{
  "nbformat": 4,
  "nbformat_minor": 5,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Chapter 5 - Modeling the Speed-Duration Curve"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import plotly.graph_objects as go\n",
        "from scipy.optimize import curve_fit\n",
        "\n",
        "distances = np.array([100, 200, 400, 800, 1500, 3000, 5000, 10000, 21100, 42200], dtype=float)\n",
        "speeds = np.array([37.6, 37.5, 33.5, 28.5, 26.2, 24.5, 23.8, 22.9, 22.0, 20.9], dtype=float)\n",
        "\n",
        "def speed_curve(x, a, b):\n",
        "    return a * np.power(x, b)\n",
        "\n",
        "params, covariance = curve_fit(speed_curve, distances, speeds, p0=(50, -0.1), maxfev=10000)\n",
        "print(f\"Fit: speed = {params[0]:.2f} * distance^{params[1]:.3f}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "fig = go.Figure()\n",
        "fig.add_trace(go.Scatter(x=distances, y=speeds, mode=\"markers\", name=\"Observed\"))\n",
        "fig.add_trace(go.Scatter(x=distances, y=speed_curve(distances, *params), mode=\"lines\", name=\"Fitted curve\"))\n",
        "fig.update_layout(title=\"Speed-Distance Curve\", xaxis_title=\"Distance (m)\", yaxis_title=\"Speed (km/h)\")\n",
        "fig.show()\n",
        "print(\"Notebook completed.\")"
      ]
    }
  ]
}