[MATH-1053] QRDecomposition.getSolver() should be able to find pseudo-inverse of non-square matrices

• Type: Improvement
• Status: Closed
• Priority: Minor
• Resolution: Fixed
• Affects Version/s: 3.2
• Fix Version/s: 3.3
• Assignee: Unassigned
• Reporter: Sean R. Owen
• Created: 02/Nov/13 11:55
• Updated: 19/May/14 15:13
• Resolved: 21/Feb/14 13:19

Description

I don't have a complete solution to this, so don't commit this as-is, but posting in case someone can get it over the line.

If you process a tall m x n matrix (non-square, m>n) with QRDecomposition and then call getSolver().getInverse(), you will get DimensionMismatchException. There's not a good reason the QR decomposition can't compute the least-squares solution here.

The issue is that it tries to invert A by solving AX = I. The dimension of I has to match the row dimension of A, or m. However it's using the length of the diagonal of R, which is min(m,n), which is n when m>n.

That patch is simple and is part of the attached patch. It also includes a test case for a tall matrix.

However it doesn't work for a fat matrix (m<n). There's a test case for that too. It returns an n x m value but the rows for i >= m are 0 and are not computed. I'm not sure enough about the shape of the computation to be able to fix it, but it is where it's solving the triangular system Rx = y.