Actual source code: borthog2.c

  1: #define PETSCKSP_DLL

  3: /*
  4:     Routines used for the orthogonalization of the Hessenberg matrix.

  6:     Note that for the complex numbers version, the VecDot() and
  7:     VecMDot() arguments within the code MUST remain in the order
  8:     given for correct computation of inner products.
  9: */
 10:  #include src/ksp/ksp/impls/gmres/gmresp.h

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

 16:      Collective on KSP

 18:   Input Parameters:
 19: +   ksp - KSP object, must be associated with GMRES, FGMRES, or LGMRES Krylov method
 20: -   its - one less then the current GMRES restart iteration, i.e. the size of the Krylov space

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

 27:     Notes: Use KSPGMRESSetCGSRefinementType() to determine if iterative refinement is to be used

 29:    Level: intermediate

 31: .seelaso:  KSPGMRESSetOrthogonalization(), KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType()

 33: @*/
 36: PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESClassicalGramSchmidtOrthogonalization(KSP  ksp,PetscInt it)
 37: {
 38:   KSP_GMRES      *gmres = (KSP_GMRES *)(ksp->data);
 40:   PetscInt       j;
 41:   PetscScalar    *hh,*hes,shh[500],*lhh;
 42:   PetscReal      hnrm, wnrm;
 43:   PetscTruth     refine = (PetscTruth)(gmres->cgstype == KSP_GMRES_CGS_REFINE_ALWAYS);

 46:   PetscLogEventBegin(KSP_GMRESOrthogonalization,ksp,0,0,0);
 47:   /* Don't allocate small arrays */
 48:   if (it < 501) lhh = shh;
 49:   else {
 50:     PetscMalloc((it+1) * sizeof(PetscScalar),&lhh);
 51:   }
 52: 
 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(it+1,VEC_VV(it+1),&(VEC_VV(0)),lhh); /* <v,vnew> */
 68:   for (j=0; j<=it; j++) {
 69:     lhh[j] = - lhh[j];
 70:   }

 72:   /*
 73:          This is really a matrix vector product: 
 74:          [h[0],h[1],...]*[ v[0]; v[1]; ...] subtracted from v[it+1].
 75:   */
 76:   VecMAXPY(VEC_VV(it+1),it+1,lhh,&VEC_VV(0));
 77:   /* note lhh[j] is -<v,vnew> , hence the subtraction */
 78:   for (j=0; j<=it; j++) {
 79:     hh[j]  -= lhh[j];     /* hh += <v,vnew> */
 80:     hes[j] -= lhh[j];     /* hes += <v,vnew> */
 81:   }

 83:   /*
 84:    *  the second step classical Gram-Schmidt is only necessary
 85:    *  when a simple test criteria is not passed
 86:    */
 87:   if (gmres->cgstype == KSP_GMRES_CGS_REFINE_IFNEEDED) {
 88:     hnrm = 0.0;
 89:     for (j=0; j<=it; j++) {
 90:       hnrm  +=  PetscRealPart(lhh[j] * PetscConj(lhh[j]));
 91:     }
 92:     hnrm = sqrt(hnrm);
 93:     VecNorm(VEC_VV(it+1),NORM_2, &wnrm);
 94:     if (wnrm < 1.0286 * hnrm) {
 95:       refine = PETSC_TRUE;
 96:       PetscLogInfo((ksp,"KSPGMRESClassicalGramSchmidtOrthogonalization:Performing iterative refinement wnorm %g hnorm %g\n",wnrm,hnrm));
 97:     }
 98:   }

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

111:   if (it >= 501) {PetscFree(lhh);}
112:   PetscLogEventEnd(KSP_GMRESOrthogonalization,ksp,0,0,0);
113:   return(0);
114: }