/* nag_dporfs (f07fhc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include int main(void) { /* Scalars */ Integer berr_len, ferr_len, i, j, n, nrhs, pda, pdaf, pdb, pdx; Integer exit_status = 0; Nag_UploType uplo; NagError fail; Nag_OrderType order; /* Arrays */ char nag_enum_arg[40]; double *a = 0, *af = 0, *b = 0, *berr = 0, *ferr = 0, *x = 0; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J-1)*pda + I - 1] #define AF(I, J) af[(J-1)*pdaf + I - 1] #define B(I, J) b[(J-1)*pdb + I - 1] #define X(I, J) x[(J-1)*pdx + I - 1] order = Nag_ColMajor; #else #define A(I, J) a[(I-1)*pda + J - 1] #define AF(I, J) af[(I-1)*pdaf + J - 1] #define B(I, J) b[(I-1)*pdb + J - 1] #define X(I, J) x[(I-1)*pdx + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dporfs (f07fhc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%ld%*[^\n] ", &n, &nrhs); #ifdef NAG_COLUMN_MAJOR pda = n; pdaf = n; pdb = n; pdx = n; #else pda = n; pdaf = n; pdb = nrhs; pdx = nrhs; #endif ferr_len = nrhs; berr_len = nrhs; /* Allocate memory */ if (!(a = NAG_ALLOC(n * n, double)) || !(af = NAG_ALLOC(n * n, double)) || !(b = NAG_ALLOC(n * nrhs, double)) || !(berr = NAG_ALLOC(berr_len, double)) || !(ferr = NAG_ALLOC(ferr_len, double)) || !(x = NAG_ALLOC(n * nrhs, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A and B from data file, and copy A to AF and B to X */ scanf(" %39s%*[^\n] ", nag_enum_arg); /* nag_enum_name_to_value (x04nac). * Converts NAG enum member name to value */ uplo = (Nag_UploType) nag_enum_name_to_value(nag_enum_arg); if (uplo == Nag_Upper) { for (i = 1; i <= n; ++i) { for (j = i; j <= n; ++j) scanf("%lf", &A(i, j)); } scanf("%*[^\n] "); } else { for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) scanf("%lf", &A(i, j)); } scanf("%*[^\n] "); } for (i = 1; i <= n; ++i) { for (j = 1; j <= nrhs; ++j) scanf("%lf", &B(i, j)); } scanf("%*[^\n] "); /* Copy A to AF and B to X */ if (uplo == Nag_Upper) { for (i = 1; i <= n; ++i) { for (j = i; j <= n; ++j) AF(i, j) = A(i, j); } } else { for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) AF(i, j) = A(i, j); } } for (i = 1; i <= n; ++i) { for (j = 1; j <= nrhs; ++j) X(i, j) = B(i, j); } /* Factorize A in the array AF */ /* nag_dpotrf (f07fdc). * Cholesky factorization of real symmetric * positive-definite matrix */ nag_dpotrf(order, uplo, n, af, pdaf, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dpotrf (f07fdc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Compute solution in the array X */ /* nag_dpotrs (f07fec). * Solution of real symmetric positive-definite system of * linear equations, multiple right-hand sides, matrix * already factorized by nag_dpotrf (f07fdc) */ nag_dpotrs(order, uplo, n, nrhs, af, pdaf, x, pdx, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dpotrs (f07fec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Improve solution, and compute backward errors and */ /* estimated bounds on the forward errors */ /* nag_dporfs (f07fhc). * Refined solution with error bounds of real symmetric * positive-definite system of linear equations, multiple * right-hand sides */ nag_dporfs(order, uplo, n, nrhs, a, pda, af, pdaf, b, pdb, x, pdx, ferr, berr, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dporfs (f07fhc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print solution */ /* nag_gen_real_mat_print (x04cac). * Print real general matrix (easy-to-use) */ fflush(stdout); nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, x, pdx, "Solution(s)", 0, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\nBackward errors (machine-dependent)\n"); for (j = 1; j <= nrhs; ++j) printf("%11.1e%s", berr[j-1], j%7 == 0?"\n":" "); printf("\nEstimated forward error bounds (machine-dependent)\n"); for (j = 1; j <= nrhs; ++j) printf("%11.1e%s", ferr[j-1], j%7 == 0 || j == nrhs?"\n":" "); END: NAG_FREE(a); NAG_FREE(af); NAG_FREE(b); NAG_FREE(berr); NAG_FREE(ferr); NAG_FREE(x); return exit_status; }