How to perform inverse between a page of a 3D matrix and a column vector without loops?

The matrix H looks like 9 x 2 x 14 and matrix A1 is 9 x1. I need to perform inversion between every page of H with A using mldivide so that output looks like 2 x 1 x14 matrix. No loops.

clear all;
close all;

load H.mat
load A1.mat
 

Answer 1

[Steven Lord]

Why do you insist to do this without looping? If you have been told "for loops in MATLAB are slow" that is not necessarily the truth anymore.

But in this particular case it is possible to use pagemldivide to accomplish this task.

Answer 2

[Kevin Holly]

load H.mat
load A1.mat

size(H)

ans = 1×3

9 2 14

size(A1)

ans = 1×2

9 1

answer = H.\A1;
size(answer)

ans = 1×3

9 2 14

[Kalasagarreddi Kottakota]

Hi,

Thanks for the reply.

But It looks wrong, as the output should be 2 x 1 x 14. Every page of H is 9 x 2 and A1 is 9 x 1. So when inverse is made it boils down to 2 x 1 . So therefore the output matrux looks like 2 x 1 x 14.

[Kevin Holly]

Ah, I see. I misread the output. So, you need to vectorize this:

load H.mat
load A1.mat

size(H)

ans = 1×3

9 2 14

size(A1)

ans = 1×2

9 1

for ii = 1:size(H,3)
answer(:,:,ii) =H(:,:,ii)\A1;
end

size(answer)

ans = 1×3

2 1 14

[Kalasagarreddi Kottakota]

Hi Kelly,

The output is correct, but I dont want to use a loop. Is there any possibility without looping?