Date: 2021-09-20T09:44:04+00:00

Actual source code: peputils.c
slepc-3.15.2 2021-09-20
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2021, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */
     10: /*
     11:    Common subroutines for several PEP solvers
     12: */

     14: #include <slepc/private/pepimpl.h>
     15: #include <slepcblaslapack.h>

     17: /*
     18:   Computes T_j=phy_idx(T) for a matrix T.
     19:     Tp (if j>0) and Tpp (if j>1) are the evaluation
     20:     of phy_(j-1) and phy(j-2)respectively.
     21: */
     22: PetscErrorCode PEPEvaluateBasisMat(PEP pep,PetscInt k,PetscScalar *T,PetscInt ldt,PetscInt idx,PetscScalar *Tpp,PetscInt ldtpp,PetscScalar *Tp,PetscInt ldtp,PetscScalar *Tj,PetscInt ldtj)
     23: {
     25:   PetscInt       i;
     26:   PetscReal      *ca,*cb,*cg;
     27:   PetscScalar    g,a;
     28:   PetscBLASInt   k_,ldt_,ldtj_,ldtp_;

     31:   if (idx==0) {
     32:     for (i=0;i<k;i++) {
     33:       PetscArrayzero(Tj+i*ldtj,k);
     34:       Tj[i+i*ldtj] = 1.0;
     35:     }
     36:   } else {
     37:     PetscBLASIntCast(ldt,&ldt_);
     38:     PetscBLASIntCast(ldtj,&ldtj_);
     39:     PetscBLASIntCast(ldtp,&ldtp_);
     40:     PetscBLASIntCast(k,&k_);
     41:     ca = pep->pbc; cb = pep->pbc+pep->nmat; cg = pep->pbc+2*pep->nmat;
     42:     for (i=0;i<k;i++) T[i*ldt+i] -= cb[idx-1];
     43:     if (idx>1) {
     44:       for (i=0;i<k;i++) {
     45:         PetscArraycpy(Tj+i*ldtj,Tpp+i*ldtpp,k);
     46:       }
     47:     }
     48:     a = 1/ca[idx-1];
     49:     g = (idx==1)?0.0:-cg[idx-1]/ca[idx-1];
     50:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&a,T,&ldt_,Tp,&ldtp_,&g,Tj,&ldtj_));
     51:     for (i=0;i<k;i++) T[i*ldt+i] += cb[idx-1];
     52:   }
     53:   return(0);
     54: }

     56: /*
     57:    PEPEvaluateBasis - evaluate the polynomial basis on a given parameter sigma
     58: */
     59: PetscErrorCode PEPEvaluateBasis(PEP pep,PetscScalar sigma,PetscScalar isigma,PetscScalar *vals,PetscScalar *ivals)
     60: {
     61:   PetscInt   nmat=pep->nmat,k;
     62:   PetscReal  *a=pep->pbc,*b=pep->pbc+nmat,*g=pep->pbc+2*nmat;

     65:   if (ivals) for (k=0;k<nmat;k++) ivals[k] = 0.0;
     66:   vals[0] = 1.0;
     67:   vals[1] = (sigma-b[0])/a[0];
     68: #if !defined(PETSC_USE_COMPLEX)
     69:   if (ivals) ivals[1] = isigma/a[0];
     70: #endif
     71:   for (k=2;k<nmat;k++) {
     72:     vals[k] = ((sigma-b[k-1])*vals[k-1]-g[k-1]*vals[k-2])/a[k-1];
     73:     if (ivals) vals[k] -= isigma*ivals[k-1]/a[k-1];
     74: #if !defined(PETSC_USE_COMPLEX)
     75:     if (ivals) ivals[k] = ((sigma-b[k-1])*ivals[k-1]+isigma*vals[k-1]-g[k-1]*ivals[k-2])/a[k-1];
     76: #endif
     77:   }
     78:   return(0);
     79: }

     81: /*
     82:    PEPEvaluateBasisDerivative - evaluate the derivative of the polynomial basis on a given parameter sigma
     83: */
     84: PetscErrorCode PEPEvaluateBasisDerivative(PEP pep,PetscScalar sigma,PetscScalar isigma,PetscScalar *vals,PetscScalar *ivals)
     85: {
     87:   PetscInt       nmat=pep->nmat,k;
     88:   PetscReal      *a=pep->pbc,*b=pep->pbc+nmat,*g=pep->pbc+2*nmat;

     91:   PEPEvaluateBasis(pep,sigma,isigma,vals,ivals);
     92:   for (k=nmat-1;k>0;k--) {
     93:     vals[k] = vals[k-1];
     94:     if (ivals) ivals[k] = ivals[k-1];
     95:   }
     96:   vals[0] = 0.0;
     97:   vals[1] = vals[1]/a[0];
     98: #if !defined(PETSC_USE_COMPLEX)
     99:   if (ivals) ivals[1] = ivals[1]/a[0];
    100: #endif
    101:   for (k=2;k<nmat;k++) {
    102:     vals[k] += (sigma-b[k-1])*vals[k-1]-g[k-1]*vals[k-2];
    103:     if (ivals) vals[k] -= isigma*ivals[k-1];
    104:     vals[k] /= a[k-1];
    105: #if !defined(PETSC_USE_COMPLEX)
    106:     if (ivals) {
    107:       ivals[k] += (sigma-b[k-1])*ivals[k-1]+isigma*vals[k-1]-g[k-1]*ivals[k-2];
    108:       ivals[k] /= a[k-1];
    109:     }
    110: #endif
    111:   }
    112:   return(0);
    113: }