Gets the maximum contributor variables from svd()

Description

This function is inspired by Jeff Leeks Data Analysis course where he suggests that one way to use the svd is to look at the most influential rows for first columns in the V matrix.

Usage

getSvdMostInfluential(mtrx, quantile, similarity_threshold,
  plot_selection = TRUE, plot_threshold = 0.05, varnames = NULL)

Arguments

Details

This function expands on that idea and adds the option of choosing more than just the most contributing variable for each row. For instance two variables may have a major impact on a certain component where the second variable has 95 important in that particular component it makes sense to include it in the selection.

It is of course useful when you have many continuous variables and you want to determine a subgroup to look at, i.e. finding the needle in the haystack.

Value

Returns a list with vector with the column numbers that were picked in the "most_influential" variable and the svd caluclation in the "svd"

Examples

org_par <- par(ask=TRUE)
set.seed(12345); 

# Simulate data with a pattern
dataMatrix <- matrix(rnorm(15*160),ncol=15)
colnames(dataMatrix) <- 
  c(paste("Pos.3:", 1:3, sep=" #"), 
    paste("Neg.Decr:", 4:6, sep=" #"), 
    paste("No pattern:", 7:8, sep=" #"),
    paste("Pos.Incr:", 9:11, sep=" #"),
    paste("No pattern:", 12:15, sep=" #"))
for(i in 1:nrow(dataMatrix)){
  # flip a coin
  coinFlip1 <- rbinom(1,size=1,prob=0.5)
  coinFlip2 <- rbinom(1,size=1,prob=0.5)
  coinFlip3 <- rbinom(1,size=1,prob=0.5)
  
  # if coin is heads add a common pattern to that row
  if(coinFlip1){
    cols <- grep("Pos.3", colnames(dataMatrix))
    dataMatrix[i, cols] <- dataMatrix[i, cols] + 3
  }
  
  if(coinFlip2){
    cols <- grep("Neg.Decr", colnames(dataMatrix))
    dataMatrix[i, cols] <- dataMatrix[i, cols] - seq(from=5, to=15, length.out=length(cols))
  }
  
  if(coinFlip3){
    cols <- grep("Pos.Incr", colnames(dataMatrix))
    dataMatrix[i,cols] <- dataMatrix[i,cols] + seq(from=3, to=15, length.out=length(cols))
  }
}

# Illustrate data
heatmap(dataMatrix, Colv=NA, Rowv=NA, margins=c(7,2), labRow="")

svd_out <- svd(scale(dataMatrix))

library(lattice)
b_clr <- c("steelblue", "darkred")
key <- simpleKey(rectangles = TRUE, space = "top", points=FALSE,
  text=c("Positive", "Negative"))
key$rectangles$col <- b_clr

b1 <- barchart(as.table(svd_out$v[,1]),
  main="First column",
  horizontal=FALSE, col=ifelse(svd_out$v[,1] > 0, 
      b_clr[1], b_clr[2]),
  ylab="Impact value", 
  scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
  key = key)

b2 <- barchart(as.table(svd_out$v[,2]),
  main="Second column",
  horizontal=FALSE, col=ifelse(svd_out$v[,2] > 0, 
      b_clr[1], b_clr[2]),
  ylab="Impact value", 
  scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
  key = key)

b3 <- barchart(as.table(svd_out$v[,3]),
  main="Third column",
  horizontal=FALSE, col=ifelse(svd_out$v[,3] > 0, 
      b_clr[1], b_clr[2]),
  ylab="Impact value", 
  scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
  key = key)

b4 <- barchart(as.table(svd_out$v[,4]),
  main="Fourth column",
  horizontal=FALSE, col=ifelse(svd_out$v[,4] > 0, 
      b_clr[1], b_clr[2]),
  ylab="Impact value", 
  scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
  key = key)

# Note that the fourth has the no pattern columns as the
# chosen pattern, probably partly because of the previous
# patterns already had been identified
print(b1, position=c(0,0.5,.5,1), more=TRUE)
print(b2, position=c(0.5,0.5,1,1), more=TRUE)
print(b3, position=c(0,0,.5,.5), more=TRUE)
print(b4, position=c(0.5,0,1,.5))

# Let's look at how well the SVD identifies
# the most influential columns
getSvdMostInfluential(dataMatrix, 
                      quantile=.8, 
                      similarity_threshold = .9,
                      plot_threshold = .05,
                      plot_selection = TRUE)
par(org_par)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(Gmisc)
Loading required package: Rcpp
Loading required package: htmlTable
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Gmisc/getSvdMostInfluential.Rd_%03d_medium.png", width=480, height=480)
> ### Name: getSvdMostInfluential
> ### Title: Gets the maximum contributor variables from svd()
> ### Aliases: getSvdMostInfluential
> 
> ### ** Examples
> 
> org_par <- par(ask=TRUE)
> set.seed(12345); 
> 
> # Simulate data with a pattern
> dataMatrix <- matrix(rnorm(15*160),ncol=15)
> colnames(dataMatrix) <- 
+   c(paste("Pos.3:", 1:3, sep=" #"), 
+     paste("Neg.Decr:", 4:6, sep=" #"), 
+     paste("No pattern:", 7:8, sep=" #"),
+     paste("Pos.Incr:", 9:11, sep=" #"),
+     paste("No pattern:", 12:15, sep=" #"))
> for(i in 1:nrow(dataMatrix)){
+   # flip a coin
+   coinFlip1 <- rbinom(1,size=1,prob=0.5)
+   coinFlip2 <- rbinom(1,size=1,prob=0.5)
+   coinFlip3 <- rbinom(1,size=1,prob=0.5)
+   
+   # if coin is heads add a common pattern to that row
+   if(coinFlip1){
+     cols <- grep("Pos.3", colnames(dataMatrix))
+     dataMatrix[i, cols] <- dataMatrix[i, cols] + 3
+   }
+   
+   if(coinFlip2){
+     cols <- grep("Neg.Decr", colnames(dataMatrix))
+     dataMatrix[i, cols] <- dataMatrix[i, cols] - seq(from=5, to=15, length.out=length(cols))
+   }
+   
+   if(coinFlip3){
+     cols <- grep("Pos.Incr", colnames(dataMatrix))
+     dataMatrix[i,cols] <- dataMatrix[i,cols] + seq(from=3, to=15, length.out=length(cols))
+   }
+ }
> 
> # Illustrate data
> heatmap(dataMatrix, Colv=NA, Rowv=NA, margins=c(7,2), labRow="")
> 
> svd_out <- svd(scale(dataMatrix))
> 
> library(lattice)
> b_clr <- c("steelblue", "darkred")
> key <- simpleKey(rectangles = TRUE, space = "top", points=FALSE,
+   text=c("Positive", "Negative"))
> key$rectangles$col <- b_clr
> 
> b1 <- barchart(as.table(svd_out$v[,1]),
+   main="First column",
+   horizontal=FALSE, col=ifelse(svd_out$v[,1] > 0, 
+       b_clr[1], b_clr[2]),
+   ylab="Impact value", 
+   scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
+   key = key)
> 
> b2 <- barchart(as.table(svd_out$v[,2]),
+   main="Second column",
+   horizontal=FALSE, col=ifelse(svd_out$v[,2] > 0, 
+       b_clr[1], b_clr[2]),
+   ylab="Impact value", 
+   scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
+   key = key)
> 
> b3 <- barchart(as.table(svd_out$v[,3]),
+   main="Third column",
+   horizontal=FALSE, col=ifelse(svd_out$v[,3] > 0, 
+       b_clr[1], b_clr[2]),
+   ylab="Impact value", 
+   scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
+   key = key)
> 
> b4 <- barchart(as.table(svd_out$v[,4]),
+   main="Fourth column",
+   horizontal=FALSE, col=ifelse(svd_out$v[,4] > 0, 
+       b_clr[1], b_clr[2]),
+   ylab="Impact value", 
+   scales=list(x=list(rot=55, labels=colnames(dataMatrix), cex=1.1)),
+   key = key)
> 
> # Note that the fourth has the no pattern columns as the
> # chosen pattern, probably partly because of the previous
> # patterns already had been identified
> print(b1, position=c(0,0.5,.5,1), more=TRUE)
> print(b2, position=c(0.5,0.5,1,1), more=TRUE)
> print(b3, position=c(0,0,.5,.5), more=TRUE)
> print(b4, position=c(0.5,0,1,.5))
> 
> # Let's look at how well the SVD identifies
> # the most influential columns
> getSvdMostInfluential(dataMatrix, 
+                       quantile=.8, 
+                       similarity_threshold = .9,
+                       plot_threshold = .05,
+                       plot_selection = TRUE)
$most_influential
 [1]  5  6  4 11 10  3  2  1 13  7

$svd
$svd$d
 [1] 22.079823 20.498937 19.366767 13.545960 13.383771 12.640558 12.547571
 [8] 11.978977 11.108905  7.040429  6.801640  6.077939  3.632932  2.318208
[15]  2.027925

$svd$u
                [,1]          [,2]          [,3]          [,4]          [,5]
  [1,]  0.0185591095  0.0865237036 -0.0978873961 -0.0877612327 -1.553266e-01
  [2,]  0.0413234145  0.0998799920  0.0703535643 -0.0726623258 -2.393896e-02
  [3,] -0.0847821804  0.0225793272  0.0916144894 -0.0691913181 -3.289293e-02
  [4,]  0.0481113252  0.1000001641  0.0349008819  0.0423924968 -4.791786e-02
  [5,]  0.1265605759  0.0066973484  0.0092468074 -0.0466327532 -2.542510e-02
  [6,] -0.0068809087 -0.1176230434  0.0635175079  0.1001700367  2.448187e-03
  [7,] -0.0261529505 -0.1299547988 -0.0269082738 -0.0771328754  3.705327e-02
  [8,]  0.1137222788 -0.0224392472  0.0299949002 -0.0252083241 -7.234376e-02
  [9,]  0.0054164673 -0.1202558784  0.1007958827 -0.0909431761  5.290797e-02
 [10,] -0.0300313180 -0.1246248106 -0.0576103749  0.0588243492  8.060576e-02
 [11,] -0.0103096233 -0.0967497011 -0.0422553926  0.0500691972  6.522078e-02
 [12,] -0.0734035903 -0.0012006571 -0.0135576737 -0.0454377108  1.592574e-01
 [13,]  0.0274569325  0.1177403103  0.0555436133 -0.0364345189 -6.097163e-02
 [14,]  0.0510149255  0.1366759163  0.0690366892 -0.0967781421  1.104872e-01
 [15,] -0.0151940321 -0.0948171990  0.0542271923  0.0073018562 -7.482951e-02
 [16,]  0.0113505115 -0.0999143290  0.1202266235 -0.1605769088 -7.737227e-02
 [17,] -0.0967907269  0.0665149765  0.0684381303 -0.0859021934 -7.366230e-02
 [18,] -0.0948238508  0.0550344930  0.0939546123  0.0525582015  9.257661e-02
 [19,]  0.1325204032 -0.0045994478  0.0786711616  0.2215528676 -2.154901e-01
 [20,] -0.1362590103  0.0290639965 -0.0898026304 -0.0928526051 -2.225302e-01
 [21,] -0.0014719106 -0.0512911542  0.1139576639 -0.0513053970 -2.441542e-02
 [22,] -0.0819087633  0.0262511677 -0.0560275269 -0.0845534353  6.871699e-02
 [23,] -0.1149728676  0.0338159988 -0.0753855853 -0.0841443790 -1.770901e-01
 [24,]  0.1120135441 -0.0257971459  0.0572188004 -0.0523081171  5.895669e-02
 [25,] -0.1163893951 -0.0260075315 -0.0864789942  0.1654911474 -3.436741e-02
 [26,]  0.0540540007  0.0658115795 -0.0714231955 -0.0509812969  2.837856e-02
 [27,]  0.0043754196 -0.0987771039  0.0829280572  0.0306462798  8.807459e-03
 [28,] -0.1041986752  0.0458225678  0.0925768613  0.0091229820  5.909117e-03
 [29,]  0.0339279515 -0.1165137029  0.0468765420 -0.0445377751  1.007554e-01
 [30,] -0.0791169021 -0.0140633269 -0.0697061361 -0.0530044526  9.472476e-02
 [31,] -0.0771342356  0.0609208629  0.0863805818  0.0066493523  3.369679e-02
 [32,]  0.0178752578  0.1582136164 -0.0992391492  0.0604593784  1.604396e-02
 [33,] -0.0061834925 -0.0899184717  0.1092317073  0.1530145216  4.676473e-03
 [34,] -0.0082101671 -0.0892975283  0.0973155188  0.0614270713  8.639697e-02
 [35,] -0.0035892549 -0.1347184272 -0.0117617347 -0.1117948040  1.289803e-01
 [36,]  0.0624570881  0.1142784855  0.0492638427  0.1215954046  5.478019e-02
 [37,]  0.1125973595 -0.0322518192  0.0774061752  0.0407005591 -1.336245e-01
 [38,]  0.1165015035 -0.0387309126 -0.1344977276 -0.1310503345 -3.424775e-03
 [39,]  0.0557751335  0.1059151896  0.0733402012 -0.1555172280 -3.449775e-02
 [40,] -0.0311620327 -0.0919126345 -0.0716965123 -0.0618729063  1.202276e-02
 [41,] -0.0932954783  0.0297433822  0.0620342287 -0.0155431592 -9.385862e-02
 [42,] -0.1072485400  0.0212852304 -0.0076944923 -0.0695182919 -1.117653e-02
 [43,] -0.1110707770 -0.0162622650 -0.0889397275  0.1007970429  2.977428e-02
 [44,]  0.0478849506  0.1198341223  0.0769242093 -0.2286760652  5.283307e-02
 [45,] -0.0830452436  0.0044842577 -0.0512124731 -0.0340044597 -6.725929e-02
 [46,]  0.0082265602 -0.1170032253  0.1231728759  0.0967148712  4.263529e-02
 [47,] -0.0147251569 -0.1143613966 -0.1067488687 -0.0640493529  4.401976e-02
 [48,]  0.1290130994 -0.0033674630  0.1000584426  0.0216294224  5.600087e-02
 [49,] -0.0988304853  0.0198203700 -0.0540770474 -0.0766997353  4.348400e-02
 [50,]  0.0570419586  0.1075177044  0.0059555687  0.0151043814  5.222797e-02
 [51,] -0.0212750724 -0.1280331651 -0.0515798685  0.0274884868  7.721056e-02
 [52,]  0.0460297015  0.1264767535  0.0803867574  0.1364797226 -3.528641e-02
 [53,] -0.0829478170  0.0443121810  0.0691433499  0.0524271925  8.789585e-02
 [54,]  0.0071536858 -0.1251847773 -0.0160831855  0.1170808975 -2.642263e-02
 [55,] -0.1276277876 -0.0147083647 -0.0777054812  0.0553813363 -2.938549e-02
 [56,] -0.1227368035  0.0371586641 -0.0720956922 -0.1197585148 -1.629777e-03
 [57,] -0.0592593182  0.0199213612  0.1144281731 -0.0586781767 -4.903217e-02
 [58,] -0.1075073662 -0.0162199144 -0.1263278390  0.1176761806  7.309234e-03
 [59,] -0.1277780897  0.0391014184 -0.0709197941 -0.0267499287  1.638695e-02
 [60,] -0.0903436930  0.0285758624  0.0735620273 -0.0175769836  1.192146e-02
 [61,]  0.0113071965  0.0993445016  0.0505452290  0.0756883926 -1.044318e-01
 [62,]  0.0178471843  0.0819133459 -0.1690941808 -0.0619401477  5.958644e-02
 [63,] -0.0971209299  0.0242462035 -0.0698152693  0.0456972852  1.364732e-01
 [64,]  0.0337977280  0.1097334887  0.0477186679  0.0530766557  6.409812e-02
 [65,] -0.0246295167 -0.1218124882 -0.0395258571  0.1670613032 -8.520687e-02
 [66,] -0.0383781576 -0.1031960672  0.0706485769 -0.0195906158  1.375336e-02
 [67,] -0.1068113258  0.0802729456  0.0885779910  0.0681373127 -3.119438e-02
 [68,]  0.0535661969  0.1154178305 -0.0585312801  0.0200573021  8.629492e-02
 [69,]  0.0455603566  0.1369191062  0.0506078785 -0.1175837996 -2.420809e-02
 [70,] -0.0806239869  0.0092687310  0.0488757645 -0.0039048924  8.406815e-02
 [71,]  0.0062326768 -0.1057073316  0.1085035043 -0.0442878376 -6.188692e-02
 [72,] -0.0958156672  0.0428481473  0.0464745937 -0.0347635383  6.764189e-02
 [73,]  0.0896073352 -0.0229664620 -0.1045609317  0.0226491246 -9.267126e-02
 [74,] -0.0962259123  0.0059777792 -0.0364103516 -0.1071143847  6.373369e-02
 [75,] -0.0294165293 -0.1326346657 -0.0155405817 -0.0353867182 -1.500852e-02
 [76,] -0.1350925345  0.0201818238 -0.0599109851 -0.0991253199 -6.620300e-02
 [77,]  0.0307528674  0.1331465110 -0.0808044131  0.1042894841 -4.092015e-02
 [78,] -0.1113969801  0.0210548335  0.0573458755  0.0247659303  3.370263e-02
 [79,] -0.1179394419  0.0204791378 -0.0586459438 -0.0172936686  4.269946e-02
 [80,]  0.0360164226  0.0838984304 -0.1132094517  0.0950060583 -3.890134e-02
 [81,]  0.1125427684  0.0007365711  0.0659615736 -0.0245471717 -2.697200e-03
 [82,] -0.0302778746 -0.0683685252  0.0857785480 -0.0661769100  5.755039e-02
 [83,]  0.1291229149 -0.0030272616  0.0459151892  0.0166672817  5.595071e-02
 [84,]  0.0378414567  0.0677912176 -0.1001976870 -0.0406638521 -7.166784e-02
 [85,]  0.0140994584 -0.0925641254  0.0958256353 -0.2501034436  7.462084e-02
 [86,]  0.0068134631 -0.0708068313  0.1320277054  0.0228459068  5.985457e-02
 [87,] -0.0009426783 -0.0681643072  0.1299928124 -0.0523940533 -2.453086e-02
 [88,]  0.0292194889  0.0822899207 -0.1122485678  0.0005271902 -2.885417e-02
 [89,]  0.0405595307  0.0961940976 -0.1194803440  0.0926583730  1.479117e-01
 [90,]  0.1349989851 -0.0272423942  0.0639113952  0.0507328128  5.674638e-02
 [91,]  0.0837609087 -0.0276161176 -0.1391905284 -0.1002113276  7.196278e-02
 [92,]  0.1184319194 -0.0446972923 -0.0954179614  0.0253290741  7.537286e-02
 [93,]  0.1105278479 -0.0328750990 -0.0324132170  0.0032928534 -7.363124e-02
 [94,]  0.1344275055 -0.0064239545  0.0188463638  0.0627973819 -3.204335e-02
 [95,] -0.0034059342 -0.1146200033  0.0568366284  0.0535927974 -7.053724e-02
 [96,]  0.0296002599  0.1331297206  0.0559768488 -0.0736955111 -7.305583e-03
 [97,] -0.0024161422 -0.0949731563  0.0712579784  0.0427589809 -8.448364e-03
 [98,]  0.0168936268  0.1167684184 -0.1037769689  0.1931135203  3.177472e-02
 [99,]  0.1232327428  0.0005589188  0.0110726530 -0.1082773393 -2.414562e-02
[100,] -0.0719421133 -0.0105213805  0.0595082473 -0.0202013933  5.945938e-02
[101,]  0.0965795558 -0.0202822226 -0.0671331478 -0.0519246955 -7.198316e-02
[102,]  0.0180703106 -0.0809257262  0.0843257192 -0.0650112019  3.130443e-02
[103,]  0.1180635756 -0.0088260457  0.0524730112 -0.0494901617 -6.983760e-02
[104,] -0.0968869101  0.0280917507  0.0450388251 -0.0902012717 -1.158504e-01
[105,] -0.1080068245  0.0420865357 -0.0393090995  0.0868841074  1.270343e-01
[106,] -0.0181433202 -0.1353284096 -0.0835978323 -0.0240687620  1.342734e-01
[107,] -0.0255053682 -0.1099674373 -0.0476337635  0.0995916917 -8.049926e-03
[108,]  0.0461018560  0.1101692478  0.0594707962  0.0609938249 -3.083882e-02
[109,] -0.0153364303 -0.1521886394 -0.0627643764  0.0231458690 -7.254739e-02
[110,]  0.0421309251  0.1144270778 -0.1086488298  0.0163056879  7.469290e-02
[111,] -0.1137264487  0.0034096325 -0.1143314731  0.0467961180 -1.972728e-01
[112,] -0.0807164384 -0.0141348727 -0.1054933310  0.0172017789  1.014120e-01
[113,]  0.1073098004 -0.0271056944 -0.0674736737  0.0082133860  1.015543e-01
[114,] -0.1078426367  0.0081995766 -0.1037258017 -0.0630359095 -1.017710e-01
[115,] -0.1188067719  0.0512080199  0.0770500550 -0.0198994079  1.440884e-02
[116,]  0.1075190188 -0.0088801436  0.0810025069 -0.0408410163  3.829902e-02
[117,] -0.0829498493  0.0598376089  0.0944341333  0.1216930605 -9.207591e-02
[118,] -0.0191357271 -0.1167469218 -0.0431601536  0.0591660130 -7.169334e-03
[119,]  0.0952470188  0.0042041744  0.0846831717  0.0107315033  8.540319e-05
[120,] -0.0758682979  0.0442119044  0.1056353634 -0.0231554966 -8.372672e-02
[121,]  0.0028827063 -0.0943768898 -0.0623606113 -0.0591722420  6.967275e-02
[122,] -0.0657088275  0.0499526073  0.1060545647  0.0154454567  8.571976e-02
[123,]  0.1223876719 -0.0477736740 -0.0997311430 -0.0166847216  1.906489e-02
[124,]  0.0500363047  0.1298195558  0.1089049607 -0.0110645080 -1.938040e-02
[125,]  0.0119231442 -0.1139564261  0.1103285159 -0.0152299180 -5.905866e-02
[126,]  0.1271235553 -0.0131456745  0.0483675365  0.0473033699  4.548310e-02
[127,]  0.1150422021 -0.0306449407  0.0177044110  0.0044002197 -5.660742e-02
[128,]  0.0443173209  0.1153271825  0.0006189243  0.0058449104  1.532595e-02
[129,] -0.1161814629  0.0172778420  0.0742129790  0.0691951570 -1.285331e-01
[130,]  0.0976190727 -0.0406035597 -0.1200410156  0.0711493665  1.590495e-02
[131,]  0.0419571976  0.0827344771 -0.0727901095 -0.1255996861 -3.003606e-03
[132,]  0.0502588492  0.1352305603  0.0503776134  0.1329880045  1.666140e-01
[133,]  0.1322464293  0.0133239155  0.0383519438  0.0658839396  8.599526e-02
[134,]  0.0856983351 -0.0329024585 -0.1142214402  0.0041029199 -1.221178e-01
[135,]  0.0158017996  0.1144660633 -0.0651171731 -0.0663435886  8.693311e-03
[136,] -0.1075585966  0.0406996796  0.0814240724  0.0163349474 -2.166208e-02
[137,] -0.0922182384 -0.0147686743 -0.0968955938  0.0442937600  7.535232e-02
[138,]  0.0734599378  0.0691106433  0.0416795947 -0.0310174291 -3.498005e-02
[139,]  0.1110856278 -0.0492038907 -0.1207524846  0.0208167735 -4.263134e-02
[140,] -0.0612147016  0.0066564694  0.0771929788  0.0895426447 -1.772709e-02
[141,] -0.0323875230 -0.1359882395 -0.0821986174 -0.0472072797 -1.422056e-02
[142,]  0.0037418528 -0.1164519855  0.0682299649 -0.0641211985 -1.838239e-02
[143,]  0.1003967849 -0.0301824707 -0.1064837878  0.0151272297 -1.795334e-01
[144,] -0.0048153714 -0.1423851523 -0.0789270215 -0.0229160631 -3.171613e-02
[145,]  0.1021076027 -0.0358527361 -0.0912911026  0.0205922170 -1.100910e-01
[146,] -0.1010653397  0.0440443488  0.0601932625  0.0545021167 -1.041623e-01
[147,]  0.0235761716  0.0954917460 -0.1286830402 -0.0332378746  7.392062e-02
[148,]  0.0153968944  0.1200395975 -0.1019770684 -0.1262447231 -6.018202e-02
[149,] -0.0767221529  0.0221496089  0.0437923412  0.0737893561  2.030322e-01
[150,]  0.0386889376  0.0861384460  0.0680024926 -0.0019681501  5.059081e-02
[151,] -0.0706282720  0.0202848360  0.0428757213  0.1601670784 -7.470087e-02
[152,]  0.0962498021 -0.0309587053 -0.0896154225 -0.0696755720  5.172475e-02
[153,] -0.1125369784 -0.0137904317 -0.0906325443  0.0285075047  3.309983e-02
[154,]  0.1000944064 -0.0442794018 -0.0597094829 -0.0557286471  1.816600e-02
[155,]  0.1130179514 -0.0484935930 -0.0404763068  0.0515069205 -5.760382e-02
[156,]  0.0968072838  0.0212535111  0.0327353478  0.0836720755 -1.288213e-01
[157,] -0.0127660847 -0.1017131027 -0.0605014718  0.1656300260  5.839968e-02
[158,] -0.0199947494 -0.0798230191  0.0424005486 -0.0165927909 -2.431838e-03
[159,] -0.1010478381  0.0116578676 -0.0334624465 -0.0104084515 -1.907992e-01
[160,]  0.0362004984  0.1228508740  0.0030820026  0.1029222781  1.699513e-01
                [,6]          [,7]          [,8]          [,9]         [,10]
  [1,] -0.0207624343  0.0326126321  0.0324628458  0.1137783686 -2.517493e-05
  [2,] -0.1537264308 -0.0325486667 -0.1517866208  0.0411475368  1.399257e-02
  [3,] -0.0245743102  0.0013237114  0.0382570085 -0.0967913353  3.310084e-02
  [4,]  0.1270687252 -0.0588858061 -0.0246456496 -0.0932470571  1.610241e-02
  [5,]  0.1001704479 -0.0694005886 -0.0348218442 -0.1369208034 -1.560912e-01
  [6,]  0.1307000642 -0.1174247806  0.1509007314  0.0511459992  8.046203e-02
  [7,] -0.1286161287 -0.0720506863  0.0019616190 -0.0221706220 -1.435567e-02
  [8,] -0.0293097260 -0.1806613287 -0.0165182340  0.1337994321 -4.145657e-02
  [9,]  0.0384639645 -0.0061820579  0.1053818822  0.0710458525  6.287674e-02
 [10,] -0.0640457784 -0.1163412584 -0.0887425885 -0.1137206893  3.234729e-02
 [11,]  0.1205146182  0.0298075874 -0.1880123139 -0.0336072937 -3.581897e-02
 [12,]  0.0585074193  0.1494417541 -0.0411422112 -0.0141361606 -3.261888e-02
 [13,] -0.0355488598  0.1704127612 -0.1740356338  0.0645435583  1.415352e-02
 [14,]  0.0622724249  0.0088768366 -0.1581716574  0.0757075367  3.781769e-02
 [15,]  0.0006724880 -0.0312272121 -0.0935122439 -0.0418206171 -7.450098e-02
 [16,]  0.0755058690  0.0115413019  0.0284339735 -0.0474156335 -6.658251e-02
 [17,]  0.0361543853  0.1023211842 -0.0476806977  0.0601795452  1.311213e-01
 [18,]  0.0132669011 -0.0224911765  0.0790103710 -0.0763516195  7.819288e-02
 [19,]  0.0564575929  0.0195279354  0.0216287238 -0.0089784387 -8.113657e-02
 [20,] -0.0263654807 -0.0024812554  0.0494369708  0.0259030835 -7.749497e-02
 [21,] -0.0135902520  0.2437960109  0.1526597877  0.0400984736 -2.257975e-02
 [22,] -0.1428641130  0.0317862697 -0.0472332504 -0.0870142202 -5.476270e-02
 [23,]  0.0840577328  0.1162318708  0.0667938912  0.0020249400  4.911115e-02
 [24,]  0.0614239929 -0.1180715592 -0.0811133331  0.0078047293  1.190093e-01
 [25,] -0.0064061352 -0.1267093451 -0.0779043742 -0.0731048634  9.517904e-02
 [26,] -0.0886631465 -0.0894773776  0.1175856744 -0.1448016090 -4.499222e-02
 [27,] -0.0311322237  0.0235391901  0.0114979246 -0.0550911063  4.143998e-02
 [28,] -0.0370628169 -0.0352713454  0.0191157518  0.0150919232 -1.749383e-02
 [29,]  0.0357946529 -0.0578623434 -0.0396281879  0.0159204159 -1.335193e-01
 [30,] -0.0595552533 -0.0467097294  0.0532957887 -0.0384817902  4.427568e-02
 [31,]  0.0697731367 -0.0057717455 -0.0664938013  0.1177582864 -3.094230e-02
 [32,] -0.0017258232  0.0382070977  0.0341036086  0.0564557574 -1.047309e-01
 [33,] -0.0463394021  0.1220854080 -0.0249799547 -0.0781203069 -1.440907e-01
 [34,] -0.0642584977  0.0654696744 -0.0802900996 -0.0123763140 -1.431898e-01
 [35,]  0.0009600674  0.0901131418 -0.0814422131  0.0319659596  5.020796e-02
 [36,] -0.0085931867 -0.0190939060  0.0057312063 -0.0697194453  3.096946e-02
 [37,]  0.0192106827 -0.1254999692 -0.0079634847 -0.1417645610  2.458040e-02
 [38,]  0.0542861150 -0.0282822496  0.0876901063  0.2142674543  1.196778e-01
 [39,] -0.0484976465 -0.0109712090  0.1371485652  0.0182971882 -4.406466e-02
 [40,]  0.0465026552  0.1794271155  0.1788666964 -0.1159993536 -3.158857e-03
 [41,]  0.0280126398 -0.1349577613 -0.0241550951 -0.1086206280 -1.823555e-01
 [42,]  0.0372185152  0.0001538108 -0.0233127125  0.0757494556  9.029071e-02
 [43,]  0.0157832692 -0.0365033859 -0.0623955762  0.1706716714  7.963859e-02
 [44,] -0.1248255152  0.0006008500 -0.0637111840 -0.0704438545  4.457423e-02
 [45,] -0.0645324338 -0.0812221027 -0.0434957800  0.0894429742 -1.010462e-02
 [46,] -0.1388736382 -0.0980689397  0.1285801113 -0.0249493551 -7.058625e-02
 [47,]  0.0404520955  0.0018043446  0.0517745349 -0.0983431393  3.710890e-03
 [48,] -0.0457786084  0.0057310084  0.0783540899 -0.0500887665  4.410598e-02
 [49,]  0.0586188235 -0.0998292456 -0.0904143523 -0.0544314180 -4.001702e-02
 [50,]  0.0208718318 -0.1203783347 -0.0562631984  0.0354033375  9.809388e-02
 [51,]  0.0058441923  0.0078270702 -0.0647651075 -0.0791382181  3.988452e-02
 [52,] -0.1106851143 -0.0199702326  0.1038665830 -0.0161456345 -5.824040e-02
 [53,] -0.0239468947 -0.0443814828 -0.0372902600 -0.0170527498 -4.234229e-03
 [54,] -0.0865855015  0.1224182728 -0.0090902653  0.1220478047  7.817705e-02
 [55,]  0.0792240091  0.1201937257  0.0467635029 -0.0436682830  1.893597e-02
 [56,] -0.0995865587  0.0563471473 -0.0976228703 -0.1587008569 -7.880366e-03
 [57,]  0.0111647533 -0.0519863254  0.0712035336 -0.0004792934  1.431906e-02
 [58,] -0.1010686171 -0.0802567158  0.0904774623  0.0482127181 -1.320696e-01
 [59,]  0.1284056460 -0.1517879959  0.0175882300  0.0110479951 -2.350612e-01
 [60,]  0.1625150872 -0.0524985523  0.0274670084 -0.0529633939  1.718608e-01
 [61,] -0.1052100028 -0.0027374969 -0.0995406157  0.0677398374  3.869424e-02
 [62,] -0.0767039528  0.0047960771  0.1082894047  0.0586767940  8.530261e-02
 [63,]  0.0099197636  0.0201953847  0.0526247442 -0.0032503886 -3.304714e-03
 [64,]  0.0162673271  0.0496451271  0.0272304629  0.0529580257 -8.427682e-02
 [65,]  0.0560188672 -0.1450899482 -0.0764573806  0.0475647340  4.565883e-02
 [66,]  0.0351767801  0.0207577262 -0.0780140076 -0.0241201376  8.935957e-02
 [67,]  0.0009802462  0.1338873139  0.0062220489  0.0439142530 -3.448160e-02
 [68,]  0.1208451103 -0.0635035365 -0.0457207315  0.0992949596 -3.689559e-02
 [69,]  0.0345126599 -0.0962324020 -0.0330409217 -0.0465996822  2.586360e-02
 [70,] -0.1482069548  0.1414963061 -0.0537610653  0.0284317107  1.203229e-01
 [71,] -0.1375283668  0.0776700662  0.0811169372 -0.0326196273  2.453821e-02
 [72,]  0.0422972428 -0.0013967346  0.0290275013  0.0989212957  3.216131e-02
 [73,]  0.1261772779 -0.0200784583  0.0429118607 -0.1029830501  4.638076e-02
 [74,] -0.0831945545  0.0458836194  0.0513647708  0.0141198210 -9.744228e-02
 [75,] -0.0678660137 -0.0553969304 -0.0235926575  0.0395511801 -7.630104e-02
 [76,] -0.0387044436 -0.0494159998  0.0289494096 -0.0065663705 -6.093920e-02
 [77,]  0.1115570200  0.1149468785 -0.0203488038 -0.0003156039  1.960477e-02
 [78,] -0.0015229961 -0.0659275193 -0.0759963164 -0.0940674936  3.644915e-03
 [79,]  0.0451994686  0.0001161504 -0.0247444010 -0.0135117975 -4.233055e-03
 [80,] -0.1203046612 -0.0444709801  0.0048646442  0.0125380918 -2.803746e-02
 [81,]  0.0343621704  0.0791168040 -0.1295856644 -0.0725850491 -8.511394e-02
 [82,] -0.0265733346 -0.0772774827  0.0930921749  0.0749143182 -1.069504e-01
 [83,]  0.1319297727  0.0967920473  0.0072586469  0.0041777055  1.163953e-02
 [84,] -0.1638959208 -0.1448089060  0.0182965363  0.0555512943 -1.598590e-01
 [85,]  0.0398212671  0.0383181130 -0.0233988960 -0.0512152046 -9.774746e-02
 [86,] -0.0299251375 -0.0722582361  0.0967322141  0.0503470716 -8.707014e-02
 [87,]  0.1342676816 -0.0443981639  0.0083282125  0.1361208707  1.440740e-02
 [88,] -0.0177472967  0.0921194199  0.0995227857 -0.1419094280  8.069622e-02
 [89,]  0.0755324339 -0.0330860473  0.0413722516 -0.0105681696  5.159310e-03
 [90,] -0.1401472339  0.0974414188  0.0290208662  0.0078675517  6.681375e-03
 [91,]  0.0444489697  0.0472150948  0.0202528444  0.0381584466  2.699742e-02
 [92,]  0.0139482412  0.0125985198  0.0256211947  0.0212787802  1.113414e-01
 [93,]  0.0042446274 -0.0829045578  0.0322736874 -0.0636447611 -8.081389e-02
 [94,]  0.0425349558  0.1092160355  0.0009132249  0.0760799439 -2.257283e-02
 [95,]  0.0216462347  0.1449738343 -0.0086593709 -0.0317645489  1.556285e-03
 [96,]  0.0634497645  0.0557519378 -0.0655759726  0.1070548020  8.623808e-03
 [97,]  0.0159672110  0.0813595302  0.0694335865  0.0802647262  2.408088e-03
 [98,] -0.0679384009  0.0856563091  0.0169637892 -0.0333962139 -1.162201e-01
 [99,] -0.0006984648  0.0303107897  0.0128851323  0.0211219908  2.219477e-03
[100,] -0.1569057707 -0.0973669560 -0.0208240904  0.1362648217  4.725908e-02
[101,] -0.1227834074  0.0886129712 -0.0362469202  0.0377787084  6.207915e-02
[102,]  0.0922381891 -0.0464371188  0.1076340694  0.0636467836  1.123578e-01
[103,]  0.0260419668 -0.0823769380 -0.0002513246 -0.1074636682 -6.288792e-02
[104,]  0.0541307529 -0.0819233390 -0.1007140974  0.0745398501  3.158627e-02
[105,]  0.1442433495  0.0201648238  0.0875854663 -0.0011584401  8.344489e-02
[106,]  0.0978579599 -0.1126932896  0.0178996460  0.0693784323 -1.612534e-02
[107,]  0.0614520615 -0.0861923200  0.1117712402  0.0142307083  2.989594e-02
[108,] -0.0967053651 -0.0317249941  0.0217800284 -0.0345763262 -4.718482e-02
[109,] -0.1588468705 -0.0710283291  0.0217388701  0.0475602769 -4.285572e-03
[110,] -0.1284698980 -0.0520590375  0.0036254962 -0.0805819724  3.379474e-02
[111,]  0.0165423946 -0.0092937064 -0.1232054752 -0.1009427736 -9.147679e-03
[112,] -0.0852381127 -0.1034935203  0.1885879807 -0.1414094123  1.109526e-01
[113,]  0.0766109976  0.0615102665  0.0480376474  0.1275857526 -2.567964e-02
[114,] -0.0417695569  0.1299001520  0.0407804836 -0.0059095075 -1.596471e-01
[115,]  0.0740155591  0.0044182698 -0.0578931446  0.0650469139  4.627914e-03
[116,] -0.0474791183 -0.0007470062 -0.0424146569 -0.1653917018  8.982686e-02
[117,]  0.1476756327 -0.0445960802  0.1546021884  0.0843528536  3.943043e-02
[118,] -0.0754211177  0.0377792658  0.0126119443  0.0506789587 -4.218720e-02
[119,]  0.0424798542  0.0259811919 -0.1558907600  0.0367190760 -2.003429e-01
[120,] -0.0501762879  0.0395565847  0.0355143043  0.0936331207  7.957284e-02
[121,]  0.0169954705  0.0394491670  0.0380267872  0.0355164560 -1.594457e-01
[122,]  0.0732552705  0.1699710005  0.1318485860 -0.1141451420 -2.773138e-02
[123,] -0.0263248046  0.0318893732  0.0240778361  0.0299883857 -2.282688e-02
[124,]  0.0980319211  0.0202300740 -0.0238386148 -0.0881316478  4.909351e-03
[125,] -0.0530392305 -0.0393639872 -0.0002511187  0.0982782494  5.688638e-02
[126,] -0.0052460850 -0.0798335748 -0.0293316643 -0.0678010068  9.401845e-02
[127,] -0.0443351946  0.0680452194 -0.0186305355 -0.0438614969  1.148971e-01
[128,] -0.1369996002 -0.0618046659  0.1805700646  0.1582085951 -4.266255e-02
[129,] -0.0403798140  0.1007545577 -0.0189151179 -0.1490289307  1.795034e-01
[130,]  0.0031257269  0.0093948041 -0.0023115620  0.0214741026  9.013185e-02
[131,] -0.0231441777 -0.0583454359  0.1209161489 -0.0080697159 -3.706605e-02
[132,]  0.0037488851  0.0494532492  0.1006729713 -0.0695210004  1.830950e-03
[133,]  0.0794191104 -0.0472603236  0.0665034133 -0.0250339043 -5.299875e-02
[134,]  0.1451428816 -0.0557332896 -0.0489234901  0.0254249697  3.814027e-02
[135,]  0.0318558193  0.0154856369 -0.1111199190  0.0121490281 -1.637865e-01
[136,]  0.0331013208 -0.1005745738  0.0130455940 -0.1609429918  7.781468e-02
[137,] -0.0428189219  0.0629202256 -0.2017740718 -0.0538538910  3.773203e-03
[138,] -0.0569478769  0.0377298540  0.1043258025  0.0878017186  3.677778e-03
[139,] -0.0126126584 -0.0115733940 -0.0433290485  0.0826681895 -4.896785e-02
[140,] -0.0042195563 -0.1488649907  0.0326730603 -0.0375090729  4.528755e-02
[141,]  0.0486655877  0.0434083417 -0.1437273528 -0.1181366800  4.299737e-03
[142,]  0.0145384530 -0.0211159190 -0.0678621131 -0.0753807574  3.143524e-02
[143,]  0.1119271393  0.0195099582  0.0082251081 -0.0409495360 -1.081618e-02
[144,] -0.0352722215  0.0415828284 -0.0938545820  0.0931455523  1.003916e-01
[145,]  0.0503694227  0.1073762659 -0.0846929690 -0.0822308728 -3.131754e-02
[146,]  0.0576056594 -0.0503026984 -0.0593122193  0.0478700638 -9.068487e-02
[147,]  0.0937755749  0.0238964305 -0.0097822122 -0.0626443344  1.734033e-01
[148,]  0.1274622741  0.0244097493  0.1752092581 -0.1034838629 -7.854097e-03
[149,] -0.1131792957  0.0794838485 -0.0269349741 -0.0539866795 -7.895374e-02
[150,] -0.1251821798 -0.1024668607 -0.1393181845  0.0869330487  8.772772e-02
[151,] -0.0317751078  0.0669976399  0.0021070987  0.1785028480  1.099622e-01
[152,] -0.0029783853  0.0831282632 -0.0284047841  0.1500904825 -1.816104e-02
[153,]  0.0502291066 -0.0084763832 -0.1302319337  0.1294180797 -2.597439e-02
[154,] -0.0570840317 -0.0630829240 -0.0426375154 -0.1293680292  1.403924e-01
[155,] -0.1915125671 -0.0332114881 -0.0384344621 -0.0373428864  1.352547e-01
[156,] -0.0375958235  0.0927999167 -0.0710000602 -0.0428608820 -2.646489e-02
[157,]  0.0118204989  0.1418692774  0.0143087466  0.0056795112 -1.537829e-01
[158,]  0.1629436973 -0.0137215060  0.0701158045  0.0316610388 -9.927196e-02
[159,] -0.0698925655  0.0351125693  0.0637567312  0.0207631015  1.175350e-01
[160,]  0.0797414359 -0.0447792720 -0.1620289170  0.0643442006  1.509739e-02
               [,11]         [,12]        [,13]         [,14]         [,15]
  [1,] -0.0301569620  0.0195197384  0.015616229 -1.453446e-03  9.068622e-02
  [2,] -0.0540179017  0.0094202726 -0.002720354  1.491970e-02  1.738685e-02
  [3,]  0.0028089637  0.1376755056  0.044394872  1.651331e-02  2.991881e-02
  [4,]  0.0641998986  0.1850734715 -0.062528487 -6.558390e-02 -6.425045e-02
  [5,]  0.0672637957 -0.0500478603  0.094488212  1.547563e-02 -6.486966e-02
  [6,] -0.0144078643  0.0739659975  0.009655770  7.934849e-02  3.077819e-02
  [7,] -0.0514468963 -0.0806225854 -0.033893872 -3.885219e-03 -5.953079e-02
  [8,] -0.1003532818  0.0103859847 -0.058338833 -2.211790e-02  1.055663e-01
  [9,]  0.1369176654 -0.0575897752  0.039655322 -9.613206e-02  2.215045e-02
 [10,] -0.1394485795 -0.0453679424 -0.002784973  1.309655e-01 -2.609754e-02
 [11,] -0.1336540768