\n",
    "\n",
    "    np.random.seed(2)\n",
    "    y_test = -1 + X_test*3.5 + 10*np.random.randn(50)\n",
    "    RMSE = np.sqrt(np.sum((y_test - func(X_test,*popt))**2) / len(X_test))\n",
    "    print('Root Mean squred error  is -',RMSE)\n",
    "\n",
    "    plt.scatter(X,y)\n",
    "    sns.lineplot(X_test,func(X_test,popt[0],popt[1]),color = 'red')\n",
    "    plt.xlabel('X')\n",
    "    plt.ylabel('Y')\n",
    "    plt.title('Resultant fit')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# that;s all.\n",
    "# play with the func, change some values and see how it goes :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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