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

Question

Kalasagarreddi Kottakota 2023-1-11

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https://ww2.mathworks.cn/matlabcentral/answers/1892270-how-to-perform-inverse-between-a-page-of-a-3d-matrix-and-a-column-vector-without-loops

回答： Steven Lord 2023-1-11

A1.mat
H.mat

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
 

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Answer 1

Steven Lord 2023-1-11

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https://ww2.mathworks.cn/matlabcentral/answers/1892270-how-to-perform-inverse-between-a-page-of-a-3d-matrix-and-a-column-vector-without-loops#answer_1146560

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.

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Answer 2

Kevin Holly 2023-1-11

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https://ww2.mathworks.cn/matlabcentral/answers/1892270-how-to-perform-inverse-between-a-page-of-a-3d-matrix-and-a-column-vector-without-loops#answer_1146525

编辑：Kevin Holly 2023-1-11

在 MATLAB Online 中打开

H.mat
A1.mat

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

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Kevin Holly 2023-1-11

在 MATLAB Online 中打开

A1.mat
H.mat

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