5 changed files with 5688 additions and 0 deletions
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253notebooks/02_fit_ex_3_sol.ipynb
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218notebooks/02_fit_ex_4_sol.ipynb
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217notebooks/02_fit_ex_5_sol.ipynb
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5000notebooks/FitTestData.txt
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BINslides/CIPpoolAccess.PDF
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{ |
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"cells": [ |
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{ |
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"cell_type": "markdown", |
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"metadata": {}, |
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"source": [ |
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"Exercise 3: Least square fit with a 3rd order polynomial with iminuit" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"import numpy as np\n", |
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"import matplotlib.pyplot as plt\n", |
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"import math" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# Data x,y and dy\n", |
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"x = np.array([0.2 , 0.4 , 0.6 , 0.8, 1. , 1.2, 1.4, 1.6, 1.8, 2., 2.2, 2.4, 2.6, 2.8 , 3., 3.2 ,3.4, 3.6, 3.8,4.],dtype='d')\n", |
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"dy = np.array([0.04,0.021,0.035,0.03,0.029,0.019,0.024,0.018,0.019,0.022,0.02,0.025,0.018,0.024,0.019,0.021,0.03,0.019,0.03,0.024 ], dtype='d')\n", |
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"y = np.array([1.792,1.695,1.541,1.514,1.427,1.399,1.388,1.270,1.262,1.228,1.189,1.182,1.121,1.129,1.124,1.089,1.092,1.084,1.058,1.057 ], dtype='d')" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# Define fit functions - a 3rd order polynomial\n", |
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"def pol3(a0, a1, a2, a3):\n", |
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" return a0 + x*a1 + a2*x**2 + a3*x**3" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# least-squares function = sum of data residuals squared\n", |
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"def LSQ(a0, a1, a2, a3):\n", |
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" return np.sum((y - pol3(a0, a1, a2, a3)) ** 2 / dy ** 2)" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# import minuit2 fitting library\n", |
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"from iminuit import Minuit" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# create instance of Minuit and use LSQ function to minimize\n", |
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"LSQ.errordef = Minuit.LEAST_SQUARES\n", |
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"m = Minuit(LSQ,a0=0.01, a1=0.05 ,a2=0.01 ,a3=0.001)" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"m.params" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# run migrad for minimization\n", |
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"m.migrad()" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# run covariance \n", |
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"m.hesse()" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"#get correlation matrix\n", |
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"cov = m.covariance\n", |
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"print (cov)" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# access elements of the numpy arrays\n", |
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"print(cov[0, 1])\n", |
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"print(cov[0, 2])" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# run minos error analysis\n", |
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"# The Minos algorithm uses the profile likelihood method to compute\n", |
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"# (generally asymmetric) confidence intervals.\n", |
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"m.minos()" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# Get a 2D contour of the function around the minimum for 2 parameters\n", |
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"# and draw a 2 D contours up to 4 sigma of a1 and a2 \n", |
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"m.draw_mncontour(\"a1\", \"a2\", cl=[1, 2, 3, 4])\n" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"m.draw_profile(\"a2\",subtract_min=True)" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# access fit results by parameter name and get minos asymetric errors\n", |
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"print (m.merrors['a2'].lower)\n", |
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"print (m.merrors['a2'].upper)" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# more print out\n", |
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"print (m.values,m.errors)\n", |
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"print (m.errors)" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# Access fit results\n", |
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"a0_fit = m.values[\"a0\"]\n", |
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"a1_fit = m.values[\"a1\"]\n", |
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"a2_fit = m.values[\"a2\"]\n", |
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"a3_fit = m.values[\"a3\"]" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# display fitted function \n", |
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"x_plot = np.linspace( 0.1, 4.1 , 100 )\n", |
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"y_fit = a0_fit + a1_fit * x_plot + a2_fit * x_plot**2 + a3_fit * x_plot**3\n" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"plt.figure()\n", |
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"\n", |
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"plt.errorbar(x, y, dy , fmt=\"o\")\n", |
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"plt.plot(x_plot,y_fit ) \n", |
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"plt.xlabel('x')\n", |
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"plt.ylabel('f(x)')\n", |
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"plt.title('iminuit exponential Fit')\n", |
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"#plt.axis([0,30,-1.2,1.2])\n", |
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"\n", |
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"# show the plot\n", |
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"plt.show()" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [] |
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} |
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], |
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"metadata": { |
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"kernelspec": { |
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"display_name": "Python 3 (ipykernel)", |
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"language": "python", |
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"name": "python3" |
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}, |
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"language_info": { |
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"codemirror_mode": { |
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"name": "ipython", |
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"version": 3 |
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}, |
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"file_extension": ".py", |
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"mimetype": "text/x-python", |
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"name": "python", |
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"nbconvert_exporter": "python", |
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"pygments_lexer": "ipython3", |
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"version": "3.8.16" |
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} |
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}, |
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"nbformat": 4, |
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"nbformat_minor": 4 |
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} |
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{ |
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"cells": [ |
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{ |
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"cell_type": "markdown", |
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"metadata": {}, |
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"source": [ |
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"Exercise 4: Least square fit to data" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"from matplotlib import pyplot as plt\n", |
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"plt.rcParams[\"font.size\"] = 20\n", |
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"import numpy as np" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# data\n", |
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"x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], dtype='d')\n", |
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"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", |
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"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", |
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"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')" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# define fit function \n", |
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"def pol3(a0, a1, a2, a3):\n", |
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" return a0 + x*a1 + a2*x**2 + a3*x**3" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# least-squares function = sum of data residuals squared\n", |
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"def LSQ(a0, a1, a2, a3):\n", |
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" return np.sum((y - pol3(a0, a1, a2, a3)) ** 2 / dy ** 2)" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# import Minuit object\n", |
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"from iminuit import Minuit" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# create instance of Minuit and use LSQ function to minimize\n", |
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"LSQ.errordef = Minuit.LEAST_SQUARES\n", |
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"m = Minuit(LSQ,a0=-1.3, a1=2.6 ,a2=-0.24 ,a3=0.005)\n", |
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"# run migrad \n", |
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"m.migrad()" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# get function value at the minimum, which is per definition a chi2\n", |
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"# obtain chi2 / degree of freedom (dof)\n", |
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"chi2 = m.fval / (len(y) - len(m.values))\n", |
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"print (\"Chi2/ndof =\" , chi2)" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# run covariance \n", |
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"m.hesse()" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"#get covariance matrix\n", |
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"m.covariance" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"#get correlation matrix in numpy array\n", |
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"cov = m.covariance\n", |
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"print (cov)" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# run minos error analysis\n", |
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"# The Minos algorithm uses the profile likelihood method to compute\n", |
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"# (generally asymmetric) confidence intervals.\n", |
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"m.minos()" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# Get a 2D contour of the function around the minimum for 2 parameters\n", |
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"# and draw a 2 D contours up to 4 sigma of a1 and a2 \n", |
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"#m.draw_profile(\"a1\")\n", |
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"m.draw_mncontour(\"a2\", \"a3\", cl=[1, 2, 3, 4])" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"print(m.values,m.errors)\n", |
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"a0_fit = m.values[\"a0\"]\n", |
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"a1_fit = m.values[\"a1\"]\n", |
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"a2_fit = m.values[\"a2\"]\n", |
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"a3_fit = m.values[\"a3\"]" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# display fitted function \n", |
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"x_plot = np.linspace( 0.1, 10.1 , 200 )\n", |
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"y_fit = a0_fit + a1_fit * x_plot + a2_fit * x_plot**2 + a3_fit * x_plot**3" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"# plot data \n", |
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"plt.figure()\n", |
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"plt.errorbar(x, y, dy , dx, fmt=\"o\")\n", |
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"plt.plot(x_plot,y_fit )\n", |
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"plt.title(\"iminuit Fit Test\")\n", |
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"plt.xlabel('x')\n", |
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"plt.ylabel('f(x)')\n", |
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"plt.xlim(-0.1, 10.1)\n", |
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"\n", |
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"# show the plot\n", |
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"plt.show()" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [] |
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} |
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], |
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"metadata": { |
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"kernelspec": { |
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"display_name": "Python 3 (ipykernel)", |
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"language": "python", |
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"name": "python3" |
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}, |
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"language_info": { |
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"codemirror_mode": { |
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"name": "ipython", |
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"version": 3 |
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|
}, |
||||
|
"file_extension": ".py", |
||||
|
"mimetype": "text/x-python", |
||||
|
"name": "python", |
||||
|
"nbconvert_exporter": "python", |
||||
|
"pygments_lexer": "ipython3", |
||||
|
"version": "3.8.16" |
||||
|
} |
||||
|
}, |
||||
|
"nbformat": 4, |
||||
|
"nbformat_minor": 4 |
||||
|
} |
||||
@ -0,0 +1,217 @@ |
|||||
|
{ |
||||
|
"cells": [ |
||||
|
{ |
||||
|
"cell_type": "markdown", |
||||
|
"metadata": {}, |
||||
|
"source": [ |
||||
|
" Exercise 5: Fit Signal and background distribution of a histogramm " |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": 1, |
||||
|
"metadata": {}, |
||||
|
"outputs": [ |
||||
|
{ |
||||
|
"ename": "ImportError", |
||||
|
"evalue": "Failed to import libcppyy3_8. Please check that ROOT has been built for Python 3.8", |
||||
|
"output_type": "error", |
||||
|
"traceback": [ |
||||
|
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", |
||||
|
"\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", |
||||
|
"File \u001b[0;32m/cern/root/lib/cppyy/__init__.py:60\u001b[0m\n\u001b[1;32m 59\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m---> 60\u001b[0m \u001b[43mimportlib\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mimport_module\u001b[49m\u001b[43m(\u001b[49m\u001b[43mlibcppyy_mod_name\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 61\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mImportError\u001b[39;00m:\n", |
||||
|
"File \u001b[0;32m~/anaconda3/envs/myML/lib/python3.8/importlib/__init__.py:127\u001b[0m, in \u001b[0;36mimport_module\u001b[0;34m(name, package)\u001b[0m\n\u001b[1;32m 126\u001b[0m level \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\n\u001b[0;32m--> 127\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_bootstrap\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_gcd_import\u001b[49m\u001b[43m(\u001b[49m\u001b[43mname\u001b[49m\u001b[43m[\u001b[49m\u001b[43mlevel\u001b[49m\u001b[43m:\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpackage\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlevel\u001b[49m\u001b[43m)\u001b[49m\n", |
||||
|
"File \u001b[0;32m<frozen importlib._bootstrap>:1014\u001b[0m, in \u001b[0;36m_gcd_import\u001b[0;34m(name, package, level)\u001b[0m\n", |
||||
|
"File \u001b[0;32m<frozen importlib._bootstrap>:991\u001b[0m, in \u001b[0;36m_find_and_load\u001b[0;34m(name, import_)\u001b[0m\n", |
||||
|
"File \u001b[0;32m<frozen importlib._bootstrap>:973\u001b[0m, in \u001b[0;36m_find_and_load_unlocked\u001b[0;34m(name, import_)\u001b[0m\n", |
||||
|
"\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'libcppyy3_8'", |
||||
|
"\nDuring handling of the above exception, another exception occurred:\n", |
||||
|
"\u001b[0;31mImportError\u001b[0m Traceback (most recent call last)", |
||||
|
"Cell \u001b[0;32mIn[1], line 5\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mos\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m path\n\u001b[1;32m 4\u001b[0m \u001b[38;5;66;03m#import ROOT\u001b[39;00m\n\u001b[0;32m----> 5\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mROOT\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m TCanvas, TFile, TFormula, TH1D, TF1, TMinuit, TFitResult, TVirtualFitter\n\u001b[1;32m 6\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mROOT\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m gROOT, gBenchmark, gRandom, gSystem\n", |
||||
|
"File \u001b[0;32m/cern/root/lib/ROOT/__init__.py:22\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[38;5;66;03m# Prevent cppyy from filtering ROOT libraries\u001b[39;00m\n\u001b[1;32m 20\u001b[0m environ[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mCPPYY_NO_ROOT_FILTER\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m1\u001b[39m\u001b[38;5;124m'\u001b[39m\n\u001b[0;32m---> 22\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mcppyy\u001b[39;00m\n\u001b[1;32m 23\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mROOTSYS\u001b[39m\u001b[38;5;124m'\u001b[39m \u001b[38;5;129;01min\u001b[39;00m environ:\n\u001b[1;32m 24\u001b[0m \u001b[38;5;66;03m# Revert setting made by cppyy\u001b[39;00m\n\u001b[1;32m 25\u001b[0m cppyy\u001b[38;5;241m.\u001b[39mgbl\u001b[38;5;241m.\u001b[39mgROOT\u001b[38;5;241m.\u001b[39mSetBatch(\u001b[38;5;28;01mFalse\u001b[39;00m)\n", |
||||
|
"File \u001b[0;32m/cern/root/lib/cppyy/__init__.py:62\u001b[0m\n\u001b[1;32m 60\u001b[0m importlib\u001b[38;5;241m.\u001b[39mimport_module(libcppyy_mod_name)\n\u001b[1;32m 61\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mImportError\u001b[39;00m:\n\u001b[0;32m---> 62\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mImportError\u001b[39;00m(\n\u001b[1;32m 63\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mFailed to import \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m. Please check that ROOT has been built for Python \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m.\u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m'\u001b[39m\u001b[38;5;241m.\u001b[39mformat(\n\u001b[1;32m 64\u001b[0m libcppyy_mod_name, major, minor))\n\u001b[1;32m 66\u001b[0m \u001b[38;5;66;03m# ensure 'import libcppyy' will find the versioned module\u001b[39;00m\n\u001b[1;32m 67\u001b[0m sys\u001b[38;5;241m.\u001b[39mmodules[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlibcppyy\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m sys\u001b[38;5;241m.\u001b[39mmodules[libcppyy_mod_name]\n", |
||||
|
"\u001b[0;31mImportError\u001b[0m: Failed to import libcppyy3_8. Please check that ROOT has been built for Python 3.8" |
||||
|
] |
||||
|
} |
||||
|
], |
||||
|
"source": [ |
||||
|
"import math\n", |
||||
|
"import numpy as np\n", |
||||
|
"from os import path\n", |
||||
|
"#import ROOT\n", |
||||
|
"from ROOT import TCanvas, TFile, TFormula, TH1D, TF1, TMinuit, TFitResult, TVirtualFitter\n", |
||||
|
"from ROOT import gROOT, gBenchmark, gRandom, gSystem" |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"#read data from text file\n", |
||||
|
"data = np.genfromtxt('FitTestData.txt', dtype='d')\n", |
||||
|
"print(data)" |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"# instanciate canvas and histogramm\n", |
||||
|
"c = TCanvas( 'c','Fit Test',200,10,700,500)\n", |
||||
|
"sig = TH1D( 'sig', 'Signal Mass', 100, 0. , 5. )" |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"# fill histogramm\n", |
||||
|
"for x in data:\n", |
||||
|
" sig.Fill(x)" |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"# fit function: gaus + exponential\n", |
||||
|
"def myN(x, p):\n", |
||||
|
" return p[0] * np.exp(-0.5 * ((x[0]-p[1])/p[2])**2) + p[3] * np.exp( p[4]*x[0])" |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"# fit function: gaussian\n", |
||||
|
"def myGauss(x, p):\n", |
||||
|
" return p[0] * np.exp(-0.5 * ((x[0]-p[1])/p[2])**2) " |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"# fit function: gaussian\n", |
||||
|
"def myExp(x, p):\n", |
||||
|
" return p[0] * np.exp( p[1]*x[0])" |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"# root formular mechanism\n", |
||||
|
"form = TFormula( 'form', '[0] * exp(-0.5 * ((x-[1])/[2])**2) + [3] * exp( [4]*x)')" |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"# define fit functions\n", |
||||
|
"#f = TF1('f','form', 0 , 5 , 5)\n", |
||||
|
"f = TF1('f',myN, 0 , 5 , 5)\n", |
||||
|
"f_exp = TF1('f_exp',myExp, 0.1 , 1.2 , 2)\n", |
||||
|
"f_gauss = TF1('f_exp',myGauss, 1.6 , 2.4 , 3)" |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"# set start values of the fit\n", |
||||
|
"f.SetParameters(250.,2.,.2,5.5,-0.7)\n", |
||||
|
"f_gauss.SetParameters(250.,2.,.1)\n", |
||||
|
"f_gauss.SetLineColor(3)\n", |
||||
|
"f_exp.SetParameters(130.,-0.5)\n", |
||||
|
"f_exp.SetLineColor(4)" |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"# perform fit\n", |
||||
|
"# Options: Q/V Quiet/Verbose mode (default is between Q and V)\n", |
||||
|
"# E Perform better errors estimation using the Minos technique\n", |
||||
|
"# M Improve fit results\n", |
||||
|
"# R Use the range specified in the function range\n", |
||||
|
"# + Add this new fitted function to the list of fitted functions\n", |
||||
|
"fit = sig.Fit(f, \"V M E S\",\"\",0.,5.)\n", |
||||
|
"fit_exp = sig.Fit(f_exp, \"R+ E S\",\"\",0.1,1.2)\n", |
||||
|
"fit_gauss = sig.Fit(f_gauss, \"R+ E S\",\"\",1.6,2.4)\n", |
||||
|
"print (\"Fit results: mean=\",fit.Parameter(1),\" +/- \",fit.ParError(1), \n", |
||||
|
" \" sigma=\",fit.Parameter(2),\" +/- \",fit.ParError(2) )" |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"# print fit summary\n", |
||||
|
"fit.Print()" |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [ |
||||
|
"# drawing \n", |
||||
|
"c.Draw() " |
||||
|
] |
||||
|
}, |
||||
|
{ |
||||
|
"cell_type": "code", |
||||
|
"execution_count": null, |
||||
|
"metadata": {}, |
||||
|
"outputs": [], |
||||
|
"source": [] |
||||
|
} |
||||
|
], |
||||
|
"metadata": { |
||||
|
"kernelspec": { |
||||
|
"display_name": "Python 3 (ipykernel)", |
||||
|
"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": "3.8.16" |
||||
|
} |
||||
|
}, |
||||
|
"nbformat": 4, |
||||
|
"nbformat_minor": 4 |
||||
|
} |
||||
5000
notebooks/FitTestData.txt
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