GLOBAL Int CAMD_valid ( /* inputs, not modified on output: */ Int n_row, /* A is n_row-by-n_col */ Int n_col, const Int Ap [ ], /* column pointers of A, of size n_col+1 */ const Int Ai [ ] /* row indices of A, of size nz = Ap [n_col] */ ) { Int nz, j, p1, p2, ilast, i, p, result = CAMD_OK ; if (n_row < 0 || n_col < 0 || Ap == NULL || Ai == NULL) { return (CAMD_INVALID) ; } nz = Ap [n_col] ; if (Ap [0] != 0 || nz < 0) { /* column pointers must start at Ap [0] = 0, and Ap [n] must be >= 0 */ CAMD_DEBUG0 (("column 0 pointer bad or nz < 0\n")) ; return (CAMD_INVALID) ; } for (j = 0 ; j < n_col ; j++) { p1 = Ap [j] ; p2 = Ap [j+1] ; CAMD_DEBUG2 (("\nColumn: "ID" p1: "ID" p2: "ID"\n", j, p1, p2)) ; if (p1 > p2) { /* column pointers must be ascending */ CAMD_DEBUG0 (("column "ID" pointer bad\n", j)) ; return (CAMD_INVALID) ; } ilast = EMPTY ; for (p = p1 ; p < p2 ; p++) { i = Ai [p] ; CAMD_DEBUG3 (("row: "ID"\n", i)) ; if (i < 0 || i >= n_row) { /* row index out of range */ CAMD_DEBUG0 (("index out of range, col "ID" row "ID"\n", j, i)); return (CAMD_INVALID) ; } if (i <= ilast) { /* row index unsorted, or duplicate entry present */ CAMD_DEBUG1 (("index unsorted/dupl col "ID" row "ID"\n", j, i)); result = CAMD_OK_BUT_JUMBLED ; } ilast = i ; } } return (result) ; }
GLOBAL size_t CAMD(aat) /* returns nz in A+A' */ ( Int n, const Int Ap [ ], const Int Ai [ ], Int Len [ ], /* Len [j]: length of column j of A+A', excl diagonal*/ Int Tp [ ], /* workspace of size n */ double Info [ ] ) { Int p1, p2, p, i, j, pj, pj2, k, nzdiag, nzboth, nz ; double sym ; size_t nzaat ; #ifndef NDEBUG CAMD_debug_init ("CAMD AAT") ; for (k = 0 ; k < n ; k++) Tp [k] = EMPTY ; ASSERT (CAMD(valid) (n, n, Ap, Ai) == CAMD_OK) ; #endif if (Info != (double *) NULL) { /* clear the Info array, if it exists */ for (i = 0 ; i < CAMD_INFO ; i++) { Info [i] = EMPTY ; } Info [CAMD_STATUS] = CAMD_OK ; } for (k = 0 ; k < n ; k++) { Len [k] = 0 ; } nzdiag = 0 ; nzboth = 0 ; nz = Ap [n] ; for (k = 0 ; k < n ; k++) { p1 = Ap [k] ; p2 = Ap [k+1] ; CAMD_DEBUG2 (("\nAAT Column: "ID" p1: "ID" p2: "ID"\n", k, p1, p2)) ; /* construct A+A' */ for (p = p1 ; p < p2 ; ) { /* scan the upper triangular part of A */ j = Ai [p] ; if (j < k) { /* entry A (j,k) is in the strictly upper triangular part, * add both A (j,k) and A (k,j) to the matrix A+A' */ Len [j]++ ; Len [k]++ ; CAMD_DEBUG3 ((" upper ("ID","ID") ("ID","ID")\n", j,k, k,j)); p++ ; } else if (j == k) { /* skip the diagonal */ p++ ; nzdiag++ ; break ; } else /* j > k */ { /* first entry below the diagonal */ break ; } /* scan lower triangular part of A, in column j until reaching * row k. Start where last scan left off. */ ASSERT (Tp [j] != EMPTY) ; ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ; pj2 = Ap [j+1] ; for (pj = Tp [j] ; pj < pj2 ; ) { i = Ai [pj] ; if (i < k) { /* A (i,j) is only in the lower part, not in upper. * add both A (i,j) and A (j,i) to the matrix A+A' */ Len [i]++ ; Len [j]++ ; CAMD_DEBUG3 ((" lower ("ID","ID") ("ID","ID")\n", i,j, j,i)) ; pj++ ; } else if (i == k) { /* entry A (k,j) in lower part and A (j,k) in upper */ pj++ ; nzboth++ ; break ; } else /* i > k */ { /* consider this entry later, when k advances to i */ break ; } } Tp [j] = pj ; } /* Tp [k] points to the entry just below the diagonal in column k */ Tp [k] = p ; } /* clean up, for remaining mismatched entries */ for (j = 0 ; j < n ; j++) { for (pj = Tp [j] ; pj < Ap [j+1] ; pj++) { i = Ai [pj] ; /* A (i,j) is only in the lower part, not in upper. * add both A (i,j) and A (j,i) to the matrix A+A' */ Len [i]++ ; Len [j]++ ; CAMD_DEBUG3 ((" lower cleanup ("ID","ID") ("ID","ID")\n", i,j, j,i)) ; } } /* --------------------------------------------------------------------- */ /* compute the symmetry of the nonzero pattern of A */ /* --------------------------------------------------------------------- */ /* Given a matrix A, the symmetry of A is: * B = tril (spones (A), -1) + triu (spones (A), 1) ; * sym = nnz (B & B') / nnz (B) ; * or 1 if nnz (B) is zero. */ if (nz == nzdiag) { sym = 1 ; } else { sym = (2 * (double) nzboth) / ((double) (nz - nzdiag)) ; } nzaat = 0 ; for (k = 0 ; k < n ; k++) { nzaat += Len [k] ; } CAMD_DEBUG1 (("CAMD nz in A+A', excluding diagonal (nzaat) = %g\n", (double) nzaat)) ; CAMD_DEBUG1 ((" nzboth: "ID" nz: "ID" nzdiag: "ID" symmetry: %g\n", nzboth, nz, nzdiag, sym)) ; if (Info != (double *) NULL) { Info [CAMD_STATUS] = CAMD_OK ; Info [CAMD_N] = n ; Info [CAMD_NZ] = nz ; Info [CAMD_SYMMETRY] = sym ; /* symmetry of pattern of A */ Info [CAMD_NZDIAG] = nzdiag ; /* nonzeros on diagonal of A */ Info [CAMD_NZ_A_PLUS_AT] = nzaat ; /* nonzeros in A+A' */ } return (nzaat) ; }