Efficiently converting a 3d matrix to a 2d matrix

Hello,

I would like to convert a 3d matrix into a 2d matrix. I want the 3rd dimension to be concatenated along dimension 1 in the 2d matrix. In the code below, the variable 'desired' illustrates what I want to achieve, but I want to do it more efficiently than via a for a loop. I tried doing the same with reshape (see variable B) but can't get it to produce the output I desire.

A(:,:,1) = ones(2,2);
A(:,:,2) = 2*ones(2,2);
A(:,:,3) = 3*ones(2,2);
desired = [];
for n = 1:size(A,3)
  desired = cat(1,desired,A(:,:,n));
end
B = reshape(A,[],size(A,2),1);

Any advice would be much appreciated. Thanks for reading.

Answer 1

[the cyclist]

You can permute the 2nd and 3rd dimension before doing the reshape:

 >> C = permute(A,[1 3 2]);
 >> C = reshape(C,[],size(A,2),1)

[Andrew Newell]

Elegant!

[Mohammed Samdani]

converting 3D to 2D matrix row wise

[Salvador Pacheco-Gutierrez]

Thank you! Excelent!

[Vasileios Siomos]

Thanks a bunch this is so elegant!

[Zoe]

Save my life!

[IndikaWM]

mine too! Thank you.

[Linjun He]

Thank you!!!

[Yue Zhang]

Thank you.

[Sem Diaz]

How can you convert it back?

Answer 2

[Andrew Newell]

You can do it with cell arrays:

Acell = num2cell(A,[1 2]); % put each page of A into a cell
Acell = reshape(Acell,size(A,3),1); %make the cell array a vector
desired = cell2mat(Acell);

EDIT: the solution by @the cyclist is nicer for this particular problem, but be careful about generalizing it. For example, suppose you want to pack your matrices into a 2x2 array:

A(:,:,1) = ones(2,2);
A(:,:,2) = 2*ones(2,2);
A(:,:,3) = 3*ones(2,2);
A(:,:,4) = 4*ones(2,2);

Acell = num2cell(A,[1 2]);
Acell = reshape(Acell,2,2);
desired = cell2mat(Acell)

desired =

     1     1     3     3
     1     1     3     3
     2     2     4     4
     2     2     4     4
C = permute(A,[1 3 2]);
C = reshape(C,[],4,1)

C =

     1     3     1     3
     1     3     1     3
     2     4     2     4
     2     4     2     4

Answer 3

[Omar Mian]

Thank you Andrew & cyclist,

Both solutions work. Cyclist's permute solution is more efficient, taking approx approx 17% of the time used by the cell array solution.