Dimension Reduction and PCA from Scratch (Iris Data).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dimension Reduction and PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import Iris Data Set..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length</th>\n",
       "      <th>sepal width</th>\n",
       "      <th>petal length</th>\n",
       "      <th>petal width</th>\n",
       "      <th>type</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.1</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>4.3</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>5.8</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    sepal length  sepal width  petal length  petal width         type\n",
       "0            5.1          3.5           1.4          0.2  Iris-setosa\n",
       "1            4.9          3.0           1.4          0.2  Iris-setosa\n",
       "2            4.7          3.2           1.3          0.2  Iris-setosa\n",
       "3            4.6          3.1           1.5          0.2  Iris-setosa\n",
       "4            5.0          3.6           1.4          0.2  Iris-setosa\n",
       "5            5.4          3.9           1.7          0.4  Iris-setosa\n",
       "6            4.6          3.4           1.4          0.3  Iris-setosa\n",
       "7            5.0          3.4           1.5          0.2  Iris-setosa\n",
       "8            4.4          2.9           1.4          0.2  Iris-setosa\n",
       "9            4.9          3.1           1.5          0.1  Iris-setosa\n",
       "10           5.4          3.7           1.5          0.2  Iris-setosa\n",
       "11           4.8          3.4           1.6          0.2  Iris-setosa\n",
       "12           4.8          3.0           1.4          0.1  Iris-setosa\n",
       "13           4.3          3.0           1.1          0.1  Iris-setosa\n",
       "14           5.8          4.0           1.2          0.2  Iris-setosa"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "url = \"https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data\"\n",
    "# load dataset into Pandas DataFrame\n",
    "\n",
    "#this data has 4 dimensions (4 variables)\n",
    "# loading dataset into Pandas DataFrame\n",
    "df = pd.read_csv(url\n",
    "                 , names=['sepal length','sepal width','petal length','petal width','type'])\n",
    "df.head(15) #head allows you to choose how many rows you want printed () empty default is 5\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standardize Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length</th>\n",
       "      <th>sepal width</th>\n",
       "      <th>petal length</th>\n",
       "      <th>petal width</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.743333</td>\n",
       "      <td>0.446</td>\n",
       "      <td>-2.358667</td>\n",
       "      <td>-0.998667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.943333</td>\n",
       "      <td>-0.054</td>\n",
       "      <td>-2.358667</td>\n",
       "      <td>-0.998667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.143333</td>\n",
       "      <td>0.146</td>\n",
       "      <td>-2.458667</td>\n",
       "      <td>-0.998667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.243333</td>\n",
       "      <td>0.046</td>\n",
       "      <td>-2.258667</td>\n",
       "      <td>-0.998667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.843333</td>\n",
       "      <td>0.546</td>\n",
       "      <td>-2.358667</td>\n",
       "      <td>-0.998667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.443333</td>\n",
       "      <td>0.846</td>\n",
       "      <td>-2.058667</td>\n",
       "      <td>-0.798667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-1.243333</td>\n",
       "      <td>0.346</td>\n",
       "      <td>-2.358667</td>\n",
       "      <td>-0.898667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.843333</td>\n",
       "      <td>0.346</td>\n",
       "      <td>-2.258667</td>\n",
       "      <td>-0.998667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-1.443333</td>\n",
       "      <td>-0.154</td>\n",
       "      <td>-2.358667</td>\n",
       "      <td>-0.998667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-0.943333</td>\n",
       "      <td>0.046</td>\n",
       "      <td>-2.258667</td>\n",
       "      <td>-1.098667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.443333</td>\n",
       "      <td>0.646</td>\n",
       "      <td>-2.258667</td>\n",
       "      <td>-0.998667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-1.043333</td>\n",
       "      <td>0.346</td>\n",
       "      <td>-2.158667</td>\n",
       "      <td>-0.998667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-1.043333</td>\n",
       "      <td>-0.054</td>\n",
       "      <td>-2.358667</td>\n",
       "      <td>-1.098667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-1.543333</td>\n",
       "      <td>-0.054</td>\n",
       "      <td>-2.658667</td>\n",
       "      <td>-1.098667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-0.043333</td>\n",
       "      <td>0.946</td>\n",
       "      <td>-2.558667</td>\n",
       "      <td>-0.998667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "    sepal length  sepal width  petal length  petal width\n",
       "0      -0.743333        0.446     -2.358667    -0.998667\n",
       "1      -0.943333       -0.054     -2.358667    -0.998667\n",
       "2      -1.143333        0.146     -2.458667    -0.998667\n",
       "3      -1.243333        0.046     -2.258667    -0.998667\n",
       "4      -0.843333        0.546     -2.358667    -0.998667\n",
       "5      -0.443333        0.846     -2.058667    -0.798667\n",
       "6      -1.243333        0.346     -2.358667    -0.898667\n",
       "7      -0.843333        0.346     -2.258667    -0.998667\n",
       "8      -1.443333       -0.154     -2.358667    -0.998667\n",
       "9      -0.943333        0.046     -2.258667    -1.098667\n",
       "10     -0.443333        0.646     -2.258667    -0.998667\n",
       "11     -1.043333        0.346     -2.158667    -0.998667\n",
       "12     -1.043333       -0.054     -2.358667    -1.098667\n",
       "13     -1.543333       -0.054     -2.658667    -1.098667\n",
       "14     -0.043333        0.946     -2.558667    -0.998667"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "features = ['sepal length', 'sepal width', 'petal length', 'petal width']\n",
    "\n",
    "# Separating out the features\n",
    "x = df.loc[:, features].values #df.loc accesses a group of rows or columns\n",
    "# Separating out the target\n",
    "y = df.loc[:,['type']].values\n",
    "\n",
    "# Standardizing the features by subtracting the mean\n",
    "mean_vec = np.mean(x, axis=0) #creating vector of means\n",
    "x1 = x - mean_vec #subtracting the means and normalizing\n",
    "\n",
    "pd.DataFrame(data = x1, columns = features).head(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find Covariance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.68569351 -0.03926846  1.27368233  0.5169038 ]\n",
      " [-0.03926846  0.18800403 -0.32171275 -0.11798121]\n",
      " [ 1.27368233 -0.32171275  3.11317942  1.29638747]\n",
      " [ 0.5169038  -0.11798121  1.29638747  0.58241432]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(4, 4)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.cov(x1.T) #can use x or x1 bc subracting the mean shouldn't affect covariance\n",
    "print(A)\n",
    "A.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find Eigenvalues and Eigenvectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.22484077 0.24224357 0.07852391 0.02368303]\n",
      "[[ 0.36158968 -0.65653988 -0.58099728  0.31725455]\n",
      " [-0.08226889 -0.72971237  0.59641809 -0.32409435]\n",
      " [ 0.85657211  0.1757674   0.07252408 -0.47971899]\n",
      " [ 0.35884393  0.07470647  0.54906091  0.75112056]]\n"
     ]
    }
   ],
   "source": [
    "e, v = np.linalg.eig(A) #command finds the eigenvalues and vectors associated, stores them separately into e and then v\n",
    "print (e)\n",
    "print (v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sort Eigenvalues/vectors Largest to Smallest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3]\n"
     ]
    }
   ],
   "source": [
    "idx = np.argsort(e)[::-1]\n",
    "e = e[idx] #orders eigen values based on index of largest to smallest eigenvalues\n",
    "e = np.real_if_close(e) #adjusts eigenvalues to be real numbers\n",
    "v = v[:, idx]#adjusts the eigenvectors to correspond to eigenvalues\n",
    "print(idx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Determine Amount of Variance and Select Principle Components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.92461621 0.05301557 0.01718514 0.00518309]\n"
     ]
    }
   ],
   "source": [
    "expvar = e/e.sum() #will give the percent of variance covered by each eigenvalue/vector\n",
    "print(expvar) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Selecting PCs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.22484077 0.24224357]\n",
      "[[ 0.36158968 -0.65653988]\n",
      " [-0.08226889 -0.72971237]\n",
      " [ 0.85657211  0.1757674 ]\n",
      " [ 0.35884393  0.07470647]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(4, 2)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nvar = 4 #number of variables\n",
    "ncomp = 2 #number of components\n",
    "remove = nvar-ncomp\n",
    "e = e[0:-remove] #indexes from 0 to everything except for the remove indexes at the end\n",
    "print(e)\n",
    "v = v[:, :-remove] #all rows and all columns except the removed\n",
    "print(v)\n",
    "v.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dimension Reduction and Change of Basis for PCA\n",
    "In this section we will perform matrix multiplication of the standardized data and the vectors of the principal components to get a new data matrix that will have n rows and m columns (where n= # of observations, and m= # of PCs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC 1</th>\n",
       "      <th>PC 2</th>\n",
       "      <th>type</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2.684207</td>\n",
       "      <td>-0.326607</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.715391</td>\n",
       "      <td>0.169557</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2.889820</td>\n",
       "      <td>0.137346</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.746437</td>\n",
       "      <td>0.311124</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.728593</td>\n",
       "      <td>-0.333925</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-2.279897</td>\n",
       "      <td>-0.747783</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-2.820891</td>\n",
       "      <td>0.082105</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-2.626482</td>\n",
       "      <td>-0.170405</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-2.887959</td>\n",
       "      <td>0.570798</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-2.673845</td>\n",
       "      <td>0.106692</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-2.506527</td>\n",
       "      <td>-0.651935</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-2.613143</td>\n",
       "      <td>-0.021521</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-2.787434</td>\n",
       "      <td>0.227740</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-3.225200</td>\n",
       "      <td>0.503280</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-2.643543</td>\n",
       "      <td>-1.186195</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        PC 1      PC 2         type\n",
       "0  -2.684207 -0.326607  Iris-setosa\n",
       "1  -2.715391  0.169557  Iris-setosa\n",
       "2  -2.889820  0.137346  Iris-setosa\n",
       "3  -2.746437  0.311124  Iris-setosa\n",
       "4  -2.728593 -0.333925  Iris-setosa\n",
       "5  -2.279897 -0.747783  Iris-setosa\n",
       "6  -2.820891  0.082105  Iris-setosa\n",
       "7  -2.626482 -0.170405  Iris-setosa\n",
       "8  -2.887959  0.570798  Iris-setosa\n",
       "9  -2.673845  0.106692  Iris-setosa\n",
       "10 -2.506527 -0.651935  Iris-setosa\n",
       "11 -2.613143 -0.021521  Iris-setosa\n",
       "12 -2.787434  0.227740  Iris-setosa\n",
       "13 -3.225200  0.503280  Iris-setosa\n",
       "14 -2.643543 -1.186195  Iris-setosa"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PCdata = x1.dot(v)\n",
    "PCdata.shape\n",
    "principalDf = pd.DataFrame(data = PCdata\n",
    "             , columns = ['PC 1', 'PC 2'])\n",
    "finalDf = pd.concat([principalDf, df[['type']]], axis = 1) #axis=1 refers to columns not rows\n",
    "\n",
    "finalDf.head(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot Data in Reduced Dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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60pfo6+ujvr6ea665ho9//OOceuqp7Lnnnuyzzz7Mnj2bE088kf333x+Ak08+mb333psHHniA//7v/6auro76+np+9atfsc0223DKKaewxx57MHz4cMaMGVPUay+URTGDsRj2228/N3/+/LK2oRbWyobauE5dY/WohesM4xr//ve/85nPfCbYwV1dXmJgX583HNDY6AUBnZ0wduyA2pFNLZYYTvL7/zGzBc65/XKdUz0CIiISrrFjvdkBHR1eTsCIEV5PQAizBSR8CgREIiy+Jk7Hog66V3TTsm0LbSPbiA2u7k88UiWammDKlHK3QgJQICASUV1Lu2id3Uqf66N3XS+N9Y1Me2AanZM6Gbtr8bpXRaS2aNaASATF18Rpnd1KfG2c3nXeVKzedb3E13rbe9b2lLmFIlItFAiIRFDHog76nH9Rlj7XR8fz4RRlERFRICASQd0rujf2BKTrXdfLkpXhFGUREVEgIBJBLdu20FjvX5Slsb6REUOLW5RFJIrKtQxxUK2trbz33nt5P++iiy7iyiuvLEKLglEgIBJBbSPbqDP/P886q6NtVHGLsogMVHxNnPaF7Uz/43TaF7YTX1O5yxCnWr9+fcZ9nZ2dbLPNNmVtQyEUCIhEUGxwjM5JncQaYht7BhrrG4k1eNubGjQfW6Kra2kXzTObmXr/VGY8OYOp90+leWYzXUujsQzxAQccsNniP+PGjWPBggX09vZy0kknMWbMGPbee2/+8Ic/ADBr1iyOOeYYvva1r/GlL30p42sMHz6cd955B4Cbb76ZPffck7322ovjjz8e8MofT5gwgT333JMJEyawdOnSfm175pln+NznPseee+7JUUcdxbvvvruxjeeeey5HHHEEV111VSj/jkmaPigSUWN3Hcvys5bT8XwHS1YuYcTQEbSNalMQIJGWOuMlKZnv0jq7leVnLQ/ld3ggyxAfd9xx3HrrrVx88cW88cYbLF++nH333Zdzzz2XL37xi9xwww2899577L///hx66KEA/OlPf+LZZ59l6NCh/PSnP836GosWLeLSSy/liSeeYNiwYaxcuRLwliQ+4YQTmDx5MjfccAPf+973uPPOOzd77gknnMAvf/lLDjnkEC644AIuvvhifv7znwPw3nvvcd9994VePVGBgEiENTU0MWUfFWWRyhFkxksYv9PZliE+6aSTWLduHf/v//0/Ro8e3e+YY489lsMOO4yLL76YW2+9lWOOOQaABx98kLvuumvjeP3q1as3fmo/7LDDGDp0aKDXeOSRR5g4cSLDhg0D2Pi8P/3pT9xxxx0AHH/88Xz/+9/f7Hnvv/8+7733HocccggAkydP3tg2gLYirdOgoQERiYR4HNrbYfp07zFenCFlKbJSzXgZyDLEzc3NbLvttjz77LN0dHRw3HHHAd4Sw7fffvvGlQqXLl26sX5/6uv5vUYq5xxmlvMaghwT5JoHSoGAiJRdVxc0N8PUqTBjhvfY3Oxtl8pS7hkvQZYhBm94YMaMGbz//vsb8wwOP/xwfvnLX5JcjO/pp58O/BqpJkyYwK233sqKFSsANg4NHHTQQcyZMweA2bNnMzZtAaatt96aj370oxtzDn77299u7B0oJg0NiEhZxePeQnWpPQC9iQ+Ura3e2jVaq6ZytI1sY9oD/ssQl2LGS5BliAEmTpzIGWecwfnnn79x2/nnn8/UqVPZc889cc4xfPhw7rnnnrxfY+TIkZx33nkccsghDBo0iL333ptZs2bxi1/8gpNOOomf/OQnfOxjH+PGG2/sd+6bbrqJ73znO6xatYpPfOITvseEzjlXE1/77ruvK7e5c+eWuwklUQvXqWsMz/XXO9fY6Bz0/2psdK69vbivr//LYF544YXAxz7+2uMudlnMNV7a6LgI13hpo4tdFnOPv/b4gNuRzQcffFDU80dBpmv0+/8B5rsA90f1CIhIWXV3b+oBSNfb661iK5VFM14qiwIBESmrlhZobPQPBhobvaXspfJoxkvlULKgiJRVWxvUZXgnqqvz9otI8SgQEJGyisWgs9N7TM6OamzctF2JgiLFpaEBESm7sWO92QEdHV5OwIgRXk+AggCR4lMgICKR0NQEUzSkLFJyGhoQEZGKUOxliO+66y6uuOKKvJ8X5LVPPvlkXnjhhUKaVXTqERARkdDF495QT3e3NzOkrc3L+wjbhg0bGDRoEE8++STxAdalPvLIIznyyCP7bV+/fj1bbJH5dhlkCeT29vYBta2Y1CMgIiKhKnbJ6GItQzxr1ixOP/10AE488USmTZvG+PHjmT59Om+//TaHHXYY++yzD9/+9rf5+Mc/vnHJ4eRrz5s3j3HjxjFx4kR23313Jk2atLFc8bhx45g/fz4A999/P/vssw977bUXEyZMALzVFA866CD23ntvDjroIBYvXhzOP1YA6hEQEZHQlKpkdDGWIX7uuec2O+6ll17ioYceYtCgQZx++ul88Ytf5JxzzuH+++/nuuuu823X008/zaJFi9hpp534/Oc/zxNPPLHZmgJvv/02p5xyCo899hi77bbbxnUIdt99dx577DG22GILHnroIc4991xuv/32gf4zBaIeARERCU1HB/T5r0JMX5+3PwzZliG+8cYbueiii3juueeI+YxHHHvssfzf//0fwGbLEKc75phjGDRoEABdXV0bVyn88pe/zEc/+tGM7dp5552pq6tj9OjRvPrqq5vt//Of/8zBBx+8se3JJYrff/99jjnmGEaNGsWZZ565WY9FsSkQEBGR0JSqZHQxliHO9hrJLv5cBg8evPH7QYMGsX79+s32uwxLFJ9//vmMHz+e559/nrvvvpvVq1cHer0wKBAQEZHQJEtG+ylFyeiBLEOczdixY7n11lsBePDBB3n33XcLat+BBx7Io48+yiuvvAJsWqL4/fffp7m5GYBZs2YVdO5CKRAQEZHQlLtk9Lx58xg9ejR77703t99+O2eccYbvcRMnTmTOnDkce+yxgc574YUX8uCDD7LPPvtw3333seOOO/oOO+TysY99jOuuu46jjz6avfbai7bEP8j3v/99zjnnHD7/+c+zYcOGvM87IEGWKKyGLy1DXDq1cJ26xupRC9dZ8mWIH3cuFtu0vHRjo/fz48VdhbioyxCvXr3arVu3zjnn3JNPPun22muvor1WNlqGWEREIq8aS0YvXbqUY489lr6+PhoaGrj++uvL3aTQKBAQEZHQVVvJ6JaWFp5++ulyN6MolCMgIiJSwxQIiIhIIC7gFDoprYH+vygQEBGRnIYMGcKKFSsUDESMc44VK1YwZMiQgs+hHAEREclp5513ZtmyZbz99tvlbkpGq1evHtANsRL4XeOQIUPYeeedCz6nAgEREcmpvr7et6RvlMybN4+999673M0oqmJco4YGREREaph6BERKLL4mTseiDrpXdNOybQttI9uIDS7CQu0iIgEoEBApgeTNf+4rc7njxTuoszpWrVtFY30j0x6YRuekTsbuOjb3iUREQha5QMDMbgC+CrzlnBvls9+Aq4BWYBVwonNuYWlbKRJc19IuWme3sqFvA6vWb742eu86b5m21tmtLD9rOU0NFVx6TUQqUhRzBGYBX86y/wigJfF1KvCrErRJpCDxNXFaZ7cSXxvvFwSk6nN9dDwf0kLtIiJ5iFwg4Jx7DFiZ5ZCvAzcn1lT4M7CNme1YmtaJ5KdjUQd9ri/ncb3relmyMqSF2kVE8mBRLA5hZsOBezIMDdwDXOGc60r8/DAw3Tk33+fYU/F6Ddh+++33nTNnTjGbnVNPTw9NlbzqRkC1cJ1Br/H1+Ou82fNmzuPqrI5dPrILw7YaFkbzQlEL/49QG9dZC9cItXGd+Vzj+PHjFzjn9st1XORyBAIwn22+0Yxz7jrgOoD99tvPjRs3rojNym3evHmUuw2lUAvXGfQa2xe2c+H9F27MBcgk1hCLXI5ALfw/Qm1cZy1cI9TGdRbjGiM3NBDAMmCXlJ93BpaXqS0iWbWNbKPOMv+ZNdY3EmuI0TmpM1JBgIjUjkoMBO4CTjDP54D3nXNvlLtRIn5ig72bfKwhRmN9IwBbbbEVgwcNZtIek7jqy1ex/KzlmjooImUTuaEBM/tfYBwwzMyWARcC9QDOuV8DnXhTB5fgTR/89/K0VCSYsbuOZflZy+l4voMlK5cwYugI2ka1qQdARCIhcoGAc+7fcux3wGklao5IKJoampiyz5RyN0NEpJ/IBQI1Kx6Hjg7o7oaWFmhrg5jKzoqISHEpEIiCri5obYW+PujthcZGmDYNOjthrMaORUSkeCoxWbC6xONeEBCPe0EAeI/J7T095W2fiIhUNQUC5dbR4fUE+Onr8/aLiIgUiQKBcuvu3tQTkK63F5ao7KyIiBSPAoFya2nxcgL8NDbCiBGlbY+IiNQUBQLl1tYGdRn+G+rqvP0iIiJFokCg3GIxb3ZALLapZ6CxcdP2Kl9AQ0REykvTB6Ng7FhYvtxLDFyyxBsOaGtTECAiIkWnQCAqmppgiirPiYhIaWloQEREpIYpEBAREalhCgRERERqmAIBERGRGqZAQEREpIYpEBAREalhmj4oIgWLr4nTsaiD7hXdtGzbQtvINmKDY+VulojkQYGAiBSka2kXrbNb6XN99K7rpbG+kWkPTKNzUidjdx1b7uaJSEAaGhCRvMXXxGmd3Up8bZzedd7qmb3reomv9bb3rO0pcwtFJCgFAiKSt45FHfS5Pt99fa6Pjuc7StwiESmUAgERyVv3iu6NPQHpetf1smTlkhK3SEQKpUBARPLWsm0LjfWNvvsa6xsZMXREiVskIoVSICAieWsb2Uad+b991FkdbaPaStwiESmUAgERyVtscIzOSZ3EGmIbewYa6xuJNXjbmxpqbwnteBza22H6dO8xHi93i0SC0fRBESnI2F3Hsvys5XQ838GSlUsYMXQEbaPaajII6OqC1lbo64PeXmhshGnToLMTxmompUScAgERKVhTQxNT9plS7maUVTzuBQGpPQC9iTzK1lZYvhyaai82kgqioQERkQLF43D66fDhh/77+/qgQzMpJeLUIyAyQCqzW5uSwwGrV8P69f7H9PbCEs2klIhTICAyACqzW5v8hgP8NDbCCM2klIjT0IBIgVRmt3Z1dHjd/rnU1UGbZlJKxCkQECmQyuzWru7uTQmBfrbYAmIxb9aAEgUl6hQIiBRIZXZrV0uL1+3vp74eJk3yZgto6qBUAgUCIgWq1jK78TVx2he283r8ddoXthNfo8o46dravG5/P0OGwNVXqydAKocCAZECVWOZ3a6lXTTPbGbq/VN5s+dNpt4/leaZzXQt7Sp30yIl2e0fi23qGWhs1HCAVCbNGhApULLMbvqsgTqrq6gyu8npj4veWsSv5v+KNRvWbNyXHPpond3K8rOWV8w1lcLYsV73f0eHN0VwxAivp0BBgFQaBQIiA1DpZXbTpz9mkkx+rPUqgumammCK/kmkwikQEBmgSi2zmzr9MRclP4pUL+UIiNSobNMf01Vy8qOIZKceAZEa4FcGOdv0x3R+yY8qrSxSHRQIiFS5TGWQ/2O//6CxvjFrMJAp+TGs0soKJkTKT4GASBXzywNI3vivnX8thvk+b8gWQ9i+cXuu+vJV/ZIfs50zn9kFWqdBJBqUIyBSxbLlATjnOG3/04g1xDYWRmqsbyTWEOOPx/+RnT+yM1P2mdLvph5GaWWt0yASHeoREKliucogG5Zx+uO8l+cVdM4gswuCBBOVOBNDpBIpEBCpYskyyH437uRMgHynPwY5Zy5ap0EkOjQ0IFLFilEGOYxzVus6DSKVSIGASBVLlkH2ywMotAxyGOesxnUaRCqVhgZEqlwxyiAP9JzVsk6DSDVQICBSA4pRBnmg56z0dRpEqoUCAREpm0pdp0GkmigQEBHJIR73lhvu7oaWFm+54ZgKIEqVUCAgIpJFVxe0tkJfH/T2QmMjTJsGnZ0wVgUQpQpo1oCISAbxuBcExONeEADeY3J7jwogShVQICAiGcXXxGlf2M70P06nfWE78TXx3E+qIh0dXk+An74+b79IpdPQgIj46lnbQ/PM5ppeFKi7e1NPQLreXliSpQDi8uVwzjnw4ouw++4Gnj4MAAAgAElEQVRw+eWw007FaafIQKhHoNzicWhvh+nTvcd4bX3ikmiKr4nTvbK75hcFamnxcgL8NDbCiAwFEK+9Fpqb4eab4amnvMfmZm+7SNQoECinri7v3WHqVJgxw3tsbva2i5RRx6LMfd5BVxisBm1tUJfhXbKuztufbvlyOO00/+ecdhq8+WZ47RMJgwKBclEWkkRY94rujKsD1tKiQLGYNzsgFtvUM9DYuGl7k0/to3POyX7Os88Ov50iA6EcgXIJkoU0RYVWpDxatm0hvsJ/mCrXokDxNXE6FnXQvaKblm1baBvZRmxw5U66HzvW+5Tf0eHlBIwY4fUE+AUB4OUEZLN4cfhtFBkIBQLlMpAsJJEiaxvZRvtL7b77si0K1LW0q9/6AVFKMPQLUoJoagoel+++u5cXkMmnPx3sPCKlokCgXJJZSH7BQLYsJJESiA2O0TK0hVhDLPCiQPE1XiJhfO2mnoRkomHr7FaWn7W8rOsIZApSfrfv70J9ncsv95IDM7niik3fq2KhRIECgXJpa/PKk/nJlIUkUkJNDU15LQrUsagjY15BMsGwXOsKZAtSuld207O2J7QgZaed4Jpr/BMGr7kGdtjB+14VCyUqFAiUSzLbKP2doK4ucxaSSInlsyhQ94rujTfXdOVOMMwWpAChBynf/S4cfbSXGLh4sTcccMUVm4KA1FzhpGTnYGurl5OgtwApFQUC5ZRvFpJIhLVs20JjfaNvMJArwbDYsgUpfa6vKEHKDjvArFn++5QrLFGiQKDc8slCEomwtpFtTHvAf7grW4JhKWQLUuqsruRBinKFJUpURyBfqgQo4is2OEbnpE5iDTEa671J9431jcQaYtx27G3MeX5O2dYsaBvZRp1lfrsrdZBSaMVCvf1IMUSuR8DMvgxcBQwC2p1zV6TtPxH4CfB6YtPVzjn/eU5hU3aPSFZjdx3bL8Fwl613YeKtE8s6pTAZpKTPGqizOlqGtpR8NkMhucJ6+5FiiVQgYGaDgGuAw4BlwF/N7C7n3Atph3Y4504vaeOU3SMSSGqCYXxNnOaZzZGYUugXpLSNamP+k/NL8vqp8s0V1tuPFFPWQMDMvgqcCWwHvABc45x7LO2YA4AnnXODQmjP/sAS59zLiXPPAb6eeO3yGmh2TzwO77zj9elpwrDUiIFMKSxGhcJ8ZkEUWz65wkoulGIy55z/DrPDgPuBPwNPAwcCo4GfA//lEk8MMxAws4nAl51zJyd+Ph44IPXTf2Jo4HLgbeAl4Ezn3D8znO9U4FSA7bffft85c+YU3rjXX8++WsgOO3gLBvnp6YHubnqam2n65z83rWLS0lKVYXxPTw9NVXhdqXSNwbwef503ezL/3ezQtAPNsf5/Nz1re+he2Q14AUNyfL8Y3fiV8H85kLcfqIxrDEMtXGc+1zh+/PgFzrn9ch7onPP9ArqAG9O2nQT0AL8HhiS2HQBsyHSefL6AY/DyApI/Hw/8Mu2YbYHBie+/AzwS5Nz77ruvG5Drr3eusdE56P/V2Ohce7v/8z74wLlYzDlwc6+8cvPnxWLOxeMDa1cEzZ07t9xNKDpdYzDXL7jeNV7a6LiIfl+Nlza69gX9/24+WP2Bi10W831O7LKYi68J92+mEv4vC337SaqEawxDLVxnPtcIzHcB7o/ZZg2MAm5JCxpuAA4BPgc8YmZDg0QleVgG7JLy887A8rQ2rHDOrUn8eD2wb8ht8FfIeqQQrE9PpEply9bPNKUwyHBCrSn07UckiGyBwGqg3wQX59wC4PPAx4Angd1CbM9fgRYz283MGoDjgLtSDzCzHVN+PBL4e4ivn1kh65GCJgxLTcs2pTDTmgVRrlBYLoW+/YgEkS1Z8FngCNJuxADOuZfN7PNAJzArrMY459ab2enAA3jTB29wzi0ys0vwujjuAr5nZkcC64GVwIlhvX5OhVQC1OJCUuMyZetnGuuPcoXCclIhUimWbIHA7cC5ZjbUObcyfadz7i0zOwQvX+DQsBrknOvECzBSt12Q8v05wDlhvV7e8q0EqMWFRPLK1o9yhcJyUyFSKYaMQwPOud845z7uFwSkHNPrnPuSc04VCjNJ7dNLDvKpT08ko0KGE0SkcJEqKFS1kn1699/vLUemPj2RrPIdThCRwikQKJWmJhg2DC6/vNwtEakIUSr+k49iFEISKSYFAiISeZVyc+1a2tVvPYNSr6sgki8FAiISaZVyc42vidM6uzUS6yqI5ENJfiISiviaOO0L20Ndajj15pq8qfau6yW+1tves7ZnwK8RFhVCkkoVKBAws0fMbPcM+z5lZo+E2ywRqSRdS7tontnM1PunMuPJGUy9fyrNM5vpWto1oPNW0s1VhZCkUgXtERgHfCTDvo8AB4fSGhGpOMX81F5JN9dkISQ/tVwISaIvn6GBfssUJsoAfxHIsi6WiFSzYn5qr6SbayHrKohEQcZAwMwuNLMNZrYBLwj4c/LnlO0f4i0JfEum84hIdSvmp/Z8b67FyFMIKmghpHgc2tth+nTvMV66Jor4yjZroBN4BzDgF8BPgVfTjlkLvOice7worRORvJRjml0x1wZI3lzTZw3UWV2/KoNRmF2QqxBSVxe0tnoLj/b2ekVGp03zioyOjc4ECKkxGQMB59xf8VYDxMziwL3OuXdK1TARyU+5boTFXhsgSJXBKE3dy1QIKR73goDUHoDkWmStrV7xURUblXIIlCPgnLtJQYBIdJVzml0p1gZoamji2JHH8smhn+SlFS8x5/k5m3X7V8Lsgo4OryfAT1+ft1+kHAIVFDKzeuAM4GhgZ2BI+jHOue3CbZqIBBXkRljMcr1+n9pbW1q5t/te7l5894CHKXL1dlTC7ILubv/VyMHbvqT8TZQaFbSy4M+AbwP3AHPxcgNEJCKicCNM7RLvWtrFp6/+dCjDFEG6/YuZpxCWlhYvJ8AvGGhs9NYiEymHoIHAMcDZzrmfFrMxVSse9/r9ttzSSxNua/OWIRYJSRRuhMlExeffep7fLPgNq9ev3rhvIOP1QXo7ip2nEIa2Ni8x0E9dnbdfpByC1hEw4NliNqRqdXVBczNMnQpvvuk9Njd720VCUu457KmVBa/6y1WbBQGpChmvD9LbUYo8BT/5TFeMxbzZAbGY1wMA3mNyuxIFpVyC9ghcD/wb8McitqX6KE1YSiSfaXZh8+u6z6SQYYqgvR1BZheEqZBZGmPHen/2HR1eTsCIEV5PgN4GpJyCBgL/AiaZ2Vy8YOC9tP3OOferUFtWDYKkCU/JkcCVHFbo7vYGGTWsIBmU6kaYXqtg9frVGbvu0xUyTJFPt3+mqXthG8h0xaam3H/2IqUUNBD4eeJxV+AQn/0OUCCQbqBpwqo+Inkq9o3Q71Pwug3rWNsXLH+4kGGKcvZ2ZFLuWRoiYQoUCDjntFxxIQaSJqxhBYmYbJ+CcxnojbvU3f65RGGWhkhYgvYISCEGkiYcxrCCSIiyfQrOZPCgwZy2/2l8dthnB1xXoFTd/kFEYZaGSFgCBwJmth1wFrAfsAtwlHNukZmdATzlnPtTkdpYuZLpwMnuffB6AurqcqcJq/qIREy2T8EA9XX1NAxq6Nd1P3bXsaHWFYiCbHkLtvYjfPjUJKZ3KK1HKkPQyoL74yUJvg08CowDBid274gXIEwsQvsqX2qa8JAhcNVVwdKEVX1EIibXp+AfH/Zjhgwa0q/rPkrrAIQlU95C32sH0Te7k7PZQmk9UjHyqSw4F6/EcB3w7yn7ngK+GXK7qksyTXjePBg3LthzVH1EIiZX9v7kvSb73tCrNbEuPW9h58Gf4ewrjqen1zYeo7QeqQRBA4F9gK875/rMzNL2rQC0zkDY0ocVkh8vggwriBRBkOx9v2WQqzmxLjVvob0dMqVQKK1HoixoIPA+8LEM+z6BV2dAwqbqIxIx2bL3MxXY+Y8x/1ETiXVK65FKFTQQ+ANwsZn9CXgtsc2Z2TDgv4A7itE4QdVHJDR+n9YLWQ3QL3s/Wx7AtU9dS/+ORE9U1gEIg9J6pFIFDQTOBh4GXgAWJLb9GhgBvAJcEH7TZDOqMCgDUEg53HxkywNwOE7f73SunX9tZAoCFUO1p/XoLah6BS0o9K6ZfQ44HpgA9AIrgXbgZufcmuI1UVRhUAaiFFn7ufIAzCxSBYGKoZrTevQWVN0C1xFwzq0F/ifxJaWiCoMyQKXI2g9SYCdKBYGKpRrTevQWVP3yrixoZlsADenbnXOrQmmRbN4H9+absGGD/3FKRZYASpG1n8/CQNWu2tJ6VOS0+gUtKPQR4DK8OgLbAX6ZP4NCbFftSd78586F22+HQYNg1SrYYgtYv97/OUpFlgBKUQ43igsDVauwx+pznU+zIapf0B6B3wBfxcsJeAEIttSYBJMcgNuwwbv5p8oUBIBSkSWQUn1a95taOND1BWRzYY7Vx+Pwox/Bz38OZrBmjf/5NBui+gUNBA4HznTOtRezMTXJbwAuqGpIRZaiK+Wn9dQ8gGpbXyCoYmXXhzlW39UFRxwBPT2bb/c7X7XPhpDggUAvsKyYDalZ2Qbg0tXXw7p1/VORNa9Hcij1Mr7VuL5AEMXMrg9rrD4ZUKQHAZnOV82zIcQTNBD4KfBdM3vQuTzXIZXssg3ApdpqKzjmGNhxR68vrrUV7r0XfvUruOMO769y1SrN65GMSpm1X63rC2RT7Oz6sMbqg3z2SD9fNc6GkE2CBgLNwF7AYjObC7yXtt8556aH2rJakW0ALtWgQXD11d5fXlcXfPrT/jkFmtcjERC19QXCqqqYTbGz6/Mdq0/tKBwzxvs5Fgv22cPvfNU2G0I2CRoITAT6Escf5rPfAQoECpFtAA68noBBgzYfBgiSU6B5PVJGpZipEFQxqir6jcYVO7s+n7H69CGKmTOhudl7Gwny2UNj/7WlLshBzrndcnx9otgNrVrJAbhYzPvrBO9xyBCYNAl+8Qvvk/1ee3nLmx1zDKwNMGlD83qkjNpGtlFn/m8vpawrkJqrkAxKetf1El/rbe9Zm2WgPIOuLu+mOnUqzJjhPTY3e/uSf8Lpwsiuz/RWkdye7PxL/ayQvNn39W3a/pWveDf6TJqaNPZfa/IuKCRFkGsALj28D0LzeqSMylVXIH0IYPX61TlzFT7JJ7OfM+XT/y67wDnnbJ5ol/yTvPZabxqen7A+YQcZq881RNHZ2T/5r6EBnPN6HH7wAwUBtSZwIGBmnwD+GxgLDMVba+Bx4Ern3MvFaV4NyTQAV+j0QvXtSZmVeqaC3xDAug3rWNvn34OWzFX45BaZA4H0GHzwYG++vR/n4PTTvYCgmNn1ucbqgwxRTJmi5D/ZJGhlwX2BucBq4B7gX8D2wDeASWY23jm3sGitrGX5TC8EzeuRSCnVTIVs0xUz2Zir8EGGc/rE4JmCAPBusmblv8EGTSpU8p8kBe0RuBJ4GjgidU0BM9sK6Ezs/2L4zZNAKb5bbeXNIJg4EcaPV2gvNSfbdMVMkrkK85+c73/OAmLwESM2v8HG4zBnTmlLfKgAkOQraCCwP3Bs+sJCzrlVZnYl0BF6y2pFrmJA2cL7hgaYMAG+8Y3Nb/7xuJdYqAJDUiOyTVcEqK+rp2FQQ165CkFLfCTlytwvVYkPvwJAdXX9kwpFkoIGAh8C22bYNxRvyEDyFeSdIlt4P3gw3Hrr5n/ZWjhcalCu6Yo/PuzHDBk0JK9chVzT7BoavAk8fqNx5V66Nz2pcJddVFZEMgsaCNwLXGFmLzvnupIbzWwscDlwdzEaV9WCvlPkU9+z3O8+ImWSa2GlyXtN3uzGH18Tp31hO90ruhmzbgzxNfF+BYayxeBNTXDFFbBsWWGZ+6Uo8ZE6RDFvnv70JbNAdQSAacDLwKNm9qaZ/c3M3gAeTWw/q1gNrFpB3imSkuH9VVfB2Wd7j8uX9/+En885RapIcrpirCFGY703yb6xvpFYQ6zfEEDX0i6aZzYz9f6pzHhyBv/84J80z2yma2nX5ufMMm//vvvgtNPg3HO92QI//KE3GpeMwbV0r1SSQD0CzrkVwFgz+zIwBtgReAP4i3PuwSK2r3rl+06RDO9feglOPNGb7LvbbjBrFnzqU4WdU6SKBJmu6De7oM/1bSwwlL4YUrZ5+9lG4bR0r1SSvAoKOefuB+4vUltqSyHvFNOmwc9+tunnN9/01hw480yvhqjefaSChbEeQK7pioUshuQ3zS7XKNzixcrcl8oRdGgAADP7kpn9wMyuSTz6rTsgQbS1Za7z6fdO8dJLmwcBqX72M/jHP/I/p0hEpHfXT71/qm93/UCFtRhS0Op9ucoBi0RBoEDAzHYys7/g9QacDnwh8fiAmT1lZs1FbGN1Clo4POnEE7Of74QT8j+nSAQUYz2ATJKzC/zksxhSkFG4oKk9IuUWdGjgOry8gLHOuSeTG83s88D/Ar8Bvhp+86qc3wBkayvcey/cfffmNQBeeSX7uV59NfM5VWBIIqyQ7vpC5ZpdkFwMKdcwhar3STUJGgh8ETgpNQgAcM49YWZnA9eH3rJakfpO0dXljfn7ZR/ttpuXE5DJ8OH+5xSJuLC664PwWwypzuo2m10QZNliVe+TahI0EPgXXlEhPx8C74TTnBqWK/vo0Udhn30yP//mm4vbPpEByPYJO1cxoKDd9UGlzy7YZe0uG2cLZFuzIHVWQT7lPUSiLmggcBlwiZktcM4tS240s52BC4FLi9G4mpIr+2jhQm92gF/C4JlnwiezL6UqUi65PmEH7a4PU+rsgnnz5m2cMpjPMIVG4aRaBA0EvoRXYvgfZrYQeAvYDtgn8f2hZnZo4ljnnFPHWL6CZB/NnOlVMTnhBC8nYPhwrydAQYBEVJBP2H7d9UHXAwhbvsMUGoWTahA0EBgGdCe+AD6Ct75AMmfgYyG3q/YEzT765CfhiSdK2zaRAgX9hB2kGFAplHqYQiQKglYWHF/shtQ8ZR9JFcrnE3auYkClUI5hikqSa7FUqUx5VRaUIlL2kVShKHzCzqdiYZSGKaJGC5tWr8CBgJntBHwNaAaGpO93zn0/xHbVplJmHym0lxIo9yfsIFMB00VlmCJKtLBpdQsUCJjZccBNgAFvA2vTDnGAAoEwlCL7SKG9lEg5P2EHnQroJwrDFFEShWWVpXiC9ghcCtwOfMc590ER2yPFptBeSqxcn7BLWbGw2hWysKk6HStH0EBgW+B/FARUAYX2Ugbl+IRdyoqF1S7fhU3V6VhZgq4+eAcwrojt2MjMvmxmi81sSaJ8cfr+wWbWkdj/FzMbXop2VY1CQnuRChTWAkOS38KmqZ2Oybea3t5N23vCW0NKQhI0EDgdGGFm7Wb2TTNrTf8KozFmNgi4BjgC+Czwb2b22bTDpgDvOudGAD8DfhzGa9eMZGjvxy+0F6lQbSPbqDP/tzhNBcxPPgubBul0lGgJOjTwKWB/YDfgJJ/9DhgUQnv2B5Y4514GMLM5wNeBF1KO+TpwUeL724Crzcyccy6E169+qlcgNUJTAcMVdFKTOh0rT9BA4EbgA+ArwBL6zxoISzPwz5SflwEHZDrGObfezN7Hy2GovYWPCsnGUb0CqUD51AJIpamA4QoyqSnffAIpPwvyQdrMeoGjnXMPFLUxZscAhzvnTk78fDywv3PuP1OOWZQ4Zlni538kjlnhc75TgVMBtt9++33nzJlTzObn1NPTQ1NYN9qeHi8AAO+GnhzAa2kJdjPv64OVK2HNGhg8GIYOzTwImHfTQrzOiNI1lrAda3voXun9rve5vo3d/S1DW0K5oUflOouplNfY1wd/+5v/8EBdHey1V2hvNf3o/3Jz48ePX+Cc2y/XcUF7BJ4Cdg147EAsA3ZJ+XlnYHmGY5aZ2RbA1sBKv5M5564DrgPYb7/93Lhx48Jub17mzZtHKG2Ix6G5efMpgEmxWNmnAIZ2nRGmayyN+Jo4zTObN6sFkBRriGWtBRBUFK6z2Ep9jQ0NmTsdizlrQP+XhQkaCEwDZpnZh8AjwHvpBzjnVoXQnr8CLWa2G/A6cBzwzbRj7gImA38CJgKP1Fx+gKYASo1QLYD8+Y0YlpqWaK4sQQOBBYnHm7IcM+BkwcSY/+nAA4nz3eCcW2RmlwDznXN3Af8D/NbMluD1BBw30NetOMrGkRqhWgDBxePwox/Bz34GZrB27ab5+7/7XenboyWaK0fQQOAkvJkBReec6wQ607ZdkPL9auCYUrQlspSNIzUiCosWVYKuLjjiiP5z9JNvEd3d3j59Ihc/QZchnlXkdkg+NAVQakS5Fy2qBEEL9WjEUDLJK3fTzHYys2+Y2SmJx52K1TDJIp/qHiIVLFkLINYQ21glsLG+kVhDTLUAErKlDCX19WnEUDILuvrgIOCXwClsnguwwcyuA/7TuQwZPVIcysaRGlHKWgCF1isop2wpQ0l1dRoxlMyC5ghcjJcncC7QAfwL2B5oAy4BVgAXZHy2ZFfoMl3KxpEaUYpFi7qWdvWrQjjtgWl0Tupk7K7lXykn09tEtpShVBoxlEyCBgInAD9wzl2Zsm0p8BMzc8D3UCBQGC3TJVJ28TVxWme3blavIJmg2Dq7NZR6BQOR7W0iW8oQeJ8XgtYZk9oUNEdgO+DZDPueTeyXfGmZLpFICFKvoFxyvU2Y9U8ZGjzYK+ozfTq88YaCAMkuaI/AS3jz9R/02XccsDi0FtUSFQYSiYQo1ysI+jahlCEpVNBA4EfAHDPbFW/Fv3/h9QIcA4ynFov6hCEqhYEKzVEQqRJRrlcQ9G1CKUNSqKB1BG41s/fwkgavAuqBdXgVB7/snPtj8ZpYxfIpDFSsm7VyFEQiXa8g6NuE4nkpVOA6As65B51zBwJbAjsAWzrnDlIQMABtbZmX4UotDNTV5S0yNHUqzJjhPTY3e9sHQjkKIkC06xUEeZvo6oKddoLTT/feIk4/3ft5oG8RUhuy9giY2R7Au8klfwES9QLeSuxvBoY6554raiurVbIAUKZlupqaNr9ZJyVv2q2tA1tpUDkKIhuVsl5BPnK9TTgHhx8Oq1KWfVuzxvs6/HD417/K13apDBkDATP7EvAHYAze0r9+Pgr8xcz+zTn3hyK0r/rlKgxUzJt1VHIURCKiFPUKCpHtbeLqqzcPAlKtWgU33QQjR5a2vVJZsvUITAVudM49n+kA59zzZvY/wHfwgobaEPZgXLYsn4HerLO1VYsXiVSMTG8T99yT/Xn33ps9EFBugWQLBD4HXBPgHPcDN4fTnApQ6uS6gdysc7VVixdJharEUsBRpFxhgezJglsBHwQ4xweJY6tfOZLrgiYUFtJWLV4kFahraRfNM5uZev9UZjw5g6n3T6V5ZjNdS2szM+6rX82+/ytf8d+uXGFJyhYILAM+E+AcnwVeD6c5ERdkvD5shd6sg7Y1Ofh41VVw9tne4/Ll+jggkZRaCjg55793XS/xtd72nrW1d/eaPBm23NJ/35Zbevv9lOPtTKIp29DAPcBZZjbbOec7SG1mTcCZwN3FaFzklCu5LlOmkHPQ3u4/uJdPW1WJRCpEkFLAUUz2K6ZYDB58EI44Atau9b4aGryv++7L/FlBucKSlC0QuAyvcuCTZnYO8LBzbg2AmTUAExLHNAGXF7uhkVDO5Lr0m3WuwT0lAkoVinIp4HIaO9ZbUyCfEsN6i5CkjEMDzrm3gC/iVRC8B4ib2etmtgyIA/cC64EvJo6tfoWO14ctyOBeVNoqEqJkKWA/5S4FXG7JzwqXX+495krxyectIh73Oh+nT/ceU8uaSOXLWlnQObfYObcfMA64BLgLbxjgh8DBzrkxzrmXit7KqIhKcl2Qwb2otFUkRG0j26gz/7etcpcCjoqgN+2gbxHFKmwq0RF0rYHHgMeK3JbKkKsAUCkEHdxLb+vOO3t5BXffDS++qAnDUnGSpYBbZ7fS5/roXddLY30jdVZH56ROnHO0L2yv2WmFmUYMf/c7/+NzvZ0Vs7CpREfQ1QclVbmT6/IZ3Eu2VROGpUpkKgX8zJvP0DyzebMAYdoD0+ic1MnYXav/dzzbTbu72xsx9LtpZ3s7UxXy2hB40SGJkHzH/zVhWKpMshTw5YdezpR9puCcq/lphdlu2sn9+dLMgtqgQKAS5Tv+rwnDUuWCTCusdtlu2n192W/amfIKkp2PfjSzoHpoaKBS5ZOroLBeqpymFWYfMayry3zTzjZqqCrktUGBQCULmqugCcNS5ZLTCv2CgVzTCvtcX1UkGGa7aSf3pwuSDJhrpXSpfNmWIW7N50TOuc6BN0cKkmv5MIX1UuXaRrYx7QH/3/Fs0wq7lnbxt3/9jfP/dH7FJxgmRwb9btotLf437aDJgOWeKCXFlavEsAMswHkcMCiUFkl+gswGyPYOobBeqkCuaYVNDf1/x5PrFlw4/MLNEgwBWme3svys5b7P8xPmaogDWRY404jh/Pn+xwcdNSz3RCkprmyBwG4la4UUJp9JvlGofyBSRJmmFWa6mYe1bkHX0q5+AUihvQphzPLN56atUUOBLIGAc+61UjZECpDvJF+F9VLlktMKgwgjwTB1NcTU50IBvQplKN6jUcPyGUjPT9jymj5oZluY2SfM7LPpX8VqoGSh2QAiBQtj3YIwpy1W0irnMjBRK9scaNaAmdUDvwAmA4MzHKYcgTAFCRfVrydSsEITDFMNpFchPa9g0YvH09vr//ZajlXOFQQURxTLNgedPngB8FVgCjAbOA3oBb4FfBL4z6K0rlYFHShUv55IwZIJhn998q8bpx7mSjBMV+i0Rb+8gvUvP8OQra5i9ar+n6lKvcp5mKLUBR4FUSzbHDQQOBa4CLgVLxB4yjm3ALjZzG4Cvg5o+mAY8gkXNRtAZEDG7jqWtf9Yy1WfuoolK5ew80d2xuG4e/HdvPjOizmz/wvpVciYV7D7TdB5OdD/9So1rtcSJ/1FcUQ3aCCwC/CSc9KvlnYAACAASURBVG6Dma0GPpqybzbwO+DbYTeuJuUbLqpfT2RA6qyOKftMKSj7v5BpixnzCgb3MOSEo2H2vQyyhoqP66PYBR4FURzRDRoIvAFsk/j+FeBg4KHEz58Mu1E1rZBwUbMBRAZkINn/+U5bzJZXsLr5IabNuZTPvnVxxcf1UewCj4IojugGDQTmAV8A7gauB640sxHAGqAN+N+itK4WRTFcFKlyA60pkM+0xVx5BZ9t3pUpXwvW7nLLNv4fxS7wKIjiiG7QQOA8YBiAc+7nZmbARGBL4JfAJcVpXg2KYrgoUuVKuWhRGLMVoiDX+L8+02QWtRHdQIGAc+5N4M2Un38G/KxYjappQcLFeBxuugnuucd7zle/CpMn13YqrkgO2coAD2TRonwVklcQNUHG//WZJrsojejmtfqgmW0DjAJ2BJYDi5xz7xWjYTUtU7jonLdg+MyZsH79puMfeMDb/sADtZuKK5JFtkRAKP2n9HzzCqIm6Ph/1LrAxV/QgkJbAJfi1Q/YKmXXKjO7FjjPObeuCO2rXanhYjwOP/xh/wAg1apVcMQR8MYb+gsTSbH8g+UcevOhrNmwZuO21ETAOz93Z1k+peeTV1AumXIAgo7/R60LXPwF7RGYCZyKlwtwB/AWsB3wDeB8YAjwvWI0sOZ1dXk3+J6e3MeuW1e7qbgiPrqWdnHYbw/bLAhI1ef6WPnhSqDyP6WHLVsOQD7j/1HqAhd/QQOB44FznXMzU7atBC5N1BX4AQoEwpcciAsSBACsWVO7qbgiaZJTAlevX53xmN51vZsFCZXwKb0UcuUALF5c2Pi/qgxGU9BAoA9YlGHf84ALpzmymWwDcX4GD67tVFyRFNmmBCY11jcyeFCm5VNqV64cgM7O/Mf/w6wyqIAiXEEDgd8CJwMP+Ow7BbgltBbJJtkG4vzU1ysVVyQh25TApDqrY+iWQ0vUosoRJAdgypTg4/9hVhnMFlBIYYIGAq8B3zCzRcBdbMoR+DpeYeyfmtl3E8c659yvQm9pLco2EJduq63gvvuUhSOSkG1KIMDgQYPpnNTJ+pczJODWsKA5AEHH/8OqMpgroLjzztznkP6CBgI/TTw2A5/x2Z+aO+AABQJhyDYRF2DQIBgzBr71LTj6aLj3Xrj7bvWViZB9SuCQLYbwyhmvsEPTDsx7eV5pGxYBubrWw64BMJAqg6ltffNN2LDB/7i+Pli5Mr92iSdoQaG6YjdEfPgVFxo82KsncOaZ8IMfeCF5Vxd8+tNa4kskRa4pgTs07VDuJpZFkLH6fMrgBhmvL7TKYHpb6+u9yVF+enu9fGnJX14FhaQMck3E1RJfIhlpSuDm8nm7CFIDIGgCYCE9DH5tzRQEgPfag5X3WZCMgYCZfRb4h3NuTeL7rJxzL4TaMtkk20CclvgSyUpTAjfJ9+0i21tPPkFFIQvt5Dtpqq4OhirvsyDZegSeBz4HPEX2KYKW2Dco3KZJIGEs8aW5OCI1IcwVAfMNKvKtMphr0tQWW3iFVlMDikyFVyW7bIHAeOCFlO8liga6xFeYk3tFqly2hYsqQZgrAhYSVORTZTBXWydOhB133DygmDcvcPMlRcZAwDn3qN/3EjEDSe9VfoFIYNkWLhq7azSC5lLOBij2MsO52nr11Xp7Ckug2QBmNsHMTsyw70QzU49BuSQH32Ix768PvMfk9vT03vZ2b6XC9nZvKeNcfXsisrFccXxtfGNdgt51vcTXett71gYsA15EXV3Q3AxTp8KMGd5jc7O3PSmft4tc2tq8G7KfMJYZDrOtkl3QWQOXAr/PsG8Y8G3gwFBaJPkrNL133TpYu9b/nPkOGIpUsWzlivtcHx3Pd5Q1ITGfQjthrQhYSAJgvrR6YWkEDQRGAudl2Pc03gqEUk6FpvdmEkbfnkiVyFauuHddL0tWljdozpW4l15oJ6wVAUtxo9bqhcUXNBBYD2SamLFtSG2Rgco0QJjvPBwIp29PpEpkK1fcWN/IiKHlDZpzJe4Vs9CObtSVL2gg0AX8t5n9wTm3sS/ZzBqAs4DHi9E4yUO27P9c83Dq66GhoX/fnnNeLoGmFUqNy1auuM7qaBtV3qA5V+KeCu1INkEDgfPwgoElZtYBvAHsCBwLbA0oHiynXAOEl12W/V3ixz+GIUM279t75hkv00jTCkVylisud6XCXBn2KrQj2QRda+BZMxsDXAQcjzccsAJ4GLjYOfdS0VooueUaIDTLnt47eXL/2QWaViiymSiXK86VuFeMQju1XIes2q498FoDzrnFwL8VsS1SqFwDhMuW5Zfeq7LFUoXCKAYU5XLF2RL3wi60U8t1yKrx2rXoUDUIUtkjn/TeMOuQikRAtmJA1aQUiXu13GFYrdceeHlhM5toZr8zs8fM7Kn0r2I2UnIIWtkj+S5x+eXeY6bf2GRg4UfTCqXC5CoGlKk+gPgL0mFYrar12oNWFrwIuBX4DPBPYJHPl5RL2CW4il0yTKSEchUDWvnhSt994q+WOwyr9dqDDg1MAa5wzp1bzMbIAIRZ2aMUJcNESiRXMaA1G4o4yb4KFXuNgSir1msPGgjE8GYIFI2ZDQU6gOHAq8Cxzrl3fY7bADyX+HGpc+7IYrarooQ5QKjanlIlchUDGjxIk+zzEebCRZWmWq89aI7AHODLxWwIcDbwsHOuBS/oODvDcR8650YnvhQEFFPQnAKRCGsb2Uad+b/V1VkdQ7cs7iT7+Jo47Qvbmf7H6bQvbCe+Jp77SRFWy4sBVeu1B+0ReBj4sZkNA/4IvJd+gHNuoOm3XwfGJb6/CZgHTB/gOWtPtU1wFRmgXMWA1r9chEn2CZWwdHEharnDsBqvPWggkMyFHA5M9tnvgEEDbMv2zrk3AJxzb5jZdhmOG2Jm8/HWP7jCOXdnhuNqR/LmP3cu3HGH10e1alV1THAVCUG2YkDzXp5XlNdMna2QlByeaJ3dyvKzlkeiGFGhanmNgWq7dnPO5T7I7OO5jnHOvRbgPA8BO/jsOg+4yTm3Tcqx7zrnPupzjp2cc8vN7BPAI8AE59w/MrzeqcCpANtvv/2+c+bMydXEourp6aEp7LCxp8f79A+Z57XU1cFee2WeCRCyolxnxOgaq0exrvOdVe/wzw/+6Ttjoc7q2OUjuzBsq2Ghv64f/V9Wj3yucfz48Qucc/vlPNA5F4kvYDGwY+L7HYHFAZ4zC5gY5Pz77ruvK7e5c+eGe8IPPnAuFnPOWx4o81djo3Pt7eG+dhahX2cE6RqrR7Gu8/sPft9xERm/zv7j2UV5XT/6v6we+VwjMN8FuD9m/IhoZlulfp/rK1B4kt1dbBp2mAz8wadNHzWzwYnvhwGfB14I4bUrU9DlhSt5gqtIhUrOVvAThaWLRZKy9RXHzWz/xPc9QDzH10BdARxmZt3AYYmfMbP9zKw9ccxngPlm9jdgLl6OQO0GArmWF06q5AmuIhUq12yFci9dLLnF495K7NOne4/xyp7wkVG2ZMGTgOTY+78XuyHOuRXABJ/t84GTE98/CexR7LZUjGzVLVJV8gRXkQoV9aWLJbtqXFwok4yBgHPuJgAzqweWAK8455aXqmESQLbqFqBqgCJlFuWli8uhUmY3V+viQpkEmT64AS87vxVQIBAlfqWAt9oKNmyAiRNh/PjKn+AqUuGivHRxKVXSJ+xaW4k9ZyDgnOtLjNtvX4L2SL6qsbqFiFSVSvuEXa2LC2UStKDQeXiVBZ9zzj2X82gprWqrbiEiVaXSPmFX6+JCmQQNBH4AbAs8Y2avA//Cqya4kXNuf78nSglVygCciNSUSvuEXa2LC2USNBBYBDxfzIbIAFXSAJyI1JRK+4RdayuxBwoEnHMnFrkdMhCVNgAnIjWlEj9h11L6VdZAwMy2xJstMBx4A2+Z4H+VoF0SRHIo4LbbYO1a/2OiOAAnIjWlUj9h10r6VcZAILGoz0N4QUDSB2Z2rHPuwWI3THJIHwrIJIoDcCJSc2rpE3alydYjMAPoA74ALAB2A64FfpP4XsrFbyggkygOwIlITaqVT9iVJttaAwcCP3DOPeGcW+2c+zvwbWBXM9uxNM0TX0EXG4LoDsCJiEgkZAsEdgReTtv2D8CAHYrWIsktyGJDjY2bBubU9yYiIhnkmjXgcuyXcsg2F6ehASZMgG98QwNwIiKSU65A4AEzW++z/eH07c657cJrlmSVbS7O4MFw663gHMyZo+JCIiKSVbZA4OKStULyk2suzjPPqLiQiIgEkm0ZYgUCUZZpLo5z0Nys4kIiIhJI0BLDEkV+c3Ha2ytrdQ8RESmrbLMGpBJV2uoeIiJSVuoR+P/t3X+UXGV9x/HPJ0AI3V1b+WHkl6JmawsRFdMoJccmiIpbjogFVkWrbVpaWxAbqELpacVftaIVjnKqaBE9UrL+QpFE+SUrxgoYFJWAmBUR4qIBori7EhLcb/947rCT2dkfs+zMnbn3/Tpnzubeeebe7zOb3fnufb73eYqm01b3ADrUyKMjGtg0oM0PbVbvPr3qP6xfPXtSkNsOWIi1MSQCRdOJq3sAHWbDvRvUd1mfxmNcYzvH1LVHl9ZcvUbrT1mvFU+jIDdPLMTaOIYGiqZyR0FPT/oJkJhcCJhHI4+OqO+yPo3sGNHYznTlbWznmEZ2pP2jO0ZzjrC8xscnZl+vXBQdG5uYlX2Ub01dJAJFVLmj4MILpbPPTl+Hh0mHgXkwsGlA41G/IHc8xjVw+0CLI0LFtm0z10pjMoYGiorVPYCm2PzQ5sevBNQa2zmmoW0U5Obl0UeplZ4LrggAQAN69+lV1x5ddZ/r2qNLS/amIDcve+45MSJai1rpqZEIAEAD+g/r1wLX/9W5wAvUv5SC3LzsvXeqia6HWumpkQgAQAN69uzR+lPWq2dhz+NXBrr26FLPwrS/eyEFuXmpzLJOrXRjqBEAgAateNoKDZ85rIHbBzS0bUhL9l6i/qX9JAFtYKrZ10kCpkYiAABz0L2wW6uPoCC3HVEr3RgSAUxgOi4AKB0SASRMxwUApUSxICam3WI6LgAoHRIBpOEApuMCgFJiaAAsXQygY1DKNP9IBMDSxQA6AqVMzcHQAFJKzXRcANoYpUzNQyIAli4G0PYoZWoehgaQMB0XgDY2m1KmZz2rtTEVBYkAJjAdF4A2RSlT85AIdKJK2eymTdK2bdKTnywtXUr5LIDC6u9PhYH1VEqZNm5sbUxFQSLQaSplszt3Stu3T+xftIjyWQCFVSlZqr1roLLiIKOYc0ci0Emqy2Zrbd+eHn19aayfnwoABUMpU3OQCHSS6cpmKyrls4z1AyggSpnmH7cPdpLpymYrmAkQANAAEoFOUimbnQ7lswCABpAIdJLpZgCsYCZAAEADSAQ6SfUMgIsW7frcokXMBAgAaBjFgp2mumz2jjukhx6S9tlHOvRQymcBAA0jEehErSqbZb1PACg8EgHUx3qfAFAK1AhgMtb7BIDSIBHAZKz3CQClQSKAyWaz3icAoBBIBDDZdBMXMWERABQKiQAmm27iIiYsAoBCIRHAZNUTF1WuDHR1MWERABQQtw+iPtb7BIBSIBHA1FjvEwAKj6EBAABKjEQAAIASIxEAAKDESAQAACgxEgEAAEqMRAAAgBIjEQAAoMRIBAAAKLG2SQRsn2R7k+1x28umaXes7btsD9k+u5UxAgBQNG2TCEi6XdKrJd04VQPbu0m6SNIrJB0q6bW2D21NeAAAFE/bTDEcEXdKku3pmi2XNBQRd2dt10o6XtIdTQ8QAIACaqcrArNxoKT7qra3ZPsAAMAcOCJadzL7OklPrfPUuRHx5azNoKSzImJjndefJOnlEfE32fYbJC2PiNOnON+pkk6VpMWLF79g7dq189KPuRodHVV3CVbvK0M/6WNxlKGfZeijVI5+NtLHVatW3RoRU9bcVbR0aCAijnmCh9gi6eCq7YMkDU9zvoslXSxJy5Yti5UrVz7B0z8xg4ODyjuGVihDP+ljcZShn2Xoo1SOfjajj502NPAdSb22n2F7oaTXSLoy55gAAOhYbZMI2D7B9hZJR0paZ/vqbP8BttdLUkQ8Juk0SVdLulPSZyNiU14xAwDQ6drproErJF1RZ/+wpL6q7fWS1rcwNAAACqttrggAAIDWIxEAAKDESAQAACgxEgEAAEqMRAAAgBIjEQAAoMTa5vZBzNHIiDQwIG3eLPX2Sv39Uk9P3lEBADoEiUAn27BB6uuTxselsTGpq0tas0Zav15asSLv6AAAHYChgU41MpKSgJGRlARI6Wtl/+hovvEBADoCiUCnGhhIVwLqGR9PzwMAMAMSgU61efPElYBaY2PS0FBr4wEAdCQSgU7V25tqAurp6pKWLGltPACAjkQi0Kn6+6UFU3z7FixIzwMAMAMSgU7V05PuDujpmbgy0NU1sb+7O9/4AAAdgdsHO9mKFdLwcCoMHBpKwwH9/SQBAIBZIxHodN3d0urVeUcBAOhQJAIAADSgaBO6kggAADBLRZzQlUSgUxUtJQWANlc9oWtFZTqXvr5UstWJJVokAp2oiCkpALS52Uzo2oklW9w+2GlYYwAAclHUCV1JBDoNawwAQC6KOqEriUCnKWpKCgBtrqgTupIIdJqipqQA0OaKOqErxYKdpr8/FQbW08kpKQB0gCJO6Eoi0GkqqWftXQMLFnR2SgoAHaJoE7qSCHSiIqakAIBckAh0qqKlpACAXFAsCABAiZEIAABQYiQCAACUGIkAAAAlRiIAAECJkQgAAFBiJAIAAJQYiQAAACVGIgAAQImRCAAAUGIkAgAAlBiJAAAAJUYiAABAiZEIAABQYixDXEYjI9LAgLR5s9TbK/X3Sz09eUcFAMgBiUDZbNgg9fVJ4+PS2JjU1SWtWSOtXy+tWJF3dACAFmNooExGRlISMDKSkgApfa3sHx3NNz4AQMuRCJTJwEC6ElDP+Hh6HgBQKgwNlMnmzRNXAmqNjUlDQ62NBwByQqnUBBKBMuntTTUB9ZKBri5pyZLWxwQALUap1K4YGiiT/n5pwRTf8gUL0vMAUGCUSk1GIlAmPT0p5e3pSSmwlL5W9nd35xsfADQZpVKTMTRQNitWSMPD6X/70FAaDujvJwkAUAqUSk1GIlBG3d3S6tV5RwEALUep1GQMDQAASoNSqclIBAAApUGp1GQMDQAASoVSqV2RCAAASodSqQkMDQAAUGIkAgAAlBiJAAAAJUYiAABAiZEIAABQYiQCAACUGIkAAAAlRiIAAECJkQgAAFBibZMI2D7J9ibb47aXTdPuHts/tH2b7Y2tjBEAgKJppymGb5f0akkfm0XbVRHxYJPjAQCg8NomEYiIOyXJdt6hAABQGm0zNNCAkHSN7Vttn5p3MAAAdDJHROtOZl8n6al1njo3Ir6ctRmUdFZE1B3/t31ARAzbfoqkayWdHhE3TtH2VEmnStLixYtfsHbt2nnoxdyNjo6quwTrXJahn/SxOMrQzzL0USpHPxvp46pVq26NiClr7ipaOjQQEcfMwzGGs69bbV8habmkuolARFws6WJJWrZsWaxcufKJnv4JGRwcVN4xtEIZ+kkfi6MM/SxDH6Vy9LMZfeyooQHbXbZ7Kv+W9DKlIkMAADAHbZMI2D7B9hZJR0paZ/vqbP8BttdnzRZL2mD7+5JukbQuIr6WT8QAAHS+ltYI5Mn2A5J+lnMY+0oqw22PZegnfSyOMvSzDH2UytHPRvr49IjYb6ZGpUkE2oHtjbMp3Oh0ZegnfSyOMvSzDH2UytHPZvSxbYYGAABA65EIAABQYiQCrXVx3gG0SBn6SR+Lowz9LEMfpXL0c977SI0AAAAlxhUBAABKjESgxWy/y/YPsmWUr7F9QN4xzTfb59v+UdbPK2z/Qd4xNcNsl87uRLaPtX2X7SHbZ+cdTzPYvsT2VtuFnZTM9sG2b7B9Z/Z/9Yy8Y5pvthfZvsX297M+npd3TM1iezfb37N91Xwel0Sg9c6PiMMj4nmSrpL0b3kH1ATXSloaEYdL+rGkc3KOp1kqS2fXneK6U9neTdJFkl4h6VBJr7V9aL5RNcWlko7NO4gme0zSmRHxx5JeJOkfC/i9fFTS0RHxXEnPk3Ss7RflHFOznCHpzvk+KIlAi0XEb6o2u5RWUyyUiLgmIh7LNm+SdFCe8TRLRNwZEXflHUcTLJc0FBF3R8QOSWslHZ9zTPMuW6xsW95xNFNE3B8R383+PaL0IXJgvlHNr0hGs809skfhfq/aPkjSn0v6xHwfm0QgB7bfY/s+SaeomFcEqv21pK/mHQQacqCk+6q2t6hgHx5lZPsQSc+XdHO+kcy/7JL5bZK2Sro2IgrXR0kXSHqbpPH5PjCJQBPYvs727XUex0tSRJwbEQdLukzSaflGOzcz9TFrc67SpcnL8ov0iZlNPwvIdfYV7i+sMrHdLekLkt5ac1WyECLid9lw60GSlttemndM88n2cZK2RsStzTh+S5chLosGllv+X0nrJP17E8Npipn6aPuNko6T9JLo4HtU52Pp7A60RdLBVdsHSRrOKRY8Qbb3UEoCLouIL+YdTzNFxK9tDyrVfhSpCPQoSa+03SdpkaQn2f5MRLx+Pg7OFYEWs91btflKST/KK5ZmsX2spLdLemVE/DbveNCw70jqtf0M2wslvUbSlTnHhDmwbUn/I+nOiPivvONpBtv7Ve5Msr2XpGNUsN+rEXFORBwUEYco/Tx+fb6SAIlEIA/vyy4t/0DSy5SqQIvmI5J6JF2b3Sb50bwDaoapls7udFmh52mSrlYqLvtsRGzKN6r5Z/tySd+W9GzbW2yvzjumJjhK0hskHZ39LN6W/VVZJPtLuiH7nfodpRqBeb29ruiYWRAAgBLjigAAACVGIgAAQImRCAAAUGIkAgAAlBiJAAAAJUYiAFSx/Q7bUfUYtv0F28+axWvflL2me55jWpkdd95nS7N9SHbs42bRdrHtC2z/xPajtn9l+6u2Xz7fcRWR7eW23zHLtstsX5qtADlu+9LmRocyIxEAJntYaW6AIyWdpbSi2fW2u2Z43brsNfM9idJ3s+P+ZJ6PO2u2ny3pe0qLnnxAaQ6Mv5R0j6QrbT83r9g6yHLNfhbRoyStULov/hdNiwgQUwwD9TwWETdl/77J9r2SvimpT9Lnahtny/buFhEPSHpgvoPJ5oa/acaGzXWZ0kp9f1ozV/1XbP+3pF/nE1ZhfTgiLpQk2xvzDgbFxhUBYGaVhT4OkaTsku1G26+yvUnSdkkvrB0aqLrsfrLtj9l+OJvB7jzbu/zs2T7c9lds/9r2qO1bbL80e27S0EC2vcb2hba3Za/7cDYlcKXN/rYvsX237Uds/9j2u6vbzIbtF0t6gaRz6i1YExE/iIh7q9qfbPuH2fDBfU6rbe5e9XzlfTrC9qDt32Yz3h1hu8v2J7P36m7br62JZdD2522favuerF/rbB9Y025f25+y/VB2/EHby2ra3GP7A7b/Kfu+/Mr2WmfT1Va12zv7/v3S9nbb/2f7hTVtwvYZtt9r+wHbW21fZHvPSp8lfbiqbTjNiV9XRMz7CnPAVEgEgJkdkn39Rc2+90v6D6UrBT+d5vXvlzQq6URJn1FaevrEypO2/0jSt5SmSv17SSdIukK7LvxTz5lKCwKdIundkk6V9J6q5/dV+it+jdIiLOdL+itlH0gN+DNJv5N03UwNbb9M0oDScMbx2bnOUpp2utanJF0u6S+UVjz8vNK8+MNK78/Nkj7ttA57tSMlnZ71a7WkwyV9qabNlyS9PDt3v9LvuhtsL6lpd7Kklyi9d29XWijrvVX92TPr90sl/bOkVyld9bnO9lNrjnWmpAMkvV7pvf47TUwhvk7SB6viP1LSP9R5T4DWiwgePHhkD0nvkPSg0rDZ7pL+UNINkn4jaf+szaVKy/I+r+a1b8r2d2fbh2Tbn65pd5uktVXblyut+LfXFDGtzI6ztGpfKC2ssqBq37lK9Ql7T3Gc3SW9TukKxsKaGI+b5j35qKT7Z/n+3STphpp9b1NKJA6qeZ/eWNWmL9t3SdW+35e0U9Kbq/YNZvueXrXvqOy1x2bbx2bbf1bVpkvpA/xjVfvuUaq72L1q3wWSflG1vVrSDkm9Ne/jTySdX/P9uLGm31+SdFPV9mnpV27D/yc3Sro0758NHsV9cEUAmGwfpQ+bnZLukvRMSf0RcX9Vm59HxG2zPN41Ndt3KP0lX3G0pIGIeKTBOL8cu15C/qKkvSQtldLKc7bfavsO248o9ecySXtKelqD55pxUZKsVuIITa6jGFD6i/zImv3XV/17KPv69cdPGPGw0of3Lpf9JX03In5W1e5bkrYqFeMp+/pARHyjqs2YpKuUCvCq3RBpkaWKOyQ9pWr45BiloaGf2t69aojjG5J2GWrQzN9noC1RLAhM9rDSB0AoDQcMR0TtB+EvGzhebSHdDqU1xSv2kXS/Grd1iu39s69vVarwf5/SB9evJP2JpItqzj+Tn0vaz/aiiNg+Tbt9Je2hye9NZXvvmv3V78uOOvsq+2tjre13ZV+l3/vXiaESx3QxVM5nSQuzf+8r6UVKSVSt2rs4ZhM70HZIBIDJHouImSq153PZzoc08SHWiKdMsV1JKk6S9LmIOLfSwPahczjPoKR3Ko2lr5um3YNKH5i1cS3Ovm6bw7nrqT1+ZV+l3/dP0WbxHGLYpnRp/s11nnu0wWMBbYmhASB/10s62Xajfz0eX3P3waslPSLp9mx7L03+sDql0eAi4ptKl8ffa7un9nnbz7F9cET8Lmt3Uk2TkyWNS/p2o+eewhG2Hx/asH2U0gf/Ldmum5Uu77+4qs3vKc2BsKHBc10vaYmkeyNiY83jhw0ea0cWC1cJ0Fa4IgDk7zyliWNutP1BpSsEz5f0UERcMs3reiR9zvbHJR2mdDfCRyKi8lfvtZLeYvtmpcvYpyh9qM3FKUpFkxttuRXN1AAAAYFJREFUf0hp/PtJSpX5fyvphZLuU5ow52rbn5S0VtJzJL1L0scjYsscz11rq6SrnGbpWyTpP5XqBr4mSRFxte1vSRqwfbbS+3mWUmJ0foPn+rTSnRyDtj8g6W6loZzlSkWFH2rgWD/Kvp5h++uSfhMRd9VraHs/pbs1JOnJkp5u+0RJiojPN9gHYFokAkDOIuIu2yuUxvI/ke2+Q9K/zPDSDyoVMl6udHXvEzWveaek/ZRuLZRSMeFbJH1ljjEeIekcpbsADlS6Q+EWSa+LiO9n7a6x/RpJ/6qUPGzN4pztjHqz8W2lW/ouUOrfoNLtf9VOyM57gVKycIukoyNiSA2IiO22Vym9l+cpDS9szY53ZYNxf1MpETlD6bbTG5XuCKnnMO1adPnMqrZu8LzAtDy5BgpAu7Mdkk6PiHr35xdWNgnPgxFx4kxtAcwONQIAAJQYiQAAACXG0AAAACXGFQEAAEqMRAAAgBIjEQAAoMRIBAAAKDESAQAASoxEAACAEvt/3GsajTuO7D4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (8,8))\n",
    "ax = fig.add_subplot(1,1,1) \n",
    "ax.set_xlabel('Principal Component 1', fontsize = 15)\n",
    "ax.set_ylabel('Principal Component 2', fontsize = 15)\n",
    "ax.set_title('2 Component PCA', fontsize = 20)\n",
    "\n",
    "targets = ['Iris-setosa', 'Iris-versicolor', 'Iris-virginica']\n",
    "colors = ['r', 'g', 'b']\n",
    "for target, color in zip(targets,colors):\n",
    "    indicesToKeep = finalDf['type'] == target\n",
    "    ax.scatter(finalDf.loc[indicesToKeep, 'PC 1']\n",
    "               , finalDf.loc[indicesToKeep, 'PC 2']\n",
    "               , c = color\n",
    "               , s = 50)\n",
    "ax.legend(targets)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare to Probablistic PCA package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length</th>\n",
       "      <th>sepal width</th>\n",
       "      <th>petal length</th>\n",
       "      <th>petal width</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.900681</td>\n",
       "      <td>1.032057</td>\n",
       "      <td>-1.341272</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.143017</td>\n",
       "      <td>-0.124958</td>\n",
       "      <td>-1.341272</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.385353</td>\n",
       "      <td>0.337848</td>\n",
       "      <td>-1.398138</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.506521</td>\n",
       "      <td>0.106445</td>\n",
       "      <td>-1.284407</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.021849</td>\n",
       "      <td>1.263460</td>\n",
       "      <td>-1.341272</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.537178</td>\n",
       "      <td>1.957669</td>\n",
       "      <td>-1.170675</td>\n",
       "      <td>-1.050031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-1.506521</td>\n",
       "      <td>0.800654</td>\n",
       "      <td>-1.341272</td>\n",
       "      <td>-1.181504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-1.021849</td>\n",
       "      <td>0.800654</td>\n",
       "      <td>-1.284407</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-1.748856</td>\n",
       "      <td>-0.356361</td>\n",
       "      <td>-1.341272</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-1.143017</td>\n",
       "      <td>0.106445</td>\n",
       "      <td>-1.284407</td>\n",
       "      <td>-1.444450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.537178</td>\n",
       "      <td>1.494863</td>\n",
       "      <td>-1.284407</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-1.264185</td>\n",
       "      <td>0.800654</td>\n",
       "      <td>-1.227541</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-1.264185</td>\n",
       "      <td>-0.124958</td>\n",
       "      <td>-1.341272</td>\n",
       "      <td>-1.444450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-1.870024</td>\n",
       "      <td>-0.124958</td>\n",
       "      <td>-1.511870</td>\n",
       "      <td>-1.444450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-0.052506</td>\n",
       "      <td>2.189072</td>\n",
       "      <td>-1.455004</td>\n",
       "      <td>-1.312977</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    sepal length  sepal width  petal length  petal width\n",
       "0      -0.900681     1.032057     -1.341272    -1.312977\n",
       "1      -1.143017    -0.124958     -1.341272    -1.312977\n",
       "2      -1.385353     0.337848     -1.398138    -1.312977\n",
       "3      -1.506521     0.106445     -1.284407    -1.312977\n",
       "4      -1.021849     1.263460     -1.341272    -1.312977\n",
       "5      -0.537178     1.957669     -1.170675    -1.050031\n",
       "6      -1.506521     0.800654     -1.341272    -1.181504\n",
       "7      -1.021849     0.800654     -1.284407    -1.312977\n",
       "8      -1.748856    -0.356361     -1.341272    -1.312977\n",
       "9      -1.143017     0.106445     -1.284407    -1.444450\n",
       "10     -0.537178     1.494863     -1.284407    -1.312977\n",
       "11     -1.264185     0.800654     -1.227541    -1.312977\n",
       "12     -1.264185    -0.124958     -1.341272    -1.444450\n",
       "13     -1.870024    -0.124958     -1.511870    -1.444450\n",
       "14     -0.052506     2.189072     -1.455004    -1.312977"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "x2 = StandardScaler().fit_transform(x) #subtracts the mean AND sets equal to unit variance\n",
    "pd.DataFrame(data = x2, columns = features).head(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC 1</th>\n",
       "      <th>PC 2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2.264542</td>\n",
       "      <td>0.505704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.086426</td>\n",
       "      <td>-0.655405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2.367950</td>\n",
       "      <td>-0.318477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.304197</td>\n",
       "      <td>-0.575368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.388777</td>\n",
       "      <td>0.674767</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-2.070537</td>\n",
       "      <td>1.518549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-2.445711</td>\n",
       "      <td>0.074563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-2.233842</td>\n",
       "      <td>0.247614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-2.341958</td>\n",
       "      <td>-1.095146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-2.188676</td>\n",
       "      <td>-0.448629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-2.163487</td>\n",
       "      <td>1.070596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-2.327378</td>\n",
       "      <td>0.158587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-2.224083</td>\n",
       "      <td>-0.709118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-2.639716</td>\n",
       "      <td>-0.938282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-2.192292</td>\n",
       "      <td>1.889979</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        PC 1      PC 2\n",
       "0  -2.264542  0.505704\n",
       "1  -2.086426 -0.655405\n",
       "2  -2.367950 -0.318477\n",
       "3  -2.304197 -0.575368\n",
       "4  -2.388777  0.674767\n",
       "5  -2.070537  1.518549\n",
       "6  -2.445711  0.074563\n",
       "7  -2.233842  0.247614\n",
       "8  -2.341958 -1.095146\n",
       "9  -2.188676 -0.448629\n",
       "10 -2.163487  1.070596\n",
       "11 -2.327378  0.158587\n",
       "12 -2.224083 -0.709118\n",
       "13 -2.639716 -0.938282\n",
       "14 -2.192292  1.889979"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=2) #choosing 2 principal components and assigning them to the variable \"pca\"\n",
    "principalComponents = pca.fit_transform(x2) #gives you 2D data, with 2 principle components\n",
    "\n",
    "principalDf1 = pd.DataFrame(data = principalComponents\n",
    "             , columns = ['PC 1', 'PC 2'])\n",
    "\n",
    "finalDf1 = pd.concat([principalDf1, df[['type']]], axis = 1)\n",
    "\n",
    "principalDf1.head(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (8,8))\n",
    "ax = fig.add_subplot(1,1,1) \n",
    "ax.set_xlabel('Principal Component 1', fontsize = 15)\n",
    "ax.set_ylabel('Principal Component 2', fontsize = 15)\n",
    "ax.set_title('2 Component PCA', fontsize = 20)\n",
    "\n",
    "targets = ['Iris-setosa', 'Iris-versicolor', 'Iris-virginica']\n",
    "colors = ['r', 'g', 'b']\n",
    "for target, color in zip(targets,colors):\n",
    "    indicesToKeep = finalDf1['type'] == target\n",
    "    ax.scatter(finalDf1.loc[indicesToKeep, 'PC 1']\n",
    "               , finalDf1.loc[indicesToKeep, 'PC 2']\n",
    "               , c = color\n",
    "               , s = 50)\n",
    "ax.legend(targets)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}