Matlab - Multiplying a matrix with every matrix of a 3d matrix - matlab

Question

I have two matlab questions that seem closely related.
I want to find the most efficient way (no loop?) to multiply a (A x A) matrix with every single matrix of a 3d matrix (A x A x N). Also, I would like to take the trace of each of those products.
http://en.wikipedia.org/wiki/Matrix_multiplication#Frobenius_product
This is the inner frobenius product. On the crappy code I have below I'm using its secondary definition which is more efficient.
I want to multiply each element of a vector (N x 1) with its "corresponding" matrix of a 3d matrix (A x A x N).
function Y_returned = problem_1(X_matrix, weight_matrix)
% X_matrix is the randn(50, 50, 2000) matrix
% weight_matrix is the randn(50, 50) matrix
[~, ~, number_of_matries] = size(X_matrix);
Y_returned = zeros(number_of_matries, 1);
for i = 1:number_of_matries
% Y_returned(i) = trace(X_matrix(:,:,i) * weight_matrix');
temp1 = X_matrix(:,:,i)';
temp2 = weight_matrix';
Y_returned(i) = temp1(:)' * temp2(:);
end
end
function output = problem_2(vector, matrix)
% matrix is the randn(50, 50, 2000) matrix
% vector is the randn(2000, 1) vector
[n1, n2, number_of_matries] = size(matrix);
output = zeros(n1, n2, number_of_matries);
for i = 1:number_of_matries
output(:, :, i) = vector(i) .* matrix(:, :, i);
end
output = sum(output, 3);
end

Answer 1

I assume you mean element-wise multiplication:
Use bsxfun:
A = 10;
N = 4;
mat1 = randn(A,A);
mat2 = randn(A,A,N);
result = bsxfun(#times, mat1, mat2);
Use bsxfun with permute to align dimensions:
A = 10;
N = 4;
vec1 = rand(N,1);
mat2 = randn(A,A,N);
result = bsxfun(#times, permute(vec1,[2 3 1]), mat2);