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"source": [
"# Interactive Gravity Model Lab\n",
"Visualize how β affects trip distribution using the doubly-constrained gravity model. Fixed P,A,C values"
]
},
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"cell_type": "markdown",
"id": "8f94cb97",
"metadata": {
"id": "8f94cb97"
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"source": [
"## Setup and Input Data\n",
"We define production, attraction, and travel cost matrices."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "ab0181e7",
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"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import ipywidgets as widgets\n",
"from IPython.display import display, clear_output\n",
"\n",
"# Input data\n",
"P = np.array([400, 350, 250], dtype=float)\n",
"A = np.array([300, 200, 500], dtype=float)\n",
"C = np.array([\n",
" [5, 10, 18],\n",
" [13, 5, 15],\n",
" [20, 16, 6]\n",
"], dtype=float)"
]
},
{
"cell_type": "markdown",
"id": "9959b192",
"metadata": {
"id": "9959b192"
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"source": [
"## Gravity Model Function\n",
"This function calculates trip distribution, shows convergence, heatmap, and F(c) plot."
]
},
{
"cell_type": "code",
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"id": "6550f7fd",
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"# Interactive gravity model function\n",
"def gravity_model(beta):\n",
" clear_output(wait=True)\n",
" print(f\"Running Gravity Model with β = {beta}\\n\")\n",
"\n",
" F = np.exp(beta * C)\n",
" Tij = np.zeros((3, 3))\n",
" row_errors = []\n",
" col_errors = []\n",
"\n",
" # Initial estimate\n",
" for i in range(3):\n",
" denom = np.sum(F[i, :] * A)\n",
" for j in range(3):\n",
" Tij[i, j] = P[i] * (F[i, j] * A[j]) / denom\n",
"\n",
" # Furness balancing\n",
" tolerance = 1e-4\n",
" max_iter = 100\n",
" for it in range(max_iter):\n",
" row_errors.append(np.abs(Tij.sum(axis=1) - P).sum())\n",
" col_errors.append(np.abs(Tij.sum(axis=0) - A).sum())\n",
"\n",
" # Column\n",
" col_sums = Tij.sum(axis=0)\n",
" for j in range(3):\n",
" if col_sums[j] != 0:\n",
" Tij[:, j] *= A[j] / col_sums[j]\n",
"\n",
" # Row\n",
" row_sums = Tij.sum(axis=1)\n",
" for i in range(3):\n",
" if row_sums[i] != 0:\n",
" Tij[i, :] *= P[i] / row_sums[i]\n",
"\n",
" if np.allclose(Tij.sum(axis=0), A, rtol=tolerance) and np.allclose(Tij.sum(axis=1), P, rtol=tolerance):\n",
" print(f\" Converged in {it+1} iterations\\n\")\n",
" break\n",
" else:\n",
" print(\" Did not converge\\n\")\n",
"\n",
" # Adjust for rounding\n",
" Tij = Tij.round(1)\n",
" for i in range(3):\n",
" Tij[i, -1] += P[i] - Tij[i, :].sum()\n",
" for j in range(3):\n",
" Tij[-1, j] += A[j] - Tij[:, j].sum()\n",
"\n",
" df = pd.DataFrame(\n",
" Tij.round(1),\n",
" index=[f\"From Zone {i+1}\" for i in range(3)],\n",
" columns=[f\"To Zone {j+1}\" for j in range(3)]\n",
" )\n",
" df[\"Row Total\"] = df.sum(axis=1)\n",
" df.loc[\"Column Total\"] = df.sum(axis=0)\n",
"\n",
" print(\"Final Trip Matrix:\")\n",
" display(df)\n",
"\n",
" avg_trip_length = (Tij * C).sum() / Tij.sum()\n",
" print(f\"Estimated Average Trip Length: {avg_trip_length:.2f}\")\n",
"\n",
"\n",
"#Plotting\n",
" # Convergence plot\n",
" plt.figure(figsize=(6, 4))\n",
" plt.plot(row_errors, label='Row Error')\n",
" plt.plot(col_errors, label='Column Error')\n",
" plt.title(f\"Convergence Plot (β = {beta})\")\n",
" plt.xlabel(\"Iteration\")\n",
" plt.ylabel(\"Error\")\n",
" plt.legend()\n",
" plt.grid(True)\n",
" plt.tight_layout()\n",
" plt.show()\n",
"\n",
" # Heatmap\n",
" plt.figure(figsize=(6, 5))\n",
" sns.heatmap(Tij, annot=True, fmt=\".1f\", cmap=\"YlGnBu\")\n",
" plt.title(f\"Trip Distribution Heatmap (β = {beta})\")\n",
" plt.tight_layout()\n",
" plt.show()\n",
"\n",
" # F(c) Curve\n",
" cost_range = np.linspace(0, 30, 100)\n",
" F_curve = np.exp(beta * cost_range)\n",
"\n",
" plt.figure(figsize=(6, 4))\n",
" plt.plot(cost_range, F_curve, color='purple')\n",
" plt.title(\"Friction Factor vs Travel Time\")\n",
" plt.xlabel(\"Travel Time (minutes)\")\n",
" plt.ylabel(\"F(c)\")\n",
" plt.grid(True)\n",
" plt.tight_layout()\n",
" plt.show()"
]
},
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"source": [
"## Select β Value\n",
"Use the slider below to run the model interactively for different β values."
]
},
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"# Slider widget for beta\n",
"beta_slider = widgets.FloatSlider(\n",
" value=-0.035,\n",
" min=-0.25,\n",
" max=-0.01,\n",
" step=0.005,\n",
" description='Select β:',\n",
" style={'description_width': 'initial'},\n",
" layout=widgets.Layout(width='60%')\n",
")\n",
"\n",
"widgets.interact(gravity_model, beta=beta_slider)"
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"Running Gravity Model with β = -0.035\n",
"\n",
" Converged in 2 iterations\n",
"\n",
"Final Trip Matrix:\n"
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\n \n \n | \n To Zone 1 | \n To Zone 2 | \n To Zone 3 | \n Row Total | \n
\n \n \n \n | From Zone 1 | \n 148.4 | \n 78.9 | \n 172.7 | \n 400.0 | \n
\n \n | From Zone 2 | \n 98.7 | \n 82.6 | \n 168.7 | \n 350.0 | \n
\n \n | From Zone 3 | \n 52.9 | \n 38.5 | \n 158.6 | \n 250.0 | \n
\n \n | Column Total | \n 300.0 | \n 200.0 | \n 500.0 | \n 1000.0 | \n
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