/* nag::ad::g02aa Adjoint Example Program.
*/
#include <dco.hpp>
#include <nagad.h>
#include <iostream>
std::stringstream filecontent(
"4 \
2.0 -1.0 0.0 0.0 \
-1.0 2.0 -1.0 0.0 \
0.0 -1.0 2.0 -1.0 \
0.0 0.0 -1.0 2.0 ");
// Function which calls NAG AD routines.
template<typename T>
void func(std::vector<T> &g, std::vector<T> &x);
// Driver with adjoint calls.
// Computes the Nearest Correlation Matrix X for an input matrix G.
// Also, computes the sum of all Jacobian elements of dX/dG.
void driver(const std::vector<double> &gv, std::vector<double> &xv, double &dxdg);
int main(void)
{
std::cout << " nag::ad::g02aa Adjoint Example Program Results\n";
Integer n;
filecontent >> n;
// Input Matrix G, whose NCM we want to compute
std::vector<double> gv(n*n);
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
filecontent >> gv[i+j*n];
}
}
// Output NCM X
std::vector<double> xv(n*n);
// Sum of all Jacobian elements dX/dG
double dxdg;
driver(gv,xv,dxdg);
std::cout.setf(std::ios::scientific,std::ios::floatfield);
std::cout.precision(12);
std::cout << "\n Nearest Correlation Matrix:\n\n";
for (int i=0; i<n; i++)
{
for (int j=0; j<n; j++)
{
std::cout.width(20); std::cout<< xv[i+j*n];
}
std::cout<<std::endl;
}
std::cout << "\n Derivatives calculated: First order adjoint\n";
std::cout << " Computational mode : algorithmic\n\n";
// Print derivatives of NCM X w.r.t. input matrix G
std::cout << "\n Sum of Jacobian elements of NCM X w.r.t. input matrix G:\n";
std::cout << " sum_ij [dX/dG]_ij = " << dxdg << std::endl;
return 0;
}
// Driver with adjoint calls.
// Computes the Nearest Correlation Matrix X for an input matrix G.
// Also, computes the sum of all Jacobian elements of dX/dG.
void driver(const std::vector<double> &gv, std::vector<double> &xv, double &dxdg)
{
using T = dco::ga1s<double>::type;
// Create AD tape
dco::ga1s<double>::global_tape = dco::ga1s<double>::tape_t::create();
// AD data types
std::vector<T> g(gv.size()), g1(gv.size());
dco::value(g) = gv;
dco::ga1s<double>::global_tape->register_variable(g);
// nag::ad::g02aa modifies input matrix g. Since we seek dx/dg, and g is overwritten,
// we must save these input nodes in the DAG. Hence we save g and overwrite a copy of it.
g1 = g;
// Variable to differentiate
std::vector<T> x(xv.size());
// Call the NAG AD Lib functions
func(g1,x);
// Extract the computed NCM
xv = dco::value(x);
dco::ga1s<double>::global_tape->register_output_variable(x);
dco::derivative(x) = std::vector<double>(xv.size(),1.0);
dco::ga1s<double>::global_tape->interpret_adjoint();
// Sum of the adjoints of g
dxdg = 0.0;
for (int i=0; i<g.size(); i++)
{
dxdg += dco::derivative(g[i]);
}
// Remove tape
dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);
}
// Function which calls NAG AD routines.
template<typename T>
void func(std::vector<T> &g, std::vector<T> &x)
{
Integer n = sqrt(g.size());
Integer pdg = n;
Integer pdx = n;
// Set up method parameters
T errtol = 1.00e-7;
Integer maxits = 200;
Integer maxit = 10;
// Output variables
Integer iter, feval;
T nrmgrd;
// Create AD configuration data object
Integer ifail = 0;
void *ad_handle = 0;
nag::ad::x10aa(ad_handle, ifail);
// Routine for computing the NCM of G.
nag::ad::g02aa(ad_handle, g.data(), pdg, n, errtol, maxits, maxit, x.data(), pdx,
iter, feval, nrmgrd, ifail);
// Remove computational data object
ifail = 0;
nag::ad::x10ab(ad_handle, ifail);
}