How to simplify the for loop for 3D matrix?

I have the following code, where I am looking to eliminate only the outer for-loop (k) and include 'k' inside the inner loop. Here, I perform inverse considering each calculation point (k=1:NFocP) in a loop, but would like to some how eliminate outer loop and perform the inverse for all points at one instance. And the other concern is that I don't want to disturb the mldivide (\) function. Is there any way to solve this issue?

clear all;

load A.mat
load s1.mat
load s2.mat

Foc = size(s1,3); % no of calculation points
Nt = size(s1,2); % length of signal
M = size(s1,1); % no of rsensors

for k=1:Foc
    for p = 1:Nt
        H = [s1(:,p,k) s2(:,p,k)];
        tmp = H\ A(:,p);
        Ainv1(k,p) = tmp(1); 
        Ainv2(k,p) = tmp(2);
    end
end

[Benjamin Thompson]

That would require calculating an inverse of a 3D matrix for H which is not possible. You may be able to use foreach to speed up the code by doing the outer loops in parallel.

[Kalasagarreddi Kottakota]

Attached H and A1

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 A1 using mldivide so that output looks like 2 x 1 x14 matrix. No loops. Is this possible?

clear all;
close all;

load H.mat
load A1.mat

Answer 1

[Bruno Luong]

load('A.mat');
load('s1.mat');
load('s2.mat');

[m,n,p] = size(s1);

% s = [reshape(s1, [m,1,n,p]),  reshape(s2, [m,1,n,p])];
% Ar = reshape(A,m,1,[]);
% C=pagemldivide(s,Ar);
% Ainv1=reshape(C(1,:,:),n,p).';
% Ainv2=reshape(C(2,:,:),n,p).';

s = reshape([s1;s2], [m,2,n,p]);
Ainv1 = zeros(p,n);
Ainv2 = zeros(p,n);
for i=1:n
    C=pagemldivide(s(:,:,i,:),A(:,i));
    Ainv1(:,i)=C(1,:);
    Ainv2(:,i)=C(2,:);
end

[Kalasagarreddi Kottakota]

Thanks Bruno, my matlab says 'Unrecognized function or variable 'pagemldivide'.' May I know if I need to install specific tool box for pagemldivide function.

[Bruno Luong]

You need R2022a or later https://fr.mathworks.com/help/matlab/ref/pagemldivide.html

[Kalasagarreddi Kottakota]

Ok, I see now. I have 2021. Is there any possibility to replace pagemldivide with any other alternate functions to do same task?

[Bruno Luong]

You might try this that requires the FEX

https://fr.mathworks.com/matlabcentral/fileexchange/27762-small-size-linear-solver#functions_tab

[m,n,p] = size(s1);
s = reshape([s1;s2], [m,2,n,p]);
Ainv1 = zeros(p,n);
Ainv2 = zeros(p,n);
Ar = reshape(A,m,1,[]);
scs = pagemtimes(s,'ctranspose',s,'none');
scA = pagemtimes(s,'ctranspose',Ar,'none');
for i=1:n
    scsi = reshape(scs(:,:,i,:),2,2,[]);
    scAi = reshape(scA(:,:,i,:),2,1,[]);
    C = inv2(scsi, scAi); % https://fr.mathworks.com/matlabcentral/fileexchange/27762-small-size-linear-solver#functions_tab
    Ainv1(:,i)=C(1,:);
    Ainv2(:,i)=C(2,:);
end