Actual source code: borthog2.c
petsc-3.10.5 2019-03-28
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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

     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: }