speed up a matlab code by replacing inv(X)*Y with X\Y in 3D dimensions

hi,

I want to speed up my code by replacing inv(X)*Y with X\Y. The main issue is that X is a 3D matrix. In details, i have the following matrixes:

A = 380; B = 380; C = 200; D=1;

X = rand(A,B,C) +1i*rand(A,B,C); X2 = zeros(A,B,C);

tic;

for m=1:C

    X2(:,:,m) = inv(X(:,:,m));

end

toc; % inverting the matrix X costs about 4.44 ~ 4.74 sec

Y = rand(A,1) + 1i*rand(A,1);

Z = reshape(reshape(permute(X2, [2 1 3]), [A B*C]), [B A*C]).' * Y;

Z = permute(reshape(Z.',[D A C]),[2 1 3]);

Output = zeros(A,C);

Output(:,:) = Z(:,1,:);

Basically i'm doing Z = inv(X)*Y on a 3D scale, Is there any simpler way to skip the for loop and use \ inside the Z= line without the need of X2=inv(X) and for ??

X, Y, X2 and Z are complex matrixes

Thanks in advance.

[Jan]

Please format your code properly.

Answer 1

[Andrei Bobrov]

A = 380; 
B = 380; 
C = 200;
X = rand(A,B,C) + 1i*rand(A,B,C);
Y = rand(A,1) + 1i*rand(A,1);
Z = zeros(A,C);

for m=1:C
   Z(:,m) = X(:,:,m)\Y;
end

Answer 2

[Sean de Wolski]

Please look into Tim Davis' comments/solutions here: Loren:Purpose of Inv

Answer 3

[Jan]

See also:

• FEX: factorize
• FEX: 2d-slice-for-arbitrary-multi-dimension-array
• FEX: mmx
• FEX: mtimesx