1: /*$Id: zerodiag.c,v 1.44 2001/08/06 21:16:10 bsmith Exp $*/

  3: /*
  4:     This file contains routines to reorder a matrix so that the diagonal
  5:     elements are nonzero.
  6:  */

 8:  #include src/mat/matimpl.h

 10: #define SWAP(a,b) {int _t; _t = a; a = b; b = _t; }

 12: #undef __FUNCT__  
 14: /*@
 15:     MatReorderForNonzeroDiagonal - Changes matrix ordering to remove
 16:     zeros from diagonal. This may help in the LU factorization to 
 17:     prevent a zero pivot.

 19:     Collective on Mat

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

 26:     Level: intermediate

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

 34:     Only works for SeqAIJ matrices

 36:     Options Database Keys (When using SLES):
 37: +      -pc_ilu_nonzeros_along_diagonal
 38: -      -pc_lu_nonzeros_along_diagonal

 40:     Algorithm Notes:
 41:     Column pivoting is used. 

 43:     1) Choice of column is made by looking at the
 44:        non-zero elements in the troublesome row for columns that are not yet 
 45:        included (moving from left to right).
 46:  
 47:     2) If (1) fails we check all the columns to the left of the current row
 48:        and see if one of them has could be swapped. It can be swapped if
 49:        its corresponding row has a non-zero in the column it is being 
 50:        swapped with; to make sure the previous nonzero diagonal remains 
 51:        nonzero


 54: @*/
 55: int MatReorderForNonzeroDiagonal(Mat mat,PetscReal atol,IS ris,IS cis)
 56: {
 57:   int         ierr,prow,k,nz,n,repl,*j,*col,*row,m,*icol,nnz,*jj,kk;
 58:   PetscScalar *v,*vv;
 59:   PetscReal   repla;
 60:   IS          icis;
 61:   PetscTruth  flg;

 67: 
 68:   PetscTypeCompare((PetscObject)mat,MATSEQAIJ,&flg);
 69:   if (!flg) SETERRQ(1,"Matrix must be of type SeqAIJ");

 71:   ISGetIndices(ris,&row);
 72:   ISGetIndices(cis,&col);
 73:   ISInvertPermutation(cis,PETSC_DECIDE,&icis);
 74:   ISGetIndices(icis,&icol);
 75:   MatGetSize(mat,&m,&n);

 77:   for (prow=0; prow<n; prow++) {
 78:     MatGetRow(mat,row[prow],&nz,&j,&v);
 79:     for (k=0; k<nz; k++) {if (icol[j[k]] == prow) break;}
 80:     if (k >= nz || PetscAbsScalar(v[k]) <= atol) {
 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(mat,row[repl],&nnz,&jj,&vv);
105:           for (kk=0; kk<nnz; kk++) {
106:             if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > atol) {
107:               MatRestoreRow(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(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(mat,row[k],&nnz,&jj,&vv);
122:         for (kk=0; kk<nnz; kk++) {
123:           if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > atol) {
124:             /* found a row */
125:             SWAP(row[prow],row[k]);
126:             goto found;
127:           }
128:         }
129:         MatRestoreRow(mat,row[k],&nnz,&jj,&vv);
130:       }

132:       found:;
133:     }
134:     MatRestoreRow(mat,row[prow],&nz,&j,&v);
135:   }
136:   ISRestoreIndices(ris,&row);
137:   ISRestoreIndices(cis,&col);
138:   ISRestoreIndices(icis,&icol);
139:   ISDestroy(icis);
140:   return(0);
141: }