/* F08GA_A1W_F C++ Header Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
* Mark 30.1, 2024.
*/
#include <dco.hpp>
#include <iostream>
#include <math.h>
#include <nag.h>
#include <nagad.h>
#include <stdio.h>
#include <string>
int main()
{
/* Scalars */
double eerrbd, eps;
Integer exit_status = 0, i, j, n;
/* Arrays */
nagad_a1w_w_rtype *ap = 0, *dummy = 0, *w = 0, *work = 0, *ap_in = 0;
double * wr = 0, *dwda = 0;
Integer ifail;
std::string uplo = "U";
#define AP(I, J) ap_in[J * (J - 1) / 2 + I - 1]
printf("F08GA_A1W_F C++ Example Program Results\n\n");
// Create AD tape
dco::ga1s<double>::global_tape = dco::ga1s<double>::tape_t::create();
nag::ad::handle_t ad_handle;
/* 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 nagad_a1w_w_rtype[n * (n + 1) / 2];
ap_in = new nagad_a1w_w_rtype[n * (n + 1) / 2];
dummy = new nagad_a1w_w_rtype[1];
w = new nagad_a1w_w_rtype[n];
work = new nagad_a1w_w_rtype[3 * n];
wr = new double[n];
dwda = new double[n * n];
/* Read the upper triangular part of the matrix A from data file */
double tmp;
for (i = 1; i <= n; ++i)
{
for (j = i; j <= n; ++j)
{
AP(i, j) = 0.0;
#ifdef _WIN32
scanf_s("%lf", &tmp);
#else
scanf("%lf", &tmp);
#endif
AP(i, j) = tmp;
}
}
#ifdef _WIN32
scanf_s("%*[^\n]");
#else
scanf("%*[^\n]");
#endif
for (int i = 0; i < n; i++)
{
dco::ga1s<double>::global_tape->register_variable(ap_in[(i * (i + 3)) / 2]);
}
for (int i = 0; i < (n * (n + 1)) / 2; i++)
{
ap[i] = ap_in[i];
}
nag::ad::f08ga(ad_handle, "N", "U", n, ap, w, dummy, 1, work, ifail);
if (ifail != 0)
{
printf("Error from F08GA_A1W_F.\n%" NAG_IFMT " ", ifail);
exit_status = 1;
goto END;
}
/* Print solution */
for (i = 0; i < n; ++i)
{
wr[i] = dco::value(w[i]);
}
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", eerrbd);
for (i = 0; i < n; i++)
{
dco::ga1s<double>::global_tape->zero_adjoints();
dco::derivative(w[i]) += 1.0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;
dco::ga1s<double>::global_tape->interpret_adjoint();
for (int j = 0; j < n; j++)
dwda[i + j * n] = dco::derivative(ap_in[j * (j + 3) / 2]);
}
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;
dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);
return exit_status;
}
#undef AP