Date: 2013-07-02T14:48:10+00:00

Actual source code: borthog2.c
petsc-3.4.2 2013-07-02

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

     46:   PetscLogEventBegin(KSP_GMRESOrthogonalization,ksp,0,0,0);
     47:   if (!gmres->orthogwork) {
     48:     PetscMalloc((gmres->max_k + 2)*sizeof(PetscScalar),&gmres->orthogwork);
     49:   }
     50:   lhh = gmres->orthogwork;

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

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

     62:   /*
     63:      This is really a matrix-vector product, with the matrix stored
     64:      as pointer to rows
     65:   */
     66:   VecMDot(VEC_VV(it+1),it+1,&(VEC_VV(0)),lhh); /* <v,vnew> */
     67:   for (j=0; j<=it; j++) lhh[j] = -lhh[j];

     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:   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:     VecNorm(VEC_VV(it+1),NORM_2, &wnrm);
     90:     if (wnrm < 1.0286 * hnrm) {
     91:       refine = PETSC_TRUE;
     92:       PetscInfo2(ksp,"Performing iterative refinement wnorm %G hnorm %G\n",wnrm,hnrm);
     93:     }
     94:   }

     96:   if (refine) {
     97:     VecMDot(VEC_VV(it+1),it+1,&(VEC_VV(0)),lhh); /* <v,vnew> */
     98:     for (j=0; j<=it; j++) lhh[j] = -lhh[j];
     99:     VecMAXPY(VEC_VV(it+1),it+1,lhh,&VEC_VV(0));
    100:     /* note lhh[j] is -<v,vnew> , hence the subtraction */
    101:     for (j=0; j<=it; j++) {
    102:       hh[j]  -= lhh[j];     /* hh += <v,vnew> */
    103:       hes[j] -= lhh[j];     /* hes += <v,vnew> */
    104:     }
    105:   }
    106:   PetscLogEventEnd(KSP_GMRESOrthogonalization,ksp,0,0,0);
    107:   return(0);
    108: }