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

Class container for the quadratic function. More...

#include <Quadratic.hh>

Inherits Optimist::Function< Real, 1, 1, Quadratic< Real > >.

Public Member Functions
	Quadratic ()
std::string	name_impl () const
void	evaluate_impl (Real x, Real &out) const
void	first_derivative_impl (Real x, Real &out) const
void	second_derivative_impl (Real, Real &out) const
Public Member Functions inherited from Optimist::Function< Real, 1, 1, Quadratic< Real > >
	Function ()
std::string	name () const
void	evaluate (const InputVector &x, OutputVector &out) const
void	jacobian (const InputVector &x, Matrix &out) const
void	hessian (const InputVector &x, Tensor &out) const
Public Member Functions inherited from Optimist::FunctionBase< Real, N, M, Quadratic< Real >, false >
	FunctionBase ()
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

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

Additional Inherited Members
Public Types inherited from Optimist::Function< Real, 1, 1, Quadratic< Real > >
using	InputVector
using	OutputVector
using	Matrix
using	Tensor
Public Types inherited from Optimist::FunctionBase< Real, N, M, Quadratic< Real >, false >
using	InputType
using	OutputType
using	FirstDerivativeType
using	SecondDerivativeType
Protected Attributes inherited from Optimist::FunctionBase< Real, N, M, Quadratic< Real >, false >
std::vector< InputType >	m_solutions
std::vector< InputType >	m_guesses

Detailed Description

template<typename Real>
class Optimist::TestSet::Quadratic< Real >

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

Real	Scalar number type.

Constructor & Destructor Documentation

Quadratic()

template<typename Real>

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

inline

< Basic constants. Class constructor for the quadratic function.

Member Function Documentation

evaluate_impl()

template<typename Real>

void Optimist::TestSet::Quadratic< Real >::evaluate_impl ( Real x, Real & out ) const

inline

Compute the function value at the input point.

Parameters

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

first_derivative_impl()

template<typename Real>

void Optimist::TestSet::Quadratic< Real >::first_derivative_impl ( Real x, Real & out ) const

inline

Compute the first derivative value at the input point.

Parameters

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

name_impl()

template<typename Real>

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

inline

Get the function name.

Returns

The function name.

second_derivative_impl()

template<typename Real>

void Optimist::TestSet::Quadratic< Real >::second_derivative_impl ( Real , Real & out ) const

inline

Compute the second derivative value at the input point.

Parameters

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

Member Data Documentation

m_a

template<typename Real>

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

private

Coefficient \(a\).

m_b

template<typename Real>

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

private

Coefficient \(b\).

m_c

template<typename Real>

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

private

Coefficient \(c\).

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

• include/Optimist/TestSet/Quadratic.hh