Subsetting an n-d array with no loop

12 Abr. 2023
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Actualizado a las 13 Abr. 2023
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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 ?

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Vilém Frynta
Vilém Frynta el 12 de Abr. de 2023
Movida: Walter Roberson el 12 de Abr. de 2023
Ran in:

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Ran in:
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

6 comentarios
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Francois Miguet
Francois Miguet el 12 de Abr. de 2023
Movida: Walter Roberson el 12 de Abr. de 2023
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
Adam Danz el 12 de Abr. de 2023
Movida: Walter Roberson el 12 de Abr. de 2023
Ran in:
Ran in:
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
Vilém Frynta el 12 de Abr. de 2023
Movida: Walter Roberson el 12 de Abr. de 2023
@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
Vilém Frynta el 12 de Abr. de 2023
Movida: Walter Roberson el 12 de Abr. de 2023
@Francois Miguet you have accepted your own answer. what i meant was my comment :p
Francois Miguet
Francois Miguet el 12 de Abr. de 2023
Editada: Adam Danz el 13 de Abr. de 2023
@Vilém Frynta weirdly it is the only option I see...
Walter Roberson
Walter Roberson el 12 de Abr. de 2023
(I moved responses around so you can accept the posting from @Vilém Frynta )

Iniciar sesión para comentar.

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Francois Miguet
Francois Miguet
el 12 de Abr. de 2023

Editada:

Adam Danz
Adam Danz
el 13 de Abr. de 2023

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