How to pass some constants in Boosts's brent_find_minima()? - c++

Question

How can I pass some constants in boost::math::tools::brent_find_minima() from main()?
struct func
{
template <class T>
T operator()(T const& x)
{ //
T Wnew = 20.0/9.0*720.0; // Goal is to pass it through main()
T W = 2500; // Goal is to pass it through main()
return abs(Wnew/2/x - atan(W/2/x));
}
};
int main(int argc, char **argv)
{
// How can I pass Wnew and W values while calling boost::math::tools::brent_find_minima() from main()
std::pair<double, double> r = boost::math::tools::brent_find_minima(func(), 1.0, 2000.0, std::numeric_limits<double>::digits);
std::cout.precision(std::numeric_limits<double>::digits10);
std::cout << "x at minimum = " << r.first << ", f(" << r.first << ") = " << r.second << std::endl;
}

Answer 1

I suppose what you want is to create different instances of func with different values for W and Wnew. You are almost there, just give your func some state:
struct func
{
double Wnew;
double W;
func(double Wnew, double W) : Wnew(Wnew),W(W) {}
double operator()(double const& x)
{
return abs(Wnew/2/x - atan(W/2/x));
}
};
And then create an instance like this:
double Wnew = 1.0;
double W = 2.0;
auto r = boost::math::tools::brent_find_minima(func(Wnew,W), 1.0, 2000.0, std::numeric_limits<double>::digits);
// ^^
I was a bit puzzled by your operator() being a template and changed that. If you had good reasons for it, simply make it a template again.
PS: Since C++11, there are lambda expressions that allow a much terser syntax for functors.

Answer 2

I like the lambda approach the best:
#include <cmath>
#include <iostream>
#include <boost/math/tools/minima.hpp>
int main(int argc, char **argv)
{
double W = 2500;
double Wnew = 20.0/9.0*720.0;
if (argc == 3) {
double W = std::stod(argv[1]);
double Wnew = std::stod(argv[2]);
}
auto f = [&W, &Wnew](double x)->double {
return std::abs(Wnew/2/x - atan(W/2/x));
};
std::pair<double, double> r = boost::math::tools::brent_find_minima(f, 1.0, 2000.0, std::numeric_limits<double>::digits);
std::cout.precision(std::numeric_limits<double>::digits10);
std::cout << "x at minimum = " << r.first << ", f(" << r.first << ") = " << r.second << std::endl;
}
The documentation for brent_find_minima was written pre-C++11, and uses what now should be regarded as overly verbose syntax. The post C++11 boost.math documentation examples (like the quadrature routines) all use lambdas.