Source code for astropy.units.core

# -*- coding: utf-8 -*-
# Licensed under a 3-clause BSD style license - see LICENSE.rst

"""
Core units classes and functions
"""

from __future__ import (absolute_import, division, print_function,
                        unicode_literals)

import inspect
import re
import sys
import textwrap
import warnings

import numpy as np
from numpy import ma

from ..utils.compat.fractions import Fraction
from . import format as unit_format

# TODO: Support functional units, e.g. log(x), ln(x)

__all__ = [
    'UnitsException', 'UnitsWarning', 'UnitBase', 'NamedUnit',
    'IrreducibleUnit', 'Unit', 'def_unit', 'CompositeUnit',
    'PrefixUnit', 'UnrecognizedUnit']


[docs]class UnitsException(Exception): """ The base class for unit-specific exceptions. """ pass
[docs]class UnitsWarning(Warning): """ The base class for unit-specific exceptions. """ pass
[docs]class UnitBase(object): """ Abstract base class for units. Most of the arithmetic operations on units are defined in this base class. Should not be instantiated by users directly. """ _registry = {} _namespace = {} # Make sure that __rmul__ of units gets called over the __mul__ of Numpy # arrays to avoid element-wise multiplication. __array_priority__ = 1000 def __deepcopy__(self, memo): # This may look odd, but the units conversion will be very # broken after deep-copying if we don't guarantee that a given # physical unit corresponds to only one instance return self def _repr_latex_(self): """ Generate latex representation of unit name. This is used by the IPython notebook to print a unit with a nice layout. Returns ------- Latex string """ return unit_format.Latex().to_string(self) def __str__(self): """Return string representation for unit""" return unit_format.Generic().to_string(self) def __repr__(self): return 'Unit("' + str(self) + '")'
[docs] def to_string(self, format='generic'): """ Output the unit in the given format as a string. Parameters ---------- format : `astropy.format.Base` instance or str The name of a format or a formatter object. If not provided, defaults to the generic format. """ f = unit_format.get_format(format) return f.to_string(self)
@staticmethod def _get_namespace(): """ Get the namespace that units will be registered to. """ return UnitBase._namespace @staticmethod def _set_namespace(d): """ Set the namespace that units will be registered to. """ UnitBase._namespace = d def __pow__(self, p): if isinstance(p, tuple) and len(p) == 2: p = Fraction(p[0], p[1]) else: # allow two possible floating point fractions, all others illegal if not int(2 * p) == 2 * p: raise ValueError( "floating values for unit powers must be integers or " "integers + 0.5") return CompositeUnit(1, [self], [p])._simplify() def __div__(self, m): # Strictly speaking, we should be using old-style division here. # However, I think it's less surprising for this to behave the # same way whether __future__ division is being used or not from .quantity import Quantity if isinstance(m, UnitBase): return CompositeUnit(1, [self, m], [1, -1])._simplify() elif isinstance(m, Quantity): return Quantity(1, self) / m elif isinstance(m, basestring): return self / Unit(m) else: return Quantity(1. / m, self) def __rdiv__(self, m): from .quantity import Quantity if isinstance(m, basestring): return Unit(m) / Quantity(1, self) else: return Quantity(m, CompositeUnit(1.0, [self], [-1])._simplify()) def __truediv__(self, m): return self.__div__(m) def __rtruediv__(self, m): return self.__rdiv__(m) def __mul__(self, m): from .quantity import Quantity if isinstance(m, UnitBase): return CompositeUnit(1, [self, m], [1, 1])._simplify() elif isinstance(m, Quantity): return Quantity(1, self) * m elif isinstance(m, basestring): return self * Unit(m) else: return Quantity(m, self) def __rmul__(self, m): from .quantity import Quantity if isinstance(m, basestring): return Unit(m) * Quantity(1, self) else: return Quantity(m, self) if sys.version_info[0] >= 3: def __hash__(self): # Since this class defines __eq__, it will become unhashable # on Python 3.x, so we need to define our own hash. return id(self) def __eq__(self, other): try: other = Unit(other, parse_strict='silent') except (ValueError, UnitsException): return False try: return np.allclose(self.to(other, 1), 1.0) except UnitsException: return False def __ne__(self, other): return not (self == other) def __lt__(self, other): other = Unit(other) return self.to(other, 1) < 1. def __gt__(self, other): other = Unit(other) return self.to(other, 1) > 1. def __le__(self, other): other = Unit(other) return self.to(other, 1) <= 1. def __ge__(self, other): other = Unit(other) return self.to(other, 1) >= 1. def __neg__(self): return self * -1. def _simplify(self): """ Compresses a possibly composite unit down to a single instance. """ return self
[docs] def is_equivalent(self, other, equivalencies=[]): """ Returns `True` if this unit is equivalent to `other`. Parameters ---------- other : unit object or string The unit to convert to. equivalencies : list of equivalence pairs, optional A list of equivalence pairs to try if the units are not directly convertible. See :ref:`unit_equivalencies`. Returns ------- bool """ other = Unit(other, parse_strict='silent') if isinstance(other, UnrecognizedUnit): return False try: (self / other)._dimensionless_constant() except UnitsException: unit = self.decompose() other = other.decompose() for equiv in equivalencies: a = equiv[0] b = equiv[1] if (unit.is_equivalent(a) and other.is_equivalent(b)): return True elif (unit.is_equivalent(b) and other.is_equivalent(a)): return True return False else: return True
def _apply_equivalences(self, unit, other, equivalencies): """ Internal function (used from `get_converter`) to apply equivalence pairs. """ def make_converter(scale1, func, scale2): def convert(v): return func(_condition_arg(v) * scale1) * scale2 return convert orig_unit = unit orig_other = other unit = self.decompose() other = other.decompose() for equiv in equivalencies: if len(equiv) == 2: funit, tunit = equiv a, b = lambda x: x if len(equiv) == 3: funit, tunit, a = equiv b = a elif len(equiv) == 4: funit, tunit, a, b = equiv else: raise ValueError("Invalid equivalence entry") if (unit.is_equivalent(funit) and other.is_equivalent(tunit)): scale1 = (unit / funit)._dimensionless_constant() scale2 = (tunit / other)._dimensionless_constant() return make_converter(scale1, a, scale2) elif (other.is_equivalent(funit) and unit.is_equivalent(tunit)): scale1 = (unit / tunit)._dimensionless_constant() scale2 = (funit / other)._dimensionless_constant() return make_converter(scale1, b, scale2) def get_err_str(unit): unit_str = unit.to_string('unscaled') physical_type = unit.physical_type if physical_type != 'unknown': unit_str = "'{0}' ({1})".format( unit_str, physical_type) else: unit_str = "'{0}'".format(unit_str) return unit_str unit_str = get_err_str(orig_unit) other_str = get_err_str(orig_other) raise UnitsException( "{0} and {1} are not convertible".format( unit_str, other_str))
[docs] def get_converter(self, other, equivalencies=[]): """ Return the conversion function to convert values from `self` to the specified unit. Parameters ---------- other : unit object or string The unit to convert to. equivalencies : list of equivalence pairs, optional A list of equivalence pairs to try if the units are not directly convertible. See :ref:`unit_equivalencies`. Returns ------- func : callable A callable that normally expects a single argument that is a scalar value or an array of values (or anything that may be converted to an array). Raises ------ UnitsException If units are inconsistent """ other = Unit(other) try: scale = (self / other)._dimensionless_constant() except UnitsException: return self._apply_equivalences( self, other, equivalencies) return lambda val: scale * _condition_arg(val)
[docs] def to(self, other, value=1.0, equivalencies=[]): """ Return the converted values in the specified unit. Parameters ---------- other : unit object or string The unit to convert to. value : scalar int or float, or sequence that can be converted to array, optional Value(s) in the current unit to be converted to the specified unit. If not provided, defaults to 1.0 equivalencies : list of equivalence pairs, optional A list of equivalence pairs to try if the units are not directly convertible. See :ref:`unit_equivalencies`. Returns ------- values : scalar or array Converted value(s). Input value sequences are returned as numpy arrays. Raises ------ UnitException If units are inconsistent """ other = Unit(other) return self.get_converter(other, equivalencies=equivalencies)(value)
[docs] def in_units(self, other, value=1.0, equivalencies=[]): """ Alias for `to` for backward compatibility with pynbody. """ return self.to( other, value=value, equivalencies=equivalencies)
[docs] def decompose(self, bases=set()): """ Return a unit object composed of only irreducible units. Parameters ---------- bases : sequence of UnitBase, optional The bases to decompose into. When not provided, decomposes down to any irreducible units. When provided, the decomposed result will only contain the given units. This will raises a `UnitsException` if it's not possible to do so. Returns ------- unit : CompositeUnit object New object containing only irreducible unit objects. """ raise NotImplementedError()
def _compose(self, equivalencies=[], namespace=[], max_depth=2, depth=0): def is_final_result(unit): # Returns True if this result contains only the expected # units for base in unit._bases: if base not in namespace: return False return True def sort_results(results): if not len(results): return [] # Sort the results so the simplest ones appear first. # Simplest is defined as "the minimum sum of absolute # powers" (i.e. the fewest bases), and preference should # be given to results where the sum of powers is positive # and the scale is exactly equal to 1.0 results = list(results) results.sort(key=lambda x: str(x)) results.sort(key=lambda x: np.sum(np.abs(x.powers))) results.sort(key=lambda x: np.sum(x.powers) < 0.0) results.sort(key=lambda x: not np.allclose(x.scale, 1.0)) last_result = results[0] filtered = [last_result] for result in results[1:]: if str(result) != str(last_result): filtered.append(result) last_result = result return filtered unit = self.decompose() # Prevent too many levels of recursion if depth >= max_depth: return [unit] # Special case for dimensionless unit if len(unit._bases) == 0: return [unit] # Make a list including all of the equivalent units units = [unit] for equiv in equivalencies: funit, tunit = equiv[:2] if self.is_equivalent(funit): units.append(tunit.decompose()) elif self.is_equivalent(tunit): units.append(funit.decompose()) # Store partial results partial_results = [] # Store final results that reduce to a single unit or pair of # units final_results = [set(), set()] for tunit in namespace: tunit_decomposed = tunit.decompose() for u in units: # If the unit is a base unit, look for an exact match # to one of the bases of the target unit. If found, # factor by the same power as the target unit's base. # This allows us to factor out fractional powers # without needing to do an exhaustive search. if len(tunit_decomposed.bases) == 1: for base, power in zip(u._bases, u._powers): if tunit_decomposed.is_equivalent(base): tunit = tunit ** power tunit_decomposed = tunit_decomposed ** power break composed = (u / tunit_decomposed).decompose() factored = composed * tunit len_bases = len(composed._bases) if is_final_result(factored) and len_bases <= 1: final_results[len_bases].add(factored) else: partial_results.append( (len_bases, composed, tunit)) # Do we have any minimal results? for final_result in final_results: if len(final_result): return sort_results(final_result) partial_results.sort(key=lambda x: x[0]) # ...we have to recurse and try to further compose results = [] for len_bases, composed, tunit in partial_results: try: composed_list = composed._compose( equivalencies=equivalencies, namespace=namespace, max_depth=max_depth, depth=depth + 1) except UnitsException: composed_list = [] for subcomposed in composed_list: results.append( (len(subcomposed._bases), subcomposed, tunit)) if len(results): results.sort(key=lambda x: x[0]) min_length = results[0][0] subresults = set() for len_bases, composed, tunit in results: if len_bases > min_length: break else: factored = composed * tunit if is_final_result(factored): subresults.add(composed * tunit) if len(subresults): return sort_results(subresults) for base in self.bases: if base not in namespace: raise UnitsException( "Cannot represent unit {0} in terms of the given " "units".format(self)) return [self]
[docs] def compose(self, equivalencies=[], units=None, max_depth=2, include_prefix_units=False): """ Return the simplest possible composite unit(s) that represent the given unit. Since there may be multiple equally simple compositions of the unit, a list of units is always returned. Parameters ---------- equivalencies : list of equivalence pairs, optional A list of equivalence pairs to also list. See :ref:`unit_equivalencies`. units : set of units to compose to, optional If not provided, any known units may be used to compose into. Otherwise, ``units`` is a dict, module or sequence containing the units to compose into. max_depth : int, optional The maximum recursion depth to use when composing into composite units. include_prefix_units : bool, optional When `True`, include prefixed units in the result. Default is `False`. Returns ------- units : list of `CompositeUnit` A list of candidate compositions. These will all be equally simple, but it may not be possible to automatically determine which of the candidates are better. """ def filter_units(units): filtered_namespace = set() for tunit in units: if (isinstance(tunit, UnitBase) and (include_prefix_units or not isinstance(tunit, PrefixUnit))): filtered_namespace.add(tunit) return filtered_namespace if units is None: units = filter_units(UnitBase._registry.values()) elif isinstance(units, dict): units = set(units.values()) elif inspect.ismodule(units): units = filter_units(vars(units).values()) else: units = set(units) return self._compose( equivalencies=equivalencies, namespace=units, max_depth=max_depth, depth=0)
[docs] def to_system(self, system): """ Converts this unit into ones belonging to the given system. Since more than one result may be possible, a list is always returned. Parameters ---------- system : module The module that defines the unit system. Commonly used ones include `astropy.units.si` and `astropy.units.cgs`. To use your own module it must contain unit objects and a sequence member named `bases` containing the base units of the system. Returns ------- units : list of `CompositeUnit` The list is ranked so that units containing only the base units of that system will appear first. """ bases = set(system.bases) def score(compose): # In case that compose._bases has no elements we return # 'np.inf' as 'score value'. It does not really matter which # number we would return. This case occurs for instance for # dimensionless quantities: if len(compose._bases) == 0: return np.inf else: sum = 0 for base in compose._bases: if base in bases: sum += 1 return sum / float(len(compose._bases)) x = self.decompose(bases=bases) composed = x.compose(units=system) composed = sorted(composed, key=score, reverse=True) return composed
@property
[docs] def physical_type(self): """ Return the physical type on the unit. Examples -------- >>> u.m.physical_type 'length' """ from . import physical return physical.get_physical_type(self)
class EquivalentUnitsList(list): """ A class to handle pretty-printing the result of `find_equivalent_units`. """ def __repr__(self): if len(self) == 0: return "[]" else: lines = [] for u in self: irred = u.decompose().to_string() if irred == u.name: irred = "irreducible" lines.append((u.name, irred, ', '.join(u.aliases))) lines.sort() lines.insert(0, ('Primary name', 'Unit definition', 'Aliases')) widths = [0, 0, 0] for line in lines: for i, col in enumerate(line): widths[i] = max(widths[i], len(col)) f = " {{0:<{0}s}} | {{1:<{1}s}} | {{2:<{2}s}}".format(*widths) lines = [f.format(*line) for line in lines] lines = (lines[0:1] + ['['] + ['{0} ,'.format(x) for x in lines[1:]] + [']']) return '\n'.join(lines)
[docs] def find_equivalent_units(self, equivalencies=[], units=None, include_prefix_units=False): """ Return a list of all the units that are the same type as the specified unit. Parameters ---------- u : Unit instance or string The `Unit` to find similar units to. equivalencies : list of equivalence pairs, optional A list of equivalence pairs to also list. See :ref:`unit_equivalencies`. units : set of units to search in, optional If not provided, all defined units will be searched for equivalencies. Otherwise, may be a dict, module or sequence containing the units to search for equivalencies. include_prefix_units : bool, optional When `True`, include prefixed units in the result. Default is `False`. Returns ------- units : list of `UnitBase` A list of unit objects that match `u`. A subclass of `list` (`EquivalentUnitsList`) is returned that pretty-prints the list of units when output. """ results = self.compose( equivalencies=equivalencies, units=units, max_depth=1, include_prefix_units=include_prefix_units) results = [ x._bases[0] for x in results if len(x._bases) == 1] return self.EquivalentUnitsList(results)
[docs]class NamedUnit(UnitBase): """ The base class of units that have a name. Parameters ---------- st : str or list of str The name of the unit. If a list, the first element is the canonical (short) name, and the rest of the elements are aliases. register : boolean, optional When `True`, also register the unit in the standard unit namespace. Default is `False`. doc : str, optional A docstring describing the unit. format : dict, optional A mapping to format-specific representations of this unit. For example, for the ``Ohm`` unit, it might be nice to have it displayed as ``\\Omega`` by the ``latex`` formatter. In that case, `format` argument should be set to:: {'latex': r'\\Omega'} Raises ------ ValueError If any of the given unit names are already in the registry. ValueError If any of the given unit names are not valid Python tokens. """ def __init__(self, st, register=False, doc=None, format=None): UnitBase.__init__(self) if isinstance(st, (bytes, unicode)): self._names = [st] else: if len(st) == 0: raise ValueError( "st list must have at least one entry") self._names = st[:] if format is None: format = {} self._format = format if doc is None: doc = self._generate_doc() doc = textwrap.dedent(doc) doc = textwrap.fill(doc) self.__doc__ = doc self._register_unit(register) def _generate_doc(self): """ Generate a docstring for the unit if the user didn't supply one. This is only used from the constructor and may be overridden in subclasses. """ names = self.names if len(self.names) > 1: return "{1} ({0})".format(*names[:2]) else: return names[0]
[docs] def get_format_name(self, format): """ Get a name for this unit that is specific to a particular format. Uses the dictionary passed into the `format` kwarg in the constructor. Parameters ---------- format : str The name of the format Returns ------- name : str The name of the unit for the given format. """ return self._format.get(format, self.name)
@property
[docs] def names(self): """ Returns all of the names associated with this unit. """ return self._names
@property
[docs] def name(self): """ Returns the canonical (short) name associated with this unit. """ return self._names[0]
@property
[docs] def aliases(self): """ Returns the alias (long) names for this unit. """ return self._names[1:]
def _register_unit(self, register): """ Registers the unit in the registry, and optionally in another namespace. It is registered under all of the names and aliases given to the constructor. The namespace used is set with `UnitBase._set_namespace`. Parameters ---------- register : bool When `True`, register the unit in the external namespace as well as the central registry. """ if not self._names: raise UnitsException("unit has no string representation") # Loop through all of the names first, to ensure of all them # are new, then add them all as a single "transaction" below. cls = self.__class__ for st in self._names: if not re.match("^[A-Za-z_]+$", st): # will cause problems for simple string parser in # unit() factory raise ValueError( "Invalid unit name {0!r}".format(st)) if (register and st in self._namespace or (st in cls._registry and cls._registry[st] != self)): raise ValueError( "Object with name {0!r} already exists " "in namespace.".format(st)) for st in self._names: if register: self._namespace[st] = self self._registry[st] = self
def _recreate_irreducible_unit(names, registered): """ This is used to reconstruct units when passed around by multiprocessing. """ namespace = UnitBase._get_namespace() if names[0] in namespace: return namespace[names[0]] else: return IrreducibleUnit(names, register=registered)
[docs]class IrreducibleUnit(NamedUnit): """ Irreducible units are the units that all other units are defined in terms of. Examples are meters, seconds, kilograms, amperes, etc. There is only once instance of such a unit per type. """ def __reduce__(self): # When IrreducibleUnit objects are passed to other processes # over multiprocessing, they need to be recreated to be the # ones already in the subprocesses' namespace, not new # objects, or they will be considered "unconvertible". # Therefore, we have a custom pickler/unpickler that # understands how to recreate the Unit on the other side. namespace = UnitBase._get_namespace() return (_recreate_irreducible_unit, (self.names, self.names[0] in namespace), self.__dict__) @property
[docs] def scale(self): """ Return the scale of the unit. """ return 1.0
@property
[docs] def bases(self): """ Return the bases of the unit. """ return [self]
@property
[docs] def powers(self): """ Return the powers of the unit. """ return [1.0]
[docs] def decompose(self, bases=set()): if len(bases) and not self in bases: for base in bases: if self.is_equivalent(base): return CompositeUnit(self.to(base), [base], [1]) raise UnitsException( "Unit {0} can not be decomposed into the requested " "bases".format(self)) return CompositeUnit(1, [self], [1])
decompose.__doc__ = UnitBase.decompose.__doc__
[docs]class UnrecognizedUnit(IrreducibleUnit): """ A unit that did not parse correctly. This allows for roundtripping it as a string, but no unit operations actually work on it. Parameters ---------- st : str The name of the unit. """ def __init__(self, st): IrreducibleUnit.__init__(self, st) def __repr__(self): return "UnrecognizedUnit({0})".format(str(self)) def __str__(self): return self.name
[docs] def to_string(self, format='generic'): return self.name
def _register_unit(self, register): pass def _unrecognized_operator(self, *args, **kwargs): raise ValueError( "The unit {0!r} is unrecognized, so all arithmetic operations " "with it are invalid.".format(self.name)) __pow__ = __div__ = __rdiv__ = __truediv__ = __rtruediv__ = __mul__ = \ __rmul__ = __lt__ = __gt__ = __le__ = __ge__ = __neg__ = \ _unrecognized_operator def __eq__(self, other): other = Unit(other, parse_strict='silent') return isinstance(other, UnrecognizedUnit) and self.name == other.name def __ne__(self, other): return not (self == other)
[docs] def is_equivalent(self, other, equivalencies=[]): return self == other
[docs] def get_converter(self, other, equivalencies=[]): raise ValueError( "The unit {0!r} is unrecognized. It can not be converted " "to other units.".format(self.name))
[docs] def get_format_name(self, format): return self.name
class _UnitMetaClass(type): """ This metaclass exists because the Unit constructor should sometimes return instances that already exist. This "overrides" the constructor before the new instance is actually created, so we can return an existing one. """ def __call__(self, s, represents=None, format=None, register=False, doc=None, parse_strict='raise'): from .quantity import Quantity if isinstance(represents, Quantity): if represents.value == 1: represents = represents.unit elif isinstance(represents.unit, CompositeUnit): represents = CompositeUnit(represents.value, bases=represents.unit.bases, powers=represents.unit.powers) else: represents = CompositeUnit(represents.value, bases=[represents.unit], powers=[1]) if isinstance(s, Quantity): if s.value == 1: s = s.unit elif isinstance(s.unit, CompositeUnit): s = CompositeUnit(s.value * s.unit.scale, bases=s.unit.bases, powers=s.unit.powers) else: s = CompositeUnit(s.value, bases=[s.unit], powers=[1]) if isinstance(represents, UnitBase): # This has the effect of calling the real __new__ and # __init__ on the Unit class. return super(_UnitMetaClass, self).__call__( s, represents, format=format, register=register, doc=doc) raise TypeError("Can not convert {0!r} to a unit".format(s)) elif isinstance(s, UnitBase): return s elif isinstance(s, (bytes, unicode)): if len(s.strip()) == 0: # Return the NULL unit return CompositeUnit(1.0, [], []) if format is None: format = 'generic' f = unit_format.get_format(format) try: return f.parse(s) except ValueError as e: msg = "'{0}' did not parse as unit format '{1}': {2}".format( s, format, str(e)) if parse_strict == 'raise': raise ValueError(msg) elif parse_strict == 'warn': warnings.warn(msg, UnitsWarning) elif parse_strict != 'silent': raise ValueError( "'parse_strict' must be 'warn', 'raise' or 'silent'") return UnrecognizedUnit(s) elif isinstance(s, (int, float, np.floating, np.integer)): return CompositeUnit(s, [], []) elif s is None: raise TypeError("None is not a valid Unit") else: raise TypeError("{0} can not be converted to a Unit".format(s))
[docs]class Unit(NamedUnit): """ The main unit class. There are a number of different ways to construct a Unit, but always returns a `UnitBase` instance. If the arguments refer to an already-existing unit, that existing unit instance is returned, rather than a new one. - From a string:: Unit(s, format=None, parse_strict='silent') Construct from a string representing a (possibly compound) unit. The optional `format` keyword argument specifies the format the string is in, by default ``"generic"``. For a description of the available formats, see `astropy.units.format`. The optional `parse_strict` keyword controls what happens when an unrecognized unit string is passed in. It may be one of the following: - ``'raise'``: (default) raise a ValueError exception. - ``'warn'``: emit a Warning, and return an `UnrecognizedUnit` instance. - ``'silent'``: return an `UnrecognizedUnit` instance. - From a number:: Unit(number) Creates a dimensionless unit. - From a `UnitBase` instance:: Unit(unit) Returns the given unit unchanged. - From `None`:: Unit() Returns the null unit. - The last form, which creates a new `Unit` is described in detail below. Parameters ---------- st : str or list of str The name of the unit. If a list, the first element is the canonical (short) name, and the rest of the elements are aliases. represents : UnitBase instance The unit that this named unit represents. register : boolean, optional When `True`, also register the unit in the standard unit namespace. Default is `False`. doc : str, optional A docstring describing the unit. format : dict, optional A mapping to format-specific representations of this unit. For example, for the ``Ohm`` unit, it might be nice to have it displayed as ``\\Omega`` by the ``latex`` formatter. In that case, `format` argument should be set to:: {'latex': r'\\Omega'} Raises ------ ValueError If any of the given unit names are already in the registry. ValueError If any of the given unit names are not valid Python tokens. """ __metaclass__ = _UnitMetaClass def __init__(self, st, represents=None, register=False, doc=None, format=None): represents = Unit(represents) self._represents = represents NamedUnit.__init__(self, st, register=register, doc=doc, format=format)
[docs] def decompose(self, bases=set()): return self._represents.decompose(bases=bases)
decompose.__doc__ = UnitBase.decompose.__doc__
[docs]class PrefixUnit(Unit): """ A unit that is simply a SI-prefixed version of another unit. For example, `mm` is a `PrefixUnit` of ``.001 * m``. The constructor is the same as for `Unit`. """ pass
[docs]class CompositeUnit(UnitBase): """ Create a composite unit using expressions of previously defined units. Direct use of this class is not recommended. Instead use the factory function `Unit(...)` and arithmetic operators to compose units. Parameters ---------- scale : number A scaling factor for the unit. bases : sequence of `UnitBase` A sequence of units this unit is composed of. powers : sequence of numbers A sequence of powers (in parallel with `bases`) for each of the base units. """ def __init__(self, scale, bases, powers): if scale == 1.: scale = 1 self._scale = scale for base in bases: if not isinstance(base, UnitBase): raise TypeError("bases must be sequence of UnitBase instances") self._bases = bases self._powers = powers self._decomposed_cache = None def __repr__(self): if len(self._bases): return super(CompositeUnit, self).__repr__() else: if self._scale != 1.0: return 'Unit(dimensionless with a scale of {0})'.format( self._scale) else: return 'Unit(dimensionless)' def __hash__(self): parts = zip((hash(x) for x in self._bases), self._powers) parts.sort() return hash(tuple([self._scale] + parts)) @property
[docs] def scale(self): """ Return the scale of the composite unit. """ return self._scale
@property
[docs] def bases(self): """ Return the bases of the composite unit. """ return self._bases
@property
[docs] def powers(self): """ Return the powers of the composite unit. """ return self._powers
def _expand_and_gather(self, decompose=False, bases=set()): def add_unit(unit, power, scale): if len(bases) and unit not in bases: for base in bases: if unit.is_equivalent(base): scale *= unit.to(base) ** power unit = base break if unit in new_parts: new_parts[unit] += power else: new_parts[unit] = power return scale new_parts = {} scale = self.scale for b, p in zip(self.bases, self.powers): if decompose and (not len(bases) or b not in bases): b = b.decompose(bases=bases) if isinstance(b, CompositeUnit): scale *= b._scale ** p for b_sub, p_sub in zip(b._bases, b._powers): scale = add_unit(b_sub, p_sub * p, scale) else: scale = add_unit(b, p, scale) new_parts = [x for x in new_parts.items() if x[1] != 0] new_parts.sort(key=lambda x: x[1], reverse=True) self._bases = [x[0] for x in new_parts] self._powers = [x[1] for x in new_parts] self._scale = scale def __copy__(self): """ For compatibility with python copy module. """ return CompositeUnit(self._scale, self._bases[:], self._powers[:]) def _simplify(self): self._expand_and_gather() return self _simplify.__doc__ = UnitBase._simplify.__doc__
[docs] def decompose(self, bases=set()): if len(bases) == 0 and self._decomposed_cache is not None: return self._decomposed_cache for base in self.bases: if (not isinstance(base, IrreducibleUnit) or (len(bases) and base not in bases)): break else: if len(bases) == 0: self._decomposed_cache = self return self x = CompositeUnit(self.scale, self.bases, self.powers) x._expand_and_gather(True, bases=bases) if len(bases) == 0: self._decomposed_cache = x return x
decompose.__doc__ = UnitBase.decompose.__doc__ def _dimensionless_constant(self): """ If this unit is dimensionless, return its scalar quantity. Direct use of this method is not recommended. It is generally better to use the `to` or `get_converter` methods instead. """ x = self.decompose() c = x.scale if len(x.bases): raise UnitsException( "'{0}' is not dimensionless".format(self.to_string())) return c
si_prefixes = [ (['Y'], ['yotta'], 1e24), (['Z'], ['zetta'], 1e21), (['E'], ['exa'], 1e18), (['P'], ['peta'], 1e15), (['T'], ['tera'], 1e12), (['G'], ['giga'], 1e9), (['M'], ['mega'], 1e6), (['k'], ['kilo'], 1e3), (['h'], ['hecto'], 1e2), (['da'], ['deka', 'deca'], 1e1), (['d'], ['deci'], 1e-1), (['c'], ['centi'], 1e-2), (['m'], ['milli'], 1e-3), (['u'], ['micro'], 1e-6), (['n'], ['nano'], 1e-9), (['p'], ['pico'], 1e-12), (['f'], ['femto'], 1e-15), (['a'], ['atto'], 1e-18), (['z'], ['zepto'], 1e-21), (['y'], ['yocto'], 1e-24) ] def _add_prefixes(u, excludes=[], register=False): """ Set up all of the standard metric prefixes for a unit. This function should not be used directly, but instead use the `prefixes` kwarg on `def_unit`. Parameters ---------- excludes : list of str, optional Any prefixes to exclude from creation to avoid namespace collisions. register : bool, optional When `True`, also register the unit in the standard unit namespace. Default is `False`. """ for short, long, factor in si_prefixes: names = [] format = {} for prefix in short: if prefix in excludes: continue for alias in [u.name] + [x for x in u.aliases if len(x) <= 2]: names.append(prefix + alias) # This is a hack to use Greek mu as a prefix # for some formatters. if prefix == 'u': format['latex'] = r'\mu ' + u.get_format_name('latex') format['unicode'] = 'μ' + u.get_format_name('unicode') for key, val in u._format.items(): format.setdefault(key, prefix + val) for prefix in long: if prefix in excludes: continue for alias in u.aliases: if len(alias) > 2: names.append(prefix + alias) if len(names): PrefixUnit(names, CompositeUnit(factor, [u], [1]), register=register, format=format)
[docs]def def_unit(s, represents=None, register=None, doc=None, format=None, prefixes=False, exclude_prefixes=[]): """ Factory function for defining new units. Parameters ---------- names : str or list of str The name of the unit. If a list, the first element is the canonical (short) name, and the rest of the elements are aliases. represents : UnitBase instance, optional The unit that this named unit represents. If not provided, a new `IrreducibleUnit` is created. register : boolean, optional When `True`, also register the unit in the standard unit namespace. Default is `False`. doc : str, optional A docstring describing the unit. format : dict, optional A mapping to format-specific representations of this unit. For example, for the ``Ohm`` unit, it might be nice to have it displayed as ``\\Omega`` by the ``latex`` formatter. In that case, `format` argument should be set to:: {'latex': r'\\Omega'} prefixes : bool, optional When `True`, generate all of the SI prefixed versions of the unit as well. For example, for a given unit `m`, will generate `mm`, `cm`, `km`, etc. Default is `False`. This function always returns the base unit object, even if multiple scaled versions of the unit were created. exclude_prefixes : list of str, optional If any of the SI prefixes need to be excluded, they may be listed here. For example, `Pa` can be interpreted either as "petaannum" or "Pascal". Therefore, when defining the prefixes for `a`, `exclude_prefixes` should be set to ``["P"]``. Returns ------- unit : `UnitBase` object The newly-defined unit, or a matching unit that was already defined. """ if register is None: register = False if represents is not None: result = Unit(s, represents, register=register, doc=doc, format=format) else: result = IrreducibleUnit(s, register=register, doc=doc, format=format) if prefixes: _add_prefixes(result, excludes=exclude_prefixes, register=register) return result
def _condition_arg(value): """ Validate value is acceptable for conversion purposes. Will convert into an array if not a scalar, and can be converted into an array Parameters ---------- value: int or float value, or sequence of such values Returns ------- Scalar value or numpy array Raises ------ ValueError If value is not as expected """ if isinstance(value, (float, int, long)): return value else: try: avalue = np.array(value) if not avalue.dtype.kind in ['i', 'f']: raise ValueError("Must be convertable to int or float array") if ma.isMaskedArray(value): return value return avalue except ValueError: raise ValueError( "Value not scalar compatible or convertable into a float or " "integer array")

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