{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Fit with Orthogonal distance regression\n", "\n", "Example from http://stackoverflow.com/questions/26058792/correct-fitting-with-scipy-curve-fit-including-errors-in-x/26085136#26085136" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# manage data and fit\n", "import pandas as pd\n", "import numpy as np\n", "\n", "# scipy ODR : orthogonal distance regression\n", "from scipy.odr import ODR, Model, Data, RealData\n", "\n", "# style and notebook integration of the plots\n", "import matplotlib.pyplot as plt \n", "import seaborn as sns\n", "%matplotlib inline \n", "sns.set(style=\"whitegrid\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def func(beta, x):\n", " y = beta[0]+beta[1]*x+beta[2]*x**3\n", " return y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## generate data" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "npts = 100\n", "np.random.seed(160810)\n", "x = np.linspace(-3, 2, npts)\n", "y = func([-2.3, 7.0, -4.0], x)\n", "\n", "sigma_x = .3\n", "sigma_y = 2\n", "\n", "# add some noise\n", "x += np.random.normal(scale=sigma_x, size=100)\n", "y += np.random.normal(scale=sigma_y, size=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define model" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "data = RealData(x, y, 0.3, 0.1)\n", "model = Model(func)\n", "odr = ODR(data, model, [1,0,0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Least squarre fit" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " stop reason: ['Iteration limit reached']\n", " params: [-2.09368488 6.0257117 -2.54574759]\n", " info: 4\n", "Sum of squares error: 5405.197746282522\n", " sd_beta: [ 0.22559351 0.80177874 0.95293199]\n", " sqrt(diag(cov): [ 0.03022085 0.1074075 0.12765622]\n", "\n", "Restart ODR till convergence is reached\n", "restart 1 5405.1977463\n", "restart 2 4325.2070339\n", "restart 3 1045.5356553\n", "restart 4 743.3175690\n", "restart 5 710.8233373\n", "restart 6 682.0088933\n", "restart 7 602.7134451\n", "restart 8 578.8585227\n", "restart 9 558.9136790\n", "restart 10 539.9567887\n", "restart 11 522.0568694\n", "restart 12 505.0221792\n", "restart 13 488.8286431\n", "restart 14 473.3871052\n", "restart 15 458.6550721\n", "restart 16 444.5728008\n", "restart 17 431.1303083\n", "restart 18 418.2785524\n", "restart 19 406.0148268\n", "restart 20 394.2378398\n", "restart 21 383.0217229\n", "restart 22 372.3116187\n", "restart 23 362.0182202\n", "restart 24 352.2750168\n", "restart 25 342.8414632\n", "restart 26 333.9524660\n", "restart 27 325.3301467\n", "restart 28 317.2122579\n", "restart 29 309.3065211\n", "restart 30 301.8936369\n", "restart 31 294.6241475\n", "restart 32 287.8565250\n", "restart 33 281.1543201\n", "restart 34 274.9756621\n", "restart 35 250.7690432\n", "restart 36 245.9163778\n", "restart 37 241.1998286\n", "restart 38 236.6336790\n", "restart 39 232.2524033\n", "restart 40 228.0534695\n", "restart 41 224.0110504\n", "restart 42 220.1177572\n", "restart 43 216.3814990\n", "restart 44 212.8300817\n", "restart 45 209.4103793\n", "restart 46 206.1065870\n", "restart 47 202.9507254\n", "restart 48 199.9235477\n", "restart 49 197.0054147\n", "restart 50 194.2163804\n", "restart 51 191.5362613\n", "restart 52 188.9598303\n", "restart 53 186.4947133\n", "restart 54 184.1129010\n", "restart 55 181.8341270\n", "restart 56 179.6356961\n", "restart 57 177.5532439\n", "restart 58 175.5140346\n", "restart 59 173.5668132\n", "restart 60 171.6843892\n", "restart 61 169.8962720\n", "restart 62 168.1662248\n", "restart 63 166.5032540\n", "restart 64 164.8891762\n", "restart 65 163.3493519\n", "restart 66 161.8492549\n", "restart 67 160.3945986\n", "restart 68 157.0580837\n", "restart 69 153.3941930\n", "restart 70 149.0470063\n", "restart 71 148.1832034\n", "restart 72 146.9758074\n", "restart 73 145.7639864\n", "restart 74 145.2494874\n", "restart 75 145.1131538\n", "restart 76 145.0754139\n", "restart 77 145.0461410\n", "restart 78 144.9885690\n", "restart 79 144.9623475\n", "restart 80 144.9537335\n", "restart 81 144.9443404\n", "restart 82 144.9438557\n", "restart 83 144.9434179\n", "restart 84 144.9430670\n", "restart 85 144.9430219\n", "restart 86 144.9429878\n", "restart 87 144.9429137\n", " stop reason: ['Sum of squares convergence']\n", " params: [ -2.01039971 12.55629008 -6.06416408]\n", " info: 1\n", "Sum of squares error: 144.94291057820132\n", " sd_beta: [ 0.48021907 0.89693549 0.49629295]\n", " sqrt(diag(cov): [ 0.39285002 0.7337508 0.40599949]\n" ] } ], "source": [ "odr.set_job(fit_type=0)\n", "lsq_output = odr.run()\n", "print(\" stop reason:\", lsq_output.stopreason)\n", "print(\" params:\", lsq_output.beta)\n", "print(\" info:\", lsq_output.info)\n", "print(\"Sum of squares error:\", lsq_output.sum_square)\n", "print(\" sd_beta:\", lsq_output.sd_beta)\n", "print(\" sqrt(diag(cov):\", np.sqrt(np.diag(lsq_output.cov_beta)))\n", "\n", "# check convergence and run again the algorithm if it is not reached\n", "if lsq_output.info != 1:\n", " print(\"\\nRestart ODR till convergence is reached\")\n", " i = 1\n", " while lsq_output.info != 1 and i < 100:\n", " print(\"restart %3d %12.7f\" % (i, lsq_output.sum_square))\n", " lsq_output = odr.restart()\n", " i += 1\n", " print(\" stop reason:\", lsq_output.stopreason)\n", " print(\" params:\", lsq_output.beta)\n", " print(\" info:\", lsq_output.info)\n", " print(\"Sum of squares error:\", lsq_output.sum_square)\n", " print(\" sd_beta:\", lsq_output.sd_beta)\n", " print(\" sqrt(diag(cov):\", np.sqrt(np.diag(lsq_output.cov_beta)))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Beta: [ -2.01039971 12.55629008 -6.06416408]\n", "Beta Std Error: [ 0.48021907 0.89693549 0.49629295]\n", "Beta Covariance: [[ 0.15433114 0.15842579 -0.04105628]\n", " [ 0.15842579 0.53839023 -0.21754393]\n", " [-0.04105628 -0.21754393 0.16483558]]\n", "Residual Variance: 1.4942568100845495\n", "Inverse Condition #: 0.037046778050718744\n", "Reason(s) for Halting:\n", " Sum of squares convergence\n" ] } ], "source": [ "lsq_output.pprint()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ODR fit" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " stop reason: ['Sum of squares convergence']\n", " params: [-1.15111597 4.5357938 -3.34692538]\n", " info: 1\n", "Sum of squares error: 821948.608722443\n", " sd_beta: [ 1.00126769 1.25522586 0.23236659]\n", " sqrt(diag(cov): [ 0.01087712 0.01363595 0.00252428]\n" ] } ], "source": [ "odr = ODR(data, model, [1,0,0])\n", "odr.set_job(fit_type=2)\n", "odr_output = odr.run()\n", "print(\" stop reason:\", odr_output.stopreason)\n", "print(\" params:\", odr_output.beta)\n", "print(\" info:\", odr_output.info)\n", "print(\"Sum of squares error:\", odr_output.sum_square)\n", "print(\" sd_beta:\", odr_output.sd_beta)\n", "print(\" sqrt(diag(cov):\", np.sqrt(np.diag(odr_output.cov_beta)))\n", "\n", "# check convergence and run again the algorithm if it is not reached\n", "if odr_output.info != 1:\n", " print(\"\\nRestart ODR till convergence is reached\")\n", " i = 1\n", " while odr_output.info != 1 and i < 100:\n", " print(\"restart\", i)\n", " odr_output = odr.restart()\n", " i += 1\n", " print(\" stop reason:\", odr_output.stopreason)\n", " print(\" params:\", odr_output.beta)\n", " print(\" info:\", odr_output.info)\n", " print(\"Sum of squares error:\", odr_output.sum_square)\n", " print(\" sd_beta:\", odr_output.sd_beta)\n", " print(\" sqrt(diag(cov):\", np.sqrt(np.diag(odr_output.cov_beta)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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2ttnPYjz1seupj11L/et66mPXqqur6/S1hofSmpoaHnzwQU6ePMnq1aubvjAzm80XBFC7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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xn = np.linspace(-3, 2, 50)\n", "\n", "plt.errorbar(x, y, marker=\"o\", linestyle=\"\", label=\"data\", xerr=sigma_x, yerr=sigma_y, elinewidth=1, capthick=1)\n", "plt.plot(xn, func(lsq_output.beta, xn), label='leastsq')\n", "plt.plot(xn, func(odr_output.beta, xn), label='odr')\n", "plt.legend()" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "language": "python", "name": "python3" }, "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" } }, "nbformat": 4, "nbformat_minor": 1 }