/* nag_dpbrfs (f07hhc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include int main(void) { /* Scalars */ Integer i, j, k, kd, n, nrhs, pdab, pdafb, pdb, pdx; Integer ferr_len, berr_len; Integer exit_status = 0; Nag_UploType uplo; NagError fail; Nag_OrderType order; /* Arrays */ char nag_enum_arg[40]; double *ab = 0, *afb = 0, *b = 0, *berr = 0, *ferr = 0, *x = 0; #ifdef NAG_COLUMN_MAJOR #define AB_UPPER(I, J) ab[(J-1)*pdab + k + I - J - 1] #define AB_LOWER(I, J) ab[(J-1)*pdab + I - J] #define AFB_UPPER(I, J) afb[(J-1)*pdafb + k + I - J - 1] #define AFB_LOWER(I, J) afb[(J-1)*pdafb + I - J] #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 AB_UPPER(I, J) ab[(I-1)*pdab + J - I] #define AB_LOWER(I, J) ab[(I-1)*pdab + k + J - I - 1] #define AFB_UPPER(I, J) afb[(I-1)*pdafb + J - I] #define AFB_LOWER(I, J) afb[(I-1)*pdafb + k + J - I - 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_dpbrfs (f07hhc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%ld%ld%*[^\n] ", &n, &kd, &nrhs); pdab = kd + 1; pdafb = kd + 1; #ifdef NAG_COLUMN_MAJOR pdb = n; pdx = n; #else pdb = nrhs; pdx = nrhs; #endif ferr_len = nrhs; berr_len = nrhs; /* Allocate memory */ if (!(berr = NAG_ALLOC(berr_len, double)) || !(ferr = NAG_ALLOC(ferr_len, double)) || !(ab = NAG_ALLOC((kd+1) * n, double)) || !(afb = NAG_ALLOC((kd+1) * n, double)) || !(b = NAG_ALLOC(n * nrhs, double)) || !(x = NAG_ALLOC(n * nrhs, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A from data file */ scanf(" %s%*[^\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); k = kd + 1; if (uplo == Nag_Upper) { for (i = 1; i <= n; ++i) { for (j = i; j <= MIN(i+kd, n); ++j) scanf("%lf", &AB_UPPER(i, j)); } scanf("%*[^\n] "); } else { for (i = 1; i <= n; ++i) { for (j = MAX(1, i-kd); j <= i; ++j) scanf("%lf", &AB_LOWER(i, j)); } scanf("%*[^\n] "); } /* Read B from data file */ 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 <= MIN(i+kd, n); ++j) AFB_UPPER(i, j) = AB_UPPER(i, j); } } else { for (i = 1; i <= n; ++i) { for (j = MAX(1, i-kd); j <= i; ++j) AFB_LOWER(i, j) = AB_LOWER(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 AFP */ /* nag_dpbtrf (f07hdc). * Cholesky factorization of real symmetric * positive-definite band matrix */ nag_dpbtrf(order, uplo, n, kd, afb, pdafb, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dpbtrf (f07hdc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Compute solution in the array X */ /* nag_dpbtrs (f07hec). * Solution of real symmetric positive-definite band system * of linear equations, multiple right-hand sides, matrix * already factorized by nag_dpbtrf (f07hdc) */ nag_dpbtrs(order, uplo, n, kd, nrhs, afb, pdafb, x, pdx, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dpbtrs (f07hec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Improve solution, and compute backward errors and */ /* estimated bounds on the forward errors */ /* nag_dpbrfs (f07hhc). * Refined solution with error bounds of real symmetric * positive-definite band system of linear equations, * multiple right-hand sides */ nag_dpbrfs(order, uplo, n, kd, nrhs, ab, pdab, afb, pdafb, b, pdb, x, pdx, ferr, berr, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dpbrfs (f07hhc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print details of 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?"\n":" "); printf("\n"); END: if (berr) NAG_FREE(berr); if (ferr) NAG_FREE(ferr); if (ab) NAG_FREE(ab); if (afb) NAG_FREE(afb); if (b) NAG_FREE(b); if (x) NAG_FREE(x); return exit_status; }