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From "Sean Owen (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-1053) QRDecomposition.getSolver() should be able to find pseudo-inverse of non-square matrices
Date Mon, 04 Nov 2013 20:40:18 GMT

    [ 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:
---------------------------------

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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