Class inte_gen (o2scl)

O2scl : Class List

template<class func_t, class lfunc_t, class ufunc_t, class vec_t = boost::numeric::ublas::vector<double>>
class inte_gen

Generalized multi-dimensional integration [abstract base].

Perform the generalized multi-dimensional integral:

\[ \int_{x_0=a_0}^{x_0=b_0} f(x_0) \int_{x_1=a_1(x_0)}^{x_1=b_1(x_0)} f(x_0, x_1) ... \int_{x_{\mathrm{n}-1}=a_{\mathrm{n}-1}(x_0,x_1,..,x_{\mathrm{n}-2})}^ {x_{\mathrm{n}-1}=b_{\mathrm{n}-1}(x_0,x_1,..,x_{\mathrm{n}-2})} f(x_0,x_1,...,x_{\mathrm{n-1}})~d x_{\mathrm{n}-1}~...~d x_1~d x_0 \]

The functions \( a_i \) and \( b_i \) are specified in the arguments a and b to the function ginteg() or ginteg_err() .

In order to allow the user to specify only three functions (for the integrand, the lower limits, and the upper limits) the first argument to the limit and integrand functions is used to distinguish among the limits for each separate integral. So first argument to a for \( a_0() \) is 0, and the first argument to a for \( a_1() \) is 1, etc., and similarly for the upper limits specified in b and the integrands specified in func.

Idea for Future:

It might be interesting to construct a child class of o2scl::inte_gen which automatically transforms variables to a hypercube and then applies a child of o2scl::inte_multi to do the integration.

Public Functions

inline inte_gen()

inline virtual ~inte_gen()

virtual double ginteg(func_t &func, size_t ndim, lfunc_t &a, ufunc_t &b) = 0

Integrate function func from \( x_i=a_i(x_i) \) to \( x_i=b_i(x_i) \) for \( 0<i<\mathrm{ndim}-1 \).

inline virtual int ginteg_err(func_t &func, size_t ndim, lfunc_t &a, ufunc_t &b, double &res, double &err)

Integrate function func from \( x_i=a_i(x_i) \) to \( x_i=b_i(x_i) \) for \( 0<i<\mathrm{ndim}-1 \).

inline double get_error()

Return the error in the result from the last call to ginteg() or ginteg_err()

This will quietly return zero if no integrations have been performed.

inline const char *type()

Return string denoting type (“inte_gen”)

Public Members

int verbose

Verbosity.

double tol_rel

The maximum “uncertainty” in the value of the integral.

bool err_nonconv

If true, call the error handler if the routine does not “converge”.

Protected Attributes

double interror

The uncertainty for the last integration computation.