diff --git a/notebooks/02_fit_ex_3_sol.ipynb b/notebooks/02_fit_ex_3_sol.ipynb new file mode 100644 index 0000000..28e75ee --- /dev/null +++ b/notebooks/02_fit_ex_3_sol.ipynb @@ -0,0 +1,253 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Exercise 3: Least square fit with a 3rd order polynomial with iminuit" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import math" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Data x,y and dy\n", + "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", + "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", + "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')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Define fit functions - a 3rd order polynomial\n", + "def pol3(a0, a1, a2, a3):\n", + " return a0 + x*a1 + a2*x**2 + a3*x**3" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# least-squares function = sum of data residuals squared\n", + "def LSQ(a0, a1, a2, a3):\n", + " return np.sum((y - pol3(a0, a1, a2, a3)) ** 2 / dy ** 2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# import minuit2 fitting library\n", + "from iminuit import Minuit" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# create instance of Minuit and use LSQ function to minimize\n", + "LSQ.errordef = Minuit.LEAST_SQUARES\n", + "m = Minuit(LSQ,a0=0.01, a1=0.05 ,a2=0.01 ,a3=0.001)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "m.params" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# run migrad for minimization\n", + "m.migrad()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# run covariance \n", + "m.hesse()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#get correlation matrix\n", + "cov = m.covariance\n", + "print (cov)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# access elements of the numpy arrays\n", + "print(cov[0, 1])\n", + "print(cov[0, 2])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# run minos error analysis\n", + "# The Minos algorithm uses the profile likelihood method to compute\n", + "# (generally asymmetric) confidence intervals.\n", + "m.minos()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Get a 2D contour of the function around the minimum for 2 parameters\n", + "# and draw a 2 D contours up to 4 sigma of a1 and a2 \n", + "m.draw_mncontour(\"a1\", \"a2\", cl=[1, 2, 3, 4])\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "m.draw_profile(\"a2\",subtract_min=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# access fit results by parameter name and get minos asymetric errors\n", + "print (m.merrors['a2'].lower)\n", + "print (m.merrors['a2'].upper)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# more print out\n", + "print (m.values,m.errors)\n", + "print (m.errors)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Access fit results\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": [ + "# display fitted function \n", + "x_plot = np.linspace( 0.1, 4.1 , 100 )\n", + "y_fit = a0_fit + a1_fit * x_plot + a2_fit * x_plot**2 + a3_fit * x_plot**3\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.figure()\n", + "\n", + "plt.errorbar(x, y, dy , fmt=\"o\")\n", + "plt.plot(x_plot,y_fit ) \n", + "plt.xlabel('x')\n", + "plt.ylabel('f(x)')\n", + "plt.title('iminuit exponential Fit')\n", + "#plt.axis([0,30,-1.2,1.2])\n", + "\n", + "# show the plot\n", + "plt.show()" + ] + }, + { + "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 +} diff --git a/notebooks/02_fit_ex_4_sol.ipynb b/notebooks/02_fit_ex_4_sol.ipynb new file mode 100644 index 0000000..3831fdb --- /dev/null +++ b/notebooks/02_fit_ex_4_sol.ipynb @@ -0,0 +1,218 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Exercise 4: Least square fit to data" + ] + }, + { + "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": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# data\n", + "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": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# define fit function \n", + "def pol3(a0, a1, a2, a3):\n", + " return a0 + x*a1 + a2*x**2 + a3*x**3" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# least-squares function = sum of data residuals squared\n", + "def LSQ(a0, a1, a2, a3):\n", + " return np.sum((y - pol3(a0, a1, a2, a3)) ** 2 / dy ** 2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# import Minuit object\n", + "from iminuit import Minuit" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# create instance of Minuit and use LSQ function to minimize\n", + "LSQ.errordef = Minuit.LEAST_SQUARES\n", + "m = Minuit(LSQ,a0=-1.3, a1=2.6 ,a2=-0.24 ,a3=0.005)\n", + "# run migrad \n", + "m.migrad()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# get function value at the minimum, which is per definition a chi2\n", + "# obtain chi2 / degree of freedom (dof)\n", + "chi2 = m.fval / (len(y) - len(m.values))\n", + "print (\"Chi2/ndof =\" , chi2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# run covariance \n", + "m.hesse()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#get covariance matrix\n", + "m.covariance" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#get correlation matrix in numpy array\n", + "cov = m.covariance\n", + "print (cov)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# run minos error analysis\n", + "# The Minos algorithm uses the profile likelihood method to compute\n", + "# (generally asymmetric) confidence intervals.\n", + "m.minos()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Get a 2D contour of the function around the minimum for 2 parameters\n", + "# and draw a 2 D contours up to 4 sigma of a1 and a2 \n", + "#m.draw_profile(\"a1\")\n", + "m.draw_mncontour(\"a2\", \"a3\", cl=[1, 2, 3, 4])" + ] + }, + { + "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": [ + "# display fitted function \n", + "x_plot = np.linspace( 0.1, 10.1 , 200 )\n", + "y_fit = a0_fit + a1_fit * x_plot + a2_fit * x_plot**2 + a3_fit * x_plot**3" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plot data \n", + "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.xlabel('x')\n", + "plt.ylabel('f(x)')\n", + "plt.xlim(-0.1, 10.1)\n", + "\n", + "# show the plot\n", + "plt.show()" + ] + }, + { + "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 +} diff --git a/notebooks/02_fit_ex_5_sol.ipynb b/notebooks/02_fit_ex_5_sol.ipynb new file mode 100644 index 0000000..08bc85b --- /dev/null +++ b/notebooks/02_fit_ex_5_sol.ipynb @@ -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:1014\u001b[0m, in \u001b[0;36m_gcd_import\u001b[0;34m(name, package, level)\u001b[0m\n", + "File \u001b[0;32m:991\u001b[0m, in \u001b[0;36m_find_and_load\u001b[0;34m(name, import_)\u001b[0m\n", + "File \u001b[0;32m: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 +} diff --git a/notebooks/FitTestData.txt b/notebooks/FitTestData.txt new file mode 100644 index 0000000..c733601 --- /dev/null +++ b/notebooks/FitTestData.txt @@ -0,0 +1,5000 @@ +4.98395 +0.346108 +0.667467 +3.2904 +0.521743 +1.45696 +3.49892 +2.06315 +1.68609 +2.05627 +2.08854 +1.9317 +0.770499 +2.16964 +1.61414 +0.359786 +1.41068 +1.043 +0.494842 +0.472404 +0.0584138 +0.829628 +0.423252 +3.22608 +1.79007 +2.58363 +1.94251 +1.52259 +1.74447 +0.393461 +0.709961 +0.240708 +0.123934 +1.91499 +2.0337 +1.89711 +2.01604 +0.201433 +1.99392 +0.219439 +0.267382 +1.54016 +0.458266 +0.686536 +0.166239 +0.264839 +1.70831 +0.164427 +0.696428 +2.51766 +0.509457 +1.2068 +0.293765 +1.07499 +1.97524 +0.364889 +1.24671 +0.0882066 +0.756521 +1.5573 +0.393774 +1.57852 +2.05758 +0.943475 +0.341065 +1.33609 +1.88151 +1.961 +1.9923 +1.42541 +0.181009 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