/* F08KP_T1W_F C++ Header Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
* Mark 30.0, 2024.
*/
#include <dco.hpp>
#include <iostream>
#include <nag.h>
#include <nagad.h>
#include <nagx04.h>
#include <stdio.h>
#include <string>
using namespace std;
int main()
{
int exit_status = 0;
nag::ad::handle_t ad_handle;
Integer ifail = 0;
NagError fail;
INIT_FAIL(fail);
cout << "F08KP_T1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline(cin, mystr);
// Read matrix dimensions
Integer m, n;
cin >> m;
cin >> n;
// Allocate arrays containing A and its factorized form, B
// and the solution X.
Integer lda = m, ldu = m, ldvt = n, lwork;
nagad_t1w_w_ctype *a = 0, *u = 0, *vt = 0, *work = 0, dummy[1];
nagad_t1w_w_rtype *ar = 0, *ai = 0, *s = 0, *rwork = 0;
Complex * uc = 0, *vtc = 0, *dsda = 0;
Charlen lena = 1;
a = new nagad_t1w_w_ctype[m * n];
ar = new nagad_t1w_w_rtype[m * n];
ai = new nagad_t1w_w_rtype[m * n];
s = new nagad_t1w_w_rtype[m];
rwork = new nagad_t1w_w_rtype[5 * n];
dsda = new Complex[n * m];
u = new nagad_t1w_w_ctype[m * m];
vt = new nagad_t1w_w_ctype[n * n];
// Read the matrix A, register and copy
double dd, di;
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
cin >> dd >> di;
Integer k = i + j * m;
ar[k] = dd;
ai[k] = di;
a[k].real(ar[k]);
a[k].imag(ai[k]);
}
}
// Create AD configuration data object
ifail = 0;
// Use routine workspace query to get optimal workspace.
ifail = 0;
lwork = -1;
nag::ad::f08kp(ad_handle, "A", "A", m, n, a, lda, s, u, ldu, vt, ldvt, dummy,
lwork, rwork, ifail);
lwork = (Integer)dco::value(real(dummy[0])) + 1;
work = new nagad_t1w_w_ctype[lwork];
double inc = 1.0, zero = 0.0;
for (int i = 0; i < 2 * m; i++)
{
if (i < m)
{
dco::derivative(ar[i]) = inc;
}
else
{
dco::derivative(ai[i - m]) = inc;
}
for (int j = 0; j < m * n; ++j)
{
a[j].real(ar[j]);
a[j].imag(ai[j]);
}
// Compute the singular values and left and right singular vectors
// of A (A = U*S*(V**T), m < n)
nag::ad::f08kp(ad_handle, "A", "A", m, n, a, lda, s, u, ldu, vt, ldvt, work,
lwork, rwork, ifail);
if (i < m)
{
dco::derivative(ar[i]) = zero;
for (int j = 0; j < n; j++)
{
dsda[j + n * i].re = dco::derivative(s[j]);
}
}
else
{
dco::derivative(ai[i - m]) = zero;
for (int j = 0; j < n; j++)
{
dsda[j + n * (i - m)].im = dco::derivative(s[j]);
}
}
}
// Print primal solution
cout.precision(4);
cout.width(12);
cout << " ";
cout << " Singular values:\n";
for (int i = 0; i < n; i++)
{
cout.width(11);
cout << dco::value(s[i]);
}
// Copy primal values to array for printing
uc = new Complex[m * m];
vtc = new Complex[n * n];
for (int i = 0; i < m * m; i++)
{
uc[i].re = dco::value(real(u[i]));
uc[i].im = dco::value(imag(u[i]));
}
for (int i = 0; i < n * n; i++)
{
vtc[i].re = dco::value(real(vt[i]));
vtc[i].im = dco::value(imag(vt[i]));
}
cout << "\n\n";
x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, m, m, uc, m,
"Left singular vectors by column", 0, &fail);
cout << "\n";
x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, vtc, n,
"Right singular vectors by row", 0, &fail);
cout << "\n\n Derivatives calculated: First order tangents\n";
cout << " Computational mode : algorithmic\n";
cout << "\n Derivatives of Singular values w.r.t first column of A\n";
cout << "\n";
x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, m, dsda, n,
" dS_i/dA_j1", 0, &fail);
ifail = 0;
delete[] a;
delete[] ar;
delete[] ai;
delete[] s;
delete[] u;
delete[] vt;
delete[] work;
delete[] rwork;
delete[] uc;
delete[] vtc;
delete[] dsda;
return exit_status;
}