Actual source code: peputils.c
slepc-3.17.1 2022-04-11
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: if (idx==0) {
30: for (i=0;i<k;i++) {
31: PetscArrayzero(Tj+i*ldtj,k);
32: Tj[i+i*ldtj] = 1.0;
33: }
34: } else {
35: PetscBLASIntCast(ldt,&ldt_);
36: PetscBLASIntCast(ldtj,&ldtj_);
37: PetscBLASIntCast(ldtp,&ldtp_);
38: PetscBLASIntCast(k,&k_);
39: ca = pep->pbc; cb = pep->pbc+pep->nmat; cg = pep->pbc+2*pep->nmat;
40: for (i=0;i<k;i++) T[i*ldt+i] -= cb[idx-1];
41: if (idx>1) {
42: for (i=0;i<k;i++) PetscArraycpy(Tj+i*ldtj,Tpp+i*ldtpp,k);
43: }
44: a = 1/ca[idx-1];
45: g = (idx==1)?0.0:-cg[idx-1]/ca[idx-1];
46: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&k_,&k_,&k_,&a,T,&ldt_,Tp,&ldtp_,&g,Tj,&ldtj_));
47: for (i=0;i<k;i++) T[i*ldt+i] += cb[idx-1];
48: }
49: PetscFunctionReturn(0);
50: }
52: /*
53: PEPEvaluateBasis - evaluate the polynomial basis on a given parameter sigma
54: */
55: PetscErrorCode PEPEvaluateBasis(PEP pep,PetscScalar sigma,PetscScalar isigma,PetscScalar *vals,PetscScalar *ivals)
56: {
57: PetscInt nmat=pep->nmat,k;
58: PetscReal *a=pep->pbc,*b=pep->pbc+nmat,*g=pep->pbc+2*nmat;
60: if (ivals) for (k=0;k<nmat;k++) ivals[k] = 0.0;
61: vals[0] = 1.0;
62: vals[1] = (sigma-b[0])/a[0];
63: #if !defined(PETSC_USE_COMPLEX)
64: if (ivals) ivals[1] = isigma/a[0];
65: #endif
66: for (k=2;k<nmat;k++) {
67: vals[k] = ((sigma-b[k-1])*vals[k-1]-g[k-1]*vals[k-2])/a[k-1];
68: if (ivals) vals[k] -= isigma*ivals[k-1]/a[k-1];
69: #if !defined(PETSC_USE_COMPLEX)
70: if (ivals) ivals[k] = ((sigma-b[k-1])*ivals[k-1]+isigma*vals[k-1]-g[k-1]*ivals[k-2])/a[k-1];
71: #endif
72: }
73: PetscFunctionReturn(0);
74: }
76: /*
77: PEPEvaluateBasisDerivative - evaluate the derivative of the polynomial basis on a given parameter sigma
78: */
79: PetscErrorCode PEPEvaluateBasisDerivative(PEP pep,PetscScalar sigma,PetscScalar isigma,PetscScalar *vals,PetscScalar *ivals)
80: {
81: PetscInt nmat=pep->nmat,k;
82: PetscReal *a=pep->pbc,*b=pep->pbc+nmat,*g=pep->pbc+2*nmat;
84: PEPEvaluateBasis(pep,sigma,isigma,vals,ivals);
85: for (k=nmat-1;k>0;k--) {
86: vals[k] = vals[k-1];
87: if (ivals) ivals[k] = ivals[k-1];
88: }
89: vals[0] = 0.0;
90: vals[1] = vals[1]/a[0];
91: #if !defined(PETSC_USE_COMPLEX)
92: if (ivals) ivals[1] = ivals[1]/a[0];
93: #endif
94: for (k=2;k<nmat;k++) {
95: vals[k] += (sigma-b[k-1])*vals[k-1]-g[k-1]*vals[k-2];
96: if (ivals) vals[k] -= isigma*ivals[k-1];
97: vals[k] /= a[k-1];
98: #if !defined(PETSC_USE_COMPLEX)
99: if (ivals) {
100: ivals[k] += (sigma-b[k-1])*ivals[k-1]+isigma*vals[k-1]-g[k-1]*ivals[k-2];
101: ivals[k] /= a[k-1];
102: }
103: #endif
104: }
105: PetscFunctionReturn(0);
106: }