I am attempting to find the roots to three equation in three unknowns, using the globally convergent Newton method. My problem is simply with the syntax. roots_multidim.h is looking for a &vecfunc object, and I have no idea how to create one. The only line from the text that seems relevant is "Its declaration as a function is
VecDoub vecfunc(VecDoub_I x); "

I have tried _many_ variations on the above line, and pre-main declaration, I won't reproduce them all here. Most produce ~50 lines of error messages and won't compile. My latest attempt, which does not work, is:

VecDoub vecfunc(VecDoub_I x) {
vecfunc[0] = x[0] * x[1] * x[2] - 6;
vecfunc[1] = x[0] * x[0] * x[1] + x[1] * x[1] * x[2]+x[2] * x[2] * x[0]-23;
vecfunc[2] = exp(x[0]+x[1]+x[2])-403;
}
using namespace std;
int main() {
const int N=3;
bool check;
int i;
VecDoub x(N);
VecDoub vecfunc(VecDoub x);
x[0] = 0;
x[1] = 5;
x[2] = 7;
newt(x,check,vecfunc);

As you can tell, I have minimal experience with C++. Any help on the basic syntax of how to create the necessary vector of functions would be much appreciated. Thanks,

Dave

...My problem is simply with the syntax....
The function takes a vector input and returns a vector output.

#include "../code/nr3.h"
#include "../code/qrdcmp.h"
#include "../code/ludcmp.h"
#include "../code/roots_multidim.h"

VecDoub vecfunc(VecDoub_I x)
{
VecDoub y(3);
y[0] = x[0] * x[1] * x[2] - 6;

y[1] = x[0] * x[0] * x[1] +
x[1] * x[1] * x[2] +
x[2] * x[2] * x[0] -
23;

y[2] = exp(x[0] + x[1] + x[2]) - 403;

return y;
}

int main()
{
bool check;

VecDoub x(3);
x[0] = 0;
x[1] = 5;
x[2] = 7;

cout << "Initial guess: " << endl;
for (int i = 0; i < x.size(); i++) {
cout << " x[" << i << "] = " << x[i] << endl;
}
cout << endl;

cout << "Calling newt . . . " << endl << endl;
newt(x, check, vecfunc);

if (check) {
cout << "Check is true (convergence to a local minimum)." << endl;
cout << "Try another initial guess." << endl;
}
else {
cout << "Check is false (a \"normal\" return)." << endl;
}
cout << endl;

cout << scientific;
cout << "Solution from newt:" << endl;
for (int i = 0; i < x.size(); i++) {
cout << " x[" << i << "] = " << x[i] << endl;
}
cout << endl;

VecDoub y;
y = vecfunc(x);
cout << "Value of the solution vector:" << endl;
for (int i = 0; i < y.size(); i++) {
cout << " y[" << i << "] = " << y[i] << endl;
}
cout << endl;


return 0;
}


Output (GNU g++ version 4.1.2)

Initial guess:
x[0] = 0
x[1] = 5
x[2] = 7

Calling newt . . .

Check is false (a "normal" return).

Solution from newt:
x[0] = 1.305823e+00
x[1] = 1.391819e+00
x[2] = 3.301295e+00

Value of the solution vector:
y[0] = -1.472073e-13
y[1] = -5.798816e-13
y[2] = -2.330580e-12


Regards,

Dave

I could have sworn I'd tried that, but I'd obviously left something out. That worked perfectly. Thank you so much!


Dave