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: }