Actual source code: agmresleja.c
petsc-3.15.0 2021-03-30
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      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;

     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:   return(0);
     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;

     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:   return(0);
     48: }

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

     58:   PetscMalloc1(m, &n_cmpl);
     59:   PetscMalloc1(m, &spos);
     60:   /* Check the proper order of complex conjugate pairs */
     61:   j = 0;
     62:   while (j  < m) {
     63:     if (im[j] != 0.0) { /* complex eigenvalue */
     64:       if (im[j] < 0.0) { /* change the order */
     65:         temp    = im[j+1];
     66:         im[j+1] = im[j];
     67:         im[j]   = temp;
     68:       }
     69:       j += 2;
     70:     } else j++;
     71:   }

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

     92:     if ((im[pos] >= 0) && (j < m)) {
     93:       rre[j]  = re[pos];
     94:       rim[j]  = im[pos];
     95:       spos[j] = pos;
     96:       j++;
     97:     }
     98:   }
     99:   PetscFree(spos);
    100:   PetscFree(n_cmpl);
    101:   return(0);
    102: }