{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Centrography of Point Patterns\n", "\n", "**Authors: Serge Rey and Wei Kang **\n", "\n", "## Introduction\n", "\n", "Centrography refers to a set of descriptive statistics that provide summary descriptions of point patterns.\n", "\n", "This notebook introduces three types of centrography analysis for point patterns in pysal.\n", "* [Central Tendency](#Central-Tendency)\n", "* [Dispersion and Orientation](#Dispersion-and-Orientation)\n", "* [Shape Analysis](#Shape-Analysis)\n", "\n", "We also illustrate centrography analysis using two simulated datasets. See [Another Example](#Another-Example)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The python file **centrography.py** contains several functions with which we can conduct centrography analysis.\n", "* Central Tendency\n", " 1. mean_center: calculate the mean center of the unmarked point pattern.\n", " 2. weighted_mean_center: calculate the weighted mean center of the marked point pattern.\n", " 3. manhattan_median: calculate the manhattan median\n", " 4. euclidean_median: calculate the Euclidean median\n", "* Dispersion and Orientation\n", " 1. std_distance: calculate the standard distance\n", "* Shape Analysis\n", " 1. hull: calculate the convex hull of the point pattern\n", " 2. mbr: calculate the minimum bounding box (rectangle)\n", " \n", "All of the above functions operate on a series of coordinate pairs. That is, the data type of the first argument should be $(n,2)$ array_like. In case that you have a point pattern (PointPattern instance), you need to pass its attribute \"points\" instead of itself to these functions." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " x y\n", "0 66.22 32.54\n", "1 22.52 22.39\n", "2 31.01 81.21\n", "3 9.47 31.02\n", "4 30.78 60.10\n", "5 75.21 58.93\n", "6 79.26 7.68\n", "7 8.23 39.93\n", "8 98.73 77.17\n", "9 89.78 42.53\n", "10 65.19 92.08\n", "11 54.46 8.48" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "from pointpats import PointPattern\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "points = [[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]]\n", "pp = PointPattern(points) #create a point pattern \"pp\" from list\n", "pp.points " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "pandas.core.frame.DataFrame" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(pp.points)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use PointPattern class method **plot** to visualize **pp**." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp.plot()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "#import centragraphy analysis functions \n", "from pointpats.centrography import hull, mbr, mean_center, weighted_mean_center, manhattan_median, std_distance,euclidean_median,ellipse" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Central Tendency\n", "\n", "Central Tendency concerns about the center point of the two-dimensional distribution. It is similar to the first moment of a one-dimensional distribution. There are several ways to measure central tendency, each having pros and cons. We need to carefully select the appropriate measure according to our objective and data status.\n", "\n", "### Mean Center $(x_{mc},y_{mc})$\n", "\n", "$$x_{mc}=\\frac{1}{n} \\sum^n_{i=1}x_i$$\n", "$$y_{mc}=\\frac{1}{n} \\sum^n_{i=1}y_i$$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([52.57166667, 46.17166667])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mc = mean_center(pp.points)\n", "mc" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp.plot()\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Weighted Mean Center $(x_{wmc},y_{wmc})$\n", "\n", "$$x_{wmc}=\\sum^n_{i=1} \\frac{w_i x_i}{\\sum^n_{i=1}w_i}$$\n", "$$y_{wmc}=\\sum^n_{i=1} \\frac{w_i y_i}{\\sum^n_{i=1}w_i}$$\n", "\n", "Weighted mean center is meant for marked point patterns. Aside from the first argument which is a seris of $(x,y)$ coordinates in **weighted_mean_center** function, we need to specify its second argument which is the weight for each event point." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "weights = np.arange(12)\n", "weights" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([60.51681818, 47.76848485])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wmc = weighted_mean_center(pp.points, weights)\n", "wmc" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp.plot() #use class method \"plot\" to visualize point pattern\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center') \n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Manhattan Median $(x_{mm},y_{mm})$\n", "\n", "$$min f(x_{mm},y_{mm})= \\sum^n_{i=1}(|x_i-x_{mm}|+|y_i-y_{mm}|)$$\n", "\n", "Manhattan median is the location which minimized the absolute distance to all the event points. It is an extension of the median measure in one-dimensional space to two-dimensional space. Since in one-dimensional space, a median is the number separating the higher half of a dataset from the lower half, we define the Manhattan median as a tuple whose first element is the median of $x$ coordinates and second element is the median of $y$ coordinates.\n", "\n", "Though Manhattan median can be found very quickly, it is not unique if you have even number of points. In this case, pysal handle the Manhattan median the same way as numpy.median: return the average of the two middle values." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#get the number of points in point pattern \"pp\"\n", "pp.n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/weikang/Google Drive (weikang@ucr.edu)/python_repos/pysal-refactor/pointpats/pointpats/centrography.py:150: UserWarning: Manhattan Median is not unique for even point patterns.\n", " warnings.warn(s)\n" ] }, { "data": { "text/plain": [ "array([59.825, 41.23 ])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Manhattan Median is not unique for \"pp\"\n", "mm = manhattan_median(pp.points)\n", "mm" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp.plot()\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Euclidean Median $(x_{em},y_{em})$\n", "\n", "$$min f(x_{em},y_{em})= \\sum^n_{i=1} \\sqrt{(x_i-x_{em})^2+(y_i-y_{em})^2}$$\n", "\n", "Euclidean Median is the location from which the sum of the Euclidean distances to all points in a distribution is a minimum. It is an optimization problem and very important for more general location allocation problems. There is no closed form solution. We can use first iterative algorithm (Kuhn and Kuenne, 1962) to approximate Euclidean Median. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, we define a function named median_center with the first argument **points** a series of $(x,y)$ coordinates and the second argument **crit** the convergence criterion." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def median_center(points, crit=0.0001):\n", " points = np.asarray(points)\n", " x0, y0 = points.mean(axis=0)\n", " dx = np.inf\n", " dy = np.inf\n", " iteration = 0\n", " while np.abs(dx) > crit or np.abs(dy) > crit:\n", " xd = points[:, 0] - x0\n", " yd = points[:, 1] - y0\n", " d = np.sqrt(xd*xd + yd*yd)\n", " w = 1./d\n", " w = w / w.sum()\n", " x1 = w * points[:, 0]\n", " x1 = x1.sum()\n", " y1 = w * points[:, 1]\n", " y1 = y1.sum()\n", " dx = x1 - x0\n", " dy = y1 - y0\n", " iteration +=1 \n", " print(x0, x1, dx, dy, d.sum(), iteration)\n", " x0 = x1\n", " y0 = y1\n", " \n", " return x1, y1" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "52.57166666666668 53.178128280602785 0.606461613936105 -0.9290354286335258 466.24479074356606 1\n", "53.178128280602785 53.56643624463614 0.388307964033352 -0.4199402653980684 465.9311160558993 2\n", "53.56643624463614 53.80720376806838 0.24076752343224683 -0.1974862190386233 465.84555867343346 3\n", "53.80720376806838 53.95348076207835 0.1462769940099662 -0.09642613786996179 465.8197750145871 4\n", "53.95348076207835 54.04117257066307 0.08769180858472225 -0.04872250646902643 465.8115372002813 5\n", "54.04117257066307 54.09327726928146 0.05210469861838618 -0.025370793047137852 465.80882301324334 6\n", "54.09327726928146 54.12405125525861 0.030773985977148755 -0.013552246205456697 465.8079149010591 7\n", "54.12405125525861 54.14215248769505 0.018101232436443127 -0.00739190209046825 465.8076087750224 8\n", "54.14215248769505 54.15276956049696 0.010617072801906602 -0.0040992658298719675 465.8075052025632 9\n", "54.15276956049696 54.15898467957115 0.0062151190741914775 -0.0023026998071102867 465.80747009858044 10\n", "54.15898467957115 54.16261796248172 0.0036332829105703013 -0.0013061853179365812 465.80745819050844 11\n", "54.16261796248172 54.16473989468326 0.002121932201539778 -0.0007463404183738476 465.80745414933307 12\n", "54.16473989468326 54.165978319450346 0.00123842476708802 -0.00042875101595285514 465.80745277762423 13\n", "54.165978319450346 54.166700756153695 0.0007224367033487056 -0.00024727631074483725 465.80745231197506 14\n", "54.166700756153695 54.16712204754273 0.0004212913890384584 -0.00014302182778891392 465.8074521538953 15\n", "54.16712204754273 54.16736766581608 0.00024561827334679265 -8.289363293556562e-05 465.8074521002288 16\n", "54.16736766581608 54.167510839857464 0.0001431740413835314 -4.8115880247223686e-05 465.80745208200943 17\n", "54.167510839857464 54.167594287646125 8.344778866131719e-05 -2.7959041396741213e-05 465.807452075824 18\n" ] }, { "data": { "text/plain": [ "(54.167594287646125, 44.42430865883205)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "median_center(pp.points, crit=.0001)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After 18 iterations, the convergence criterion is reached. The Euclidean Median is $(54.167594287646125,44.424308658832047)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also call the function **euclidean_median** in pysal to calculate the Euclidean Median." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([54.16770671, 44.4242589 ])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "em = euclidean_median(pp.points)\n", "em" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The two results we get from **euclidean_median** function in pysal and the **median_center** function we define here are very much the same." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp.plot()\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dispersion and Orientation\n", "\n", "### Standard Distance & Standard Distance Circle\n", "\n", "$$SD = \\displaystyle \\sqrt{\\frac{\\sum^n_{i=1}(x_i-x_{m})^2}{n} + \\frac{\\sum^n_{i=1}(y_i-y_{m})^2}{n}}$$\n", "\n", "Standard distance is obviously closely related to the usual definition of the standard deviation of a data set, and it provides a measure of how dispersed the events are around their mean center $(x_m,y_m)$. Taken together, these measurements can be used to plot a summary circle (standard distance circle) for the point pattern, centered at $(x_m,y_m)$ with radius $SD$, as shown below." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "40.14980648908671" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stdd = std_distance(pp.points)\n", "stdd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot mean center as well as the standard distance circle." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "circle1=plt.Circle((mc[0], mc[1]),stdd,color='r')\n", "ax = pp.plot(get_ax=True, title='Standard Distance Circle')\n", "ax.add_artist(circle1)\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "ax.set_aspect('equal')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the above figure, we can observe that there are five points outside the standard distance circle which are potential outliers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Standard Deviational Ellipse\n", "\n", "Compared with standard distance circle which measures dispersion using a single parameter $SD$, standard deviational ellipse measures dispersion and trend in two dimensions through angle of rotation $\\theta$, dispersion along major axis $s_x$ and dispersion along minor axis $s_y$:\n", "\n", "* Major axis defines the direction of maximum spread in the distribution. $s_x$ is the semi-major axis (half the length of the major axis):\n", "\n", "$$ s_x = \\displaystyle \\sqrt{\\frac{2(\\sum_{i=1}^n (x_i-\\bar{x})\\cos(\\theta) - \\sum_{i=1}^n (y_i-\\bar{y})\\sin(\\theta))^2}{n-2}}$$\n", "\n", "* Minor axis defines the direction of minimum spread and is orthogonal to major axis. $s_y$ is the semi-minor axis (half the length of the minor axis):\n", "\n", "$$ s_y = \\displaystyle \\sqrt{\\frac{2(\\sum_{i=1}^n (x_i-\\bar{x})\\sin(\\theta) - \\sum_{i=1}^n (y_i-\\bar{y})\\cos(\\theta))^2}{n-2}}$$\n", "\n", "* The ellipse is rotated clockwise through an angle $\\theta$:\n", "\n", "$$\\theta = \\displaystyle \\arctan{\\{ (\\sum_i(x_i-\\bar{x})^2-\\sum_i(y_i-\\bar{y})^2) + \\frac{[(\\sum_i(x_i-\\bar{x})^2-\\sum_i(y_i-\\bar{y})^2)^2 + 4(\\sum_i(x-\\bar{x})(y_i-\\bar{y}))^2]^\\frac{1}{2}}{2\\sum_i(x-\\bar{x})(y_i-\\bar{y})}\\}}$$\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(39.62386788646298, 42.753818949026815, 1.1039268428650906)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sx, sy, theta = ellipse(pp.points)\n", "sx, sy, theta" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "63.250348987371304" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta_degree = np.degrees(theta) #need degree of rotation to plot the ellipse\n", "theta_degree" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Standard Deviational Ellipse for the point pattern is rotated clockwise by $63.25^{\\circ}$." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib.patches import Ellipse\n", "from pylab import figure, show,rand\n", "fig = figure()\n", "#ax = fig.add_subplot(111, aspect='equal')\n", "e = Ellipse(xy=mean_center(pp.points), width=sx*2, height=sy*2, angle=-theta_degree) #angle is rotation in degrees (anti-clockwise)\n", "ax = pp.plot(get_ax=True, title='Standard Deviational Ellipse')\n", "ax.add_artist(e)\n", "e.set_clip_box(ax.bbox)\n", "e.set_facecolor([0.8,0,0])\n", "e.set_edgecolor([1,0,0])\n", "ax.set_xlim(0,100)\n", "ax.set_ylim(0,100)\n", "ax.set_aspect('equal')\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.legend(numpoints=1)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Shape Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### [Convex Hull](https://en.wikipedia.org/wiki/Convex_hull)\n", "\n", "The convex hull of a point pattern *pp* is the smallest convex set that contains *pp*. We can call function **hull** to caculate the convex hull." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[31.01, 81.21],\n", " [ 8.23, 39.93],\n", " [ 9.47, 31.02],\n", " [22.52, 22.39],\n", " [54.46, 8.48],\n", " [79.26, 7.68],\n", " [89.78, 42.53],\n", " [98.73, 77.17],\n", " [65.19, 92.08]])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hull(pp.points)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By specifying \"hull\" argument **True** in PointPattern class method **plot**, we can easily plot convex hull of the point pattern." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp.plot(title='Centers', hull=True ) #plot point pattern \"pp\" as well as its convex hull\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### [Minimum Bounding Rectangle](https://en.wikipedia.org/wiki/Minimum_bounding_rectangle)\n", "\n", "Minimum Bounding Rectangle (Box) is the same as the minimum bounding Rectangle of its convex hull. Thus, it is almost always bigger than convex hull.\n", "\n", "We can call **mbr** function to calculate the leftmost, downmost, rightmost, and upmost value of the vertices of minimum bounding rectangle." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(8.23, 7.68, 98.73, 92.08)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mbr(pp.points)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus, four vertices of the minimum bounding rectangle is $(8.23,7.68),(98.73,7.68),(98.73,92.08),(8.23,92.08)$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp.plot(title='Centers', window=True ) #plot point pattern \"pp\" as well as its Minimum Bounding Rectangle\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp.plot(title='Centers', hull=True , window=True )#plot point pattern \"pp\", convex hull, and Minimum Bounding Rectangle\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot Standard Distance Circle and Convex Hull." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "circle1=plt.Circle((mc[0], mc[1]),stdd,color='r',alpha=0.2)\n", "ax = pp.plot(get_ax=True, title='Standard Distance Circle', hull=True)\n", "ax.add_artist(circle1)\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "ax.set_aspect('equal')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Another Example\n", "\n", "We apply the above centragraphy statistics and visualization to 2 simulated random datasets." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "#from pysal.contrib import shapely_ext\n", "from libpysal.cg import shapely_ext\n", "from pointpats import PoissonPointProcess as csr\n", "import libpysal as ps\n", "from pointpats import as_window\n", "#import pysal_examples\n", "\n", "# open \"vautm17n\" polygon shapefile\n", "va = ps.io.open(ps.examples.get_path(\"vautm17n.shp\"))\n", "\n", "# Create the exterior polygons for VA from the union of the county shapes\n", "polys = [shp for shp in va]\n", "state = shapely_ext.cascaded_union(polys)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Simulate a 100-point dataset within VA state border from a CSR (complete spatial randomness) process." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp = csr(as_window(state), 100, 1, asPP=True).realizations[0]\n", "pp.plot(window=True)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp.plot(window=True, hull=True)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/weikang/Google Drive (weikang@ucr.edu)/python_repos/pysal-refactor/pointpats/pointpats/centrography.py:150: UserWarning: Manhattan Median is not unique for even point patterns.\n", " warnings.warn(s)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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dtE9M8GJnJ0bNoBil5MWODp6Kj2ezEwKHH/3oR/m3f/s3jh07Rk/PP/ZZkVLyu9/9jpSUlFn1n3nmGaKioigrK8NiscwS6JsZyPTw8JgXrwgKCsLf35/6+nq2bds265yUkvT0dM6ePWtznNN92+p3qTF/8MEHK55KUaw+3d3dGI1GIiIiVtyXj48PeXl51hjdwMAAlZWVhIeHc+TIEZtBd09PTyYnJ/Hz82PXrl2UlJRw6NAhJSK5DlBaXnYy0zuZZtpLcQYPPvggX/nKV9i9e/es8ptuuonvfve71jhIaWkpAAMDA9YA5y9+8QuH9/t+4oknePjhh615/oODg/zkJz8hJSUFg8FgNSgmk4mLFy8u2ldgYCBDQ0NLjlmxPmhoaCAlJcUhwcfFCAoKIiMjg8nJSaqrq8nKyiI7O3vBDC4vLy+MRiNDQ0Ns2bKFkJAQKioqnDIWxeqiDIqdnB0ctHon0xil5MzAgFP6j42N5dFHH51X/tRTT2EymcjIyGDXrl089dRTAPzLv/wLL7/8Mvn5+dTU1Dj8y/9zn/sc1157LXv37mXXrl0cPnwYPz8/9Ho9r776Kl/84hfJzMwkKyvLGvBfiGuvvZbKykprUH6hMSvcn4mJCbq7u4mKinJKfxaLhbq6Oi5dukR6ejqHDx9e0vPx8vJi27Zt1NbWMjw8zO7du+nu7rYmhyjcFyHl8lJF1xt79uyRRUVFs8ouXbrEzp07XTQihbugPgdTtLa2Ul5eTnx8vFPuR29vL+Xl5Xh7e7N7926Hf/R0dHTQ399PSkoK/f39FBYWUlBQsOhKe4XzEUIUSyn32FNXxVAUCgVSSqqrq9m7d++81F5HMZlMXLp0ic7OTtLT0xdcGb8UmzZtoq+vj0uXppayjY+P88ILL3DrrbfOi/0p3ANlUBQKBe3t7ej1+hUbk5aWFiorK4mJieHIkSMr2jRLp9ORkpLCwMAAHh4eJCYmcubMGc6ePcvIyAi7du1aMFtR4RqUQVEoFNTW1pKamrrs9sPDw5SXl2MymcjLyyMkJMQp49LpdISG/mPL7f379/Pee+/R1tbG+Pg4ubm5dikiK9YGZVAUig1OW9uUDN5CGluLMTk5yeXLl2lsbGTHjh0kJCSsqtfg6+tLdnY2Fy9eZGBggP7+frWuyY1Qpl2h2MBYLBYuXrxo3XnREQwGA8ePH2doaIjDhw+TmJg4r4/ipj6+/95lipscUy5ejOjoaCIjI+nu7l5Q1VjhGpSHolBsYIQQeHh42LWOqbipj/fre8iJDcR7qJW+vj527969oGczLUdvNFvQe+r41UP55MaH2qzrKLt27aKqqoq6ujqH9m1RrC7KQ3ExqyFfHxAQ4FD9Y8eOzVpr8oc//IHKysplX38uznqPR44cYTr1+8Mf/rDaJtaJLLWIceZeJZ9+sYjGYR1HjhxZdJpsrhz9+/U9C9Z1FA8PD/bt20dhYSHHjx+nsrJS7Z3iBiiDYi/Z2SDE/Fd29oq6dZV8/UxW26Csxnt88803nRb43chMZ3fNDHzb4mxdN0bTlHGwSGifDFhSCiV/Wzh6Tx0eArw8deRvW1kG2Vy2bt3KbbfdxuDgIF5eXpSXlzu8KZjCuSiDYi/79oFeP7tMr4f9+1fc9WLy9efOnWP//v1kZ2ezf/9+qqurgSkp+DvvvJObb76Z5ORkHn/88Vl9Pvnkk2RmZpKfn09nZycAf/rTn7jmmmvIzs7mQx/6EJ2dnTQ2NvKjH/2Ib3/722RlZXH8+HFef/11vvCFL5CVlUVdXR3PP/88e/fuJTMzk7vuuovR0VEA7r//fj7/+c+zf/9+tm3bxquvvrqs97iQ3P3Y2Bj33nsvGRkZ3HPPPVaDBFN7j3d3dwNwxx13kJubS3p6Oj/5yU+sdQICAmzeB8WUXldNTQ21tbUkJycvWnd8fBz/kVY8PXDIOOTGh/Krh/J57MYUp053zSQ1NZXIyEgsFgspKSlUVVU5/RoKB7BXlni9v1YsX9/WJqWPj5Twj5evr5Tt7fb3YYOl5OsHBgakyWSSUkr5zjvvyDvvvFNKOSUZn5iYKPv7++XY2JjcunWrvHLlipRSSkC+/vrrUkopv/CFL8hnn31WSillb2+vtFgsUkopn3/+easU/dNPPy2/8Y1vWMd03333yd/+9rfW4+7ubuvfTz75pHzuuees9e6++245OTkpL168KLdv376s97iQ3P23vvUtq3R+WVmZ9PDwkIWFhVJKKePj461S6NNy+KOjozI9Pd063oXuw1w2onx9cXGx/Nvf/iZPnDixaL2+vj759ttvy5qaGlnU2Cu/9/daWdTYO6/eYudWm7GxMfnWW29Jg8EgT506Jc+cOSNHRkbWfBxXKyj5+lUgOhoeeAB++lMwGqe8kwcegBXIe0+zmHz9wMAA9913H7W1tQghZm2rev3111tlvdPS0mhqaiIuLg69Xm+NT+Tm5vLOO+8AU4vO7rnnHtrb2zEajSQmJto1voqKCr785S/T39/P8PAwN910k/XcHXfcgU6nIy0tbVEPYDkS/SdOnODzn/+8tX1GRobNvp977jlee+01AJqbm6mtrSU8PHzB+7DRsVgsGAwGDh06NEulei6tra1UVFSQmZlplbG35WWsZvDdHnx8fMjMzOT8+fMcOnSIuro6ysvLueaaa9ZsDIop1JSXIzz1FEwvovLwmDp2EtPy9TOngqYu+RTXXnstFRUV/OlPf2J8fNx6biGZei8vL2v65szyf/3Xf+WRRx6hvLycH//4x7P6Woz777+f733ve5SXl/P0008vOAa5hC7cQu9RanL358+f5/z581y5csWqJbVUKuuxY8d49913OXv2LGVlZWRnZ1vHt9B92KgMDg5axRrDwsLw9fW1eX+llFy6dImqqir27du35J4oqxl8t5eoqCg2b95MeXk527Zto6+vb8nPo8L5KIPiCNNeik7nNO9kmoXk6wcGBqwB7JdeemlF15jZ18svv2wtnys/P/d4aGiI6OhoTCYTv/rVr5Z9fUcl+g8dOmS9XkVFxaztZGe+p9DQUPz8/KiqquL9999f9viuZnp7ezl+/DhVVVXU19eTnp5us57ZbKawsJC+vj4KCgrs2tN9tYPv9rJz506Ghobo6uoiICCA5uZml4xjI6MMiqM89RQcPOhU7wQWlq9//PHHeeKJJzhw4IDDe57M5ZlnnuHjH/84BQUFsyTEP/KRj/Daa6+RlZXFyZMnuffee/nGN75BdnY2dXV1PPvss1xzzTXccMMNK5LncFSi/3Of+xzDw8NkZGTwX//1X+Tl5c1re/PNN2M2m8nIyOCpp54iPz9/2eO7mmloaLD+m5GRgZ+f37w6IyMjnDx5El9fX/Lz89HPTUJZgLUIvk+z2EJJDw8PcnNzqaysJCkpiUuXLmE0GldtLIr5KPl6JVu+4bnaPwetra3U1NSwd+9eLBaLTa+ju7ubkpISq3yKO2JvrKaxsZErV65YdcUCAwNdMNqrB0fk65WHolBcxZjNZioqKsjJySEgIMCmMWloaKCkpITc3Fy3NSZgf6wmISEBHx8fGhsb1bbBa4zdBkUI4SGEKBVCvKEd/1QIUSaEuCCEeFUIEaCVewshXhFCXBZCfCCESJjRxxNaebUQ4qYZ5TdrZZeFEF+aUZ6o9VGr9alf6hoKheIf9Pb2EhgYaM0GnInFYqGsrIympiYOHjy4Yun61WaxWM3cqbCsrCzGx8dpaWlx1XA3JI54KI8Cl2Yc/28pZaaUMgO4AjyilX8G6JNSJgHfBv4TQAiRBtwLpAM3Az/QjJQH8H3gFiAN+IRWF63tt6WUyUCf1veC11AoNiqDg4M2y3t7e20aiomJCc6ePYvRaOTgwYM2YyruxkKxmpmyMJ984X2Km/rQ6/Xk5uZy/vx5FUdZQ+wyKEKIWOBW4IXpMinloHZOAL7AdDDmdmA6hehV4Hqtzu3AUSnlhJSyAbgM5Gmvy1LKeimlETgK3K61uU7rA63PO5a4hkKx4RgeHub48ePU1tbOO9fT0zNP3n1wcJCTJ08SERHBnj17ltTxcidy40N5+NqkWbGThabCfH19SU5OpqyszFXD3XDY66F8B3gcsMwsFEK8CHQAqcB3teItQDOAlNIMDADhM8s1WrSyhcrDgX6tj5nli11jFkKIzwohioQQRQaDwc63qlCsL2pqakhMTKSxsZGuri5r+fj4OENDQ7M8lPb2ds6ePUtaWhopKSlO2btkNSTqHWGhqTCLxcLOnTsZGxujsbHRJWPbaCxpUIQQtwFdUsriueeklA8AMUxNhd0z3cRGN9KJ5YtdY+74fiKl3COl3BMZGWmjiUKxvhkeHsZgMJCamkpubi6lpaXWPUJaW1uJjo5Gp9NZ94y/ePEi+fn5y97nfS62ppvWmoWmwoQQCCHIycmhurp61toqxepgj4dyAPioEKKRqemo64QQv5w+KaWcBF4B7tKKWoA4ACGEJxAM9M4s14gF2hYp7wZCtD5mli92jXWHh4cHWVlZ1tfXv/71ZfUzUyxx/wKClffff/+iAo7OQEnVrx0mk4ni4mKSk5Px9PQkLCyMlJQUCgsLMZvNtLS0EBsbi9lspri4mO7ubgoKCmwG6JfL70tamDC5dpU82J4KE0IgpSQgIICdO3dSUlKCxWJZpBfFSlnSoEgpn5BSxkopE5gKqv8d+JQQIgmsMZSPANMyn68D92l/3w38XRMYex24V8vQSgSSgXNAIZCsZXTptWu8rrV5T+sDrc8/LnGNNaHhmQan9eXr62uVHDl//jxf+tKXlm60BDOl6NcaJVW/dvT39+Pp6cm2bdusZQkJCYSGhvLBBx9gNBrx8fHh9OnTeHp6sm/fvllSOSuluKmP3xY1W6cGPDxct0reFkIIqwHZunUr/v7+Tt2WQTGf5a5DEcDLQohyoByIBr6qnfspEC6EuAw8BnwJQEp5EfgNUAn8FXhYSjmpxUAeAd5iaursN1pdgC8Cj2l9hWt9L3iNtaLp35tW/RozPY6ioiKOHDkCTE1xPPDAA+zevZuMjAx+97vfzWs7vcGWlJJHHnmEtLQ0br311lnz68XFxRw+fJjc3Fxuuukm2tvbAZRU/TrCYrHYDKjv3r3b+sv89OnTxMXFkZWVhU7n3GVn79f3YLZMmRMB3J0bu6aikAthNpupra3FZDLNWoeSmZlJR0fHrO+Bwrk49AmTUh6TUt4mpbRIKQ9IKXdLKXdJKT85nfUlpRyXUn5cSpkkpcyTUtbPaP81KeV2KWWKlPIvM8rflFLu0M59bUZ5vdZHktbnxFLXWG+MjY3NmvJ65ZVXFq3/7LPPEhwcTHl5ORcuXOC6665bsO5rr71GdXU15eXlPP/881bPxWQy8a//+q+8+uqrFBcX8+CDD/Lkk08CcOedd1JYWEhZWRk7d+7kpz/9qbW/9vZ2Tp06xRtvvLGoJ3Xvvfdy9OhRxsfHuXDhwizV16997Wtcd911FBYW8t577/GFL3yBkZERfvjDH+Ln58eFCxd48sknKS6eF7ID4Gc/+xnFxcUUFRXx3HPP0dMzNcUyMjJCfn4+ZWVlHDp0iOeff37R+3g1MDQ0hL+//7xynU7Hli1bGBwcxCMqib80WVYltjEzGO7tpeOunFjrOVcG6js6OrBYLCQlJc3yyLy8vMjOzub8+fNMTEys+bg2AusnX9DFNDzTMMszOSaOARD/dDyJz9gnA2+L6Skve3n33Xc5evSo9XixnfZOnDjBJz7xCTw8PIiJibEan+rqaioqKrjhhhsAmJycJDo6GlBS9euJrq4utm/fPqvMYrFw8eJFuru7CUjYzWd+WbZqsvLTwfD363vI3xY+b12IK+TsJyYm6OrqIj093eb0Xnh4OFu3buX8+fPk5eU5JctN8Q+UQbGTxGcSrYbjmDjGEXlkVa/n6elpnf+dKRcvpXToS7CQPHl6ejpnz56dd+7+++/nD3/4A5mZmbz00kscO3bMem45UvXHjh2zehHT7X73u9+RkpJi11hnMlOq3s/PjyNHjmxYqXqz2czAwMAskU+j0UhxcTE6nY6DBw/yk1NN89ZnOPvBnhsfOq9PW+tC1sqgGAwGIiIiFo0V7dixgzNnztDQ0DAr/qRYOUqd2xxkAAAgAElEQVTLy01JSEiwTvvMjJPceOONfO9737MeL7aH9qFDhzh69CiTk5O0t7fz3nvvAZCSkoLBYLAaFJPJxMWLU2ErJVW/Pujt7SU4ONgaIxgaGuLkyZOEhISQl5eHl5eXy2Tl1/q6g4OD1NTUIKXEZDItumkYTE0J5uTkUFtbu6DCgGJ5KIOyDOKfjndaX3NjKNOxiaeffppHH32UgoKCWYHFL3/5y/T19bFr1y4yMzOtRsIWH/vYx0hOTmb37t187nOf4/DhwwDo9XpeffVVvvjFL5KZmUlWVpY1vqKk6tcHZrPZKi/f0dHBmTNnSElJYefOnVZPzVWy8mt53fHxcWpra61TtP39/UsaFAA/Pz927dpFcXHxireFUPwDJV9/FcuWK+xjPX4O2traaGtrIzg4mMbGRvbu3euy1GpXxkwMBgODg4P09PTg6elJYmLionHFuZSWluLh4bFgzE6h5OsViquapqYmKioqqKqqoqOjg4KCApeu03HlFsCDg4MEBQURGRnJzp07HTImMJVibTAY6OjoWKURbiyUQVEo1hnl5eX09fWRmJjI/v377ZriWU1cuQXw0NAQAQEBJCYm4uvr63B7T09PcnJyuHDhwqzkF8Xy2PBZXo5mTSmuLtbblG9TUxO1tbV85CMfISkpydXDARZOH3YGxU19C/Y7MTGBxWJZliGZSWhoKImJiZSWlpKfn6+eBytgQxsUHx8fenp6CA8PVx+iDYiUkp6eHpf/wreX5uZmjh8/TkFBgdsYk2lspQ+vlKViM8PDw1ZViJWSlJREV1cXdXV1bndv1xMb2qDExsbS0tKCkrbfuPj4+BAbG7t0RRcipaSyspLOzk527ty5YR54S61nmY6fOINpVeITJ04QERGhtOOWyYY2KF5eXiQmLn+Vu0LhCPX19WzZssUhgcZpRWGA/Px8Ll265LSHqLszHZsxmS02YzPDw8M4c1sKX19fMjIyKCkp4dChQ+tq4zF3Qd0xhWINGBgYoLq6msuXL5OWlmaXVzQ8PMy5c+eIiooiLS3Nuj+8s0Ue3ZXFYjMmkwmj0WhTy2wlREdH09XVRUVFBVlZWU7teyOgDIpCsQa0t7eTkJBATEwM58+fp62tjYyMjAXjN11dXZSWlrJz5062bt0KTMnVh4SELBqovtpYKDYzPDyMv7//qsQ+09PTOXHiBK2trSveemGjsTF+6igULqajo4Po6GiCg4MpKCggKCjIppYaQF1dHWVlZezdu9dqTKSU9Pf30zCIy3dIdAeGhoZWberP09OT3NxcKioqrNs3KOxDGRSFYg2YnJzEy8sLmNKSSk1NxWw2Mzw8bK1jsVgoLS2lpaWFgwcPEhYWZj03PDyMt7c3Rc2DLltE6E4MDg4SGBi4av0HBweTlJREaWnpukstdyXKoCgUa4BOp8NkMs0q27x5s3WF9vj4OGfOnMFisXDw4MF5ayump7tcuYjQXTCbzUxMTDg9fjKXbdu24eHhQU1Nzape52pCxVAUilWmpaUFnU43b4omKiqK2tpaIiIiKCoqIj4+nuTkZJt99Pf3k5iYSGxAwKotIlwvTG8sttrJCUIIsrKyOHHiBJGRkbM8RoVtlEFRKFaZ9vZ2kpKS5j0AIyIieOutt+jr62PPnj1s3rzZZvuJiQlMJpP1F/lyFhG6YyB/uWNy5vqTpfDx8SEzM5OSkhIOHz5snbZU2EYZFIVilfHy8ponkS6lpKamBpPJRHp6+oLGBKYUdcPCwpad0eRKNeCVjsmW0RFCWDefWwuioqLo6uriwoUL5Obmrtl11yMqhqJQrDJ6vR6j0Wg9NpvNFBYW0tvbyy233MLg4OCCG6WZzWa6urqsWzQvB1eqAa9kTNNGZ25GW0REBAaDYU2D5WlpaQwNDdHc3Lxm11yPKIOiUKwyMw3KyMgIp06dwsfHh/z8fKKjo9m6dSutra1UVlbO20Gws7OT4ODgJVfXz9zgai7uGMi3Z0wLGR0/Pz/0ej0DAwNrNl4PDw9ycnKorKxkZGRkza673rB7yksI4QEUAa1SytuEEL8C9gAm4Bzwv6SUJiHEEeCPQIPW9PdSyq9qfdwM/DfgAbwgpfy6Vp4IHAXCgBLgU1JKoxDCG/g5kAv0APdIKRu1Nk8AnwEmgc9LKd9a9l1QKFYRT09PRkZG6O7upqSkhB07dpCQkGA9HxoaSkhICL29vTQ0NODt7U1sbCwmk4muri7S0tIW7X+p6aPFVpy7KrZij0LxYtIrkZGRGAyGBTW3RkdHaWlpwd/f32mLE4OCgtixYwclJSUcOHBgwygWOIIjMZRHgUvAdDTsV8A/aX//D/AQ8EPt+KSU8raZjTWD9H3gBqAFKBRCvC6lrAT+E/i2lPKoEOJHTBmKH2r/9kkpk4QQ92r17hFCpAH3AulADPCuEGKHlFLt5alwO9ra2pBSUlJSQk5ODhEREfPqCCEIDw8nNDSUnp4eamtrsVgspKSkLOmdLCWiCLYD+a6OrSyVXLCY0QkPD6e5uRmz2TxLc2tsbIzW1laGhoaIjIykq6uLmJgYp62oT0xMxGAwUF1dve52+VwL7DKxQohY4FbghekyKeWbUoMpD2UpcaI84LKUsl5KaWTKI7ldTP1PXwe8qtV7GbhD+/t27Rjt/PVa/duBo1LKCSllA3BZ61+hcCs6OzuprKzEaDRy8OBBm8ZkJjqdjsjISDIzM9m1a5dd8uzLndJyx9jKXHLjQ3n42qR5hqe7uxsvLy+roRgfH6euro5Lly7h5+dHRkYGsbGxeHl5MTQ05NQxZWVl0dLSQnd3t1P7vRqw10P5DvA4MG9pqhDCC/gUUx7MNPuEEGVAG/BvUsqLwBZgZkSrBbgGCAf6pZTmGeXTPqq1jZTSLIQY0OpvAd6f05cS3VG4FRMTE7z55pvExsZSUFDgkHqtTqezW5V4uRtcTRsio9mCEIJQP73d43M1w8PDGI1Gqqqq0Ov1DA0NERUVRUJCAh4eHtZ64eHh9PT0ODXNWK/Xk5WVRWlpKYcPH0avXz/3bbVZ0kMRQtwGdEkpixeo8gPghJTypHZcAsRLKTOB7wJ/mO7KRlu5SPly28wc+2eFEEVCiCK154liLRkcHOTkyZOEh4fjH7+bH59sXFXdrYV+yS/V5iu3paMTgkmL5KtvXHQLbbDFEgym2b59O9nZ2WzdupWQkBAyMjLYsmXLLGMCEBYWRl9fn9PTjCMjI9myZQtlZWVO7Xe9Y8+U1wHgo0KIRqamqa4TQvwSQAjxNBAJPDZdWUo5KKUc1v5+E/ASQkQw5UXEzeg3likPphsIEUJ4zilnZhvtfDDQu0hfs5BS/kRKuUdKuceZ+yYoFIvR3t7O6dOniYqKYsg7gn/+nwtuK+bYN2rEIiUSmDBZ+H1Ji0vHs1CqsC08PDwIDAwkMjJyQe/P29sbHx+fedlzziA1NZWxsTGampqc3vd6ZUmDIqV8QkoZK6VMYCoQ/ncp5T8JIR4CbgI+IaW0mn8hxGYtzoEQIk+7Rg9QCCQLIRKFEHqtr9e1GMx7wN1aF/cxlSUG8Lp2jHb+71r914F7hRDeWoZYMlNxHIXCZUgpqa6u5uLFi2zfvh2AxlG9W8cp8reF4+kx9RiQwG+Lml1q9FYjrhMWFkZPj/Pvu06nIycnh6qqKqfHadYrK8l7+xEQBZwVQpwXQnxFK78bqNBiKM8B92qxezPwCPAWU9liv9FiKwBfBB4TQlxmKkbyU638p0C4Vv4Y8CUArd1vgErgr8DDKsNL4UrMZjPFxcV0d3dz4MABRkdHSUxM5Oac7W63BmQmufGh3J0ba51DnrRIlxq91VgzEx4eTn9//6zFpc4iICCAnTt3UlJSsqar990VsVGkmffs2SOLiopcPQzFVcjo6CiFhYUEBweTkZFBX18fBoOB1NRUwD11tGYyPc00vd7D1dIsq3G/pqel4uPjndLfXIqKivD19SU9PX1V+nclQohiKeUeu+oqg6JQLJ/e3l6KiopISkpi27ZtALS2tjI5OWndHGs94O5Gb6UYjUbKy8vJyMhYFYFHk8nE8ePHycjIYNOmTU7v35U4YlDUUk+FYplcuXKFoqIisrOzrcYEpla+GwyGdTUFspwssfWEXq8nLCyMrq6uVenfy8uL7OxsysrKmJiYWJVrrAeUQVEoHMRisVBRUUFdXR0HDhxgbgahlBKdTqekORbBntRgZxMdHU1nZyeDg4OrIiwZHh5OXFwc58+f37C7PCr5eoXCAYxGI8XFxeh0Og4ePDhv+mR0dJSamhq3ne5aztSWs6fDXCX54uPjQ1xcHFeuXGFycpKIiAgiIiLsXkBqDzt27OD06dM0NDTM8lo3CsqgKBR2MjQ0xLlz54iOjmbnzp3z9KEsFgt1dXXExcURHu5e2VywvAf5ajz87dEeWy0iIyOJjIxkZGQEg8HAxYsX8fPzIzIykpCQkHkLIx1lOpX41KlTRERErNlGYO6C8skVCjvo7OzkzJkzpKSkkJaWZlNssKOjA71ev6Rel6tYzhqP1VgX4g5y+v7+/iQkJJCVlWVVLj5//jwNDQ0MDw+vuO/09HSKi4vnbax2taM8FIViCWpra2lsbCQvL4/QUNu/pCcmJujo6HDrtNHF5OCd2WYplqs95gzmTt/pdDrCw8MJDw/HaDTS3d1NXV0dOp3OOiW2nKyw2NhYurq6uHjxIhkZGavwTtwTlTasUCzA5OQkZWVljIyMsHfvXnx8fBasW11dTWBgIDExMWs4QsdxhxiKq3Bk+m5oaAiDwUBfXx9btmxZdIvmhTCZTJw4cWLJLZ7dHUfShpWHolDYYHx8nHPnzhEQEMD+/fsXnVvv6+vDaDSui4fGUnuQOKuNO+JI7CYwMJDAwEAmJia4ePEioaGhDgfvvby8yMnJobCwkJCQkEV/kFwtqBiKQjGHvr4+Tp48SUxMDDk5OUsGak0mE/7+/ipN2M2ZG7sJ9dMvmbrs7e3N5s2bly0AGRoaSkJCAqWlpS5JJe7u7ubixYtrtjZGeSgKxQyam5uprKwkKyuLqKgou9qYzWZlTNYBM2M3oX56vvrGRbumvzZv3syFCxcYGRnB39/f4esmJydjMBioq6sjKSlppW9jQSYnJ+nr68Pb25vAwECklBQWFmI2m1f1ujNRBkWhYGoxYmVlJZ2dnezfv5/AwHl7yS1If3+/0/Yt38isRaxmevru++9dtnv6S6fTodfrl618IIQgJyeHEydOEBERQUhIyEreghWTyURvby89PT309vZaJfq3b99OSkoK/f39mM1moqOjnbrWZjGUQVFseEwmE8XFxUgpKSgocCirx2QyMTY25pABulpwpgFY68WOjmavzd273lF8fX3ZvXs3JSUlHDp0aFl9TU5O0tnZaTUgo6OjhIaGEhYWRmpqKiEhIRw7dsyaGNLe3g6sniCmLZRBUWxohoeHOXfuHJs2bSI9Pd3m+pLF0Ol0G1Jmw9kGYK0XOzqaujw5ObkigwIQExODwWCgoqKCrKwsh9tXV1fT09NDTEwMcXFxBAUFzZpq7enpwcvLy/rjpq6uDmBN10Upg6LYsHR1dVFaWsrOnTuXLZViMpk2ZPzE2QbAEY/BHs/Injr2Zq+NjY1hMplobGwkICCAqKioZf+fp6enc+LECdra2hxKMbdYLLS0tHDgwIEF4zgtLS3ExsYCWKe/UlJSHP6RtBKUQVFsSOrq6qirq2Pv3r2EhYUtu5/Ozk42bdq04YyKsxc82usx2OMZOdt7Gh8fx8/Pj6CgIAYGBujq6mLr1q0LLnJdDE9PT3Jzc3n//fcJDQ3F19fXrnZDQ0Po9foFjYnFYqG9vZ0jR44A/5juWmspfWVQFBsKi8XChQsXGBgYoKCgwO4v9EJ0d3eza9cuJ41u/bAaq93t8Rjs8Yyc7T2FhoZajUdUVBT9/f00NTVZDYujn6Hg4GCSkpIoKSlh//79S3oQUkp6enoICAhYsE5nZyfBwcHWtS5XrlwBWHMtMWVQFBuG8fFxioqK8PHx4eDBgysWAjQajQgh1iyDZinWekW7KxY82uMZrYZczExCQkIICgqis7OTS5cuERERQWxsrENe6rZt2+jq6qK2tpYdO3bYrCOlpLq6mpaWFjw9PReV9WltbbVmGvb09DA+Pk5ERMSae87KoCg2BP39/RQWFhIfH7/gF9hRRkZG8PPzc0pfy2GmAQFcIgm/1tjjGa2FVphOpyM6OpqIiAjq6+upr69n+/btdscrhBBkZ2dbU4ltTbtKKWlsbCQ7O3vRNVEmkwmDwUBmZiZGo5EzZ84AaxuMn0YZFMVVT2trKxUVFWRmZjpVHqWnp2feg2CtvIS5cYK7cmJdJgm/1tjjGa2V9+Tl5UVycjI1NTU0NDSQmJhot1Hx8fEhIyOD0tJSDh06NC9dXafTERsbS39//6IGpb29ncjISLy8vDCbzdZyV2yhsLEiiYoNhZSSqqoqqqqq2Ldvn1ONidlsZmBgYJZBmX7If+vtaj75wvuruhvh3DiBBLsk4V2xU6IrrrmW6HQ6kpOTGR8fd1iiZfPmzWzatIny8nKb5+Pj47ly5cqiqekzs7s6OjoAyMnJWVGyyXJRHoriqsRsNlNSUoLZbKagoAC9Xu/U/g0GA0FBQbPWJqzlWoq5cYK7cmK5Kyd2Ue/IFTslump3RnuZjlPAVPDdXrmduXh4eJCSkkJVVRVNTU0OLSZMS0vj5MmTswzDNIGBgfj5+dHZ2WnzB9HY2BiDg4PWbK6YmBiio6NXHB9cLnZ7KEIIDyFEqRDiDe34V0KIaiFEhRDiZ0IIL61cCCGeE0JcFkJcEELkzOjjPiFErfa6b0Z5rhCiXGvznNB8RiFEmBDiHa3+O0KI0KWuoVCMjIxw6tQpfHx8yM/Pd7oxGRwcpKOjg7i4uFnla7lx1HSc4LEbU6wP6dz4UB6+NmnBB/ZqbJa1FK64piMIIbBYLPj6+tLW1raizbWmjUpPT49DYoweHh7k5ORw8eJFRkZG5p3funUrzc3NNtu2trYSExNjDb7rdDqXGRNwbMrrUeDSjONfAanAbsAXeEgrvwVI1l6fBX4IU8YBeBq4BsgDnp42EFqdz85od7NW/iXgb1LKZOBv2vGC11Aouru7OX36NAkJCWRkZDg9y2ViYoK6ujq2b98+T47c1kN+NVnKgMzFFTslusPujEuxadMmxsbG2Lp1K3V1dSvaZdHT0xM/Pz/Gx8cdahcUFMSOHTsoKSmZpxnm5eW14JTXzOwud8CuKS8hRCxwK/A14DEAKeWbM86fA6Z9tduBn8upO/C+ECJECBENHAHekVL2am3eAW4WQhwDgqSUZ7XynwN3AH/R+jqi9fsycAz44kLXkFK2L+MeKK4SGhoaqK2tJScnZ1UyXKSU1NXVER0dvWB+vzvvHeKKnRJduTujvYSFhdHc3Iyfnx8BAQG0tLSsSP9Kr9cvSy4+MTGRrq4uampqSE1NtZaPjo7a3EtlcHAQk8nkkljJQtj78+07wOPAPLlNbarrU8BftaItwEz/rEUrW6y8xUY5QNS0kdD+nV72uVBfc8f2WSFEkRCiyGAwLP0uFesSi8VCWVkZTU1NHDx4cNXSJTs7OwGWPc/uDjjq1azXazqCTqcjMjKSrq4u4uPjZyn3OorRaKS/v39ZMvcAWVlZNDc3093dDUx95mpra23KtEx7J2sprbIUSxoUIcRtQJeUsniBKj8ATkgpT043sVFHLqN80WHZ00ZK+RMp5R4p5Z7IyMglulSsRyYmJjh79ixGo5GDBw+u2roQo9FIW1ubQ2mhCvtxdSZYZGQk3d3dCCFITEykoaFhWVNfDQ0NbNq0adkGxdvbm8zMTEpLS6murubChQvk5eXN+5EkpbQZxHc19ngoB4CPCiEagaPAdUKIXwIIIZ4GItGmwTRagJnRyligbYnyWBvlAJ3adBnav11LXEOxgRgcHOTkyZOEh4ezZ8+eFavBLkZ/fz/BwcErlmpRzGct060Xwtvbm6CgILq7u60r4aflS+ylq6sLk8nkkOijLTZt2oSPjw/Hjh3jwIEDNjXDent70ev1brdtwpIGRUr5hJQyVkqZANwL/F1K+U9CiIeAm4BPSClnToW9Dnxay8TKBwa06aq3gBuFEKFaMP5G4C3t3JAQIl/L7vo08McZfU1ng903p9zWNRQbhPb2ds6ePUtaWhqpqamr6jX09fXR2trqVnPV65GFvBB3yQSLioqiq2vqN+vWrVsZHBykr88+4yalpLm5mW3btjklESQ2Npbw8HAWmqp3R+8EVrYO5UdAE3BW+zL/Xkr5VeBN4MPAZWAUeABAStkrhHgWKNTaf3U6QA98DniJqWyxv2gvgK8DvxFCfAa4AnxcK7d5DcXVj5SS2tparly5Qn5+PsHBwat6vdHRURobG9m+ffuaC+1dTSy2HmW1tbfsZfr/t6Ojg82bN5OYmEhdXR1eXl6LCjPCVPqxEMKhzdkWw2KxsHfvXqqqqggPD591/bnKwu6EQwZFSnmMqUwrpJQ222qZVw8vcO5nwM9slBcB8yRbpZQ9wPWOXENx9TI5OUlpaSnj4+MUFBSsiShjb28vERERypiskMUWfbpTJlhycjK1tbWMjo6SkJBAQkICNTU1JCYmLilX7+3tzcTEhFOMislkIiIigtTUVIqLiykoKLB6PnOVhd0JJb2iWBeMjY1x6tQpPD092b9//5op/JpMJpcuFLtaWGo9irtkgvn4+JCWlsb4+Dg9PT2EhoayY8cO6uvrlwzSTxsUZzC95XB8fDx+fn5cuvSPJYAtLS1utfZkJsqgKNye3t5eTp48SVxcHFlZWWsmyT0yMkJfX59LVFuvNtZ60edK8PDwIC4ujtbWViwWCwEBAfj7+9Pf379oO2caFJPJZE0yyczMpK2tDYPBgMlkoru7m+joaKdcx9koLS+FW3PlyhWqqqrIzs5mLVO/LRYLDQ0NbN261enSLRsVd170OZfAwEB8fHzo6ekhMjKSyMhIDAbDogq+np6eDq+Qt8W0/Mr0506v15OdnU1paSkZGRlu7TErD0XhllgsFioqKqirq+PAgQNrakxgKk1Yp9Mp78QBXL2WxNls2bKFtrY2LBYLoaGhjI6OLuiB9Pb20t7e7pRMwK6uLqKiomZlLkZERBAXF8fbxbWc6PbltRPnV3yd1UB5KAq3w2g0UlxcjE6n4+DBg07LnHEEIYRb/xJcLqu1X4u7qwovh8DAQLy9va1eynQar6103ZaWFqKiolacdWg2m+nt7SUjI2PeuWGfSJ49VYfJIvmt5xDbk/rc7h4rD0XhVgwNDXHq1CmCg4PJy8tziTGZTst0t0VjK2U1FxC6y1oSZzPTS5me9rIl1JiUlERnZydjY2Mrup7BYCAkJMTm5/6Dhj7MEiQC86R0y3usDIrCbejs7OTMmTPs2LGDtLQ0l0mcdHd3W7d4vZpYzYf+elAVXg4zvRQ/Pz/0ej0DAwPz6vn5+eHh4bHoRlhLIaW0TnfZYk9cEB5i6qHtrvdYTXkp3ILLly/T0NBAXl7ekvn+q40QAr1ef9VpdtlaQNjwTAOJzySuuG93WkvibLZs2UJ9fT3h4eFs2rSJpqYmRkdHCQ0NtUrxTE5OYjKZVrQ2pL+/H09PzwUXUUaIIZ7I96NpVM9H96W55T1WBkXhUiYnJykrK2NkZISCggK3WKwlpVzRnhjuiq2H/rF/L3OKQZnu3x0fcitl2ktpbm4mNjYWvV5PX18fVVVV6HQ6QkND8fHxwcfHZ0Up7Z2dnQt6J4ODgwwNDbFrsz83xsQQG+ue91lNeSlcxvj4OKdPnwZg//79bmFMzGYzra2tV9101zTusoBwvbFt2zaMRiMVFRVMTk6SkJBAdnY227dvR6fT0dXVtaKY29jYGGNjYwtmiV25coXY2FiGh4dXXW5oJSgPReES+vr6KCoqIjExkaSkJFcPx8qVK1cICwtbUrtpPdPwTANN/95kPT4mjgEQ/3S807yVqw29Xk9ycjKDg4M0NTXR2dlJfHw8AQEBBAQErEiocXx8nEuXLmE2mxeMwQQEBNDW1sbIyIhbfzaVQVGsOc3NzVRWVpKVleVWm1UZjUZ6e3vJzs529VBWlcRnEq2G45g4xhF5xLUDWkcEBQWxa9cuurq6qKqqIjQ0lNjY2BVlI/b19eHn57fgVr99fX14eHhgMBgwGAxuHdtTBkWxZkgpuXTpEh0dHezfv9/t0nI9PT1XlKWznlmt9SmuYjXfjxCCqKgowsPDaW1tpby8nJiYGDZt2rSsGMrQ0JB1h8jh4WEyMzOt58xmM/X19WzevJmQkJBlb9y1ViiDolgTTCYTJSUlWCwWCgoKXLK+ZCnGxsbQ6/UYjUb0er1dCxvX04PY1ljjn46/6hYlrtX7mRZvjIyM5MqVK3R1dZGQkOCwMrWfnx+Tk5N4e3vP+14MDAwQGBjIli1b6O7udnvlBmVQFKvO8PAw586dY9OmTaSlpa2ZuKOjeHt7o9PpqKmpQUrJjh07Ft1S2N0exO0TE9xbWckraWlsnqPGvNBYE59J5M33Li8oLb8eWUwqf6WMj49TX19PQEAAgYGBBAQE4OfnR2pqKo2NjbS1tTlsUHp7e9m2bZvN2MjAwIA1CD8wMMDWrVud8j5WC2VQFKuKwWCgpKSEnTt3uv+XwdOT3bt3A9Da2kpjYyNpaWkL1l/NB9dyeLaxkVMDAzzb1MT3d+yYdW6xsbrLBlfOoLipj7b+MTx1gkmLdPr78fb2JjAwkPb2dnp6erBYLHh5eREYGEh/fz875tz3pTCZTJhMpgWnsoxGIxMTE/j6+jI8POz2+/Iog6JYNerr67l8+TJ79+5dd9vnDgwMsGnTpkXruNODuH1ighc7O7EAL3Z08FR8/CwvZbGxXi2LEmd6YZ4eOu7Ji+OunFinvh8hBHFxcfj7+9PY2EhYWBjDw8MYDOs+TJkAACAASURBVAbCwsIcjnGYTKZFF9Fu3bqV6upqysvL8fX1dXt9OWVQFE7HYrFw4cIFBgYGKCgosK4mXg9MTk7S2NgIsKhUObjXg/jZxkYsWkLBpJTzvJSlxno1LEqc6YVNTlrYEuK7au8pLCwMX19fa4xDSmndP8WRKV2TyYTRaKS5uZm4uDhr+cTEBG1tbfT19bF582ZrBqK7owyKwqmMj49TVFSEj48PBw8edPtfVDOZmJigtrYWX19fUlJS7ErPdIcH8bR3YtQMilFKm16KO4x1NVlrj9HX13fWj6Wenh6rMrG9+Pj44Ovri9lsnlVeV1eHv78/GRkZeHp6UlFR4dYLGqdRBkXhNPr7+yksLCQ+Pp7k5GS3zpe3RUtLC8HBwbN+Ka4HZnon09jyUq52XO0xxsTE0NDQQEREhN2ffW9vb7y9vecF5E0mE1FRUdZdGwcGBti8ebPTx+xslEFROIXW1lYqKirIyMhYt7IlY2NjREVFOTxt4WrODg5avZNpjFJyxoYq7tXOWnphPT09s4xBUFAQXl5e9Pb2LjldOpPh4eF53xmLxWL17qWUDA4OrgsPxe5vjRDCQwhRKoR4Qzt+RAhxWQghhRARM+odEUIMCCHOa6+vzDh3sxCiWmv3pRnliUKID4QQtUKIV4QQeq3cWzu+rJ1PmNHmCa28Wghx08pug8IW01pbi21rKqWkqqqKqqoq9u3bt26NCUwtIqurq6OpqWnpyi5m5u6IpXv3Io8cmfcq3bvX1cO8qmlra6O6uprh4WFrWUxMDG1tbXYvkDWbzZjN5llTZ0ajEZPJRH19PQCjo6N4eXm55dqtuTjyM+xR4NKM49PAhwBb376TUsos7fVVmDJIwPeBW4A04BNCiOmczP8Evi2lTAb6gM9o5Z8B+qSUScC3tXpo7e4F0oGbgR9o/SuchMViobCwEKPRSE1Njc06ZrOZwsJCent7KSgocPuUxqVITU21ubjM3VjNjbKWO56raetfe5icnGRiYoLExERqamqsRiUkJAQhBP39/Xb1Mzw8jJ+f36wpsoaGBgICAhgYGMBsNs9ai+Lu2GVQhBCxwK3AC9NlUspSKWWjA9fKAy5LKeullEbgKHC7mLqT1wGvavVeBu7Q/r5dO0Y7f71W/3bgqJRyQkrZAFzW+lc4iek0xdTUVJtfjpGREU6dOoWPjw/5+fno9XoXjNJ5mEwmWltbGR8fd/sUZ3faHdHdjJuzOFXVynfevkRhQ7fN8yaTyboh1qZNm2YZlWkvxR7mij0aDAZMJhOpqank5eXh6el59RkU4DvA44DFzvr7hBBlQoi/CCHStbItQPOMOi1aWTjQL6U0zymf1UY7P6DVX6ivWQghPiuEKBJCFBkMhv+/vTMPbuw4D/yvARAAr+EJHkPOkMMZzn3PSHNJsuK4FEuRJZePLTmJLSlOXPHaGyeqLVuK184mWW852d2sozjrxLGzsZOyZDtxYkWRI2sjK3HJmhkNRzNDci6Sw/s+wQvE2fvHew8DgAAIkiDxQPav6hUe+r0+HtCvv+7v+7o7xaIrurq6mJycxOVyce3aNfbt2xd1fWxsjDfffJP6+noOHz6cVfaGRNy5cweLxcKhQ4eSzo43A2baHdFMwi1dNHVP8qt/c5XnX7/DL3/jAufbhxfd43Q6OXr0KAUFBVEjFWPjrVAoFF6fKxmzs7NhgeL1eunt7aWhoSHqnXK73Vkz+l+yJRBCPAqMSCmbUkzzMlAnpTwC/Cnwj0ZSce6VScJXGudugJRfl1KelFKeXI4r32ZmYmKC27dvc88994QnJUb+dl1dXVy+fJnjx49TX1+fuYIuEyklQ0NDtLS00N/fHw4PhUL09fUxOztLbW1tVrg5G95Mzzy0J+PLvZhJuKWL83fGCYQkISAYgh81dRAKxe9LFxQUMDs7S0lJCVVVVQwNDSGEwOl04vf7l8xrdnY2PBlyaGgIl8u1qEOTLQZ5SM3L6xzwmBDiEcAJbBFC/K2U8lfi3SylnI44f0UI8X90o30fEOmPWQsMAGNAsRDCpo9CjHAi4vQJIWxAETCRJC3FKlhYWKCpqYmjR4+Sn59PQUFBeAZwKBSipaWFiYkJ7rvvPtP34iMxVmwNBALU1tbS2dkZnpg2MDDA7Owshw4dMr3tJJK0eTMdOwZXriwOP3oU3nknpXKYZXJnujCEpC8QIsdq4ejWPAYGBhbtedLR0cHs7Gx4L3ljRB8MBllYWFhyQu/CwgJWqzWsLg4EAotGIgsLC0gps2Zy8JIjFCnlc1LKWillPZoh/PVEwgRACFGl2zkQQtyr5zEOvA006h5ddj2tl6TmDvET4EN6Ek8CP9TPX9K/o19/Xb//JeAJ3QtsB9AIXFzGcytiMIzwO3bsCC85cuTIkfBmQm+99RZerzfrhInf7+fGjRvY7Xb27t1LcXExDoeDQCDA/Pw8IyMjNDQ0ZL0NaMWcOQOxz263w9mzUUHJDO8bbRdIQ0j++qkq/uiRbTx6+gCjo6OLVFgul4v8/HyOHTuGEIKcnBy2bNnC+Pg4CwsLOGIW6IwlUt0F0a7CBtlkP4FVbAEshPhNIUQf2ujgmhDCMNh/CGgRQlwFngeekBoB4NPAq2jeYt+TUrbqcT4HPCOEaEezkXxTD/8mUKaHPwM8C6DH+x5wHfgX4FNSyo23Cfg6cu3aNfLy8qJ2T3Q6ndTX1/PCCy9QXFzMyZMnwxOtzILb7cbr9ca95vf7w5sg1dfXh/XSdrudnp4ebty4QV1d3boIE9N6Qn3hCxBrA7NatXCdjWp4T8aJuhI++76jbMvVlkZpaGigo6MjSo1VUlKC1+uNcht2uVz09/djs9mWVJ/GCpRgMLjIHjk9PZ019hNY5sRGKeUbwBv6+fNoAiP2nq8CX00Q/xXglTjhd4jjpSWlXAA+nCCtLwFfSrnwioR0dnbidru57777osIHBwfp7Ozk2LFjVFZWmm7mu9frpb29HdDcNXfu3Bm+FilMYlUV27ZtY2JiApfLtS4C0mzL3EdRXQ1PPw3f/Cb4fNro5OmnIWJWttlWVV4vrFYrNTU19Pb2snfvXsrKyvjnC9fp9+eH1XuVlZUMDw+HBUNxcTH19fUpzUOZn5+P8ihMNELJprld2e+eo1gV4+PjtLW1cc8990TNzL19+zatra2cPn2a6upqU3pyjY6OUl5ezpEjR5icnCQUCuHxeJienk4oTEBb7qK6unrdRlum94SKHKXEjE4g2vButVron/JsmFHK5ORk0sbf5XLh8/mYmppiJJTPZ3/UHzVSc7lcTE1NRY2SS0pKUnI9t1qtBIN3FSvxVmjYNCovRfbj8Xi4fPkyx44d48aol8//QzO/84OrfOfHbzEyMsL9999PUVERgUDAlAZr42WzWq0UFBRw6dIlmpub6e7uprS0NK4wyQRm8IRKqnIzRikWy6LRCdy1KTxx73aQkhcv9mwY1VdbW1uUyioWY7n63t5eLnROaN5fER0Dm81GaWkpK5mWkJeXh8fjCX8PBoNRIxS/34/X6zX9tr+RmEshrlg3gsEgly5doqGhgZ55Gx/5S00lA2CzwIufOB02KgohUnKBXG9KSkqYmJiguLiYvXv3cuXKFQoLC6NUX2Yg055QKancvvAFaG1dNDoxOFFXcteddoOpvhYWFigsLEx4vaSkhOHhYbY7veHVjK0Wwb31xczNzTE5ObnsjbVAEyiTk3eFcuwIxbCfmE3VnAwlUDYpzc3N5Ofns3PnTv7sJ+34A3f97IMhuNA5ycl6rSddVVVFf3+/6WaQG26agUAAm83GkSNHTPvyZXLp+JRsINXV8G//ljQdM20olk7m5+eXvKexsRFLRwdfek8lA/586vL8lASnuH27l/r6+rjb9y5Fbm7uojlRkSOUbFN3gRIom5JYI/zBCjtWAQFdlZxjFVGNRUlJCQMDA3R3d7N9+/ZVN9qzs7O43W5qahYtbrAsYveQMKswyTTpEgSZHmmtFckWPzWwWq00NjaSl9fP2NgYDQ0NdHV1UV1dveKOltPpxOv1hlVdsV5ebrd7WasWmwElUDYZhhHe2PxqcnKShb4bfO3De3ij24OEuNum7tmzh1u3bjE6Orrk1rjJCIVCdHZ24vV6KSoqWlHPDjSh1NbWRl1dnelcmc1GOgVBukZaTd2TGRVMxg6LoHkLprKirxCC2tpa8vLyaG9vp66ublUNvsViITc3l4WFBZxOJxaLJapT5Ha7aWhoWHH6mUC9iZsIj8dDU1MTx44dIy8vj/HxcS5dusSxY8eoqKigtGwyoQeSzWajrKyMubm5VZVhbGyMnJwcqqqq6OnpYf/+/UtH0hkfH6eoqIiZmRk6OztpaGiguLh4VeXZLJhpt8ZMu1GHQqHwCtqHDx/mzp07tLe34/f72blzJ8XFxczMzNDX14fT6aSioiLKMF5aWorT6eT27dt4PB5qampWPDrOzc1lfn4eu90eNToJhULMz88nte2YESVQNgnBYJC3336bXbt24XK5GB0d5fLly5w4cYLy8vKUXvLS0lKam5uprq7G4/FQVFS0bHfiqakpXC4XpaWlDA0NMT4+vmQvLxgM0t/fz9DQULgHuXv37hWPbhSZxQzzWrxeL9u3b8fpdIY7NW63m66uLgoKCrhz5w6VlZUEAgE6Ozs5ePBgVPy8vDwOHDhAW1sboVCI7du3r6gchkDZsmVLlP1kenqa/Px8U7rrJ0MJlE3C1atXKSwspKGhgeHhYa5cucI999wT1v+m8pLb7Xa2bt1Kc3Mzdrs9rFdeaokJg8nJSWZmZqivr0cIQUNDA7du3cJut0f1xLxeL2NjY8zPzzM/P4/P56OwsJAjR44wOztLcXFxViziqIhPpo37FouFHTt20NHREZ67ZNQzIQStra3k5ubicDjC80ympqYWjYZzcnLYvn37qjZky8vLY2hoaJH9JJsWhIxECZQNjN/vp7e3N7yD3NmzZxkaGuLatWvce++9lJTcFRipvuTV1dVUVlZisVjo6emhv79/ST1vMBikt7cXt9vN7t27w0udGF5m7e3t7N27l9zcXCYnJ+ns7KSsrIzS0lJqamrC+mUgZeGlMC9mMO5v2bKFqqoqxsfHycvLo7y8HJ/PR39/f7jjdP36dRobG6murmZgYCCuetXhcDA3N8fo6CiFhYXcvn2b/fv3p2zXM+aixPPwyqYlVwyUQNmgDA4O0tLSQllZGbt376a8vJzBwUFaW1s5derUot7Pcl5yo3GvrKykpaUl6XpDMzMz3Lp1i5KSEg4cOLDoRSsqKmLbtm3cunWL0tJSxsfHlTpLJ9OG67XEDDad6urqRcuazM3NYbFYmJycxGKxMD8/T0VFBV1dXXHTMFSwnZ2d5Ofn4/f7GRgYSFkFZrfbCYVCTE1NLfLw2rp168oeLIMogbLBWFhYoLm5mdnZWU6cOBFWafX29nLz5k1Onz6dsPFf7kvucDjYtWsXHR0dNDQ0xB2iDw8Ps3Xr1qQvR3l5OX6/n+npaQ4ePJiRWflma7wzbbjerNTV1dHa2orf72fr1q3Mzs7i9XqTjowLCwspKSmhv78/7A1ZWVmZ8mg6Ly+PsbGx8ORIKWXWLQppoATKBkFKSVdXF7dv32bHjh2cOHEi3OPp7u7m9u3bnDlzJu09/6KiorBP/sGDB6OG7d3d3Xi93pQ24orXW1wvzNh4m8FwvRmx2Wzs3LkTt9tNcXExY2NjeL1enE5nwjjGjqYVFRVYLBZKS0vp7e2NWrk7GXV1dVEuy3NzczgcDlMud7QUSqBsAObm5mhqasJqtXLu3LkoodHZ2UlHRwdnz55dszWBjPkkzc3NWCwWpJSEQiHsdjt79uwx/TwRMzbemTZcb2YKCgooKCjA5/OFjeULCwsEg0Hm5ubijhxmZ2cZHx9namoKgOXsEBu7v1A2zpA3MPebrliSubk5fvazn9HY2LhoJNDR0UFXVxdnz55d802xduzYwcLCAkKI8JGTk5MVbo9mbLzNYLje7FitVgKBQHgtr46ODqampti+fTtVEQtoSinp7OwMz0nZunXrqlZtUAJFkRFmZ2d566232LNnzyIj4O3bt+nr6+PcuXNJh+vpwmKxZNVOjpGYtfE2g+F6tZjNNrUcDPVtMBikvr6elpYWnE5neD6UMX9KCMHBgweZmJhgaGiIsbExqqqqqKioWJFgcbvdplvgNFWUQMlSDGGyd+9etm3bFnXt5s2bDA0Nce7cuYSGwaVe9GxuCFbCRmi8zYYZbVPLxWazEQwGcTqd1NbWMjMzg9VqxefzRd0nhKCsrIyysjJmZmZob28nPz9/RTbLbHUZBiVQspJkwqS1tZWxsTHOnj2bcGvbpV70jdAQKDLPcmxTZu3AGGovu91OVVUVlZWVXL9+PWoOVyzGJN2VGNU9Hg8Wi2VdtAprgfkV3IooZmZmeOutt9i3b1+UMJFS0tzczMTERFJhAkvvIGj6HQbTgGn3eN9ApLqxmJn3rG+fCvHH/9LKxTtjgDYSqampoaenh1AoFDeOlHLFm9Jls/0E1Agl67h+/Tq7du2K2o1QSsm1a9eYnZ3l9OnTS1bkpYzQZjRSp5PNMgLLdK8/VduUGb3sQPv9fufHg/iCIb7dNMJXP7ib9xzVFo8cGRlhcHAw7hYM8/Pz2Gy2FTmkKIGiWFcCgUCUXlZKyZUrV/B4PJw6dSolF92lXnSzGqnThVkbsHRiFqGZim3KrB2Y83fG8QW1ehIMwb/fGOTYtmJcLld4AmRZWVmUemp4eJj+/v5FquhUmZ6eXvU+QZkkZREqhLAKId4RQrysf/+0EKJdCCGFEOUR9wkhxPP6tWtCiOMR154UQrTpx5MR4SeEEM16nOeF7hohhCgVQrym3/+aEKJkqTw2OsZkK9CWuL58+TJerzdlYWJwoq6ET/3croQv+1LX00Gm1E5m2ON9rckmtaXRgXnmoT2mGi1G1ROrhb2lVoaGhhgcHMThcFBVVRVeGNLv94f3C9q3b9+y5qFEsplGKJ8BbgCG+8GbwMvAGzH3PQw06scp4GvAKSFEKfC7wElAAk1CiJeklJP6PZ8AzgOvAO8FfgQ8C/yrlPLLQohn9e+fS5THMp4la5mYmGDv3r2EQiGampqQUnLvvfdmxXyPSDLZg97oIzAwb68/EWb0sousJzvy/ewqtuJyueju7g7v6TM+Ps74+DjDw8Pk5+drWwWv8F30+Xz4/f6sdb+HFAWKEKIW+EXgS8AzAFLKd/Rrsbc/DnxbSimB80KIYiFENfAg8JqUckKP9xrwXiHEG8AWKeVbevi3gfejCZTH9XgA30ITXp9LlIeUcnCZz591GMtAvP3221it1qglVtLFWuneI9PNtNrJjA1YOtkMQnM9iFdPHA4HN2/exG63U1dXx82bNykpKaGuri58z+DgIBaLBZfLlfL7abgLZ/NW1qmOUL4CfBZIZfuwGqA34nufHpYsvC9OOEClISSklINCCGPv2URpRQkUIcQn0EY+K94AxywEAgHa29vxer1cvXqVvLw8jh07lvbKt5KRQyoCKDbdLz56IKt60NnIRheamSIvL4/t27fT19fH/v372bVrV5Saan5+nsHBwfBeJ7W1tZSWliKECC9LFLvdL2TvHiiRLClQhBCPAiNSyiYhxIMppBmvhZMrCF9JHtEBUn4d+DrAyZMnl0rTlEgp6enpCS/vnpubS0FBAUeOHFmTnsxyRw6RgsJmtfChE7Vx96SPTXdy3qd60IqsxefzhdfGM1b0NnC73ZSWllJfX8/09DRdXV1IKcnPz6etrQ2fzxcWKlarFafTyb59+3C73Su2vZiFVEYo54DHhBCPAE5gixDib6WUv5Lg/j4g0sWhFhjQwx+MCX9DD6+Ncz/AsKHK0tVmI0vksaEw3IGnp6c5fvw4N27coLy8nEOHDq3ZsHi5uvdIQeELhHjhQg8/uNy3aGQTL13Vg1ZkK9PT0xQXFyOljHoXvV4vOTk5zM/PA9pGXpWVlQwNDeHz+di2bRsulys8UgkGg7S2tuL1enG73SmvUGxWllTuSSmfk1LWSinrgSeA15MIE4CXgI/pnlinAbeutnoVeEgIUaJ7az0EvKpfmxFCnNa9uz4G/DAiLcMb7MmY8Hh5bCgi9zW5fv06paWlHD58eE11rMv1uDEEhVEiSXyvIrN68igWoyZ9JkdKyczMDD09PXg8HqSUjI6O0tLSwtWrV5FSRi3NYqix9uzZEx6BCCGwWq3Y7Xby8/Nxu914PJ6s31huxfNQhBC/iWZXqQKuCSFekVL+GpqX1iNAOzAPPA0gpZwQQvwB8LaexO8bBnrgk8BfA7loxvgf6eFfBr4nhPg40AN8WA+Pm8dGYnZ2Nrwe18WLF6msrAzvu7DWLGfkYAiKH1zu4/uXegmGZMKRjRqRmB+zzF8xM0II9u/fz61btwgEAty4cQOA2tpa+vo0c3CkQHE6nRw8eDBhegUFBQwPD1NQUJB13pqxLEugSCnfQHcTllI+Dzwf5x4JfCpB/L8C/ipO+CVg0S8upRwHfn45eWwUjDWELl68SE1NTXg3NzNiCIoPHK9VNpEsJ9Ped9mC2+0OO8ps3bqVyspKhBCMjIwghMDv96ecVn5+PtevX896+wmomfKmJRAIcP36dd7//vevWK+63ktvqBGIOVjN/56qDS3Ty7pkAuOZj23Nx+buw2q1snfv3qh5I0IIQqEQQggCgUBKk43z8/MZHh7O2iXrI1ECxYTMzc3x05/+lMbGxlUJk2xTXWzGRirdrPZ/N1SYf3+5L64rZTryyEaivBktgi/eV8SH330kanuIgYEBJicnCQaDBINBfD5fSgLFZrMxPz+f1fNPDLJbYbcBmZ2d5Wc/+xlVVVUcOHBgxelk09IbYO4VZ5fLSoza6TKEp+t//8HlPl642BP3v8i2upUOIp85EJS0TYsoYTI0NBS2nxgjltg9UxJheHslWr04m1AjFBMxMzPD+fPn2bVrFx6PZ1Wb7GTb0hup6O6zYQSz0omh6erxp+N/X+q/yLa6lQ6MZ9ZGKHD/nqqo6xaLhbKyMurq6rDZbLhcriiBk6zuzs7OUlRUxMzMzLo8y1qiBIpJcLvdXLhwgbq6OtxuN8XFxZSXly8dMQHZtvTGUo1UtqhZVmLUTqchPB3/+1L/RbbVrXRgPPNrVzqpdSzw4MHolTcqKiqoqKgIf8/NzQ2fJ6u7Td2T/PidO7icFUxNTa3Pw6whSqBkEL/fT0dHB0NDQ7S2trJ//37m5+epr69PuiNcqmSTkXypRipbvI9W0ntPd49/tf97KgIjm+pWujhRV0KNw8v09PSyVvZOVHfDgsYfIscq+E+HFrgvGAzvZZ+NKIGSQS5duoTX62VoaIiHHnqIrVu34nA4llVZNxLJGqlsUbOspPduxh5/KgIjG1SQ6cblclFWtry6l6juvtk2ogkaIBCSdHsc4WVbshWhTenY+Jw8eVJeunQp08UIMzk5yeuvv05eXh4nT57cED7oa81mbMDMSraoIM2CUXcPVTioyvEwMjLC1b5p/qRZEgiB3WbhD37OxfG6EtO5DwshmqSUJ1O5d3N2hU3A22+/zcLCAg8++OCyezyblc2oZjEr2aKCzDSBQICxsTFsU8PsDowQGLbir6xkz549nD1bxukz7nAnyTrZnfV2FCVQMkB7ezstLS189KMfVcJkFaRzxLKZRz8refZsUUGmg+X+PnNzcwwPDzMyMsLk5CQlJSVUVFSwa9eu8ArFBkYnKRQK8c/XtB05Tpw4sSbPsR4ogbLODA4O8pOf/ISHH35YqblWQTpVLptZfbPSZzej3WctiLePz+S8L+qZQ6EQ4+PjjIyMMDw8TDAYpKKigvr6ek6ePJmSTdTj8YTPvV5vlMtxNqEEyjrS399Pa2sr+/btY8eOHZkuTlaTTpXLZlbfrObZN4MKMmp7Bn+IL/6whZCU2K0W/vixelxilrGxMQoLC6msrOTEiRMr2iTL4/FgtVoJBoNMTU1RWVm5Bk+z9iiBsk709vZy8+ZNzpw5Q1dX14aYFZtJ0qlyyRb1zVqo5bLl2TNF5O+DEARDEom298+bt0f45IM7OXLkCHa7fVX5zM/PU1VVRX9/P8PDw1krUJSX1zpw584dLl++zOHDh7FarUxPT3Po0KFN6x6cLjaTDWUt1XJmf/ZM4ff7GRkZ4d+v93Ghc4Jip40XbvkJ6Fs0pPM/uHXrFgBtbW1IKXnf+96XlnTTgfLyMgGhUIjR0VEuXLhAV1cX999/P3l5eTgcDmpra5UwSQPpVLmYXX2zlmo5sz/7ejIzM8Pw8DDDw8NMT09TVlbGmcZK3n/fYXJzc3nfGglfj8dDaWkpe/bs4ebNm2lLd71RrVqaCYVCdHd309bWxuTkJEIInnrqqVWty6VYGRup561UU2tDMBhkbGwsbFAHqKyspLGxkbKyskWz1tdK+M7Pz1NTU0NlZSU3b95kZmaGwsLCtOez1iiBkkamp6dpamoiNzeXsrIycnJyOHPmDE6nMyPl2UgN6nLZaJ5bm8Wraj3weDzhUcjExARFRUVUVFRw6tSpdW3EgxHLrHg8nrAGA6Cjo4OjR4+uW1nShRIoaSAUCjExMUFzczM7d+4M+6GfPXs2Y+5/G61BXS7pUBGZTSAr1dTSxPvPQqEQk5OT4bkhXq+XiooKtm3bxvHjx8nJyclIWV955RXq6uo4dOgQCwsLUQtK9vX1KYGyWZiYmODatWssLCxgsVgIBoMUFBRQV1fHzMwM4+PjnD17lubBOc7f6c1Ig7SZXWFh9SqizS6Qs5Go/8xq4SuPN+CyzDI6OkpeXh6VlZUcOXKE4uJiU2xmVVJSQnd3N42NjeTk5IT3k3c4HHi93gyXbmUogbIMgsEgN2/eZGBggIMHD1JeXk4wGMRisZCTk0NzczPT09OcOXOGawOz4cptEYLff/wgv3RqHXcglAAADfRJREFU+9KZpInNrnNfrYposwvk9cbYZGo1x9+3TuPza4st+gIh/v3WEL/xwA4OHDiQMbVzMnbv3h122oncRjg3Nxev10soFAoLmWxBCZQUGR8f58qVK5SWlvKud70Lu91+d3i9oxTrVA9zc3OcPn0am80W1SCFpOSLP2xhT1Vh1D4Ia6lOUTr31amINrtANjB2EoxsuAOBQFoEgHEYe7Bbrdakh8Viifpus9lwOBzh7w9SyN/faiMQ1Nx6P3j/YbZvX796HwwG8fv9+Hw+fD4fXq834aff78fv9wPahOfa2tpwOnV1dbhcLlOMopaLEigpMDg4SHNzM0eOHAlPOIreYxo+f7aQX3nvubCR7XRDGRYhCOnzfEIhuXgfhDVWpyid+8pJJJDNYFeRUi67QV+pAIhtxFM5cnJycDqdKQkF40hH41lbC98pK1/1/yOlJBAI4PP5wgIi9jNSQBjhUkrsdjs5OTnY7XYcDkf4c8uWLeHvxhGp5opk+/b102Skm5QnNgohrMAloF9K+agQYgfwIlAKXAY+KqX0CSGeAv4H0K9H/aqU8ht6Gk8C/0UP/29Sym/p4SeAvwZygVeAz0gppRCiFPguUA90Af9BSjkptNr3J8AjwDzwlJTycrLyr3Rio5SSV199lVAoFNUbevmOj+/fWCAECCTvKpnm/nIPFosFIQQWi4VLk05eHspDSoHNAp+9x0FjiY2X7/j5wW0fIcACfHCPg8cbneGXSggRPpJ9T+V8NfGM74FAAClluFdovASplHEl+aWjzGvRu1uqI7CShn4pARAIBOIKhZU09Ms9jLqcbfj9/vAowPj9kn3GCgy/34/NZgsLhsjPWGEReWTzxljJWKuJjZ8BbgDGhIo/BP63lPJFIcSfAx8HvqZf+66U8tMxhSoFfhc4CUigSQjxkpRyUo/3CeA8mkB5L/Aj4FngX6WUXxZCPKt//xzwMNCoH6f0+KeW8SwpI4TgPe95T9SLHQwG8RdN8Y9tN/AHJTkWCx+47xB7XQ5CoRBSSoLBIEeCQXa19NCzYOdwdS57yrTlGQ5XWXmp3UcgBDYLHKywR73AFoslfBjfjbIA4fDYhtS4J/YwOg1SyvARCoXCh5Qy6j4jPeO+8+fPA0Q1ZsZhs9nCZS8sLKSmpmZRfrF5J/uezniRv0fsb5PoWrI4/9Thu6uj94f4zmsXmaizRDX4y22wrVZruDHa6A19Khijg9jDEA6x58b3yBGD8Zsav6tRRyM/7XY7NpstoeDYqL/vWpOSQBFC1AK/CHwJeEYfIbwb+CX9lm8B/5W7AiUevwC8JqWc0NN8DXivEOINYIuU8i09/NvA+9EEyuPAgxF5vIEmUB4Hvi21VuO8EKJYCFEtpRxM5XmWi1HxInl3SQnfKSpecni9b98+JiYm8Hq94QbP5ZL8r5ISrg7Mc7g6jwOVuVG928ieaCgUwu/3RzX+kcIgMiz2M1JYGI2QcQ1YJHTiNcxCCA4fPszp06fD14yeXeTR1tZGIBCgvr6e3NxcHA5HxtwxDZYjoFK5Jsrd/NOdFgLBEDlWCx+4/xDHt5dENfabnWAwyMLCQtQIYTkCwpibEdnYxzvPzc0NnxsCwuFw4HA4ss6QvZFIdYTyFeCzgDHrpwyYklIG9O99QE3E/R8UQjwA3AZ+W0rZq1/vjbjHiFOjn8eGA1QaQkJKOSiEqNDDE6UVJVCEEJ9AG/msiV4yFRuF3W6nqqpqUXhDA6zXaj2RQsYwfqbSA4unDhVCxBWwXq+X4eFh2tvbWVhYYGFhASklTqcz4RHbU4/8TAeRo4x08MCBLXzn1wsybkNZb0KhUFhIRB5GmM/nC59LKXE4HDidzigBYAiESEEQe9041Ogge1lSoAghHgVGpJRNQogHjeA4txqtzz8BL0gpvUKI30AbWbw7SZxkaSUsVipxpJRfB74Omg1liTQ3LEYDvdwe9HJe7JqaGmpqaqLCAoFAWLgYx/z8fHjEFuktFPkppVwkZOIJnsiebCLVRrze7moarNU6OiQaUaZqW5FShp/FarWG48dLM9651+vF4/EQCGh9wVgVYeynka/R+488DENz5KHWqNvcpPLvnwMeE0I8AjjRbChfAYqFEDZ9lFILDABIKccj4v4lmq0FtFHEgxHXatFUWH36eWT4gH4+bKiyhBDVwEhEWtsSxFGYBJvNRkFBAQUFBcuKZzSwiVSAxmekYTUQCISFVKzRNfYw5g0ZDgaxNpNEn5GCyNDPxytXPON6pPoxUgVpfC7HhuLz+ZibmwuPOCPtbrHpRz6jxWKhrKwsPHpI5ZkNry2FIhWWFChSyueA5wD0Ecp/llL+shDi+8CH0Dy9ngR+qN8Tact4DM2QD/Aq8N+FEEb37iHgOSnlhBBiRghxGrgAfAz4U/2el/S0vxyZhx7+aSHEi2jGePda2U8U64/REK4FhrAy9PZGQ29cS/XT5/OF9f3x3GHjqfGUbl+x0VnNW/s54EUhxH8D3gG+qYf/phDiMSAATABPAeiC4w+At/X7ft8w0AOf5K7b8I/0AzRB8j0hxMeBHuDDevgraC7D7Whuw0+v4jkUm4hENiCFQrF61AZbCoVCoUjIcuahqDG4QqFQKNKCEigKhUKhSAtKoCgUCoUiLSiBolAoFIq0oASKQqFQKNKCEigKhUKhSAtKoCgUCoUiLWyaeShCiFGgO0PZlwNjGco7VVQZ04MqY3pQZUwP6ShjnZTSlcqNm0agZBIhxKVUJwZlClXG9KDKmB5UGdPDepdRqbwUCoVCkRaUQFEoFApFWlACZX34eqYLkAKqjOlBlTE9qDKmh3Uto7KhKBQKhSItqBGKQqFQKNKCEigKhUKhSA/GftPqWHygbXl8EbgKtAK/p4fvQNtdsg34LmDXwx3693b9en1EWs/p4beAX4gIf68e1g48GxEeN48kZbWibXT2shnLCHQBzcAV4JIeVgq8psd/DSjRwwXwvJ7fNeB4RDpP6ve3AU9GhJ/Q02/X44pkeSQoYzHwd8BNtJ1Gz5ipjMAe/fczjmngt8xURv3e30Z7X1qAF9DeI9PUR+Azetlagd8yS10E/gptm/OWiLCMlStZHgn/+3Q2wBvt0H/QAv08R6+sp4HvAU/o4X8OfFI//4/An+vnTwDf1c/3owklh17pO9AEgFU/bwDs+j379Thx80hS1meA73BXoJiqjGgCpTwm7I/QGwTgWeAP9fNH0HbtFPrvfSGi4t/RP0v0c6PyX0QTAEKP+3CyPBKU8VvAr+nndjQBY6oyRpTVCgwBdWYqI1ADdAK5EXXkqUR1hXWuj8BBNGGSh7Zj7f8DGs3wGwIPAMeJFigZK1eiPJLWy7VskDfSoVfAy2h72I8BNj38DPCqfv4qcEY/t+n3CbSe1nMRab2qxwvH1cOf0w+RKI8EZasF/hV4N/BysvgZLGMXiwXKLaBaP68GbunnfwF8JPY+4CPAX0SE/4UeVg3cjAgP35cojzjl24LWEAqzljGmXA8Bb5qtjGgCpRetQbOh1cdfSFRXWOf6iLaN+Dcivn8B+KxZfkOgnmiBkrFyJcojWb1UNpQlEEJYhRBX0Iair6H1jqaklAH9lj60lwjuvkzo191AWWR4TJxE4WVJ8ojHV9BeipD+PVn8TJVRAj8WQjQJIT6hh1VKKQf1sgwCFbFlTLEsNfp5bHiyPGJpAEaB/yuEeEcI8Q0hRL7JyhjJE2jqpGTx172MUsp+4H8CPcAgWv1qwjz1sQV4QAhRJoTIQ+uFb0vyfJn+nzNZrkRpJUQJlCWQUgallEfRRgH3Avvi3aZ/igTX0hW+CCHEo8CIlLIpMthMZdQ5J6U8DjwMfEoI8UCSe9e6LPGwoakbvialPAbMoQ3/zVRGLWMh7MBjwPeXunWZZVl1GYUQJcDjaGqqrUA+2n+eKN11rY9SyhvAH6J1Dv8FTWUWiL0vgoz9z0uwHuVadhwlUFJESjkFvIGmSywWQtj0S7XAgH7eh9bbQb9eBExEhsfESRQ+liSPWM4BjwkhuoAX0dReXzFZGZFSDuifI8A/oAnnYSFEtV6WarRRYFQZUyxLn34eG06SPGLpA/qklBf073+HJmDMVEaDh4HLUsrhJeJnoozvATqllKNSSj/wA+AsJqqPUspvSimPSykf0PNqS/J8mfyfk8VZj3IlSishSqAkQQjhEkIU6+e5aC/LDeAnwIf0254Efqifv6R/R7/+utSUjy8BTwghHEKIHWhGwIvA20CjEGKH3ut8AnhJj5MojyiklM9JKWullPV6/NellL9spjIKIfKFEIXGOZr+vyWmLLFl/JjQOA249aH4q8BDQogSvSf8EJqefBCYEUKcFkII4GMJnjfZ7zgE9Aoh9uhBPw9cN1MZI/gId9VdyeJnoow9wGkhRJ6ehvE7mqk+Vuif24EP6L+lmX7DSDJZrkR5JCaZgWWzH8BhNFfca2gN4Bf18Aa0yt2OpnZw6OFO/Xu7fr0hIq3Po9lfbqF7V+jhjwC39WufjwiPm8cS5X2Qu15epimjft9V7rpff14PL0NzJmjTP0v1cAH8mZ5fM3AyIq1f1fNrB56OCD+p/0cdwFe56xIZN48E5TwKXNL/739E85IxWxnzgHGgKCLMbGX8PTTX6xbgb9A8tcxUH3+KJuSuAj9vlt8QTbANAn600cHHM1muZHkkOtTSKwqFQqFIC0rlpVAoFIq0oASKQqFQKNKCEigKhUKhSAtKoCgUCoUiLSiBolAoFIq0oASKQqFQKNKCEigKhUKhSAv/H20TiSVJNUwLAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mc = mean_center(pp.points)\n", "mm = manhattan_median(pp.points)\n", "em = euclidean_median(pp.points)\n", "pp.plot(title='Centers', hull=True , window=True )#plot point pattern \"pp\", convex hull, and Minimum Bounding Rectangle\n", "plt.plot(mc[0], mc[1], 'c^', label='Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot Standard Distance Circle of the simulated point pattern." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sx, sy, theta = ellipse(pp.points)\n", "sx, sy, theta\n", "theta_degree = np.degrees(theta) #need degree of rotation to plot the ellipse\n", "from matplotlib.patches import Ellipse\n", "from pylab import figure, show,rand\n", "fig = figure()\n", "#ax = fig.add_subplot(111, aspect='equal')\n", "e = Ellipse(xy=mean_center(pp.points), width=sx*2, height=sy*2, angle=-theta_degree)\n", "ax = pp.plot(get_ax=True, title='Standard Distance Circle')\n", "ax.add_artist(e)\n", "e.set_clip_box(ax.bbox)\n", "e.set_facecolor([0.8,0,0])\n", "e.set_edgecolor([1,0,0])\n", "ax.set_xlim(300000,1000000)\n", "ax.set_ylim(4050000,4350000)\n", "#ax.set_aspect('equal')\n", "plt.plot(mc[0], mc[1], 'c^', label='Mean Center')\n", "plt.legend(numpoints=1)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Simulate a 500-point dataset within VA state border from a CSR (complete spatial randomness) process." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp = csr(as_window(state), 500, 1, asPP=True).realizations[0]\n", "pp.plot(window=True)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pp.plot(window=True, hull=True)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/weikang/Google Drive (weikang@ucr.edu)/python_repos/pysal-refactor/pointpats/pointpats/centrography.py:150: UserWarning: Manhattan Median is not unique for even point patterns.\n", " warnings.warn(s)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mc = mean_center(pp.points)\n", "mm = manhattan_median(pp.points)\n", "em = euclidean_median(pp.points)\n", "pp.plot(title='Centers', hull=True , window=True )#plot point pattern \"pp\", convex hull, and Minimum Bounding Rectangle\n", "plt.plot(mc[0], mc[1], 'c^', label='Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sx, sy, theta = ellipse(pp.points)\n", "sx, sy, theta\n", "theta_degree = np.degrees(theta) #need degree of rotation to plot the ellipse\n", "from matplotlib.patches import Ellipse\n", "from pylab import figure, show,rand\n", "fig = figure()\n", "#ax = fig.add_subplot(111, aspect='equal')\n", "e = Ellipse(xy=mean_center(pp.points), width=sx*2, height=sy*2, angle=-theta_degree)\n", "ax = pp.plot(get_ax=True, title='Standard Distance Circle')\n", "ax.add_artist(e)\n", "e.set_clip_box(ax.bbox)\n", "e.set_facecolor([0.8,0,0])\n", "e.set_edgecolor([1,0,0])\n", "ax.set_xlim(300000,1000000)\n", "ax.set_ylim(4050000,4350000)\n", "#ax.set_aspect('equal')\n", "plt.plot(mc[0], mc[1], 'c^', label='Mean Center')\n", "plt.legend(numpoints=1)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we calculate the Euclidean distances between every event point and Mean Center (Euclidean Median), and sum them up, we can see that Euclidean Median is the optimal point in iterms of minimizing the Euclidean distances to all the event points." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "74214411.72342663\n", "73835502.40107813\n", "True\n" ] } ], "source": [ "from pointpats import dtot\n", "print(dtot(mc, pp.points))\n", "print(dtot(em, pp.points))\n", "print(dtot(mc, pp.points) > dtot(em, pp.points))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.5" }, "widgets": { "state": {}, "version": "1.1.2" } }, "nbformat": 4, "nbformat_minor": 1 }