Actual source code: agmresleja.c

  1: #define PETSCKSP_DLL
  2: /*
  3:    Functions in this file reorder the Ritz values in the (modified) Leja order.

  5:    References : [1] Bai, Zhaojun and  Hu, D. and Reichel, L. A Newton basis GMRES implementation. IMA J. Numer. Anal. 14 (1994), no. 4, 563-581.
  6: */
  7: #include <../src/ksp/ksp/impls/gmres/agmres/agmresimpl.h>

  9: static PetscErrorCode KSPAGMRESLejafmaxarray(PetscScalar *re, PetscInt pt, PetscInt n, PetscInt *pos)
 10: {
 11:   PetscInt    i;
 12:   PetscScalar mx;

 14:   PetscFunctionBegin;
 15:   mx   = re[0];
 16:   *pos = 0;
 17:   for (i = pt; i < n; i++) {
 18:     if (mx < re[i]) {
 19:       mx   = re[i];
 20:       *pos = i;
 21:     }
 22:   }
 23:   PetscFunctionReturn(PETSC_SUCCESS);
 24: }

 26: static PetscErrorCode KSPAGMRESLejaCfpdMax(PetscScalar *rm, PetscScalar *im, PetscInt *spos, PetscInt nbre, PetscInt n, PetscInt *rpos)
 27: {
 28:   PetscScalar rd, id, pd, max;
 29:   PetscInt    i, j;

 31:   PetscFunctionBegin;
 32:   pd    = 1.0;
 33:   max   = 0.0;
 34:   *rpos = 0;
 35:   for (i = 0; i < n; i++) {
 36:     for (j = 0; j < nbre; j++) {
 37:       rd = rm[i] - rm[spos[j]];
 38:       id = im[i] - im[spos[j]];
 39:       pd = pd * PetscSqrtReal(rd * rd + id * id);
 40:     }
 41:     if (max < pd) {
 42:       *rpos = i;
 43:       max   = pd;
 44:     }
 45:     pd = 1.0;
 46:   }
 47:   PetscFunctionReturn(PETSC_SUCCESS);
 48: }

 50: PetscErrorCode KSPAGMRESLejaOrdering(PetscScalar *re, PetscScalar *im, PetscScalar *rre, PetscScalar *rim, PetscInt m)
 51: {
 52:   PetscInt    *spos;
 53:   PetscScalar *n_cmpl, temp;
 54:   PetscInt     i, pos, j;

 56:   PetscFunctionBegin;
 57:   PetscCall(PetscMalloc1(m, &n_cmpl));
 58:   PetscCall(PetscMalloc1(m, &spos));
 59:   /* Check the proper order of complex conjugate pairs */
 60:   j = 0;
 61:   while (j < m) {
 62:     if (im[j] != 0.0) {  /* complex eigenvalue */
 63:       if (im[j] < 0.0) { /* change the order */
 64:         temp      = im[j + 1];
 65:         im[j + 1] = im[j];
 66:         im[j]     = temp;
 67:       }
 68:       j += 2;
 69:     } else j++;
 70:   }

 72:   for (i = 0; i < m; i++) n_cmpl[i] = PetscSqrtReal(re[i] * re[i] + im[i] * im[i]);
 73:   PetscCall(KSPAGMRESLejafmaxarray(n_cmpl, 0, m, &pos));
 74:   j = 0;
 75:   if (im[pos] >= 0.0) {
 76:     rre[0] = re[pos];
 77:     rim[0] = im[pos];
 78:     j++;
 79:     spos[0] = pos;
 80:   }
 81:   while (j < (m)) {
 82:     if (im[pos] > 0) {
 83:       rre[j]  = re[pos + 1];
 84:       rim[j]  = im[pos + 1];
 85:       spos[j] = pos + 1;
 86:       j++;
 87:     }
 88:     PetscCall(KSPAGMRESLejaCfpdMax(re, im, spos, j, m, &pos));
 89:     if (im[pos] < 0) pos--;

 91:     if ((im[pos] >= 0) && (j < m)) {
 92:       rre[j]  = re[pos];
 93:       rim[j]  = im[pos];
 94:       spos[j] = pos;
 95:       j++;
 96:     }
 97:   }
 98:   PetscCall(PetscFree(spos));
 99:   PetscCall(PetscFree(n_cmpl));
100:   PetscFunctionReturn(PETSC_SUCCESS);
101: }