MATLAB: Create sparse matrix with zig-zag diagonal

diag sparse shift rows down

Is there a way to shift every column c by (c-1)*n rows down, where n is size(A,1) in the following example, without a loop and without excessive memory usage? So to get
   A = [
      a11 a12 a13 a14 ...
      a21 a22 a23 a24 ...
      ... ... ... ... ...
   ]
to read
    B = [
       a11   0   0   0 ...
       a21   0   0   0 ...
       ... ... ... ... ...
         0 a12   0   0 ...
         0 a22   0   0 ...
       ... ... ... ... ...
         0   0 a13   0 ...
         0   0 a23   0 ...
       ... ... ... ... ...
         0   0   0 a14 ...
         0   0   0 a24 ...
       ... ... ... ... ...
   ]
I tried diag and sparse with no luck so far. I need Matrix A in an operation X=J\A afterwards. It is crucial that the zero elements do not consume memory as A can have up to 20e6 columns and probably 10 rows.
Thanks in advance.

Best Answer

You could use sparse(), building appropriate vectors of indices and values, e.g.:
 nCol = size(A, 2) ;
 nRow = nCol * size(A, 1) ;
 I = (1:nRow).' ;
 J = reshape(repmat(1:nCol, size(A, 1), 1), [], 1) ;
 B = sparse(I, J, A(:), nRow, nCol) ;
(that you can write in two lines actually, but I wanted to keep it clear)
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