bug in svd() and work-around

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Hi,

I find PDL very useful in my work. Thanks!

I noticed that svd (Singular Value Decomposition) does not work properly
when there is only one row or one column in the input matrix. Attached
is a little wrapper "mysvd.pl" that I use to work around this bug.

When I say "does not work properly", what I mean is that it should
always be possible to reconstruct the input matrix from its SVD. That
is, given an input matrix $mat, we should be able to make an identical
matrix $matcopy from the SVD of $mat, as follows:

       ($u, $s_diag, $v) = svd($mat)
       $s = zeroes($v)
       $s->diagonal(0,1) .= $s_diag
       $vt = transpose($v)
       $matcopy = $u x $s x $vt
 
This assumes:

       $mat    = m rows x n columns
       $u      = m rows x n columns
       $s_diag = n elements
       $s      = n rows x n columns
       $v      = n rows x n columns

With the current svd routine in PDL, $matcopy does not equal $mat when
there is only one row or column in $mat.

Best wishes,
Peter.

mysvd.pl
Description: Perl program