1: #define PETSCMAT_DLL

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

 8:  #include include/private/matimpl.h

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

 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 KSP):
 37: .      -pc_factor_nonzeros_along_diagonal

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

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


 53: @*/
 54: PetscErrorCode  MatReorderForNonzeroDiagonal(Mat mat,PetscReal abstol,IS ris,IS cis)
 55: {
 56:   PetscErrorCode ierr,(*f)(Mat,PetscReal,IS,IS);

 59:   PetscObjectQueryFunction((PetscObject)mat,"MatReorderForNonzeroDiagonal_C",(void (**)(void))&f);
 60:   if (f) {
 61:     (*f)(mat,abstol,ris,cis);
 62:   }
 63:   return(0);
 64: }

 66: EXTERN PetscErrorCode MatGetRow_SeqAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**);
 67: EXTERN PetscErrorCode MatRestoreRow_SeqAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**);

 72: PetscErrorCode  MatReorderForNonzeroDiagonal_SeqAIJ(Mat mat,PetscReal abstol,IS ris,IS cis)
 73: {
 75:   PetscInt       prow,k,nz,n,repl,*j,*col,*row,m,*icol,nnz,*jj,kk;
 76:   PetscScalar    *v,*vv;
 77:   PetscReal      repla;
 78:   IS             icis;

 81:   ISGetIndices(ris,&row);
 82:   ISGetIndices(cis,&col);
 83:   ISInvertPermutation(cis,PETSC_DECIDE,&icis);
 84:   ISGetIndices(icis,&icol);
 85:   MatGetSize(mat,&m,&n);

 87:   for (prow=0; prow<n; prow++) {
 88:     MatGetRow_SeqAIJ(mat,row[prow],&nz,&j,&v);
 89:     for (k=0; k<nz; k++) {if (icol[j[k]] == prow) break;}
 90:     if (k >= nz || PetscAbsScalar(v[k]) <= abstol) {
 91:       /* Element too small or zero; find the best candidate */
 92:       repla = (k >= nz) ? 0.0 : PetscAbsScalar(v[k]);
 93:       /*
 94:           Look for a later column we can swap with this one
 95:       */
 96:       for (k=0; k<nz; k++) {
 97:         if (icol[j[k]] > prow && PetscAbsScalar(v[k]) > repla) {
 98:           /* found a suitable later column */
 99:           repl  = icol[j[k]];
100:           SWAP(icol[col[prow]],icol[col[repl]]);
101:           SWAP(col[prow],col[repl]);
102:           goto found;
103:         }
104:       }
105:       /* 
106:            Did not find a suitable later column so look for an earlier column
107:            We need to be sure that we don't introduce a zero in a previous
108:            diagonal 
109:       */
110:       for (k=0; k<nz; k++) {
111:         if (icol[j[k]] < prow && PetscAbsScalar(v[k]) > repla) {
112:           /* See if this one will work */
113:           repl  = icol[j[k]];
114:           MatGetRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);
115:           for (kk=0; kk<nnz; kk++) {
116:             if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > abstol) {
117:               MatRestoreRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);
118:               SWAP(icol[col[prow]],icol[col[repl]]);
119:               SWAP(col[prow],col[repl]);
120:               goto found;
121:             }
122:           }
123:           MatRestoreRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);
124:         }
125:       }
126:       /* 
127:           No column  suitable; instead check all future rows 
128:           Note: this will be very slow 
129:       */
130:       for (k=prow+1; k<n; k++) {
131:         MatGetRow_SeqAIJ(mat,row[k],&nnz,&jj,&vv);
132:         for (kk=0; kk<nnz; kk++) {
133:           if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > abstol) {
134:             /* found a row */
135:             SWAP(row[prow],row[k]);
136:             goto found;
137:           }
138:         }
139:         MatRestoreRow_SeqAIJ(mat,row[k],&nnz,&jj,&vv);
140:       }

142:       found:;
143:     }
144:     MatRestoreRow_SeqAIJ(mat,row[prow],&nz,&j,&v);
145:   }
146:   ISRestoreIndices(ris,&row);
147:   ISRestoreIndices(cis,&col);
148:   ISRestoreIndices(icis,&icol);
149:   ISDestroy(icis);
150:   return(0);
151: }