{ "metadata": { "name": "", "signature": "sha256:85803ac598aef29d5de2555d7ee246f55a8ccbe8c5b71fd2c09f0e19e0428563" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Matrix Algebra\n", "====\n", "\n", "Date: October 14, 2014\n", "\n", "Copyright (c) 2014 Rafael A. Irizarry MIT License" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# special IPython command to prepare the notebook for matplotlib\n", "%matplotlib inline \n", "\n", "import numpy as np\n", "import scipy\n", "import pandas as pd # pandas\n", "import matplotlib.pyplot as plt # module for plotting \n", "from mpl_toolkits.mplot3d import Axes3D #3D plotting\n", "import datetime as dt # module for manipulating dates and times\n", "\n", "import requests \n", "import scipy.stats as stats\n", "import statsmodels.api as sm\n", "from scipy.stats import binom\n", "from __future__ import division\n", "import re\n", "from StringIO import StringIO\n", "from zipfile import ZipFile \n", "from pandas import read_csv\n", "from urllib import urlopen\n", "\n", "import sklearn\n", "import sklearn.preprocessing\n", "import sklearn.datasets\n", "\n", "#nice defaults for matplotlib\n", "from matplotlib import rcParams\n", "\n", "dark2_colors = [(0.10588235294117647, 0.6196078431372549, 0.4666666666666667),\n", " (0.8509803921568627, 0.37254901960784315, 0.00784313725490196),\n", " (0.4588235294117647, 0.4392156862745098, 0.7019607843137254),\n", " (0.9058823529411765, 0.1607843137254902, 0.5411764705882353),\n", " (0.4, 0.6509803921568628, 0.11764705882352941),\n", " (0.9019607843137255, 0.6705882352941176, 0.00784313725490196),\n", " (0.6509803921568628, 0.4627450980392157, 0.11372549019607843),\n", " (0.4, 0.4, 0.4)]\n", "\n", "rcParams['figure.figsize'] = (10, 6)\n", "rcParams['figure.dpi'] = 150\n", "rcParams['axes.color_cycle'] = dark2_colors\n", "rcParams['lines.linewidth'] = 2\n", "rcParams['axes.grid'] = True\n", "rcParams['axes.facecolor'] = '#eeeeee'\n", "rcParams['font.size'] = 14\n", "rcParams['patch.edgecolor'] = 'none'" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 392 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Motivation\n", "====" ] }, { "cell_type": "code", "collapsed": false, "input": [ "url_exprs = \"https://raw.githubusercontent.com/cs109/2014_data/master/exprs_GSE5859.csv\"\n", "X = pd.read_csv(url_exprs, index_col=0)\n", "\n", "url_sampleinfo = \"https://raw.githubusercontent.com/cs109/2014_data/master/sampleinfo_GSE5859.csv\"\n", "sampleid = pd.read_csv(url_sampleinfo)\n", "\n", "a = list(sampleid.filename)\n", "b = list(X.columns)\n", "matchIndex = [b.index(x) for x in a]\n", "X = X[matchIndex]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 393 }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", " Our data is usually saved in matrices. \n", "\n", "\n", "\n", "In the gene expression example data, $X$, was $8793 \\times 208$.\n", "\n", "\n", "Say you want to compute the average of each column:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "A = np.repeat(1/float(X.shape[0]), X.shape[0]).reshape(1, X.shape[0])\n", "colmeans = np.dot(A, X)\n", "print \"Column averages:\",np.round(colmeans,2)[0]\n", "pd.DataFrame(np.array([X.columns.values, np.round(colmeans,2)[0]]).transpose(), \n", " columns = [\"Gene\", \"Average\"]).head(15)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Column averages: [ 5.74 5.75 5.69 5.73 5.72 5.72 5.72 5.75 5.62 5.73 5.72 5.72\n", " 5.62 5.71 5.68 5.7 5.71 5.74 5.71 5.72 5.69 5.71 5.76 5.71\n", " 5.74 5.71 5.71 5.71 5.71 5.72 5.71 5.69 5.74 5.73 5.73 5.73\n", " 5.73 5.75 5.75 5.7 5.81 5.84 5.72 5.68 5.72 5.7 5.73 5.74\n", " 5.81 5.73 5.74 5.73 5.69 5.72 5.69 5.7 5.7 5.71 5.72 5.71\n", " 5.74 5.71 5.71 5.74 5.7 5.72 5.71 5.73 5.73 5.69 5.7 5.72\n", " 5.73 5.69 5.72 5.73 5.73 5.72 5.72 5.69 5.73 5.69 5.73 5.72\n", " 5.75 5.75 5.73 5.75 5.72 5.72 5.73 5.72 5.72 5.71 5.74 5.71\n", " 5.69 5.65 5.68 5.73 5.74 5.74 5.74 5.73 5.73 5.74 5.75 5.74\n", " 5.75 5.73 5.73 5.73 5.73 5.74 5.68 5.73 5.74 5.74 5.73 5.73\n", " 5.73 5.72 5.72 5.73 5.74 5.74 5.73 5.73 5.75 5.73 5.74 5.74\n", " 5.73 5.74 5.73 5.73 5.73 5.74 5.74 5.73 5.73 5.73 5.75 5.74\n", " 5.74 5.74 5.74 5.73 5.74 5.75 5.76 5.74 5.74 5.74 5.75 5.72\n", " 5.75 5.72 5.72 5.75 5.71 5.73 5.73 5.73 5.75 5.73 5.75 5.73\n", " 5.74 5.73 5.74 5.75 5.73 5.73 5.73 5.73 5.74 5.75 5.74 5.74\n", " 5.74 5.74 5.74 5.74 5.75 5.75 5.74 5.75 5.75 5.76 5.75 5.74\n", " 5.75 5.74 5.75 5.74 5.76 5.75 5.75 5.75 5.76 5.75 5.75 5.76\n", " 5.74 5.73 5.74 5.73]\n" ] }, { "html": [ "
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GeneAverage
0 GSM25349.CEL.gz 5.74
1 GSM25350.CEL.gz 5.75
2 GSM25356.CEL.gz 5.69
3 GSM25357.CEL.gz 5.73
4 GSM25358.CEL.gz 5.72
5 GSM25359.CEL.gz 5.72
6 GSM25360.CEL.gz 5.72
7 GSM25361.CEL.gz 5.75
8 GSM25377.CEL.gz 5.62
9 GSM25378.CEL.gz 5.73
10 GSM25385.CEL.gz 5.72
11 GSM25386.CEL.gz 5.72
12 GSM25399.CEL.gz 5.62
13 GSM25400.CEL.gz 5.71
14 GSM25401.CEL.gz 5.68
\n", "

15 rows \u00d7 2 columns

\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 394, "text": [ " Gene Average\n", "0 GSM25349.CEL.gz 5.74\n", "1 GSM25350.CEL.gz 5.75\n", "2 GSM25356.CEL.gz 5.69\n", "3 GSM25357.CEL.gz 5.73\n", "4 GSM25358.CEL.gz 5.72\n", "5 GSM25359.CEL.gz 5.72\n", "6 GSM25360.CEL.gz 5.72\n", "7 GSM25361.CEL.gz 5.75\n", "8 GSM25377.CEL.gz 5.62\n", "9 GSM25378.CEL.gz 5.73\n", "10 GSM25385.CEL.gz 5.72\n", "11 GSM25386.CEL.gz 5.72\n", "12 GSM25399.CEL.gz 5.62\n", "13 GSM25400.CEL.gz 5.71\n", "14 GSM25401.CEL.gz 5.68\n", "\n", "[15 rows x 2 columns]" ] } ], "prompt_number": 394 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the distribution of the averages: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.hist(colmeans[0], bins = np.arange(5.60, 5.86, 0.02))\n", "plt.xlim(5.60, 5.84)\n", "plt.xticks(np.arange(5.60, 5.86, 0.04))\n", "plt.xlabel(\"Average\")\n", "plt.ylabel(\"Frequency\")\n", "plt.title(\"Histogram of colmeans\")\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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epnv37mrTpk2hafQAAADCnVd79IoVK6bq1aurb9++6t69u8qVK3faNgcOHNDN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\nE3Xvvfdq1KhRkqSjR48qPj5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"text": [ "" ] } ], "prompt_number": 395 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matrix Notation\n", "====\n", "\n", "* Let $X$ be a data matrix with $N$ rows and $p$ columns\n", "\n", "* The vector of column averages:\n", "\n", "$$ \\left( \\frac{1}{N}\\sum_{i=1}^N X_{i,1}, \\dots, \\frac{1}{N}\\sum_{i=1}^N X_{i,p}\\right)$$\n", "\n", "can be written like this $AX$ with $A=(\\frac{1}{N},\\dots,\\frac{1}{N})$\n", "\n", "Here are the **matrix operations**:\n", "$$AX = \\begin{pmatrix}\n", " \\frac{1}{N} & \\frac{1}{N} & \\dots & \\frac{1}{N}\n", " \\end{pmatrix}\n", "\\begin{pmatrix}\n", " X_{1,1}&\\dots & X_{1,p} \\\\\n", " X_{2,1}&\\dots & X_{2,p} \\\\\n", " & \\vdots & \\\\\n", " X_{N,1}&\\dots & X_{N,p} \\\\\n", " \\end{pmatrix}$$\n", " \n", "$$ =\n", " \\begin{pmatrix}\n", " \\bar{X}_1 & \\bar{X}_2 & \\dots &\\bar{X}_N\n", " \\end{pmatrix}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the ** row averages**:\n", "\n", "$$\n", "XB = \\begin{pmatrix}\n", " X_{1,1}&\\dots & X_{1,p} \\\\\n", " X_{2,1}&\\dots & X_{2,p} \\\\\n", " & \\vdots & \\\\\n", " X_{N,1}&\\dots & X_{N,p} \\\\\n", " \\end{pmatrix}\n", " \\begin{pmatrix}\n", " 1/p\\\\\n", " 1/p\\\\\n", " \\vdots\\\\\n", " 1/p\\\\\n", " \\end{pmatrix}=\n", " \\begin{pmatrix}\n", " \\bar{X}_1 \\\\\n", " \\bar{X}_2 \\\\\n", " \\vdots\\\\\n", " \\bar{X}_q\\\\\n", " \\end{pmatrix}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matrix Notation (more general)\n", "====\n", "$$AX = \\begin{pmatrix}\n", " a_1 & a_2 & \\dots & a_N\n", " \\end{pmatrix}\n", "\\begin{pmatrix}\n", " X_{1,1}&\\dots & X_{1,p} \\\\\n", " X_{2,1}&\\dots & X_{2,p} \\\\\n", " & \\vdots & \\\\\n", " X_{N,1}&\\dots & X_{N,p} \\\\\n", " \\end{pmatrix}$$\n", " \n", "$$ =\n", " \\begin{pmatrix}\n", " \\sum_{i=1}^N a_i X_{i,1} & \\dots & \\sum_{i=1}^N a_i X_{i,p}\n", " \\end{pmatrix}\n", "$$\n", "Convenient and fast for coding" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matrix Notation\n", "====\n", "\n", "* Say for each gene you want to compute\n", " 1. the average across all samples\n", " + the difference between males and females" ] }, { "cell_type": "code", "collapsed": false, "input": [ "sex = sampleid['sex']=='M'\n", "A = np.repeat(1/float(X.shape[1]), X.shape[1]).reshape(1, X.shape[1])[0]\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 396 }, { "cell_type": "code", "collapsed": false, "input": [ "A = np.repeat(1/float(X.shape[1]), X.shape[1]).reshape(1, X.shape[1])[0]\n", "B = [1./sum(sex) if x == True else -1./sum(1-sex) for x in sex]\n", "pd.DataFrame([A,B], columns = sampleid.filename.values)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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2 rows \u00d7 208 columns

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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 397, "text": [ " GSM25349.CEL.gz GSM25350.CEL.gz GSM25356.CEL.gz GSM25357.CEL.gz \\\n", "0 0.004808 0.004808 0.004808 0.004808 \n", "1 0.008197 0.008197 0.008197 0.008197 \n", "\n", " GSM25358.CEL.gz GSM25359.CEL.gz GSM25360.CEL.gz GSM25361.CEL.gz \\\n", "0 0.004808 0.004808 0.004808 0.004808 \n", "1 0.008197 0.008197 -0.011628 0.008197 \n", "\n", " GSM25377.CEL.gz GSM25378.CEL.gz GSM25385.CEL.gz GSM25386.CEL.gz \\\n", "0 0.004808 0.004808 0.004808 0.004808 \n", "1 0.008197 0.008197 0.008197 0.008197 \n", "\n", " GSM25399.CEL.gz GSM25400.CEL.gz GSM25401.CEL.gz GSM25402.CEL.gz \\\n", "0 0.004808 0.004808 0.004808 0.004808 \n", "1 -0.011628 -0.011628 0.008197 -0.011628 \n", "\n", " GSM25409.CEL.gz GSM25410.CEL.gz GSM25426.CEL.gz GSM25427.CEL.gz \n", "0 0.004808 0.004808 0.004808 0.004808 ... \n", "1 0.008197 -0.011628 0.008197 0.008197 ... \n", "\n", "[2 rows x 208 columns]" ] } ], "prompt_number": 397 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matrix Notation\n", "===\n", "$$\\begin{pmatrix}\n", " X_{1,1}&\\dots & X_{1,p} \\\\\n", " X_{2,1}&\\dots & X_{2,p} \\\\\n", " & \\vdots & \\\\\n", " X_{N,1}&\\dots & X_{N,p} \\\\\n", " \\end{pmatrix}\n", " \\begin{pmatrix}\n", " 1/p&a_1\\\\\n", " 1/p&a_2\\\\\n", " \\vdots\\\\\n", " 1/p&a_p\\\\\n", " \\end{pmatrix}\n", "$$\n", "with \n", "$$\n", "\\begin{align*}\n", " a_j &=\n", " \\begin{cases}\n", " -1/N_F & \\text{if female } \\\\\n", " 1/N_M & \\text{if male}\n", " \\end{cases}\n", "\\end{align*}\n", "$$\n", "\n", "with\n", "$N_F$=number of females and $N_M$=number of males." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matrix Notation (even more general)\n", "====\n", "$$AX = \\begin{pmatrix}\n", " a_{1,1} & a_{1,2} & \\dots & a_{1,N}\\\\\n", " a_{2,1} & a_{2,2} & \\dots & a_{2,N}\\\\\n", " & & \\vdots & \\\\\n", " a_{M,1} & a_{M,2} & \\dots & a_{M,N}\\\\\n", " \\end{pmatrix}\n", "\\begin{pmatrix}\n", " X_{1,1}&\\dots & X_{1,p} \\\\\n", " X_{2,1}&\\dots & X_{2,p} \\\\\n", " & \\vdots & \\\\\n", " X_{N,1}&\\dots & X_{N,p} \\\\\n", " \\end{pmatrix}=\n", " \\begin{pmatrix}\n", " \\sum_{i=1}^N a_{1,i} X_{i,1} & \\dots & \\sum_{i=1}^N a_{1,i} X_{i,p}\\\\\n", " & \\vdots & \\\\\n", " \\sum_{i=1}^N a_{M,i} X_{i,1} & \\dots & \\sum_{i=1}^N a_{M,i} X_{i,p}\n", "\\end{pmatrix}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Regression Models\n", "====\n", "\n", "We used regression with our Baseball data. For example\n", "\n", "$$\n", "Y_i= \\beta_0 + X_{i}\\beta_1 + \\varepsilon_i, i=1,\\dots,N\n", "$$ \n", "\n", "with $Y_i$ = runs for team $i$ and $X_{i}$ = BB for team $i$.\n", "\n", "We need to find the $\\beta_0,\\beta_1$ pair that minimizes \n", "\n", "$$\\sum_{i=1}^N (Y_i- \\beta_0 - X_i\\beta_1)^2$$\n", "\n", "How do we do this?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear Algebra Representation\n", "====\n", "\n", "We can write it like this:\n", "\n", "$$\n", "\\begin{pmatrix}\n", "Y_1\\\\\n", "Y_2\\\\\n", "\\vdots\\\\\n", "Y_N\\\\\n", "\\end{pmatrix}\n", "=\n", "\\begin{pmatrix}\n", "1\\\\\n", "1\\\\\n", "\\vdots \\\\\n", "1\\\\\n", "\\end{pmatrix} \n", "\\beta_0 +\n", "\\begin{pmatrix}\n", "X_{1}\\\\\n", "X_{2}\\\\\n", "\\vdots \\\\\n", "X_{N}\\\\\n", "\\end{pmatrix} \\beta_1+ \n", "\\begin{pmatrix}\n", "\\varepsilon_1\\\\\n", "\\varepsilon_2\\\\\n", "\\vdots\\\\\n", "\\varepsilon_N\\\\\n", "\\end{pmatrix}\\\\\n", "$$\n", "\n", "The $Y$ column is a point in $\\mathbb{R}^N$\n", "\n", "The $1$ and $X$ vectors define a subspace, each point defined by the pair $(\\beta_0,\\beta_1)\\in \\mathbb{R}^2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Projections\n", "====\n", "\n", "Recall: The projection of the point $Y$ to the smaller space minimizes the distance.\n", "
\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simplest example\n", "====\n", "\n", "$\\vec{y} \\in \\mathbb{R}^N$ \n", "and $L \\subset \\mathbb{R}^N$ is the space spanned by \n", "\n", "$$\\vec{v}=\\begin{pmatrix} 1\\\\ \\vdots \\\\ 1\\end{pmatrix};\n", "L = \\{ c \\vec{v}; c \\in \\mathbb{R}\\}$$\n", "\n", "What $c$ minimizes distance between $c\\vec{v}$ and $\\vec{y}$? \n", "\n", "Answer: The projection of $\\vec{y}$ onto $L$:\n", "$$\n", "\\mbox{Proj}_L(\\vec{y}) = \\hat{c} \\vec{v}\n", "$$\n", "\n", "So how do we find $\\hat{c}$? \n", "\n", "The projection is orthogonal to the space so:\n", "\n", "$$\n", "(\\vec{y}-\\hat{c}\\vec{v}) \\cdot \\vec{v} = 0\n", "$$\n", "\n", "$$\n", "\\vec{y}\\cdot\\vec{v} - \\hat{c}\\vec{v}\\cdot\\vec{v} = 0\n", "$$\n", "\n", "$$\n", "\\hat{c} = \\frac{\\vec{y}\\cdot\\vec{v}}\n", "{\\vec{v}\\cdot\\vec{v}}\n", "$$\n", "\n", "$$\n", "\\hat{c} = \\frac{\\vec{y}\\cdot\\vec{v}}\n", "{\\vec{v}\\cdot\\vec{v}}\n", "$$\n", "\n", "\n", "Going back to our original notation this means $\\hat{\\beta}_0 = \\bar{Y}$\n", "\n", "In this case calculus would have been just as easy:\n", "\n", "$$\\frac{\\partial}{\\partial\\beta_0}\\sum_{i=1}^N (Y_i - \\beta_0)^2 = 0 \\implies \n", " - 2 \\sum_{i=1}^N (Y_i - \\beta_0) = 0 \\implies$$\n", "\n", "$$ N \\beta_0 = \\sum_{i=1}^N Y_i \\implies \\hat{\\beta_0}=\\bar{Y}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Regression Model\n", "===\n", "Make it slightly more complicated.\n", "\n", "The space is now\n", "\n", "$$ L = \\{ \\beta_0 \\vec{v}_0 + \\beta_1 \\vec{v}_1 ; \\vec{\\beta}=(\\beta_0,\\beta_1) \\in \\mathbb{R}^2 \\}$$\n", "\n", "with \n", "\n", "$$\n", "\\vec{v}_0=\n", "\\begin{pmatrix}\n", "1\\\\\n", "1\\\\\n", "\\vdots \\\\\n", "1\\\\\n", "\\end{pmatrix} \n", "\\mbox{ and }\n", "\\vec{v}_1=\n", "\\begin{pmatrix}\n", "X_{1}\\\\\n", "X_{2}\\\\\n", "\\vdots \\\\\n", "X_{N}\\\\\n", "\\end{pmatrix} \n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Transpose\n", "====\n", "\n", "The columns become the rows\n", "\n", "$$X = \\begin{pmatrix}\n", " X_{1,1}&\\dots & X_{1,p} \\\\\n", " X_{2,1}&\\dots & X_{2,p} \\\\\n", " & \\vdots & \\\\\n", " X_{N,1}&\\dots & X_{N,p} \\\\\n", " \\end{pmatrix} , \\,\n", "X^\\top = \\begin{pmatrix}\n", " X_{1,1}&\\dots & X_{N,1} \\\\\n", " X_{1,2}&\\dots & X_{N,2} \\\\\n", " & \\vdots & \\\\\n", " X_{1,p}&\\dots & X_{N,p} \\\\\n", " \\end{pmatrix}\n", " $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Variance\n", "===\n", "This helps us define projections but also:\n", "\n", "If $X$ is $N\\times p$ matrix of features for which the columns have average 0, \n", "\n", "$$ S = \\frac{1}{N} X^\\top X $$\n", "\n", "* is called the sample covariance matrix\n", "* $S_{i,i}$ is the variance of column $i$\n", "* $S_{i,j}$ entry is the covariance between columns $i$ and $j$. \n", "* $$\\frac{S_{i,j}}{\\sqrt{S_{i,i}S_{j,j}}}$$ is the correlation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Regression Model\n", "====\n", "\n", "Let $X = [ \\vec{v}_0 \\,\\, \\vec{v}_1]$. It's a $N\\times 2$ matrix\n", "\n", "Any point $L$ can be writen as $X\\beta$. \n", "\n", "The orthogonal projection must have\n", "\n", "$X^\\top (\\vec{y}-X\\vec{\\beta}) = 0$\n", "\n", "$$X^\\top X \\vec{\\beta}= X^\\top y $$\n", "\n", "$$\\vec{\\beta}= (X^\\top X)^{-1}X^\\top y$$\n", "\n", "In general, we can write this\n", "\n", "$$\n", "Y_i= \\beta_0 + X_{i,1}\\beta_1 + \\dots X_{i,p} \\beta_p + \\varepsilon_i, i=1,\\dots,N\n", "$$ as\n", "\n", "$$\n", "\\begin{pmatrix}\n", "Y_1\\\\\n", "Y_2\\\\\n", "\\vdots\\\\\n", "Y_N\\\\\n", "\\end{pmatrix}\n", "=\n", "\\begin{pmatrix}\n", "1\\\\\n", "1\\\\\n", "\\vdots \\\\\n", "1\\\\\n", "\\end{pmatrix} \n", "\\beta_0 +\n", "\\begin{pmatrix}\n", "X_{1,1}\\\\\n", "X_{2,1}\\\\\n", "\\vdots \\\\\n", "X_{N,1}\\\\\n", "\\end{pmatrix} \\beta_1+ \n", "\\dots\n", "+\n", "\\begin{pmatrix}\n", "X_{1,p}\\\\\n", "X_{2,p}\\\\\n", " \\vdots \\\\\n", "X_{N,p}\\\\\n", "\\end{pmatrix}\\beta_p\n", "+\n", "\\begin{pmatrix}\n", "\\varepsilon_1\\\\\n", "\\varepsilon_2\\\\\n", "\\vdots\\\\\n", "\\varepsilon_N\\\\\n", "\\end{pmatrix}\\\\\n", "$$\n", "\n", "We can simplify to:\n", "\n", "$$Y = X\\beta + \\varepsilon$$\n", "\n", "with\n", "$$\n", "Y = \\begin{pmatrix}\n", "Y_1\\\\\n", "\\vdots\\\\\n", "Y_N\\\\\n", "\\end{pmatrix}, \\,\n", "X=\\begin{pmatrix}\n", "1&X_{1,1}&\\dots&X_{1,p}\\\\\n", "1&X_{2,1}&\\dots&X_{2,p}\\\\\n", " & \\vdots & \\\\\n", "1&X_{N,1}&\\dots&X_{N,p}\n", "\\end{pmatrix}, \\,\n", "\\beta = \\begin{pmatrix}\n", "\\beta_1\\\\\n", "\\vdots\\\\\n", "\\beta_p\n", "\\end{pmatrix}, \\,\n", "\\varepsilon = \\begin{pmatrix}\n", "\\varepsilon_1\\\\\n", "\\vdots\\\\\n", "\\varepsilon_N\n", "\\end{pmatrix}\n", "$$\n", "\n", "Solution is still \n", "\n", "$$\\hat{\\beta} = (X^\\top X)^{-1} X^\\top Y$$\n", "\n", "### Application to baseball data:\n", "\n", "Read in the data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "zip_folder = requests.get('http://seanlahman.com/files/database/lahman-csv_2014-02-14.zip').content\n", "zip_files = StringIO()\n", "zip_files.write(zip_folder)\n", "csv_files = ZipFile(zip_files)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 398 }, { "cell_type": "code", "collapsed": false, "input": [ "teams = csv_files.open('Teams.csv')\n", "teams = read_csv(teams)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 399 }, { "cell_type": "code", "collapsed": false, "input": [ "teams = csv_files.open('Teams.csv')\n", "teams = read_csv(teams)\n", "dat = teams[(teams['G']==162) & (teams['yearID'] < 2002)]\n", "dat['Singles'] = dat['H']-dat['2B']-dat['3B']-dat['HR']\n", "dat = dat[['R','Singles', 'HR', 'BB']]\n", "dat.head(5)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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RSinglesHRBB
437 505 997 11 344
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5 rows \u00d7 4 columns

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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 400, "text": [ " R Singles HR BB\n", "437 505 997 11 344\n", "1366 744 902 189 681\n", "1367 683 989 90 580\n", "1377 817 1041 199 584\n", "1379 718 973 137 602\n", "\n", "[5 rows x 4 columns]" ] } ], "prompt_number": 400 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Get X and Y:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y = dat.R\n", "X = np.column_stack((np.repeat(1, dat.shape[0]) , dat.BB))\n", "print X" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[ 1 344]\n", " [ 1 681]\n", " [ 1 580]\n", " ..., \n", " [ 1 519]\n", " [ 1 678]\n", " [ 1 511]]\n" ] } ], "prompt_number": 401 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solve for $\\beta$:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "beta = np.linalg.inv(np.dot(X.T, X)).dot(X.T).dot(y)\n", "print beta" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 326.82416279 0.71264016]\n" ] } ], "prompt_number": 402 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The projection: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "proj = X.dot(beta)\n", "print proj" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 571.97237855 812.13211317 740.1554568 743.00601745 755.83354037\n", " 768.66106329 684.56952416 694.54648643 723.05209291 658.91447832\n", " 681.71896351 740.86809696 678.1557627 685.99480448 733.74169534\n", " 661.05239881 661.05239881 748.70713875 703.81080854 681.00632335\n", " 653.21335703 641.09847427 614.01814811 664.61559962 639.67319395\n", " 650.36279638 651.7880767 652.50071687 727.32793388 663.1903193\n", " 685.99480448 693.1212061 631.121512 640.38583411 686.70744465\n", " 673.16728157 617.58134892 682.43160367 598.34006455 721.62681259\n", " 706.66136918 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"language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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8LajtK6wOO/VXf5TlfjMaduGxu6vnwxndntQBFEKIfDRnTgpPP52K2azw2GM2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\nKsMGkIiIiEhl/gL7axSGVx3eLAAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 404 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's add Home Runs:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y = dat.R\n", "X = np.column_stack((np.repeat(1, dat.shape[0]) , dat.BB, dat.HR))\n", "print X" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[ 1 344 11]\n", " [ 1 681 189]\n", " [ 1 580 90]\n", " ..., \n", " [ 1 519 206]\n", " [ 1 678 161]\n", " [ 1 511 213]]\n" ] } ], "prompt_number": 405 }, { "cell_type": "code", "collapsed": false, "input": [ "beta = np.linalg.inv(np.dot(X.T, X)).dot(X.T).dot(y)\n", "print beta\n", "beta.shape" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 287.72267563 0.38971779 1.52204481]\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 406, "text": [ "(3,)" ] } ], "prompt_number": 406 }, { "cell_type": "code", "collapsed": false, "input": [ "new_prox = X.dot(beta)\n", "len(new_prox)\n", "len(y)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 407, "text": [ "663" ] } ], "prompt_number": 407 }, { "cell_type": "code", "collapsed": false, "input": [ "#this requires some 3D plotting\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.scatter(X[:,1], X[:,2], y)\n", "ax.set_xlabel('BB')\n", "ax.set_ylabel('HR')\n", "ax.set_zlabel('R')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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jFSGUa9+XdBGtX9LDDz9M//79Oe+887pr07JCLGO2iPBEQJIknE4nkiR1micq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\nijlz5hAeHo5SqZSqRt9///0888wz0tcQTfKMV/fu3fn888+bNVYmk2FlZ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"text": [ "" ] } ], "prompt_number": 408 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Singular Value Decomposition (SVD)\n", "===\n", "\n", "We have a data matrix with $N$ observations (rows) and $p$ columns. \n", "\n", "We can write our data matrix as\n", "\n", "$$X = U D V^\\top , \\mbox{ with } $$\n", "* $U$ is $N\\times p$ with $U^\\top U=I$\n", "* $V$ is $p\\times p$ with $V^\\top V=I$ and\n", "* $D$ is $p \\times p$ diagonal matrix \n", "\n", "We are changing basis: $XV = UD$ \n", "\n", "And can change back $XVV^\\top = X$\n", "\n", "\n", "SVD\n", "====\n", "\n", "* Say the columns of $X$ are perfectly correlated" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Y1 = np.random.normal(0, size = (100,1))\n", "Y = np.column_stack((Y1,Y1,Y1,Y1,Y1))\n", "Y.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 409, "text": [ "(100, 5)" ] } ], "prompt_number": 409 }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Then we really have just one column, the SVD catches this:\n", "\n", " X = U[:,0] d[0,0] Vh[0,:] " ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Singular Value Decomposition\n", "#U are the left singular vectors\n", "#d are the singular values\n", "#U*d gives PCA scores\n", "#V are the right singular vectors -- PCA loadings\n", "U, d, Vh = scipy.linalg.svd(Y, full_matrices=False)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 410 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Print the eigenvalues:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print np.round(d, 6)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 22.872792 0. 0. 0. 0. ]\n" ] } ], "prompt_number": 411 }, { "cell_type": "code", "collapsed": false, "input": [ "U1 = U[:,0].reshape(100,1)\n", "dV1 = (d[0] * Vh[0,:].reshape(1,5))\n", "newY = np.dot(U1, dV1)\n", "print dV1" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[-10.22902343 -10.22902343 -10.22902343 -10.22902343 -10.22902343]]\n" ] } ], "prompt_number": 412 }, { "cell_type": "code", "collapsed": false, "input": [ "np.round(np.abs(Y-newY).max(),6)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 413, "text": [ "0.0" ] } ], "prompt_number": 413 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Motivating SVD\n", "====\n", "Consider this simple linear combination:\n", "\n", "$$ \\Delta_j = (Y_{1,j}, \\dots, Y_{N,j})'(1/N_1,\\dots,1/N_1,-1/N_2,\\dots,-1/N_2) =$$ \n", "\n", "$$\\frac{1}{N_1}\\sum_{i=1}^{N_1} Y_{i,j} - \\frac{1}{N_2}\\sum_{i=N_1+1}^{N} Y_{i,j}, N_2=N-N_1$$\n", "\n", "Try to find the $N_1$ that maximizes the variance\n", "\n", "$$\n", "\\frac{1}{p}\\sum_{j=1}^p \\Delta_j^2\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Back to gene expression example" ] }, { "cell_type": "code", "collapsed": false, "input": [ "url_exprs = \"https://raw.githubusercontent.com/cs109/2014_data/master/exprs_GSE5859.csv\"\n", "exprs = pd.read_csv(url_exprs, index_col=0)\n", "\n", "url_sampleinfo = \"https://raw.githubusercontent.com/cs109/2014_data/master/sampleinfo_GSE5859.csv\"\n", "sampleinfo = pd.read_csv(url_sampleinfo)\n", "## Re-order the columns in the `exprs` DataFrame to match the order of the file names in the `sampleinfo` DataFrame.\n", "fns = list(sampleinfo.filename)\n", "cns = list(exprs.columns)\n", "matchIndex = [cns.index(x) for x in fns]\n", "exprs = exprs[matchIndex]\n", "\n", "##Add a column to the `sampleinfo` DataFrame titled `days` containing the days since October 31, 2002.\n", "sampleinfo[\"date\"] = pd.to_datetime(sampleinfo.date)\n", "oct31 = dt.datetime(2002,10,31,0,0)\n", "\n", "sampleinfo[\"days\"] = map(lambda x: (x - oct31).days, sampleinfo.date)\n", "\n", "##Subset for CEU only samples only. \n", "sampleinfoCEU = sampleinfo[sampleinfo.ethnicity == \"CEU\"]\n", "exprsCEU = exprs[sampleinfoCEU.filename]\n", "\n", "###Remove the mean\n", "X = exprsCEU.apply(lambda x: x - exprsCEU.mean(axis=1), \\\n", " axis = 0)\n", "X=X.T\n", "X.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 415, "text": [ "(102, 8793)" ] } ], "prompt_number": 415 }, { "cell_type": "markdown", "metadata": {}, "source": [ "** SVD **" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Singular Value Decomposition\n", "#U are the left singular vectors\n", "#d are the singular values\n", "#U*d gives PCA scores\n", "#V are the right singular vectors -- PCA loadings\n", "U, d, Vh = scipy.linalg.svd(X,full_matrices=False)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 416 }, { "cell_type": "code", "collapsed": false, "input": [ "Vh.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 417, "text": [ "(102, 8793)" ] } ], "prompt_number": 417 }, { "cell_type": "markdown", "metadata": {}, "source": [ "** First PC correlates with batch **" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(sampleinfoCEU.days, U.transpose()[0,:])\n", "plt.xlabel('Date sample was processed (Number of days since Oct 31, 2012)')\n", "plt.ylabel('PC1')\n", "plt.title('Relationship between the PC1 and the date the samples were processed')\n", "plt.ylim()\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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hl19+wdy5c1GpUiWUL18eERERstqqjZc5+/aUKVOwf/9+tG/fHr6+vnj48CGW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"text": [ "" ] } ], "prompt_number": 418 }, { "cell_type": "code", "collapsed": false, "input": [ "rankDays = scipy.stats.mstats.rankdata(sampleinfoCEU.days)\n", "plt.scatter(rankDays, U.transpose()[0,:])\n", "plt.xlabel('Ranked Date (Number of days since Oct 31, 2012)')\n", "plt.ylabel('PC1')\n", "plt.title('Relationship between the PC1 and the ranked date')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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FIQSmTJmCKVOmpFtfkiQ8efIEFSpUyHD7L168wPjx47F169Z0tTC5HUbk3r17kCQJFStW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"text": [ "" ] } ], "prompt_number": 419 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.hist(U.transpose()[0,:], bins = np.arange(-0.2,0.3,0.05))\n", "plt.xlabel('PC1')\n", "plt.ylabel('Frequency')\n", "plt.title('Distribution of the values from PC1')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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cxtaeGVtz29o7Yut825rb1nVObhQXRRwAAIADUcQ5jK09M7bmtrV3xNb5tjW3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\nQBEHAADgQPTEOQw9cQAQGui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"text": [ "" ] } ], "prompt_number": 420 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Applications of SVD: Iris Example\n", "\n", "### Load in iris data" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Load the dataset from sklearn's library of example datasets\n", "iris = sklearn.datasets.load_iris()\n", "\n", "#data are the features (here, flower measurements)\n", "X = iris.data\n", "#target are the classes we wish to recover (here, flower species)\n", "Y = iris.target" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 421 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Take only the petal length attributes and scale." ] }, { "cell_type": "code", "collapsed": false, "input": [ "X = X[:,2:4]\n", "X = sklearn.preprocessing.scale(X, axis = 0)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 422 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(X[:,0], X[:,1])\n", "plt.axvline(x=0, color = 'black', ls='--')\n", "plt.axhline(y=0, color = 'black', ls='--')\n", "plt.gca().set_aspect('equal')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Hzw945JGq2/OBB0qQnp6Offs8//qTJvn+93Pw4FKkp6fj/HmgZUv+fqanp2Pt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\ntLQ0OT4+Xg4ICJAjIiLkO++8U/7+++9Vl1OW674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"text": [ "" ] } ], "prompt_number": 424 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What transformation has more varinace?\n", "\n", "This is the projection of $(0,1)$ and $(1,0)$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "np.apply_along_axis(np.std, 0, X)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 425, "text": [ "array([ 1., 1.])" ] } ], "prompt_number": 425 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How about this direction?\n", "\n", "Line represents the space spaned by \n", "\n", "$$\\vec{v}=\\begin{pmatrix}1/\\sqrt{2}&-1/\\sqrt{2}\\end{pmatrix}$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(X[:,0], X[:,1])\n", "plt.axvline(x=0, color = 'black', ls='--')\n", "plt.axhline(y=0, color = 'black', ls='--')\n", "plt.plot([-2,2], [2, -2], c='black')\n", "plt.gca().set_aspect('equal')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Gyp06dZKnTp0qf/fdd6HaJVVlZGTIkiTJJpNJliTJ92My\nmeTMzMxQ754qnnrqqWpxVf5r1Ol0S5cula+88krZarXKgwcPlrdv3x7qXVJF5Wux5uvxvvvuC/Wu\nqaKu95kkSfIzzzwT6l1Txb333itfccUVstVqldu0aSOPGTNG3rJlS4PPYUsBIiLBcN4dEZFgmNiJ\niATDxE5EJBgmdiIiwTCxExEJhomdiEgwTOxERIJhYiciEgwTOxGRYP4/m7kLbTXRpTAAAAAASUVO\nRK5CYII=\n", "text": [ "" ] } ], "prompt_number": 426 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Here is the projection\n", "\n", "$$d\\vec{u} = X \\vec{v}$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "V = (-1,1)/np.sqrt(2)\n", "V = V.reshape(2,1)\n", "dat = np.dot(np.dot(X, V), V.T)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 427 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(X[:,0], X[:,1])\n", "plt.axvline(x=0, color = 'black', ls='--')\n", "plt.axhline(y=0, color = 'black', ls='--')\n", "plt.plot([-2,2], [2, -2], c=\"black\")\n", "\n", "plt.scatter(dat[:,0], dat[:,1], c='red')\n", "plt.gca().set_aspect('equal')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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mG1Zotcq47LL6b4BR2YABLlQerihJMuLjPa/v2tW/7fi7XkPExroRFuZrV3i4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\ntF0b1tgFc/SoCRMmRCI72wS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"text": [ "" ] } ], "prompt_number": 428 }, { "cell_type": "code", "collapsed": false, "input": [ "np.std(np.dot(X, V))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 429, "text": [ "0.19298420388475782" ] } ], "prompt_number": 429 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How about this one?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "V = (1,1)/np.sqrt(2)\n", "V = V.reshape(2,1)\n", "dat = np.dot(np.dot(X, V), V.T)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 430 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(X[:,0], X[:,1])\n", "plt.axvline(x=0, color = 'black', ls='--')\n", "plt.axhline(y=0, color = 'black', ls='--')\n", "plt.plot([-2,2], [-2, 2], c=\"black\")\n", "\n", "plt.scatter(dat[:,0], dat[:,1], c='red')\n", "plt.gca().set_aspect('equal')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ETJ6M3DlzPEL9q8hIhM+fH9ShLvKxuxRcK4ZIQHY7MGNGBLZsCUG7djL69bNj/fpQhIZG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\n2rdvj2PHjl10uxr7JI0bN0bjxo1rNQB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"text": [ "" ] } ], "prompt_number": 431 }, { "cell_type": "code", "collapsed": false, "input": [ "np.std(np.dot(X, V))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 432, "text": [ "1.4009843314794663" ] } ], "prompt_number": 432 }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is $\\vec{v}$ here?\n", "\n", "### Transformation\n", "\n", "Note these two are orthogonal so let\n", "\n", "$$V=\\frac{1}{\\sqrt{2}}\\begin{pmatrix}\n", "1&1\\\\\n", "1&-1\\\\\n", "\\end{pmatrix}\n", "$$\n", "\n", "$XV$ reports something proportional to the average and the difference.\n", "\n", "The orthogonality is convenient because we can change back and forth: \n", "\n", "$$XVV^\\top = X$$\n", "\n", "** SVD gives us that transformation **\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Projection to first and second PC" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Singular Value Decomposition\n", "#U are the left singular vectors\n", "#d are the singular values\n", "#U*d gives PCA scores\n", "#V are the right singular vectors -- PCA loadings\n", "U, d, V = scipy.linalg.svd(X, full_matrices=False)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 433 }, { "cell_type": "code", "collapsed": false, "input": [ "print V" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[ 0.70710678 0.70710678]\n", " [-0.70710678 0.70710678]]\n" ] } ], "prompt_number": 434 }, { "cell_type": "code", "collapsed": false, "input": [ "np.sqrt((d ** 2) / X.shape[0])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 435, "text": [ "array([ 1.40098433, 0.1929842 ])" ] } ], "prompt_number": 435 }, { "cell_type": "code", "collapsed": false, "input": [ "#Plot components of left singular vectors\n", "plt.scatter(U.transpose()[0],U.transpose()[1])\n", "plt.xlabel('Projection to first PC')\n", "plt.ylabel('Projection to second PC')\n", "plt.axvline(x=0, color = 'black', ls='--')\n", "plt.axhline(y=0, color = 'black', ls='--')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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szj4LFwC8vU2TBh8ffmigYmb1BLZv3x69e/fGu+++a3L+q6++wqZNm7Bnzx6b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\ndSvWrVvXXKdCREREZLJMLgkEgFWrVsHW1hYxMTF4+PAhoqK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CgnDixAmtfcePH4e3t3ej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\nEVmh/wONs9j0odCoHQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 436 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compression based on SVD \n", "\n", "Get rid of one dimension and recuperate data XV[:,1]V.T " ] }, { "cell_type": "code", "collapsed": false, "input": [ "xnew = np.dot(U.transpose()[0][None].T, [d[0]*V[0]])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 437 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(xnew[:, 0], X[:, 0])\n", "plt.plot(xnew[:, 0],xnew[:, 0])\n", "plt.xlabel(\"Original 1st column\")\n", "plt.ylabel(\"Approximation\")\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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iokKdPCkDPNQIil4AWYX8CSJFmZULACdOmKYMJ08yhXA1rOkjI9bdiGNcxDEu4hgXc4yJ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\nPvp18eJF9OnTB5aWlvDw8MDu3bthY2ODNWvWqNs8fno3OTlZ/XrAgAG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"text": [ "" ] } ], "prompt_number": 438 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(xnew[:, 1], X[:, 1])\n", "plt.plot(xnew[:, 1],xnew[:, 1])\n", "plt.xlabel(\"Original 2nd column\")\n", "plt.ylabel(\"Approximation\")\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Xe+2Va28VnYsn450+IiIiL8OpXO/Emj4iIiIvwalc98WaPiIiIioV98olgDV99ADWUYgx\nFzHmIsZcrDETseJyycyUID7euEVa375BOHZMim7djO1nngnC0aNSdOpkbA8ZEoS//pKiQ4cQhIeH\nYsSIQOTnW57vnT37HbZXrsi6dQo8+qgSkZGhWLKk7Fuq8XpxHN7pIyIiciEzZ/ojLc34z3NqqgKj\nRgXh3DkZAODXX43t8+eN7R07FDh1KggXLxrbW7f6YPlyHRITC4RTubm72uHNFvFoX9VyMWZ7uXtX\ngoSEQKjVxh013nwzAN26aRAVpXfI91HZcNBHJrGxsRXdBZfEXMSYixhzscZMxIrL5fp1y0m47GxJ\nie2cHMu26qYW8T8nWdzZM+gluPaPGTDcC8CNmkVuBdrR3bsS04Dvvps3pQBsH/TxenEcTu8SERG5\nkFGjCiGVGgv25XIDhg9XQyIxtn18DBg2zHyXztfXgGefNbcrPfMLfmo7x2LA1+PyKFx97j0Y7gUg\nJESPZ55xzF0+AKhVS4/u3c1bqDVpokWbNlqHfR+VDZ/eJZPU1FT+hiXAXMSYixhzscZMxErKJS1N\nhsOHZWjdWofmzXU4cECGo0flaN9eiyZNdNi3T44TJ6SIidGicWM9Vu+8ibnZX1ic48GncnfskOPS\nJSm6dtWibl3HTrVqNMD69T4oLAT69VMjJKRsn+f1Isand4mIiDxQmzY6tGlj3i+3fXvL/XM7dNCi\nQ4f7CyyX/lRuXJzz7rYpFMCQIY67m0gPj3f6iIiI3BAXWPYuvNNHRETkZbjAMj0sPshBJlwbSYy5\niDEXMeZijZmIlTUXV90r1954vTgO7/QRERG5OE7lkj2wpo+IiMhFcSqX7rNHTR+nd4mIiIqRmSnB\nk08GIyIiFP36GbdE697duAXagAHGdufOxveHDjVuidaxYwgiIkIxalQgCgoe7nsrair38899Ubt2\nKB55RIm1a31KPf699/xQs2YoGjZUIiWFk4euzmUHfXv27EHfvn0RGRkJqVSKlStXlvqZI0eOoHPn\nzggICEBkZCRmzZrlhJ56DtZRiDEXMeYixlysuXMmM2f64+BBOTQaCX77zbgF2p9/yqHVSrB7twIj\nRwbhyBHj+ykpxvePH5dBo5FgyxYfLF9e/N6zxeXyycl9Tt0r976//5Zi2jR/5OZKcPeuFJMnB+DG\nDUmxx+/fL8eCBf7Iz5fgxg0pJkwIgtYOK8O48/Xi6lx2WJ6Xl4dmzZphzJgxGD16NCSS4i88AMjO\nzkaPHj3QpUsXpKWl4fjx4xg3bhwCAwPx6quvOqnXRETkScq6Jdrdu5btop8vSUVP5d68KYHBYO6/\nRiPB7dsSVK0qnlK8ft3yZ83NleDePZR5MWZyHreo6QsODsbSpUsxevToYo9JSkrC9OnTkZmZCV9f\n429Wc+bMQVJSEi5fvmx1PGv6iIioNOvXK/D884HQ6yWQyw146aVCLF3qC4NBAoXCgOefL8CyZf4A\njFuijRtXgOXLjW1/fwN+/DEHLVvqSvoKFOg06Luj9AWWHa2wEOjZMxgZGcb7QbGxGqxfnwuZTHz8\nnTsSdOsWjPPnjQf076/Gl1/mOau7Xofr9D1g//79eOKJJ0wDPgCIj4/HjBkzcOHCBdSpU6cCe0dE\nRO7omWc0iIzMweHDcrRpo0Xz5jo89ZQaf/1l3BKtaVMdevXS4sQJGWJiNIiK0qNnTy1On5bhiSc0\naNCg5C3PXOmpXF9fYPPmHKxf7wO5HBgwQF3sgA8AQkMN2LEjB5s2KRAcbED//priDyaX4DGDPpVK\nhdq1a1u8FhERYXqPg77Scb9DMeYixlzEmIs1d8+kbVsd2rYtfku0jh216NjRXMzWqZMWnTqVXNx2\n/E4m+i1/B76NzP9uucJTuUFBwKhRtm+hFhZmwNix9t1yzd2vF1fmMYO+0mr+iIiIKpqrTOWSd/KY\nQV+1atWgUqksXsvMzDS9J5KQkGC6O6hUKhEdHW367eL+00Pe1r7PVfrjCu3Y2FiX6o8rte9zlf64\nQpvXi3X7/muu0p+Kah+tKsWS47+h8MRFAIBvo9r4rONQaE9expHf0yq8f67Svv+aq/SnIv9+TU1N\nxcWLF2EvHvMgx/LlyzFt2jRcv37dVNf37rvvIikpCZcuXbI6ng9yEBGRM1T0U7nkGTx6cea8vDyk\np6cjPT0der0eFy5cQHp6umkAN336dMTFxZmOHz58OAICAjB27FgcPXoU69atw7x587hcSxkUvXtD\nRsxFjLmIMRdr3ppJaQsse2supWEujuOyg76DBw+iVatWaNWqFQoKCvDWW2+hVatWeOuttwAYH844\ne/as6fiQkBCkpKTg6tWraNOmDSZPnoypU6ciMTGxon4EIiLyUhW1wDJRSdxietcROL1LREQPSk+X\nYcKEQFy9KsXgwWq0aqXFv/4VAJ0OaNxYh99+y4H0gVslv/4qR0JCIO7ckeDFFwvw5psFTp3K/fBD\nPyxc6Ad/fwMWLbqHXr24ZIons8f0Lgd9REREAGJiQnDypHlhOqnUAL3evDLExIn5mDPHuJmuwQDU\nq6fEnTv/GwUqNGj62QLc1jvnqdxDh2SIizNvfREQYMDp03fg72/3ryIX4dE1feR8rKMQYy5izEWM\nuVhzl0yKbiumL7Ku8tWr5gFhYSFMA77gp39BzU9mWAz4bJnKLU8uN25Y/vN9754EubmesXSZu1wv\n7oiDPiIiIgCjR5sXGa5USY8GDcwLMEskBkyalG9q+/kBvZ87j5pfvo6QASmm14fUbYEj/ac5fEeN\nmBgN6tc3969XL3Wxe+QS3cfpXSIiov/ZulWBK1ekiI/XoHZtPWbO9MOlSzJMnJiPNm2Mt/5cZYHl\nO3ck2LBBgYAA45ZpcrnTvpoqAGv6yoGDPiIiKitX2iuXvAtr+siuWEchxlzEmIsYc7HmCZkcv5OJ\n6A3zLAZ85Z3K9YRcHIG5OA5vBhMRERXDVaZyieyB07tEREQCnMolV2KP6V3e6SMiInoA98olT8Wa\nPjJhHYUYcxFjLmLMxZq7ZFLaXrn25i65OBtzcRwO+oiIyO0lJvojLCwUYWGhaNIkBPPn+6JKFWO7\nb98gq+PXr1egfn0latcOxfLlvmXeK3fEiECEhYWicuVQzJjhh48+8kWtWqFo2FCJbdsUVse//bY/\nIiND0bSpEr/9ZjnJZjAAU6f6o0aNULRsGYI//pBZff5BajUwYUIgqlcPRYcOITh9mv+Uk21Y00dE\nRG5NrQaqVQsF8OCOFAaL9gcf5GHcOOPiy3fuSNC4sRKFhRIoal9B+MzFFucrbSp382Y5xowJLva7\nAgMNOHXKvCXazp1yDBpkPj4sTI8zZ+6a2uvWKfDcc+aB6SOP6PDHH+bBZ1HLlvnijTcCTO2YGA22\nbMkt9njyDKzpIyIir3f7NmA54LNuX7hgvht2964EhXotIuZ/AHmVO6bXbX0q9+zZonfiLL8rL0+C\nvDwJ/P2N/0Bfv255J+72bQnUasDHB8L3i26xVlRZjye6j1cKmbCOQoy5iDEXMeZizdGZREQAAQEP\nbpRrQOXK5rZcbsCECeYt1q4HXECtRe9ZDPiWtC59r9z7hg8vhI+P+Y5LaKgejzxiuSValSrm97t3\n16BGDXN/hg5Vw8fHnEvv3hqL/o4YUVji9w8apEZAgPn8I0eWfLy74X9DjsM7fURE5PbOnr2LYcMC\nceuWFLNm3UObNjr8+9/+uHtXgmnTClCrlh43CnLxwV+7sOXyMeB/Y7vmha2xrFccQkJs/66qVYGD\nB7Mxa5Yf/PyAd9+9B41GgvXrFQgMBAYOVBc53oBffsnGjz/6IDRUj2ee0Vi8X6uWHjt35mDbNgWq\nVdOjTx/L94tq2lSHnTuzsXu3Ao8+qkNcnNb2zpNXY00fERF5NI1ehzVnD2HZiVTkadXwlcoxoUF7\njH+sHXxlvPdB7oE1fURERCVIu3kJcw5vx5nsmwCALtXqY1p0d0QGhlZwz4icjzV9ZMI6CjHmIsZc\nxJiLtYrI5EZBLl5P24xxqV/jTPZNRAaEYkn7gVjcfqDLDPh4rYgxF8fhnT4iIvIYnMolKh5r+oiI\nyCNwKpc8GWv6iIjI61k8lQsgMiAUrzfrjs7V6ldwz4hcC2v6yIR1FGLMRYy5iDEXa0Uz2bpVgYYN\njVugLV7s+9Dn1eh1WHXmIJ786TNsuXwMBo0c3SWdsKH7BLcY8PFaEWMujsM7fURE5DR5ecDzzwfi\n3j3jLhZvvRWAzp21aNZMV8onLVlM5UqB/D8b4+6aPlibWwnvdL0D3zKsu0fkLVjTR0RETqNSSRAV\nZVljt3Ztjs0LDBedyq0iDcXJD/uhIKOx6ZjDh+8gMtIr/2kjD2aPmj5O7xIRkdNUq2ZAjx7mHSce\ne0yHdu1KH/Ddn8rts8M4lesrlSOhUSx+6DIBdQoamI7r2lWDmjU54CMS4aCPTFhHIcZcxJiLGHOx\nVjSTr77KxdKleXj//Tz8/HMOgoNL/nzazUsYsnsFFvy1E3laNbpUq48N3SdgYqOOCAuRY9u2HLz/\nfh6WLMnDmjW5kEgc+MPYEa8VMebiOKzpIyIip1IogGHD1KUeZ+tTuUqlAePHl34+Im/Hmj4iInIp\nXGCZyBrX6SMiIo/CBZaJHKdMNX1Xr15Feno6Dh06ZPGHPAPrKMSYixhzEWMu1mzJxB32yrU3Xiti\nzMVxbLrT9+eff2LEiBE4ceKE1XsSiQQ6XdnWVyIiIgI4lUvkTDbV9LVt2xaVK1fGm2++ierVq0NS\n5NGounXrOqp/WLZsGRYsWACVSoUmTZrgo48+QmxsrPDY8+fP49FHH7V6fdu2bYiPj7d4jTV9REQV\ni1O5RLZzWk3fsWPHcOjQITRs2LBcX1ZW3377LaZMmYKkpCTExsZi6dKl6NWrF44dO4ZatWoV+7mf\nf/4ZzZs3N7UrVarkjO4SEXm95ct98d57/vDzM2Dhwnvo3Vtj8f68eX5Y9h81ggdthaRFOgDb98rV\n64HExAB8/70PIiP1+OKLPDRt6riZpqwsCcaODcQff8jRrp0Wycl5CA31ymcfyUPYVNPXtGlTqFQq\nR/fFysKFCzFu3DhMmDABDRs2xMcff4zq1asjKSmpxM+FhYUhPDzc9EehUDipx+6NdRRizEWMuYh5\ncy7Hjknx73/7IydHghs3pHjhhUBkZ5sz+W2fBEsOpSHo3wshaZEOg1qOiQ1jbd4r95tvfPCf//gi\nP1+C06dlSEgIcOjP8/bb/ti7V4GCAgl+/VWBd9/1s+v5vflaKQlzcRybBn3vvfcepk2bhpSUFGRm\nZuLWrVsWfxxBrVbj0KFDVtOy8fHx2LdvX4mfHTBgACIiIhAbG4sffvjBIf0jIiJLmZlSGAzm8p/8\nfAmys43ttJuXMDPzC4QO2wKpfyHy/2yMzDdexehaHW2u3cvMlJbYtrei51epuJ8BuTeb/kuLi4sD\nADz55JNW7znqQY6bN29Cp9MhIiLC4vXw8PBi7zoGBwfjgw8+QMeOHSGXy7Fx40YMHToUK1euxIgR\nI+zeR09TXK2kt2MuYsxFzJtzadtWiwYNdDh1SgbAuCWaT+Uc/Ki6jS2pewEJgFthyPpPHxRkNEa/\nfmoEBeXZfP4+fdRYtMgX2dnGwdeIEYWO+DFMhg8vxC+/yKHXSyCTGWxaULosvPlaKQlzcRybBn07\nd+50dD/sonLlykhMTDS1W7VqhaysLMyfP5+DPiIiBwsKAn7+OQfff+8DhZ8WujYH0PcXy6dy+4S2\nxzZ9AIJfysOgQWUbRNWvr8euXTnYvl2ByEi9Vb2gvfXrp0FERA7+/FOONm20aNuWK1WQe7Np0Nel\nSxcHd8NalSpVIJPJkJmZafF6ZmYmqlevbvN52rZtiy+//FL4XkJCAmrXrg0AUCqViI6ONv2Gcb+m\nwJvaR44cwcSJE12mP67SfrC+xBX64yptXi+8XkRtpdIAVFuD5L/TcPO4EgAQsf8cJvXoj2cadQQA\nNGr0CwBAJiv7+R95RI8mTX65n7DDf5727XXQan9FYaH9v+/+a670/z9XaCclJXn9v8f3paam4uLF\ni7AXm7dhU6lUWLp0KY4dOwapVIqoqCgkJCRYTb/aU/v27dG8eXN88sknptcaNGiAwYMHY86cOTad\nIzExEZswzNT7AAAgAElEQVQ3b8aZM2csXueSLdZSU1NNFx2ZMRcx5iLmzbkUt1eu7IzKazMpiTdf\nKyVhLmL2WLLFpkHf3r170bNnT0RERCAmJgYGgwH79+/HjRs3sG3bNnTo0KFcnSjO2rVrMWrUKCxb\ntgwdOnTA8uXLkZycjKNHj6JWrVqYPn06Dh48iB07dgAAVq5cCR8fH7Ro0QJSqRSbN2/Gv//9b8yf\nPx+vvPKK5Q/OQR8RkV1wgWUix3PaOn1Tp07FsGHDsHz5ckilxgJanU6HiRMnYurUqaU+TfuwhgwZ\ngqysLMyePRvXrl1DdHQ0fvrpJ9MafSqVCmfPnjUdL5FIMHv2bFy4cAEymQwNGzZEcnIyhg8f7pD+\nERF5Oy6wTOQ+bLrT5+/vj/T0dKvFmY8fP46WLVuioKDAYR10FN7ps8Zb6mLMRYy5iHlLLsVN5YrW\n2/OWTMqKuYgxFzGn3elTKpU4e/as1aDv/PnzCA3lb3NERN6CU7lE7sumO31TpkzB2rVrMX/+fHTs\naHz6KjU1FdOmTcPQoUPx4YcfOryj9sY7fUTk7ebP98OSJX4ICTFg6dI8dO6sLfZYjQao0+k2QkZs\nhCLSuKpClRsN8feSvqjuF4pPP83Dp5/6YuNGH9SurUdyci4aNtSbPn/nDtCxoxLXrkng7w989VUO\nPv/cD7t3KxAVpcOSJbmYMSMQe/fK0ayZDitW5CIiglueEd3ntAc5CgsL8dprr2H58uXQaIzrIvn4\n+GDixImYN28efHx8ytWJisBBHxF5s3375Hj66WBTW6nU4++/70Iq2HTiRkEuus1LBZpnAAC018Nw\nd83TKMiIMh1TvboO167JTO02bbTYvj3H1B4wIAi7d5u3xPT3NyA/37x7x6OP6nD2rPnzgwcX4pNP\n7pXvhyTyIPYY9Nm0p4yvry8WLVqEW7duIT09Henp6cjKysKHH37olgM+EntwbSAyYy5izEXMXXJR\nqSQW7bt3pbhXZIyl0euw6sxB9NnxGdA8Awa1HNnr45D5RiIKMhpbfb6486empuL6dcvvUxdZl/nO\nHcv3vWHLM3e5VpyNuThOmf6rCgwMRLNmzdCsWTMEBgY6qk9ERORgXbpoERlp3mHCuCWa+f20m5cw\nZPcKLPhrJ/K0atTMaYDMNxKRszkO0CoglQLBwea7Ds88o0ZQkLk9YoTlqO6FFwoBmN9//HEtFApz\ne9AgNeRyY1sisf+WZ0RUwvRunz59sHr1aoSEhKBPnz6QSCTC24oSiQSbNm1yeEftjdO7ROTtrl+X\nYONGH4SEGDBokBoyWclP5b73ng+WL/dHpUp6pKfn4OxZKbZvV6BmTT369NHg9GkpduxQoG5dPXr1\nst4ibeNGBb77zgctW2rxz38W4vBhGVJT5WjSRIfOnbU4dEiGAweMNX2xscXXFxJ5I4fW9I0dOxaL\nFy9GcHAwxo4dW+KgLzk5uVydqAgc9BERmfGpXCLX5rQHOTwRB33WuDaSGHMRYy5i7piLoxdYdsdM\nnIG5iDEXMac9yDF+/Hjk5ORYvZ6Xl4fx48eXqwNERFQxbhTk4vW0zRiX+jXOZN9EZEAolrQfiMXt\nB3JHDSIPZNOdPqlUCpVKhfDwcIvXb9y4gWrVqkGn0xXzSdfFO31E5K04lUvkfhy+I8etW7dMX3Dr\n1i3I5ebDdTodfvzxR0RERJSrA0RE5DzcK5fIe5U4vVulShVUrVoVABAVFYUqVaqY/kREROC5555D\nQkKCUzpKjse1kcSYixhzEXPVXCpyKtdVM6lozEWMuThOiXf6du7cCQDo1q0bfvjhB1SqVMn0no+P\nD+rUqYOaNWs6todERIQZM/yxcqUvqlbV45NP8tCmjW1lNaKp3BG12+PzMT3wzCUfBAQAP/yQg3bt\nzOfLyQGeey7of1uiaTF7dj4GDw7C7dsSKJUGrF2bi1mz/HHokByPP65FcnIelErnPRN48KAML70U\niBs3pBg7thDvvJPvtO8mcmc21fSdP38etWvXhlS0P4+bYk0fEbmLn35SYORI88rJtWrpkJGRXern\nipvK/ceoSIst0apU0ePUqbum9ptv+mPJEj9TW6nUW+y4ERKiR3a2uf388wWYN895A69mzUJw+bJ5\ny7bVq3OF6wISeRKH1/TdV7duXQDA1atXcfHiRaiL7J/TqVOncnWCiIiKV3TLtMzMkn8BL2mBZQBW\nW6Ll5hbdAs2y/eAeuaL2tWvOuyFgMFj//EX7S0RiNv2XevXqVXTu3BmRkZHo0KEDunTpYvrTtWtX\nR/eRnIR1FGLMRYy5iDkil/h4DapU0ZvaxW1R9uBeuVsuH4OvVI6ERrHY0H2CacAHABMmWG6JFhdn\neZdsyBA1ZDLzlmhdu2oeON6Azp01kEiMbanUgGefLXnLNHtmIpFY/vxVqugRH++ed/n435AYc3Ec\nm+70TZkyBTKZDMeOHUPbtm2xbds2ZGZmYsaMGfjwww8d3UciIq8WGWnAL7/kYMsWBapW1WPAAOtB\nTlmeyh03To1KlQz47jsftGpl3BLtQXFxWmzbloMDB+Ro3ty4JVpysg9SUhTo2lWL558vxP79chw6\nJEPbtlo8/rhzl+368MN7eOIJDW7ckOLpp9WoWdMr9xggKjObavoiIiLw448/om3btggJCUFaWhoa\nNGiALVu2YNasWThw4IAz+mpXrOkjIk9Q2lQuEXkGp9X05efnm5ZuCQsLw/Xr19GgQQM0btwYGRkZ\n5eoAERGVHRdYJqKysqmmr2HDhjhx4gQAoHnz5khKSsKFCxewbNkyLtniQVhHIcZcxJiLmDNySbt5\nCUN2r8CCv3YiT6tGl2r1saH7BExs1NElB3y8VsSYixhzcRyb/nZ45ZVXcO3aNQDAW2+9hSeffBJr\n1qyBr68vVq5c6dAOEhGREadyiag8bKrpKyovLw8nTpxA7dq1TdO+7oY1fUTkLjiVS0T2qOl7qEGf\nJ+Cgj4jcAffKJSLAPoM+m1fU3LBhAyZPnoyhQ4di8ODBGDJkiOn/kmdgHYUYcxFjLmJ79qQiMTEA\ntWuHIiYmBMeOlW3h4suXgerVQ1HlESnqv/6zaa9c7fUw3Pt0NPrlDkHnZnUQFhaKRx9V4pdf5Hjk\nESXCwkJRr54Sf/4pRe/eQahVKxTPPhuIU6ckePLJYNSqFYrRowNx8qQU3bsb2+PGBaKwsPQ+lRev\nFTHmIsZcHMemeYF//etfWLRoETp27IiIiAjIZObtbyQSroRORHTfzp1yrFzpCwA4eVKGhIRA7N6d\nY/Pne/UOhLxTKsL674DUvxAGtRw5W7ogZ2tnQKvAiBEGaDTGv3fv3JFg+PAgU/v2bQkGDAg2bZm2\nfbsP/v5bhr//Nv6d/eOPPjh6VIZz54ztjRt90Ly5FlOmOGHkR0QVzqbp3SpVquDzzz9H//79ndEn\np+D0LhE5wsKFfpg929/UDg/X48SJuyV8wizt5iWMXvsLZDUyAQD5fzbG3TVPQ3ezsukYicQAg0FS\nbNvHxwC12twOC9Pj1i3z3cZKlfS4fdvcfuGFAsyd67x9c4no4Thtetff3x+NGzcu1xcREXmDp59W\nIyjI/BdzaVuUAcancl9P24xxqV9DViMT2uthyFo0BrcWj0G4IhQPbpnWpIkOD26JFhVl2e7Sxbxb\nh0xmwMCB5u9XKAwYMMDc9vGxbBORZ7PpTt/ixYuRnp6OTz75BHK5Zzwpxjt91lJTUxEbG1vR3XA5\nzEWMuYilpqaiWrVO2L5dgchIPfr2LX5f2OKeyr29qRM2rw/A449rsWhRPv7zHx/89JMCsbFaTJpU\niC++8MGOHQp062bcEu3TT32xa5cc8fEajBunxp49chw+LENMjBatW+uwa5ccx47J0LGjFi1a6JCS\nIsepUzJ07qxF06aO30KN14oYcxFjLmJOe3pXo9Ggd+/eyMjIQIMGDSwGfhKJBDt37ixXJyoCB33W\n+B+aGHMRYy5itubiTU/l8loRYy5izEXMaYO+8ePH47vvvkPPnj0RHh5u8fCGRCLB4sWLy9WJisBB\nHxFVBC6wTEQPw2mDvqCgIKxbtw7x8fHl+jJXwkEfETkTF1gmovJw2oMcVapUQWRkZLm+6GEsW7YM\njzzyCPz9/dGmTZtS1+45cuQIOnfujICAAERGRmLWrFlO6qln4NpIYsxFjLmIiXJxt71y7Y3Xihhz\nEWMujmPToO/tt9/Gm2++iZwc29eaKq9vv/0WU6ZMwRtvvIH09HR06NABvXr1wqVLl4THZ2dno0eP\nHqhevTrS0tKwaNEiLFiwAAsXLnRan4mIHvTgU7lnsm8iMiAUS9oPxOL2Az2ydo+IXJtN07vR0dE4\nf/48dDodateuDYVCYT6BRILDhw/bvWPt2rVDixYt8Mknn5hea9CgAQYNGoR3333X6vikpCRMnz4d\nmZmZ8PU1Low6Z84cJCUl4fLly1bHc3qXiByFU7lEZG/2mN616W+fgQMHFvueI3bkUKvVOHToEF57\n7TWL1+Pj47Fv3z7hZ/bv348nnnjCNOC7f/yMGTNw4cIF1KlTx+79JCIqquhTuf4XGiEzuQ9+iwpG\nj3fu4eWXg3DsmAxdumjwySd58Dev44yzZ6WYMCEQf/8tQ+/eanz88T088Ds2jh2T4rnngnDlihSD\nBxdiwYJ8lPRX8P79ckyaFIDbtyV44YVCTJ9e4KCfmojcgU2DvpkzZzq4G5Zu3rwJnU6HiIgIi9fD\nw8OhUqmEn1GpVKhdu7bFa/c/r1KpOOizAR+TF2MuYszF0v2nctft2AbfRrURGRCKwF97Y2dSNABg\n20Xg9GnLLdE+/liHadPMA7FXXglARobxr+Vvv/VFixY6vPiieYu0F18MxIkTxs9/+aUf2rbVYejQ\n4hdXHjMmEDdvGqt4FizwR4cOWnTurLXvD24DXitizEWMuTiOx8wzPMwdx4SEBNNAUalUIjo62nSh\n3S8k9ab2kSNHXKo/bLt2m9eLsa3R6/DOd8nYePEIDI/VgEIiQ897SjwV1ggLDzeC0W4AwO3bnSza\n167FWJxPpXqqyPvti7zfu8j7jxfbP40GyMp6usjxbSskryNHjjj1+9ylfZ+r9MdV2rxezNdHamoq\nLl68CHsptqYvODgY586dQ5UqVRAcHFz8CSQSZGdn261DgHF6NzAwEN98843F1PKkSZNw7Ngx7Nq1\ny+ozY8aMQVZWFn788UfTawcPHkS7du1w7tw5qzt9rOkjovIqbYHl1at9MHlyIADjlmjjxhXi88/9\nAAByuQHr1uUiNlZrOt8HH/hhzhzjfK+fnwE//ZSDFi3MO2bMmOGPpUuNnw8ONmDHjmw89pi+2P49\n/3wgfvjBBwAQEaHH7t3ZiIgoX00QEVUMh9b0LV68GEFBQab/7Uw+Pj5o3bo1tm/fbjHoS0lJweDB\ng4WfiYmJwbRp01BYWGiq60tJSUHNmjU5tUtEdmXrAssjRqgRGanHkSMytG+vRZs2Ojz5pAbHj8sQ\nG6u1GNABwD//WYCoKB3+/luKbt00iIqyHNDNmpWP1q21uHJFip49NahXr/gBHwAsX56H7t01uH1b\ngr591RzwEXk5m57erQhr167FqFGjsGzZMnTo0AHLly9HcnIyjh49ilq1amH69Ok4ePAgduzYAcC4\nZEvDhg3RpUsXvPHGGzh58iTGjRuHmTNnIjEx0er8vNNnLTWVdRQizEXMG3Ox5alcb8ylNMxEjLmI\nMRcxpz29+8MPPwif4DUYDJg/fz6mTZtWrk6IDBkyBFlZWZg9ezauXbuG6Oho/PTTT6hVqxYA48MZ\nZ8+eNR0fEhKClJQUTJo0CW3atEFYWBimTp0qHPAREZWVN+2VS0SeyaY7fX5+fhgxYgQWL16MgIAA\nAMClS5cwevRoHDt2DJmZmQ7vqL3xTh8R2YJ75RKRK3DaNmy///47Dhw4gBYtWuDgwYP45ptv0Lx5\nc/j5+TlkYWYiooqm0euw6sxB9NnxGbZcPgZfqRwJjWKxofsEDviIyC3ZNOhr1qwZ0tLS0LFjR8TE\nxGD06NF46623sHXrVqu19Mh9FV1GgIyYi5gn51KevXI9OZeHxUzEmIsYc3Ecm2r6ACAjIwN79uxB\n/fr1cenSJfz+++/Izs5GSEiII/tHROQ0nMolIk9mU03fO++8gzlz5iAhIQHz5s3DuXPnMHz4cGRl\nZWHVqlXo1KlTaadwOazpI3Iv9+4BL70UiF9/VaBpUy2++CIP1arZZ/EBW57KPXVKiuefD8SFC1L0\n76/Bc88V4MUXg3DligSDB6sxf37JW6IREZWHPWr6bBr0Va9eHStXrkR8fLzpNY1GgxkzZmDhwoVQ\nq4vfBshVcdBH5F7mzPHDBx+YN6rt10+N5OS8cp/X1qdye/QIxh9/mCdHqlfX4do1mam9fHkehgxx\nv78Licg9OO1BjsOHD1sM+ABAoVBg7ty5SElJKVcHyHWwjkKMuYg5O5dr16QltsvqRkEuXk/bjHGp\nX+NM9k1EBoRiSfuBWNx+oHAZlqLfd+dO0f4Yb/PxerHGTMSYixhzcRybavqqVq2KgoICrF69GseP\nH4dEIkFUVBSGDx+Ozp07O7qPREQYNEiNtWt9oNUaB1fPPlv4UOexZSpX5NlnC7FwofFOY2CgAU8/\nrca33xp3/wkKMuCppzQP1R8iImexaXr32LFj6NmzJ7KzsxEdHQ2DwYC//voLSqUS27ZtQ+PGjZ3R\nV7vi9C6R+/njDxn27pWjaVMdunXTlv6BIsq7wPKmTQpcuCBFfLwGDRvqsX69wrQlWv36JW+JRkRU\nHk6r6evRowcCAgLwn//8x/S0bnZ2NkaOHImCggJs3769XJ2oCBz0EXkPPpVLRO7OaTV9e/fuxZw5\ncyyWZwkJCcGcOXM49+5B+P9LMeYi5g65VMQCy+6Qi7MxEzHmIsZcHMemmj4/Pz/cuXPH6vW7d+/C\nz8/P7p0iIiov7pVLRGTJpundMWPG4ODBg/j0008RExMDANi3bx9efPFFPP7441ixYoWj+2l3nN4l\n8kycyiUiT+S0mr7bt29j7Nix2Lx5M6RS44ywXq9Hv379kJycjNBQ9/vNmYM+Is/ysE/lEhG5A6fU\n9On1ely7dg2rV6/GyZMnsW7dOqxbtw4nT57E+vXr3XLAR2KsoxBjLmKulEt59sq1N1fKxVUwEzHm\nIsZcHMemBzmaN28OlUqFxx57DH379kXfvn3x2GOPObpvRERC27fLUaNGKKo8IkWL2dusFljucuVZ\ntKlXF5Urh6Jbt2Crzx84IEObNiGoX1+J+fNLr0vetk2B6GglGjZUIjnZB5s2KdCkiRKNGimxerWP\nI35EIiK7s2l6t2nTpvjss89M9XyegNO7RO6rVp1goP1+hPTfAal/IaQ6OV5qYp7KjYgIhUZj3gh3\n0qR8zJpVAAAwGICGDZW4edP8O++GDTno1Em87l92NtC4cSjy8++fzwAfH0CtNrZlMgMOHsxG3bpc\np4+IHMdpS7YsWLAAU6dOxZ9//lnuLyQiKo+0m5cQ+K/FCB22BVL/QuT/2RjVv/+HxVSupsjmGBcu\nmPfIVathMeADSt7S7c4d6QMDPgCQmAZ8AKDTSZCZKbH+IBGRi7Fp0DdkyBD8/vvvaN26NXx9fREc\nHGz68+DafeTeWEchxlzEnJ3Lg3vlKiIzob0ehqxFY3Br8WhMGu5vcWzDhg/edTPghRcKTC1fX6B/\nf7WpHRGhR5cuxW+hFhmpR8eO5vfr1dOhVSvzXcHGjXVo1kxnavN6scZMxJiLGHNxHJsqnBcvXuzo\nfhARCRX3VO7FPzrjXIQvxqzORa9ellOze/dm47XX/HHlihQTJxYiNlZn8f6nn+ahe3cN7tyRoH9/\nNSIiip/BkEqBtWtz8c03PigslGDIEDV8fQ345htfaLXAs8+q4e9f7MeJiFyGTTV9nog1fUSujwss\nExEZ2aOmz+a1DPLz8/H111/j+PHjAIDGjRtj+PDh8OevuERkZ1xgmYjI/myq6Tt06BDq1auHqVOn\n4vfff8d///tf/Otf/8Kjjz6KP/74w9F9JCdhHYUYcxFzRC4VsVeuvfF6scZMxJiLGHNxHJvu9L3w\nwguIjY1FcnIyAgMDAQB5eXkYP348XnzxRaSlpTm0k0Tk+TiVS0TkWDbV9Pn7+yMtLQ1NmjSxeP3o\n0aNo3bo1CgoKivmk62JNH5Fr4FQuEVHpnFbT17BhQ1y9etVq0Hft2jU0bNiwXB0gIu/EvXKJiJzL\nppq+OXPm4B//+AfWrFmD8+fP4/z581izZg2mTJmCOXPm4NatW6Y/5L5YRyHGXMTKk4sr7ZVrb7xe\nrDETMeYixlwcx6a/Xfv06QMAGDFihNV7ffv2Nf1viUQCnU5ndQwREcCpXCKiimRTTd/u3bttPmGX\nLl3K0R3nYU0fkfNwKpeIqHzsUdPHxZmJyKH4VC4RUfnZY9BnU00fAFy9ehUzZszAwIEDMWjQIMyY\nMQNXr14t15eTa2EdhRhzESstlwf3yj2TfRORAaFY0n4gFrcf6NEDPl4v1piJGHMRYy6OY9OgLyUl\nBfXr18fatWsRGBgIf39/rF27FvXr18fPP/9s904VFhZi8uTJqFq1KoKCgtCvXz9cuXKlxM+sWLEC\nUqnU4o9MJoNarS7xc0RkX56wwDIRkSeyaXq3cePG6NGjBxYtWgSJRAIAMBgMmDJlCrZv327ams1e\nJk6ciE2bNmHVqlUICwvDq6++ijt37uCPP/6AVCoep65YsQIvv/wyzp07Z3H7Mzw8XHg8p3eJ7I9T\nuUREjuG0mj5/f39kZGSgQYMGFq+fPHkSLVq0QH5+frk68aC7d+8iPDwcK1aswLBhwwAAly9fRp06\ndbB161bEx8cLP7dixQpMnjwZOTk5Nn0PB31E9sOncomIHMtpNX2tW7fG4cOHrV7/66+/0KpVq3J1\noKg//vgDGo3GYnAXGRmJxo0bY9++fSV+Nj8/H3Xr1kWtWrXQp08fpKen27Vvno51FGLMRSw1NZVT\nuQK8XqwxEzHmIsZcHMemtRImTZqExMREnD59GjExMQCA/fv3Y/ny5Zg7dy4OHTpkOra8g0CVSgWZ\nTIbKlStbvB4REYHMzMxiP9eoUSMkJyejefPmyM7OxqJFi9CxY0dkZGSgfn3v/MeHyJFO3r2OD3av\n4FQuEZGbsGl6t7g6OquTlbA48xtvvIF33323xM/v3r0bly9fxpgxY6DRaCze6969Oxo0aICkpCSb\n+qLX69GyZUt06dIFixYtEvaV07tEZcepXCIi53Pa3rtnz561ek0ikcBgMCAlJQU9evQo9RyJiYkY\nPXp0icfUqlULWq0WOp0OWVlZFnf7VCoVOnXqZEt3ARgHqq1atcLp06eLPSYhIQG1a9cGACiVSkRH\nRyM2NhaA+fYy22yzbWxr9XpcrOGPZSdSceuvM1BIZHi531CMf6wdDu4/gNQzKpfqL9tss822O7fv\n/++LFy/CXh5qcebLly8jOTkZycnJuHDhgl23XivpQY5t27bZNMAEjE8Xt27dGq1atcLnn39u9T7v\n9FlLTU01XXRkxlzET+V2yw3EM3E9K7hnrofXizVmIsZcxJiLmNPu9AGAVqvFxo0b8cUXX2D79u1o\n1qwZXnrpJQwaNKhcHShKqVRiwoQJeO211xAeHm5asqV58+aIi4szHde9e3e0a9fONGX89ttvIyYm\nBvXr10d2djY+/vhjHD16FJ9++qld+0fkTUqayn3wt1EiInJ9pd7pO3HiBL744gusWrUKEokEY8aM\nwQcffICMjAw0adLEIZ1Sq9WYOnUqvv76a+Tn5yMuLg7Lli1DzZo1Tcc88sgj6Nq1K7788ksAwKuv\nvop169ZBpVJBqVSiVatWmDlzJtq1ayf8Dt7pIyoe98olInItDl+nLzY2FgcOHEC3bt3wwgsvoH//\n/pDL5VAoFMjIyEBUVFS5vrwicdBHJMYFlomIXI/D1+nbt28fWrdujVdffRWDBg2CXM7f8D0Zp+vE\nvCWXsu6V6y25lBVzscZMxJiLGHNxnBJHcWlpafj8888xbNgwKJVKjB8/HuPGjXNW34jICTiVS0Tk\nHWx6ejc/Px/ff/89vvjiC+zduxc6nQ5z587F888/j0qVKjmjn3bH6V0iTuUSEbkLp+29+6AzZ87g\n888/x8qVK5GVlYVu3bph27Zt5epEReCgj7wZF1gmInIvTtt790H169fH3LlzcenSJXz33Xfw9fUt\nVwfIdbCOQsyTcrHnXrmelIs9MRdrzESMuYgxF8d56IIduVyOfv36oV+/fvbsDxE5CKdyiYi820Pt\nyOEJOL1L3oJTuURE7s+pO3IQkXvhU7lERPSgMtf0kediHYWYO+aSdvMShuxegQV/7USeVo0u1epj\nQ/cJmNioo90GfO6YizMwF2vMRIy5iDEXx+Gv+0QehFO5RERUHNb0EXkATuUSEXk21vQREZ/KJSIi\nm7Cmj0xYRyHmqrmI9spd2n5QsXvl2pur5lLRmIs1ZiLGXMSYi+PwTh+Rm+FULhERPQzW9BG5EU7l\nEhF5J9b0EXkJ0VO505vFoVO1ehXcMyIiches6SMT1lGIVWQuJe2VW9EDPl4vYszFGjMRYy5izMVx\neKePSODQIRkmTQrErVsSxMX5IDbW+X3gVC4REdkTa/qIBKKjlbhyxXwj/Pvvc9Ctm9Yp382pXCIi\nKoo1fUQOoNMB165JLF57cADoKHwql4iIHIk1fWTCOgojmQwYMEBtagcH70TXrhqHfqcz9sq1N14v\nYszFGjMRYy5izMVxXPNfE6IKtmzZPcTGanHrlgSRkfcQGemYKghO5RIRkbOwpo+oAnAql4iIyoI1\nfURuiE/lEhFRRWBNH5mwjkLMXrlU9F659sbrRYy5WGMmYsxFjLk4Du/0ETkYp3KJiMgVsKaPyIE4\nlUtERPbAmj4iF8WncomIyNWwpo9MvLWOYt06BaKjlWjWLAQbNyqs3i9LLq68V669eev1UhrmYo2Z\niIxN04QAACAASURBVDEXMebiOLzTR17t6lUJJk4MhEZj3IHjxRcD0b79XURElP0WOqdyiYjIlbGm\nj7zan3/K0L17iMVre/Zko2lTnc3n4FQuERE5mj1q+lxyevfTTz9F165dERoaCqlUiosXL9r0uR9+\n+AFRUVHw8/NDkyZNsGHDBgf3lNxd48Y6REVpTe3oaC0aNLBtwOdNU7lEROT+XHLQl5+fj549e+Lt\nt9+2+TP79+/Hs88+i1GjRiEjIwMjRozA4MGD8fvvvzuwp57FG+so/PyALVty8c479zB79j1s3pwD\nHx/LY0S5uONeufbmjdeLLZiLNWYixlzEmIvjuOS/Tq+88goAIC0tzebPfPTRR+jWrRumT58OAPi/\n//s/7Nq1Cx999BG+/vprh/STPINSacDLLxfadCyncomIyF25dE1fWloaHn/8cZw/fx61a9cu8dg6\ndergH//4B/75z3+aXluwYAGWLl2K8+fPWx3Pmj4qCy6wTEREFYnr9D1ApVIhIiLC4rWIiAioVKoK\n6hF5Cj6VS0REnsBpNX1vvPEGpFJpiX/27NnjrO6QAOsoLN3fK3f453M9Yq9ce+P1IsZcrDETMeYi\nxlwcx2l3+hITEzF69OgSj6lVq9ZDn79atWpWd/UyMzNRrVq1Yj+TkJBgmjZWKpWIjo5GbGwsAPNF\n503tI0eOuFR/Kqqt0evwznfJ2HjxCAyP1YBCIkPPe0o8FdbIVLvnSv2tqDavF7ZtbR85csSl+uMq\n7ftcpT+u0ub1Yr4+UlNTbV7BxBYeU9P37LPP4vbt2/j5559Nr8XHx6Nq1apYvXq11fGs6SMRTuUS\nEZEr8tiaPpVKBZVKhVOnTgEAjh49ilu3bqFOnTqoVKkSAKB79+5o164d3n33XQDGJ347deqEefPm\noV+/fli/fj12796NvXv3VtjPQeX37bc+mD3bH3K5AXPn5uPJJzUW73fpEozDh2UAgHHjCvHoo3os\nXeqH4GADFi3Kw/79Cnz2mS9CQw1YvDgPrVtbrsH39tv+WLPGB+GP3kWTf/6I1JyjAPhULhEReR6X\nXKdv+fLlaNWqFUaOHAmJRILevXujdevW2Lx5s+mYs2fPWkznxsTE4JtvvsGKFSvQvHlzfPXVV1i7\ndi3atm1bET+CWyo65VDRzp2T4uWXA3DlihQXLsgwfnwgbt+WmN7/8EPf/w34JAAkSE72xYwZAVCp\npDh9WoahQ4Mwa5Y/VCopTpyQYfToIIvzb96swKIlCuQ134usUR8hNeeocIFlV8vFVTAXMeZijZmI\nMRcx5uI4Lnmnb+bMmZg5c2aJx5w7d87qtYEDB2LgwIEO6hU527VrUuh05kFefr4EWVkSVKpkvL2d\nkXF/wHefxOLzOTmWv9OoVBKo1TAtvvzfzEsIf2sbFJGZAADNkcbY+monTuUSEZFHcumaPkdiTZ/r\ny8sDunULwenTxunb1q212Lo1B/L//aqSni5Dt27BuD/Yk8kMqFLFgMxM42CvUycNjh6VISvL2O7b\nV40VK/KsFljWXg/Dna/7YmiLR/DRR/ec+0MSERHZwB41fRz0kUu7dUuCr77ygUIBjBpViCDLGVr8\n8osM06YFIDAQWLs2BxqNBN9/74OQEANGjlTj2jUp1q3zQaVKegwdno/vLlousNy/cgwU/+2EyAgp\nhg1TQ+qSBQ9EROTtOOgrBw76rKWmppoeGfc05Xkq15NzKQ/mIsZcrDETMeYixlzEPPbpXSJ7+S3z\nbyTs/97U5lO5RETkrXinjzxSnqYQ7bd8ZPFaQqNY7pVLRERuiXf6iARe2Pst9t84b/Ha+2374cma\njSqmQ0RERC6AZetk4u5rI/2W+TeiN8yzGPBV8w/Gkf7TyjXgc/dcHIW5iDEXa8xEjLmIMRfH4Z0+\ncnuiqVwA2NVzEqr4BQk+QURE5H1Y00cV5umng3DggBw+PsCSJXl44w3j7hkSCTBnzj1cuiTDDz/4\nIDJSj6SkPDz2mN70WZ0OmDo1ADs6v2V13pktemJg3ebO/FGIiIgciku2lAMHfRVr/nxfzJ0b8MAr\nBljuqGHZbtlSi19+yTG1n//qdxwI2mVxzmr+wUh5MsEh/SUiIqpI9hj0saaPTJxZR3HqlKxMx1++\nbLxUbxXeQ/SGeVYDPr9PpjhswMf6EjHmIsZcrDETMeYixlwch4M+qhDjxxfCeDfPKCzMYNEODDQg\nIMDcfuYZNaI3zEPnrYstznPvQHNcGT8XAzsrHd1lIiIit8bpXaowv/wix5IlfoiI0OPjj+/hq698\nsHixH6pX12PDhlycOSPFTz/54EKdPdit2GX1+VV1/g87dihQr54OAwZoKuAnICIicg7W9JUDB32u\n71bhPas7ewCwsftzeDS4cgX0iIiIqGKwpo/sypXqKERTuU9FRuFI/2lOH/C5Ui6uhLmIMRdrzESM\nuYgxF8fhOn3kUj49uQ+Lj/9m9fqR/tMqoDdERESeg9O75BJU97LRY3uS1eucyiUiIuLeu+QhojfM\ns3rtqcgozGvTpwJ6Q0RE5JlY00cmzq6jePX39cIB35H+01xqwMf6EjHmIsZcrDETMeYixlwch4M+\nKpXBAMyY4Y+oKCV69AjGmTOWl41aDbRvH4IqVUJRt64SO3ZIER4eirCwUFSuHIoFC+QICws1/ZmQ\nmI/oDfOQcvWUxXmuz56IK+Pfw48/SjBiRCAaNVJizJhA5OZa9uf6dQkGDAhCo0ZKTJwYgMJCRydA\nRETk/ljTR6X67jsfvPji/7d351FVnHcfwL9zwYuAa4koyKbiBlUDCkhQBFGiHtEkNtalJmr6mogl\niMmpcWkFTY0Jr1uTmBybilpNogYlS12QI4qoGFlExVCXiiJwyRs1LBZB5Xn/SBm93mG5yF3gfj/n\ncMLMPHPvM1+fxF9mnpmxl5d9fR8gJeXRK9HmzLHH11+r5WVJEhBC+ZVqPbe8o/P5D3/uCM2iZYrt\nASAy8h7efbdKXp471x5JSY++b+nSKrz99j39D4yIiKiV4Jw+MoobN7TP7BUWai9fv669rDQmn1ny\nCWz6XtdZXzR3DR5/E0dTvr+x/hAREZEu/m1JsvrmUYwfXwNbW+1Xoj1u1iztV6p17VorL1s9cxs9\ntyzRKfh+uZS75r9L2kVfx47ay09+30svPVpWqQQmTdLe3tI4v0QZc1HGXHQxE2XMRRlzMRye6aNG\neXnVIjm5Avv3t4OLSy2mTdMusubMqYFaLbBrlw0GDnyI99+vwuuv2+Hk+BWKn3f+hcUIfL8jrljV\nwslJ4Ny5cowe3QE//GCFvn0fIi2tEocPWyM72xr+/g8QGvpAa//IyGq4udUiL88KwcEPEBj4QPF7\niIiI6BHO6aMW99mlU9h4MU1nPR+wTERE1Dyc00dmpazmHkbs36izfkvQdPh1czNBj4iIiKgO5/SR\n7GnmUQz95n91Cr4hv3LG+RcWt/qCj/NLlDEXZcxFFzNRxlyUMRfD4Zk+eir7rp/Dn3MO6KznpVwi\nIiLzwjl91Cz1Xco9OPYN9LTvbIIeERERtV2c00cmMfSb/0VN7UOtdf/TLxBvegWbqEdERETUGM7p\nI1l6ejoqKoBXX7XHwIGdMWuWPcrLH23fd/0cBiW9r1Pw9fvHKnwyJQKRkXb44gtrODj88rq17t27\n4KefjHwQBsD5JcqYizLmoouZKGMuypiL4Zhl0bd582aEhoaiS5cuUKlUuHHjRqP7bN26FSqVSuvH\nysoKNTWGfXBvW/Pee7b49ls1SktV+Oc/1Vi1yhb3Ht6Hz9fxOnP3Do59A37frERqajuUlqrw5Zc2\nWLCgw39fwSbh/n0JQUGdTHMgREREpMUsi76qqiqMGzcOcXFxeu1nZ2eH0tJSaDQaaDQalJSUQK1W\nN74jAQBGjBih80qzrI7H4fftOjwQtfK6/+kXiPMvLEZP+846r0R7Unm5WQ4xvYwYMcLUXTBLzEUZ\nc9HFTJQxF2XMxXDMck5fdHQ0ACAzM1Ov/SRJQrdu3QzRJYvxwgs1+Oc/1WjnVgTH2A/xf49tm+rx\nLP707PNa7V98sQbZ2b8MI5VKwNZW4O5d6b9bBcLC7hun40RERNSg1n8a5jFVVVXw8PCAq6srIiIi\ncPbsWVN3qVVJT0/HlCn3sX7XJTjGfiivt5IknJgQrVPwAcCCBdXYtq0SixdX4dtvK1FYWIZBgx6g\nU6davPxyDXbsuGvMQzAIzi9RxlyUMRddzEQZc1HGXAzHLM/0NceAAQOQkJCAIUOGoLy8HBs3bkRQ\nUBByc3Ph6elp6u61Kh6DyoCMX37/W9BvMbybR4PtIyLuIyLi0Rm9Y8cqDNg7IiIiag6jPadv+fLl\nWL16dYNtjh49iuDgR4/9yMzMhL+/PwoKCuDmpt9bHWpra+Hj44OQkBBs3Kj7PDk+p69hVQ/uw9a6\nnam7QURERGhlz+mLiYnBK6+80mAbV1fXFvs+lUoFX19fXL58ud42kZGRcjHZuXNnDBo0SJ5AWnd6\n2VKXszJOm1V/uMxlLnOZy1y2pOW635vyBJOmMus3cjzNmT4hBIYOHQpfX1989tlnOtt5pk9Xenq6\nPOjoEeaijLkoYy66mIky5qKMuShrVWf69FH3yJVLly4BAPLy8nD79m24u7uja9euAICwsDAEBATI\nl4zj4uIQGBgIT09PlJeX469//Svy8vKwefNmkx0HERERkbkwyzN9sbGxWLlyJYBfzsgJISBJEhIS\nEuRLxL169UJoaCi2bNkCAFi0aBH27t0LjUaDzp07w9fXF7GxsQgICFD8Dp7pIyIiotaiJc70mWXR\nZwws+oiIiKi1aImir009p4+ezuOTR+kR5qKMuShjLrqYiTLmooy5GA6LPiIiIiILwMu7RERERGaO\nl3eJiIiIqElY9JGM8yiUMRdlzEUZc9HFTJQxF2XMxXBY9BERERFZAM7pIyIiIjJznNNHRERERE3C\noo9knEehjLkoYy7KmIsuZqKMuShjLobDoo+IiIjIAnBOHxEREZGZ45w+IiIiImoSFn0k4zwKZcxF\nGXNRxlx0MRNlzEUZczEcFn1EREREFoBz+oiIiIjMHOf0EREREVGTsOgjGedRKGMuypiLMuaii5ko\nYy7KmIvhsOgjIiIisgCc00dERERk5jinj4iIiIiahEUfyTiPQhlzUcZclDEXXcxEGXNRxlwMh0Uf\nERERkQXgnD4iIiIiM8c5fURERETUJCz6SMZ5FMqYizLmooy56GImypiLMuZiOCz6iIiIiCwA5/QR\nERERmTnO6SMiIiKiJmHRRzLOo1DGXJQxF2XMRRczUcZclDEXw2HRR0RERGQBOKePiIiIyMy1yTl9\nd+7cQVRUFAYOHAg7Ozu4ubkhMjKySQVaYmIivLy80L59e3h7eyMpKckIPSYiIiIyf2ZX9BUXF6O4\nuBjx8fG4cOECduzYgbS0NEyfPr3B/U6dOoVp06Zh1qxZyM3NxcyZM/Hyyy/j+++/N1LPWz/Oo1DG\nXJQxF2XMRRczUcZclDEXwzG7os/b2xuJiYmYOHEievfujeDgYMTHxyMlJQWVlZX17rdhwwaMHj0a\nS5YsQf/+/bF06VKEhIRgw4YNRux963b+/HlTd8EsMRdlzEUZc9HFTJQxF2XMxXDMruhTUlZWBhsb\nG9jZ2dXbJiMjA+Hh4VrrwsPDcfLkSUN3r80oKyszdRfMEnNRxlyUMRddzEQZc1HGXAzH7Iu+n3/+\nGX/6058wb948qFT1d1ej0aB79+5a67p37w6NRmPoLhIRERGZPaMVfcuXL4dKpWrwJy0tTWufyspK\nREREwNXVFR988IGxumqxbty4YeoumCXmooy5KGMuupiJMuaijLkYjtEe2XLr1i3cunWrwTaurq6w\ntbUF8EvBN2HCBEiShAMHDjR4aRcA3N3dERUVhbffflteFx8fj48//hgFBQU67T09PXH16lX9D4SI\niIjIyPr06YMrV6481WeY5XP6KioqMH78eEiShIMHD8Le3r7RfaZNm4Y7d+7g0KFD8rrw8HB069YN\nO3fuNGR3iYiIiMyetak78KSKigqEh4ejoqICSUlJqKioQEVFBQDAwcEB7dq1AwCEhYUhICAAq1ev\nBgBER0cjODgY77//PiZPnox9+/bh6NGjOHHihMmOhYiIiMhcmN2NHFlZWTh9+jR++OEH9OvXD87O\nznB2dkbPnj1x6tQpud2///1vrZs0AgMD8eWXX2Lr1q0YMmQIduzYgd27d8PPz88Uh0FERERkVszy\n8i4RERERtSyzO9PX0vhat/pt3rwZoaGh6NKlC1QqVZPumNq6davOXddWVlaoqakxQo8NrzmZAG1/\nrFRXVyMqKgrdunVDhw4dMHnyZBQVFTW4T1sdK5s2bUKvXr1ga2uLYcOGNfr2gPPnz2PUqFGws7OD\ni4sLVq1aZaSeGo8+mRQUFCg+vSE5OdmIPTastLQ0TJo0CS4uLlCpVNi2bVuj+1jCONE3F0sYKwDw\n3nvvwc/PD507d4ajoyMmTZqEvLy8Rvdrzphp80UfX+tWv6qqKowbNw5xcXF67WdnZ4fS0lJoNBpo\nNBqUlJRArVYbqJfG1ZxMLGGsLFy4EHv37sWXX36J48ePo7y8HBMnTkRtbW2D+7W1sbJr1y4sXLgQ\ny5cvx9mzZ/Hcc89h/PjxKCwsVGxfXl6OsWPHwsnJCZmZmdi4cSPi4+Oxbt06I/fccPTNpM6hQ4fk\ncaHRaBAaGmqkHhve3bt3MXjwYGzcuBG2traQJKnB9pYwTgD9c6nTlscKABw7dgx/+MMfcOrUKRw5\ncgTW1tYYM2YM7ty5U+8+zR4zwgLt379fqFQqUVFRUW+bqVOnivDwcK11Y8aMEdOnTzd094zuzJkz\nQpIkcf369UbbJiQkiA4dOhihV6alTyZtfaz8/PPPQq1Wi88//1xeV1hYKFQqlTh06FC9+7XFseLv\n7y/mzZunta5v375iyZIliu03bdokOnfuLO7duyeve/fdd0XPnj0N2k9j0jeTa9euCUmSRGZmpjG6\nZ3IdOnQQ27Zta7CNJYyTJzUlF0sbK3UqKyuFlZWV+O677+pt09wx0+bP9Cnha92eTlVVFTw8PODq\n6oqIiAicPXvW1F0yqbY+VrKysnD//n2tY3RxccHAgQMbPca2NFZqamqQnZ2t15/1qVOnMHLkSNjY\n2Gi1Ly4uxvXr1w3aX2NoTiZ1XnrpJXTv3h0jRoxAYmKiIbtp9tr6OHlaljZWysvLUVtbi65du9bb\nprljxuKKPr7W7ekMGDAACQkJ+Oabb/DFF1+gffv2CAoKeuoHRrZmbX2saDQaWFlZwcHBQWt99+7d\nUVpaWu9+bW2s/PTTT3j48KHOn7Wjo2O9f9b1jY26ba1dczLp2LEj1q5diz179uDAgQMICwvDb3/7\nW4t+nmpbHyfNZaljJTo6Gj4+PggMDKy3TXPHTKst+vhaN2XNyUUfw4cPx6xZszB48GCMGDECu3bt\ngqenJz788MMWPIqWZehMWiuOFcNr6pwlS+Lg4ICYmBj4+/vD19cXcXFxeOONN9rsf5ObguNEmSWO\nlUWLFuHkyZNITExscFw0d8yY3cOZmyomJgavvPJKg21cXV3l3+te66ZSqfDdd981Opm8R48eOtVy\naWkpevTo0fxOG4G+uTwtlUoFX19fXL58ucU+s6UZOpO2PlYePHiAhw8f4tatW1pn+zQaDYKDg5v8\nfa1hrDTkmWeegZWVlc7ZzdLSUjg5OSnuU9/YqNvW2jUnEyV+fn7YsmVLS3ev1Wjr46QlteWxEhMT\ng927dyM1NRUeHh4Ntm3umGm1RZ+Dg4PO5ab6PP5at6a8xxf45WHPhw8f1nqX7+HDhxEUFNTsPhuD\nPrm0BCEEcnNz4evra7Tv1JehM2nrY2Xo0KFo164dkpOT5bveb968ifz8fDz33HNN/r7WMFYaolar\nMXToUCQnJ2PKlCny+sOHD+Pll19W3CcwMBCLFy9GdXW1PPfm8OHD6NmzJ9zd3Y3Sb0NqTiZKzp49\nC2dnZ0N0sVVo6+OkJbXVsRIdHY09e/YgNTUV/fr1a7R9s8dMC91sYrbKy8vF8OHDhbe3t7h8+bIo\nKSmRf2pqauR2o0eP1rrb7OTJk8La2lqsWbNG/PDDD2L16tWiXbt24vvvvzfFYRhESUmJyMnJETt3\n7hSSJIn9+/eLnJwccfv2bbnNk7nExsaKQ4cOiatXr4qcnBwxZ84coVarxZkzZ0xxCC2uOZlYwliZ\nP3++cHFxESkpKSI7O1uEhIQIHx8fUVtbK7exhLGya9cuoVarxWeffSYuXrwo3nzzTdGxY0dx48YN\nIYQQ77zzjggLC5Pbl5WViR49eohp06aJCxcuiMTERNGpUyexbt06Ux1Ci9M3k61bt4rPP/9cXLx4\nUeTn54v4+HihVqvFhg0bTHUILa6yslLk5OSInJwcYWdnJ1auXClycnIsepwIoX8uljBWhBAiMjJS\ndOrUSRw5ckSrRqmsrJTbtNSYafNFX2pqqpAkSahUKiFJkvyjUqnEsWPH5HYeHh5izpw5Wvt+9dVX\nYsCAAUKtVgsvLy+xb98+Y3ffoFasWKGVR90/H7+N/slcYmJihLu7u7CxsRGOjo5i3LhxIiMjwxTd\nN4jmZCJE2x8r1dXVIioqSjg4OAg7OzsxadIkcfPmTa02ljJWNm3aJDw8PISNjY0YNmyYOH78uLxt\n9uzZolevXlrtz58/L4KDg0X79u2Fs7OzWLlypbG7bHD6ZLJt2zbh5eUl7O3tRadOnYSfn5/YuXOn\nKbptMHV/7zz5d0/dvx+WOk70zcUSxooQQrFGkSRJxMXFyW1aaszwNWxEREREFqDV3r1LRERERE3H\noo+IiIjIArDoIyIiIrIALPqIiIiILACLPiIiIiILwKKPiIiIyAKw6CMiIiKyACz6iMhkevXqhXXr\n1um1j0qlwt69e1u0H7GxsRg0aFCLfmZTffXVV1CpDPuf4pCQEERFRRn0O4jI/LHoI6JmKyoqwrx5\n8+Dq6gobGxu4uLhg3rx5KCoqatL+mZmZmD9/vl7fqdFoMHHixOZ0t9kKCgrw2muvoU+fPrCzs0Of\nPn2wdOlS3Lt3z6j9aC5JkiBJkqm7QUQmxqKPiJrl2rVrGDZsGC5evIjt27fj6tWr2LFjB/Ly8uDn\n54fr16/Xu29NTQ0AwMHBAba2tnp9r6OjI9Rq9VP1XV//+te/UFtbi08//RQXL17Ehx9+iO3btyM6\nOtqo/SAiehos+oioWRYsWABra2ukpKQgNDQULi4uCAkJQUpKClQqFRYsWCC3DQkJQWRkJN5++204\nOjpi5MiRAAAPDw+sXbtWbnfp0iWMGjUKtra28PLywsGDB9GhQwds27ZNbvP45d2CggJ5eezYsbC3\nt4e3tzdSUlLk9rW1tXjttdfQu3dv2NnZoV+/foiPj4c+b6B8/vnnkZCQgLFjx8LDwwMTJkzAsmXL\nkJiYKLc5evQoVCoVjhw5goCAANjb28PPzw85OTlan7V9+3a4u7vD3t4eERERKC0tbfT7y8rKMH/+\nfDg7O8vZ7N69W96+d+9eDBo0CO3bt4ebmxtWr17d4Oc9mTugewnYw8MDq1atwuzZs9GpUye4ublh\n9+7duHPnDqZOnYqOHTuif//+OHLkiN4ZEJFpsOgjIr3dvn0bhw4dwoIFC9C+fXutbba2toiMjMSB\nAwdQVlYmr9+xYwckSUJ6ejq2b98OQPuyY21tLV588UWo1WqcPn0aW7ZswYoVK1BTU9Popclly5Zh\n4cKFOHfuHPz8/DBt2jTcvXtX/lwXFxfs2bMH+fn5+Mtf/oLVq1cjISHhqTIoKyvDr371K531S5cu\nxQcffIDs7Gw4ODhg5syZ8rbTp09jzpw5eOONN5Cbm4uIiAj8+c9/bvD4hBCYMGECjh8/jq1btyI/\nPx8bN26EjY0NACArKwtTp07Fb37zG1y4cAFr1qzBe++9h48++qjez1S63Ku0bsOGDRg+fDhycnIw\ndepUzJ49G9OnT8ekSZOQm5uLkSNHYubMmaiurm5yBkRkQoKISE8ZGRlCkiSRlJSkuH3v3r1CkiRx\n5swZIYQQo0aNEkOGDNFp5+HhIdauXSuEEOLgwYPC2tpaFBcXy9tPnjwpJEkS27Ztk9dJkiQSExOF\nEEJcu3ZNSJIkNm/eLG8vKioSkiSJEydO1Nv/xYsXizFjxsjLK1asEL/+9a+bcuhCCCEKCgrEM888\nI9avXy+vS01NFZIkieTkZHndiRMnhCRJoqioSAghxPTp00V4eLjWZ/3+978XkiTV+13JyclCpVKJ\n/Px8xe0zZswQYWFhWutiY2OFi4uLvBwSEiKioqLk5cdzr6+Nu7u7mDFjhrxcWVkpJEkS0dHRWjlI\nkiSysrKanAERmQ7P9BGRUQwdOrTB7fn5+XB2doaTk5O8btiwYU26s3Xw4MHy73X7//jjj/K6Tz/9\nFMOGDYOjoyM6duyIDRs2oLCwUN9DAACUlpZi3LhxCA8Px8KFC/XqS35+PgIDA7XaDx8+vMHvy8nJ\ngZOTE/r376+4PT8/H0FBQVrrgoKCUFRUhMrKysYPqB6SJGkdi729Pezs7LTucnZ0dASgnTXQ+J8H\nEZkGiz4i0punpyckSUJeXp7i9osXL0KSJHh6egL4pYCwt7c3WH/atWsn//745WIA2LVrF2JiYjB3\n7lwkJycjNzcXkZGROpckm0Kj0SA0NBSDBw/GP/7xD737YiiinvmJ9V02VqlUOvvU3VzzuMePpe7z\nmnJ8psiAiBrHoo+I9Obg4IDnn38emzZtQlVVlda2//znP/j4448xYcIEdOnSpcmfOWDAABQXF6Ok\npERel5mZ+dTFQnp6OgICAhAZGYlnn30WvXv3xpUrV/R+hElJSQlCQkLg7e2NL774olnP1hs4cCBO\nnTqltS4jI6PBvvj6+qKkpAT5+fn1fuaJEye01qWnp8PV1bXeQrtbt24oLi6Wl+/du1fv5xNRxYKn\n3wAAAnpJREFU28Gij4ia5aOPPsKDBw8wZswYpKamorCwEEePHsXYsWMhSZLWjQRCiEbvlg0PD0f/\n/v3x6quv4ty5c8jIyMCiRYtgbW39VM+Y69+/P7Kzs3Hw4EFcvnwZq1atQlpaml537xYXF2PUqFFw\ncnLC+vXr8eOPP0Kj0UCj0ehVlL755ptISUnBmjVrcPnyZfztb39DUlJSg30JCwtDQEAApkyZguTk\nZFy7dg2HDx/G119/DQB46623cOzYMcTFxeHSpUvYuXMn1q1bhz/+8Y/yZzyZ/+jRo7Fz504cO3YM\neXl5mDt3Lh4+fNjk4yCi1olFHxE1S+/evZGZmQlvb2/MmjULffr0wcyZM+Ht7Y0zZ87A3d1dbtuU\nhwNLkoR9+/ahuroa/v7+mDNnDpYtWwZJknTuEH5yv4a8/vrrmDp1KmbMmAF/f3/cuHEDb731ltZ+\njfUvOTkZV65cQVpaGtzc3ODs7AxnZ2f07NkTN2/ebLAvj68LCAjA3//+d3zyyScYMmQIkpKSEBsb\n2+B3S5KEAwcOICgoCL/73e/g5eWFmJgY3L9/HwDg4+ODPXv2IDExEYMGDcLSpUuxZMkSrUfmPHl8\nS5YswejRozF58mSMGzcOwcHB8PHxaTDHpmosAyIyHUno87+7RERGlJubCx8fH2RlZbVYUUJEZKlY\n9BGR2di3bx/s7e3Rt29fFBQUYNGiRZAkCdnZ2abuGhFRq2dt6g4QEdWprKzEO++8g8LCQnTt2hWh\noaFYv369qbtFRNQm8EwfERERkQXgjRxEREREFoBFHxEREZEFYNFHREREZAFY9BERERFZABZ9RERE\nRBaARR8RERGRBfh/khecIdPx4GUAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 439 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Proportion of variance" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#d^2 is proportional to the variance explained by the dimension\n", "#For variance explained, normalize d^2\n", "\n", "var_exp = d**2/sum(d**2)\n", "\n", "print \"The first component explains %0.2f%% of the variance.\"%(var_exp[0]*100)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The first component explains 98.14% of the variance.\n" ] } ], "prompt_number": 440 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Iris example\n", "====\n", "\n", "We take all four features now and apply SVD:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Load the dataset from sklearn's library of example datasets\n", "iris = sklearn.datasets.load_iris()\n", "\n", "#data are the features (here, flower measurements)\n", "X = iris.data\n", "#target are the classes we wish to recover (here, flower species)\n", "Y = iris.target" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 441 }, { "cell_type": "code", "collapsed": false, "input": [ "train = np.array(range(0,35)+range(50,85)+range(100,135))\n", "X = X[:, 0:4]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 442 }, { "cell_type": "code", "collapsed": false, "input": [ "colmeans = np.dot(np.matrix([np.zeros(len(train))+1/len(train)]),X[train])\n", "colmeans = np.array(colmeans)[0]\n", "X = np.array([a-colmeans for a in X])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 443 }, { "cell_type": "code", "collapsed": false, "input": [ "names = {0:'setosa', 1:'versicolor', 2:'virginica'}" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 444 }, { "cell_type": "code", "collapsed": false, "input": [ "cols = np.zeros(len(X))\n", "cols[train] = Y[train]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 445 }, { "cell_type": "code", "collapsed": false, "input": [ "U, d, V = scipy.linalg.svd(X[train,], full_matrices=False)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 446 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(range(1,5), d**2/np.sum(d**2), s=70)\n", "plt.xlabel(\"Dimension\")\n", "plt.ylabel(\"Percent explained\")\n", "plt.xlim(0.9, 4.1)\n", "plt.ylim(-0.1,1)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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YUNHR0e4Ot2CNuKztbdu2adSoUR4fz7bn24mJieX+78E2+frD9i/nS/yhnuq0XbDPX+qp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\nKvbnww8/rKKKA8NTTz2lbt2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"text": [ "" ] } ], "prompt_number": 447 }, { "cell_type": "code", "collapsed": false, "input": [ "colors = [dark2_colors[i] for i in Y[train]]\n", "plt.scatter(U[:,0], U[:,1], color = colors, s=50)\n", "x = np.array([-0.15, 0.15])\n", "plt.plot(x, -3*x-.165, color='k', linestyle='-', linewidth=1)\n", "plt.plot(x, -3.2*x+0.2, color='k', linestyle='-', linewidth=1)\n", "plt.xlabel(\"PC1\")\n", "plt.ylabel(\"PC2\")\n", "plt.ylim(-0.3,0.3)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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L9wHUuZ/PCpR4EhMTadeuHRMnTuSBBx7gyy+/pFWrVj59/sTExIDKRyD9fFZ1739l10sp\nfPcvfH+4BIB+lyjgsvP9URs8N56bF16LITI+YH6/i/m5QYMG3HrrrSxatIioqCgMBkNAxefPn8/e\nFijxyM+B/fPZ2wIlHn9+vq5bt46srCy8JaAXhlxxxRV079690sKQe+65h9TUVN3HfP311yQlJfHU\nU0/x2GOPud23LAwJPq+++irp6emsWrWKmJgYf4cjaqDoy5cp/vQZcJRW3mgKJ+q2JwlPHO37wDzE\n4XBw55130r9/f6ZPn+7vcIQQIaROLQwBmDJlCq+99hrp6ens2bOHRx99lOzsbMaOHQvA9OnTueGG\nG8rvv3btWoYMGcK4ceMYPnw42dnZZGdnc/LkSX/9CkHl90d3Ao2/ZgwHel78pSZ50fKO6ReAAPYS\nXIXB/V41Go08/PDDvPHGG6xatcrf4QQMeQ/pk7zok7z4TkAXgcnJyfzrX/9i1qxZ9OzZkw0bNvDJ\nJ5/QvHlzALKzs9m3b1/5/ZcsWYLVamXu3Lk0btyYJk2a0KRJE/r16+evX0F4mKwYDm7GFj3AEqm/\n0RKFsUkX3wbkBXFxcaSnpzNx4kT279/v73CEEMKtgD4d7E1yOjh4yYzh4KXZrZx+qgda4WngvI8e\nxYAh5hLiZ2xFUY1+i8+T0tLSWLp0KStXriQiIsLf4Qghgpw3TgdLESiC0t69e0lKSmLRokVcddVV\n/g5HXATHib3kLRyGVnS6rAzUQI1pROwf30Zt0MrP0XmOpmmMHTsWg8HA/PnzURTF3yEJIYJYnesJ\nFL4VTH0YvpwxHEx58aWa5sWY0I74x7cQ89B/ib57LvXGvkPc374PmQLwbF4UReH5559nx44ddX6G\nubyH9Ele9ElefEeKQBG0ZMZw8FIUBXPbKwnrk4ypdd+QPUoWGRlJRkYGzz77LJs2bfJ3OEIIUYGc\nDhZBT2YMi0D36aefMnXqVNasWUPDhg39HY4QIgjJ6WAhdMiKYRHohgwZwvDhwxkzZgwOh8Pf4Qgh\nBCBFoDhPsPZheHvGcLDmxdskL/rc5WXatGmoqsqsWbN8HJH/yWtFn+RFn+TFd6QIFCFBZgyLQKeq\nKmlpabz//vt8+OGH/g5HCCGkJ1CElrVr1zJ27FhWrlxJq1at/B2OEJVkZmaSnJzMihUraN++vb/D\nEUIECekJFOICZMWwCHQ9e/ZkxowZpKSkUFhY6O9whBB1mBSBolyo9GF4esZwqOTF0yQv+qqTl5SU\nFPr27cukSZM8/s0+EMlrRZ/kRZ/kxXekCBQhSVYMi0A3Z84cDhw4wIIFC/wdihCijpKeQBGyZMaw\nCHRZWVkMHjyYRYsW0b9/f3+HI4QIYNITKMRFkBXDItC1aNGCefPmMWbMGI4dO+bvcIQQdYwUgaJc\nKPZheGLGcCjmxRMkL/rc5cWZd4yiT2aTu+Bu8v87CXtWJgADBw5k9OjRjBo1CpvN5stQfUZeK/ok\nL/okL74jRaAIebJiWPib7dcN5MzuR/Gaedh//orSjf8l9+XbKFo1F4ApU6YQFxcnPaxCCJ+SnkBR\nZ8iMYeEPmtPO6Rmd0EpyK280hVNv0gpMzbqRl5fHgAEDmD59OkOHDvV9oEKIgCY9gULUgqwYFv5g\n+3ENmsvNvGCHDeuG1wCIjY1lyZIlTJ8+nd27d/suQCFEnSVFoCgX6n0YNZ0xHOp5qSnJi77f58VV\neBI0l/6dNSfO3KPlP3bp0oXU1FRSUlJCqnWhpq+VgoJSjh4poLjI7uGIAoO8h/RJXnzH6O8AhPCl\nsyuGk5KSaNu2LVdddZW/QxIhzti4cxUbwzC17F3hpuTkZDZv3sz48ePJyMjAYKh739ULC2188N7P\nHDmUj9FowOFw0fbSOG65vR1hYfJnSwhPkZ5AUSfJjGHhS2eeG4jj6G5wVTyipVgiif/7JgzRCRVu\nt9lsJCUlMWTIECZPnuzLUP3O6XTxyryt5OeX4jrvAKqqKjS6JJKU0d1QFMV/AQrhJ9ITKISHyIph\n4UuxD/8XY9PLwBwO5kgUSxRKZDyxf3ynUgEIYDabWbx4MWlpaaxZs8YPEfvPzz/lUFxsr1AAAjid\nGidPFHPkcIF/AhMiBEkRKMrVtT6M6s4Yrmt5qS7Jiz69vBiiGxI35QvqTVxB9NA5xIxcRP0nd2Nq\n3dftfpo2bcorr7zCuHHjOHz4sDdD9rqLea0c2J+LzabfQ+l0ujicFTpf2uQ9pE/y4jtSBIo6TVYM\ni5rQHDZKt31A4SfPULJuEa6iM9V6nKlZN8L6DMPccQCKeuHetsTERCZMmMCIESOwWq21DTvgWa0O\nTp0odrvdYDBgMsvlnYTwFOkJFHWezBgWF8Nx4hdyX74NbMVopYVgCgc0ou+dT1iP2zz+fJqmMXLk\nSOLj43nhhRc8vv9AUVxsZ3HadooKbTid+n+WVKPC+Em9iYoy+zg6IfxPegKF8AKZMSyqS3O5yPvP\nPWiFJ8sKQAB7CditFLw5Aefpgx5/TkVRePnll9mwYQOvv/66x/cfKNZ9lUVhgfsC0GQycO11LaUA\nFMKDpAgU5epyH0ZVM4brcl6qUhfzYt+3AVfxGdD7Nu5yULJ+sVfyEh0dTUZGBk8++STbt2/3+P69\nrTo52bnjJC6X+6Mct9/Vnn79m3oyLL+ri++h6pC8+I4UgUL8RlYMi6rYszIp/uz5siN/epx2HNk/\neu35O3TowNy5cxkxYkRItrI47G4uqE3Z5WGaNIv2YTRC1A3SEyjE78iMYXE+TdMoWDaZ0q3LwW4F\n3HxkqibCr36IqNuf8mo8M2bMYM+ePSxbtiykXp9LF+/g8CH9L19R0WYeeay3XB9Q1GnSEyiED8iK\nYXG+0sz3Kc1877cjgFV8ABuMhF81yuvxPPHEE5SWljJnzhyvP5cvXTegBUZj5T9JJpOB6wa0kAJQ\nCC+QIlCUkz6MMr+fMSx50RdKedGcDqyblnHmXzeSM7sf+f99DMeJXwAoWTsfbO4vW4JqAVMY0ckv\noDZo7fW8GI1G0tPTeeONN1i1apVXn8tTqpOT5i1juePu9kRGmjCZDZjNKhaLyvU3tKJr90Y+iNL3\nQuk95EmSF9+RIYxC6Dh/xvDkyZNJTEz0d0jCSzSng7y04dj3f19e7DlPH6Q08z1iH3oLZ+5R9w9W\nTYQljiZy4CQM0Q19FDEkJCSQnp7OAw88wKpVq2jdurXPntub2nWoz6Xt4zlxvBiXy0VCo0hUVY5V\nCOEt0hMoRBVkxnDos255l4K3p+ge7TPEXIKhYVscv7q5dJDRQv0nd2GIqOflKPWlpaWxdOlSVq5c\nSUREhF9iEEL4hvQECuFjsmI49JWsf83t6V6ttBBLt6TfLgj9O0YLlm5JfisAoWz0YadOnfjTn/7k\n8T8OQojQJ0WgKCd9GPo6duxYrRnDdU2ovF60klz3GxUDxkbtiBwyDYwWMIeDagZTOKZWvYlOfr7S\nQ3yZF0VReP7559mxYweLFy/22fNerFB5rXia5EWf5MV3pAgUohpkxXDoMrW7GlST7jbNUYqxaVci\nrp9A/ZnbiLp9FpFJM6g38SPqTfgAxRLp42gri4yMJCMjg2effZZNmzb5O5xqKSmxk32skKIim79D\nEaJOk55AIapJZgyHJmfOIXL+mQi2ooobTOGE9b5H92hfIPr000+ZOnUqa9asoWFD3y1SuRilpQ4+\n+fAX9u7NQVUNOB0uWrWuR9Id7YiI0C/EhRBlvNETKEWgqDWHy8Xa7L18kLUTm8vJDY3bc0vzzkQY\nQ2/G5969e0lKSmLRokVcddVV/g5HeIj94FbyM8bgKjyFYjCiOUoJ6zucqLueQXFzlDAQpaamsnHj\nRpYvX47RGFgXf9A0jYxFP3A8u6jCfGCDQaFeXBgPjeuJwSDXAhTCHVkYIryqJn0YNqeDB9e/xd+3\nrGBt9i9sOLGfuTu/5I7V6ZyyFl14B0Hg/LxUNWO4rgmlvh1Ty17EP76FuEmfEPNgBvX/sZPoe/6v\nRgWgP/Mybdo0VFVl1qxZfotBz7p16zh8qICTJ4orFIAALpdGQUEpv+yte1/KQ+k95EmSF9+RIlDU\nypJfNrLrTDbFTnv5bSVOOyethTy1baUfI/MeWTEcmhRFwdi0C+ZLEzFExvk7nBpRVZW0tDTef/99\nPvzwQ3+HU8Ghg3k4HPrzge02Fwf25fk4IiGEnA4WtTJw5TxOWAt1t5kMKt8MmUikyeLjqHxDZgyL\nsxzH91LyzSs4ju5CbdiW8KsfwtSsm9/iyczMJDk5mRUrVtC+fXu/xXG+Td8fZc0XByodCQRQFLji\nqqZcN6CV28cXF9vJ3JLNzz+exqAqdOveiC7dGmIyyXtP1A1yOlgEnDyb1e02VVEocJT6MBrfkhXD\nAsCa+T5nnhuA9dulOPZvpHTT2+S+dAvFX6f5LaaePXsyY8YMUlJSKCzU/5Lmax061Xe7TVUNXNYl\nwe32vFwrafO3suGbQ2QfK+Lo4UJWf7afJek/YLPJZZuEqCkpAkW5mvRhtI12/8FuVAzUD4BLaNSW\nu7z8fsZwXSN9O+AqzqXgrYlgLwGXA4DvjznAXkLRR//AmZPlt9hSUlLo27cvkyZN8vuFpNetW0dM\njIX+VzfDZKr4Z8dkMtC9VyMaJrifePLpx79SUuLA4Tj3e9jtLnJySvh23eFK9z+TU8Jnn/7K4rRt\nvLtsD/t/zfV7DvTIe0if5MV3pAisYzRN45S1kDxbiUf2N75TImE6zfNhqpGUS/tgMoT2qZqzM4ZT\nU1NZv97NaDERskq3fwiKm49RzYV10zLfBvQ7c+bM4cCBAyxYsMCvcZyVeE0L7hjagWYtYoiMNNG4\nSRRJt7dj0I3uZx+XljrIOpiHXg3ndGhszzxe4bYD+3JJX7iNzC3ZZB8rYu9POSx/ew+fr9wXkIWg\nEP4kPYF1yGdHfuT/dq7hdGkRmqbRIbYRM3oMpnO9S2q13zd+3cy/dn+F+tsfQ7vLyR0tuvL37oMx\nKHXjkg8yY7huKv7iXxR9Mhs0/QUPYf1HEn3P//k4qoqysrIYPHgwixYton///n6NpSYK8kv5z8tb\n3S4qMZoMTJ1+JQBOp4uXntuI1Vr5FLHJZGDYvZ1p3jLWq/EK4S3e6AkMrAtJCa9ZdeRHHt+6AqvT\nUX7bztxjjPzmTf57XQptohvUeN/3te3NHS26suHEAeyak74NWtAgLMoTYQeN81cMr1q1ipiYGH+H\nJHzA2LRr2Si5Up3LIZkjMbXsfcF9aJqG4/B2tOJcjE06Y4h23xtXEy1atGDevHmMGTOG1atX07hx\n41rvU9M0sFvBaEExePeEUmSUGaPJ4LYIbNToXMvJgX15uPTvht3uYuuWbCkChThPQJ8Onj9/Pq1b\ntyY8PJzevXtX2SdQWlrKyJEj6d69O2azmeuvv96HkQY2TdOYs2N1hQLwrFKng/l7yk5j1qYPI9Jk\nYVDTDtzcrHPIFYDVzcuYMWPq1Ixh6dsBU4frMUQ1hPPaHr7P1kBRUExhWHrcXuXj7VlbyXm6F7kv\n307+a6M5/VRP8l8fh+bhBVUDBw5k9OjRjBo1Cput5qPaNJeL4rX/4fTMTpya1pJT01tR8N40NL0i\n+Dy1ea0YDApXXd0Mo6nynyuj0cA117Uo/7nEakfD/ZGSokK7223+IO8hfZIX3wnYInDZsmU89thj\nPP7442zbto3+/fszZMgQDh06pHt/p9NJeHg4EydO5JZbbkGpI6chqyO7pIB8u/4qXhcaG07s93FE\noUtWDNctisFAvUc+RL2kI5gjwBIFpjAM8S2pN+ljFHO428c6c4+SN/8uXGcOga0IzZoPjlJKf/iI\n/Dcf8XisU6ZMIS4urlavzcL3/krRp7PRCk+VnQK3FWP9dim5L9+GpvMl01P69GtCvyuaYDQaMFtU\nzBYVi0VlSFJbWrWpV36/xo2j3J2ZRzUqtGgpR+iFOF/A9gT269ePHj16sHDhwvLb2rdvz9ChQ5k9\ne3aVj33kkUfYtWsXa9ascXufutQTeNJayE2f/QebS//oVD1zON/cPMnHUYUumTFcN9kP/4Dz5K+o\ncc0xtrz8gl9ECz96kpKvFoJT58ic0UL845tRY2t26tZVko8rJwtDTCMM0efmCOfl5TFgwACmT5/O\n0KFDL2o4lQkrAAAgAElEQVSfzjNHyJndF/SOUpojibl/AZauN9co3uoqLXVw5FABqqrQrEUMqlr5\nOMZbS3dyKCu/0vUIzRaVsRN6ERkVeuMsRd1QZ3oCbTYbW7du5S9/+UuF2wcPHsyGDRv8FFXwahgW\nRYvIOH4pOFVpm1ExcFPTjn6IKnSdXTGclJRE27ZtZcZwHWFq1u2iLhBt3/uNfgEIKEYzjkPbLroI\n1GwlFLz7Z0ozP0AxmtAcNkxtriTmvnkYYhoRGxvLkiVLuPPOO+ncuTOdO3eu9r5tP31Z4bR3xY1F\nlGb+z+tFoMVipM2lVU9zuSu5I/979yeyDuZhUA2gaVjCjNyd3EkKQCF+JyBPB586dQqn00mjRo0q\n3J6QkEB2drafogpuT/S4kTDVyPnHJlTFQIw5jIc7lK0YlD4MfTXJS12YMSyvF33VzYsSGe92m6Zp\nKOH13G53J29RCqWZ/wOHFc1aAI5S7L+s48yLQ8r7DLt06UJqaiopKSkXOfbwAi02VSwQ8eVrxWIx\nMuy+y3hoXC9uvaMdw+67jAmP9qZxk8DrVZb3kD7Ji+8EZBEoPK9H/WYsvfp+rm7UlnDVRLTRwp0t\nu/Hu9aNoGGILOQKFzBgWVQnvP7Ksj1CHYgrD1LrvRe3PcXQX9n3fVT5d63KgFZ2mdPtH5TclJycz\nYMAAxo8fj8vdctrfMXccCG5aShRzJJYed1xUvN5WLy6M9h3q06x5TLV6xF0ujY3fHeHlFzbxz1kb\nmP/SZjK3ZMu1BUVIC8jTwQ0aNEBVVY4fr3gR0OPHj3vk8gZnjR8/nhYtylaWxcbG0rVrVxITE4Fz\n30RC7ed5iUPP/VxIeQH4+29egRJvIPycmJhY48ePGTOGn376ibvuuouZM2dyzTXX+P338eTPZwVK\nPIHwc3VfL5orim4dB2L7cTXfZ5Wtru3XxARGMzsum4Rpw7cX9fzW7R/R/bdVEd9nlxUu/S4pK36+\nO1iI6aO3uPHyc+//IUOG8Mwzz/Diiy/Sp0+fav1+3a8ahfXbjHPxXqKA0cKm0qZE5URwNeg+/uxt\ngfD/x93PX6/NwqS2xmF3kXVoBwDFRXays4uIjj3m9/jq0s9nbwuUePz5+bpu3Tqysrw3eShgF4Zc\nccUVdO/evdLCkHvuuYfU1NQqHysLQ0QgsdvtJCcn07lz5wu+dkXdorlc2H74mJJ16biKTmFqcyUR\n141HbdjmovdV8t3rFL7/N7AVV96oGMouXD10ToWbjxw5wqBBg5g3b161LqulaRolG16j5PMXcOUd\nRQmLJqz/SCJv/EuVK6ED3dEjBbyZsRO7vfJRUaPRwIN/7EF8/eD9/URo8MbCkIA9HTxlyhRee+01\n0tPT2bNnD48++ijZ2dmMHTsWgOnTp3PDDTdUeMzu3bvZtm0bp06dorCwkO3bt7Nt2zZ/hB+Ufn90\nR5SpbV5CdcawvF70XUxeFIMBS4/bqPfIB8T/dT3R9/xfjQpAAEuXIW5P12IKI6zPsEo3N23alFde\neYVx48Zx+PDhC8erKERcNYr6//iBBs+doMEz+4m69YkLFoCB/lr5cc9p3QIQyk4T7/3JOwcMAj0v\n/iJ58R2jvwNwJzk5mdOnTzNr1iyOHTtG165d+eSTT2jevDkA2dnZ7Nu3r8JjbrnlFg4ePAiUfVj1\n7NkTRVHqxIV7RWCTFcPC2wxR9Ym85fGyMXb282aDmyOwdEvC2KKX7uMSExOZMGECI0aMYMWKFYSF\nhVXr+bw9KcSXXM6q+iI1nK6APGEmRK0F7Olgb5PTwcIfZMaw8DbbT2sp/vx5HMf3YohtRMR147Fc\nfk+ViyM0TWPkyJHEx8fzwgsv+DDawHBgXy7vvr0Hu03ndLDJQMqorjS6RBbQCf/yxulgKQKF8LFX\nX32V9PR0mTEsfMJ55jDW797AmZOFsVk3wvoMwxBR+fIzBQUF3HDDDUycOJH777/fD5G657IW4Dy6\nG8USidrkMo9PhNI0jaWLd5CdXYjTce5PotFooGXrWJKHV/96ikJ4S53qCRS+J30Y+jydl1CZMSyv\nF32BlJeSTcvIeeYKile/SOnmZRStmEXOUz2wH9hc6b7R0dFkZGTw5JNPsn37do/GUdOcaC4XhR8/\nzemZnclL+wNnXrqFnKe6Y/vFszlWFIXhD1xG9x6NMBoNqEYFs9nA5X0bc3ey9y6mH0ivlUAiefEd\nKQKF8AOZMSy8zZmTReE7fwK79dxkEnsJWmkhea/8Ac1ReVpJhw4dmDt3LiNGjAiIMyXFK5+l5OtX\nyuK2FoCtCFfuUfJeGY4j+yePPpfJpHLjzW2Z8td+THi0N49N7ceAG1rpjqYTIlTI6WAh/ERmDAtv\nKlwxi5I188Bpr7RNsUQRfd98t2PeZsyYwZ49e1i2bBmq6mZUnJdptmJOzejo5pI3KpZedxFz/wLf\nByaEn8jpYCFCyNkVw6mpqaxfv97f4YgQ4zx1QLcABNCcdlxnjrh97BNPPEFpaSlz5sxxex9vcxz/\nGcXdrGLNif1Xec8IUVtSBIpy0oehz5t5CeYZw8H4enEVnsZxdDeukjyvPUeg5MXYtAuY3FzuRTWh\nNmrn/rFGI+np6bzxxhusWrWq1rHUJCdKWDSa0+F+uyX4V+sGymsl0EhefEeKQCH8TGYMe5+r8BR5\nr/yB0092Jfelmzk9szP5r49DKy3yd2heE97vPlD0P+IVkwVTu2uqfHxCQgLp6elMnDiR/fv3eyPE\nKhkbtkWNa6q/0RRO2JUjfBuQECFIegKFT2UVnqHYYaN1dH0sasBeq9wvpk6dysGDB3nrrbf81ocV\nijSngzP/7I8zJwvOP7JktGBseTlxj3zov+C8rPTHNeS/Mgy0313/zhRG5K3/IOLqMRfcR1paGkuX\nLmXlypVERER4KVJ99qxM8ubdUbaIxfXbqW1TOMZLOlJv4kco7o50ChGC5DqBHiRFoG/tPHOMv235\nmGMl+aiKoezitO36MbZDf49f8ytYyYxh7yj94WPy35wAekf9zBHUm/A/TG6maQQ769b3KFj2mP7i\nClM4DZ7ec8HTqpqmMXbsWAwGA/Pnz/f5+9V5+iDFa17G9tNaFEsUYVemEN7vXhSjxadxCOFvsjBE\neJW3+jAOFZ3hwXVvsb8wB6vTQZHDRrHTzuK937Pgx8Bv7vZVf0qwzRgOlr4d249r9AtAAKcN+68b\nPPp8gZQX66Zl+gUgoBiM2H7++oL7UBSF559/nh07drB48eIaxVGbnKj1WxI9dC71/76J+D+vIeKq\nUSFTAAbSayWQSF58R87HCa9b9PP3lLoqN3iXOO289stGRrXrR7jR5IfIAo/MGPY8xRJZ1hv3+1Oi\nAAYjism3pzihrEexeO0CSrf9DzQNS/dbibhuPIaYRp59ImflawGepaG5XT38e5GRkWRkZHDTTTfR\ntWtX+vTp46kIhRB+JKeDhdfd9Nl/OFKsvxozymhmYf9hdItv4uOoApvMGPYc+6Ht5P47CewllTca\nLcQ/vgU19hKvPLfj+M9Yv38DV8EJTK2vJOzyu3BZCzjz3AC04rxzRZpqRgmLIm7KatT45h57/uJ1\n6RR99KT+0UCjhfozt2GIbljt/X366adMnTqVNWvW0LBh9R93MRwnfsGZ/SOG6ASMrfpIu4gQv/HG\n6WA5Eii8Llx1f5TPqWlyFFDH+SuGZcZw7Ziadyfs8qFYty6vWAyZI4i44TGvFYBFnz1H8RcvlC1G\ncTko/WEFRZ/MwtiqN1rRGTj/6LjThlacS+H/Hid29BKPxRDeZxglq1/C5bBVfD5TOGFXPnBRBSDA\nkCFD2Lp1K2PGjGH58uUYjZ77E+IqziV/0QjsWVtANaFoLpTwesQ8uBRTs24eex4hxDnSEyjKeasP\n466W3Qkz6P+xiDOHc2l0A688r6f4qz8l0GcMB1PfTlTy80QnP4/atCtKZH2MrfsSk/IqkYOmePy5\n1q1bh33/Roq/+FfZyLazxZetGK3oDPZdn1UsyM7SXNh2rary2ngXS7FEETf5M8ydB4NqBlMYSngM\nEYOmEHX7rBrtc9q0aaiqyqxZ1X98dV4reWnDsR/YWJYzawFaaRGu3CPkzbsDV1FonrUJpveQL0le\nfEeOBAqvu6d1dz48tIP9BTnlvYEGRcFsUEm9PElO91Rh9uzZJCcnM3PmTFkxXAuKohB2+VDCLh/q\nk+cr/nohOKw6Wy5wKkdzlRWIHrx8kiGmEbEPZqCVFuKyFmCIaohSi/2rqkpaWhoDBgygV69e3Hbb\nbbWO0XFkB44jO3V7FDWnjZLvXidy4KRaP48QoiLpCRQ+UeKws+xAJu/u30ax006fBi14uP2VtI0J\n7KOAgUBmDAefM88PwnEoU3+ju0UqgJpwKfHTv/NiZJ6TmZlJcnIyK1asoH379rXaV8n3b1C4fDrY\n9VcymzoNot7Db9XqOYQIdtITKIJWuNHEyEv7MvLSvv4OJejIimHfsO/7jqLPX8BxdCeGqAZEXDsW\nS+9hKIaL75oxNu2C48gP4NI5jW8wgqKAo7Ti7aZwIpNm1jB63+vZsyczZswgJSWFL774gqiomo9x\nM0TEoRgM+sdJFYPnV00LIQDpCRTn8UYfRp6thMV7v2fy9+/z7A9f8Ev+SY8/h7cFQn9KIM4YDoS8\neErJxv+S+597sP+4Gi3/OM6juyhY/lfyXxt10d+8161bR/i1Y8t68H7PYMLYvDvR985DiWoAlkiw\nRKFExhN1z3NYut7sod/IN1JSUujbty+TJk2qMk8Xeq2YOw0E3LSFGC2EXxmaR8BD6T3kSZIX35Ei\nUHjNzjPHuPGz/zB/zzq+OPYz/923lT+szSD95+A43RVoZMawd2ilhRS+O7XyJWRsxdh+Wov9568u\nep/GSzoQPfzfYAoHc2RZQWiORG10KbGjMwjreQf1n9xF3MQVxE38iPpP7SG8T7KHfiPfmjNnDgcO\nHGDBggU13oditBAz4tWyfJVfTUABcwThiQ9iahmaE12E8DfpCRRe4dRcDFw5j9OllXt8wlQjGVff\nT6d6coqnJmTGsGeVbvuQgv9OQist1N1u7nknsSlpNdq3y1qAbccnuIpyMDbvjqnNlSG5ECorK4vB\ngwezaNEi+vfvX+P9OE/tp/jrhTiyMjHUa0J44hjMl0r7gxAgs4M9SopA7/r2xAEmb3yfIkfliQUG\nReHOFl35R88hFW7fX3Ca/YU5GBUDmacPsSfvBC0i4xjWuqcsIDmPzBj2LOvG/1Kw/K9g0x8tZ+o0\nkHoPL/NxVMFn9erVTJw4kdWrV9O4cWN/hyNEyJHZwcKrPNmHcdJa6PbF6tK0ChNEckqLSfn6de5Z\n8xp/3fQhE757l1f3fs/6E/t5e38mw9Yu4a19Wz0W28UKtP6UQJkxHGh5qSlTm3761+0DMEeUXWPv\nIoRKXi7WwIEDGT16NKNGjcJmq/jlr67m5Pc0TeNQVj4/bDtO1oE8vvnmG7f3dbk09v6cwzdfZbFl\n0zGKi6o34i8UyOvFd2R1sPCKttH13V4RzWRQuaxe2ZQGTdMYs/6/7C84jUPnshlONJwuB8/tXENi\no9Y0j4zzYtTBQ1YMe47aoDXmzoOx7fm87ELFZykGFEskYb2Ds1fPH6ZMmcKWLVuYOXMmzz77rL/D\nqRG73cnen3IoKLDRoEEErdvWw2Co3Sl8TdP4ac9pPl+5j9LSshXjigLHjv9Mp46X06BhxfnV+fml\nvP7aDkqK7dhsLoxGA19+vp8bb25Ltx7SRiM8R04HC6/QNI171rzGLwUncf7uJWYxGLmt+WWUOO3U\nt0Ty9oFtlFxgkL1RMTCqXV8mdb7Wm2EHHZkx7Bmao5TC5dOwbn4HxWhCc9gwNutGzAMLUeNb+Du8\noJKXl8eAAQOYPn06Q4fW/uLcmqZx+FABP2w7jtXqoE3belzWNQGz2fP9sAcP5PHusj2ggdPpQlUV\nwsKM3JvShbj48BrtM+tgHv9790eKivSPNkdEGJnwWB+MxnMn5hYt3MaJE0X8/q+z0WhgxIPdSGgU\nWaNYRHCTnkAPkiLQ+05aC3l4/TKOFOfh0jSMBgN2lxNN09AAh+bCqBh0jwDqSWrWmWd63+rdoIPQ\nq6++Snp6uswY9gBXST7O0wcwRDVArdfE3+EErZ07d3LnnXfywQcf0Llz5xrvR9M0Pv5wLz/tPo3d\nXvY5YTIZMJtVUh7sRr16YZ4KmaIiGwte2lL+PGcpCsTEWBg36fKLXtSTk1PCooXbKu3zfCazgZtu\nbkuXbgkAHM8uYuniH3QfoyjQtXsCt9zW7qLiEKFBegKFV9WmD6PYYeOnvBOctJ5bYdkwLIr3Boxm\nYf9kpnYdwIPtrkAB7JqrvPCrbgEYrproGuefP8qB3p/irxnDgZ6XmjCEx2Bq1q1WBWAo5uVidenS\nhdTUVFJSUsjPz68yJ1arg80bj/LJR7/w7frDFBWe6yf8cffpCgUggN3uorjYzgfLf/JozNszj+v+\ngdU0KCmxc2Bfns6jqrbx26M4ne4/47IO7cBuc5F97NznZu4ZK4qb08+aBidP6k9VCSXyHvId6QkU\ntWJ3OZm740vez/oBVSk70tc1rjGzL0+iSUQsiqLQs34zetZvxl83f4hNb4JCNRgVA7e26OLh6EOH\nzBgWvuDI/gn7z1+DyYKly00YohPc3jc5OZnNmzczfvx4Hn74Yd37HMrK5+03d+HSwGF3oRoV1n11\niNvubEeHTg3Y+N0R3SNimgYnjheTm2v12NHA49lFOBz6R1mcTo3Tp0to3bZehdtPnSxm65Zscs9Y\nuaRxFD0vb0R0tKV8e9bBPFwX+J6rqgpR0ecuLB5bz4Lm0o9DUaB+/ZqdlhZCjxSBolxiYuJFP+bx\nrSv48uherOetrszMOcK9X2Ww4oaHiTSd+0A8VJTrdrEIgAEF13n3MCoGLKqRcNXEzB438swPn/P1\n8V8xYGBw0w483P5KEsKjLzrmi1WTvPja2RXDgwYNokOHDj6ZMRwMefGHYM2L5nJS8k06JV8twFV4\nEjW+BRGDpmDpdTc4beQvGYPtp7VlFZjBQOF704kYNIXIwX9yu89Zs2aRlJTEli1buOaaaypss9ud\nvPPWbmy2c1WS06EBGh++v5dxzWMoLHTfK6yqCkWFdo8VgXFxYaiqgtNZ+VNKVRViYipOgNm88Shr\nvjiI0+lC0+DAvlw2fnuEocM60apNWbEYHl71n9gWzbuCAl26niumG10SSUyshZzTJZV6AlWjgT79\nQr9NIVjfQ8FIikBRY0eL8/ji6M+Vju65NI1ih50PsnZyb9vLy2/vGNuI3bnZlRaKAJgNKlc3asOx\nkgKahsdwRUIrTAaVRuHR1LdEMOKbNylx2MuLxOUHtvPZkR95+/qRXBIufXAgK4ZFzWmaRv5ro8qK\nPFvZ6Ubn8Z8peHsKjqO70WxF2H5aU3H1NFC8+kWMjTu5HXdnNpvLv5z06NGD66+/vnzbzz/l4HLT\n36ShsWPbCRIaRZCfV6p7H4fTRVy853oCe/S6hE3fHwOdr6oGg4G27c5dmSDndAlrvjiIw3FeAevU\ncDo1lr/9I5P+1AeTSaVXn8Yczy5y2xNoNBq48eY2FY4EKorCPcM78/riH7DZnNhsZQtUUOD6gS25\npHHNZzQL8XvSEyjKXWwfxtbThzEa9FfolTjtfHX8lwq33d+2Nyad+xsVAx1jG/Gvfnex7LoRPN/v\nTpJb9+TOlt3on9Caf+5YTZHDVuEooUNzkW+z8tLury8q5poIpv4UX84YDqa8+FIw5sWxf2OFArCc\nrZiSrxdi/e6NSgXg2e3Fnz1X5b6bNm3KxIkTGTduHIcPHy6/PT+3FIeb4sjp0DhzpoQrr2qG0VT5\nz5RqVOjQsT4RESadR9dMvbgwbry5DUajoazooqxIM5tV7hneCVU9F8f2zOO4qjjP+8vPZwDo1LkB\nLVrFYvrd76Ao0LFzfS7rXqR7yZe4uDDGTerNTUmX0rtfYxKvbc7YCZfTu2/oHwWE4HwPBSspAkWN\nhalGdyPfgbLTu9nF52bctomuz+xeSYSpRiKMJlQUDJSNmNubf4JHv3uPEyUFFfZR7LCx9fQR3f07\n0fj8qGebw0OBzBgWF8ua+V7l2cnnq2IBl/PUvgvuv2vXrkyYMIERI0ZgtZYVk/H1wysVR2cZjQYa\nJkTSrHkMNw5p81sxZsBoLPvXrHkMnTo34Ne9Z7DZPLcYqluPRjw8oRdXXtWMLt0act3Alox/tDfN\nmlc825CXV+q218/pdFH42+IWg0Fh6LBO3HzbpbRoGUPDhAh692vM2ImXc+fQjsTEuj+SaTQauKxL\nQwbd2Ib+ic2JibW4va8QNSWXiBE1Vuywce2nL2N1c40/k0HFgELjiBhm9riRPg3KrrdWZC9l+YHt\nPLdrbYWje1BWOC4fMIpLYxoCkG+zcu2n/3a7itioGMi8faoHf6vQITOGRXUVLJuM9bul+htVM2hO\ncLOoyxDfgrjHVla5SATKTjmPHDmS+Ph4XnjhBZxOFy+/sJni4sqfH6pRYdzE3kT/dpq0tNTBL3vP\nYCt1knvGypZNxzAYFDTA5dRIvLY5V17V7KJ+59r4/tsjfL02S/dIpsls4J5hnWjZup7OI4WoOblE\njAgoEUYzf+t2A2Gqfmup3eWk1OXgQGEO4799h51njgEQabLwftaOSgUggAuNCd++W/5ztMlCk4hY\ntzH0rN+0lr9F6Jo9ezZ2u52ZM2f6OxThJZrTTumOTyheM4/SHz5G05nVXR3mywaD2c0FiA0qxksT\nQdU/9erKPcbpp3pw5oVBOI7tcfsciqLw8ssvs2HDBl5//XVU1cC9KZcREWHCZKp4TkFBIW3BVg4f\nKjuSbbEYuaxLQywWlc2bjmG3uygtdWIrdeJwuFj/9SF2bD9eo9+9Jrr1SNCdIqIoEBVlpkUr959Z\nQgQSKQJFuZr0YdzZshsLrkzmioYtiTOFY1T0X1JWp4MXd39V/vMvBafc7vNoST7Fv/0xUxSFqV0G\n6BaaYaqRR30wQSRY+1O8PWM4WPPibb7Ki+PITk4/0YX8N8ZTtGIW+W8+wuknumA/tP2i92XuPBi1\nfsuyo37nM4Vh7nAdsSlpZZNTLGcLxfMKIJcdHDYcWdvIfelmnDmHKuxCc9r55uuy3t3o6GgyMjJ4\n8skn2b59Ow0TIhn/6OUV+u0AHA4XpVYny97YjdV67soDX6/RP/pmt7v4eu2hSrd7S3i4ieH3X0ZE\nhBGzWcVkMmAyGYivH869D3Sp9kWl5T2kT/LiO1IEilrr3aA5aVf9gQ8HPVRlj+DW02VN4VU1VJ9V\nfN4RjesaX8rsXkk0CosmTDViMRhpERnHy1cMpXu8HAmsytkVw6mpqaxfv97f4QgP0exWcuffiVZ0\nGkoLwWmH0kK04hzyFtyF9vsFHhegGFTqTfwYS887wGgBUziYIwjrP4qYEekYIuOJ++s6ooe9WHbJ\nGN0FYRqa3UrxmpcBsP26gTPPD+LU1Kbk/educhcOw3F8Lx06dGDu3LmMGDGCnJwcDuzLddtf59I0\ndv5wouy/XRpnzugsTvlNQX5phdW63takaTQTp/Tljrs7cMONrfnDfZfx0Lie0rsngor0BAqPKbKX\nkvjJS2779yKMZr5PmgxArw/mYndzPwMKmbf9GYOh4ncUTdM4WpyPqig0Co++6BFOdZnMGA4t1i3v\nUPDOn6G0qPJGcyTRdz9LWN/hNdq3ZivGVZyHISoexVi5oLFnbSVvwd1o1gKdR4MhvjnRf3iRvLT7\nfrfYREEJiyJuymrUhm2YMWMGe/bs4bFJz7H+68NuC8FuPcrGpGmaxv89853bQk9VFab+7Ur5XBAh\nS3oCRUCLNFnoGtdYd5uqKNzYpEP5z/e37e12P0nNL6tUAEJZ4d40MpZLImLkg/4iyYrh0OLI3qtf\nAALYinBk/1jjfSvmCNR6jXULQADFGIZWxdF8xRhG4bt/1VltrKGVFlG08p8APPHEE5SWlvLe+69i\nNOr/KVKNCnFxZStoFUWhS7eGur14BoNC5y4N5XNBiIskRaAo54k+jMe730ik0YzhvA9jo2Ig1hTO\nhE5Xl982pcv1DD6vKDyrf8NWpF5+S61i2J2bzUeHdrHx5EG3F6O9GKHSn+LpGcOhkhdP80ReNFsJ\n1k3LKHj3LxR99hzOM4crbFfjmoA5Qv/BpnDUuOa1jsEdtXEnDO4u0G4Kw9z9dpw5Byvc/H32b+9D\nzYVt1yoAjEYj6enpfPb5++z9daPu7hQUuvY4t+r4uoGtiK1nqXDtQJPJQHSMmQGDWtX8l/ITeQ/p\nk7z4jkwMER7VPrYhy64bwX9+Ws832ftQFQM3Nu3IQx2upGFYxSvdP9f3Ds6UFrP84HacLo27W3Wj\nQVjNr4Z/0lrI+G/f4WDhGRTKjhxEGM28fMXddK53SS1/s9AgM4YDn+PEXnL/fSuavaTsaJ9qpvjz\nF4i87R9EXD0GAEvPOyn8wP2qb0uvu70Wn6IoRA//N3npD/x2AenfCjyjBbVeU8L6DqNkzUvV2ldC\nQgLp6ence+/9/OHuf1KvXmMcjrIJGYqikHT7pRVm8YaHGxn9cA92bD/Brp0nQYPOXRrQrUcjzGa5\nDJIQF0t6AkVI0DSNO79M50BhTqWxdFFGC6sGjyXG7LkRU8EsNzeXQYMGMXHiRJ/MGBbVp2kaOal9\ncOUcpNLgWFM4cY9+grFpVwBse1aT99qosgs5261lCzoUAzEjXsVy2Y1ej9WelUnxqjnY929EMYVj\n6TuciIGTMIRFk/Nsf5zHf678IMWApdddxNz/nwo3p6WlsWRJBqlPLyY/z0VcXBjdezYiOkYWWQhx\nljd6Ai9YBK5bt47//e9/xMfH88ADD9C8+bnTDDk5OQwdOpQvv/zSo0H5ghSBoWXzqUNM+PYdinUu\nXB2mGpnU6RoeuLSPHyILTHv37iUpKYlFixbJjOEAYj+wmdwFd4NNp99PUbH0HUbMH84dZXMVnKTk\n+xf1d0cAACAASURBVDdxHv8RNaE94f3uxRBTeQyZr9n2fkNe2r0V+wIVBcUSRdyfvkRt0LrC/TVN\nY+zYsRgMBubPny+9fb+xWh38sO04P+05jdFooGuPBDp1blDpkjqibvD5wpCPPvqI6667jm+++Yal\nS5fSpUsXVqxYUb7dZrOxdu1ajwYk/CeY+zB+yjvhdlWy1enghzNHa7zvYM6LO56YMRyKefGE2uTF\neeZQ2RWH9WhOnCd+rXCTIbohkTc8Ssx9C4gcNDkgCkAAc7urif3j2xhbXg6KwvfHFcydbqDe5M8q\nFYBQ9qX8+eefZ8eOHSxevNgPEftHVa+V/PxS0uZv5as1WRw+VMCB/Xms/PhXli7egd3uvqc3N9fK\nkcMFupNYgoV8tvhOlT2BqampzJw5s3ziwLx580hOTmbp0qXcddddPglQ1C15thL2F5ymniWCVlHx\n1X5cfUsERkXFRuUPR1VRSAiL9mSYIeH8FcOrVq0iJsZNs7/wGbVBG/dzeg1GjE06+zagWjC3vRLz\nY6vQXE5i160n9pprqrx/ZGQkGRkZ3HTTTXTt2pU+fer2kftPP/6FoiJ7ha4Au93FyRNFbPz2KFdd\nU3HxT+4ZK/9b/hMnTxSjqgoOh4uOneoz5NZLMZmkX1Loq/J0cExMDNu2baNNmzblty1fvpyUlBSW\nLFlCYmIiTZo0qdbFfwONnA4OLDang6e2f8anh3djNqg4NBctIuOY2+c22kQ3uODjSxx2rvv037qn\ngy0GI29fP6Ja+6mLZMZw4NA0jTNzr8GZ/XPZvN7zmcKJ+9OXGBu1809wPvLpp58ydepU1qxZQ8OG\nDf0djl9YrQ5eem4jTqf+n+eoaDMTJ58rkm02Jwv+vYWS4opFo9Go0KJVLMPuvczbIQsf8Pnp4LCw\nsEqF0t13382SJUtISUnhnXfe8Wgwou6avuVjVh7eg83lpNBhw+p0sDf/JA98/Qa5tt9fb6yycKOJ\n5/reQZhqxPTb6DqDohCmGhnfMVEKwCrIjOHAoSgKsQ/9F0NcUxRLFCiGskvBmMKI/sOLIV8AAgwZ\nMoThw4czZswYHA7HhR8QgkpLnbrXQyzfbq2Yl50/nMBuc1ZaS+RwaGQdyOf0qYubICPqjiqLwB49\neugu+hg6dCivvfYaU6ZM8WoD7/z582ndujXh4eH07t37gn0CO3bs4NprryUiIoJmzZrx9NNPey22\nUOSvPoyjxXmszf6FUlfFDzYNKHU6eHf/tmrtJ7FRG/43YAz3te1N3wYtuKNFVzKuvp/R7fvVKr5Q\n70+p6YzhUM9LTdU2L2pcU+L/vonolDQihkwj6vanqf/EDsJ6BW8LzsXmZNq0aaiqyqxZs7wUUWBw\nl5eoKFOVRWBCo8gKP+/7NRe7zkxlKGsxPZQVXBeIl88W36myJ3Ds2LF8/dvg799LTk7G5XKxcOFC\nrwS2bNkyHnvsMRYsWEBiYiLz5s1jyJAh7N69u8IK5bPy8/MZNGgQ1113HZs3b2bPnj2MGjWKyMhI\npkyZ4pUYhWf8kHMUk0HF5qrcz1fqcrD+5H7GdLiyWvtqGhnLn7pc7+kQQ97ZGcNJSUm0bdtWVgz7\nmWJQsXQehKXzIH+H4heqqpKWlsaAAQPo1asXt912m79D8ilVNdCvf1O+XXe4UnFnNBm4+toWFW6z\nhLlv41AUMFukzUPoC9jrBPbr148ePXpUKDLbt2/P0KFDmT17dqX7L1iwgOnTp3P8+HEslrJrS6Wm\nprJgwQIOHz5c6f7SExg4vs7+lb9s/pAih013+4DG7XixX/AeBQkmMmNYBJLMzEySk5NZsWIF7du3\n93c4PqVpGl98tp/MzdmoRgNoZbfdcGNrevSqePH7rAN5vP3Wbt2jgUajgUf/3Fcuph0CfN4TePLk\nSZ5++mny8vIqbcvLy+Opp57ixIkTHg0Iyi49s3XrVgYPHlzh9sGDB7Nhwwbdx3z77bdcffXV5QXg\n2fsfPXqUgwcP6j5GBIYrGrbE3YmPcNXE3S27+zSeukxmDItA0rNnT2bMmEFKSgqFhYX+DsenFEVh\n0I1teGRyH269vR23392eR//ct1IBCNC8ZQztO9bHZKr4J91oMnDTLW2kABRuVVkEvvjii/z444/E\nxsZW2hYbG8vevXv55z//6fGgTp06hdPppFGjite8SkhIIDs7W/cx2dnZle5/9md3jxEV+asPw6wa\nmdXrFv6fvTuPi6pe/wD+OXPODDsICCjiggtuoOK+kCWgpaHpzYtRiRt1DdPSsrKfS97U27UyW9SS\ncEEt65Yt5oIb5pbmLi7kLoLggrLDbOf8/iBHkTMIOHPOmZnn/Xr1unc4M2eeefwCX855vt/HmeWg\num866MKq0cc/GBEBzat5tfU5Wn1KTXsMO1peaoryUtWj5CQ+Ph7du3fHpEmTLH4V5FEYDDyuZRfh\nxvWSOsdVk7y4uqoR0sYXLVv5mN3qhWEYDB7aCoMGt0RgI3d4ejqhZYg3nh8ZirCOytg7sjboe0g6\n1dYE/vrrr/j000/NHh83bhwmTpxo8aDqoi4LVBITE9GkSUVthZeXF8LCwhAREQHg3iB0pMfp6emy\nvb/TxRuYrA7BkQAeJ/NzIJzNRnRga7zRfShUDKOI/DjS46effhqzZ8829RhW2nihx7b1OD09/ZFe\nP3ToULz99ttYsmQJEhMTZf08giBg6Vc/4+SJG2jWtCMEXkBO7in07BOEf8Y+Vavz3WXJ+NqF+v39\nuByNgtpJnh9LPH7U8WIvj+/+/8zMTFhLtTWB7u7uOHPmjOhCDAC4cuUK2rdvb/HL9DqdDm5ubli7\ndi2effZeI/QJEybg9OnTSEtLq/KaUaNGIS8vD7/99pvpawcPHkSPHj1w6dIlNG3atNLzqSbQMdzW\nluJoXhbUKhbd/ZrAmVXLHZLNoB7DREkyMzMxYMAALFu2DL1795Ytjj/3Z2NXWqbogo0XR4WhYaC7\nTJEReyd5TaBarcbVq1fNHs/KygLHVXsxsU40Gg26dOmCLVu2VPr61q1bzX7z9+rVC7t374ZWq630\n/EaNGlWZABL7xwsC5h3fiv6pi/F/RzbgrUO/4vGNn+OnKyfkDs1m3F0xPHfuXOzdu1fucIiDa9Kk\nCRYtWoSEhATk5OTIEgPPC9iz66roAgyDnsee3613xYYQa6h2EhgeHo5169aZPb5u3TqEh4dbPCgA\nmDJlClasWIHk5GScOXMGr732GnJzczF+/HgAwLRp0xAdHW16/vPPPw9XV1eMHj0ap06dwrp16/Df\n//6Xtod5QLFei4M3M3HyTg74B/6iePAWhS37MmMvfso8AR1vRIlBhxKDDqVGPead2Ir9Ny/X6lz2\nlJfaqq7HsCPnpTqUF0DQlaL8z7Uo3jAHZftWYtf2VIucNyoqCmPHjsWYMWOg04nvJmBN+fnl4M10\n8QCArKu1W0xFY0Uc5UU61V7Ge/XVVxEbG4ugoCBMnDjR1FJKr9fjiy++wKeffoq1a9daJbDY2Fjk\n5eVhzpw5yMnJQVhYGDZu3Gi6NZ2bm4uLFy+anu/p6YmtW7diwoQJ6Nq1K3x8fPDmm29i8uTJVonP\n1vCCgE9O7cS3F49ArWLBCzxcOQ3mdnkavf2rNnRXMl4QcKX4NlQMgyZu3lXqQfW8ESkXDqLcaKjy\n2nKjAUsy9qKnXzOJorV91GOY1IY+8ygKvhwOwWgAdCWAxhWF1wzQBX0LTevHH/n8U6ZMweHDhzFz\n5kx88MEHFoi45jQaFjxvfhJIPXqJrXnoPoH/93//h//85z9wc3NDy5YtIQgCLly4gJKSErz11luS\nfxNaiqPVBH5+ehdWXTiIsgcmRs4sh9V9R6K1l79MkdVOanYGPjixDSUGHQQIqKdxwYyOT6Jvgxam\n51wtycezO5ahTKSPMAC4cRrsj6E/DmqLegyThxEMWuTNCoVQeqfqQY0rfGceg8rN55Hfp6CgAJGR\nkZg2bRqGDx/+yOerCb3eiPNn72D71ksoKqx6FZJlGfTs3Qh9+1H5EbEOyWsCgYoNlw8cOIBx48Yh\nMDAQDRs2xLhx47B//36bnQA6mnKjHqsuHKoyAQQAndGIpX+J772oNL/nnsf0IxtwS1uCMqMe5UYD\ncsuK8MbBn3Hw1r1aHE+1EwyCeAuliuPOUoRrd6jHMHkYbfomwMwfXxAElB/8ziLv4+XlhZUrV2La\ntGk4ffq0Rc5ZnYvn7+Czjw9i4/rzKCmpOgHkOAb1vJ3Ro3cjq8dCiCVVOwksLS3FhAkTMHToUKxe\nvRqenp5ISUnBwoUL0b17d6liJI/oclHFrVMxPAQcycsCoPw6jA/T08ze4l146nfTYy+NC7r4Bol+\nZicVh9hmnWr1vkrPi1Tu7zG8atUqyosZjpwXPu8yBF1Zla8fyBUAfRmM189a7L1CQ0Mxd+5cxMfH\nW3Vj84ICLdb9LwM6nRE6nRH3d7dUqRj41nfBY080xeiEjnByqt1CSUceK9WhvEin2kngrFmzsGLF\nCsTExOD555/H1q1b8corr0gVG7EQd7UTDLz5K2Puaiezx6R0R1uKfTcu4cTta1UWrZQadMgSu8X0\nt5N3cipdJv93+CB4a1zgzN77oezCqtGmnj9Gtuxm+eAdxN0Vw3PmzMHJkyflDocojMq3KRiNi/hB\ntTPYAMu2fouNjUVkZCQSExPBV/Mz7lEcOZhjtg6QZRkMHhqCnr0bUVcOYpOqrQls0aIF5syZg7i4\nOADAn3/+id69e0Or1dp8TZCj1QT+Y8cynCu8WeXrzioOk9r1lXVipOeNmHt8C9ZfPQWNigMPAW6s\nGv/tOgTd/Co289YZDej+2ycwmrnN66RicWjIm5W+Vqgrx0+ZJ7Dj2jk4sRyGNQ1DdGBrqFW2PXaV\ngHoMEzGCQYu8me0hlOVXPWjBmsD76XQ6xMTEYODAgVZZCPjNqpO4cqlq61QAUGtUeHJQC4R1sI2a\namLbJK8JvHr1Kvr27Wt63L17d6jValy7ds2iQRDr+0+XGLhxGqiZe//kziyHVp5+iA22zjY/NfWf\nE9uwIes0dLwRxQYtSg063NSWIHH/D7hcXDFR17Cc2R7DLBj0b9S6ytc9Nc4Y1bI7VvZ9AUv7jMDA\noHY0AbQQ6jFMxDCcE7zGfw/G2RPQuFZ8Ue0CaFzhNWalxSeAQMW+ssuXL0dSUpJoI4FHVa+eE8w1\npGIAeHhoLP6ehEil2kmgwWCAWl25wwLHcdDrzRT+EsVq7eWPnyPH4bnmnRHs7ov29Rrg7bAorHjs\neTj9fctUjjqMAl05fs1MF6310/MGLD93wPT43Q794a52AnffRFbNqOCpccFr7R596wlzqD5FXJs2\nbRAR8fAew45G6eOFL7mDko3zkPd+Z+TN7oCiH6bCeCfLYudXN+kM3/fS4fGPD+AS+Srcn5mNMwOS\noGnTz2Lv8aBGjRph6dKleOWVV5CVZbnPAgBdujUEy4r/qlRrWDRt5lXncyt9rMiF8iKdh1axjhw5\nEhqNBgzDQBAElJeX4+WXX4aLS0XdB8Mw+PXXX60eKHl0DVw98VZYFN4KkzuSe84W3oBaxUHLV51E\nGAUBh27d61jTxN0bP/Ybi6/P/oEdOefAMAyeatQGY1v1QH1natUkh3nz5iE2NtbUY5goG198C3c+\njgRfnAcYKrorlf+xGtrDP6Le66ngAlpZ5H0YJzc493je9FglwS/1iIgITJgwAaNGjcKGDRvg7GyZ\nXQACGrij7xNNsGtnJnieB88DHKcCyzKIjWtXp771hChFtTWBo0ePNk3+zJ6AYbB8+XKrBGdNjlYT\nqFR/FdzAyF2rze7pF+bdEN88Tn1rlexuj+FJkyZh5MiRcodDqlH0w9so358iso0LA3WL3qj36i+y\nxGUpgiBg9OjR8PHxwSeffGLRc+fdKsWxI9dRWKhFoyAPhHUMgIuL5dumEmKONWoCH7pZtL2iSaAy\nCIKAQVuXIqu0aiG5C6vGjI4DMLhJqAyRkdo4d+4cYmJisGzZMvTp00fucIgZt95tDqHMTA0nq4bv\nnLNQOXtIG5SFFRUVITo6GhMnTsSLL74odziEWIwsm0UTxyFHHQbDMJjfbTBcWXWlRSsurBqdfYMw\nMKid5DE9iOpTxN2fl+p6DDsaJY8XQa81f5BRAfqqe/xZgpQ58fDwQEpKCmbPno3jx49L9r51oeSx\nIifKi3RoEkhkF+YdiJ+iKhattPL0QxffxpjV6Sl80XM4OBUNUVtBK4aVT920q9ljKjdfMO5+EkZj\nPa1bt8aHH36IUaNG0R0fQqpBt4MJIRZFPYaVS3/pT+QvebbqFT+1C9xjF8Cl6z/lCcxKZsyYgTNn\nzuC7775TzFjkeQGFhVpo1Cxc3dQPfwEhf6OaQAuiSSAh1qHX6xEbG4t27drRimEF0p7ZhuLvpoAv\nywcYBoxKDbfBM+HSy/4WYBkMBgwbNgy9e/fGtGnTZI1FEAQcOZSL3TszoTfwEHgB/g3c8PTglvDz\nd5M1NmIbqCaQWBXVYYijvIgzl5cHeww7GqWPF6e20fCZdRzeU7bBe9JG+L6fYfUJoFw54TgOycnJ\nWLNmDX79dQP278vGzz/+hZ3bL+POnXJJYzl04BrStl1GWZkBBj0Po1HAgf1/IGV5OgrypY1F6ZT+\nPWRPaH07IcTi7vYYjomJQfPmzWnFsMIwDAPOwn18jXeyUbZrKfQX9kLl5gvnPmOgaf+k7Pvo+fv7\n44N5n2N84ljEP/8xPNwDoFIxOHggB/2fCkanzg2sHoPBwGPX71eh11dte2nQG7F/XzaeHNTC6nEQ\n8iC6HUwIsRrqMewY9JcPVdQaGvWAUVfxRY0rnNo/CY+RS2WdCBqNPD79+E/8sf8XnDi5BS+MmA+1\numIjaY5TIWF8J3j7uFg1hpxrxfgm5SR0OvHOOp5eTpjwmvlFO4QAdDuYEGJjaMWw/RMEAYUrxgK6\nknsTQADQlUJ7KhW6k5tqf07eCO2pVJRs+Rhlf6SALyuoc3znz92BwAPhHZ9G/fpNsWXHYtMvUp4X\ncOzI9Tqfu6Y4rvqmCyxLXUeIPGgSSEzkrMPQGg0oqW4PMxlRfYq4muYlISHBoXoMO9p4MWQegVBu\nZoKvK0XZ71/VKifG21dxe04XFK36F0o3/xfFP09H3qxQlB9fX6PXC39PPrXHfoGxIBdFhTrwvACG\nYTAgagJu3LyEYycqJqY8LyBfgtrA+n6ucBbpLpJ5NR0cp0KHTv5Wj8GWONr3kJxoEkhkdakoDy/v\n/Q491i9A7w2fInLTImzJzpA7LGJh8+bNg16vx8yZM+UOhVgYX3K7YqNpM/QX9qLkt/fBF9966LkE\nQUDBV7Hg869B0BYDAg/oSgF9GYrWJMJ482K1ry/7cy1uzWiDolXjUbj2Ndye0wWuJ1fg7najGrUz\nhsZMw7793+BaTgY4jkFAQ+uvzGUYBoMGtwTHVc6TigU8PDXo0q2h1WMgRAzVBBLJ6Hkjtl77C7ty\nL6DUoMOV4ju4WJwn+ty44HC823GAxBESa6Iew/bJWJCD23O6AoZqruSzarA+TeD99h4wrPm98Uy1\nhboS0XM49xkLj2Hi2w7pzu9BwdK4KnsgCmpX/M9nGYr0Lrj72+78hQPYlvYlxsZ/iqnToiXbry/n\nWhF277yKrKuF4DgVwjr6o1dEEJydaY2mUun1RhgMApydWdkXOVmjJpBGHpFEnrYEI39fjTxtCUqr\nNK+v6ttLRxEd2Brd/ZpKEB2RAq0Ytk+sV0NoQp+C7lQqoDdza9Woh7HwOnQnN8Op42Cz5zLevAiG\nAUR/zRn1MF47bfa1pakfiba9Y/SlGJj/NjY3/BJlZUYYjTzate2FG7fOYd/BL6Bx6v+QT2g5DQM9\nEPu8/K0wycPdvl2G1I0XkHm5otTBw0ODJ6Kaol2ofXTVuYtuBxMTa9ZhzDyyCTllhTWaAN618PTv\nVounNqg+RVxd8uIIPYbtfbwIvBECX7m20zPuC2jaDai4vyniQK4AaIuh+yut2nOrfIKqOciCDWhp\n9rDh2kmzxzxxCy8954V//LMN+kU3w9NDWuGHdZ/Bzc0Jc+bMqTYma7L3sVJXcuelqFCLlV8fx5VL\nBeB5ATwvoKBAiw3rz+P4UesvJJISTQKJ1RXoyrD/5mUYhKp7ZFXnUpH4rWJi22jFsG0yZKcjf/Ew\n3HqzIW692RD5XzwD/dXjAABG4wKv0cvg+uTbgLnbvYwKjFP19Xfq4J5gXH0AiNx2YzVw6TPO7GsZ\nl3pmjwlGA1g3HwS3qIduPQLRpl19ODmpkZSUhJ9++gm//vprtXERx7J/XzZ0Oh4P3nk16Hns2HYZ\nPG8/VXQ0CSQmERERVjlvnrYUnJkrBNXx0lh3766aslZebN2j5MWeVwzb43gxZKfjzmdPQ39ud8Vi\nDYGH/sJe5H8x2DQRBADnHnGii0R6NGAAzglOnYdX+z6MSgWvl9eCcfMGNH9PGDkNwDnBfehccA3b\nmH2tS8Q4QC3yM4NhoW7WFSr3+lUO+fr6YsWKFXjjjTdw9uzZamOzhgfHik5nxNXMQlzPLbZ47Zct\nkft76Oxft81O9HijgJs3SiWOyHpoYQixulKDDn03fg4tb6jxa9QMi5jG7eHCqeHCcniqUVu0qRdg\nxSiJ1KjHsG0wFuTgzoL+EApzRY+rW/RBvVd/MT0u2bIApds/AXT31edpXOEUPhSez31Wo/cUdKXQ\nHvsF+syjUHk1gHPXEWC9G1X/GoMOBV/FQp959N7CErULGCd3eE/eAtansdnXpqSkYPHixdi2bRvc\n3d1rFKMlCYKAnTuu4NCBHKhYBgIvwNmFw+ChIWjazEvyeBzd4s8OoSBffKGTWq3CqHEd4efvKnFU\ntFk0sTJr1WG4choMaRIKJ1XN1iE5qViwKgabs07jm4uHsfzcnxi5ezVmHNkoy1/HctenKNWj5sVe\newzb03gxFuTgzkf9zE4AAUB/8Q8Ixnt/4LkNmALP+GRwzbqBcfMFG9ge6a1fhseIT2v8vozGFc7d\n4+AxfD7c+k956AQQABhOA6/xP8Dz+S+gadsf6hZ94DZoGnze3V/tBBAA4uPj0b17d0yaNEnSnzF3\nx8qunZk4/GcODAYeOq0Rej2PokId/vftady6aT9XnWpK7u+h9qF+ZjfwdnJiUd9PGXepLIFWBxNJ\nvB0WhRtlRdh/8woAAQIAHW8EA0AFBg1dPeGhdoa3xgUlBh1O5eeaagh5CCg3GpCanYEuvo0xtGmY\nnB+FWBCtGFa20tSPIJTm1/p1Tu0HwKn9vS2eNHv2SLK9BsNycOo4uNoVyObMnz8fgwYNwpIlS5CY\nmGiF6MTp9UYc3H9NvK+wgcfe3VfxzD9aP9J7FBZqcfzoddy+VYb6/q7oGB4Ad3fNI53TnnXrGYgT\nx2+gtEQH/r5/Fo5T4amnW8q+VYwl0e1gIqnzhTdx8NZVOLMc+ga0gFrFQq1i4cJVFJMX67V4fNPn\n0PHidWItPHzxc1RCjd/vVnkJrpUWoIGLB/xdPCzyGYjlUY9hZbr1bksIZdVPAtUteqPeq/axsCIz\nMxMDBgzAsmXL0Lt3b0neMzenGGtWmu8r7OGhwauTu9X5/BlnbmH9T+cgCAKMRgEsy4BRMfjH8DZo\n0cq7zue1dyUlOvy+IxOnT92E0SCgYaA7nohsiiYy3p6nfQKJzWvp6YeWnub3WcrTloBjVNBB/Afi\n9bLiGr1Pga4c049swL4bl6BRcdDxBnTxbYz/dI2B70NWKBLp3b9iODU1FZ6ennKHRACAf8iWTmpn\nuD3zb2likUCTJk2waNEiJCQkYPv27WjY0PqdPDROLPhqfrFrnCovqisrM+DEseu4fKkArm4cwsMb\noFFjD9GrU6Uleqz/6RwMhnuXs4xGATAK+OmHDEyc0g1OTjQNEOPmpsGgwS0xaLD5bYnsAdUEEhO5\n6zAAwM/ZHcZqfiAGuVX+K2z/zcuI27kSnX6Zj+7rF+C9o5txq7wYCXvXYu+Ni9DxRhQbtNDxRhy8\nlYlRu9bAwNduqxol5EWJLJ0Xe1kxbE/jRd3qccDcrS/OCV6vroe6caeHnseWchIVFYWxY8dizJgx\n0Ol0Vn2vPXv2wMfHBV5eTqLHOU6F8C4NTI9v3SzFl58fwq60TFw8fwcnj9/E2jWnkLrxougVopPp\nN2Bm620AwJlTD2/lZ44gCLhyKR9HDuXg3F+3YTTW7udqdWxpvNg6mgQSRXHlNBgY1FZ0EQnHqPBi\ni66mx1uyMzBx/484mZ8LoyCgzKjHL5np+MeOZbhSlAf9A5M9g8DjprYEu65fsPrnIHVDPYaVxW3Q\nNPFtV9TO8HjxS2iahEsflASmTJkCb29vycbh4KEh0GhYU49jAODUKvj5u5omgYIg4MfvM1Bebqx0\nZU+v53HyxA1cOH+nynkL8rUwGMQngXo9j6Kiuk1y8++U48svjuCH785g+5bL+PWns/h8wUFkZxXV\n6XxEPlQTSBSnzKDHC7tW4VzhzUpfVwFo7OaN7/uNhhPLod+mRbijq7pyjmWYaq8mvti8C97uEG3p\nsImFUI9hZdFfOYKiH96EMScDYBioPPzg9sz7cK7D4gtbUlBQgMjISEybNg3Dh1e/v6El5OeX48C+\nbFy6mA+NhkWnzgHo0CkAHFcxM7xxvQQpy06ILiABgODm9fDci+0rfe340evYuvmi6Gs0GhUGDm6J\ndu2rb4PG8wIuXcxH3q0yeHpq0KKVN5IWH0VhobbKZsoaDYsJr3elXshWQjWBxCE4sRxul1dtIM8D\nyC0rwveXjqKnXzNozdQrVTcB5BgV3NXit16IMtCKYWVRN+0Mnzd2gC+5DcGgg8ozwK5WR5rj5eWF\nlStXYtiwYWjXrh3atbNuz9969Zzx5KAWZo8XF+mgUpnPu9hVvbbt62P71kuAyI9KjlMhpLVvtTHd\nzivDN6tOQltuMC0qEYSKq5JiP2Z5XkD68Rvo1iOw2vMS5aDbwcREKXUYZwtuoMxMj2Etb8DP53Im\n0gAAIABJREFUmekwQgAj1lrqIVhGhUFBtfthrpS8KI0182LLPYbtdbyo3HzAejWo0wTQVnMSGhqK\nuXPnIj4+3iotDmuTl/r+rjCYqbtjGKBhYNVNrjUaFs+PDIWLKweNhgXLMtBoWLi5q/F8fKjpKqMY\nnhfwzaqTKCrUQafjYTQK0Ol46PW82VvMBgOPnGs1W7xXHVsdL7aIrgQSxdHxxmp/0WiNRoR4+kFl\n5jlqlQodvANxOv96pcmkC6vGc807I9ij+r9+iTLQimGiBLGxsTh06BASExORkpIClUqeayeenk4I\nbl4Ply7kV6zwvQ/LqtCjl/iG2g0aumPi5G64cP4OCvK18PZ2RvOW3tVeVQSASxfyoS2veZenijgY\neNWjOy22hGoCieJojQb03fgZSkWuBnKMCiOCw/FOh2j8cPk4/pu+DeX3dStQgYGH2gk/R43D2cKb\nWHb2AC4X30aQWz2MadUdjzew7+X+9mjq1Km4cuUKvv32W7Bs7XtQE/KodDodYmJiMHDgQEyePFm2\nOLRaA378PgPZV4vAMBW/xwQIGDIs5KG3dmvrzz+ysXPHlSoTzupwnAovJYajXj1ni8ZCKlijJpAm\ngUSRlp89gMV/7ak0wWMAuHFO+ClyLBq4VlwV2pR1GgtP/Y4b5RW3IHr5N8O7HfojyK2eHGETK6Ae\nw0QJsrOz0b9/fyxatAj9+vWTNZabN0pxLbsIzi4cmreoB7Xa8n8cnTl1CxvXn4NOV/UW9N2LoSqV\nCgYDD5Wq4v/3fyoYnTo3qPJ8Yhk0CbQgmgRWtWfPHkRERMgdBoCKwuNvLh7Gkoy90PFGGAQebb0C\n8O/wgWjhWb/Kc4sNOmhULJxYy1c4KCkvSiJlXmxpxTCNl6rsJSd79uxBQkICtm3bhqCgIIucT6l5\nMRh4fPbxn9Bqq+7ZyXEqvDg6FBfO38H1nBJ4+zijU5cG8PGxTE9dJedFTrQ6mDiEW+UlOJJ3FUFu\n9bCp/3gU6Mvgymng4+Qq+nyGqbgFTOwXrRhWBmNBDgyXD4HRuELdKgIM51jfdxEREZgwYQJGjRqF\nDRs2wNnZfm97cpwKw59ri++/OQ1BqJgUsiwDhmHw1NMt0DDQAw0DqRWnraMrgUQxjAKP/5zYhp+u\nnIBaxYJBxXYv73SIxj+adpA7PKIA1GNYHoJRj6Lvp0B7ZB3AaSrW5QsC3EcshHP4ULnDk5QgCBg9\nejR8fHzwySefyB2O1ZWW6nHi2HXcyC2Fl7cTOoUHwItq/mRBt4MtiCaByvP56V1IuXCwUh0gADiz\nHD7v+Sx6+jWTJzCiKF9//TWSk5NpxbCEitZNQ/n+1YC+rPIBtQvqTfgZ6qZd5AlMJkVFRYiOjsbE\niRPx4osvSva+xUU6ZGcXQaNm0aSZJ1iWdnlzJNaYBNIIIiZy7s2kMxqw+uLhKhNAACg3GrAkY68M\nUVWgPavEyZUXpfcYtrfxwpcXoXz/qqoTQADQl6N0y8cPPYe95cTDwwMpKSmYPXs2jh8/Xufz1DQv\nRiOPDb+cw+LPDuG3X85h3Q8Z+PSjP3E2I6/O761kjzJerucW4/DBHJw4fgNlZbXb4sYR0SSQKML1\n8qJq/8I5W3BDwmiI0lGPYekYb10Cw6rNHBWgz6r7JMiWtW7dGh9++CFGjRpl9btK27dexulTtyo2\nbNYaodMaodUa8ctPZy2yObM90OmMWJOSjpRl6dix9TK2bLqALz45iGNHcuUOTdFoEkhM5FyN5al2\nhlEQ3w3/7nG50Co1cXLmRa1WY/ny5diyZQtWrVolWxxi7G28qNx8IBiqtiQzHXf1fug5LJ0TQVeG\nsv2rkf/5YNz5dBBKdyWBLy+y6HvUxNChQzF48GC8/PLLdboqXZO8aLUGHD9yHQZD1Z+PBj2Pfbuv\n1vp9la4u42XDr+eQnVUEg4GHwcBDr6v4322pl5CVafluL/ZCkZNArVaLiRMnws/PD+7u7njmmWeQ\nnZ1d7WtOnTqF4cOHo0WLFlCpVJg9e7ZE0RJL8NK4oItvY7AiXUCcVRyea95ZhqiIkt1dMTxnzhzs\n3StfuYC9Y72DwDVsV9Gb7EEaV7g89pKk8fDlRbizIBrFP70L/cU/YLj8J0p++zfu/DcCfJH0dwxm\nzZoFrVaL+fPnW+X8t/PKoWLNd/e4RlcCUVqix7m/bsMo0s5Or+fxx94sGaKyDYqcBL7++utYt24d\n1q5di927d6OwsBAxMTHgefNXisrKytC8eXPMmTMHwcHBDtHg3NLkrtv5d/hAeGtc4XzfXn8urBrt\nvBvghebyFZ7LnRelUkJelNhjWAl5sTSPkV+CcakH3H9FXuMGdXAPOPd44aGvt2ROSjd/AGPeZUBX\neu+L+jLwhddRtO5di71PTXEch+TkZKxZswapqam1em1N8uLiyoGvpmuHi4v97fRW2/Fy+3ZZtX2Q\nb9woNXvM0Slu9BQUFGDZsmVYsWIFoqKiAACrVq1C06ZNsW3bNgwYMED0dV27dkXXrl0BVNQLEdvT\nwNUT66Nfwk9X0rEj5yycWQ7DmnZAZMMQcDL16yTKRz2GrY/zawGfdw+g7I8U6E5vgcrZE849X4Qm\ndCAYlbSt/MoPfAsYtFUP8Abo0jdAMOjAcBpJY/L390dycjJGjhyJ1NRUBAcHW+zc9eo5w7e+C67n\nllQ5plar0LV7Q4u9l63y8NBU297Ow1Pa8WBLFLdFzI4dOxAdHY2bN2/C1/deL8TQ0FAMHz4c7733\n3kPPERYWhn/+85/VFo3TFjGE2BfqMewYbk7xB8zVD7Nq+L6fAZWLl7RB/S0pKQmrVq3C5s2b4eoq\nvrl9XeTdKkXKshN/17tV/MpWq1UIauyJ2OfbQaWiO18py07gWnYRHpzRqNUqxAxthTZt64u/0IY4\nxBYxubm5YFm20gQQAAICAnD9+nWZoiKEKB2tGHYMbECI2WOMqzcYZ/muBCckJKBt27Z44403LPrL\n2re+K/71ahf0jmiMRkEeaN6iHmKGtqIJ4H2eebY13Nw0UGsqpjUMUzEBbB/mh9ZtfB/yascl2SRw\n+vTpUKlU1f63a9cuqcIhIuyxlskSKC/ilJYXpawYVlpelMCSOXEb9C6gFulRq3GF25NTZa0HZxgG\nCxYsQHp6OpYvX/7Q59cmL66uavTp2xjxYztgxAvt0aZtfbudANZlvHh5OWH8xM4Y8FRztG1fH506\nN0DcyFAMjGlJawSqIVlN4OTJkxEfH1/tcxo3bgyDwQCj0Yi8vLxKVwNzc3PRt29fi8aUmJiIJk2a\nAAC8vLwQFhZmWpp+dxA60uP09HRFxUOPlf1YqePlm2++wYABA1BSUoLx48fLHg89BtLT0y12Pqew\nQTje7EWU/7ESPYMqehfvv1oO586DEdV7tOyf183NDZMmTcJbb72FsLAwdOvWzezz77JmPAYDj6Vf\n/oRzf91GQEA71KvnDDePa2jWvB4ee+wx2fMl9ri68XL5Uj6+TvoFd/LKEBzcEe1D/aB2zoKzM4eI\niAh06BSAwuJzAIBGQS0U8Xnq+vju/8/MzIS1KK4msKCgAP7+/lixYgXi4uIAAFlZWWjatCk2b96M\n/v37P/QcVBNIiGOjHsP2T9CVQndhH8AboW7RGypnD7lDqmTTpk2YOnUq0tLS4OfnJ0sMgiBgTcpJ\n5GQXV9pnUK1WoVuPQDwe2VSWuOoq4/QtrP/lHAz6e59FpWLg5q7GuH+F2+VK6fs5RE2gl5cXxo0b\nh7feegvbt2/H0aNHMXLkSHTs2BHR0dGm50VFReHdd+9tB6DX63Hs2DEcO3YMZWVlyMnJwbFjx3D+\n/Hk5PgYhREb3rxguLKSNYu0Ro3GFU9toOLV/UnETQAAYOHAg4uLikJCQAIPBIEsMF87fQW5OcZWN\npvV6Hgf+yEZJiflNwJWG5wWkbrxYaQJ49+tlpXocPnhNpshsm+ImgQCwcOFCDBs2DCNGjEBERAQ8\nPT2xfv36Svf1L168iNzce+1gsrOz0blzZ3Tu3BmXLl3CV199hc6dO+Pll1+W4yPYpLrUYUjFwPPY\nd+MS1meexF8St5BTcl7kpPS8yNVjWOl5kYOj5uSdd94By7KYM2eO6HFr5+V0+k3odeIrqVUqBhfO\n3bHq+9eVWF5uXC8R7ZoCAAaDgJMnblo7LLukyGunGo0Gn332GT777DOzz7l06VKlx82aNat2M2li\nu47mZeG1A+ug440QBIAHj9ae/vii13DU04gUiBPyt3nz5iE2NhYzZ87E3Llz5Q6HOBiWZZGUlITI\nyEh07twZQ4YMkfT9eb76W4cPO64kD7sNqrDKNpuhuJpAqVBNoG24WV6MmK1LUWrUV/o6x6jQvl4D\nrH58pEyREVuRn5+P/v37Y9KkSRg5ksYLkd7Ro0cRGxuLDRs2ICTE/BY3lnbm1C1sWH9O9GogyzH4\n14Qu8PJykiyeR2E08vj0oz+h1Va9qs+yDLr1CES/6GbSByYhh6gJJOR+3186CoPIxrAGgcdfhTck\nvzVMbA/1GCZyCw8Px4wZMxAfH4/iYul6/Ya08YGXlzPYB3oPq9UqtA/1s5kJIACwrAr9opuBU1ee\ntjAMoNGw6NYzUKbIbBtNAomJEut2jt3Oho4Xr+dSgZFkEqjEvCiBLeVFyh7DtpQXqVBOgPj4eHTv\n3h2TJk0yXc2xdl5YVoWRY8LQLtQPLMeAZRk4ObPoFRGEQYNbWvW9H4W5vIR3aYBBMS3h6eUElYqB\nSsUguEU9jE7oCHd3ag1XF4qsCSTkrgBnD6jAgEfVS+AMw8DHyXKtmYh9ox7DRG7z58/HoEGDsGTJ\nEiQmJkryns7OHGKeaYWBMS2g1Rrh7MzZ9CbT7cP80C60PsrLjeA4Bmo1tYh8FFQTSBQt/c41jN3z\nLcqNVbdY8FI7Y+fAieBUdEGb1Bz1GCZyyszMxIABA7Bs2TL07t1b7nCIDaGaQOJwwrwDEd+iG5xZ\nNVSo+OtVo2LhyqrxaY9/0ASQ1Br1GCZyatKkCRYtWoSEhATk5OTIHQ5xcPQblJgotW5nYru+WBbx\nHGIat0eP+k0xumV3rI9+CV3qN5bk/ZWaF7nZal6s3WPYVvNiTZSTyqKiojB27Fg8++yz0OlsZ8Nm\nqdB4kQ7VBBKbEOYdiLAudV/9xQsCGIAaiRMA91YMx8TEoHnz5ujTp4/cITk8feYRlP+5FnzJHWha\n94Vz+D/AOLnJHZbVTJkyBVu3bsXMmTPxwQcfyB0OcVBUE0js2tG8LHx8Mg0n7lyDimHwWEALvBna\nD03dfeQOjSgA9RiWnyAIKF73Dsr//AbQawGBBzRuYJxc4f3aZrC+ttXftjYKCgoQGRmJadOmYfjw\n4XKHQxTOGjWBNAkkduvgzUwk7v9fpUUlDAA3zgnf9xuNxm715AuOKMbXX3+N5ORkWjEsE236RhSu\nHg/oSisfYFTggjrAe8o2eQKTyMmTJzFs2DD88ssvaNeundzhEAWjhSHEquytDmPuiS1VVhULAEoN\nOiw6s7vG57G3vFiKveTF0j2G7SUvllRdTsp+/6rqBBAABB6G3AwYb160YmTy2rNnD0JDQzF37lzE\nx8ejsLBQ7pAUgb6HpEOTQGKXbmtLcbUkX/QYDwE7c89LHBFRMloxLB9jfrbZYwyrgbEwV8Jo5BEb\nG4vIyEgkJiaC56t2SCLEWuh2MLFLedoS9E9dAr2ZbiOunAYHYiZLHBVRMuoxLI+C5aOhS98AiP0q\n4pzgM/0wWK8G0gcmMZ1Oh5iYGAwcOBCTJ9PPJlIV3Q4mpIZ8ndzQyNVL9JgKDB4PaCFxRETpqMew\nPFwjJwKcc9UDnAaaNlEOMQEEAI1Gg+XLlyMpKQlpaWlyh0McBE0CiYncdRi3yktwrvAmSg2W2Tfr\n3Q794cxW3gWJAeDCqTGhbUSNzyN3XpTKHvNiiR7D9piXR1VdTtRNu8B9+HxA7Qxo3ComhBoXcE26\nwOOFRRJGKb0H89KoUSMsXboUr7zyCrKysmSKSn70PSQd2ieQyEprNOD7S0eRfG4/7mhLofl70jas\nSQdMDYuEWlX3tl69/Jthcc9/4qOTO5BRcANggJ5+TfF2WBRtEUPMoh7D0nPpHgensKehO7UZQnkR\nuGbdoA7qIHdYsoiIiMCECRMwatQobNiwAc7OIldJZcTzAi6cv4OiQi18fV3QpJkX7b9qw6gmkMgm\nt6wQz/++CjfLi6scc2JYRAaGYH63IRZ5Lz1vBAOG2syRGqMew0QugiBg9OjR8PHxwSeffCJ3OCbX\nsovw/benYTQI4HkBjApwc1PjuRdD4e2trMmqPaKaQGJXph78FbfKS0SPaQUjtuecRXZJgUXeS61i\naQJIaoVWDBO5MAyDL774Avv27cPq1avlDgcAUF5uwNrVp1BWaoBOZ4TBwEOv41GQr8U3KSfB8w55\nPcnm0W9FYiJlHca10gKcyb8OAeZ/cHCMCkfyrkoWkzlUnyLO3vNS1x7D9p6XuqCciKsuLx4eHkhJ\nScHs2bNx/PhxCaMSd/LEDdGJniAA5WV6XLooviVXXdB4kQ5NAoksbpQVPbTej2EYOLFUtkrkQyuG\niZxat26NDz/8EKNGjZK9fCk3pxh6vfgehgYDj1s3RTb8JopHNYFEFrfKS/DkliXQmdnHDwCcWQ6/\nD5wIV04jYWSEVEU9homcZsyYgTNnzuC7776TrT51985M/LE3C0Zj1SmDRqPCU0+3RPswPxkicxxU\nE0jsRn1nNzwW0AIaM1cDNSoW74RF0wSQKML9K4aptReR2qxZs6DVajF//nzZYujQyR/VLQIOaUM7\nLtgimgQSE6nrMOZ2HoT29RrCmeXAMgzu/nxp5uaDL3vF4tlmHa36/rwgoNyof+hfVlSfIs7R8lLT\nHsOOlpeaoJyIq2leOI5DcnIy1qxZg9TUVCtHJc6rnjMGDGwBjlPh7ho7lmOgVqvwj3+2hVptuSuU\nNF6kQwVXRDZuaiek9H0Bp+7k4OjtbLhxGkQ2bAUvjYtV37fUoMMnp37Hz5knoOON8Na44qWQnni+\neRfa74pUa968eYiNjcXMmTMxd+5cucMhDsTf3x/JyckYOXIkUlNTERwcLHkMHcMD0LipJ44ezkX+\n7XIENHBDx84B8PBwkjwWYhlUE0gcip434vnfU3CxKK9SPaIzy+HZph3xTodoGaMjtoB6DBM5JSUl\nYdWqVdi8eTNcXV3lDodIiGoCCXlEaTnnkFl8p8qClHKjAf+7fAw3yopkiozYCloxTOSUkJCAtm3b\n4o033rD4hIA4HpoEEhNHqMNIzc5AqVEveoxlVNh343KVrztCXurCkfNSXY9hR86LOZQTcXXJC8Mw\nWLBgAdLT07F8+XIrRCU/Gi/SoUkgcSgPq/mjkkBSU7RimMjFzc0NKSkp+OCDD3Dw4EG5wyE2jGoC\niUPZdu0v/N/hDaJXAzUqFqkDxqO+s7sMkRFbRT2GiVw2bdqEqVOnIi0tDX5+tEefvaOaQEIe0RMN\nWiHYw7fK/oQurBpxwZ1pAkhqjXoME7kMHDgQcXFxSEhIgMFgkDscYoNoEkhMHKEOg1OpsCwiDs8F\nd4bb3xtRBzh74M3QfngjtJ/oaxwhL3VBeanwYI9hyktVlBNxlsjLO++8A5ZlMWfOHAtEpAw0XqRD\n+wQSh+PKaTA1LBJTwyJhFHiwDP0tRB7N3RXDMTExmDx5MiIiIuQOiTgIlmWRlJSEyMhIdO7cGUOG\nDJE7JGJDqCaQEEIshHoME7kcPXoUsbGx2LBhA0JCQuQOh1gB1QQSQoiC0YphIpfw8HDMmDED8fHx\nKC4uljscYiNoEkhMqA5DHOVFHOVFXJs2bWrUY9iR0FgRZ+m8xMfHo3v37pg0aZJNbyRN40U6NAkk\nhBALoxXDRC7z58/H5cuXsWTJErlDITaAagIJIcQKqMcwkUtmZiYGDBiAZcuWoXfv3nKHQyyEagIJ\nIcRGUI9hIpcmTZpg0aJFSEhIQE5OjtzhEAWjSSAxoToMcZQXcZQXcffnpboew46Exoo4a+YlKioK\nY8eOxZgxY6DT6az2PtZA40U6NAkkhBArohXDRC5TpkyBt7c31aYSs6gmkBBCJEA9hokcCgoKEBkZ\niWnTpmH48OFyh0MeAdUEEkKIjaIVw0QOXl5eWLlyJaZNm4bTp0/LHQ5RGJoEEhOqwxBHeRFHeRFn\nLi8P9hh2JDRWxEmVl9DQUMydOxfx8fE2UZJA40U6NAkkhBCJ0IphIpfY2FhERkYiMTERPM/LHQ5R\nCKoJJIrCCwKulRZArWIR4OIhdziEWAX1GCZy0Ol0iImJwcCBAzF58mS5wyG15DA1gVqtFhMnToSf\nnx/c3d3xzDPPIDs7u9rXJCUl4bHHHoOPjw+8vb0RGRlJf2nbmA1XTyNq8yIM25GMp7d+hWe2f41j\neVlyh0WIxdGKYSIHjUaD5cuXIykpCWlpaXKHQxRAkZPA119/HevWrcPatWuxe/duFBYWIiYmptpL\n2L///jvi4uKQlpaGAwcOoHXr1njyySdx/vx5CSO3bXLWYWzKOoP3jm3CLW0Jyo0GaHkjLhbl4aV9\n3yEj/7pscQFUn2IO5UVcTfOSkJDgMD2GaayIkyMvjRo1wtKlS/HKK68gK0uZf2TTeJGO4iaBBQUF\nWLZsGT766CNERUUhPDwcq1atwokTJ7Bt2zazr1u9ejUSExPRsWNHhISEYMmSJfDw8EBqaqqE0ZO6\nEAQBH59MQ7nRUOWY1mjAFxm7ZYiKEOujFcNEDhEREZgwYQJGjRqF8vJyucMhMlLcJPDw4cPQ6/UY\nMGCA6WtBQUFo27Yt9u3bV+PzaLValJeXw9vb2xph2qWIiAhZ3vdGeTHydWWixwQAB29mShvQA+TK\ni9JRXsTVJi+OsmKYxoo4OfPy6quvIigoCNOmTZMtBnNovEhHcZPA3NxcsCwLX1/fSl8PCAjA9es1\nvy04ffp0eHh4YMiQIZYOkViYRsWCh/liV7WKNtYl9otWDBM5MAyDL774Avv27cPq1avlDofIRLJJ\n4PTp06FSqar9b9euXRZ5r08//RRLly7FunXr4O7ubpFzOgK56jC8nVwR4ukneoxjVBgU1E7iiCqj\n+hRxlBdxdcmLvfcYprEiTu68eHh4ICUlBbNnz8bx48dljeV+cufFkXBSvdHkyZMRHx9f7XMaN24M\ng8EAo9GIvLy8SlcDc3Nz0bdv34e+z8KFCzFz5kxs3rwZXbt2rfa5iYmJaNKkCYCKXdXDwsJMl6Hv\nDkJHepyeni7b+8eUe+PU2cNQhQSBhwBtRiZYhoFfhzZ4uXVvReSHHitnvNjjY47jTCuG33vvPbi5\nuSkqvkd5nJ6erqh4lPL4Ljnjad26NcaNG4cRI0Zg37598PHxkT0/NF7ujY89e/YgM9N6JVGK2yew\noKAA/v7+WLFiBeLi4gAAWVlZaNq0KTZv3oz+/fubfe2CBQvw3nvvYePGjaZkmkP7BCrPxaI8fJmx\nF3tvXAKnUuHpoHYYF9ITvk5ucodGiGSoxzCRw4wZM3DmzBl89913NO4Uyhr7BCpuEghUXKFbv349\nVqxYAR8fH0yZMgUFBQU4fPgwGIYBAERFRaFHjx6YN28eAODDDz/E9OnTsXr1ajz22GOmc7m6usLT\n07PKe9AkkBCiRHq9HrGxsWjXrh3mzp0rdzjEQRgMBgwbNgy9e/dW5GIR4kCbRS9cuBDDhg3DiBEj\nEBERAU9PT6xfv940AQSAixcvIjc31/R48eLFMBgMGDFiBAIDA03/vf7663J8BJv04C0KqZTotdiV\newG7ci+gRK+VJYbqyJUXpaO8iHvUvNjjimEaK+KUlBeO45CcnIw1a9bIvrWakvJi7zi5AxCj0Wjw\n2Wef4bPPPjP7nEuXLlX7mNiG5LP78eVfe8ExFX+PGAQer7Tug7EhPWWOjBD53F0xHBMTg+bNm6NP\nnz5yh0QcgL+/P5KTkzFy5EikpqYiODhY7pCIlSnydrAU6Haw/H7LPInZx1OrbBLtzHKY2fFJDG4S\nKlNkhCgD9RgmckhKSsKqVauwefNmuLq6yh0O+ZvD3A4mjuGLjD2iXULKjQYsyqDbAYRQj2Eih4SE\nBLRt2xZvvPGGxScdRFloEkhMpKzD0PNGXCstMHv8WmkB9Lwy+qlSfYo4yos4S+fFHnoM01gRp9S8\nMAyDBQsWID09HcuXL5f8/ZWaF3tEk0AiC45RQaMyX5KqUXGmOkFCHB31GCZSc3NzQ0pKCj744AMc\nPHhQ7nCqVVqix84dV7Dk80NY8tkhpG27jJJindxh2QSqCSSymXV0E9ZnnoRe4Ct9Xc2oMKRJGN4L\nf0qmyAhRnvz8fPTv3x+TJk3CyJEj5Q6HOIhNmzZh6tSpSEtLg5+feGcnORUVabF86XGUlxtgNFZM\nZ1iWgcaJxZiXOsHLy0nmCC2HagKJXZnS/gk0cPWEC6s2fc2FVaOBqycmt39cxsgIUR7qMUzkMHDg\nQMTFxSEhIQEGQ9UabrmlbbuM0lK9aQIIAEajgPIyA7anXpQxMttAk0BiInUdhpfGBT/0G4M3Q/uh\ns08QOvsE4c3Qfvih3xh4aVwkjaU6VJ8ijvIizpp5sdUewzRWxNlKXt555x2wLIs5c+ZI8n41zYsg\nCMg4nQexi2OCAJw7ewc875A3O2tMkfsEEsfhymkQGxyO2OBwuUMhxCbcv2I4NTVVtCMSIZbEsiyS\nkpIQGRmJzp07Y8iQIXKHZHL/FcAHCYIAnhegUjFmn+PoqCaQEEJsEPUYJlI7evQoYmNjsWHDBoSE\nhMgdDgDg6y+P4uaNUtFjPr4u+NeEzhJHZD1UE0gIIQQArRgm0gsPD8eMGTMQHx+P4uJiucMBAPSL\nbgZOXXUqw3Eq9ItuKkNEtoUmgcTEVupTpEZ5EUd5ESdVXmypxzCNFXG2mJf4+Hh0794dkyZNstpG\n0rXJS4uW3nh6cEu4unLQaFTQaFi4uHAYGNMCIa19rRKfPaGaQEIIsVHUY5jIYf78+RiEGVsZAAAU\ndUlEQVQ0aBCWLFmCxMREucNBu1A/tGlXHzdvlEAQAP8AN6oDrCGqCSSEEBtHPYaJ1DIzMzFgwAAs\nW7YMvXv3ljsch0A1gYQQQqqgHsNEak2aNMGiRYuQkJCAnJwcucMhdUSTQGJii/UpAHDg5hW8tHct\nojYvwgu/p2BLdoZF/1qy1bxYG+VFnFx5UXKPYRor4mw9L1FRURg7dizGjBkDnc5ybdpsPS+2hCaB\nxKatunAQr+7/AftvXsGN8mKcuJOD6Uc2Ys7xLXKHRojkaMUwkdqUKVPg7e1NY85GUU0gsVm3taXo\nn7oYOr7qVQ9nlkPKYy+ibb0AGSIjRD7UY5hIraCgAJGRkZg2bRqGDx8udzh2i2oCCbnP9pyzYBnx\nFWA6oxG/Zp6UOCJC5Ec9honUvLy8sHLlSkybNg2nT5+WOxxSCzQJJCa2VodRatDBYKYvJA8BxQat\nRd7H1vIiFcqLOCXkRWk9hpWQEyWyp7yEhoZi7ty5iI+Pf+TFSfaUF6WjSSCxWV19G4NViQ9hV06D\n3v7NpA2IEAWhFcNEarGxsYiMjERiYiJ4npc7HFIDVBNIbNro3WuQfienUl0gyzBo4OKJ9dEvQa2i\nnqrEsVGPYSIlnU6HmJgYDBw4EJMnT5Y7HLtCNYGEPGBxr3+iX4NW0KhYuHMaaFQsuvg2xqq+L9IE\nkBDQimEiLY1Gg+XLlyMpKQlpaWlyh0MegiaBxMQW6zBcOQ0+6v4Mtj81AV/3eQ6b+v8LyRFx8HN2\nt9h72GJepEB5Eae0vCihx7DScqIU9pqXRo0aYenSpXjllVeQlZVV69fba16UiCaBxC7U07igvXdD\n+Lt4yB0KIYpDK4aJ1CIiIjBhwgSMGjUK5eXlcodDzKCaQEIIcRDUY5hISRAEjB49Gj4+Pvjkk0+q\nfV5uTjHKygwICHCDm7tGwihthzVqAmkSSAghDuTrr79GcnIyUlNT4enpKXc4xM4VFRUhOjoaEydO\nxIsvvljleHZWEX7+IQNlZQaoVAwMBh6t2/ri6SGtwHF0s/J+tDCEWBXVYYijvIijvIhTel7k6DGs\n9JzIxRHy4uHhgZSUFMyePRvHjx+vdKygQItvV59EYaEOej0PrdYIo1HA1i1p2PDLOZkidiw0CSSE\nEAdDK4aJlFq3bo0PP/wQo0aNqnQH7tCBa+CNVa9sGY3AXxl5KCqyzIb/xDy6HUwIIQ6IegwTqc2Y\nMQNnzpzBd999B5ZlsWzpMVzPLRF9rpMTi8HDQtAqxEfiKJWLbgcTQgixCFoxTKQ2a9YsaLVazJ8/\nHwDg4sqZfa4gAC7O5o8Ty6BJIDFxhPqUuqC8iKO8iLOlvEjVY9iWciIlR8sLx3FITk7GmjVrkJqa\nis5dG0KtrjoNybyaDrVahUaNacsva6NJICGEODDqMUyk5O/vj+TkZEycOBFqTQGat/CuNBFUqQCO\nYzD02dZgGEbGSB0D1QQSQgihHsNEUklJSVi1ahU2bdqEq1fKcPhQLspK9WjcxBPdewbC28dF7hAV\nh/YJtCCaBBJCyD16vR6xsbFo164d5s6dK3c4xM4JgoDx48dDpVJh8eLFdNWvBmhhCLEqR6tPqSnK\nizjKizhbzYs1ewzbak6szZHzwjAMFixYgPT0dCxfvrzSMUfOi9Ro6Q0hhBAA91YMx8TEoHnz5ujT\np4/cIRE75ubmhpSUFDz11FMICwtDt27d5A7J4dDtYEIIIZVQj2EipU2bNmHq1KlIS0uDn5+f3OEo\nFt0OJoQQYnW0YphIaeDAgYiLi0NCQgIMBoPc4TgUmgQSE6rDEEd5EUd5EWcvebFkj2F7yYmlUV7u\neeedd8CyLObMmUN5kRBNAgkhhIiiHsNEKizLIikpCT/99BNOnjwpdzgOg2oCCSGEmEU9homUsrKy\n0LBhQ9qrUoQ1agJpdTAhhBCzaMUwkVJQUJDcITgUuh1MTKgOQxzlRRzlRZw95uVRewzbY04sgfIi\njvIiHZoEEkIIeShaMUyI/aGaQEIIITVGPYYJkYfD7BOo1WoxceJE+Pn5wd3dHc888wyys7Orfc3/\n/vc/dO3aFd7e3nB3d0d4eDhSUlIkipgQQhwDrRgmxH4ochL4+uuvY926dVi7di12796NwsJCxMTE\ngOd5s6+pX78+Zs6ciQMHDiA9PR1jxozBuHHjsGHDBgkjt21UhyGO8iKO8iLO3vNSlx7D9p6TuqK8\niKO8SEdxk8CCggIsW7YMH330EaKiohAeHo5Vq1bhxIkT2LZtm9nX9evXD0OGDEFISAiCg4MxadIk\ndOjQAfv27ZMwetuWnp4udwiKRHkRR3kR5wh5ubtieM6cOdi7d+9Dn+8IOakLyos4yot0FDcJPHz4\nMPR6PQYMGGD6WlBQENq2bVvjCZ0gCNi+fTvOnj2LqKgoa4VqdwoKCuQOQZEoL+IoL+IcJS+1WTHs\nKDmpLcqLOMqLdBQ3CczNzQXLsvD19a309YCAAFy/fr3a1xYUFMDd3R1OTk4YNGgQPvnkE0RGRloz\nXEIIcVi0YpgQ2ybZJHD69OlQqVTV/rdr165Heg9PT0+cOHEChw4dwn/+8x+89tpr+PXXXy30Cexf\nZmam3CEoEuVFHOVFnKPlpSY9hh0tJzVFeRFHeZGOZFvE5OXlIS8vr9rnNG7cGH/88Qeio6Nx8+bN\nSlcD27dvj9jYWMyaNavG7/nSSy/h/PnzSEtLq3KsU6dOOH78eM0/ACGEEEKITDp27Ihjx45Z9JyS\ntY3z9fWtcotXTJcuXaBWq7FlyxbExcUBqOglmJGRgd69e9fqPY1Go9kVxZZOJCGEEEKILVFc72Av\nLy+MGzcOb731Fvz9/eHj44MpU6agY8eOiI6ONj0vKioKPXr0wLx58wAAc+fORc+ePREcHAytVouN\nGzdi9erVWLx4sVwfhRBCCCFEsRQ3CQSAhQsXguM4jBgxAmVlZYiOjsbq1avBMIzpORcvXkTTpk1N\nj0tKSvDKK68gKysLLi4uaNu2LVatWoURI0bI8REIIYQQQhTNYdvGEUIIIYQ4MsVtEfOo6tJyLikp\nCY899hh8fHzg7e2NyMhI0Q1QFy9ejODgYLi4uKBr1642tat5XfJy6tQpDB8+HC1atIBKpcLs2bOr\nPOe9996rsso7MDDQWh/D4qyVF8DxxgsA/Pjjj2jXrh2cnZ3Rvn17/Pzzz5WO29p4qe2/YXp6Oh5/\n/HG4uroiKCgI77//fpXn/P777+jSpQtcXFzQokULfPXVV9YK32osnZedO3eK7hhx9uxZa34Mi6pN\nTrRaLUaPHo2OHTtCo9GgX79+os9ztLFSk7zYw1gBapeXnTt34plnnkFgYCDc3NzQsWNHLF++vMrz\n6jReBDszfvx4ITAwUNi2bZtw5MgR4YknnhA6deokGI1Gs6954YUXhEWLFgnHjh0T/vrrL2H8+PGC\nm5ubcO7cOdNz1q5dK6jVauHrr78WMjIyhIkTJwru7u5CZmamFB/rkdUlLwcPHhSmTp0qfPPNN0Lz\n5s2F2bNnV3nOrFmzhLZt2wrXr183/Xfr1i1rfhSLslZeHHG87Nu3T+A4Tpg3b56QkZEhzJ07V+A4\nTjhw4IDpObY0Xmr7b1hQUCAEBAQII0aMEE6dOiX88MMPgoeHh/Dxxx+bnnPx4kXB1dVVmDRpkpCR\nkSEkJSUJarVa+PHHH6X6WI/MGnlJS0sTGIYRzpw5U2lsVDfelKS2OSkpKRHGjx8vJCUlCUOHDhX6\n9etX5TmOOFZqkhdbHyuCUPu8zJs3T5gxY4awb98+4dKlS8KSJUsEjuOEb775xvScuo4Xu5oE5ufn\nCxqNplJirl69KqhUKiE1NbVW52rQoIHw+eefmx53795dePnllys9p1WrVsK0adMeLWgJWCIvoaGh\nZieBoaGhFotVStbMiyOOl9jYWGHAgAGVvhYdHS3ExcWZHtvSeKntv+HixYsFLy8voby83PS1OXPm\nCI0aNTI9fuutt4SQkJBKr0tISBB69eplwcityxp5ufuLXal/EDzMo3y/T5gwQXjiiSeqfN0Rx8r9\nzOXF1seKIFjm90NsbKzw7LPPmh7XdbzY1e1gS7ScAyouSZeXl8PHxwcAoNPpcOTIkUrnBYABAwbY\nRG9iS+XFnIsXL6JRo0Zo3rw54uLicOnSpUc+pxSslRdHHS/79++v0We2hfFSl3/DP/74A4899hic\nnJwqPf/atWu4cuWK6Tli5zx06JDZjZaVxFp5uatr164IDAxEdHQ0du7cafH4rcFa3++OOFZqwxbH\nCmC5vBQUFJjmKEDdx4tdTQIfpeXc/aZPnw4PDw8MGTIEAHDr1i0YjUYEBARUep6/vz9yc3MfPXAr\ns1RexPTs2RMrV65EamoqkpKSkJubi969e+P27duPdF4pWCsvjjpecnNzq3zmgICASp/ZVsZLXf4N\nzX3+u8cA4Pr166LPMRgMuHXrlqXCtxpr5SUwMBBffvkl1q1bh3Xr1qF169aIioqyiTpaa32/O+JY\nqQlbHiuAZfLy22+/YceOHXj55ZdNX6vreFHkFjEPmj59umk/QHMs9ZfAp59+iqVLl2L79u1wd3e3\nyDmtRcq8mPPUU0+Z/n9oaCh69eqF4OBgrFy5EpMnT7bqe5ujhLwokRLyosTxYin3b2FF7qlJXkJC\nQhASEmJ63LNnT1y+fBkffvghIiIirBkesTGOPlb27t2LF154AZ9//jm6du36yOeziUng5MmTER8f\nX+1zGjduDIPBAKPRiLy8vEpXMXJzc9G3b9+Hvs/ChQsxc+ZMbN68uVJy69evD5Zlq1wFuX79Oho2\nbFjLT2M5UuWlNlxdXdG+fXucP3/eouetDbnz4qjjpUGDBlX+kr1+/ToaNGhg9jVKGC9i6vJvaO7z\n3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"text": [ "" ] } ], "prompt_number": 448 }, { "cell_type": "code", "collapsed": false, "input": [ "newd = np.array(np.matrix([1/d]).T)\n", "newd = np.diag(newd[:,0])\n", "a = list(set(range(0,len(X))) - set(train))\n", "a.sort()\n", "newu = np.dot(X[a, ],V.T).dot(newd)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 449 }, { "cell_type": "code", "collapsed": false, "input": [ "colors = [dark2_colors[i] for i in Y[train]]\n", "plt.scatter(U[:,0], U[:,1], color = colors, s=50)\n", "x = np.array([-0.15, 0.15])\n", "plt.plot(x, -3*x-.165, color='k', linestyle='-', linewidth=1)\n", "plt.plot(x, -3.2*x+0.2, color='k', linestyle='-', linewidth=1)\n", "plt.xlabel(\"PC1\")\n", "plt.ylabel(\"PC2\")\n", "plt.ylim(-0.3,0.3)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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L9wHUuZ/PCpR4EhMTadeuHRMnTuSBBx7gyy+/pFWrVj59/sTExIDKRyD9fFZ1739l10sp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"text": [ "" ] } ], "prompt_number": 450 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obtain $V$ from $X_{train}=UDV^\\top$\n", "\n", "Apply to $X_{test} V$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "colors = [dark2_colors[i] for i in Y[train]]\n", "plt.scatter(U[:,0], U[:,1], color = colors, s=50)\n", "colors = [dark2_colors[i] for i in Y[a]]\n", "plt.scatter(newu[:,0], newu[:,1], s=70, marker = '^', facecolors=colors, edgecolors='k')\n", "x = np.array([-0.15, 0.15])\n", "plt.plot(x, -3*x-.165, color='k', linestyle='-', linewidth=1)\n", "plt.plot(x, -3.2*x+0.2, color='k', linestyle='-', linewidth=1)\n", "plt.xlabel(\"PC1\")\n", "plt.ylabel(\"PC2\")\n", "plt.ylim(-0.3,0.3)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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qMn5PJfr/LZK9e/eyatUqdDrP2vxBVVViFh4gMSEjX31gjUYhsJI3fx/RFo1G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\nDIRzWW9cIPv3L7Bej0dXuxX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TObM5k5bEL5dPsiXhDz4+vJnh21cwZf8G/ki1v8dgeSU1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o0ld46SeGfz1VrroIGG28xRk3GPYVKKEAITJkxAUFAQli9frnQ5Nid+voB//u8x1FkErFYBjRbw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\ncpHSv39/bNmypZUVO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