pyoculus.solvers.fixed_point.FixedPoint Class Reference

Class that used to setup the fixed point finder. More...

Inheritance diagram for pyoculus.solvers.fixed_point.FixedPoint:

Public Member Functions
	__init__ (self, problem, params=dict(), integrator=None, integrator_params=dict())
	Set up the class of the fixed point finder.
	compute (self, guess, pp, qq, sbegin=-1.0, send=1.0, tol=None)
	Looks for the fixed point with rotation number pp/qq.
	plot (self, plottype=None, xlabel=None, ylabel=None, xlim=None, ylim=None, **kwargs)
	Generates the plot for fixed points.
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
bool	is_theta_fixed = False
bool	is_Z_fixed = False
	Nfp = problem.Nfp
	niter = params["niter"]
	nrestart = params["nrestart"]
	pp = pp
	qq = qq
int	dzeta = 2 * np.pi / self.Nfp
	s = np.zeros([qq + 1], dtype=np.float64)
	theta = np.zeros([qq + 1], dtype=np.float64)
	zeta = np.zeros([qq + 1], dtype=np.float64)
	x = np.zeros([qq + 1], dtype=np.float64)
	y = np.zeros([qq + 1], dtype=np.float64)
	z = np.zeros([qq + 1], dtype=np.float64)
list	history = []
	GreenesResidue = rdata.GreenesResidue
	MeanResidue = rdata.MeanResidue
Public Attributes inherited from pyoculus.solvers.base_solver.BaseSolver
bool	successful = False
	flagging if the computation is done and successful

Protected Member Functions
	_newton_method_1 (self, pp, qq, s_guess, sbegin, send, theta, zeta, dzeta, niter, tol)
	_newton_method_2 (self, pp, qq, s_guess, sbegin, send, theta_guess, zeta, dzeta, niter, tol)
	_newton_method_3 (self, pp, qq, R_guess, Rbegin, Rend, Z, zeta, dzeta, niter, tol)

Protected Attributes
bool	_is_cylindrical_problem = False
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 fixed point finder.

Constructor & Destructor Documentation

__init__()

pyoculus.solvers.fixed_point.FixedPoint.__init__	(		self,
			problem,
			params = dict(),
			integrator = None,
			integrator_params = dict() )

Set up the class of the fixed point finder.

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['niter']=100 – the maximum number of Newton iterations

params['theta']=None – if we look for fixed point on some symmetry line =None : theta is also a free variable to look for =somenumber : only look for theta with this number

params['zeta']=0.0 – the toroidal plane we are after

params['nrestart']=1 – if search failed, the number of time to restart (randomly within the domain)

Member Function Documentation

_newton_method_1()

pyoculus.solvers.fixed_point.FixedPoint._newton_method_1 ( self, pp, qq, s_guess, sbegin, send, theta, zeta, dzeta, niter, tol )

protected

driver to run Newton's method for one variable s
pp,qq -- integers, the numerator and denominator of the rotation number
s_guess -- the guess of s
sbegin -- the allowed minimum s
send -- the allowed maximum s
theta -- the theta value (fixed)
zeta -- the toroidal plain to investigate
dzeta -- period in zeta
niter -- the maximum number of iterations
tol -- the tolerance of finding a fixed point

_newton_method_2()

pyoculus.solvers.fixed_point.FixedPoint._newton_method_2 ( self, pp, qq, s_guess, sbegin, send, theta_guess, zeta, dzeta, niter, tol )

protected

driver to run Newton's method for two variable (s,theta)
pp,qq -- integers, the numerator and denominator of the rotation number
s_guess -- the guess of s
sbegin -- the allowed minimum s
send -- the allowed maximum s
theta_guess -- the guess of theta
zeta -- the toroidal plain to investigate
dzeta -- period in zeta
niter -- the maximum number of iterations
tol -- the tolerance of finding a fixed point

_newton_method_3()

pyoculus.solvers.fixed_point.FixedPoint._newton_method_3 ( self, pp, qq, R_guess, Rbegin, Rend, Z, zeta, dzeta, niter, tol )

protected

driver to run Newton's method for one variable R, for cylindrical problem
pp,qq -- integers, the numerator and denominator of the rotation number
R_guess -- the guess of R
Rbegin -- the allowed minimum R
Rend -- the allowed maximum R
Z -- the Z value (fixed)
zeta -- the toroidal plain to investigate
dzeta -- period in zeta
niter -- the maximum number of iterations
tol -- the tolerance of finding a fixed point

compute()

pyoculus.solvers.fixed_point.FixedPoint.compute	(		self,
			guess,
			pp,
			qq,
			sbegin = -1.0,
			send = 1.0,
			tol = None )

Looks for the fixed point with rotation number pp/qq.

Parameters

guess	the initial guess, [s, theta], if ‘params['theta’] == None,[s], ifparams['theta'] ==‘ somevalue
pp	integer, the numerator of the rotation number
qq	integer, the denominator of the rotation number
sbegin=-1.0	the allowed minimum s or R
send=1.0	the allowed maximum s or R
tol=self._integrator_params['rtol’]*qq	– the tolerance of the fixed point

Returns

rdata a class that contains the results that contains rdata.x,rdata.y,rdata,z – the fixed points in xyz coordinates

rdata.s,rdata,theta,rdata,zeta – the fixed points in s,theta,zeta coordinates

rdata.jacobian – the Jacobian of the fixed point constructed by following the tangent map

rdata.GreenesResidue – the Greene's Residue of the fixed point

rdata.MeanResidue – the 'Average Residue' f as defined by Greene

plot()

pyoculus.solvers.fixed_point.FixedPoint.plot	(		self,
			plottype = None,
			xlabel = None,
			ylabel = None,
			xlim = None,
			ylim = None,
		**	kwargs )

Generates the plot for fixed points.

Parameters

plottype	which variables to plot: 'RZ' or 'yx', by default using "poincare_plot_type" in problem
xlabel,ylabel	what to put for the xlabel and ylabel, by default using "poincare_plot_xlabel" in problem
xlim,ylim	the range of plotting, by default plotting the range of all data
**kwargs	passed to the plotting routine "plot"

Member Data Documentation

_is_cylindrical_problem

bool pyoculus.solvers.fixed_point.FixedPoint._is_cylindrical_problem = False

protected

dzeta

int pyoculus.solvers.fixed_point.FixedPoint.dzeta = 2 * np.pi / self.Nfp

GreenesResidue

pyoculus.solvers.fixed_point.FixedPoint.GreenesResidue = rdata.GreenesResidue

history

list pyoculus.solvers.fixed_point.FixedPoint.history = []

is_theta_fixed

bool pyoculus.solvers.fixed_point.FixedPoint.is_theta_fixed = False

is_Z_fixed

bool pyoculus.solvers.fixed_point.FixedPoint.is_Z_fixed = False

MeanResidue

pyoculus.solvers.fixed_point.FixedPoint.MeanResidue = rdata.MeanResidue

Nfp

pyoculus.solvers.fixed_point.FixedPoint.Nfp = problem.Nfp

niter

pyoculus.solvers.fixed_point.FixedPoint.niter = params["niter"]

nrestart

pyoculus.solvers.fixed_point.FixedPoint.nrestart = params["nrestart"]

pp

pyoculus.solvers.fixed_point.FixedPoint.pp = pp

qq

pyoculus.solvers.fixed_point.FixedPoint.qq = qq

s

pyoculus.solvers.fixed_point.FixedPoint.s = np.zeros([qq + 1], dtype=np.float64)

theta

pyoculus.solvers.fixed_point.FixedPoint.theta = np.zeros([qq + 1], dtype=np.float64)

x

pyoculus.solvers.fixed_point.FixedPoint.x = np.zeros([qq + 1], dtype=np.float64)

y

pyoculus.solvers.fixed_point.FixedPoint.y = np.zeros([qq + 1], dtype=np.float64)

z

pyoculus.solvers.fixed_point.FixedPoint.z = np.zeros([qq + 1], dtype=np.float64)

zeta

pyoculus.solvers.fixed_point.FixedPoint.zeta = np.zeros([qq + 1], dtype=np.float64)

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

• pyoculus/solvers/fixed_point.py