MATLAB: Compare matrices built with repelem and repmat

Question

I have an array a of size ZxW.

Z = 20;
W = 30;
A = 40; %will be used below
size(a)
20      30

Then I apply to a two different transformations, and then after those I delete a and I cannot go back to it.

First transformation:

b = repelem(a(:,1),A,A);

Second transformation:

c = repmat(a,[1,1,A,A]);
d = c(:,1,:,:);

After those transformation and deleting a (which cannot be used for the following), I want to compare d and b using

assert( isequal(b,f) )

Where f is a transformation of d that makes the assertion true.

My first idea was a simple reshape:

    f = reshape(squeeze(d),[Z*A,A]);

Which does not work as repelem and repmat move entries differently. How can I do this?

Thanks for the attention.

Sincerely

Luca

Answer 1

The transformation

c = repmat(a, [1,1,A,A]);
d = c(:,1,:,:);

is an indirection to reproduce b.

Z = 2;
W = 3;  
A = 4;  % Smaller to check the output manually
a = rand(Z, W);
b = repelem(a(:,1),A,A);
c = reshape(repmat(a(:,1).', [A, A]), Z*A, A);
isequal(b, c)

But if you really want

c = repmat(a, [1,1,A,A]);
d = c(:,1,:,:);

Then:

f = reshape(permute(d, [3,1,4,2]), [Z*A,A]);
isequal(b, f)    % 1: equal