Optimist::FiniteDifferences Namespace Reference

Classes
class	Epsilon

Functions
template<typename Real>
Real	SideFiniteDifferences (Real const f_0, Real const f_1, Real const f_2, Real h_1, Real h_2)
template<typename Real>
Real	CenteredFiniteDifferences (Real const f_l, Real const f_c, Real const f_r, Real h)
template<typename Vector, typename Real = typename Vector::Scalar>
Vector	SideFiniteDifferences (Vector const &f_0, Vector const &f_1, Vector const &f_2, Real h_1, Real h_2)
template<typename Vector, typename Real = typename Vector::Scalar>
Vector	CenteredFiniteDifferences (Vector const &f_l, Vector const &f_c, Vector const &f_r, Real h)
template<typename Function, typename Vector, typename Real = typename Vector::Scalar>
bool	Gradient (Vector const &x, Function &&function, Vector &out)
template<typename Function, typename Vector, typename Matrix, typename Real = typename Vector::Scalar>
bool	Jacobian (Vector const &x, Function &&function, Matrix &out)
template<typename Function, typename Vector, typename Matrix, typename Real = typename Vector::Scalar>
bool	Hessian (Vector const &x, Function &&function, Matrix &out)

Function Documentation

CenteredFiniteDifferences() [1/2]

template<typename Real>

Real Optimist::FiniteDifferences::CenteredFiniteDifferences ( Real const f_l, Real const f_c, Real const f_r, Real h )

inline

Compute centered finite differences (for scalars).

Parameters

[in]	f_l	Function value at \( x-h \).
[in]	f_c	Function value at \( x \).
[in]	f_r	Function value at \( x+h \).
[in]	h	Step size.

Template Parameters

Real	Scalar number type.

Returns

Approximated derivative.

CenteredFiniteDifferences() [2/2]

template<typename Vector, typename Real = typename Vector::Scalar>

Vector Optimist::FiniteDifferences::CenteredFiniteDifferences ( Vector const & f_l, Vector const & f_c, Vector const & f_r, Real h )

inline

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

Parameters

[in]	f_l	Vector at \( x-h \).
[in]	f_c	Vector at \( x \).
[in]	f_r	Vector at \( x+h \).
[in]	h	Step size.

Template Parameters

Vector	Fixed-size Eigen vector type.
Real	Scalar number type.

Returns

Approximated derivative vector.

Gradient()

template<typename Function, typename Vector, typename Real = typename Vector::Scalar>

bool Optimist::FiniteDifferences::Gradient	(	Vector const &	x,
		Function &&	function,
		Vector &	out )

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

Template Parameters

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

Parameters

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

Returns

True if successful, false otherwise.

Hessian()

template<typename Function, typename Vector, typename Matrix, typename Real = typename Vector::Scalar>

bool Optimist::FiniteDifferences::Hessian	(	Vector const &	x,
		Function &&	function,
		Matrix &	out )

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

Template Parameters

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

Parameters

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

Returns

True if successful, false otherwise.

Jacobian()

template<typename Function, typename Vector, typename Matrix, typename Real = typename Vector::Scalar>

bool Optimist::FiniteDifferences::Jacobian	(	Vector const &	x,
		Function &&	function,
		Matrix &	out )

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

Template Parameters

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

Parameters

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

Returns

True if successful, false otherwise.

SideFiniteDifferences() [1/2]

template<typename Real>

Real Optimist::FiniteDifferences::SideFiniteDifferences ( Real const f_0, Real const f_1, Real const f_2, Real h_1, Real h_2 )

inline

Compute one-sided finite differences (for scalars).

Parameters

[in]	f_0	Function value at \( x \).
[in]	f_1	Function value at \( x+h_1 \).
[in]	f_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() [2/2]

template<typename Vector, typename Real = typename Vector::Scalar>

Vector Optimist::FiniteDifferences::SideFiniteDifferences ( Vector const & f_0, Vector const & f_1, Vector const & f_2, Real h_1, Real h_2 )

inline

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

Parameters

[in]	f_0	Vector at \( x \).
[in]	f_1	Vector at \( x+h_1 \).
[in]	f_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.
Real	Scalar number type.

Returns

Approximated derivative vector.