Date: 2022-03-31T04:48:11+00:00

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

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

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

     48: PetscErrorCode KSPAGMRESLejaOrdering(PetscScalar *re, PetscScalar *im, PetscScalar *rre, PetscScalar *rim, PetscInt m)
     49: {
     50:   PetscInt       *spos;
     51:   PetscScalar    *n_cmpl,temp;
     52:   PetscInt       i, pos, j;

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

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

     88:     if ((im[pos] >= 0) && (j < m)) {
     89:       rre[j]  = re[pos];
     90:       rim[j]  = im[pos];
     91:       spos[j] = pos;
     92:       j++;
     93:     }
     94:   }
     95:   PetscFree(spos);
     96:   PetscFree(n_cmpl);
     97:   return 0;
     98: }