Transforming matrices in a sophisticated way

[My problem]

You have three regular matrices (a1, a2, and a3), and two matrices (allR and allC), which combine the three regular matrices.

% code
a1 = [1 2 ; 3 4];
a2 = [5 6 ; 7 8];
a3 = [9 10; 11 12];
allR = [a1 a2 a3];
allC = [a1 ; a2; a3];

I need matrix transformations "from allR to allC" and "from allC to allR" in my simulation. Unfortunately, the number of regular matrices a* (a1, a2, ....., an) is not previously determined.

Is there a sophisticated way of transformations "from allR to allC" and "from allC to allR" quickly? (transpose(allR) and transpose(allC) are not appropriate solutions to my problem.) My (ugly) solution is below.

[My (ugly) solution (from allR to allC, and vice versa)]

Transformation from allR to allC:

% code
clear allC
allR = [a1 a2 a3]
[m, n] = size(allR);
maxItr = n/m;
tmpMat = allR.';
% From allR to allC
for i = 1:maxItr
    tmpMat( (m*(i-1)+1):(m*i) ,  :) = allR(:,  (m*(i-1)+1):(m*i));
end
allC = repmat(tmpMat,1)

Answer 1

[Roger Stafford]

If a1, a2, a3, ..., an are each p-by-q in size

   allC = reshape(permute(reshape(allR,p,q,n),[1,3,2]),p*n,q);
   allR = reshape(permute(reshape(allC,p,n,q),[1,3,2]),p,q*n);

[Koiti Yano]

Dear Roger, thank you for your great help! It perfectly works. Thank you, Roger, Azzi, and all. My test code is below.

% test code
a1 = [1 2 0 ; 4 3 4];
a2 = [5 6 0 ; 7 8 0];
a3 = [9 10 4; 11 0 12];
allR = [a1 a2 a3]
allC = [a1 ; a2; a3]
[p, q] = size(a1);
n = 3;
clear allC;
allC = reshape(permute(reshape(allR,p,q,n),[1,3,2]),p*n,q);
allC
clear allR;
allR = reshape(permute(reshape(allC,p,n,q),[1,3,2]),p,q*n);
allR

Answer 2

[Azzi Abdelmalek]

It's better to put your matrics inside a cell array, instead of creating a new variabl for each matrix

a{1} = [1 2 0 ; 4 3 4];
a{2} = [5 6 0 ; 7 8 0];
a{3} = [9 10 4; 11 0 12]
allR=cat(2,a{:})
allC=cat(1,a{:})

read this link http://matlab.wikia.com/wiki/FAQ#How_can_I_create_variables_A1.2C_A2.2C....2CA10_in_a_loop.3F

[Koiti Yano]

Dear Azzi, Thank you for your great suggestion! Using a cell array is a brilliant idea (I'm new to matlab).

The solution, which I am searching, is transforming matrices "form allR to allC" and "from allC to allR". Do you and others have any suggestions? Many thanks. Koiti