{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Probability distributions\n", "\n", "Probability distribution is the backbone of uncertainty quantification.\n", "Creating a probability distribution in `chaospy` is done by as follows:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:12.698334Z", "iopub.status.busy": "2021-05-18T10:56:12.698032Z", "iopub.status.idle": "2021-05-18T10:56:12.706508Z", "shell.execute_reply": "2021-05-18T10:56:12.706773Z" } }, "outputs": [ { "data": { "text/plain": [ "Normal(mu=2, sigma=2)" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import chaospy\n", "\n", "normal = chaospy.Normal(mu=2, sigma=2)\n", "normal" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The distribution have a few methods that the user can used, which has names\n", "and syntax very similar to that of\n", "[scipy.stats](https://docs.scipy.org/doc/scipy/reference/stats.html). Below\n", "some of these methods are demonstrated. For a full overview of the\n", "distribution methods, see\n", "[chaospy.Distribution](../../api/chaospy.Distribution.rst).\n", "\n", "For an overview of available distributions, see then take a look at the\n", "[collection listed in the reference](../../reference/distribution/collection.rst)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (Pseudo-)random samples\n", "\n", "The most important property a random variable has, is to create\n", "(pseudo-)random samples. This can be created using\n", "[chaospy.Distribution.sample()](../../api/chaospy.Distribution.sample.rst#chaospy.Distribution.sample):" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:12.708954Z", "iopub.status.busy": "2021-05-18T10:56:12.708621Z", "iopub.status.idle": "2021-05-18T10:56:12.716671Z", "shell.execute_reply": "2021-05-18T10:56:12.716331Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.2553786 , 2.62204779, 1.68653451, 3.58083895])" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "samples = normal.sample(4, seed=1234)\n", "samples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These can be used to create e.g. histograms:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:12.718782Z", "iopub.status.busy": "2021-05-18T10:56:12.718465Z", "iopub.status.idle": "2021-05-18T10:56:12.803777Z", "shell.execute_reply": "2021-05-18T10:56:12.804034Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib import pyplot\n", "\n", "pyplot.hist(normal.sample(10000, seed=1234), 30)\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The input can be both be a integer, but also a sequence of integers. For\n", "example:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:12.806367Z", "iopub.status.busy": "2021-05-18T10:56:12.805941Z", "iopub.status.idle": "2021-05-18T10:56:12.814580Z", "shell.execute_reply": "2021-05-18T10:56:12.814241Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0.2553786 , 2.62204779],\n", " [1.68653451, 3.58083895]])" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "normal.sample([2, 2], seed=1234)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Random seed\n", "\n", "Note that the `seed` parameters was passed to ensure reproducability. In\n", "addition to having this flag, all `chaospy` distributions respects `numpy`'s\n", "random seed. So the sample generation can also be done as follows:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:12.816776Z", "iopub.status.busy": "2021-05-18T10:56:12.816465Z", "iopub.status.idle": "2021-05-18T10:56:12.824359Z", "shell.execute_reply": "2021-05-18T10:56:12.824021Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.2553786 , 2.62204779, 1.68653451, 3.58083895])" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy\n", "\n", "numpy.random.seed(1234)\n", "normal.sample(4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Probability density function\n", "\n", "The probability density function, is a function whose value at any given\n", "sample in the sample space can be interpreted as providing a relative\n", "likelihood that the value of the random variable would equal that sample.\n", "This method is available through\n", "[chaospy.Distribution.pdf()](../../api/chaospy.Distribution.pdf.rst):" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:12.826483Z", "iopub.status.busy": "2021-05-18T10:56:12.826171Z", "iopub.status.idle": "2021-05-18T10:56:12.833879Z", "shell.execute_reply": "2021-05-18T10:56:12.833582Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.02699548, 0.12098536, 0.19947114])" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "normal.pdf([-2, 0, 2])" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:12.835996Z", "iopub.status.busy": "2021-05-18T10:56:12.835684Z", "iopub.status.idle": "2021-05-18T10:56:12.897885Z", "shell.execute_reply": "2021-05-18T10:56:12.897594Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "q_loc = numpy.linspace(-4, 8, 200)\n", "pyplot.plot(q_loc, normal.pdf(q_loc))\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cumulative probability function\n", "\n", "the cumulative distribution function, defines the probability that a random\n", "variables is at most the argument value provided. This method is available\n", "through\n", "[chaospy.Distribution.cdf()](../../api/chaospy.Distribution.cdf.rst):" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:12.900117Z", "iopub.status.busy": "2021-05-18T10:56:12.899804Z", "iopub.status.idle": "2021-05-18T10:56:12.907770Z", "shell.execute_reply": "2021-05-18T10:56:12.907483Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.02275013, 0.15865525, 0.5 ])" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "normal.cdf([-2, 0, 2])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:12.909949Z", "iopub.status.busy": "2021-05-18T10:56:12.909641Z", "iopub.status.idle": "2021-05-18T10:56:12.965778Z", "shell.execute_reply": "2021-05-18T10:56:12.966051Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pyplot.plot(q_loc, normal.cdf(q_loc))\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Statistical moments\n", "\n", "The moments of a random variable giving important descriptive information\n", "about the variable reduced to single scalars. The raw moments is the building\n", "blocks to build these descriptive statistics. The moments are available\n", "through\n", "[chaospy.Distribution.mom()](../../api/chaospy.Distribution.mom.rst):" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:12.968234Z", "iopub.status.busy": "2021-05-18T10:56:12.967918Z", "iopub.status.idle": "2021-05-18T10:56:12.992303Z", "shell.execute_reply": "2021-05-18T10:56:12.992575Z" } }, "outputs": [ { "data": { "text/plain": [ "array([1., 2., 8.])" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "normal.mom([0, 1, 2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Not all random variables have raw moment variables, but for these variables\n", "the raw moments are estimated using quadrature integration. This allows for\n", "the moments to be available for all distributions. This approximation can\n", "explicitly be evoked through\n", "[chaospy.approximate_moment()](../../api/chaospy.approximate_moment.rst):" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:12.994707Z", "iopub.status.busy": "2021-05-18T10:56:12.994399Z", "iopub.status.idle": "2021-05-18T10:56:13.011144Z", "shell.execute_reply": "2021-05-18T10:56:13.011416Z" } }, "outputs": [ { "data": { "text/plain": [ "8.0" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chaospy.approximate_moment(normal, [2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See [quadrature integration](./quadrature_integration.ipynb) for more details on how this\n", "is done in practice.\n", "\n", "Central moments can be accessed through wrapper functions. The four first\n", "central moments of our random variable are:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.013593Z", "iopub.status.busy": "2021-05-18T10:56:13.013274Z", "iopub.status.idle": "2021-05-18T10:56:13.086324Z", "shell.execute_reply": "2021-05-18T10:56:13.086742Z" } }, "outputs": [ { "data": { "text/plain": [ "(array(2.), array(4.), array(0.), array(0.))" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(chaospy.E(normal), chaospy.Var(normal),\n", " chaospy.Skew(normal), chaospy.Kurt(normal))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See [descriptive statistics](./descriptive_statistics.ipynb) for details on\n", "the functions extracting metrics of interest from random variables." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Truncation\n", "\n", "In the [collection of distributions](../../reference/distribution/collection.rst) some\n", "distribution are truncated by default. However for those that are not, and\n", "that is the majority of distributions, truncation can be invoiced using\n", "[chaospy.Trunc()](../../api/chaospy.Trunc.rst). It supports one-sided\n", "truncation:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.090472Z", "iopub.status.busy": "2021-05-18T10:56:13.089797Z", "iopub.status.idle": "2021-05-18T10:56:13.184478Z", "shell.execute_reply": "2021-05-18T10:56:13.184177Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "normal_trunc = chaospy.Trunc(normal, upper=4)\n", "\n", "pyplot.plot(q_loc, normal_trunc.pdf(q_loc))\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and two-sided truncation:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.186956Z", "iopub.status.busy": "2021-05-18T10:56:13.186637Z", "iopub.status.idle": "2021-05-18T10:56:13.242816Z", "shell.execute_reply": "2021-05-18T10:56:13.242482Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "normal_trunc2 = chaospy.Trunc(normal, lower=-1, upper=5)\n", "\n", "pyplot.plot(q_loc, normal_trunc2.pdf(q_loc))\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multivariate variables\n", "\n", "`chaospy` also supports joint random variables. Some have their own\n", "constructors defined in the\n", "[collection of distributions](../../reference/distribution/collection.rst).\n", "But more practical, multivariate variables can be constructed from univariate\n", "ones through [chaospy.J](../../api/chaospy.J.rst):" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.244981Z", "iopub.status.busy": "2021-05-18T10:56:13.244673Z", "iopub.status.idle": "2021-05-18T10:56:13.252117Z", "shell.execute_reply": "2021-05-18T10:56:13.251761Z" } }, "outputs": [], "source": [ "normal_gamma = chaospy.J(chaospy.Normal(0, 1), chaospy.Gamma(1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The multivariate variables have the same functionality as the univariate\n", "ones, except that inputs and the outputs of the methods\n", "[chaospy.Distribution.sample](../../api/chaospy.Distribution.sample.rst),\n", "[chaospy.Distribution.pdf()](../../api/chaospy.Distribution.pdf.rst)\n", "and\n", "[chaospy.Distribution.cdf()](../../api/chaospy.Distribution.cdf.rst)\n", "assumes an extra axis for dimensions. For example:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.255041Z", "iopub.status.busy": "2021-05-18T10:56:13.254725Z", "iopub.status.idle": "2021-05-18T10:56:13.464743Z", "shell.execute_reply": "2021-05-18T10:56:13.465005Z" } }, "outputs": [ { "data": { "image/png": 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GQpxPfFHPpatrlFVuUd9QSg8FMI0xdiml1Cp3KwDsA2NFoV3Ksir6i8KnJBCo5NIk0PEKBDtmoxyv5TLfoUsV6+1KFvsXyxXHffX7lCpD26p90W9f0pZVDM8HlWMUKnIq2YL6XPk7WBl6PliS/x9Q/vYXhp4PlOT2BorKfqUKBotKmyV1WRmDhbK2HgAKyjbFYhlFZd+ibhkAFJTjFApDxcZKRfn/srKN+pz3f6k4CANFizoWBZvrbYGnXgwA8zHqhe5c8s//kmvMDotILgn++ytSxPnElxDP5RQAA5TSSyDnk3wvpfQi0zbvAhilez5aWSYQCOqPGLMCAEA63SBSK9MadQ+cSbcOPTgR2RUEggZA8ewBACilrQBGMsauppSOAJBjjHVDrsDzIQDLKKWdAFoBWFbNEggE4SLGrEAQPULkCgQNBKX0NMgXxQyldD7keuaHAzgfcrnN2ZTSHwCYAOBsxphT+VuBQBAyYswKmo50S3SWBY8IkSsQNBCMsTsB3GmzrgJ5hrYgxth5HJPJ5rHtCIYQY1YQKelWa1/uMKFBjCICgUDQmJTLkuFR63YCgaC5yGSCizeSdAvHAbOBHS/uCJHbpOSLZcfnAoEgPIIQq0LwCgTNRTotUiDXGyFym5AlT27EObe8gJ5+uXx8T38B59zyApY8uTHajgkETU5YolSIXYEg3rRkwhGwqXRMXaU8EeMYwPXqUUovhlxycDuAQwB8kTHWHIlNm4x8sYwV67Zjw45+nH/7GlwxZxouve8VbNjRjxXrtuOsow5EVvyaFAgCpx4itFyWhHdXIAiYllRCy29bTzKZhJYrVxAOrpFcSul+AL4L4OuMsR8AGAHg1LA7JvBHNp3E4rkzMHlMDht29GP+0uexYUc/Jo/JYfHcGULgCgQBU+8oq4jqCgSNTaxtC3HPlesRHrtCP4AC5CTVADASIo9frOnMZXDFnGmGZVfMmYbOXCaiHgkEzUmUYlMIXYFAIHDG1a7AGNul2BWWU0q3AngLwHr9Nm1t2VhXrUomE2hvz0XdjcBwO58dewbx/b8yw7Lv/5Xh5vOOwpiR8fPRNNP700znInAmDiJT2BcEAkFkNEC+XFeRSymdBeBiAEcwxkqU0v8FcBmAb6vb9PXF257b3p7Dzp39UXcjMJzOJ18s45xbXtAsCqond333Hsz/3TNYeubs2FkWmun9Uc+lq2uU+8aChiQO4laP2h8hdgUCgcAIj11hPIAexlhJeb4VculBQQzJppM4YepYzYM7ZewIzaN7wtSxsRO4AkEjETeBqyfOfRMIBIIo4Mmu8CCATykR3J0ApgO4KMQ+CWpk4TGTDFkUOnOZWEZwBYJGohFEpLAvCATh05JOYjBGuedT6RRKxZL7hnoyWaAQwF34mFsWeDy5ZQAX1KEvggAxC1o3gZsvlg3bmJ8LBMOZRhC4KkLoCgTNiS8x64dMK1BojlLAohiEQBSPEAgEAoGgWUkPX4epELnDHHPxiPXb9+L829doxSNEOWDBcKeRorgqjdhngSCOtKbieVckVpXQYlz9TIjcYY4oHiEQ2NPIYrGR+y4QDHeS4tobCELkCkTxCIHAgmYQic1wDgJBI9GSil5WkSgiqzGN5kb/bggip6e/gEvve8Ww7NL7XtE8ugLBcKOZxGEznYtAIKgTTVLeV4jcYU6+WNY8uJPH5HDrOUdq1oXzb18jPLmCYUczisJmPCeBQBAzYhjNFSJ3mCOKRwgEAoFAMAzJZKPuQejEaHqeICpE8QiBQKaZI54if65AIAidmBWHECJXAMB78QhB/aGUJgDcC+AZABkABwM4jzGW121zLoDzAaiZvH/PGFtW5642JM0scFWE0K0fYrw2Hq2pBAZKlai7IQgQIXIFgsbiKcbYTwCAUno3gFMB3GLaZh5jbGO9OyYQCKoQ4zViMokkChUxtwTpVqDosYqZ38pnMYrmCpErEDQIjLEKAPWCmQJwAABmsenXKKXbAOQAXMsY66lfLxuT4RDFVRHR3Pogxmu0tCQTGCxHF5XNpJMo+Ji4XbfSvcMEMfFMIGgwKKUnArgPwH2MsedMqx8HcCVj7CoAzwH4U73712gMJ4GrMhzPOSrEeG1eMjHIiasSqwpoQGwyLcTnHRIIBFwwxh5ijH0CwGRK6VdN6zYwxrqVp48COI5SKgzWAkFEiPEaDzLJxpU7oQpYtwwLteTLjYHQbdx3XSAYZlBKD6WUnqRbtAHAQZTSTkrpaGWbnyq3RgHgEAAbGWPCkGbDcI5oDudzrwdivAqiJJKqZ1ZE3I+YxbcFAoEDgwC+SCmdDSANYBqAbwC4BEAPgEUAtgH4DaV0A4DDASyIqK+xR4g84c8NGTFeQyKVIChVxPgVuEMkqfYPSnf37lh/2trbc9i5sz/qbgSGOJ/4op5LV9eoWCuH/mIAA7/BESJXRohcIJcmsX4RohyvvOPETnSWLPYvmiaEmffV71OqDG1bNiyXDNuq2+n3VSeeqdkVCuUKCsqyQWV77bmSOmygVEF/Yeh/+a/c5kCxom03qEwqK5QqGCzJ/w8Wyoa21IlnxWIZxWJF+1//t1AYOr9CQZ5wpk48K+smrukno/H8DwCSOcOBXXaFQt56ubbeR4YFMwFnW8g/fSXXmHWN5FJKJwF4BMBmZdFoAGsYY+f67ZxAIBBEiRC4Q4horkAgcMRvKjE9EaUV47Er7AbwFcbYCgCglF4OYEWYnRIIBIKwEAK3GiF0Bc1CKkkso8cC+MuVG+jx6y90XSeeMcZ26ARuC4D/YIz9K/SeCQQCgUAgEARIVFkW0mnr42YyMZj/75ZhIUjSLXWdjOZ14tl8ALeZF7a1ZUFibGlKJhNob89F3Y3AaIbz6S+UkMvIH79kMoFMLqM9b2Sa4b1pZkQU1x4RzRUIBLYEYVnQU6eorldV8TkAnzUv7OtzMS1HTDNNbAIa/3yWPLkRK9Ztx+K5M9CZy6CcSmL+757BCVPHYuExk6LuXk3oJp5F3RWBQCAQ1IGWVFKbfOZGOp1EsVjW/jqRTCcNk8+ajjoIXe44OaX0eMh1uIvhdUfQ7OSLZaxYtx0bdvTj/NvXYP32vVhww7PYsKMfK9ZtR76ZB7QgUkQU1x3xGgkEQC4OFgIfxK7qGQ8h2xe8vJNfAbA4rI4IhgfZdBKL587A5DE5bNjRj/lLn8f67j2YPCaHxXNnIJsWxX4EAoFAIKgVTwUheHy5tVQ/cyMkscstchlj8xlj2wPvgWDY0ZnL4Io50wzLrpgzDZ25TEQ9EjQ7IkLJj3itBIImJh2iUA0CVewGJHgbMyYvaGh6+gu49L5XDMsuve8V9PQXIuqRQCAQCAQCV8KM5prRC16foleIXEFdyRfLOP/2Ndiwox+Tx+Rw6zlHYkrXSM2jKzy5gqARkUnviNdM0Oy0JPzJn5aUkE2R4UPwindLUFey6SROmDpW8+BOGTsCN593FCaPyeGEqWOFJ1fQtJQqEtdDIBhupBIidZ0bdpPKAp1sxpsvt57R3BppwKl4gkZn4TGTcNZRB2qCdszIFiw9c7YQuILAiToi6Ue06veJ8uIv8uYKBN5oySQxWKj9bmQqnUKpWPK9XjCEiOQKIsEsaIXAFTQTQUVlRXRXIOAj5dN+0OxYZlgIYvJZg0RzxadCIBA0JVFEccMSpVGJ3agj4QKBQFALQuQKBAJBjdRLhIrIrqDRSDWw5aW1ASeZ1ezR5fXlAg0RzW28d1AgEAhcqGcEMgrRWc9jimiuQCBoVITIFQgEAh9EHVWN+vgCgV/SyfhIj0wIffGbZiyTacBcADGP5sbnkyYQCAQBUI/IY5zEZT36IqK5AoGRljpNlk6GdRynyWdeLAtArIWuELkCgUDggTgJXJU49kkgEMQDywwLw4QGjI0LBMMTSmkCwL0AngGQAXAwgPMYY3ndNq0ArgLwNoBDACxijK2LoLuREHbEMc5islSRQs2rK/LmekOMV0EmnUSBo4pnJpNAoVDxfZxY5M3NtAKFgWj7YIGI5AoEjcVTjLEfMcb+G0AOwKmm9RcB2MQY+ymAXwD4fZ3717TEWeCqNEIfhxlivAoaE6+WBSCWtgUhcgWCBoExVmGM/QQAKKUpAAcAYKbNTgLwlLL9iwBmUkpH17WjERFmFLeRxGOYfRXeXH7EeBWopG18tXbL7dCnB3NKFcadRiyIohBmYiZ0hcgVCBoMSumJAO4DcB9j7DnT6n0A7NY936UsE/ikkQSuSiP2uVkR47XxaU0FY9NJpxPK3wap8OknmgvESugKkSsQNBiMsYcYY58AMJlS+lXT6ncBjNI9H60sa2rCijA2slgMq+8imusNMV4bA99pv0IqGFFzUQcTdZ98FhOhK0SuQNAgUEoPpZSepFu0AcBBlNJO3S3O+wG8X9n+cACrGWO76txVgWDYI8aroCnwG80FZKEbsdjl+qlAKaUA5gPIAzgOwOWMsX+H2TGBQFDFIIAvUkpnA0gDmAbgGwAuAdADYBGAXwK4ilL63wCmAPhiRH1teBo5iqsSdsYFgSNivAriT7oVKIacFSHCzAuuIpdSmgTwfwA+zRirUEpvAhBxrgqBYPjBGHsd1bOzAeDbum3yAC6oW6diQBi3z5tB4KqEIXRFOjF3xHgNhlQigVLFf3qt4YI5jVgs0orpUSO6dRa7PJHcowAQAF+nlOYA7ABwfai9EggEgohoJoGrIiK6gmYllSQoCZ94uGSyQCHvvh1XW/WN6vKI3ImQPUPzGWN9lNKbARQA3Khu0NaWBSHx/QJNJhNob89F3Y3AEOcTX5rpXBqBoKO4zShwVYIWuiKaKxAM0ZJKYrDkXvjBjUwmhULBGIFNppMoWxSV8BqtJekWSMXB6hU8loWgha5KyIKXR+TuAvAqY6xPef4vAMdDJ3L7+gI68ZBob89h587+qLsRGOJ84ot6Ll1do9w3FggEAkGsaE0lMFCytke0phMYKEZrnYidDaFWQrYx8GRXeAbAGMWbC8iRXVF2UCAQRIqI4non6HMU6cQEgmFELZkWXNtuNT4CwlXkMsZ6AHwHwNWU0ssAdEEuPzisyJtuFZifCwSCxmU4CFyV4XSuAkG9acn4K/SQyQSf0dVTrt0wqp/Vgln0+hS/XK8AY+wuAHd5br1JWPLkRqxYtx2L585AZy6Dnv4Czr99DU6YOhYLj5kUdfcEAkEDwDs5JiV8rgKBJckkEXcPHOCxMtj6cnkJ0pvr6/jehK4oBuFCvljGinXbsWFHP86/fQ3Wb9+L829fgw07+rFi3XYR0RUIIiDIC12Ykc1SWdIeYe7juV8BnrMQHQJBOARd9cwV3mhumLaFgBEi14VsOonFc2dg8pgcNuzox/ylz2PDjn5MHpPD4rkzkG2UGtQCgaCKsARuUCI1TLErbAuCuBKHuxk5B/sATwlg3jLB6UbVEA0idIXI5aAzl8EVc6YZll0xZxo6c5mIeiQQDF/iHDkMS5SGHdmtlTi/JwJBJhGdkMzYiNigxK2faC9Jt9iv9OLNbQChK0QuBz39BVx63yuGZZfe9wp6+gsR9UggENRKkJHMeonQoI8jormC4UQmGZ3kUUVtOu2vD0mdKPYibOtueYgZQuS6kC+WNQ/u5DE53HrOkZp14fzb1whPrkDQgAQtcOuNELoCgTstNqI2SrHLQybjX5jWXdTGPJob73c6BmTTSZwwdazmwZ0ydoTm0T1h6ljhyRUI6kicbotHbSGI+vhm4vTeCAT1oKWBr/+BWRYAWejGVOwO7zg2JwuPmYSzjjpQE7SduQyWnjlbCFyBoAEJInIZJ3FZKks1T9QJuuSvQNAsOFVAaxR8VUnjKfVrJur0YhaISC4nZkErBK5AUF/iEimMk8BViUuf4vIeCQQ8tCSaQwLFyncbs4huc7zDTY7Z99tfaKK61QJBHak1ihsXMWlFrX0T3lxBs1DvFGQZznRhru1YpC3zI2B593G0LAD+q6DFyL4gRG7MWfLkRpxzywtaJoee/gJOW/w0ljy5sWpbUXpYIAiPOAtclUboo0Ag8IffDAuREQOxK0RujLGrtra+e09VtTUrMXzOLS9YiuEg++f0XCAIiiBug9cSqWwk8VhLX4OI5grLwvCk3p7uII/Hk22hNRXe+dWjIISdKA4tmqsnQrErRG6Msau2NqVrpKHaWhSlh6MQ1QJBFDSSwFVpxD4LBI1OS6pJ5+oEIXSBSMSuELkxx6ra2i/PmGmotlbv0sNRiGqBoBb8RigbWSz67bvw5goEtdGS4bvmOkVwvebKNUdqY21nUMVuHQRvjF8FAWBdbe3C5atx3enTDUJXFcPzlz6vLQur9LAqqlVhqx4zLFEtkKGUHgzgJwBWAjgAwA7G2I9M25wL4HwAau6X3zPGltWzn0FT6+1vIdq8U2tKsXJZQrLOk3/ixnAdr41MSyqBwQZPF+aEXSoxkm6BVBx03tlPSjEerIRugGnIRCQ3xthVW1vfvaeq2lq9Sw9bRZjDEtUCjU4AtzHGfs4YuxDAPErpkRbbzWOMHa88xAXTJ40cxVVphnNoYJpivDbSj5VUHVKCtXooy9uiZF3IaCV9ayvtaybIaK2rNxcIzrbghj7Sa354RERyY4xabW3Fuu1YPHcGOnMZLJ47AxfcsRYfntJp8OTqxfAVc6bh0vte0ewEfgpX5Itlwz7m53aiWu2nIHgYY8+aFiUA7LXY9GuU0m0AcgCuZYz1hN65mBIXm0Kx7C06lA6w7KjfYhGiQERtiPEqCAp9BDaZTqIcpSUwrIguLx6FLtc3KaX0aUrpY8rjEV8dE/hi4TGTsPTM2Zpw7MxlcOf578PCYyZp2wRdethtUpldhFkV1cKTGz6U0lMAPMQYe9W06nEAVzLGrgLwHIA/1b1zARLFTP2gBG6xXNEe9dzXiigiuiLLwhDDZbwKascqVy4vPL5cp+gvVzQXqF9ENwB4X80HdbdTPhpqjwRVmEVqzsKQbiWGl5452yCGeeCZVBa0qBZ4g1L6YQAfBvBN8zrG2AbGWLfy9FEAx1FKh+Ub4ieKG4QYDFKcBtmen3MTfubaEeO18WjlKO7QElABiIalQYQur13hcErpdwBkATzLGLs/xD4JfBJE6WHeSWULj5mEs446UHuuimohcMOFUnoSgA8CuBDA/pTSiQAYgBJjbBel9KcAvs8YKwE4BMBGxlhDhtYbLRIYpLB1aj9IK0PYDPcJaMNpvApqI51Oolinu6B2E9AAzkloKqrQjdK+4AKvyL2SMfZv5RfmPyiluxlj/wizY4LoqGemBgE/yqSV5ZBva/4dwAgA1wE4BUAPgEUAtgH4DaV0A4DDASyIprfRUu8obtgC13wsv0LXjz9XeHP9Icbr8KAlncRgSOI0k0mhULAWoypOgpVnfSBE7dN1gEiSty92SukiAHnG2A/VZYVCSSIkvl+CyWQC5TpehMIm7PPZsWcQC254Fuu792jLpnSNxM3nHYUxI2XPzjWPvoYH1r6jLVP3+eT0ffGNjxzi6XjN9P6o55JOxzt81V/0OPAjoJZIrleR61fg1lPcWuFX7HoVurWI3EaI5ObSMb6AIfrxyjsW7cad1fgyjx3zvvp9SpWhbcuG5ZLttuqyQeU4hYosRAvqc+XvYMX0XEkhNqD87S9UtP8HSnKbA0XjtoPFMgrq/yX5OIOFsmGbgiKEi9rfoXMqmtYVCkPr9CJXL1b1k8/MItbtudtyAPzRXD11FLr5B77JNWZdI7mU0vcAOJYx9ntl0SEA7tJv09cXXE6zMGhvz2Hnzv6ouxEYYZ5PvljGObe8UJWpYX33Hsz/3TNYeuZsAMB9a7bKdobfPWPI5nDfmgo+d/h+nmwLzfT+qOfS1TUq6q40NPUUuH6JWuCqfaiHfaGWaO5wtywI+EglSEN7wDOphCZ0mwFPtgWVGNoXeL4ddwE4iVL6fUrpzwFsBvDHcLsliAqeSWX1rrAmEISJnyhuHASuip++iPy5AgE/PBPRVHhL+zrlyq0lw4IVdhkV3PLscmdbMJNujc3ENNdILmNsC4BT69AXQUzgmVQWtG/XLS+vQBAGjS5wVfxEdP3mzxUI4kYqSWL3w60lk9QsC3rCmGBm9t0G6cP1FdFV0QvdiKK7jTNNt8kx55aNOtesW6aGICusXfPoa455eQXDizhbFeIocFXC7lstr22jZcoQCILCXPXMKxmLlKGAXBTCC36juYGhRnfrHOEVIjcGuBVfiBtBFoPIF8t4YO07jnl5BYIw8Br5ibPAVfHax7hFvwTDh3qnwsskZFGYUY6b8XH81lS4dz7SLsK1boLUhG/bgh16wRuy6BUiN2J4ii/EjSCLQWTTSdx83lHC3yuoGS+RxmYUuCphCt1GnhgkiI5abTGpRHhSpSXEtutJLdXOeMRz4EJXj1n0BiiAPacQs6K7e3esv/niPnu/p7+gCVsVVeRZeVzjcj5B+Wjb23N4bn23wd976zlHYsrYEYH0s57osivE2uwYdUoiO+plVfAi7AKpNuZRHAaRl9ZLpMyLCGnGdGIihZgztaYQA7ynETNvr6YGs0ohpt/enEIM8JZGzCqFmP65Po2YPoUYgEjTiJnXWT23W8azTo9vj26A5O/5T64x2xw/YRocdRKXnkYovhBEhTVAzssblL9XMDyJo8AtVSTtUc99Vbz0XURzBY1CXH8oBQ1PhgWvvlwgGMtDqFHdgBEiNwYEOYmr0cgXy1hww7OB+HsFgiDxK3BrFadBttdINguBIA60eEoXVpuEckojpkc/+cxJpPJYFpzwsn2jCF0hciMmyElcjUg2ncQnp+8biL9X0Nj4tSqEEcX1lXs2YHEbVPu851KPaK7IsiCoF/VMj9fi8TrlNsEsbLwIZSdIuiX2YleI3IgJchJXo/KNjxyCpWfO1uwZal7ehcdMirZjAgEn9byFL+wCguFA1DmcvRSAUMm47MOTRixoAezHnuB1nziL3WjyUQgM8BRfaHaC8vcKBHaEEcWNSnCqx+WdBMZbLEIUiBAIaqcllcRgqawVhGhJJbTJZ0GTTCcNE9B4C0G4beenoIQqdOMwMU1FRHJjAq/Ii1vRiLj1R9CY1MOqwEMjCFy/fQjanyssC4LhQC7gErt2WEVw9ZPPeH25VvidbOZ3PzWyG4forhC5DYRaNGLHHvlXUtRFIxqtiIVg+MITxW00gasStNAVBSIEjUIQqfZ48WNfiDs8IrbWbAxRC97me9ealHyxjL+xbmzY0Y8FNzyL9dv3YuHy1ZEVjWjEIhaC5oJX3AUt2uIkcFWC7hPvaxbH10IwvAmzcEQY8GZYcMKcSizoQhBBVVrTC956id7G+jQMY5Y9uxmSBEzoyGJ99x7MX/o83uzJoz2b8lUZrFabQTad1CbIiUplglqIw+1r7gwEMRZ1vH2LQ1qxOLznAoEfwi7tC/BNPqt3id8wjmcWvWGIYCFyGwA1arqpN4+y6UI2IpPyLCiDshk0ahELwfAhSJtCLQK3VJY8PXwfJ0ChK2wLAoE9rTVGYHmzKNj5ct0IOprrZbugCEIAC5FrgV2UM6pJVmrUdEJHFm/3DRjWJRPEUz+CtBkM5yIWgmipd0TVV9WyGkRrTfs2wGsjEDQLakEIt1y56nZOacRqSR/mp/qZHi9Ct95itxaEyDVhF+X8yvJVkU6yyqaTVVHc8W2t2NSb91Q0IiibwXAvYiEIhjBvWwcVxfUq4mqNxgbRHk+fo47mCsuCICoySjo99W9LgD5eNVduS0q+lrZkorPueYnmuq2z2rYRxG78e1hHzFHOK+ZMw6X3vYINO/rxVpKgWJaqlq9Yt92Q4zbMvu0tGIVjMkEwoSPruWiEajOYv/R5bRmPzSBfLGvHyaaTOO7gMQCAxXNnoDOXweK5M3D+7WuGTRGLekMpPRjATwCsBHAAgB2MsR+ZtmkFcBWAtwEcAmARY2xdvfsaJkFFDoMWuGHf3lfb581jW6pIrrPPefPnBnGs4YYYr/Ejk0iiULEPwGSSCRQi8Kyn0wkUixXTsiSKLsEicy5bc85c3v1419ltD8BzTt16wf3tRinNUkrXUEqvCrNDUeIU5bx5wRGRTbJSo6Y780VM6szi/q8di8ljctjUm0eCAGcddaDlPvpoqv65H5uBVYT78dd34LiDO0WlsvrRCeA2xtjPGWMXAphHKT3StM1FADYxxn4K4BcAfl/nPsaCIARnnASu32MF8YNAeHN9I8ZrHQmyiElLzNKF+fXlAvWpeKbuE8fIrpd38icAXgirI3HBbjLVQWNHhDrJysnvqy/9+9szZmLqvqM0Mf4x2lUlspc8uREnX/9vLFi2Ej39BfT0F7Bg2UqcfP0zuO6fGzzbDJx8vI+/3lPVV0E4MMaeZYzdrVuUALDXtNlJAJ5Stn8RwExK6eg6dbFhCCrDQNDWhCiOG4dsC83IcByvcY3mt/i8WxF2blwrD65XX65ZWPJ6c90EaS0FJOIkeLneQUrpWQCeALAh3O5Ej12U843te0ObZGXnA77un29o2yw8ZpJmCwCGoqbmKG5PfwEPs27szBexqTeP8/64Cuf9cRU29eaxM1/C39dvx3EHd2pR6CljR2iC2c5mINKFxQ9K6SkAHmKMvWpatQ+A3brnu5RlscOPJ7Nek5x4jhOHCCdPH+L0mpkZLr7cZhivw5mgq545TT4LA79ZFWoVq3rBG5XodT0qpfRQANMYY5dSSmdYbdPWlgUh8fwFBwDJZALt7TnX7foLJVxw00ps2NGPKV0j8cszZuLC5auxvnsPzrr5BRTKlarlF9yxFnee/z7kPN5C0B/z7+t7sGFHPy64Y63c9h1rsWFHP97eOYCzP3AQDuzIYceeQVxwx1p8cvq++ObHKNrbc7jp0dfwwNp3cPN5R2HMyBZtm49O2xePvvqu3IYuG8OkMTnc9qWjMWZkC75ZKGl9bm/P4S9fPcbxHNrbc7h2/mycdO0T2rJr58/GQfuO8nXeenjfn0agHudCKf0wgA9DvtVp5l0A+jdltLJs2OAm/Nwil40icFVKZcn1Vq2bZ9bNm8tzDIE1Yrzyk0qQWGfraE0lMFCqoDVFMFDy3s+WVAKDJf47J3pfbiaTQKFQUf5PoVCw98DyenMBPg+uV5+uUztWhOnnJZLk/EZRSr8HIAmgAOAEABkAf2aMXa1u0929O76fSsgCbefOfq5tlzy5ESvWbdeipj39BZx/+xp0ZFPozZeqlp8wdWzNHlS1rQ07hvqYVia6TR6TM0x0mzxGFqR9fXmcc8sL2jLzNpedOBVf+OMqw3FuPedITBk7IrA+qpHcWi0bXt6fuKOeS1fXqFAUAaX0JAAfBPBdAPsDmAiAASgxxnZRSi8BUGGM/YxSejiAXzPGPmhup7/oMvDrgNcoXlAVzpxEbpgCt1Thu7j5rdjEI0KdhK7bBDRekev1lnUyBuI5lw4nStMs49XLWLUbQ1bjxmos6vc376OOIX1/rLbXjzV12aByLHXimTrBTP07WDE9V8TogPK3v2B8rorcgeLQ9oOKsCzohOxgSV42qEwcV9stKNvqJ5epk8+My4b+V0Wu/L9RGJqFopXIdRKTPEIzTpPLdt12NteYdRW5eiillwMYyRj7L/3yZhK5gDGLgP653fIgWL99ryHbweK5M3DlI+stReVB49qxc2e/rfBcNGcaLr7nZWzqzRuOMaEji+vnzdREKe/55ItlR0G99MzZNb0OQuTyoUxaeRzAc8qiEQCuA3AogB7G2CJKaRbybO2tAKYAuMJqtnYjXTRVghCgtUZxvafyqs3v6lXwuglRNwEahND148uMWuiGIXKH63ith8jV9ylOIhdAldB1E7nAkJDVZ1goWohgvciVnw+JTisBGobQ9bJdmAQucimlpwG4AHIk9zrG2K3qumYTufXGTqxe8tEp+Mrta7RlaiRWfz5mcXzjmbNw+QMMG3tkgTu+rRUANNvCxM4sli04Asue3WwZsbaLTNtFuIOIZMf9/fFC2JHcoGiki6ZKrSK3ngK3VnFrxovYDVPoCpEbDVGPV4B/zAqRG6zINf8fZjSXZ73fbYMmlEiuHULk+scpSqpaFlR4I7nHTu7AfS+9i9GtKVw/byYA4Mu3rcaugSI+N2sczjrqQMfIrNmCEHYkO87vj1eEyOUjDKtCmDYFXoEbtLg1wyt2axG6UURzhch1JurxCoQjcoHqcTlcRC5QbVkIWuQC4QvdWvapBV6RG69kcMMUNT3Y4rkzML6tFVefcpjBk2tO89VfKCFfLOMry1dbpgJ7YkMvlp97JG4+6wh05jLozGVw81lH4J4vH42Fx0xyzJZw7OQOnH/7Gi3TwxbF+7vkyY2a0FURWRUEfohiRn3YArdUqYQucL0cp5aJcVGkFBsuWRaGM34mLvr9QeXX114PnHLwptPe+m3OmeulNG8t6+32iVPqMJX4fhKGAWrqsNNnjcPSM2cDAM655QXc99I7OPPIAwxpvo6d3IF0kuDYyR3IZVLIF8vYmS+iPZu2TAXWmcsYRGg2nTQ8t8oH/INPTMUTG3o1Mb1oxWs4/Q/PaZXd9IJXIKgXUWY74BW49aZWoVvLDPY4ZZYQCPxiV9pXe66I0aBy5Xot76vPl6v/P+MxnZld3tyw8uSq+8ZF8AqRGxHmAgtv9w1o1oMV67bjvPdNwNIzZ6Mzl0G+WMYTG3pRLEt4YkMv1r2zW6mAVkJbNqWJVy8Vx6zyAf/wwXVYNGeaFuG9c/VWFMsS0kmCSz46BRfd9ZLWP6uiEQJBHPEbxY2rwPVybL9Ct9ZobpzTQAmGN5mEvzuQaq5cXtGbSali2f14XgtAGI7DEc2tRejWKlTNuXLrLX6FyI0IngILqng1b3vStU9o2y45Y2ZVxFaPVSU1tUywldXhkvtewWUnTjXsUyxL+Ipue1EAQuCXMG5LhxFZdGuzFntCuSxZPvzA048oXh+BoNlpTck2ida0MfLb4uHaaFUUgsey4DWa6wSP4AxDmNqJ36DFsBC5EWJXQliN3urJppOuZYXN+1z3zw2WldSWPbvZ4APWWx2OndyBHz1UlcHG9pgCQZjUGhGsNSeu9X7exC2vmK1F9PoV3HGK5gpfriBM/Jb2jRI7y4KZWqK5dtvbbVdvC0Kt4rfx3vWYYxU5tcOuhPAvH38d59zyArb05bXtFixbif+8fXXVtqqANZcG3tKXxy3Pv6XZIdZv32uwQ5x11IGG/LaduQwWz52heXJVAZw2Gf+DKmUsEESJX5sCr5isNULrpw2nvoXlzxUI4kSjVOWzmnxWi2XBirCErrptHPy2PAiRGxD5YtkgNPPFshY5tZqo5WQZWP7CFmzY0Y/T//Acnt+8EwuXr8am3jx25ktoz6Zw/9eONWRb6OkvGPy967fvxUV3vaT5afV2iHSSYNGcaVqmBH3/OnMZLcJ79SmH4cpH1mttnDZzP8MxhSdXEAdqyYvrtT0egVursK21Xb9C1w7HSLiIvAoEnuCdfGZnWXCagGaO5toRlNBVt4+74BUiNwCWPLkRZ9+8Eg+92o0NO/rx5dtWY/7S53HGjc/ZTtTKppO2loHTZuyvpRA7//Y1eLMnDzVLyujWNA7oyFZlUrDz91572uGG4xbLEi6575WqyK7av4XHTMLSM2djXFtW698dX/gPXHLCVMMxhSdX4JWwyvh6xWseT3kfPoEbNmEJ3Xq/1nYIy4IgaKKM7vJMPrPy5eqpJcJrJz7dhG4zpRATxSBqRF/MYUJHFuWKpFUXA4ADO1rxu3mzuEvpqmLz5W1yBgU9EzuzWHLGTK0YhHlfntLAdgUm7Hy2YZYyVhHFIOpPFMnlgxa5fqO4XkWum8CNSpi5FVCwyxVqd9H3WyCi1gprZqIoDCGKQbhTazEIgK/qmXl//T5WxSDM+wRZEAKQize4FYQAvBeF0G/rt/oZ4FzqVzt/m0INVoUiePbzQ9DFInqWfV4Ug6gH+swHm3rzBoELAPrro5V9wSwYlz27GQuWrcQVD79WdaxLTzjEIEb1+1r5e79+54tVdoii6UvGbSKZuX8igitoZJpF4PIc267v9Y7mCgRhEOSPIbtcuSpq2jBzGjE1w0IY6C0LvBPQAGvbgp+IrrpfUJHZMDMoOCFEbgBYZUlQebtvAF+6dZXBHvAw67b0tOaLZTzMurGpN49NvXmYvekX3LFGm4ym39/O36v6aa8+5TBMGTsCi+ZMExPJBJFQT6uCXRTXj03BCS/nVKpInh5h9MHQH49Ct5ZMC8KyIPCCU+TfSyUznm3NYrYeWPly3SwLTtSaTsxN6ALhTzTjTScmsitERE9/Ad+992XDsvFtrRjf1goA2LxzQPPJTujIoiIBNzy9qaqdbDqJ354xE+1Z+Q1US1yPbElqzy/881ps7u3XIsKqfcDO33vmkeMxri2LfLGMS+57xbZUsJhIJmgk6jHpySmKy+eN9S5a/ezr1Je6lBoWolQQMV4tMX4LQtQCT1EIgM+Da96GZxKakzDkEbpqG3H03TohRG6NqFHUjT15tGfTGN/WigkdWbzdN4AEAcx3VMoVCZt65fRe1/3zjar2OnMZ/GbuTMOyttY0ACBBgB17C/jiUnlC20OvduOsm1diyZMbtQlj5upn571vIgDniW76iWReUqCFRRz6IGhMgori2olDniwHfoVtLe059Sso20KteXMFwwOvgrNZUYtCZBwqpFmlEtNjZ1ngwY/Q5RW7aluNIHiFyK0RvXhcfu6RuPWcI/GhgzuRThIcPbED+49uNWz/dt8AkkTOcvD46z1aBTIVK29tMkFwYHsrKhKwe7CMDTv6Mb6tFRVJwps9eS07wrJnN+Psm1dq9oN8sYyzFREMDGVOUD245jLA5ly7TinQwiIOfRBESy0TzoI5vr3Add4vWHHrp32vQjco3CvEiWivwBqnSY1AsNkRwiwIYa585tiPACwLbtFceZk3oQvwR3XNbcZV9AqRGwBm8fjEhl4UyxLuXrsNb/UNVP2yLUvAAe2tWDx3hiFXrZ23Vs2Rq+ftvgG8tXMA7dkUrj7lMADAn1ZtxcaePL5822qs374XX75tNTb25PGnVVs1IW03kSxfLFfl2rVKMRYmceiDIHjq5bEMIopbi8CtF0EK3bhGc4UvVxBXapl85sey4CWay+vPdROjXqO6du3HQfgKkRsQqljUZ1tQMxlYXTDKFQk9/UWDiANgaSk4sL0Vey3SgqjH+8af1+KGp9/E6Fb5g7SpN4/5S5/Hpl55kpq63K3/drl2F8+dUZesCn76IKwNAj8EFQ327bktS4ZHvY5r1xeBoFmwivz6iQZrGRdSRlHrh1osC07wWBicikTwRHVrEbvmYwU1mcwLQuSGgFW2BXM0d+uuQUsRZ44KZ9NJJBIEFcna6/Tu7kG82ZPH46/34FenTdcmu6mMb2vF9fNmcolUq367pRgLGi99ENaG5iNoq4IXIeg1isvbtlnQWkaQObbx0ocgbAteRbSwLAjciHPZXXMasSBocbjuulkWeKO5fm0LKjziUhW7QQlep77UPbsCpTRBKb2fUnoZpfQnlNJbKaXZms6kyenpL+ASU7aFUkVC2saQbxZxekGaTSfxcdqFSZ1ZjB1RLfTKErQ0Ya01fgCt/MD1TjHG2wdhbWgMorYqWBGETYFHjPuN0nptIwih66WfwrIwPImiSEc9CCONWC3RWR782BbchC6vcKyX4A0K3nfiKcbYjxhj/w0gB+DUEPvU0Ki+2jd78pjQkTVEVosVCQe2t2Lc6BbDPm5CcuExk/DLU6drVVbMnDx9X3TkMvjybaurilG83TeAL9+22lb0qcvt/MD1TDHmpQ9xsFcI6kuYUVwrahG4QRO00OU+bsDRXIEgLgSZRkz15bamOSadWfhy9aLYbgJa2qFtK9HrVegCfFFdPY0geF3fEcZYhTH2EwCglKYAHACABdmJRvZVWvW1I5tCOknw85MPxVWfPcywriIBW3YNYlJnlltI5otlXHTXS9iZL+LA9lYc2GEMpD+3uQ+9/QXsGigCACZ0yG1PULZTl5vR3+7PppM4dnIH0kmCYyd32KYYCxPeNGcqcbBX1BNK6X6U0t9RSp+1WX88pXQVpfQx5XFxvftYC35FaRhRXD8Ct9bIrRtu7XsRulFFc4ebZaHZx2zU+C1tXSvmyWc8WPlyrSwLepwitm62BcBe6AYV1dWjF7xxEr5E4iyJTSk9EcA3ATzDGPuBfl2hUJKIz9Lf1zz6Gh5Y+w5uPu8ojBnZgh17BrHghmfxyen74hsfOcRXm2aSyQTKPr6U+wsl5HQfBvNzq75//vf/Rm9/Ab39RUwak0NFkrCpJ6/t05FLoy2bxm1fOtr1fPXHu+bR13Dfmq2QAGzc0a+1vXughN7+IqZ0jcQJ07rwt5ffxR+/+F6t7Xm/ewafnrG/1rbaZn+hhNMWP4313XswpWskfnnGTFy4fLX2/M7z36dtl3P59Vcr5vfH7XVXUV+79d17tGVTukZq70c9+m5GPZe0ubRcAFBKTwcwCOAHjLH/sFh/PAAwxh5za6u/yDnwa8RrVTDH9TZtWQkuq7bCErhRRS/t/I12eUqtBIGVCLCcuGPRpl3qJzffpZc8qvW6RZ5L+7yAuRDUmK3XeHWDdzy7/Rg0Yx7D5v3N++jHrb5P6n4lw7JK1bJB5XiFihxYKqjPlb+DFeNzABhU7qSqd1T7C8bnAyW5/YFixbA9AAwqAaxCSV03FNAaLOj+V9YXdAGvoin4VSxWbNfZLSsUrPVPwWZCu55S0X0bv5RrCGhu+e2pXGOWW+SqUEpvAvA0Y+zX6rLu7t2+BqCaPku9zXzFnGm49L5XtOf64ga10N6ew86d/Z72WfLkRqxYtx2L585AZy6Dnv4Czr99DU6YOhYLj5nk2PcJHVlIkLC5d8g6ML6tFckEwabePCZ1ZnHTgiMM6bvM52l1/IXLV2NMLo1dgxVcd/p0ZNNJ7Ra/vl9qW0ue3Ii/sW4sOWOm5TmozzfsGHpt9Lf79X2y6mNQ+Hl/zK//EQeMxj1r39Equl19ymG46K6XtHOtF+q5dHWNCuuieTyAqxwumGcBeAXAaADXM8Y2W7VTj4tmkKV8vQhcu7ZqEbm1ClyveWp5I1BehG7QIhfwJ3S9Fguoh9ANS+QCwYzZ4SZyzW3UW+QC1ULXq8jV72MWufI6eZmVyAXsha5e5JrXWT3X2qtB6KqEKXi9svnaz3CNWZ6JZ4dSSk/SLdoA4CC/HdMTV18lz6Qmp75fP28mfnay0aZw1WcPw/XzZmLymBw+RruqJpfxHP/Nnjx68yUsO+8odOYyyKaTVQUdzHlv3+zJO56D1e3+O1ZtccxaEAd7id7acPUph2HlW7tQLEtIJwmOOKANF9310nCchPYygB8zxq4CsBzAw5TShsigEnSFsKplEQjcUqWiPbzCu6+XPLe12BbCfn+GMQ07ZpuRWiah8fhy/VgWzJi9uTy2BcA+h66bfUFPHPLeesU1kkspPRjAzwGsBJAGMA3ANxhj29RtvEZyzVHBtVt34Qt/XKU9v/WcIzFl7AgvTTriJ1LoFOXUez7Xb9+L+Uuf157fes6R6MyluSOkXo4/qTOL354xEweNa8fOnf2u0dWe/gK+slwuCGFu445VW/DQq90AoOXTBYC21hTasmls6s1bRtePO7gTj7/eUxVh/jjt0oS216ivn/dHRT0W7/sVNlFGci223QbgaMbYm+Z1cYvkxsGqEJTADau6mFN0t5aIrrAsRBfJtdjWcswO90iueT+3SK5+e/226jJzJBdwtyzYRXL1y7xYFuT1/qK58vNgI7pD6/1Fa+sd5Q0skssYe50xdipj7CeMsR8wxubqBa5XzLlN39i+FwuXrzZsU++0VVbwTGqySnf13XtfxpdvW22bIaCW4xd1g5knJ+wdq7YY9lHbuPX5t/A31o1NvXls6s1jfFurlgWib6AESZIwqTNbFaG++pTD8PjrPYYI8xk3Poc3e/J46NVu5IvluueqVcX0cJuEpkIpHUEp7VL+v4RS2qn83wkgA+CdKPsXBPXy4vK05dQfv1FbXpza91q5zNwuT3tWbdnaRUSWBVuGw5j1iltp3zihTjbLcVQX400lxhPN5Sn8wLO9W1U0L5FdPfUs8OCFun6yzLfhX9q2CwtuXqndZv7D52fVPW2VHW75Wu3SXW3syWPXQAkTO7NcGQLsbv1bHf/tvgF86dZVWPfObtecsPliGQ+92m2ZUuzR13bgmlOnoz2b0pa93TeACR1ZTOjI4hPT9sFPP32oYb8r5kzDuLZslUVDX2747b6ByHLVxiHHb9hQSo+D7N/bn1L630q+6nMB/FjZZAOAX1JKvwvglwDOZowNWDYWMkFGcYOGx6bgR+ByH9+i8IMXUVir0OW1LYSJl/e8kfPlNtKYDRKvvuuo4EkjZq58xoNXy4IennRigLttwW4ZIAvdsMSumaCLO3jF88QzK7zYFaxuK6eTBDcvOAIHjR1RNTnKC+bb5Opzr7fDeSfEOU1OO+uoA10nbtntf9zBY/D46zuwYUc/0kmCa087HP/z8GsGWwFgvB1vde4Llq2s2geQU4zdfNYReLtvoMpqMb6tFb39Bc3TanUss0VjfFurQUyrlgg1iupmX6jFrqC2X48JjDyEbVcIirBvfwYlcmudcBakTcF3RNinSOOpDlWL1cCPbSGqCWhhWxbCtCsEQaPZFQDvPxS9ZFjwYlfQbx/25DP5/2AtC0BttgW35YC7hWFou/hMPNvwi5OCsSsEjdVt5evnzcRBigfXPJGKlyBLvKqTmiaZorGTOrOGaKy5BK++72ZR5TS5bOHy1YaJYX9fvx3HTJJz1hbLEhY9sh6XfuyQqovCdz46RRPH5olh2XQSJ76ny7LM74nv6UK+WLa0Wvz6n2/g9D88hw07+mWxOncG0kmiRde39OWr9jPj1VZRK17z6wqaE7+35nna8Spw61XxLMiJY7VYOAQCXoIu7Rv0DyAvk8948uVaRYDdJqA5RY2rJ5q5R3SdlgPuFoah7VKGRyNQd5FrdVv5hw+uM9xW9ipK3LIh9Pv89WH+OpeAKo+renwVNa2XeZ35LwAsnjsD7dkU3uzJa97XVEL+ZZrLJPG7eTMNAtN8gfn6nS9i5eadhnO97p9vaGL/9FnjYI5PpJIEcw7bt8pq0Z5NY2NPHneu3ibbRxIEA8UKvnPvK5qd5NjJHVqEV91vQkfWtspaPUvtOv3gENSXuFgVeAQmj03Bi8ANqyCEU7t+hS7P+xRqcYthYlkQBI/dJMxabBJexC1PEQie6meAdQU0eTmfbcEKv0KXV+wO7ZOKvfCtq10hzNvKTrPr1WwETv3SH1fflrmf6STBHV/4D4xry6Knv4AzbnwegISlZ87WlsmWg06kkwmsWLcdx07uwBMbevHdEw7GT1e8rj1/74Ft+NeG3iqRCKh5dYFNvQNVy3922uE4d+lzBsGtTgz7xp/X4s0eORdvsSxpbY9va0UqSfBmT17JkiBbItSMD6q1YXRrEqNa0lX2g1+eOh3j2rIGi4V+v/ZsGr+ZOwPfuedlR1uFFbXaFeKEsCtEY1XgEad+bApeBW49sM+k4M9u4GZbCDPTQlwsC8KuwEeYYzvoghD6fYLKsACEa1kA+DItAO62BatteNdpx+S0MXghKMsDr12h7p5ctyILtWCVzmvK2BGOIsquP6oQNXuH1WIDl504FT98kGnpuVIJ4NrTZ+DKR9ZrYjiXTqJvoKTtZ24HADJJgoLDF0c6QVDUDdrRrSnc9qWjcd5Nz2HbrkHDuebSCXz9zrXYNVA0TAib0JHF9fNmAoBt4Qg1FdibPdUeXnNKN3PBiYdZt+bB7ekv4Lw/rjKIZLeUcELk1p9mF7l+vLh+BS6PuB208RDb0cIRVbIWn96FblDeXCFywyMuIhdonIIQ+n2cRC7gXvnMsMxHKjH9foM6cVkPoWu1ndtyK8IQvLXArjwxniIXsJ8gVgt+IrlukeUffGIqzr1llbb9b+fOwCJFxKoc0N6KbX0DKOleAVXETujIghBYCkc9+41uMQhWM6kEMQzcVAIw+dIxqiWFfLGMUkWqmgimF5k9/YWqiKr6+pt/JKi4RWLdxLKI5MaPOIhcP7lxw4rihiFwvQpbO5wEb72Ebi3R3KBy5gqRGw8aMVeufnsvIhdwn3wG2Fc/A4KN5gLBC123dXZELXp5RW4kyencJmV5xS6dl+pl1Xtyzf7Zq085zLJq2aI50/DDB9cZjrPokfW46Dhjsbfzjp6ArlEthmXFspxn9vp5M7HIlIrLTJLju7VqoCufLX1+292DJZQqElIJgrJp+2/f/RJ6+gvaDwH9JDB1wt4b2/fikntfNuw3vq0VEzqyrind9FXW1MpsVu/DMKo8NmwJyjtZ64Qtw3OPAteyTQ8Cd7BcCUzgurUXVA7g6tfEdOs4wPfDL8KXKwgSpx+PPP5cJ1+uWv3McDyXCWh6b67TJDSzP9dqIpp5MprVduZ16oMX1cOrf8SRePbKI26z63OKGdoqA8NFd72EIw4YbWjvshOn4hJdRFcv1v7r7pcM2/7ooXXYahGFHShVsOzZza6ZCMqSZBnFHd/Wiv1Ht1jsITOqJYkbPj8LV33WWD64VJGwbbexvc07B3DeH1fhK8tXGyaB6SfsLbh5Jd7syUMNqqQS0KLB5qwSdogsB4J6E8bENTeRbLUNELy45W2fR+iGMhlOZFoQBEgtBSGCivI7iVuefLlWwtdqAlqLx2uhW45e6xy51kLXTch6Fbt6rIRv1AI4ErtCWDjlyd3avdvWmmD2zE4ek9M8uept9i19eZzy+2dRkWSP67nvPRA/emidVTc0rGwFToxqSWFkSxLpZAIfOrgTj63fgbd2WucFTycJrjt9On664nWDfULPfqNakEoQvKWzLpitA1Y2j4mdWfzs04fi2/e+jI/TLi3nL6+txKsdJZPLoKDLrhGEfSUqhrtdoZ4TU6zaCNqmwCsW3cStfnILD25J6u2iUNW2BGfbQa22hSAsC3Hw5Qq7Aj9xyZUrr3e2LNjZG+JkWQD4bAvm/c22BcDadmBnX7Dbvpbt6smLP/5YfO0KYeFkg8imk1XVuvQCd2Jn1hCx/ecbPQYx2JHLYFSL3F65IuH3T29y7c+ITAoTO7OYc2gX9zmkEgQ/P3ka/vlGD97aOYAkAczXALXPC5e/aMhnW3XBShBcaLJXmEvdWuUtXvTpQ7FiXTcIgNNnjUM2nfSU79aLHWXJkxtx2uKnA8lvLGgc/Ew4Cxs/AtcpeluolLWHV9z25Y3q1iOiy4Nzrt/Y6DdBnQg6V25Ux6nFsmAXzbWzLZixSitmF9G1iuqq2/NEbfV2Br9R3qiItci1K3nrFytBd/L0/dCeTUGSgM5cGovnzsCEjiz68iXcsWqLtl02ncSnp++HJBkqg+tEKkFw8Ngcli04Aj/45DRM7coZ1o8dka7aZ/dgCZt3DmDh8jXo2VtEOkFQlqpF4o9PPhRpZfAmiOwB/tFD66ouFm/3DeDie4w+W3OpW6u8xZfc+zIeerUbG3vylnmHg/LWqnaJ9d17Qj2OoD6E6ZnknXBmXO/fi8srcK3wK2ztcBO7ZnjsFkPrvHlz3fYPG+HLFfjFakKmX19uEJYFw7Gcikl48OcCTjlynQtMeBGvZtEbZ/EbW5EbZAUzFStB99zmnRjVksKmXlnQ9fQXkSDAznzRILTyxTL+9UYPeL9jSxUJ2/cWteOa7xj09MvrJnRkceOZszChIwtAFq19AyXsHiyhWJGw36gWw60MALjkrpe06PO+ozJ4u28AW3fZi+4EkTNDmCeB2U3YUzMjTOrMVk3IU/PjesHux4oaXZ/SNbLqOFefcljDWhYE0eAlSsmTTcEJK3EZtLjlbd+rD7haBHt43TheJ7uSywKBV8x3J+sRAebx5VqRs/Cdeonm2k1Cc9ofsBe6XqO6+v38ClY78RulEI6lyHWrYOY1wtdfKBkEnd6a8GZPHoQQg6DbqGQH0Au6Zc9u1iqB8VKRpCohedrM/ZBOEqjXlYs/fBB++OA6vHdCG1IJgO5jzCe7bfcgihW54tiHDuowrJu2z0h07y5gdGsK+uuUuYv7jmrBJOV89JPAnCaKnfieLvzUlBnCbHXgwe3HSmcug/dOMp7Xdz46BRfd9ZKwLDQpQVgVao3iOh3TLYprJ3DtKJQrvh627XEI3VpsC2FFc4VlQRAXrMSykw++xabCGmATufURza06poNtwUroeo3qOolddd8wxCmPEA5SLMdS5Nr5Z/1EElXPZ75YxglTx2JCRxaSBDy6rptb0OWLZfyNdePtvgFDYQYnkgTYZ2QGnbkMTpg6FpM6s7j6lMOw8q1dhklu37r7ZWzY0Y+7176DUgVYv916EtnlJ07FP9/oNSx78NVulCRg94Cxgoi5iwlC8OXbVuOOVVuqSt3alcM9fda4qqi32ergBs+PlS19edyx8m3Dfl+/80VhWRBo8EQGa4niGtd5E7hO0Vs3seqG0/5Wx/UqdI3rRDRXwEeY+YprQd8vfQS4luivV8tCkNHcqn1chC7gLaorr3MXu+Z24m5PMBNLkQtY+2e9RhLNns+PTO1CggCbevNYsW47sumko6B7Y/seALLovubU6Rjdyl+XuSwB2/cWNZGmXhZUz6+KKniLZUmbUJZOEOwz0nie3/srg92lxemSs89I2c6wqTePB199FwA0q4KK1Y8Gp7zD+n2dfNNuP1YA4KK7XkKhXNE8xvrXQlgWGoc4eyV5o7h+BK4VtYpbL+3VInS9RHPjRJz7JqgNr2nErHy2XrHy5Xq1LPiJ5vqxLfgVuoBbntyEJ8GrbzMutgQ7XM+IUnowpfRWSunFlNJfUkovq0fHrPyzXiOJVp5PKyuCPoXWz08+VBNlZyxdiS/dKt9a/9qdL2KEw0xHKyqShN7+Alas2443e/I4/Q/Pgb2zu6pYg8qnpu0jC92KhHf38J2n+Tei2aqgb0eqyJHtBctW4uTrn7G1A/Dmu+XxTTv9WFGPM6VrJK497XDDNidP3xfj2rKBTz4UREsYVgW/EUvH2+c+BK6rzaBWm4LNeq9C125dLRFuYVkQNAK1iGIry0It0VwnghC6XqO6Q9v4E7x2xwrTisCDa55cSulRAMYxxu5Wnr8M4CzGmFb/Neg8uW7ldpeeOdtThO/dwTJOuvYJ7bm+zC0AXP3Y67jlefmWeTpJ8P6JHfjHGz3aczkaal921459R2aQa0nh8k9MxZduW22wKVgxeUwOl39iKr5x51r0mSwIXkglCDLJBPotBKG+RPDEziyWLTjC9rV0ynfL+x45lVtWo/K7JeCLS5+r2sacq1ht64SpYw2WizgxXPPkxqXUp7zevdyneT+nCKebwHUTprXgJaJk9hSaI1Qpw+3chOVyed3Q86TNPm77qYSVMzfoW+YiT643osyH7We815IvV///YMVimUPOXP1yq7y5+v0B+9y58namH7MFC2++RWJ+q3y6erzmwHXKu1tPnvnuccHkyWWMPasKXN0+e/12jIcgK2f19Bdw4fLVhmXmiPBFxx+MpWfO0uwCqsAFgEtPOASkKl7Ke+wiNuzox+UPrsN3TzjEcht1Ils6SbRtf3nadM/H+slJFO1Z2U6xz8gM7K6N6sCf0JHFkjNmakUeVMx2A721QS9weXzT5kl3f/j8LIPtoae/gHyxjIXLVlpaI5a/sCWwyYeC5qCWKK7dfk77+BW4QVkWHK0KLn1zyrrAa1uw28dqPxGJFdQDpx9Jdr5cP/CU9tXjlDNXXj/UH6+2BXk754iuuS2tHZuororXCKo+0htU1DdMPFU8o5SeAuB4xtiF+uWFQkkiIfwQ7i+UtJK8Vs959j9t8dNY370HU7pG4pdnzMSFy1drz+88/31ae/2FEv61fjsuuHWVZVsEzt5XKyZ0ZJFKJvDGduvfBOPaWnHtvFn49p/X4ripY/F31o0PThmDe9ds1VKM2ZEigO6HISaNyeHX82fjq7e+gN7+AvryzpHg3599JD50SBd27BnEghuexSen7wsAeGDtO7j5vKMwZmQLduwZxKd+9S9IAB74+ge0Zer23/jIIVj3zm5DlPz+rx2LqfuO0p5f8+hreGDtOzhu6lg8vm47rjljJr6xfDWOmzoGj6/bgU9O3xeEEPz1xW2G4y644Vltn/Xde7T2pnSN1LaLI8lkAuVyBel0TGdnKAQZGWqkCkhW+9kJPj8Cl0fYDtqIaqcZ3CpWF14vEd16R3PtPJZ2QiWq6mcikuuNOFU2dMqk4hbNtRrv+nHOU/0MCDaaC9Qe0bVqU2svBlXOgogG80ZyuUUupfTDAE4BcBFjzNDDqMr68pSPXfLkRvx9fQ+uO3267S3vJU9uxF9ffhfvKum6guLMI8fhQ1PG4CvLX7RcnwAwvr0V155+OO5asw0PvfouuvcUuCMiEzqy2LG3gL3Kh3xCRxY//uRUfOPPL2HXQAmEVGdaUEklgOtOn4FFj6zHhh39mNCRBSHAmz15TOrM4vJPUlz+AMNGJWfuxM4sFn36UIMl4epTDsNFd73kaEUAjKWDJ4/J4QefmIofPrhOe/6Xrx6Dvr685Xu5fvtezF+qOWOqrCZxYzjaFeJiVajlYmde7lXgOolbO1HrhpPorRK2AQtdO5HrtI95P5VGsCwIkeuNMEUuEM6PW16RC/i3LABDgtZK5Mr/e7MtAO5CF+C3Lxja9SBk41ba91//9cHgRC6l9CQAHwTwXQD7A5jIGHtKXR+FyF3y5EasWLedy6+ZyWVQ0NkTVAGl3vJesOx5bOqViymkEgRtrSnscImkujGqJYkT39OFu9e+U+XFPWHqGDyybocWGW5rTWHvYEmLzCYJQdnlfUkQ4MpPT8N373sF6uc4RQAQ4vilYtV2ggD7j27F/332MFx8z8vY1JvX1qmZIPTLzAKXxzft5M3db+xIy/eHx88bN8IUuZTS/QD8BMBMxthRFusTAK4AsBvAJAC/Z4w9bdVWI4rcsC50VuusLnjacw6B61fY2mEleL0IXTuRC3gXukFEc4eLyA1qzAqRG97Yd/LlAsFHc+X/6yd0ze1a4UXsmolK/PKKXJ7sCkcCWA7gfQD+DuBuALSm3tWI12IRZotDNp3UMgPki2VcP28WWpQvzFJFqlngAsDuwTLuWL1NS4f14SljtHWPrd+B/UfLt9vVCmd664GbwAXkCO3F98gCV/X1lqShQZ2z8ci0pgmSpotIRZJLAH/rLy9hwPTa/ehTFFeebMwh/INPTMW4tqzmm776lMNcfdN2WRbuWLUFpy1+uipDw3X/fIM7jdkw4gOQx5/d4J4LYDRj7H8AfAfATZTS+ORyscFrtTHLNmoUlX4ErpVfdrBS4RK4vBkVnNo17+vk0dWfU62vd62vdRB9aCCacszWO1eu38pnXvLlOpX4BfisQoDRm2uVacGxDzb+XMDao2vl07Xz6jqVIlZ9u27+XSuiyJjgBZ6JZ88zxkYyxo5XHkcxxm6sQ99s8VMswjy56m+sWzcBqoixJo+nOji8VDgz0zUiDUDO+/r39Tu05dP2HYU/nDkbEzpabe0EXvj6hyZXLes3eV7U89lbqFSlMFPXvd03UJW67LK/MnznnpcNy75822q8vHUXFh4zSYvoXvfPN7RCElaZD6xSwl1y78t46NVuLY+x/sfK46/34LiDxwQy+bBZYIzdATniY8dJAJ5Stu0BMADgsDD7FEQU1wq3YgK8OV5rsSm4CVwzduKWJ00Ybyoxq2PUKnTtXgv9a+elYpwZr4UheD8rjZAvN45jtt44RebDKNPLI8DdUok5VT8D+NOJ6dGLX7tJaOZ23ISuvL2FqHURu259rUX02hFUpbOmqHjGg5diEdc8+pohn2u+WIYkAe3ZlCaS3+4bMOyTTSdwYHurlrFAxcuQTNt8kPYUyhgolg23KaxIEWDOoftU/4o1Pf+/x96wbaNrZAYTOrJVF44D2lpx6zlHWq4DgBOmjkU6QbCpN49NvXkc0N6K/Ua3IEFk0X7OH1fh7691a5aFm597C9f9c4MhA4OKOcuCvqQyABw0doTlj5ULPjjZshpbXNOHxYB9YLyg7lKWNTxecriGgZOQdIqyBlHxjPd4dv0Lg6Cqpwmad8zWk1ry37oJbbcsC16iubxCV4+V0OWJ6gL2Ylfeh0/wAtWiN0jxGzYNK3J5i0Xki2U8sPadKmvDpt48RphsDOPaZCEHyHaDHXsL6N5rtC4kE0MJxdx+MCZAYPX5+eqxk/Cff1rjWvChJAHPv9WHitmPVJGw7yjr7AJmK0JLKoHvfaw6fVlC2a5g4esBZEuFOgkvkyTYNVDCtl2D6NJFvL99j+zBTRCgVAEefU22igxZDjYAGEoJN7EzWxWVPfE9XfjVvFmGY+t/rJgjtk45fZ2eDxPeBTBK93y0siy28E444yWMKK6bwNXDI2wHSxXLhxN2Yte8jeX/dYjmumE5ibABIrF1oOHGbD3wWvksKPSWBatorpvgbUlZC1o7nNKKOUV0Af6oLuAsdvXH4xG8hj7YiN84CeKGFLl2kcENO/rxleWrqwTOzecdVWVtULMJ6KlUJKR0C/W3/C87capWSCGZIBjX1gK77+h9RmVwYHsr3uobgNW16+J7XsYWpbhEKkEwJpc2rM/qPuxbdw1C34SqYbfvqS5OkSRAuSIhlSAY1ZJESyqBt3YO4II71lRtu6k3j/lLn8e23dZCW39xK5Ql7FKKU7SkEvjORw82bKvX4K/rLAe3PP8WtvTJ0drTZ40DAXDHqi0AhqKyp88a55rH2A2eymvNCqV0BKW0S3l6P4D3K8s7AbQCeCmqvgWF26QT3+2GIHCt4BWzPNuFKXRrQeTM5Wc4jNl64CdfLm8KPTNW4lZvWXATv3bRXDNu1gVe+4Kb2OUVvH6Erx1eBHGQorkhRa5dsYj2bBo780VN5Kpi55Z/b6qyNpQrEt7aOYAJHVmMb2sFAGzbPYi3+ga0aK6eHz20DqWKhAQBTp+5v2OBiHd3F1yrmwHy4Pv156ZXieVSWULWVAbwA5M6kE4QTVBaNV+W5Db3GZXBydP3wxjFE1yqAPuNcs5GkE0p2RkcGNfWik29eVz5yOtV6/Yb1YJNvXl84Y+rsGFHv1ZY46K7XtKi5xt78lUTA8+/fQ3Wd+/xPbnM6yTERoZSehyAswDsTyn9b0ppFsC5AH6sbHI7gN2U0h8A+DmAsxljob0AYflxvVBrRgXAu8A12wUso6ycEVon7NowH8+qP5b/2whdFa/R3DBtIs3iy43bmG1kai3uwIuXCWhu3lyvtgXAWegCfPYFeT97sQvwCV59H+weccdTMQg7wkghxpMD11xm9qybV+LNnnxVSqtJY3KAJGk5XwGgPZvG6NYUrp83Ez39RUMuVn3pWzP7j27B4rkzcPbNLxhK7yYTBESStCwJ5uIRVm2Ob2tBMpHApl45N+13TzgEX7vzRS6B7MZoJS1ZKpngutCmEgRfPXYSrlEsBtbbwDIybcU1p07HLx5/wzX9F08eYzfilGpsOOXJrVXk1rukpxebgpPA1WMlbp0YcFnvdovTfFExR5Dsokvq/zxpxdQIV63pxGrNmVvPVGIiT64/gvqhG1VJb7/WJbvvBKuUYoD3tGIAqubsWH23mNOMAdWpxoxt8P1+sktFFiS1BAAA4KGvHh1MCrEo4L39rBe92XQSS86YWWVLmNiZBQGwURG/arRwZ76IBAEGiuUqb29JueU/doTRRgAoYvBPL6JvoITRLQmMapH7UK5I6ByR0Xy6kra9LIzNg2zfURm83TeIbbvkCW+zxo3GEQe247iDx8ALVu/yfqMz6B8soSzxf5BKFclS4KYSBNecdpgngQsAv3j8DXzno1MMy6wmBi48ZhLuPP99NU0u8zIJUdBY8E4444niWuGUTQGoXeAOlCqGhxtu21tFdQ3rbS642jKXaK6eWqO5wrIgUKlXFFYPT4lfO8tCrdFcXmqJ6AL2Xl2ryK7cRtI1wgsYo7y80V6vOEWHeR68xE7kern9bL4VnU0nq8TOok8fijkz9rdMRXX8lLGGgga3nnMkRrfKk9FKFQnbTZPOUglg884BbFEyMYxsTeN382ZiXJtsb3h3T6HKRvB/pxwGq9/g7+wuoGtEWrsQ/GXtO7j8gVfx6GvbXV8j/VCwuoxs21VAKaDrS6ki4WcrXsc+nGV0L/nowdoPja/faaz0Zue1tcpj7AXeSYiC+hMXoWMXsVGxsymoOAlcK0sBr6h1w6od8/HcfLrmbazEvJulIwri8tkRRAPP5LMwUpCZ0d/98JJpgce2YF7HI3St7Atexa7cFp/g1ba3EL5hiuCgiKVdgef2s1XFsy/fthq7BkrYmS8a9rv1S0ejkC9Y2h+s2jnt989ij0u4PpOQJ1x1jWzBnkIJuwett0+SIf9sOkFwxZxpuNiUdzZuqP285N6XUVZSrX328P3xN9atCXzbfZMEn5rWhb++0o1iWeKqhqbe4vdDvljGObe8wF15LWyGi10hjCpnQVgVgqpVb/6f55YkYG9H0N+i5MEuibzZzqC/4NlFl6xsC8DQxdvKtuBWBS1Iy0Icqp8Ju4I/6l35zKodXsuCeV8vGVeC+o6wsy2Y18nPvdsXAGsLg9YvDz+8ea0N9URvo7hn4VGNa1dwu/1sFe1duHw1NvXmsTNfxKTOrGES04Ibnq06hip8Fh4zyZCLdaBYrvrwWH3RFipyiq+tuwdtBS4wJHBTCYKbzzoCM8aPRtfIcG6je30z7T4hxYqEXz+xEVeeLL8HrakETpmxH9IcF5JiWcJfX+nGqYfvV5dCDnaTEIdz0YhGgGdWvx+rgtu2Kla36mu9eJkvUv2Fivbwit2+5uPYRXR5JqJp27pMQrMiSMuCSCUmCCsiG1RlNrtoLs8PSz8RXfm596guYB/ZBYaiu04R3qH2k5aPKPETOW7YSK7VNu3ZFEa3pnH9vJmGSUxzZuyPs48YD8B5Qps+Kpgg8FyNzDzZTE+SAJ+dsT+eebMXb+10joZGwYcO6sQ/3ujRnk/qzOKtnXmUKnLasgSxn4xn5vQZ++E7H5vKNXkQsI7k8u7rd/uwEJFcI7VMOnOK2Lj5cWuJ4tYSnQHco7Z20V63SWdOF0UvEd1aork8E9DMgsUcJIjj5DMRyfWH1+wWQURzrdpwstvwTEAz71fPOz5eI7pAdVTX6hiGdZxZhrxEenkJKyL8p3OPaMxIrlMOXH1aKato7y9OmY6bzzrCUEhg6Zmz8Y2PyMUQ3Ca06aOCv/ncjKq+7T+6Bfs4RGGdhntZAu5cvTV2Ale9Nq7e0oeuEUPntrFHFrgEwLjRrdwC9xPvGYvn396FJU9u5C7kYIZn4qFbajCryms8+wmCw4un0ksZX94Z1OZtVZyiuG4XLLMf1nyxshK4vJPP3LYzt2+O6Kr9cjuHWqK5PBPQgozMCl9uvAkqUuoFtx8+TtXPapkAF1Q0F/Ae0bWK6vJGdoGh6K5dhFfrsy7SyxvxdcMuIlzrg5fYiVze289Wk40WLl+NrYpnVBVGy57dDIBvQlu+WMbCYybh6lMOw6JH1lf1beuuQdcqZVFQy8DNZVIY1ZJE30AZ3Xurz22fUS247nOHV5U3tuOR13Zgw45+/I11W04SdBOdPO8Tb/aN4VwkIkxqzU1aq1XBT/tOk83cJprpBa6KWYja2QpqmXxm14ZZ6FrZF5yyQujXu01Cc1rGi/m9DKP6Wdzz5Qqig1eI82RaCFPomvPoutkXAGexyyN43UQvYC18gxbCYRJLuwLAbyuYPCaHy06cioXLV6NYlpBOElw/byZ++OA6bf1fvnoMCv0FRxvEHau24GHWjV+eOl3LuJBOEpw8fV88vXEn3naZcGUmmSAo21yoR7UkMSKTwrbd1VXLosApL3CSAHMO2xf3v/wOdwqxBJGj3jd8frbBNtKRTaE3XzJM8jPbSQBnu0o2ncTZN6/UUsJdMWcavnvvy9pzdaKZ24Q0cw7doOwNw8GuUG+rgt3EEj95cXlsCjwCV8XtVuPQcm8vt9UFTV5uvKDYJZhXL3BWF18e24KfvLleJqDFzbIg7Ar+CWryGRCcZUHeJvgJaIC/ioheJqvyfKfYfZ9Y2RjsjusEr70hSm6Yd3hj2hVUnG51m6O90/cfjZsXHKFV2Tr3llUGMaPSmcvgB5+YamhXff6nVVuxsSePr9+5FjP2H4V0Qm5rBdteVf4XADJJYnjxzJsQG/PC+LZW7B4sY0dI6a1GekzlkUoQQxlhPUnINou71/ILXEB+f97uG8QZNz5niMS+uHU3Nuzox8Llqw3L739xmyGi6zTxcNmzm1GRgAkdWS0f8saePNqzaU0Eq31Q7wDo8yZPHpPDsZM7cP7ta0SEN0TCus3sNiHKKQrJa1Mwr9Pj1UunPrxit69bVNeM03k52Rb8RHPDSj0mLAvNQ1D5cr22U+9oLuAvogtY2xd4LAyAdWRXf1zePLPmaK+XyG/ciG0klwdz9O2lbbtw7i2rtOe3nnMkOnNpXHDHWnx4SifyxTKWv7DFUFEsQYCRLSmMaklZRmvVIggTO7NY9OlDcfHdL1X5apNETiVmjszq04epjGtrwTu7BlFWhNr2PYPod/j15ZURmQT2FiqOkWSVBIBcOoE9xYplX3nasCKdICia9pvUmcWVnz4UX7l9NXbmhyrFTejIIpkghgpndpHcq085TIuyj29rNbxf49taces5R1b9OFq/fa+hmt2NZ84yRPmDTjkmIrky9Zxw5jeKaxWFUaMvVpEXnqpF8nPvURY9dhepKl+eS8lQq8lo5miu/n+/0dy4TEATkdzoiHsqMaD2aC7grwS4HqcCMnY+fDNeIrsA//eOuT9hEVSUuOEjuTzoxUhPfwGXP8AM6//rLy/hy7etxvruPXjw1Xc1gZtOEvzs5EORUnLd7hoogQBVk8r2H92CeUeMx+QxOSw5YyamjB2B604/HONGGwsjjBmR0QSu/geSPn3YfqNb0JJKYEvfICoSMLoliWK5EqjABYC9yqDgEacVAHuU41t9t6htZBLAfqP4ikEAqBK4gJxa7IFX3sUIU+GHckWq8kXbTTy86K6XcPUph2FCR7bqB0kyQar8vVa+7R8+uA6L5kyzjPDqI8ECa+rtfeSZcGa1rXmZU3WvoASuZeS1WNEevNjtY27frU9W6cWsztGM12huPSag8SB8uY2P3Y8cyx9Eph8+1T+qjPs4/Qiy+kHn1B8zPP5c8zqgOr2YW1TXbjs1susU3XWK8ur7U0t1MR6cosReHrw0tMhVUYXRxp48JnRkMb6tFQDwdt8ANvXmcdDYEfjdvFk4Y/Y4zdLw7XteRqkii9K21hTe6huomlSWIARnHXWglkd3yZMb8fU712JPoWTYTt1vdGsS150+w7AuqfhdK5KkXXQkAC2palEGyIIyDGpptgJSs3/47b4BPMy6sWugWLU8nSQ4dnIHsumk68TDjlymSsCPb2vFpt68IfuGk1i+5L5XcNmJRtuKKAPcmPBmVFAxR3EdxZ5HgavHTtiqWRDsHmbsxK5VH9yErhnza2A1CU3FLdOCQMBLFCV+reDtB49tAXAWunbWBYDPvsArduXl9oIXqBa9bsJX7WNYZXfDxrUnlNL9KKW/o5RWV1SICXphdP28mbjqs4cZ1v9q3ix05jLIppMYO8IoZLpGtuD4KWMs2327bwBfvHUVAFk0Pcy6sak3j10D8sUgmTDfPkziO/caq5mpguzd3UYB3b23ZLhtr+IjbzwXtTSrv5iZh42X76t3bApnFMsS/vlGjyZQzQU6OnMZLD1zNhYeMwn5Yhl7TT8ykgmCCR1ZQ/YNJ7F87OQO/OihdYY2RBng4KgldRjPvtwT3xwmm5kxRzh5BW5VdNUkSt1EbFU/bLY3t6s/Lq/QtZpYZ0Z9jZyiuVb4sbC4pY1z2lcgsCKMaK4ZP0IXsPfoAtXpv+yiul7ErrzOWfBq21kIXx7x64QfYRyGiObZ8gMA7oZ9gaxYoAojAFW3qC9cvhpvbN+DB195F1t3GSOSW3cN4v6X3zUsG9/WqkWDt/QNYGvfALLpJGaNG2XYzhxR7OkvasLVLICbBf0ZJwhw5aen2W5rJpmotoSo7fzs04casmdYTTxUo7M78yVM1FW129SbByHAWUcdaNjHSiwvnjsDT2zodc3DLAger7evnRK8223LM/nJLpuCVSYFFVU86lN28YhbOwaLZcPDdjsOsWvul5WPz07o8kS0VayKajhtx7Nt1b7CctCQBJkvtxbLgudjOezvZFsISujyRHXtxK7dBDWeCC+P8AXsxW8YojgsXHvFGLsDwO469CUQ1FvU6STRInfru/dg3tKVtoUYShUJLakEkgQ4QJnQpN5Wr0jAgptX4m+vvoO/rH3Xcn99O0kiDxw/E7YajR998j249l8bubZNEWCwJFnmGa5IwMX3vIx8seyY6UAfnVU90up7/HHaZemnNS/rzGVEGWCfxM3zyDOBxW6yGY+oM4tGO3uCm7g1C1orUeu2jZXYteyLQ5/tsLMt8ERz4xZhjdtnVGBNmJYFr9FcfV+c9nXy5/oVupbrLSKVdsLVLrqr38epkqKV8OUVwJbteRTFtTx44cquQCk9HsBVjLH/sFpfKJQkEpPJqf/7MMMNT7yJQrmCKV0jMWP8aPx51RZtvTmLAAHQlk1DgoS+fAkHdmRRkSRs7RvwVNY3gSGv7cen7Yt7XtwW1ClFwgEdWfRwZn5oz6Zw3fzZ+MLS5y3Fg+qDdqItm8Ifv3g0LlwuTxSc0jUSd57/PuQy1UUo+gslw3Lzcx6CaMOKZDKBcrmCdDqCUkAe8DNbO+j8uH6yKjiV8PWSUcEtiutX4Gr/u9wRMJfPdEuorp9oYbitqfuy11+Y1AubegE0Z1ywy7bgJ9OCW85cr1kWosiXK7Ir1E6QJX6BYDMtyNvYT1zlzehiXmee0Gq2RJmvh065dK3WA/a+eqcfsG6lxd3294qfNIm1suhTU7nGbCAiN6oUYna8sX0vLlHSQqmkEwQduXRVJPHA9lZc9ZlDcfE9r2BTb77eXY0lo1uS2GXhnbUjqVgFtu8ZxH0vV0e7c5kEBosVw4+LVEL2Q5vtIwAsizU0Cs2cQqyeqcNqSRsWtMDVL9PsAR7Erd968FbC103sqkLXKr1YUEK31nRicUwlJkRuMERRGMKurVpSipn3r6fQtdoG8Cd2AT7B67XNOHD5xw9p/hRiVix5ciMuue8VXPLRKYblxUr1rfLxba3YvHMAl9z3Kn512nTsb0oNFutvvZAYkUnggwdbT8SzoywBd67eggdfHRK4CUB7PfsLssDNJIk2Ua1Ukf3QqQTBqBbjrR6R6UDASz08nH4EbqFU0R5WDJbKhocVVm3oj2FlX7CajBYWwj8rqAW/lgVeb24ttoXq9u3vNrQkE9weXavn5uwL6jZ2NgY7K4ObpcHOy2uFuU2nR9zhya5wHICzAOxPKf1vSmk2zA6ZJ/54mQiUL5axYt12bNjRj6/d+aLr9rsHS0gn5PRVrelklY/Wz1f4uNGNLc72FipVE/F42D1YRqkiTyJLEjmbQzqZMPxwkCRUWUBKFanqgiwyHcSPoL2OvFkV3HLjmrcLy6bgJHD1HlorYWsWtFai1m0bfbv64/EIXfO58E5Cs/PmOk3us8uZq6eWLAs8CF9uc8Cbo7YWeLMtAM5CF6iejGaujGb26foVu4C94AXcRS9gLXx5BbDb8er14CVWFc+WPLkRK9Zt125Vq5Wv9NWw3NjSl8fpf3jO0QM6vq0VhECbiDahI4sdewvYWxAz6/UQeBf6N545Cx3ZtFaZTGViZxZf/8AkfPf+Vy3fmzCqj0VB2HYFSukJAE4F8C4AiTH2Q9P6cwGcD0CdZfl7xtgyczteb3/W048btlWhVoHrFL3VlttEZwFg0OZ7psWhJHdLSnfB1H3BW9kX7KwLPLaFuFgW6u3LDcuuENV4jZIgvblOdwuisC1Y7e9UFQ1wty/YLbNL9ceT29uNoO/0+LFE1MolHzmYa8zWPtMmIPRR2PNvX2MQPCvWbcdZRx3IJXjGtWVx8vT9cOfqrYblCQKMyKTQkUtjU69cNGL/0Rnki1LkXtzjD+rEY2/0RNoHK/x8q37//lfxu/mzqmZnLnzfRPzXPa9Y7pNOElx9ymEY15bF4rkzsHD5apHpwAJKaQ7AYgCHMcYGKaV3Uko/yhh7xLTpPMbYxnr3z4sf1ytOFc68RnGtqEXguolbO1Hrtp1e9KrttqSS2vEyqQQGi2VN6A6WKmhJJTBQrKA1ncBASUJrimCgVEFrKoH+QgW5TEJ7bkWhXEEmmRj6Wykjk0hisFxBSzKBUllCKklQqlSQSgw911MuSzWnlLJqF5A/Y3EpJuBG3MdrI5BKEk/fHyml+JLzNgmDUE0mieH7xdyGuQ/m/c3rW5IJg9DNJJIGoav+gNR/H1ktU6O6ZrGrj+yav9PMkV070esUCfUjgP1EgOtFbERuNp3E4rkztBRg85c+DwCeyq2qZWFXvtVnWJ5JJnD9vBmYPGaElmu1f7CEnnwRV5w0DRff87JNi/UhjgLXD/uOymDzzgF84Y+rsMVUdvd7f33Vcp8Ekd/7Vt372xiXsEh4P4A3GWPqbL0nAJwEwHzR/BqldBuAHIBrGWOx+oD5ieJabesHnpy4QQhcO2HrFmnRX6T0baiCd7BU1qK6hVLFs9A196UlNSRoByuVqtulXrASoKoYBozC1bxtsVyx9Fo2OE0xXr1iFo21Yid008kEl9XFav96CF1g6Ae3ekekFrELOAte835AtejV2nH4HqrFZxvHCWux+lbpzGVwxRxjcQG3SUiqZ3fJkxtx9s0r8cVbV2HDjn4c0C4XdGjPplAoV3DZAwyALKjee+BovLOngGJZilzgNgstKYIlZ8zEge2t2LbLOh+xSpIQjMgkkSCyR3fXQAkLl6/G+u17tfLMK9ZtF4UZqtkHxpzVu5Rleh4HcCVj7CoAzwH4U536VleCiOI6ZVNQ4RG4eg/tYKFsEKdBVTzTt6s/nt6nW3VeFun/7Py5erx6c8UENFvEeOWglsi830lo8nbeJqJZeXTNdhwnny5Q7dUFrH236jI7366Vf9e8n5WXV2snoGpiZuLoyY1NJBcAevoLVdXKLr3vFdt0UqqH9+pTDsOKdduxsSePBJFn8b+zaxDFioQJHVm0ZTPoyxdw0Z9fRE9/0VP+WwEfgyUJT23oRSJBtNf3P4+ZgN88ualq27IkVfmf3+zJ+4reDzPeBaAvuzdaWabBGNuge/oogHsopUnGmO9fDEGnDgvj+E7YTbAC3G0KgLvA1dYVqoWmoR+cP9oyab1NQW5HvfAMFspVUV2riK4eHtuCOZqrPvdL1JaFII4fAJGM10bEzWYQhG2Bpw2eiC6AmqK6AH9kV7/cap1Z6LpFeu3aMVOL0DXD6xMOi9hEclUbAW+51Z7+gubhveiul/DN4w5COikLrEJZQrEiIZ0k+N7HDkFfXi63++KW3djYk0evmLkfGCN1XpxFj6zHmz15qOPDSuCaIQB+PX+WYZlIIWbLUwAmUkrVlBXHArifUtpJKR0NAJTSn1JK1R+vhwDYGOcLph+rgtuFyhzFNazzYVNQsRO4xiirMQJbKJa1By9W++jbNUd1DX0yZV3gSS1mzrZg6IspmuuG5cQfmzK/cauWFgJNN155qecPDDubC29aMZ6ILk9U17zeKqrrJbJrJVDdorTmSK+d/cgc8XV61Ipb1Njvg5eGzK6gbrdozrSqog9OjG9rlauZWRQgcKI1CQw0/NdOeGSSgD4wm00R5DkroCQJwcjWJPryJW1ZezaF5ef+R0MK3TpkV/gYgNMBdAMoMsZ+SCn9GYAextgiSumFAKYD2ADgcAC/ZIw9bW7Hy2ztICO5QWRV8GJVcEoZZhXFtfPhOglc/XaAdcS26NF6k7aIyGYsMimoUV3Vp6tmXlAjulYZF6yyLTgViPCaaSEuWRa8CK0QsyvUfbzGiXpVQQP4sy3YteOWdcGqPZ527LYzZ2FQsftByVOKnGcbQx8c0gHGnfmzxwdX8cyNICue5Ytlw21qq+fn3PKCFvE9eEwWK9btCOrwgojYf3QLEoTgbWXC2sTOLJYtOCJWlgW3zybQnBXPohS5PGV89SLXKS+uVcowK5tCUALXTtgWbUplp23qsesFb61C1yqtmFVKMacqaLwiF3Av89vsIjcohMjVbRMzocvblt12gHfBC3gTtF7FrxNxEcYNK3J5UCO8vBFcP3SNzKB7j7A11JsD21tBCMGJ7+nizo1cD3jvMjSbyA2zlK9dVCTMKK7VZLMgBK6TuLUTtW6YRa+V2K1V6Frlzg07mlt9q3foeVQlfoXIDY96Cl27bAu1CF0gerEL8FmG/IrZIEVwvTh15v7NW9a3M5fBDz4xlXt7P7M3hcCNhooEfOSQMbESuOYczmoWCDWHs8gCwYdTuh+rL32/E87ckq1bZVOwmmhmmUVB8cPqPbKqwC0Wy5rALRYr2kNFXe/2GNre2IZ+vXpMLROD1i9nj675XM2RbJ7XzwtO+Y2tCLr6maDxCDrbglObPFkXAOsfS3aeXx7fr7qdnW/Xyb+rf5jx66314tGth483SGLVG96Svj39BVyupATjYRhMcIgl/3nMRM/7vN03gEdf2xEr4ajmcFYnQs5f+rxmlxFZIMLHLQpjjuIC1RkVAKPQc/LhAvYCV9+OfnKYWdyqWIlXN5wEr/5Y+uMbJqU5pBfTT0SzEvuGTBIW2Sjs0omZEd+5AhU/k9DchK5TyV8noeslvZjVhDSeSWlqm3Zil1fwAs6iF7AWvlbiF/AuZGshaNFcS/9iI3KXPLkR59zyAnqUzAc9/QWcc8sLWPLkRsN2ahaGjT1y1bJ9R1lPTjqgvRW3nnMkJnRkw+66wIbfPPmm7bp9R2UapnIR4C+H83DGLQOCrXB18HtZ2RnM8EZxq/7X2RR4BS5QHb1VMS7ni+BaRXStxK55Oa/Qtcqfa/d6eI3m8uTMtXvfaplsJGgMwsi24CZ0vWZd8BLVrUXsqu26CV4e0WslfAF78eskgqvaqINQbVqRq1YmU+npL+BvrNvxdrC6fTadxAlTx2JiZxa/Om161YdkVIv8BiYIwfi2VmWbxhFTw4X+QgXZdKLqvRnVksL7J7ZXTfCKGrsczj3DPB1dEBG7WqwKtURxAft8uJZ5cC0ErvzX2lJgFcEtFCqODz12bdlFdc3nYBa65vVWtoWqNiyEqTma64ZXywIvIlrc3PBct52ELhCcfcGr2LVKOeZV8Jr3sztXK+HrJIABdxHM82gU6i5ylzy5ESdf/28sWLYSPf0F9PQX8OXbVqO3v4j2bMrydvANT28yRHlPnzUOBMCfVm2pKirQkcvggPZWnPieLq1c7KjWWNW8aHqsvj/My/YWStg9WK66UO0eLGH5qq04748rAdhH9OuJ1xzOzUKQpTn9ei3dJpzpqSWKa/bhAqY8uA4CV31uJUidRKwVVts7iV19Xww+XVMeXf25DZYqnqO5TpXj7N4bvyI0SF9ukJ9hQW2EYVsA7KOlKn7sC7WKXZ723QQvj+itRQDzCmI7ghDK9RDZdVV/+WIZD7Nu7MwXsTNfxHl/XAUAWtqo/Ue3YKcuX+oVc6ZhoFjGLc+/hWJZwvm3r8EVc6bh0vtewcaePN7u24JiWcKkzix++ulDcamSM3dSZxZnHXWgJk56+4uY0JHFYKmMd3YP78hbPahIcpEHybQslSAYOyKDgVLZ8D6rJACol7cXt+7Bys07seiR9VpE/6yjDozE/6rePdBnV1g8d4aWXUF4coPByYbghNWsY6corlU2BcDow/UqcPV/AVhGZb2gZlJQ28lkElob6XQSxWJZ+VtBOp3QnheKZWTSyaFKaZmkdi7mqmjyuSe0amjAUO7cwVJlqMqaUgVNT6FS9hXNKVUqlhdvwfDAXFGMB7dqaNp2DhXN0smE7Y8nu/atqpvJ28ufX/P3lV7omqum6bGqoKatszmWGavvSreotlX7evwI3Uag7inE1Mjtpt68Yfn4tlYkCLB554BhWTJBsKk3j3SSoKh7gyaPyeHYyR14YkOvJjy29OVx0V0vaWmd8sUylj27GX9f34MjDxiFP6/ehqLDYEkQiJK/IbLf6BYsPXM2AOD829cgkwTYu+5p4NSIvtn/ypO3NkiGW55cv+nDvKQO85MblzdtmLnwg91kM30U186Ha21RqE4bphe3VanECsWq18WKdCZtfK5PHaaIUP2ydDqppRtTl2fSSUN6MX1qMX1aMbsiEeYCEbzpxILKmcubSiyoNGIihVh98RthrzWPLuCS5cWhfT9+c8D5XIM4Hy99CYo4+OTfP6U9HinEzLdys+kkrjz5UMttN+8cwISOLMa3tQKQI7ybevOY2JnFtacdbtj2ijnTcOFxB2PpmbORTSex5MmNuOiul3D1KYdh4TGTtNvcALDsvKPw7019KFYkOH3fCYEbLmrUrDOXwaI570HBJrjVmTXeYLhizrQqMXndP9/gmqgYJOY+DPcILu/t6KCtCnqsSvjaRXEB68lmAL/AHUrrZbQP2NoLCkXtoadcLBseesz7WNkfqi0Mxn4VdBPNzBPRrLItmF8b82unf02dSv3W27IgfLmNid+JaEHZF7xaGNzadbIYqHYGJ0uDnZdXf1xei4LZ8sDz8IpTn+r14IUrkkspPQHAqQDeBSAxxn6oX28XybVKoP/l21ajL19E34DxdvXo1hTas2lcP28mevqLmL/0eW3d4rkzcKVy21plQkcW18+bCQD4yvLVigWihMljcpqlQfVQ/uWrx2Db9j344q2r8JYuUiwIn1SC4BPTuvDQq90oliVMHpPDojnvwYKbX0CxLGF8Wyve2T3oeLFqz6YxujWF6+fN1CL2p//hOa098/ut/vCJgmaJ5Na7ypnXAhBBRnHNNgUngav+r/+rF7faOetErVnE8pLUR2t10V0tWmuK6g79TThGdPWFIoKM5tZaGCLK6mcikhsNYUZ0Ab6Io9sPKr/RXXlf9x9rvK9BLT/o4hB5DZrZE/musa4il1KaA7AGwGGMsUFK6Z0Afs0Ye0TdxkrkmsvvXjFnGi6592W82TNkU9BHbAFgQkcrfnXa4bjorpcMgla1KkzszKJUlrTtx7e1Ip0kWjoxQmBoX73NfdC4dmzt3o35S5/X9tXD6/kReKdrRBrZTEqznJw8fT+sfKsPG3b0Q75+2r/2v507Az9d8Ro2Ku/pxM4sFum811YWFitbQz0RItdZ5Pq1KjhVONNPijJXN3OqbGa2Kdj5cL0IXFXcmoVtqVjtQXcilTbezVAFryp2eYWuvjKaviqalW3BXAnNrgqavtSvUwW0oC0LQuQ2L40udnmPw2slCPv1qAdhC2tekcsTp34/gDcZY4PK8ycAnOS2k1UC/Td78mjPptDWmsKEjixu+Pws3PD5WZjQkUV7NoWPHNKlCVz9LPZiWUI6SXDNqdO17QFZHG/syWPymByunzcTiz5ttEHo85jmi2XsLRgvNKkEcEBbKxb8x3gsP+dIpEPI5Tfc6d5bRLkiTw4sliXcuXqr9v7ectYRSCoXqPFtrbjxzFlaCrhMkmDafqPw2zNmap+PN3vyhswbv7KwsIi8tdES1BebOYprhVXaMPP/QHXKMDubAmAtcFX0AtdsG1DtBXr7QalY0h7aeemWWT2stgOG7A2alcFkk7Ca/FYsli0zLgDWtgVzSjG3TAuAc6nRWi0Ldu0Jmo9a7AtBWBiAIRuDm5WBx9LAmz2Bx+Jg9bA9Twv7g9dHUMTFrsCTXWEfALt1z3cpyzTa2rIgFj+E29tzuHb+bJx07RPaslu+eDQOUERqLiMf/t6vHas9H/Xoa3hg7Tu4+byjMGZkC2790mgsuOFZnDCtC4dOHAMA+M2ZRxjavHb+bLSNyOCCO9Yajv/9vzLcfN5RGCxXcMEda7EzX8JBY0fgV/Nm4cLlq7G+ew8y6SS+eeJ7kMuksPjMI/DFm56HwJ0RmWRV+jY9uUxCExf9hRKuP/s/cPpvn9bWXzt/NqbuOwoLPzgZ9724Fbd+8WiMGdmChy/qwNzrn8ZnZo7D/l2jAMifj7d684b3/CefOQw/uNeYt1Z9v8eMbAnyVD2RTCbQ3p6L7Pj1Ikg/rteJEoM2gsvsxTWnxjLnxDWnCzOIwKq8tEaBq/4PVEdvzWLVCvNyNXJrtVxdlkqnUC6WkUwnUSwUkc6kh7IqKH1SMy/I/w9lZFAjuuo5qhPR1NdAtSXIr1FFi+Kqr5VVpoVCuaJFdQfLFU+zs3myLBTLFVvBYWxLErnQmwBVvPmJYqrvv9v3kl4cOf1o0n/unLIyaG3ZHNdKjFkd12ksWH0/+v1RwPPaNttY4rErfBTApYyxjyrPvwXgAMbYt9Rt7Dy5Pf0FLb+oCs8tZadZ7FZtTurMoiIBm3rztp7ca1esq/IHqymgFh4zyeDzFPAxMk0wWAGKZakqM0U6QdA1MoO9hTI+PX1fPLGh1/ZzkMllUNAVVTC//1bvuWpVEJ5cf9RqV4jaquDXi8tjU/AqcN3ErVergoresmD1fzKdtLQv6K0L+qwLqj+Xx7bgx5sbZ8uCsCs0FrXmN/Z698DLXYKwJkUGUyAl/MwKcWHqvrnA7ApPAZhIKVXDY8cCuN9tp1oS6NvNYrdrc2NPHrsGSpjYmcXiuTMwZewIzSpxwtSxyGVSWHjMJCw9c7YmrjtzGSw9c7aWauyiu15qOIG7z0j5Akcg394HgLSPfBl23/+pBMHIzFCD+41uwYHtso86QYDTZ4/HGbPHIZ0kqEiyZ/bnn5kmC9CKhHQqgZsWzNYErt3nQI3oq5h/4Fi956qF5epTDqt6v4d71oNaiTqBvpNVwa7KlltGBX0UF7C3KRSK+tv99gJXb08AhoSs3mJg9T/vw60tAFX2BQBV1gV9qWE144KTbUF+vSTuTAuGbRwLRUT7mYr6My3wBs+teSe83n73citcb2twutPg1RIQxK16P5kVwnzEAVe7AmOsn1L6nwCuoZR2A1ijn3RmRxgJ9N3a1BcLUEWs/jh24lnf7nsntOHfm/pw+Sem4vIH1+HoCe14ZtNOjEgnsXlnHm3ZNI6Z1I5/bejFO7sGUaxIOHhsFm9sz0OCLP4kSS6EQAAcuu8I9OZL2LZ7EPuMzCBfLEOSgPZcBu+d0I67X9wGSBJKEpAigEQIDh6bw2vdew2R0VSCoDWdgCQB/YUyMimCzxy+P06fNQ4AcMeqLfgb68aSM2bihqc24qk3+9CzdwCpZBJjchm8vqMfuTTB2JGtmD1+FO5e+y4AYHRLCicfvi8efW0HtvUNIJNK4JCuHF59dy/OmD0O2XQSD7wib/vJafvg9FnjsHD5anx4ylhc8MHJWt8ef71He0/u+MJILV/xuLZsTZ8Dp/f8uIPHYFxb1vb9FtQXt6wKlvtwRh54KpyZq5v1mwoy6KO4KqpNQb/cLA6tBC4gi0yz8NT/b47gSsVB8EDSLZbRX711QY9qXwBQZV2Q+2x8rj9X1bagX96q+6WsvoZqZFdvUbB6DsjvFVdieh+WBd62Bc1DLTYGgM9WULWP6TPGa23Q4/T9xyO+nfoa1hgI2vceB6EbejGIMBL2e21TvYXM267TXwCG/3v7CxjXltXytarre/sLaE0n0ZmThW2+WNb+12/X01+oOoZqpzCjnmM6m0ExX6g6Z/3rYD7Olr48OpQotnrcgWIZHbmMdlx1f3W9ftKe/vhWr7fbe+L0nOf9qXfhB780g10hDKuCeT9zWjCzVcGuVKybVUEVaqrItUsZ5mRTMJfq5RW4VuK2StgWXVIYplsNT0l6yF+u2hSs/uqzL5itC1YZF+xsC1YpxawyLXixLKjPnSwLtaYSqzXDgrArNBZBRuajTM0VZAlrO6K+ixIWEzpbuMZs6GV9w0igH1ZSfn1k1+mvYZkukmhoS1mubmvVhn4/83onz3L7yBbsLFXbPZyi1uN0/bHsr66P5vU8r7fbNrW+Z6IQQ2Nj58d12s6M04Qz3iiu+da8lQ8X8CZwHcWtnagtGCs+IpO13F59NXiiu3YRXfW5eh56VKELwPDauEVzAXiegOY0QUwfofUzkUxMPhtemH+w1CJ6rT43fiO+Ve249ItnYqUTPCJ5uI+L0EWuQCBoHOrpXfRjVbBLGwbYe3H1KcMAY9EH8z6qD7dK8JoErl301lLcmgWtFVbbZLJaO2axy2tdUPuvktaJV/O5Z3QZFeTXLAGnTAuAUeAWKmUtb26QloWgKJcl3x5PQbyxel+DFr56ghLBtu1z9r1WkTwcECJXIGgg3KoPUkpbAVwF4G0AhwBYxBhbF3a//PhxVdwqnDlhngRlFcUFYLApmNHbFPSCUMuD6yBwbcWtWbQWPFZazLRaCl/1VdbLW7Pg1QtdYKhghDmKmzHdDSkYvLrGi6c5mgsY04nZoYpYs+j1Ijgb2Zcb1/E6HHD6fNX6Y95PdNSLbaBRPt+NgBC5AkGDoFQfXAxd9UFK6UdNE0EvArCJMfYzSunhAH4P4IMRdFeD16rghJ1VQX3OG8UFjJPNzDYFYGiimSeBayVu9cKWc9KZJRaCV4LRwuAmdIGhyK56jmb0k9AA52guANsJaFFZFuJGo47X4YCfiH4UwjgONLqnV4hcgaBxsKs+qL9ongTgUgBgjL1IKZ1JKR3NGNsVRAfq/YXnZFXwE8UdtPCyA0abgj4NF2AvcG2jt6q41QtbtwlnPKhiV7ExmKO6VkJXPrfqc05b5Bo0vza80VwANVkWgiKGwjjy8SoIjrhZXeplLYvZmPJMICI37jPJAaBLqZ7VLIjziS8hnotr9UGHbQwXTdvZ5OnYD2WBoFEIf7wKhi/iu5oL4VoWCBqHdwHoFfRoZZnXbQQCQfiI8SoQRIwQuQJB42BZfZBS2kkpHa0sux/ybVIoHr/V4tanQBAJYrwKBBETSDEIgUBQHyilHwNwOoBuAEXG2A8ppT8D0MMYW0QpzUKerb0VwBQAV4jZ2gJBNIjxKhBEy7ARuZTSXwDoB7AHwEwAFzHGtkXbK2+4paNpJCilBwP4CYCVAA4AsIMx9qNoe1UbygXrGQB/Y4z9V9T9cYJSeiGAwwGsgxxhWsQYe6rOfYh8TFJKEwC+DODHAD7CGFtbp+NGPpYppftBHoMzGWNHRXD8yL8DlPf/XsjjNgPgYADnMcY4khvXl6jH7HAer8qxIx2zYrz6G6/Dya6wlzH2PcbYTwG8AOB7UXfIC7p0NN9kjF0OYAal9KPR9qomOgHcxhj7OWPsQgDzKKVHRt2pGvkJ5M9WI9AC4OuMsZ8BuBFAFD8w4jAmZ0L+wnSv+x0QMRrLHwBwN4CoZrDE5TvgKcbYjxhj/w0gB1nIxJGox+ywHK9AbMasGK8ynsbrsEkhprwgKgnIv0YbCZ50NA0DY+xZ06IEgL1R9CUIKKVnQX5PZgAYGXF3XFEulCpTALwcQR8iH5OMsRcAgFJaz8PGYiwzxu6glB5fz2Oajh/5dwBjrAL5xykopSnIESpWzz7wEvWYHcbjFYjBmBXj1d94bSqRSyl9CMC+FqsuY4zdo2zTDuDjAE6rY9eCgCcdTUNCKT0FwEOMsVej7osfKKWHApjGGLuUUjoj6v6ouI0H5fbXdwHMRkjRqziMSZ4+1JmmHct+ifo7gFJ6IoBvAriPMfZcFH1Q+hHpmBXj1RYxZnU00nhtKpHLGDvRaT2ltA3AdZA9HD316VVgNGWqGUrphwF8GHLln0blFAADlNJLIN9SylBKL2KMXR1lp9zGg+Knu5BS+hEAfwXw3nr3oR5j0q0PEdCUY9kvcfgOYIw9BOAhSulNlNKvMsZ+HVE/Ih2zYrzaIsasQqON12HjyaWUjoU8OL/NGNtAKW20SK5lOpoI+1MzlNKTAJwI4EIA+1FK3x9xl3zBGPsfxSO0CMC/APw7aoHrBqX0Yt3TDQAOiqAPjT4m/dJ0Y9kvUX8HUEoPVfqgEslY4CHqMTuMxysgxiyAxhyvwym7wkrIkWv11+duxtinI+ySZ6zS0UTcJd8ohvXHAai3GkYAuI4xdmNknaoR5Uv/AsizPq9jjN0acZdsoZT+CkABwHbIkzluY4z9pc59iHxMUko7IL9n/w/AMgB/ZIw9XYfjRj6WKaXHATgbwCcA/AbA/9Yzq0AcvgOUGeM/hzxjPA1gGoBvxDHzTtRjdjiPV+XYkY5ZMV79jddhI3IFAoFAIBAIBMOHYWNXEAgEAoFAIBAMH4TIFQgEAoFAIBA0HULkCgQCgUAgEAiaDiFyBQKBQCAQCARNhxC5AoFAIBAIBIKmQ4hcgUAgEAgEAkHTIUSuQCAQCAQCgaDpECJXIBAIBAKBQNB0/H8uVW5f3AvWBwAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pyplot.rc(\"figure\", figsize=[12, 4])\n", "\n", "pyplot.subplot(131)\n", "pyplot.title(\"random scatter\")\n", "pyplot.scatter(*normal_gamma.sample(1000, seed=1000), marker=\"x\")\n", "\n", "pyplot.subplot(132)\n", "pyplot.title(\"probability density\")\n", "grid = numpy.mgrid[-3:3:100j, 0:4:100j]\n", "pyplot.contourf(grid[0], grid[1], normal_gamma.pdf(grid), 50)\n", "\n", "pyplot.subplot(133)\n", "pyplot.title(\"cumulative distibution\")\n", "pyplot.contourf(grid[0], grid[1], normal_gamma.cdf(grid), 50)\n", "\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rosenblatt transformation\n", "\n", "One of the more sure-fire ways to create random variables, is to first\n", "generate classical uniform samples and then use a inverse transformation to\n", "map the sample to have the desired properties. In one-dimension, this mapping\n", "is the inverse of the cumulative distribution function, and is available as\n", "[chaospy.Distribution.ppf()](../../api/chaospy.Distribution.ppf.rst):" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.467553Z", "iopub.status.busy": "2021-05-18T10:56:13.467235Z", "iopub.status.idle": "2021-05-18T10:56:13.614112Z", "shell.execute_reply": "2021-05-18T10:56:13.614368Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pyplot.subplot(121)\n", "pyplot.title(\"standard uniform\")\n", "u_samples = chaospy.Uniform(0, 1).sample(10000, seed=1234)\n", "pyplot.hist(u_samples, 30)\n", "\n", "pyplot.subplot(122)\n", "pyplot.title(\"transformed normal\")\n", "q_samples = normal.inv(u_samples)\n", "pyplot.hist(q_samples, 30)\n", "\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that `u_samples` and `q_samples` here consist of independently\n", "identical distributed samples, the joint set `(u_samples, q_samples)` are\n", "not. In fact, they are highly dependent by following the line of the normal\n", "cumulative distribution function shape:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.616901Z", "iopub.status.busy": "2021-05-18T10:56:13.616589Z", "iopub.status.idle": "2021-05-18T10:56:13.734943Z", "shell.execute_reply": "2021-05-18T10:56:13.735206Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pyplot.subplot(121)\n", "pyplot.title(\"coupled samples\")\n", "pyplot.scatter(q_samples, u_samples)\n", "\n", "pyplot.subplot(122)\n", "pyplot.title(\"normal cumulative distribution\")\n", "pyplot.plot(q_loc, normal.cdf(q_loc))\n", "\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This idea also generalizes to the multivariate case. There the mapping\n", "function is called an inverse Rosenblatt transformation $T^{-1}$, and is\n", "defined in terms of conditional distribution functions:\n", "\n", "$$\n", "T^{-1}(q_0, q_1, q_2, \\dots) =\n", " \\left[ F^{-1}_{Q_0}(q_0),\n", " F^{-1}_{Q_1\\mid Q_0}(q_1),\n", " F^{-1}_{Q_2\\mid Q_1,Q_0}(q_2), \\dots \\right]\n", "$$\n", "\n", "And likewise a forward Rosenblatt transformation is defined as:\n", "\n", "$$\n", "T(q_0, q_1, q_2, \\dots) =\n", " \\left[ F_{Q_0}(q_0),\n", " F_{Q_1\\mid Q_0}(q_1),\n", " F_{Q_2\\mid Q_1,Q_0}(q_2), \\dots \\right]\n", "$$\n", "\n", "These functions can be used to map samples from standard multivariate uniform\n", "distribution to a distribution of interest, and vise-versa.\n", "\n", "In `chaospy` these methods are available through\n", "[chaospy.Distribution.inv()](../../api/chaospy.Distribution.inv.rst)\n", "and\n", "[chaospy.Distribution.fwd()](../../api/chaospy.Distribution.fwd.rst):" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.737674Z", "iopub.status.busy": "2021-05-18T10:56:13.737404Z", "iopub.status.idle": "2021-05-18T10:56:13.854356Z", "shell.execute_reply": "2021-05-18T10:56:13.854064Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pyplot.subplot(121)\n", "pyplot.title(\"standard uniform\")\n", "uu_samples = chaospy.Uniform(0, 1).sample((2, 500), seed=1234)\n", "pyplot.scatter(*uu_samples)\n", "\n", "pyplot.subplot(122)\n", "pyplot.title(\"transformed normal-gamma\")\n", "qq_samples = normal_gamma.inv(uu_samples)\n", "pyplot.scatter(*qq_samples)\n", "\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### User-defined distributions\n", "\n", "The [collection of distributions](../../reference/distribution/collection.rst) contains a\n", "lot of distributions, but if one needs something custom, `chaospy` allows for\n", "the construction of user-defined distributions through\n", "[chaospy.UserDistribution](../../api/chaospy.UserDistribution.rst).\n", "These can be constructed by providing three functions: cumulative\n", "distribution function, a lower bounds function, and a upper bounds function.\n", "As an illustrative example, let us recreate the uniform distribution:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.856829Z", "iopub.status.busy": "2021-05-18T10:56:13.856510Z", "iopub.status.idle": "2021-05-18T10:56:13.863668Z", "shell.execute_reply": "2021-05-18T10:56:13.863384Z" } }, "outputs": [], "source": [ "def cdf(x_loc, lo, up):\n", " \"\"\"Cumulative distribution function.\"\"\"\n", " return (x_loc-lo)/(up-lo)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.865617Z", "iopub.status.busy": "2021-05-18T10:56:13.865345Z", "iopub.status.idle": "2021-05-18T10:56:13.872334Z", "shell.execute_reply": "2021-05-18T10:56:13.872025Z" } }, "outputs": [], "source": [ "def lower(lo, up):\n", " \"\"\"Lower bounds function.\"\"\"\n", " return lo" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.874336Z", "iopub.status.busy": "2021-05-18T10:56:13.874025Z", "iopub.status.idle": "2021-05-18T10:56:13.880740Z", "shell.execute_reply": "2021-05-18T10:56:13.881002Z" } }, "outputs": [], "source": [ "def upper(lo, up):\n", " \"\"\"Upper bounds function.\"\"\"\n", " return up" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The user-define distribution takes these functions, and a dictionary with the\n", "parameter defaults as part of its initialization:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.883128Z", "iopub.status.busy": "2021-05-18T10:56:13.882809Z", "iopub.status.idle": "2021-05-18T10:56:13.889655Z", "shell.execute_reply": "2021-05-18T10:56:13.889368Z" } }, "outputs": [], "source": [ "user_distribution = chaospy.UserDistribution(\n", " cdf=cdf, lower=lower, upper=upper, parameters=dict(lo=-1, up=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The distribution can then be used in the same was as any other\n", "[chaospy.Distribution](../../api/chaospy.Distribution.rst):" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:13.892229Z", "iopub.status.busy": "2021-05-18T10:56:13.891905Z", "iopub.status.idle": "2021-05-18T10:56:14.062173Z", "shell.execute_reply": "2021-05-18T10:56:14.061877Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pyplot.subplot(131)\n", "pyplot.title(\"binned random samples\")\n", "pyplot.hist(user_distribution.sample(10000), 30)\n", "\n", "pyplot.subplot(132)\n", "pyplot.title(\"probability density\")\n", "x_loc = numpy.linspace(-2, 2, 200)\n", "pyplot.plot(x_loc, user_distribution.pdf(x_loc))\n", "\n", "pyplot.subplot(133)\n", "pyplot.title(\"cumulative distribution\")\n", "pyplot.plot(x_loc, user_distribution.cdf(x_loc))\n", "\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternative, it is possible to define the same distribution using cumulative\n", "distribution and point percentile function without the bounds:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:14.064567Z", "iopub.status.busy": "2021-05-18T10:56:14.064249Z", "iopub.status.idle": "2021-05-18T10:56:14.071542Z", "shell.execute_reply": "2021-05-18T10:56:14.071196Z" } }, "outputs": [], "source": [ "def ppf(q_loc, lo, up):\n", " \"\"\"Point percentile function.\"\"\"\n", " return q_loc*(up-lo)+lo\n", "\n", "\n", "user_distribution = chaospy.UserDistribution(\n", " cdf=cdf, ppf=ppf, parameters=dict(lo=-1, up=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition to the required fields, there are a few optional ones. These does\n", "not provide new functionality, but allow for increased accuracy and/or lower\n", "computational cost for the operations where they are used. These include raw\n", "statistical moments which is used by\n", "[chaospy.Distribution.mom()](../../api/chaospy.Distribution.rst):" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:14.073785Z", "iopub.status.busy": "2021-05-18T10:56:14.073474Z", "iopub.status.idle": "2021-05-18T10:56:14.080663Z", "shell.execute_reply": "2021-05-18T10:56:14.080318Z" } }, "outputs": [], "source": [ "def mom(k_loc, lo, up):\n", " \"\"\"Raw statistical moment.\"\"\"\n", " return (up**(k_loc+1)-lo**(k_loc+1))/(k_loc+1)/(up-lo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And three terms recurrence coefficients which is used by the method\n", "[chaospy.Distribution.ttr()](../../api/chaospy.Distribution.ttr.rst)\n", "to pass analytically to Stieltjes' method:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:14.082858Z", "iopub.status.busy": "2021-05-18T10:56:14.082545Z", "iopub.status.idle": "2021-05-18T10:56:14.089330Z", "shell.execute_reply": "2021-05-18T10:56:14.089037Z" } }, "outputs": [], "source": [ "def ttr(k_loc, lo, up):\n", " \"\"\"Three terms recurrence.\"\"\"\n", " return 0.5*up+0.5*lo, k_loc**2/(4*k_loc**2-1)*lo**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What these coefficients are and why they are important are discussed in the\n", "section [orthogonal polynomials](../polynomial/orthogonality.ipynb)." ] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "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": "3.9.5" } }, "nbformat": 4, "nbformat_minor": 4 }