1 #ifndef lint 2 static char vcid[] = "$Id: zerodiag.c,v 1.9 1996/11/19 16:31:54 bsmith Exp balay $"; 3 #endif 4 5 /* 6 This file contains routines to reorder a matrix so that the diagonal 7 elements are nonzero. 8 */ 9 10 #include "src/mat/matimpl.h" /*I "mat.h" I*/ 11 #include <math.h> 12 13 #define SWAP(a,b) {int _t; _t = a; a = b; b = _t; } 14 15 #undef __FUNCTION__ 16 #define __FUNCTION__ "MatZeroFindPre_Private" 17 /* Given a current row and current permutation, find a column permutation 18 that removes a zero diagonal */ 19 int MatZeroFindPre_Private(Mat mat,int prow,int* row,int* col,double repla, 20 double atol,int* rc,double* rcv ) 21 { 22 int k, nz, repl, *j, kk, nnz, *jj,ierr; 23 Scalar *v, *vv; 24 25 ierr = MatGetRow( mat, row[prow], &nz, &j, &v ); CHKERRQ(ierr); 26 for (k=0; k<nz; k++) { 27 if (col[j[k]] < prow && PetscAbsScalar(v[k]) > repla) { 28 /* See if this one will work */ 29 repl = col[j[k]]; 30 ierr = MatGetRow( mat, row[repl], &nnz, &jj, &vv ); CHKERRQ(ierr); 31 for (kk=0; kk<nnz; kk++) { 32 if (col[jj[kk]] == prow && PetscAbsScalar(vv[kk]) > atol) { 33 *rcv = PetscAbsScalar(v[k]); 34 *rc = repl; 35 ierr = MatRestoreRow( mat, row[repl], &nnz, &jj, &vv ); CHKERRQ(ierr); 36 ierr = MatRestoreRow( mat, row[prow], &nz, &j, &v ); CHKERRQ(ierr); 37 return 1; 38 } 39 } 40 ierr = MatRestoreRow( mat, row[repl], &nnz, &jj, &vv ); CHKERRQ(ierr); 41 } 42 } 43 ierr = MatRestoreRow( mat, row[prow], &nz, &j, &v ); CHKERRQ(ierr); 44 return 0; 45 } 46 47 #undef __FUNCTION__ 48 #define __FUNCTION__ "MatReorderForNonzeroDiagonal" 49 /*@ 50 MatReorderForNonzeroDiagonal - Changes matrix ordering to remove 51 zeros from diagonal. This may help in the LU factorization to 52 prevent a zero pivot. 53 54 Input Parameters: 55 . mat - matrix to reorder 56 . rmap,cmap - row and column permutations. Usually obtained from 57 . MatGetReordering(). 58 59 Notes: 60 This is not intended as a replacement for pivoting for matrices that 61 have ``bad'' structure. It is only a stop-gap measure. 62 63 Algorithm: 64 Column pivoting is used. Choice of column is made by looking at the 65 non-zero elements in the row. This algorithm is simple and fast but 66 does NOT guarentee that a non-singular or well conditioned 67 principle submatrix will be produced. 68 @*/ 69 int MatReorderForNonzeroDiagonal(Mat mat,double atol,IS ris,IS cis ) 70 { 71 int ierr, prow, k, nz, n, repl, *j, *col, *row, m; 72 Scalar *v; 73 double repla; 74 75 PetscValidHeaderSpecific(mat,MAT_COOKIE); 76 PetscValidHeaderSpecific(ris,IS_COOKIE); 77 PetscValidHeaderSpecific(cis,IS_COOKIE); 78 79 ierr = ISGetIndices(ris,&row); CHKERRQ(ierr); 80 ierr = ISGetIndices(cis,&col); CHKERRQ(ierr); 81 ierr = MatGetSize(mat,&m,&n); CHKERRQ(ierr); 82 83 for (prow=0; prow<n; prow++) { 84 ierr = MatGetRow( mat, row[prow], &nz, &j, &v ); CHKERRQ(ierr); 85 for (k=0; k<nz; k++) {if (col[j[k]] == prow) break;} 86 if (k >= nz || PetscAbsScalar(v[k]) <= atol) { 87 /* Element too small or zero; find the best candidate */ 88 repl = prow; 89 repla = (k >= nz) ? 0.0 : PetscAbsScalar(v[k]); 90 for (k=0; k<nz; k++) { 91 if (col[j[k]] > prow && PetscAbsScalar(v[k]) > repla) { 92 repl = col[j[k]]; 93 repla = PetscAbsScalar(v[k]); 94 } 95 } 96 if (prow == repl) { 97 /* Now we need to look for an element that allows us 98 to pivot with a previous column. To do this, we need 99 to be sure that we don't introduce a zero in a previous 100 diagonal */ 101 if (!MatZeroFindPre_Private(mat,prow,row,col,repla,atol,&repl,&repla)){ 102 SETERRQ(1,"MatReorderForNonzeroDiagonal:Can not reorder matrix"); 103 } 104 } 105 SWAP(col[prow],col[repl]); 106 } 107 ierr = MatRestoreRow( mat, row[prow], &nz, &j, &v ); CHKERRQ(ierr); 108 } 109 ierr = ISRestoreIndices(ris,&row); CHKERRQ(ierr); 110 ierr = ISRestoreIndices(cis,&col); CHKERRQ(ierr); 111 return 0; 112 } 113 114 115 116