pyoculus.solvers.lyapunov_exponent.LyapunovExponent Class Reference

Class that used to setup the Lyapunov exponent computation. More...

Inheritance diagram for pyoculus.solvers.lyapunov_exponent.LyapunovExponent:

Public Member Functions
	__init__ (self, problem, params=dict(), integrator=None, integrator_params=dict())
	Sets up the class that compute the Lyapunov exponent.
	compute (self, t0, ic, dic=[1.0, 0.0])
	Compute the maximal Lyapunov exponents.
	plot (self, **kwargs)
Public Member Functions inherited from pyoculus.solvers.base_solver.BaseSolver
	__init__ (self, problem, params=dict(), integrator=None, integrator_params=dict())
	Sets up the solver.
	is_successful (self)
	Returns True if the computation is successfully completed.

Public Attributes
	nPpts = params["nPpts"]
	nsave = params["nsave"]
	Nfp = problem.Nfp
	ile = np.arange(0, self.nPpts + 1, self.nsave, dtype=np.int)
	le = np.zeros(self.ile.shape, dtype=np.float64)
int	dt = 2 * np.pi / self.Nfp
	t0 = t0
	ic = icnp.copy()
	dic = dic_norm.copy()
	di = np.ones((self.nPpts), dtype=np.float64)
Public Attributes inherited from pyoculus.solvers.base_solver.BaseSolver
bool	successful = False
	flagging if the computation is done and successful

Additional Inherited Members
Protected Attributes inherited from pyoculus.solvers.base_solver.BaseSolver
	_integrator_type = RKIntegrator
	_params = dict(params)
	_integrator = self._integrator_type(integrator_params)
	_problem = problem
	_integrator_params = dict(integrator_params)

Detailed Description

Class that used to setup the Lyapunov exponent computation.

Constructor & Destructor Documentation

__init__()

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.__init__	(		self,
			problem,
			params = dict(),
			integrator = None,
			integrator_params = dict() )

Sets up the class that compute the Lyapunov exponent.

Parameters

problem	must inherit pyoculus.problems.BaseProblem, the problem to solve
params	dict, the parameters for the solver
integrator	the integrator to use, must inherit \pyoculus.integrators.BaseIntegrator, if set to None by default using RKIntegrator
integrator_params	dict, the parmaters passed to the integrator

params['nPpts']=2000 – the number of iterations

params['nsave']=100 – save the Lyapunov Exponent each nsave iteration

params['Nfp']=1 – period in zeta direction

Member Function Documentation

compute()

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.compute	(		self,
			t0,
			ic,
			dic = [1.0, 0.0] )

Compute the maximal Lyapunov exponents.

Parameters

t0	the start time (or angle)
ic	the initial conidition
dic	the initial perturbation direction (non-zero, for most of the cases it doesn't matter)

Returns

a class with results

result.le – the computed maximal Lyapunov Exponent (as a function of number of map iterations)

result.ile – the number of iterations

plot()

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.plot	(		self,
		**	kwargs )

Member Data Documentation

di

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.di = np.ones((self.nPpts), dtype=np.float64)

dic

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.dic = dic_norm.copy()

dt

int pyoculus.solvers.lyapunov_exponent.LyapunovExponent.dt = 2 * np.pi / self.Nfp

ic

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.ic = icnp.copy()

ile

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.ile = np.arange(0, self.nPpts + 1, self.nsave, dtype=np.int)

le

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.le = np.zeros(self.ile.shape, dtype=np.float64)

Nfp

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.Nfp = problem.Nfp

nPpts

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.nPpts = params["nPpts"]

nsave

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.nsave = params["nsave"]

t0

pyoculus.solvers.lyapunov_exponent.LyapunovExponent.t0 = t0

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

• pyoculus/solvers/lyapunov_exponent.py