Should SVD should return U,S,V' or U,S,V

[ViralBShah]

LAPACK returns V', which is what julia returns currently. Should it return V instead? Unless there is a clear reason, I would prefer not doing the extra transpose in svd.

[ViralBShah]

cc @alanedelman

[timholy]

For reasons of performance and Matlab compatibility, I vote with keep the current behavior.

Matlab:

help svd
svd Singular value decomposition.
[U,S,V] = svd(X) produces a diagonal matrix S, of the same
dimension as X and with nonnegative diagonal elements in
decreasing order, and unitary matrices U and V so that
X = U_S_V'.

(They really should have named that matrix Vt or Vp in their documentation!)

[JeffBezanson]

No, matlab does it the other way. We return V', while matlab returns V such that X=U*S*V'.

[timholy]

Ah. Thanks for explaining.

In general I'm in favor of doing less (i.e., return whatever LAPACK gives us), but the Matlab compatibility would be an issue for people migrating over.

[StefanKarpinski]

I think we should do the Matlab-compatible version even though I generally find it annoying. It's also the more mathematically correct form since that's how the factorization is always written (so that U and V are both column-orthonormal, rather than V being row-orthonormal). It's kind of annoying though since I frequently transpose V immediately.

[StefanKarpinski]

I propose that we define svdt that returns V' and for now we can define svd in terms of that.

[timholy]

I like it.

[JeffBezanson]

But we may end up modifying lapack, in which case we won't be able to compute both svd and svdt efficiently. And if multiplication by the transpose is wanted we're better off writing X*V' so we make the right BLAS call.

[alanedelman]

i like stephan's answer
and i'm hoping we realize that this is a minor alternative
to lapack
i suspect 10 minutes of thought would convince us we have to multiply
householders right to left instead of left to right, but i haven't given it
the five minutes of thought

On Fri, Jul 6, 2012 at 4:48 AM, Jeff Bezanson <
reply@reply.github.com

wrote:

But we may end up modifying lapack, in which case we won't be able to
compute both svd and svdt efficiently. And if multiplication by the
transpose is wanted we're better off writing X*V' so we make the right
BLAS call.

---

Reply to this email directly or view it on GitHub:
#912 (comment)

[StefanKarpinski]

The X*V' doesn't actually need a transpose in any case. When/if we modify LAPACK for this, we can either just implement svd in terms of svdt, or allow a stride parameter in the outputs, or have two different routines.

[ViralBShah]

Decision is to have svd and svdt. Tests will then need to be updated, and we should ensure the same is done for svds.

[StefanKarpinski]

To clarify svd returns (U,S,V) like Matlab and svdt returns (U,S,V') like LAPACK. That means that svd does a transpose even though it doesn't return V transposed.

[ViralBShah]

Closed by commit afcace2