1: /*
  2:     Routines used for the orthogonalization of the Hessenberg matrix.

  4:     Note that for the complex numbers version, the VecDot() and
  5:     VecMDot() arguments within the code MUST remain in the order
  6:     given for correct computation of inner products.
  7: */
  8: #include <../src/ksp/ksp/impls/gmres/gmresimpl.h>

 10: /*@C
 11:   KSPGMRESClassicalGramSchmidtOrthogonalization -  This is the basic orthogonalization routine
 12:   using classical Gram-Schmidt with possible iterative refinement to improve the stability

 14:   Collective

 16:   Input Parameters:
 17: + ksp - `KSP` object, must be associated with `KSPGMRES`, `KSPFGMRES`, or `KSPLGMRES` Krylov method
 18: - it  - one less than the current GMRES restart iteration, i.e. the size of the Krylov space

 20:   Options Database Keys:
 21: + -ksp_gmres_classicalgramschmidt                                             - Activates `KSPGMRESClassicalGramSchmidtOrthogonalization()`
 22: - -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is
 23:                                    used to increase the stability of the classical Gram-Schmidt  orthogonalization.

 25:   Level: intermediate

 27:   Note:
 28:   Use `KSPGMRESSetCGSRefinementType()` to determine if iterative refinement is to be used.
 29:   This is much faster than `KSPGMRESModifiedGramSchmidtOrthogonalization()` but has the small possibility of stability issues
 30:   that can usually be handled by using a single step of iterative refinement with `KSPGMRESSetCGSRefinementType()`

 32: .seealso: [](ch_ksp), `KSPGMRESCGSRefinementType`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESSetCGSRefinementType()`,
 33:            `KSPGMRESGetCGSRefinementType()`, `KSPGMRESGetOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`
 34: @*/
 35: PetscErrorCode KSPGMRESClassicalGramSchmidtOrthogonalization(KSP ksp, PetscInt it)
 36: {
 37:   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);

 43:   PetscFunctionBegin;
 44:   PetscCall(PetscLogEventBegin(KSP_GMRESOrthogonalization, ksp, 0, 0, 0));
 45:   if (!gmres->orthogwork) PetscCall(PetscMalloc1(gmres->max_k + 2, &gmres->orthogwork));
 46:   lhh = gmres->orthogwork;

 48:   /* update Hessenberg matrix and do unmodified Gram-Schmidt */
 49:   hh  = HH(0, it);
 50:   hes = HES(0, it);

 52:   /* Clear hh and hes since we will accumulate values into them */
 53:   for (j = 0; j <= it; j++) {
 54:     hh[j]  = 0.0;
 55:     hes[j] = 0.0;
 56:   }

 58:   /*
 59:      This is really a matrix-vector product, with the matrix stored
 60:      as pointer to rows
 61:   */
 62:   PetscCall(VecMDot(VEC_VV(it + 1), it + 1, &(VEC_VV(0)), lhh)); /* <v,vnew> */
 63:   for (j = 0; j <= it; j++) {
 64:     KSPCheckDot(ksp, lhh[j]);
 65:     if (ksp->reason) goto done;
 66:     lhh[j] = -lhh[j];
 67:   }

 69:   /*
 70:          This is really a matrix-vector product:
 71:          [h[0],h[1],...]*[ v[0]; v[1]; ...] subtracted from v[it+1].
 72:   */
 73:   PetscCall(VecMAXPY(VEC_VV(it + 1), it + 1, lhh, &VEC_VV(0)));
 74:   /* note lhh[j] is -<v,vnew> , hence the subtraction */
 75:   for (j = 0; j <= it; j++) {
 76:     hh[j] -= lhh[j];  /* hh += <v,vnew> */
 77:     hes[j] -= lhh[j]; /* hes += <v,vnew> */
 78:   }

 80:   /*
 81:      the second step classical Gram-Schmidt is only necessary
 82:      when a simple test criteria is not passed
 83:   */
 84:   if (gmres->cgstype == KSP_GMRES_CGS_REFINE_IFNEEDED) {
 85:     hnrm = 0.0;
 86:     for (j = 0; j <= it; j++) hnrm += PetscRealPart(lhh[j] * PetscConj(lhh[j]));

 88:     hnrm = PetscSqrtReal(hnrm);
 89:     PetscCall(VecNorm(VEC_VV(it + 1), NORM_2, &wnrm));
 90:     KSPCheckNorm(ksp, wnrm);
 91:     if (ksp->reason) goto done;
 92:     if (wnrm < hnrm) {
 93:       refine = PETSC_TRUE;
 94:       PetscCall(PetscInfo(ksp, "Performing iterative refinement wnorm %g hnorm %g\n", (double)wnrm, (double)hnrm));
 95:     }
 96:   }

 98:   if (refine) {
 99:     PetscCall(VecMDot(VEC_VV(it + 1), it + 1, &(VEC_VV(0)), lhh)); /* <v,vnew> */
100:     for (j = 0; j <= it; j++) {
101:       KSPCheckDot(ksp, lhh[j]);
102:       if (ksp->reason) goto done;
103:       lhh[j] = -lhh[j];
104:     }
105:     PetscCall(VecMAXPY(VEC_VV(it + 1), it + 1, lhh, &VEC_VV(0)));
106:     /* note lhh[j] is -<v,vnew> , hence the subtraction */
107:     for (j = 0; j <= it; j++) {
108:       hh[j] -= lhh[j];  /* hh += <v,vnew> */
109:       hes[j] -= lhh[j]; /* hes += <v,vnew> */
110:     }
111:   }
112: done:
113:   PetscCall(PetscLogEventEnd(KSP_GMRESOrthogonalization, ksp, 0, 0, 0));
114:   PetscFunctionReturn(PETSC_SUCCESS);
115: }