Date: 2021-03-03T22:26:40+00:00

Actual source code: zerodiag.c
petsc-3.14.5 2021-03-03
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      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

     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

     50: @*/
     51: PetscErrorCode  MatReorderForNonzeroDiagonal(Mat mat,PetscReal abstol,IS ris,IS cis)
     52: {

     56:   PetscTryMethod(mat,"MatReorderForNonzeroDiagonal_C",(Mat,PetscReal,IS,IS),(mat,abstol,ris,cis));
     57:   return(0);
     58: }

     60: PETSC_INTERN PetscErrorCode MatGetRow_SeqAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**);
     61: PETSC_INTERN PetscErrorCode MatRestoreRow_SeqAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**);

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

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

     74:   /* access the indices of the IS directly, because it changes them */
     75:   row  = ((IS_General*)ris->data)->idx;
     76:   col  = ((IS_General*)cis->data)->idx;
     77:   ISInvertPermutation(cis,PETSC_DECIDE,&icis);
     78:   icol = ((IS_General*)icis->data)->idx;
     79:   MatGetSize(mat,&m,&n);

     81:   for (prow=0; prow<n; prow++) {
     82:     MatGetRow_SeqAIJ(mat,row[prow],&nz,&j,&v);
     83:     for (k=0; k<nz; k++) {
     84:       if (icol[j[k]] == prow) break;
     85:     }
     86:     if (k >= nz || PetscAbsScalar(v[k]) <= abstol) {
     87:       /* Element too small or zero; find the best candidate */
     88:       repla = (k >= nz) ? 0.0 : PetscAbsScalar(v[k]);
     89:       /*
     90:           Look for a later column we can swap with this one
     91:       */
     92:       for (k=0; k<nz; k++) {
     93:         if (icol[j[k]] > prow && PetscAbsScalar(v[k]) > repla) {
     94:           /* found a suitable later column */
     95:           repl = icol[j[k]];
     96:           SWAP(icol[col[prow]],icol[col[repl]]);
     97:           SWAP(col[prow],col[repl]);
     98:           goto found;
     99:         }
    100:       }
    101:       /*
    102:            Did not find a suitable later column so look for an earlier column
    103:            We need to be sure that we don't introduce a zero in a previous
    104:            diagonal
    105:       */
    106:       for (k=0; k<nz; k++) {
    107:         if (icol[j[k]] < prow && PetscAbsScalar(v[k]) > repla) {
    108:           /* See if this one will work */
    109:           repl = icol[j[k]];
    110:           MatGetRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);
    111:           for (kk=0; kk<nnz; kk++) {
    112:             if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > abstol) {
    113:               MatRestoreRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);
    114:               SWAP(icol[col[prow]],icol[col[repl]]);
    115:               SWAP(col[prow],col[repl]);
    116:               goto found;
    117:             }
    118:           }
    119:           MatRestoreRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);
    120:         }
    121:       }
    122:       /*
    123:           No column  suitable; instead check all future rows
    124:           Note: this will be very slow
    125:       */
    126:       for (k=prow+1; k<n; k++) {
    127:         MatGetRow_SeqAIJ(mat,row[k],&nnz,&jj,&vv);
    128:         for (kk=0; kk<nnz; kk++) {
    129:           if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > abstol) {
    130:             /* found a row */
    131:             SWAP(row[prow],row[k]);
    132:             goto found;
    133:           }
    134:         }
    135:         MatRestoreRow_SeqAIJ(mat,row[k],&nnz,&jj,&vv);
    136:       }

    138: found:;
    139:     }
    140:     MatRestoreRow_SeqAIJ(mat,row[prow],&nz,&j,&v);
    141:   }
    142:   ISDestroy(&icis);
    143:   return(0);
    144: }