Multiply each element of a vector with a matrix

Question

Lars Kluken 2012-3-8

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I want to multiply each element of a vector with a matrix such that I end up with a 3D matrix (or higher dimentions).

For example if A is a vector and B is a matrix I would write:

for indx=1:length(A)
    result(:,:,indx)=A(indx).*B
end

Is for-loops the way to go here or are there any better solutions?

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Answer 1

Sean de Wolski 2012-3-8

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BSXFUN!!!

B = [1 2; 3 4];
A = 1:5;
D = bsxfun(@times,B,reshape(A,1,1,numel(A)));

kron is notorious (at least in older versions) for being very slow.

And obligatory timings:

B = repmat([1 2; 3 4],10,10);
A = 1:50;
t1 = 0;
t2 = 0;
t3 = 0;
for ii = 1:100
      tic
      C = reshape(kron(A,B),[size(B),numel(A)]);
      t1=t1+toc;
      tic
      D = bsxfun(@times,B,reshape(A,1,1,numel(A)));
      t2=t2+toc;
      tic
      for indx = length(A):-1:1  % Backwards for pre-allocation
          result(:, :, indx) = A(indx) .* B;
      end
      t3=t3+toc;
  end
  isequal(C,D,result)
  [t1 t2 t3]
%{
ans =
     1
ans =
    0.0128    0.0069    0.0098
%}

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Lars Kluken 2012-3-9

I was also wondering if there is something similar for multiplicating a 2d matrix with slices 3d matrix?

Sean de Wolski 2012-3-9

for matrix multiplication, use a for-loop or James Tursa's mtimex on the FEX.

for element by element:

bsxfun(@times,magic(3),rand(3,3,10));

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Answer 2

James Tursa 2012-3-8

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Yet another method for completeness using an outer product formulation. May not be any faster than bsxfun et al:

result = reshape(B(:)*A(:).',[size(B) numel(A)]);

(This tip actually comes from Bruno via another thread)

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Sean de Wolski 2012-3-8

Nice

Lars Kluken 2012-3-9

This is also a good solution. Sometimes a little faster than the bsxfun, and sometimes a little slower. It seems to depend on the sizes of the matrix and the vector.

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Answer 3

Friedrich 2012-3-8

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Hi,

try kron and reshape:

B = [1 2; 3 4]
A = 1:5
reshape(kron(A,B),[size(B),numel(A)])

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Jan 2012-3-8

I feel so blind without a Matlab installation. Is MESHGRID free of FOR loops now? I've read all the basic function in Matlab 4, 5.3, 6.5, 2008b, 2009a. Now I'm starting to get confused when I read them in 2011b again. It would be so nice to have a list of changes for each function...

Sean de Wolski 2012-3-8

Looking in meshgrid in 2012a it is just a series of reshapes and ones() used for indexing.

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Answer 4

Jan 2012-3-8

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Did you pre-allocate the output?

result = zeros([size(B), length(A)]);
for indx = 1:length(A)
  result(:, :, indx) = A(indx) .* B;
end

Or:

for indx = length(A):-1:1  % Backwards for pre-allocation
  result(:, :, indx) = A(indx) .* B;
end

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Lars Kluken 2012-3-8

Yes I did. In my case the for-loop is fast enough. I was just hoping for a neater solution. I never thought of backwards for-loops for pre-allocation.

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