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;
 51: 
 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++) {
 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++) {
 89:       hnrm  +=  PetscRealPart(lhh[j] * PetscConj(lhh[j]));
 90:     }
 91:     hnrm = PetscSqrtReal(hnrm);
 92:     VecNorm(VEC_VV(it+1),NORM_2, &wnrm);
 93:     if (wnrm < 1.0286 * hnrm) {
 94:       refine = PETSC_TRUE;
 95:       PetscInfo2(ksp,"Performing iterative refinement wnorm %G hnorm %G\n",wnrm,hnrm);
 96:     }
 97:   }

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