how to solve diagonal matrix of each page of a 3D vector ? pagediag?

There is a 3D vector A, it has 100 pages, each page is a 1×20 vector. I want to solve diagonal matrix of each 1×20 vector.

A=rand(1,20,100);

for k=1:100

B(:,:,k)=diag(A(:,:,k));

end

B is a 20×20×100 matrix.

I'm trying to vectorize this expression, is there a matlab function maybe called 'pagediag' that can solve B=pagediag(A) ?

[Matt J]

I am concerned about why you think you need a pagediag.If you plan to use it in conjunction with pagemtimes to scale the rows or columns of a stack of matrices, it's the wrong approach.

Answer 1

[Matt J]

A=rand(1,4,3)

A = 
A(:,:,1) =

    0.0986    0.2790    0.2407    0.2268


A(:,:,2) =

    0.4894    0.0108    0.5699    0.2451


A(:,:,3) =

    0.5105    0.6127    0.1543    0.3238

[~,n,p]=size(A);

B=zeros(n^2,p);
B(1:n+1:end,:)=reshape(A,n,p);
B=reshape(B,n,n,p)

B = 
B(:,:,1) =

    0.0986         0         0         0
         0    0.2790         0         0
         0         0    0.2407         0
         0         0         0    0.2268


B(:,:,2) =

    0.4894         0         0         0
         0    0.0108         0         0
         0         0    0.5699         0
         0         0         0    0.2451


B(:,:,3) =

    0.5105         0         0         0
         0    0.6127         0         0
         0         0    0.1543         0
         0         0         0    0.3238

Answer 2

[Bruno Luong]

[~,n,p] = size(A);
[J,K] = ndgrid(1:n,1:p);
B = accumarray([J(:) J(:) K(:)], A(:), [n,n,p]);

Answer 3

[shobun]

A.*eye(20)

[Bruno Luong]

@shobun please read the question.

This answer is not appriopriate. The question is how to build diagonal matrix from multiple vectors of diagonal.

[shobun]

A=rand(1,3,5)

A = 
A(:,:,1) =

    0.3838    0.7549    0.5770


A(:,:,2) =

    0.2478    0.3948    0.3644


A(:,:,3) =

    0.7509    0.8237    0.9942


A(:,:,4) =

    0.5378    0.6055    0.1165


A(:,:,5) =

    0.9689    0.1000    0.9162

diagA=A.*eye(3)

diagA = 
diagA(:,:,1) =

    0.3838         0         0
         0    0.7549         0
         0         0    0.5770


diagA(:,:,2) =

    0.2478         0         0
         0    0.3948         0
         0         0    0.3644


diagA(:,:,3) =

    0.7509         0         0
         0    0.8237         0
         0         0    0.9942


diagA(:,:,4) =

    0.5378         0         0
         0    0.6055         0
         0         0    0.1165


diagA(:,:,5) =

    0.9689         0         0
         0    0.1000         0
         0         0    0.9162

size(diagA)

ans = 1×3

3 3 5

[shobun]

I thought I got the same output, sorry if it was inappropriate.

[Bruno Luong]

Oh sorry, my fault. Your answer is appropriate.

[shobun]

Thanks!

for column vectors

A=rand(3,1,5)

A = 
A(:,:,1) =

    0.2270
    0.3032
    0.1406


A(:,:,2) =

    0.7674
    0.6613
    0.2126


A(:,:,3) =

    0.3058
    0.1203
    0.2630


A(:,:,4) =

    0.9825
    0.3091
    0.3544


A(:,:,5) =

    0.7992
    0.5751
    0.6762

diagA=eye(3).*A

diagA = 
diagA(:,:,1) =

    0.2270         0         0
         0    0.3032         0
         0         0    0.1406


diagA(:,:,2) =

    0.7674         0         0
         0    0.6613         0
         0         0    0.2126


diagA(:,:,3) =

    0.3058         0         0
         0    0.1203         0
         0         0    0.2630


diagA(:,:,4) =

    0.9825         0         0
         0    0.3091         0
         0         0    0.3544


diagA(:,:,5) =

    0.7992         0         0
         0    0.5751         0
         0         0    0.6762

[Bruno Luong]

Neat and compact syntax