gauss_kronrod Namespace Reference

Namespace with utility functions for adaptive numerical integration. More...

Classes
struct	control
	User control parameters for R's integrate. More...
struct	Integral
	Interface to R's adaptive integrate routine. More...
struct	mvIntegral
	Multivariate integral class. More...

Functions
template<class Integrand >
Integrand::Scalar	integrate (Integrand f, typename Integrand::Scalar a=-INFINITY, typename Integrand::Scalar b=INFINITY, control c=control())
	Integrate function over finite or infinite interval. More...
template<class Integrand >
mvIntegral0< Integrand >	mvIntegrate (Integrand &f, control c=control())
	Multivariate integration. More...

Detailed Description

Namespace with utility functions for adaptive numerical integration.

Interfaces to R's integrator that can be used with forward mode AD.

Function Documentation

integrate()

template<class Integrand >

Integrand::Scalar gauss_kronrod::integrate	(	Integrand	f,
		typename Integrand::Scalar	a = -INFINITY,
		typename Integrand::Scalar	b = INFINITY,
		control	c = control()
	)

Integrate function over finite or infinite interval.

Parameters

f	Univariate integrand (functor)
a	Lower integration limit. Default is negative infinity.
a	Upper integration limit. Default is positive infinity.
c	Optional control parameters.

Example:

template<class Float>
struct Gauss_t {
  typedef Float Scalar;
  Float a;  // Parameter
  // Evaluate integrand
  Float operator(Float x) () {
    Float ans = exp(- a*x*x);
    return ans;
  }
  // Integrate wrt x
  Float my_integrate() {
    using gauss_kronrod::integrate;
    Float ans = integrate(*this);
    return ans;
  }
};

Examples:

adaptive_integration.cpp.

Definition at line 163 of file tiny_ad/integrate/integrate.hpp.

mvIntegrate()

template<class Integrand >

mvIntegral0<Integrand> gauss_kronrod::mvIntegrate	(	Integrand &	f,
		control	c = control()
	)

Multivariate integration.

Parameters

f	Multivariate integrand (functor)
c	Optional control parameters

Example:

template<class Float>
struct Gauss2D_t {
  typedef Float Scalar;
  Float a, b;  // Parameters
  Float x, y;  // Integration variables
  // Evaluate integrand (u1,u2)
  Float operator() () {
    Float ans = exp(- a*x*x - b*y*y);
    return ans;
  }
  // Integrate wrt (x,y)
  Float my_integrate() {
    using gauss_kronrod::mvIntegrate;
    Float ans = mvIntegrate(*this).
      wrt(x, -INFINITY, INFINITY).
      wrt(y, -INFINITY, INFINITY) ();
    return ans;
  }
};

Definition at line 259 of file tiny_ad/integrate/integrate.hpp.