# Efficient way to multiply a vector of size (Nx,1) with a matrix of size (Nx+1,Nx+1)

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Matthew Kehoe on 28 Jul 2021
Commented: the cyclist on 29 Jul 2021
My code repeatedly computes a vector of size (Nx,1) by a matrix of size (Nx+1,Nx+1):
clc; clear all;
Nx = 32;
a = 1.5;
b = 2;
gamma = rand(Nx,1);
D = rand(Nx+1,Nx+1);
D2 = D*D;
identy = eye(Nx+1,Nx+1);
% Computation performed by my code millions of times
for j=1:Nx
A = a*D2 + b*D + gamma(j)*identy;
% Can gamma(j)*identy be avoided through vectorization or a faster
% technique?
end
Is there an alternative way to compute A without using the for loop (would vectorization or repmat also work)?
##### 2 CommentsShowHide 1 older comment
Matthew Kehoe on 28 Jul 2021
Edited: Matthew Kehoe on 28 Jul 2021
I agree @Matt J. I didn't want to ask about all of my code (as it might have appeared to be a difficult question) so I only asked about a small portion of my code. This might have been a mistake. The answer provided by the cyclist has helped me fix/improve my own code significantly.

the cyclist on 28 Jul 2021
If you permute gamma to be a vector along the dimension 3, then you can multiply it by identy, and the result will be a 33x33x32 array, where each "slice" along dimension 3 is the multiple with the corresponding value of gamma.
So, this calculation will do all of the calculations of your for loop (and store them all, rather than overwriting as your code does).
A = a*D2 + b*D + permute(gamma,[3,2,1]) .* identy;
You may now have a memory problem, though, if your arrays are large.
the cyclist on 29 Jul 2021
That's fine, but if the question is self-contained, it might be better to open a new one, because it might get wider exposure.
You can always tag me as you did in your comment, and I will get a notification.

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