chebyshev::prec::estimator Namespace Reference

Precision estimators. More...

Functions
template<typename FloatType = double>
auto	quadrature1D ()
	Use Simpson's quadrature scheme to approximate error integrals for univariate real functions (endofunctions on real number types). More...
template<typename IntType = int, typename ReturnType = IntType>
auto	discrete1D ()
	Use a discrete estimator over a lattice of points, here implemented in one dimension, to compute error sums over a discrete domain. More...
template<typename FloatType = double>
auto	montecarlo1D ()
	Use crude Monte Carlo integration to approximate error integrals for univariate real functions. More...
template<typename FloatType = double, typename Vector = std::vector<FloatType>>
auto	montecarlo (unsigned int dimensions)
	Use crude Monte Carlo integration to approximate error integrals for multivariate real functions. More...

Detailed Description

Precision estimators.

Function Documentation

discrete1D()

template<typename IntType = int, typename ReturnType = IntType>

auto chebyshev::prec::estimator::discrete1D ( )

inline

Use a discrete estimator over a lattice of points, here implemented in one dimension, to compute error sums over a discrete domain.

The function is evaluated at the discrete integer values inside the prec::interval domain and the errors are summed and averaged, returning a prec::estimate_result.

ReturnType must be a type that has operator-() and is castable to long double.

montecarlo()

template<typename FloatType = double, typename Vector = std::vector<FloatType>>

auto chebyshev::prec::estimator::montecarlo ( unsigned int  dimensions )

inline

Use crude Monte Carlo integration to approximate error integrals for multivariate real functions.

Parameters

dimensions

The dimension of the space of inputs

Note

You may specify a custom vector type to use as input, but it must provide a constructor taking in the number of elements.

montecarlo1D()

template<typename FloatType = double>

auto chebyshev::prec::estimator::montecarlo1D ( )

inline

Use crude Monte Carlo integration to approximate error integrals for univariate real functions.

A uniform random sampler is used to sample points over the one-dimensional domain

quadrature1D()

template<typename FloatType = double>

auto chebyshev::prec::estimator::quadrature1D ( )

inline

Use Simpson's quadrature scheme to approximate error integrals for univariate real functions (endofunctions on real number types).

The estimator is returned as a lambda function.