Date: 2022-03-31T04:47:21+00:00

Actual source code: zerodiag.c

      2: /*
      3:     This file contains routines to reorder a matrix so that the diagonal
      4:     elements are nonzero.
      5:  */

      7: #include <petsc/private/matimpl.h>

      9: #define SWAP(a,b) {PetscInt _t; _t = a; a = b; b = _t; }

     11: /*@
     12:     MatReorderForNonzeroDiagonal - Changes matrix ordering to remove
     13:     zeros from diagonal. This may help in the LU factorization to
     14:     prevent a zero pivot.

     16:     Collective on Mat

     18:     Input Parameters:
     19: +   mat  - matrix to reorder
     20: -   rmap,cmap - row and column permutations.  Usually obtained from
     21:                MatGetOrdering().

     23:     Level: intermediate

     25:     Notes:
     26:     This is not intended as a replacement for pivoting for matrices that
     27:     have ``bad'' structure. It is only a stop-gap measure. Should be called
     28:     after a call to MatGetOrdering(), this routine changes the column
     29:     ordering defined in cis.

     31:     Only works for SeqAIJ matrices

     33:     Options Database Keys (When using KSP):
     34: .      -pc_factor_nonzeros_along_diagonal - Reorder to remove zeros from diagonal

     36:     Algorithm Notes:
     37:     Column pivoting is used.

     39:     1) Choice of column is made by looking at the
     40:        non-zero elements in the troublesome row for columns that are not yet
     41:        included (moving from left to right).

     43:     2) If (1) fails we check all the columns to the left of the current row
     44:        and see if one of them has could be swapped. It can be swapped if
     45:        its corresponding row has a non-zero in the column it is being
     46:        swapped with; to make sure the previous nonzero diagonal remains
     47:        nonzero

     49: @*/
     50: PetscErrorCode  MatReorderForNonzeroDiagonal(Mat mat,PetscReal abstol,IS ris,IS cis)
     51: {
     52:   PetscTryMethod(mat,"MatReorderForNonzeroDiagonal_C",(Mat,PetscReal,IS,IS),(mat,abstol,ris,cis));
     53:   return 0;
     54: }

     56: PETSC_INTERN PetscErrorCode MatGetRow_SeqAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**);
     57: PETSC_INTERN PetscErrorCode MatRestoreRow_SeqAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**);

     59: #include <../src/vec/is/is/impls/general/general.h>

     61: PETSC_INTERN PetscErrorCode  MatReorderForNonzeroDiagonal_SeqAIJ(Mat mat,PetscReal abstol,IS ris,IS cis)
     62: {
     63:   PetscInt       prow,k,nz,n,repl,*j,*col,*row,m,*icol,nnz,*jj,kk;
     64:   PetscScalar    *v,*vv;
     65:   PetscReal      repla;
     66:   IS             icis;

     68:   /* access the indices of the IS directly, because it changes them */
     69:   row  = ((IS_General*)ris->data)->idx;
     70:   col  = ((IS_General*)cis->data)->idx;
     71:   ISInvertPermutation(cis,PETSC_DECIDE,&icis);
     72:   icol = ((IS_General*)icis->data)->idx;
     73:   MatGetSize(mat,&m,&n);

     75:   for (prow=0; prow<n; prow++) {
     76:     MatGetRow_SeqAIJ(mat,row[prow],&nz,&j,&v);
     77:     for (k=0; k<nz; k++) {
     78:       if (icol[j[k]] == prow) break;
     79:     }
     80:     if (k >= nz || PetscAbsScalar(v[k]) <= abstol) {
     81:       /* Element too small or zero; find the best candidate */
     82:       repla = (k >= nz) ? 0.0 : PetscAbsScalar(v[k]);
     83:       /*
     84:           Look for a later column we can swap with this one
     85:       */
     86:       for (k=0; k<nz; k++) {
     87:         if (icol[j[k]] > prow && PetscAbsScalar(v[k]) > repla) {
     88:           /* found a suitable later column */
     89:           repl = icol[j[k]];
     90:           SWAP(icol[col[prow]],icol[col[repl]]);
     91:           SWAP(col[prow],col[repl]);
     92:           goto found;
     93:         }
     94:       }
     95:       /*
     96:            Did not find a suitable later column so look for an earlier column
     97:            We need to be sure that we don't introduce a zero in a previous
     98:            diagonal
     99:       */
    100:       for (k=0; k<nz; k++) {
    101:         if (icol[j[k]] < prow && PetscAbsScalar(v[k]) > repla) {
    102:           /* See if this one will work */
    103:           repl = icol[j[k]];
    104:           MatGetRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);
    105:           for (kk=0; kk<nnz; kk++) {
    106:             if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > abstol) {
    107:               MatRestoreRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);
    108:               SWAP(icol[col[prow]],icol[col[repl]]);
    109:               SWAP(col[prow],col[repl]);
    110:               goto found;
    111:             }
    112:           }
    113:           MatRestoreRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);
    114:         }
    115:       }
    116:       /*
    117:           No column  suitable; instead check all future rows
    118:           Note: this will be very slow
    119:       */
    120:       for (k=prow+1; k<n; k++) {
    121:         MatGetRow_SeqAIJ(mat,row[k],&nnz,&jj,&vv);
    122:         for (kk=0; kk<nnz; kk++) {
    123:           if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > abstol) {
    124:             /* found a row */
    125:             SWAP(row[prow],row[k]);
    126:             goto found;
    127:           }
    128:         }
    129:         MatRestoreRow_SeqAIJ(mat,row[k],&nnz,&jj,&vv);
    130:       }

    132: found:;
    133:     }
    134:     MatRestoreRow_SeqAIJ(mat,row[prow],&nz,&j,&v);
    135:   }
    136:   ISDestroy(&icis);
    137:   return 0;
    138: }