mrdivide for sparse blockdiagonal matrices

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Frank 2011-9-2

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https://ww2.mathworks.cn/matlabcentral/answers/15030-mrdivide-for-sparse-blockdiagonal-matrices

when computing A/B where A and B are sparse block diagonal and have the same block structure, does it matter in terms of computation time whether to:

1. construct A and B as sparse matrices, and then compute C=A/B 2. for each block i, compute C_i=A_i/B_i, store them in a cell Ccell, and then define C=blkdiag(Ccell{:})

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Answer 1

Fangjun Jiang 2011-9-3

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I don't know. You could write a test to find out. From the code below, it seems that as N grows, approach 2 is faster.

N=20;
a=cell(N,1);
b=cell(N,1);
for k=1:N
    a{k}=rand(k);
    b{k}=rand(k);
end
t1=0;t2=0;
for k=1:100
    tic;
    A=blkdiag(a{:});
    B=blkdiag(b{:});
    C=A/B;
    t1=t1+toc;
      tic;
      d=cell(N,1);
      for j=1:N
          d{j}=a{j}/b{j};
      end
      D=blkdiag(d{:});
      t2=t2+toc;
  end
  fprintf('time for approach 1: %f\n',t1);
  fprintf('time for approach 2: %f\n',t2);
time for approach 1: 0.503683
time for approach 2: 0.129935