1 2 /* 3 This file contains routines to reorder a matrix so that the diagonal 4 elements are nonzero. 5 */ 6 7 #include <petsc-private/matimpl.h> /*I "petscmat.h" I*/ 8 9 #define SWAP(a,b) {PetscInt _t; _t = a; a = b; b = _t; } 10 11 #undef __FUNCT__ 12 #define __FUNCT__ "MatReorderForNonzeroDiagonal" 13 /*@ 14 MatReorderForNonzeroDiagonal - Changes matrix ordering to remove 15 zeros from diagonal. This may help in the LU factorization to 16 prevent a zero pivot. 17 18 Collective on Mat 19 20 Input Parameters: 21 + mat - matrix to reorder 22 - rmap,cmap - row and column permutations. Usually obtained from 23 MatGetOrdering(). 24 25 Level: intermediate 26 27 Notes: 28 This is not intended as a replacement for pivoting for matrices that 29 have ``bad'' structure. It is only a stop-gap measure. Should be called 30 after a call to MatGetOrdering(), this routine changes the column 31 ordering defined in cis. 32 33 Only works for SeqAIJ matrices 34 35 Options Database Keys (When using KSP): 36 . -pc_factor_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 PetscErrorCode MatReorderForNonzeroDiagonal(Mat mat,PetscReal abstol,IS ris,IS cis) 54 { 55 PetscErrorCode ierr; 56 57 PetscFunctionBegin; 58 ierr = PetscTryMethod(mat,"MatReorderForNonzeroDiagonal_C",(Mat,PetscReal,IS,IS),(mat,abstol,ris,cis));CHKERRQ(ierr); 59 PetscFunctionReturn(0); 60 } 61 62 extern PetscErrorCode MatGetRow_SeqAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**); 63 extern PetscErrorCode MatRestoreRow_SeqAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**); 64 65 #include <../src/vec/is/impls/general/general.h> 66 67 EXTERN_C_BEGIN 68 #undef __FUNCT__ 69 #define __FUNCT__ "MatReorderForNonzeroDiagonal_SeqAIJ" 70 PetscErrorCode MatReorderForNonzeroDiagonal_SeqAIJ(Mat mat,PetscReal abstol,IS ris,IS cis) 71 { 72 PetscErrorCode ierr; 73 PetscInt prow,k,nz,n,repl,*j,*col,*row,m,*icol,nnz,*jj,kk; 74 PetscScalar *v,*vv; 75 PetscReal repla; 76 IS icis; 77 78 PetscFunctionBegin; 79 /* access the indices of the IS directly, because it changes them */ 80 row = ((IS_General*)ris->data)->idx; 81 col = ((IS_General*)cis->data)->idx; 82 ierr = ISInvertPermutation(cis,PETSC_DECIDE,&icis);CHKERRQ(ierr); 83 icol = ((IS_General*)icis->data)->idx; 84 ierr = MatGetSize(mat,&m,&n);CHKERRQ(ierr); 85 86 for (prow=0; prow<n; prow++) { 87 ierr = MatGetRow_SeqAIJ(mat,row[prow],&nz,&j,&v);CHKERRQ(ierr); 88 for (k=0; k<nz; k++) {if (icol[j[k]] == prow) break;} 89 if (k >= nz || PetscAbsScalar(v[k]) <= abstol) { 90 /* Element too small or zero; find the best candidate */ 91 repla = (k >= nz) ? 0.0 : PetscAbsScalar(v[k]); 92 /* 93 Look for a later column we can swap with this one 94 */ 95 for (k=0; k<nz; k++) { 96 if (icol[j[k]] > prow && PetscAbsScalar(v[k]) > repla) { 97 /* found a suitable later column */ 98 repl = icol[j[k]]; 99 SWAP(icol[col[prow]],icol[col[repl]]); 100 SWAP(col[prow],col[repl]); 101 goto found; 102 } 103 } 104 /* 105 Did not find a suitable later column so look for an earlier column 106 We need to be sure that we don't introduce a zero in a previous 107 diagonal 108 */ 109 for (k=0; k<nz; k++) { 110 if (icol[j[k]] < prow && PetscAbsScalar(v[k]) > repla) { 111 /* See if this one will work */ 112 repl = icol[j[k]]; 113 ierr = MatGetRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 114 for (kk=0; kk<nnz; kk++) { 115 if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > abstol) { 116 ierr = MatRestoreRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 117 SWAP(icol[col[prow]],icol[col[repl]]); 118 SWAP(col[prow],col[repl]); 119 goto found; 120 } 121 } 122 ierr = MatRestoreRow_SeqAIJ(mat,row[repl],&nnz,&jj,&vv);CHKERRQ(ierr); 123 } 124 } 125 /* 126 No column suitable; instead check all future rows 127 Note: this will be very slow 128 */ 129 for (k=prow+1; k<n; k++) { 130 ierr = MatGetRow_SeqAIJ(mat,row[k],&nnz,&jj,&vv);CHKERRQ(ierr); 131 for (kk=0; kk<nnz; kk++) { 132 if (icol[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > abstol) { 133 /* found a row */ 134 SWAP(row[prow],row[k]); 135 goto found; 136 } 137 } 138 ierr = MatRestoreRow_SeqAIJ(mat,row[k],&nnz,&jj,&vv);CHKERRQ(ierr); 139 } 140 141 found:; 142 } 143 ierr = MatRestoreRow_SeqAIJ(mat,row[prow],&nz,&j,&v);CHKERRQ(ierr); 144 } 145 ierr = ISDestroy(&icis);CHKERRQ(ierr); 146 PetscFunctionReturn(0); 147 } 148 EXTERN_C_END 149 150 151