Array multiplication along certain dimension?

I have a 4-D array with dimensions A = A1 x A2 x A3 x N and a vector with dimensions V = 1 x N. I would like to multiply each element in the array A with vector V along fourth dimension and take a sum along the same dimension to form a matrix B = A1 x A2 x A3. Currently I am using a loop to achieve this, but is there any faster method to achieve the same result? Thanks!

A1 = 3;
A2 = 3;
A3 = 3;
N = 10;

A = ones(A1, A2, A3, N);
V = ones(1, N);
B = NaN(A1, A2, A3);

for i = 1:A1
for j = 1:A2
for k = 1:A3
  B(i,j,k) = squeeze(A(i,j,k,:))' * V';
end
end
end

Answer 1

[David Goodmanson]

Hi Visa,

This seems to work

A1 = 2;
A2 = 3;
A3 = 4;
N =  7;

A = rand(A1, A2, A3, N);
V = rand(1, N);

% ---- method 1

B1 = NaN(A1, A2, A3);

for i = 1:A1
  for j = 1:A2
    for k = 1:A3
      B1(i,j,k) = squeeze(A(i,j,k,:))' * V';
    end
  end
end

% ---- method 2

D = permute(A,[4 1 2 3]);
E = reshape(D,N,A1*A2*A3);
F = V*E;
B2 = reshape(F,A1,A2,A3);

max(max(max(max(abs(B1-B2)))))     ans = 8.8818e-16

[Visa Suomi]

Hi David,

That works great. Thank you!

Answer 2

[James Tursa]

Another way:

B = sum(bsxfun(@times,A,reshape(V,1,1,1,numel(V))),4);

Or in later versions of MATLAB:

B = sum(A.*reshape(V,1,1,1,numel(V)),4);

[Visa Suomi]

Thanks, they work with smaller grids, but I encounter memory problems with my array sizes with these functions. My array A = 120 x 132 x 132 x 120.