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From: Ritajit Kundu (ritajit2014_at_[hidden])
Date: 2020-05-10 18:28:31

I am trying to compute a 2 Dimensional numerical integration with the help
of Boost. I've been reading the documentation for a couple of days and my
CPP language knowledge is just up to legacy CPP level so I'm a noob.

I saw this page
<https://www.boost.org/doc/libs/1_73_0/libs/math/doc/html/math_toolkit/gauss_kronrod.html>
in documentation which calculates the quadrature using* Gauss-Kronrod *rule.
I was trying to build upon it and calculate a 2-d integral using
Gauss-Kronrod rule. My understanding is *a 2D integral is basically 2 1D
integrals with the Cartesian product.* So I was thinking If I can nest two
integration function then I'm done. I've started from the aforementioned
example and extended it a bit so the code for a 2d integration looks like,

    #include <boost/math/quadrature/gauss_kronrod.hpp>
    #include <iostream>

    int main(int argc, char *argv[])
    {
      using namespace boost::math::quadrature;
      auto f1 = [](double t, double s) { return std::exp(-(t*t+s*s+t*s) /
2); };
      double error;
      double Q = gauss_kronrod<double, 15>::integrate(gauss_kronrod<double,
61>::integrate(f1, 0, std::numeric_limits<double>::infinity(), 5), 0,
std::numeric_limits<double>::infinity(), 5, 1e-9, &error);
      std::cout << Q << " " << error<<std::endl;
      return 0;
    }
.
I've just added a lambda function (which is the integrand) of two variables
and nested 2 1D Gauss-Kronrod integration functions. I'm compiling this with

g++ -Wall -I /path/to/boost_1_73_0  2d-gauss.cpp

This gives error and compilation fails. I don't know what wrong I'm doing.
How do you suggest to do such an integral?
Thanks in advance.