On 3/6/2011 12:20 AM, Dima Kogan wrote:
>
> It seems that the current implementation of PDL::MatrixOps::svd has a
> bug where rank-deficient matrices can produce a non-unitary singular
> vector matrix:
>
> pdl> p $x
>
> [
> [1 2 3]
> [4 5 6]
> [4 5 6]
> ]
>
> pdl> ($u,$s,$v) = svd($x)
>
> pdl> p $u
>
> [
> [ 0.28303265 0.95911028 -4.0699249e-10]
> [ 0.67819338 -0.2001343 -9.7522246e-10]
> [ 0.67819338 -0.2001343 -9.7522246e-10]
> ]
>
> pdl> p $s
> [ 12.936563 0.80332812 3.9580815e-19]
> pdl> p $v
>
> [
> [ 0.44127483 -0.79913069 0.40824829]
> [ 0.56800242 -0.10347264 -0.81649658]
> [ 0.69473 0.59218541 0.40824829]
> ]
>
>
> We see that $u has a column of 0s, which is wrong. Here
>
> $x == $u x stretcher($s) x $v->transpose
>
> is still true despite the wrong $u because the associated singular
> value is 0 (as it should be). PDL has 2 other implementations of the
> SVD that do NOT have this issue: PDL::LinearAlgebra::{msvd,mdsvd}.
> These seem to call LAPACK directly. Is this a bug worth fixing? Should
> the non-LAPACK SVD method simply be deprecated and removed? Is there a
> reason multiple SVD implementation exist in parallel?
I don't appear to have PDL::LinearAlgebra in my PDL
version 2.4.7_010 so I'm, not sure to what you are
referring as far as SVD implementations.
Bug fixes are preferred unless there is an option
that is available for *all* PDL users. I see no
documentation for PDL::LinearAlgebra is the latest
PDL distribution so a working svd decomp in PDL::MatrixOps
would be of use to me....
--Chris
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