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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      "cell_type": "markdown",
      "metadata": {
        "id": "9Z1353j4wPUA"
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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": "b736d31c-3b23-42be-df28-d29df15903a2"
      },
      "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')"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Populating the interactive namespace from numpy and matplotlib\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-1-dfb1f5c682e1>:9: DeprecationWarning: `set_matplotlib_formats` is deprecated since IPython 7.23, directly use `matplotlib_inline.backend_inline.set_matplotlib_formats()`\n",
            "  set_matplotlib_formats('svg')\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MdZv9D0WuPxV"
      },
      "source": [
        "Enter your data below"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "collapsed": true,
        "id": "oMG6to8tuPxW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 461
        },
        "outputId": "c1b2afce-b84f-4f0a-f1d0-81c81f27e4cf"
      },
      "source": [
        "# Measure the mass of each set of filters\n",
        "m1 = 0.89\n",
        "m2 = 1.80\n",
        "m3 = 2.67\n",
        "m4 = 3.57\n",
        "m5 = 4.46\n",
        "m = np.array([m1, m2, m3, m4, m5])*.001\n",
        "g=9.81\n",
        "\n",
        "# Measure the terminal velocity for each set of filters 5 times and record the values\n",
        "v1 = np.array([1.150, 1.026, 1.014, 1.134, 1.010])\n",
        "v2 = np.array([1.443, 1.492, 1.583, 1.563, 1.589])\n",
        "v3 = np.array([2.031, 1.939, 1.941, 2.067, 1.941])\n",
        "v4 = np.array([2.181, 2.202, 2.199, 2.109, 2.269])\n",
        "v5 = np.array([2.507, 2.292, 2.303, 2.364, 2.267])\n",
        "\n",
        "\n",
        "################################################################\n",
        "############## DO NOT EDIT BELOW THIS LINE #####################\n",
        "################################################################\n",
        "\n",
        "\n",
        "# Calculate the mean and std dev of each set of 5 velocity measurements.\n",
        "v = np.array([mean(v1), mean(v2), mean(v3), mean(v4), mean(v5)])\n",
        "sigma_v=np.array([np.std(v1, ddof=1), np.std(v2, ddof=1), np.std(v3, ddof=1), np.std(v4, ddof=1), np.std(v5, ddof=1)]/np.sqrt(np.size(v1)));\n",
        "\n",
        "# x,y data arrays and y-error array\n",
        "x = m*g\n",
        "y = v**2\n",
        "yerr = 2*v*sigma_v\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",
        "\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": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    5 points   chisq min = 17.47    best slope = 137.04 +/- 1.96 \n"
          ]
        },
        {
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