Local Adaptive integration
Everything is in LAInt.hpp. The class LocalAdaptive has two static methods: partialIntegral and integrate. The first calculates
the integral in a cell, and subdivides it until two consecutive subdivisions give almost the same result. The second method, runs
the first in the entire integration region.
The signature of integrate is:
template< class LD >
lai::LocalAdaptive< LD >::integrate(funcType integrand, const std::vector<std::vector> &X,
const LD & atol, const LD & rtol, const unsigned int & maxDivisions,
integrationRuleType integrationRule)
,
where LD is the numeric type, funcType = std::function<LD(LD x,...)>, and integrationRuleType = std::function<LD(std::function<LD(LD)> integrand, const LD & x0, const LD & x1)>.
The arguments are:
- integrand: the integrand.
- X: integration cells for each dimension. These are the ones that will be subdivided.
- atol,rtol: absolute and relative tolerance. These are used to decide whether the integral in a cell has converged.
- maxDivisions: Maximum number of subdivisions of each cell.
- integrationRule: Integration rule to be used.
For one dimesnional integrals, one can use functions of the type std::function<LD(LD x)> and X as std::vector<LD>. Other than that, everything is identical.
Note: You can implement a new integration rule as
template< class LD >
LD Rule(std::function< LD(LD) > integrand, const LD & x0, const LD & x1)
{return integral for [x0,x1];}