MATLAB: Sparse Block Matrix Construction

matrix manipulationsparse

I want to construct a matrix that looks like

X = [0, A,
     B, 0]

Where the A and B blocks are, in themselves, sparse matrices. I already have code for generating the A and B blocks, and I was hoping to reuse that. Is there a way I can then create the X matrix so that it is also sparse?

Best Answer

[Am,An] = size(A);
[Bm,Bn] = size(B);
X = spalloc(Am+Bm,An+Bn,nnz(A)+nnz(B));
X(Am+1:Am+Bm,1:Bn) = B;
X(1:Am,Bn+1:An+Bn) = A;

Related Solutions

MATLAB: Matrix construction

The are a few problems with your code. One is the square brackets in the expression MATRIX([cont1:p*11,cont2:q*11]). This builds a 1-D matrix which is then used as the indexing expression - not what you want. You need to give the row and column index expressions separately, so no square brackets.

Another is the arithmetic for cont1 and cont2. These get reset to 1 just before the assignment to MATRX, so they are always 1 at this point, which again isn't what you want.

Also, if you want the second SOL matrix to go in MATRIX(12:23, 1:71), you need to make the row index change fastest - that is, the row needs to change in the inner loop.

Other points: it's better to use variables to hold values of things like the matrix sizes, because then your code becomes far more flexible, and it's a good idea to preallocate the results matrix for efficiency.

Here is a version of your code that I think does what you want. Look at how cont1 and cont2 are initialised and incremented.

nr = 11;
nc = 71;
nblocksr = 9;
nblocksc = 9;
MATRIX = zeros(nblocksr*nr, nblocksc*nc);  % preallocate

cont2 = 1;
for q=1:nblocksc
    cont1 = 1;
    for p=1:nblocksr       
        SOL = rand(nr, nc);    % example only
        MATRIX(cont1:cont1+nr-1, cont2:cont2+nc-1)=SOL;
        cont1 = cont1+nr;
    end
    cont2 = cont2+nc;
end

Here's another way to do it - it's more concise because it doesn't use the extra variables but just works out where to put the results directly from the indices.

nr = 11;
nc = 71;
nblocksr = 9;
nblocksc = 9;
MATRIX = zeros(nblocksr*nr, nblocksc*nc);  % preallocate
for q=1:nblocksc
    for p=1:nblocksr       
        SOL = rand(nr, nc);    % example only    
        MATRIX((p-1)*nr+1:p*nr, (q-1)*nc+1:q*nc)=SOL;
    end
end

MATLAB: While loop construction

http://matlab.wikia.com/wiki/FAQ#How_can_I_process_a_sequence_of_files.3F

But remember that by default plot() will clear all previous plots in the axis, so you will either want to subplot() or figure() or "hold on"

Best Answer

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MATLAB: Matrix construction

MATLAB: While loop construction

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