CDPL.Math.FVectorBFGSMinimizer Class Reference

Fletcher's implementation of the BFGS method. More...

Inheritance diagram for CDPL.Math.FVectorBFGSMinimizer:

Classes
class	Status
	Status bitmask reported by minimize() and getStatus(). More...

Public Member Functions
None	__init__ (FloatFVectorFunctor func, object grad_func)
	Constructs the BFGSMinimizer instance with the given objective and gradient functions. More...
int	getObjectID ()
	Returns the numeric identifier (ID) of the wrapped C++ class instance. More...
float	getGradientNorm ()
	Returns the L2 norm of the gradient at the end of the most recent iterate() call. More...
float	getFunctionDelta ()
	Returns the magnitude of the function-value decrease produced by the most recent iterate() call. More...
float	getFunctionValue ()
	Returns the function value at the end of the most recent iterate() call. More...
int	getNumIterations ()
	Returns the number of iterations performed by the most recent minimize() or iterate() loop. More...
Status	getStatus ()
	Returns the current status of the minimizer. More...
Status	minimize (FVector x, FVector g, int max_iter, float g_norm, float delta_f, bool do_setup=True)
	Runs the BFGS minimization loop on x. More...
float	setup (FVector x, FVector g, float step_size=0.001, float tol=0.15)
	Initializes the minimizer state for a subsequent iterate() / minimize() loop. More...
tuple	iterate (float f, FVector x, FVector g)
	Performs a single BFGS iteration: line search along the current search direction, BFGS update of the inverse Hessian approximation, and selection of the new search direction. More...

Properties
	objectID = property(getObjectID)
	gradientNorm = property(getGradientNorm)
	functionDelta = property(getFunctionDelta)
	functionValue = property(getFunctionValue)
	numIterations = property(getNumIterations)
	status = property(getStatus)

Detailed Description

Fletcher's implementation of the BFGS method.

The implementation has been taken from the GNU Scientific Library.

See also

R. Fletcher, "Practical Method's of Optimization", Second Edition, ISBN 0471915475. Algorithms 2.6.2 and 2.6.4.

Constructor & Destructor Documentation

__init__()

None CDPL.Math.FVectorBFGSMinimizer.__init__	(	FloatFVectorFunctor	func,
		object	grad_func
	)

Constructs the BFGSMinimizer instance with the given objective and gradient functions.

Parameters

func	The objective function.
grad_func	The gradient function (also computes the objective value).

Member Function Documentation

getObjectID()

int CDPL.Math.FVectorBFGSMinimizer.getObjectID

(

)

Returns the numeric identifier (ID) of the wrapped C++ class instance.

Different Python FVectorBFGSMinimizer instances may reference the same underlying C++ class instance. The commonly used Python expression a is not b thus cannot tell reliably whether the two FVectorBFGSMinimizer instances a and b reference different C++ objects. The numeric identifier returned by this method allows to correctly implement such an identity test via the simple expression a.getObjectID() != b.getObjectID().

Returns

The numeric ID of the internally referenced C++ class instance.

getGradientNorm()

float CDPL.Math.FVectorBFGSMinimizer.getGradientNorm

(

)

Returns the L2 norm of the gradient at the end of the most recent iterate() call.

Returns

The gradient norm.

getFunctionDelta()

float CDPL.Math.FVectorBFGSMinimizer.getFunctionDelta

(

)

Returns the magnitude of the function-value decrease produced by the most recent iterate() call.

Returns

The function-value delta (positive when the function decreased).

getFunctionValue()

float CDPL.Math.FVectorBFGSMinimizer.getFunctionValue

(

)

Returns the function value at the end of the most recent iterate() call.

Returns

The function value.

getNumIterations()

int CDPL.Math.FVectorBFGSMinimizer.getNumIterations

(

)

Returns the number of iterations performed by the most recent minimize() or iterate() loop.

Returns

The iteration count.

getStatus()

Status CDPL.Math.FVectorBFGSMinimizer.getStatus

(

)

Returns the current status of the minimizer.

Returns

The Status bitmask.

minimize()

Status CDPL.Math.FVectorBFGSMinimizer.minimize	(	FVector	x,
		FVector	g,
		int	max_iter,
		float	g_norm,
		float	delta_f,
		bool	do_setup = True
	)

Runs the BFGS minimization loop on x.

Parameters

x	The variable vector to be minimized (modified in place).
g	The gradient vector (modified in place).
max_iter	The maximum number of iterations (0 means unlimited).
g_norm	The gradient-norm threshold below which the minimization is stopped (negative values disable this stop condition).
delta_f	The function-value-delta threshold below which the minimization is stopped (negative values disable this stop condition).
do_setup	If True, setup() is invoked at the start to initialize the minimizer.

Returns

The terminal Status bitmask of the minimization.

setup()

float CDPL.Math.FVectorBFGSMinimizer.setup	(	FVector	x,
		FVector	g,
		float	step_size = 0.001,
		float	tol = 0.15
	)

Initializes the minimizer state for a subsequent iterate() / minimize() loop.

Parameters

x	The starting variable vector.
g	The gradient vector (filled with the gradient at x).
step_size	The initial step-size guess.
tol	The line-search tolerance.

Returns

The objective-function value at x.

iterate()

tuple CDPL.Math.FVectorBFGSMinimizer.iterate	(	float	f,
		FVector	x,
		FVector	g
	)

Performs a single BFGS iteration: line search along the current search direction, BFGS update of the inverse Hessian approximation, and selection of the new search direction.

Parameters

f	The current function value (updated in place).
x	The current variable vector (updated in place).
g	The current gradient vector (updated in place).

Returns

Status.SUCCESS if the iteration produced a step, otherwise the bitmask of stop conditions met.