Use Boost-Python in C++ to Access to Array of Functions Defined in Python

Your question is a bit confusing to me: you have a typedef for function pointers, but you are aware that you will be calling functors. Anyway, the code that you posted doesn't work because you forgot to import math, try with

  bp::exec(
    "from math import *\n"
    "def f1(x):\n"
    "  return  sin(x)*cos(x)\n"
    "def f2(x):\n"
    "  return  sin(x)*cos(x)\n"
    "f=[f1, f2]",
    main_dict
  );

Then for the c++ type, you might want to use:

  typedef std::function<double (double, double, double)> CPP_Function; // (a bad name)

Use the standard library, it doesn't bite:

  typedef vector< CPP_Function > CPP_Function_vector;

And then build an adaptor that constructs CPP_Function objects from python objects. It is extremely easy using lambda functions these days. All together:

#include <boost/python.hpp>

#include <functional>
#include <vector>

using namespace std;
namespace bp = boost::python;

typedef function<double(double, double, double)> CPP_Function;
typedef vector< CPP_Function > CPP_Function_vector; 

CPP_Function_vector convert_functions( bp::object const& functions ) 
{
    int l = bp::len( functions );
    CPP_Function_vector result;
    for (int i=0; i < l; i++ )
    {
        bp::object f = functions[i];
        result.push_back( [f]( double a, double b, double c)->double { return bp::extract<double>(f(a,b,c)); } );
    }
    return result;
}

int main( int argc, char* argv[] )
{

    Py_Initialize();

    bp::object main_module = bp::import("__main__");
    bp::object main_dict   = main_module.attr("__dict__");

    bp::exec(
        "from math import *\n"
        "def f1(x,y,z):\n"
        "  return  sin(x)*cos(y)*tan(z)\n"
        "def f2(x,y,z):\n"
        "  return  sin(x)*cos(z)\n"
        "f=[f1, f2]",
        main_dict
    );

    bp::object f = main_dict["f"];

    CPP_Function_vector function_vector = convert_functions( f );

    cout << function_vector[1](1.0, 0.2, 0.3) << endl;

    return 0;

}