FiniteDifference.hpp File Reference

Finite difference weights, derivative approximations, and integration defects. More...

#include "metis/core/MetisError.hpp"
#include "metis/core/MetisTypes.hpp"
#include <Eigen/Dense>
#include <cmath>
#include <string>
#include <vector>

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Namespaces
namespace	metis

Enumerations
enum class	metis::IntegrationMethod { metis::ForwardEuler , metis::BackwardEuler , metis::Trapezoidal , metis::Midpoint }
	Integration/differentiation method for trajectory optimization. More...

Functions
IntegrationMethod	metis::parse_integration_method (const std::string &method)
	Parse integration method from string.
template<typename Scalar>
std::pair< Scalar, Scalar >	metis::forward_euler_weights (Scalar h)
	Forward Euler (explicit) differentiation weights.
template<typename Scalar>
std::pair< Scalar, Scalar >	metis::backward_euler_weights (Scalar h)
	Backward Euler (implicit) differentiation weights.
template<typename Scalar>
std::pair< Scalar, Scalar >	metis::central_difference_weights (Scalar h)
	Central difference differentiation weights.
template<typename Scalar>
std::pair< Scalar, Scalar >	metis::trapezoidal_weights (Scalar h)
	Trapezoidal integration weights.
template<typename Scalar>
MetisVector< Scalar >	metis::forward_difference (const MetisVector< Scalar > &f, const MetisVector< Scalar > &x)
	Compute derivative using forward difference.
template<typename Scalar>
MetisVector< Scalar >	metis::backward_difference (const MetisVector< Scalar > &f, const MetisVector< Scalar > &x)
	Compute derivative using backward difference.
template<typename Scalar>
MetisVector< Scalar >	metis::central_difference (const MetisVector< Scalar > &f, const MetisVector< Scalar > &x)
	Compute derivative using central difference.
template<typename Scalar>
MetisVector< Scalar >	metis::integration_defects (const MetisVector< Scalar > &x, const MetisVector< Scalar > &xdot, const MetisVector< Scalar > &t, IntegrationMethod method=IntegrationMethod::Trapezoidal)
	Compute integration defects for derivative constraints.
template<typename Scalar>
MetisVector< Scalar >	metis::finite_difference_coefficients (const MetisVector< Scalar > &x, Scalar x0=Scalar(0.0), int derivative_degree=1)
	Computes finite difference coefficients for arbitrary grids.

Detailed Description

Finite difference weights, derivative approximations, and integration defects.

See also

Calculus.hpp, AutoDiff.hpp