I have question regarding the difference between the sparse and non-sparse QR as implimented R2012b. I have a matrix, X, that is mostly zeros which I wish to upper-triangularize. Because the matrix X is formed piecemeal from several sparse multiplications, the X is sparse. The results of:
a1 = qr(X)
a2 = triu(qr(full(X)))
are completely different. The few nonzero values end up in very different places. The code is for a square root DWY backward (Fisher type) filter as in Park and Kailath 96. Based on what I know of the problem and what the answer should be, a2 is correct (or at least I know a1 is incorrect because what should be the multiplication of 2 nonzero submatrices is zero in a1 but not a2).
Does anyone know why the two are different? Further is there a way to force qr(X) to produce the same result as triu(qr(full(X))) without resorting to the full() call?