bug in lsqfit?

scipy-comparison.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import curve_fit\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initializing Julia interpreter. This may take some time...\n"
     ]
    }
   ],
   "source": [
    "%load_ext julia.magic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "res_norm = np.array([1.0, 0.78117 , 0.606603, 0.470121])\n",
    "t = np.array([0, .25, .5, .75])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0aa2f48358>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, res_norm)\n",
    "plt.plot(t, np.exp(-t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(x, τ):\n",
    "    return -x / τ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "popt, pcov = curve_fit(func, t, np.log(res_norm))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.99686146]), array([[8.75553818e-06]]))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "popt, pcov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%julia \n",
    "using LsqFit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.  , 0.25, 0.5 , 0.75])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%julia\n",
    "res_norm = [1.0, 0.78117 , 0.606603, 0.470121]\n",
    "t = [0, .25, .5, .75]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<PyCall.jlwrap LsqFit.LsqFitResult{Float64,1}(3, [0.996861], [-0.0, -0.00382462, -0.00169347, 0.00240386], [0.0; 0.251577; 0.503153; 0.75473], true, [1.0, 1.0, 1.0, 1.0])>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%julia\n",
    "func(x, p) = -x / p[1]\n",
    "fit = curve_fit(func, t, log.(res_norm), ones(size(res_norm)), [1., ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9968614610778082, array([[1.12857694]]))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%julia\n",
    "fit.param[1], estimate_covar(fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}