{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\nUsing an ExpressionModel\n========================\n\nExpressionModels allow a model to be built from a user-supplied expression.\nSee: https://lmfit.github.io/lmfit-py/builtin_models.html#user-defined-models\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\nimport numpy as np\n\nfrom lmfit.models import ExpressionModel"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Generate synthetic data for the user-supplied model:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "x = np.linspace(-10, 10, 201)\namp, cen, wid = 3.4, 1.8, 0.5\n\ny = amp * np.exp(-(x-cen)**2 / (2*wid**2)) / (np.sqrt(2*np.pi)*wid)\ny = y + np.random.normal(size=x.size, scale=0.01)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Define the ExpressionModel and perform the fit:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "gmod = ExpressionModel(\"amp * exp(-(x-cen)**2 /(2*wid**2))/(sqrt(2*pi)*wid)\")\nresult = gmod.fit(y, x=x, amp=5, cen=5, wid=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "this results in the following output:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "print(result.fit_report())\n\nplt.plot(x, y, 'bo')\nplt.plot(x, result.init_fit, 'k--', label='initial fit')\nplt.plot(x, result.best_fit, 'r-', label='best fit')\nplt.legend(loc='best')\nplt.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "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": "3.7.6"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}