ML-Kurs-SS2023/notebooks/02_fit_iminuitFit.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit with the python interface to Minuit 2 called iminuit\n",
    "https://iminuit.readthedocs.io/en/stable/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "plt.rcParams[\"font.size\"] = 20\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], dtype='d')\n",
    "dx =  np.array([0.1,0.1,0.5,0.1,0.5,0.1,0.5,0.1,0.5,0.1], dtype='d')\n",
    "y = np.array([1.1 ,2.3 ,2.7 ,3.2 ,3.1 ,2.4 ,1.7 ,1.5 ,1.5  ,1.7 ], dtype='d')\n",
    "dy = np.array([0.15,0.22,0.29,0.39,0.31,0.21,0.13,0.15,0.19,0.13], dtype='d')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define fit function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pol3(a0, a1, a2, a3):\n",
    "    return a0 + x*a1 + a2*x**2 + a3*x**3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "least-squares function: sum of data residuals squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LSQ(a0, a1, a2, a3):\n",
    "    return np.sum((y - pol3(a0, a1, a2, a3)) ** 2 / dy ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "import Minuit object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from iminuit import Minuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Minuit instance using LSQ function to minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "LSQ.errordef = Minuit.LEAST_SQUARES\n",
    "#LSQ.errordef = Minuit.LIKELIHOOD\n",
    "m = Minuit(LSQ,a0=-1.3, a1=2.6 ,a2=-0.24 ,a3=0.005)\n",
    "m.fixed[\"a3\"] = True \n",
    "m.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "run migrad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m.fixed[\"a3\"] = False\n",
    "m.params\n",
    "m.migrad()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get contour"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m.draw_mncontour(\"a2\", \"a3\",  cl=[1, 2, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Improve the fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m.hesse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m.minos()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "access fit results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(m.values,m.errors)\n",
    "a0_fit = m.values[\"a0\"]\n",
    "a1_fit = m.values[\"a1\"]\n",
    "a2_fit = m.values[\"a2\"]\n",
    "a3_fit = m.values[\"a3\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print (m.covariance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "prepare data to display fitted function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_plot = np.linspace( 0.5, 10.5 , 500 )\n",
    "y_fit = a0_fit + a1_fit * x_plot + a2_fit * x_plot**2 +  a3_fit * x_plot**3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Minos algorithm uses the profile likelihood method to compute (generally asymmetric) confidence intervals. This can be plotted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m.draw_profile(\"a2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get a 2D contour of the function around the minimum for 2 parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m.draw_mncontour(\"a2\", \"a3\" , cl=[1, 2, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "lotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "plt.errorbar(x, y, dy , dx, fmt=\"o\")\n",
    "plt.plot(x_plot, y_fit)\n",
    "plt.title(\"iminuit Fit Test\")\n",
    "plt.xlim(-0.1, 10.1)\n",
    "plt.show()"
   ]
  }
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