Subsetting an n-d array with no loop

I have an n-d array that I want to subset along specific dimensions accordingly.

For instance, consider the following array,

Consider also a permutation or selection of specific indices from the last dimension:

I want to extract an n-d array B that contains all the diagonal elements of the 1st and last dimensions (applying for that last dimension the σ transformation) :

One option, rather brute-force, is to do the following:

A = rand(10,25,7,10);
sigma = [5,5,4,1,1,9,8,7,2,4];

for i=1:10
    B(i,:,:)= A (i,:,:,sigma(i))
end

However, if I deal with very large arrays, this requires a loop which really slows down my code.

I have tried subsetting like below, but Matlab doesn't understand that the index for the 1st dimension runs with the index for last dimension.

C = A(1:10,:,:,sigma(1:10))

If I do this, I end up with a matrix, which would be the following

Is there a way of subsetting an n-d array along specific dimensions simultaneously without a loop ?

Answer 1

[Vilém Frynta]

Could this work for you? It may be too "sample specific" instead working for every example.

This script generates a 4D array A of random numbers, and an array sigma of indices (which you provided). It then uses these indices to extract elements from A along the fourth dimension, and saves the results in a new array B, creating a new 3D array that only contains the elements of A selected by the sigma array.

sub2ind function needs same length vectors, so it's been workarounded a bit.

A = rand(10,25,7,10);
sigma = [5,5,4,1,1,9,8,7,2,4];
idx = sub2ind(size(A), repmat((1:10)',25*7,1), ...
    repmat(reshape(repmat((1:25)',1,7),[],1),10,1), ...
    repmat(reshape(repmat((1:7)',25,1),[],1),10,1), ...
    repmat(sigma',25*7,1));
B = reshape(A(idx), [10, 25, 7]);
disp(B)

(:,:,1) =

  Columns 1 through 19

    0.8419    0.1654    0.4302    0.0222    0.1194    0.4118    0.8931    0.6330    0.7192    0.4322    0.2011    0.2726    0.9072    0.1600    0.8224    0.5720    0.2752    0.6638    0.9715
    0.1068    0.2722    0.2647    0.3641    0.5543    0.1652    0.7239    0.3740    0.8143    0.3968    0.7299    0.7016    0.2639    0.0332    0.9909    0.0442    0.9355    0.4878    0.3770
    0.1411    0.5408    0.4414    0.0513    0.8026    1.0000    0.0751    0.5718    0.8551    0.5188    0.3871    0.0247    0.1508    0.5312    0.5501    0.1578    0.6124    0.7138    0.7429
    0.3241    0.2109    0.7512    0.1503    0.8854    0.9613    0.2702    0.2072    0.3297    0.1601    0.5885    0.8163    0.7043    0.2722    0.3613    0.4253    0.2086    0.1753    0.7646
    0.9964    0.0846    0.2339    0.6096    0.4706    0.6881    0.8045    0.1918    0.5795    0.3290    0.7296    0.9661    0.8417    0.4322    0.3425    0.8539    0.1077    0.4708    0.4340
    0.5386    0.4330    0.4899    0.2925    0.3641    0.7586    0.9642    0.9607    0.5449    0.2362    0.3217    0.0573    0.5500    0.5746    0.0740    0.8235    0.1572    0.2822    0.3274
    0.4756    0.8898    0.5960    0.0507    0.0921    0.1475    0.1726    0.9654    0.9958    0.4072    0.4900    0.9518    0.4734    0.7550    0.4443    0.7000    0.9827    0.4097    0.2692
    0.6074    0.0632    0.8178    0.9912    0.7856    0.1898    0.9194    0.8009    0.5920    0.4843    0.8502    0.5559    0.3164    0.8014    0.0337    0.2448    0.6822    0.9138    0.1172
    0.7617    0.0669    0.1958    0.1749    0.5044    0.0657    0.3261    0.2607    0.5235    0.2774    0.3124    0.7538    0.7401    0.2160    0.3764    0.1029    0.6114    0.0423    0.9861
    0.0539    0.0552    0.0603    0.1992    0.8039    0.2940    0.6013    0.1736    0.8238    0.6903    0.4683    0.0435    0.2153    0.3781    0.3374    0.2396    0.0657    0.8695    0.4397

  Columns 20 through 25

    0.0297    0.0033    0.2927    0.4264    0.1332    0.2415
    0.2785    0.1678    0.4385    0.4717    0.4377    0.0106
    0.3901    0.6661    0.8665    0.8876    0.7462    0.0204
    0.7250    0.7851    0.9598    0.5317    0.9935    0.3177
    0.3933    0.3303    0.7820    0.7344    0.4992    0.7589
    0.6290    0.5364    0.9495    0.8766    0.1682    0.5318
    0.1893    0.4017    0.1995    0.4424    0.5875    0.8294
    0.7882    0.0410    0.4026    0.0419    0.3005    0.2005
    0.8363    0.2756    0.6467    0.7691    0.9012    0.1762
    0.3174    0.3921    0.7081    0.0927    0.6641    0.8973


(:,:,2) =

  Columns 1 through 19

    0.7295    0.9767    0.9107    0.1318    0.7118    0.9255    0.6909    0.4158    0.2962    0.7614    0.8419    0.1654    0.4302    0.0222    0.1194    0.4118    0.8931    0.6330    0.7192
    0.5105    0.3614    0.6143    0.7640    0.8465    0.8773    0.4293    0.6849    0.2809    0.3280    0.1068    0.2722    0.2647    0.3641    0.5543    0.1652    0.7239    0.3740    0.8143
    0.5359    0.8440    0.4746    0.5335    0.3952    0.7718    0.3380    0.0489    0.8560    0.7551    0.1411    0.5408    0.4414    0.0513    0.8026    1.0000    0.0751    0.5718    0.8551
    0.3204    0.1051    0.8214    0.3956    0.1964    0.0831    0.2789    0.0179    0.6262    0.8167    0.3241    0.2109    0.7512    0.1503    0.8854    0.9613    0.2702    0.2072    0.3297
    0.0027    0.0980    0.0290    0.3765    0.0310    0.8001    0.7793    0.5528    0.4243    0.4869    0.9964    0.0846    0.2339    0.6096    0.4706    0.6881    0.8045    0.1918    0.5795
    0.6930    0.7368    0.3657    0.7719    0.1206    0.0464    0.1892    0.8462    0.6369    0.9851    0.5386    0.4330    0.4899    0.2925    0.3641    0.7586    0.9642    0.9607    0.5449
    0.6023    0.9826    0.5895    0.4044    0.6841    0.8209    0.3883    0.0739    0.0371    0.8075    0.4756    0.8898    0.5960    0.0507    0.0921    0.1475    0.1726    0.9654    0.9958
    0.7721    0.1879    0.2124    0.6136    0.5076    0.1983    0.1037    0.2933    0.7815    0.2867    0.6074    0.0632    0.8178    0.9912    0.7856    0.1898    0.9194    0.8009    0.5920
    0.0809    0.2578    0.1787    0.9215    0.9610    0.9895    0.7791    0.6516    0.1358    0.7782    0.7617    0.0669    0.1958    0.1749    0.5044    0.0657    0.3261    0.2607    0.5235
    0.8553    0.3136    0.3753    0.0828    0.3849    0.4778    0.2705    0.3805    0.5815    0.8126    0.0539    0.0552    0.0603    0.1992    0.8039    0.2940    0.6013    0.1736    0.8238

  Columns 20 through 25

    0.4322    0.2011    0.2726    0.9072    0.1600    0.8224
    0.3968    0.7299    0.7016    0.2639    0.0332    0.9909
    0.5188    0.3871    0.0247    0.1508    0.5312    0.5501
    0.1601    0.5885    0.8163    0.7043    0.2722    0.3613
    0.3290    0.7296    0.9661    0.8417    0.4322    0.3425
    0.2362    0.3217    0.0573    0.5500    0.5746    0.0740
    0.4072    0.4900    0.9518    0.4734    0.7550    0.4443
    0.4843    0.8502    0.5559    0.3164    0.8014    0.0337
    0.2774    0.3124    0.7538    0.7401    0.2160    0.3764
    0.6903    0.4683    0.0435    0.2153    0.3781    0.3374


(:,:,3) =

  Columns 1 through 19

    0.5720    0.2752    0.6638    0.9715    0.0297    0.0033    0.2927    0.4264    0.1332    0.2415    0.7295    0.9767    0.9107    0.1318    0.7118    0.9255    0.6909    0.4158    0.2962
    0.0442    0.9355    0.4878    0.3770    0.2785    0.1678    0.4385    0.4717    0.4377    0.0106    0.5105    0.3614    0.6143    0.7640    0.8465    0.8773    0.4293    0.6849    0.2809
    0.1578    0.6124    0.7138    0.7429    0.3901    0.6661    0.8665    0.8876    0.7462    0.0204    0.5359    0.8440    0.4746    0.5335    0.3952    0.7718    0.3380    0.0489    0.8560
    0.4253    0.2086    0.1753    0.7646    0.7250    0.7851    0.9598    0.5317    0.9935    0.3177    0.3204    0.1051    0.8214    0.3956    0.1964    0.0831    0.2789    0.0179    0.6262
    0.8539    0.1077    0.4708    0.4340    0.3933    0.3303    0.7820    0.7344    0.4992    0.7589    0.0027    0.0980    0.0290    0.3765    0.0310    0.8001    0.7793    0.5528    0.4243
    0.8235    0.1572    0.2822    0.3274    0.6290    0.5364    0.9495    0.8766    0.1682    0.5318    0.6930    0.7368    0.3657    0.7719    0.1206    0.0464    0.1892    0.8462    0.6369
    0.7000    0.9827    0.4097    0.2692    0.1893    0.4017    0.1995    0.4424    0.5875    0.8294    0.6023    0.9826    0.5895    0.4044    0.6841    0.8209    0.3883    0.0739    0.0371
    0.2448    0.6822    0.9138    0.1172    0.7882    0.0410    0.4026    0.0419    0.3005    0.2005    0.7721    0.1879    0.2124    0.6136    0.5076    0.1983    0.1037    0.2933    0.7815
    0.1029    0.6114    0.0423    0.9861    0.8363    0.2756    0.6467    0.7691    0.9012    0.1762    0.0809    0.2578    0.1787    0.9215    0.9610    0.9895    0.7791    0.6516    0.1358
    0.2396    0.0657    0.8695    0.4397    0.3174    0.3921    0.7081    0.0927    0.6641    0.8973    0.8553    0.3136    0.3753    0.0828    0.3849    0.4778    0.2705    0.3805    0.5815

  Columns 20 through 25

    0.7614    0.8419    0.1654    0.4302    0.0222    0.1194
    0.3280    0.1068    0.2722    0.2647    0.3641    0.5543
    0.7551    0.1411    0.5408    0.4414    0.0513    0.8026
    0.8167    0.3241    0.2109    0.7512    0.1503    0.8854
    0.4869    0.9964    0.0846    0.2339    0.6096    0.4706
    0.9851    0.5386    0.4330    0.4899    0.2925    0.3641
    0.8075    0.4756    0.8898    0.5960    0.0507    0.0921
    0.2867    0.6074    0.0632    0.8178    0.9912    0.7856
    0.7782    0.7617    0.0669    0.1958    0.1749    0.5044
    0.8126    0.0539    0.0552    0.0603    0.1992    0.8039


(:,:,4) =

  Columns 1 through 19

    0.4118    0.8931    0.6330    0.7192    0.4322    0.2011    0.2726    0.9072    0.1600    0.8224    0.5720    0.2752    0.6638    0.9715    0.0297    0.0033    0.2927    0.4264    0.1332
    0.1652    0.7239    0.3740    0.8143    0.3968    0.7299    0.7016    0.2639    0.0332    0.9909    0.0442    0.9355    0.4878    0.3770    0.2785    0.1678    0.4385    0.4717    0.4377
    1.0000    0.0751    0.5718    0.8551    0.5188    0.3871    0.0247    0.1508    0.5312    0.5501    0.1578    0.6124    0.7138    0.7429    0.3901    0.6661    0.8665    0.8876    0.7462
    0.9613    0.2702    0.2072    0.3297    0.1601    0.5885    0.8163    0.7043    0.2722    0.3613    0.4253    0.2086    0.1753    0.7646    0.7250    0.7851    0.9598    0.5317    0.9935
    0.6881    0.8045    0.1918    0.5795    0.3290    0.7296    0.9661    0.8417    0.4322    0.3425    0.8539    0.1077    0.4708    0.4340    0.3933    0.3303    0.7820    0.7344    0.4992
    0.7586    0.9642    0.9607    0.5449    0.2362    0.3217    0.0573    0.5500    0.5746    0.0740    0.8235    0.1572    0.2822    0.3274    0.6290    0.5364    0.9495    0.8766    0.1682
    0.1475    0.1726    0.9654    0.9958    0.4072    0.4900    0.9518    0.4734    0.7550    0.4443    0.7000    0.9827    0.4097    0.2692    0.1893    0.4017    0.1995    0.4424    0.5875
    0.1898    0.9194    0.8009    0.5920    0.4843    0.8502    0.5559    0.3164    0.8014    0.0337    0.2448    0.6822    0.9138    0.1172    0.7882    0.0410    0.4026    0.0419    0.3005
    0.0657    0.3261    0.2607    0.5235    0.2774    0.3124    0.7538    0.7401    0.2160    0.3764    0.1029    0.6114    0.0423    0.9861    0.8363    0.2756    0.6467    0.7691    0.9012
    0.2940    0.6013    0.1736    0.8238    0.6903    0.4683    0.0435    0.2153    0.3781    0.3374    0.2396    0.0657    0.8695    0.4397    0.3174    0.3921    0.7081    0.0927    0.6641

  Columns 20 through 25

    0.2415    0.7295    0.9767    0.9107    0.1318    0.7118
    0.0106    0.5105    0.3614    0.6143    0.7640    0.8465
    0.0204    0.5359    0.8440    0.4746    0.5335    0.3952
    0.3177    0.3204    0.1051    0.8214    0.3956    0.1964
    0.7589    0.0027    0.0980    0.0290    0.3765    0.0310
    0.5318    0.6930    0.7368    0.3657    0.7719    0.1206
    0.8294    0.6023    0.9826    0.5895    0.4044    0.6841
    0.2005    0.7721    0.1879    0.2124    0.6136    0.5076
    0.1762    0.0809    0.2578    0.1787    0.9215    0.9610
    0.8973    0.8553    0.3136    0.3753    0.0828    0.3849


(:,:,5) =

  Columns 1 through 19

    0.9255    0.6909    0.4158    0.2962    0.7614    0.8419    0.1654    0.4302    0.0222    0.1194    0.4118    0.8931    0.6330    0.7192    0.4322    0.2011    0.2726    0.9072    0.1600
    0.8773    0.4293    0.6849    0.2809    0.3280    0.1068    0.2722    0.2647    0.3641    0.5543    0.1652    0.7239    0.3740    0.8143    0.3968    0.7299    0.7016    0.2639    0.0332
    0.7718    0.3380    0.0489    0.8560    0.7551    0.1411    0.5408    0.4414    0.0513    0.8026    1.0000    0.0751    0.5718    0.8551    0.5188    0.3871    0.0247    0.1508    0.5312
    0.0831    0.2789    0.0179    0.6262    0.8167    0.3241    0.2109    0.7512    0.1503    0.8854    0.9613    0.2702    0.2072    0.3297    0.1601    0.5885    0.8163    0.7043    0.2722
    0.8001    0.7793    0.5528    0.4243    0.4869    0.9964    0.0846    0.2339    0.6096    0.4706    0.6881    0.8045    0.1918    0.5795    0.3290    0.7296    0.9661    0.8417    0.4322
    0.0464    0.1892    0.8462    0.6369    0.9851    0.5386    0.4330    0.4899    0.2925    0.3641    0.7586    0.9642    0.9607    0.5449    0.2362    0.3217    0.0573    0.5500    0.5746
    0.8209    0.3883    0.0739    0.0371    0.8075    0.4756    0.8898    0.5960    0.0507    0.0921    0.1475    0.1726    0.9654    0.9958    0.4072    0.4900    0.9518    0.4734    0.7550
    0.1983    0.1037    0.2933    0.7815    0.2867    0.6074    0.0632    0.8178    0.9912    0.7856    0.1898    0.9194    0.8009    0.5920    0.4843    0.8502    0.5559    0.3164    0.8014
    0.9895    0.7791    0.6516    0.1358    0.7782    0.7617    0.0669    0.1958    0.1749    0.5044    0.0657    0.3261    0.2607    0.5235    0.2774    0.3124    0.7538    0.7401    0.2160
    0.4778    0.2705    0.3805    0.5815    0.8126    0.0539    0.0552    0.0603    0.1992    0.8039    0.2940    0.6013    0.1736    0.8238    0.6903    0.4683    0.0435    0.2153    0.3781

  Columns 20 through 25

    0.8224    0.5720    0.2752    0.6638    0.9715    0.0297
    0.9909    0.0442    0.9355    0.4878    0.3770    0.2785
    0.5501    0.1578    0.6124    0.7138    0.7429    0.3901
    0.3613    0.4253    0.2086    0.1753    0.7646    0.7250
    0.3425    0.8539    0.1077    0.4708    0.4340    0.3933
    0.0740    0.8235    0.1572    0.2822    0.3274    0.6290
    0.4443    0.7000    0.9827    0.4097    0.2692    0.1893
    0.0337    0.2448    0.6822    0.9138    0.1172    0.7882
    0.3764    0.1029    0.6114    0.0423    0.9861    0.8363
    0.3374    0.2396    0.0657    0.8695    0.4397    0.3174


(:,:,6) =

  Columns 1 through 19

    0.0033    0.2927    0.4264    0.1332    0.2415    0.7295    0.9767    0.9107    0.1318    0.7118    0.9255    0.6909    0.4158    0.2962    0.7614    0.8419    0.1654    0.4302    0.0222
    0.1678    0.4385    0.4717    0.4377    0.0106    0.5105    0.3614    0.6143    0.7640    0.8465    0.8773    0.4293    0.6849    0.2809    0.3280    0.1068    0.2722    0.2647    0.3641
    0.6661    0.8665    0.8876    0.7462    0.0204    0.5359    0.8440    0.4746    0.5335    0.3952    0.7718    0.3380    0.0489    0.8560    0.7551    0.1411    0.5408    0.4414    0.0513
    0.7851    0.9598    0.5317    0.9935    0.3177    0.3204    0.1051    0.8214    0.3956    0.1964    0.0831    0.2789    0.0179    0.6262    0.8167    0.3241    0.2109    0.7512    0.1503
    0.3303    0.7820    0.7344    0.4992    0.7589    0.0027    0.0980    0.0290    0.3765    0.0310    0.8001    0.7793    0.5528    0.4243    0.4869    0.9964    0.0846    0.2339    0.6096
    0.5364    0.9495    0.8766    0.1682    0.5318    0.6930    0.7368    0.3657    0.7719    0.1206    0.0464    0.1892    0.8462    0.6369    0.9851    0.5386    0.4330    0.4899    0.2925
    0.4017    0.1995    0.4424    0.5875    0.8294    0.6023    0.9826    0.5895    0.4044    0.6841    0.8209    0.3883    0.0739    0.0371    0.8075    0.4756    0.8898    0.5960    0.0507
    0.0410    0.4026    0.0419    0.3005    0.2005    0.7721    0.1879    0.2124    0.6136    0.5076    0.1983    0.1037    0.2933    0.7815    0.2867    0.6074    0.0632    0.8178    0.9912
    0.2756    0.6467    0.7691    0.9012    0.1762    0.0809    0.2578    0.1787    0.9215    0.9610    0.9895    0.7791    0.6516    0.1358    0.7782    0.7617    0.0669    0.1958    0.1749
    0.3921    0.7081    0.0927    0.6641    0.8973    0.8553    0.3136    0.3753    0.0828    0.3849    0.4778    0.2705    0.3805    0.5815    0.8126    0.0539    0.0552    0.0603    0.1992

  Columns 20 through 25

    0.1194    0.4118    0.8931    0.6330    0.7192    0.4322
    0.5543    0.1652    0.7239    0.3740    0.8143    0.3968
    0.8026    1.0000    0.0751    0.5718    0.8551    0.5188
    0.8854    0.9613    0.2702    0.2072    0.3297    0.1601
    0.4706    0.6881    0.8045    0.1918    0.5795    0.3290
    0.3641    0.7586    0.9642    0.9607    0.5449    0.2362
    0.0921    0.1475    0.1726    0.9654    0.9958    0.4072
    0.7856    0.1898    0.9194    0.8009    0.5920    0.4843
    0.5044    0.0657    0.3261    0.2607    0.5235    0.2774
    0.8039    0.2940    0.6013    0.1736    0.8238    0.6903


(:,:,7) =

  Columns 1 through 19

    0.2011    0.2726    0.9072    0.1600    0.8224    0.5720    0.2752    0.6638    0.9715    0.0297    0.0033    0.2927    0.4264    0.1332    0.2415    0.7295    0.9767    0.9107    0.1318
    0.7299    0.7016    0.2639    0.0332    0.9909    0.0442    0.9355    0.4878    0.3770    0.2785    0.1678    0.4385    0.4717    0.4377    0.0106    0.5105    0.3614    0.6143    0.7640
    0.3871    0.0247    0.1508    0.5312    0.5501    0.1578    0.6124    0.7138    0.7429    0.3901    0.6661    0.8665    0.8876    0.7462    0.0204    0.5359    0.8440    0.4746    0.5335
    0.5885    0.8163    0.7043    0.2722    0.3613    0.4253    0.2086    0.1753    0.7646    0.7250    0.7851    0.9598    0.5317    0.9935    0.3177    0.3204    0.1051    0.8214    0.3956
    0.7296    0.9661    0.8417    0.4322    0.3425    0.8539    0.1077    0.4708    0.4340    0.3933    0.3303    0.7820    0.7344    0.4992    0.7589    0.0027    0.0980    0.0290    0.3765
    0.3217    0.0573    0.5500    0.5746    0.0740    0.8235    0.1572    0.2822    0.3274    0.6290    0.5364    0.9495    0.8766    0.1682    0.5318    0.6930    0.7368    0.3657    0.7719
    0.4900    0.9518    0.4734    0.7550    0.4443    0.7000    0.9827    0.4097    0.2692    0.1893    0.4017    0.1995    0.4424    0.5875    0.8294    0.6023    0.9826    0.5895    0.4044
    0.8502    0.5559    0.3164    0.8014    0.0337    0.2448    0.6822    0.9138    0.1172    0.7882    0.0410    0.4026    0.0419    0.3005    0.2005    0.7721    0.1879    0.2124    0.6136
    0.3124    0.7538    0.7401    0.2160    0.3764    0.1029    0.6114    0.0423    0.9861    0.8363    0.2756    0.6467    0.7691    0.9012    0.1762    0.0809    0.2578    0.1787    0.9215
    0.4683    0.0435    0.2153    0.3781    0.3374    0.2396    0.0657    0.8695    0.4397    0.3174    0.3921    0.7081    0.0927    0.6641    0.8973    0.8553    0.3136    0.3753    0.0828

  Columns 20 through 25

    0.7118    0.9255    0.6909    0.4158    0.2962    0.7614
    0.8465    0.8773    0.4293    0.6849    0.2809    0.3280
    0.3952    0.7718    0.3380    0.0489    0.8560    0.7551
    0.1964    0.0831    0.2789    0.0179    0.6262    0.8167
    0.0310    0.8001    0.7793    0.5528    0.4243    0.4869
    0.1206    0.0464    0.1892    0.8462    0.6369    0.9851
    0.6841    0.8209    0.3883    0.0739    0.0371    0.8075
    0.5076    0.1983    0.1037    0.2933    0.7815    0.2867
    0.9610    0.9895    0.7791    0.6516    0.1358    0.7782
    0.3849    0.4778    0.2705    0.3805    0.5815    0.8126

[Francois Miguet]

Thanks, I didn't think about using linear indices.

I have tweaked your code a bit to make it a little more generic, and it works great!

A = rand(10,25,7,10);
sigma = [5,5,4,1,1,9,8,7,2,4];
[idI,idJ,idK] = ndgrid(1:10,1:1:25,1:1:7);

idA = {idI(:),idJ(:),idK(:),repmat(sigma',[25*7,1])};

B = reshape(A(sub2ind([10,25,7,10],idA{:})),[10,25,7]);
disp(B)

[Adam Danz]

Even more generic:

A = rand(10,25,7,10);
sigma = [5,5,4,1,1,9,8,7,2,4];

[idI,idJ,idK] = ndgrid(1:size(A,1),1:size(A,2),1:size(A,3));
idA = {idI(:),idJ(:),idK(:),repmat(sigma',[prod(size(A,[2,3])),1])};
B = reshape(A(sub2ind(size(A),idA{:})),size(A,[1,2,3]));
disp(B)

(:,:,1) =

  Columns 1 through 19

    0.8813    0.3298    0.7865    0.1427    0.8151    0.4347    0.0297    0.9471    0.3619    0.4638    0.3218    0.6070    0.6661    0.1832    0.8625    0.3020    0.1389    0.8537    0.3161
    0.1544    0.7348    0.8033    0.4073    0.7639    0.9193    0.8492    0.3257    0.8663    0.1844    0.0475    0.8053    0.1869    0.7286    0.7670    0.7760    0.5751    0.4092    0.7083
    0.3041    0.4739    0.4587    0.0987    0.9339    0.9146    0.2383    0.9134    0.7246    0.6171    0.2522    0.1147    0.2065    0.7261    0.1794    0.7158    0.4429    0.0910    0.5259
    0.9056    0.6959    0.8764    0.7206    0.6501    0.6842    0.3972    0.9941    0.3167    0.0526    0.8369    0.5901    0.8623    0.9346    0.4686    0.3594    0.9869    0.7096    0.1894
    0.9005    0.2708    0.8788    0.4281    0.9598    0.0733    0.1801    0.0207    0.8346    0.8549    0.0305    0.8835    0.7175    0.0439    0.0912    0.9733    0.9229    0.0911    0.0660
    0.3171    0.7970    0.2240    0.5311    0.2255    0.2534    0.4293    0.4370    0.8417    0.0065    0.4150    0.9114    0.7056    0.7542    0.8089    0.8022    0.7667    0.8431    0.9668
    0.7019    0.8264    0.7454    0.7192    0.3190    0.5806    0.1708    0.5521    0.7368    0.0030    0.8855    0.2513    0.3646    0.9209    0.0021    0.1310    0.0013    0.2870    0.5060
    0.3754    0.8257    0.8819    0.7097    0.0218    0.3463    0.4148    0.2213    0.9992    0.7035    0.7487    0.1149    0.6332    0.8549    0.5372    0.6726    0.7135    0.5932    0.7472
    0.7556    0.3964    0.2566    0.2028    0.8778    0.2245    0.8121    0.2046    0.3699    0.5459    0.5242    0.3265    0.0222    0.0902    0.5272    0.0214    0.5151    0.3717    0.6060
    0.1587    0.5312    0.2727    0.3998    0.5424    0.7251    0.2298    0.5471    0.6626    0.4785    0.2940    0.4131    0.5016    0.1287    0.0222    0.2766    0.4340    0.7835    0.1171

  Columns 20 through 25

    0.3950    0.5354    0.1849    0.4438    0.2787    0.0059
    0.9061    0.6323    0.4026    0.7729    0.2608    0.2150
    0.1835    0.1111    0.8339    0.6703    0.7184    0.4140
    0.4113    0.9582    0.1829    0.7343    0.5213    0.7621
    0.0630    0.0583    0.0581    0.0963    0.5968    0.5443
    0.0154    0.2325    0.4582    0.9570    0.5239    0.2582
    0.4598    0.3054    0.0194    0.1836    0.5956    0.8956
    0.8591    0.3099    0.4003    0.3817    0.7255    0.6468
    0.2278    0.0270    0.9803    0.5546    0.5751    0.7145
    0.8252    0.9796    0.8190    0.2295    0.0033    0.5777


(:,:,2) =

  Columns 1 through 19

    0.2082    0.5193    0.9032    0.2339    0.3858    0.7963    0.8341    0.1368    0.6613    0.6476    0.4259    0.5130    0.6958    0.2704    0.9218    0.7284    0.5892    0.9525    0.2237
    0.2094    0.1654    0.1420    0.7623    0.1502    0.6476    0.0978    0.4550    0.0210    0.0982    0.9335    0.4247    0.1442    0.3515    0.5038    0.7183    0.6259    0.3756    0.8924
    0.7136    0.4102    0.8953    0.3785    0.5345    0.6538    0.8032    0.9218    0.0714    0.1776    0.7898    0.5252    0.2868    0.3026    0.0273    0.7093    0.7985    0.9821    0.3303
    0.2310    0.9310    0.1793    0.9112    0.9358    0.2389    0.4253    0.8044    0.2894    0.8713    0.6668    0.4156    0.4377    0.8353    0.2742    0.1578    0.5771    0.8312    0.2146
    0.0551    0.9209    0.1833    0.2460    0.6668    0.8184    0.0214    0.7507    0.3500    0.3271    0.3087    0.1017    0.5328    0.6972    0.4042    0.3181    0.5783    0.6623    0.6241
    0.2456    0.5259    0.3159    0.8955    0.0047    0.3406    0.5106    0.8760    0.2416    0.9637    0.8248    0.2812    0.3856    0.6563    0.3771    0.0742    0.2579    0.1031    0.6261
    0.1407    0.5358    0.8048    0.4204    0.5084    0.1335    0.1661    0.8686    0.5540    0.7321    0.3510    0.0055    0.9907    0.0648    0.8367    0.4463    0.3115    0.6205    0.3656
    0.6695    0.6370    0.6678    0.1881    0.1920    0.0673    0.2062    0.1464    0.1764    0.9458    0.0433    0.5862    0.9869    0.7496    0.4745    0.1600    0.9027    0.0495    0.9110
    0.7114    0.9822    0.9127    0.8847    0.4290    0.5520    0.1693    0.2436    0.7901    0.2595    0.6834    0.8155    0.6979    0.0442    0.2600    0.0020    0.1944    0.1537    0.9513
    0.9039    0.5641    0.6023    0.0057    0.5278    0.0427    0.8478    0.7725    0.7326    0.7719    0.1054    0.8631    0.8141    0.6868    0.3387    0.6421    0.9116    0.7745    0.1361

  Columns 20 through 25

    0.8186    0.9508    0.9868    0.2730    0.6237    0.8278
    0.6821    0.4453    0.4717    0.7845    0.8570    0.4686
    0.8973    0.5473    0.3850    0.4729    0.8141    0.1737
    0.0188    0.0551    0.7440    0.0655    0.1006    0.2357
    0.8907    0.4380    0.0023    0.6815    0.7306    0.7740
    0.3544    0.9925    0.2473    0.1599    0.2927    0.3973
    0.1947    0.6697    0.3329    0.0201    0.9341    0.3425
    0.5973    0.3427    0.9437    0.8491    0.1707    0.8262
    0.4420    0.9198    0.5507    0.3002    0.4964    0.8874
    0.7152    0.2009    0.4625    0.8489    0.5532    0.7058


(:,:,3) =

  Columns 1 through 19

    0.5984    0.3165    0.0768    0.9112    0.8768    0.1350    0.0164    0.9483    0.5626    0.7649    0.2998    0.0761    0.6490    0.1818    0.0369    0.3632    0.9267    0.1369    0.9047
    0.6192    0.3113    0.9483    0.1475    0.2948    0.2224    0.3633    0.1341    0.3069    0.3365    0.3791    0.1547    0.1387    0.9365    0.3775    0.5772    0.8666    0.6971    0.8668
    0.0873    0.0247    0.1477    0.2051    0.8148    0.2990    0.0829    0.8879    0.1835    0.4828    0.8805    0.0999    0.2462    0.5208    0.1752    0.6808    0.3582    0.5255    0.6968
    0.0677    0.2062    0.2278    0.3141    0.8664    0.5966    0.7108    0.7601    0.4381    0.9687    0.2827    0.5149    0.2197    0.1425    0.5344    0.1981    0.2004    0.9674    0.7527
    0.5214    0.6760    0.3502    0.7227    0.3594    0.4905    0.4041    0.6801    0.5209    0.6044    0.2768    0.5028    0.0462    0.3394    0.1459    0.0936    0.1122    0.9428    0.0293
    0.6103    0.3026    0.9497    0.7317    0.2565    0.9056    0.1516    0.5014    0.1837    0.0757    0.2450    0.0143    0.3696    0.9044    0.9457    0.6668    0.7184    0.6040    0.9658
    0.7799    0.8508    0.2506    0.3215    0.5820    0.6523    0.0860    0.4533    0.1280    0.3045    0.4499    0.4991    0.5271    0.7134    0.3700    0.8061    0.3398    0.5944    0.3726
    0.1479    0.6864    0.1532    0.3269    0.6930    0.7833    0.7062    0.8559    0.1283    0.8605    0.1924    0.3785    0.9546    0.9316    0.9375    0.2118    0.3179    0.7951    0.8802
    0.9507    0.4450    0.2269    0.9753    0.5384    0.7636    0.0469    0.5815    0.2423    0.1880    0.3627    0.7765    0.9621    0.8960    0.1676    0.4127    0.5036    0.3739    0.0988
    0.1019    0.1687    0.9974    0.9900    0.4315    0.3535    0.7490    0.8353    0.7882    0.2590    0.2078    0.8028    0.5729    0.9353    0.9527    0.7306    0.8881    0.1009    0.2450

  Columns 20 through 25

    0.4931    0.7439    0.1386    0.1189    0.5192    0.8543
    0.5926    0.9979    0.1910    0.9586    0.6197    0.6955
    0.9176    0.0550    0.8846    0.0531    0.8810    0.5605
    0.2743    0.8689    0.2590    0.8068    0.3570    0.7955
    0.2972    0.8760    0.5100    0.7373    0.0855    0.5055
    0.5642    0.9110    0.9453    0.8204    0.6172    0.8432
    0.9910    0.0329    0.8490    0.3467    0.7049    0.9819
    0.6807    0.2033    0.0341    0.5200    0.7543    0.6395
    0.4630    0.6721    0.1671    0.5712    0.3159    0.2335
    0.7974    0.4052    0.5349    0.4088    0.4896    0.3699


(:,:,4) =

  Columns 1 through 19

    0.7741    0.6394    0.0962    0.5015    0.8449    0.5746    0.2140    0.5010    0.0486    0.3288    0.9166    0.3170    0.9634    0.8985    0.9871    0.5053    0.0981    0.8741    0.1410
    0.5678    0.9299    0.9810    0.9823    0.6036    0.0757    0.7521    0.2777    0.5777    0.0930    0.2837    0.8574    0.3691    0.4892    0.3798    0.6131    0.3661    0.9088    0.6693
    0.1798    0.5159    0.7416    0.5663    0.4213    0.3206    0.8424    0.1938    0.4628    0.0615    0.2773    0.1894    0.8347    0.1026    0.4199    0.3375    0.1592    0.3988    0.1741
    0.1103    0.4234    0.9024    0.0830    0.6216    0.4151    0.8468    0.9320    0.6732    0.0718    0.7686    0.3573    0.6426    0.2476    0.2072    0.3961    0.0167    0.0669    0.7681
    0.8426    0.5283    0.8038    0.2168    0.5302    0.4349    0.5603    0.5196    0.4931    0.5320    0.4970    0.1368    0.9016    0.4579    0.3042    0.0207    0.9993    0.0261    0.8101
    0.2538    0.9300    0.0851    0.1457    0.1538    0.3107    0.5554    0.2680    0.6788    0.3468    0.8115    0.3531    0.6572    0.2278    0.1961    0.0095    0.7694    0.2362    0.2552
    0.0697    0.9301    0.9560    0.3538    0.7927    0.8918    0.3596    0.9355    0.0122    0.5807    0.4910    0.1452    0.1670    0.9016    0.2179    0.5665    0.5540    0.9018    0.3945
    0.9087    0.4075    0.6045    0.6746    0.7095    0.8160    0.5737    0.3066    0.5002    0.0123    0.9915    0.6263    0.1112    0.9171    0.8982    0.5238    0.2907    0.3319    0.4362
    0.5467    0.0934    0.0824    0.0396    0.4685    0.3575    0.5351    0.9446    0.7863    0.4008    0.4180    0.9544    0.9909    0.5980    0.5099    0.7405    0.5259    0.4010    0.7382
    0.7032    0.5806    0.9857    0.3370    0.4120    0.8853    0.3996    0.9419    0.5655    0.0807    0.9484    0.1607    0.4168    0.0992    0.1136    0.5103    0.4905    0.4612    0.4051

  Columns 20 through 25

    0.1814    0.7170    0.7098    0.2190    0.0565    0.6735
    0.1307    0.5529    0.9095    0.1199    0.5076    0.9700
    0.1941    0.2622    0.4618    0.8730    0.1662    0.6515
    0.8909    0.3045    0.5177    0.4113    0.3961    0.2095
    0.6247    0.8914    0.4274    0.0693    0.1871    0.4767
    0.0602    0.1182    0.6885    0.1675    0.4765    0.7531
    0.7474    0.6540    0.2785    0.3785    0.2507    0.2087
    0.7191    0.9815    0.4354    0.2289    0.4218    0.0526
    0.5116    0.6119    0.8197    0.4918    0.2148    0.2923
    0.7354    0.3769    0.4892    0.9460    0.3132    0.2188


(:,:,5) =

  Columns 1 through 19

    0.5566    0.9732    0.6031    0.8425    0.5459    0.1345    0.4237    0.1129    0.0863    0.0536    0.3106    0.8668    0.4594    0.8486    0.1706    0.0443    0.9473    0.2168    0.2251
    0.9396    0.3941    0.4968    0.7187    0.4833    0.0602    0.8076    0.3073    0.2901    0.9924    0.1731    0.4674    0.7011    0.5080    0.7728    0.8160    0.9531    0.0129    0.8094
    0.3646    0.9889    0.8054    0.5807    0.9920    0.2850    0.8325    0.4742    0.3921    0.5331    0.0600    0.3467    0.2817    0.4567    0.4869    0.4180    0.3097    0.2827    0.4579
    0.8475    0.5779    0.6148    0.9464    0.6138    0.7744    0.1215    0.2492    0.2904    0.7906    0.2416    0.1525    0.5786    0.2896    0.7944    0.8579    0.7881    0.6981    0.6916
    0.7154    0.3492    0.8103    0.2439    0.8254    0.2766    0.3390    0.7277    0.0816    0.1111    0.8274    0.4180    0.9681    0.3569    0.7655    0.3092    0.7869    0.3950    0.7170
    0.2657    0.8091    0.7699    0.5940    0.7708    0.6525    0.1759    0.5963    0.0106    0.0223    0.5654    0.9227    0.3842    0.8443    0.7337    0.4251    0.2107    0.9510    0.0473
    0.4230    0.5660    0.5306    0.8513    0.1775    0.2221    0.8494    0.5572    0.5294    0.1747    0.5043    0.8821    0.7180    0.0796    0.6474    0.4481    0.4666    0.7631    0.7367
    0.7103    0.8342    0.1889    0.1355    0.3672    0.0484    0.3709    0.7559    0.4123    0.3920    0.7927    0.6316    0.1186    0.7917    0.0559    0.9213    0.2020    0.7075    0.0086
    0.5023    0.5754    0.5043    0.0807    0.4136    0.2773    0.4004    0.0306    0.5169    0.1756    0.6321    0.1646    0.2066    0.2683    0.0678    0.5439    0.7557    0.9593    0.4279
    0.3249    0.1202    0.3859    0.2211    0.7989    0.5925    0.6212    0.5932    0.3864    0.0883    0.0133    0.7946    0.9024    0.4522    0.5320    0.7574    0.7675    0.5247    0.9620

  Columns 20 through 25

    0.0695    0.2646    0.7857    0.1114    0.9040    0.7828
    0.3979    0.3854    0.6579    0.5178    0.3237    0.5521
    0.6045    0.9961    0.5543    0.9229    0.6937    0.5939
    0.0259    0.2665    0.4658    0.5023    0.9787    0.0783
    0.5626    0.0134    0.1578    0.2356    0.6212    0.7004
    0.5758    0.4673    0.0510    0.6227    0.1476    0.6789
    0.1493    0.4266    0.8624    0.1656    0.7156    0.4331
    0.5756    0.5204    0.2051    0.5363    0.1148    0.6864
    0.3027    0.6816    0.0631    0.2590    0.8178    0.0263
    0.6164    0.9762    0.6507    0.0248    0.7181    0.4725


(:,:,6) =

  Columns 1 through 19

    0.5401    0.7014    0.8840    0.5181    0.5196    0.6219    0.5193    0.6446    0.6882    0.3093    0.2213    0.8105    0.1195    0.1727    0.7237    0.4949    0.1676    0.6589    0.3486
    0.2859    0.2807    0.4905    0.8399    0.1846    0.0476    0.1189    0.5970    0.6250    0.1111    0.8713    0.5336    0.2190    0.3566    0.8644    0.4622    0.7408    0.7096    0.2503
    0.7286    0.1002    0.1612    0.2516    0.7473    0.1722    0.7077    0.6073    0.3281    0.2815    0.9232    0.0129    0.2291    0.7102    0.2751    0.2288    0.1968    0.9101    0.9108
    0.9720    0.3848    0.2131    0.1532    0.3908    0.3508    0.7146    0.2424    0.2279    0.3525    0.2911    0.6443    0.3088    0.9514    0.3190    0.0163    0.1300    0.4507    0.7273
    0.2332    0.4013    0.7693    0.0057    0.6885    0.5579    0.6724    0.1718    0.3049    0.5409    0.6776    0.4554    0.0656    0.7633    0.7268    0.4101    0.6086    0.5822    0.5947
    0.6460    0.4193    0.7690    0.9086    0.5729    0.4273    0.7731    0.9803    0.0090    0.7485    0.8108    0.9751    0.4200    0.1626    0.6823    0.7174    0.3976    0.6593    0.0215
    0.2320    0.5010    0.6943    0.6259    0.8359    0.8367    0.2700    0.1967    0.6802    0.2314    0.4164    0.1535    0.0564    0.3485    0.6610    0.8250    0.5809    0.3925    0.7720
    0.1961    0.5781    0.6183    0.1150    0.5884    0.5905    0.7850    0.6990    0.6456    0.6484    0.8324    0.1069    0.5500    0.0475    0.9544    0.7070    0.3353    0.4825    0.5544
    0.4272    0.9882    0.0720    0.1344    0.9908    0.0600    0.8173    0.0624    0.3137    0.9499    0.5265    0.0879    0.2807    0.7663    0.2930    0.1479    0.7690    0.3529    0.8294
    0.3519    0.3931    0.4164    0.2768    0.1226    0.3753    0.8008    0.7708    0.7880    0.9000    0.4969    0.9458    0.7362    0.5048    0.2209    0.8786    0.1602    0.1361    0.6317

  Columns 20 through 25

    0.2299    0.7061    0.1590    0.8198    0.3567    0.2683
    0.4842    0.4748    0.8296    0.5325    0.8132    0.2471
    0.6607    0.2606    0.0511    0.8991    0.0871    0.9423
    0.2188    0.3051    0.0741    0.0316    0.3390    0.5170
    0.1993    0.4924    0.0302    0.7602    0.0909    0.8663
    0.1443    0.0940    0.0815    0.4107    0.1191    0.4911
    0.1083    0.7259    0.7327    0.7139    0.5697    0.0720
    0.5760    0.7890    0.8702    0.9155    0.1315    0.7326
    0.8569    0.3700    0.3762    0.0648    0.5967    0.3808
    0.6157    0.6033    0.4988    0.7513    0.3045    0.0493


(:,:,7) =

  Columns 1 through 19

    0.1463    0.4935    0.3419    0.9883    0.5345    0.1640    0.3111    0.3722    0.9942    0.9045    0.2456    0.8052    0.3360    0.7961    0.8708    0.8309    0.0485    0.4915    0.2730
    0.8281    0.4622    0.8572    0.7414    0.6796    0.3181    0.8121    0.4392    0.5375    0.4857    0.3776    0.9154    0.7234    0.7959    0.7291    0.9189    0.7891    0.7152    0.4635
    0.9563    0.0069    0.5477    0.2373    0.3518    0.4063    0.6004    0.0263    0.4052    0.0368    0.3457    0.4254    0.0677    0.0152    0.9748    0.7382    0.6287    0.7053    0.4513
    0.0030    0.0089    0.4098    0.6782    0.5622    0.6792    0.2810    0.8950    0.7392    0.8218    0.1041    0.8548    0.1021    0.2203    0.7198    0.9091    0.9556    0.3401    0.7982
    0.8246    0.6090    0.5926    0.9178    0.6637    0.5362    0.9992    0.1461    0.6343    0.0184    0.1078    0.4766    0.8077    0.5808    0.5060    0.1397    0.0114    0.6827    0.8354
    0.8986    0.4497    0.1148    0.4367    0.7546    0.5736    0.9130    0.9524    0.6283    0.6785    0.5723    0.3762    0.9211    0.7544    0.3263    0.7634    0.8693    0.4370    0.7278
    0.8655    0.6580    0.8876    0.6880    0.7296    0.9037    0.3059    0.4645    0.3799    0.1493    0.4753    0.1641    0.1729    0.6952    0.6019    0.8646    0.1339    0.3963    0.3314
    0.4616    0.5354    0.9956    0.0104    0.1437    0.9831    0.2992    0.8755    0.4434    0.3903    0.7014    0.1136    0.3043    0.9371    0.5756    0.7052    0.6574    0.8191    0.4846
    0.7759    0.8633    0.3335    0.0841    0.7532    0.1266    0.9042    0.4498    0.7539    0.9656    0.0598    0.3554    0.3525    0.1216    0.4601    0.1220    0.4776    0.0026    0.0574
    0.8036    0.0351    0.9809    0.2693    0.1352    0.4119    0.4381    0.3737    0.1467    0.5987    0.7201    0.2388    0.6566    0.4268    0.6519    0.1084    0.3941    0.8555    0.5033

  Columns 20 through 25

    0.3892    0.7326    0.9699    0.5795    0.0905    0.9306
    0.9051    0.9447    0.2242    0.9916    0.3119    0.5010
    0.9959    0.0343    0.8200    0.9366    0.2939    0.0318
    0.5377    0.4163    0.1636    0.0810    0.3618    0.9892
    0.3598    0.6675    0.1051    0.1856    0.9876    0.2834
    0.1135    0.3392    0.0075    0.2018    0.1027    0.5761
    0.6096    0.7331    0.0922    0.3379    0.4132    0.5190
    0.5613    0.3024    0.1237    0.8570    0.8847    0.2421
    0.0163    0.1079    0.9000    0.3114    0.1879    0.4787
    0.8658    0.0113    0.4300    0.8040    0.2767    0.4005

[Vilém Frynta]

@Francois Miguet glad I could help!

If my answer was helpful to you, I'd be happy if you could formally accept it.

[Vilém Frynta]

@Francois Miguet you have accepted your own answer. what i meant was my comment :p

[Francois Miguet]

@Vilém Frynta weirdly it is the only option I see...

[Walter Roberson]

(I moved responses around so you can accept the posting from @Vilém Frynta )