/* nag_lapackeig_dggevx (f08wbc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.2, 2024.
*/
#include <math.h>
#include <nag.h>
#include <stdio.h>
int main(void) {
/* Scalars */
Complex eig, eigl, eigr;
double abnorm, abnrm, bbnrm, eps, sign, small, tol;
Integer i, ihi, ilo, j, k, n, pda, pdb, pdvl, pdvr;
Integer verbose = 0;
Integer exit_status = 0;
/* Arrays */
double *a = 0, *alphai = 0, *alphar = 0, *b = 0, *beta = 0;
double *lscale = 0, *rconde = 0, *rcondv = 0, *rscale = 0;
double *vl = 0, *vr = 0;
char nag_enum_arg[40];
/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_LeftVecsType jobvl;
Nag_RightVecsType jobvr;
Nag_RCondType sense;
#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define B(I, J) b[(J - 1) * pdb + I - 1]
#define VL(I, J) vl[(J - 1) * pdvl + 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 B(I, J) b[(I - 1) * pdb + J - 1]
#define VL(I, J) vl[(I - 1) * pdvl + J - 1]
#define VR(I, J) vr[(I - 1) * pdvr + J - 1]
order = Nag_RowMajor;
#endif
INIT_FAIL(fail);
printf("nag_lapackeig_dggevx (f08wbc) Example Program Results\n");
/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%*[^\n]", &n);
if (n < 0) {
printf("Invalid n\n");
exit_status = 1;
goto END;
}
scanf(" %39s%*[^\n]", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
jobvl = (Nag_LeftVecsType)nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobvr = (Nag_RightVecsType)nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
sense = (Nag_RCondType)nag_enum_name_to_value(nag_enum_arg);
pda = n;
pdb = n;
pdvl = (jobvl == Nag_LeftVecs ? n : 1);
pdvr = (jobvr == Nag_RightVecs ? n : 1);
/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, double)) || !(alphai = NAG_ALLOC(n, double)) ||
!(alphar = NAG_ALLOC(n, double)) || !(b = NAG_ALLOC(n * n, double)) ||
!(beta = NAG_ALLOC(n, double)) || !(lscale = NAG_ALLOC(n, double)) ||
!(rconde = NAG_ALLOC(n, double)) || !(rcondv = NAG_ALLOC(n, double)) ||
!(rscale = NAG_ALLOC(n, double)) ||
!(vl = NAG_ALLOC(pdvl * pdvl, double)) ||
!(vr = NAG_ALLOC(pdvr * pdvr, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read in the matrices A and B */
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
scanf("%lf", &A(i, j));
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
scanf("%lf", &B(i, j));
scanf("%*[^\n]");
/* Solve the generalized eigenvalue problem using nag_lapackeig_dggevx
* (f08wbc). */
nag_lapackeig_dggevx(order, Nag_BalanceBoth, jobvl, jobvr, sense, n, a, pda,
b, pdb, alphar, alphai, beta, vl, pdvl, vr, pdvr, &ilo,
&ihi, lscale, rscale, &abnrm, &bbnrm, rconde, rcondv,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dggevx (f08wbc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* nag_machine_real_safe (x02amc), nag_machine_precision (x02ajc) */
eps = nag_machine_precision;
small = nag_machine_real_safe;
if (abnrm == 0.0)
abnorm = ABS(bbnrm);
else if (bbnrm == 0.0)
abnorm = ABS(abnrm);
else if (ABS(abnrm) >= ABS(bbnrm))
abnorm = ABS(abnrm) * sqrt(1.0 + (bbnrm / abnrm) * (bbnrm / abnrm));
else
abnorm = ABS(bbnrm) * sqrt(1.0 + (abnrm / bbnrm) * (abnrm / bbnrm));
tol = eps * abnorm;
/* Print out eigenvalues and vectors and associated condition
* number and bounds.
*/
for (j = 0; j < n; ++j) {
/* Print out information on the j-th eigenvalue */
printf("\n");
if ((fabs(alphar[j]) + fabs(alphai[j])) * small >= fabs(beta[j])) {
printf("Eigenvalue %2" NAG_IFMT " is numerically infinite or "
"undetermined\n",
j + 1);
printf("alpha = (%13.4e, %13.4e), beta = %13.4e\n", alphar[j], alphai[j],
beta[j]);
} else if (alphai[j] == 0.0) {
printf("Eigenvalue %2" NAG_IFMT " = %13.4e\n", j + 1,
alphar[j] / beta[j]);
} else {
eig.re = alphar[j] / beta[j], eig.im = alphai[j] / beta[j];
printf("Eigenvalue %2" NAG_IFMT " = (%13.4e, %13.4e)\n", j + 1, eig.re,
eig.im);
}
if (verbose) {
if (sense == Nag_RCondEigVals || sense == Nag_RCondBoth) {
printf("\n Reciprocal condition number = %10.1e\n", rconde[j]);
if (rconde[j] > 0.0)
printf(" Error bound = %10.1e\n", tol / rconde[j]);
else
printf(" Error bound is infinite\n");
}
}
printf("\n\n");
/* Normalize and print out information on the j-th eigenvector(s) */
if (jobvl == Nag_LeftVecs)
printf("%21s%8s", "Left Eigenvector", "");
if (jobvr == Nag_RightVecs)
printf("%21s", "Right Eigenvector");
printf(" %2" NAG_IFMT "\n", j + 1);
if (alphai[j] == 0.0)
for (i = 1; i <= n; ++i) {
if (jobvl == Nag_LeftVecs)
printf("%7s%13.4e%12s", "", VL(i, j + 1) / VL(n, j + 1), "");
if (jobvr == Nag_RightVecs)
printf("%7s%13.4e", "", VR(i, j + 1) / VR(n, j + 1));
printf("\n");
}
else {
k = (alphai[j] > 0.0 ? j + 1 : j);
sign = (alphai[j] > 0.0 ? 1.0 : -1.0);
if (jobvl == Nag_LeftVecs)
eigl = nag_complex_create(VL(n, k), VL(n, k + 1));
if (jobvr == Nag_RightVecs)
eigr = nag_complex_create(VR(n, k), VR(n, k + 1));
for (i = 1; i <= n; ++i) {
if (jobvl == Nag_LeftVecs) {
eig = nag_complex_divide(nag_complex_create(VL(i, k), VL(i, k + 1)),
eigl);
printf(" (%13.4e,%13.4e) ", eig.re, sign * eig.im);
}
if (jobvr == Nag_RightVecs) {
eig = nag_complex_divide(nag_complex_create(VR(i, k), VR(i, k + 1)),
eigr);
printf(" (%13.4e,%13.4e)", eig.re, sign * eig.im);
}
printf("\n");
}
}
if (verbose) {
if (sense == Nag_RCondEigVecs || sense == Nag_RCondBoth) {
printf("\n Reciprocal condition number = %10.1e\n", rcondv[j]);
if (rcondv[j] > 0.0)
printf(" Error bound = %10.1e\n\n", tol / rcondv[j]);
else
printf(" Error bound is infinite\n\n");
}
}
}
END:
NAG_FREE(a);
NAG_FREE(alphai);
NAG_FREE(alphar);
NAG_FREE(b);
NAG_FREE(beta);
NAG_FREE(lscale);
NAG_FREE(rconde);
NAG_FREE(rcondv);
NAG_FREE(rscale);
NAG_FREE(vl);
NAG_FREE(vr);
return exit_status;
}