/* nag_lapackeig_dhseqr (f08pec) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/
#include <math.h>
#include <nag.h>
#include <stdio.h>
int main(void) {
/* Scalars */
double alpha, beta, norm;
Integer i, j, n, pdc, pdd, pdh, pdz, wi_len, wr_len;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;
/* Arrays */
double *c = 0, *d = 0, *h = 0, *wi = 0, *wr = 0, *z = 0;
#ifdef NAG_COLUMN_MAJOR
#define H(I, J) h[(J - 1) * pdh + I - 1]
#define D(I, J) d[(J - 1) * pdd + I - 1]
order = Nag_ColMajor;
#else
#define H(I, J) h[(I - 1) * pdh + J - 1]
#define D(I, J) d[(I - 1) * pdd + J - 1]
order = Nag_RowMajor;
#endif
INIT_FAIL(fail);
printf("nag_lapackeig_dhseqr (f08pec) Example Program Results\n\n");
/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
pdc = n;
pdd = n;
pdh = n;
pdz = n;
#else
pdc = n;
pdd = n;
pdh = n;
pdz = n;
#endif
wr_len = n;
wi_len = n;
/* Allocate memory */
if (!(c = NAG_ALLOC(n * n, double)) || !(d = NAG_ALLOC(n * n, double)) ||
!(h = NAG_ALLOC(n * n, double)) || !(wi = NAG_ALLOC(wi_len, double)) ||
!(wr = NAG_ALLOC(wr_len, double)) || !(z = NAG_ALLOC(n * n, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read H from data file */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= n; ++j)
scanf("%lf", &H(i, j));
}
scanf("%*[^\n] ");
/* Copy H into D */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= n; ++j)
D(i, j) = H(i, j);
}
/* nag_file_print_matrix_real_gen (x04cac): Print Matrix H. */
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
n, h, pdh, "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;
}
/* Calculate the eigenvalues and Schur factorization of H */
/* nag_lapackeig_dhseqr (f08pec).
* Eigenvalues and Schur factorization of real upper
* Hessenberg matrix reduced from real general matrix
*/
nag_lapackeig_dhseqr(order, Nag_Schur, Nag_InitZ, n, 1, n, h, pdh, 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 H - Z*T*Z^T from the factorization of */
/* H 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, h,
pdh, 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("\n%s\n%s\n", "Norm of H-(Z*T*Z^H) is much greater than 0.",
"Schur factorization has failed.");
} else {
printf(" Eigenvalues\n");
for (i = 1; i <= n; ++i)
printf(" (%8.4f,%8.4f)", wr[i - 1], wi[i - 1]);
printf("\n");
}
END:
NAG_FREE(c);
NAG_FREE(d);
NAG_FREE(h);
NAG_FREE(wi);
NAG_FREE(wr);
NAG_FREE(z);
return exit_status;
}