1 /* 2 This file contains routines to reorder a matrix so that the diagonal 3 elements are nonzero. 4 */ 5 6 #include "src/mat/matimpl.h" /*I "petscmat.h" I*/ 7 8 #define SWAP(a,b) {int _t; _t = a; a = b; b = _t; } 9 10 #undef __FUNCT__ 11 #define __FUNCT__ "MatReorderForNonzeroDiagonal" 12 /*@ 13 MatReorderForNonzeroDiagonal - Changes matrix ordering to remove 14 zeros from diagonal. This may help in the LU factorization to 15 prevent a zero pivot. 16 17 Collective on Mat 18 19 Input Parameters: 20 + mat - matrix to reorder 21 - rmap,cmap - row and column permutations. Usually obtained from 22 MatGetOrdering(). 23 24 Level: intermediate 25 26 Notes: 27 This is not intended as a replacement for pivoting for matrices that 28 have ``bad'' structure. It is only a stop-gap measure. Should be called 29 after a call to MatGetOrdering(), this routine changes the column 30 ordering defined in cis. 31 32 Only works for SeqAIJ matrices 33 34 Options Database Keys (When using KSP): 35 + -pc_ilu_nonzeros_along_diagonal 36 - -pc_lu_nonzeros_along_diagonal 37 38 Algorithm Notes: 39 Column pivoting is used. 40 41 1) Choice of column is made by looking at the 42 non-zero elements in the troublesome row for columns that are not yet 43 included (moving from left to right). 44 45 2) If (1) fails we check all the columns to the left of the current row 46 and see if one of them has could be swapped. It can be swapped if 47 its corresponding row has a non-zero in the column it is being 48 swapped with; to make sure the previous nonzero diagonal remains 49 nonzero 50 51 52 @*/ 53 int MatReorderForNonzeroDiagonal(Mat mat,PetscReal atol,IS ris,IS cis) 54 { 55 int ierr,(*f)(Mat,PetscReal,IS,IS); 56 57 PetscFunctionBegin; 58 ierr = PetscObjectQueryFunction((PetscObject)mat,"MatReorderForNonzeroDiagonal_C",(void (**)(void))&f);CHKERRQ(ierr); 59 if (f) { 60 ierr = (*f)(mat,atol,ris,cis);CHKERRQ(ierr); 61 } 62 PetscFunctionReturn(0); 63 } 64 65 EXTERN_C_BEGIN 66 #undef __FUNCT__ 67 #define __FUNCT__ "MatReorderForNonzeroDiagonal_SeqAIJ" 68 int MatReorderForNonzeroDiagonal_SeqAIJ(Mat mat,PetscReal atol,IS ris,IS cis) 69 { 70 int ierr,prow,k,nz,n,repl,*j,*col,*row,m,*icol,nnz,*jj,kk; 71 PetscScalar *v,*vv; 72 PetscReal repla; 73 IS icis; 74 75 PetscFunctionBegin; 76 ierr = ISGetIndices(ris,&row);CHKERRQ(ierr); 77 ierr = ISGetIndices(cis,&col);CHKERRQ(ierr); 78 ierr = ISInvertPermutation(cis,PETSC_DECIDE,&icis);CHKERRQ(ierr); 79 ierr = ISGetIndices(icis,&icol);CHKERRQ(ierr); 80 ierr = MatGetSize(mat,&m,&n);CHKERRQ(ierr); 81 82 for (prow=0; prow<n; prow++) { 83 ierr = MatGetRow(mat,row[prow],&nz,&j,&v);CHKERRQ(ierr); 84 for (k=0; k<nz; k++) {if (icol[j[k]] == prow) break;} 85 if (k >= nz || PetscAbsScalar(v[k]) <= atol) { 86 /* Element too small or zero; find the best candidate */ 87 repla = (k >= nz) ? 0.0 : PetscAbsScalar(v[k]); 88 /* 89 Look for a later column we can swap with this one 90 */ 91 for (k=0; k<nz; k++) { 92 if (icol[j[k]] > prow && PetscAbsScalar(v[k]) > repla) { 93 /* found a suitable later column */ 94 repl = icol[j[k]]; 95 SWAP(icol[col[prow]],icol[col[repl]]); 96 SWAP(col[prow],col[repl]); 97 goto found; 98 } 99 } 100 /* 101 Did not find a suitable later column so look for an earlier column 102 We need to be sure that we don't introduce a zero in a previous 103 diagonal 104 */ 105 for (k=0; k<nz; k++) { 106 if (icol[j[k]] < prow && PetscAbsScalar(v[k]) > repla) { 107 /* See if this one will work */ 108 repl = icol[j[k]]; 109 ierr = MatGetRow(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 110 for (kk=0; kk<nnz; kk++) { 111 if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > atol) { 112 ierr = MatRestoreRow(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 113 SWAP(icol[col[prow]],icol[col[repl]]); 114 SWAP(col[prow],col[repl]); 115 goto found; 116 } 117 } 118 ierr = MatRestoreRow(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 119 } 120 } 121 /* 122 No column suitable; instead check all future rows 123 Note: this will be very slow 124 */ 125 for (k=prow+1; k<n; k++) { 126 ierr = MatGetRow(mat,row[k],&nnz,&jj,&vv);CHKERRQ(ierr); 127 for (kk=0; kk<nnz; kk++) { 128 if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > atol) { 129 /* found a row */ 130 SWAP(row[prow],row[k]); 131 goto found; 132 } 133 } 134 ierr = MatRestoreRow(mat,row[k],&nnz,&jj,&vv);CHKERRQ(ierr); 135 } 136 137 found:; 138 } 139 ierr = MatRestoreRow(mat,row[prow],&nz,&j,&v);CHKERRQ(ierr); 140 } 141 ierr = ISRestoreIndices(ris,&row);CHKERRQ(ierr); 142 ierr = ISRestoreIndices(cis,&col);CHKERRQ(ierr); 143 ierr = ISRestoreIndices(icis,&icol);CHKERRQ(ierr); 144 ierr = ISDestroy(icis);CHKERRQ(ierr); 145 PetscFunctionReturn(0); 146 } 147 EXTERN_C_END 148 149 150