Actual source code: borthog2.c
petsc-3.13.0 2020-03-29
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:
27: Use KSPGMRESSetCGSRefinementType() to determine if iterative refinement is to be used
29: Level: intermediate
31: .seelaso: KSPGMRESSetOrthogonalization(), KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
32: KSPGMRESGetCGSRefinementType(), KSPGMRESGetOrthogonalization()
34: @*/
35: PetscErrorCode KSPGMRESClassicalGramSchmidtOrthogonalization(KSP ksp,PetscInt it)
36: {
37: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
39: PetscInt j;
40: PetscScalar *hh,*hes,*lhh;
41: PetscReal hnrm, wnrm;
42: PetscBool refine = (PetscBool)(gmres->cgstype == KSP_GMRES_CGS_REFINE_ALWAYS);
45: PetscLogEventBegin(KSP_GMRESOrthogonalization,ksp,0,0,0);
46: if (!gmres->orthogwork) {
47: PetscMalloc1(gmres->max_k + 2,&gmres->orthogwork);
48: }
49: lhh = gmres->orthogwork;
51: /* update Hessenberg matrix and do unmodified Gram-Schmidt */
52: hh = HH(0,it);
53: hes = HES(0,it);
55: /* Clear hh and hes since we will accumulate values into them */
56: for (j=0; j<=it; j++) {
57: hh[j] = 0.0;
58: hes[j] = 0.0;
59: }
61: /*
62: This is really a matrix-vector product, with the matrix stored
63: as pointer to rows
64: */
65: VecMDot(VEC_VV(it+1),it+1,&(VEC_VV(0)),lhh); /* <v,vnew> */
66: for (j=0; j<=it; j++) {
67: KSPCheckDot(ksp,lhh[j]);
68: lhh[j] = -lhh[j];
69: }
71: /*
72: This is really a matrix vector product:
73: [h[0],h[1],...]*[ v[0]; v[1]; ...] subtracted from v[it+1].
74: */
75: VecMAXPY(VEC_VV(it+1),it+1,lhh,&VEC_VV(0));
76: /* note lhh[j] is -<v,vnew> , hence the subtraction */
77: for (j=0; j<=it; j++) {
78: hh[j] -= lhh[j]; /* hh += <v,vnew> */
79: hes[j] -= lhh[j]; /* hes += <v,vnew> */
80: }
82: /*
83: * the second step classical Gram-Schmidt is only necessary
84: * when a simple test criteria is not passed
85: */
86: if (gmres->cgstype == KSP_GMRES_CGS_REFINE_IFNEEDED) {
87: hnrm = 0.0;
88: for (j=0; j<=it; j++) hnrm += PetscRealPart(lhh[j] * PetscConj(lhh[j]));
90: hnrm = PetscSqrtReal(hnrm);
91: VecNorm(VEC_VV(it+1),NORM_2, &wnrm);
92: if (wnrm < hnrm) {
93: refine = PETSC_TRUE;
94: PetscInfo2(ksp,"Performing iterative refinement wnorm %g hnorm %g\n",(double)wnrm,(double)hnrm);
95: }
96: }
98: if (refine) {
99: VecMDot(VEC_VV(it+1),it+1,&(VEC_VV(0)),lhh); /* <v,vnew> */
100: for (j=0; j<=it; j++) lhh[j] = -lhh[j];
101: VecMAXPY(VEC_VV(it+1),it+1,lhh,&VEC_VV(0));
102: /* note lhh[j] is -<v,vnew> , hence the subtraction */
103: for (j=0; j<=it; j++) {
104: hh[j] -= lhh[j]; /* hh += <v,vnew> */
105: hes[j] -= lhh[j]; /* hes += <v,vnew> */
106: }
107: }
108: PetscLogEventEnd(KSP_GMRESOrthogonalization,ksp,0,0,0);
109: return(0);
110: }