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Package PyDSTool :: Module Symbolic
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Module Symbolic

source code

Symbolic expression support, and associated utilities.

Robert Clewley, October 2005.

   Includes code for symbolic differentiation by Pearu Peterson
   and Ryan Gutenkunst.


 Symbolic Differentiation code:
    Copyright 1999 Pearu Peterson, <pearu@ioc.ee>
    March 11-12, 1999
    Pearu Peterson

    Modified by Ryan Gutenkunst, <rng7@cornell.edu>
    April 28th, 2005
    General clean-up of code.
    Also changed saving mechanism to explicitly save the results,
    rather than doing it each time a derivative is taken.

    Modified by Robert Clewley, <rhc28@cornell.edu>
    September 15th, 2005
    As this branch of Peterson's development of symbolic features in Python
      seems to be stopped, I have increased the version number to 0.3 from 0.2.
    Added division by zero check in function dodiv().
    Added decimal point to integer constants in division to avoid Python
      integer division rules being applied to the expressions. This involves
      an added optional argument to trysimple(), and a new function
      ensuredecimalconst(). This option is conrolled using the global DO_DEC
      switch.
    Added functionality in dofun() for using "pow(x,y)" (with two arguments only)
      in input expressions.
    Also, added DO_POW option to make all output involving powers to use this
      "pow(x,y)" syntax, rather than "x**y". (Set the global DO_POW switch).
    dopower(), domul(), etc. also accept decimals 1.0 and 0.0 to perform
      simplifications if the DO_DEC switch is set.
    Adapted Diff function to accept PyDSTool Var and QuantSpec types, and
      always return those types, and also to accept an array (acts like Jacobian).
      Code is entirely backwards compatible if PyDSTool is not used (except
      Jacobians won't work).
    Renamed original, pure-string Diff function to DiffStr.
    test3() augmented with test for "pow(x,y)" syntax.
    Added test4() for Diff as Jacobian and using Var and QuantSpec objects,
      if available.
    Note that with DO_DEC option off you get "incorrect" results for the derivative
      of f[1] in test4().

    25 February 2006
    Moved package into Symbolic.py
    Added scopes to eval statements to prevent argument names clashing with
      names appearing in the eval'd string.
    Made title case symbolic versions of math functions and constants
      from ModelSpec compatible with Diff.
    Improved support for pow(x,y) syntax under differentiation.
    Added support for symbolic vectors.
Classes [hide private]
  _mathobj
  QuantSpec
Specification for a symbolic numerical quantity.
  Quantity
Abstract class for symbolic numerical quantities.
  Par
  Var
  Input
  Fun
Functions [hide private]
 
resolveSpecTypeCombos(t1, t2)
Resolve Quantity and QuantSpec types when combined.		 source code
 
getdim(s)
If s is a representation of a vector, return the dimension.		 source code
 
strIfSeq(x)
Convert sequence of QuantSpecs or strings to a string representation of that sequence, otherwise return the argument untouched.		 source code
 
ensureQlist(thelist) source code
 
ensureStrArgDict(d, renderForCode=True)
Optional renderForCode argument converts any uppercase built-in symbolic function names to lowercase numeric function names (default True)		 source code
 
_eval(q, math_globals, local_free, eval_at_runtime) source code
 
_propagate_str_eval(s) source code
 
_join_sublist(qspec, math_globals, local_free, eval_at_runtime) source code
 
expr2fun(qexpr, ensure_args=None, **values)
qexpr is a string, Quantity, or QuantSpec object.		 source code
 
subs(qexpr, *bindings)
Substitute pars or other name bindings (as a dictionary) into a Quantity, QuantSpec, or string containing a symbolic expression.		 source code
 
_parse_func_deriv(fname)
Internal utility to test whether a function name is generated from a symbolic differentiation call.		 source code
 
_generate_subderivatives(symbols, fnspecs)
Internal utility for prepJacobian		 source code
 
prepJacobian(varspecs, coords, fnspecs=None, max_iter_depth=20)
Returns a symbolic Jacobian and updated function specs to support its definition from variable specifications.		 source code
 
checkbraces(s)
Internal utility to verify that braces match.		 source code
 
whoQ(objdict=None, deepSearch=False, frameback=3) source code
 
processMultiDef(s, specstr, specType) source code
 
isMultiDef(s)
Determine whether string is a candidate multiple Quantity definition.		 source code
 
findMultiRefs(s) source code
 
isMultiRef(s)
Simple litmus test for candidate multiple quantity reference (or definition).		 source code
 
processMultiRef(s, rootname, ixname, ok_range) source code
 
isMultiDefClash(obj, multiDefRefs, parentname=None) source code
 
evalMultiRefToken(mref, ixname, val)
Helper function for evaluating multi-reference tokens for given index values.		 source code
 
getlftrtD(t, a) source code
 
dofun(l, r) source code
 
Diff(t, a)
Diff expects strings, Quantity, or QuantSpec types, a mixture of these, or a list of strings in second argument.		 source code
 
DiffStr(t, a='x')
Diff for strings only.		 source code
Variables [hide private]
  builtin_auxnames = ['globalindepvar', 'initcond', 'heav', 'if'...
  re
  replaceSepStr
  num_chars = ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
  builtinFnSigInfo = {'for': 4, 'getbound': 2, 'getindex': 1, 'g...
  token
  specialfns
  alphabet_chars_RE
  collect_numbers
  toCircumflexSyntax
  np
  syms = {0: 'ENDMARKER', 1: 'NAME', 2: 'NUMBER', 3: 'STRING', 4...
  protected_allnames = ['acos', 'asin', 'atan', 'atan2', 'ceil',...
  ZEROS = ['0', '0.0', '0.', '(0)', '(0.0)', '(0.)']
  reserved_keywords
  isVectorClause
  protected_mathnames = ['acos', 'asin', 'atan', 'atan2', 'ceil'...
  parser
  temp_macro_names
  replaceSepQSpec
  protected_macronames = ['for', 'if', 'max', 'min', 'sum']
  protected_auxnamesDB = ModelSpec internal helper class: auxfnD...
  DO_DEC
  protected_specialfns = ['special_airy', 'special_airye', 'spec...
  ensureints
  convert_power_reserved_keywords
  name_chars_RE = re.compile(r'\w')
  protected_randomnames = ['BPF', 'LOG4', 'NV_MAGICCONST', 'RECI...
  temp_macro_names_inv
  protected_scipynames = ['sign', 'mod']
  toDoubleStarSyntax
  symbol
  TENS
  POW_STR
  NAMESEP = '.'
  ONES = ['1', '1.0', '1.', '(1)', '(1.0)', '(1.)']
  DO_POW
  all
  predicate_op
  less
  shape
  complexfloating
  DomainType
  putmask
  swapaxes
  newton_meth
  float32
  take
  float
  greater
  float96
  complex_
  ones
  API = API_class()
  targetLangs = ['c', 'python', 'matlab']
  concatenate
  API_class
  argmax
  sign
  Macheps
  mat
  asarray
  Continuous = Continuous Domain
  null_predicate = null_predicate_class(None)
  complex64
  transpose
  atleast_1d
  Discrete = Discrete Domain
  float_
  less_equal
  platform
  complex128
  zeros
  int_
  complex192
  int0
  int8
  argmin
  double
  norm
  finfo
  integer
  spy
  clip
  int
  logical_or
  floating
  argsort
  any
  null_predicate_class
  rout
  redirc
  complex
  LargestInt32 = 2147483647
  int64
  int16
  npy
  minpack
  ndarray
  searchsorted
  fit_function
  time
  rerr
  Inf = inf
  NaN = nan
  isfinite = <ufunc 'isfinite'>
  mod = <ufunc 'remainder'>
  arccos = <ufunc 'arccos'>
  arcsin = <ufunc 'arcsin'>
  arctan = <ufunc 'arctan'>
  arctan2 = <ufunc 'arctan2'>
  arccosh = <ufunc 'arccosh'>
  arcsinh = <ufunc 'arcsinh'>
  arctanh = <ufunc 'arctanh'>
  ceil = <ufunc 'ceil'>
  cos = <ufunc 'cos'>
  cosh = <ufunc 'cosh'>
  exp = <ufunc 'exp'>
  fabs = <ufunc 'fabs'>
  floor = <ufunc 'floor'>
  fmod = <ufunc 'fmod'>
  frexp = <ufunc 'frexp'>
  hypot = <ufunc 'hypot'>
  ldexp = <ufunc 'ldexp'>
  log = <ufunc 'log'>
  log10 = <ufunc 'log10'>
  modf = <ufunc 'modf'>
  power = <ufunc 'power'>
  sin = <ufunc 'sin'>
  sinh = <ufunc 'sinh'>
  sqrt = <ufunc 'sqrt'>
  tan = <ufunc 'tan'>
  tanh = <ufunc 'tanh'>
  pi = 3.14159265359
  e = 2.71828182846
  asin = <ufunc 'arcsin'>
  acos = <ufunc 'arccos'>
  atan = <ufunc 'arctan'>
  atan2 = <ufunc 'arctan2'>
  acosh = <ufunc 'arccosh'>
  asinh = <ufunc 'arcsinh'>
  atanh = <ufunc 'arctanh'>
  pow = <ufunc 'power'>
  math_dir = ['__doc__', '__file__', '__name__', 'acos', 'asin',...
  math_globals = {'Abs': Abs (ModelSpec wrapper), 'Acos': Acos (...
  allmathnames = ['acos', 'asin', 'atan', 'atan2', 'ceil', 'cos'...
  allmathnames_symbolic = ['Acos', 'Asin', 'Atan', 'Atan2', 'Cei...
  mathNameMap = {'Abs': 'abs', 'Acos': 'acos', 'Asin': 'asin', '...
  inverseMathNameMap = {'Random': 'Random', 'SystemRandom': 'Sys...
  specTypes = ('RHSfuncSpec', 'ImpFuncSpec', 'ExpFuncSpec')
  _functions = ['isMultiDef', 'isMultiRef', 'isMultiDefClash', '...
  _classes = ['QuantSpec', 'Quantity', 'Var', 'Par', 'Input', 'F...
  _constants = ['specTypes', 'allmathnames_symbolic', 'allmathna...
  feval_map_const = {'e': '2.7182818284590451', 'pi': '3.1415926...
  feval_map_symb = {'Abs': 'abs', 'Acos': 'acos', 'Asin': 'asin'...
  mathlookup = {'acos': 'math.', 'asin': 'math.', 'atan': 'math....
  randomlookup = {'BPF': 'random.', 'LOG4': 'random.', 'NV_MAGIC...
  builtinlookup = {'abs': '', 'max': '', 'min': '', 'pow': '', '...
  modlookup = {'BPF': 'random.', 'LOG4': 'random.', 'NV_MAGICCON...
  funcnames = ['acos', 'asin', 'atan', 'atan2', 'ceil', 'cos', '...
  _localfuncnames = ['for', 'if', 'max', 'min', 'sum', 'globalin...
  _avoid_math_symbols = ['e', 'pi', 'Acos', 'Asin', 'Atan', 'Ata...
  local_fndef = {'for_': Fun for_ (ExpFuncSpec), 'getbound_': Fu...
  qtypes = (<class 'PyDSTool.Symbolic.Quantity'>, <class 'PyDSTo...
  Abs = Abs (ModelSpec wrapper)
  Acos = Acos (ModelSpec wrapper)
  Asin = Asin (ModelSpec wrapper)
  Atan = Atan (ModelSpec wrapper)
  Atan2 = Atan2 (ModelSpec wrapper)
  Betavariate = Betavariate (ModelSpec wrapper)
  Ceil = Ceil (ModelSpec wrapper)
  Choice = Choice (ModelSpec wrapper)
  Cos = Cos (ModelSpec wrapper)
  Cosh = Cosh (ModelSpec wrapper)
  Degrees = Degrees (ModelSpec wrapper)
  E = QuantSpec e (ExpFuncSpec)
  Exp = Exp (ModelSpec wrapper)
  Expovariate = Expovariate (ModelSpec wrapper)
  Fabs = Fabs (ModelSpec wrapper)
  Floor = Floor (ModelSpec wrapper)
  Fmod = Fmod (ModelSpec wrapper)
  Frexp = Frexp (ModelSpec wrapper)
  Gammavariate = Gammavariate (ModelSpec wrapper)
  Gauss = Gauss (ModelSpec wrapper)
  Getrandbits = Getrandbits (ModelSpec wrapper)
  Getstate = Getstate (ModelSpec wrapper)
  Hypot = Hypot (ModelSpec wrapper)
  Jumpahead = Jumpahead (ModelSpec wrapper)
  Ldexp = Ldexp (ModelSpec wrapper)
  Log = Log (ModelSpec wrapper)
  Log10 = Log10 (ModelSpec wrapper)
  Lognormvariate = Lognormvariate (ModelSpec wrapper)
  Max = Max (ModelSpec wrapper)
  Min = Min (ModelSpec wrapper)
  Modf = Modf (ModelSpec wrapper)
  Normalvariate = Normalvariate (ModelSpec wrapper)
  Paretovariate = Paretovariate (ModelSpec wrapper)
  Pi = QuantSpec pi (ExpFuncSpec)
  Pow = Pow (ModelSpec wrapper)
  Radians = Radians (ModelSpec wrapper)
  Randint = Randint (ModelSpec wrapper)
  Random = Random (ModelSpec wrapper)
  Randrange = Randrange (ModelSpec wrapper)
  Sample = Sample (ModelSpec wrapper)
  Seed = Seed (ModelSpec wrapper)
  Setstate = Setstate (ModelSpec wrapper)
  Shuffle = Shuffle (ModelSpec wrapper)
  Sin = Sin (ModelSpec wrapper)
  Sinh = Sinh (ModelSpec wrapper)
  Sqrt = Sqrt (ModelSpec wrapper)
  Sum = Sum (ModelSpec wrapper)
  Systemrandom = Systemrandom (ModelSpec wrapper)
  Tan = Tan (ModelSpec wrapper)
  Tanh = Tanh (ModelSpec wrapper)
  Uniform = Uniform (ModelSpec wrapper)
  Vonmisesvariate = Vonmisesvariate (ModelSpec wrapper)
  Weibullvariate = Weibullvariate (ModelSpec wrapper)
  Wichmannhill = Wichmannhill (ModelSpec wrapper)
  _1DimplicitSolveMethods = ['newton', 'bisect', 'steffe']
  _all_complex = (<type 'complex'>, <type 'numpy.complexfloating...
  _all_float = (<type 'float'>, <type 'numpy.floating'>, <type '...
  _all_int = (<type 'int'>, <type 'numpy.integer'>, <type 'numpy...
  _all_numpy_complex = (<type 'numpy.complex128'>, <type 'numpy....
  _all_numpy_float = (<type 'numpy.float64'>, <type 'numpy.float...
  _all_numpy_int = (<type 'numpy.int32'>, <type 'numpy.int32'>, ...
  _complex_types = (<type 'complex'>, <type 'numpy.complexfloati...
  _float_types = (<type 'float'>, <type 'numpy.floating'>)
  _implicitSolveMethods = ['newton', 'bisect', 'steffe', 'fsolve']
  _indentstr = ' '
  _int_types = (<type 'int'>, <type 'numpy.integer'>)
  _num_equivtype = {<type 'float'>: <type 'numpy.float64'>, <typ...
  _num_maxmin = {<type 'numpy.int32'>: [-2147483648, 2147483647]...
  _num_name2equivtypes = {'float': (<type 'float'>, <type 'numpy...
  _num_name2type = {'float': <type 'numpy.float64'>, 'int': <typ...
  _num_type2name = {<type 'float'>: 'float', <type 'int'>: 'int'...
  _num_types = (<type 'float'>, <type 'int'>, <type 'numpy.float...
  _pytypefromtype = {<type 'numpy.int32'>: <type 'int'>, <type '...
  _real_types = (<type 'int'>, <type 'numpy.integer'>, <type 'fl...
  _seq_types = (<type 'list'>, <type 'tuple'>, <type 'numpy.ndar...
  a = 'sum'
  argstr = '\'arg0\',\'arg1\',\'arg2\','
  c = 'pi'
  f = 'sum'
  fname = 'if'
  funcstr = 'Fun(\'\', [\'arg0\',\'arg1\',\'arg2\',], \'if_\')'
  i = 2
  m = 'tanh'
  n = 'sum'
  symb = 'Sum'
Function Details [hide private]

resolveSpecTypeCombos(t1, t2)

source code 

Resolve Quantity and QuantSpec types when combined. QuantSpec <op> QuantSpec -> specType rules: same types -> that type ExpFuncSpec o RHSfuncSpec -> RHSfuncSpec ImpFuncSpec o RHSfuncSpec -> RHSfuncSpec (should this be an error?) ImpFuncSpec o ExpFuncSpec -> ImpFuncSpec

expr2fun(qexpr, ensure_args=None, **values)

source code 

qexpr is a string, Quantity, or QuantSpec object. values is a dictionary binding free names to numerical values or other objects defined at runtime that are in local scope.

If values contains pairs (fnsig, fndef) from a FuncSpec function definition then the function will be incorporated into the result. The function definition can contain math names that are still in non-code-rendered (lowercase) form (i.e. "Exp" rather than "exp").

If any names use the hierarchical naming convention (using the '.' separator) then those names will be converted to use the '_' separator instead. For end-use convenience, the necessary name map for arguments is stored in the '_namemap' attribute, which will otherwise be the ID map. Calling with keyed objects that use hierarchical names (especially Point objects) can then be done using the return object's alt_call method, which takes any keyed_object that will be filtered for the function arguments and name-mapped appropriately before evaluation.

You can force the function to accept the named arguments in the ensure_args list of strings, e.g. when creating a Jacobian that is expected to always take 't' as an argument even if the system is autonomous.

The arguments to the returned callable function object are given by its attribute '_args', and its definition string by '_call_spec'.

prepJacobian(varspecs, coords, fnspecs=None, max_iter_depth=20)

source code 

Returns a symbolic Jacobian and updated function specs to support its definition from variable specifications. Only makes the Jacobian with respect to the named coordinates, which will be sorted into alphabetical order.

isMultiRef(s)

source code 

Simple litmus test for candidate multiple quantity reference (or definition).

Requires further testing using one of the other associated multiple quantity reference/definition tests.

Diff(t, a)

source code 

Diff expects strings, Quantity, or QuantSpec types, a mixture of these, or a list of strings in second argument.

The return type is a QuantSpec.

DiffStr(t, a='x')

source code 

Diff for strings only.

This is Pearu's original Diff function renamed to DiffStr.


Variables Details [hide private]

builtin_auxnames

Value:
['globalindepvar', 'initcond', 'heav', 'if', 'getindex', 'getbound']

builtinFnSigInfo

Value:
{'for': 4,
 'getbound': 2,
 'getindex': 1,
 'globalindepvar': 1,
 'heav': 1,
 'if': 3,
 'initcond': 1,
 'max': 1,
...

syms

Value:
{0: 'ENDMARKER',
 1: 'NAME',
 2: 'NUMBER',
 3: 'STRING',
 4: 'NEWLINE',
 5: 'INDENT',
 6: 'DEDENT',
 7: 'LPAR',
...

protected_allnames

Value:
['acos',
 'asin',
 'atan',
 'atan2',
 'ceil',
 'cos',
 'cosh',
 'degrees',
...

protected_mathnames

Value:
['acos',
 'asin',
 'atan',
 'atan2',
 'ceil',
 'cos',
 'cosh',
 'degrees',
...

protected_auxnamesDB

Value:
ModelSpec internal helper class: auxfnDBclass object

protected_specialfns

Value:
['special_airy',
 'special_airye',
 'special_ai_zeros',
 'special_bi_zeros',
 'special_ellipj',
 'special_ellipk',
 'special_ellipkinc',
 'special_ellipe',
...

protected_randomnames

Value:
['BPF',
 'LOG4',
 'NV_MAGICCONST',
 'RECIP_BPF',
 'Random',
 'SG_MAGICCONST',
 'SystemRandom',
 'TWOPI',
...

math_dir

Value:
['__doc__',
 '__file__',
 '__name__',
 'acos',
 'asin',
 'atan',
 'atan2',
 'ceil',
...

math_globals

Value:
{'Abs': Abs (ModelSpec wrapper),
 'Acos': Acos (ModelSpec wrapper),
 'Asin': Asin (ModelSpec wrapper),
 'Atan': Atan (ModelSpec wrapper),
 'Atan2': Atan2 (ModelSpec wrapper),
 'Betavariate': Betavariate (ModelSpec wrapper),
 'Ceil': Ceil (ModelSpec wrapper),
 'Choice': Choice (ModelSpec wrapper),
...

allmathnames

Value:
['acos',
 'asin',
 'atan',
 'atan2',
 'ceil',
 'cos',
 'cosh',
 'degrees',
...

allmathnames_symbolic

Value:
['Acos',
 'Asin',
 'Atan',
 'Atan2',
 'Ceil',
 'Cos',
 'Cosh',
 'Degrees',
...

mathNameMap

Value:
{'Abs': 'abs',
 'Acos': 'acos',
 'Asin': 'asin',
 'Atan': 'atan',
 'Atan2': 'atan2',
 'Betavariate': 'betavariate',
 'Ceil': 'ceil',
 'Choice': 'choice',
...

inverseMathNameMap

Value:
{'Random': 'Random',
 'SystemRandom': 'Systemrandom',
 'WichmannHill': 'Wichmannhill',
 'abs': 'Abs',
 'acos': 'Acos',
 'asin': 'Asin',
 'atan': 'Atan',
 'atan2': 'Atan2',
...

_functions

Value:
['isMultiDef',
 'isMultiRef',
 'isMultiDefClash',
 'checkbraces',
 'findMultiRefs',
 'processMultiRef',
 'evalMultiRefToken',
 'expr2fun',
...

_classes

Value:
['QuantSpec', 'Quantity', 'Var', 'Par', 'Input', 'Fun']

_constants

Value:
['specTypes',
 'allmathnames_symbolic',
 'allmathnames',
 'Acos',
 'Asin',
 'Atan',
 'Atan2',
 'Ceil',
...

feval_map_const

Value:
{'e': '2.7182818284590451', 'pi': '3.1415926535897931'}

feval_map_symb

Value:
{'Abs': 'abs',
 'Acos': 'acos',
 'Asin': 'asin',
 'Atan': 'atan',
 'Atan2': 'atan2',
 'Betavariate': 'betavariate',
 'Ceil': 'ceil',
 'Choice': 'choice',
...

mathlookup

Value:
{'acos': 'math.',
 'asin': 'math.',
 'atan': 'math.',
 'atan2': 'math.',
 'ceil': 'math.',
 'cos': 'math.',
 'cosh': 'math.',
 'degrees': 'math.',
...

randomlookup

Value:
{'BPF': 'random.',
 'LOG4': 'random.',
 'NV_MAGICCONST': 'random.',
 'RECIP_BPF': 'random.',
 'Random': 'random.',
 'SG_MAGICCONST': 'random.',
 'SystemRandom': 'random.',
 'TWOPI': 'random.',
...

builtinlookup

Value:
{'abs': '', 'max': '', 'min': '', 'pow': '', 'sum': ''}

modlookup

Value:
{'BPF': 'random.',
 'LOG4': 'random.',
 'NV_MAGICCONST': 'random.',
 'RECIP_BPF': 'random.',
 'Random': 'random.',
 'SG_MAGICCONST': 'random.',
 'SystemRandom': 'random.',
 'TWOPI': 'random.',
...

funcnames

Value:
['acos',
 'asin',
 'atan',
 'atan2',
 'ceil',
 'cos',
 'cosh',
 'degrees',
...

_localfuncnames

Value:
['for',
 'if',
 'max',
 'min',
 'sum',
 'globalindepvar',
 'initcond',
 'heav',
...

_avoid_math_symbols

Value:
['e',
 'pi',
 'Acos',
 'Asin',
 'Atan',
 'Atan2',
 'Ceil',
 'Cos',
...

local_fndef

Value:
{'for_': Fun for_ (ExpFuncSpec),
 'getbound_': Fun getbound_ (ExpFuncSpec),
 'getindex_': Fun getindex_ (ExpFuncSpec),
 'globalindepvar_': Fun globalindepvar_ (ExpFuncSpec),
 'heav_': Fun heav_ (ExpFuncSpec),
 'if_': Fun if_ (ExpFuncSpec),
 'initcond_': Fun initcond_ (ExpFuncSpec),
 'max_': Fun max_ (ExpFuncSpec),
...

qtypes

Value:
(<class 'PyDSTool.Symbolic.Quantity'>,
 <class 'PyDSTool.Symbolic.QuantSpec'>)

_all_complex

Value:
(<type 'complex'>,
 <type 'numpy.complexfloating'>,
 <type 'numpy.complex128'>,
 <type 'numpy.complex64'>,
 <type 'numpy.complex128'>)

_all_float

Value:
(<type 'float'>,
 <type 'numpy.floating'>,
 <type 'numpy.float64'>,
 <type 'numpy.float32'>,
 <type 'numpy.float64'>)

_all_int

Value:
(<type 'int'>,
 <type 'numpy.integer'>,
 <type 'numpy.int32'>,
 <type 'numpy.int32'>,
 <type 'numpy.int8'>,
 <type 'numpy.int16'>,
 <type 'numpy.int32'>,
 <type 'numpy.int64'>)

_all_numpy_complex

Value:
(<type 'numpy.complex128'>,
 <type 'numpy.complex64'>,
 <type 'numpy.complex128'>)

_all_numpy_float

Value:
(<type 'numpy.float64'>,
 <type 'numpy.float32'>,
 <type 'numpy.float64'>)

_all_numpy_int

Value:
(<type 'numpy.int32'>,
 <type 'numpy.int32'>,
 <type 'numpy.int8'>,
 <type 'numpy.int16'>,
 <type 'numpy.int32'>,
 <type 'numpy.int64'>)

_complex_types

Value:
(<type 'complex'>, <type 'numpy.complexfloating'>)

_num_equivtype

Value:
{<type 'float'>: <type 'numpy.float64'>,
 <type 'int'>: <type 'numpy.int32'>,
 <type 'numpy.integer'>: <type 'numpy.int32'>,
 <type 'numpy.floating'>: <type 'numpy.float64'>,
 <type 'numpy.int8'>: <type 'numpy.int32'>,
 <type 'numpy.int16'>: <type 'numpy.int32'>,
 <type 'numpy.int32'>: <type 'numpy.int32'>,
 <type 'numpy.int32'>: <type 'numpy.int32'>,
...

_num_maxmin

Value:
{<type 'numpy.int32'>: [-2147483648, 2147483647],
 <type 'numpy.float64'>: [-inf, inf]}

_num_name2equivtypes

Value:
{'float': (<type 'float'>,
           <type 'numpy.floating'>,
           <type 'numpy.float64'>,
           <type 'numpy.float32'>,
           <type 'numpy.float64'>),
 'int': (<type 'int'>,
         <type 'numpy.integer'>,
         <type 'numpy.int32'>,
...

_num_name2type

Value:
{'float': <type 'numpy.float64'>, 'int': <type 'numpy.int32'>}

_num_type2name

Value:
{<type 'float'>: 'float',
 <type 'int'>: 'int',
 <type 'numpy.integer'>: 'int',
 <type 'numpy.floating'>: 'float',
 <type 'numpy.int8'>: 'int',
 <type 'numpy.int16'>: 'int',
 <type 'numpy.int32'>: 'int',
 <type 'numpy.int32'>: 'int',
...

_num_types

Value:
(<type 'float'>,
 <type 'int'>,
 <type 'numpy.floating'>,
 <type 'numpy.integer'>)

_pytypefromtype

Value:
{<type 'numpy.int32'>: <type 'int'>,
 <type 'numpy.float64'>: <type 'float'>}

_real_types

Value:
(<type 'int'>,
 <type 'numpy.integer'>,
 <type 'float'>,
 <type 'numpy.floating'>)

_seq_types

Value:
(<type 'list'>, <type 'tuple'>, <type 'numpy.ndarray'>)

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