Actual source code: borthog2.c
petsc-3.9.3 2018-07-02
2: /*
3: Routines used for the orthogonalization of the Hessenberg matrix.
5: Note that for the complex numbers version, the VecDot() and
6: VecMDot() arguments within the code MUST remain in the order
7: given for correct computation of inner products.
8: */
9: #include <../src/ksp/ksp/impls/gmres/gmresimpl.h>
11: /*@C
12: KSPGMRESClassicalGramSchmidtOrthogonalization - This is the basic orthogonalization routine
13: using classical Gram-Schmidt with possible iterative refinement to improve the stability
15: Collective on KSP
17: Input Parameters:
18: + ksp - KSP object, must be associated with GMRES, FGMRES, or LGMRES Krylov method
19: - its - one less then the current GMRES restart iteration, i.e. the size of the Krylov space
21: Options Database Keys:
22: + -ksp_gmres_classicalgramschmidt - Activates KSPGMRESClassicalGramSchmidtOrthogonalization()
23: - -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is
24: used to increase the stability of the classical Gram-Schmidt orthogonalization.
26: Notes: Use KSPGMRESSetCGSRefinementType() to determine if iterative refinement is to be used
28: Level: intermediate
30: .seelaso: KSPGMRESSetOrthogonalization(), KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
31: KSPGMRESGetCGSRefinementType(), KSPGMRESGetOrthogonalization()
33: @*/
34: PetscErrorCode KSPGMRESClassicalGramSchmidtOrthogonalization(KSP ksp,PetscInt it)
35: {
36: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
38: PetscInt j;
39: PetscScalar *hh,*hes,*lhh;
40: PetscReal hnrm, wnrm;
41: PetscBool refine = (PetscBool)(gmres->cgstype == KSP_GMRES_CGS_REFINE_ALWAYS);
44: PetscLogEventBegin(KSP_GMRESOrthogonalization,ksp,0,0,0);
45: if (!gmres->orthogwork) {
46: PetscMalloc1(gmres->max_k + 2,&gmres->orthogwork);
47: }
48: lhh = gmres->orthogwork;
50: /* update Hessenberg matrix and do unmodified Gram-Schmidt */
51: hh = HH(0,it);
52: hes = HES(0,it);
54: /* Clear hh and hes since we will accumulate values into them */
55: for (j=0; j<=it; j++) {
56: hh[j] = 0.0;
57: hes[j] = 0.0;
58: }
60: /*
61: This is really a matrix-vector product, with the matrix stored
62: as pointer to rows
63: */
64: VecMDot(VEC_VV(it+1),it+1,&(VEC_VV(0)),lhh); /* <v,vnew> */
65: for (j=0; j<=it; j++) {
66: KSPCheckDot(ksp,lhh[j]);
67: lhh[j] = -lhh[j];
68: }
70: /*
71: This is really a matrix vector product:
72: [h[0],h[1],...]*[ v[0]; v[1]; ...] subtracted from v[it+1].
73: */
74: VecMAXPY(VEC_VV(it+1),it+1,lhh,&VEC_VV(0));
75: /* note lhh[j] is -<v,vnew> , hence the subtraction */
76: for (j=0; j<=it; j++) {
77: hh[j] -= lhh[j]; /* hh += <v,vnew> */
78: hes[j] -= lhh[j]; /* hes += <v,vnew> */
79: }
81: /*
82: * the second step classical Gram-Schmidt is only necessary
83: * when a simple test criteria is not passed
84: */
85: if (gmres->cgstype == KSP_GMRES_CGS_REFINE_IFNEEDED) {
86: hnrm = 0.0;
87: for (j=0; j<=it; j++) hnrm += PetscRealPart(lhh[j] * PetscConj(lhh[j]));
89: hnrm = PetscSqrtReal(hnrm);
90: VecNorm(VEC_VV(it+1),NORM_2, &wnrm);
91: if (wnrm < hnrm) {
92: refine = PETSC_TRUE;
93: PetscInfo2(ksp,"Performing iterative refinement wnorm %g hnorm %g\n",(double)wnrm,(double)hnrm);
94: }
95: }
97: if (refine) {
98: VecMDot(VEC_VV(it+1),it+1,&(VEC_VV(0)),lhh); /* <v,vnew> */
99: for (j=0; j<=it; j++) lhh[j] = -lhh[j];
100: VecMAXPY(VEC_VV(it+1),it+1,lhh,&VEC_VV(0));
101: /* note lhh[j] is -<v,vnew> , hence the subtraction */
102: for (j=0; j<=it; j++) {
103: hh[j] -= lhh[j]; /* hh += <v,vnew> */
104: hes[j] -= lhh[j]; /* hes += <v,vnew> */
105: }
106: }
107: PetscLogEventEnd(KSP_GMRESOrthogonalization,ksp,0,0,0);
108: return(0);
109: }