{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Example of an unbinned maximum likelihood fit with iminuit" ] }, { "cell_type": "code", "execution_count": 113, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from iminuit import Minuit" ] }, { "cell_type": "code", "execution_count": 114, "metadata": {}, "outputs": [], "source": [ "# x = np.loadtxt(\"data/data_ml_fit.txt\")\n", "x = np.loadtxt(\"https://www.physi.uni-heidelberg.de/~reygers/lectures/2020/smipp/data_ml_fit.txt\")" ] }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [], "source": [ "def f(x, a, b):\n", " \"\"\"normalized fit function\"\"\"\n", " xmin = -0.95\n", " xmax = 0.95\n", " return (6 * (1 + a * x + b * x * x)) / \\\n", " ((xmax - xmin) * (3 * a * (xmax + xmin) + \\\n", " 2 * (3 + b * (xmax * xmax + xmax * xmin + xmin * xmin))))" ] }, { "cell_type": "code", "execution_count": 116, "metadata": {}, "outputs": [], "source": [ "def negative_log_likelihood(a, b):\n", " p = np.log(f(x, a, b))\n", " return -np.sum(p)" ] }, { "cell_type": "code", "execution_count": 117, "metadata": {}, "outputs": [], "source": [ "m = Minuit(negative_log_likelihood, a=1, b=1)\n", "m.errordef = Minuit.LIKELIHOOD" ] }, { "cell_type": "code", "execution_count": 118, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Migrad
FCN = 606.5 Nfcn = 50
EDM = 2.23e-08 (Goal: 0.0001)
Valid Minimum No Parameters at limit
Below EDM threshold (goal x 10) Below call limit
Covariance Hesse ok Accurate Pos. def. Not forced
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Name Value Hesse Error Minos Error- Minos Error+ Limit- Limit+ Fixed
0 a 0.53 0.08
1 b 0.51 0.16
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a b
a 0.00571 0.00575 (0.476)
b 0.00575 (0.476) 0.0255
" ], "text/plain": [ "┌─────────────────────────────────────────────────────────────────────────┐\n", "│ Migrad │\n", "├──────────────────────────────────┬──────────────────────────────────────┤\n", "│ FCN = 606.5 │ Nfcn = 50 │\n", "│ EDM = 2.23e-08 (Goal: 0.0001) │ │\n", "├──────────────────────────────────┼──────────────────────────────────────┤\n", "│ Valid Minimum │ No Parameters at limit │\n", "├──────────────────────────────────┼──────────────────────────────────────┤\n", "│ Below EDM threshold (goal x 10) │ Below call limit │\n", "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n", "│ Covariance │ Hesse ok │ Accurate │ Pos. def. │ Not forced │\n", "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n", "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n", "│ │ Name │ Value │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit- │ Limit+ │ Fixed │\n", "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n", "│ 0 │ a │ 0.53 │ 0.08 │ │ │ │ │ │\n", "│ 1 │ b │ 0.51 │ 0.16 │ │ │ │ │ │\n", "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n", "┌───┬─────────────────┐\n", "│ │ a b │\n", "├───┼─────────────────┤\n", "│ a │ 0.00571 0.00575 │\n", "│ b │ 0.00575 0.0255 │\n", "└───┴─────────────────┘" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.migrad()" ] }, { "cell_type": "code", "execution_count": 119, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
a b
a 0.00571 0.00575 (0.476)
b 0.00575 (0.476) 0.0255
" ], "text/plain": [ "┌───┬─────────────────┐\n", "│ │ a b │\n", "├───┼─────────────────┤\n", "│ a │ 0.00571 0.00575 │\n", "│ b │ 0.00575 0.0255 │\n", "└───┴─────────────────┘" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# covariance matrix\n", "m.covariance" ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
a b
a 1 0.476
b 0.476 1
" ], "text/plain": [ "┌───┬─────────────┐\n", "│ │ a b │\n", "├───┼─────────────┤\n", "│ a │ 1 0.476 │\n", "│ b │ 0.476 1 │\n", "└───┴─────────────┘" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# correlation matrix\n", "m.covariance.correlation()" ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [], "source": [ "# function with fitted parameters\n", "xf = np.linspace(-1, 1., 1000)\n", "a_fit = m.values['a']\n", "b_fit = m.values['b']\n", "yf = f(xf, a_fit, b_fit)" ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "data": { "image/png": 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MsnVJ4rIWGmY2H1gEXOvur2ZruSKypdZ2BQK0fI5h0ZSwZzE/6tC6745w9LWw35nQJXZnD9KBZXNPoywaXjazJ9391CwuW0QiFRUV2b+o6+Np8PKNMPfv4XmPvnD4FeGai249s7suadeyFhru3sXMegNHA8dna7kikkNLZ8MrN8K7j4fn3UrgkxfDIZepF1pJK6vnNNy9CngiGkSkUC2fB//8GUx/AHDo2gM+cVHYu+g9OOnqpIDpRLhIZ7J0Fkz6FbzzMHg9dOkGB54HY74FfXdIujppBzIODTPrCuwJbEOaiwN1ElykAH30X3j1lzD7qfC8S1G4J/enroJtdAGexJdRaJjZd4Craf5e4GpiIVIoPngjhMX7z4fnXXvAAefCYZdD/6HJ1ibtUuzQMLMLgZuAfwL/AH4C/BrYBFwIzAduzUGNIpKJ+voQEv/6HVS8FsZ1K4HR58OhX4M+2yVbn7RrmexpXAK84e5HmdlAQmg8Hd0g6bfA22gvQyQ5mzbC9Pvg37fCsjlhXI9+cPD/haazag0lWZBJaOwFXBs9bmgk3hXA3T82swnA1wl34hORfFm3DCbfBm/+GdYvC+P67ggHXxxOchf3S7Y+6VAyCY06YF30uOHfgSnTywF1pC+SL0tnw3/+CNPuhdqNYdz2I8O9uEecCl27JVqedEyZhMYHwC4A7l5tZguBMcB90fRPACuyW56IbKFuE2fsVQR3nQTlkzaPHz42XJBXdjiYJVefdHiZhMarwGeAa6LnDwLfMLOehKa3X0KHpkRyY83H8NbdMPUuHvpCrxAY3Upg5JnhMNTgPZKuUDqJTELjt8A0M+vp7huAHwLDgfOi6f8gNMcVkWyorw/hMOWOcH1FfS0Asyrr2Ovcm0Ng6HyF5Fns0HD3OcCclOfrgJPNrB9QF3UhIiJttWphOE/x33tgVdSbrXWFvU6GT1zE3rsdid8yPtkapdNqczci7r46G4WIdGq11TD76RAU817ifw0U++4E+4+DA86DfjsmWqIIqO8pkeS4w4dTQ6eBMx6ADSvD+K7dYc/PwP7nwK5H6j4WUlAUGiL5tnQ2zHgQ3nkIVpZvHj9kXzjgHNj387oQTwqWQiOdTRtDG3f9wpNsWbUw9Cw74yFYMmPz+N7bwT5nwH5fgB1GJVaeSFwKjXSm3A6v/Rr2+DTs+VnY9Qgo6pF0Va2+zWdpaSnl5eXZL0iat+x9mP0kzHoKPpyyeXxxv3BSe9/Ph+sq9ONE2hGFRjqLpsC6SnjrL2Ho3gd2Pw72OgmGHQfFzXXymzutvc2n6WKv/HCHxdNhVhQUlbM2TyvqCXuMDUEx7NiC+BEi0hqW9XsNF5DRo0f7lClTWp6xMXdYMjO0jZ/11JaHE7p2Dycnh58QAiSP9yIws1aHRkf+Oydq0wYofw3eex7mPgurPtg8rUe/EBR7ngTDjoHuJVlZpf6eArl9H5jZVHcfnXZaR37ztTo0GltZHppDznoKPvg3m/trBAbuHvZChh0DpYdBt55tX18TFBoFYvm8EBLvPx8Co6HfJ4DeQ0LLpz1PgrIxUNQ966vX31OgHYSGme0KvAC4u++WZvp8YBFwbaHcvS9roZGqqjL8onz/BZj3ClSnXKZS1DMco97t6PDvkH2gy1Y3N2w1hUZC1i0LV2YvmATzX4YV87ecvv2o8MNh9+Nhx9FZ/Zuno7+nQPsIjT2AWYTQ2OrMnZnVRw8deNLdT21dudmTk9BIVbcpnP94//kQIh9P23J6cf8QHg3DtiOgS5e8n9DWl0yGNqyE8n9tDoqlM7ecXtw/7FkOO47RZ32HqXMWtmo1+ntKWxR8aMRcUW/gaOB4d78sawtupZyHRmNrl8C8F2HBq+HLZs2iLaf33AaGHsLVtzzCTye+ADvsDz1657wsfck0wx2Wvw8L34RFb8LCybD0XbY4BFlUDDsfDLuMgV2OgB0OgK6hDUlbtq32HKUtOkRoFJpchkacvYWy/sZRZUUcWdaVo8qK2Llfo8MW1gWGjICdPhGGHQ+EgcOy3gRTXzIp1i0Le4QfvRUCYtGbm6/EjlTXOm8squPl8jpeWlDLfz6so6Yu/eLa0pxZoSFt0SFCw8z6FVJfVLkMjYz/YO6wckH0i3ZyGBa/A97o26ioJwzZG7bbNxr2g233btMeSaf8knEPnf19PD00g108Izxe+9HW8/YewiOTF3H65TfBTgeFi+xy2KChgUJD2qLgQ8PMXgTGufviJqYfBtzj7rtkUNgA4HbgeGAZcI27/62Z+bsD04A+7r5TS8svqNBIp2Y9fPx2CJCFb4YvtdUfpJnRYMAuMGg4DNo9+jcaYnQ30aG/ZOo2wYoF4Z7YlXNg2Xvh8bL3oCZNx8vde4cGCtuPhJ0PCnt4/YdiXbrkfRspNKQtkgqNTC7uO5RwP43z3f2ZlIUb4d7h3wc+zrC2W4AaYAgwCnjazKa5+8wm5r8SqAT6ZLiewtS9F5QeGoYG61eEa0Qafh0vngGVs0OLnRXzYe7ft1xGr4EwYDfoP7TRUAr9doJuxfn9P2WbeziktKoiDCsb/bvqg//dZ2IrJYPDntr2+0X/joRtdsl566a4SktLW3XhZWlp/q4NEmkskz2N/YD7CTde+i3wHWBb4B7gCOBx4AJ3X9nkQrZcXgmwEtjH3edG4yYCH7r7VjdzMrNdgGeAbwJ/7hB7GnHVVodrA5bNjX5Jz4Xl7zX9azpVyWCmzVvMyEOPDdcQ9N42+ncIlAwMF6AVpww5uK5gC+5QvRY2roINq2Dj6vB4/fLQkKAqGtYuhqql4XFddfPL7D8UBu0R9rwGDw+PB++RUad/+vUu7U3B72m4+3QzOwD4f8A3gGOAHYAS4DJ3vzXDuoYDtQ2BEZlGCKB0fg98F9jQ3ELNbDwwHmDo0KEZllSginqE8xxD9t5yvDus+SicK1m1MPzqXvXB5l/gaz6EdZWM3K5ruL4ghvWbnNUbnbU1zsZa8K7dGXnAQeFK+KLiUEuXhreNb66jQX1tuNittjpcLV1bHT3fGAJu42rw+q3W26we/WCbaO9pm7Lo39LNe1TdewGt75sL9OtdJK6M+p5y9w1mdjHhC/8wwrfG11oRGAC9gTWNxq0mzaEnMzsN6Oruj5rZkS3UOAGYAGFPoxV1tR9m4cY8Td2cp64W1i+Lfr0v3fwrvmppGNYvg41rwhd5dfi3V7daenUztt+8kOgq+Czq3jtc61DcD3r2D497bgN9hoReX3tvC32227xXFLP7jdb2zSUi8WUUGma2G3AfcADwV+Bw4DdmNhC4wTP7xFYBjXv+6wusbbTOEuDnwImZ1CqEawn6bBeGONxh0/oQJDVVUFvNJw4cyeTXJ0V7CzXh39RzCP87Jh/926VraAFW1CO0QCoqDkO3YujWKwRF125Z/W+KSP7EDg0zGwfcCtQDZ7n7g9H9we8AfgQcZWbj3D3uyfC5QJGZ7e7u70XjRgKNT4LvDpQBk6KTht2Bfma2GPiku5fH/T9IC8zCr/qUX/ZTPqrf8kS9iHRqmTQjmQi8C+zv7g9CuD+4u58BXAocTDgnEYu7rwMeAa43s5Koye4p0XpSvQPsTGhdNQq4CFgSPW5d/w0iItIqmYTGL4Ax6X7Zu/sfCaGxJMP1Xwr0BJYC9wKXuPtMMxtjZlXRsmvdfXHDAKwA6qPnTVynK9nS0Cw006GsrCzp0kUkB7J9RXixu29sec786DBNbtuhJLaP/ibSmSTV5DarVzkVUmCIiEj2NRkaZvZjM8v4vqZm1t/MbmhbWSIiUoia29P4ElBuZr80s5EtLcjMRpvZb4EFwNnZKlDap9aeC2nLoAv0RHKvuSa3ewLfAr4NXBE1cX0TmEc4GW3AAEKT2IOBQYRuQX4K/CZ3JUt70NruwkWksDUZGu5eDdxoZjcD44DPE7oOOaXRrGuAScCDwP3R60REpANq8eK+6OT27cDtZtYFGAoMJnQhUgksdM+0MyEREWmPmjsRfoeZHZzy/FPAQHcvd/fJ7j7F3SsUGCIinUdzJ8K/DOyW8vxl4LicViMiIgWtudBYRrg5UoPM7xYjIiIdSnPnNF4HrjWzoYRWUQCnm9mwZl7j7v7jrFUnIiIFpbnQ+AZwN3A5YS/DgdOjoSkOKDRERDqo5prclgNHmFl3YDugnBAkj+ejMBERKTxxmtzWAB+Y2d3Af9y9dffTFBGRdi+Te4Sfn8tCRESk8GW1l1sREenYFBoiIhKbQkNERGJTaIiISGwKDRERiU2hISIisSk0REQkNoWGiIjEptAQEZHYFBoiIhKbQkNERGJTaIiISGwKDRERiU2hISIisSk0REQkNoWGiIjEptAQEZHYFBoiIhKbQkNERGJTaIiISGyJhoaZDTCzR81snZlVmNnZTcx3pZm9Y2ZrzWyBmV2Z71pFRASKEl7/LUANMAQYBTxtZtPcfWaj+Qw4F5gO7Ab8w8wWuvt9+SxWRKSzS2xPw8xKgDOA77t7lbu/BjwBnNN4Xnf/ubu/5e617j4HeBw4LL8Vi4hIkoenhgO17j43Zdw0YERzLzIzA8YAjfdGGqaPN7MpZjalsrIya8WKiEiyodEbWNNo3GqgTwuvu45Q953pJrr7BHcf7e6jBw8e3OYiRURksyTPaVQBfRuN6wusbeoFZnYZ4dzGGHevzmFtIiKSRpJ7GnOBIjPbPWXcSJo+7HQBcDVwjLsvykN9IiLSSGKh4e7rgEeA682sxMwOA04BJjae18zGATcCx7n7/PxWKiIiDZK+uO9SoCewFLgXuMTdZ5rZGDOrSpnvBmAgMNnMqqLhjwnUKyLSqSV6nYa7rwBOTTN+EuFEecPzXfJYloiINCHpPQ0REWlHFBoiIhKbQkNERGJTaIiISGwKDRERiU2hISIisSk0REQkNoWGiIjEptAQEZHYFBoiIhKbQkNERGJTaIiISGwKDRERiU2hISIisSk0REQkNoWGiIjEptAQEZHYFBoiIhKbQkNERGJTaIiISGwKDRERiU2hISIisSk0REQkNoWGiIjEptAQEZHYFBoiIhKbQkNERGJTaIiISGwKDRERiU2hISIisSk0REQkNoWGiIjEptAQEZHYFBoiIhKbQkNERGJLNDTMbICZPWpm68yswszObmI+M7OfmdnyaPiZmVm+6xUR6eyKEl7/LUANMAQYBTxtZtPcfWaj+cYDpwIjAQeeBxYAf8xbpSIiktyehpmVAGcA33f3Knd/DXgCOCfN7OcBv3L3Re7+IfAr4Mt5K1ZERIBk9zSGA7XuPjdl3DTgiDTzjoimpc43It1CzWw8Yc8EoMrM5rSyvkHAsuZmSOgIWYt1JahQa1NdmVFdmUmsrha+g9pSV2lTE5IMjd7AmkbjVgN9mph3daP5epuZubunzujuE4AJbS3OzKa4++i2LifbCrUuKNzaVFdmVFdmOltdSZ4IrwL6NhrXF1gbY96+QFXjwBARkdxKMjTmAkVmtnvKuJFA45PgRONGxphPRERyKLHQcPd1wCPA9WZWYmaHAacAE9PM/hfgm2a2o5ntAHwLuCvHJbb5EFeOFGpdULi1qa7MqK7MdKq6LMkjPGY2ALgDOA5YDlzt7n8zszHAs+7eO5rPgJ8BF0UvvQ34jg5PiYjkV6KhISIi7Yu6ERERkdgUGiIiElunDQ0zu8zMpphZtZndFWP+K8xssZmtMbM7zKxHyrQyM3vZzNab2WwzO7aNtcXqkyua91kzq0oZasxsRsr0cjPbkDL9H3mq6zoz29Sotl1Tpo8ys6nRNptqZqPyVNeVZvaOma01swVmdmWj6a3eXtnqSy2b2ybDunK2bdpYV97eSxnWlbfPXrS82N9ZlsvvK3fvlANwOqE/qz8Ad7Uw7wnAEsJV6NsArwA/TZn+b+BmoCeha5RVwOA21HYvcD/hosbDCRczjoj52leAH6Q8LweOzdI2i10XcB1wTxPTugMVwBVAD+Dy6Hn3PNR1FXAA4cLWPaL1npWN7RW3DuD/gDnATsCOwLvAxbnYNhnWlbNt08a68vZeyvT91Oh1OfvsRcuL9Z1Fjr+vsvKfac8DcENzf4Bonr8BN6Y8PwZYHD0eDlQDfVKmT2r4EmhFPSWEThyHp4ybmPpHb+a1ZUAdUJYyLitv3EzrauGDfjzwIVFDjGjcB8DYfG6vaN7fAb9v6/bKpA7gdWB8yvMLgTeyvW2y8H7KyrbJwvbKy3upLdsrl5+9NOtq9juLHH9fddrDUxlK1/fVEDMbGE2b7+5rG01P2zdWDE31yRVneecCk9y9vNH4v5pZpZn9w8xGpnldrur6rJmtMLOZZnZJyvgRwHSP3rGR6S0sK5t1Af9ryj2GrS8Ubc32yqSO5vpSy+a2ybSu/8nytslGXfl4L7Wmrga5/OxlKqffVwqNeNL1fQWhn6zG0xqmp+tDK+664vbJ1di5bH3R4zjCr6BS4GXgOTPrn4e6HgD2AgYDXwF+YGZfTFlWtrZZW7bXdYTPwJ0p41q7vbLSl1qaac0tJ47Wbp/ryN62aWtd+XovZVpXqlx+9jKV0++rDhkaZvaKmXkTw2utWGS6vq8g9JOVSR9acWrLaHkpyz0c2A54KHW8u//L3Te4+3p3v4lw/HJMruty93fd/SN3r3P314HfAp+LJsdeVg6312WED/pn3L06pe5Y2yuNbPWl1qr/T5bqAnKybdpUV7beS9muq0FbP3s5kLXvq3Q6ZGi4+5Hubk0Mh7diken6vlri7sujabuaWZ9G09P2jRWjtkz65Ep1HvCIu1e1MJ8DW/WnnMO60q13JrBf9Mu6wX7plpWLuszsAuBq4Bh3X5RB3c3JVl9qsbdNTBltnxxtmzbX1cx6E91ekTZ99nIga99XaWX7JE17GQgtRIqBmwgnuoqBoibmHQssBvYG+gMvsWVrhDeAX0bLOI22t566j9CCowQ4jBZabxBaQawGjm40fmj0+u5RbVcClcDAXNdF6EdsG8KH5CDCycrzomkNLV6+Tmjxchltaz2VSV3jor/lXmmmtWl7xa0DuBiYRWg5tQPhA9u49VRWtk2GdeVs27Sxrry9l1rxfsrLZy9aZqzvLHL8fdWq4jvCQDhm642G61L+4FXA0JT5v0loxraGcJy3R8q0MkKztg2EppRtajEBDAAeA9YRWoKcnTJtDOFQRur8X4w+KNZo/AjCScF1hL69XgRG56Ou6EO3PNqOs4HLGy1rf2BqtM3eAvbPU10LgE1RXQ3DH7OxvZqqI00NBvwcWBENP2fL1j9Z2zYZ1pWzbdPGuvL2Xsqkrnx+9qJlXkea7yzy/H2lvqdERCS2DnlOQ0REckOhISIisSk0REQkNoWGiIjEptAQEZHYFBoiIhKbQkNERGJTaIiISGwKDRERiU2hISIisSk0RPLAzIrM7F/Rfaf3bDRtfNTV+/VJ1ScSl/qeEskTMysF3iZ0cHewu1eb2QhgMqHDvSPdvS7BEkVapD0NkTxx9wrC/cBHAr8ys57A/cBGYJwCQ9oD7WmI5JmZ3QpcArwOHAqc4e6PJFuVSDwKDZE8M7Ni4B1gN+DP7j4+4ZJEYtPhKZH8G0m4cQ7APmZWlGQxIplQaIjkkZn1JdyJbhnwPeAQ4EeJFiWSAf3CEcmvCUApcJy7v2Rm+wNXm9kL7v5ywrWJtEjnNETyxMwuBG4DbnT370Xj+hOa4XYD9nP35YkVKBKDQkMkD6IL+qYSAuIId69NmXYI8CrwrLufnEyFIvEoNEREJDadCBcRkdgUGiIiEptCQ0REYlNoiIhIbAoNERGJTaEhIiKxKTRERCQ2hYaIiMSm0BARkdj+P2QADNTsQwcIAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.hist(x, bins=20, density=True, ec=\"black\", histtype='step');\n", "plt.plot(xf, yf, linewidth=2)\n", "plt.xticks(fontsize=12)\n", "plt.yticks(fontsize=12)\n", "plt.xlabel(\"x\", fontsize=18)\n", "plt.ylabel(\"f(x; a, b)\", fontsize=18);\n", "plt.savefig(\"ml_fit_example.pdf\")" ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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