```/* nag_sparse_direct_real_gen_refine (f11mhc) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/

#include <stdio.h>
#include <nag.h>

/* Table of constant values */

static Integer c__1 = 1;
static Integer c__80 = 80;
static Integer c__0 = 0;

int main(void)
{
double flop, thresh;
Integer exit_status = 0, i, j;
Integer n, nnz, nnzl, nnzu, nrhs, nzlmx, nzlumx, nzumx;
double *a = 0, *b = 0, *berr = 0, *ferr = 0, *lval = 0;
double *uval = 0, *x = 0;
Integer *icolzp = 0, *il = 0, *iprm = 0, *irowix = 0;
Integer *iu = 0;
/* Nag types */
Nag_OrderType order = Nag_ColMajor;
Nag_MatrixType matrix = Nag_GeneralMatrix;
Nag_DiagType diag = Nag_NonUnitDiag;
Nag_ColumnPermutationType ispec;
Nag_TransType trans;
NagError fail;

INIT_FAIL(fail);

printf("nag_sparse_direct_real_gen_refine (f11mhc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
/* Read order of matrix and number of right hand sides */
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &nrhs);
/* Read the matrix A */
if (!(icolzp = NAG_ALLOC(n + 1, Integer)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
for (i = 1; i <= n + 1; ++i)
scanf("%" NAG_IFMT "%*[^\n] ", &icolzp[i - 1]);
nnz = icolzp[n] - 1;
/* Allocate memory */
if (!(irowix = NAG_ALLOC(nnz, Integer)) ||
!(a = NAG_ALLOC(nnz, double)) ||
!(il = NAG_ALLOC(7 * n + 8 * nnz + 4, Integer)) ||
!(iu = NAG_ALLOC(2 * n + 8 * nnz + 1, Integer)) ||
!(uval = NAG_ALLOC(8 * nnz, double)) ||
!(lval = NAG_ALLOC(8 * nnz, double)) ||
!(b = NAG_ALLOC(n * nrhs, double)) ||
!(x = NAG_ALLOC(n * nrhs, double)) ||
!(berr = NAG_ALLOC(nrhs, double)) ||
!(ferr = NAG_ALLOC(nrhs, double)) ||
!(iprm = NAG_ALLOC(7 * n, Integer)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
for (i = 0; i < nnz; ++i)
scanf("%lf%" NAG_IFMT "%*[^\n] ", &a[i], &irowix[i]);
/* Read the right hand sides */
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < n; ++i) {
scanf("%lf", &x[j * n + i]);
b[j * n + i] = x[j * n + i];
}
scanf("%*[^\n] ");
}
/* Calculate COLAMD permutation */
ispec = Nag_Sparse_Colamd;
/* nag_sparse_direct_real_gen_setup (f11mdc).
* Real sparse nonsymmetric linear systems, setup for
* nag_sparse_direct_real_gen_lu (f11mec)
*/
nag_sparse_direct_real_gen_setup(ispec, n, icolzp, irowix, iprm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparse_direct_real_gen_setup (f11mdc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Factorise */
thresh = 1.;
nzlmx = 8 * nnz;
nzlumx = 8 * nnz;
nzumx = 8 * nnz;
/* nag_sparse_direct_real_gen_lu (f11mec).
* LU factorization of real sparse matrix
*/
nag_sparse_direct_real_gen_lu(n, irowix, a, iprm, thresh, nzlmx, &nzlumx, nzumx,
il, lval, iu, uval, &nnzl, &nnzu, &flop, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparse_direct_real_gen_lu (f11mec).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Compute solution in array X */
trans = Nag_NoTrans;
/* nag_sparse_direct_real_gen_solve (f11mfc).
* Solution of real sparse simultaneous linear equations
*/
nag_sparse_direct_real_gen_solve(order, trans, n, iprm, il, lval, iu, uval, nrhs, x,
n, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparse_direct_real_gen_solve (f11mfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Improve solution, and compute backward errors and estimated */
/* bounds on the forward errors */
/* nag_sparse_direct_real_gen_refine (f11mhc).
* Refined solution with error bounds of real system of
* linear equations, multiple right-hand sides
*/
nag_sparse_direct_real_gen_refine(order, trans, n, icolzp, irowix, a, iprm, il, lval,
iu, uval, nrhs, b, n, x, n, ferr, berr, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparse_direct_real_gen_refine (f11mhc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print solution */
printf("\n");
/* nag_file_print_matrix_real_gen (x04cac).
* Print real general matrix (easy-to-use)
*/
fflush(stdout);
nag_file_print_matrix_real_gen(order, matrix, diag, n, nrhs,
x, n, "Solutions", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_file_print_matrix_real_gen_comp (x04cbc).
* Print real general matrix (comprehensive)
*/
fflush(stdout);
nag_file_print_matrix_real_gen_comp(order, matrix, diag, nrhs, c__1, ferr, nrhs,
"%8.2g", "Estimated Forward Error",
Nag_NoLabels, NULL, Nag_NoLabels, NULL, c__80,
c__0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen_comp (x04cbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* nag_file_print_matrix_real_gen_comp (x04cbc), see above. */
fflush(stdout);
nag_file_print_matrix_real_gen_comp(order, matrix, diag, nrhs, c__1, berr, nrhs,
"%8.2g", "Backward Error", Nag_NoLabels, NULL,
Nag_NoLabels, NULL, c__80, c__0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen_comp (x04cbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(berr);
NAG_FREE(ferr);
NAG_FREE(lval);
NAG_FREE(uval);
NAG_FREE(x);
NAG_FREE(icolzp);
NAG_FREE(il);
NAG_FREE(iprm);
NAG_FREE(irowix);
NAG_FREE(iu);
return exit_status;
}
```