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**画像ノイズ除去をしてみる(2010-09-17) [#kaf51261]

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。

***Rでの行列操作によるノイズデータの除去 [#tdcc0e68]
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 ⇒ :http://www.okada.jp.org/RWiki/?%B9%D4%CE%F3Tips%C2%E7%C1%B4#l2354237]] ("-"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。

***孤立点を判定する [#c21e2296]
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)

***孤立点の除去 [#e4c40e31]
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。

***フローサイトメトリデータ処理への応用 [#sb2fa544] 
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)

**<<37編>> [#oe530143]
***処理結果 37C/100124 37-2_limit.csv [#pd57553d]
&ref(100124 37-2_limit.png);
 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

***処理結果 37C/100207 37-2_limit.csv [#pd57553d]
&ref(100207 37-2_limit.png);
 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

***処理結果 37C/100222 37-2_limit.csv [#pd57553d]
&ref(100222 37-2_limit.png);
 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

// 〜〜〜〜〜〜

|37-0124|37-0207|37-0222|
|&ref(100124 37-2_limit.png,,350x350);|&ref(100207 37-2_limit.png,,350x350);|&ref(100222 37-2_limit.png,,350x350);|


**<<40編>> [#u5553204]

***処理結果 40C/100130 40C_limit.csv [#pd57553d]
&ref(100130 40C_limit.png);
 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

***処理結果 40C/100131 40C-2_limit.csv [#pd57553d]
&ref(100131 40C-2_limit.png);
 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


> 




***処理結果 40C/100202 40C-2_limit.csv [#pd57553d]
&ref(100202 40C-2_limit.png);
 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

***処理結果 40C/100206 40C-2_limit.csv [#pd57553d]
&ref(100206 40C-2_limit.png);
 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

***処理結果 40C/100213 40C-2_limit.csv [#pd57553d]
&ref(100213 40C-2_limit.png);
 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

***処理結果 40C/100222 40C-2_limit.csv [#w3b989c2]
&ref(100222 40C-2_limit.png);
 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


//〜〜〜〜

|40-0130|40-0131|
|&ref(100130 40C_limit.png,,350x350);|&ref(100131 40C-2_limit.png,,350x350);|
|40-0202|40-0206|40-0213|
|&ref(100202 40C-2_limit.png,,350x350);|&ref(100206 40C-2_limit.png,,350x350);|&ref(100213 40C-2_limit.png,,350x350);|
|40-0130|40-0131|40-0202|
|&ref(100130 40C_limit.png,,350x350);|&ref(100131 40C-2_limit.png,,350x350);|&ref(100202 40C-2_limit.png,,350x350);|
|40-0206|40-0213|40-0222|
|&ref(100206 40C-2_limit.png,,350x350);|&ref(100213 40C-2_limit.png,,350x350);|&ref(100222 40C-2_limit.png,,350x350);|

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