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

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.

Answer 1

[Bruno Luong]

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

[Anne Davenport]

Thank-you for the quick reply.

Unfortunately, all the elements for TRR1 and TRR don't agree, only the last row. Is there another line for this?

[Bruno Luong]

My code when run the last test line

norm(TRR-TRR1, 'inf')

returns 0 meaning they match perfectly

[Dyuman Joshi]

@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]

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')