Optimist::CostFunction< Real, N, DerivedFunction > Class Template Reference

Class container for the cost function. More...

#include <CostFunction.hh>

Inherits Optimist::Function< Real, N, 1, DerivedFunction >.

Public Types
using	Vector = typename Function<Real, N, 1, DerivedFunction>::InputType
using	RowVector = typename Function<Real, N, 1, DerivedFunction>::FirstDerivativeType
using	Matrix = typename Function<Real, N, 1, DerivedFunction>::SecondDerivativeType
Public Types inherited from Optimist::Function< Real, N, 1, DerivedFunction >
using	InputType
using	OutputType
using	FirstDerivativeType
using	SecondDerivativeType

Public Member Functions
	CostFunction ()
std::string	name () const
void	evaluate (const Vector &x, Vector &out) const
void	gradient (const Vector &x, RowVector &out) const
void	hessian (const Vector &x, Matrix &out) const
Public Member Functions inherited from Optimist::Function< Real, N, 1, DerivedFunction >
	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

Public Attributes
friend	Function< Real, N, 1, CostFunction< Real, N, DerivedFunction > >

Additional Inherited Members
Protected Attributes inherited from Optimist::Function< Real, N, 1, DerivedFunction >
std::vector< InputType >	m_solutions
std::vector< InputType >	m_guesses

Detailed Description

template<typename Real, Integer N, typename DerivedFunction>
class Optimist::CostFunction< Real, N, 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

N	The dimension of the cost function input.
DerivedFunction	Derived cost function class.

Member Typedef Documentation

Matrix

template<typename Real, Integer N, typename DerivedFunction>

using Optimist::CostFunction< Real, N, DerivedFunction >::Matrix = typename Function<Real, N, 1, DerivedFunction>::SecondDerivativeType

Hessian matrix type.

RowVector

template<typename Real, Integer N, typename DerivedFunction>

using Optimist::CostFunction< Real, N, DerivedFunction >::RowVector = typename Function<Real, N, 1, DerivedFunction>::FirstDerivativeType

Gradient (row) vector type.

Vector

template<typename Real, Integer N, typename DerivedFunction>

using Optimist::CostFunction< Real, N, DerivedFunction >::Vector = typename Function<Real, N, 1, DerivedFunction>::InputType

Vector type.

Constructor & Destructor Documentation

CostFunction()

template<typename Real, Integer N, typename DerivedFunction>

Optimist::CostFunction< Real, N, DerivedFunction >::CostFunction ( )

inline

Class constructor for the function.

Member Function Documentation

evaluate()

template<typename Real, Integer N, typename DerivedFunction>

void Optimist::CostFunction< Real, N, DerivedFunction >::evaluate ( const Vector & x, Vector & out ) const

inline

Compute the function value at the input point.

Parameters

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

gradient()

template<typename Real, Integer N, typename DerivedFunction>

void Optimist::CostFunction< Real, N, DerivedFunction >::gradient ( const Vector & x, RowVector & out ) const

inline

Compute the function first derivative at the input point.

Parameters

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

hessian()

template<typename Real, Integer N, typename DerivedFunction>

void Optimist::CostFunction< Real, N, DerivedFunction >::hessian ( const Vector & x, Matrix & out ) const

inline

Compute the function second derivative at the input point.

Parameters

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

name()

template<typename Real, Integer N, typename DerivedFunction>

std::string Optimist::CostFunction< Real, N, DerivedFunction >::name ( ) const

inline

Get the function name.

Returns

The function name.

Member Data Documentation

Function< Real, N, 1, CostFunction< Real, N, DerivedFunction > >

template<typename Real, Integer N, typename DerivedFunction>

friend Optimist::CostFunction< Real, N, DerivedFunction >::Function< Real, N, 1, CostFunction< Real, N, DerivedFunction > >

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

• include/Optimist/Function/CostFunction.hh