Optimist::TestSet::Quadratic< Scalar > Class Template Reference

Class container for the quadratic function. More...

#include <Quadratic.hh>

Inherits Optimist::Function< Scalar, Scalar, Quadratic< Scalar > >.

Public Member Functions
	Quadratic ()
constexpr std::string	name_impl () const
bool	evaluate_impl (const Scalar x, Scalar &out) const
bool	first_derivative_impl (const Scalar x, Scalar &out) const
bool	second_derivative_impl (Scalar, Scalar &out) const
Public Member Functions inherited from Optimist::Function< Scalar, Scalar, Quadratic< Scalar > >
	Function ()
constexpr std::string	name () const
bool	evaluate (const Scalar &x, Scalar &out) const
bool	jacobian (const Scalar &x, FirstDerivative &out) const
bool	hessian (const Scalar &x, SecondDerivative &out) const
Public Member Functions inherited from Optimist::FunctionBase< Scalar, Scalar, Quadratic< Scalar > >
	FunctionBase ()
constexpr std::string	name () const
bool	evaluate (const Scalar &x, Scalar &out) const
bool	first_derivative (const Scalar &x, FirstDerivative &out) const
bool	second_derivative (const Scalar &x, SecondDerivative &out) const
constexpr Integer	input_dimension () const
constexpr Integer	output_dimension () const
const std::vector< Scalar > &	solutions () const
const std::vector< Scalar > &	guesses () const
const Scalar &	solution (const Integer i) const
const Scalar &	guess (const Integer i) const
bool	is_solution (const Scalar &x, const Scalar tol=FunctionBase::SQRT_EPSILON) const

Private Attributes
Scalar	m_a {1.0}
Scalar	m_b {1.0}
Scalar	m_c {-1.0}

Additional Inherited Members
Public Types inherited from Optimist::FunctionBase< Scalar, Scalar, Quadratic< Scalar > >
using	InputTrait
using	OutputTrait
using	Scalar
using	FirstDerivative
using	SecondDerivative
Protected Attributes inherited from Optimist::FunctionBase< Scalar, Scalar, Quadratic< Scalar > >
std::vector< Scalar >	m_solutions
std::vector< Scalar >	m_guesses

Detailed Description

template<typename Scalar>
requires TypeTrait<Scalar>::IsScalar
class Optimist::TestSet::Quadratic< Scalar >

Class container for the quadratic function, which is defined as:

\[f(x) = ax^2 + bx + c \text{.} \]

The function has roots at

\[x = \sqrt{\displaystyle\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}} \text{,} \]

and a minimum at

\[x = -\displaystyle\frac{b}{2a} \text{.} \]

The default coefficients are \(a = 1\), \(b = 1\), and \(c = -1\), and the function initial guess is \(x = 0\).

Template Parameters

Scalar

Floating-point number type.

Constructor & Destructor Documentation

Quadratic()

template<typename Scalar>

Optimist::TestSet::Quadratic< Scalar >::Quadratic ( )

inline

Class constructor for the quadratic function.

Member Function Documentation

evaluate_impl()

template<typename Scalar>

bool Optimist::TestSet::Quadratic< Scalar >::evaluate_impl ( const Scalar x, Scalar & out ) const

inline

Compute the function value at the input point.

Parameters

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

Returns

The boolean flag for successful evaluation.

first_derivative_impl()

template<typename Scalar>

bool Optimist::TestSet::Quadratic< Scalar >::first_derivative_impl ( const Scalar x, Scalar & out ) const

inline

Compute the first derivative value at the input point.

Parameters

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

Returns

The boolean flag for successful evaluation.

name_impl()

template<typename Scalar>

std::string Optimist::TestSet::Quadratic< Scalar >::name_impl ( ) const

inlineconstexpr

Get the function name.

Returns

The function name.

second_derivative_impl()

template<typename Scalar>

bool Optimist::TestSet::Quadratic< Scalar >::second_derivative_impl ( Scalar , Scalar & out ) const

inline

Compute the second derivative value at the input point.

Parameters

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

Returns

The boolean flag for successful evaluation.

Member Data Documentation

m_a

template<typename Scalar>

Scalar Optimist::TestSet::Quadratic< Scalar >::m_a {1.0}

private

Coefficient \(a\).

m_b

template<typename Scalar>

Scalar Optimist::TestSet::Quadratic< Scalar >::m_b {1.0}

private

Coefficient \(b\).

m_c

template<typename Scalar>

Scalar Optimist::TestSet::Quadratic< Scalar >::m_c {-1.0}

private

Coefficient \(c\).

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

• core/include/Optimist/TestSet/Quadratic.hh