Class container for the generic function. More...

#include <Function.hh>

Public Types
using	InputType = typename std::conditional_t<FunInDim == 1, Real, Eigen::Vector<Real, FunInDim>>

using	OutputType = typename std::conditional_t<FunOutDim == 1, Real, Eigen::Vector<Real, FunOutDim>>

using	FirstDerivativeType = std::conditional_t<FunInDim == 1 && FunOutDim == 1, Real, Eigen::Matrix<Real, FunOutDim, FunInDim>>

using	SecondDerivativeType

Public Member Functions
	Function ()

std::string	name () const

void	evaluate (const InputType &x, OutputType &out) const

void	first_derivative (const InputType &x, FirstDerivativeType &out) const

void	second_derivative (const InputType &x, SecondDerivativeType &out) const

constexpr Integer	input_dimension () const

constexpr Integer	output_dimension () const

const std::vector< InputType > &	solutions () const

const std::vector< InputType > &	guesses () const

const InputType &	solution (const Integer i) const

const InputType &	guess (const Integer i) const

bool	is_solution (const InputType &x, const Real tol=EPSILON_LOW) const

Protected Attributes
std::vector< InputType >	m_solutions

std::vector< InputType >	m_guesses

Detailed Description

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>
class Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >

Function

The Function class in Optimist provides a common interface for representing and evaluating mathematical functions. This class is designed to handle a generic function \(\mathbf{f}(\mathbf{x}): \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}\), where \(\mathbf{x}\) is a vector of input variables and \(\mathbf{f}(\mathbf{x})\) is a vector of output values.

The Function class serves as a base class for developing specific function representations that can be used in various numerical algorithms. In general, the Function class and its derived classes are designed to support:

Root-finding problems of the form
\[ \mathbf{f}(\mathbf{x}) = \mathbf{0} \text{,} \quad \text{with} \quad \mathbf{f}: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n} \text{,} \]
Optimization problems of the form
\[ \min_{\mathbf{x}} f(\mathbf{x}) \text{,} \quad f: \mathbb{R}^{n} \rightarrow \mathbb{R} \text{.} \]

If \(n > 1\), the function is multi-dimensional, otherwise, it is scalar. The linear algebra operations required for multi-dimensional functions are performed using the Eigen library, which provides a high-level interface for matrix operations. For scalar functions ( \(n = 1\)), the base type changes to Real, a scalar type defined in the Optimist library.

Template Parameters

Real	Scalar number type.
FunInDim	The function problem input dimension.
FunOutDim	The function problem output dimension.
DerivedFunction	Derived function class.

Member Typedef Documentation

◆ FirstDerivativeType

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

using Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::FirstDerivativeType = std::conditional_t<FunInDim == 1 && FunOutDim == 1, Real, Eigen::Matrix<Real, FunOutDim, FunInDim>>

First derivative type.

◆ InputType

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

using Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::InputType = typename std::conditional_t<FunInDim == 1, Real, Eigen::Vector<Real, FunInDim>>

Basic constants. Input type.

◆ OutputType

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

using Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::OutputType = typename std::conditional_t<FunOutDim == 1, Real, Eigen::Vector<Real, FunOutDim>>

Output type.

◆ SecondDerivativeType

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

using Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::SecondDerivativeType

Initial value:

 std::conditional_t<FunInDim == 1 && FunOutDim == 1, Real,
      std::conditional_t<FunInDim == 1 || FunOutDim == 1, Eigen::Matrix<Real, FunInDim, FunInDim>,
      std::vector<Eigen::Matrix<Real, FunInDim, FunInDim>>>>

Second derivative type.

Constructor & Destructor Documentation

◆ Function()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::Function ( )

inline

Suggested initial guess used for testing. Class constructor for the function.

Member Function Documentation

◆ evaluate()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

void Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::evaluate	(	const InputType &	x,
		OutputType &	out ) const

inline

Compute the function value at the input point.

Parameters

[in]	x	Input point.
[out]	out	The function value.

◆ first_derivative()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

void Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::first_derivative	(	const InputType &	x,
		FirstDerivativeType &	out ) const

inline

Compute the function first derivative at the input point.

Parameters

[in]	x	Input point.
[out]	out	The function first derivative.

◆ guess()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

const InputType & Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::guess ( const Integer i ) const

inline

Retrieve the initial guess at the index.

Parameters

[in] i The index of the initial guess.

Returns: The initial guess.

◆ guesses()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

const std::vector< InputType > & Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::guesses ( ) const

inline

Get the vector of initial guesses.

Returns: The vector of initial guesses.

◆ input_dimension()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

Integer Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::input_dimension ( ) const

inlineconstexpr

Get the input dimension of the function.

Returns: The input dimension of the function.

◆ is_solution()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

bool Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::is_solution	(	const InputType &	x,
		const Real	tol = EPSILON_LOW ) const

inline

Check if the input point is a known solution.

Parameters

[in]	x	Input point.
[in]	tol	Tolerance.

Returns: True if the input point is a known solution, false otherwise.

◆ name()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

std::string Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::name ( ) const

inline

Get the function name.

Returns: The function name.

◆ output_dimension()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

Integer Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::output_dimension ( ) const

inlineconstexpr

Get the output dimension of the function.

Returns: The output dimension of the function.

◆ second_derivative()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

void Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::second_derivative	(	const InputType &	x,
		SecondDerivativeType &	out ) const

inline

Compute the function second derivative at the input point.

Parameters

[in]	x	Input point.
[out]	out	The function second derivative.

◆ solution()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

const InputType & Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::solution ( const Integer i ) const

inline

Retrieve the known solution at the index.

Parameters

[in] i The index of the known solution.

Returns: The known solution.

◆ solutions()

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

const std::vector< InputType > & Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::solutions ( ) const

inline

Get the vector of known solutions.

Returns: The vector of known solutions.

Member Data Documentation

◆ m_guesses

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

std::vector<InputType> Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::m_guesses

protected

Known solutions used for test purposes.

◆ m_solutions

template<typename Real, Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

std::vector<InputType> Optimist::Function< Real, FunInDim, FunOutDim, DerivedFunction >::m_solutions

protected

The documentation for this class was generated from the following file:

include/Optimist/Function.hh

Public Types

Public Member Functions

Protected Attributes

Detailed Description

Function

Member Typedef Documentation

◆ FirstDerivativeType

◆ InputType

◆ OutputType

◆ SecondDerivativeType

Constructor & Destructor Documentation

◆ Function()

Member Function Documentation

◆ evaluate()

◆ first_derivative()

◆ guess()

◆ guesses()

◆ input_dimension()

◆ is_solution()

◆ name()

◆ output_dimension()

◆ second_derivative()

◆ solution()

◆ solutions()

Member Data Documentation

◆ m_guesses

◆ m_solutions