Can you index matrices?

Suppose I have a (n x p) matrix M. Can a "for" loop be written to partition M into a set of smaller matrices A_i where A_1 = the first r_1 rows of M, A_2 = the next r_2 rows of M, A_3 = the next r_3 rows of M,........., A_k = the last r_k rows of M where k<=n ?

I know I can index into M easily with A(i,j) being the element corresponding to the i'th row and j'th column of M. What I want to do is "pull out'' matrices from M: A_1, A_2, A_3, .... , A_k as described above. I don't want to define each matrix manually however as I would have to define thousands of sub matrices A_i !

Any help would be greatly appreciated.

Jonathan

[Image Analyst]

These sentences seem contradictory: "What I want to do is "pull out'' matrices from M: A_1, A_2, A_3, .... , A_k as described above. I don't want to define each matrix manually however" So do you want separate matrices (A_1, A_2, etc.), or separate cells in a cell array (A{1}, A{2}, etc.) or not? I can tell from what you said. You said you do but in the next sentence you said you don't.

[Cedric]

The way I understood it is that he doesn't want to write manually expressions like:

 A_1 = [M(1,1),M(1,2),M(1,3); M(2,1),M(2,2),M(2,3)] ;
 ...

Answer 1

[Cedric]

The following:

 M(5:8, 3:7)

is an array that corresponds to the block defined by rows 5 to 8 of M and columns 3 to 7. As these ranges can be defined by vectors/arrays content, you can build flexible solutions for block-indexing M.

 rIds = ... ;           % rIds and cIds could be defined as a function of a loop
 cIds = ... ;           % index variable, e.g. based on vectors of block 
                        % boundaries in terms of row IDs and column IDs:
                        % rIds = rBoundaries(ii):rBoundaries(ii+1) ; ..
 block = M(rIds, cIds) ;

If you wanted your blocks to be stored separately in a cell arrays, you could use the function mat2cell(). It would take M as a first arg and essentially the two vectors of block boundaries mentioned above as second/third args.

[Jonathan Ross]

Thank you Cedric. Just what I needed. I wasn't aware of the mat2cell function in Matlab.