Date: 2026-05-01T06:11:50+00:00

Actual source code: borthog.c

      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, No Fortran Support

     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: }