Extract elements of each cell to form a matrix and store it. Can anyone give me suggestions?

Hi,

I have a cell array of 4*4 size, each cell has a vector of 10 elements.

{0×0 double} {10×1 double} {10×1 double} {10×1 double}

{0×0 double} {0×0 double} {10×1 double} {10×1 double}

{0×0 double} {0×0 double} {0×0 double} {10×1 double}

{0×0 double} {0×0 double} {0×0 double} {0×0 double}

I want to extract individual elements of the cell sequentially and form a matrix like in the following. How can I form the matrix, A_1? Can you help me?

A_1 is a matrix consist of first element of each cell (as follows)=

0 x1 x2 x3

0 0 y1 y2

0 0 0 z3

0 0 0 0 ]; then the 2nd element of of every cell will form another 4*4 matrix=A_2,

3rd element of every cell will form 4*4 matrix=A_3,.....and so on up to A_10. With these A_1, A_2,...,A_10 matrices, I want to add its transpose+ Identity matrix(i.e. eye(4)). Finally, it should be like this

FullMatrix(1) = A_1+A_1(transpose)+eye(4)=

1 x1 x2 x3

x1 1 y1 y2

x2 y1 1 z3

x3 y2 z3 1;

FullMatrix(2), FullMatrix(3),......,FullMatrix(10). I've tried but failed to do it. Your support is highly appriciate. Thanks & Regards, sa

Answer 1

[DGM]

This is what I did:

% build test array
a = [1 2 3 4].';
b = [2 3 4 5].';
c = [5 4 4 5].';
d = [7 3 4 5].';
e = [1 3 4 5].';
f = [9 7 6 5].';
CC = {0 a b c;
      0 0 d e;
      0 0 0 f;
      0 0 0 0};

% these are the indices of triu for 4x4
idx = [5 9 10 13 14 15];
% make sure vectors share the same orientation
% this may or may not be necessary depending on how CC is made
CC = cellfun(@(x) x(:),CC,'UniformOutput',false);
% extract just the nonzero part of CC
C = [CC{idx}];

% build the outputs
A1 = zeros(4,4);
A1(idx) = C(1,:)

A2 = zeros(4,4);
A2(idx) = C(2,:)
% ... and so on

At that point, you can do whatever you want with A1, A2, etc.

[SA]

@DGM, Thanks for your support. However, I've 2 questions:

1. How to choose triu of a big matrix of size 16*16 or 32*32? I mean manually (e.g. above) or any other ways?
2. How to save these matrix A1,A2,....A10? Thanks & grateful/sa

[DGM]

For a bit more generalization

% build test array
a = [1 2 3 4].';
b = [2 3 4 5].';
c = [5 4 4 5].';
d = [7 3 4 5].';
e = [1 3 4 5].';
f = [9 7 6 5].';
CC = {0 a b c;
	  0 0 d e;
	  0 0 0 f;
	  0 0 0 0};
 
% this is a logical mask of triu for any size
s = size(CC); 
mask = triu(true(s),1); 
% extract just the nonzero part of CC
CC = cellfun(@(x) x(:),CC,'UniformOutput',false);
C = [CC{mask}];

% build the outputs as a single 3D array instead of
% having a bunch of loose numbered variables
A = zeros([s size(C,1)]);
thispage = zeros(s);
for p = 1:size(C,1)
	thispage(mask) = C(p,:);
	A(:,:,p) = thispage;
end
% A1-An are now pages of A
A

% use them how you want
% if you don't need A for anything else, you could
% just do this while building the pages of A, i.e.
% A(:,:,p) = thispage + thispage.' + eye(s)
B = A(:,:,1) + A(:,:,1).' + eye(s)

It depends what you mean when you say "save these matrices". If you need to save them to disk, you can use save()

save('mydata.mat','A')

and then load it using load().

S = load('mydata.mat') % load into a struct
A = S.A; % explicitly allocate the desired variable

[SA]

It works well. Your effort is highly acknowledged. Like this piece of code.