Creating a 3 dimensional matrix from a matrix and vector in MATLAB

Question

I have a matrix A of size pxp and a vector y = [y1,y2,...,yn] .

What do I want to do is to create a 3 dimensional matrix of size pxpxn , that is, it contains n bands where each one is of size pxp .

How each band is created?:

Each band is equal to the matrix A multiplied by one value in y . For example, the first band is A * y1 , the second band is A * y2 . On the other hand, the band number i , where i = 1, ..., n , is equal to A * yi

Well, this can be easily done using a for loop, but this is trivial and expensive in computation. How can I prevent using a for loop? Is there any very fast automatic method that can directly create the 3-D matrix?

Any help will be very appreciated.

Answer 1

You can use bsxfun to multiply your pxp matrix by each value in y . We must reshape y to be 1 x 1 xn though so that the multiplication creates a third dimension.

out = bsxfun(@times, A, reshape(y, 1, 1, []));

If you're on R2016b or newer (when MATLAB introduced implicit broadcasting), you can replace bsxfun with simply .*

out = A .* reshape(y, 1, 1, []);