PEPSetScale#

Specifies the scaling strategy to be used.

Synopsis#

#include "slepcpep.h" 
PetscErrorCode PEPSetScale(PEP pep,PEPScale scale,PetscReal alpha,Vec Dl,Vec Dr,PetscInt its,PetscReal lambda)

Collective

Input Parameters#

  • pep - the polynomial eigensolver context

  • scale - scaling strategy, see PEPScale for possible values

  • alpha - the scaling factor used in the scalar strategy

  • Dl - the left diagonal matrix of the diagonal scaling algorithm

  • Dr - the right diagonal matrix of the diagonal scaling algorithm

  • its - number of iterations of the diagonal scaling algorithm

  • lambda - approximation to wanted eigenvalues (modulus)

Options Database Keys#

  • -pep_scale <scale> - set the scaling type, one of none,scalar,diagonal,both

  • -pep_scale_factor <alpha> - set the scaling factor

  • -pep_scale_its <its> - set the number of iterations

  • -pep_scale_lambda <lambda> - set the approximation to eigenvalues

Notes#

There are two non-exclusive scaling strategies, scalar and diagonal. See discussion in section Scaling.

In the scalar strategy, scaling is applied to the eigenvalue, that is, \(\mu = \lambda/\alpha\) is the new eigenvalue and all matrices are scaled accordingly. After solving the scaled problem, the original \(\lambda\) is recovered. Parameter alpha must be positive. Use PETSC_DETERMINE to let the solver compute a reasonable scaling factor, and PETSC_CURRENT to retain a previously set value.

In the diagonal strategy, the solver works implicitly with matrix \(D_\ell P(\lambda)D_r\), where \(D_\ell\) and \(D_r\) are appropriate diagonal matrices. This improves the accuracy of the computed results in some cases. The user may provide the Dl and Dr matrices represented as Vec objects storing diagonal elements. If not provided, these matrices are computed internally. This option requires that the polynomial coefficient matrices are of MATAIJ type. The parameter its is the number of iterations performed by the method. Parameter lambda must be positive. Use PETSC_DETERMINE or set lambda = 1.0 if no information about eigenvalues is available. PETSC_CURRENT can also be used to leave its and lambda unchanged.

See Also#

PEP: Polynomial Eigenvalue Problems, Scaling, PEPGetScale()

Level#

intermediate

Location#

src/pep/interface/pepopts.c

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