static scs_int _ldl_factor(cs *A, scs_int P[], scs_int Pinv[], cs **L, scs_float **D) { scs_int kk, n = A->n; scs_int *Parent = (scs_int *)scs_malloc(n * sizeof(scs_int)); scs_int *Lnz = (scs_int *)scs_malloc(n * sizeof(scs_int)); scs_int *Flag = (scs_int *)scs_malloc(n * sizeof(scs_int)); scs_int *Pattern = (scs_int *)scs_malloc(n * sizeof(scs_int)); scs_float *Y = (scs_float *)scs_malloc(n * sizeof(scs_float)); (*L)->p = (scs_int *)scs_malloc((1 + n) * sizeof(scs_int)); /*scs_int Parent[n], Lnz[n], Flag[n], Pattern[n]; */ /*scs_float Y[n]; */ LDL_symbolic(n, A->p, A->i, (*L)->p, Parent, Lnz, Flag, P, Pinv); (*L)->nzmax = *((*L)->p + n); (*L)->x = (scs_float *)scs_malloc((*L)->nzmax * sizeof(scs_float)); (*L)->i = (scs_int *)scs_malloc((*L)->nzmax * sizeof(scs_int)); *D = (scs_float *)scs_malloc(n * sizeof(scs_float)); if (!(*D) || !(*L)->i || !(*L)->x || !Y || !Pattern || !Flag || !Lnz || !Parent) { return -1; } #if EXTRA_VERBOSE > 0 scs_printf("numeric factorization\n"); #endif kk = LDL_numeric(n, A->p, A->i, A->x, (*L)->p, Parent, Lnz, (*L)->i, (*L)->x, *D, Y, Pattern, Flag, P, Pinv); #if EXTRA_VERBOSE > 0 scs_printf("finished numeric factorization\n"); #endif scs_free(Parent); scs_free(Lnz); scs_free(Flag); scs_free(Pattern); scs_free(Y); return (kk - n); }
int main (void) #endif { /* ---------------------------------------------------------------------- */ /* local variables */ /* ---------------------------------------------------------------------- */ #ifdef USE_AMD double Info [AMD_INFO] ; #endif double r, rnorm, flops, maxrnorm = 0. ; double *Ax, *Lx, *B, *D, *X, *Y ; LDL_int matrix, *Ai, *Ap, *Li, *Lp, *P, *Pinv, *Perm, *PermInv, n, i, j, p, nz, *Flag, *Pattern, *Lnz, *Parent, trial, lnz, d, jumbled ; FILE *f ; char s [LEN] ; /* ---------------------------------------------------------------------- */ /* check the error-checking routines with null matrices */ /* ---------------------------------------------------------------------- */ i = 1 ; n = -1 ; if (LDL_valid_perm (n, (LDL_int *) NULL, &i) || !LDL_valid_perm (0, (LDL_int *) NULL, &i) || LDL_valid_matrix (n, (LDL_int *) NULL, (LDL_int *) NULL) || LDL_valid_matrix (0, &i, &i)) { printf (PROGRAM ": ldl error-checking routine failed\n") ; EXIT_ERROR ; } /* ---------------------------------------------------------------------- */ /* read in a factorize a set of matrices */ /* ---------------------------------------------------------------------- */ for (matrix = 1 ; matrix <= NMATRICES ; matrix++) { /* ------------------------------------------------------------------ */ /* read in the matrix and the permutation */ /* ------------------------------------------------------------------ */ sprintf (s, "../Matrix/A%02d", (int) matrix) ; if ((f = fopen (s, "r")) == (FILE *) NULL) { printf (PROGRAM ": could not open file: %s\n", s) ; EXIT_ERROR ; } fgets (s, LEN, f) ; printf ("\n\n--------------------------------------------------------"); printf ("\nInput matrix: %s", s) ; printf ("--------------------------------------------------------\n\n"); fscanf (f, LDL_ID " " LDL_ID, &n, &jumbled) ; n = (n < 0) ? (0) : (n) ; ALLOC_MEMORY (P, LDL_int, n) ; ALLOC_MEMORY (Ap, LDL_int, n+1) ; for (j = 0 ; j <= n ; j++) { fscanf (f, LDL_ID, &Ap [j]) ; } nz = Ap [n] ; ALLOC_MEMORY (Ai, LDL_int, nz) ; ALLOC_MEMORY (Ax, double, nz) ; for (p = 0 ; p < nz ; p++) { fscanf (f, LDL_ID , &Ai [p]) ; } for (p = 0 ; p < nz ; p++) { fscanf (f, "%lg", &Ax [p]) ; } for (j = 0 ; j < n ; j++) { fscanf (f, LDL_ID , &P [j]) ; } fclose (f) ; /* ------------------------------------------------------------------ */ /* check the matrix A and the permutation P */ /* ------------------------------------------------------------------ */ ALLOC_MEMORY (Flag, LDL_int, n) ; /* To test the error-checking routines, some of the input matrices * are not valid. So this error is expected to occur. */ if (!LDL_valid_matrix (n, Ap, Ai) || !LDL_valid_perm (n, P, Flag)) { printf (PROGRAM ": invalid matrix and/or permutation\n") ; FREE_MEMORY (P, LDL_int) ; FREE_MEMORY (Ap, LDL_int) ; FREE_MEMORY (Ai, LDL_int) ; FREE_MEMORY (Ax, double) ; FREE_MEMORY (Flag, LDL_int) ; continue ; } /* ------------------------------------------------------------------ */ /* get the AMD permutation, if available */ /* ------------------------------------------------------------------ */ #ifdef USE_AMD /* recompute the permutation with AMD */ /* Assume that AMD produces a valid permutation P. */ #ifdef LDL_LONG if (amd_l_order (n, Ap, Ai, P, (double *) NULL, Info) < AMD_OK) { printf (PROGRAM ": call to AMD failed\n") ; EXIT_ERROR ; } amd_l_control ((double *) NULL) ; amd_l_info (Info) ; #else if (amd_order (n, Ap, Ai, P, (double *) NULL, Info) < AMD_OK) { printf (PROGRAM ": call to AMD failed\n") ; EXIT_ERROR ; } amd_control ((double *) NULL) ; amd_info (Info) ; #endif #endif /* ------------------------------------------------------------------ */ /* allocate workspace and the first part of LDL factorization */ /* ------------------------------------------------------------------ */ ALLOC_MEMORY (Pinv, LDL_int, n) ; ALLOC_MEMORY (Y, double, n) ; ALLOC_MEMORY (Pattern, LDL_int, n) ; ALLOC_MEMORY (Lnz, LDL_int, n) ; ALLOC_MEMORY (Lp, LDL_int, n+1) ; ALLOC_MEMORY (Parent, LDL_int, n) ; ALLOC_MEMORY (D, double, n) ; ALLOC_MEMORY (B, double, n) ; ALLOC_MEMORY (X, double, n) ; /* ------------------------------------------------------------------ */ /* factorize twice, with and without permutation */ /* ------------------------------------------------------------------ */ for (trial = 1 ; trial <= 2 ; trial++) { if (trial == 1) { printf ("Factorize PAP'=LDL' and solve Ax=b\n") ; Perm = P ; PermInv = Pinv ; } else { printf ("Factorize A=LDL' and solve Ax=b\n") ; Perm = (LDL_int *) NULL ; PermInv = (LDL_int *) NULL ; } /* -------------------------------------------------------------- */ /* symbolic factorization to get Lp, Parent, Lnz, and Pinv */ /* -------------------------------------------------------------- */ LDL_symbolic (n, Ap, Ai, Lp, Parent, Lnz, Flag, Perm, PermInv) ; lnz = Lp [n] ; /* find # of nonzeros in L, and flop count for LDL_numeric */ flops = 0 ; for (j = 0 ; j < n ; j++) { flops += ((double) Lnz [j]) * (Lnz [j] + 2) ; } printf ("Nz in L: "LDL_ID" Flop count: %g\n", lnz, flops) ; /* -------------------------------------------------------------- */ /* allocate remainder of L, of size lnz */ /* -------------------------------------------------------------- */ ALLOC_MEMORY (Li, LDL_int, lnz) ; ALLOC_MEMORY (Lx, double, lnz) ; /* -------------------------------------------------------------- */ /* numeric factorization to get Li, Lx, and D */ /* -------------------------------------------------------------- */ d = LDL_numeric (n, Ap, Ai, Ax, Lp, Parent, Lnz, Li, Lx, D, Y, Flag, Pattern, Perm, PermInv) ; /* -------------------------------------------------------------- */ /* solve, or report singular case */ /* -------------------------------------------------------------- */ if (d != n) { printf ("Ax=b not solved since D("LDL_ID","LDL_ID") is zero.\n", d, d) ; } else { /* construct the right-hand-side, B */ for (i = 0 ; i < n ; i++) { B [i] = 1 + ((double) i) / 100 ; } /* solve Ax=b */ if (trial == 1) { /* the factorization is LDL' = PAP' */ LDL_perm (n, Y, B, P) ; /* y = Pb */ LDL_lsolve (n, Y, Lp, Li, Lx) ; /* y = L\y */ LDL_dsolve (n, Y, D) ; /* y = D\y */ LDL_ltsolve (n, Y, Lp, Li, Lx) ; /* y = L'\y */ LDL_permt (n, X, Y, P) ; /* x = P'y */ } else { /* the factorization is LDL' = A */ for (i = 0 ; i < n ; i++) /* x = b */ { X [i] = B [i] ; } LDL_lsolve (n, X, Lp, Li, Lx) ; /* x = L\x */ LDL_dsolve (n, X, D) ; /* x = D\x */ LDL_ltsolve (n, X, Lp, Li, Lx) ; /* x = L'\x */ } /* compute the residual y = Ax-b */ /* note that this code can tolerate a jumbled matrix */ for (i = 0 ; i < n ; i++) { Y [i] = -B [i] ; } for (j = 0 ; j < n ; j++) { for (p = Ap [j] ; p < Ap [j+1] ; p++) { Y [Ai [p]] += Ax [p] * X [j] ; } } /* rnorm = norm (y, inf) */ rnorm = 0 ; for (i = 0 ; i < n ; i++) { r = (Y [i] > 0) ? (Y [i]) : (-Y [i]) ; rnorm = (r > rnorm) ? (r) : (rnorm) ; } maxrnorm = (rnorm > maxrnorm) ? (rnorm) : (maxrnorm) ; printf ("relative maxnorm of residual: %g\n", rnorm) ; } /* -------------------------------------------------------------- */ /* free the size-lnz part of L */ /* -------------------------------------------------------------- */ FREE_MEMORY (Li, LDL_int) ; FREE_MEMORY (Lx, double) ; } /* free everything */ FREE_MEMORY (P, LDL_int) ; FREE_MEMORY (Ap, LDL_int) ; FREE_MEMORY (Ai, LDL_int) ; FREE_MEMORY (Ax, double) ; FREE_MEMORY (Pinv, LDL_int) ; FREE_MEMORY (Y, double) ; FREE_MEMORY (Flag, LDL_int) ; FREE_MEMORY (Pattern, LDL_int) ; FREE_MEMORY (Lnz, LDL_int) ; FREE_MEMORY (Lp, LDL_int) ; FREE_MEMORY (Parent, LDL_int) ; FREE_MEMORY (D, double) ; FREE_MEMORY (B, double) ; FREE_MEMORY (X, double) ; } printf ("\nLargest residual during all tests: %g\n", maxrnorm) ; if (maxrnorm < 1e-8) { printf ("\n" PROGRAM ": all tests passed\n") ; EXIT_OK ; } else { printf ("\n" PROGRAM ": one more tests failed (residual too high)\n") ; EXIT_ERROR ; } }