/* nag_lapackeig_dspgv (f08tac) 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 anorm, bnorm, eps, rcond, rcondb, t1, t2;
Integer i, j, n;
Integer exit_status = 0;
/* Arrays */
double *ap = 0, *bp = 0, *dummy = 0, *eerbnd = 0, *w = 0;
char nag_enum_arg[40];
/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_UploType uplo;
#ifdef NAG_COLUMN_MAJOR
#define A_UPPER(I, J) ap[J * (J - 1) / 2 + I - 1]
#define A_LOWER(I, J) ap[(2 * n - J) * (J - 1) / 2 + I - 1]
#define B_UPPER(I, J) bp[J * (J - 1) / 2 + I - 1]
#define B_LOWER(I, J) bp[(2 * n - J) * (J - 1) / 2 + I - 1]
order = Nag_ColMajor;
#else
#define A_UPPER(I, J) ap[(2 * n - I) * (I - 1) / 2 + J - 1]
#define A_LOWER(I, J) ap[I * (I - 1) / 2 + J - 1]
#define B_UPPER(I, J) bp[(2 * n - I) * (I - 1) / 2 + J - 1]
#define B_LOWER(I, J) bp[I * (I - 1) / 2 + J - 1]
order = Nag_RowMajor;
#endif
INIT_FAIL(fail);
printf("nag_lapackeig_dspgv (f08tac) Example Program Results\n\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
*/
uplo = (Nag_UploType)nag_enum_name_to_value(nag_enum_arg);
/* Allocate memory */
if (!(ap = NAG_ALLOC(n * (n + 1) / 2, double)) ||
!(bp = NAG_ALLOC(n * (n + 1) / 2, double)) ||
!(dummy = NAG_ALLOC(1 * 1, double)) || !(eerbnd = NAG_ALLOC(n, double)) ||
!(w = NAG_ALLOC(n, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read the triangular parts of the matrices A and B from data file. */
if (uplo == Nag_Upper) {
for (i = 1; i <= n; ++i)
for (j = i; j <= n; ++j)
scanf("%lf", &A_UPPER(i, j));
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = i; j <= n; ++j)
scanf("%lf", &B_UPPER(i, j));
} else if (uplo == Nag_Lower) {
for (i = 1; i <= n; ++i)
for (j = 1; j <= i; ++j)
scanf("%lf", &A_LOWER(i, j));
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = 1; j <= i; ++j)
scanf("%lf", &B_LOWER(i, j));
}
scanf("%*[^\n]");
/* Compute the one-norms of the symmetric matrices A and B
* using nag_blast_dsp_norm (f16rdc).
*/
nag_blast_dsp_norm(order, Nag_OneNorm, uplo, n, ap, &anorm, &fail);
nag_blast_dsp_norm(order, Nag_OneNorm, uplo, n, bp, &bnorm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dsp_norm (f16rdc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Solve the generalized symmetric eigenvalue problem A*x = lambda*B*x
* using nag_lapackeig_dspgv (f08tac).
*/
nag_lapackeig_dspgv(order, 1, Nag_EigVals, uplo, n, ap, bp, w, dummy, 1,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dspgv (f08tac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Print solution */
printf("Eigenvalues\n ");
for (j = 0; j < n; ++j)
printf(" %11.4f%s", w[j], j % 6 == 5 ? "\n" : "");
printf("\n");
/* Estimate the reciprocal condition number of the Cholesky factor of B.
* nag_lapacklin_dtpcon (f07ugc)
* Note that: cond(B) = 1/(rcond*rcond).
*/
nag_lapacklin_dtpcon(order, Nag_OneNorm, uplo, Nag_NonUnitDiag, n, bp, &rcond,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_dtpcon (f07ugc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Print the reciprocal condition number of B */
rcondb = rcond * rcond;
printf("\nEstimate of reciprocal condition number for B\n %11.1e\n",
rcondb);
/* Get the machine precision, using nag_machine_precision (x02ajc) */
eps = nag_machine_precision;
if (rcond < eps) {
printf("\nB is very ill-conditioned, error estimates have not been "
"computed\n");
}
t1 = eps / rcondb;
t2 = anorm / bnorm;
for (i = 0; i < n; ++i)
eerbnd[i] = t1 * (t2 + fabs(w[i]));
/* Print the approximate error bounds for the eigenvalues */
printf("\nError estimates for the eigenvalues\n ");
for (i = 0; i < n; ++i)
printf(" %11.1e%s", eerbnd[i], i % 6 == 5 ? "\n" : "");
printf("\n");
END:
NAG_FREE(ap);
NAG_FREE(bp);
NAG_FREE(dummy);
NAG_FREE(eerbnd);
NAG_FREE(w);
return exit_status;
}