Matrix Multiplication Along Pages of Multidimensional Matrix

조회 수: 13 (최근 30일)
Mark Whirdy
Mark Whirdy 2014년 8월 27일
댓글: Mark Whirdy 2014년 8월 27일
What is the most efficient way of matrix-multiplying along a page (2d plane) of a multidimensional matrix. Speed is important here as this operation will be in the objective-function of a calibration.
Specifically I have a 4d matrix of dimension [m,n,p,2], and I want to matrix-multiply it by a [2x1] vector
So conceptually I need
b*y0'
Taking for example:
b = rand(5,3,4,2); %
y0 = [0.1;0.2]; y0 = reshape(y0,[1,1,1,2]); %
I should end up with a 3d matrix of size [5,3,4]
I could, of course, dot-multiply by a repmatted y0 and then sum along the 4d but is this really the most efficient?
y0 = y0(ones(5,1,1),ones(1,3,1),ones(1,1,4),:);
sum(b.*y0,4);
All the best

채택된 답변

Matt J
Matt J 2014년 8월 27일
If size(b,4)=2 all the time, it would probably be best just to generate two separate 3D arrays b1 and b2
result=b1*y0(1)+b2*y0(2);
  댓글 수: 2
Matt J
Matt J 2014년 8월 27일
Note, this is different from (and faster than)
result=b(:,:,:,1)*y0(1)+b(:,:,:,2)*y0(2);
Mark Whirdy
Mark Whirdy 2014년 8월 27일
you're right - talk about overengineering :-D
thanks!

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추가 답변 (2개)

Matt J
Matt J 2014년 8월 27일
편집: Matt J 2014년 8월 27일
I could, of course, dot-multiply by a repmatted y0 and then sum along the 4d but is this really the most efficient?
Probably, if you're stuck with b in the shape you describe. However, it is better to use bsxfun, rather than repmat;
y0 = [0.1;0.2]; y0 = reshape(y0,[1,1,1,2]); %
result = sum( bsxfun(@times, b,y0) , 4)
  댓글 수: 3
Matt J
Matt J 2014년 8월 27일
It's not a meaningful test with m,n,p that small. If your dimensions are truly that size, you should be thinking about vectorizing across the different batches of b.
Mark Whirdy
Mark Whirdy 2014년 8월 27일
[4000,10,2,2] is the real size

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Matt J
Matt J 2014년 8월 27일
편집: Matt J 2014년 8월 27일
If you can re-organize the code that generates b so that, without using permute() , it is instead 2 x m x n x p , that would be ideal. You can then do it all by straight matrix multiplication
result=squeeze( y0.'*reshape(b,2,[]) );

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