1: /*
  2:     Routines used for the orthogonalization of the Hessenberg matrix.

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

 10: /*@C
 11:   KSPGMRESModifiedGramSchmidtOrthogonalization -  This is the basic orthogonalization routine
 12:   using modified Gram-Schmidt.

 14:   Collective

 16:   Input Parameters:
 17: + ksp - `KSP` object, must be associated with `KSPGMRES`, `KSPFGMRES`, or `KSPLGMRES` Krylov method
 18: - it  - one less than the current GMRES restart iteration, i.e. the size of the Krylov space

 20:   Options Database Key:
 21: . -ksp_gmres_modifiedgramschmidt - Activates `KSPGMRESModifiedGramSchmidtOrthogonalization()`

 23:   Level: intermediate

 25:   Note:
 26:   In general this is much slower than `KSPGMRESClassicalGramSchmidtOrthogonalization()` but has better stability properties.

 28: .seealso: [](ch_ksp), `KSPGMRESSetOrthogonalization()`, `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESGetOrthogonalization()`
 29: @*/
 30: PetscErrorCode KSPGMRESModifiedGramSchmidtOrthogonalization(KSP ksp, PetscInt it)
 31: {
 32:   KSP_GMRES   *gmres = (KSP_GMRES *)(ksp->data);
 33:   PetscInt     j;
 34:   PetscScalar *hh, *hes;

 36:   PetscFunctionBegin;
 37:   PetscCall(PetscLogEventBegin(KSP_GMRESOrthogonalization, ksp, 0, 0, 0));
 38:   /* update Hessenberg matrix and do Gram-Schmidt */
 39:   hh  = HH(0, it);
 40:   hes = HES(0, it);
 41:   for (j = 0; j <= it; j++) {
 42:     /* (vv(it+1), vv(j)) */
 43:     PetscCall(VecDot(VEC_VV(it + 1), VEC_VV(j), hh));
 44:     KSPCheckDot(ksp, *hh);
 45:     if (ksp->reason) break;
 46:     *hes++ = *hh;
 47:     /* vv(it+1) <- vv(it+1) - hh[it+1][j] vv(j) */
 48:     PetscCall(VecAXPY(VEC_VV(it + 1), -(*hh++), VEC_VV(j)));
 49:   }
 50:   PetscCall(PetscLogEventEnd(KSP_GMRESOrthogonalization, ksp, 0, 0, 0));
 51:   PetscFunctionReturn(PETSC_SUCCESS);
 52: }