{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# CS 109A/STAT 121A/AC 209A/CSCI E-109A\n", "\n", "## Standard Section 5: Partial Components Analysis (PCA) Fitting and Model Selection\n", "\n", "**Harvard University**
\n", "**Fall 2017**
\n", "**Section Leaders: Albert Wu, Nathaniel Burbank
**\n", "**Instructors: Pavlos Protopapas, Kevin Rader, Rahul Dave, Margo Levine** " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Download this notebook from the CS109 repo or here:\n", "http://bit.ly/Sec_5_109a (right click save to computer)\n", "\n", "For this section, our goal is to review and further our understanding of the Partial Components Analysis (PCA) model. PCA is highly effective in applications to high dimensionional datasets, which we will use here. Specifically, this section is designed to help us answer Homework 4, part (h). \n", "\n", "Specifically, we will: \n", " \n", " 1. Review the basics of Partial Components Analysis and hone our intution\n", " 2. Discuss implementation of PCA within Python and coding issues to keep in mind\n", " 3. Use the principles of model selection we have learned in lecture to find a \"best\" PCA feature set.\n", " 4. Compare our PCA model with other models we have fit in labs and lecture and discuss coefficient meanings.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this section we will be using the following packages:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda/lib/python3.6/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n", " from pandas.core import datetools\n" ] } ], "source": [ "import sys\n", "import numpy as np\n", "import pandas as pd\n", "pd.set_option('display.max_rows', 999)\n", "pd.set_option('display.max_columns', 999)\n", "pd.set_option('display.width', 1000)\n", "pd.set_option('display.notebook_repr_html', True)\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "import statsmodels.api as sm\n", "from statsmodels.api import OLS\n", "from statsmodels.api import add_constant\n", "from statsmodels.regression.linear_model import RegressionResults\n", "from sklearn.preprocessing import MinMaxScaler\n", "from sklearn.model_selection import KFold\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.linear_model import Ridge\n", "from sklearn.linear_model import Lasso\n", "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.neighbors import KNeighborsRegressor\n", "from sklearn.decomposition import PCA\n", "from sklearn.model_selection import train_test_split\n", "# Note -- Requires sklearn version .18 or higher \n", "\n", "from sklearn.metrics import r2_score\n", "from collections import Counter\n", "sns.set(style=\"ticks\")\n", "%matplotlib inline\n", "\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "matplotlib.rcParams['figure.figsize'] = (13.0, 6.0)\n", "\n", "assert(sys.version_info.major==3),print(sys.version)\n", "# Python 3 or higher is required" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part (1): Load in our data and conduct basic EDA\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will first load in our dataset below and look at the first few rows. Then, we use the describe function to get a sense of the data." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
IncidenceTempDewpointWindspeedPressurePrecipitationTMAX_CTMIN_CMonthDOWWeekendSeason
018226.44444415.9444448.51008.50.031.72222221.7222227Sunday1Summer
129524.3333339.6666677.91012.20.031.72222220.0000007Monday0Summer
226722.7222229.6666675.51016.00.028.88888918.2777787Tuesday0Summer
325023.16666714.5000006.71020.10.028.27777818.2777787Wednesday0Summer
425924.50000015.6111118.61021.30.030.00000018.8888897Thursday0Summer
\n", "
" ], "text/plain": [ " Incidence Temp Dewpoint Windspeed Pressure Precipitation TMAX_C TMIN_C Month DOW Weekend Season\n", "0 182 26.444444 15.944444 8.5 1008.5 0.0 31.722222 21.722222 7 Sunday 1 Summer\n", "1 295 24.333333 9.666667 7.9 1012.2 0.0 31.722222 20.000000 7 Monday 0 Summer\n", "2 267 22.722222 9.666667 5.5 1016.0 0.0 28.888889 18.277778 7 Tuesday 0 Summer\n", "3 250 23.166667 14.500000 6.7 1020.1 0.0 28.277778 18.277778 7 Wednesday 0 Summer\n", "4 259 24.500000 15.611111 8.6 1021.3 0.0 30.000000 18.888889 7 Thursday 0 Summer" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crime_df = pd.read_csv('https://raw.githubusercontent.com/albertw1/data/master/Crime.csv').drop(['Date', 'Year'], axis=1)\n", "crime_df.head()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
IncidenceTempDewpointWindspeedPressurePrecipitationTMAX_CTMIN_CMonthWeekend
count1095.0000001095.0000001095.0000001095.0000001095.0000001095.0000001095.0000001095.0000001095.0000001095.000000
mean238.10776310.5838153.7130909.1687671016.4635620.11491316.3090825.8417556.5260270.285845
std31.5398439.91381710.8485713.2699697.6322740.30340910.4456459.8062763.4494270.452022
min115.000000-14.222222-24.2777782.200000987.4000000.000000-10.000000-19.3888891.0000000.000000
25%219.0000002.500000-4.0555566.9000001011.3000000.0000007.222222-1.1111114.0000000.000000
50%240.00000011.3333334.7222228.7000001016.4000000.00000017.2222226.7222227.0000000.000000
75%259.00000019.11111112.88888911.0000001021.4000000.05500025.61111115.00000010.0000001.000000
max349.00000030.94444422.44444425.8000001040.4000003.54000037.22222226.11111112.0000001.000000
\n", "
" ], "text/plain": [ " Incidence Temp Dewpoint Windspeed Pressure Precipitation TMAX_C TMIN_C Month Weekend\n", "count 1095.000000 1095.000000 1095.000000 1095.000000 1095.000000 1095.000000 1095.000000 1095.000000 1095.000000 1095.000000\n", "mean 238.107763 10.583815 3.713090 9.168767 1016.463562 0.114913 16.309082 5.841755 6.526027 0.285845\n", "std 31.539843 9.913817 10.848571 3.269969 7.632274 0.303409 10.445645 9.806276 3.449427 0.452022\n", "min 115.000000 -14.222222 -24.277778 2.200000 987.400000 0.000000 -10.000000 -19.388889 1.000000 0.000000\n", "25% 219.000000 2.500000 -4.055556 6.900000 1011.300000 0.000000 7.222222 -1.111111 4.000000 0.000000\n", "50% 240.000000 11.333333 4.722222 8.700000 1016.400000 0.000000 17.222222 6.722222 7.000000 0.000000\n", "75% 259.000000 19.111111 12.888889 11.000000 1021.400000 0.055000 25.611111 15.000000 10.000000 1.000000\n", "max 349.000000 30.944444 22.444444 25.800000 1040.400000 3.540000 37.222222 26.111111 12.000000 1.000000" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crime_df.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Convert the columns that are categorical variables into dummy variables by one-hot encoding." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
IncidenceTempDewpointWindspeedPressurePrecipitationTMAX_CTMIN_CMonth_2Month_3Month_4Month_5Month_6Month_7Month_8Month_9Month_10Month_11Month_12Weekend_1Season_SpringSeason_SummerSeason_WinterDOW_MondayDOW_SaturdayDOW_SundayDOW_ThursdayDOW_TuesdayDOW_Wednesday
018226.44444415.9444448.51008.50.031.72222221.722222000001000001010001000
129524.3333339.6666677.91012.20.031.72222220.000000000001000000010100000
226722.7222229.6666675.51016.00.028.88888918.277778000001000000010000010
325023.16666714.5000006.71020.10.028.27777818.277778000001000000010000001
425924.50000015.6111118.61021.30.030.00000018.888889000001000000010000100
\n", "
" ], "text/plain": [ " Incidence Temp Dewpoint Windspeed Pressure Precipitation TMAX_C TMIN_C Month_2 Month_3 Month_4 Month_5 Month_6 Month_7 Month_8 Month_9 Month_10 Month_11 Month_12 Weekend_1 Season_Spring Season_Summer Season_Winter DOW_Monday DOW_Saturday DOW_Sunday DOW_Thursday DOW_Tuesday DOW_Wednesday\n", "0 182 26.444444 15.944444 8.5 1008.5 0.0 31.722222 21.722222 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0\n", "1 295 24.333333 9.666667 7.9 1012.2 0.0 31.722222 20.000000 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0\n", "2 267 22.722222 9.666667 5.5 1016.0 0.0 28.888889 18.277778 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0\n", "3 250 23.166667 14.500000 6.7 1020.1 0.0 28.277778 18.277778 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1\n", "4 259 24.500000 15.611111 8.6 1021.3 0.0 30.000000 18.888889 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "categorical_columns = ['Month', 'Weekend', 'Season', 'DOW']\n", "numerical_columns = ['Temp', 'Dewpoint', 'Windspeed', 'Pressure', 'Precipitation', 'TMAX_C', 'TMIN_C']\n", "crime_df = pd.get_dummies(crime_df, columns=categorical_columns, drop_first=True)\n", "crime_df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's split this dataset up into a testing and training set." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((876, 29), (219, 29))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "train, test = train_test_split(crime_df, test_size=.2, random_state=123)\n", "train.shape,test.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let us standarize the numerical variables only." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "mean = train[numerical_columns].mean()\n", "std = train[numerical_columns].std()\n", "\n", "train[numerical_columns] = (train[numerical_columns] - mean)/std\n", "test[numerical_columns] = (test[numerical_columns] - mean)/std" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now to let us subset and create convenient formats for parts in train and test" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(219,)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "all_predictors = ['Temp','Dewpoint','Windspeed','Pressure','Precipitation','TMAX_C','TMIN_C','Month_2','Month_3','Month_4','Month_5','Month_6','Month_7','Month_8','Month_9','Month_10','Month_11','Month_12','Weekend_1','Season_Spring','Season_Summer','Season_Winter','DOW_Monday','DOW_Saturday','DOW_Sunday','DOW_Thursday','DOW_Tuesday','DOW_Wednesday']\n", "\n", "X_train_df = train[all_predictors]\n", "X_test_df = test[all_predictors]\n", "X_train_np = train[all_predictors].values\n", "X_test_np = test[all_predictors].values\n", "y_train = train['Incidence'].values\n", "y_test = test['Incidence'].values\n", "y_test.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part (2): Use subset selection to fit a linear regression model\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use the forward/backward subset selection method from HW 3 to fit a linear regression model on the data." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def step_forwards_backwards(df, y_val, direction='forward'):\n", " \n", " assert direction in ['forward', 'backward']\n", " \n", " y = y_val.reshape(-1,1)\n", " \n", " predictors = set(df.columns)\n", " selected_predictors = set() if direction=='forward' else set(predictors)\n", " \n", " n = df.shape[0]\n", " best_bic = np.inf\n", " \n", " best_bics = []\n", " best_models = []\n", " \n", " if direction == 'forward':\n", " X = np.ones(n).reshape(-1,1)\n", " X = np.concatenate([X, df[list(selected_predictors)].values], axis=1)\n", " while (True):\n", " \n", " possible_bic_scores = []\n", " possible_predictors = list(selected_predictors ^ predictors)\n", " \n", " if len(possible_predictors) == 0:\n", " break\n", " \n", " for predictor in possible_predictors:\n", " \n", " x_temp = np.concatenate([X, df[predictor].values.reshape(-1,1)], axis=1)\n", " model = OLS(endog=y, exog=x_temp).fit()\n", " bic = model.bic\n", " possible_bic_scores.append(bic)\n", " \n", " best_predictor_ix = np.argmin(possible_bic_scores)\n", " best_predictor = possible_predictors[best_predictor_ix]\n", " \n", " best_bic = np.min(possible_bic_scores)\n", " best_bics.append(best_bic)\n", " \n", " selected_predictors.add(best_predictor) \n", " X = np.concatenate([X, df[best_predictor].values.reshape(-1,1)], axis=1)\n", " best_models.append(list(selected_predictors))\n", "\n", " else:\n", "\n", " while (True):\n", " possible_bic_scores = []\n", " possible_predictors = list(selected_predictors)\n", "\n", " if len(possible_predictors) == 0:\n", " break\n", "\n", " for predictor in possible_predictors:\n", " X = np.concatenate([np.ones(n).reshape(-1,1), df[list(selected_predictors - set([predictor]))].values], axis=1)\n", " model = OLS(endog=y, exog=X).fit()\n", " bic = model.bic\n", " possible_bic_scores.append(bic)\n", "\n", " best_predictor_ix = np.argmin(possible_bic_scores)\n", " best_predictor = possible_predictors[best_predictor_ix] \n", "\n", " best_bic = possible_bic_scores[best_predictor_ix]\n", " selected_predictors.discard(best_predictor)\n", " \n", " best_bics.append(best_bic)\n", " best_models.append(list(selected_predictors))\n", " \n", " index_of_best_bic = np.argmin(best_bics)\n", "\n", " return best_models[index_of_best_bic]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's run the subset selection function and see which variables were included in the best model:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "ename": "SyntaxError", "evalue": "invalid syntax (, line 1)", "output_type": "error", "traceback": [ "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m predictors_forward = # Your code goes here\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" ] } ], "source": [ "predictors_forward = # Your code goes here\n", "predictors_forward" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "ename": "SyntaxError", "evalue": "invalid syntax (, line 1)", "output_type": "error", "traceback": [ "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m predictors_backward = # Your code goes here\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" ] } ], "source": [ "predictors_backward = # Your code goes here\n", "predictors_backward" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Based on these variables, we can see what the R-squared values are for our training and testing sets." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'predictors_backward' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_constant\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train_df\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpredictors_backward\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mX_test\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_constant\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_test_df\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpredictors_backward\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrain\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Incidence'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mmodel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mOLS\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mendog\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexog\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'predictors_backward' is not defined" ] } ], "source": [ "X = sm.add_constant(X_train_df[predictors_backward])\n", "X_test = sm.add_constant(X_test_df[predictors_backward])\n", "y = train['Incidence'].values.reshape(-1,1)\n", "\n", "model = OLS(endog=y, exog=X)\n", "result = model.fit()\n", "\n", "y_hat_train = result.predict()\n", "y_hat_test = result.predict(exog=X_test)\n", "\n", "print('Backward Selection Training R2 = ', r2_score(y_train, y_hat_train))\n", "print('Backward Selection Testing R2 = ', r2_score(y_test, y_hat_test))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'predictors_forward' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_constant\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train_df\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpredictors_forward\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mX_test\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_constant\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_test_df\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpredictors_forward\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrain\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Incidence'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mmodel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mOLS\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mendog\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexog\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'predictors_forward' is not defined" ] } ], "source": [ "X = sm.add_constant(X_train_df[predictors_forward])\n", "X_test = sm.add_constant(X_test_df[predictors_forward])\n", "y = train['Incidence'].values.reshape(-1,1)\n", "\n", "model = OLS(endog=y, exog=X)\n", "result = model.fit()\n", "\n", "y_hat_train = result.predict()\n", "y_hat_test = result.predict(exog=X_test)\n", "\n", "print('Forward Selection Training R2 = ', r2_score(y_train, y_hat_train))\n", "print('Forward Selection Testing R2 = ', r2_score(y_test, y_hat_test))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part (3): Create a data frame with continuous predictors taken to polynomial power" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we will work with an example where we will manually take numeric predictors and take them to a polynomial power. The next step is a simple example to help you see how we can do this." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 1, 2, 3, 1, 4, 9, 1, 8, 27],\n", " [ 4, 5, 6, 16, 25, 36, 64, 125, 216],\n", " [ 7, 8, 9, 49, 64, 81, 343, 512, 729],\n", " [ 10, 11, 12, 100, 121, 144, 1000, 1331, 1728]])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.hstack((np.array([[1, 2,3], [4, 5,6],[7,8,9],[10,11,12]])**(i+1) for i in range(3)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We want to create a data frame with the continuous predictors taken up to a power 3, while keeping the rest of the categorical predictors the same. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "ename": "SyntaxError", "evalue": "invalid syntax (, line 1)", "output_type": "error", "traceback": [ "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m X_train_numerical_powers = # Your code goes here\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" ] } ], "source": [ "X_train_numerical_powers = # Your code goes here\n", "\n", "print('Number of Total Predictors with Continuous Polynomial Terms Added is', X_train_numerical_powers.shape[1])" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": true }, "outputs": [ { "ename": "NameError", "evalue": "name 'X_train_numerical_powers' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mX_train_np_powers\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconcatenate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train_numerical_powers\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mX_train_df\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdrop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnumerical_columns\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mX_train_df_powers\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDataFrame\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train_np_powers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mnewcolname\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'Temp'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Dewpoint'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Windspeed'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Pressure'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Precipitation'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'TMAX_C'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'TMIN_C'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Temp^2'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Dewpoint^2'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Windspeed^2'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Pressure^2'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Precipitation^2'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'TMAX_C^2'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'TMIN_^2'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'Temp^3'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Dewpoint^3'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Windspeed^3'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Pressure^3'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Precipitation^3'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'TMAX_C^3'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'TMIN_C^3'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train_df\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdrop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnumerical_columns\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mX_train_df_powers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolumns\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnewcolname\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mX_train_df_powers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhead\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'X_train_numerical_powers' is not defined" ] } ], "source": [ "X_train_np_powers = np.concatenate((X_train_numerical_powers,X_train_df.drop(numerical_columns, axis=1)),axis=1)\n", "X_train_df_powers = pd.DataFrame(X_train_np_powers)\n", "newcolname = ['Temp', 'Dewpoint', 'Windspeed', 'Pressure', 'Precipitation', 'TMAX_C', 'TMIN_C', 'Temp^2', 'Dewpoint^2', 'Windspeed^2', 'Pressure^2', 'Precipitation^2', 'TMAX_C^2', 'TMIN_^2','Temp^3', 'Dewpoint^3', 'Windspeed^3', 'Pressure^3', 'Precipitation^3', 'TMAX_C^3', 'TMIN_C^3'] + list(X_train_df.drop(numerical_columns, axis=1))\n", "X_train_df_powers.columns = newcolname\n", "X_train_df_powers.head() \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can do the same with the test set:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": false }, "outputs": [ { "ename": "SyntaxError", "evalue": "invalid syntax (, line 1)", "output_type": "error", "traceback": [ "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m X_test_numerical_powers = # Your code goes here\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" ] } ], "source": [ "X_test_numerical_powers = # Your code goes here\n", "X_test_np_powers = np.concatenate((X_test_numerical_powers,X_test_df.drop(numerical_columns, axis=1)),axis=1)\n", "X_test_df_powers = pd.DataFrame(X_test_np_powers)\n", "newcolname = ['Temp', 'Dewpoint', 'Windspeed', 'Pressure', 'Precipitation', 'TMAX_C', 'TMIN_C', 'Temp^2', 'Dewpoint^2', 'Windspeed^2', 'Pressure^2', 'Precipitation^2', 'TMAX_C^2', 'TMIN_^2','Temp^3', 'Dewpoint^3', 'Windspeed^3', 'Pressure^3', 'Precipitation^3', 'TMAX_C^3', 'TMIN_C^3'] + list(X_train_df.drop(numerical_columns, axis=1))\n", "X_test_df_powers.columns = newcolname\n", "X_test_df_powers.head() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can do forward and backward selection as well on this new data frame. " ] }, { "cell_type": "code", "execution_count": 317, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['DOW_Sunday',\n", " 'DOW_Monday',\n", " 'Windspeed',\n", " 'Temp',\n", " 'DOW_Wednesday',\n", " 'Weekend_1',\n", " 'Windspeed^3',\n", " 'DOW_Thursday',\n", " 'Season_Summer',\n", " 'DOW_Tuesday',\n", " 'Dewpoint^3']" ] }, "execution_count": 317, "metadata": {}, "output_type": "execute_result" } ], "source": [ "predictors_forward = step_forwards_backwards(X_train_df_powers, y_train, direction='forward')\n", "predictors_forward" ] }, { "cell_type": "code", "execution_count": 319, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['DOW_Wednesday',\n", " 'Windspeed',\n", " 'DOW_Thursday',\n", " 'Dewpoint',\n", " 'DOW_Sunday',\n", " 'TMIN_C^3',\n", " 'Season_Summer',\n", " 'DOW_Monday',\n", " 'DOW_Saturday',\n", " 'DOW_Tuesday',\n", " 'Temp']" ] }, "execution_count": 319, "metadata": {}, "output_type": "execute_result" } ], "source": [ "predictors_backward = step_forwards_backwards(X_train_df_powers, y_train, direction='backward')\n", "predictors_backward" ] }, { "cell_type": "code", "execution_count": 320, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Forward Selection Training R2 = 0.422425372293\n", "Forward Selection Testing R2 = 0.361986140851\n" ] } ], "source": [ "X = sm.add_constant(X_train_df_powers[predictors_backward])\n", "X_test = sm.add_constant(X_test_df_powers[predictors_backward])\n", "y = train['Incidence'].values.reshape(-1,1)\n", "\n", "model = OLS(endog=y, exog=X)\n", "result = model.fit()\n", "\n", "y_hat_train = result.predict()\n", "y_hat_test = result.predict(exog=X_test)\n", "\n", "print('Forward Selection Training R2 = ', r2_score(y_train, y_hat_train))\n", "print('Forward Selection Testing R2 = ', r2_score(y_test, y_hat_test))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "X = sm.add_constant(X_train_df_powers[predictors_forward])\n", "X_test = sm.add_constant(X_test_df_powers[predictors_forward])\n", "y = train['Incidence'].values.reshape(-1,1)\n", "\n", "model = OLS(endog=y, exog=X)\n", "result = model.fit()\n", "\n", "y_hat_train = result.predict()\n", "y_hat_test = result.predict(exog=X_test)\n", "\n", "print('Forward Selection Training R2 = ', r2_score(y_train, y_hat_train))\n", "print('Forward Selection Testing R2 = ', r2_score(y_test, y_hat_test))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part (4) Create the expanded matrix containing all terms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now create a design matrix that includes all polynomial terms up to the third order, including all interactions. " ] }, { "cell_type": "code", "execution_count": 416, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of total predictors 4494\n" ] } ], "source": [ "all_poly_terms = PolynomialFeatures(degree=3, interaction_only=False, include_bias=False)\n", "\n", "X_train_full_poly = all_poly_terms.fit_transform(X_train_df)\n", "X_test_full_poly = all_poly_terms.fit_transform(X_test_df)\n", "\n", "print('number of total predictors', X_train_full_poly.shape[1])" ] }, { "cell_type": "code", "execution_count": 417, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(876, 4494)" ] }, "execution_count": 417, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_train_full_poly.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the following function to get an idea of the interactions between the variables (print first 25)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'all_poly_terms' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mall_poly_terms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_feature_names\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhead\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mNameError\u001b[0m: name 'all_poly_terms' is not defined" ] } ], "source": [ "all_poly_terms.get_feature_names()[0:25]" ] }, { "cell_type": "code", "execution_count": 419, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "array([[ 1.42281184, 1.58038879, -0.57476883, ..., 0. ,\n", " 0. , 0. ],\n", " [-1.51727206, -1.79988626, 1.10635803, ..., 0. ,\n", " 0. , 0. ],\n", " [-0.47203311, 0.001912 , -1.05509079, ..., 0. ,\n", " 0. , 0. ],\n", " ..., \n", " [-0.11430427, -0.2112585 , 0.35585497, ..., 0. ,\n", " 0. , 0. ],\n", " [ 0.42228899, 0.05774237, 0.5359757 , ..., 0. ,\n", " 0. , 0. ],\n", " [ 0.41669948, -0.05391837, -1.02507067, ..., 0. ,\n", " 0. , 0. ]])" ] }, "execution_count": 419, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_train_full_poly" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we wanted to drop the 0's, we can use the following function:" ] }, { "cell_type": "code", "execution_count": 420, "metadata": { "collapsed": true }, "outputs": [], "source": [ "zero_column_index = np.where(~X_train_full_poly.any(axis=0))[0]" ] }, { "cell_type": "code", "execution_count": 421, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1.42281184 1.58038879 -0.57476883 ..., 0. 0. 0. ]\n", " [-1.51727206 -1.79988626 1.10635803 ..., 0. 0. 0. ]\n", " [-0.47203311 0.001912 -1.05509079 ..., 0. 0. 0. ]\n", " ..., \n", " [-0.11430427 -0.2112585 0.35585497 ..., 0. 0. 0. ]\n", " [ 0.42228899 0.05774237 0.5359757 ..., 0. 0. 0. ]\n", " [ 0.41669948 -0.05391837 -1.02507067 ..., 0. 0. 0. ]]\n" ] } ], "source": [ "X_train_full_poly_nonzero_col = np.delete(X_train_full_poly, zero_column_index, axis = 1)\n", "X_test_full_poly_nonzero_col = np.delete(X_test_full_poly, zero_column_index, axis = 1)\n", "\n", "print(X_train_full_poly_nonzero_col)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can fit our PCA model:" ] }, { "cell_type": "code", "execution_count": 447, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Explained variance ratio: [ 0.8129783 0.04373497 0.03401266 0.02028036 0.01556333]\n" ] } ], "source": [ "pca = PCA(n_components=5)\n", "pca.fit(X_train_full_poly)\n", "train_pca = pca.transform(X_train_full_poly)\n", "test_pca = pca.transform(X_test_full_poly)\n", "\n", "print('Explained variance ratio:', pca.explained_variance_ratio_)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can obtain the corresponding coefficients of each principal component." ] }, { "cell_type": "code", "execution_count": 428, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 2.89699969e-04, 8.16273796e-04, 2.21196880e-03, ...,\n", " 0.00000000e+00, 0.00000000e+00, 1.63373238e-05],\n", " [ -2.10903042e-02, -1.89535884e-02, 3.16788138e-02, ...,\n", " -0.00000000e+00, -0.00000000e+00, 1.56530336e-04],\n", " [ 6.60108855e-02, 6.63252686e-02, -1.68813579e-02, ...,\n", " -0.00000000e+00, -0.00000000e+00, -1.08743378e-04],\n", " [ -1.22151524e-02, -1.10596786e-02, -3.84026203e-02, ...,\n", " 0.00000000e+00, 0.00000000e+00, 2.21319814e-03],\n", " [ 8.82561724e-03, 1.13001835e-02, 4.94705788e-02, ...,\n", " 0.00000000e+00, 0.00000000e+00, 2.29230565e-03]])" ] }, "execution_count": 428, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pca.components_\n", "# First \"row\" of array corresponds to first component weights. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you recall, our weights squared had to sum to one. Let's see if this is the case:" ] }, { "cell_type": "code", "execution_count": 429, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1., 1., 1., 1., 1.])" ] }, "execution_count": 429, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Your code goes here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will look at each of the components, or weights from our 5 principal components. Because we centered our dataset, each value is essentially a correlation value. " ] }, { "cell_type": "code", "execution_count": 430, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
x0x1x2x3x4x5x6x7x8x9x10x11x12x13x14x15x16x17x18x19x20x21x22x23x24x25x26x27x0^2x0 x1x0 x2x0 x3x0 x4x0 x5x0 x6x0 x7x0 x8x0 x9x0 x10x0 x11x0 x12x0 x13x0 x14x0 x15x0 x16x0 x17x0 x18x0 x19x0 x20x0 x21x0 x22x0 x23x0 x24x0 x25x0 x26x0 x27x1^2x1 x2x1 x3x1 x4x1 x5x1 x6x1 x7x1 x8x1 x9x1 x10x1 x11x1 x12x1 x13x1 x14x1 x15x1 x16x1 x17x1 x18x1 x19x1 x20x1 x21x1 x22x1 x23x1 x24x1 x25x1 x26x1 x27x2^2x2 x3x2 x4x2 x5x2 x6x2 x7x2 x8x2 x9x2 x10x2 x11x2 x12x2 x13x2 x14x2 x15x2 x16x2 x17x2 x18x2 x19x2 x20x2 x21x2 x22x2 x23x2 x24x2 x25x2 x26x2 x27x3^2x3 x4x3 x5x3 x6x3 x7x3 x8x3 x9x3 x10x3 x11x3 x12x3 x13x3 x14x3 x15x3 x16x3 x17x3 x18x3 x19x3 x20x3 x21x3 x22x3 x23x3 x24x3 x25x3 x26x3 x27x4^2x4 x5x4 x6x4 x7x4 x8x4 x9x4 x10x4 x11x4 x12x4 x13x4 x14x4 x15x4 x16x4 x17x4 x18x4 x19x4 x20x4 x21x4 x22x4 x23x4 x24x4 x25x4 x26x4 x27x5^2x5 x6x5 x7x5 x8x5 x9x5 x10x5 x11x5 x12x5 x13x5 x14x5 x15x5 x16x5 x17x5 x18x5 x19x5 x20x5 x21x5 x22x5 x23x5 x24x5 x25x5 x26x5 x27x6^2x6 x7x6 x8x6 x9x6 x10x6 x11x6 x12x6 x13x6 x14x6 x15x6 x16x6 x17x6 x18x6 x19x6 x20x6 x21x6 x22x6 x23x6 x24x6 x25x6 x26x6 x27x7^2x7 x8x7 x9x7 x10x7 x11x7 x12x7 x13x7 x14x7 x15x7 x16x7 x17x7 x18x7 x19x7 x20x7 x21x7 x22x7 x23x7 x24x7 x25x7 x26x7 x27x8^2x8 x9x8 x10x8 x11x8 x12x8 x13x8 x14x8 x15x8 x16x8 x17x8 x18x8 x19x8 x20x8 x21x8 x22x8 x23x8 x24x8 x25x8 x26x8 x27x9^2x9 x10x9 x11x9 x12x9 x13x9 x14x9 x15x9 x16x9 x17x9 x18x9 x19x9 x20x9 x21x9 x22x9 x23x9 x24x9 x25x9 x26x9 x27x10^2x10 x11x10 x12x10 x13x10 x14x10 x15x10 x16x10 x17x10 x18x10 x19x10 x20x10 x21x10 x22x10 x23x10 x24x10 x25x10 x26x10 x27x11^2x11 x12x11 x13x11 x14x11 x15x11 x16x11 x17x11 x18x11 x19x11 x20x11 x21x11 x22x11 x23x11 x24x11 x25x11 x26x11 x27x12^2x12 x13x12 x14x12 x15x12 x16x12 x17x12 x18x12 x19x12 x20x12 x21x12 x22x12 x23x12 x24x12 x25x12 x26x12 x27x13^2x13 x14x13 x15x13 x16x13 x17x13 x18x13 x19x13 x20x13 x21x13 x22x13 x23x13 x24x13 x25x13 x26x13 x27x14^2x14 x15x14 x16x14 x17x14 x18x14 x19x14 x20x14 x21x14 x22x14 x23x14 x24x14 x25x14 x26x14 x27x15^2x15 x16x15 x17x15 x18x15 x19x15 x20x15 x21x15 x22x15 x23x15 x24x15 x25x15 x26x15 x27x16^2x16 x17x16 x18x16 x19x16 x20x16 x21x16 x22x16 x23x16 x24x16 x25x16 x26x16 x27x17^2x17 x18x17 x19x17 x20x17 x21x17 x22x17 x23x17 x24x17 x25x17 x26x17 x27x18^2x18 x19x18 x20x18 x21x18 x22x18 x23x18 x24x18 x25x18 x26x18 x27x19^2x19 x20x19 x21x19 x22x19 x23x19 x24x19 x25x19 x26x19 x27x20^2x20 x21x20 x22x20 x23x20 x24x20 x25x20 x26x20 x27x21^2x21 x22x21 x23x21 x24x21 x25x21 x26x21 x27x22^2x22 x23x22 x24x22 x25x22 x26x22 x27x23^2x23 x24x23 x25x23 x26x23 x27x24^2x24 x25x24 x26x24 x27x25^2x25 x26x25 x27x26^2x26 x27x27^2x0^3x0^2 x1x0^2 x2x0^2 x3x0^2 x4x0^2 x5x0^2 x6x0^2 x7x0^2 x8x0^2 x9x0^2 x10x0^2 x11x0^2 x12x0^2 x13x0^2 x14x0^2 x15x0^2 x16x0^2 x17x0^2 x18x0^2 x19x0^2 x20x0^2 x21x0^2 x22x0^2 x23x0^2 x24x0^2 x25x0^2 x26x0^2 x27x0 x1^2x0 x1 x2x0 x1 x3x0 x1 x4x0 x1 x5x0 x1 x6x0 x1 x7x0 x1 x8x0 x1 x9x0 x1 x10x0 x1 x11x0 x1 x12x0 x1 x13x0 x1 x14x0 x1 x15x0 x1 x16x0 x1 x17x0 x1 x18x0 x1 x19x0 x1 x20x0 x1 x21x0 x1 x22x0 x1 x23x0 x1 x24x0 x1 x25x0 x1 x26x0 x1 x27x0 x2^2x0 x2 x3x0 x2 x4x0 x2 x5x0 x2 x6x0 x2 x7x0 x2 x8x0 x2 x9x0 x2 x10x0 x2 x11...x14 x19 x20x14 x19 x21x14 x19 x22x14 x19 x23x14 x19 x24x14 x19 x25x14 x19 x26x14 x19 x27x14 x20^2x14 x20 x21x14 x20 x22x14 x20 x23x14 x20 x24x14 x20 x25x14 x20 x26x14 x20 x27x14 x21^2x14 x21 x22x14 x21 x23x14 x21 x24x14 x21 x25x14 x21 x26x14 x21 x27x14 x22^2x14 x22 x23x14 x22 x24x14 x22 x25x14 x22 x26x14 x22 x27x14 x23^2x14 x23 x24x14 x23 x25x14 x23 x26x14 x23 x27x14 x24^2x14 x24 x25x14 x24 x26x14 x24 x27x14 x25^2x14 x25 x26x14 x25 x27x14 x26^2x14 x26 x27x14 x27^2x15^3x15^2 x16x15^2 x17x15^2 x18x15^2 x19x15^2 x20x15^2 x21x15^2 x22x15^2 x23x15^2 x24x15^2 x25x15^2 x26x15^2 x27x15 x16^2x15 x16 x17x15 x16 x18x15 x16 x19x15 x16 x20x15 x16 x21x15 x16 x22x15 x16 x23x15 x16 x24x15 x16 x25x15 x16 x26x15 x16 x27x15 x17^2x15 x17 x18x15 x17 x19x15 x17 x20x15 x17 x21x15 x17 x22x15 x17 x23x15 x17 x24x15 x17 x25x15 x17 x26x15 x17 x27x15 x18^2x15 x18 x19x15 x18 x20x15 x18 x21x15 x18 x22x15 x18 x23x15 x18 x24x15 x18 x25x15 x18 x26x15 x18 x27x15 x19^2x15 x19 x20x15 x19 x21x15 x19 x22x15 x19 x23x15 x19 x24x15 x19 x25x15 x19 x26x15 x19 x27x15 x20^2x15 x20 x21x15 x20 x22x15 x20 x23x15 x20 x24x15 x20 x25x15 x20 x26x15 x20 x27x15 x21^2x15 x21 x22x15 x21 x23x15 x21 x24x15 x21 x25x15 x21 x26x15 x21 x27x15 x22^2x15 x22 x23x15 x22 x24x15 x22 x25x15 x22 x26x15 x22 x27x15 x23^2x15 x23 x24x15 x23 x25x15 x23 x26x15 x23 x27x15 x24^2x15 x24 x25x15 x24 x26x15 x24 x27x15 x25^2x15 x25 x26x15 x25 x27x15 x26^2x15 x26 x27x15 x27^2x16^3x16^2 x17x16^2 x18x16^2 x19x16^2 x20x16^2 x21x16^2 x22x16^2 x23x16^2 x24x16^2 x25x16^2 x26x16^2 x27x16 x17^2x16 x17 x18x16 x17 x19x16 x17 x20x16 x17 x21x16 x17 x22x16 x17 x23x16 x17 x24x16 x17 x25x16 x17 x26x16 x17 x27x16 x18^2x16 x18 x19x16 x18 x20x16 x18 x21x16 x18 x22x16 x18 x23x16 x18 x24x16 x18 x25x16 x18 x26x16 x18 x27x16 x19^2x16 x19 x20x16 x19 x21x16 x19 x22x16 x19 x23x16 x19 x24x16 x19 x25x16 x19 x26x16 x19 x27x16 x20^2x16 x20 x21x16 x20 x22x16 x20 x23x16 x20 x24x16 x20 x25x16 x20 x26x16 x20 x27x16 x21^2x16 x21 x22x16 x21 x23x16 x21 x24x16 x21 x25x16 x21 x26x16 x21 x27x16 x22^2x16 x22 x23x16 x22 x24x16 x22 x25x16 x22 x26x16 x22 x27x16 x23^2x16 x23 x24x16 x23 x25x16 x23 x26x16 x23 x27x16 x24^2x16 x24 x25x16 x24 x26x16 x24 x27x16 x25^2x16 x25 x26x16 x25 x27x16 x26^2x16 x26 x27x16 x27^2x17^3x17^2 x18x17^2 x19x17^2 x20x17^2 x21x17^2 x22x17^2 x23x17^2 x24x17^2 x25x17^2 x26x17^2 x27x17 x18^2x17 x18 x19x17 x18 x20x17 x18 x21x17 x18 x22x17 x18 x23x17 x18 x24x17 x18 x25x17 x18 x26x17 x18 x27x17 x19^2x17 x19 x20x17 x19 x21x17 x19 x22x17 x19 x23x17 x19 x24x17 x19 x25x17 x19 x26x17 x19 x27x17 x20^2x17 x20 x21x17 x20 x22x17 x20 x23x17 x20 x24x17 x20 x25x17 x20 x26x17 x20 x27x17 x21^2x17 x21 x22x17 x21 x23x17 x21 x24x17 x21 x25x17 x21 x26x17 x21 x27x17 x22^2x17 x22 x23x17 x22 x24x17 x22 x25x17 x22 x26x17 x22 x27x17 x23^2x17 x23 x24x17 x23 x25x17 x23 x26x17 x23 x27x17 x24^2x17 x24 x25x17 x24 x26x17 x24 x27x17 x25^2x17 x25 x26x17 x25 x27x17 x26^2x17 x26 x27x17 x27^2x18^3x18^2 x19x18^2 x20x18^2 x21x18^2 x22x18^2 x23x18^2 x24x18^2 x25x18^2 x26x18^2 x27x18 x19^2x18 x19 x20x18 x19 x21x18 x19 x22x18 x19 x23x18 x19 x24x18 x19 x25x18 x19 x26x18 x19 x27x18 x20^2x18 x20 x21x18 x20 x22x18 x20 x23x18 x20 x24x18 x20 x25x18 x20 x26x18 x20 x27x18 x21^2x18 x21 x22x18 x21 x23x18 x21 x24x18 x21 x25x18 x21 x26x18 x21 x27x18 x22^2x18 x22 x23x18 x22 x24x18 x22 x25x18 x22 x26x18 x22 x27x18 x23^2x18 x23 x24x18 x23 x25x18 x23 x26x18 x23 x27x18 x24^2x18 x24 x25x18 x24 x26x18 x24 x27x18 x25^2x18 x25 x26x18 x25 x27x18 x26^2x18 x26 x27x18 x27^2x19^3x19^2 x20x19^2 x21x19^2 x22x19^2 x23x19^2 x24x19^2 x25x19^2 x26x19^2 x27x19 x20^2x19 x20 x21x19 x20 x22x19 x20 x23x19 x20 x24x19 x20 x25x19 x20 x26x19 x20 x27x19 x21^2x19 x21 x22x19 x21 x23x19 x21 x24x19 x21 x25x19 x21 x26x19 x21 x27x19 x22^2x19 x22 x23x19 x22 x24x19 x22 x25x19 x22 x26x19 x22 x27x19 x23^2x19 x23 x24x19 x23 x25x19 x23 x26x19 x23 x27x19 x24^2x19 x24 x25x19 x24 x26x19 x24 x27x19 x25^2x19 x25 x26x19 x25 x27x19 x26^2x19 x26 x27x19 x27^2x20^3x20^2 x21x20^2 x22x20^2 x23x20^2 x24x20^2 x25x20^2 x26x20^2 x27x20 x21^2x20 x21 x22x20 x21 x23x20 x21 x24x20 x21 x25x20 x21 x26x20 x21 x27x20 x22^2x20 x22 x23x20 x22 x24x20 x22 x25x20 x22 x26x20 x22 x27x20 x23^2x20 x23 x24x20 x23 x25x20 x23 x26x20 x23 x27x20 x24^2x20 x24 x25x20 x24 x26x20 x24 x27x20 x25^2x20 x25 x26x20 x25 x27x20 x26^2x20 x26 x27x20 x27^2x21^3x21^2 x22x21^2 x23x21^2 x24x21^2 x25x21^2 x26x21^2 x27x21 x22^2x21 x22 x23x21 x22 x24x21 x22 x25x21 x22 x26x21 x22 x27x21 x23^2x21 x23 x24x21 x23 x25x21 x23 x26x21 x23 x27x21 x24^2x21 x24 x25x21 x24 x26x21 x24 x27x21 x25^2x21 x25 x26x21 x25 x27x21 x26^2x21 x26 x27x21 x27^2x22^3x22^2 x23x22^2 x24x22^2 x25x22^2 x26x22^2 x27x22 x23^2x22 x23 x24x22 x23 x25x22 x23 x26x22 x23 x27x22 x24^2x22 x24 x25x22 x24 x26x22 x24 x27x22 x25^2x22 x25 x26x22 x25 x27x22 x26^2x22 x26 x27x22 x27^2x23^3x23^2 x24x23^2 x25x23^2 x26x23^2 x27x23 x24^2x23 x24 x25x23 x24 x26x23 x24 x27x23 x25^2x23 x25 x26x23 x25 x27x23 x26^2x23 x26 x27x23 x27^2x24^3x24^2 x25x24^2 x26x24^2 x27x24 x25^2x24 x25 x26x24 x25 x27x24 x26^2x24 x26 x27x24 x27^2x25^3x25^2 x26x25^2 x27x25 x26^2x25 x26 x27x25 x27^2x26^3x26^2 x27x26 x27^2x27^3
PC-10.0002900.0008160.002212-0.0018930.0118730.0003300.000413-0.0001100.000031-0.000119-0.0001120.0004010.000032-0.000075-0.0001100.000105-0.0000680.0001350.000329-0.0001990.000357-0.000084-0.0001750.000354-0.0000250.000108-0.0001730.000016-0.000866-0.0008540.0002610.0003680.002569-0.000736-0.0007940.0001540.0000220.000023-0.0000480.000194-0.000006-0.000085-0.000077-0.0000280.000016-0.0000260.000279-0.0000030.0001030.000278-0.0000200.000391-0.0001120.000048-0.000015-0.000080-0.0007440.001265-0.0003450.006456-0.000735-0.0007660.0001410.0001250.000040-0.0000380.000334-0.000026-0.000049-0.0000700.0000870.0000350.0000890.0004770.0001270.0002600.0003780.0000040.000482-0.0000050.000188-0.0000080.0000470.004738-0.0025470.017019-0.0000590.000623-0.0000330.000235-0.0000310.0000100.0004310.0001630.0000480.0000520.0010090.0000660.0002890.0008660.0002140.0006410.0002300.0000050.0005570.0003100.0009950.0000660.0002450.001297-0.0142420.0004210.000325-0.000009-0.000173-0.000023-0.000030-0.000491-0.000058-0.000012-0.000025-0.000309-0.000121-0.000595-0.000744-0.000226-0.000560-0.000653-0.000040-0.000552-0.000192-0.000386-0.000102-0.0005020.1017050.0033010.0033320.0000160.0011500.0000430.0000400.0051970.0010570.0002790.0000560.0017030.0002710.0020230.0069520.0012340.0065320.0020760.0001540.0057780.0011740.0021740.0001640.001962-0.000540-0.0006380.0001550.0000280.000022-0.0000560.0003470.000016-0.000087-0.000079-0.0001180.000036-0.0000730.000436-0.0000060.0002760.000222-0.0000290.000538-0.000103-0.000011-0.000023-0.000127-0.0007240.0001570.0000830.000024-0.0000390.000245-0.000004-0.000082-0.0000790.0000370.000023-0.0001080.0003700.0000680.0001600.000203-0.0000100.000432-0.0000620.000131-0.000011-0.000154-0.0001100.00.00.00.00.00.00.00.00.00.0-0.0000240.00.0-0.000110-0.000021-0.000011-0.000013-0.000015-0.000014-0.0000190.0000310.00.00.00.00.00.00.00.00.00.0001050.0000310.00.0-0.000011-0.0000220.000127-0.000017-0.000016-0.000017-0.0001190.00.00.00.00.00.00.00.0-0.000032-0.0001190.00.0-0.000018-0.000015-0.000018-0.000016-0.000017-0.000016-0.0001120.00.00.00.00.00.00.0-0.000036-0.0001120.00.0-0.000014-0.000017-0.000019-0.000012-0.000014-0.0000180.0004010.00.00.00.00.00.00.0004220.00.0004010.0-0.0000104.281049e-04-0.000006-0.000021-0.000012-0.0000070.0000320.00.00.00.00.00.0000750.00.0000320.0-0.0000230.000093-0.0000180.000036-0.000024-0.000020-0.0000750.00.00.00.0-0.0000230.0-0.0000750.0-0.000018-0.000009-0.000015-0.000013-1.806578e-05-0.000017-0.0001100.00.00.0-0.0000320.00.00.0-0.000020-0.000015-0.000016-0.000015-0.000018-0.0000090.0001050.00.0-0.0000280.00.00.0-0.000015-0.000014-0.0000140.000196-0.000010-0.000025-0.0000680.0-0.0000450.00.00.0-0.000012-0.000024-0.0000210.0000238.494807e-07-0.0000200.000135-0.0000290.00.00.0001353.755264e-07-0.000021-0.000008-0.000015-0.0000150.0002030.0003290.0000360.000474-0.0000760.00.000354-0.0000250.00.00.0-0.0001990.00.0-0.000044-0.0000540.000090-0.000044-0.000047-0.0000510.0003570.0-0.0000510.000512-0.0000380.000002-0.000054-0.000045-0.000084-0.000033-0.000051-0.000026-0.000053-0.0000440.000166-0.0001750.00.00.00.00.00.0003540.00.00.00.0-0.0000250.00.00.00.0001080.00.0-0.0001730.00.0000160.0006520.0008960.000277-0.0008090.0047100.0006640.000720-0.000238-0.000076-0.000020-0.0000370.000061-0.000066-0.000101-0.000067-0.000019-0.000018-0.000040-0.000036-0.000133-0.000106-0.000522-0.0002010.000056-0.000092-0.000110-0.000206-0.0001720.0010980.000093-0.0006930.0043770.0009190.000954-0.000225-0.000150-0.000021-0.0000250.000156-0.000075-0.000056-0.000061-0.000021-0.000038-0.000092-0.000018-0.0001960.000024-0.000561-0.0001930.000110-0.000128-0.000112-0.000196-0.0002180.0002660.0000800.0007660.0003430.0002980.000064-0.000137-0.000001-0.0000080.000238...0.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0000200.00.00.00.00.0-0.0000150.00.00.00.0-0.0000160.00.00.0-0.0000150.00.0-0.0000180.0-0.0000090.0001050.00.0-0.0000280.00.00.0-0.000015-0.000014-0.0000140.000196-0.000010-0.0000250.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0000280.00.00.00.0-0.000014-0.0000140.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0000150.00.00.00.00.0-0.0000140.00.00.00.0-0.0000140.00.00.00.0001960.00.0-0.0000100.0-0.000025-0.0000680.0-0.0000450.00.00.0-0.000012-0.000024-0.0000210.0000238.494807e-07-0.0000200.00.00.00.00.00.00.00.00.00.00.0-0.0000450.00.00.00.0-0.000024-0.0000210.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0000120.00.00.00.00.0-0.0000240.00.00.00.0-0.0000210.00.00.00.0000230.00.08.494807e-070.0-0.0000200.000135-0.0000290.00.00.0001353.755264e-07-0.000021-0.000008-0.000015-0.0000150.000203-0.0000290.00.0-0.0000290.0-0.000021-0.0000080.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0001353.755264e-07-0.000021-0.000008-0.000015-0.0000150.0002033.755264e-070.00.00.00.00.0-0.0000210.00.00.00.0-0.0000080.00.00.0-0.0000150.00.0-0.0000150.00.0002030.0003290.0000360.000474-0.0000760.00.000354-0.0000250.00.00.00.0000360.00.00.0-0.0000540.0000900.00.00.00.0004740.00.00.000512-0.0000380.00.00.0-0.0000760.0-0.000051-0.0000260.00.00.00.00.00.00.00.00.00.0003540.00.00.00.0-0.0000250.00.00.00.00.00.00.00.00.0-0.0001990.00.0-0.000044-0.0000540.000090-0.000044-0.000047-0.0000510.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0000440.00.00.00.00.0-0.0000540.00.00.00.00.0000900.00.00.0-0.0000440.00.0-0.0000470.0-0.0000510.0003570.0-0.0000510.000512-0.0000380.000002-0.000054-0.0000450.00.00.00.00.00.00.0-0.0000510.00.00.00.00.00.0005120.00.00.00.0-0.0000380.00.00.00.0000020.00.0-0.0000540.0-0.000045-0.000084-0.000033-0.000051-0.000026-0.000053-0.0000440.000166-0.0000330.00.00.00.00.0-0.0000510.00.00.00.0-0.0000260.00.00.0-0.0000530.00.0-0.0000440.00.000166-0.0001750.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0003540.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0000250.00.00.00.00.00.00.00.00.00.0001080.00.00.00.00.0-0.0001730.00.00.000016
PC-2-0.021090-0.0189540.031679-0.0070520.009876-0.021639-0.0205260.0023510.0015510.000012-0.000700-0.002477-0.002753-0.002158-0.0013080.0016670.0005530.001005-0.0016730.000863-0.0073880.0056140.000161-0.0018140.0001420.002061-0.0004570.0001570.0080020.007928-0.0166250.005613-0.0176090.0064090.007661-0.004243-0.0017570.000040-0.000317-0.001993-0.003577-0.002634-0.001150-0.000114-0.000629-0.001129-0.006437-0.002033-0.008204-0.008961-0.002981-0.003969-0.002468-0.003243-0.002183-0.0030070.008905-0.0071360.001708-0.0073140.0056900.007685-0.004004-0.001620-0.000006-0.000301-0.002148-0.003399-0.002541-0.0011930.001140-0.000563-0.000735-0.005925-0.001927-0.008088-0.008323-0.002814-0.004006-0.001919-0.001988-0.002039-0.0029320.089820-0.0341970.078531-0.020423-0.0130350.0041620.0034800.0012320.000294-0.0003190.0007760.0009120.0006930.0114670.0026510.0020470.0055390.0050060.0013690.0104930.0047210.0020040.0035340.0140920.0018780.0028990.015957-0.0251370.0081500.005207-0.000736-0.000690-0.000521-0.0002520.0016300.0008200.0004970.000159-0.004040-0.001359-0.001507-0.000700-0.0014630.002947-0.003296-0.0011770.001165-0.001864-0.004279-0.000192-0.0007150.029817-0.027895-0.0145680.0002520.0028570.0003150.000066-0.011763-0.002656-0.001195-0.0002090.0155990.0019000.004513-0.0083440.003238-0.0156150.0049620.000510-0.0124080.0040630.0146310.0009350.0031120.0054450.005915-0.003991-0.0017660.000096-0.000377-0.002348-0.003613-0.002480-0.001134-0.001054-0.000385-0.001154-0.006465-0.002048-0.008442-0.008577-0.002941-0.004042-0.002424-0.003926-0.002158-0.0030350.007738-0.004179-0.0015420.000064-0.000257-0.002073-0.003644-0.002706-0.0011880.000583-0.000469-0.001319-0.006463-0.001734-0.008423-0.009294-0.002857-0.004110-0.002353-0.002865-0.002077-0.0030680.002351-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.000643-0.0-0.00.0023510.0006060.0004290.0002140.0001360.0002600.0002510.001551-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.0004420.001551-0.0-0.00.0001950.0000220.0004200.0003700.0001360.0003220.000012-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0000900.000012-0.0-0.0-0.000065-0.000021-0.0000690.0000570.0000990.000058-0.000700-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.000206-0.000700-0.0-0.0-0.000076-0.000126-0.000079-0.000122-0.000087-0.000076-0.002477-0.0-0.0-0.0-0.0-0.0-0.0-0.001466-0.0-0.002477-0.0-0.000265-1.246766e-03-0.000219-0.000201-0.000154-0.000171-0.002753-0.0-0.0-0.0-0.0-0.0-0.000787-0.0-0.002753-0.0-0.000376-0.000509-0.000278-0.000560-0.000450-0.000342-0.002158-0.0-0.0-0.0-0.0-0.000640-0.0-0.002158-0.0-0.000223-0.000450-0.000190-0.000343-2.505720e-04-0.000251-0.001308-0.0-0.0-0.0-0.000418-0.0-0.0-0.0-0.000238-0.000201-0.000217-0.000150-0.000124-0.0001860.001667-0.0-0.0-0.000165-0.0-0.0-0.00.000316-0.000113-0.0000520.001779-0.000008-0.0001610.000553-0.00.000089-0.0-0.0-0.00.000017-0.0000470.0001360.0003872.879226e-06-0.0000050.0010050.000320-0.0-0.00.0010051.581754e-04-0.0000110.000331-0.0000270.0000280.000412-0.0016730.000146-0.0028920.001567-0.0-0.0018140.000142-0.0-0.0-0.00.000863-0.0-0.00.000055-0.0001260.0002720.0003050.0001470.000304-0.007388-0.0-0.000864-0.002206-0.000687-0.001104-0.000854-0.0007630.0056140.0008750.0008780.0006890.0008430.0003790.0009680.000161-0.0-0.0-0.0-0.0-0.0-0.001814-0.0-0.0-0.0-0.00.000142-0.0-0.0-0.00.002061-0.0-0.0-0.000457-0.00.000157-0.051553-0.0496590.0350850.002346-0.004067-0.048680-0.0505560.0080400.0021250.000061-0.000239-0.001909-0.004898-0.003294-0.001204-0.0001230.0007220.0014350.0009110.001947-0.0101010.0167620.0016750.0007250.0001870.0010180.0003400.001252-0.0500640.0327030.004294-0.010616-0.046657-0.0489270.0076410.0021700.000134-0.000183-0.001852-0.004559-0.003164-0.001255-0.0001000.0006970.0010870.0003630.002121-0.0095750.0160410.0018830.000387-0.0000240.0010560.0004750.001406-0.0515700.011346-0.0182480.0324890.034259-0.007574-0.0034580.000012-0.000006-0.000249...-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.000238-0.0-0.0-0.0-0.0-0.0-0.000201-0.0-0.0-0.0-0.0-0.000217-0.0-0.0-0.0-0.000150-0.0-0.0-0.000124-0.0-0.0001860.001667-0.0-0.0-0.000165-0.0-0.0-0.00.000316-0.000113-0.0000520.001779-0.000008-0.000161-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.000165-0.0-0.0-0.0-0.0-0.000113-0.000052-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.000316-0.0-0.0-0.0-0.0-0.0-0.000113-0.0-0.0-0.0-0.0-0.000052-0.0-0.0-0.00.001779-0.0-0.0-0.000008-0.0-0.0001610.000553-0.00.000089-0.0-0.0-0.00.000017-0.0000470.0001360.0003872.879226e-06-0.000005-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.000089-0.0-0.0-0.0-0.0-0.0000470.000136-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.000017-0.0-0.0-0.0-0.0-0.0-0.000047-0.0-0.0-0.0-0.00.000136-0.0-0.0-0.00.000387-0.0-0.02.879226e-06-0.0-0.0000050.0010050.000320-0.0-0.00.0010051.581754e-04-0.0000110.000331-0.0000270.0000280.0004120.000320-0.0-0.00.000320-0.0-0.0000110.000331-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.0010051.581754e-04-0.0000110.000331-0.0000270.0000280.0004121.581754e-04-0.0-0.0-0.0-0.0-0.0-0.000011-0.0-0.0-0.0-0.00.000331-0.0-0.0-0.0-0.000027-0.0-0.00.000028-0.00.000412-0.0016730.000146-0.0028920.001567-0.0-0.0018140.000142-0.0-0.0-0.00.000146-0.0-0.0-0.0-0.0001260.000272-0.0-0.0-0.0-0.002892-0.0-0.0-0.002206-0.000687-0.0-0.0-0.00.001567-0.00.0008780.000689-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.001814-0.0-0.0-0.0-0.00.000142-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.000863-0.0-0.00.000055-0.0001260.0002720.0003050.0001470.000304-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.000055-0.0-0.0-0.0-0.0-0.0-0.000126-0.0-0.0-0.0-0.00.000272-0.0-0.0-0.00.000305-0.0-0.00.000147-0.00.000304-0.007388-0.0-0.000864-0.002206-0.000687-0.001104-0.000854-0.000763-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.000864-0.0-0.0-0.0-0.0-0.0-0.002206-0.0-0.0-0.0-0.0-0.000687-0.0-0.0-0.0-0.001104-0.0-0.0-0.000854-0.0-0.0007630.0056140.0008750.0008780.0006890.0008430.0003790.0009680.000875-0.0-0.0-0.0-0.0-0.00.000878-0.0-0.0-0.0-0.00.000689-0.0-0.0-0.00.000843-0.0-0.00.000379-0.00.0009680.000161-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.001814-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.000142-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.002061-0.0-0.0-0.0-0.0-0.0-0.000457-0.0-0.00.000157
PC-30.0660110.066325-0.016881-0.0227930.0069620.0626770.065717-0.008503-0.0035150.0005780.0014960.0030870.0072950.0053480.0029910.002409-0.000471-0.0023200.000921-0.0014410.015730-0.0192170.000019-0.0006870.0016080.0000840.000605-0.000109-0.041244-0.0460840.0272210.013977-0.015471-0.036615-0.0417340.0151650.0051430.0001520.0008220.0035940.0102660.0066330.0029620.0006330.0011620.0035580.0158790.0061170.0204930.0346440.0096410.0102920.0055870.0097910.0092810.010385-0.0505720.0292650.014895-0.011836-0.041457-0.0456540.0148330.0062360.0001660.0007200.0030060.0096010.0060210.0030080.0013630.0015620.0034610.0151500.0071230.0186290.0346410.0097700.0099160.0052340.0104330.0092890.010535-0.011092-0.0002230.0293090.0228930.026424-0.007562-0.0015360.0001880.000099-0.000464-0.001689-0.002014-0.0009280.003594-0.000276-0.000294-0.004164-0.001249-0.004166-0.013857-0.005630-0.003076-0.0010890.001559-0.001330-0.002525-0.018495-0.0055890.0130420.013562-0.001407-0.003151-0.0004280.000170-0.001148-0.002546-0.001103-0.000836-0.002078-0.001965-0.003064-0.005934-0.003409-0.004798-0.009706-0.001538-0.004352-0.001583-0.005050-0.003782-0.0033410.019481-0.019213-0.0132610.0011150.0020570.000044-0.000128-0.004686-0.001518-0.0007980.0003340.0063990.0008500.001255-0.0036300.001973-0.0070020.0044080.000353-0.0041870.0005570.0075840.0004290.001515-0.032695-0.0373610.0144070.0048230.0002640.0009520.0035400.0100900.0063430.0029350.0001810.0010690.0032680.0149290.0060380.0199720.0324810.0089630.0094340.0054950.0091490.0089750.010126-0.0422050.0153430.0053570.0000910.0006400.0033710.0102040.0066930.0029890.0009350.0010490.0033290.0160550.0060880.0202680.0343880.0094540.0105070.0055480.0101540.0089230.010105-0.008503-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.001678-0.0-0.0-0.008503-0.001917-0.001071-0.000608-0.000846-0.001262-0.001155-0.003515-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.000632-0.003515-0.0-0.0-0.000630-0.000398-0.000235-0.000624-0.000558-0.0003880.000578-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.0001660.000578-0.0-0.00.0000850.0000950.0000710.0000670.0000990.0000810.001496-0.0-0.0-0.0-0.0-0.0-0.0-0.00.0004980.001496-0.0-0.00.0001760.0002490.0002490.0001920.0001860.0002440.003087-0.0-0.0-0.0-0.0-0.0-0.00.000908-0.00.003087-0.00.0005482.053817e-040.0007020.0005450.0004030.0003790.007295-0.0-0.0-0.0-0.0-0.00.001845-0.00.007295-0.00.0012170.0009410.0009040.0008380.0014880.0012290.005348-0.0-0.0-0.0-0.00.001429-0.00.005348-0.00.0006830.0009110.0005170.0008447.650545e-040.0007130.002991-0.0-0.0-0.00.000990-0.0-0.0-0.00.0004890.0004930.0004970.0002930.0002950.0005270.002409-0.0-0.00.000350-0.0-0.0-0.00.0002190.0001950.0001560.0010040.0003180.000308-0.000471-0.0-0.000261-0.0-0.0-0.0-0.000180-0.000170-0.0000910.000052-1.853918e-05-0.000086-0.002320-0.000733-0.0-0.0-0.002320-3.901327e-04-0.000438-0.000295-0.000248-0.000466-0.0003260.0009210.0000320.004182-0.004373-0.0-0.0006870.001608-0.0-0.0-0.0-0.001441-0.0-0.0-0.000370-0.0000540.000086-0.000365-0.000273-0.0000630.015730-0.00.0024480.0020580.0021240.0022260.0026560.002321-0.019217-0.002586-0.003209-0.001164-0.003127-0.002373-0.0031150.000019-0.0-0.0-0.0-0.0-0.0-0.000687-0.0-0.0-0.0-0.00.001608-0.0-0.0-0.00.000084-0.0-0.00.000605-0.0-0.0001090.1858100.183678-0.066726-0.0500060.0067000.1743280.182741-0.028416-0.007564-0.0000170.0006930.0046000.0151240.0084530.0033550.000406-0.001371-0.005358-0.004944-0.0068880.028176-0.064921-0.005753-0.0059730.001029-0.007933-0.004225-0.0063020.187307-0.067880-0.0528840.0104690.1714730.181107-0.027942-0.009082-0.0000830.0005320.0037450.0138270.0076370.0034150.000530-0.001783-0.005125-0.006088-0.0086340.025209-0.064821-0.006503-0.0065560.000468-0.008846-0.004831-0.0070670.095980-0.017856-0.002321-0.060830-0.0661350.0150820.0016870.0003150.0002700.000128...-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.000489-0.0-0.0-0.0-0.0-0.00.000493-0.0-0.0-0.0-0.00.000497-0.0-0.0-0.00.000293-0.0-0.00.000295-0.00.0005270.002409-0.0-0.00.000350-0.0-0.0-0.00.0002190.0001950.0001560.0010040.0003180.000308-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.000350-0.0-0.0-0.0-0.00.0001950.000156-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.000219-0.0-0.0-0.0-0.0-0.00.000195-0.0-0.0-0.0-0.00.000156-0.0-0.0-0.00.001004-0.0-0.00.000318-0.00.000308-0.000471-0.0-0.000261-0.0-0.0-0.0-0.000180-0.000170-0.0000910.000052-1.853918e-05-0.000086-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.000261-0.0-0.0-0.0-0.0-0.000170-0.000091-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.000180-0.0-0.0-0.0-0.0-0.0-0.000170-0.0-0.0-0.0-0.0-0.000091-0.0-0.0-0.00.000052-0.0-0.0-1.853918e-05-0.0-0.000086-0.002320-0.000733-0.0-0.0-0.002320-3.901327e-04-0.000438-0.000295-0.000248-0.000466-0.000326-0.000733-0.0-0.0-0.000733-0.0-0.000438-0.000295-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.002320-3.901327e-04-0.000438-0.000295-0.000248-0.000466-0.000326-3.901327e-04-0.0-0.0-0.0-0.0-0.0-0.000438-0.0-0.0-0.0-0.0-0.000295-0.0-0.0-0.0-0.000248-0.0-0.0-0.000466-0.0-0.0003260.0009210.0000320.004182-0.004373-0.0-0.0006870.001608-0.0-0.0-0.00.000032-0.0-0.0-0.0-0.0000540.000086-0.0-0.0-0.00.004182-0.0-0.00.0020580.002124-0.0-0.0-0.0-0.004373-0.0-0.003209-0.001164-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.000687-0.0-0.0-0.0-0.00.001608-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.001441-0.0-0.0-0.000370-0.0000540.000086-0.000365-0.000273-0.000063-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.000370-0.0-0.0-0.0-0.0-0.0-0.000054-0.0-0.0-0.0-0.00.000086-0.0-0.0-0.0-0.000365-0.0-0.0-0.000273-0.0-0.0000630.015730-0.00.0024480.0020580.0021240.0022260.0026560.002321-0.0-0.0-0.0-0.0-0.0-0.0-0.00.002448-0.0-0.0-0.0-0.0-0.00.002058-0.0-0.0-0.0-0.00.002124-0.0-0.0-0.00.002226-0.0-0.00.002656-0.00.002321-0.019217-0.002586-0.003209-0.001164-0.003127-0.002373-0.003115-0.002586-0.0-0.0-0.0-0.0-0.0-0.003209-0.0-0.0-0.0-0.0-0.001164-0.0-0.0-0.0-0.003127-0.0-0.0-0.002373-0.0-0.0031150.000019-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.000687-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.001608-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.0-0.00.000084-0.0-0.0-0.0-0.0-0.00.000605-0.0-0.0-0.000109
PC-4-0.012215-0.011060-0.0384030.021049-0.000039-0.012307-0.013006-0.0004320.000835-0.0005010.000240-0.001832-0.002189-0.000974-0.000018-0.0011410.0007440.004840-0.0006690.000574-0.0049950.004836-0.001065-0.0016770.001008-0.0015320.0010610.002213-0.003041-0.0039070.019208-0.009009-0.034570-0.002889-0.0025440.001107-0.000799-0.000288-0.000055-0.001486-0.002770-0.001323-0.000363-0.000171-0.000663-0.003554-0.003672-0.001143-0.005579-0.004296-0.000074-0.002394-0.001279-0.002312-0.002397-0.002177-0.0047760.013859-0.011363-0.023475-0.003903-0.0039380.000930-0.000374-0.0001010.000016-0.001818-0.002435-0.001509-0.000444-0.000995-0.000678-0.001701-0.003384-0.000460-0.005762-0.002720-0.000273-0.002770-0.000614-0.002848-0.002406-0.000371-0.1116820.0340070.0007340.0217420.017483-0.006605-0.005549-0.003227-0.000701-0.001413-0.001329-0.000211-0.000764-0.008949-0.0040180.001432-0.009835-0.009477-0.002953-0.012242-0.007866-0.007406-0.002429-0.011433-0.003151-0.0026050.010637-0.036463-0.008064-0.0076420.0034340.0014380.0017420.0004810.0019670.0018160.0008690.0008570.0036820.002675-0.0035920.0084030.0036600.0046520.0055230.0041340.0060530.0023500.0063480.001629-0.0025430.026113-0.040225-0.041199-0.0007770.006838-0.000061-0.000192-0.011738-0.007910-0.003502-0.001092-0.0048660.0019070.022065-0.0115390.006585-0.0231510.0205780.001415-0.0168230.005284-0.0075380.0006890.019232-0.002834-0.0022440.000877-0.000440-0.000341-0.000042-0.001834-0.002924-0.001218-0.0003160.000382-0.000653-0.004135-0.004185-0.000823-0.005976-0.0049200.000009-0.002729-0.001455-0.001871-0.002388-0.002377-0.0020850.000841-0.000826-0.000343-0.000028-0.001576-0.002763-0.001373-0.000371-0.000605-0.000785-0.004037-0.003614-0.001197-0.005712-0.004337-0.000171-0.002560-0.001054-0.002159-0.002406-0.003013-0.0004320.00.00.00.00.00.00.00.00.00.0-0.0002880.00.0-0.000432-0.000610-0.000202-0.0000860.0002100.0002980.0002730.0008350.00.00.00.00.00.00.00.00.00.0012360.0008350.00.00.0002680.0001760.001060-0.0004820.000088-0.000665-0.0005010.00.00.00.00.00.00.00.00.000087-0.0005010.00.00.000065-0.0000340.000121-0.000205-0.000386-0.0000710.0002400.00.00.00.00.00.00.0-0.0000260.0002400.00.00.0000220.000019-0.0000450.0000910.0000420.000018-0.0018320.00.00.00.00.00.0-0.0012740.0-0.0018320.0-0.000142-9.556352e-04-0.0003190.000002-0.000085-0.000125-0.0021890.00.00.00.00.0-0.0009120.0-0.0021890.0-0.000079-0.000841-0.000071-0.000642-0.000243-0.000214-0.0009740.00.00.00.0-0.0002350.0-0.0009740.0-0.000007-0.0002800.000044-0.0002762.492292e-05-0.000029-0.0000180.00.00.0-0.0000710.00.00.0-0.000028-0.0000750.0000040.0000910.000058-0.000126-0.0011410.00.00.0000840.00.00.0-0.0010310.000095-0.000011-0.0004620.0000390.0001450.0007440.0-0.0000150.00.00.00.0000640.000212-0.0002270.0001695.461344e-040.0000930.0048400.0006040.00.00.0048405.525942e-040.0003990.0002050.0003480.0004850.002546-0.0006690.001298-0.0024220.0004580.0-0.0016770.0010080.00.00.00.0005740.00.00.0003560.0001610.001136-0.000596-0.000256-0.000718-0.0049950.0-0.000229-0.002076-0.000345-0.000916-0.000304-0.0003680.004836-0.0001970.0000060.0004510.0001830.0009780.003187-0.0010650.00.00.00.00.0-0.0016770.00.00.00.00.0010080.00.00.0-0.0015320.00.00.0010610.00.002213-0.015181-0.015643-0.0468010.036834-0.014489-0.015328-0.015895-0.0026270.001251-0.000164-0.000097-0.001444-0.003734-0.001782-0.0006500.0000030.0001960.003454-0.0020860.000991-0.0069600.003377-0.002838-0.0024110.0003250.0006240.0018190.000514-0.016758-0.0449580.040025-0.024610-0.015477-0.016403-0.0022350.001086-0.000345-0.000086-0.001581-0.003277-0.002002-0.000738-0.0001110.0002000.002481-0.0018180.000655-0.0068600.002948-0.003385-0.001677-0.0001410.0009560.001887-0.0004060.052325-0.002956-0.025595-0.044594-0.0445450.0114820.006871-0.000443-0.000264-0.000955...0.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0000280.00.00.00.00.0-0.0000750.00.00.00.00.0000040.00.00.00.0000910.00.00.0000580.0-0.000126-0.0011410.00.00.0000840.00.00.0-0.0010310.000095-0.000011-0.0004620.0000390.0001450.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0000840.00.00.00.00.000095-0.0000110.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0010310.00.00.00.00.00.0000950.00.00.00.0-0.0000110.00.00.0-0.0004620.00.00.0000390.00.0001450.0007440.0-0.0000150.00.00.00.0000640.000212-0.0002270.0001695.461344e-040.0000930.00.00.00.00.00.00.00.00.00.00.0-0.0000150.00.00.00.00.000212-0.0002270.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0000640.00.00.00.00.00.0002120.00.00.00.0-0.0002270.00.00.00.0001690.00.05.461344e-040.00.0000930.0048400.0006040.00.00.0048405.525942e-040.0003990.0002050.0003480.0004850.0025460.0006040.00.00.0006040.00.0003990.0002050.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0048405.525942e-040.0003990.0002050.0003480.0004850.0025465.525942e-040.00.00.00.00.00.0003990.00.00.00.00.0002050.00.00.00.0003480.00.00.0004850.00.002546-0.0006690.001298-0.0024220.0004580.0-0.0016770.0010080.00.00.00.0012980.00.00.00.0001610.0011360.00.00.0-0.0024220.00.0-0.002076-0.0003450.00.00.00.0004580.00.0000060.0004510.00.00.00.00.00.00.00.00.0-0.0016770.00.00.00.00.0010080.00.00.00.00.00.00.00.00.00.0005740.00.00.0003560.0001610.001136-0.000596-0.000256-0.0007180.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0003560.00.00.00.00.00.0001610.00.00.00.00.0011360.00.00.0-0.0005960.00.0-0.0002560.0-0.000718-0.0049950.0-0.000229-0.002076-0.000345-0.000916-0.000304-0.0003680.00.00.00.00.00.00.0-0.0002290.00.00.00.00.0-0.0020760.00.00.00.0-0.0003450.00.00.0-0.0009160.00.0-0.0003040.0-0.0003680.004836-0.0001970.0000060.0004510.0001830.0009780.003187-0.0001970.00.00.00.00.00.0000060.00.00.00.00.0004510.00.00.00.0001830.00.00.0009780.00.003187-0.0010650.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0016770.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0010080.00.00.00.00.00.00.00.00.0-0.0015320.00.00.00.00.00.0010610.00.00.002213
PC-50.0088260.0113000.049471-0.0569080.0105710.0081810.0076410.0006110.0007470.000429-0.0004400.0003280.0006830.000012-0.000377-0.001224-0.0002640.000569-0.0014850.0007360.0010230.0001050.002398-0.0023480.000864-0.001798-0.0009880.002292-0.003565-0.008040-0.0428080.045771-0.031402-0.002650-0.004807-0.0012570.0005350.000414-0.0000440.0009790.0017360.0001940.0001160.0001780.0006590.0013320.0017570.0009050.0029090.004058-0.0011230.002425-0.0006690.0024780.0036390.001093-0.010969-0.0383280.042172-0.024921-0.006803-0.009799-0.0007720.0014270.000158-0.0001410.0007580.0015560.0000190.000152-0.0004380.0011020.0028780.0026100.0014440.0023340.006707-0.0006920.002951-0.0003410.0021800.0040270.0017870.094382-0.039798-0.045976-0.041438-0.0453350.0109510.0109240.0035650.0007410.0003920.0005420.0007020.000892-0.0019720.0064330.0062240.0161830.0152310.0016360.0272500.0105280.0080660.0081170.0033820.0044540.009235-0.002126-0.0179530.0451670.047662-0.007518-0.008320-0.003499-0.000926-0.001050-0.001882-0.000692-0.001044-0.000873-0.007825-0.011709-0.018590-0.012745-0.003623-0.030797-0.007538-0.009295-0.009296-0.007251-0.005644-0.0109330.007692-0.029271-0.0408670.0019190.0033730.0002330.000120-0.001613-0.005113-0.0010400.000302-0.0143450.0028190.0207360.0003400.003727-0.0077660.0258350.001670-0.0036620.004002-0.0125090.0024480.017228-0.001999-0.003363-0.0009500.0000830.000494-0.0000240.0010530.0016980.0002410.0001450.0007260.0007890.0005720.0017060.0005530.0029920.002974-0.0014440.002275-0.0005690.0031560.0035300.000166-0.005462-0.0007460.0012330.000423-0.0000950.0007820.0015940.0001210.000107-0.0001580.0008800.0002550.0018890.0015610.0024980.002752-0.0009800.002438-0.0005480.0015680.0034770.0004620.0006110.00.00.00.00.00.00.00.00.00.00.0002480.00.00.0006110.001159-0.0000960.000344-0.000345-0.000460-0.0004650.0007470.00.00.00.00.00.00.00.00.0-0.0002520.0007470.00.0-0.000032-0.0002770.0000250.000676-0.0003040.0011100.0004290.00.00.00.00.00.00.00.0-0.0001360.0004290.00.0-0.0001920.000041-0.0001770.0001800.0004690.000155-0.0004400.00.00.00.00.00.00.0-0.000135-0.0004400.00.0-0.000014-0.0001630.000027-0.000073-0.000041-0.0000450.0003280.00.00.00.00.00.0-0.0000270.00.0003280.00.0000888.713002e-08-0.0000270.0000330.0000190.0001270.0006830.00.00.00.00.0-0.0004480.00.0006830.00.000184-0.0004990.0000520.0001150.0003960.0004100.0000120.00.00.00.0-0.0001370.00.0000120.00.000053-0.000047-0.0000900.0000958.776719e-070.000054-0.0003770.00.00.0-0.0000180.00.00.0-0.0000260.000035-0.000053-0.000166-0.000068-0.000030-0.0012240.00.00.0000360.00.00.00.001040-0.0000480.000084-0.002096-0.000065-0.000091-0.0002640.0-0.0002440.00.00.0-0.000142-0.0004820.0002380.000228-1.847632e-04-0.0001180.000569-0.0003880.00.00.0005692.102541e-05-0.0007460.000358-0.000363-0.0003970.001683-0.001485-0.000524-0.000612-0.0001220.0-0.0023480.0008640.00.00.00.0007360.00.0-0.000238-0.000399-0.0001250.0007830.0001230.0012210.0010230.00.000324-0.000547-0.0000650.0002440.0004150.0005910.0001050.001439-0.0009070.000785-0.000791-0.0012100.0007200.0023980.00.00.00.00.0-0.0023480.00.00.00.00.0008640.00.00.0-0.0017980.00.0-0.0009880.00.0022920.0271760.0314290.080853-0.0869330.0172890.0257980.0278020.002941-0.0024730.0001030.0000240.0015860.0034850.0004650.0004840.000022-0.000409-0.003135-0.001785-0.0023460.005536-0.0068530.005314-0.0027350.000950-0.003756-0.003466-0.0004820.0346030.074672-0.0855430.0092580.0298970.0321110.002045-0.0034630.000371-0.0000040.0013880.0030750.0002300.0005150.000109-0.000745-0.004008-0.003674-0.0030950.004693-0.0095160.005472-0.0039660.000292-0.004726-0.003945-0.000926-0.0992870.021867-0.0276240.0778280.078127-0.018867-0.0123710.0003330.0002410.000714...0.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0000260.00.00.00.00.00.0000350.00.00.00.0-0.0000530.00.00.0-0.0001660.00.0-0.0000680.0-0.000030-0.0012240.00.00.0000360.00.00.00.001040-0.0000480.000084-0.002096-0.000065-0.0000910.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0000360.00.00.00.0-0.0000480.0000840.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0010400.00.00.00.00.0-0.0000480.00.00.00.00.0000840.00.00.0-0.0020960.00.0-0.0000650.0-0.000091-0.0002640.0-0.0002440.00.00.0-0.000142-0.0004820.0002380.000228-1.847632e-04-0.0001180.00.00.00.00.00.00.00.00.00.00.0-0.0002440.00.00.00.0-0.0004820.0002380.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0001420.00.00.00.00.0-0.0004820.00.00.00.00.0002380.00.00.00.0002280.00.0-1.847632e-040.0-0.0001180.000569-0.0003880.00.00.0005692.102541e-05-0.0007460.000358-0.000363-0.0003970.001683-0.0003880.00.0-0.0003880.0-0.0007460.0003580.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0005692.102541e-05-0.0007460.000358-0.000363-0.0003970.0016832.102541e-050.00.00.00.00.0-0.0007460.00.00.00.00.0003580.00.00.0-0.0003630.00.0-0.0003970.00.001683-0.001485-0.000524-0.000612-0.0001220.0-0.0023480.0008640.00.00.0-0.0005240.00.00.0-0.000399-0.0001250.00.00.0-0.0006120.00.0-0.000547-0.0000650.00.00.0-0.0001220.0-0.0009070.0007850.00.00.00.00.00.00.00.00.0-0.0023480.00.00.00.00.0008640.00.00.00.00.00.00.00.00.00.0007360.00.0-0.000238-0.000399-0.0001250.0007830.0001230.0012210.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0002380.00.00.00.00.0-0.0003990.00.00.00.0-0.0001250.00.00.00.0007830.00.00.0001230.00.0012210.0010230.00.000324-0.000547-0.0000650.0002440.0004150.0005910.00.00.00.00.00.00.00.0003240.00.00.00.00.0-0.0005470.00.00.00.0-0.0000650.00.00.00.0002440.00.00.0004150.00.0005910.0001050.001439-0.0009070.000785-0.000791-0.0012100.0007200.0014390.00.00.00.00.0-0.0009070.00.00.00.00.0007850.00.00.0-0.0007910.00.0-0.0012100.00.0007200.0023980.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0-0.0023480.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0008640.00.00.00.00.00.00.00.00.0-0.0017980.00.00.00.00.0-0.0009880.00.00.002292
\n", "

5 rows × 4494 columns

\n", "
" ], "text/plain": [ " x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x0^2 x0 x1 x0 x2 x0 x3 x0 x4 x0 x5 x0 x6 x0 x7 x0 x8 x0 x9 x0 x10 x0 x11 x0 x12 x0 x13 x0 x14 x0 x15 x0 x16 x0 x17 x0 x18 x0 x19 x0 x20 x0 x21 x0 x22 x0 x23 x0 x24 x0 x25 x0 x26 x0 x27 x1^2 x1 x2 x1 x3 x1 x4 x1 x5 x1 x6 x1 x7 x1 x8 x1 x9 x1 x10 x1 x11 x1 x12 x1 x13 x1 x14 x1 x15 x1 x16 x1 x17 x1 x18 x1 x19 x1 x20 x1 x21 x1 x22 x1 x23 x1 x24 x1 x25 x1 x26 x1 x27 x2^2 x2 x3 x2 x4 x2 x5 x2 x6 x2 x7 x2 x8 x2 x9 x2 x10 x2 x11 x2 x12 x2 x13 x2 x14 x2 x15 x2 x16 x2 x17 \\\n", "PC-1 0.000290 0.000816 0.002212 -0.001893 0.011873 0.000330 0.000413 -0.000110 0.000031 -0.000119 -0.000112 0.000401 0.000032 -0.000075 -0.000110 0.000105 -0.000068 0.000135 0.000329 -0.000199 0.000357 -0.000084 -0.000175 0.000354 -0.000025 0.000108 -0.000173 0.000016 -0.000866 -0.000854 0.000261 0.000368 0.002569 -0.000736 -0.000794 0.000154 0.000022 0.000023 -0.000048 0.000194 -0.000006 -0.000085 -0.000077 -0.000028 0.000016 -0.000026 0.000279 -0.000003 0.000103 0.000278 -0.000020 0.000391 -0.000112 0.000048 -0.000015 -0.000080 -0.000744 0.001265 -0.000345 0.006456 -0.000735 -0.000766 0.000141 0.000125 0.000040 -0.000038 0.000334 -0.000026 -0.000049 -0.000070 0.000087 0.000035 0.000089 0.000477 0.000127 0.000260 0.000378 0.000004 0.000482 -0.000005 0.000188 -0.000008 0.000047 0.004738 -0.002547 0.017019 -0.000059 0.000623 -0.000033 0.000235 -0.000031 0.000010 0.000431 0.000163 0.000048 0.000052 0.001009 0.000066 0.000289 \n", "PC-2 -0.021090 -0.018954 0.031679 -0.007052 0.009876 -0.021639 -0.020526 0.002351 0.001551 0.000012 -0.000700 -0.002477 -0.002753 -0.002158 -0.001308 0.001667 0.000553 0.001005 -0.001673 0.000863 -0.007388 0.005614 0.000161 -0.001814 0.000142 0.002061 -0.000457 0.000157 0.008002 0.007928 -0.016625 0.005613 -0.017609 0.006409 0.007661 -0.004243 -0.001757 0.000040 -0.000317 -0.001993 -0.003577 -0.002634 -0.001150 -0.000114 -0.000629 -0.001129 -0.006437 -0.002033 -0.008204 -0.008961 -0.002981 -0.003969 -0.002468 -0.003243 -0.002183 -0.003007 0.008905 -0.007136 0.001708 -0.007314 0.005690 0.007685 -0.004004 -0.001620 -0.000006 -0.000301 -0.002148 -0.003399 -0.002541 -0.001193 0.001140 -0.000563 -0.000735 -0.005925 -0.001927 -0.008088 -0.008323 -0.002814 -0.004006 -0.001919 -0.001988 -0.002039 -0.002932 0.089820 -0.034197 0.078531 -0.020423 -0.013035 0.004162 0.003480 0.001232 0.000294 -0.000319 0.000776 0.000912 0.000693 0.011467 0.002651 0.002047 \n", "PC-3 0.066011 0.066325 -0.016881 -0.022793 0.006962 0.062677 0.065717 -0.008503 -0.003515 0.000578 0.001496 0.003087 0.007295 0.005348 0.002991 0.002409 -0.000471 -0.002320 0.000921 -0.001441 0.015730 -0.019217 0.000019 -0.000687 0.001608 0.000084 0.000605 -0.000109 -0.041244 -0.046084 0.027221 0.013977 -0.015471 -0.036615 -0.041734 0.015165 0.005143 0.000152 0.000822 0.003594 0.010266 0.006633 0.002962 0.000633 0.001162 0.003558 0.015879 0.006117 0.020493 0.034644 0.009641 0.010292 0.005587 0.009791 0.009281 0.010385 -0.050572 0.029265 0.014895 -0.011836 -0.041457 -0.045654 0.014833 0.006236 0.000166 0.000720 0.003006 0.009601 0.006021 0.003008 0.001363 0.001562 0.003461 0.015150 0.007123 0.018629 0.034641 0.009770 0.009916 0.005234 0.010433 0.009289 0.010535 -0.011092 -0.000223 0.029309 0.022893 0.026424 -0.007562 -0.001536 0.000188 0.000099 -0.000464 -0.001689 -0.002014 -0.000928 0.003594 -0.000276 -0.000294 \n", "PC-4 -0.012215 -0.011060 -0.038403 0.021049 -0.000039 -0.012307 -0.013006 -0.000432 0.000835 -0.000501 0.000240 -0.001832 -0.002189 -0.000974 -0.000018 -0.001141 0.000744 0.004840 -0.000669 0.000574 -0.004995 0.004836 -0.001065 -0.001677 0.001008 -0.001532 0.001061 0.002213 -0.003041 -0.003907 0.019208 -0.009009 -0.034570 -0.002889 -0.002544 0.001107 -0.000799 -0.000288 -0.000055 -0.001486 -0.002770 -0.001323 -0.000363 -0.000171 -0.000663 -0.003554 -0.003672 -0.001143 -0.005579 -0.004296 -0.000074 -0.002394 -0.001279 -0.002312 -0.002397 -0.002177 -0.004776 0.013859 -0.011363 -0.023475 -0.003903 -0.003938 0.000930 -0.000374 -0.000101 0.000016 -0.001818 -0.002435 -0.001509 -0.000444 -0.000995 -0.000678 -0.001701 -0.003384 -0.000460 -0.005762 -0.002720 -0.000273 -0.002770 -0.000614 -0.002848 -0.002406 -0.000371 -0.111682 0.034007 0.000734 0.021742 0.017483 -0.006605 -0.005549 -0.003227 -0.000701 -0.001413 -0.001329 -0.000211 -0.000764 -0.008949 -0.004018 0.001432 \n", "PC-5 0.008826 0.011300 0.049471 -0.056908 0.010571 0.008181 0.007641 0.000611 0.000747 0.000429 -0.000440 0.000328 0.000683 0.000012 -0.000377 -0.001224 -0.000264 0.000569 -0.001485 0.000736 0.001023 0.000105 0.002398 -0.002348 0.000864 -0.001798 -0.000988 0.002292 -0.003565 -0.008040 -0.042808 0.045771 -0.031402 -0.002650 -0.004807 -0.001257 0.000535 0.000414 -0.000044 0.000979 0.001736 0.000194 0.000116 0.000178 0.000659 0.001332 0.001757 0.000905 0.002909 0.004058 -0.001123 0.002425 -0.000669 0.002478 0.003639 0.001093 -0.010969 -0.038328 0.042172 -0.024921 -0.006803 -0.009799 -0.000772 0.001427 0.000158 -0.000141 0.000758 0.001556 0.000019 0.000152 -0.000438 0.001102 0.002878 0.002610 0.001444 0.002334 0.006707 -0.000692 0.002951 -0.000341 0.002180 0.004027 0.001787 0.094382 -0.039798 -0.045976 -0.041438 -0.045335 0.010951 0.010924 0.003565 0.000741 0.000392 0.000542 0.000702 0.000892 -0.001972 0.006433 0.006224 \n", "\n", " x2 x18 x2 x19 x2 x20 x2 x21 x2 x22 x2 x23 x2 x24 x2 x25 x2 x26 x2 x27 x3^2 x3 x4 x3 x5 x3 x6 x3 x7 x3 x8 x3 x9 x3 x10 x3 x11 x3 x12 x3 x13 x3 x14 x3 x15 x3 x16 x3 x17 x3 x18 x3 x19 x3 x20 x3 x21 x3 x22 x3 x23 x3 x24 x3 x25 x3 x26 x3 x27 x4^2 x4 x5 x4 x6 x4 x7 x4 x8 x4 x9 x4 x10 x4 x11 x4 x12 x4 x13 x4 x14 x4 x15 x4 x16 x4 x17 x4 x18 x4 x19 x4 x20 x4 x21 x4 x22 x4 x23 x4 x24 x4 x25 x4 x26 x4 x27 x5^2 x5 x6 x5 x7 x5 x8 x5 x9 x5 x10 x5 x11 x5 x12 x5 x13 x5 x14 x5 x15 x5 x16 x5 x17 x5 x18 x5 x19 x5 x20 x5 x21 x5 x22 x5 x23 x5 x24 x5 x25 x5 x26 x5 x27 x6^2 x6 x7 x6 x8 x6 x9 x6 x10 x6 x11 x6 x12 x6 x13 x6 x14 x6 x15 x6 x16 x6 x17 x6 x18 x6 x19 x6 x20 x6 x21 x6 x22 \\\n", "PC-1 0.000866 0.000214 0.000641 0.000230 0.000005 0.000557 0.000310 0.000995 0.000066 0.000245 0.001297 -0.014242 0.000421 0.000325 -0.000009 -0.000173 -0.000023 -0.000030 -0.000491 -0.000058 -0.000012 -0.000025 -0.000309 -0.000121 -0.000595 -0.000744 -0.000226 -0.000560 -0.000653 -0.000040 -0.000552 -0.000192 -0.000386 -0.000102 -0.000502 0.101705 0.003301 0.003332 0.000016 0.001150 0.000043 0.000040 0.005197 0.001057 0.000279 0.000056 0.001703 0.000271 0.002023 0.006952 0.001234 0.006532 0.002076 0.000154 0.005778 0.001174 0.002174 0.000164 0.001962 -0.000540 -0.000638 0.000155 0.000028 0.000022 -0.000056 0.000347 0.000016 -0.000087 -0.000079 -0.000118 0.000036 -0.000073 0.000436 -0.000006 0.000276 0.000222 -0.000029 0.000538 -0.000103 -0.000011 -0.000023 -0.000127 -0.000724 0.000157 0.000083 0.000024 -0.000039 0.000245 -0.000004 -0.000082 -0.000079 0.000037 0.000023 -0.000108 0.000370 0.000068 0.000160 0.000203 -0.000010 \n", "PC-2 0.005539 0.005006 0.001369 0.010493 0.004721 0.002004 0.003534 0.014092 0.001878 0.002899 0.015957 -0.025137 0.008150 0.005207 -0.000736 -0.000690 -0.000521 -0.000252 0.001630 0.000820 0.000497 0.000159 -0.004040 -0.001359 -0.001507 -0.000700 -0.001463 0.002947 -0.003296 -0.001177 0.001165 -0.001864 -0.004279 -0.000192 -0.000715 0.029817 -0.027895 -0.014568 0.000252 0.002857 0.000315 0.000066 -0.011763 -0.002656 -0.001195 -0.000209 0.015599 0.001900 0.004513 -0.008344 0.003238 -0.015615 0.004962 0.000510 -0.012408 0.004063 0.014631 0.000935 0.003112 0.005445 0.005915 -0.003991 -0.001766 0.000096 -0.000377 -0.002348 -0.003613 -0.002480 -0.001134 -0.001054 -0.000385 -0.001154 -0.006465 -0.002048 -0.008442 -0.008577 -0.002941 -0.004042 -0.002424 -0.003926 -0.002158 -0.003035 0.007738 -0.004179 -0.001542 0.000064 -0.000257 -0.002073 -0.003644 -0.002706 -0.001188 0.000583 -0.000469 -0.001319 -0.006463 -0.001734 -0.008423 -0.009294 -0.002857 \n", "PC-3 -0.004164 -0.001249 -0.004166 -0.013857 -0.005630 -0.003076 -0.001089 0.001559 -0.001330 -0.002525 -0.018495 -0.005589 0.013042 0.013562 -0.001407 -0.003151 -0.000428 0.000170 -0.001148 -0.002546 -0.001103 -0.000836 -0.002078 -0.001965 -0.003064 -0.005934 -0.003409 -0.004798 -0.009706 -0.001538 -0.004352 -0.001583 -0.005050 -0.003782 -0.003341 0.019481 -0.019213 -0.013261 0.001115 0.002057 0.000044 -0.000128 -0.004686 -0.001518 -0.000798 0.000334 0.006399 0.000850 0.001255 -0.003630 0.001973 -0.007002 0.004408 0.000353 -0.004187 0.000557 0.007584 0.000429 0.001515 -0.032695 -0.037361 0.014407 0.004823 0.000264 0.000952 0.003540 0.010090 0.006343 0.002935 0.000181 0.001069 0.003268 0.014929 0.006038 0.019972 0.032481 0.008963 0.009434 0.005495 0.009149 0.008975 0.010126 -0.042205 0.015343 0.005357 0.000091 0.000640 0.003371 0.010204 0.006693 0.002989 0.000935 0.001049 0.003329 0.016055 0.006088 0.020268 0.034388 0.009454 \n", "PC-4 -0.009835 -0.009477 -0.002953 -0.012242 -0.007866 -0.007406 -0.002429 -0.011433 -0.003151 -0.002605 0.010637 -0.036463 -0.008064 -0.007642 0.003434 0.001438 0.001742 0.000481 0.001967 0.001816 0.000869 0.000857 0.003682 0.002675 -0.003592 0.008403 0.003660 0.004652 0.005523 0.004134 0.006053 0.002350 0.006348 0.001629 -0.002543 0.026113 -0.040225 -0.041199 -0.000777 0.006838 -0.000061 -0.000192 -0.011738 -0.007910 -0.003502 -0.001092 -0.004866 0.001907 0.022065 -0.011539 0.006585 -0.023151 0.020578 0.001415 -0.016823 0.005284 -0.007538 0.000689 0.019232 -0.002834 -0.002244 0.000877 -0.000440 -0.000341 -0.000042 -0.001834 -0.002924 -0.001218 -0.000316 0.000382 -0.000653 -0.004135 -0.004185 -0.000823 -0.005976 -0.004920 0.000009 -0.002729 -0.001455 -0.001871 -0.002388 -0.002377 -0.002085 0.000841 -0.000826 -0.000343 -0.000028 -0.001576 -0.002763 -0.001373 -0.000371 -0.000605 -0.000785 -0.004037 -0.003614 -0.001197 -0.005712 -0.004337 -0.000171 \n", "PC-5 0.016183 0.015231 0.001636 0.027250 0.010528 0.008066 0.008117 0.003382 0.004454 0.009235 -0.002126 -0.017953 0.045167 0.047662 -0.007518 -0.008320 -0.003499 -0.000926 -0.001050 -0.001882 -0.000692 -0.001044 -0.000873 -0.007825 -0.011709 -0.018590 -0.012745 -0.003623 -0.030797 -0.007538 -0.009295 -0.009296 -0.007251 -0.005644 -0.010933 0.007692 -0.029271 -0.040867 0.001919 0.003373 0.000233 0.000120 -0.001613 -0.005113 -0.001040 0.000302 -0.014345 0.002819 0.020736 0.000340 0.003727 -0.007766 0.025835 0.001670 -0.003662 0.004002 -0.012509 0.002448 0.017228 -0.001999 -0.003363 -0.000950 0.000083 0.000494 -0.000024 0.001053 0.001698 0.000241 0.000145 0.000726 0.000789 0.000572 0.001706 0.000553 0.002992 0.002974 -0.001444 0.002275 -0.000569 0.003156 0.003530 0.000166 -0.005462 -0.000746 0.001233 0.000423 -0.000095 0.000782 0.001594 0.000121 0.000107 -0.000158 0.000880 0.000255 0.001889 0.001561 0.002498 0.002752 -0.000980 \n", "\n", " x6 x23 x6 x24 x6 x25 x6 x26 x6 x27 x7^2 x7 x8 x7 x9 x7 x10 x7 x11 x7 x12 x7 x13 x7 x14 x7 x15 x7 x16 x7 x17 x7 x18 x7 x19 x7 x20 x7 x21 x7 x22 x7 x23 x7 x24 x7 x25 x7 x26 x7 x27 x8^2 x8 x9 x8 x10 x8 x11 x8 x12 x8 x13 x8 x14 x8 x15 x8 x16 x8 x17 x8 x18 x8 x19 x8 x20 x8 x21 x8 x22 x8 x23 x8 x24 x8 x25 x8 x26 x8 x27 x9^2 x9 x10 x9 x11 x9 x12 x9 x13 x9 x14 x9 x15 x9 x16 x9 x17 x9 x18 x9 x19 x9 x20 x9 x21 x9 x22 x9 x23 x9 x24 x9 x25 x9 x26 x9 x27 x10^2 x10 x11 x10 x12 x10 x13 x10 x14 x10 x15 x10 x16 x10 x17 x10 x18 x10 x19 x10 x20 x10 x21 x10 x22 x10 x23 x10 x24 x10 x25 x10 x26 x10 x27 x11^2 x11 x12 x11 x13 x11 x14 x11 x15 x11 x16 x11 x17 x11 x18 x11 x19 x11 x20 x11 x21 x11 x22 x11 x23 x11 x24 x11 x25 x11 x26 x11 x27 x12^2 x12 x13 x12 x14 x12 x15 x12 x16 x12 x17 x12 x18 x12 x19 \\\n", "PC-1 0.000432 -0.000062 0.000131 -0.000011 -0.000154 -0.000110 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000024 0.0 0.0 -0.000110 -0.000021 -0.000011 -0.000013 -0.000015 -0.000014 -0.000019 0.000031 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000105 0.000031 0.0 0.0 -0.000011 -0.000022 0.000127 -0.000017 -0.000016 -0.000017 -0.000119 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000032 -0.000119 0.0 0.0 -0.000018 -0.000015 -0.000018 -0.000016 -0.000017 -0.000016 -0.000112 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000036 -0.000112 0.0 0.0 -0.000014 -0.000017 -0.000019 -0.000012 -0.000014 -0.000018 0.000401 0.0 0.0 0.0 0.0 0.0 0.0 0.000422 0.0 0.000401 0.0 -0.000010 4.281049e-04 -0.000006 -0.000021 -0.000012 -0.000007 0.000032 0.0 0.0 0.0 0.0 0.0 0.000075 0.0 \n", "PC-2 -0.004110 -0.002353 -0.002865 -0.002077 -0.003068 0.002351 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000643 -0.0 -0.0 0.002351 0.000606 0.000429 0.000214 0.000136 0.000260 0.000251 0.001551 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000442 0.001551 -0.0 -0.0 0.000195 0.000022 0.000420 0.000370 0.000136 0.000322 0.000012 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000090 0.000012 -0.0 -0.0 -0.000065 -0.000021 -0.000069 0.000057 0.000099 0.000058 -0.000700 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000206 -0.000700 -0.0 -0.0 -0.000076 -0.000126 -0.000079 -0.000122 -0.000087 -0.000076 -0.002477 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.001466 -0.0 -0.002477 -0.0 -0.000265 -1.246766e-03 -0.000219 -0.000201 -0.000154 -0.000171 -0.002753 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000787 -0.0 \n", "PC-3 0.010507 0.005548 0.010154 0.008923 0.010105 -0.008503 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.001678 -0.0 -0.0 -0.008503 -0.001917 -0.001071 -0.000608 -0.000846 -0.001262 -0.001155 -0.003515 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000632 -0.003515 -0.0 -0.0 -0.000630 -0.000398 -0.000235 -0.000624 -0.000558 -0.000388 0.000578 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000166 0.000578 -0.0 -0.0 0.000085 0.000095 0.000071 0.000067 0.000099 0.000081 0.001496 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000498 0.001496 -0.0 -0.0 0.000176 0.000249 0.000249 0.000192 0.000186 0.000244 0.003087 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000908 -0.0 0.003087 -0.0 0.000548 2.053817e-04 0.000702 0.000545 0.000403 0.000379 0.007295 -0.0 -0.0 -0.0 -0.0 -0.0 0.001845 -0.0 \n", "PC-4 -0.002560 -0.001054 -0.002159 -0.002406 -0.003013 -0.000432 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000288 0.0 0.0 -0.000432 -0.000610 -0.000202 -0.000086 0.000210 0.000298 0.000273 0.000835 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.001236 0.000835 0.0 0.0 0.000268 0.000176 0.001060 -0.000482 0.000088 -0.000665 -0.000501 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000087 -0.000501 0.0 0.0 0.000065 -0.000034 0.000121 -0.000205 -0.000386 -0.000071 0.000240 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000026 0.000240 0.0 0.0 0.000022 0.000019 -0.000045 0.000091 0.000042 0.000018 -0.001832 0.0 0.0 0.0 0.0 0.0 0.0 -0.001274 0.0 -0.001832 0.0 -0.000142 -9.556352e-04 -0.000319 0.000002 -0.000085 -0.000125 -0.002189 0.0 0.0 0.0 0.0 0.0 -0.000912 0.0 \n", "PC-5 0.002438 -0.000548 0.001568 0.003477 0.000462 0.000611 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000248 0.0 0.0 0.000611 0.001159 -0.000096 0.000344 -0.000345 -0.000460 -0.000465 0.000747 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000252 0.000747 0.0 0.0 -0.000032 -0.000277 0.000025 0.000676 -0.000304 0.001110 0.000429 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000136 0.000429 0.0 0.0 -0.000192 0.000041 -0.000177 0.000180 0.000469 0.000155 -0.000440 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000135 -0.000440 0.0 0.0 -0.000014 -0.000163 0.000027 -0.000073 -0.000041 -0.000045 0.000328 0.0 0.0 0.0 0.0 0.0 0.0 -0.000027 0.0 0.000328 0.0 0.000088 8.713002e-08 -0.000027 0.000033 0.000019 0.000127 0.000683 0.0 0.0 0.0 0.0 0.0 -0.000448 0.0 \n", "\n", " x12 x20 x12 x21 x12 x22 x12 x23 x12 x24 x12 x25 x12 x26 x12 x27 x13^2 x13 x14 x13 x15 x13 x16 x13 x17 x13 x18 x13 x19 x13 x20 x13 x21 x13 x22 x13 x23 x13 x24 x13 x25 x13 x26 x13 x27 x14^2 x14 x15 x14 x16 x14 x17 x14 x18 x14 x19 x14 x20 x14 x21 x14 x22 x14 x23 x14 x24 x14 x25 x14 x26 x14 x27 x15^2 x15 x16 x15 x17 x15 x18 x15 x19 x15 x20 x15 x21 x15 x22 x15 x23 x15 x24 x15 x25 x15 x26 x15 x27 x16^2 x16 x17 x16 x18 x16 x19 x16 x20 x16 x21 x16 x22 x16 x23 x16 x24 x16 x25 x16 x26 x16 x27 x17^2 x17 x18 x17 x19 x17 x20 x17 x21 x17 x22 x17 x23 x17 x24 x17 x25 x17 x26 x17 x27 x18^2 x18 x19 x18 x20 x18 x21 x18 x22 x18 x23 x18 x24 x18 x25 x18 x26 x18 x27 x19^2 x19 x20 x19 x21 x19 x22 x19 x23 x19 x24 x19 x25 x19 x26 x19 x27 x20^2 x20 x21 x20 x22 x20 x23 x20 x24 x20 x25 x20 x26 x20 x27 x21^2 \\\n", "PC-1 0.000032 0.0 -0.000023 0.000093 -0.000018 0.000036 -0.000024 -0.000020 -0.000075 0.0 0.0 0.0 0.0 -0.000023 0.0 -0.000075 0.0 -0.000018 -0.000009 -0.000015 -0.000013 -1.806578e-05 -0.000017 -0.000110 0.0 0.0 0.0 -0.000032 0.0 0.0 0.0 -0.000020 -0.000015 -0.000016 -0.000015 -0.000018 -0.000009 0.000105 0.0 0.0 -0.000028 0.0 0.0 0.0 -0.000015 -0.000014 -0.000014 0.000196 -0.000010 -0.000025 -0.000068 0.0 -0.000045 0.0 0.0 0.0 -0.000012 -0.000024 -0.000021 0.000023 8.494807e-07 -0.000020 0.000135 -0.000029 0.0 0.0 0.000135 3.755264e-07 -0.000021 -0.000008 -0.000015 -0.000015 0.000203 0.000329 0.000036 0.000474 -0.000076 0.0 0.000354 -0.000025 0.0 0.0 0.0 -0.000199 0.0 0.0 -0.000044 -0.000054 0.000090 -0.000044 -0.000047 -0.000051 0.000357 0.0 -0.000051 0.000512 -0.000038 0.000002 -0.000054 -0.000045 -0.000084 \n", "PC-2 -0.002753 -0.0 -0.000376 -0.000509 -0.000278 -0.000560 -0.000450 -0.000342 -0.002158 -0.0 -0.0 -0.0 -0.0 -0.000640 -0.0 -0.002158 -0.0 -0.000223 -0.000450 -0.000190 -0.000343 -2.505720e-04 -0.000251 -0.001308 -0.0 -0.0 -0.0 -0.000418 -0.0 -0.0 -0.0 -0.000238 -0.000201 -0.000217 -0.000150 -0.000124 -0.000186 0.001667 -0.0 -0.0 -0.000165 -0.0 -0.0 -0.0 0.000316 -0.000113 -0.000052 0.001779 -0.000008 -0.000161 0.000553 -0.0 0.000089 -0.0 -0.0 -0.0 0.000017 -0.000047 0.000136 0.000387 2.879226e-06 -0.000005 0.001005 0.000320 -0.0 -0.0 0.001005 1.581754e-04 -0.000011 0.000331 -0.000027 0.000028 0.000412 -0.001673 0.000146 -0.002892 0.001567 -0.0 -0.001814 0.000142 -0.0 -0.0 -0.0 0.000863 -0.0 -0.0 0.000055 -0.000126 0.000272 0.000305 0.000147 0.000304 -0.007388 -0.0 -0.000864 -0.002206 -0.000687 -0.001104 -0.000854 -0.000763 0.005614 \n", "PC-3 0.007295 -0.0 0.001217 0.000941 0.000904 0.000838 0.001488 0.001229 0.005348 -0.0 -0.0 -0.0 -0.0 0.001429 -0.0 0.005348 -0.0 0.000683 0.000911 0.000517 0.000844 7.650545e-04 0.000713 0.002991 -0.0 -0.0 -0.0 0.000990 -0.0 -0.0 -0.0 0.000489 0.000493 0.000497 0.000293 0.000295 0.000527 0.002409 -0.0 -0.0 0.000350 -0.0 -0.0 -0.0 0.000219 0.000195 0.000156 0.001004 0.000318 0.000308 -0.000471 -0.0 -0.000261 -0.0 -0.0 -0.0 -0.000180 -0.000170 -0.000091 0.000052 -1.853918e-05 -0.000086 -0.002320 -0.000733 -0.0 -0.0 -0.002320 -3.901327e-04 -0.000438 -0.000295 -0.000248 -0.000466 -0.000326 0.000921 0.000032 0.004182 -0.004373 -0.0 -0.000687 0.001608 -0.0 -0.0 -0.0 -0.001441 -0.0 -0.0 -0.000370 -0.000054 0.000086 -0.000365 -0.000273 -0.000063 0.015730 -0.0 0.002448 0.002058 0.002124 0.002226 0.002656 0.002321 -0.019217 \n", "PC-4 -0.002189 0.0 -0.000079 -0.000841 -0.000071 -0.000642 -0.000243 -0.000214 -0.000974 0.0 0.0 0.0 0.0 -0.000235 0.0 -0.000974 0.0 -0.000007 -0.000280 0.000044 -0.000276 2.492292e-05 -0.000029 -0.000018 0.0 0.0 0.0 -0.000071 0.0 0.0 0.0 -0.000028 -0.000075 0.000004 0.000091 0.000058 -0.000126 -0.001141 0.0 0.0 0.000084 0.0 0.0 0.0 -0.001031 0.000095 -0.000011 -0.000462 0.000039 0.000145 0.000744 0.0 -0.000015 0.0 0.0 0.0 0.000064 0.000212 -0.000227 0.000169 5.461344e-04 0.000093 0.004840 0.000604 0.0 0.0 0.004840 5.525942e-04 0.000399 0.000205 0.000348 0.000485 0.002546 -0.000669 0.001298 -0.002422 0.000458 0.0 -0.001677 0.001008 0.0 0.0 0.0 0.000574 0.0 0.0 0.000356 0.000161 0.001136 -0.000596 -0.000256 -0.000718 -0.004995 0.0 -0.000229 -0.002076 -0.000345 -0.000916 -0.000304 -0.000368 0.004836 \n", "PC-5 0.000683 0.0 0.000184 -0.000499 0.000052 0.000115 0.000396 0.000410 0.000012 0.0 0.0 0.0 0.0 -0.000137 0.0 0.000012 0.0 0.000053 -0.000047 -0.000090 0.000095 8.776719e-07 0.000054 -0.000377 0.0 0.0 0.0 -0.000018 0.0 0.0 0.0 -0.000026 0.000035 -0.000053 -0.000166 -0.000068 -0.000030 -0.001224 0.0 0.0 0.000036 0.0 0.0 0.0 0.001040 -0.000048 0.000084 -0.002096 -0.000065 -0.000091 -0.000264 0.0 -0.000244 0.0 0.0 0.0 -0.000142 -0.000482 0.000238 0.000228 -1.847632e-04 -0.000118 0.000569 -0.000388 0.0 0.0 0.000569 2.102541e-05 -0.000746 0.000358 -0.000363 -0.000397 0.001683 -0.001485 -0.000524 -0.000612 -0.000122 0.0 -0.002348 0.000864 0.0 0.0 0.0 0.000736 0.0 0.0 -0.000238 -0.000399 -0.000125 0.000783 0.000123 0.001221 0.001023 0.0 0.000324 -0.000547 -0.000065 0.000244 0.000415 0.000591 0.000105 \n", "\n", " x21 x22 x21 x23 x21 x24 x21 x25 x21 x26 x21 x27 x22^2 x22 x23 x22 x24 x22 x25 x22 x26 x22 x27 x23^2 x23 x24 x23 x25 x23 x26 x23 x27 x24^2 x24 x25 x24 x26 x24 x27 x25^2 x25 x26 x25 x27 x26^2 x26 x27 x27^2 x0^3 x0^2 x1 x0^2 x2 x0^2 x3 x0^2 x4 x0^2 x5 x0^2 x6 x0^2 x7 x0^2 x8 x0^2 x9 x0^2 x10 x0^2 x11 x0^2 x12 x0^2 x13 x0^2 x14 x0^2 x15 x0^2 x16 x0^2 x17 x0^2 x18 x0^2 x19 x0^2 x20 x0^2 x21 x0^2 x22 x0^2 x23 x0^2 x24 x0^2 x25 x0^2 x26 x0^2 x27 x0 x1^2 x0 x1 x2 x0 x1 x3 x0 x1 x4 x0 x1 x5 x0 x1 x6 x0 x1 x7 x0 x1 x8 x0 x1 x9 x0 x1 x10 x0 x1 x11 x0 x1 x12 x0 x1 x13 x0 x1 x14 x0 x1 x15 x0 x1 x16 x0 x1 x17 x0 x1 x18 x0 x1 x19 x0 x1 x20 x0 x1 x21 x0 x1 x22 x0 x1 x23 x0 x1 x24 x0 x1 x25 x0 x1 x26 x0 x1 x27 x0 x2^2 x0 x2 x3 x0 x2 x4 x0 x2 x5 x0 x2 x6 x0 x2 x7 x0 x2 x8 x0 x2 x9 x0 x2 x10 x0 x2 x11 ... x14 x19 x20 x14 x19 x21 x14 x19 x22 x14 x19 x23 \\\n", "PC-1 -0.000033 -0.000051 -0.000026 -0.000053 -0.000044 0.000166 -0.000175 0.0 0.0 0.0 0.0 0.0 0.000354 0.0 0.0 0.0 0.0 -0.000025 0.0 0.0 0.0 0.000108 0.0 0.0 -0.000173 0.0 0.000016 0.000652 0.000896 0.000277 -0.000809 0.004710 0.000664 0.000720 -0.000238 -0.000076 -0.000020 -0.000037 0.000061 -0.000066 -0.000101 -0.000067 -0.000019 -0.000018 -0.000040 -0.000036 -0.000133 -0.000106 -0.000522 -0.000201 0.000056 -0.000092 -0.000110 -0.000206 -0.000172 0.001098 0.000093 -0.000693 0.004377 0.000919 0.000954 -0.000225 -0.000150 -0.000021 -0.000025 0.000156 -0.000075 -0.000056 -0.000061 -0.000021 -0.000038 -0.000092 -0.000018 -0.000196 0.000024 -0.000561 -0.000193 0.000110 -0.000128 -0.000112 -0.000196 -0.000218 0.000266 0.000080 0.000766 0.000343 0.000298 0.000064 -0.000137 -0.000001 -0.000008 0.000238 ... 0.0 0.0 0.0 0.0 \n", "PC-2 0.000875 0.000878 0.000689 0.000843 0.000379 0.000968 0.000161 -0.0 -0.0 -0.0 -0.0 -0.0 -0.001814 -0.0 -0.0 -0.0 -0.0 0.000142 -0.0 -0.0 -0.0 0.002061 -0.0 -0.0 -0.000457 -0.0 0.000157 -0.051553 -0.049659 0.035085 0.002346 -0.004067 -0.048680 -0.050556 0.008040 0.002125 0.000061 -0.000239 -0.001909 -0.004898 -0.003294 -0.001204 -0.000123 0.000722 0.001435 0.000911 0.001947 -0.010101 0.016762 0.001675 0.000725 0.000187 0.001018 0.000340 0.001252 -0.050064 0.032703 0.004294 -0.010616 -0.046657 -0.048927 0.007641 0.002170 0.000134 -0.000183 -0.001852 -0.004559 -0.003164 -0.001255 -0.000100 0.000697 0.001087 0.000363 0.002121 -0.009575 0.016041 0.001883 0.000387 -0.000024 0.001056 0.000475 0.001406 -0.051570 0.011346 -0.018248 0.032489 0.034259 -0.007574 -0.003458 0.000012 -0.000006 -0.000249 ... -0.0 -0.0 -0.0 -0.0 \n", "PC-3 -0.002586 -0.003209 -0.001164 -0.003127 -0.002373 -0.003115 0.000019 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000687 -0.0 -0.0 -0.0 -0.0 0.001608 -0.0 -0.0 -0.0 0.000084 -0.0 -0.0 0.000605 -0.0 -0.000109 0.185810 0.183678 -0.066726 -0.050006 0.006700 0.174328 0.182741 -0.028416 -0.007564 -0.000017 0.000693 0.004600 0.015124 0.008453 0.003355 0.000406 -0.001371 -0.005358 -0.004944 -0.006888 0.028176 -0.064921 -0.005753 -0.005973 0.001029 -0.007933 -0.004225 -0.006302 0.187307 -0.067880 -0.052884 0.010469 0.171473 0.181107 -0.027942 -0.009082 -0.000083 0.000532 0.003745 0.013827 0.007637 0.003415 0.000530 -0.001783 -0.005125 -0.006088 -0.008634 0.025209 -0.064821 -0.006503 -0.006556 0.000468 -0.008846 -0.004831 -0.007067 0.095980 -0.017856 -0.002321 -0.060830 -0.066135 0.015082 0.001687 0.000315 0.000270 0.000128 ... -0.0 -0.0 -0.0 -0.0 \n", "PC-4 -0.000197 0.000006 0.000451 0.000183 0.000978 0.003187 -0.001065 0.0 0.0 0.0 0.0 0.0 -0.001677 0.0 0.0 0.0 0.0 0.001008 0.0 0.0 0.0 -0.001532 0.0 0.0 0.001061 0.0 0.002213 -0.015181 -0.015643 -0.046801 0.036834 -0.014489 -0.015328 -0.015895 -0.002627 0.001251 -0.000164 -0.000097 -0.001444 -0.003734 -0.001782 -0.000650 0.000003 0.000196 0.003454 -0.002086 0.000991 -0.006960 0.003377 -0.002838 -0.002411 0.000325 0.000624 0.001819 0.000514 -0.016758 -0.044958 0.040025 -0.024610 -0.015477 -0.016403 -0.002235 0.001086 -0.000345 -0.000086 -0.001581 -0.003277 -0.002002 -0.000738 -0.000111 0.000200 0.002481 -0.001818 0.000655 -0.006860 0.002948 -0.003385 -0.001677 -0.000141 0.000956 0.001887 -0.000406 0.052325 -0.002956 -0.025595 -0.044594 -0.044545 0.011482 0.006871 -0.000443 -0.000264 -0.000955 ... 0.0 0.0 0.0 0.0 \n", "PC-5 0.001439 -0.000907 0.000785 -0.000791 -0.001210 0.000720 0.002398 0.0 0.0 0.0 0.0 0.0 -0.002348 0.0 0.0 0.0 0.0 0.000864 0.0 0.0 0.0 -0.001798 0.0 0.0 -0.000988 0.0 0.002292 0.027176 0.031429 0.080853 -0.086933 0.017289 0.025798 0.027802 0.002941 -0.002473 0.000103 0.000024 0.001586 0.003485 0.000465 0.000484 0.000022 -0.000409 -0.003135 -0.001785 -0.002346 0.005536 -0.006853 0.005314 -0.002735 0.000950 -0.003756 -0.003466 -0.000482 0.034603 0.074672 -0.085543 0.009258 0.029897 0.032111 0.002045 -0.003463 0.000371 -0.000004 0.001388 0.003075 0.000230 0.000515 0.000109 -0.000745 -0.004008 -0.003674 -0.003095 0.004693 -0.009516 0.005472 -0.003966 0.000292 -0.004726 -0.003945 -0.000926 -0.099287 0.021867 -0.027624 0.077828 0.078127 -0.018867 -0.012371 0.000333 0.000241 0.000714 ... 0.0 0.0 0.0 0.0 \n", "\n", " x14 x19 x24 x14 x19 x25 x14 x19 x26 x14 x19 x27 x14 x20^2 x14 x20 x21 x14 x20 x22 x14 x20 x23 x14 x20 x24 x14 x20 x25 x14 x20 x26 x14 x20 x27 x14 x21^2 x14 x21 x22 x14 x21 x23 x14 x21 x24 x14 x21 x25 x14 x21 x26 x14 x21 x27 x14 x22^2 x14 x22 x23 x14 x22 x24 x14 x22 x25 x14 x22 x26 x14 x22 x27 x14 x23^2 x14 x23 x24 x14 x23 x25 x14 x23 x26 x14 x23 x27 x14 x24^2 x14 x24 x25 x14 x24 x26 x14 x24 x27 x14 x25^2 x14 x25 x26 x14 x25 x27 x14 x26^2 x14 x26 x27 x14 x27^2 x15^3 x15^2 x16 x15^2 x17 x15^2 x18 x15^2 x19 x15^2 x20 x15^2 x21 x15^2 x22 x15^2 x23 x15^2 x24 x15^2 x25 x15^2 x26 x15^2 x27 x15 x16^2 x15 x16 x17 x15 x16 x18 x15 x16 x19 x15 x16 x20 x15 x16 x21 x15 x16 x22 x15 x16 x23 x15 x16 x24 x15 x16 x25 x15 x16 x26 x15 x16 x27 x15 x17^2 x15 x17 x18 x15 x17 x19 x15 x17 x20 x15 x17 x21 x15 x17 x22 x15 x17 x23 x15 x17 x24 x15 x17 x25 x15 x17 x26 x15 x17 x27 x15 x18^2 x15 x18 x19 x15 x18 x20 x15 x18 x21 \\\n", "PC-1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000020 0.0 0.0 0.0 0.0 0.0 -0.000015 0.0 0.0 0.0 0.0 -0.000016 0.0 0.0 0.0 -0.000015 0.0 0.0 -0.000018 0.0 -0.000009 0.000105 0.0 0.0 -0.000028 0.0 0.0 0.0 -0.000015 -0.000014 -0.000014 0.000196 -0.000010 -0.000025 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000028 0.0 0.0 0.0 \n", "PC-2 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000238 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000201 -0.0 -0.0 -0.0 -0.0 -0.000217 -0.0 -0.0 -0.0 -0.000150 -0.0 -0.0 -0.000124 -0.0 -0.000186 0.001667 -0.0 -0.0 -0.000165 -0.0 -0.0 -0.0 0.000316 -0.000113 -0.000052 0.001779 -0.000008 -0.000161 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000165 -0.0 -0.0 -0.0 \n", "PC-3 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000489 -0.0 -0.0 -0.0 -0.0 -0.0 0.000493 -0.0 -0.0 -0.0 -0.0 0.000497 -0.0 -0.0 -0.0 0.000293 -0.0 -0.0 0.000295 -0.0 0.000527 0.002409 -0.0 -0.0 0.000350 -0.0 -0.0 -0.0 0.000219 0.000195 0.000156 0.001004 0.000318 0.000308 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000350 -0.0 -0.0 -0.0 \n", "PC-4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000028 0.0 0.0 0.0 0.0 0.0 -0.000075 0.0 0.0 0.0 0.0 0.000004 0.0 0.0 0.0 0.000091 0.0 0.0 0.000058 0.0 -0.000126 -0.001141 0.0 0.0 0.000084 0.0 0.0 0.0 -0.001031 0.000095 -0.000011 -0.000462 0.000039 0.000145 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000084 0.0 0.0 0.0 \n", "PC-5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000026 0.0 0.0 0.0 0.0 0.0 0.000035 0.0 0.0 0.0 0.0 -0.000053 0.0 0.0 0.0 -0.000166 0.0 0.0 -0.000068 0.0 -0.000030 -0.001224 0.0 0.0 0.000036 0.0 0.0 0.0 0.001040 -0.000048 0.000084 -0.002096 -0.000065 -0.000091 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000036 0.0 0.0 0.0 \n", "\n", " x15 x18 x22 x15 x18 x23 x15 x18 x24 x15 x18 x25 x15 x18 x26 x15 x18 x27 x15 x19^2 x15 x19 x20 x15 x19 x21 x15 x19 x22 x15 x19 x23 x15 x19 x24 x15 x19 x25 x15 x19 x26 x15 x19 x27 x15 x20^2 x15 x20 x21 x15 x20 x22 x15 x20 x23 x15 x20 x24 x15 x20 x25 x15 x20 x26 x15 x20 x27 x15 x21^2 x15 x21 x22 x15 x21 x23 x15 x21 x24 x15 x21 x25 x15 x21 x26 x15 x21 x27 x15 x22^2 x15 x22 x23 x15 x22 x24 x15 x22 x25 x15 x22 x26 x15 x22 x27 x15 x23^2 x15 x23 x24 x15 x23 x25 x15 x23 x26 x15 x23 x27 x15 x24^2 x15 x24 x25 x15 x24 x26 x15 x24 x27 x15 x25^2 x15 x25 x26 x15 x25 x27 x15 x26^2 x15 x26 x27 x15 x27^2 x16^3 x16^2 x17 x16^2 x18 x16^2 x19 x16^2 x20 x16^2 x21 x16^2 x22 x16^2 x23 x16^2 x24 x16^2 x25 x16^2 x26 x16^2 x27 x16 x17^2 x16 x17 x18 x16 x17 x19 x16 x17 x20 x16 x17 x21 x16 x17 x22 x16 x17 x23 x16 x17 x24 x16 x17 x25 x16 x17 x26 x16 x17 x27 x16 x18^2 x16 x18 x19 x16 x18 x20 x16 x18 x21 x16 x18 x22 \\\n", "PC-1 0.0 -0.000014 -0.000014 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000015 0.0 0.0 0.0 0.0 0.0 -0.000014 0.0 0.0 0.0 0.0 -0.000014 0.0 0.0 0.0 0.000196 0.0 0.0 -0.000010 0.0 -0.000025 -0.000068 0.0 -0.000045 0.0 0.0 0.0 -0.000012 -0.000024 -0.000021 0.000023 8.494807e-07 -0.000020 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000045 0.0 0.0 0.0 0.0 \n", "PC-2 -0.0 -0.000113 -0.000052 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000316 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000113 -0.0 -0.0 -0.0 -0.0 -0.000052 -0.0 -0.0 -0.0 0.001779 -0.0 -0.0 -0.000008 -0.0 -0.000161 0.000553 -0.0 0.000089 -0.0 -0.0 -0.0 0.000017 -0.000047 0.000136 0.000387 2.879226e-06 -0.000005 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000089 -0.0 -0.0 -0.0 -0.0 \n", "PC-3 -0.0 0.000195 0.000156 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000219 -0.0 -0.0 -0.0 -0.0 -0.0 0.000195 -0.0 -0.0 -0.0 -0.0 0.000156 -0.0 -0.0 -0.0 0.001004 -0.0 -0.0 0.000318 -0.0 0.000308 -0.000471 -0.0 -0.000261 -0.0 -0.0 -0.0 -0.000180 -0.000170 -0.000091 0.000052 -1.853918e-05 -0.000086 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000261 -0.0 -0.0 -0.0 -0.0 \n", "PC-4 0.0 0.000095 -0.000011 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.001031 0.0 0.0 0.0 0.0 0.0 0.000095 0.0 0.0 0.0 0.0 -0.000011 0.0 0.0 0.0 -0.000462 0.0 0.0 0.000039 0.0 0.000145 0.000744 0.0 -0.000015 0.0 0.0 0.0 0.000064 0.000212 -0.000227 0.000169 5.461344e-04 0.000093 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000015 0.0 0.0 0.0 0.0 \n", "PC-5 0.0 -0.000048 0.000084 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.001040 0.0 0.0 0.0 0.0 0.0 -0.000048 0.0 0.0 0.0 0.0 0.000084 0.0 0.0 0.0 -0.002096 0.0 0.0 -0.000065 0.0 -0.000091 -0.000264 0.0 -0.000244 0.0 0.0 0.0 -0.000142 -0.000482 0.000238 0.000228 -1.847632e-04 -0.000118 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000244 0.0 0.0 0.0 0.0 \n", "\n", " x16 x18 x23 x16 x18 x24 x16 x18 x25 x16 x18 x26 x16 x18 x27 x16 x19^2 x16 x19 x20 x16 x19 x21 x16 x19 x22 x16 x19 x23 x16 x19 x24 x16 x19 x25 x16 x19 x26 x16 x19 x27 x16 x20^2 x16 x20 x21 x16 x20 x22 x16 x20 x23 x16 x20 x24 x16 x20 x25 x16 x20 x26 x16 x20 x27 x16 x21^2 x16 x21 x22 x16 x21 x23 x16 x21 x24 x16 x21 x25 x16 x21 x26 x16 x21 x27 x16 x22^2 x16 x22 x23 x16 x22 x24 x16 x22 x25 x16 x22 x26 x16 x22 x27 x16 x23^2 x16 x23 x24 x16 x23 x25 x16 x23 x26 x16 x23 x27 x16 x24^2 x16 x24 x25 x16 x24 x26 x16 x24 x27 x16 x25^2 x16 x25 x26 x16 x25 x27 x16 x26^2 x16 x26 x27 x16 x27^2 x17^3 x17^2 x18 x17^2 x19 x17^2 x20 x17^2 x21 x17^2 x22 x17^2 x23 x17^2 x24 x17^2 x25 x17^2 x26 x17^2 x27 x17 x18^2 x17 x18 x19 x17 x18 x20 x17 x18 x21 x17 x18 x22 x17 x18 x23 x17 x18 x24 x17 x18 x25 x17 x18 x26 x17 x18 x27 x17 x19^2 x17 x19 x20 x17 x19 x21 x17 x19 x22 x17 x19 x23 x17 x19 x24 x17 x19 x25 x17 x19 x26 \\\n", "PC-1 -0.000024 -0.000021 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000012 0.0 0.0 0.0 0.0 0.0 -0.000024 0.0 0.0 0.0 0.0 -0.000021 0.0 0.0 0.0 0.000023 0.0 0.0 8.494807e-07 0.0 -0.000020 0.000135 -0.000029 0.0 0.0 0.000135 3.755264e-07 -0.000021 -0.000008 -0.000015 -0.000015 0.000203 -0.000029 0.0 0.0 -0.000029 0.0 -0.000021 -0.000008 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 \n", "PC-2 -0.000047 0.000136 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000017 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000047 -0.0 -0.0 -0.0 -0.0 0.000136 -0.0 -0.0 -0.0 0.000387 -0.0 -0.0 2.879226e-06 -0.0 -0.000005 0.001005 0.000320 -0.0 -0.0 0.001005 1.581754e-04 -0.000011 0.000331 -0.000027 0.000028 0.000412 0.000320 -0.0 -0.0 0.000320 -0.0 -0.000011 0.000331 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 \n", "PC-3 -0.000170 -0.000091 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000180 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000170 -0.0 -0.0 -0.0 -0.0 -0.000091 -0.0 -0.0 -0.0 0.000052 -0.0 -0.0 -1.853918e-05 -0.0 -0.000086 -0.002320 -0.000733 -0.0 -0.0 -0.002320 -3.901327e-04 -0.000438 -0.000295 -0.000248 -0.000466 -0.000326 -0.000733 -0.0 -0.0 -0.000733 -0.0 -0.000438 -0.000295 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 \n", "PC-4 0.000212 -0.000227 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000064 0.0 0.0 0.0 0.0 0.0 0.000212 0.0 0.0 0.0 0.0 -0.000227 0.0 0.0 0.0 0.000169 0.0 0.0 5.461344e-04 0.0 0.000093 0.004840 0.000604 0.0 0.0 0.004840 5.525942e-04 0.000399 0.000205 0.000348 0.000485 0.002546 0.000604 0.0 0.0 0.000604 0.0 0.000399 0.000205 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 \n", "PC-5 -0.000482 0.000238 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000142 0.0 0.0 0.0 0.0 0.0 -0.000482 0.0 0.0 0.0 0.0 0.000238 0.0 0.0 0.0 0.000228 0.0 0.0 -1.847632e-04 0.0 -0.000118 0.000569 -0.000388 0.0 0.0 0.000569 2.102541e-05 -0.000746 0.000358 -0.000363 -0.000397 0.001683 -0.000388 0.0 0.0 -0.000388 0.0 -0.000746 0.000358 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 \n", "\n", " x17 x19 x27 x17 x20^2 x17 x20 x21 x17 x20 x22 x17 x20 x23 x17 x20 x24 x17 x20 x25 x17 x20 x26 x17 x20 x27 x17 x21^2 x17 x21 x22 x17 x21 x23 x17 x21 x24 x17 x21 x25 x17 x21 x26 x17 x21 x27 x17 x22^2 x17 x22 x23 x17 x22 x24 x17 x22 x25 x17 x22 x26 x17 x22 x27 x17 x23^2 x17 x23 x24 x17 x23 x25 x17 x23 x26 x17 x23 x27 x17 x24^2 x17 x24 x25 x17 x24 x26 x17 x24 x27 x17 x25^2 x17 x25 x26 x17 x25 x27 x17 x26^2 x17 x26 x27 x17 x27^2 x18^3 x18^2 x19 x18^2 x20 x18^2 x21 x18^2 x22 x18^2 x23 x18^2 x24 x18^2 x25 x18^2 x26 x18^2 x27 x18 x19^2 x18 x19 x20 x18 x19 x21 x18 x19 x22 x18 x19 x23 x18 x19 x24 x18 x19 x25 x18 x19 x26 x18 x19 x27 x18 x20^2 x18 x20 x21 x18 x20 x22 x18 x20 x23 x18 x20 x24 x18 x20 x25 x18 x20 x26 x18 x20 x27 x18 x21^2 x18 x21 x22 x18 x21 x23 x18 x21 x24 x18 x21 x25 x18 x21 x26 x18 x21 x27 x18 x22^2 x18 x22 x23 x18 x22 x24 x18 x22 x25 x18 x22 x26 x18 x22 x27 x18 x23^2 x18 x23 x24 \\\n", "PC-1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000135 3.755264e-07 -0.000021 -0.000008 -0.000015 -0.000015 0.000203 3.755264e-07 0.0 0.0 0.0 0.0 0.0 -0.000021 0.0 0.0 0.0 0.0 -0.000008 0.0 0.0 0.0 -0.000015 0.0 0.0 -0.000015 0.0 0.000203 0.000329 0.000036 0.000474 -0.000076 0.0 0.000354 -0.000025 0.0 0.0 0.0 0.000036 0.0 0.0 0.0 -0.000054 0.000090 0.0 0.0 0.0 0.000474 0.0 0.0 0.000512 -0.000038 0.0 0.0 0.0 -0.000076 0.0 -0.000051 -0.000026 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000354 0.0 \n", "PC-2 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.001005 1.581754e-04 -0.000011 0.000331 -0.000027 0.000028 0.000412 1.581754e-04 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000011 -0.0 -0.0 -0.0 -0.0 0.000331 -0.0 -0.0 -0.0 -0.000027 -0.0 -0.0 0.000028 -0.0 0.000412 -0.001673 0.000146 -0.002892 0.001567 -0.0 -0.001814 0.000142 -0.0 -0.0 -0.0 0.000146 -0.0 -0.0 -0.0 -0.000126 0.000272 -0.0 -0.0 -0.0 -0.002892 -0.0 -0.0 -0.002206 -0.000687 -0.0 -0.0 -0.0 0.001567 -0.0 0.000878 0.000689 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.001814 -0.0 \n", "PC-3 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.002320 -3.901327e-04 -0.000438 -0.000295 -0.000248 -0.000466 -0.000326 -3.901327e-04 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000438 -0.0 -0.0 -0.0 -0.0 -0.000295 -0.0 -0.0 -0.0 -0.000248 -0.0 -0.0 -0.000466 -0.0 -0.000326 0.000921 0.000032 0.004182 -0.004373 -0.0 -0.000687 0.001608 -0.0 -0.0 -0.0 0.000032 -0.0 -0.0 -0.0 -0.000054 0.000086 -0.0 -0.0 -0.0 0.004182 -0.0 -0.0 0.002058 0.002124 -0.0 -0.0 -0.0 -0.004373 -0.0 -0.003209 -0.001164 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000687 -0.0 \n", "PC-4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.004840 5.525942e-04 0.000399 0.000205 0.000348 0.000485 0.002546 5.525942e-04 0.0 0.0 0.0 0.0 0.0 0.000399 0.0 0.0 0.0 0.0 0.000205 0.0 0.0 0.0 0.000348 0.0 0.0 0.000485 0.0 0.002546 -0.000669 0.001298 -0.002422 0.000458 0.0 -0.001677 0.001008 0.0 0.0 0.0 0.001298 0.0 0.0 0.0 0.000161 0.001136 0.0 0.0 0.0 -0.002422 0.0 0.0 -0.002076 -0.000345 0.0 0.0 0.0 0.000458 0.0 0.000006 0.000451 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.001677 0.0 \n", "PC-5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000569 2.102541e-05 -0.000746 0.000358 -0.000363 -0.000397 0.001683 2.102541e-05 0.0 0.0 0.0 0.0 0.0 -0.000746 0.0 0.0 0.0 0.0 0.000358 0.0 0.0 0.0 -0.000363 0.0 0.0 -0.000397 0.0 0.001683 -0.001485 -0.000524 -0.000612 -0.000122 0.0 -0.002348 0.000864 0.0 0.0 0.0 -0.000524 0.0 0.0 0.0 -0.000399 -0.000125 0.0 0.0 0.0 -0.000612 0.0 0.0 -0.000547 -0.000065 0.0 0.0 0.0 -0.000122 0.0 -0.000907 0.000785 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.002348 0.0 \n", "\n", " x18 x23 x25 x18 x23 x26 x18 x23 x27 x18 x24^2 x18 x24 x25 x18 x24 x26 x18 x24 x27 x18 x25^2 x18 x25 x26 x18 x25 x27 x18 x26^2 x18 x26 x27 x18 x27^2 x19^3 x19^2 x20 x19^2 x21 x19^2 x22 x19^2 x23 x19^2 x24 x19^2 x25 x19^2 x26 x19^2 x27 x19 x20^2 x19 x20 x21 x19 x20 x22 x19 x20 x23 x19 x20 x24 x19 x20 x25 x19 x20 x26 x19 x20 x27 x19 x21^2 x19 x21 x22 x19 x21 x23 x19 x21 x24 x19 x21 x25 x19 x21 x26 x19 x21 x27 x19 x22^2 x19 x22 x23 x19 x22 x24 x19 x22 x25 x19 x22 x26 x19 x22 x27 x19 x23^2 x19 x23 x24 x19 x23 x25 x19 x23 x26 x19 x23 x27 x19 x24^2 x19 x24 x25 x19 x24 x26 x19 x24 x27 x19 x25^2 x19 x25 x26 x19 x25 x27 x19 x26^2 x19 x26 x27 x19 x27^2 x20^3 x20^2 x21 x20^2 x22 x20^2 x23 x20^2 x24 x20^2 x25 x20^2 x26 x20^2 x27 x20 x21^2 x20 x21 x22 x20 x21 x23 x20 x21 x24 x20 x21 x25 x20 x21 x26 x20 x21 x27 x20 x22^2 x20 x22 x23 x20 x22 x24 x20 x22 x25 x20 x22 x26 x20 x22 x27 x20 x23^2 x20 x23 x24 \\\n", "PC-1 0.0 0.0 0.0 -0.000025 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000199 0.0 0.0 -0.000044 -0.000054 0.000090 -0.000044 -0.000047 -0.000051 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000044 0.0 0.0 0.0 0.0 0.0 -0.000054 0.0 0.0 0.0 0.0 0.000090 0.0 0.0 0.0 -0.000044 0.0 0.0 -0.000047 0.0 -0.000051 0.000357 0.0 -0.000051 0.000512 -0.000038 0.000002 -0.000054 -0.000045 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000051 0.0 0.0 0.0 0.0 0.0 0.000512 0.0 \n", "PC-2 -0.0 -0.0 -0.0 0.000142 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000863 -0.0 -0.0 0.000055 -0.000126 0.000272 0.000305 0.000147 0.000304 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000055 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000126 -0.0 -0.0 -0.0 -0.0 0.000272 -0.0 -0.0 -0.0 0.000305 -0.0 -0.0 0.000147 -0.0 0.000304 -0.007388 -0.0 -0.000864 -0.002206 -0.000687 -0.001104 -0.000854 -0.000763 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000864 -0.0 -0.0 -0.0 -0.0 -0.0 -0.002206 -0.0 \n", "PC-3 -0.0 -0.0 -0.0 0.001608 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.001441 -0.0 -0.0 -0.000370 -0.000054 0.000086 -0.000365 -0.000273 -0.000063 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000370 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000054 -0.0 -0.0 -0.0 -0.0 0.000086 -0.0 -0.0 -0.0 -0.000365 -0.0 -0.0 -0.000273 -0.0 -0.000063 0.015730 -0.0 0.002448 0.002058 0.002124 0.002226 0.002656 0.002321 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.002448 -0.0 -0.0 -0.0 -0.0 -0.0 0.002058 -0.0 \n", "PC-4 0.0 0.0 0.0 0.001008 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000574 0.0 0.0 0.000356 0.000161 0.001136 -0.000596 -0.000256 -0.000718 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000356 0.0 0.0 0.0 0.0 0.0 0.000161 0.0 0.0 0.0 0.0 0.001136 0.0 0.0 0.0 -0.000596 0.0 0.0 -0.000256 0.0 -0.000718 -0.004995 0.0 -0.000229 -0.002076 -0.000345 -0.000916 -0.000304 -0.000368 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000229 0.0 0.0 0.0 0.0 0.0 -0.002076 0.0 \n", "PC-5 0.0 0.0 0.0 0.000864 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000736 0.0 0.0 -0.000238 -0.000399 -0.000125 0.000783 0.000123 0.001221 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000238 0.0 0.0 0.0 0.0 0.0 -0.000399 0.0 0.0 0.0 0.0 -0.000125 0.0 0.0 0.0 0.000783 0.0 0.0 0.000123 0.0 0.001221 0.001023 0.0 0.000324 -0.000547 -0.000065 0.000244 0.000415 0.000591 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000324 0.0 0.0 0.0 0.0 0.0 -0.000547 0.0 \n", "\n", " x20 x23 x25 x20 x23 x26 x20 x23 x27 x20 x24^2 x20 x24 x25 x20 x24 x26 x20 x24 x27 x20 x25^2 x20 x25 x26 x20 x25 x27 x20 x26^2 x20 x26 x27 x20 x27^2 x21^3 x21^2 x22 x21^2 x23 x21^2 x24 x21^2 x25 x21^2 x26 x21^2 x27 x21 x22^2 x21 x22 x23 x21 x22 x24 x21 x22 x25 x21 x22 x26 x21 x22 x27 x21 x23^2 x21 x23 x24 x21 x23 x25 x21 x23 x26 x21 x23 x27 x21 x24^2 x21 x24 x25 x21 x24 x26 x21 x24 x27 x21 x25^2 x21 x25 x26 x21 x25 x27 x21 x26^2 x21 x26 x27 x21 x27^2 x22^3 x22^2 x23 x22^2 x24 x22^2 x25 x22^2 x26 x22^2 x27 x22 x23^2 x22 x23 x24 x22 x23 x25 x22 x23 x26 x22 x23 x27 x22 x24^2 x22 x24 x25 x22 x24 x26 x22 x24 x27 x22 x25^2 x22 x25 x26 x22 x25 x27 x22 x26^2 x22 x26 x27 x22 x27^2 x23^3 x23^2 x24 x23^2 x25 x23^2 x26 x23^2 x27 x23 x24^2 x23 x24 x25 x23 x24 x26 x23 x24 x27 x23 x25^2 x23 x25 x26 x23 x25 x27 x23 x26^2 x23 x26 x27 x23 x27^2 x24^3 x24^2 x25 x24^2 x26 x24^2 x27 x24 x25^2 x24 x25 x26 \\\n", "PC-1 0.0 0.0 0.0 -0.000038 0.0 0.0 0.0 0.000002 0.0 0.0 -0.000054 0.0 -0.000045 -0.000084 -0.000033 -0.000051 -0.000026 -0.000053 -0.000044 0.000166 -0.000033 0.0 0.0 0.0 0.0 0.0 -0.000051 0.0 0.0 0.0 0.0 -0.000026 0.0 0.0 0.0 -0.000053 0.0 0.0 -0.000044 0.0 0.000166 -0.000175 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000354 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.000025 0.0 0.0 0.0 0.0 0.0 \n", "PC-2 -0.0 -0.0 -0.0 -0.000687 -0.0 -0.0 -0.0 -0.001104 -0.0 -0.0 -0.000854 -0.0 -0.000763 0.005614 0.000875 0.000878 0.000689 0.000843 0.000379 0.000968 0.000875 -0.0 -0.0 -0.0 -0.0 -0.0 0.000878 -0.0 -0.0 -0.0 -0.0 0.000689 -0.0 -0.0 -0.0 0.000843 -0.0 -0.0 0.000379 -0.0 0.000968 0.000161 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.001814 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.000142 -0.0 -0.0 -0.0 -0.0 -0.0 \n", "PC-3 -0.0 -0.0 -0.0 0.002124 -0.0 -0.0 -0.0 0.002226 -0.0 -0.0 0.002656 -0.0 0.002321 -0.019217 -0.002586 -0.003209 -0.001164 -0.003127 -0.002373 -0.003115 -0.002586 -0.0 -0.0 -0.0 -0.0 -0.0 -0.003209 -0.0 -0.0 -0.0 -0.0 -0.001164 -0.0 -0.0 -0.0 -0.003127 -0.0 -0.0 -0.002373 -0.0 -0.003115 0.000019 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000687 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.001608 -0.0 -0.0 -0.0 -0.0 -0.0 \n", "PC-4 0.0 0.0 0.0 -0.000345 0.0 0.0 0.0 -0.000916 0.0 0.0 -0.000304 0.0 -0.000368 0.004836 -0.000197 0.000006 0.000451 0.000183 0.000978 0.003187 -0.000197 0.0 0.0 0.0 0.0 0.0 0.000006 0.0 0.0 0.0 0.0 0.000451 0.0 0.0 0.0 0.000183 0.0 0.0 0.000978 0.0 0.003187 -0.001065 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.001677 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.001008 0.0 0.0 0.0 0.0 0.0 \n", "PC-5 0.0 0.0 0.0 -0.000065 0.0 0.0 0.0 0.000244 0.0 0.0 0.000415 0.0 0.000591 0.000105 0.001439 -0.000907 0.000785 -0.000791 -0.001210 0.000720 0.001439 0.0 0.0 0.0 0.0 0.0 -0.000907 0.0 0.0 0.0 0.0 0.000785 0.0 0.0 0.0 -0.000791 0.0 0.0 -0.001210 0.0 0.000720 0.002398 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.002348 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000864 0.0 0.0 0.0 0.0 0.0 \n", "\n", " x24 x25 x27 x24 x26^2 x24 x26 x27 x24 x27^2 x25^3 x25^2 x26 x25^2 x27 x25 x26^2 x25 x26 x27 x25 x27^2 x26^3 x26^2 x27 x26 x27^2 x27^3 \n", "PC-1 0.0 0.0 0.0 0.0 0.000108 0.0 0.0 0.0 0.0 0.0 -0.000173 0.0 0.0 0.000016 \n", "PC-2 -0.0 -0.0 -0.0 -0.0 0.002061 -0.0 -0.0 -0.0 -0.0 -0.0 -0.000457 -0.0 -0.0 0.000157 \n", "PC-3 -0.0 -0.0 -0.0 -0.0 0.000084 -0.0 -0.0 -0.0 -0.0 -0.0 0.000605 -0.0 -0.0 -0.000109 \n", "PC-4 0.0 0.0 0.0 0.0 -0.001532 0.0 0.0 0.0 0.0 0.0 0.001061 0.0 0.0 0.002213 \n", "PC-5 0.0 0.0 0.0 0.0 -0.001798 0.0 0.0 0.0 0.0 0.0 -0.000988 0.0 0.0 0.002292 \n", "\n", "[5 rows x 4494 columns]" ] }, "execution_count": 430, "metadata": {}, "output_type": "execute_result" } ], "source": [ "feature_frame = pd.DataFrame(pca.components_,columns=all_poly_terms.get_feature_names(),index = ['PC-1','PC-2','PC-3','PC-4','PC-5'])\n", "feature_frame" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's take a look at the top correlation values for the first partial component. " ] }, { "cell_type": "code", "execution_count": 426, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
PC-1
x4^30.960024
x2 x4^20.146450
x4^20.101705
\n", "
" ], "text/plain": [ " PC-1\n", "x4^3 0.960024\n", "x2 x4^2 0.146450\n", "x4^2 0.101705" ] }, "execution_count": 426, "metadata": {}, "output_type": "execute_result" } ], "source": [ "feature_frame[0:1].sort_values(by=['PC-1'], axis = 1, ascending = False).T[0:3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first partial component really depends on x4^3, x2 x4^2 and x4^2. When each of these values increase, we would expect each of them to increase together." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, let's look at the R-squared models fo the first 10 partial components. " ] }, { "cell_type": "code", "execution_count": 435, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Explained variance ratio for Model with 1 components: [ 0.8129783]\n", "Explained variance ratio for Model with 2 components: [ 0.8129783 0.04373497]\n", "Explained variance ratio for Model with 3 components: [ 0.8129783 0.04373497 0.03401266]\n", "Explained variance ratio for Model with 4 components: [ 0.8129783 0.04373497 0.03401266 0.02028036]\n", "Explained variance ratio for Model with 5 components: [ 0.8129783 0.04373497 0.03401266 0.02028036 0.01556333]\n", "Explained variance ratio for Model with 6 components: [ 0.8129783 0.04373497 0.03401266 0.02028036 0.01556333 0.00778059]\n", "Explained variance ratio for Model with 7 components: [ 0.8129783 0.04373497 0.03401266 0.02028036 0.01556333 0.00778059\n", " 0.00562893]\n", "Explained variance ratio for Model with 8 components: [ 0.8129783 0.04373497 0.03401266 0.02028036 0.01556333 0.00778059\n", " 0.00562893 0.00509171]\n", "Explained variance ratio for Model with 9 components: [ 0.8129783 0.04373497 0.03401266 0.02028036 0.01556333 0.00778059\n", " 0.00562893 0.00509171 0.00434038]\n", "Explained variance ratio for Model with 10 components: [ 0.8129783 0.04373497 0.03401266 0.02028036 0.01556333 0.00778059\n", " 0.00562893 0.00509171 0.00434038 0.0033645 ]\n" ] } ], "source": [ "\n", "R2_pca_train = []\n", "R2_pca_test = []\n", "\n", "for i in range(10):\n", " pca = PCA(n_components=i+1)\n", " pca.fit(X_train_full_poly_nonzero_col)\n", " \n", " X_train_pca = pca.transform(X_train_full_poly_nonzero_col)\n", " X_test_pca = pca.transform(X_test_full_poly_nonzero_col)\n", " \n", " regression_model = LinearRegression(fit_intercept=True) \n", " regression_model.fit(X_train_pca, y_train)\n", " \n", " R2_pca_train.append(regression_model.score(X_train_pca, y_train)) \n", " R2_pca_test.append(regression_model.score(X_test_pca, y_test)) \n", " \n", " print('Explained variance ratio for Model with',i+1, 'components:', pca.explained_variance_ratio_)\n", " " ] }, { "cell_type": "code", "execution_count": 436, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.0010658459075083559,\n", " 0.03830594358760786,\n", " 0.13381819106030979,\n", " 0.13382136439024239,\n", " 0.13585955685136197,\n", " 0.13676941737898085,\n", " 0.14451154996044147,\n", " 0.14712808866011484,\n", " 0.17240002211375349,\n", " 0.17960666107411249]" ] }, "execution_count": 436, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R2_pca_train" ] }, { "cell_type": "code", "execution_count": 437, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-0.0053200353011577661,\n", " 0.051752057220783021,\n", " 0.10653207172873704,\n", " 0.10667438546230867,\n", " 0.11083439698814734,\n", " 0.11371485746532772,\n", " 0.115030280594421,\n", " 0.11572373943930712,\n", " 0.13615410672470851,\n", " 0.14113152029249787]" ] }, "execution_count": 437, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R2_pca_test" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }