Actual source code: borthog2.c

petsc-3.14.3 2021-01-09
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  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.
 28:     This is much faster than KSPGMRESModifiedGramSchmidtOrthogonalization() but has the small possibility of stability issues
 29:     that can usually be handled by using a a single step of iterative refinement with KSPGMRESSetCGSRefinementType()

 31:    Level: intermediate

 33: .seelaso:  KSPGMRESSetOrthogonalization(), KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
 34:            KSPGMRESGetCGSRefinementType(), KSPGMRESGetOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization()

 36: @*/
 37: PetscErrorCode  KSPGMRESClassicalGramSchmidtOrthogonalization(KSP ksp,PetscInt it)
 38: {
 39:   KSP_GMRES      *gmres = (KSP_GMRES*)(ksp->data);
 41:   PetscInt       j;
 42:   PetscScalar    *hh,*hes,*lhh;
 43:   PetscReal      hnrm, wnrm;
 44:   PetscBool      refine = (PetscBool)(gmres->cgstype == KSP_GMRES_CGS_REFINE_ALWAYS);

 47:   PetscLogEventBegin(KSP_GMRESOrthogonalization,ksp,0,0,0);
 48:   if (!gmres->orthogwork) {
 49:     PetscMalloc1(gmres->max_k + 2,&gmres->orthogwork);
 50:   }
 51:   lhh = gmres->orthogwork;

 53:   /* update Hessenberg matrix and do unmodified Gram-Schmidt */
 54:   hh  = HH(0,it);
 55:   hes = HES(0,it);

 57:   /* Clear hh and hes since we will accumulate values into them */
 58:   for (j=0; j<=it; j++) {
 59:     hh[j]  = 0.0;
 60:     hes[j] = 0.0;
 61:   }

 63:   /*
 64:      This is really a matrix-vector product, with the matrix stored
 65:      as pointer to rows
 66:   */
 67:   VecMDot(VEC_VV(it+1),it+1,&(VEC_VV(0)),lhh); /* <v,vnew> */
 68:   for (j=0; j<=it; j++) {
 69:     KSPCheckDot(ksp,lhh[j]);
 70:     if (ksp->reason) goto done;
 71:     lhh[j] = -lhh[j];
 72:   }

 74:   /*
 75:          This is really a matrix vector product:
 76:          [h[0],h[1],...]*[ v[0]; v[1]; ...] subtracted from v[it+1].
 77:   */
 78:   VecMAXPY(VEC_VV(it+1),it+1,lhh,&VEC_VV(0));
 79:   /* note lhh[j] is -<v,vnew> , hence the subtraction */
 80:   for (j=0; j<=it; j++) {
 81:     hh[j]  -= lhh[j];     /* hh += <v,vnew> */
 82:     hes[j] -= lhh[j];     /* hes += <v,vnew> */
 83:   }

 85:   /*
 86:      the second step classical Gram-Schmidt is only necessary
 87:      when a simple test criteria is not passed
 88:   */
 89:   if (gmres->cgstype == KSP_GMRES_CGS_REFINE_IFNEEDED) {
 90:     hnrm = 0.0;
 91:     for (j=0; j<=it; j++) hnrm +=  PetscRealPart(lhh[j] * PetscConj(lhh[j]));

 93:     hnrm = PetscSqrtReal(hnrm);
 94:     VecNorm(VEC_VV(it+1),NORM_2, &wnrm);
 95:     KSPCheckNorm(ksp,wnrm);
 96:     if (ksp->reason) goto done;
 97:     if (wnrm < hnrm) {
 98:       refine = PETSC_TRUE;
 99:       PetscInfo2(ksp,"Performing iterative refinement wnorm %g hnorm %g\n",(double)wnrm,(double)hnrm);
100:     }
101:   }

103:   if (refine) {
104:     VecMDot(VEC_VV(it+1),it+1,&(VEC_VV(0)),lhh); /* <v,vnew> */
105:     for (j=0; j<=it; j++) {
106:        KSPCheckDot(ksp,lhh[j]);
107:        if (ksp->reason) goto done;
108:        lhh[j] = -lhh[j];
109:     }
110:     VecMAXPY(VEC_VV(it+1),it+1,lhh,&VEC_VV(0));
111:     /* note lhh[j] is -<v,vnew> , hence the subtraction */
112:     for (j=0; j<=it; j++) {
113:       hh[j]  -= lhh[j];     /* hh += <v,vnew> */
114:       hes[j] -= lhh[j];     /* hes += <v,vnew> */
115:     }
116:   }
117: done:
118:   PetscLogEventEnd(KSP_GMRESOrthogonalization,ksp,0,0,0);
119:   return(0);
120: }