1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, 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: {
 24:   PetscInt       i;
 25:   PetscReal      *ca,*cb,*cg;
 26:   PetscScalar    g,a;
 27:   PetscBLASInt   k_,ldt_,ldtj_,ldtp_;

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

 53: /*
 54:    PEPEvaluateBasis - evaluate the polynomial basis on a given parameter sigma
 55: */
 56: PetscErrorCode PEPEvaluateBasis(PEP pep,PetscScalar sigma,PetscScalar isigma,PetscScalar *vals,PetscScalar *ivals)
 57: {
 58:   PetscInt   nmat=pep->nmat,k;
 59:   PetscReal  *a=pep->pbc,*b=pep->pbc+nmat,*g=pep->pbc+2*nmat;

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

 78: /*
 79:    PEPEvaluateBasisDerivative - evaluate the derivative of the polynomial basis on a given parameter sigma
 80: */
 81: PetscErrorCode PEPEvaluateBasisDerivative(PEP pep,PetscScalar sigma,PetscScalar isigma,PetscScalar *vals,PetscScalar *ivals)
 82: {
 83:   PetscInt       nmat=pep->nmat,k;
 84:   PetscReal      *a=pep->pbc,*b=pep->pbc+nmat,*g=pep->pbc+2*nmat;

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