Optimist::FiniteDifferences Namespace Reference

Classes
class	Epsilon

Typedefs
template<typename Real>
using	VectorXd = Eigen::Vector<Real, Eigen::Dynamic>
template<typename Real>
using	MatrixXd = Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic>

Functions
template<typename Real>
Real	SideFiniteDifferences (Real const fun_0, Real const fun_1, Real const fun_2, Real h_1, Real h_2)
template<typename Real>
Real	CenteredFiniteDifferences (Real const fun_l, Real const fun_c, Real const fun_r, Real h)
template<typename Real>
VectorXd< Real >	SideFiniteDifferences (VectorXd< Real > const &fun_0, VectorXd< Real > const &fun_1, VectorXd< Real > const &fun_2, Real h_1, Real h_2)
template<typename Real>
VectorXd< Real >	CenteredFiniteDifferences (VectorXd< Real > const &fun_l, VectorXd< Real > const &fun_c, VectorXd< Real > const &fun_r, Real h)
template<typename Function, typename Real>
bool	Gradient (VectorXd< Real > const &x, Function fun, VectorXd< Real > &grad)
template<typename Function, typename Real>
bool	Jacobian (VectorXd< Real > const &x, Function fun, MatrixXd< Real > &jac)
template<typename Function, typename Real>
bool	Hessian (VectorXd< Real > const &x, Function fun, MatrixXd< Real > &hes)
template<typename Vector>
Vector	SideFiniteDifferences (Vector const &fun_0, Vector const &fun_1, Vector const &fun_2, typename Vector::Scalar h_1, typename Vector::Scalar h_2)
template<typename Vector>
Vector	CenteredFiniteDifferences (Vector const &fun_l, Vector const &fun_c, Vector const &fun_r, typename Vector::Scalar h)
template<typename Function, typename Vector>
bool	Gradient (Vector const &x, Function fun, Vector &grad)
template<typename Function, typename Vector, typename Matrix>
bool	Jacobian (Vector const &x, Function fun, Matrix &jac)
template<typename Function, typename Vector, typename Matrix>
bool	Hessian (Vector const &x, Function fun, Matrix &hes)

Typedef Documentation

MatrixXd

template<typename Real>

using Optimist::FiniteDifferences::MatrixXd = Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic>

VectorXd

template<typename Real>

using Optimist::FiniteDifferences::VectorXd = Eigen::Vector<Real, Eigen::Dynamic>

< Template alias for VectorXd<Real>. Template alias for MatrixXd<Real>.

Function Documentation

CenteredFiniteDifferences() [1/3]

template<typename Real>

Real Optimist::FiniteDifferences::CenteredFiniteDifferences ( Real const fun_l, Real const fun_c, Real const fun_r, Real h )

inline

Compute centered finite differences (for scalars).

Parameters

[in]	fun_l	Function value at \( x-h \).
[in]	fun_c	Function value at \( x \).
[in]	fun_r	Function value at \( x+h \).
[in]	h	Step size.

Template Parameters

Real	Scalar number type.

Returns

Approximated derivative.

CenteredFiniteDifferences() [2/3]

template<typename Vector>

Vector Optimist::FiniteDifferences::CenteredFiniteDifferences ( Vector const & fun_l, Vector const & fun_c, Vector const & fun_r, typename Vector::Scalar h )

inline

Compute centered finite differences (for fixed-size Eigen vectors).

Parameters

[in]	fun_l	Vector at \( x-h \).
[in]	fun_c	Vector at \( x \).
[in]	fun_r	Vector at \( x+h \).
[in]	h	Step size.

Template Parameters

Vector

Fixed-size Eigen vector type.

Returns

Approximated derivative vector.

CenteredFiniteDifferences() [3/3]

template<typename Real>

VectorXd< Real > Optimist::FiniteDifferences::CenteredFiniteDifferences ( VectorXd< Real > const & fun_l, VectorXd< Real > const & fun_c, VectorXd< Real > const & fun_r, Real h )

inline

Compute centered finite differences (for dynamic-size Eigen vectors).

Parameters

[in]	fun_l	Vector at \( x-h \).
[in]	fun_c	Vector at \( x \).
[in]	fun_r	Vector at \( x+h \).
[in]	h	Step size.

Template Parameters

Real	Scalar number type.

Returns

Approximated derivative vector.

Gradient() [1/2]

template<typename Function, typename Vector>

bool Optimist::FiniteDifferences::Gradient	(	Vector const &	x,
		Function	fun,
		Vector &	grad )

Compute finite differences gradient for a scalar function (for fixed-size Eigen vectors).

Parameters

[in]	x	Point at which to compute gradient.
[in]	fun	Function to differentiate.
[out]	grad	Gradient vector.

Template Parameters

Function	Callable type bool(Vector const &, Real &).
Vector	Fixed-size Eigen vector type.

Returns

True if successful, false otherwise.

Gradient() [2/2]

template<typename Function, typename Real>

bool Optimist::FiniteDifferences::Gradient	(	VectorXd< Real > const &	x,
		Function	fun,
		VectorXd< Real > &	grad )

Compute finite differences gradient of a scalar function (for dynamic-size Eigen vectors).

Parameters

[in]	x	Point at which to compute gradient.
[in]	fun	Function to differentiate.
[out]	grad	Gradient vector.

Template Parameters

Function	Callable type bool(VectorXd const &, Real &).
Real	Scalar number type.

Returns

True if successful, false otherwise.

Hessian() [1/2]

template<typename Function, typename Vector, typename Matrix>

bool Optimist::FiniteDifferences::Hessian	(	Vector const &	x,
		Function	fun,
		Matrix &	hes )

Compute finite differences Hessian for a scalar function (for fixed-size Eigen vectors).

Parameters

[in]	x	Point at which to compute Hessian.
[in]	fun	Function to differentiate.
[out]	hes	Hessian matrix.

Template Parameters

Function	Callable type bool(Vector const &, Real &).
Vector	Fixed-size Eigen vector type.
Matrix	Fixed-size Eigen matrix type.

Returns

True if successful, false otherwise.

Hessian() [2/2]

template<typename Function, typename Real>

bool Optimist::FiniteDifferences::Hessian	(	VectorXd< Real > const &	x,
		Function	fun,
		MatrixXd< Real > &	hes )

Compute finite differences Hessian of a scalar function (for dynamic-size Eigen vectors).

Parameters

[in]	x	Point at which to compute Hessian.
[in]	fun	Function to differentiate.
[out]	hes	Hessian matrix.

Template Parameters

Function	Callable type bool(VectorXd<Real> const &, Real&).
Real	Scalar number type.

Returns

True if successful, false otherwise.

Jacobian() [1/2]

template<typename Function, typename Vector, typename Matrix>

bool Optimist::FiniteDifferences::Jacobian	(	Vector const &	x,
		Function	fun,
		Matrix &	jac )

Compute finite differences Jacobian for a vector function (for fixed-size Eigen vectors).

Parameters

[in]	x	Point at which to compute Jacobian.
[in]	fun	Function to differentiate.
[out]	jac	Jacobian matrix.

Template Parameters

Function	Callable type bool(Vector const &, Vector &).
Vector	Fixed-size Eigen vector type.
Matrix	Fixed-size Eigen matrix type.

Returns

True if successful, false otherwise.

Jacobian() [2/2]

template<typename Function, typename Real>

bool Optimist::FiniteDifferences::Jacobian	(	VectorXd< Real > const &	x,
		Function	fun,
		MatrixXd< Real > &	jac )

Compute finite differences Jacobian of a vector function (for dynamic-size Eigen vectors).

Parameters

[in]	x	Point at which to compute Jacobian.
[in]	fun	Function to differentiate.
[out]	jac	Output Jacobian matrix.

Template Parameters

Function	Callable type bool(VectorXd<Real> const &, VectorXd<Real> &).
Real	Scalar number type.

Returns

True if successful, false otherwise.

SideFiniteDifferences() [1/3]

template<typename Real>

Real Optimist::FiniteDifferences::SideFiniteDifferences ( Real const fun_0, Real const fun_1, Real const fun_2, Real h_1, Real h_2 )

inline

Compute one-sided finite differences (for scalars).

Parameters

[in]	fun_0	Function value at \( x \).
[in]	fun_1	Function value at \( x+h_1 \).
[in]	fun_2	Function value at \( x+h_2 \).
[in]	h_1	Step size 1.
[in]	h_2	Step size 2.

Template Parameters

Real	Scalar number type.

Returns

Approximated derivative.

SideFiniteDifferences() [2/3]

template<typename Vector>

Vector Optimist::FiniteDifferences::SideFiniteDifferences ( Vector const & fun_0, Vector const & fun_1, Vector const & fun_2, typename Vector::Scalar h_1, typename Vector::Scalar h_2 )

inline

Compute one-sided finite differences (for fixed-size Eigen vectors).

Parameters

[in]	fun_0	Vector at \( x \).
[in]	fun_1	Vector at \( x+h_1 \).
[in]	fun_2	Vector at \( x+h_2 \).
[in]	h_1	Step size 1.
[in]	h_2	Step size 2.

Template Parameters

Vector

Fixed-size Eigen vector type.

Returns

Approximated derivative vector.

SideFiniteDifferences() [3/3]

template<typename Real>

VectorXd< Real > Optimist::FiniteDifferences::SideFiniteDifferences ( VectorXd< Real > const & fun_0, VectorXd< Real > const & fun_1, VectorXd< Real > const & fun_2, Real h_1, Real h_2 )

inline

Compute one-sided finite differences (for dynamic-size Eigen vectors).

Parameters

[in]	fun_0	Vector at \( x \).
[in]	fun_1	Vector at \( x+h_1 \).
[in]	fun_2	Vector at \( x+h_2 \).
[in]	h_1	Step size 1.
[in]	h_2	Step size 2.

Template Parameters

Real	Scalar number type.

Returns

Approximated derivative vector.