BVDotQuadrature#

Computes the projection terms required in the quadrature rule to approximate the contour integral.

Synopsis#

#include "slepcbv.h" 
PetscErrorCode BVDotQuadrature(BV Y,BV V,PetscScalar Mu[],PetscInt M,PetscInt L,PetscInt L_max,PetscScalar w[],PetscScalar zn[],PetscSubcomm subcomm,PetscInt npoints,PetscBool useconj)

Collective

Input Parameters#

  • Y - first basis vectors

  • V - second basis vectors

  • M - number of moments

  • L - block size

  • L_max - maximum block size

  • w - quadrature weights

  • zn - normalized quadrature points

  • subcomm - subcommunicator layout

  • npoints - number of points to process by the subcommunicator

  • useconj - whether conjugate points can be used or not

Output Parameter#

  • Mu - computed result

Notes#

This is a generalization of BVDot(). The resulting matrix Mu consists of M blocks of size L*L (placed horizontally), each of them computed as \(Mu_k = \sum_j w_j\zeta_j^k V^*Y_j\), where \(Y_j\) is the \(j\)-th panel of \(Y\) containing the result of solving \(T(z_j)^{-1}X\) for each integration point \(j\). L_max is the width of the panels in \(Y\).

When using subcommunicators, \(Y\) is stored in the subcommunicators for a subset of integration points. In that case, the computation is done in the subcomm and then the final result is combined via reduction. The value npoints is the number of points to be processed in this subcomm and the flag useconj indicates whether symmetric points can be reused.

See Also#

BV: Basis Vectors, BVDot(), BVScatter(), BVSumQuadrature(), RGComputeQuadrature(), RGCanUseConjugates()

Level#

developer

Location#

src/sys/classes/bv/interface/bvcontour.c

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