Cells and Matrix division

Hi,

I have a problem where I want to find the solution to A*x=B

Where A is a matrix of 4x4 where each element in the matrix is of the size 1x10. B is a matrix 4x1 where each element is of the size 1x10. The x matrix should be a matrix 4x1 where each element is of the size 4x1 where each element is the size of 1x10. How can I succed with this?

If needed I can write a code with exemples of the matrices.

[Star Strider]

Simply out of curiosity, find a solution to what problem?

[Filip Wadman]

Hi I have updated it now

Answer 1

[Filip Wadman]

Hi I updated my text to make it better.

Answer 2

[DGM]

I'm still assuming you're using cell arrays, since that's the only way that the description makes sense.

I'm sure someone can whip up a more elegant solution, maybe even directly dealing with the cell array without converting it. ... but this is what I did as a simplified example.

sa = 4; % size of system
nsys = 10; % number of systems

% generate a test array (all coefficient matrixes)
A = repmat(randi([-100 100],sa,sa),[1 1 nsys]);
% rearrange to mimic the array you have
A = cellfun(@(x) permute(x,[1 3 2]),num2cell(A,3),'uniform',false)

A = 4×4 cell array
    {[95 95 95 95 95 95 95 95 95 95]}    {[100 100 100 100 100 100 100 100 100 100]}    {[          40 40 40 40 40 40 40 40 40 40]}    {[          36 36 36 36 36 36 36 36 36 36]}
    {[22 22 22 22 22 22 22 22 22 22]}    {[          39 39 39 39 39 39 39 39 39 39]}    {[          44 44 44 44 44 44 44 44 44 44]}    {[-46 -46 -46 -46 -46 -46 -46 -46 -46 -46]}
    {[43 43 43 43 43 43 43 43 43 43]}    {[-82 -82 -82 -82 -82 -82 -82 -82 -82 -82]}    {[-30 -30 -30 -30 -30 -30 -30 -30 -30 -30]}    {[          40 40 40 40 40 40 40 40 40 40]}
    {[37 37 37 37 37 37 37 37 37 37]}    {[-68 -68 -68 -68 -68 -68 -68 -68 -68 -68]}    {[          17 17 17 17 17 17 17 17 17 17]}    {[-18 -18 -18 -18 -18 -18 -18 -18 -18 -18]}

% turn it back into a regular array
A = cell2mat(cellfun(@(x) permute(x,[1 3 2]),A,'uniform',false))

A = 
A(:,:,1) =

    95   100    40    36
    22    39    44   -46
    43   -82   -30    40
    37   -68    17   -18


A(:,:,2) =

    95   100    40    36
    22    39    44   -46
    43   -82   -30    40
    37   -68    17   -18


A(:,:,3) =

    95   100    40    36
    22    39    44   -46
    43   -82   -30    40
    37   -68    17   -18


A(:,:,4) =

    95   100    40    36
    22    39    44   -46
    43   -82   -30    40
    37   -68    17   -18


A(:,:,5) =

    95   100    40    36
    22    39    44   -46
    43   -82   -30    40
    37   -68    17   -18


A(:,:,6) =

    95   100    40    36
    22    39    44   -46
    43   -82   -30    40
    37   -68    17   -18


A(:,:,7) =

    95   100    40    36
    22    39    44   -46
    43   -82   -30    40
    37   -68    17   -18


A(:,:,8) =

    95   100    40    36
    22    39    44   -46
    43   -82   -30    40
    37   -68    17   -18


A(:,:,9) =

    95   100    40    36
    22    39    44   -46
    43   -82   -30    40
    37   -68    17   -18


A(:,:,10) =

    95   100    40    36
    22    39    44   -46
    43   -82   -30    40
    37   -68    17   -18

% all b vectors as you describe
b = repmat({repmat(10,[1 nsys])},[sa 1]);
% turn it into a regular array
b = cell2mat(b)

b = 4×10

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

x = zeros(sa,nsys);
for k = 1:nsys
    x(:,k) = A(:,:,k)\b(:,k);
end
x % the answers

x = 4×10

0.4316 0.4316 0.4316 0.4316 0.4316 0.4316 0.4316 0.4316 0.4316 0.4316 0.0755 0.0755 0.0755 0.0755 0.0755 0.0755 0.0755 0.0755 0.0755 0.0755 -0.5436 -0.5436 -0.5436 -0.5436 -0.5436 -0.5436 -0.5436 -0.5436 -0.5436 -0.5436 -0.4669 -0.4669 -0.4669 -0.4669 -0.4669 -0.4669 -0.4669 -0.4669 -0.4669 -0.4669

% turn it back into an unweildy cell array??
x = num2cell(x,2)

x = 4×1 cell array
    {[          0.4316 0.4316 0.4316 0.4316 0.4316 0.4316 0.4316 0.4316 0.4316 0.4316]}
    {[          0.0755 0.0755 0.0755 0.0755 0.0755 0.0755 0.0755 0.0755 0.0755 0.0755]}
    {[-0.5436 -0.5436 -0.5436 -0.5436 -0.5436 -0.5436 -0.5436 -0.5436 -0.5436 -0.5436]}
    {[-0.4669 -0.4669 -0.4669 -0.4669 -0.4669 -0.4669 -0.4669 -0.4669 -0.4669 -0.4669]}