Interactive.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPHkaEYkWIgvfzkOzHTd+My",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/witkov/chi-squared/blob/master/chisq.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "5RxlAiQDhWVZ",
        "outputId": "b66c22a6-c530-4779-e0bf-f46d76b4d80c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Enter distinct (no repeating) x values, separated by spaces: 0.89 1.80 2.67 3.57 4.46\n",
            "Enter the repeated measurements of y for each distinct x value (separated by ';'): 1.150 1.026 1.014 1.134 1.010; 1.443 1.492 1.583 1.563 1.589; 2.031 1.939 1.941 2.067 1.941; 2.181 2.202 2.199 2.109 2.269; 2.507 2.292 2.303 2.364 2.267\n",
            "Enter the coefficient of the dependent variable: 1\n",
            "What is the functional relationship between the dependent and measured variables?\n",
            "1. Dependent variable is the measured variable.\n",
            "2. Dependent variable is the square of the measured variable.\n",
            "3. Dependent variable is the square root of the measured variable.\n",
            "4. Dependent variable is the log of the measured variable.\n",
            "5. Dependent variable is the reciprocal of the measured variable.\n",
            "Select an option (1-5): 4\n",
            "Enter the coefficient of the independent variable: 1\n",
            "What is the functional relationship between the independent and measured variables?\n",
            "1. Independent variable is the measured variable.\n",
            "2. Independent variable is the square of the measured variable.\n",
            "3. Independent variable is the square root of the measured variable.\n",
            "4. Independent variable is the log of the measured variable.\n",
            "5. Independent variable is the reciprocal of the measured variable.\n",
            "Select an option (1-5): 4\n",
            "\n",
            "\n",
            "Number of data points: 5\n",
            "Best-fit slope: 0.494 ± 0.016\n",
            "Best-fit intercept: 0.156 ± 0.017\n",
            "Min_chi2: 17.673\n",
            "Good fit min_chi2 range: 1.838 to 8.162\n",
            "\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.patches import Ellipse\n",
        "from scipy.optimize import minimize_scalar\n",
        "\n",
        "def mean(arr):\n",
        "    return np.mean(arr)\n",
        "\n",
        "def plot_chi_squared_ellipses(A_best, B_best, var_A, var_B, cov_AB):\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.scatter(A_best, B_best, color='red', marker='x', label='Best-fit parameters')\n",
        "\n",
        "    # Define the chi-squared contours at delta_chi2 = 2.3 and delta_chi2 = 6.17\n",
        "    delta_chi2 = [2.3, 6.17]\n",
        "\n",
        "    for chi2 in delta_chi2:\n",
        "        # Calculate the semi-major and semi-minor axes and rotation angle for the ellipse\n",
        "        a = np.sqrt(2.0 * chi2 * var_A)\n",
        "        b = np.sqrt(2.0 * chi2 * var_B)\n",
        "        theta = 0.5 * np.arctan(2.0 * cov_AB / (var_A - var_B))\n",
        "        theta = np.degrees(theta)\n",
        "\n",
        "        # Create the ellipse\n",
        "        ellipse = Ellipse(xy=(A_best, B_best), width=a * 2, height=b * 2, angle=theta, edgecolor='blue', fill=False)\n",
        "        ax.add_patch(ellipse)\n",
        "\n",
        "    ax.set_xlabel('Slope (A)')\n",
        "    ax.set_ylabel('Intercept (B)')\n",
        "    ax.legend(loc='best')\n",
        "    plt.title('68% and 95% chi-squared contours in slope-intercept plane')\n",
        "    plt.show()\n",
        "\n",
        "def get_distinct_x_values():\n",
        "    while True:\n",
        "        # Ask the user to enter the data points for x (space-separated)\n",
        "        x_input = input(\"Enter distinct (no repeating) x values, separated by spaces: \")\n",
        "        x = np.array([float(val) for val in x_input.split()])\n",
        "        \n",
        "        # Check if all x values are distinct\n",
        "        if len(np.unique(x)) == len(x):\n",
        "            return x\n",
        "        else:\n",
        "            print(\"Error: All x values must be distinct. Please enter distinct (no repeating) x values again.\")\n",
        "\n",
        "# Get distinct x values from user input\n",
        "x = get_distinct_x_values()\n",
        "\n",
        "# Ask the user to enter the repeated measurements of y for each distinct x value\n",
        "y_input = input(\"Enter the repeated measurements of y for each distinct x value (separated by ';'): \")\n",
        "y_measurements = [np.array([float(val) for val in group.split()]) for group in y_input.split(';')]\n",
        "\n",
        "# Verify that the number of x values matches the number of groups of y measurements\n",
        "if len(x) != len(y_measurements):\n",
        "    print(\"Error: The number of x values must match the number of groups of y measurements.\")\n",
        "    exit()\n",
        "\n",
        "# Calculate the mean and standard error of the dependent variable\n",
        "y_mean = np.array([mean(group) for group in y_measurements])\n",
        "sigma_y = np.array([np.std(group, ddof=1) / np.sqrt(len(group)) for group in y_measurements])\n",
        "\n",
        "\n",
        "# Function to validate yes/no input\n",
        "def get_yes_no_input(prompt):\n",
        "    while True:\n",
        "        response = input(prompt).strip().lower()\n",
        "        if response in ['y', 'n']:\n",
        "            return response\n",
        "        else:\n",
        "            print(\"Invalid input. Please enter 'y' or 'n'.\")\n",
        "\n",
        "# Function to validate numerical input within a given range\n",
        "def get_numerical_input(prompt, lower_bound, upper_bound):\n",
        "    while True:\n",
        "        try:\n",
        "            response = int(input(prompt))\n",
        "            if lower_bound <= response <= upper_bound:\n",
        "                return response\n",
        "            else:\n",
        "                print(f\"Invalid input. Please enter a number between {lower_bound} and {upper_bound}.\")\n",
        "        except ValueError:\n",
        "            print(\"Invalid input. Please enter a valid number.\")\n",
        "\n",
        "# Validate input for coefficient in the dependent variable\n",
        "K = float(input(\"Enter the coefficient of the dependent variable: \"))\n",
        "\n",
        "# Validate input for functional relationship between dependent and measured variables\n",
        "print(\"What is the functional relationship between the dependent and measured variables?\")\n",
        "print(\"1. Dependent variable is the measured variable.\")\n",
        "print(\"2. Dependent variable is the square of the measured variable.\")\n",
        "print(\"3. Dependent variable is the square root of the measured variable.\")\n",
        "print(\"4. Dependent variable is the log of the measured variable.\")\n",
        "print(\"5. Dependent variable is the reciprocal of the measured variable.\")\n",
        "relationship_option = get_numerical_input(\"Select an option (1-5): \", 1, 5)\n",
        "\n",
        "# Update the equation for y_mean and yerr based on the selected option\n",
        "if relationship_option == 1:\n",
        "    yerr = K * sigma_y\n",
        "    y = K * y_mean\n",
        "elif relationship_option == 2:\n",
        "    yerr = K * 2 * sigma_y * y_mean\n",
        "    y = K * y_mean**2\n",
        "elif relationship_option == 3:\n",
        "    yerr = K * 0.5 * sigma_y * np.sqrt(1 / y_mean)\n",
        "    y = K * np.sqrt(y_mean)\n",
        "elif relationship_option == 4:\n",
        "    yerr = K * sigma_y / y_mean\n",
        "    y = K * np.log(y_mean)\n",
        "elif relationship_option == 5:\n",
        "    yerr = K * sigma_y / (y_mean ** 2)\n",
        "    y = K * 1/y_mean\n",
        "\n",
        "# Validate input for coefficient in the independent variable\n",
        "K2 = float(input(\"Enter the coefficient of the independent variable: \"))\n",
        "\n",
        "# Validate input for functional relationship between independent and measured variables\n",
        "print(\"What is the functional relationship between the independent and measured variables?\")\n",
        "print(\"1. Independent variable is the measured variable.\")\n",
        "print(\"2. Independent variable is the square of the measured variable.\")\n",
        "print(\"3. Independent variable is the square root of the measured variable.\")\n",
        "print(\"4. Independent variable is the log of the measured variable.\")\n",
        "print(\"5. Independent variable is the reciprocal of the measured variable.\")\n",
        "relationship_option2 = get_numerical_input(\"Select an option (1-5): \", 1, 5)\n",
        "\n",
        "# Update the equation for y_mean and yerr based on the selected option\n",
        "if relationship_option2 == 1:\n",
        "    x = K2 * x\n",
        "elif relationship_option2 == 2:\n",
        "    x = K2 * x**2\n",
        "elif relationship_option2 == 3:\n",
        "    x = K2 * np.sqrt(x)\n",
        "elif relationship_option2 == 4:\n",
        "    x = K2* np.log(x)\n",
        "elif relationship_option2 == 5:\n",
        "    x = K2 * 1/x\n",
        "\n",
        "# calculate sums needed to calculate chi-squared in closed-form\n",
        "s_yy = sum(y ** 2 / yerr ** 2)\n",
        "s_xx = sum(x ** 2 / yerr ** 2)\n",
        "s_0 = sum(1 / yerr ** 2)\n",
        "s_xy = sum((y * x) / yerr ** 2)\n",
        "s_y = sum(y / yerr ** 2)\n",
        "s_x = sum(x / yerr ** 2)\n",
        "\n",
        "# Calculate the best-fit slope and intercept\n",
        "A_best = (s_0 * s_xy - s_x * s_y) / (s_0 * s_xx - s_x ** 2)\n",
        "B_best = (s_y * s_xx - s_x * s_xy) / (s_0 * s_xx - s_x ** 2)\n",
        "\n",
        "# Calculate the variance and covariance\n",
        "var_A = 1 / s_xx\n",
        "var_B = 1 / s_0\n",
        "cov_AB = -s_x / (s_xx * s_0)\n",
        "\n",
        "# Calculate the chi-squared min value\n",
        "min_chi2 = s_yy + (s_0 * s_xy ** 2 - 2 * s_x * s_y * s_xy + s_y ** 2 * s_xx) / (s_x ** 2 - s_0 * s_xx)\n",
        "\n",
        "# Define the chi-squared function in terms of slope\n",
        "def chi_squared(slope):\n",
        "    intercept = (s_y - s_x * slope) / s_0\n",
        "    return s_yy + s_xx * slope ** 2 + s_0 * intercept ** 2 - 2 * (s_x * s_y * slope + s_x * intercept * slope - s_y * intercept)\n",
        "\n",
        "# Find the slope values that correspond to chi_squared_min + 1\n",
        "target_chi_squared = min_chi2 + 1\n",
        "result_1 = minimize_scalar(lambda slope: (chi_squared(slope) - target_chi_squared) ** 2, bounds=(A_best - 5 * np.sqrt(var_A), A_best))\n",
        "result_2 = minimize_scalar(lambda slope: (chi_squared(slope) - target_chi_squared) ** 2, bounds=(A_best, A_best + 5 * np.sqrt(var_A)))\n",
        "\n",
        "# Calculate the uncertainties in the slope and intercept\n",
        "slope_uncertainty = np.abs(result_1.x - result_2.x) / 2\n",
        "intercept_uncertainty = np.abs((s_y - s_x * result_1.x) / s_0 - (s_y - s_x * result_2.x) / s_0) / 2\n",
        "\n",
        "# Display the results\n",
        "print(\"\\n\")\n",
        "print(\"Number of data points:\", len(x))\n",
        "print(f\"Best-fit slope: {A_best:.3f} ± {slope_uncertainty:.3f}\")\n",
        "print(f\"Best-fit intercept: {B_best:.3f} ± {intercept_uncertainty:.3f}\")\n",
        "print(f\"Min_chi2: {min_chi2:.3f}\")\n",
        "#print(f\"s_0: {s_0:.3f}\")\n",
        "#print(f\"s_x: {s_x:.3f}\")\n",
        "#print(f\"s_xx: {s_xx:.3f}\")\n",
        "#print(f\"s_y: {s_y:.3f}\")111\n",
        "#print(f\"s_xy: {s_xy:.3f}\")\n",
        "#print(f\"s_yy: {s_yy:.3f}\")\n",
        "\n",
        "# Calculate the good fit range\n",
        "N = len(x)  # Number of distinct x values\n",
        "lower_bound = N - np.sqrt(2*N)\n",
        "upper_bound = N + np.sqrt(2*N)\n",
        "good_fit_range = f\"{lower_bound:.3f} to {upper_bound:.3f}\"\n",
        "\n",
        "print(f\"Good fit min_chi2 range: {good_fit_range}\")\n",
        "print(\"\\n\")\n",
        "\n",
        "# Generate scatter plot with vertical error bars and best-fit line\n",
        "plt.errorbar(x, y, yerr=yerr, fmt='o', label='Data Points', capsize=3)\n",
        "plt.plot(x, A_best * x + B_best, label='Best-fit Line', color='red')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.legend()\n",
        "plt.title('Dependent vs independent variable with error bars and best-fit line')\n",
        "plt.show()\n",
        "\n",
        "# Plot the chi-squared ellipses\n",
        "plot_chi_squared_ellipses(A_best, B_best, var_A, var_B, cov_AB)\n"
      ]
    }
  ]
}