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How to do a layered matrix--vector multiplication without a for loop?

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Anne Davenport
Anne Davenport 2024-1-26
移动：Bruno Luong 2024-1-29
I would like to multiply a 3-D matrix of NNN transformations by a 2-D matrix of NNN vectors without the for loop below:
% RR is an (NNN x 3) array of vectors.
% TT is a 3-D array of NNN (3 x 3) matrices.
for iii = 1:1:NNN
TRR(iii,:) = TT(:,:,iii) * RR(iii, 3);
end
The array of transformed vectors is an (NNN x 3) matrix.
I have tried pagemtimes() with no luck. Any help would be much appreciated.

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Bruno Luong
Bruno Luong 2024-1-26
编辑：Bruno Luong 2024-1-26
Ran in:
NNN = 10;
RR = rand(NNN, 3);
TT = rand(3,3,NNN);
for iii = 1:1:NNN
TRR(iii,:) = TT(:,:,iii) * RR(iii, :).'; % Bug fix
end
TRR1 = permute(pagemtimes(TT, reshape(RR.', 3, 1, [])), [3 1 2]);
norm(TRR-TRR1, 'inf')
ans = 0
% EDIT:
TRR
TRR = 10×3
0.5562 0.5086 1.2347 1.1149 0.9370 0.9763 0.6643 0.4458 0.6342 0.3462 0.4368 0.3715 0.3473 0.4736 0.2898 1.6595 0.6729 1.2345 0.9500 1.4171 1.9221 0.9745 1.1071 0.8333 0.4928 1.1708 1.0786 1.0319 0.6400 1.3485
TRR1
TRR1 = 10×3
0.5562 0.5086 1.2347 1.1149 0.9370 0.9763 0.6643 0.4458 0.6342 0.3462 0.4368 0.3715 0.3473 0.4736 0.2898 1.6595 0.6729 1.2345 0.9500 1.4171 1.9221 0.9745 1.1071 0.8333 0.4928 1.1708 1.0786 1.0319 0.6400 1.3485
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Dyuman Joshi
Dyuman Joshi 2024-1-27
Ran in:
@Anne Davenport, the elements do match, see the edit above.
You can directly check like this as well -
NNN = 10;
RR = rand(NNN, 3);
TT = rand(3,3,NNN);
for iii = 1:1:NNN
TRR(iii,:) = TT(:,:,iii) * RR(iii, :).'; % Bug fix
end
TRR1 = permute(pagemtimes(TT, reshape(RR.', 3, 1, [])), [3 1 2]);
all(TRR-TRR1==0, 'all')
ans = logical
1
Anne Davenport
Anne Davenport 2024-1-29
移动：Bruno Luong 2024-1-29
Thank-you again for your quick response. It worked for me this time.
I don't know how many times I can stare at a typo in my code and not see it, but my pride prevents me from saying just what dastardly typo I fat-fingered into your solution. This bit of code from above works just fine and answers my question.
TRR1 = permute(pagetimes(TT, reshape(RR.', 3, 1,[])),[3 1 2])
norm(TRR-TRR1, 'inf')

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