— Loadable Function: r = spqr (a)
— Loadable Function: r = spqr (a,0)
— Loadable Function: [c, r] = spqr (a,b)
— Loadable Function: [c, r] = spqr (a,b,0)

Compute the sparse QR factorization of a, using CSparse. As the matrix Q is in general a full matrix, this function returns the Q-less factorization r of a, such that r = chol (a' * a).

If the final argument is the scalar 0 and the number of rows is larger than the number of columns, then an economy factorization is returned. That is r will have only size (a,1) rows.

If an additional matrix b is supplied, then spqr returns c, where c = q' * b. This allows the least squares approximation of a \ b to be calculated as

          [c,r] = spqr (a,b)
          x = r \ c
     

See also: spchol, qr.