call BLAS syrk for A'*A

[ViralBShah]

1. Add the matrix cross product to cross
2. Add the transposed version tcross
3. Add crossprod and tcrossprod aliases
4. Make cross and tcross use the BLAS function dsyrk wherever possible

https://groups.google.com/forum/?hl=en&fromgroups#!searchin/julia-dev/dsyrk/julia-dev/1f-QaxYPdNY/V7qkrnBsqTIJ

[dmbates]

Overloading the name cross may not be the best choice in that the current meaning as the cross-product of 3-dimensional vectors is quite different from the X'*X operation. In the one case it is a binary operation producing a 3-vector from two other 3-vectors and in the other case it takes one m by n matrix and produces an n by n positive semidefinite symmetric matrix.

[ViralBShah]

Oh, I didn't realize that. In that case, we should just have crossprod. Note, that julia already optimizes A'_B by calling the appropriate dgemm routine, but I am not sure if we detect A'_A. I don't think so.

@JeffBezanson In the AtB operator, can we check somehow if A and B are the same objects and call a different BLAS function?

@dmbates If julia can do A'_B, A_B', A'_B', A'_A, A*A' the right way calling BLAS directly, would you still want crossprod() and tcrossprod()?

[JeffBezanson]

Yes you can test is(x,y)
On Apr 2, 2012 10:47 AM, "Viral B. Shah" <
reply@reply.github.com>
wrote:

Oh, I didn't realize that. In that case, we should just have crossprod.
Note, that julia already optimizes A'_B by calling the appropriate dgemm
routine, but I am not sure if we detect A'_A. I don't think so.

@JeffBezanson In the AtB operator, can we check somehow if A and B are the
same objects and call a different BLAS function?

@dmbates If julia can do A'_B, A_B', A'_B', A'_A, A*A' the right way
calling BLAS directly, would you still want to implement crossprod() and
tcrossprod()?

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[StefanKarpinski]

Is there a BLAS function that computes A'*A?

[JeffBezanson]

Yes, dsyrk I believe.
On Apr 5, 2012 6:32 PM, "Stefan Karpinski" <
reply@reply.github.com>
wrote:

Is there a BLAS function that computes A'*A?

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#659 (comment)

[JeffBezanson]

So is the only thing to do for this issue call the BLAS function specialized for A'*A?

[ViralBShah]

Yes, I think so.

-viral

On 13-Apr-2012, at 5:33 AM, JeffBezanson wrote:

So is the only thing to do for this issue call the BLAS function specialized for A'*A?

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[Nosferican]

What happened with this issue? It seems DSYRK was used for
cross(::AbstractVector{T}, ::AbstractVector{T}) where T, but never implemented it for A'A or a crossprod(::AbstractVecOrMat{T}) where T <: Number, no?

[andreasnoack]

Take a look inside matmul.jl. We are using syrk.