The Generalized Rosenbrock function in n dimensions, defined by f(x) = sum_i^{n - 1} (f(i)(x)) f_i(x) = 100 * (x_i^2 - x_{i + 1})^2 + (1 - x_i)^2 x_0 = [-1.2, 1, -1.2, 1, ...]. More...

Public Member Functions
	GeneralizedRosenbrockFunction (const size_t n)

double	Evaluate (const arma::mat &coordinates, const size_t begin, const size_t batchSize=1) const

double	Evaluate (const arma::mat &coordinates) const

const arma::mat &	GetInitialPoint () const
	Get the starting point. More...

void	Gradient (const arma::mat &coordinates, const size_t begin, arma::mat &gradient, const size_t batchSize=1) const

void	Gradient (const arma::mat &coordinates, const size_t begin, arma::sp_mat &gradient, const size_t count) const

void	Gradient (const arma::mat &coordinates, arma::mat &gradient) const

size_t	NumFunctions () const
	Return 1 (the number of functions). More...

void	Shuffle ()
	Shuffle the order of function visitation. More...

Detailed Description

The Generalized Rosenbrock function in n dimensions, defined by f(x) = sum_i^{n - 1} (f(i)(x)) f_i(x) = 100 * (x_i^2 - x_{i + 1})^2 + (1 - x_i)^2 x_0 = [-1.2, 1, -1.2, 1, ...].

This should optimize to f(x) = 0, at x = [1, 1, 1, 1, ...].

This function can also be used for stochastic gradient descent (SGD) as a decomposable function (DecomposableFunctionType), so there are other overloads of Evaluate() and Gradient() implemented, as well as NumFunctions().

For more information, please refer to:

@phdthesis{Jong1975,
  title  = {Analysis of the behavior of a class of genetic adaptive
            systems},
  author = {De Jong, Kenneth Alan},
  school = {Queensland University of Technology},
  year   = {1975},
  type   = {{PhD} dissertation},
}

Definition at line 48 of file generalized_rosenbrock_function.hpp.

Constructor & Destructor Documentation

◆ GeneralizedRosenbrockFunction()

GeneralizedRosenbrockFunction ( const size_t n )

Member Function Documentation

◆ Evaluate() [1/2]

double Evaluate	(	const arma::mat &	coordinates,
		const size_t	begin,
		const size_t	batchSize = `1`
	)		const

Referenced by GeneralizedRosenbrockFunction::GetInitialPoint().

◆ Evaluate() [2/2]

double Evaluate ( const arma::mat & coordinates ) const

◆ GetInitialPoint()

const arma::mat& GetInitialPoint ( ) const

inline

Get the starting point.

Definition at line 68 of file generalized_rosenbrock_function.hpp.

References GeneralizedRosenbrockFunction::Evaluate(), and GeneralizedRosenbrockFunction::Gradient().

◆ Gradient() [1/3]

void Gradient	(	const arma::mat &	coordinates,
		const size_t	begin,
		arma::mat &	gradient,
		const size_t	batchSize = `1`
	)		const

Referenced by GeneralizedRosenbrockFunction::GetInitialPoint().

◆ Gradient() [2/3]

void Gradient	(	const arma::mat &	coordinates,
		const size_t	begin,
		arma::sp_mat &	gradient,
		const size_t	count
	)		const

◆ Gradient() [3/3]

void Gradient	(	const arma::mat &	coordinates,
		arma::mat &	gradient
	)		const

◆ NumFunctions()

size_t NumFunctions ( ) const

inline

Return 1 (the number of functions).

Definition at line 65 of file generalized_rosenbrock_function.hpp.

◆ Shuffle()

void Shuffle ( )

Shuffle the order of function visitation.

This may be called by the optimizer.

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

src/mlpack/core/optimizers/problems/generalized_rosenbrock_function.hpp

Public Member Functions