/* nag_lapackeig_dorghr (f08nfc) Example Program.
*
* Copyright 2020 Numerical Algorithms Group.
*
* Mark 27.1, 2020.
*/

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

int main(void) {
/* Scalars */
double norm, alpha, beta;
Integer i, j, n, pda, pdc, pdd, pdz, tau_len, wi_len;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;
/* Arrays */
double *a = 0, *c = 0, *d = 0, *tau = 0, *wi = 0, *wr = 0, *z = 0;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define D(I, J) d[(J - 1) * pdd + I - 1]
#define Z(I, J) z[(J - 1) * pdz + I - 1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define D(I, J) d[(I - 1) * pdd + J - 1]
#define Z(I, J) z[(I - 1) * pdz + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_dorghr (f08nfc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);

pda = n;
pdc = n;
pdd = n;
pdz = n;
tau_len = n - 1;
wi_len = n;

/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, double)) || !(c = NAG_ALLOC(n * n, double)) ||
!(d = NAG_ALLOC(n * n, double)) || !(tau = NAG_ALLOC(tau_len, double)) ||
!(wi = NAG_ALLOC(wi_len, double)) || !(wr = NAG_ALLOC(wi_len, double)) ||
!(z = NAG_ALLOC(n * n, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read A from data file */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= n; ++j)
scanf("%lf", &A(i, j));
}
scanf("%*[^\n] ");

/* Copy A into D */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= n; ++j)
D(i, j) = A(i, j);
}

/* nag_file_print_matrix_real_gen (x04cac): Print Matrix A. */
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
n, a, pda, "Matrix A", 0, &fail);
printf("\n");
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_lapackeig_dgehrd (f08nec): Reduce A to upper Hessenberg form H =
* (Q^T)*A*Q */
nag_lapackeig_dgehrd(order, n, 1, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dgehrd (f08nec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Copy A into Z */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= n; ++j)
Z(i, j) = A(i, j);
}

/* nag_lapackeig_dorghr (f08nfc): Form Q explicitly, storing the result in Z
*/
nag_lapackeig_dorghr(order, n, 1, n, z, pdz, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dorghr (f08nfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_lapackeig_dhseqr (f08pec):
*       Calculate the Schur factorization of H = Y*T*(Y^T) and form
*       Z=Q*Y explicitly. Note that A = Z*T*(Z^T).
*/
nag_lapackeig_dhseqr(order, Nag_Schur, Nag_UpdateZ, n, 1, n, a, pda, wr, wi,
z, pdz, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dhseqr (f08pec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_blast_dgemm (f16yac): Compute A - Z*T*Z^T from the factorization of */
/* A and store in matrix D */
alpha = 1.0;
beta = 0.0;
nag_blast_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, z, pdz, a,
pda, beta, c, pdc, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dgemm (f16yac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
alpha = -1.0;
beta = 1.0;
nag_blast_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, alpha, c, pdc, z, pdz,
beta, d, pdd, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dgemm (f16yac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_blast_dge_norm (f16rac): Find norm of matrix D and print warning if */
/* it is too large */
nag_blast_dge_norm(order, Nag_OneNorm, n, n, d, pdd, &norm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
if (norm > pow(x02ajc(), 0.8)) {
printf("%s\n%s\n", "Norm of A-(Z*T*Z^T) is much greater than 0.",
"Schur factorization has failed.");
}

END:
NAG_FREE(a);
NAG_FREE(c);
NAG_FREE(d);
NAG_FREE(tau);
NAG_FREE(wi);
NAG_FREE(wr);
NAG_FREE(z);

return exit_status;
}

#undef A
#undef D
#undef Z