This class provides a nonlinear conjugate-gradient optimizer. More...

#include <conjugate_gradient.h>

Public Member Functions
template<class Func , class Deriv >
	ConjugateGradient (const Vector< Size > &start, const Func &func, const Deriv &deriv)
template<class Func >
	ConjugateGradient (const Vector< Size > &start, const Func &func, const Vector< Size > &deriv)
void	init (const Vector< Size > &start, const Precision &func, const Vector< Size > &deriv)
template<class Func >
void	find_next_point (const Func &func)
bool	finished ()
void	update_vectors_PR (const Vector< Size > &grad)
template<class Func , class Deriv >
bool	iterate (const Func &func, const Deriv &deriv)
Public Attributes
const int	size
Vector< Size >	g
Vector< Size >	h
Vector< Size >	minus_h
Vector< Size >	old_g
Vector< Size >	old_h
Vector< Size >	x
Vector< Size >	old_x
Precision	y
Precision	old_y
Precision	tolerance
Precision	epsilon
int	max_iterations
Precision	bracket_initial_lambda
Precision	linesearch_tolerance
Precision	linesearch_epsilon
int	linesearch_max_iterations
Precision	bracket_epsilon
int	iterations

Detailed Description

template<int Size = Dynamic, class Precision = double>
struct TooN::ConjugateGradient< Size, Precision >

This class provides a nonlinear conjugate-gradient optimizer.

The following code snippet will perform an optimization on the Rosenbrock Bananna function in two dimensions:

double Rosenbrock(const Vector<2>& v)
{
        return sq(1 - v[0]) + 100 * sq(v[1] - sq(v[0]));
}

Vector<2> RosenbrockDerivatives(const Vector<2>& v)
{
    double x = v[0];
    double y = v[1];

    Vector<2> ret;
    ret[0] = -2+2*x-400*(y-sq(x))*x;
    ret[1] = 200*y-200*sq(x);

    return ret;
}

int main()
{
    ConjugateGradient<2> cg(makeVector(0,0), Rosenbrock, RosenbrockDerivatives);

    while(cg.iterate(Rosenbrock, RosenbrockDerivatives))
        cout << "y_" << iteration << " = " << cg.y << endl;

    cout << "Optimal value: " << cg.y << endl;
}

The chances are that you will want to read the documentation for ConjugateGradient::ConjugateGradient and ConjugateGradient::iterate.

Linesearch is currently performed using golden-section search and conjugate vector updates are performed using the Polak-Ribiere equations. There many tunable parameters, and the internals are readily accessible, so alternative termination conditions etc can easily be substituted. However, ususally these will not be necessary.

Constructor & Destructor Documentation

ConjugateGradient	(	const Vector< Size > &	start,
		const Func &	func,
		const Deriv &	deriv
	)

Initialize the ConjugateGradient class with sensible values.

Parameters:

start	Starting point, x
func	Function f to compute
deriv	Function to compute $\nabla f(x)$

References ConjugateGradient< Size, Precision >::init().

ConjugateGradient	(	const Vector< Size > &	start,
		const Func &	func,
		const Vector< Size > &	deriv
	)

Initialize the ConjugateGradient class with sensible values.

Parameters:

start	Starting point, x
func	Function f to compute
deriv	$\nabla f(x)$

References ConjugateGradient< Size, Precision >::init().

Member Function Documentation

void init	(	const Vector< Size > &	start,
		const Precision &	func,
		const Vector< Size > &	deriv
	)

Initialize the ConjugateGradient class with sensible values.

Used internally.

Parameters:

start	Starting point, x
func
deriv	$\nabla f(x)$

Referenced by ConjugateGradient< Size, Precision >::ConjugateGradient().

void find_next_point ( const Func & func )

Perform a linesearch from the current point (x) along the current conjugate vector (h).

The linesearch does not make use of derivatives. You probably do not want to use this function. See iterate() instead. This function updates:

x
old_c
y
old_y
iterations Note that the conjugate direction and gradient are not updated. If bracket_minimum_forward detects a local maximum, then essentially a zero sized step is taken.
Parameters:

func Functor returning the function value at a given point.

Referenced by ConjugateGradient< Size, Precision >::iterate().

bool finished ( )

Check to see it iteration should stop.

You probably do not want to use this function. See iterate() instead. This function updates nothing.

References ConjugateGradient< Size, Precision >::epsilon, ConjugateGradient< Size, Precision >::iterations, ConjugateGradient< Size, Precision >::max_iterations, ConjugateGradient< Size, Precision >::old_y, ConjugateGradient< Size, Precision >::tolerance, and ConjugateGradient< Size, Precision >::y.

Referenced by ConjugateGradient< Size, Precision >::iterate().

void update_vectors_PR ( const Vector< Size > & grad )

After an iteration, update the gradient and conjugate using the Polak-Ribiere equations.

This function updates:

g
old_g
h
old_h
Parameters:

grad The derivatives of the function at x

References ConjugateGradient< Size, Precision >::g, ConjugateGradient< Size, Precision >::h, ConjugateGradient< Size, Precision >::minus_h, ConjugateGradient< Size, Precision >::old_g, and ConjugateGradient< Size, Precision >::old_h.

Referenced by ConjugateGradient< Size, Precision >::iterate().

bool iterate	(	const Func &	func,
		const Deriv &	deriv
	)

Use this function to iterate over the optimization.

Note that after iterate returns false, g, h, old_g and old_h will not have been updated. This function updates:

x
old_c
y
old_y
iterations
g*
old_g*
h*
old_h* 'd variables not updated on the last iteration.
Parameters:

func Functor returning the function value at a given point.

deriv Functor to compute derivatives at the specified point.

Returns:
Whether to continue.

References ConjugateGradient< Size, Precision >::find_next_point(), ConjugateGradient< Size, Precision >::finished(), ConjugateGradient< Size, Precision >::update_vectors_PR(), and ConjugateGradient< Size, Precision >::x.

func	Functor returning the function value at a given point.
deriv	Functor to compute derivatives at the specified point.

Public Member Functions

Public Attributes

Detailed Description

template<int Size = Dynamic, class Precision = double> struct TooN::ConjugateGradient< Size, Precision >

Constructor & Destructor Documentation

Member Function Documentation

template<int Size = Dynamic, class Precision = double>
struct TooN::ConjugateGradient< Size, Precision >