/* F08GA_T1W_F C++ Header Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
* Mark 28.3, 2022.
*/
#include <dco.hpp>
#include <iostream>
#include <math.h>
#include <nag.h>
#include <nagad.h>
#include <stdio.h>
#include <string>
typedef double DCO_BASE_TYPE;
typedef dco::gt1s<DCO_BASE_TYPE> DCO_MODE;
typedef DCO_MODE::type DCO_TYPE;
int main()
{
/* Scalars */
double eerrbd, eps;
Integer exit_status = 0, i, j, n;
/* Arrays */
DCO_TYPE * ap = 0, *dummy = 0, *w = 0, *work = 0, *ap_in = 0;
Integer ifail;
std::string uplo = "U";
double * wr = 0, *dwda = 0;
#define AP(I, J) ap_in[J * (J - 1) / 2 + I - 1]
printf("F08GA_T1W_F C++ Example Program Results\n\n");
nag::ad::handle_t ad_handle;
ifail = 0;
/* Skip heading in data file */
#ifdef _WIN32
scanf_s("%*[^\n]");
#else
scanf("%*[^\n]");
#endif
#ifdef _WIN32
scanf_s("%" NAG_IFMT "%*[^\n]", &n);
#else
scanf("%" NAG_IFMT "%*[^\n]", &n);
#endif
/* Allocate memory */
ap = new DCO_TYPE[n * (n + 1) / 2];
ap_in = new DCO_TYPE[n * (n + 1) / 2];
dummy = new DCO_TYPE[1];
w = new DCO_TYPE[n];
work = new DCO_TYPE[3 * n];
wr = new double[n];
dwda = new double[n * n];
/* Read the upper or lower triangular part of the matrix A from data file */
for (i = 1; i <= n; ++i)
{
for (j = i; j <= n; ++j)
{
#ifdef _WIN32
scanf_s("%lf", &dco::value(AP(i, j)));
#else
scanf("%lf", &dco::value(AP(i, j)));
#endif
}
}
#ifdef _WIN32
scanf_s("%*[^\n]");
#else
scanf("%*[^\n]");
#endif
for (int i = 0; i < (n * (n + 1)) / 2; i++)
{
dco::derivative(ap_in[i]) = 0.0;
ap[i] = ap_in[i];
}
for (int j = 0; j < n; j++)
{
dco::derivative(ap[j * (j + 3) / 2]) = 1.0;
nag::ad::f08ga(ad_handle, "N", "U", n, ap, w, dummy, 1, work, ifail);
if (ifail != 0)
{
printf("Error from nag::ad::f08ga.\n%" NAG_IFMT " ", ifail);
exit_status = 1;
goto END;
}
if (j == 0)
{
for (i = 0; i < n; ++i)
{
wr[i] = dco::value(w[i]);
}
}
for (int i = 0; i < n; i++)
dwda[i + j * n] = dco::derivative(w[i]);
for (int i = 0; i < (n * (n + 1)) / 2; i++)
ap[i] = ap_in[i];
}
/* Print solution */
printf("Eigenvalues\n");
for (j = 0; j < n; ++j)
printf("%8.4f%s", wr[j], (j + 1) % 8 == 0 ? "\n" : " ");
printf("\n");
/* Get the machine precision, eps, using nag_machine_precision (X02AJC)
* and compute the approximate error bound for the computed eigenvalues.
* Note that for the 2-norm, ||A|| = max {|w[i]|, i=0..n-1}, and since
* the eigenvalues are in ascending order ||A|| = max( |w[0]|, |w[n-1]|).
*/
eps = X02AJC;
eerrbd = eps * MAX(fabs(wr[0]), fabs(wr[n - 1]));
/* Print the approximate error bound for the eigenvalues */
printf("\nError estimate for the eigenvalues\n");
printf("%11.1e\n", dco::value(eerrbd));
printf("\nDerivatives of eigenvalues w.r.t. diagonals of A\n");
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, dwda, n,
" dW_i/dA_jj", 0, &fail);
END:
delete[] ap;
delete[] ap_in;
delete[] dummy;
delete[] w;
delete[] work;
delete[] wr;
delete[] dwda;
return exit_status;
}
#undef AP