[petsc-users] HermitianTranspose version of MatCreateTranspose.

[Barry Smith]

   We've had a small amount of debate over the years on how to handle the Hermitian transpose and non-Hermitian transpose that never got fully resolved.

Approach 1) Each (complex) matrix has a full set of transpose and Hermitian transpose operations (MatTranspose(), MatHermitianTranspose(), MatMultTranspose()), MatMultHermitianTranspose(), MatSolveTranspose(), MatSolveHermitianTranspose(), MatMatMultTranspose(), MatMatMultHermitianTranspose(), MatTranposeMatMult(), MatHermitianTransposeMatMult().......)  plus there are two vector "inner" products; VecDot() and VecTDot(). 

Approach 2) Consider a (complex) vector (and hence the associated matrix operators on it) to live in the usual Hermitian inner product space or the non-Hermitian "inner product space". Then one only needs a single VecDot() and MatTranspose(), MatMultTranspose() ... that just "does the right thing" based on what space the user has declared the vectors/matrices to be in. 

Approach 2) seems nicer since it only requires 1/2 the functions :-) and so long as the two vector "spaces" never interact directly (for example what would be the meaning of the "inner" product of a vector in the usual Hermitian inner product space with a vector from the non-Hermitian "inner product space"?) certain seems simpler.  Approach 1) might be simpler for some people who like to always see exactly what they are doing. 

I personally wish I had started with Approach 2 (but I did not), but there could be some flaw with it I am not seeing.

  Barry







> On Feb 23, 2015, at 6:50 PM, Andrew Spott <ansp6066 at colorado.edu> wrote:
> 
> I’m definitely willing to submit it as a pull request.
> 
> Also, while I’m at it, I’m going to write a “duplicate” function for transpose and hermitian_transpose.  Just because this seems 1) easy ( MatHermitianTranspose can return a new copy, as well as MatTranspose), and 2) necessary to use these for EPS.
> 
> Also, is “transpose” a good enough MatType?  Or does a new one need to be written?
> 
> -Andrew
> 
> 
> 
> On Mon, Feb 23, 2015 at 3:12 PM, Jed Brown <jed at jedbrown.org> wrote:
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