Package PyDSTool :: Package PyCont :: Module Continuation

Module Continuation

Curve classes: Continuation, EquilibriumCurve, FoldCurve, HopfCurveOne, HopfCurveTwo

Drew LaMar, March 2006

Continuation is the ancestral class of all curve classes and contains the continuation algorithms (Moore-Penrose, etc.) It also contains all methods that are general to any curve found using continuation.

Classes

[hide private]

Continuation
Abstract continuation class

EquilibriumCurve
Child of Continuation class that represents curves of equilibrium points.

FoldCurve
Child of Continuation class that represents curves of limit points.

HopfCurveOne
Child of Continuation class that represents curves of Hopf points.

HopfCurveTwo
Child of Continuation class that represents curves of Hopf points.

FixedPointCurve

LimitCycleCurve
Wrapper for auto limit cycle computations.

UserDefinedCurve
User defined curve.

Functions

[hide private]

random(size=None)
Return random floats in the half-open interval [0.0, 1.0).

source code

Variables

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FLOQ_TOL

clock

sum

pointsToPointset

negate

argmax

ndarray

conjugate

sqrt

multiply

identity

evec1_standard

ver = ['0', '99', '0']

failed = False

rcParamsDefault = {'figure.subplot.right': 0.90000000000000002...

colorbar_doc = '\n\nAdd a colorbar to a plot.\n\nFunction sign...

rcParams = {'figure.subplot.right': 0.90000000000000002, 'math...

log10 = <ufunc 'log10'>

Inf = inf

NaN = nan

isfinite = <ufunc 'isfinite'>

r_ = <numpy.lib.index_tricks.RClass object at 0x115c2f0>

c_ = <numpy.lib.index_tricks.CClass object at 0x115c330>

sign = <ufunc 'sign'>

mod = <ufunc 'remainder'>

subtract = <ufunc 'subtract'>

divide = <ufunc 'divide'>

isnan = <ufunc 'isnan'>

_classes = ['Continuation', 'EquilibriumCurve', 'FoldCurve', '...

_constants = ['cont_args_list', 'cont_bif_points', 'equilibriu...

cont_args_list = ['name', 'force', 'freepars', 'MaxNumPoints',...

cont_bif_points = ['BP', 'B', 'SP']

equilibrium_args_list = ['LocBifPoints']

equilibrium_bif_points = ['LP', 'H']

fold_args_list = ['LocBifPoints']

fold_bif_points = ['BT', 'ZH', 'CP']

hopf_args_list = ['LocBifPoints']

hopf_bif_points = ['BT', 'ZH', 'GH', 'DH']

fixedpoint_args_list = ['LocBifPoints', 'period']

fixedpoint_bif_points = ['PD', 'LPC', 'NS']

limitcycle_args_list = ['LocBifPoints', 'NumCollocation', 'Num...

limitcycle_bif_points = ['PD', 'LPC', 'NS']

userdefined_args_list = ['LocBifPoints']

other_special_points = ['RG', 'UZ', 'P', 'MX']

auto_point_types = {-9: 'MX', -4: 'UZ', 1: 'BP', 2: 'LP', 3: '...

solution_measures_list = ['max', 'min', 'avg', 'nm2']

solution_measures = {'avg': 1, 'max': 0, 'min': 0, 'nm2': 2}

all_args_list = ['force', 'NumIntervals', 'SPOut', 'period', '...

all_point_types = ['NS', 'B', 'ZH', 'PD', 'DH', 'UZ', 'H', 'SP...

all_curve_types = ['EP-C', 'LP-C', 'H-C1', 'H-C2', 'FP-C', 'LC...

bif_curve_colors = {'EP-C': 'k', 'FP-C': 'g', 'H-C1': 'b', 'H-...

bif_point_colors = {'B': 'dr', 'BP': 'og', 'BT': 'sy', 'CP': '...

stab_line_styles = {'N': '-.', 'S': '-', 'U': '--', 'X': ':'}

Function Details

[hide private]

random(size=None)

source code

Return random floats in the half-open interval [0.0, 1.0).

Results are from the "continuous uniform" distribution over the
stated interval.  To sample :math:`Unif[a, b), b > a` multiply
the output of `random_sample` by `(b-a)` and add `a`::

  (b - a) * random_sample() + a

Parameters
----------
size : int or tuple of ints, optional
    Defines the shape of the returned array of random floats. If None
    (the default), returns a single float.

Returns
-------
out : float or ndarray of floats
    Array of random floats of shape `size` (unless ``size=None``, in which
    case a single float is returned).

Examples
--------
>>> np.random.random_sample()
0.47108547995356098
>>> type(np.random.random_sample())
<type 'float'>
>>> np.random.random_sample((5,))
array([ 0.30220482,  0.86820401,  0.1654503 ,  0.11659149,  0.54323428])

Three-by-two array of random numbers from [-5, 0):

>>> 5 * np.random.random_sample((3, 2)) - 5
array([[-3.99149989, -0.52338984],
       [-2.99091858, -0.79479508],
       [-1.23204345, -1.75224494]])

Variables Details

[hide private]

rcParamsDefault

Value:

{'figure.subplot.right': 0.90000000000000002, 'mathtext.cal': 'cursive
', 'font.fantasy': ['Comic Sans MS', 'Chicago', 'Charcoal', 'ImpactWes
tern', 'fantasy'], 'xtick.minor.pad': 4, 'tk.pythoninspect': False, 'i
mage.aspect': 'equal', 'font.cursive': ['Apple Chancery', 'Textile', '
Zapf Chancery', 'Sand', 'cursive'], 'figure.subplot.hspace': 0.2000000
0000000001, 'xtick.direction': 'in', 'axes.facecolor': 'w', 'mathtext.
fontset': 'cm', 'ytick.direction': 'in', 'axes.axisbelow': False, 'lin
es.markersize': 6, 'figure.dpi': 80, 'text.usetex': False, 'text.fonta
...

colorbar_doc

Value:

'''

Add a colorbar to a plot.

Function signatures for the :mod:`~matplotlib.pyplot` interface; all
but the first are also method signatures for the
:meth:`~matplotlib.figure.Figure.colorbar` method::

...

rcParams

Value:

{'figure.subplot.right': 0.90000000000000002, 'mathtext.cal': 'cursive
', 'font.fantasy': ['Comic Sans MS', 'Chicago', 'Charcoal', 'ImpactWes
tern', 'fantasy'], 'xtick.minor.pad': 4, 'tk.pythoninspect': False, 'i
mage.aspect': 'equal', 'font.cursive': ['Apple Chancery', 'Textile', '
Zapf Chancery', 'Sand', 'cursive'], 'figure.subplot.hspace': 0.2000000
0000000001, 'xtick.direction': 'in', 'axes.facecolor': 'w', 'mathtext.
fontset': 'cm', 'ytick.direction': 'in', 'axes.axisbelow': False, 'lin
es.markersize': 6, 'figure.dpi': 100.0, 'text.usetex': True, 'text.fon
...

_classes

Value:

['Continuation',
 'EquilibriumCurve',
 'FoldCurve',
 'HopfCurveOne',
 'HopfCurveTwo',
 'FixedPointCurve',
 'LimitCycleCurve',
 'UserDefinedCurve']

_constants

Value:

['cont_args_list',
 'cont_bif_points',
 'equilibrium_args_list',
 'equilibrium_bif_points',
 'fold_args_list',
 'fold_bif_points',
 'hopf_args_list',
 'hopf_bif_points',
...

cont_args_list

Value:

['name',
 'force',
 'freepars',
 'MaxNumPoints',
 'MaxCorrIters',
 'MaxTestIters',
 'MaxStepSize',
 'MinStepSize',
...

limitcycle_args_list

Value:

['LocBifPoints',
 'NumCollocation',
 'NumIntervals',
 'AdaptMesh',
 'NumSPOut',
 'DiagVerbosity',
 'SolutionMeasures',
 'SaveFlow']

auto_point_types

Value:

{-9: 'MX',
 -4: 'UZ',
 1: 'BP',
 2: 'LP',
 3: 'H',
 4: 'RG',
 5: 'LPC',
 6: 'BP',
...

all_args_list

Value:

['force',
 'NumIntervals',
 'SPOut',
 'period',
 'ClosedCurve',
 'SolutionMeasures',
 'NumSPOut',
 'SaveEigen',
...

all_point_types

Value:

['NS',
 'B',
 'ZH',
 'PD',
 'DH',
 'UZ',
 'H',
 'SP',
...

all_curve_types

Value:

['EP-C', 'LP-C', 'H-C1', 'H-C2', 'FP-C', 'LC-C']

bif_curve_colors

Value:

{'EP-C': 'k',
 'FP-C': 'g',
 'H-C1': 'b',
 'H-C2': 'b',
 'LC-C': 'm',
 'LP-C': 'r',
 'UD-C': 'k'}

bif_point_colors

Value:

{'B': 'dr',
 'BP': 'og',
 'BT': 'sy',
 'CP': 'sr',
 'DH': 'sg',
 'GH': 'sb',
 'H': 'ob',
 'LP': 'or',
...