{ "cells": [ { "cell_type": "markdown", "id": "5212af16", "metadata": {}, "source": [ "# Simulating random point patterns with `pointpats.random`\n", "\n", "This notebook illustrates how to use the `pointpats.random` module to simulate\n", "random point patterns inside a study region (the *hull*).\n", "\n", "We will look at several families of random patterns:\n", "\n", "1. **Homogeneous Poisson** (`random.poisson`)\n", "2. **Normal cluster** (`random.normal`)\n", "3. **Poisson cluster (Neyman–Scott)** (`random.cluster_poisson`)\n", "4. **Normal cluster with random seeds** (`random.cluster_normal`)\n", "\n", "All examples use a simple square window as the hull:\n", "\n", "$$[0, 1] \\times [0, 1].$$\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "6003346e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0., 0., 1., 1.])" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from pointpats import random as ppr # pointpats.random\n", "\n", "# Make results reproducible\n", "np.random.seed(12345)\n", "\n", "# Define a simple square hull as a bounding box:\n", "# [xmin, ymin, xmax, ymax]\n", "hull = np.array([0.0, 0.0, 1.0, 1.0])\n", "\n", "hull" ] }, { "cell_type": "markdown", "id": "11dc1585", "metadata": {}, "source": [ "## Helper function for plotting point patterns\n", "\n", "We'll use a small helper to visualize realizations of the random point processes." ] }, { "cell_type": "code", "execution_count": 2, "id": "fd2889cf", "metadata": {}, "outputs": [], "source": [ "def plot_pattern(points, hull, ax=None, title=None):\n", " \"\"\"Plot a 2D point pattern inside a rectangular hull.\n", "\n", " Parameters\n", " ----------\n", " points : array-like, shape (n_points, 2)\n", " Coordinates of the points.\n", " hull : array-like, shape (4,)\n", " Bounding box [xmin, ymin, xmax, ymax].\n", " ax : matplotlib.axes.Axes, optional\n", " Axis to plot on.\n", " title : str, optional\n", " Title for the plot.\n", " \"\"\"\n", " points = np.asarray(points)\n", "\n", " if ax is None:\n", " fig, ax = plt.subplots(figsize=(4, 4))\n", "\n", " xmin, ymin, xmax, ymax = hull\n", " ax.scatter(points[:, 0], points[:, 1], s=10, alpha=0.7)\n", " ax.set_xlim(xmin, xmax)\n", " ax.set_ylim(ymin, ymax)\n", " ax.set_aspect(\"equal\", adjustable=\"box\")\n", " ax.set_xlabel(\"x\")\n", " ax.set_ylabel(\"y\")\n", " if title:\n", " ax.set_title(title)\n", "\n", " return ax" ] }, { "cell_type": "markdown", "id": "f05bca84", "metadata": {}, "source": [ "## 1. Homogeneous Poisson process (`random.poisson`)\n", "\n", "The **homogeneous Poisson point process** is the canonical model of\n", "*complete spatial randomness* (CSR):\n", "\n", "- Each point is independently and uniformly distributed in the hull.\n", "- The expected number of points is controlled by the **intensity**\n", " (points per unit area).\n", "\n", "A typical interface (check the installed `pointpats` version for details) allows usage patterns like:\n", "\n", "- `poisson(hull, size=n)` — simulate `n` points once.\n", "- `poisson(hull, intensity=lambda_, size=r)` — draw `r` *replications* from a Poisson\n", " process with intensity `lambda_` points per unit area.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "870559d8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(100, 2)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# A single realization with exactly 100 points\n", "points_poisson_fixed = ppr.poisson(hull, size=100)\n", "\n", "points_poisson_fixed.shape" ] }, { "cell_type": "code", "execution_count": 4, "id": "bb7f6f94", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(4, 4))\n", "plot_pattern(points_poisson_fixed, hull, ax=ax,\n", " title=\"Homogeneous Poisson process (n = 100)\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "id": "0ac04ea4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(4, 200, 2)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Simulate 4 replications with intensity λ = 200 points per unit area\n", "lambda_ = 200 # expected number of points in unit square\n", "n_replications = 4\n", "\n", "points_poisson_intensity = ppr.poisson(hull, intensity=lambda_, size=n_replications)\n", "\n", "points_poisson_intensity.shape" ] }, { "cell_type": "code", "execution_count": 6, "id": "b0e48b36", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(2, 2, figsize=(6, 6))\n", "\n", "for i, ax in enumerate(axes.ravel()):\n", " plot_pattern(points_poisson_intensity[i], hull, ax=ax,\n", " title=f\"Poisson, λ={lambda_}, rep {i+1}\")\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ff89ebf4", "metadata": {}, "source": [ "## 2. Normal cluster (`random.normal`)\n", "\n", "`random.normal` simulates points from a **bivariate normal distribution**\n", "truncated to the hull.\n", "\n", "A typical interface looks like:\n", "\n", "```python\n", "ppr.normal(hull, center=None, cov=None, size=None)\n", "```\n", "\n", "Key arguments:\n", "\n", "- `center`: 2D location of the cluster center. If `None`, often the centroid of the hull.\n", "- `cov`: covariance structure (scalar = iid variance, or 2×2 matrix).\n", "- `size`: number of points (and optionally replications).\n", "\n", "We'll start with a single tight cluster in the center of the window." ] }, { "cell_type": "code", "execution_count": 7, "id": "c34bfe45", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(200, 2)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 200 points in a single bivariate normal cluster\n", "points_normal = ppr.normal(hull, size=200)\n", "\n", "points_normal.shape" ] }, { "cell_type": "code", "execution_count": 8, "id": "7fbf7901", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(4, 4))\n", "plot_pattern(points_normal, hull, ax=ax,\n", " title=\"Normal cluster (default center & spread)\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "id": "a58f6a59", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Three different covariance structures\n", "covariances = [\n", " 0.05, # scalar: isotropic variance\n", " np.array([[0.05, 0.0], [0.0, 0.01]]), # elongated along x\n", " np.array([[0.01, 0.0], [0.0, 0.05]]), # elongated along y\n", "]\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(12, 4))\n", "\n", "for cov, ax in zip(covariances, axes):\n", " pts = ppr.normal(hull, size=300, cov=cov)\n", " plot_pattern(pts, hull, ax=ax, title=f\"cov =\\n{cov}\")\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f74ce910", "metadata": {}, "source": [ "## 3. Poisson cluster process (`random.cluster_poisson`)\n", "\n", "`cluster_poisson` implements a simple **Neyman–Scott**–type cluster process:\n", "\n", "1. \"Seed\" points are drawn from a Poisson process.\n", "2. Around each seed, a small cloud of points is placed within a radius.\n", "\n", "A typical use looks like:\n", "\n", "```python\n", "ppr.cluster_poisson(\n", " hull,\n", " intensity=None,\n", " size=None,\n", " n_seeds=2,\n", " cluster_radius=None,\n", ")\n", "```\n", "\n", "Key arguments:\n", "\n", "- `n_seeds`: number of cluster centers.\n", "- `cluster_radius`: radius of each cluster. If `None`, it may default to a value\n", " based on distances between seeds.\n", "- `size`: controls how many points you simulate in total and how many replications.\n", "\n", "Here we simulate 300 points organized into a few clusters." ] }, { "cell_type": "code", "execution_count": 10, "id": "f1137841", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(300, 2)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n_points = 300\n", "n_replications = 1\n", "n_seeds = 4\n", "\n", "points_cluster_poisson = ppr.cluster_poisson(\n", " hull,\n", " size=(n_points, n_replications),\n", " n_seeds=n_seeds,\n", " # cluster_radius can be None (default) or a scalar / array\n", ")\n", "\n", "points_cluster_poisson.shape" ] }, { "cell_type": "code", "execution_count": 11, "id": "3601664c", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(4, 4))\n", "plot_pattern(points_cluster_poisson, hull, ax=ax,\n", " title=f\"Poisson cluster process (n={n_points}, seeds={n_seeds})\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "b43e4bc9", "metadata": {}, "source": [ "## 4. Normal clusters with random seeds (`random.cluster_normal`)\n", "\n", "`cluster_normal` builds clusters whose centers are themselves drawn from a\n", "Poisson process, but the points within clusters are drawn from a **normal**\n", "distribution around each seed:\n", "\n", "```python\n", "ppr.cluster_normal(hull, cov=None, size=None, n_seeds=2)\n", "```\n", "\n", "- `cov` controls the within-cluster spread.\n", "- `n_seeds` controls how many clusters you get.\n", "- `size` controls total number of points and replications.\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "7baf7061", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(300, 2)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n_points = 300\n", "n_replications = 1\n", "n_seeds = 5\n", "\n", "points_cluster_normal = ppr.cluster_normal(\n", " hull,\n", " size=(n_points, n_replications),\n", " n_seeds=n_seeds,\n", " # cov=None uses a default based on distances between seeds\n", ")\n", "\n", "points_cluster_normal.shape" ] }, { "cell_type": "code", "execution_count": 13, "id": "2d02eb84", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(4, 4))\n", "plot_pattern(points_cluster_normal, hull, ax=ax,\n", " title=f\"Normal cluster process (n={n_points}, seeds={n_seeds})\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f21340aa", "metadata": {}, "source": [ "## Recap\n", "\n", "In this notebook we have:\n", "\n", "- Used `pointpats.random.poisson` to simulate homogeneous Poisson\n", " point patterns under complete spatial randomness.\n", "- Used `pointpats.random.normal` to generate truncated bivariate normal clusters.\n", "- Used `pointpats.random.cluster_poisson` for Poisson cluster processes\n", " (Neyman–Scott–like).\n", "- Used `pointpats.random.cluster_normal` for clustered patterns with\n", " normally distributed clusters.\n", "\n", "These simulated patterns are useful as:\n", "\n", "- **Null models** for hypothesis testing (e.g., against observed patterns).\n", "- **Toy data** for teaching, examples, and algorithm development.\n", "\n", "You can adapt the hull, intensities, and covariance structures to match\n", "your own study regions and applications." ] }, { "cell_type": "code", "execution_count": null, "id": "92eec114-d372-4458-b4f3-514bd34a2b7f", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.2" } }, "nbformat": 4, "nbformat_minor": 5 }