Small vector and matrix proposed for phobos2 now on github

[Robert Jacques]

On Fri, 30 Apr 2010 17:23:33 -0400, Jérôme M. Berger <jeberger at free.fr>  
wrote:
> Robert Jacques wrote:
>> On Thu, 29 Apr 2010 19:16:49 -0400, Gareth Charnock
>> <gareth.tpc at gmail.com> wrote:
>>
>>> Jérôme M. Berger wrote:
>>>> Gareth Charnock wrote:
>>>>> PS: Okay so I just had a looked at the matrix and vector classes in
>>>>> Ogre3D and irrlicht. Looks like they both define v*v as element wise
>>>>> multiplication but m*m is matrix multiplication. That just seems even
>>>>> more inconsistent.
>>>>      Eigen (http://eigen.tuxfamily.org/ ) uses '*' for the matrix
>>>> multiplication. v*v is an error (incompatible shapes). Element wise
>>>> operations can be done like this: v.cwise()*v
>>>>          Jerome
>>> That's an very impressive looking library if even half of what they
>>> claim is true. I can't believe I've missed this for so long (found the
>>> boost matrix library, blitz++, the matrix template library, FLENS,
>>> something called armadillo but not eigen. I do believe all my C++
>>> linear algebra woes are over.
>>>
>>> Eigen seems to treat vectors as 1 by n matrices and if you do this you
>>> get the matrix-vector product and the dot product for free as these
>>> are all the same operation. Probably v^T*v would be the dot product.
>>> Expression templates should make these operations efficient.
>>>
>>
>> Actually, express templates, though they give nice syntax result in a
>> lot of temporaries, which hurt performance. Check out Don's BLADE
>> library and the associated talks and posts.
>
> 	According to the documentation, Eigen expression templates do not
> result in temporaries, except for multiplication. And even then, you
> can remove the temporaries by using the .lazy function in Eigen2 or
> the .noalias() function in the upcoming Eigen3:
> http://eigen.tuxfamily.org/dox-devel/Eigen2ToEigen3.html#LazyVsNoalias
>
> 	An yes, it is very impressive :) and very comfortable to use. I had
> seen about the same selection as you before discovering Eigen and
> moving to it. The only drawback is that it currently doesn't
> multithread.
>
> 		Jerome

No, according to the documentation, Eigen expression templates do not  
result in any temporary vectors. They do however, result in a a lot of  
stack temporaries. And stack temporaries of stack temporaries. The  
overhead of using expression templates has generally been ignored in CS,  
which is why when I first saw Don's BLADE library and talk it was so  
refreshing. The weaknesses of expression templates was also a major reason  
for the inclusion of array ops as a language feature.