[petsc-users] VecPow clarification

[Barry Smith]

   Good question. Looking at the commit logs from 2014 I see 

move tao vector operations over to Vec directory, fix a couple names and calling sequences


 So previously, the function was  problem-specific for Tao (which did not support complex numbers) used inside the semi-smooth methods where roots of negative numbers should be mapped to infinity (indicating a "bad" domain point).

 When we merged the Tao and PETSc source code base  just blindly copied over the code without realizing it was not a general-purpose VecPow() and that it did not make sense for complex numbers.

 I should rework it for general use without breaking the use in Tao.

 Thanks for pointing out the problem.

  Barry





> On Nov 14, 2024, at 9:39 AM, Peder Jørgensgaard Olesen via petsc-users <petsc-users at mcs.anl.gov> wrote:
> 
> Given a vector containing roots of unity, v[i] = exp(i*k*x[i]) I wanted to compute the vector u[i]=exp(i*n*k*x[i]), for some real number n. From the face of it this should be easily achieved with VecPow, as u[i] = v[i]^n.
> 
> That didn't work as expected, though I got around it using VecGetArray() and a loop with PetscPowComplex(). The source designated in the docs (src/vec/vec/utils/projection.c) reveals that VecPow() maps v[i] to PETSC_INFINITY when the PetscRealPart(v[i]) < 0, unless the power is any of 0, ±0.5, ±1 or ±2. Even in the simple case of a purely real vector (with negative entries) raised to any other integer power, the results would not be what one might  reasonably expect from the description of VecPow().
> 
> While I do have a solution suiting my need, I'm left wondering what might be the rationale for VecPow working the way it does.
> 
> Best,
> Peder

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