Package PyDSTool :: Package PyCont :: Module Continuation
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Module Continuation

source code

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 [hide private]
  FLOQ_TOL
  clock
  sum
  PI
  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',
...