IST 707 HW2
Jing Wang
__download package and install, and read.csv
library(lattice)
library(ggplot2)
library(rattle)## Rattle: A free graphical interface for data science with R.
## Version 5.2.0 Copyright (c) 2006-2018 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.library(caret)
library(factoextra)## Welcome! Related Books: `Practical Guide To Cluster Analysis in R` at https://goo.gl/13EFCZlibrary(caret)
library(rpart)
library(e1071)
setwd("~/Desktop")
origndata<- read.csv('Disputed_Essay_data.csv' ,stringsAsFactors = F)__#Section 1: Data preparation # Create vectors for Author labels
index <- rep(NA,85)
for (i in 1:85){
index[i] <- paste(substr(origndata$author[i],1,2),i)
}
rownames(origndata) <- index
#create new dataset remove that 11 unknow author essay
origndata1<-data.frame(origndata)
cleandf<-origndata1[-1:-11,]
unknow<-origndata1[1:11,]
# Remove HM and Jay for DTree model and also remove the filename in dataset.
origndatadf<-origndata1
origndatadf<-origndatadf[-63:-70,]
origndatadf<-origndatadf[-1:-11,]
origndatadf2<-origndata1
origndatadf2<- origndatadf2[,-2]
# Make 80% as sampling
Ham <- origndatadf2[12:62,]
Mad <- origndatadf2[71:85,]
HSize <- floor(nrow(Ham)*0.8)
MSize <- floor(nrow(Mad)*0.8)
#Index sample
H <- sample(12:62,HSize,replace = F)
M <- sample(71:85,MSize,replace = F)
# Make Training data and testing data
traindata <- origndatadf2[c(H,M),]
testdata <- origndatadf2[-c(H,M,63:70),]
testdata <- testdata[-1:-11,]
colnames(traindata) <- make.names(colnames(traindata))
colnames(testdata) <- make.names(colnames(testdata))
rownames(testdata) <- NULL
rownames(traindata) <- NULL__#Section 2: Build and tune cluster analysis and decision tree models
origndata11<-data.frame(origndata)
origndata11<-origndata
origndata11$author<-NULL
origndata11$filename<-NULL
origndata11<- na.omit(origndata11)
origndata11<- scale(origndata11)
distance <- get_dist(origndata11, method = "euclidean")
fviz_dist(distance, gradient = list(low = "navy", mid = "ghostwhite", high = "orange1"))
# This step chang centers=4, because there are 4 classfication.
km_output <- kmeans(origndata11, centers = 4, nstart = 25, iter.max = 100, algorithm = "Hartigan-Wong")
str(km_output)## List of 9
## $ cluster : Named int [1:85] 1 4 1 1 1 1 1 1 1 1 ...
## ..- attr(*, "names")= chr [1:85] "di 1" "di 2" "di 3" "di 4" ...
## $ centers : num [1:4, 1:70] -0.0627 0.2896 -1.3703 -0.576 0.0387 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:4] "1" "2" "3" "4"
## .. ..$ : chr [1:70] "a" "all" "also" "an" ...
## $ totss : num 5880
## $ withinss : num [1:4] 1181 2768 335 636
## $ tot.withinss: num 4920
## $ betweenss : num 960
## $ size : int [1:4] 24 46 4 11
## $ iter : int 4
## $ ifault : int 0
## - attr(*, "class")= chr "kmeans"fviz_cluster(km_output, data = origndata11)
set.seed(8)
wss <- function(k){
return(kmeans(origndata11, k, nstart = 25)$tot.withinss)
}
k_values <- 1:15
wss_values <- purrr::map_dbl(k_values, wss)
plot(x = k_values, y = wss_values,
type = "b", frame = F,
xlab = "Number of clusters K",
ylab = "Total within-clusters sum of square")
#After look this plots, we can see 4 is best suitable for the centers.__#PCA
pca <- prcomp(origndata11, scale. = T, center = T)
pca$sdev## [1] 2.58033029 2.23088581 2.04483499 1.96570202 1.70617987 1.68274177
## [7] 1.64753321 1.53862104 1.50712338 1.44973334 1.42800946 1.33541831
## [13] 1.32883833 1.29861245 1.27039898 1.24777907 1.19813461 1.17438899
## [19] 1.16503860 1.11535765 1.08156644 1.04718072 1.00577487 0.99012756
## [25] 0.97266176 0.95427055 0.93436695 0.89695923 0.89163580 0.86870391
## [31] 0.82527776 0.80818454 0.80666440 0.78152436 0.76275427 0.73526804
## [37] 0.72856974 0.67445062 0.66271753 0.64553949 0.61559121 0.60148482
## [43] 0.58678292 0.55873335 0.53664799 0.52889727 0.51813646 0.49467116
## [49] 0.45973651 0.44349108 0.43429757 0.38994704 0.37220406 0.34898723
## [55] 0.34047511 0.32823667 0.32708957 0.31411901 0.27296832 0.26325998
## [61] 0.24283359 0.23205274 0.21811185 0.18035713 0.17119369 0.14656337
## [67] 0.13745632 0.12999387 0.11807871 0.06883288pcs <- as.data.frame(predict(pca, newdata = origndata11))
head(pcs, 5)## PC1 PC2 PC3 PC4 PC5 PC6
## di 1 -0.3778149 -0.2139072 -1.7263782 0.9793304 1.71786801 1.0794551
## di 2 -3.5873506 -3.7355183 -0.8165473 -0.7036312 -2.20865397 4.2869484
## di 3 -0.5910984 1.4354747 -3.4946355 -0.6628195 3.43499514 1.1118983
## di 4 -1.4122962 -1.2670197 -2.4400567 -1.9558714 0.03316503 -0.1712289
## di 5 -1.9246760 1.4724608 -2.9702620 0.4431899 0.22062437 -0.6388908
## PC7 PC8 PC9 PC10 PC11 PC12
## di 1 -0.8102195 0.5423284 0.3766260 0.05939187 -0.6346672 -2.5933113
## di 2 -2.2178713 0.3116561 4.4654417 -1.06453155 0.9389065 -1.1776901
## di 3 -1.8584424 -1.8270564 1.3531007 -0.27284683 -1.0066947 1.0464127
## di 4 -0.4386193 -1.3952403 1.8518411 0.14468543 1.5724665 -0.8026828
## di 5 -1.1196062 1.4319391 0.4208459 -2.31753086 0.2945245 1.0320933
## PC13 PC14 PC15 PC16 PC17 PC18
## di 1 0.2077845 0.02453289 -1.8163811 -1.7777091 -1.0092868 1.63271980
## di 2 -0.9084088 -0.64982064 -1.2078906 -1.7811439 0.3247868 -0.56594526
## di 3 2.0434873 0.68308276 0.1209994 0.4667111 -2.2762267 0.73640062
## di 4 0.5266931 1.99290785 1.3224561 0.1348521 -0.1978696 0.09227076
## di 5 -0.2323347 0.14236534 2.3104305 2.6663419 -0.2480200 -1.59622529
## PC19 PC20 PC21 PC22 PC23 PC24
## di 1 -0.4729345 -0.6479645 -0.5011214 1.0885105 1.01691491 -0.1967622
## di 2 0.1542830 -1.0272788 1.7034772 -1.4219367 -0.50639706 0.7290882
## di 3 -0.1590518 -0.2372311 0.2700438 0.1628784 0.06753983 -2.4068322
## di 4 3.7012554 -0.1863586 -0.5555702 -0.6171765 0.16456546 0.6592927
## di 5 -0.4569008 1.1489804 -0.7393948 1.1943151 0.15820069 0.1520482
## PC25 PC26 PC27 PC28 PC29 PC30
## di 1 -1.4457243 -1.46040709 -1.1839326 -1.4808346 -0.9188426 0.8533936
## di 2 1.2337810 -0.02091012 -0.6636506 -1.3075521 -0.5872868 -0.9136147
## di 3 1.5180942 1.44266517 0.1842148 0.5822960 0.8159110 0.9139242
## di 4 -1.3995278 -0.79345472 -0.4490524 0.2429757 -0.6122527 -0.7306795
## di 5 -0.6903863 -1.04386990 0.4031576 -1.4432554 0.1560557 -1.3914198
## PC31 PC32 PC33 PC34 PC35 PC36
## di 1 -1.0753645 1.9480526 1.4721687 0.5486298 -0.02419735 0.1336663
## di 2 -0.3864853 1.0778226 -0.8916559 0.6480450 -1.52969436 1.3003451
## di 3 0.4937133 -1.1309169 -1.2700247 0.3135114 -0.49889639 0.9115177
## di 4 0.7436638 -0.9561101 0.3592043 -0.7886410 0.45469008 -0.5930307
## di 5 -0.9804727 -0.1189807 -0.8263461 -0.4491288 -0.07526734 0.1546534
## PC37 PC38 PC39 PC40 PC41 PC42
## di 1 0.97732536 0.1072429 0.19460699 -0.89253462 -0.6109353 0.07604576
## di 2 0.12932072 0.2259817 0.19087957 0.39361593 1.1126512 0.21016219
## di 3 0.07270422 -0.8605397 -0.05460513 0.16305361 -0.3752659 -0.56772839
## di 4 -0.56564143 -0.5333531 -0.97077402 1.04438165 -0.6029690 0.25121783
## di 5 -0.88598302 -0.4443370 0.14248080 -0.03234246 -0.4082852 -0.91894277
## PC43 PC44 PC45 PC46 PC47 PC48
## di 1 -0.08058227 0.05338608 0.6326994 1.1568835 0.17610253 0.04673128
## di 2 -0.79260138 0.73777833 0.4430608 -0.6748997 -0.09778026 -0.15573948
## di 3 -0.44045573 -0.40893694 -0.5996414 -0.2082303 0.03098862 -0.18987515
## di 4 -0.61674683 0.14222592 1.4667109 -0.2340859 -0.22140583 0.45769726
## di 5 -0.19732772 -0.35674601 0.1402707 -0.7067342 -0.58764573 0.42722500
## PC49 PC50 PC51 PC52 PC53 PC54
## di 1 -0.9148228 0.7074467 -0.53392881 0.3564814 -0.26863638 -0.154725388
## di 2 0.4471787 -0.5201117 -0.35538756 0.3895519 0.28517966 -0.276564054
## di 3 -0.3689852 0.1895063 -0.04348436 -0.3284680 -0.82501807 0.007279562
## di 4 -1.3015345 -0.6390304 -0.83020134 -0.7308819 0.04370876 0.188504393
## di 5 0.2083083 0.5812354 -0.02255917 0.2391645 0.04845862 -0.005669647
## PC55 PC56 PC57 PC58 PC59
## di 1 0.5476847 -0.20595028 0.43153181 0.45582238 0.16207906
## di 2 -0.4999054 -0.30106638 0.05901064 -0.25335495 0.15950446
## di 3 0.0267157 0.33680433 0.37514763 -0.12600971 0.42689081
## di 4 -0.2120713 0.07877001 -0.22907923 0.03241203 -0.07651465
## di 5 0.4410619 -0.16063421 0.13014889 0.52472950 -0.16680230
## PC60 PC61 PC62 PC63 PC64
## di 1 0.45710221 0.01711886 0.04601017 -0.121553501 0.138865268
## di 2 0.26951876 0.11454118 0.10573061 0.005937115 -0.007445833
## di 3 0.04267183 0.17553240 -0.13090109 -0.106459168 0.174998663
## di 4 -0.36194260 -0.01318951 0.07055586 -0.174951815 0.176562069
## di 5 0.35009671 -0.21167627 0.26693788 0.088338281 -0.115119576
## PC65 PC66 PC67 PC68 PC69
## di 1 0.08078192 0.07556686 0.10328565 -0.03493345 0.12314800
## di 2 0.06545278 0.02557472 -0.25036746 0.03872739 -0.05787324
## di 3 0.29096432 0.20860974 -0.13851173 -0.03240667 -0.05402984
## di 4 0.17819562 -0.10769616 0.06128564 -0.05926029 0.24578733
## di 5 -0.05453665 -0.34612419 0.09199768 0.31463534 0.15065744
## PC70
## di 1 0.1059461141
## di 2 -0.0006518049
## di 3 0.0361891416
## di 4 0.0026467968
## di 5 0.0178184991cov(pcs) ## covariance is zero## PC1 PC2 PC3 PC4 PC5
## PC1 6.658104e+00 3.392695e-15 -6.989080e-16 3.418811e-16 7.358059e-16
## PC2 3.392695e-15 4.976852e+00 -1.892555e-15 2.122601e-15 7.656565e-16
## PC3 -6.989080e-16 -1.892555e-15 4.181350e+00 3.920785e-16 8.518731e-17
## PC4 3.418811e-16 2.122601e-15 3.920785e-16 3.863984e+00 -1.224550e-15
## PC5 7.358059e-16 7.656565e-16 8.518731e-17 -1.224550e-15 2.911050e+00
## PC6 1.144514e-15 -8.247277e-16 -1.404602e-16 4.279775e-15 1.034235e-15
## PC7 -4.255869e-16 9.052840e-16 4.980954e-16 -3.684480e-16 -9.419135e-17
## PC8 1.206237e-15 3.417931e-17 -5.258377e-16 -3.473772e-16 -1.529411e-15
## PC9 -4.321233e-16 -1.067243e-15 4.832237e-16 1.045754e-15 4.777950e-16
## PC10 9.751851e-16 -1.602457e-15 1.309163e-15 -7.449059e-16 7.398944e-16
## PC11 -1.584430e-15 3.388490e-16 -1.618345e-15 4.553081e-16 -4.754188e-16
## PC12 -1.438597e-16 -6.151730e-16 -7.683625e-16 -4.269690e-16 2.890875e-17
## PC13 -3.419699e-16 -3.608867e-16 -1.625423e-15 -4.429702e-16 -3.454655e-16
## PC14 4.293475e-16 1.244182e-16 1.142000e-15 5.435622e-16 -6.178210e-16
## PC15 8.552176e-16 1.735319e-16 -2.717217e-16 -6.995840e-16 2.243660e-16
## PC16 1.087568e-15 -2.860793e-16 1.955151e-15 -1.543420e-16 -4.305051e-16
## PC17 4.858777e-16 6.497396e-16 1.025154e-15 -7.584239e-16 -9.007603e-16
## PC18 -1.404452e-15 -2.795697e-16 1.344129e-15 -3.993859e-16 -6.889011e-16
## PC19 -7.461189e-16 2.223076e-16 -1.765236e-16 2.368388e-16 -1.998456e-16
## PC20 8.820545e-17 -4.885338e-16 9.196487e-17 5.254702e-16 2.849980e-16
## PC21 4.985194e-16 3.961155e-16 -1.240895e-15 -7.838627e-16 6.758452e-17
## PC22 5.948597e-16 -1.882586e-16 2.561647e-16 2.850109e-16 2.115666e-16
## PC23 -4.603536e-16 -7.475590e-16 7.157119e-16 3.221510e-16 7.339833e-16
## PC24 -5.808218e-17 1.563938e-15 -1.496400e-15 6.047009e-17 5.739043e-17
## PC25 3.532985e-16 -5.669349e-17 -5.003425e-16 3.798184e-16 2.609736e-16
## PC26 -3.577034e-16 1.487363e-16 6.975405e-16 4.794915e-16 2.540957e-16
## PC27 -7.229030e-16 -4.757524e-16 -7.238018e-16 -3.253239e-16 4.260147e-16
## PC28 1.604354e-15 -2.157475e-16 -1.115771e-15 3.825685e-17 7.806127e-17
## PC29 -9.395186e-16 -3.950790e-16 1.381812e-15 1.004127e-15 -9.055766e-16
## PC30 -8.793876e-16 -1.510398e-16 1.043862e-15 -3.530027e-16 -5.555917e-16
## PC31 -6.534153e-16 9.738414e-16 3.280538e-16 -9.859012e-17 -1.870739e-16
## PC32 -2.862974e-16 -5.328460e-16 4.849020e-16 -4.318797e-16 5.484893e-16
## PC33 5.730893e-16 8.385674e-16 2.970843e-17 7.500394e-16 1.841730e-16
## PC34 -7.868517e-17 -7.907803e-16 -1.419789e-17 -8.562506e-16 -8.487651e-16
## PC35 -1.533556e-15 -4.867878e-16 8.693551e-16 -2.835530e-16 1.736446e-16
## PC36 8.556937e-16 8.657815e-16 -3.671418e-16 5.654321e-16 -1.424972e-16
## PC37 7.082938e-17 -1.514353e-16 -7.196521e-16 4.702391e-16 2.239897e-16
## PC38 8.076053e-16 1.563897e-15 1.308511e-15 1.032269e-15 -7.356183e-16
## PC39 -3.687254e-16 -1.665724e-16 -1.109356e-16 1.959557e-16 1.975501e-16
## PC40 -1.867929e-16 -1.384768e-15 -2.637322e-17 2.798210e-16 -2.406845e-16
## PC41 -1.074763e-15 4.084062e-16 1.788262e-16 -2.127915e-16 -1.845815e-16
## PC42 -8.350693e-16 -1.987849e-17 -1.300397e-17 2.561395e-16 -2.594347e-16
## PC43 -1.144603e-15 1.436143e-15 -5.086036e-16 4.517224e-16 3.816385e-16
## PC44 7.628806e-16 2.277434e-16 2.954044e-16 -3.948432e-17 -2.314213e-16
## PC45 -7.199390e-17 -1.620599e-16 3.416720e-16 -5.040683e-16 -3.137418e-16
## PC46 2.821852e-16 -5.390175e-17 -7.587608e-17 -2.425128e-17 9.625037e-17
## PC47 5.954058e-16 -8.052186e-17 1.178838e-16 -1.022674e-16 -4.956353e-17
## PC48 5.079204e-16 -5.532718e-16 -2.419449e-16 -6.499082e-16 -3.016218e-16
## PC49 2.162005e-16 5.920446e-16 3.147600e-16 -1.031359e-15 -1.147473e-16
## PC50 5.565150e-16 4.698464e-17 -5.687221e-17 -1.501962e-16 -7.247165e-17
## PC51 -9.696400e-17 -2.280321e-16 -2.808439e-16 1.817336e-16 -1.470281e-16
## PC52 7.068348e-16 -1.220041e-15 -2.486682e-16 5.650694e-16 1.332610e-16
## PC53 3.835869e-17 -1.288713e-16 2.612927e-16 9.888498e-16 -4.237617e-17
## PC54 -3.887944e-17 -2.585788e-16 -1.828573e-16 4.148720e-16 1.948724e-16
## PC55 -1.269119e-15 -3.258952e-16 -1.230678e-15 -6.153841e-16 -1.020328e-16
## PC56 -8.453516e-16 3.659776e-16 3.115855e-17 -7.682857e-16 -1.572603e-16
## PC57 -1.805853e-16 2.987423e-16 -2.853930e-16 -6.075582e-16 3.853661e-16
## PC58 1.822562e-16 5.393887e-16 2.169876e-16 -6.213573e-16 -3.746636e-17
## PC59 9.219294e-16 -5.237197e-16 -8.352371e-16 5.201028e-16 4.288988e-17
## PC60 1.390008e-15 1.722625e-16 -3.223540e-16 4.684657e-18 -2.401250e-17
## PC61 2.639264e-16 8.807848e-16 7.905586e-16 -7.329045e-17 2.873176e-16
## PC62 3.989937e-16 -4.124405e-17 -3.360388e-16 5.809065e-17 2.186691e-16
## PC63 4.011544e-16 -4.046438e-17 9.307359e-18 -2.785554e-16 2.999110e-17
## PC64 -2.082177e-16 2.026718e-16 -4.787905e-16 1.026639e-16 2.555990e-17
## PC65 -5.873197e-17 -1.679699e-16 -4.188131e-16 6.696355e-16 -1.411302e-17
## PC66 7.248176e-16 -5.118210e-16 -1.081063e-16 -2.845224e-16 -3.489508e-16
## PC67 5.024191e-16 1.273494e-18 -1.832941e-16 -2.492981e-16 2.478015e-18
## PC68 1.354803e-15 -3.282902e-16 2.646686e-16 -5.920212e-17 -1.342726e-16
## PC69 -1.272961e-15 3.729347e-16 5.858983e-16 4.397448e-16 -2.695081e-16
## PC70 -7.174288e-18 -7.410354e-16 -1.287293e-16 -3.924895e-16 9.444813e-17
## PC6 PC7 PC8 PC9 PC10
## PC1 1.144514e-15 -4.255869e-16 1.206237e-15 -4.321233e-16 9.751851e-16
## PC2 -8.247277e-16 9.052840e-16 3.417931e-17 -1.067243e-15 -1.602457e-15
## PC3 -1.404602e-16 4.980954e-16 -5.258377e-16 4.832237e-16 1.309163e-15
## PC4 4.279775e-15 -3.684480e-16 -3.473772e-16 1.045754e-15 -7.449059e-16
## PC5 1.034235e-15 -9.419135e-17 -1.529411e-15 4.777950e-16 7.398944e-16
## PC6 2.831620e+00 3.835239e-16 4.519337e-16 3.298669e-16 1.353856e-16
## PC7 3.835239e-16 2.714366e+00 -8.184545e-16 -5.023470e-16 5.953164e-16
## PC8 4.519337e-16 -8.184545e-16 2.367355e+00 -1.549422e-15 -2.026897e-16
## PC9 3.298669e-16 -5.023470e-16 -1.549422e-15 2.271421e+00 -3.920362e-16
## PC10 1.353856e-16 5.953164e-16 -2.026897e-16 -3.920362e-16 2.101727e+00
## PC11 4.102093e-16 1.804432e-15 -1.171171e-16 9.439271e-17 6.289851e-16
## PC12 1.418357e-16 -1.691993e-17 1.570366e-16 3.878207e-16 1.617874e-16
## PC13 9.630820e-16 8.268190e-16 -1.228154e-15 5.572851e-16 1.017285e-16
## PC14 2.718939e-16 -5.897750e-16 1.102715e-15 -1.576603e-15 -5.194216e-17
## PC15 -3.281665e-16 -6.755335e-16 -3.427345e-17 4.482763e-16 -2.623491e-16
## PC16 -2.783833e-16 7.768031e-16 -3.039677e-16 -8.533458e-16 -1.681032e-16
## PC17 -2.907353e-16 -3.814262e-16 1.877672e-16 9.822097e-17 -1.129187e-16
## PC18 -7.225160e-16 7.628230e-16 -1.857618e-16 6.600726e-17 -4.727012e-16
## PC19 1.104198e-15 -4.492934e-16 8.786891e-16 -3.197880e-17 2.929827e-16
## PC20 -1.091116e-15 -4.340810e-17 2.174731e-16 -3.400355e-16 4.642876e-16
## PC21 4.750343e-16 1.574132e-16 -1.548450e-16 1.219211e-16 -3.213875e-16
## PC22 6.151351e-16 3.710011e-16 1.624900e-16 -9.507550e-17 4.942279e-16
## PC23 -4.428555e-16 -3.349999e-16 8.722457e-17 -2.440655e-16 2.766086e-16
## PC24 5.778952e-16 1.229356e-16 -7.238032e-16 -1.763455e-16 -1.905353e-16
## PC25 6.387581e-16 -1.689950e-16 4.539853e-17 4.654035e-17 2.813763e-19
## PC26 -5.152748e-16 1.791041e-16 9.151050e-17 -3.622358e-16 -1.142286e-16
## PC27 1.752491e-16 -1.801363e-16 -2.417003e-16 1.908222e-16 2.627407e-17
## PC28 2.213366e-16 -2.925926e-17 2.305554e-16 6.581572e-16 3.080330e-16
## PC29 -2.734225e-16 1.352188e-15 -1.454130e-16 -4.878484e-16 1.111922e-16
## PC30 -1.921572e-16 -1.841208e-18 -4.192473e-16 -1.790728e-16 -1.235577e-16
## PC31 -1.322540e-16 -1.170964e-16 1.967036e-17 4.963813e-16 4.242806e-16
## PC32 1.630259e-16 -4.680988e-16 -1.205665e-16 -9.109041e-17 -1.687866e-16
## PC33 1.483599e-16 -2.718272e-16 -1.261207e-16 3.578267e-16 -2.564634e-16
## PC34 3.116986e-17 2.598090e-16 3.437183e-16 -1.088345e-16 3.470457e-16
## PC35 9.320970e-17 -4.461210e-17 2.138828e-16 2.646982e-16 -1.641022e-16
## PC36 2.202724e-17 -2.766163e-16 3.262776e-16 -6.456553e-17 -1.192664e-16
## PC37 -2.758165e-17 -2.129528e-16 -2.631885e-17 2.586958e-16 -3.516719e-17
## PC38 -3.242422e-16 -3.324377e-16 -9.817612e-17 -1.451948e-15 -2.073914e-16
## PC39 1.276666e-16 4.245180e-16 2.978260e-16 2.546158e-16 -1.969817e-16
## PC40 -2.963151e-16 7.946273e-16 -6.703313e-16 -2.901493e-16 2.031542e-16
## PC41 3.306827e-16 -1.114102e-16 2.835598e-16 1.496535e-16 1.061208e-16
## PC42 2.085819e-16 -5.199072e-17 3.862884e-16 -8.718663e-17 -2.248181e-16
## PC43 -4.804611e-16 -3.185651e-16 8.091091e-16 7.048597e-17 4.701785e-16
## PC44 -1.172866e-17 -2.040307e-16 -1.368751e-16 7.883247e-17 -7.716010e-17
## PC45 2.805480e-16 -1.927413e-16 4.496750e-16 2.079706e-16 -2.958454e-16
## PC46 -2.497973e-17 1.701863e-16 3.516172e-16 -4.438808e-16 2.409521e-16
## PC47 1.899646e-16 1.325218e-16 -1.264578e-16 -4.779266e-17 3.793917e-16
## PC48 -3.934251e-16 6.223127e-17 1.457519e-16 1.912817e-16 -5.188795e-17
## PC49 3.688376e-17 -3.702454e-17 -6.929286e-17 1.679629e-16 -3.622924e-16
## PC50 -3.103586e-16 1.863602e-17 4.495274e-16 -4.772719e-16 -4.876960e-16
## PC51 3.121998e-17 -2.045573e-16 3.627985e-16 2.182738e-16 1.634474e-16
## PC52 -4.781960e-16 4.064790e-17 -8.655370e-17 -4.354504e-16 -2.219381e-16
## PC53 -5.166459e-16 7.419170e-17 -2.743976e-16 9.812933e-17 -1.570572e-16
## PC54 -1.857382e-16 -2.017443e-16 -1.371707e-16 -1.548389e-16 -5.083893e-17
## PC55 -3.720405e-17 -1.076287e-16 2.182033e-16 2.331164e-16 -1.523159e-17
## PC56 7.689057e-17 5.716295e-17 -4.380463e-17 3.162443e-16 4.601894e-16
## PC57 1.845828e-16 -1.914291e-16 6.609557e-17 1.769237e-16 6.353774e-17
## PC58 1.458088e-16 -9.333561e-17 2.521258e-16 5.417784e-18 8.496850e-17
## PC59 1.371176e-16 -3.654149e-17 -4.940776e-16 1.765817e-16 1.563146e-16
## PC60 2.452712e-16 -8.589011e-17 -3.167067e-16 -5.279032e-17 1.340075e-16
## PC61 -4.834193e-16 6.638418e-16 -3.593397e-16 6.376235e-16 8.678397e-18
## PC62 2.329373e-16 3.057450e-17 2.999378e-16 2.884597e-16 2.213030e-16
## PC63 -3.711605e-16 4.454587e-17 -3.728414e-16 -8.797010e-17 -9.285897e-17
## PC64 3.957812e-16 4.865502e-17 -1.691310e-16 4.857345e-16 -3.123413e-16
## PC65 3.144851e-16 -4.745998e-17 -3.978843e-16 4.242696e-16 4.568718e-16
## PC66 -4.073435e-16 2.536295e-16 1.790486e-16 -2.768496e-16 1.091765e-16
## PC67 -3.557812e-16 -3.241205e-16 -4.741519e-16 -5.249152e-17 8.941560e-17
## PC68 -4.368887e-17 -2.434774e-16 -2.715553e-16 -1.236158e-16 2.195741e-16
## PC69 -2.763304e-16 -4.808566e-17 -2.596107e-16 7.718906e-17 3.035872e-16
## PC70 -1.733421e-16 5.563803e-16 1.752095e-16 -2.623660e-16 9.133203e-18
## PC11 PC12 PC13 PC14 PC15
## PC1 -1.584430e-15 -1.438597e-16 -3.419699e-16 4.293475e-16 8.552176e-16
## PC2 3.388490e-16 -6.151730e-16 -3.608867e-16 1.244182e-16 1.735319e-16
## PC3 -1.618345e-15 -7.683625e-16 -1.625423e-15 1.142000e-15 -2.717217e-16
## PC4 4.553081e-16 -4.269690e-16 -4.429702e-16 5.435622e-16 -6.995840e-16
## PC5 -4.754188e-16 2.890875e-17 -3.454655e-16 -6.178210e-16 2.243660e-16
## PC6 4.102093e-16 1.418357e-16 9.630820e-16 2.718939e-16 -3.281665e-16
## PC7 1.804432e-15 -1.691993e-17 8.268190e-16 -5.897750e-16 -6.755335e-16
## PC8 -1.171171e-16 1.570366e-16 -1.228154e-15 1.102715e-15 -3.427345e-17
## PC9 9.439271e-17 3.878207e-16 5.572851e-16 -1.576603e-15 4.482763e-16
## PC10 6.289851e-16 1.617874e-16 1.017285e-16 -5.194216e-17 -2.623491e-16
## PC11 2.039211e+00 1.353851e-16 -8.317734e-16 -7.408392e-16 -2.597113e-16
## PC12 1.353851e-16 1.783342e+00 -2.700625e-16 -4.129987e-17 8.086447e-16
## PC13 -8.317734e-16 -2.700625e-16 1.765811e+00 9.360976e-16 3.462251e-16
## PC14 -7.408392e-16 -4.129987e-17 9.360976e-16 1.686394e+00 -7.704392e-16
## PC15 -2.597113e-16 8.086447e-16 3.462251e-16 -7.704392e-16 1.613914e+00
## PC16 1.494042e-16 -1.804130e-15 2.277796e-16 -8.844766e-17 7.561516e-16
## PC17 -9.868563e-17 -5.357904e-16 -3.967851e-16 1.454728e-16 9.779826e-17
## PC18 2.548358e-16 -1.758402e-16 3.830790e-16 5.637830e-16 -1.826211e-16
## PC19 -6.074643e-16 -8.578748e-16 -1.280520e-17 -9.158540e-17 -8.000431e-16
## PC20 2.588881e-16 -1.034060e-15 -2.195006e-16 8.730925e-16 -6.058919e-16
## PC21 1.822892e-16 3.997189e-18 -3.043072e-16 -8.608694e-17 4.125389e-17
## PC22 4.236817e-16 7.955987e-16 2.378533e-17 3.066976e-16 -8.061172e-18
## PC23 4.556715e-17 7.194702e-16 1.481098e-17 -3.142686e-16 -1.566270e-16
## PC24 2.104307e-16 -1.567832e-16 3.770629e-16 4.202187e-17 1.569976e-16
## PC25 -3.361829e-16 2.029592e-16 -4.638590e-16 -2.438751e-16 -5.434160e-17
## PC26 -1.199431e-16 -5.987191e-16 2.090394e-16 8.468773e-17 -2.354718e-16
## PC27 -3.497326e-16 4.106955e-16 -3.772765e-17 -7.870082e-17 9.659951e-17
## PC28 1.866202e-16 1.518754e-16 -4.521639e-17 -3.464768e-16 -2.583486e-16
## PC29 -3.791408e-17 6.848520e-17 7.197049e-16 2.832217e-16 5.026505e-16
## PC30 -8.996329e-17 1.871051e-16 -7.319655e-18 -1.476319e-16 6.428038e-16
## PC31 7.517780e-17 -3.348954e-16 1.371819e-16 2.151896e-16 4.425268e-16
## PC32 1.337275e-16 2.769645e-16 6.622265e-17 6.769052e-17 -5.831088e-17
## PC33 5.945084e-16 -2.885183e-16 -1.134343e-16 2.398665e-16 1.511026e-17
## PC34 3.417951e-16 -2.608060e-16 2.402318e-16 -3.910582e-16 -1.378376e-16
## PC35 1.601028e-16 -2.583922e-16 1.920712e-16 -6.652754e-17 2.227858e-16
## PC36 -2.484670e-16 -4.055423e-16 2.747304e-16 4.341939e-16 2.202272e-16
## PC37 -5.217787e-17 3.578706e-17 -6.466104e-17 1.176088e-16 -2.496053e-17
## PC38 -5.317250e-16 1.234980e-16 -2.268074e-16 7.025824e-17 -2.448542e-16
## PC39 -1.505183e-16 5.599965e-16 -1.200068e-16 2.656878e-17 1.576335e-16
## PC40 -1.977062e-16 -2.463218e-16 3.517597e-16 -3.770249e-17 -4.593555e-16
## PC41 -1.838368e-17 3.782720e-16 -1.046507e-16 1.487487e-17 2.311971e-16
## PC42 2.656815e-16 2.289800e-16 2.239265e-17 -2.903403e-17 -3.428467e-18
## PC43 2.900172e-16 -2.351857e-16 -1.822655e-17 -4.318781e-17 4.733517e-17
## PC44 3.081277e-16 8.135473e-17 -3.643074e-16 -8.883165e-17 -2.424587e-16
## PC45 -2.566344e-16 2.238276e-16 7.566469e-17 2.511194e-16 -1.990920e-16
## PC46 1.590246e-16 -5.000538e-16 -1.988269e-17 1.835203e-16 2.696254e-16
## PC47 -4.880330e-17 -3.781754e-16 1.429391e-16 2.465637e-16 9.183451e-18
## PC48 1.666670e-17 5.390356e-17 -9.322783e-17 -1.435890e-16 -7.287742e-17
## PC49 -4.123202e-16 4.049981e-16 3.242479e-16 -1.701867e-16 1.326337e-16
## PC50 -1.082645e-16 -7.729609e-17 3.510871e-17 1.832385e-16 1.085792e-16
## PC51 3.536069e-16 2.927646e-16 -3.278001e-17 2.145904e-16 -1.559631e-16
## PC52 3.560765e-19 1.912544e-16 -7.539723e-18 3.689869e-17 -3.112880e-16
## PC53 -7.299198e-17 3.801812e-16 1.979911e-16 2.316001e-16 -2.117531e-16
## PC54 -3.787532e-16 -6.789062e-17 1.494729e-16 -1.569026e-16 -1.585879e-16
## PC55 6.531560e-17 1.438163e-17 2.331520e-16 -1.001164e-16 6.111399e-17
## PC56 2.806102e-16 6.800412e-16 2.557042e-16 -3.637282e-16 1.503650e-16
## PC57 7.822825e-17 -1.933379e-16 5.084924e-17 1.098915e-16 8.439046e-17
## PC58 3.392786e-17 4.052076e-16 1.652163e-16 -1.806280e-16 8.015689e-17
## PC59 2.151367e-17 -2.480704e-16 -2.359902e-16 5.198649e-16 -3.823716e-16
## PC60 -4.980070e-17 4.278513e-16 -1.933842e-16 1.346650e-16 1.463134e-16
## PC61 2.331525e-16 -2.465683e-16 -4.168402e-16 1.748281e-16 1.871273e-17
## PC62 2.218486e-16 1.383681e-16 -8.394564e-17 -8.509406e-17 3.045559e-17
## PC63 -1.532605e-16 -3.570350e-16 1.217930e-16 6.507956e-18 3.010129e-17
## PC64 1.456714e-16 1.953747e-16 4.951916e-18 1.695644e-16 1.942935e-16
## PC65 9.729311e-17 -1.240581e-16 -4.424931e-16 5.124612e-16 -1.888409e-16
## PC66 -1.254648e-16 -9.004586e-17 1.196745e-16 -2.190774e-17 3.710004e-17
## PC67 2.009424e-16 -1.137079e-17 -8.457471e-17 7.186582e-17 -1.471337e-16
## PC68 6.471437e-17 -1.370633e-16 -1.467248e-16 3.142912e-17 6.754741e-17
## PC69 1.632426e-17 9.459178e-17 -1.039398e-16 -2.317191e-16 -1.786885e-17
## PC70 3.170202e-17 1.119945e-16 -7.214438e-17 -3.857751e-17 -8.955458e-17
## PC16 PC17 PC18 PC19 PC20
## PC1 1.087568e-15 4.858777e-16 -1.404452e-15 -7.461189e-16 8.820545e-17
## PC2 -2.860793e-16 6.497396e-16 -2.795697e-16 2.223076e-16 -4.885338e-16
## PC3 1.955151e-15 1.025154e-15 1.344129e-15 -1.765236e-16 9.196487e-17
## PC4 -1.543420e-16 -7.584239e-16 -3.993859e-16 2.368388e-16 5.254702e-16
## PC5 -4.305051e-16 -9.007603e-16 -6.889011e-16 -1.998456e-16 2.849980e-16
## PC6 -2.783833e-16 -2.907353e-16 -7.225160e-16 1.104198e-15 -1.091116e-15
## PC7 7.768031e-16 -3.814262e-16 7.628230e-16 -4.492934e-16 -4.340810e-17
## PC8 -3.039677e-16 1.877672e-16 -1.857618e-16 8.786891e-16 2.174731e-16
## PC9 -8.533458e-16 9.822097e-17 6.600726e-17 -3.197880e-17 -3.400355e-16
## PC10 -1.681032e-16 -1.129187e-16 -4.727012e-16 2.929827e-16 4.642876e-16
## PC11 1.494042e-16 -9.868563e-17 2.548358e-16 -6.074643e-16 2.588881e-16
## PC12 -1.804130e-15 -5.357904e-16 -1.758402e-16 -8.578748e-16 -1.034060e-15
## PC13 2.277796e-16 -3.967851e-16 3.830790e-16 -1.280520e-17 -2.195006e-16
## PC14 -8.844766e-17 1.454728e-16 5.637830e-16 -9.158540e-17 8.730925e-16
## PC15 7.561516e-16 9.779826e-17 -1.826211e-16 -8.000431e-16 -6.058919e-16
## PC16 1.556953e+00 -8.065432e-17 2.881631e-16 -3.135732e-17 -4.010031e-17
## PC17 -8.065432e-17 1.435527e+00 7.932439e-17 -3.153066e-16 2.526049e-16
## PC18 2.881631e-16 7.932439e-17 1.379189e+00 2.899434e-17 -5.994513e-16
## PC19 -3.135732e-17 -3.153066e-16 2.899434e-17 1.357315e+00 -6.192563e-16
## PC20 -4.010031e-17 2.526049e-16 -5.994513e-16 -6.192563e-16 1.244023e+00
## PC21 -3.258802e-17 -1.177263e-16 -4.757644e-16 -1.513830e-16 3.011591e-16
## PC22 -1.895558e-16 -7.020854e-18 7.052359e-16 5.977226e-16 7.187925e-16
## PC23 3.660692e-16 -4.448331e-16 2.222093e-16 -5.231663e-17 1.029151e-16
## PC24 2.767810e-16 -4.941122e-17 1.500899e-16 -2.140163e-16 -1.201528e-16
## PC25 7.161232e-17 4.241917e-17 2.156383e-16 -5.463379e-17 -3.737868e-17
## PC26 4.630187e-16 7.566189e-16 2.980154e-17 1.665439e-16 -3.219961e-16
## PC27 3.399597e-16 -2.071375e-16 -1.767153e-17 -3.375225e-16 1.043664e-16
## PC28 -1.724424e-16 1.076025e-16 -1.479187e-16 7.722875e-17 3.432726e-17
## PC29 -2.631471e-16 -1.466764e-16 -1.215053e-16 7.818898e-16 -7.132847e-16
## PC30 3.178713e-18 1.807126e-16 -2.736881e-16 -1.686367e-16 -7.653048e-17
## PC31 -1.513340e-16 5.093814e-18 -2.779722e-16 -3.924760e-16 1.316415e-16
## PC32 1.105515e-16 -1.109329e-16 -2.965273e-17 1.949176e-16 1.292687e-16
## PC33 -1.504452e-16 -1.301640e-16 -3.479846e-16 4.026814e-16 1.302500e-16
## PC34 -1.535743e-16 -3.554402e-16 1.241773e-16 -3.396302e-16 2.758249e-16
## PC35 1.599496e-16 6.340805e-16 4.582771e-18 1.220038e-16 -5.565186e-17
## PC36 -1.886701e-16 1.992641e-17 5.142539e-17 -2.368569e-16 1.830699e-16
## PC37 1.033606e-17 -2.740373e-16 -7.793413e-17 1.839556e-16 3.052907e-16
## PC38 4.039502e-16 2.750698e-16 3.773695e-16 2.371034e-16 -6.792656e-17
## PC39 -1.362448e-16 1.544971e-16 2.595617e-16 2.842023e-16 -4.800144e-17
## PC40 -4.987695e-16 2.319651e-16 1.427576e-16 -5.347440e-17 -3.881937e-16
## PC41 -1.420176e-17 -1.814490e-16 2.349382e-16 1.695537e-16 -1.899419e-17
## PC42 -3.208138e-16 3.281835e-16 -2.178097e-16 4.353588e-18 -1.379873e-17
## PC43 -1.380382e-16 -3.082443e-16 -3.766625e-17 1.409700e-16 1.803860e-16
## PC44 1.345177e-16 4.072289e-16 6.721682e-17 2.967294e-17 1.561961e-17
## PC45 5.650992e-16 4.023780e-16 -9.912520e-17 -2.265696e-16 1.865791e-16
## PC46 1.208756e-17 1.678660e-16 -2.654998e-16 1.899232e-16 4.507829e-17
## PC47 -4.442615e-17 6.720634e-16 -7.933649e-17 -1.229279e-16 9.498063e-17
## PC48 -4.614032e-16 -2.134620e-16 -3.919007e-16 5.646628e-17 -2.431488e-16
## PC49 4.510636e-17 -2.806228e-17 2.584952e-16 3.399584e-16 1.598592e-16
## PC50 -1.329146e-16 -2.096049e-16 6.726468e-17 -5.416864e-17 1.299188e-16
## PC51 2.837657e-17 -2.579223e-16 -7.552630e-18 1.520858e-16 -6.816728e-17
## PC52 -4.807081e-17 3.603682e-16 -7.295390e-17 3.871641e-16 -1.602425e-16
## PC53 2.482968e-17 -3.704428e-16 -2.567946e-17 -5.969049e-17 -1.631647e-16
## PC54 1.558575e-16 2.393181e-16 1.528048e-16 1.193578e-16 2.954396e-17
## PC55 6.333620e-17 -2.222585e-16 -6.565300e-17 1.277484e-16 2.306293e-16
## PC56 1.250032e-16 -9.621810e-17 2.310146e-16 9.116559e-17 -1.111793e-16
## PC57 4.053398e-16 -1.764044e-16 1.029291e-16 -1.218056e-16 1.798374e-16
## PC58 2.942170e-16 2.821961e-16 1.500599e-16 -1.200298e-17 -1.232726e-16
## PC59 -2.924894e-17 -3.641306e-17 1.137568e-16 1.018827e-16 4.352652e-16
## PC60 1.028822e-16 1.196849e-16 3.072606e-16 1.183136e-16 3.353692e-16
## PC61 3.186611e-17 1.253931e-18 2.505757e-16 -1.276317e-16 5.976398e-17
## PC62 6.284162e-17 4.898803e-16 -3.870190e-17 4.167693e-16 4.270853e-16
## PC63 9.878429e-17 5.890348e-17 -6.956968e-17 1.641243e-17 -1.475825e-16
## PC64 4.921459e-17 -3.468705e-17 1.590188e-16 2.122224e-16 2.115533e-16
## PC65 3.491770e-16 7.957108e-17 -2.635779e-16 3.513299e-16 1.456864e-17
## PC66 -6.042757e-17 7.021989e-16 -4.356910e-17 2.849241e-16 -4.953989e-17
## PC67 9.689831e-17 2.107086e-16 -2.394310e-16 8.628023e-17 -3.559023e-17
## PC68 2.643897e-16 2.108725e-16 -2.322998e-16 3.045361e-16 1.514782e-16
## PC69 -2.845711e-16 1.030191e-16 1.540839e-16 -5.695788e-17 -1.880916e-16
## PC70 -2.181217e-16 -5.430239e-17 3.338275e-16 -1.233108e-16 -3.557970e-16
## PC21 PC22 PC23 PC24 PC25
## PC1 4.985194e-16 5.948597e-16 -4.603536e-16 -5.808218e-17 3.532985e-16
## PC2 3.961155e-16 -1.882586e-16 -7.475590e-16 1.563938e-15 -5.669349e-17
## PC3 -1.240895e-15 2.561647e-16 7.157119e-16 -1.496400e-15 -5.003425e-16
## PC4 -7.838627e-16 2.850109e-16 3.221510e-16 6.047009e-17 3.798184e-16
## PC5 6.758452e-17 2.115666e-16 7.339833e-16 5.739043e-17 2.609736e-16
## PC6 4.750343e-16 6.151351e-16 -4.428555e-16 5.778952e-16 6.387581e-16
## PC7 1.574132e-16 3.710011e-16 -3.349999e-16 1.229356e-16 -1.689950e-16
## PC8 -1.548450e-16 1.624900e-16 8.722457e-17 -7.238032e-16 4.539853e-17
## PC9 1.219211e-16 -9.507550e-17 -2.440655e-16 -1.763455e-16 4.654035e-17
## PC10 -3.213875e-16 4.942279e-16 2.766086e-16 -1.905353e-16 2.813763e-19
## PC11 1.822892e-16 4.236817e-16 4.556715e-17 2.104307e-16 -3.361829e-16
## PC12 3.997189e-18 7.955987e-16 7.194702e-16 -1.567832e-16 2.029592e-16
## PC13 -3.043072e-16 2.378533e-17 1.481098e-17 3.770629e-16 -4.638590e-16
## PC14 -8.608694e-17 3.066976e-16 -3.142686e-16 4.202187e-17 -2.438751e-16
## PC15 4.125389e-17 -8.061172e-18 -1.566270e-16 1.569976e-16 -5.434160e-17
## PC16 -3.258802e-17 -1.895558e-16 3.660692e-16 2.767810e-16 7.161232e-17
## PC17 -1.177263e-16 -7.020854e-18 -4.448331e-16 -4.941122e-17 4.241917e-17
## PC18 -4.757644e-16 7.052359e-16 2.222093e-16 1.500899e-16 2.156383e-16
## PC19 -1.513830e-16 5.977226e-16 -5.231663e-17 -2.140163e-16 -5.463379e-17
## PC20 3.011591e-16 7.187925e-16 1.029151e-16 -1.201528e-16 -3.737868e-17
## PC21 1.169786e+00 5.387917e-16 1.552129e-16 -6.170569e-16 1.565348e-16
## PC22 5.387917e-16 1.096587e+00 -8.166292e-16 -3.994420e-16 6.756846e-17
## PC23 1.552129e-16 -8.166292e-16 1.011583e+00 -6.132158e-16 1.046823e-16
## PC24 -6.170569e-16 -3.994420e-16 -6.132158e-16 9.803526e-01 1.408132e-16
## PC25 1.565348e-16 6.756846e-17 1.046823e-16 1.408132e-16 9.460709e-01
## PC26 -2.348732e-16 -2.936641e-16 -3.714892e-16 7.414120e-18 3.776730e-17
## PC27 -9.908704e-17 -2.807471e-17 -3.352775e-16 -2.493452e-16 8.139139e-16
## PC28 3.259318e-16 -2.194658e-16 1.495473e-17 8.515246e-17 -1.326233e-16
## PC29 5.659161e-16 1.379171e-17 -1.497062e-16 3.099473e-16 -1.486841e-17
## PC30 -8.243615e-17 2.448929e-16 -2.458412e-16 -7.008818e-17 -4.496687e-16
## PC31 -2.510070e-16 -1.971889e-16 2.188064e-17 -6.300634e-18 -5.956394e-16
## PC32 -1.438778e-16 1.434566e-16 -2.712319e-16 -6.867162e-17 -2.220169e-16
## PC33 -1.441550e-16 -7.659775e-17 -1.705373e-16 2.066707e-16 2.873850e-16
## PC34 7.497161e-16 -1.691894e-16 1.317863e-16 -3.556822e-16 7.758991e-17
## PC35 9.913770e-17 -1.939644e-16 1.722340e-16 3.400830e-16 -8.409116e-18
## PC36 -3.696904e-17 -1.302723e-16 5.489818e-17 -1.815151e-16 3.381158e-16
## PC37 -5.498970e-17 1.839575e-16 -8.320477e-17 2.602731e-17 2.654592e-16
## PC38 1.570815e-16 -1.399218e-16 1.188500e-16 -1.012819e-16 -1.877095e-16
## PC39 7.240490e-17 -1.091812e-16 -1.997676e-16 -9.214938e-17 -2.228795e-16
## PC40 1.400363e-16 -4.024871e-16 2.486358e-16 1.815006e-16 -2.632745e-16
## PC41 -1.768502e-16 1.580712e-16 5.210559e-17 8.711887e-17 7.595377e-17
## PC42 9.360924e-18 -1.389821e-16 2.583667e-16 4.914050e-17 -6.935582e-17
## PC43 -1.252020e-16 1.678104e-16 -7.661910e-17 -3.515797e-16 -1.136334e-16
## PC44 -6.577041e-17 7.631025e-17 -1.638839e-17 9.362634e-17 2.576493e-16
## PC45 1.540631e-16 -6.257968e-17 8.748058e-17 -1.249139e-16 2.809324e-16
## PC46 2.978694e-16 1.359721e-16 4.955863e-16 1.846209e-18 -1.410672e-16
## PC47 4.048463e-17 1.532571e-16 -8.306320e-17 -1.080330e-17 4.419971e-17
## PC48 1.758240e-16 -1.002668e-16 -1.823686e-17 -4.608182e-17 3.308083e-17
## PC49 1.825525e-16 5.469590e-17 7.714048e-17 2.206776e-16 6.982742e-17
## PC50 2.533032e-18 -1.507039e-16 -2.218752e-18 1.877985e-16 -1.651265e-16
## PC51 3.496907e-17 1.292416e-16 6.067051e-17 2.519576e-17 -1.098678e-16
## PC52 1.381441e-16 3.185376e-17 -3.496124e-17 9.901089e-18 -2.093273e-16
## PC53 -9.361053e-17 -1.517886e-16 -2.389320e-16 -2.890186e-16 1.195072e-16
## PC54 -4.532498e-17 5.498801e-17 1.527611e-16 8.964856e-17 -1.656219e-16
## PC55 3.597596e-16 -3.240784e-16 1.842512e-16 -1.199879e-16 -1.130098e-16
## PC56 2.815002e-16 -1.134868e-16 6.188080e-17 2.627064e-16 1.589110e-16
## PC57 -7.792897e-17 1.557194e-16 1.505237e-16 1.652429e-16 6.317837e-17
## PC58 -1.806697e-16 1.263552e-16 -2.141631e-16 -2.548320e-16 -1.346539e-16
## PC59 3.199777e-16 -5.359282e-17 2.342365e-17 -3.918229e-17 7.321902e-17
## PC60 -1.319106e-16 7.009415e-17 -1.633298e-16 3.100012e-17 2.789930e-16
## PC61 -8.464360e-17 2.970111e-16 1.931332e-17 3.422437e-16 -8.504229e-17
## PC62 1.330600e-16 -2.501453e-16 -1.874696e-16 9.416199e-17 -3.647768e-17
## PC63 -2.727188e-17 4.349377e-17 1.337755e-16 -6.196022e-17 -7.896360e-17
## PC64 1.738742e-16 -2.627970e-16 -1.191493e-18 1.090091e-16 -9.734373e-17
## PC65 -3.848466e-17 1.340463e-16 3.165368e-17 -6.628315e-18 -1.011132e-16
## PC66 -3.304251e-17 3.071951e-17 -3.142628e-16 -1.459371e-16 -1.194186e-16
## PC67 -1.094131e-16 2.302682e-16 1.277447e-18 -6.762969e-17 -1.149309e-16
## PC68 1.821169e-17 1.307061e-17 -2.003265e-16 -1.195592e-16 -1.810852e-17
## PC69 2.402579e-16 -8.180346e-17 -3.416925e-16 2.717984e-17 5.424568e-17
## PC70 -3.873941e-17 3.007818e-17 -7.787689e-17 -9.265766e-17 9.769799e-18
## PC26 PC27 PC28 PC29 PC30
## PC1 -3.577034e-16 -7.229030e-16 1.604354e-15 -9.395186e-16 -8.793876e-16
## PC2 1.487363e-16 -4.757524e-16 -2.157475e-16 -3.950790e-16 -1.510398e-16
## PC3 6.975405e-16 -7.238018e-16 -1.115771e-15 1.381812e-15 1.043862e-15
## PC4 4.794915e-16 -3.253239e-16 3.825685e-17 1.004127e-15 -3.530027e-16
## PC5 2.540957e-16 4.260147e-16 7.806127e-17 -9.055766e-16 -5.555917e-16
## PC6 -5.152748e-16 1.752491e-16 2.213366e-16 -2.734225e-16 -1.921572e-16
## PC7 1.791041e-16 -1.801363e-16 -2.925926e-17 1.352188e-15 -1.841208e-18
## PC8 9.151050e-17 -2.417003e-16 2.305554e-16 -1.454130e-16 -4.192473e-16
## PC9 -3.622358e-16 1.908222e-16 6.581572e-16 -4.878484e-16 -1.790728e-16
## PC10 -1.142286e-16 2.627407e-17 3.080330e-16 1.111922e-16 -1.235577e-16
## PC11 -1.199431e-16 -3.497326e-16 1.866202e-16 -3.791408e-17 -8.996329e-17
## PC12 -5.987191e-16 4.106955e-16 1.518754e-16 6.848520e-17 1.871051e-16
## PC13 2.090394e-16 -3.772765e-17 -4.521639e-17 7.197049e-16 -7.319655e-18
## PC14 8.468773e-17 -7.870082e-17 -3.464768e-16 2.832217e-16 -1.476319e-16
## PC15 -2.354718e-16 9.659951e-17 -2.583486e-16 5.026505e-16 6.428038e-16
## PC16 4.630187e-16 3.399597e-16 -1.724424e-16 -2.631471e-16 3.178713e-18
## PC17 7.566189e-16 -2.071375e-16 1.076025e-16 -1.466764e-16 1.807126e-16
## PC18 2.980154e-17 -1.767153e-17 -1.479187e-16 -1.215053e-16 -2.736881e-16
## PC19 1.665439e-16 -3.375225e-16 7.722875e-17 7.818898e-16 -1.686367e-16
## PC20 -3.219961e-16 1.043664e-16 3.432726e-17 -7.132847e-16 -7.653048e-17
## PC21 -2.348732e-16 -9.908704e-17 3.259318e-16 5.659161e-16 -8.243615e-17
## PC22 -2.936641e-16 -2.807471e-17 -2.194658e-16 1.379171e-17 2.448929e-16
## PC23 -3.714892e-16 -3.352775e-16 1.495473e-17 -1.497062e-16 -2.458412e-16
## PC24 7.414120e-18 -2.493452e-16 8.515246e-17 3.099473e-16 -7.008818e-17
## PC25 3.776730e-17 8.139139e-16 -1.326233e-16 -1.486841e-17 -4.496687e-16
## PC26 9.106323e-01 4.745455e-16 -8.474269e-16 2.495863e-17 3.981852e-16
## PC27 4.745455e-16 8.730416e-01 2.819177e-16 3.699921e-17 -4.803580e-16
## PC28 -8.474269e-16 2.819177e-16 8.045359e-01 1.732931e-16 -2.822320e-16
## PC29 2.495863e-17 3.699921e-17 1.732931e-16 7.950144e-01 4.844707e-16
## PC30 3.981852e-16 -4.803580e-16 -2.822320e-16 4.844707e-16 7.546465e-01
## PC31 2.611887e-17 -1.167169e-16 6.780839e-16 -3.764327e-16 4.955675e-16
## PC32 -6.827313e-17 -7.819050e-17 -2.345410e-16 1.536235e-17 1.656226e-16
## PC33 8.961806e-17 -4.083844e-16 -2.343435e-16 -1.010253e-16 -3.249880e-17
## PC34 2.674826e-16 -2.182331e-16 3.451629e-16 2.579612e-16 2.189485e-16
## PC35 -5.325631e-17 -8.912826e-17 -1.838157e-16 2.302200e-17 3.775203e-16
## PC36 1.689781e-16 -2.243155e-16 -1.978401e-16 -2.812452e-16 -7.813008e-17
## PC37 -6.584721e-17 2.987648e-16 5.978213e-17 -4.441615e-17 -3.955854e-17
## PC38 -2.277010e-17 7.993022e-17 -1.978598e-16 -1.024839e-16 1.257707e-17
## PC39 4.773461e-16 -1.672376e-16 -3.681554e-16 -1.691804e-16 -1.091833e-16
## PC40 -6.160987e-16 -2.189846e-16 -5.376223e-17 1.366317e-16 1.210386e-16
## PC41 1.256986e-16 -2.939337e-16 -1.425861e-16 -2.835334e-17 4.958063e-17
## PC42 -4.175011e-16 -1.320468e-17 1.467300e-16 1.929410e-16 -1.038088e-16
## PC43 -6.076536e-17 -1.148880e-16 -6.485194e-17 1.890628e-16 -3.611436e-19
## PC44 -6.566970e-17 4.307154e-17 5.476479e-17 1.011389e-16 -5.136246e-17
## PC45 1.463685e-16 -1.039149e-16 7.236033e-17 3.302089e-16 1.123498e-16
## PC46 1.013940e-16 7.182839e-18 1.829072e-16 -4.755017e-17 2.065516e-16
## PC47 8.688977e-17 7.849882e-17 4.755646e-18 -2.547133e-17 -1.200534e-16
## PC48 -2.165844e-16 1.839265e-16 -3.906032e-17 -1.057007e-16 4.589305e-17
## PC49 -5.214633e-17 -8.379060e-17 -1.944813e-16 -7.032866e-17 1.833471e-16
## PC50 -5.717000e-17 -6.881618e-18 -6.358233e-18 -9.801349e-17 -1.666848e-16
## PC51 -1.061574e-16 5.932377e-17 -3.910614e-17 8.372743e-17 2.828041e-17
## PC52 -9.878417e-17 2.476563e-17 -7.601225e-17 -1.043446e-16 1.578037e-16
## PC53 2.563745e-16 -1.239701e-17 -2.746871e-16 -3.892665e-17 -3.958693e-17
## PC54 -1.353635e-16 7.736912e-17 1.514156e-17 -7.737656e-17 2.890778e-17
## PC55 1.246526e-16 -1.665694e-16 -2.445118e-16 1.041251e-16 -2.796501e-16
## PC56 3.552451e-16 -1.537107e-16 8.688073e-17 1.470581e-16 1.323640e-16
## PC57 1.791319e-16 2.281116e-17 1.829064e-16 6.835225e-17 1.461626e-16
## PC58 -1.094584e-16 -2.186823e-16 3.139467e-18 -3.029131e-17 1.567567e-16
## PC59 -6.382833e-17 -3.701260e-17 -1.583703e-16 6.507819e-17 -6.558810e-17
## PC60 2.634758e-16 3.323919e-17 1.124585e-16 6.353255e-17 7.223820e-18
## PC61 4.733281e-18 6.144877e-17 8.559357e-17 1.984082e-16 -8.891023e-17
## PC62 1.518583e-16 -8.081630e-17 -3.139249e-17 1.185816e-16 -2.332212e-17
## PC63 -6.326172e-17 6.840961e-18 -5.796384e-17 1.937015e-17 4.706510e-17
## PC64 1.042099e-16 -1.108305e-16 1.752535e-16 -5.961944e-17 -6.587044e-17
## PC65 -6.595194e-17 -2.617880e-17 2.000772e-17 -2.616137e-16 -4.639506e-17
## PC66 5.455537e-16 3.989457e-16 1.238834e-16 -6.905900e-17 1.046484e-16
## PC67 2.744701e-16 4.812599e-17 -2.044954e-16 1.244241e-16 5.946728e-17
## PC68 -1.396596e-18 9.855083e-17 -4.955933e-17 -2.160928e-17 3.211372e-17
## PC69 -8.538263e-17 2.067226e-16 6.028325e-17 -1.302707e-16 4.756437e-17
## PC70 -2.894931e-17 4.383871e-17 -3.365036e-17 -1.558737e-16 -1.270888e-16
## PC31 PC32 PC33 PC34 PC35
## PC1 -6.534153e-16 -2.862974e-16 5.730893e-16 -7.868517e-17 -1.533556e-15
## PC2 9.738414e-16 -5.328460e-16 8.385674e-16 -7.907803e-16 -4.867878e-16
## PC3 3.280538e-16 4.849020e-16 2.970843e-17 -1.419789e-17 8.693551e-16
## PC4 -9.859012e-17 -4.318797e-16 7.500394e-16 -8.562506e-16 -2.835530e-16
## PC5 -1.870739e-16 5.484893e-16 1.841730e-16 -8.487651e-16 1.736446e-16
## PC6 -1.322540e-16 1.630259e-16 1.483599e-16 3.116986e-17 9.320970e-17
## PC7 -1.170964e-16 -4.680988e-16 -2.718272e-16 2.598090e-16 -4.461210e-17
## PC8 1.967036e-17 -1.205665e-16 -1.261207e-16 3.437183e-16 2.138828e-16
## PC9 4.963813e-16 -9.109041e-17 3.578267e-16 -1.088345e-16 2.646982e-16
## PC10 4.242806e-16 -1.687866e-16 -2.564634e-16 3.470457e-16 -1.641022e-16
## PC11 7.517780e-17 1.337275e-16 5.945084e-16 3.417951e-16 1.601028e-16
## PC12 -3.348954e-16 2.769645e-16 -2.885183e-16 -2.608060e-16 -2.583922e-16
## PC13 1.371819e-16 6.622265e-17 -1.134343e-16 2.402318e-16 1.920712e-16
## PC14 2.151896e-16 6.769052e-17 2.398665e-16 -3.910582e-16 -6.652754e-17
## PC15 4.425268e-16 -5.831088e-17 1.511026e-17 -1.378376e-16 2.227858e-16
## PC16 -1.513340e-16 1.105515e-16 -1.504452e-16 -1.535743e-16 1.599496e-16
## PC17 5.093814e-18 -1.109329e-16 -1.301640e-16 -3.554402e-16 6.340805e-16
## PC18 -2.779722e-16 -2.965273e-17 -3.479846e-16 1.241773e-16 4.582771e-18
## PC19 -3.924760e-16 1.949176e-16 4.026814e-16 -3.396302e-16 1.220038e-16
## PC20 1.316415e-16 1.292687e-16 1.302500e-16 2.758249e-16 -5.565186e-17
## PC21 -2.510070e-16 -1.438778e-16 -1.441550e-16 7.497161e-16 9.913770e-17
## PC22 -1.971889e-16 1.434566e-16 -7.659775e-17 -1.691894e-16 -1.939644e-16
## PC23 2.188064e-17 -2.712319e-16 -1.705373e-16 1.317863e-16 1.722340e-16
## PC24 -6.300634e-18 -6.867162e-17 2.066707e-16 -3.556822e-16 3.400830e-16
## PC25 -5.956394e-16 -2.220169e-16 2.873850e-16 7.758991e-17 -8.409116e-18
## PC26 2.611887e-17 -6.827313e-17 8.961806e-17 2.674826e-16 -5.325631e-17
## PC27 -1.167169e-16 -7.819050e-17 -4.083844e-16 -2.182331e-16 -8.912826e-17
## PC28 6.780839e-16 -2.345410e-16 -2.343435e-16 3.451629e-16 -1.838157e-16
## PC29 -3.764327e-16 1.536235e-17 -1.010253e-16 2.579612e-16 2.302200e-17
## PC30 4.955675e-16 1.656226e-16 -3.249880e-17 2.189485e-16 3.775203e-16
## PC31 6.810834e-01 -1.979258e-16 -3.955810e-16 -2.848580e-17 5.188819e-17
## PC32 -1.979258e-16 6.531623e-01 -2.565964e-16 8.776859e-17 -1.508925e-16
## PC33 -3.955810e-16 -2.565964e-16 6.507075e-01 1.965472e-16 -1.316972e-16
## PC34 -2.848580e-17 8.776859e-17 1.965472e-16 6.107803e-01 -2.519130e-16
## PC35 5.188819e-17 -1.508925e-16 -1.316972e-16 -2.519130e-16 5.817941e-01
## PC36 5.233437e-17 6.862052e-17 -6.125928e-17 3.811184e-16 2.275056e-16
## PC37 -1.883414e-17 -1.394390e-16 3.446817e-16 -3.298621e-17 4.246757e-17
## PC38 1.260320e-16 3.207480e-17 -5.343019e-17 1.928673e-16 4.250438e-17
## PC39 1.690265e-16 1.662211e-16 -1.408476e-16 -6.325494e-17 2.138447e-16
## PC40 -5.638303e-17 1.979548e-16 7.080018e-17 -2.246615e-16 -2.769347e-16
## PC41 -2.503855e-16 6.124484e-17 1.977072e-16 2.832823e-16 -7.768000e-17
## PC42 -1.028182e-16 3.474683e-16 7.146780e-18 1.671480e-16 -5.447295e-17
## PC43 -2.031866e-16 -5.568110e-17 -9.523578e-17 2.810836e-16 1.149272e-16
## PC44 -5.980311e-17 -3.768236e-17 -9.933196e-18 -6.304668e-18 -1.409875e-16
## PC45 2.286864e-16 1.373326e-16 -1.154913e-16 1.249633e-16 8.127860e-17
## PC46 2.450720e-16 -7.534995e-17 -6.964620e-17 -2.607353e-17 -5.342905e-17
## PC47 -1.205588e-16 -7.285322e-17 5.883120e-17 -6.844381e-17 -4.947205e-17
## PC48 2.635902e-17 1.005189e-16 2.239549e-16 -1.521310e-16 -5.574215e-17
## PC49 5.116353e-17 1.841241e-16 1.416360e-17 2.396834e-16 5.556437e-17
## PC50 5.914912e-17 -1.313933e-16 -1.269421e-16 -2.961344e-17 1.837172e-16
## PC51 3.273710e-17 1.023563e-17 -3.468084e-17 9.757658e-18 -3.162823e-17
## PC52 -8.516569e-17 -1.933099e-17 5.998090e-17 5.241359e-17 -3.188474e-19
## PC53 -1.459885e-16 7.286266e-17 -5.896616e-17 1.361279e-16 5.438744e-17
## PC54 4.665558e-17 -2.579894e-16 8.601075e-17 6.525292e-17 4.458573e-17
## PC55 -2.014582e-16 1.692929e-16 -4.961056e-17 -1.927040e-17 2.945428e-17
## PC56 2.792798e-16 -1.221899e-16 2.474127e-17 1.530721e-16 -2.164314e-17
## PC57 -5.410927e-17 5.729908e-17 1.339204e-16 9.007994e-18 9.788053e-17
## PC58 2.000431e-16 -3.149259e-17 -9.223145e-17 3.085240e-17 -2.201572e-16
## PC59 7.744818e-17 -2.645381e-17 -2.556988e-16 -5.360896e-17 -1.456627e-16
## PC60 1.224219e-16 1.100031e-16 2.864811e-17 1.677512e-17 -5.820240e-17
## PC61 1.680344e-16 2.193636e-17 9.960938e-17 -1.512034e-16 -2.148701e-17
## PC62 -9.036502e-17 -4.648291e-17 7.045112e-17 -6.909369e-18 4.924193e-17
## PC63 -7.782636e-17 -3.467366e-17 1.111389e-16 -1.629421e-16 -3.620968e-17
## PC64 2.497113e-16 -9.257909e-17 -6.345152e-17 1.184167e-16 4.010714e-17
## PC65 -2.844095e-17 -1.716645e-17 -2.190266e-18 2.547270e-17 1.203473e-16
## PC66 -1.849402e-16 -8.595944e-17 3.641760e-17 2.987699e-17 9.400425e-17
## PC67 1.113453e-17 -7.402951e-17 1.769855e-17 1.630498e-18 -6.702157e-17
## PC68 -3.873361e-17 5.577266e-17 6.996305e-17 1.526595e-17 1.336278e-16
## PC69 -3.124108e-17 -9.562768e-17 2.022273e-16 -9.973115e-17 -1.044144e-16
## PC70 -1.583000e-16 -1.015918e-16 -2.005782e-17 -2.049987e-16 9.280384e-17
## PC36 PC37 PC38 PC39 PC40
## PC1 8.556937e-16 7.082938e-17 8.076053e-16 -3.687254e-16 -1.867929e-16
## PC2 8.657815e-16 -1.514353e-16 1.563897e-15 -1.665724e-16 -1.384768e-15
## PC3 -3.671418e-16 -7.196521e-16 1.308511e-15 -1.109356e-16 -2.637322e-17
## PC4 5.654321e-16 4.702391e-16 1.032269e-15 1.959557e-16 2.798210e-16
## PC5 -1.424972e-16 2.239897e-16 -7.356183e-16 1.975501e-16 -2.406845e-16
## PC6 2.202724e-17 -2.758165e-17 -3.242422e-16 1.276666e-16 -2.963151e-16
## PC7 -2.766163e-16 -2.129528e-16 -3.324377e-16 4.245180e-16 7.946273e-16
## PC8 3.262776e-16 -2.631885e-17 -9.817612e-17 2.978260e-16 -6.703313e-16
## PC9 -6.456553e-17 2.586958e-16 -1.451948e-15 2.546158e-16 -2.901493e-16
## PC10 -1.192664e-16 -3.516719e-17 -2.073914e-16 -1.969817e-16 2.031542e-16
## PC11 -2.484670e-16 -5.217787e-17 -5.317250e-16 -1.505183e-16 -1.977062e-16
## PC12 -4.055423e-16 3.578706e-17 1.234980e-16 5.599965e-16 -2.463218e-16
## PC13 2.747304e-16 -6.466104e-17 -2.268074e-16 -1.200068e-16 3.517597e-16
## PC14 4.341939e-16 1.176088e-16 7.025824e-17 2.656878e-17 -3.770249e-17
## PC15 2.202272e-16 -2.496053e-17 -2.448542e-16 1.576335e-16 -4.593555e-16
## PC16 -1.886701e-16 1.033606e-17 4.039502e-16 -1.362448e-16 -4.987695e-16
## PC17 1.992641e-17 -2.740373e-16 2.750698e-16 1.544971e-16 2.319651e-16
## PC18 5.142539e-17 -7.793413e-17 3.773695e-16 2.595617e-16 1.427576e-16
## PC19 -2.368569e-16 1.839556e-16 2.371034e-16 2.842023e-16 -5.347440e-17
## PC20 1.830699e-16 3.052907e-16 -6.792656e-17 -4.800144e-17 -3.881937e-16
## PC21 -3.696904e-17 -5.498970e-17 1.570815e-16 7.240490e-17 1.400363e-16
## PC22 -1.302723e-16 1.839575e-16 -1.399218e-16 -1.091812e-16 -4.024871e-16
## PC23 5.489818e-17 -8.320477e-17 1.188500e-16 -1.997676e-16 2.486358e-16
## PC24 -1.815151e-16 2.602731e-17 -1.012819e-16 -9.214938e-17 1.815006e-16
## PC25 3.381158e-16 2.654592e-16 -1.877095e-16 -2.228795e-16 -2.632745e-16
## PC26 1.689781e-16 -6.584721e-17 -2.277010e-17 4.773461e-16 -6.160987e-16
## PC27 -2.243155e-16 2.987648e-16 7.993022e-17 -1.672376e-16 -2.189846e-16
## PC28 -1.978401e-16 5.978213e-17 -1.978598e-16 -3.681554e-16 -5.376223e-17
## PC29 -2.812452e-16 -4.441615e-17 -1.024839e-16 -1.691804e-16 1.366317e-16
## PC30 -7.813008e-17 -3.955854e-17 1.257707e-17 -1.091833e-16 1.210386e-16
## PC31 5.233437e-17 -1.883414e-17 1.260320e-16 1.690265e-16 -5.638303e-17
## PC32 6.862052e-17 -1.394390e-16 3.207480e-17 1.662211e-16 1.979548e-16
## PC33 -6.125928e-17 3.446817e-16 -5.343019e-17 -1.408476e-16 7.080018e-17
## PC34 3.811184e-16 -3.298621e-17 1.928673e-16 -6.325494e-17 -2.246615e-16
## PC35 2.275056e-16 4.246757e-17 4.250438e-17 2.138447e-16 -2.769347e-16
## PC36 5.406191e-01 -1.741842e-16 1.534386e-16 2.592189e-16 -2.697631e-17
## PC37 -1.741842e-16 5.308139e-01 -9.654562e-18 3.123759e-16 -7.141472e-17
## PC38 1.534386e-16 -9.654562e-18 4.548836e-01 -6.424233e-17 1.202767e-16
## PC39 2.592189e-16 3.123759e-16 -6.424233e-17 4.391945e-01 9.737265e-17
## PC40 -2.697631e-17 -7.141472e-17 1.202767e-16 9.737265e-17 4.167212e-01
## PC41 -1.949176e-17 -1.558979e-16 1.599295e-16 5.343890e-16 1.815006e-17
## PC42 2.972198e-18 -1.764597e-16 -1.277639e-16 2.689627e-16 1.856480e-16
## PC43 -4.700569e-18 7.302025e-17 -7.874885e-19 -2.262743e-16 1.612816e-16
## PC44 3.760375e-17 -9.767016e-17 -1.206870e-16 -3.510993e-16 2.566741e-16
## PC45 4.201298e-17 -1.886165e-17 -1.416294e-16 -3.718434e-17 1.197713e-17
## PC46 4.386743e-17 -6.175370e-17 1.082863e-17 3.180437e-16 9.201198e-18
## PC47 8.385158e-17 -1.746766e-16 6.932569e-17 4.860680e-17 1.490746e-16
## PC48 -3.727526e-17 1.776788e-16 -3.925851e-16 -9.404238e-17 7.661018e-17
## PC49 -4.616285e-17 -6.438677e-17 -8.403858e-18 4.069817e-17 -1.654200e-16
## PC50 6.993997e-17 6.981730e-17 6.571814e-17 -1.926628e-16 8.000089e-17
## PC51 -5.642909e-17 -8.685072e-17 -8.177046e-17 -5.412372e-17 8.774406e-17
## PC52 -6.316446e-18 7.384837e-17 6.553970e-17 3.112032e-17 -1.087316e-17
## PC53 -7.776892e-18 -1.650220e-16 7.192778e-17 -3.373466e-17 9.516746e-17
## PC54 -6.899134e-17 1.263129e-16 1.232824e-17 -1.910004e-17 6.927439e-18
## PC55 -3.502961e-17 -1.293711e-16 -6.461006e-18 1.471279e-16 3.305994e-17
## PC56 5.422306e-17 2.682400e-17 -2.799610e-16 -1.306167e-16 -3.534725e-17
## PC57 -2.961437e-17 8.856931e-17 -1.436407e-17 -9.157915e-17 -1.360351e-17
## PC58 4.607091e-17 -2.399479e-17 -3.189676e-17 -2.124527e-17 -2.184942e-18
## PC59 -1.635225e-17 3.497197e-17 -8.495014e-17 -1.491748e-16 -5.930779e-17
## PC60 1.319550e-16 6.348778e-17 7.479607e-17 4.247122e-17 -1.744727e-18
## PC61 1.085632e-16 -7.119433e-18 1.516996e-17 6.918654e-17 5.660044e-17
## PC62 -1.145253e-16 1.649084e-17 8.308570e-17 -4.584447e-17 1.351355e-16
## PC63 -4.873432e-17 -6.858515e-17 2.734577e-17 8.650848e-18 -4.135328e-17
## PC64 -1.720066e-17 -1.042880e-16 -3.222654e-17 8.297760e-17 -3.085378e-17
## PC65 8.625744e-17 -5.167708e-17 1.066832e-16 1.881169e-18 6.848334e-17
## PC66 -1.812813e-16 3.798023e-17 -1.805600e-17 -7.867258e-17 -2.223950e-17
## PC67 6.447574e-18 -2.712025e-16 4.873166e-17 1.965561e-17 1.080990e-16
## PC68 -3.283727e-17 4.062128e-17 -1.102409e-16 4.768663e-17 -4.690772e-17
## PC69 -5.599723e-17 -3.334244e-18 -2.027321e-17 1.354738e-18 -1.425540e-16
## PC70 1.631105e-17 8.451090e-17 3.872114e-17 -6.563298e-17 -9.680937e-17
## PC41 PC42 PC43 PC44 PC45
## PC1 -1.074763e-15 -8.350693e-16 -1.144603e-15 7.628806e-16 -7.199390e-17
## PC2 4.084062e-16 -1.987849e-17 1.436143e-15 2.277434e-16 -1.620599e-16
## PC3 1.788262e-16 -1.300397e-17 -5.086036e-16 2.954044e-16 3.416720e-16
## PC4 -2.127915e-16 2.561395e-16 4.517224e-16 -3.948432e-17 -5.040683e-16
## PC5 -1.845815e-16 -2.594347e-16 3.816385e-16 -2.314213e-16 -3.137418e-16
## PC6 3.306827e-16 2.085819e-16 -4.804611e-16 -1.172866e-17 2.805480e-16
## PC7 -1.114102e-16 -5.199072e-17 -3.185651e-16 -2.040307e-16 -1.927413e-16
## PC8 2.835598e-16 3.862884e-16 8.091091e-16 -1.368751e-16 4.496750e-16
## PC9 1.496535e-16 -8.718663e-17 7.048597e-17 7.883247e-17 2.079706e-16
## PC10 1.061208e-16 -2.248181e-16 4.701785e-16 -7.716010e-17 -2.958454e-16
## PC11 -1.838368e-17 2.656815e-16 2.900172e-16 3.081277e-16 -2.566344e-16
## PC12 3.782720e-16 2.289800e-16 -2.351857e-16 8.135473e-17 2.238276e-16
## PC13 -1.046507e-16 2.239265e-17 -1.822655e-17 -3.643074e-16 7.566469e-17
## PC14 1.487487e-17 -2.903403e-17 -4.318781e-17 -8.883165e-17 2.511194e-16
## PC15 2.311971e-16 -3.428467e-18 4.733517e-17 -2.424587e-16 -1.990920e-16
## PC16 -1.420176e-17 -3.208138e-16 -1.380382e-16 1.345177e-16 5.650992e-16
## PC17 -1.814490e-16 3.281835e-16 -3.082443e-16 4.072289e-16 4.023780e-16
## PC18 2.349382e-16 -2.178097e-16 -3.766625e-17 6.721682e-17 -9.912520e-17
## PC19 1.695537e-16 4.353588e-18 1.409700e-16 2.967294e-17 -2.265696e-16
## PC20 -1.899419e-17 -1.379873e-17 1.803860e-16 1.561961e-17 1.865791e-16
## PC21 -1.768502e-16 9.360924e-18 -1.252020e-16 -6.577041e-17 1.540631e-16
## PC22 1.580712e-16 -1.389821e-16 1.678104e-16 7.631025e-17 -6.257968e-17
## PC23 5.210559e-17 2.583667e-16 -7.661910e-17 -1.638839e-17 8.748058e-17
## PC24 8.711887e-17 4.914050e-17 -3.515797e-16 9.362634e-17 -1.249139e-16
## PC25 7.595377e-17 -6.935582e-17 -1.136334e-16 2.576493e-16 2.809324e-16
## PC26 1.256986e-16 -4.175011e-16 -6.076536e-17 -6.566970e-17 1.463685e-16
## PC27 -2.939337e-16 -1.320468e-17 -1.148880e-16 4.307154e-17 -1.039149e-16
## PC28 -1.425861e-16 1.467300e-16 -6.485194e-17 5.476479e-17 7.236033e-17
## PC29 -2.835334e-17 1.929410e-16 1.890628e-16 1.011389e-16 3.302089e-16
## PC30 4.958063e-17 -1.038088e-16 -3.611436e-19 -5.136246e-17 1.123498e-16
## PC31 -2.503855e-16 -1.028182e-16 -2.031866e-16 -5.980311e-17 2.286864e-16
## PC32 6.124484e-17 3.474683e-16 -5.568110e-17 -3.768236e-17 1.373326e-16
## PC33 1.977072e-16 7.146780e-18 -9.523578e-17 -9.933196e-18 -1.154913e-16
## PC34 2.832823e-16 1.671480e-16 2.810836e-16 -6.304668e-18 1.249633e-16
## PC35 -7.768000e-17 -5.447295e-17 1.149272e-16 -1.409875e-16 8.127860e-17
## PC36 -1.949176e-17 2.972198e-18 -4.700569e-18 3.760375e-17 4.201298e-17
## PC37 -1.558979e-16 -1.764597e-16 7.302025e-17 -9.767016e-17 -1.886165e-17
## PC38 1.599295e-16 -1.277639e-16 -7.874885e-19 -1.206870e-16 -1.416294e-16
## PC39 5.343890e-16 2.689627e-16 -2.262743e-16 -3.510993e-16 -3.718434e-17
## PC40 1.815006e-17 1.856480e-16 1.612816e-16 2.566741e-16 1.197713e-17
## PC41 3.789525e-01 -9.443207e-18 -5.743972e-17 1.780058e-16 2.336068e-17
## PC42 -9.443207e-18 3.617840e-01 -2.060744e-16 -1.878558e-17 -9.461100e-17
## PC43 -5.743972e-17 -2.060744e-16 3.443142e-01 -1.185678e-16 2.537317e-21
## PC44 1.780058e-16 -1.878558e-17 -1.185678e-16 3.121830e-01 6.727077e-17
## PC45 2.336068e-17 -9.461100e-17 2.537317e-21 6.727077e-17 2.879911e-01
## PC46 -1.127615e-16 -1.464447e-16 -1.014634e-16 1.211593e-16 -2.445673e-16
## PC47 2.247783e-18 -2.843256e-17 3.502034e-17 1.510478e-16 -2.019545e-16
## PC48 -1.724275e-16 -1.906198e-16 -2.427645e-16 -3.880992e-17 -7.808756e-18
## PC49 -2.066599e-17 7.367412e-18 1.221235e-16 -1.344203e-16 -3.553823e-17
## PC50 5.320440e-17 4.107525e-17 8.550762e-17 -2.228511e-17 1.331739e-16
## PC51 -4.136957e-17 -1.444748e-17 -1.293248e-16 -1.117119e-16 -3.026531e-17
## PC52 1.410324e-16 -1.505199e-16 -5.997498e-17 1.163235e-16 -1.689052e-16
## PC53 -1.049808e-16 -1.469357e-16 -5.306021e-17 -4.790383e-17 7.341037e-17
## PC54 -4.872856e-17 -7.703180e-17 -4.450945e-17 2.139340e-17 4.144278e-18
## PC55 -1.944513e-17 8.397105e-17 -4.191227e-17 -1.841692e-18 5.885270e-17
## PC56 -9.757932e-17 1.026541e-16 1.005546e-16 -5.791689e-18 -5.070402e-17
## PC57 -1.259094e-17 -1.122455e-16 7.303537e-17 -4.797639e-17 -1.139874e-16
## PC58 -4.253531e-17 4.226868e-17 1.123234e-16 -9.178001e-17 -1.298994e-17
## PC59 -8.640381e-17 4.845593e-17 -2.412103e-16 -1.947208e-18 1.384888e-16
## PC60 4.317964e-17 7.928712e-18 -1.745466e-17 2.517829e-16 -8.940324e-17
## PC61 -1.918885e-17 6.110286e-17 -3.203837e-17 -3.601084e-17 -7.036415e-17
## PC62 7.464538e-17 -6.217819e-17 5.375754e-17 5.949559e-18 -1.927367e-17
## PC63 2.974118e-17 -3.657650e-17 1.589974e-17 5.733703e-17 -2.837112e-17
## PC64 -8.932156e-17 -7.269390e-17 -3.681493e-17 7.745471e-18 7.623111e-17
## PC65 -7.152185e-18 3.904064e-17 -4.518262e-17 -1.588985e-17 4.401173e-17
## PC66 2.974780e-18 2.507020e-17 4.305613e-17 1.142232e-17 -1.126809e-16
## PC67 9.262087e-17 4.424255e-18 -3.715872e-17 1.768161e-17 4.689599e-17
## PC68 5.483820e-17 -3.196553e-17 7.787150e-17 9.170140e-18 6.879994e-17
## PC69 4.851740e-17 5.616252e-17 -1.623462e-17 4.815286e-17 1.240188e-17
## PC70 -1.417247e-18 1.905830e-17 5.998433e-17 3.913454e-17 -2.205807e-17
## PC46 PC47 PC48 PC49 PC50
## PC1 2.821852e-16 5.954058e-16 5.079204e-16 2.162005e-16 5.565150e-16
## PC2 -5.390175e-17 -8.052186e-17 -5.532718e-16 5.920446e-16 4.698464e-17
## PC3 -7.587608e-17 1.178838e-16 -2.419449e-16 3.147600e-16 -5.687221e-17
## PC4 -2.425128e-17 -1.022674e-16 -6.499082e-16 -1.031359e-15 -1.501962e-16
## PC5 9.625037e-17 -4.956353e-17 -3.016218e-16 -1.147473e-16 -7.247165e-17
## PC6 -2.497973e-17 1.899646e-16 -3.934251e-16 3.688376e-17 -3.103586e-16
## PC7 1.701863e-16 1.325218e-16 6.223127e-17 -3.702454e-17 1.863602e-17
## PC8 3.516172e-16 -1.264578e-16 1.457519e-16 -6.929286e-17 4.495274e-16
## PC9 -4.438808e-16 -4.779266e-17 1.912817e-16 1.679629e-16 -4.772719e-16
## PC10 2.409521e-16 3.793917e-16 -5.188795e-17 -3.622924e-16 -4.876960e-16
## PC11 1.590246e-16 -4.880330e-17 1.666670e-17 -4.123202e-16 -1.082645e-16
## PC12 -5.000538e-16 -3.781754e-16 5.390356e-17 4.049981e-16 -7.729609e-17
## PC13 -1.988269e-17 1.429391e-16 -9.322783e-17 3.242479e-16 3.510871e-17
## PC14 1.835203e-16 2.465637e-16 -1.435890e-16 -1.701867e-16 1.832385e-16
## PC15 2.696254e-16 9.183451e-18 -7.287742e-17 1.326337e-16 1.085792e-16
## PC16 1.208756e-17 -4.442615e-17 -4.614032e-16 4.510636e-17 -1.329146e-16
## PC17 1.678660e-16 6.720634e-16 -2.134620e-16 -2.806228e-17 -2.096049e-16
## PC18 -2.654998e-16 -7.933649e-17 -3.919007e-16 2.584952e-16 6.726468e-17
## PC19 1.899232e-16 -1.229279e-16 5.646628e-17 3.399584e-16 -5.416864e-17
## PC20 4.507829e-17 9.498063e-17 -2.431488e-16 1.598592e-16 1.299188e-16
## PC21 2.978694e-16 4.048463e-17 1.758240e-16 1.825525e-16 2.533032e-18
## PC22 1.359721e-16 1.532571e-16 -1.002668e-16 5.469590e-17 -1.507039e-16
## PC23 4.955863e-16 -8.306320e-17 -1.823686e-17 7.714048e-17 -2.218752e-18
## PC24 1.846209e-18 -1.080330e-17 -4.608182e-17 2.206776e-16 1.877985e-16
## PC25 -1.410672e-16 4.419971e-17 3.308083e-17 6.982742e-17 -1.651265e-16
## PC26 1.013940e-16 8.688977e-17 -2.165844e-16 -5.214633e-17 -5.717000e-17
## PC27 7.182839e-18 7.849882e-17 1.839265e-16 -8.379060e-17 -6.881618e-18
## PC28 1.829072e-16 4.755646e-18 -3.906032e-17 -1.944813e-16 -6.358233e-18
## PC29 -4.755017e-17 -2.547133e-17 -1.057007e-16 -7.032866e-17 -9.801349e-17
## PC30 2.065516e-16 -1.200534e-16 4.589305e-17 1.833471e-16 -1.666848e-16
## PC31 2.450720e-16 -1.205588e-16 2.635902e-17 5.116353e-17 5.914912e-17
## PC32 -7.534995e-17 -7.285322e-17 1.005189e-16 1.841241e-16 -1.313933e-16
## PC33 -6.964620e-17 5.883120e-17 2.239549e-16 1.416360e-17 -1.269421e-16
## PC34 -2.607353e-17 -6.844381e-17 -1.521310e-16 2.396834e-16 -2.961344e-17
## PC35 -5.342905e-17 -4.947205e-17 -5.574215e-17 5.556437e-17 1.837172e-16
## PC36 4.386743e-17 8.385158e-17 -3.727526e-17 -4.616285e-17 6.993997e-17
## PC37 -6.175370e-17 -1.746766e-16 1.776788e-16 -6.438677e-17 6.981730e-17
## PC38 1.082863e-17 6.932569e-17 -3.925851e-16 -8.403858e-18 6.571814e-17
## PC39 3.180437e-16 4.860680e-17 -9.404238e-17 4.069817e-17 -1.926628e-16
## PC40 9.201198e-18 1.490746e-16 7.661018e-17 -1.654200e-16 8.000089e-17
## PC41 -1.127615e-16 2.247783e-18 -1.724275e-16 -2.066599e-17 5.320440e-17
## PC42 -1.464447e-16 -2.843256e-17 -1.906198e-16 7.367412e-18 4.107525e-17
## PC43 -1.014634e-16 3.502034e-17 -2.427645e-16 1.221235e-16 8.550762e-17
## PC44 1.211593e-16 1.510478e-16 -3.880992e-17 -1.344203e-16 -2.228511e-17
## PC45 -2.445673e-16 -2.019545e-16 -7.808756e-18 -3.553823e-17 1.331739e-16
## PC46 2.797323e-01 1.038979e-16 -2.941511e-17 -6.435167e-17 -6.036243e-17
## PC47 1.038979e-16 2.684654e-01 9.428364e-17 -4.344101e-17 -3.458282e-17
## PC48 -2.941511e-17 9.428364e-17 2.446996e-01 -1.190147e-16 -7.562738e-17
## PC49 -6.435167e-17 -4.344101e-17 -1.190147e-16 2.113577e-01 7.284990e-17
## PC50 -6.036243e-17 -3.458282e-17 -7.562738e-17 7.284990e-17 1.966843e-01
## PC51 -9.247034e-17 3.100721e-17 4.325047e-17 -1.480370e-16 7.438930e-17
## PC52 1.869075e-16 -8.587462e-18 8.664486e-17 -9.810263e-17 -6.068422e-17
## PC53 6.639367e-18 8.555969e-17 1.049969e-16 -1.238130e-16 -5.838852e-17
## PC54 -3.538244e-17 -6.096056e-18 5.715306e-17 -1.050872e-16 -9.220681e-17
## PC55 4.167507e-17 -2.282713e-17 -1.761714e-16 5.905086e-17 4.818682e-17
## PC56 3.194907e-17 -6.597854e-17 -1.509322e-16 1.161285e-16 5.112481e-17
## PC57 4.430144e-17 2.918634e-19 -1.284817e-16 3.093155e-17 1.628058e-18
## PC58 -3.413538e-18 -9.243814e-17 -1.894415e-17 5.553621e-17 1.108245e-16
## PC59 1.579168e-17 8.287983e-17 1.788708e-17 -2.619018e-17 -2.277958e-17
## PC60 9.521820e-17 -2.119228e-17 -5.200621e-18 3.757551e-17 9.610553e-17
## PC61 -3.377350e-17 3.502280e-17 1.205876e-16 7.329900e-17 1.734155e-17
## PC62 1.747336e-16 -1.643147e-17 6.968096e-17 2.309020e-17 -5.803446e-17
## PC63 6.827872e-17 -3.632029e-17 3.221662e-17 3.673558e-17 -6.739849e-17
## PC64 -1.441137e-16 7.278998e-18 -4.218934e-17 -6.134467e-17 2.979002e-17
## PC65 2.076199e-17 4.908370e-17 1.291507e-17 -1.914585e-17 -6.099706e-18
## PC66 6.543098e-17 -6.298295e-17 -8.561970e-18 1.273958e-17 3.549119e-17
## PC67 -1.003936e-18 2.820926e-17 4.809405e-17 6.741430e-17 -2.233670e-17
## PC68 -1.029064e-16 -7.048282e-17 -6.356329e-17 7.163945e-17 3.090450e-18
## PC69 6.757173e-17 1.996989e-17 2.700301e-17 1.997324e-17 -5.583225e-17
## PC70 4.239021e-17 -1.219776e-17 3.807260e-17 -2.179652e-17 -3.524640e-17
## PC51 PC52 PC53 PC54 PC55
## PC1 -9.696400e-17 7.068348e-16 3.835869e-17 -3.887944e-17 -1.269119e-15
## PC2 -2.280321e-16 -1.220041e-15 -1.288713e-16 -2.585788e-16 -3.258952e-16
## PC3 -2.808439e-16 -2.486682e-16 2.612927e-16 -1.828573e-16 -1.230678e-15
## PC4 1.817336e-16 5.650694e-16 9.888498e-16 4.148720e-16 -6.153841e-16
## PC5 -1.470281e-16 1.332610e-16 -4.237617e-17 1.948724e-16 -1.020328e-16
## PC6 3.121998e-17 -4.781960e-16 -5.166459e-16 -1.857382e-16 -3.720405e-17
## PC7 -2.045573e-16 4.064790e-17 7.419170e-17 -2.017443e-16 -1.076287e-16
## PC8 3.627985e-16 -8.655370e-17 -2.743976e-16 -1.371707e-16 2.182033e-16
## PC9 2.182738e-16 -4.354504e-16 9.812933e-17 -1.548389e-16 2.331164e-16
## PC10 1.634474e-16 -2.219381e-16 -1.570572e-16 -5.083893e-17 -1.523159e-17
## PC11 3.536069e-16 3.560765e-19 -7.299198e-17 -3.787532e-16 6.531560e-17
## PC12 2.927646e-16 1.912544e-16 3.801812e-16 -6.789062e-17 1.438163e-17
## PC13 -3.278001e-17 -7.539723e-18 1.979911e-16 1.494729e-16 2.331520e-16
## PC14 2.145904e-16 3.689869e-17 2.316001e-16 -1.569026e-16 -1.001164e-16
## PC15 -1.559631e-16 -3.112880e-16 -2.117531e-16 -1.585879e-16 6.111399e-17
## PC16 2.837657e-17 -4.807081e-17 2.482968e-17 1.558575e-16 6.333620e-17
## PC17 -2.579223e-16 3.603682e-16 -3.704428e-16 2.393181e-16 -2.222585e-16
## PC18 -7.552630e-18 -7.295390e-17 -2.567946e-17 1.528048e-16 -6.565300e-17
## PC19 1.520858e-16 3.871641e-16 -5.969049e-17 1.193578e-16 1.277484e-16
## PC20 -6.816728e-17 -1.602425e-16 -1.631647e-16 2.954396e-17 2.306293e-16
## PC21 3.496907e-17 1.381441e-16 -9.361053e-17 -4.532498e-17 3.597596e-16
## PC22 1.292416e-16 3.185376e-17 -1.517886e-16 5.498801e-17 -3.240784e-16
## PC23 6.067051e-17 -3.496124e-17 -2.389320e-16 1.527611e-16 1.842512e-16
## PC24 2.519576e-17 9.901089e-18 -2.890186e-16 8.964856e-17 -1.199879e-16
## PC25 -1.098678e-16 -2.093273e-16 1.195072e-16 -1.656219e-16 -1.130098e-16
## PC26 -1.061574e-16 -9.878417e-17 2.563745e-16 -1.353635e-16 1.246526e-16
## PC27 5.932377e-17 2.476563e-17 -1.239701e-17 7.736912e-17 -1.665694e-16
## PC28 -3.910614e-17 -7.601225e-17 -2.746871e-16 1.514156e-17 -2.445118e-16
## PC29 8.372743e-17 -1.043446e-16 -3.892665e-17 -7.737656e-17 1.041251e-16
## PC30 2.828041e-17 1.578037e-16 -3.958693e-17 2.890778e-17 -2.796501e-16
## PC31 3.273710e-17 -8.516569e-17 -1.459885e-16 4.665558e-17 -2.014582e-16
## PC32 1.023563e-17 -1.933099e-17 7.286266e-17 -2.579894e-16 1.692929e-16
## PC33 -3.468084e-17 5.998090e-17 -5.896616e-17 8.601075e-17 -4.961056e-17
## PC34 9.757658e-18 5.241359e-17 1.361279e-16 6.525292e-17 -1.927040e-17
## PC35 -3.162823e-17 -3.188474e-19 5.438744e-17 4.458573e-17 2.945428e-17
## PC36 -5.642909e-17 -6.316446e-18 -7.776892e-18 -6.899134e-17 -3.502961e-17
## PC37 -8.685072e-17 7.384837e-17 -1.650220e-16 1.263129e-16 -1.293711e-16
## PC38 -8.177046e-17 6.553970e-17 7.192778e-17 1.232824e-17 -6.461006e-18
## PC39 -5.412372e-17 3.112032e-17 -3.373466e-17 -1.910004e-17 1.471279e-16
## PC40 8.774406e-17 -1.087316e-17 9.516746e-17 6.927439e-18 3.305994e-17
## PC41 -4.136957e-17 1.410324e-16 -1.049808e-16 -4.872856e-17 -1.944513e-17
## PC42 -1.444748e-17 -1.505199e-16 -1.469357e-16 -7.703180e-17 8.397105e-17
## PC43 -1.293248e-16 -5.997498e-17 -5.306021e-17 -4.450945e-17 -4.191227e-17
## PC44 -1.117119e-16 1.163235e-16 -4.790383e-17 2.139340e-17 -1.841692e-18
## PC45 -3.026531e-17 -1.689052e-16 7.341037e-17 4.144278e-18 5.885270e-17
## PC46 -9.247034e-17 1.869075e-16 6.639367e-18 -3.538244e-17 4.167507e-17
## PC47 3.100721e-17 -8.587462e-18 8.555969e-17 -6.096056e-18 -2.282713e-17
## PC48 4.325047e-17 8.664486e-17 1.049969e-16 5.715306e-17 -1.761714e-16
## PC49 -1.480370e-16 -9.810263e-17 -1.238130e-16 -1.050872e-16 5.905086e-17
## PC50 7.438930e-17 -6.068422e-17 -5.838852e-17 -9.220681e-17 4.818682e-17
## PC51 1.886144e-01 1.024474e-17 1.443368e-16 2.886700e-17 2.189274e-17
## PC52 1.024474e-17 1.520587e-01 -5.898996e-17 5.877673e-17 -7.224465e-17
## PC53 1.443368e-16 -5.898996e-17 1.385359e-01 -1.402566e-16 5.015548e-17
## PC54 2.886700e-17 5.877673e-17 -1.402566e-16 1.217921e-01 -1.233048e-16
## PC55 2.189274e-17 -7.224465e-17 5.015548e-17 -1.233048e-16 1.159233e-01
## PC56 -2.085919e-17 1.298760e-17 -4.356347e-17 1.302121e-16 2.609047e-17
## PC57 -1.160809e-16 8.332239e-17 -1.300107e-17 8.948363e-17 5.634068e-17
## PC58 -2.666111e-17 3.079734e-17 4.297218e-17 -5.230732e-17 3.436739e-17
## PC59 5.415122e-17 1.193477e-17 -6.676556e-17 3.801185e-17 2.262844e-17
## PC60 3.364068e-17 5.642546e-17 4.205914e-17 7.258050e-17 2.009001e-17
## PC61 -7.520757e-17 2.052756e-17 6.159519e-17 -2.229219e-18 -6.558068e-17
## PC62 -1.561606e-17 8.051927e-17 -1.900516e-17 2.027696e-18 -6.206420e-17
## PC63 1.890279e-17 8.116851e-17 -1.074118e-17 7.545228e-18 6.120378e-18
## PC64 -3.309535e-17 -8.566444e-17 2.990873e-17 3.402862e-17 1.217183e-16
## PC65 -1.924459e-17 2.765603e-17 -1.203126e-17 -3.767088e-18 4.182624e-17
## PC66 1.267706e-18 -2.048368e-18 -2.049908e-17 -5.576336e-18 5.085560e-17
## PC67 -1.082262e-17 5.195143e-17 -6.176500e-17 4.032559e-17 3.519422e-18
## PC68 8.594569e-17 -6.738982e-17 8.977944e-18 9.127541e-18 2.562960e-17
## PC69 1.816075e-17 -3.270991e-17 2.189201e-17 5.282057e-17 3.361668e-17
## PC70 -6.487518e-17 -3.291473e-17 -1.199461e-17 1.027488e-17 -2.577451e-17
## PC56 PC57 PC58 PC59 PC60
## PC1 -8.453516e-16 -1.805853e-16 1.822562e-16 9.219294e-16 1.390008e-15
## PC2 3.659776e-16 2.987423e-16 5.393887e-16 -5.237197e-16 1.722625e-16
## PC3 3.115855e-17 -2.853930e-16 2.169876e-16 -8.352371e-16 -3.223540e-16
## PC4 -7.682857e-16 -6.075582e-16 -6.213573e-16 5.201028e-16 4.684657e-18
## PC5 -1.572603e-16 3.853661e-16 -3.746636e-17 4.288988e-17 -2.401250e-17
## PC6 7.689057e-17 1.845828e-16 1.458088e-16 1.371176e-16 2.452712e-16
## PC7 5.716295e-17 -1.914291e-16 -9.333561e-17 -3.654149e-17 -8.589011e-17
## PC8 -4.380463e-17 6.609557e-17 2.521258e-16 -4.940776e-16 -3.167067e-16
## PC9 3.162443e-16 1.769237e-16 5.417784e-18 1.765817e-16 -5.279032e-17
## PC10 4.601894e-16 6.353774e-17 8.496850e-17 1.563146e-16 1.340075e-16
## PC11 2.806102e-16 7.822825e-17 3.392786e-17 2.151367e-17 -4.980070e-17
## PC12 6.800412e-16 -1.933379e-16 4.052076e-16 -2.480704e-16 4.278513e-16
## PC13 2.557042e-16 5.084924e-17 1.652163e-16 -2.359902e-16 -1.933842e-16
## PC14 -3.637282e-16 1.098915e-16 -1.806280e-16 5.198649e-16 1.346650e-16
## PC15 1.503650e-16 8.439046e-17 8.015689e-17 -3.823716e-16 1.463134e-16
## PC16 1.250032e-16 4.053398e-16 2.942170e-16 -2.924894e-17 1.028822e-16
## PC17 -9.621810e-17 -1.764044e-16 2.821961e-16 -3.641306e-17 1.196849e-16
## PC18 2.310146e-16 1.029291e-16 1.500599e-16 1.137568e-16 3.072606e-16
## PC19 9.116559e-17 -1.218056e-16 -1.200298e-17 1.018827e-16 1.183136e-16
## PC20 -1.111793e-16 1.798374e-16 -1.232726e-16 4.352652e-16 3.353692e-16
## PC21 2.815002e-16 -7.792897e-17 -1.806697e-16 3.199777e-16 -1.319106e-16
## PC22 -1.134868e-16 1.557194e-16 1.263552e-16 -5.359282e-17 7.009415e-17
## PC23 6.188080e-17 1.505237e-16 -2.141631e-16 2.342365e-17 -1.633298e-16
## PC24 2.627064e-16 1.652429e-16 -2.548320e-16 -3.918229e-17 3.100012e-17
## PC25 1.589110e-16 6.317837e-17 -1.346539e-16 7.321902e-17 2.789930e-16
## PC26 3.552451e-16 1.791319e-16 -1.094584e-16 -6.382833e-17 2.634758e-16
## PC27 -1.537107e-16 2.281116e-17 -2.186823e-16 -3.701260e-17 3.323919e-17
## PC28 8.688073e-17 1.829064e-16 3.139467e-18 -1.583703e-16 1.124585e-16
## PC29 1.470581e-16 6.835225e-17 -3.029131e-17 6.507819e-17 6.353255e-17
## PC30 1.323640e-16 1.461626e-16 1.567567e-16 -6.558810e-17 7.223820e-18
## PC31 2.792798e-16 -5.410927e-17 2.000431e-16 7.744818e-17 1.224219e-16
## PC32 -1.221899e-16 5.729908e-17 -3.149259e-17 -2.645381e-17 1.100031e-16
## PC33 2.474127e-17 1.339204e-16 -9.223145e-17 -2.556988e-16 2.864811e-17
## PC34 1.530721e-16 9.007994e-18 3.085240e-17 -5.360896e-17 1.677512e-17
## PC35 -2.164314e-17 9.788053e-17 -2.201572e-16 -1.456627e-16 -5.820240e-17
## PC36 5.422306e-17 -2.961437e-17 4.607091e-17 -1.635225e-17 1.319550e-16
## PC37 2.682400e-17 8.856931e-17 -2.399479e-17 3.497197e-17 6.348778e-17
## PC38 -2.799610e-16 -1.436407e-17 -3.189676e-17 -8.495014e-17 7.479607e-17
## PC39 -1.306167e-16 -9.157915e-17 -2.124527e-17 -1.491748e-16 4.247122e-17
## PC40 -3.534725e-17 -1.360351e-17 -2.184942e-18 -5.930779e-17 -1.744727e-18
## PC41 -9.757932e-17 -1.259094e-17 -4.253531e-17 -8.640381e-17 4.317964e-17
## PC42 1.026541e-16 -1.122455e-16 4.226868e-17 4.845593e-17 7.928712e-18
## PC43 1.005546e-16 7.303537e-17 1.123234e-16 -2.412103e-16 -1.745466e-17
## PC44 -5.791689e-18 -4.797639e-17 -9.178001e-17 -1.947208e-18 2.517829e-16
## PC45 -5.070402e-17 -1.139874e-16 -1.298994e-17 1.384888e-16 -8.940324e-17
## PC46 3.194907e-17 4.430144e-17 -3.413538e-18 1.579168e-17 9.521820e-17
## PC47 -6.597854e-17 2.918634e-19 -9.243814e-17 8.287983e-17 -2.119228e-17
## PC48 -1.509322e-16 -1.284817e-16 -1.894415e-17 1.788708e-17 -5.200621e-18
## PC49 1.161285e-16 3.093155e-17 5.553621e-17 -2.619018e-17 3.757551e-17
## PC50 5.112481e-17 1.628058e-18 1.108245e-16 -2.277958e-17 9.610553e-17
## PC51 -2.085919e-17 -1.160809e-16 -2.666111e-17 5.415122e-17 3.364068e-17
## PC52 1.298760e-17 8.332239e-17 3.079734e-17 1.193477e-17 5.642546e-17
## PC53 -4.356347e-17 -1.300107e-17 4.297218e-17 -6.676556e-17 4.205914e-17
## PC54 1.302121e-16 8.948363e-17 -5.230732e-17 3.801185e-17 7.258050e-17
## PC55 2.609047e-17 5.634068e-17 3.436739e-17 2.262844e-17 2.009001e-17
## PC56 1.077393e-01 -5.246724e-17 -6.924340e-17 -7.906480e-17 1.235281e-17
## PC57 -5.246724e-17 1.069876e-01 5.213327e-17 4.695233e-17 8.635912e-17
## PC58 -6.924340e-17 5.213327e-17 9.867075e-02 -3.457993e-17 5.469249e-17
## PC59 -7.906480e-17 4.695233e-17 -3.457993e-17 7.451171e-02 -6.704145e-18
## PC60 1.235281e-17 8.635912e-17 5.469249e-17 -6.704145e-18 6.930581e-02
## PC61 9.212718e-17 -5.128837e-17 -8.223228e-18 -2.697873e-17 -4.902094e-17
## PC62 4.714989e-18 -1.320629e-17 2.817221e-18 -2.252624e-18 4.227162e-17
## PC63 1.617267e-16 -2.231227e-16 3.696171e-17 -6.039748e-19 -9.237661e-17
## PC64 1.210965e-16 -7.334119e-17 -7.221075e-17 -2.696453e-17 -4.380245e-17
## PC65 5.467719e-18 2.036921e-17 1.829843e-17 -6.019799e-17 -4.369440e-17
## PC66 1.544281e-16 -3.746033e-16 -3.009311e-17 -1.542173e-17 -1.280548e-17
## PC67 -1.932883e-16 3.485703e-16 1.649676e-17 2.865674e-17 2.577650e-17
## PC68 8.966977e-17 -2.530257e-16 7.202699e-18 9.375687e-18 -1.456086e-17
## PC69 -6.387415e-17 -6.613311e-17 2.176644e-17 3.308664e-17 1.912887e-17
## PC70 -6.408236e-17 3.900012e-18 -1.913111e-17 3.326411e-17 -6.491102e-17
## PC61 PC62 PC63 PC64 PC65
## PC1 2.639264e-16 3.989937e-16 4.011544e-16 -2.082177e-16 -5.873197e-17
## PC2 8.807848e-16 -4.124405e-17 -4.046438e-17 2.026718e-16 -1.679699e-16
## PC3 7.905586e-16 -3.360388e-16 9.307359e-18 -4.787905e-16 -4.188131e-16
## PC4 -7.329045e-17 5.809065e-17 -2.785554e-16 1.026639e-16 6.696355e-16
## PC5 2.873176e-16 2.186691e-16 2.999110e-17 2.555990e-17 -1.411302e-17
## PC6 -4.834193e-16 2.329373e-16 -3.711605e-16 3.957812e-16 3.144851e-16
## PC7 6.638418e-16 3.057450e-17 4.454587e-17 4.865502e-17 -4.745998e-17
## PC8 -3.593397e-16 2.999378e-16 -3.728414e-16 -1.691310e-16 -3.978843e-16
## PC9 6.376235e-16 2.884597e-16 -8.797010e-17 4.857345e-16 4.242696e-16
## PC10 8.678397e-18 2.213030e-16 -9.285897e-17 -3.123413e-16 4.568718e-16
## PC11 2.331525e-16 2.218486e-16 -1.532605e-16 1.456714e-16 9.729311e-17
## PC12 -2.465683e-16 1.383681e-16 -3.570350e-16 1.953747e-16 -1.240581e-16
## PC13 -4.168402e-16 -8.394564e-17 1.217930e-16 4.951916e-18 -4.424931e-16
## PC14 1.748281e-16 -8.509406e-17 6.507956e-18 1.695644e-16 5.124612e-16
## PC15 1.871273e-17 3.045559e-17 3.010129e-17 1.942935e-16 -1.888409e-16
## PC16 3.186611e-17 6.284162e-17 9.878429e-17 4.921459e-17 3.491770e-16
## PC17 1.253931e-18 4.898803e-16 5.890348e-17 -3.468705e-17 7.957108e-17
## PC18 2.505757e-16 -3.870190e-17 -6.956968e-17 1.590188e-16 -2.635779e-16
## PC19 -1.276317e-16 4.167693e-16 1.641243e-17 2.122224e-16 3.513299e-16
## PC20 5.976398e-17 4.270853e-16 -1.475825e-16 2.115533e-16 1.456864e-17
## PC21 -8.464360e-17 1.330600e-16 -2.727188e-17 1.738742e-16 -3.848466e-17
## PC22 2.970111e-16 -2.501453e-16 4.349377e-17 -2.627970e-16 1.340463e-16
## PC23 1.931332e-17 -1.874696e-16 1.337755e-16 -1.191493e-18 3.165368e-17
## PC24 3.422437e-16 9.416199e-17 -6.196022e-17 1.090091e-16 -6.628315e-18
## PC25 -8.504229e-17 -3.647768e-17 -7.896360e-17 -9.734373e-17 -1.011132e-16
## PC26 4.733281e-18 1.518583e-16 -6.326172e-17 1.042099e-16 -6.595194e-17
## PC27 6.144877e-17 -8.081630e-17 6.840961e-18 -1.108305e-16 -2.617880e-17
## PC28 8.559357e-17 -3.139249e-17 -5.796384e-17 1.752535e-16 2.000772e-17
## PC29 1.984082e-16 1.185816e-16 1.937015e-17 -5.961944e-17 -2.616137e-16
## PC30 -8.891023e-17 -2.332212e-17 4.706510e-17 -6.587044e-17 -4.639506e-17
## PC31 1.680344e-16 -9.036502e-17 -7.782636e-17 2.497113e-16 -2.844095e-17
## PC32 2.193636e-17 -4.648291e-17 -3.467366e-17 -9.257909e-17 -1.716645e-17
## PC33 9.960938e-17 7.045112e-17 1.111389e-16 -6.345152e-17 -2.190266e-18
## PC34 -1.512034e-16 -6.909369e-18 -1.629421e-16 1.184167e-16 2.547270e-17
## PC35 -2.148701e-17 4.924193e-17 -3.620968e-17 4.010714e-17 1.203473e-16
## PC36 1.085632e-16 -1.145253e-16 -4.873432e-17 -1.720066e-17 8.625744e-17
## PC37 -7.119433e-18 1.649084e-17 -6.858515e-17 -1.042880e-16 -5.167708e-17
## PC38 1.516996e-17 8.308570e-17 2.734577e-17 -3.222654e-17 1.066832e-16
## PC39 6.918654e-17 -4.584447e-17 8.650848e-18 8.297760e-17 1.881169e-18
## PC40 5.660044e-17 1.351355e-16 -4.135328e-17 -3.085378e-17 6.848334e-17
## PC41 -1.918885e-17 7.464538e-17 2.974118e-17 -8.932156e-17 -7.152185e-18
## PC42 6.110286e-17 -6.217819e-17 -3.657650e-17 -7.269390e-17 3.904064e-17
## PC43 -3.203837e-17 5.375754e-17 1.589974e-17 -3.681493e-17 -4.518262e-17
## PC44 -3.601084e-17 5.949559e-18 5.733703e-17 7.745471e-18 -1.588985e-17
## PC45 -7.036415e-17 -1.927367e-17 -2.837112e-17 7.623111e-17 4.401173e-17
## PC46 -3.377350e-17 1.747336e-16 6.827872e-17 -1.441137e-16 2.076199e-17
## PC47 3.502280e-17 -1.643147e-17 -3.632029e-17 7.278998e-18 4.908370e-17
## PC48 1.205876e-16 6.968096e-17 3.221662e-17 -4.218934e-17 1.291507e-17
## PC49 7.329900e-17 2.309020e-17 3.673558e-17 -6.134467e-17 -1.914585e-17
## PC50 1.734155e-17 -5.803446e-17 -6.739849e-17 2.979002e-17 -6.099706e-18
## PC51 -7.520757e-17 -1.561606e-17 1.890279e-17 -3.309535e-17 -1.924459e-17
## PC52 2.052756e-17 8.051927e-17 8.116851e-17 -8.566444e-17 2.765603e-17
## PC53 6.159519e-17 -1.900516e-17 -1.074118e-17 2.990873e-17 -1.203126e-17
## PC54 -2.229219e-18 2.027696e-18 7.545228e-18 3.402862e-17 -3.767088e-18
## PC55 -6.558068e-17 -6.206420e-17 6.120378e-18 1.217183e-16 4.182624e-17
## PC56 9.212718e-17 4.714989e-18 1.617267e-16 1.210965e-16 5.467719e-18
## PC57 -5.128837e-17 -1.320629e-17 -2.231227e-16 -7.334119e-17 2.036921e-17
## PC58 -8.223228e-18 2.817221e-18 3.696171e-17 -7.221075e-17 1.829843e-17
## PC59 -2.697873e-17 -2.252624e-18 -6.039748e-19 -2.696453e-17 -6.019799e-17
## PC60 -4.902094e-17 4.227162e-17 -9.237661e-17 -4.380245e-17 -4.369440e-17
## PC61 5.896815e-02 3.087548e-17 1.865977e-17 -1.929838e-17 -1.948765e-17
## PC62 3.087548e-17 5.384847e-02 4.617782e-18 -1.523615e-17 1.542132e-17
## PC63 1.865977e-17 4.617782e-18 4.757278e-02 -1.733118e-17 -2.774719e-18
## PC64 -1.929838e-17 -1.523615e-17 -1.733118e-17 3.252870e-02 7.429689e-19
## PC65 -1.948765e-17 1.542132e-17 -2.774719e-18 7.429689e-19 2.930728e-02
## PC66 1.068702e-17 3.431883e-17 4.044284e-17 1.563204e-17 6.057959e-18
## PC67 -5.459295e-17 1.380502e-18 9.144406e-18 -5.477076e-19 -2.654198e-17
## PC68 -3.460924e-17 8.434310e-18 -2.254459e-18 -1.828681e-17 -5.338395e-17
## PC69 -2.585453e-17 -7.355110e-18 -1.913191e-17 7.696676e-18 5.008580e-17
## PC70 -1.087072e-17 8.921818e-18 4.176951e-18 2.194215e-17 -6.306685e-18
## PC66 PC67 PC68 PC69 PC70
## PC1 7.248176e-16 5.024191e-16 1.354803e-15 -1.272961e-15 -7.174288e-18
## PC2 -5.118210e-16 1.273494e-18 -3.282902e-16 3.729347e-16 -7.410354e-16
## PC3 -1.081063e-16 -1.832941e-16 2.646686e-16 5.858983e-16 -1.287293e-16
## PC4 -2.845224e-16 -2.492981e-16 -5.920212e-17 4.397448e-16 -3.924895e-16
## PC5 -3.489508e-16 2.478015e-18 -1.342726e-16 -2.695081e-16 9.444813e-17
## PC6 -4.073435e-16 -3.557812e-16 -4.368887e-17 -2.763304e-16 -1.733421e-16
## PC7 2.536295e-16 -3.241205e-16 -2.434774e-16 -4.808566e-17 5.563803e-16
## PC8 1.790486e-16 -4.741519e-16 -2.715553e-16 -2.596107e-16 1.752095e-16
## PC9 -2.768496e-16 -5.249152e-17 -1.236158e-16 7.718906e-17 -2.623660e-16
## PC10 1.091765e-16 8.941560e-17 2.195741e-16 3.035872e-16 9.133203e-18
## PC11 -1.254648e-16 2.009424e-16 6.471437e-17 1.632426e-17 3.170202e-17
## PC12 -9.004586e-17 -1.137079e-17 -1.370633e-16 9.459178e-17 1.119945e-16
## PC13 1.196745e-16 -8.457471e-17 -1.467248e-16 -1.039398e-16 -7.214438e-17
## PC14 -2.190774e-17 7.186582e-17 3.142912e-17 -2.317191e-16 -3.857751e-17
## PC15 3.710004e-17 -1.471337e-16 6.754741e-17 -1.786885e-17 -8.955458e-17
## PC16 -6.042757e-17 9.689831e-17 2.643897e-16 -2.845711e-16 -2.181217e-16
## PC17 7.021989e-16 2.107086e-16 2.108725e-16 1.030191e-16 -5.430239e-17
## PC18 -4.356910e-17 -2.394310e-16 -2.322998e-16 1.540839e-16 3.338275e-16
## PC19 2.849241e-16 8.628023e-17 3.045361e-16 -5.695788e-17 -1.233108e-16
## PC20 -4.953989e-17 -3.559023e-17 1.514782e-16 -1.880916e-16 -3.557970e-16
## PC21 -3.304251e-17 -1.094131e-16 1.821169e-17 2.402579e-16 -3.873941e-17
## PC22 3.071951e-17 2.302682e-16 1.307061e-17 -8.180346e-17 3.007818e-17
## PC23 -3.142628e-16 1.277447e-18 -2.003265e-16 -3.416925e-16 -7.787689e-17
## PC24 -1.459371e-16 -6.762969e-17 -1.195592e-16 2.717984e-17 -9.265766e-17
## PC25 -1.194186e-16 -1.149309e-16 -1.810852e-17 5.424568e-17 9.769799e-18
## PC26 5.455537e-16 2.744701e-16 -1.396596e-18 -8.538263e-17 -2.894931e-17
## PC27 3.989457e-16 4.812599e-17 9.855083e-17 2.067226e-16 4.383871e-17
## PC28 1.238834e-16 -2.044954e-16 -4.955933e-17 6.028325e-17 -3.365036e-17
## PC29 -6.905900e-17 1.244241e-16 -2.160928e-17 -1.302707e-16 -1.558737e-16
## PC30 1.046484e-16 5.946728e-17 3.211372e-17 4.756437e-17 -1.270888e-16
## PC31 -1.849402e-16 1.113453e-17 -3.873361e-17 -3.124108e-17 -1.583000e-16
## PC32 -8.595944e-17 -7.402951e-17 5.577266e-17 -9.562768e-17 -1.015918e-16
## PC33 3.641760e-17 1.769855e-17 6.996305e-17 2.022273e-16 -2.005782e-17
## PC34 2.987699e-17 1.630498e-18 1.526595e-17 -9.973115e-17 -2.049987e-16
## PC35 9.400425e-17 -6.702157e-17 1.336278e-16 -1.044144e-16 9.280384e-17
## PC36 -1.812813e-16 6.447574e-18 -3.283727e-17 -5.599723e-17 1.631105e-17
## PC37 3.798023e-17 -2.712025e-16 4.062128e-17 -3.334244e-18 8.451090e-17
## PC38 -1.805600e-17 4.873166e-17 -1.102409e-16 -2.027321e-17 3.872114e-17
## PC39 -7.867258e-17 1.965561e-17 4.768663e-17 1.354738e-18 -6.563298e-17
## PC40 -2.223950e-17 1.080990e-16 -4.690772e-17 -1.425540e-16 -9.680937e-17
## PC41 2.974780e-18 9.262087e-17 5.483820e-17 4.851740e-17 -1.417247e-18
## PC42 2.507020e-17 4.424255e-18 -3.196553e-17 5.616252e-17 1.905830e-17
## PC43 4.305613e-17 -3.715872e-17 7.787150e-17 -1.623462e-17 5.998433e-17
## PC44 1.142232e-17 1.768161e-17 9.170140e-18 4.815286e-17 3.913454e-17
## PC45 -1.126809e-16 4.689599e-17 6.879994e-17 1.240188e-17 -2.205807e-17
## PC46 6.543098e-17 -1.003936e-18 -1.029064e-16 6.757173e-17 4.239021e-17
## PC47 -6.298295e-17 2.820926e-17 -7.048282e-17 1.996989e-17 -1.219776e-17
## PC48 -8.561970e-18 4.809405e-17 -6.356329e-17 2.700301e-17 3.807260e-17
## PC49 1.273958e-17 6.741430e-17 7.163945e-17 1.997324e-17 -2.179652e-17
## PC50 3.549119e-17 -2.233670e-17 3.090450e-18 -5.583225e-17 -3.524640e-17
## PC51 1.267706e-18 -1.082262e-17 8.594569e-17 1.816075e-17 -6.487518e-17
## PC52 -2.048368e-18 5.195143e-17 -6.738982e-17 -3.270991e-17 -3.291473e-17
## PC53 -2.049908e-17 -6.176500e-17 8.977944e-18 2.189201e-17 -1.199461e-17
## PC54 -5.576336e-18 4.032559e-17 9.127541e-18 5.282057e-17 1.027488e-17
## PC55 5.085560e-17 3.519422e-18 2.562960e-17 3.361668e-17 -2.577451e-17
## PC56 1.544281e-16 -1.932883e-16 8.966977e-17 -6.387415e-17 -6.408236e-17
## PC57 -3.746033e-16 3.485703e-16 -2.530257e-16 -6.613311e-17 3.900012e-18
## PC58 -3.009311e-17 1.649676e-17 7.202699e-18 2.176644e-17 -1.913111e-17
## PC59 -1.542173e-17 2.865674e-17 9.375687e-18 3.308664e-17 3.326411e-17
## PC60 -1.280548e-17 2.577650e-17 -1.456086e-17 1.912887e-17 -6.491102e-17
## PC61 1.068702e-17 -5.459295e-17 -3.460924e-17 -2.585453e-17 -1.087072e-17
## PC62 3.431883e-17 1.380502e-18 8.434310e-18 -7.355110e-18 8.921818e-18
## PC63 4.044284e-17 9.144406e-18 -2.254459e-18 -1.913191e-17 4.176951e-18
## PC64 1.563204e-17 -5.477076e-19 -1.828681e-17 7.696676e-18 2.194215e-17
## PC65 6.057959e-18 -2.654198e-17 -5.338395e-17 5.008580e-17 -6.306685e-18
## PC66 2.148082e-02 3.980849e-17 -3.174822e-17 1.483883e-17 5.085409e-18
## PC67 3.980849e-17 1.889424e-02 -1.135998e-17 4.198641e-18 7.203945e-18
## PC68 -3.174822e-17 -1.135998e-17 1.689840e-02 5.306631e-18 -1.867760e-17
## PC69 1.483883e-17 4.198641e-18 5.306631e-18 1.394258e-02 2.138195e-17
## PC70 5.085409e-18 7.203945e-18 -1.867760e-17 2.138195e-17 4.737965e-03hac_output <- hclust(dist(origndata11, method = "euclidean"), method = "complete")
cluster <- km_output$cluster
pcs$cluster <- cluster[match(rownames(pcs), names(cluster))]
plot(hac_output)
__#tune cluster, change parameter
km_output <- kmeans(origndata11, centers = 3, nstart = 90, iter.max = 800, algorithm = "Hartigan-Wong")
str(km_output)## List of 9
## $ cluster : Named int [1:85] 2 2 2 2 2 2 3 2 2 2 ...
## ..- attr(*, "names")= chr [1:85] "di 1" "di 2" "di 3" "di 4" ...
## $ centers : num [1:3, 1:70] -1.37027 -0.24965 0.27489 -0.61716 0.00961 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:3] "1" "2" "3"
## .. ..$ : chr [1:70] "a" "all" "also" "an" ...
## $ totss : num 5880
## $ withinss : num [1:3] 335 1856 2968
## $ tot.withinss: num 5159
## $ betweenss : num 721
## $ size : int [1:3] 4 32 49
## $ iter : int 3
## $ ifault : int 0
## - attr(*, "class")= chr "kmeans"fviz_cluster(km_output, data = origndata11)
set.seed(8)
wss <- function(k){
return(kmeans(origndata11, k, nstart = 25)$tot.withinss)
}
plot(x = k_values, y = wss_values,
type = "b", frame = F,
xlab = "Number of clusters K",
ylab = "Total within-clusters sum of square")
#So we can found Jay's writting style is different with Ham and Mad, Ham and Mad has similiar writting style
#so I think three cluster is better than four cluster. __#Test data in Kmean
testdata1<-testdata
testdata1$author<-NULL
testdata1$filename<-NULL
testdata1 <- na.omit(testdata1)
testdata1 <- scale(testdata1)
distance <- get_dist(testdata1, method = "euclidean")
fviz_dist(distance, gradient = list(low = "#00AFBB", mid = "white", high = "#FC4E07"))
km_output2 <- kmeans(testdata1, centers = 3, nstart = 25, iter.max = 100, algorithm = "Hartigan-Wong")
str(km_output2)## List of 9
## $ cluster : Named int [1:14] 1 3 2 2 2 2 2 2 2 1 ...
## ..- attr(*, "names")= chr [1:14] "1" "2" "3" "4" ...
## $ centers : num [1:3, 1:70] -0.833 0.39 1.043 0.875 -0.495 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:3] "1" "2" "3"
## .. ..$ : chr [1:70] "a" "all" "also" "an" ...
## $ totss : num 910
## $ withinss : num [1:3] 246 411 0
## $ tot.withinss: num 657
## $ betweenss : num 253
## $ size : int [1:3] 5 8 1
## $ iter : int 2
## $ ifault : int 0
## - attr(*, "class")= chr "kmeans"table(testdata$author, km_output2$cluster)##
## 1 2 3
## Hamilton 2 8 1
## Madison 3 0 0fviz_cluster(km_output2, data = testdata1)
__#For DTree
library(C50)
traindata1<-traindata
dt_model <- train(author ~ ., data = traindata1, metric = "Accuracy", method = "rpart")
names(dt_model)## [1] "method" "modelInfo" "modelType" "results"
## [5] "pred" "bestTune" "call" "dots"
## [9] "metric" "control" "finalModel" "preProcess"
## [13] "trainingData" "resample" "resampledCM" "perfNames"
## [17] "maximize" "yLimits" "times" "levels"
## [21] "terms" "coefnames" "xlevels"print(dt_model)## CART
##
## 52 samples
## 70 predictors
## 2 classes: 'Hamilton', 'Madison'
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 52, 52, 52, 52, 52, 52, ...
## Resampling results across tuning parameters:
##
## cp Accuracy Kappa
## 0.0000000 0.9202746 0.7220923
## 0.4583333 0.9202746 0.7220923
## 0.9166667 0.8430961 0.3802280
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.4583333.print(dt_model$finalModel)## n= 52
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 52 12 Hamilton (0.76923077 0.23076923)
## 2) upon>=0.019 39 0 Hamilton (1.00000000 0.00000000) *
## 3) upon< 0.019 13 1 Madison (0.07692308 0.92307692) *confusionMatrix(dt_model,traindata1$authorship)## Bootstrapped (25 reps) Confusion Matrix
##
## (entries are un-normalized aggregated counts)
##
## Reference
## Prediction Hamilton Madison
## Hamilton 356 20
## Madison 19 86
##
## Accuracy (average) : 0.9189traindata2<-traindata
dt_model2 <- train(author ~ ., data = traindata2, metric = "Accuracy", method = "rpart")
print(dt_model2)## CART
##
## 52 samples
## 70 predictors
## 2 classes: 'Hamilton', 'Madison'
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 52, 52, 52, 52, 52, 52, ...
## Resampling results across tuning parameters:
##
## cp Accuracy Kappa
## 0.0000000 0.9287182 0.7867283
## 0.4583333 0.9196273 0.7595439
## 0.9166667 0.8536085 0.4972554
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.print(dt_model2$finalModel)## n= 52
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 52 12 Hamilton (0.76923077 0.23076923)
## 2) upon>=0.019 39 0 Hamilton (1.00000000 0.00000000) *
## 3) upon< 0.019 13 1 Madison (0.07692308 0.92307692) *dt_model_tune <- train(author ~ ., data = traindata2, method = "rpart",
metric = "Accuracy",
tuneLength = 8)
print(dt_model_tune$finalModel)## n= 52
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 52 12 Hamilton (0.76923077 0.23076923)
## 2) upon>=0.019 39 0 Hamilton (1.00000000 0.00000000) *
## 3) upon< 0.019 13 1 Madison (0.07692308 0.92307692) *dt_model_tune2 <- train(author ~ ., data = traindata2, method = "rpart",
tuneGrid = expand.grid(cp = seq(0, 0.1, 0.01)))
print(dt_model_tune2$finalModel)## n= 52
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 52 12 Hamilton (0.76923077 0.23076923)
## 2) upon>=0.019 39 0 Hamilton (1.00000000 0.00000000) *
## 3) upon< 0.019 13 1 Madison (0.07692308 0.92307692) *library(rattle)
fancyRpartPlot(dt_model$finalModel)
library(rpart.plot)
prp(dt_model$finalModel)
__#section 3 prediction and interpretion
#DTree prediction
dt_prediction <- predict(dt_model, newdata = testdata, na.action = na.omit, type = "prob")
head(dt_prediction)## Hamilton Madison
## 1 1 0
## 2 1 0
## 3 1 0
## 4 1 0
## 5 1 0
## 6 1 0dt_prediction## Hamilton Madison
## 1 1.00000000 0.0000000
## 2 1.00000000 0.0000000
## 3 1.00000000 0.0000000
## 4 1.00000000 0.0000000
## 5 1.00000000 0.0000000
## 6 1.00000000 0.0000000
## 7 1.00000000 0.0000000
## 8 1.00000000 0.0000000
## 9 1.00000000 0.0000000
## 10 1.00000000 0.0000000
## 11 1.00000000 0.0000000
## 12 0.07692308 0.9230769
## 13 0.07692308 0.9230769
## 14 0.07692308 0.9230769dt_prediction2 <- predict(dt_model,newdata = testdata,type = 'raw')
dt_prediction2## [1] Hamilton Hamilton Hamilton Hamilton Hamilton Hamilton Hamilton
## [8] Hamilton Hamilton Hamilton Hamilton Madison Madison Madison
## Levels: Hamilton MadisonfancyRpartPlot(dt_model$finalModel)
#cluster prediction
origndata22<-origndata
origndata22$author<-NULL
origndata22$filename<-NULL
distance1 <- get_dist(origndata22, method = "euclidean")
fviz_dist(distance1, gradient = list(low = "gold", mid = "ghostwhite", high = "orange1"))
km_output3 <- kmeans(origndata22, centers = 2, nstart = 30, iter.max = 1000, algorithm = "Hartigan-Wong")
str(km_output3)## List of 9
## $ cluster : Named int [1:85] 2 1 2 2 1 2 2 1 2 1 ...
## ..- attr(*, "names")= chr [1:85] "di 1" "di 2" "di 3" "di 4" ...
## $ centers : num [1:2, 1:70] 0.28037 0.301 0.05125 0.05379 0.00866 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:2] "1" "2"
## .. ..$ : chr [1:70] "a" "all" "also" "an" ...
## $ totss : num 12.6
## $ withinss : num [1:2] 4.82 5.48
## $ tot.withinss: num 10.3
## $ betweenss : num 2.28
## $ size : int [1:2] 32 53
## $ iter : int 1
## $ ifault : int 0
## - attr(*, "class")= chr "kmeans"table(origndata$author, km_output3$cluster)##
## 1 2
## dispt 4 7
## Hamilton 14 37
## HM 3 0
## Jay 5 0
## Madison 6 9fviz_cluster(km_output3, data = origndata22)
#Kmeans can give more detial about the predict dataset #Desition Tree is clear and more accuracy __#The root is upon. and unknow essay looks like is madsion writting style, maybe he wrote those.