levenberg-marquardt.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def mean_square_error(y, y_exp):\n",
    "    ''' Compute the Mean Square Error bewteen 2 arrays (y and y_exp) '''\n",
    "    residus = (y - y_exp)\n",
    "    return np.sum(residus**2) / len(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class curve_fitting():\n",
    "    def __init__(self):\n",
    "        ''' Parameters values (X), \n",
    "        number of points for the curve (nb_points),\n",
    "        abscisse curve points (x) '''\n",
    "        self.X = 0.5 * np.ones(2)\n",
    "        self.nb_points = 30\n",
    "        self.x = np.linspace(0, 1, self.nb_points)\n",
    "        \n",
    "    def scale_parameters(self, X_raw):\n",
    "        ''' Return scaled parameters between [0, 1] for gradient convergence optimization '''\n",
    "        X0 = ( X_raw[0] - 0 ) / ( 2000 - 0 )\n",
    "        X1 = ( X_raw[1] - 0.01 ) / ( 0.5 - 0.01 )\n",
    "        return np.array([X0, X1])\n",
    "    \n",
    "    def unscale_parameters(self):\n",
    "        ''' Return unscaled parameters between [min, max] for computing function '''\n",
    "        X0 = self.X[0] * ( 2000 - 0 ) + 0\n",
    "        X1 = self.X[1] * ( 0.5 - 0.01 ) + 0.01\n",
    "        return np.array([X0, X1])\n",
    "    \n",
    "    def print_parameters(self):\n",
    "        ''' Print value of raw and scaled parameters '''\n",
    "        X_raw = self.unscale_parameters()\n",
    "        print(f'Raw parameters {X_raw}')\n",
    "        print(f'Scaled parameters {np.round(self.X, 2)}')\n",
    "    \n",
    "    def set_parameters_norm(self, X):\n",
    "        ''' Update parameters values (scaled or norm) '''\n",
    "        self.X = X\n",
    "    \n",
    "    def set_parameters_raw(self, X_raw):\n",
    "        ''' Update parameters values (given raw values) '''\n",
    "        X = self.scale_parameters(X_raw)\n",
    "        self.X = X\n",
    "        \n",
    "    def function(self):\n",
    "        ''' Define the function to fit using parameters X[i] '''\n",
    "        X = self.unscale_parameters()\n",
    "        return X[0] * self.x ** X[1]\n",
    "    \n",
    "    def optim(self, lamdba = 0.01, mu = 0.95, steps=10, delta = 0.001, y_exp=None, debug=False):\n",
    "        ''' Perform Levenberg Marquardt optimization '''\n",
    "        print(f'X init: {self.X}')\n",
    "        y = self.function()\n",
    "        error = mean_square_error(y, y_exp)\n",
    "        errors = [error]\n",
    "\n",
    "        for step in range(steps):\n",
    "            y = self.function()\n",
    "            error = mean_square_error(y, y_exp)\n",
    "            print(f'Iteration {step}: error = {np.round(error)}')\n",
    "            errors.append(error)\n",
    "            \n",
    "            ''' Compute jacobian with finite difference method \n",
    "            for each curve point (y) and each parameter (X) '''\n",
    "            J = np.zeros((len(y), len(self.X)))\n",
    "            for i in range(len(self.X)):\n",
    "                X2 = self.X.copy()  \n",
    "                X2[i] = X2[i] + delta\n",
    "                self.set_parameters_norm(X2)\n",
    "                Y2 = self.function()\n",
    "                X3 = self.X.copy()  \n",
    "                X3[i] = X3[i] - delta\n",
    "                self.set_parameters_norm(X3)\n",
    "                Y3 = self.function()\n",
    "                J[:, i] = (Y2 - Y3) / (2*delta)\n",
    "            \n",
    "            JJ = np.dot(np.transpose(J), J)\n",
    "            G = np.dot(np.linalg.inv( JJ + mu * np.diag(np.diag(JJ)))  , np.transpose(J))\n",
    "            X = self.X + np.dot(G, (y_exp-y))\n",
    "            self.set_parameters_norm(X)\n",
    "            \n",
    "            if debug:\n",
    "                print(f'jacobian: {J}')\n",
    "                print(f'gradient: {np.dot(np.transpose(J), y-y_exp)}')\n",
    "                print(f'G: {G}')\n",
    "                print(f'np.dot(G, (y_exp-y): {np.dot(G, (y_exp-y))}')\n",
    "                print(f'next iteration: {X}')\n",
    "        \n",
    "        fig, ax = plt.subplots(1, 2)\n",
    "        plt.title('Levenberg Marquardt Curve Fitting')\n",
    "        ax[0].plot(self.x, y, linestyle='dashed', color='red')\n",
    "        ax[0].scatter(self.x, y_exp, color='grey', alpha=0.9)\n",
    "        ax[0].title.set_text('Fitted experimental points')\n",
    "        ax[0].set_xlabel('x')\n",
    "        ax[0].set_ylabel('y')\n",
    "        \n",
    "        ax[1].plot(errors, color='black')\n",
    "        ax[1].title.set_text('Convergence')\n",
    "        ax[1].set_xlabel('iterations')\n",
    "        ax[1].set_ylabel('mean square error')\n",
    "        \n",
    "        fig.tight_layout()\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def generate_experimental_noisy_points(X, nb_points):\n",
    "    ''' Simulation the generation of noisy experimental dataset \n",
    "    from true parameters values (set_parameters_raw([600, 0.15])) and number of points (nb_points) '''\n",
    "    noisy_model = curve_fitting()\n",
    "    noisy_model.set_parameters_raw(X)\n",
    "    target = noisy_model.function()\n",
    "    noise = 0.15 * np.random.random(nb_points) * target\n",
    "    return target + noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raw parameters [1.00e+03 2.55e-01]\n",
      "Scaled parameters [0.5 0.5]\n",
      "X init: [0.5 0.5]\n",
      "Iteration 0: error = 217493.0\n",
      "Iteration 1: error = 92022.0\n",
      "Iteration 2: error = 15162.0\n",
      "Iteration 3: error = 5287.0\n",
      "Iteration 4: error = 2808.0\n",
      "Iteration 5: error = 2075.0\n",
      "Iteration 6: error = 1868.0\n",
      "Iteration 7: error = 1809.0\n",
      "Iteration 8: error = 1792.0\n",
      "Iteration 9: error = 1787.0\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raw parameters [1.61667224e+03 3.00107440e-01]\n",
      "Scaled parameters [0.81 0.59]\n"
     ]
    }
   ],
   "source": [
    "# Initiate model \n",
    "model = curve_fitting()\n",
    "\n",
    "# generate noisy dataset\n",
    "model.print_parameters()\n",
    "y_exp = generate_experimental_noisy_points(X=[1500,0.3], nb_points=30)\n",
    "\n",
    "# perform curve fitting optimization\n",
    "model.optim(lamdba = 0.001, mu = 0.95, steps=10, delta = 0.001, y_exp=y_exp, debug=False)\n",
    "model.print_parameters()"
   ]
  }
 ],
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