/* nag_dgbrfs (f07bhc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include int main(void) { /* Scalars */ Integer i, ipiv_len, j, kl, ku, n, nrhs, pdab, pdafb, pdb, pdx; Integer exit_status=0; NagError fail; Nag_OrderType order; /* Arrays */ double *ab=0, *afb=0, *b=0, *berr=0, *ferr=0, *x=0; Integer *ipiv=0; #ifdef NAG_COLUMN_MAJOR #define AB(I,J) ab[(J-1)*pdab + ku + I - J] #define AFB(I,J) afb[(J-1)*pdafb + kl + ku + 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(I,J) ab[(I-1)*pdab + kl + J - I] #define AFB(I,J) afb[(I-1)*pdafb + kl + J - I] #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); Vprintf("nag_dgbrfs (f07bhc) Example Program Results\n\n"); /* Skip heading in data file */ Vscanf("%*[^\n] "); Vscanf("%ld%ld%ld%ld%*[^\n] ", &n, &nrhs, &kl, &ku); ipiv_len = n; pdab = kl + ku + 1; pdafb = 2*kl + ku + 1; #ifdef NAG_COLUMN_MAJOR pdb = n; pdx = n; #else pdb = nrhs; pdx = nrhs; #endif /* Allocate memory */ if ( !(ab = NAG_ALLOC((kl+ku+1) * n, double)) || !(afb = NAG_ALLOC((2*kl+ku+1) * n, double)) || !(b = NAG_ALLOC(nrhs * n, double)) || !(x = NAG_ALLOC(nrhs * n, double)) || !(berr = NAG_ALLOC(nrhs, double)) || !(ferr = NAG_ALLOC(nrhs, double)) || !(ipiv = NAG_ALLOC(ipiv_len, Integer)) ) { Vprintf("Allocation failure\n"); exit_status = -1; goto END; } /* Set A to zero to avoid referencing unitialized elements */ for (i = 0; i < n*(kl+ku+1); ++i) ab[i] = 0.0; /* Read A from data file */ for (i = 1; i <= n; ++i) { for (j = MAX(i-kl,1); j <= MIN(i+ku,n); ++j) Vscanf("%lf", &AB(i,j)); } Vscanf("%*[^\n] "); /* Read B from data file */ for (i = 1; i <= n; ++i) { for (j = 1; j <= nrhs; ++j) Vscanf("%lf", &B(i,j)); } Vscanf("%*[^\n] "); /* Copy A to AFB and B to X */ for (i = 1; i <= n; ++i) { for (j = MAX(i-kl,1); j <= MIN(i+ku,n); ++j) AFB(i,j) = AB(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 AFB */ /* nag_dgbtrf (f07bdc). * LU factorization of real m by n band matrix */ nag_dgbtrf(order, n, n, kl, ku, afb, pdafb, ipiv, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dgbtrf (f07bdc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Compute solution in the array X */ /* nag_dgbtrs (f07bec). * Solution of real band system of linear equations, * multiple right-hand sides, matrix already factorized by * nag_dgbtrf (f07bdc) */ nag_dgbtrs(order, Nag_NoTrans, n, kl, ku, nrhs, afb, pdafb, ipiv, x, pdx, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dgbtrs (f07bec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Improve solution, and compute backward errors and */ /* estimated bounds on the forward errors */ /* nag_dgbrfs (f07bhc). * Refined solution with error bounds of real band system of * linear equations, multiple right-hand sides */ nag_dgbrfs(order, Nag_NoTrans, n, kl, ku, nrhs, ab, pdab, afb, pdafb, ipiv, b, pdb, x, pdx, ferr, berr, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dgbrfs (f07bhc).\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) */ nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, x, pdx, "Solution(s)", 0, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print forward and backward errors */ Vprintf("\nBackward errors (machine-dependent)\n"); for (j = 1; j <= nrhs; ++j) Vprintf("%11.1e%s", berr[j-1], j%7==0 ?"\n":" "); Vprintf("\nEstimated forward error bounds (machine-dependent)\n"); for (j = 1; j <= nrhs; ++j) Vprintf("%11.1e%s", ferr[j-1], j%7==0 ?"\n":" "); Vprintf("\n"); END: if (ab) NAG_FREE(ab); if (afb) NAG_FREE(afb); if (b) NAG_FREE(b); if (x) NAG_FREE(x); if (berr) NAG_FREE(berr); if (ferr) NAG_FREE(ferr); if (ipiv) NAG_FREE(ipiv); return exit_status; }