Sean Owen created MATH-1053:
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Summary: QRDecomposition.getSolver() should be able to find
pseudo-inverse of non-square matrices
Key: MATH-1053
URL: https://issues.apache.org/jira/browse/MATH-1053
Project: Commons Math
Issue Type: Bug
Affects Versions: 3.2
Reporter: Sean Owen
Priority: Minor
Attachments: MATH-1053.patch
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.
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