/* nag_lapackeig_dormhr (f08ngc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.2, 2024.
*/
#include <math.h>
#include <nag.h>
#include <stdio.h>
int main(void) {
/* Scalars */
Integer i, j, k, l, m, n, pda, pdh, pdvl, pdvr, pdz;
Integer tau_len, ifaill_len, select_len, w_len;
Integer exit_status = 0;
double thresh, r, s;
Complex eig, eig1;
/* Arrays */
double *a = 0, *h = 0, *vl = 0, *vr = 0, *z = 0, *wi = 0, *wr = 0;
double *tau = 0;
Integer *ifaill = 0, *ifailr = 0;
/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_Boolean *select = 0;
#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define H(I, J) h[(J - 1) * pdh + I - 1]
#define VR(I, J) vr[(J - 1) * pdvr + I - 1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define H(I, J) h[(I - 1) * pdh + J - 1]
#define VR(I, J) vr[(I - 1) * pdvr + J - 1]
order = Nag_RowMajor;
#endif
INIT_FAIL(fail);
printf("nag_lapackeig_dormhr (f08ngc) Example Program Results\n\n");
/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);
pda = n;
pdh = n;
pdvl = n;
pdvr = n;
pdz = 1;
tau_len = n;
w_len = n;
ifaill_len = n;
select_len = n;
/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, double)) || !(h = NAG_ALLOC(n * n, double)) ||
!(vl = NAG_ALLOC(n * n, double)) || !(vr = NAG_ALLOC(n * n, double)) ||
!(z = NAG_ALLOC(1 * 1, double)) || !(wi = NAG_ALLOC(w_len, double)) ||
!(wr = NAG_ALLOC(w_len, double)) ||
!(ifaill = NAG_ALLOC(ifaill_len, Integer)) ||
!(ifailr = NAG_ALLOC(ifaill_len, Integer)) ||
!(select = NAG_ALLOC(select_len, Nag_Boolean)) ||
!(tau = NAG_ALLOC(tau_len, 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]");
scanf("%lf%*[^\n]", &thresh);
/* Reduce A to upper Hessenberg form */
/* nag_lapackeig_dgehrd (f08nec).
* Orthogonal reduction of real general matrix to upper
* Hessenberg form
*/
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 to H */
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
H(i, j) = A(i, j);
/* Calculate the eigenvalues of H (same as A) */
/* nag_lapackeig_dhseqr (f08pec).
* Eigenvalues and Schur factorization of real upper
* Hessenberg matrix reduced from real general matrix
*/
nag_lapackeig_dhseqr(order, Nag_EigVals, Nag_NotZ, 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;
}
/* Print eigenvalues */
printf(" Eigenvalues\n");
for (i = 0; i < n; ++i)
printf(" (%8.4f,%8.4f)\n", wr[i], wi[i]);
printf("\n");
for (i = 0; i < n; ++i)
select[i] = wr[i] < thresh ? Nag_TRUE : Nag_FALSE;
/* Calculate the eigenvectors of H (as specified by SELECT), */
/* storing the result in VR */
/* nag_lapackeig_dhsein (f08pkc).
* Selected right and/or left eigenvectors of real upper
* Hessenberg matrix by inverse iteration
*/
nag_lapackeig_dhsein(order, Nag_RightSide, Nag_HSEQRSource, Nag_NoVec, select,
n, a, pda, wr, wi, vl, pdvl, vr, pdvr, n, &m, ifaill,
ifailr, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dhsein (f08pkc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Calculate the eigenvectors of A = Q * VR */
/* nag_lapackeig_dormhr (f08ngc).
* Apply orthogonal transformation matrix from reduction to
* Hessenberg form determined by nag_lapackeig_dgehrd (f08nec)
*/
nag_lapackeig_dormhr(order, Nag_LeftSide, Nag_NoTrans, n, m, 1, n, a, pda,
tau, vr, pdvr, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dormhr (f08ngc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Scale selected eigenvectors */
j = 0;
for (k = 0; k < n; k++) {
if (select[k]) {
j++;
if (wi[k] == 0.0) {
r = 0.0;
l = 0;
s = 0.0;
for (i = 1; i <= n; i++) {
h[i - 1] = VR(i, j) * VR(i, j);
s += h[i - 1];
if (h[i - 1] > r) {
l = i - 1;
r = h[l];
}
}
if (VR(l, j) < 0.0) {
for (i = 1; i <= n; i++) {
VR(i, j) = -VR(i, j) / sqrt(s);
}
} else {
for (i = 1; i <= n; i++) {
VR(i, j) = VR(i, j) / sqrt(s);
}
}
} else {
r = 0.0;
l = 0;
s = 0.0;
for (i = 1; i <= n; i++) {
h[i - 1] = VR(i, j) * VR(i, j) + VR(i, j + 1) * VR(i, j + 1);
s += h[i - 1];
if (h[i - 1] > r) {
l = i - 1;
r = h[l];
}
}
r = sqrt(r * s);
eig1.re = VR(l + 1, j) / r;
eig1.im = -VR(l + 1, j + 1) / r;
for (i = 1; i <= n; i++) {
eig = nag_complex_create(VR(i, j), VR(i, j + 1));
eig = nag_complex_multiply(eig, eig1);
if (fabs(eig.re) < 10.0 * x02ajc()) {
VR(i, j) = 0.0;
} else {
VR(i, j) = eig.re;
}
if (fabs(eig.im) < 10.0 * x02ajc()) {
VR(i, j + 1) = 0.0;
} else {
VR(i, j + 1) = eig.im;
}
}
j++;
k++;
}
}
}
/* Print Eigenvectors */
/* nag_file_print_matrix_real_gen (x04cac).
* Print real general matrix (easy-to-use)
*/
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
m, vr, pdvr, "Contents of array VR", 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;
}
END:
NAG_FREE(a);
NAG_FREE(h);
NAG_FREE(vl);
NAG_FREE(vr);
NAG_FREE(z);
NAG_FREE(wi);
NAG_FREE(wr);
NAG_FREE(ifaill);
NAG_FREE(ifailr);
NAG_FREE(select);
NAG_FREE(tau);
return exit_status;
}