Optimist::FiniteDifferences Namespace Reference

Classes
class	Epsilon

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

Function Documentation

CenteredFiniteDifferences() [1/2]

template<typename Vector, typename Scalar>

void Optimist::FiniteDifferences::CenteredFiniteDifferences ( const Scalar f_l, const Scalar f_c, const Scalar f_r, const Scalar h, const Integer i, Vector & out )

inline

Compute centered finite differences.

Template Parameters

Scalar

Floating-point number type.

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.
[in]	i	Index of the variable.
[out]	out	The approximated derivative.

CenteredFiniteDifferences() [2/2]

template<typename Vector, typename Matrix, typename Scalar>

void Optimist::FiniteDifferences::CenteredFiniteDifferences ( const Vector & f_l, const Vector & f_c, const Vector & f_r, const Scalar h, const Integer i, Matrix && out )

inline

Compute centered finite differences (for dense and Eigen vectors).

Template Parameters

Vector	Dense or sparse Eigen vector type.
Matrix	Dense or sparse Eigen matrix type.
Scalar	Floating-point number type.

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.
[in]	i	Index of the variable.
[out]	out	The approximated derivative vector.

Gradient()

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

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

inline

Compute finite differences gradient for a scalar function (for dense Eigen vectors).

Template Parameters

Function	Callable type bool(Vector const &, Scalar &).
Vector	Dense Eigen vector type.
Scalar	Floating-point number type.

Parameters

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

Returns

True if successful, false otherwise.

Hessian()

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

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

inline

Compute finite differences Hessian for a scalar function (for dense Eigen vectors).

Template Parameters

Function	Callable type bool(Vector const &, Scalar &).
Vector	Dense Eigen vector type.
Matrix	Dense Eigen matrix type.
Scalar	Floating-point number type.

Parameters

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

Returns

True if successful, false otherwise.

Jacobian()

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

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

inline

Compute finite differences Jacobian for a vector function (for dense Eigen vectors).

Template Parameters

Function	Callable type bool(Vector const &, Vector &).
Vector	Dense Eigen vector type.
Matrix	Dense Eigen matrix type.
Scalar	Floating-point number type.

Parameters

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

Returns

True if successful, false otherwise.

SideFiniteDifferences() [1/2]

template<typename Vector, typename Scalar>

void Optimist::FiniteDifferences::SideFiniteDifferences ( const Scalar f_0, const Scalar f_1, const Scalar f_2, const Scalar h_1, const Scalar h_2, const Integer i, Vector & out )

inline

Compute one-sided finite differences.

Template Parameters

Scalar

Floating-point number type.

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.
[in]	i	Index of the variable.
[out]	out	The approximated derivative.

SideFiniteDifferences() [2/2]

template<typename Vector, typename Matrix, typename Scalar>

void Optimist::FiniteDifferences::SideFiniteDifferences ( const Vector & f_0, const Vector & f_1, const Vector & f_2, const Scalar h_1, const Scalar h_2, const Integer i, Matrix & out )

inline

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

Template Parameters

Vector	Dense or sparse Eigen vector type.
Matrix	Dense or sparse Eigen matrix type.
Scalar	Floating-point number type.

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.
[in]	i	Index of the variable.
[out]	out	The approximated derivative.