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ノート/R/画像ノイズ除去をしてみるhttp://pepper.is.sci.toho-u.ac.jp/pepper/index.php?%A5%CE%A1%BC%A5%C8%2FR%2F%B2%E8%C1%FC%A5%CE%A5%A4%A5%BA%BD%FC%B5%EE%A4%F2%A4%B7%A4%C6%A4%DF%A4%EB |
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ノート/ノート
ノート/R
訪問者数 2038 最終更新 2010-09-17 (金) 18:15:20
背景: 岸本プロジェクトで、フローサイトメトリデータをクラスタ化。その時の 雑音データを取り除く。
Mclustをそのまま使うには、入力データ(=点のX-Y値の列挙)を行列(ベクトル)で与えることになる。
(FSC-H) (SSC-H) 253 327 310 332 289 132
そのデータは、読み込んだままでは雑音(X-Yに描画した時の孤立点)があって不可なので、雑音データを除去したい。
上記のデータから、雑音と判定された「行」を除きたいのだが、全部コピーすることは実行効率上したくない。配列の指定した行を除去するにはどうするか? 参考 ⇒ ("-"は除外を意味する、を使う)
> x <- cbind(c(1,3,5,7), c(2,4,6,8), c(3,5,7,9)) > x [,1] [,2] [,3] [1,] 1 2 3 [2,] 3 4 5 [3,] 5 6 7 [4,] 7 8 9 > x[-2,] [,1] [,2] [,3] [1,] 1 2 3 [2,] 5 6 7 [3,] 7 8 9 > x[c(-2,-4),] [,1] [,2] [,3] [1,] 1 2 3 [2,] 5 6 7
のように、指定した行(複数もできる)を除去することができる。
これを使えば、もし消したい行(行番号)のリストが与えられれば、それらの行を全て消す、という操作ができる。
点の落ちる場所(X-Y座標)ごとに、点を順番にカウントするのもよいが、そうでない方法を考える。
まず、XとYでソートする。ソートした結果が、N行目≠N+1行目であれば、N行目は孤立と言えるだろう。但し両端(N=1とN=max)は片側だけでいい。ソートしたものを2つコピーして、1行ずらして(N行目とN+1行目を)横に並べる。
XとYでソートするには、うまい関数が見つからないので(ありそうなのだが)、 Xの値の範囲が0〜1023のはずなので、(x[,1]*10000) + x[,2]を値としてソートする。 その結果の順で、xを並べなおす(表示しなおす)と
> x <- cbind(c(1,3,1,5,7,9,11), c(2,4,1,6,8,10,12)) > x [,1] [,2] [1,] 1 2 [2,] 3 4 [3,] 1 1 [4,] 5 6 [5,] 7 8 [6,] 9 10 [7,] 11 12 > y <- x[order(x[,1]*10000+x[,2]), ] > y [,1] [,2] [1,] 1 1 [2,] 1 2 [3,] 3 4 [4,] 5 6 [5,] 7 8 [6,] 9 10 [7,] 11 12
次に3つずつコピーして並べるところは、
> l <- length(y[,1]) > z <- cbind(y[1:(l-1),], y[2:l,]) > z [,1] [,2] [,3] [,4] [1,] 1 1 1 2 [2,] 1 2 3 4 [3,] 3 4 5 6 [4,] 5 6 7 8 [5,] 7 8 9 10
で作ることができる。
重複のある例でやってみると、
> x <- cbind(c(1,3,1,5,7,9,1,11), c(2,4,1,6,8,10,2,12)) > x [,1] [,2] [1,] 1 2 [2,] 3 4 [3,] 1 1 [4,] 5 6 [5,] 7 8 [6,] 9 10 [7,] 1 2 <-- 重複あり [8,] 11 12 > y <- x[order(x[,1]*10000+x[,2]), ] > l <- length(y[,1]) > z <- cbind(y[1:(l-1),], y[2:l,]) > z [,1] [,2] [,3] [,4] [1,] 1 1 1 2 [2,] 1 2 1 2 <-- 重複ありの情報 [3,] 1 2 3 4 [4,] 3 4 5 6 [5,] 5 6 7 8 [6,] 7 8 9 10 [7,] 9 10 11 12
ここで、重複ありの行を抽出するためには
> t <- (z[,1]==z[,3]) & (z[,2]==z[,4]) > t <- c(FALSE, t) <-- 1行減らした分を先頭に補う。2行目==3行目だと3がTRUEになる。
なお、&は1つだけ(vectorized)である。
しかし、重複がXの値がまったく同値、かつ、Yの値がまったく同値、としてしまうと、少し細かすぎるので、ここは、
> t <- (abs(z[,1]-z[,3])<=N) & (abs(z[,2]-z[,4])<=N) > t <- c(FALSE, t) <-- 1行減らした分を先頭に補う。2行目==3行目だと3がTRUEに
のようにしたほうがよさそうである。(結果を見ると)
このtを使って、行列yから、tが値TRUEの行のみ(つまり近隣に落ちるデータが無い)取り出す操作は、
> y[t,]
と書ける。
尚、余分なこととして、
> s <- cbind(c(1;length(t)), t) > s t [1,] 1 0 [2,] 2 0 [3,] 3 1 <-- (ソート後)データyの3行目が(2行目と)重複 [4,] 4 0 [5,] 5 0 [6,] 6 0 [7,] 7 0 [8,] 8 0
もできるが、yから行を抜き取る操作は上記の方が簡単である。
全体をまとめると、
> y <- x[order(x[,1]*10000*x[,2]), ] > l <- length(y[,1]) > z <- cbind(y[1:(l-1),], y[2:l,]) > t <- (abs(z[,1]-z[,3])<=N) & (abs(z[,2]-z[,4])<=N) > t <- c(FALSE, t) <-- 1行減らした分を先頭に補う。2行目==3行目だと3がTRUEになる。 > m <- y[t,]
と書ける。
これを使って、フローサイトメトリデータを処理してみると、次のようになる
# Need to "download" the library "mclust" beforehand. # # First, filter the data (1) remove x=0 data, (2) remove isolated data. # Then, apply Mclust, and display. # install.packages("mclust") library(mclust) memory.limit(3071) # Temporary datalimit <- 10000 N <- 4 # Read the data f <- file("37C/100124 37-2_limit.csv", "r") readLines(f, n=3) ## Read 3 lines to ignore them. #u <- matrix(scan(f, sep=","), ncol=8, byrow=TRUE) u <- matrix(scan(f, sep=","), ncol=8, byrow=TRUE) # ncol should be 8 because lines end with comma (with one more hidden column.) close(f) u <- u[,1:2] # erase the hidden=empty column # Reduce to "datalimit" samples, two dimensions(FSC vs SSC). if (length(u[,1])>datalimit) u <- u[1:datalimit,] print(length(u[,1])) y <- u[order(u[,1]*10000+u[,2]), ] l <- length(y[,1]) z <- cbind(y[1:(l-1),], y[2:l,]) #s <- (z[,1]==z[,3]) & (z[,2]==z[,4]) s <- ((abs(z[,1]-z[,3])<=N) & (abs(z[,2]-z[,4])<=N)) | (z[,1]<N) | (z[,2]<N) s <- c(FALSE, s) u <- y[s,] print(length(u[,1])) # Now calculate Mclust #x <- Mclust(u, G=3, modelNames="VII") # modelNames may be either "EII", "VII", "EEI", "VEI". # This calculation takes a long time, possibly due to the data size(1987440 items). # Instead, calculate BIC #BIC <- mclustBIC(u) x <- Mclust(u, G=5, modeNames="VEV") mclust2Dplot(data=u, what="classification", identify=TRUE, parameters=x$parameters, z=x$z, scale=TRUE)
Read 147648 items [1] 10000 [1] 5928 $Vinv NULL $pro [1] 0.008365081 0.139807240 0.119567031 0.196275078 0.217181430 0.076706666 [7] 0.116521647 0.125575827 $mean [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 276.4347 426.9785 572.0128 486.4956 479.0643 529.0192 537.5909 566.7286 [2,] 384.2431 476.0807 526.4424 511.7898 475.8735 522.8688 490.9496 533.1137 $variance $variance$modelName [1] "VVV" $variance$d [1] 2 $variance$G [1] 8 $variance$sigma , , 1 [,1] [,2] [1,] 17628.748 -5867.392 [2,] -5867.392 8566.723 , , 2 [,1] [,2] [1,] 4181.9544 159.9707 [2,] 159.9707 214.7473 , , 3 [,1] [,2] [1,] 5361.645 3208.185 [2,] 3208.185 2535.281 , , 4 [,1] [,2] [1,] 1465.4985 175.4553 [2,] 175.4553 251.2087 , , 5 [,1] [,2] [1,] 1304.28096 97.71196 [2,] 97.71196 175.27455 , , 6 [,1] [,2] [1,] 654.6105 -137.2886 [2,] -137.2886 114.2930 , , 7 [,1] [,2] [1,] 556.6931 131.3741 [2,] 131.3741 180.0008 , , 8 [,1] [,2] [1,] 711.91442 13.11913 [2,] 13.11913 108.89344 $variance$cholsigma , , 1 [,1] [,2] [1,] -132.7733 44.19105 [2,] 0.0000 -81.32572 , , 2 [,1] [,2] [1,] -64.66803 -2.473722 [2,] 0.00000 -14.443961 , , 3 [,1] [,2] [1,] -73.22325 -43.81374 [2,] 0.00000 -24.81204 , , 4 [,1] [,2] [1,] -38.28183 -4.583252 [2,] 0.00000 15.172426 , , 5 [,1] [,2] [1,] -36.11483 -2.705591 [2,] 0.00000 -12.959719 , , 6 [,1] [,2] [1,] -25.58536 5.365904 [2,] 0.00000 9.246622 , , 7 [,1] [,2] [1,] -23.59434 -5.568035 [2,] 0.00000 -12.206465 , , 8 [,1] [,2] [1,] -26.68172 -0.4916899 [2,] 0.00000 10.4236115
Read 133800 items [1] 10000 [1] 4353 $Vinv NULL $pro [1] 0.04699748 0.14027222 0.09260779 0.23007086 0.26211838 0.09559291 [7] 0.09629144 0.03604891 $mean [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 306.0208 418.6529 439.8381 493.5509 572.6118 497.0098 537.7538 643.8109 [2,] 361.4996 492.4958 455.9503 493.0856 528.3183 526.6853 511.7776 593.3946 $variance $variance$modelName [1] "VEV" $variance$d [1] 2 $variance$G [1] 8 $variance$sigma , , 1 [,1] [,2] [1,] 11693.40 -5307.200 [2,] -5307.20 8209.293 , , 2 [,1] [,2] [1,] 1941.3360 216.0946 [2,] 216.0946 588.6128 , , 3 [,1] [,2] [1,] 2416.137 1433.995 [2,] 1433.995 2722.357 , , 4 [,1] [,2] [1,] 922.159679 8.647484 [2,] 8.647484 259.248368 , , 5 [,1] [,2] [1,] 591.2982 261.6259 [2,] 261.6259 400.7722 , , 6 [,1] [,2] [1,] 666.6134 128.2134 [2,] 128.2134 232.1553 , , 7 [,1] [,2] [1,] 220.1749 -147.9005 [2,] -147.9005 372.9192 , , 8 [,1] [,2] [1,] 1607.0957 568.3284 [2,] 568.3284 837.9530 $variance$scale [1] 8235.7848 1046.8994 2126.3222 488.8697 410.5213 371.9128 245.4239 [8] 1011.7675 $variance$shape [1] 1.8865403 0.5300708 $variance$orientation , , 1 [,1] [,2] [1,] -0.8098987 0.5865698 [2,] 0.5865698 0.8098987 , , 2 [,1] [,2] [1,] -0.9880697 -0.1540073 [2,] -0.1540073 0.9880697 , , 3 [,1] [,2] [1,] -0.6685177 -0.7436962 [2,] -0.7436962 0.6685177 , , 4 [,1] [,2] [1,] -0.99991496 -0.01304138 [2,] -0.01304138 0.99991496 , , 5 [,1] [,2] [1,] -0.8191897 0.5735226 [2,] -0.5735226 -0.8191897 , , 6 [,1] [,2] [1,] -0.9646724 -0.2634525 [2,] -0.2634525 0.9646724 , , 7 [,1] [,2] [1,] -0.5201847 0.8540538 [2,] 0.8540538 0.5201847 , , 8 [,1] [,2] [1,] -0.8832959 -0.4688159 [2,] -0.4688159 0.8832959
Read 128200 items [1] 10000 [1] 4356 $Vinv NULL $pro [1] 0.0862894 0.2481755 0.1795777 0.2320187 0.2539387 $mean [,1] [,2] [,3] [,4] [,5] [1,] 362.0790 483.1855 545.4415 535.3017 584.2430 [2,] 340.3189 505.1435 534.5480 534.8650 533.5848 $variance $variance$modelName [1] "VVV" $variance$d [1] 2 $variance$G [1] 5 $variance$sigma , , 1 [,1] [,2] [1,] 9147.5254 -677.4772 [2,] -677.4772 7311.8394 , , 2 [,1] [,2] [1,] 2051.84683 62.33014 [2,] 62.33014 398.44143 , , 3 [,1] [,2] [1,] 5608.921 3480.902 [2,] 3480.902 2932.788 , , 4 [,1] [,2] [1,] 1070.4228 188.3379 [2,] 188.3379 257.9111 , , 5 [,1] [,2] [1,] 672.1205 423.0666 [2,] 423.0666 512.7710 $variance$cholsigma , , 1 [,1] [,2] [1,] -95.6427 7.083418 [2,] 0.0000 -85.215401 , , 2 [,1] [,2] [1,] -45.29732 -1.376023 [2,] 0.00000 19.913513 , , 3 [,1] [,2] [1,] -74.89273 -46.47850 [2,] 0.00000 27.79455 , , 4 [,1] [,2] [1,] -32.71732 -5.75652 [2,] 0.00000 14.99245 , , 5 [,1] [,2] [1,] -25.92529 -16.31868 [2,] 0.00000 -15.69941
Read 132728 items [1] 10000 [1] 2717 $Vinv NULL $pro [1] 0.08627891 0.08369000 0.17293510 0.21230533 0.08960009 0.13767879 [7] 0.21751179 $mean [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 272.4490 331.3218 473.3830 590.2983 657.1372 641.3339 725.5653 [2,] 256.1549 398.3479 520.5002 549.8457 628.3205 657.4361 668.5336 $variance $variance$modelName [1] "VVV" $variance$d [1] 2 $variance$G [1] 7 $variance$sigma , , 1 [,1] [,2] [1,] 10986.1228 -78.7728 [2,] -78.7728 1656.4718 , , 2 [,1] [,2] [1,] 6806.218 1196.392 [2,] 1196.392 6875.475 , , 3 [,1] [,2] [1,] 3287.212 1666.060 [2,] 1666.060 2221.489 , , 4 [,1] [,2] [1,] 1528.4977 969.9005 [2,] 969.9005 913.7396 , , 5 [,1] [,2] [1,] 1045.9485 299.5733 [2,] 299.5733 232.4328 , , 6 [,1] [,2] [1,] 5096.412 1882.042 [2,] 1882.042 1830.718 , , 7 [,1] [,2] [1,] 2025.672 1938.037 [2,] 1938.037 2024.082 $variance$cholsigma , , 1 [,1] [,2] [1,] -104.8147 0.7515434 [2,] 0.0000 -40.6928372 , , 2 [,1] [,2] [1,] -82.4998 -14.50175 [2,] 0.0000 81.64052 , , 3 [,1] [,2] [1,] -57.33422 -29.05873 [2,] 0.00000 37.10901 , , 4 [,1] [,2] [1,] -39.09601 -24.80817 [2,] 0.00000 -17.27119 , , 5 [,1] [,2] [1,] -32.34113 -9.262922 [2,] 0.00000 12.109134 , , 6 [,1] [,2] [1,] -71.38916 -26.36313 [2,] 0.00000 33.70020 , , 7 [,1] [,2] [1,] -45.00746 -43.06035 [2,] 0.00000 -13.03414
Read 138504 items [1] 10000 [1] 3867 $Vinv NULL $pro [1] 0.0708716 0.1769284 0.1491971 0.2780176 0.1609299 0.1640554 $mean [,1] [,2] [,3] [,4] [,5] [,6] [1,] 301.0512 479.3534 481.4737 553.1853 643.9201 646.4777 [2,] 325.0113 481.0801 519.9109 521.1925 589.2686 628.2585 $variance $variance$modelName [1] "VVV" $variance$d [1] 2 $variance$G [1] 6 $variance$sigma , , 1 [,1] [,2] [1,] 7845.995 1967.291 [2,] 1967.291 9829.285 , , 2 [,1] [,2] [1,] 1857.7216 330.3594 [2,] 330.3594 234.9704 , , 3 [,1] [,2] [1,] 2692.0382 659.3057 [2,] 659.3057 341.5811 , , 4 [,1] [,2] [1,] 1110.8005 450.6766 [2,] 450.6766 363.0634 , , 5 [,1] [,2] [1,] 3622.571 3387.179 [2,] 3387.179 3288.265 , , 6 [,1] [,2] [1,] 3976.527 1861.752 [2,] 1861.752 1388.307 $variance$cholsigma , , 1 [,1] [,2] [1,] -88.57762 -22.20979 [2,] 0.00000 96.62303 , , 2 [,1] [,2] [1,] -43.10129 -7.664721 [2,] 0.00000 -13.274880 , , 3 [,1] [,2] [1,] -51.88486 -12.70709 [2,] 0.00000 -13.42054 , , 4 [,1] [,2] [1,] -33.32867 -13.52219 [2,] 0.00000 -13.42438 , , 5 [,1] [,2] [1,] -60.1878 -56.27684 [2,] 0.0000 -11.00825 , , 6 [,1] [,2] [1,] -63.05971 -29.52363 [2,] 0.00000 22.73021
Read 127000 items [1] 10000 [1] 2987 $Vinv NULL $pro [1] 0.08337143 0.05570773 0.17876734 0.12477475 0.23229551 0.20140907 [7] 0.12367416 $mean [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 349.9035 374.7882 611.4276 499.6387 607.7975 662.6251 762.0650 [2,] 411.9781 256.9926 617.4432 494.8893 562.5699 610.3566 691.4602 $variance $variance$modelName [1] "VVV" $variance$d [1] 2 $variance$G [1] 7 $variance$sigma , , 1 [,1] [,2] [1,] 16072.626 9225.822 [2,] 9225.822 11034.045 , , 2 [,1] [,2] [1,] 2712.66456 25.34234 [2,] 25.34234 1722.33045 , , 3 [,1] [,2] [1,] 10771.492 7047.211 [2,] 7047.211 5343.205 , , 4 [,1] [,2] [1,] 5213.002 3713.708 [2,] 3713.708 3662.314 , , 5 [,1] [,2] [1,] 925.7252 539.2082 [2,] 539.2082 749.8059 , , 6 [,1] [,2] [1,] 738.1418 429.2458 [2,] 429.2458 414.4744 , , 7 [,1] [,2] [1,] 1607.196 1552.762 [2,] 1552.762 1790.061 $variance$cholsigma , , 1 [,1] [,2] [1,] -126.7779 -72.77156 [2,] 0.0000 75.75187 , , 2 [,1] [,2] [1,] -52.08325 -0.4865736 [2,] 0.00000 -41.4981168 , , 3 [,1] [,2] [1,] -103.7858 -67.90149 [2,] 0.0000 27.06644 , , 4 [,1] [,2] [1,] -72.20112 -51.43560 [2,] 0.00000 -31.88562 , , 5 [,1] [,2] [1,] -30.42573 -17.72211 [2,] 0.00000 -20.87421 , , 6 [,1] [,2] [1,] -27.16877 -15.79924 [2,] 0.00000 -12.83972 , , 7 [,1] [,2] [1,] -40.08985 -38.73204 [2,] 0.00000 -17.02617
Read 143512 items [1] 10000 [1] 4352 $Vinv NULL $pro [1] 0.02547121 0.29099435 0.07388858 0.22176791 0.07915986 0.18513305 [7] 0.12358504 $mean [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 326.5259 488.1971 535.3663 566.5123 595.7151 650.5835 683.7027 [2,] 368.9300 504.8604 595.9315 528.9039 606.3186 612.4143 650.6195 $variance $variance$modelName [1] "VVV" $variance$d [1] 2 $variance$G [1] 7 $variance$sigma , , 1 [,1] [,2] [1,] 12142.045 -2211.784 [2,] -2211.784 10760.556 , , 2 [,1] [,2] [1,] 2265.2013 604.6191 [2,] 604.6191 578.4554 , , 3 [,1] [,2] [1,] 13499.441 6467.233 [2,] 6467.233 3768.151 , , 4 [,1] [,2] [1,] 1198.8135 690.9153 [2,] 690.9153 781.3351 , , 5 [,1] [,2] [1,] 1101.48659 -84.76034 [2,] -84.76034 288.74142 , , 6 [,1] [,2] [1,] 530.4911 217.3745 [2,] 217.3745 246.5619 , , 7 [,1] [,2] [1,] 1186.0582 433.9824 [2,] 433.9824 426.4151 $variance$cholsigma , , 1 [,1] [,2] [1,] -110.1909 20.07229 [2,] 0.0000 -101.77259 , , 2 [,1] [,2] [1,] -47.59413 -12.70365 [2,] 0.00000 -20.42236 , , 3 [,1] [,2] [1,] -116.1871 -55.66223 [2,] 0.0000 -25.88178 , , 4 [,1] [,2] [1,] -34.62389 -19.95488 [2,] 0.00000 -19.57391 , , 5 [,1] [,2] [1,] -33.18865 2.553895 [2,] 0.00000 16.799376 , , 6 [,1] [,2] [1,] -23.03239 -9.437774 [2,] 0.00000 12.549514 , , 7 [,1] [,2] [1,] -34.43920 -12.60141 [2,] 0.00000 16.35908
Read 139224 items [1] 10000 [1] 4111 $Vinv NULL $pro [1] 0.03772979 0.19006704 0.31427003 0.16695336 0.10767037 0.18330941 $mean [,1] [,2] [,3] [,4] [,5] [,6] [1,] 348.4743 479.9382 563.7061 644.9337 625.0681 691.0621 [2,] 359.8323 494.3479 524.7628 606.8775 625.2827 625.0112 $variance $variance$modelName [1] "VVV" $variance$d [1] 2 $variance$G [1] 6 $variance$sigma , , 1 [,1] [,2] [1,] 10240.881 1626.031 [2,] 1626.031 10977.447 , , 2 [,1] [,2] [1,] 2768.2229 609.9427 [2,] 609.9427 678.0838 , , 3 [,1] [,2] [1,] 1340.6985 585.8402 [2,] 585.8402 639.4631 , , 4 [,1] [,2] [1,] 800.3198 371.3095 [2,] 371.3095 465.1034 , , 5 [,1] [,2] [1,] 6596.206 3492.190 [2,] 3492.190 2381.841 , , 6 [,1] [,2] [1,] 1799.778 1543.032 [2,] 1543.032 1528.821 $variance$cholsigma , , 1 [,1] [,2] [1,] -101.1972 -16.06794 [2,] 0.0000 -103.53390 , , 2 [,1] [,2] [1,] -52.6139 -11.59280 [2,] 0.0000 -23.31718 , , 3 [,1] [,2] [1,] -36.61555 -15.99977 [2,] 0.00000 -19.58241 , , 4 [,1] [,2] [1,] -28.28992 -13.12515 [2,] 0.00000 17.11239 , , 5 [,1] [,2] [1,] -81.21703 -42.99825 [2,] 0.00000 -23.08661 , , 6 [,1] [,2] [1,] -42.42379 -36.37184 [2,] 0.00000 -14.34956
Read 134408 items [1] 10000 [1] 3969 $Vinv NULL $pro [1] 0.06542553 0.16157240 0.14877678 0.18182725 0.17895889 0.26343916 $mean [,1] [,2] [,3] [,4] [,5] [,6] [1,] 361.0161 523.3542 559.6788 649.4959 608.7483 725.5666 [2,] 302.7612 513.4298 542.3724 609.8812 558.8478 664.8292 $variance $variance$modelName [1] "VVV" $variance$d [1] 2 $variance$G [1] 6 $variance$sigma , , 1 [,1] [,2] [1,] 9309.3649 342.6209 [2,] 342.6209 7529.9921 , , 2 [,1] [,2] [1,] 3453.989 1547.289 [2,] 1547.289 1698.183 , , 3 [,1] [,2] [1,] 1230.5867 142.9697 [2,] 142.9697 247.2928 , , 4 [,1] [,2] [1,] 1336.2549 703.8288 [2,] 703.8288 909.8132 , , 5 [,1] [,2] [1,] 558.7936 200.6191 [2,] 200.6191 282.5990 , , 6 [,1] [,2] [1,] 2480.592 1970.225 [2,] 1970.225 2072.693 $variance$cholsigma , , 1 [,1] [,2] [1,] -96.48505 -3.551026 [2,] 0.00000 86.702839 , , 2 [,1] [,2] [1,] -58.77065 -26.32758 [2,] 0.00000 31.70239 , , 3 [,1] [,2] [1,] -35.07972 -4.075564 [2,] 0.00000 15.188238 , , 4 [,1] [,2] [1,] -36.55482 -19.25406 [2,] 0.00000 23.21840 , , 5 [,1] [,2] [1,] -23.63881 -8.48685 [2,] 0.00000 14.51111 , , 6 [,1] [,2] [1,] -49.80554 -39.55836 [2,] 0.00000 -22.53507