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 KSP): 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,(*f)(Mat,PetscReal,IS,IS); 58 59 PetscFunctionBegin; 60 ierr = PetscObjectQueryFunction((PetscObject)mat,"MatReorderForNonzeroDiagonal_C",(void (**)(void))&f);CHKERRQ(ierr); 61 if (f) { 62 ierr = (*f)(mat,atol,ris,cis);CHKERRQ(ierr); 63 } 64 PetscFunctionReturn(0); 65 } 66 67 EXTERN_C_BEGIN 68 #undef __FUNCT__ 69 #define __FUNCT__ "MatReorderForNonzeroDiagonal_SeqAIJ" 70 int MatReorderForNonzeroDiagonal_SeqAIJ(Mat mat,PetscReal atol,IS ris,IS cis) 71 { 72 int ierr,prow,k,nz,n,repl,*j,*col,*row,m,*icol,nnz,*jj,kk; 73 PetscScalar *v,*vv; 74 PetscReal repla; 75 IS icis; 76 77 PetscFunctionBegin; 78 PetscValidHeaderSpecific(mat,MAT_COOKIE); 79 PetscValidHeaderSpecific(ris,IS_COOKIE); 80 PetscValidHeaderSpecific(cis,IS_COOKIE); 81 82 ierr = ISGetIndices(ris,&row);CHKERRQ(ierr); 83 ierr = ISGetIndices(cis,&col);CHKERRQ(ierr); 84 ierr = ISInvertPermutation(cis,PETSC_DECIDE,&icis);CHKERRQ(ierr); 85 ierr = ISGetIndices(icis,&icol);CHKERRQ(ierr); 86 ierr = MatGetSize(mat,&m,&n);CHKERRQ(ierr); 87 88 for (prow=0; prow<n; prow++) { 89 ierr = MatGetRow(mat,row[prow],&nz,&j,&v);CHKERRQ(ierr); 90 for (k=0; k<nz; k++) {if (icol[j[k]] == prow) break;} 91 if (k >= nz || PetscAbsScalar(v[k]) <= atol) { 92 /* Element too small or zero; find the best candidate */ 93 repla = (k >= nz) ? 0.0 : PetscAbsScalar(v[k]); 94 /* 95 Look for a later column we can swap with this one 96 */ 97 for (k=0; k<nz; k++) { 98 if (icol[j[k]] > prow && PetscAbsScalar(v[k]) > repla) { 99 /* found a suitable later column */ 100 repl = icol[j[k]]; 101 SWAP(icol[col[prow]],icol[col[repl]]); 102 SWAP(col[prow],col[repl]); 103 goto found; 104 } 105 } 106 /* 107 Did not find a suitable later column so look for an earlier column 108 We need to be sure that we don't introduce a zero in a previous 109 diagonal 110 */ 111 for (k=0; k<nz; k++) { 112 if (icol[j[k]] < prow && PetscAbsScalar(v[k]) > repla) { 113 /* See if this one will work */ 114 repl = icol[j[k]]; 115 ierr = MatGetRow(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 116 for (kk=0; kk<nnz; kk++) { 117 if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > atol) { 118 ierr = MatRestoreRow(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 119 SWAP(icol[col[prow]],icol[col[repl]]); 120 SWAP(col[prow],col[repl]); 121 goto found; 122 } 123 } 124 ierr = MatRestoreRow(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 125 } 126 } 127 /* 128 No column suitable; instead check all future rows 129 Note: this will be very slow 130 */ 131 for (k=prow+1; k<n; k++) { 132 ierr = MatGetRow(mat,row[k],&nnz,&jj,&vv);CHKERRQ(ierr); 133 for (kk=0; kk<nnz; kk++) { 134 if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > atol) { 135 /* found a row */ 136 SWAP(row[prow],row[k]); 137 goto found; 138 } 139 } 140 ierr = MatRestoreRow(mat,row[k],&nnz,&jj,&vv);CHKERRQ(ierr); 141 } 142 143 found:; 144 } 145 ierr = MatRestoreRow(mat,row[prow],&nz,&j,&v);CHKERRQ(ierr); 146 } 147 ierr = ISRestoreIndices(ris,&row);CHKERRQ(ierr); 148 ierr = ISRestoreIndices(cis,&col);CHKERRQ(ierr); 149 ierr = ISRestoreIndices(icis,&icol);CHKERRQ(ierr); 150 ierr = ISDestroy(icis);CHKERRQ(ierr); 151 PetscFunctionReturn(0); 152 } 153 EXTERN_C_END 154 155 156