chi2_1D.ipynb

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        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/witkov/chi-squared/blob/master/chi2_1D.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# chi2_1D.ipynb version 1/8/2022\n",
        "# This script does chi-square curve fitting to the 1-parameter linear model y = Ax\n",
        "#\n",
        "# Three arrays are needed:\n",
        "    # x is an array of mean values for the independent variable\n",
        "    # y is an array of mean values for the dependent variable\n",
        "    # y_err is an array of standard errors (SD/(sqrt of N)) for y\n",
        "#\n",
        "# This script assumes errors on the dependent (y) variable only.\n",
        "#\n",
        "# SOFTWARE DEPENDENCIES: Numpy, Matplotlib\n",
        "# ---------------------------------------------------------------------------\n",
        "# Copyright (C) 2021 Carey Witkov and Keith Zengel\n",
        "\n",
        "# This program is free software: you can redistribute it and/or modify it under \n",
        "# the terms of the GNU General Public License as published by the Free Software \n",
        "# Foundation; either version 3 of the License, or (at your option) any later version.\n",
        "\n",
        "# This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; \n",
        "# without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. \n",
        "# See the GNU General Public License for more details.\n",
        "\n",
        "# You should have received a copy of the GNU General Public License along with this program. \n",
        "# If not, see https://www.gnu.org/licenses/.\n",
        "# ---------------------------------------------------------------------------"
      ],
      "metadata": {
        "id": "jaLlcOyRV5-U"
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      "execution_count": null,
      "outputs": []
    },
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      "source": [
        "Run the section below to import all the necessary python \n",
        "\n",
        "---\n",
        "\n",
        "libraries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OAIxlqyIuPxT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0f26821f-d8e9-4d4f-ca5c-3d98bb1ec10f"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy as sp\n",
        "from scipy import optimize\n",
        "%pylab inline\n",
        "\n",
        "# this sets the figure format to a vector format\n",
        "from IPython.display import set_matplotlib_formats\n",
        "set_matplotlib_formats('svg', quality=50)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Populating the interactive namespace from numpy and matplotlib\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MdZv9D0WuPxV"
      },
      "source": [
        "Enter your data below"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oMG6to8tuPxW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 796
        },
        "outputId": "20d2a079-804a-448b-d9f2-a6bfa0f935be"
      },
      "source": [
        "# It is assumed that experimental variation is in the dependent, not the independent, variable.\n",
        "# Therefore, enter either a single measurement or a mean for each independent variable value)\n",
        "x1 = 0.89\n",
        "x2 = 1.80\n",
        "x3 = 2.67\n",
        "x4 = 3.57\n",
        "x5 = 4.46\n",
        "x = np.array([x1, x2, x3, x4, x5])\n",
        "\n",
        "# Dependent variable\n",
        "# Enter repeated measurements of the dependent variable.\n",
        "y1 = np.array([1.150, 1.026, 1.014, 1.134, 1.010])\n",
        "y2 = np.array([1.443, 1.492, 1.583, 1.563, 1.589])\n",
        "y3 = np.array([2.031, 1.939, 1.941, 2.067, 1.941])\n",
        "y4 = np.array([2.181, 2.202, 2.199, 2.109, 2.269])\n",
        "y5 = np.array([2.507, 2.292, 2.303, 2.364, 2.267])\n",
        "\n",
        "################################################################\n",
        "############## DO NOT EDIT BELOW THIS LINE #####################\n",
        "################################################################\n",
        "\n",
        "# Calculate the mean and std dev of each set of measurements.\n",
        "y_mean = np.array([mean(y1), mean(y2), mean(y3), mean(y4), mean(y5)])\n",
        "sigma_y=np.array([np.std(y1, ddof=1), np.std(y2, ddof=1), np.std(y3, ddof=1), np.std(y4, ddof=1), np.std(y5, ddof=1)]/np.sqrt(np.size(y1)));\n",
        "\n",
        "# x,y data arrays and y-error array\n",
        "x = x\n",
        "y = y_mean**2\n",
        "yerr = 2*y_mean*sigma_y\n",
        "\n",
        "# calculate sums needed to obtain chi-square\n",
        "s_yy=sum((y**2)/(yerr**2));\n",
        "s_xx=sum((x**2)/(yerr**2));\n",
        "s_xy=sum((y*x)/(yerr**2));\n",
        "\n",
        "A_best = s_xy/s_xx\n",
        "sigma_A = 1/sqrt(s_xx)\n",
        "minchi2 = s_yy - s_xy**2/s_xx;\n",
        "\n",
        "# plot data with errorbars \n",
        "#plt.figure()\n",
        "plt.figure(facecolor='white')\n",
        "plt.errorbar(x,y,yerr,linestyle='None',fmt='none',capsize=5)\n",
        "plt.xlabel('x', fontsize=16)\n",
        "plt.ylabel('y', fontsize=16)\n",
        "plt.grid(True)\n",
        "plt.plot(x, A_best*x)\n",
        "#plt.ylim(0,7);\n",
        "\n",
        "# create parameter range for slope\n",
        "xmin = A_best-2*sigma_A\n",
        "xmax = A_best+2*sigma_A\n",
        "delta_x = xmax-xmin \n",
        "A = np.linspace(xmin,xmax,200)\n",
        "\n",
        "# calculate chi-square \n",
        "chi2 = s_yy + (A**2)*(s_xx) - 2*A*s_xy \n",
        "     \n",
        "# display chi-square vs. slope\n",
        "plt.figure()\n",
        "plt.plot(A,chi2)\n",
        "plt.errorbar(A,chi2)\n",
        "plt.xlabel('slope',fontsize=16)\n",
        "plt.ylabel('chisq',fontsize=16)\n",
        "plt.grid(True)\n",
        "plt.title(\"Chisquared vs Slope and minchi2 + 1 \\n %4d points   chisq min =%6.2f    best slope =%7.2f \" %(x.size,minchi2,A_best))\n",
        "#plt.hlines(minchi2+1,xmin,ymin);\n",
        "\n",
        "print(\" %4d points   chisq min =%6.2f    best slope =%7.2f +/- %.2f \" %(x.size,minchi2,A_best,sigma_A))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    5 points   chisq min = 17.47    best slope =   1.34 +/- 0.02 \n"
          ]
        },
        {
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