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https://issues.apache.org/jira/browse/MATH-1053?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13813240#comment-13813240
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Sean Owen commented on MATH-1053:
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As a more conservative change for now, it could merely reject a tall matrix
with an exception, and document this. That would probably be nicer than the
current DimesnionMismatchException.
> 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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