Perform "outer product" of 2-D matrix and return a 3-D array in MATLAB -

i operation on 2-d matrix somehow looks outer product of vector. have written codes task, pretty slow, know if there can accelerate it.

i show code wrote first, followed example illustrate task wanted do.

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my code, version row-by-row

function b = outer2d(a)     b = zeros(size(a,1),size(a,2),size(a,2)); %pre-allocate output array     j = 1 : size(a,1)         b(j,:,:) = transpose(a(j,:))*a(j,:); %perform outer product on each row of , assign j-th layer of b     end end 

using matrix = randn(30000,20) input testing, spends 0.317 sec.

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my code, version page-by-page

function b = outer2d(a)     b = zeros(size(a,1),size(a,2),size(a,2)); %pre-allocate output array     j = 1 : size(a,2)         b(:,:,j) = repmat(a(:,j),1,size(a,2)).*a; %evaluate b page-by-page     end end 

using matrix = randn(30000,20) input testing, spends 0.146 sec.

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example 1

a = [3 0; 1 1; 1 0; -1 1; 0 -2]; %a input matrix. b = outer2d(a); disp(b) 

then expect

(:,:,1) =       9     0      1     1      1     0      1    -1      0     0   (:,:,2) =       0     0      1     1      0     0     -1     1      0     4 

the first row of b, [9 0; 0 0], outer product of [3 0], i.e. [3; 0]*[3 0] = [9 0; 0 0].

the second row of b, [1 1; 1 1], outer product of [1 1], i.e. [1; 1]*[1 1] = [1 1; 1 1].

the third row of b, [1 0; 0 0], outer product of [1 0], i.e. [1; 0]*[1 0] = [1 0; 0 0].

and same remaining rows.

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example 2

a =  0   -1  -2 0   1   0 -3  0   2 0   0   0 1   0   0  b = outer2d(a) disp(b) 

then, similar example 1, expected output is

(:,:,1) =  0     0     0  0     0     0  9     0    -6  0     0     0  1     0     0   (:,:,2) =  0     1     2  0     1     0  0     0     0  0     0     0  0     0     0   (:,:,3) =  0     2     4  0     0     0 -6     0     4  0     0     0  0     0     0 

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because real input in project in size of 30000 × 2000 , task performed many times. acceleration of task quite essential me.

i thinking of eliminating for-loop in function. may have opinions on problem?

with auto expansion:

function b = outer2d(a)     b=permute(permute(a,[3 1 2]).*a',[2 3 1]); end 

without auto expansion:

function b = outer2dold(a)     b=permute(bsxfun(@times,permute(a,[3 1 2]),a'),[2 3 1]); end