{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Distance Based Statistical Method for Planar Point Patterns\n", "\n", "**Authors: Serge Rey and Wei Kang **\n", "\n", "## Introduction\n", "\n", "Distance based methods for point patterns are of three types:\n", "\n", "* [Mean Nearest Neighbor Distance Statistics](#Mean-Nearest-Neighbor-Distance-Statistics)\n", "* [Nearest Neighbor Distance Functions](#Nearest-Neighbor-Distance-Functions)\n", "* [Interevent Distance Functions](#Interevent-Distance-Functions)\n", "\n", "In addition, we are going to introduce a computational technique [Simulation Envelopes](#Simulation-Envelopes) to aid in making inferences about the data generating process. An [example](#CSR-Example) is used to demonstrate how to use and interprete simulation envelopes." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from scipy import spatial\n", "import libpysal as ps\n", "import numpy as np\n", "from pointpats import ripley\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mean Nearest Neighbor Distance Statistics\n", "\n", "The nearest neighbor(s) for a point $u$ is the point(s) $N(u)$ which meet the condition\n", "$$d_{u,N(u)} \\leq d_{u,j} \\forall j \\in S - u$$\n", "\n", "The distance between the nearest neighbor(s) $N(u)$ and the point $u$ is nearest neighbor distance for $u$. After searching for nearest neighbor(s) for all the points and calculating the corresponding distances, we are able to calculate mean nearest neighbor distance by averaging these distances.\n", "\n", "It was demonstrated by Clark and Evans(1954) that mean nearest neighbor distance statistics distribution is a normal distribution under null hypothesis (underlying spatial process is CSR). We can utilize the test statistics to determine whether the point pattern is the outcome of CSR. If not, is it the outcome of cluster or regular\n", "spatial process?" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "points = np.array([[66.22, 32.54], [22.52, 22.39], [31.01, 81.21],\n", " [9.47, 31.02], [30.78, 60.10], [75.21, 58.93],\n", " [79.26, 7.68], [8.23, 39.93], [98.73, 77.17],\n", " [89.78, 42.53], [65.19, 92.08], [54.46, 8.48]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Nearest Neighbor Distance Functions\n", "\n", "Nearest neighbour distance distribution functions (including the nearest “event-to-event” and “point-event” distance distribution functions) of a point process are cumulative distribution functions of several kinds -- $G, F, J$. By comparing the distance function of the observed point pattern with that of the point pattern from a CSR process, we are able to infer whether the underlying spatial process of the observed point pattern is CSR or not for a given confidence level." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### $G$ function - event-to-event\n", "\n", "The $G$ function is a kind of \"cumulative\" density describing the distribution of distances within a point pattern. For a given distance $d$, $G(d)$ is the proportion of nearest neighbor distances that are less than $d$. To express this, we first need to define the nearest neighbor distance, which is the smallest distance from each observation $i$ to some other observation $j$, where $j \\neq i$:\n", "$$ min_{j\\neq i}\\{d_{ij}\\} = d^*_i $$\n", "\n", "With this, we can define the $G$ function as a cumulative density function:\n", "$$G(d) = \\frac{1}{N}\\sum_{i=1}^N \\mathcal{I}(d^*_i < d)$$\n", "where $\\mathcal{I}(.)$ is an *indicator function* that is $1$ when the argument is true and is zero otherwise. In simple terms, $G(d)$ gives the percentage of of nearest neighbor distances ($d^*_i$) that are smaller than $d$; when $d$ is very small, $G(d)$ is close to zero. When $d$ is large, $G(d)$ approaches one. \n", "\n", "Analytical results about $G$ are available assuming that the \"null\" process of locating points in the study area is completely spatially random. In a completely spatially random process, the $G(d)$ value should be:\n", "$$\n", "G(d) = 1-e^{-\\lambda \\pi d^2}\n", "$$\n", "Practically, we assess statistical significance for the $G(d)$ function using simulations, where a known spatially-random process is generated and then analyzed. This partially accounts for issues with irregularly-shaped study areas, where locations of points are constrained. \n", "\n", "In practice, we use the `ripley.g_test` function to conduct a test on the $G(d)$. It estimates a value of $G(d)$ for a set of values (called the `support`). To compute the $G$ function for ten values of $d$ ranging from the smallest possible to the largest values in the data:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "g_test = ripley.g_test(points, support=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All statistical tests in the `pointpats.distance_statistics` return a `collections.namedtuple` object with the following properties:\n", "- `support`, which contains the distance values ($d$) used to compute the distance statistic. \n", "- `statistic`, which expresses the value of the requested function at each value of $d$ in the `support`. \n", "- `pvalue`, which expresses the fraction of observed simulations (under a completely spatially random process) that are more extreme than the observed statistics. \n", "- `simulations`, which stores the simulated values of the statistic under a spatially random process. Generally, this is *not* saved (for efficiency reasons), but can be requested using `keep_simulations`. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0. , 3.84791574, 7.69583148, 11.54374723, 15.39166297,\n", " 19.23957871, 23.08749445, 26.93541019, 30.78332593, 34.63124168])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g_test.support" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0. , 0. , 0. , 0.16666667, 0.16666667,\n", " 0.25 , 0.58333333, 0.83333333, 0.91666667, 1. ])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g_test.statistic" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.00e+00, 0.00e+00, 0.00e+00, 2.89e-02, 1.10e-03, 1.00e-04,\n", " 4.30e-03, 6.10e-02, 7.33e-02, 0.00e+00])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g_test.pvalue" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "g_test.simulations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To make a plot of the statistic, the `statistic` is generally plotted on the vertical axis and the `support` on the horizontal axis. Here, we will show the median simulated value of $G(d)$ as well." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "g_test = ripley.g_test(points, support=10, keep_simulations=True)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(g_test.support, np.median(g_test.simulations, axis=0), \n", " color='k', label='simulated')\n", "plt.plot(g_test.support, g_test.statistic, \n", " marker='x', color='orangered', label='observed')\n", "plt.legend()\n", "plt.xlabel('Distance')\n", "plt.ylabel('G Function')\n", "plt.title('G Function Plot')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the $G$ function increases very slowly at small distances and the line is below the typical simulated value (shown in black). We can verify the visual intuition here by looking at the p-value for each point and plotting the simulated $G(d)$ curves, too:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# grab the middle 95% of simulations using numpy:\n", "middle_95pct = np.percentile(g_test.simulations, q=(2.5, 97.5), axis=0)\n", "# use the fill_between function to color between the 2.5% and 97.5% envelope\n", "plt.fill_between(g_test.support, *middle_95pct, \n", " color='lightgrey', label='simulated')\n", "\n", "# plot the line for the observed value of G(d)\n", "plt.plot(g_test.support, g_test.statistic, \n", " color='orangered', label='observed')\n", "# and plot the support points depending on whether their p-value is smaller than .05\n", "plt.scatter(g_test.support, g_test.statistic, \n", " cmap='viridis', c=g_test.pvalue < .01)\n", "plt.legend()\n", "plt.xlabel('Distance')\n", "plt.ylabel('G Function')\n", "plt.title('G Function Plot')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From this, we can see that there is statistically significant \"dispersion\" at small values of $d$, since there are *too few* nearest neighbor distances observed between $0 < d < 25$. Once we get to very large distances, the simulation envelope covers the observed statistic. As such, we can say that the point pattern recorded in `points` is unusally dispersed. \n", "\n", "To evaluate the $G(d)$ function without considering any statistical significance or simulations, you can use the `g_function` in the `ripley` module, which simply returns the distances & values of $G(d)$. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([ 0. , 1.82269693, 3.64539386, 5.46809079, 7.29078772,\n", " 9.11348465, 10.93618158, 12.75887851, 14.58157544, 16.40427237,\n", " 18.2269693 , 20.04966623, 21.87236316, 23.69506009, 25.51775702,\n", " 27.34045395, 29.16315088, 30.98584782, 32.80854475, 34.63124168]),\n", " array([0. , 0. , 0. , 0. , 0. ,\n", " 0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.25 ,\n", " 0.25 , 0.25 , 0.41666667, 0.58333333, 0.75 ,\n", " 0.83333333, 0.83333333, 0.91666667, 0.91666667, 1. ]))" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ripley.g_function(points)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### $F$ function - \"point-event\" \n", "\n", "When the number of events in a point pattern is small, $G$ function is rough. For the pattern contained in `points`, there are only 12 observations! This means that there are only 12 nearest neighbor distances, and thus only 12 possible values for the $G(d)$ statistic, at any $d$. \n", "\n", "One way to get around this is to turn to an alternative, the $F(d)$ function. This is analogous to the $G(d)$ function, but measures the nearest neighbor distance *from* a set of known randomly-distributed points *to* a point in the observed pattern. Another way of thinking about $F(d)$ is that it reflects a *between-pattern* measure of dispersion, where one pattern is completely spatially random and the other pattern is our observed pattern. In contrast, $G(d)$ is a *within-pattern* measure of dispersion. \n", "\n", "For a randomly simulated point pattern of size $N_s$, this makes the $F(d)$ function:\n", "\n", "$$F(d) = \\frac{1}{N_s} \\sum_k^{N_s} \\mathcal{I}(d^*_k < d)$$\n", "\n", "This can have $N_s$ possible values for any $d$, and thus can give a much more fine-grained view of the point pattern. In this sense, the $F(d)$ function is often called the *empty space function*, as it measures the distance from random points in \"empty space\" to the \"filled\" points in our point pattern. The number of those random points governs how \"fine-grained\" our measure of the observed point pattern can be. \n", "\n", "Just like the `ripley.g_test`, this function is evaluated for every $d$ in a support. Further, we can provide *custom* values for `support`, just in case we have known distance values of interest. \n", "\n", "Below, we'll use the same ten `support` values from $G(d)$ function. And, let's constrain the \"simulated\" point patterns to fall within the convex hull of our original point pattern: " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "f_test = ripley.f_test(points, support = g_test.support, keep_simulations=True, hull='convex')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the $F(d)$ function is very smooth, we can see the $F(d)$ statistic and its simulations clearly by plotting their values directly as lines. For the simulated values, we will make them very transparent. As before we will visualize statistical significance using the `pvalue` attribute:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(f_test.support, f_test.simulations.T, alpha=.01, color='k')\n", "plt.plot(f_test.support, f_test.statistic, color='red')\n", "\n", "plt.scatter(f_test.support, f_test.statistic, \n", " cmap='viridis', c=f_test.pvalue < .05,\n", " zorder=4 # make sure they plot on top\n", " )\n", "\n", "plt.xlabel('Distance')\n", "plt.ylabel('F Function')\n", "plt.title('F Function Plot')\n", "plt.show()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From this we see that the values of the $F$ function are *too high* for distances from about 15 to 25, and (in contrast) for values between $5 < d < 10$, the $F(d)$ function has too few short distances. When the observed $F(d)$ values are too large, then the pattern is too dispersed, or regular. If the empirical $F(d)$ tends to fall below the simulated values, then it reflects clustering. This is the *opposite* of the interpretation of the $G(d)$ function above, so be careful!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### $J$ function - a combination of \"event-event\" and \"point-event\"\n", "\n", "The $J$ function combines the $G$ and $F$ function, in an attempt to provide an immediate graphical indication of the clustering both internally and with respect to the empty space distribution. Practically, the $J(d)$ function is computed as a kind of \"relative clustering ratio\":\n", "\n", "$$J(d) = \\frac{1-G(d)}{1-F(d)}$$\n", "\n", "where the numerator captures the clustering due to within-pattern distances and the denominator captures that for the pattern-to-empty distances. This means that when $J(d)<1$, the underlying point process is a cluster point process, and when $J(d)=1$, the underlying point process is a random point process; otherwise, it is a dispersed point process.\n", "\n", "This function can suffer from numerical stability issues; as $G(d)$ and $F(d)$ both approach $1$, the $J$ ratio can become chaotic. Further, when $G$ or $F$ reaches one, the $J$ function changes abruptly. As such, the $J$ function is often *truncated* to the first $1$ (either in $F(d)$ or $G(d)$), and any $d$ where both $F$ and $G$ are $1$ is assigned a $J$ value of $1$. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/lw17329/Dropbox/dev/pointpats/pointpats/ripley.py:894: UserWarning: requested 20 bins to evaluate the J function, but it reaches infinity at d=25.5178, meaning only 14 bins will be used to characterize the J function.\n", " tree, distances=distances, **core_kwargs\n" ] } ], "source": [ "jp1 = ripley.j_test(points, support=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see from the warning above, the $J$ function did encounter numerical stability issues at about $d=25$. To address this, `pointpats` truncated the $J$ function to only have 14 values in its support, rather than the $20$ requested. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'J Function')" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(jp1.support, jp1.statistic, color='orangered')\n", "plt.axhline(1, linestyle=':', color='k')\n", "plt.xlabel('Distance')\n", "plt.ylabel('J Function')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the above figure, we see that the $J$ function is above the $J(d)=1$ horizontal line, especially as $d$ gets large. This suggests that the process is over-dispersed. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interevent Distance Functions\n", "\n", "While both the $F(d)$ and $G(d)$ functions are useful, they only consider the distance between each point $i$ and its nearest point. Earlier we spelled this distance $d_i^*$, and the distance between $i$ and $j$ was $d_{ij}$. So, note that $d_{i}^*$ is the *only* term that matters for $F$ and $G$, if $d_{ij}$ changes (but $j$ isn't closest to $i$), then the $F$ and $G$ functions generally remain the same. \n", "\n", "So, further statistical summary functions have been developed to consider the *whole* distance distribution, not only the nearest neighbor distances. These functions (still considered part of the \"Ripley\" alphabet, are the $K$, and $L$ functions. \n", "\n", "#### $K$ function\n", "\n", "The $K(d)$ function is a scaled version of the cumulative density function for *all* distances within a point pattern. As such, it's a \"relative\" of the $G$ function that considers all distances, not just the nearest neighbor distances. Practically, the $K(d)$ function can be thought of as the percentage of all distances that are less than $d$. Therefore, for a threshold distance $d$, the $K$ function is defined as:\n", "\n", "$$K(d) = \\frac{1}{N\\hat\\lambda} \\underset{i=1}{\\overset{N}{\\sum}}\\underset{j=1}{\\overset{N}{\\sum}} \\mathcal{I}\\left(d_ij < d\\right)$$\n", "\n", "In this equation, $\\hat\\lambda$ is the *intensity* of the point process. This represents how many points (on average) you would expect in a unit area. You can think of this as an analogue to the *density* of the points in the pattern: large values of $\\hat\\lambda$ mean many points per area, and small values of $\\hat\\lambda$ mean there are fewer points per area. Generally, this parameter is unknown, and is modelled using the average number of points in the study area. This assumes that the intensity of the point pattern is *constant* or *homogeneous* over the study area.\n", "\n", "In the same manner as before, we can construct a set of $K(d)$ function evaluations for random point patterns, and compare them to the observed $K(d)$ function we saw in our original data." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "k_test = ripley.k_test(points, keep_simulations=True)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(k_test.support, k_test.simulations.T, color='k', alpha=.01)\n", "plt.plot(k_test.support, k_test.statistic, color='orangered')\n", "\n", "plt.scatter(k_test.support, k_test.statistic, \n", " cmap='viridis', c=k_test.pvalue < .05,\n", " zorder=4 # make sure they plot on top\n", " )\n", "\n", "plt.xlabel('Distance')\n", "plt.ylabel('K Function')\n", "plt.title('K Function Plot')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we can see that the envelopes are generally above the observed function, meaining that our point pattern is dispersed. We can draw this conclusion because the distances are *too small*, suggesting the pattern is less clustered than otherwise woudl be expected. When points are too regular, their distances tend to be smaller than if they were distributed randomly. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### $L$ function - \"interevent\"\n", "\n", "The $L$ function is a scaled version of $K$ function, defined in order to assist with interpretation. The expected value of the $K(d)$ function *increases* with $d$; this makes sense, since the number of pairs of points closer than $d$ will increase as $d$ increases. So, we can define a normalization of $K$ that *removes* this increase as $d$ increases. \n", "\n", "$$L(d) = \\sqrt{\\frac{K(d)}{\\pi}}-d$$\n", "\n", "For a pattern that is spatially random, $L(d)$ is $0$ at all $d$ values. So, we can use this standardization to make it easier to visualize the results of the $K$ function:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "l_test = ripley.l_test(points, keep_simulations=True)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(l_test.support, l_test.simulations.T, color='k', alpha=.01)\n", "plt.plot(l_test.support, l_test.statistic, color='orangered')\n", "\n", "plt.scatter(l_test.support, l_test.statistic, \n", " cmap='viridis', c=l_test.pvalue < .05,\n", " zorder=4 # make sure they plot on top\n", " )\n", "\n", "plt.xlabel('Distance')\n", "plt.ylabel('K Function')\n", "plt.title('K Function Plot')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## CSR Example\n", "\n", "In this example, we are going to generate a point pattern as the \"observed\" point pattern. This ensures that the data generating process is completely spatially random. Then, we will simulate CSR in the same domain for 100 times and construct evaluate the ripley functions for these simulations. " ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "import geopandas\n", "df = geopandas.read_file(ps.examples.get_path(\"vautm17n.shp\"))\n", "state = df.geometry.cascaded_union" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate the point pattern **pp** (size 100) from CSR as the \"observed\" point pattern." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "pattern = ripley.simulate(state, size=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "before we go any further, let's visualize these simulated values:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "df.plot()\n", "plt.scatter(*pattern.T, color='orangered', marker='.')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And, let's check if there are 100 points:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(100, 2)" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pattern.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yep! So, next to simulate a set of realizations in the same manner, we can use the `size` argument again, just like the `numpy.random` simulators. This means that, to simulate $K$ realizations of a pattern of size $N$, then we use `simulate(hull, size=(N,K)`. For just one realization, we can use `size=N`. " ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "random_realizations = ripley.simulate(state, size=(100,100))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To show the random pattern is truly random, we can visualize all of the points:" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "df.plot(facecolor='none', edgecolor='k')\n", "plt.scatter(*random_realizations.T, marker='.', s=2)\n", "plt.scatter(*pattern.T, color='orangered', marker='.')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now compute the `G` function for the observed pattern as well as all the realizations we just made. " ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "observed_g = ripley.g_function(pattern)\n", "comparison_g = [ripley.g_function(realization, support=observed_g[0]) \n", " for realization in random_realizations]" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(*observed_g, color='orangered')\n", "[plt.plot(*comparison, color='k', alpha=.01) \n", " for comparison in comparison_g]\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All other functions work identically!" ] } ], "metadata": { "kernelspec": { "display_name": "Analysis", "language": "python", "name": "ana" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" }, "widgets": { "state": {}, "version": "1.1.2" } }, "nbformat": 4, "nbformat_minor": 4 }