1 /*$Id: zerodiag.c,v 1.44 2001/08/06 21:16:10 bsmith Exp $*/ 2 3 /* 4 This file contains routines to reorder a matrix so that the diagonal 5 elements are nonzero. 6 */ 7 8 #include "src/mat/matimpl.h" /*I "petscmat.h" I*/ 9 10 #define SWAP(a,b) {int _t; _t = a; a = b; b = _t; } 11 12 #undef __FUNCT__ 13 #define __FUNCT__ "MatReorderForNonzeroDiagonal" 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. 18 19 Collective on Mat 20 21 Input Parameters: 22 + mat - matrix to reorder 23 - rmap,cmap - row and column permutations. Usually obtained from 24 MatGetOrdering(). 25 26 Level: intermediate 27 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. 33 34 Only works for SeqAIJ matrices 35 36 Options Database Keys (When using SLES): 37 + -pc_ilu_nonzeros_along_diagonal 38 - -pc_lu_nonzeros_along_diagonal 39 40 Algorithm Notes: 41 Column pivoting is used. 42 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 52 53 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; 62 63 PetscFunctionBegin; 64 PetscValidHeaderSpecific(mat,MAT_COOKIE); 65 PetscValidHeaderSpecific(ris,IS_COOKIE); 66 PetscValidHeaderSpecific(cis,IS_COOKIE); 67 68 ierr = PetscTypeCompare((PetscObject)mat,MATSEQAIJ,&flg);CHKERRQ(ierr); 69 if (!flg) SETERRQ(1,"Matrix must be of type SeqAIJ"); 70 71 ierr = ISGetIndices(ris,&row);CHKERRQ(ierr); 72 ierr = ISGetIndices(cis,&col);CHKERRQ(ierr); 73 ierr = ISInvertPermutation(cis,PETSC_DECIDE,&icis);CHKERRQ(ierr); 74 ierr = ISGetIndices(icis,&icol);CHKERRQ(ierr); 75 ierr = MatGetSize(mat,&m,&n);CHKERRQ(ierr); 76 77 for (prow=0; prow<n; prow++) { 78 ierr = MatGetRow(mat,row[prow],&nz,&j,&v);CHKERRQ(ierr); 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 ierr = MatGetRow(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 105 for (kk=0; kk<nnz; kk++) { 106 if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > atol) { 107 ierr = MatRestoreRow(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 108 SWAP(icol[col[prow]],icol[col[repl]]); 109 SWAP(col[prow],col[repl]); 110 goto found; 111 } 112 } 113 ierr = MatRestoreRow(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 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 ierr = MatGetRow(mat,row[k],&nnz,&jj,&vv);CHKERRQ(ierr); 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 ierr = MatRestoreRow(mat,row[k],&nnz,&jj,&vv);CHKERRQ(ierr); 130 } 131 132 found:; 133 } 134 ierr = MatRestoreRow(mat,row[prow],&nz,&j,&v);CHKERRQ(ierr); 135 } 136 ierr = ISRestoreIndices(ris,&row);CHKERRQ(ierr); 137 ierr = ISRestoreIndices(cis,&col);CHKERRQ(ierr); 138 ierr = ISRestoreIndices(icis,&icol);CHKERRQ(ierr); 139 ierr = ISDestroy(icis);CHKERRQ(ierr); 140 PetscFunctionReturn(0); 141 } 142 143 144 145