```/* F08KD_A1W_F C++ Header Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
* Mark 26.2, 2017.
*/

#include <nag.h>
#include <nagx04.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <iostream>
using namespace std;

int main(void)
{
int       exit_status = 0;
Integer   ifail = 0;
NagError  fail;
INIT_FAIL(fail);

cout << "F08KD_A1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline (cin, mystr);

// Read matrix dimensions and algorithmic mode
Integer m, n, mode;
cin >> m;
cin >> n;
cin >> mode;

// Allocate arrays containing A and its factorized form, B
// and the solution X.
Integer           lda = m, ldu = m, ldvt = n, lwork;
nagad_a1w_w_rtype *a=0, *a_in=0, *s=0, *u=0, *vt=0, *work=0;
double            *ur=0, *vtr = 0;
Integer           *iwork=0;
Charlen           lena = 1;
if (!(a     = NAG_ALLOC(m*n, nagad_a1w_w_rtype)) ||
!(iwork = NAG_ALLOC(8*n, Integer))) {
cout << "Allocation failure\n";
exit_status = -1;
goto END;
}

// Read the matrix A, register and copy
double dd;
for (int i = 0; i<m; i++) {
for (int j = 0; j<n; j++) {
cin >> dd;
Integer k = i + j*m;
a_in[k].value = dd;
a_in[k].id = 0;
a[k] = a_in[k];
}
}

// Create AD configuration data object
ifail = 0;

ifail = 0;

// Use routine workspace query to get optimal workspace.
ifail = 0;
lwork = -1;
lena);

lwork = (Integer) dummy[0].value + 1;
if (!(work = NAG_ALLOC(lwork, nagad_a1w_w_rtype))) {
cout << "Allocation failure\n";
exit_status = -2;
goto END;
}

//  Compute the singular values and left and right singular vectors
//  of A (A = U*S*(V**T), m < n)
lena);

// Print primal solution
cout.precision(4);
cout.width(12); cout << " ";
cout << " Singular values:\n";
for (int i=0; i<m; i++) {
}

// Copy primal values to array for printing
if (!(ur     = NAG_ALLOC(m*m, double)) ||
!(vtr    = NAG_ALLOC(n*n, double))) {
cout << "Allocation failure\n";
exit_status = -3;
goto END;
}

for (int i=0; i<m*m; i++) {
}
for (int j=0; j<n; j++) {
Integer k = j*n;
for (int i=0; i<m; i++) {
k++;
}
}

cout << "\n\n";
x04cac(Nag_ColMajor,Nag_GeneralMatrix,Nag_NonUnitDiag,m,m,ur,ldu,
"Left singular vectors by column",0,&fail);
cout << "\n";
x04cac(Nag_ColMajor,Nag_GeneralMatrix,Nag_NonUnitDiag,m,n,vtr,ldvt,
"Right singular vectors by row",0,&fail);

cout << "\n\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode    : symbolic\n";
} else {
cout << " Computational mode    : algorithmic\n";
}

cout << "\n Derivatives of Singular values w.r.t first column of A\n";
// Obtain derivatives for each singular value w.r.t first column of A
cout.setf(ios::scientific,ios::floatfield);
cout.setf(ios::right);
cout.precision(2);
for (int i=0; i<m; i++) {
cout << "\n Singular value " << i+1 << endl;
// Setup evaluation of derivatives via adjoints
Integer inc = 1.0;
ifail = -1;
if (ifail != 0) {
exit_status = 1;
goto END;
}
// Get derivatives
cout.width(10); cout << " ";
for (int j=0; j<m; j++) {
cout.width(10); cout << dsda;
}
cout << endl;
}
END:
// Remove computational data object and tape
ifail = 0;

NAG_FREE(a);
NAG_FREE(a_in);
NAG_FREE(s);
NAG_FREE(u);
NAG_FREE(vt);
NAG_FREE(iwork);
NAG_FREE(work);
NAG_FREE(ur);
NAG_FREE(vtr);

return exit_status;
}
```