Re: [eigen] fix double-promotion in 3.3 Core/SpecialFunctions.h

[Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx>]

On 2016-05-05 15:04, Ilja Honkonen wrote:
> Looks like boost has this covered:
> http://www.boost.org/doc/libs/1_60_0/libs/math/doc/html/math_toolkit/powers/ct_pow.html
> This overload would be nice for Eigen types also.

I'm really not sure how often this is needed and I guess this is very 
hard to implement optimally, e.g. for big matrices it could be worth to 
implementing  pow<31>(A) as
  A.colPivLu().solve(pow<32>(A));
in case A is invertible.
cf: https://en.wikipedia.org/wiki/Addition-chain_exponentiation

And it gets really complicated if powers are part of bigger expressions, 
like for matrix A and vector x
  pow<k>(A)*x
might be cheapest to compute by k Matrix-vector products (which is 
O(k*n²) before doing any O(n³) matrix products.


Also, for Arrays the exponentiation should happen packet-by-packet if 
possible, of course.

But if someone likes to implement that, I would not object integrating 
it into Eigen.


Christoph




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