# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Core units classes and functions
"""
import inspect
import operator
import textwrap
import warnings
import numpy as np
from astropy.utils.decorators import lazyproperty
from astropy.utils.exceptions import AstropyWarning
from astropy.utils.misc import isiterable
from .utils import (is_effectively_unity, sanitize_scale, validate_power,
resolve_fractions)
from . import format as unit_format
__all__ = [
'UnitsError', 'UnitsWarning', 'UnitConversionError', 'UnitTypeError',
'UnitBase', 'NamedUnit', 'IrreducibleUnit', 'Unit', 'CompositeUnit',
'PrefixUnit', 'UnrecognizedUnit', 'def_unit', 'get_current_unit_registry',
'set_enabled_units', 'add_enabled_units',
'set_enabled_equivalencies', 'add_enabled_equivalencies',
'set_enabled_aliases', 'add_enabled_aliases',
'dimensionless_unscaled', 'one',
]
UNITY = 1.0
def _flatten_units_collection(items):
"""
Given a list of sequences, modules or dictionaries of units, or
single units, return a flat set of all the units found.
"""
if not isinstance(items, list):
items = [items]
result = set()
for item in items:
if isinstance(item, UnitBase):
result.add(item)
else:
if isinstance(item, dict):
units = item.values()
elif inspect.ismodule(item):
units = vars(item).values()
elif isiterable(item):
units = item
else:
continue
for unit in units:
if isinstance(unit, UnitBase):
result.add(unit)
return result
def _normalize_equivalencies(equivalencies):
"""
Normalizes equivalencies, ensuring each is a 4-tuple of the form::
(from_unit, to_unit, forward_func, backward_func)
Parameters
----------
equivalencies : list of equivalency pairs
Raises
------
ValueError if an equivalency cannot be interpreted
"""
if equivalencies is None:
return []
normalized = []
for i, equiv in enumerate(equivalencies):
if len(equiv) == 2:
funit, tunit = equiv
a = b = lambda x: x
elif len(equiv) == 3:
funit, tunit, a = equiv
b = a
elif len(equiv) == 4:
funit, tunit, a, b = equiv
else:
raise ValueError(
f"Invalid equivalence entry {i}: {equiv!r}")
if not (funit is Unit(funit) and
(tunit is None or tunit is Unit(tunit)) and
callable(a) and
callable(b)):
raise ValueError(
f"Invalid equivalence entry {i}: {equiv!r}")
normalized.append((funit, tunit, a, b))
return normalized
class _UnitRegistry:
"""
Manages a registry of the enabled units.
"""
def __init__(self, init=[], equivalencies=[], aliases={}):
if isinstance(init, _UnitRegistry):
# If passed another registry we don't need to rebuild everything.
# but because these are mutable types we don't want to create
# conflicts so everything needs to be copied.
self._equivalencies = init._equivalencies.copy()
self._aliases = init._aliases.copy()
self._all_units = init._all_units.copy()
self._registry = init._registry.copy()
self._non_prefix_units = init._non_prefix_units.copy()
# The physical type is a dictionary containing sets as values.
# All of these must be copied otherwise we could alter the old
# registry.
self._by_physical_type = {k: v.copy() for k, v in
init._by_physical_type.items()}
else:
self._reset_units()
self._reset_equivalencies()
self._reset_aliases()
self.add_enabled_units(init)
self.add_enabled_equivalencies(equivalencies)
self.add_enabled_aliases(aliases)
def _reset_units(self):
self._all_units = set()
self._non_prefix_units = set()
self._registry = {}
self._by_physical_type = {}
def _reset_equivalencies(self):
self._equivalencies = set()
def _reset_aliases(self):
self._aliases = {}
@property
def registry(self):
return self._registry
@property
def all_units(self):
return self._all_units
@property
def non_prefix_units(self):
return self._non_prefix_units
def set_enabled_units(self, units):
"""
Sets the units enabled in the unit registry.
These units are searched when using
`UnitBase.find_equivalent_units`, for example.
Parameters
----------
units : list of sequence, dict, or module
This is a list of things in which units may be found
(sequences, dicts or modules), or units themselves. The
entire set will be "enabled" for searching through by
methods like `UnitBase.find_equivalent_units` and
`UnitBase.compose`.
"""
self._reset_units()
return self.add_enabled_units(units)
def add_enabled_units(self, units):
"""
Adds to the set of units enabled in the unit registry.
These units are searched when using
`UnitBase.find_equivalent_units`, for example.
Parameters
----------
units : list of sequence, dict, or module
This is a list of things in which units may be found
(sequences, dicts or modules), or units themselves. The
entire set will be added to the "enabled" set for
searching through by methods like
`UnitBase.find_equivalent_units` and `UnitBase.compose`.
"""
units = _flatten_units_collection(units)
for unit in units:
# Loop through all of the names first, to ensure all of them
# are new, then add them all as a single "transaction" below.
for st in unit._names:
if (st in self._registry and unit != self._registry[st]):
raise ValueError(
"Object with name {!r} already exists in namespace. "
"Filter the set of units to avoid name clashes before "
"enabling them.".format(st))
for st in unit._names:
self._registry[st] = unit
self._all_units.add(unit)
if not isinstance(unit, PrefixUnit):
self._non_prefix_units.add(unit)
hash = unit._get_physical_type_id()
self._by_physical_type.setdefault(hash, set()).add(unit)
def get_units_with_physical_type(self, unit):
"""
Get all units in the registry with the same physical type as
the given unit.
Parameters
----------
unit : UnitBase instance
"""
return self._by_physical_type.get(unit._get_physical_type_id(), set())
@property
def equivalencies(self):
return list(self._equivalencies)
def set_enabled_equivalencies(self, equivalencies):
"""
Sets the equivalencies enabled in the unit registry.
These equivalencies are used if no explicit equivalencies are given,
both in unit conversion and in finding equivalent units.
This is meant in particular for allowing angles to be dimensionless.
Use with care.
Parameters
----------
equivalencies : list of tuple
List of equivalent pairs, e.g., as returned by
`~astropy.units.equivalencies.dimensionless_angles`.
"""
self._reset_equivalencies()
return self.add_enabled_equivalencies(equivalencies)
def add_enabled_equivalencies(self, equivalencies):
"""
Adds to the set of equivalencies enabled in the unit registry.
These equivalencies are used if no explicit equivalencies are given,
both in unit conversion and in finding equivalent units.
This is meant in particular for allowing angles to be dimensionless.
Use with care.
Parameters
----------
equivalencies : list of tuple
List of equivalent pairs, e.g., as returned by
`~astropy.units.equivalencies.dimensionless_angles`.
"""
# pre-normalize list to help catch mistakes
equivalencies = _normalize_equivalencies(equivalencies)
self._equivalencies |= set(equivalencies)
@property
def aliases(self):
return self._aliases
def set_enabled_aliases(self, aliases):
"""
Set aliases for units.
Parameters
----------
aliases : dict of str, Unit
The aliases to set. The keys must be the string aliases, and values
must be the `astropy.units.Unit` that the alias will be mapped to.
Raises
------
ValueError
If the alias already defines a different unit.
"""
self._reset_aliases()
self.add_enabled_aliases(aliases)
def add_enabled_aliases(self, aliases):
"""
Add aliases for units.
Parameters
----------
aliases : dict of str, Unit
The aliases to add. The keys must be the string aliases, and values
must be the `astropy.units.Unit` that the alias will be mapped to.
Raises
------
ValueError
If the alias already defines a different unit.
"""
for alias, unit in aliases.items():
if alias in self._registry and unit != self._registry[alias]:
raise ValueError(
f"{alias} already means {self._registry[alias]}, so "
f"cannot be used as an alias for {unit}.")
if alias in self._aliases and unit != self._aliases[alias]:
raise ValueError(
f"{alias} already is an alias for {self._aliases[alias]}, so "
f"cannot be used as an alias for {unit}.")
for alias, unit in aliases.items():
if alias not in self._registry and alias not in self._aliases:
self._aliases[alias] = unit
class _UnitContext:
def __init__(self, init=[], equivalencies=[]):
_unit_registries.append(
_UnitRegistry(init=init, equivalencies=equivalencies))
def __enter__(self):
pass
def __exit__(self, type, value, tb):
_unit_registries.pop()
_unit_registries = [_UnitRegistry()]
def get_current_unit_registry():
return _unit_registries[-1]
def set_enabled_units(units):
"""
Sets the units enabled in the unit registry.
These units are searched when using
`UnitBase.find_equivalent_units`, for example.
This may be used either permanently, or as a context manager using
the ``with`` statement (see example below).
Parameters
----------
units : list of sequence, dict, or module
This is a list of things in which units may be found
(sequences, dicts or modules), or units themselves. The
entire set will be "enabled" for searching through by methods
like `UnitBase.find_equivalent_units` and `UnitBase.compose`.
Examples
--------
>>> from astropy import units as u
>>> with u.set_enabled_units([u.pc]):
... u.m.find_equivalent_units()
...
Primary name | Unit definition | Aliases
[
pc | 3.08568e+16 m | parsec ,
]
>>> u.m.find_equivalent_units()
Primary name | Unit definition | Aliases
[
AU | 1.49598e+11 m | au, astronomical_unit ,
Angstrom | 1e-10 m | AA, angstrom ,
cm | 0.01 m | centimeter ,
earthRad | 6.3781e+06 m | R_earth, Rearth ,
jupiterRad | 7.1492e+07 m | R_jup, Rjup, R_jupiter, Rjupiter ,
lyr | 9.46073e+15 m | lightyear ,
m | irreducible | meter ,
micron | 1e-06 m | ,
pc | 3.08568e+16 m | parsec ,
solRad | 6.957e+08 m | R_sun, Rsun ,
]
"""
# get a context with a new registry, using equivalencies of the current one
context = _UnitContext(
equivalencies=get_current_unit_registry().equivalencies)
# in this new current registry, enable the units requested
get_current_unit_registry().set_enabled_units(units)
return context
def add_enabled_units(units):
"""
Adds to the set of units enabled in the unit registry.
These units are searched when using
`UnitBase.find_equivalent_units`, for example.
This may be used either permanently, or as a context manager using
the ``with`` statement (see example below).
Parameters
----------
units : list of sequence, dict, or module
This is a list of things in which units may be found
(sequences, dicts or modules), or units themselves. The
entire set will be added to the "enabled" set for searching
through by methods like `UnitBase.find_equivalent_units` and
`UnitBase.compose`.
Examples
--------
>>> from astropy import units as u
>>> from astropy.units import imperial
>>> with u.add_enabled_units(imperial):
... u.m.find_equivalent_units()
...
Primary name | Unit definition | Aliases
[
AU | 1.49598e+11 m | au, astronomical_unit ,
Angstrom | 1e-10 m | AA, angstrom ,
cm | 0.01 m | centimeter ,
earthRad | 6.3781e+06 m | R_earth, Rearth ,
ft | 0.3048 m | foot ,
fur | 201.168 m | furlong ,
inch | 0.0254 m | ,
jupiterRad | 7.1492e+07 m | R_jup, Rjup, R_jupiter, Rjupiter ,
lyr | 9.46073e+15 m | lightyear ,
m | irreducible | meter ,
mi | 1609.34 m | mile ,
micron | 1e-06 m | ,
mil | 2.54e-05 m | thou ,
nmi | 1852 m | nauticalmile, NM ,
pc | 3.08568e+16 m | parsec ,
solRad | 6.957e+08 m | R_sun, Rsun ,
yd | 0.9144 m | yard ,
]
"""
# get a context with a new registry, which is a copy of the current one
context = _UnitContext(get_current_unit_registry())
# in this new current registry, enable the further units requested
get_current_unit_registry().add_enabled_units(units)
return context
def set_enabled_equivalencies(equivalencies):
"""
Sets the equivalencies enabled in the unit registry.
These equivalencies are used if no explicit equivalencies are given,
both in unit conversion and in finding equivalent units.
This is meant in particular for allowing angles to be dimensionless.
Use with care.
Parameters
----------
equivalencies : list of tuple
list of equivalent pairs, e.g., as returned by
`~astropy.units.equivalencies.dimensionless_angles`.
Examples
--------
Exponentiation normally requires dimensionless quantities. To avoid
problems with complex phases::
>>> from astropy import units as u
>>> with u.set_enabled_equivalencies(u.dimensionless_angles()):
... phase = 0.5 * u.cycle
... np.exp(1j*phase) # doctest: +FLOAT_CMP
<Quantity -1.+1.2246468e-16j>
"""
# get a context with a new registry, using all units of the current one
context = _UnitContext(get_current_unit_registry())
# in this new current registry, enable the equivalencies requested
get_current_unit_registry().set_enabled_equivalencies(equivalencies)
return context
def add_enabled_equivalencies(equivalencies):
"""
Adds to the equivalencies enabled in the unit registry.
These equivalencies are used if no explicit equivalencies are given,
both in unit conversion and in finding equivalent units.
This is meant in particular for allowing angles to be dimensionless.
Since no equivalencies are enabled by default, generally it is recommended
to use `set_enabled_equivalencies`.
Parameters
----------
equivalencies : list of tuple
list of equivalent pairs, e.g., as returned by
`~astropy.units.equivalencies.dimensionless_angles`.
"""
# get a context with a new registry, which is a copy of the current one
context = _UnitContext(get_current_unit_registry())
# in this new current registry, enable the further equivalencies requested
get_current_unit_registry().add_enabled_equivalencies(equivalencies)
return context
def set_enabled_aliases(aliases):
"""
Set aliases for units.
This is useful for handling alternate spellings for units, or
misspelled units in files one is trying to read.
Parameters
----------
aliases : dict of str, Unit
The aliases to set. The keys must be the string aliases, and values
must be the `astropy.units.Unit` that the alias will be mapped to.
Raises
------
ValueError
If the alias already defines a different unit.
Examples
--------
To temporarily allow for a misspelled 'Angstroem' unit::
>>> from astropy import units as u
>>> with u.set_enabled_aliases({'Angstroem': u.Angstrom}):
... print(u.Unit("Angstroem", parse_strict="raise") == u.Angstrom)
True
"""
# get a context with a new registry, which is a copy of the current one
context = _UnitContext(get_current_unit_registry())
# in this new current registry, enable the further equivalencies requested
get_current_unit_registry().set_enabled_aliases(aliases)
return context
def add_enabled_aliases(aliases):
"""
Add aliases for units.
This is useful for handling alternate spellings for units, or
misspelled units in files one is trying to read.
Since no aliases are enabled by default, generally it is recommended
to use `set_enabled_aliases`.
Parameters
----------
aliases : dict of str, Unit
The aliases to add. The keys must be the string aliases, and values
must be the `astropy.units.Unit` that the alias will be mapped to.
Raises
------
ValueError
If the alias already defines a different unit.
Examples
--------
To temporarily allow for a misspelled 'Angstroem' unit::
>>> from astropy import units as u
>>> with u.add_enabled_aliases({'Angstroem': u.Angstrom}):
... print(u.Unit("Angstroem", parse_strict="raise") == u.Angstrom)
True
"""
# get a context with a new registry, which is a copy of the current one
context = _UnitContext(get_current_unit_registry())
# in this new current registry, enable the further equivalencies requested
get_current_unit_registry().add_enabled_aliases(aliases)
return context
class UnitsError(Exception):
"""
The base class for unit-specific exceptions.
"""
class UnitScaleError(UnitsError, ValueError):
"""
Used to catch the errors involving scaled units,
which are not recognized by FITS format.
"""
pass
class UnitConversionError(UnitsError, ValueError):
"""
Used specifically for errors related to converting between units or
interpreting units in terms of other units.
"""
class UnitTypeError(UnitsError, TypeError):
"""
Used specifically for errors in setting to units not allowed by a class.
E.g., would be raised if the unit of an `~astropy.coordinates.Angle`
instances were set to a non-angular unit.
"""
class UnitsWarning(AstropyWarning):
"""
The base class for unit-specific warnings.
"""
class UnitBase:
"""
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.
"""
# Make sure that __rmul__ of units gets called over the __mul__ of Numpy
# arrays to avoid element-wise multiplication.
__array_priority__ = 1000
_hash = None
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 __bytes__(self):
"""Return string representation for unit"""
return unit_format.Generic.to_string(self).encode('unicode_escape')
def __str__(self):
"""Return string representation for unit"""
return unit_format.Generic.to_string(self)
def __repr__(self):
string = unit_format.Generic.to_string(self)
return f'Unit("{string}")'
def _get_physical_type_id(self):
"""
Returns an identifier that uniquely identifies the physical
type of this unit. It is comprised of the bases and powers of
this unit, without the scale. Since it is hashable, it is
useful as a dictionary key.
"""
unit = self.decompose()
r = zip([x.name for x in unit.bases], unit.powers)
# bases and powers are already sorted in a unique way
# r.sort()
r = tuple(r)
return r
@property
def names(self):
"""
Returns all of the names associated with this unit.
"""
raise AttributeError(
"Can not get names from unnamed units. "
"Perhaps you meant to_string()?")
@property
def name(self):
"""
Returns the canonical (short) name associated with this unit.
"""
raise AttributeError(
"Can not get names from unnamed units. "
"Perhaps you meant to_string()?")
@property
def aliases(self):
"""
Returns the alias (long) names for this unit.
"""
raise AttributeError(
"Can not get aliases from unnamed units. "
"Perhaps you meant to_string()?")
@property
def scale(self):
"""
Return the scale of the unit.
"""
return 1.0
@property
def bases(self):
"""
Return the bases of the unit.
"""
return [self]
@property
def powers(self):
"""
Return the powers of the unit.
"""
return [1]
def to_string(self, format=unit_format.Generic):
"""
Output the unit in the given format as a string.
Parameters
----------
format : `astropy.units.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)
def __format__(self, format_spec):
"""Try to format units using a formatter."""
try:
return self.to_string(format=format_spec)
except ValueError:
return format(str(self), format_spec)
@staticmethod
def _normalize_equivalencies(equivalencies):
"""
Normalizes equivalencies, ensuring each is a 4-tuple of the form::
(from_unit, to_unit, forward_func, backward_func)
Parameters
----------
equivalencies : list of equivalency pairs, or None
Returns
-------
A normalized list, including possible global defaults set by, e.g.,
`set_enabled_equivalencies`, except when `equivalencies`=`None`,
in which case the returned list is always empty.
Raises
------
ValueError if an equivalency cannot be interpreted
"""
normalized = _normalize_equivalencies(equivalencies)
if equivalencies is not None:
normalized += get_current_unit_registry().equivalencies
return normalized
def __pow__(self, p):
p = validate_power(p)
return CompositeUnit(1, [self], [p], _error_check=False)
def __div__(self, m):
if isinstance(m, (bytes, str)):
m = Unit(m)
if isinstance(m, UnitBase):
if m.is_unity():
return self
return CompositeUnit(1, [self, m], [1, -1], _error_check=False)
try:
# Cannot handle this as Unit, re-try as Quantity
from .quantity import Quantity
return Quantity(1, self) / m
except TypeError:
return NotImplemented
def __rdiv__(self, m):
if isinstance(m, (bytes, str)):
return Unit(m) / self
try:
# Cannot handle this as Unit. Here, m cannot be a Quantity,
# so we make it into one, fasttracking when it does not have a
# unit, for the common case of <array> / <unit>.
from .quantity import Quantity
if hasattr(m, 'unit'):
result = Quantity(m)
result /= self
return result
else:
return Quantity(m, self**(-1))
except TypeError:
return NotImplemented
__truediv__ = __div__
__rtruediv__ = __rdiv__
def __mul__(self, m):
if isinstance(m, (bytes, str)):
m = Unit(m)
if isinstance(m, UnitBase):
if m.is_unity():
return self
elif self.is_unity():
return m
return CompositeUnit(1, [self, m], [1, 1], _error_check=False)
# Cannot handle this as Unit, re-try as Quantity.
try:
from .quantity import Quantity
return Quantity(1, self) * m
except TypeError:
return NotImplemented
def __rmul__(self, m):
if isinstance(m, (bytes, str)):
return Unit(m) * self
# Cannot handle this as Unit. Here, m cannot be a Quantity,
# so we make it into one, fasttracking when it does not have a unit
# for the common case of <array> * <unit>.
try:
from .quantity import Quantity
if hasattr(m, 'unit'):
result = Quantity(m)
result *= self
return result
else:
return Quantity(m, self)
except TypeError:
return NotImplemented
def __rlshift__(self, m):
try:
from .quantity import Quantity
return Quantity(m, self, copy=False, subok=True)
except Exception:
return NotImplemented
def __rrshift__(self, m):
warnings.warn(">> is not implemented. Did you mean to convert "
"to a Quantity with unit {} using '<<'?".format(self),
AstropyWarning)
return NotImplemented
def __hash__(self):
if self._hash is None:
parts = ([str(self.scale)] +
[x.name for x in self.bases] +
[str(x) for x in self.powers])
self._hash = hash(tuple(parts))
return self._hash
def __getstate__(self):
# If we get pickled, we should *not* store the memoized hash since
# hashes of strings vary between sessions.
state = self.__dict__.copy()
state.pop('_hash', None)
return state
def __eq__(self, other):
if self is other:
return True
try:
other = Unit(other, parse_strict='silent')
except (ValueError, UnitsError, TypeError):
return NotImplemented
# Other is unit-like, but the test below requires it is a UnitBase
# instance; if it is not, give up (so that other can try).
if not isinstance(other, UnitBase):
return NotImplemented
try:
return is_effectively_unity(self._to(other))
except UnitsError:
return False
def __ne__(self, other):
return not (self == other)
def __le__(self, other):
scale = self._to(Unit(other))
return scale <= 1. or is_effectively_unity(scale)
def __ge__(self, other):
scale = self._to(Unit(other))
return scale >= 1. or is_effectively_unity(scale)
def __lt__(self, other):
return not (self >= other)
def __gt__(self, other):
return not (self <= other)
def __neg__(self):
return self * -1.
def is_equivalent(self, other, equivalencies=[]):
"""
Returns `True` if this unit is equivalent to ``other``.
Parameters
----------
other : `~astropy.units.Unit`, str, or tuple
The unit to convert to. If a tuple of units is specified, this
method returns true if the unit matches any of those in the tuple.
equivalencies : list of tuple
A list of equivalence pairs to try if the units are not
directly convertible. See :ref:`unit_equivalencies`.
This list is in addition to possible global defaults set by, e.g.,
`set_enabled_equivalencies`.
Use `None` to turn off all equivalencies.
Returns
-------
bool
"""
equivalencies = self._normalize_equivalencies(equivalencies)
if isinstance(other, tuple):
return any(self.is_equivalent(u, equivalencies=equivalencies)
for u in other)
other = Unit(other, parse_strict='silent')
return self._is_equivalent(other, equivalencies)
def _is_equivalent(self, other, equivalencies=[]):
"""Returns `True` if this unit is equivalent to `other`.
See `is_equivalent`, except that a proper Unit object should be
given (i.e., no string) and that the equivalency list should be
normalized using `_normalize_equivalencies`.
"""
if isinstance(other, UnrecognizedUnit):
return False
if (self._get_physical_type_id() ==
other._get_physical_type_id()):
return True
elif len(equivalencies):
unit = self.decompose()
other = other.decompose()
for a, b, forward, backward in equivalencies:
if b is None:
# after canceling, is what's left convertible
# to dimensionless (according to the equivalency)?
try:
(other/unit).decompose([a])
return True
except Exception:
pass
else:
if(a._is_equivalent(unit) and b._is_equivalent(other) or
b._is_equivalent(unit) and a._is_equivalent(other)):
return True
return False
def _apply_equivalencies(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
for funit, tunit, a, b in equivalencies:
if tunit is None:
try:
ratio_in_funit = (other.decompose() /
unit.decompose()).decompose([funit])
return make_converter(ratio_in_funit.scale, a, 1.)
except UnitsError:
pass
else:
try:
scale1 = funit._to(unit)
scale2 = tunit._to(other)
return make_converter(scale1, a, scale2)
except UnitsError:
pass
try:
scale1 = tunit._to(unit)
scale2 = funit._to(other)
return make_converter(scale1, b, scale2)
except UnitsError:
pass
def get_err_str(unit):
unit_str = unit.to_string('unscaled')
physical_type = unit.physical_type
if physical_type != 'unknown':
unit_str = f"'{unit_str}' ({physical_type})"
else:
unit_str = f"'{unit_str}'"
return unit_str
unit_str = get_err_str(unit)
other_str = get_err_str(other)
raise UnitConversionError(
f"{unit_str} and {other_str} are not convertible")
def _get_converter(self, other, equivalencies=[]):
"""Get a converter for values in ``self`` to ``other``.
If no conversion is necessary, returns ``unit_scale_converter``
(which is used as a check in quantity helpers).
"""
# First see if it is just a scaling.
try:
scale = self._to(other)
except UnitsError:
pass
else:
if scale == 1.:
return unit_scale_converter
else:
return lambda val: scale * _condition_arg(val)
# if that doesn't work, maybe we can do it with equivalencies?
try:
return self._apply_equivalencies(
self, other, self._normalize_equivalencies(equivalencies))
except UnitsError as exc:
# Last hope: maybe other knows how to do it?
# We assume the equivalencies have the unit itself as first item.
# TODO: maybe better for other to have a `_back_converter` method?
if hasattr(other, 'equivalencies'):
for funit, tunit, a, b in other.equivalencies:
if other is funit:
try:
return lambda v: b(self._get_converter(
tunit, equivalencies=equivalencies)(v))
except Exception:
pass
raise exc
def _to(self, other):
"""
Returns the scale to the specified unit.
See `to`, except that a Unit object should be given (i.e., no
string), and that all defaults are used, i.e., no
equivalencies and value=1.
"""
# There are many cases where we just want to ensure a Quantity is
# of a particular unit, without checking whether it's already in
# a particular unit. If we're being asked to convert from a unit
# to itself, we can short-circuit all of this.
if self is other:
return 1.0
# Don't presume decomposition is possible; e.g.,
# conversion to function units is through equivalencies.
if isinstance(other, UnitBase):
self_decomposed = self.decompose()
other_decomposed = other.decompose()
# Check quickly whether equivalent. This is faster than
# `is_equivalent`, because it doesn't generate the entire
# physical type list of both units. In other words it "fails
# fast".
if(self_decomposed.powers == other_decomposed.powers and
all(self_base is other_base for (self_base, other_base)
in zip(self_decomposed.bases, other_decomposed.bases))):
return self_decomposed.scale / other_decomposed.scale
raise UnitConversionError(
f"'{self!r}' is not a scaled version of '{other!r}'")
def to(self, other, value=UNITY, equivalencies=[]):
"""
Return the converted values in the specified unit.
Parameters
----------
other : unit-like
The unit to convert to.
value : int, float, or scalar array-like, optional
Value(s) in the current unit to be converted to the
specified unit. If not provided, defaults to 1.0
equivalencies : list of tuple
A list of equivalence pairs to try if the units are not
directly convertible. See :ref:`unit_equivalencies`.
This list is in addition to possible global defaults set by, e.g.,
`set_enabled_equivalencies`.
Use `None` to turn off all equivalencies.
Returns
-------
values : scalar or array
Converted value(s). Input value sequences are returned as
numpy arrays.
Raises
------
UnitsError
If units are inconsistent
"""
if other is self and value is UNITY:
return UNITY
else:
return self._get_converter(Unit(other),
equivalencies=equivalencies)(value)
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)
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 `UnitsError` if it's not possible
to do so.
Returns
-------
unit : `~astropy.units.CompositeUnit`
New object containing only irreducible unit objects.
"""
raise NotImplementedError()
def _compose(self, equivalencies=[], namespace=[], max_depth=2, depth=0,
cached_results=None):
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
unit = self.decompose()
key = hash(unit)
cached = cached_results.get(key)
if cached is not None:
if isinstance(cached, Exception):
raise cached
return cached
# Prevent too many levels of recursion
# And special case for dimensionless unit
if depth >= max_depth:
cached_results[key] = [unit]
return [unit]
# Make a list including all of the equivalent units
units = [unit]
for funit, tunit, a, b in equivalencies:
if tunit is not None:
if self._is_equivalent(funit):
scale = funit.decompose().scale / unit.scale
units.append(Unit(a(1.0 / scale) * tunit).decompose())
elif self._is_equivalent(tunit):
scale = tunit.decompose().scale / unit.scale
units.append(Unit(b(1.0 / scale) * funit).decompose())
else:
if self._is_equivalent(funit):
units.append(Unit(unit.scale))
# Store partial results
partial_results = []
# Store final results that reduce to a single unit or pair of
# units
if len(unit.bases) == 0:
final_results = [set([unit]), set()]
else:
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):
results = final_results[0].union(final_results[1])
cached_results[key] = results
return results
partial_results.sort(key=operator.itemgetter(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,
cached_results=cached_results)
except UnitsError:
composed_list = []
for subcomposed in composed_list:
results.append(
(len(subcomposed.bases), subcomposed, tunit))
if len(results):
results.sort(key=operator.itemgetter(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(factored)
if len(subresults):
cached_results[key] = subresults
return subresults
if not is_final_result(self):
result = UnitsError(
f"Cannot represent unit {self} in terms of the given units")
cached_results[key] = result
raise result
cached_results[key] = [self]
return [self]
def compose(self, equivalencies=[], units=None, max_depth=2,
include_prefix_units=None):
"""
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 tuple
A list of equivalence pairs to also list. See
:ref:`unit_equivalencies`.
This list is in addition to possible global defaults set by, e.g.,
`set_enabled_equivalencies`.
Use `None` to turn off all equivalencies.
units : set of `~astropy.units.Unit`, 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 `True` if a sequence is passed in to ``units``,
`False` otherwise.
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.
"""
# if units parameter is specified and is a sequence (list|tuple),
# include_prefix_units is turned on by default. Ex: units=[u.kpc]
if include_prefix_units is None:
include_prefix_units = isinstance(units, (list, tuple))
# Pre-normalize the equivalencies list
equivalencies = self._normalize_equivalencies(equivalencies)
# The namespace of units to compose into should be filtered to
# only include units with bases in common with self, otherwise
# they can't possibly provide useful results. Having too many
# destination units greatly increases the search space.
def has_bases_in_common(a, b):
if len(a.bases) == 0 and len(b.bases) == 0:
return True
for ab in a.bases:
for bb in b.bases:
if ab == bb:
return True
return False
def has_bases_in_common_with_equiv(unit, other):
if has_bases_in_common(unit, other):
return True
for funit, tunit, a, b in equivalencies:
if tunit is not None:
if unit._is_equivalent(funit):
if has_bases_in_common(tunit.decompose(), other):
return True
elif unit._is_equivalent(tunit):
if has_bases_in_common(funit.decompose(), other):
return True
else:
if unit._is_equivalent(funit):
if has_bases_in_common(dimensionless_unscaled, other):
return True
return False
def filter_units(units):
filtered_namespace = set()
for tunit in units:
if (isinstance(tunit, UnitBase) and
(include_prefix_units or
not isinstance(tunit, PrefixUnit)) and
has_bases_in_common_with_equiv(
decomposed, tunit.decompose())):
filtered_namespace.add(tunit)
return filtered_namespace
decomposed = self.decompose()
if units is None:
units = filter_units(self._get_units_with_same_physical_type(
equivalencies=equivalencies))
if len(units) == 0:
units = get_current_unit_registry().non_prefix_units
elif isinstance(units, dict):
units = set(filter_units(units.values()))
elif inspect.ismodule(units):
units = filter_units(vars(units).values())
else:
units = filter_units(_flatten_units_collection(units))
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: np.abs(x.scale))
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 is_effectively_unity(x.scale))
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
return sort_results(self._compose(
equivalencies=equivalencies, namespace=units,
max_depth=max_depth, depth=0, cached_results={}))
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:
compose_bases = compose.bases
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
@lazyproperty
def si(self):
"""
Returns a copy of the current `Unit` instance in SI units.
"""
from . import si
return self.to_system(si)[0]
@lazyproperty
def cgs(self):
"""
Returns a copy of the current `Unit` instance with CGS units.
"""
from . import cgs
return self.to_system(cgs)[0]
@property
def physical_type(self):
"""
Physical type(s) dimensionally compatible with the unit.
Returns
-------
`~astropy.units.physical.PhysicalType`
A representation of the physical type(s) of a unit.
Examples
--------
>>> from astropy import units as u
>>> u.m.physical_type
PhysicalType('length')
>>> (u.m ** 2 / u.s).physical_type
PhysicalType({'diffusivity', 'kinematic viscosity'})
Physical types can be compared to other physical types
(recommended in packages) or to strings.
>>> area = (u.m ** 2).physical_type
>>> area == u.m.physical_type ** 2
True
>>> area == "area"
True
`~astropy.units.physical.PhysicalType` objects can be used for
dimensional analysis.
>>> number_density = u.m.physical_type ** -3
>>> velocity = (u.m / u.s).physical_type
>>> number_density * velocity
PhysicalType('particle flux')
"""
from . import physical
return physical.get_physical_type(self)
def _get_units_with_same_physical_type(self, equivalencies=[]):
"""
Return a list of registered units with the same physical type
as this unit.
This function is used by Quantity to add its built-in
conversions to equivalent units.
This is a private method, since end users should be encouraged
to use the more powerful `compose` and `find_equivalent_units`
methods (which use this under the hood).
Parameters
----------
equivalencies : list of tuple
A list of equivalence pairs to also pull options from.
See :ref:`unit_equivalencies`. It must already be
normalized using `_normalize_equivalencies`.
"""
unit_registry = get_current_unit_registry()
units = set(unit_registry.get_units_with_physical_type(self))
for funit, tunit, a, b in equivalencies:
if tunit is not None:
if self.is_equivalent(funit) and tunit not in units:
units.update(
unit_registry.get_units_with_physical_type(tunit))
if self._is_equivalent(tunit) and funit not in units:
units.update(
unit_registry.get_units_with_physical_type(funit))
else:
if self.is_equivalent(funit):
units.add(dimensionless_unscaled)
return units
class EquivalentUnitsList(list):
"""
A class to handle pretty-printing the result of
`find_equivalent_units`.
"""
HEADING_NAMES = ('Primary name', 'Unit definition', 'Aliases')
ROW_LEN = 3 # len(HEADING_NAMES), but hard-code since it is constant
NO_EQUIV_UNITS_MSG = 'There are no equivalent units'
def __repr__(self):
if len(self) == 0:
return self.NO_EQUIV_UNITS_MSG
else:
lines = self._process_equivalent_units(self)
lines.insert(0, self.HEADING_NAMES)
widths = [0] * self.ROW_LEN
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] +
['['] +
[f'{x} ,' for x in lines[1:]] +
[']'])
return '\n'.join(lines)
def _repr_html_(self):
"""
Outputs a HTML table representation within Jupyter notebooks.
"""
if len(self) == 0:
return f"<p>{self.NO_EQUIV_UNITS_MSG}</p>"
else:
# HTML tags to use to compose the table in HTML
blank_table = '<table style="width:50%">{}</table>'
blank_row_container = "<tr>{}</tr>"
heading_row_content = "<th>{}</th>" * self.ROW_LEN
data_row_content = "<td>{}</td>" * self.ROW_LEN
# The HTML will be rendered & the table is simple, so don't
# bother to include newlines & indentation for the HTML code.
heading_row = blank_row_container.format(
heading_row_content.format(*self.HEADING_NAMES))
data_rows = self._process_equivalent_units(self)
all_rows = heading_row
for row in data_rows:
html_row = blank_row_container.format(
data_row_content.format(*row))
all_rows += html_row
return blank_table.format(all_rows)
@staticmethod
def _process_equivalent_units(equiv_units_data):
"""
Extract attributes, and sort, the equivalent units pre-formatting.
"""
processed_equiv_units = []
for u in equiv_units_data:
irred = u.decompose().to_string()
if irred == u.name:
irred = 'irreducible'
processed_equiv_units.append(
(u.name, irred, ', '.join(u.aliases)))
processed_equiv_units.sort()
return processed_equiv_units
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 ``self``.
Parameters
----------
equivalencies : list of tuple
A list of equivalence pairs to also list. See
:ref:`unit_equivalencies`.
Any list given, including an empty one, supersedes global defaults
that may be in effect (as set by `set_enabled_equivalencies`)
units : set of `~astropy.units.Unit`, 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 = set(
x.bases[0] for x in results if len(x.bases) == 1)
return self.EquivalentUnitsList(results)
def is_unity(self):
"""
Returns `True` if the unit is unscaled and dimensionless.
"""
return False
class NamedUnit(UnitBase):
"""
The base class of units that have a name.
Parameters
----------
st : str, list of str, 2-tuple
The name of the unit. If a list of strings, the first element
is the canonical (short) name, and the rest of the elements
are aliases. If a tuple of lists, the first element is a list
of short names, and the second element is a list of long
names; all but the first short name are considered "aliases".
Each name *should* be a valid Python identifier to make it
easy to access, but this is not required.
namespace : dict, optional
When provided, inject the unit, and all of its aliases, in the
given namespace dictionary. If a unit by the same name is
already in the namespace, a ValueError is raised.
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, doc=None, format=None, namespace=None):
UnitBase.__init__(self)
if isinstance(st, (bytes, str)):
self._names = [st]
self._short_names = [st]
self._long_names = []
elif isinstance(st, tuple):
if not len(st) == 2:
raise ValueError("st must be string, list or 2-tuple")
self._names = st[0] + [n for n in st[1] if n not in st[0]]
if not len(self._names):
raise ValueError("must provide at least one name")
self._short_names = st[0][:]
self._long_names = st[1][:]
else:
if len(st) == 0:
raise ValueError(
"st list must have at least one entry")
self._names = st[:]
self._short_names = [st[0]]
self._long_names = st[1:]
if format is None:
format = {}
self._format = format
if doc is None:
doc = self._generate_doc()
else:
doc = textwrap.dedent(doc)
doc = textwrap.fill(doc)
self.__doc__ = doc
self._inject(namespace)
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]
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
def names(self):
"""
Returns all of the names associated with this unit.
"""
return self._names
@property
def name(self):
"""
Returns the canonical (short) name associated with this unit.
"""
return self._names[0]
@property
def aliases(self):
"""
Returns the alias (long) names for this unit.
"""
return self._names[1:]
@property
def short_names(self):
"""
Returns all of the short names associated with this unit.
"""
return self._short_names
@property
def long_names(self):
"""
Returns all of the long names associated with this unit.
"""
return self._long_names
def _inject(self, namespace=None):
"""
Injects the unit, and all of its aliases, in the given
namespace dictionary.
"""
if namespace is None:
return
# Loop through all of the names first, to ensure all of them
# are new, then add them all as a single "transaction" below.
for name in self._names:
if name in namespace and self != namespace[name]:
raise ValueError(
"Object with name {!r} already exists in "
"given namespace ({!r}).".format(
name, namespace[name]))
for name in self._names:
namespace[name] = self
def _recreate_irreducible_unit(cls, names, registered):
"""
This is used to reconstruct units when passed around by
multiprocessing.
"""
registry = get_current_unit_registry().registry
if names[0] in registry:
# If in local registry return that object.
return registry[names[0]]
else:
# otherwise, recreate the unit.
unit = cls(names)
if registered:
# If not in local registry but registered in origin registry,
# enable unit in local registry.
get_current_unit_registry().add_enabled_units([unit])
return unit
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.
registry = get_current_unit_registry().registry
return (_recreate_irreducible_unit,
(self.__class__, list(self.names), self.name in registry),
self.__getstate__())
@property
def represents(self):
"""The unit that this named unit represents.
For an irreducible unit, that is always itself.
"""
return self
def decompose(self, bases=set()):
if len(bases) and self not in bases:
for base in bases:
try:
scale = self._to(base)
except UnitsError:
pass
else:
if is_effectively_unity(scale):
return base
else:
return CompositeUnit(scale, [base], [1],
_error_check=False)
raise UnitConversionError(
f"Unit {self} can not be decomposed into the requested bases")
return self
class UnrecognizedUnit(IrreducibleUnit):
"""
A unit that did not parse correctly. This allows for
round-tripping it as a string, but no unit operations actually work
on it.
Parameters
----------
st : str
The name of the unit.
"""
# For UnrecognizedUnits, we want to use "standard" Python
# pickling, not the special case that is used for
# IrreducibleUnits.
__reduce__ = object.__reduce__
def __repr__(self):
return f"UnrecognizedUnit({str(self)})"
def __bytes__(self):
return self.name.encode('ascii', 'replace')
def __str__(self):
return self.name
def to_string(self, format=None):
return self.name
def _unrecognized_operator(self, *args, **kwargs):
raise ValueError(
"The unit {!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):
try:
other = Unit(other, parse_strict='silent')
except (ValueError, UnitsError, TypeError):
return NotImplemented
return isinstance(other, type(self)) and self.name == other.name
def __ne__(self, other):
return not (self == other)
def is_equivalent(self, other, equivalencies=None):
self._normalize_equivalencies(equivalencies)
return self == other
def _get_converter(self, other, equivalencies=None):
self._normalize_equivalencies(equivalencies)
raise ValueError(
"The unit {!r} is unrecognized. It can not be converted "
"to other units.".format(self.name))
def get_format_name(self, format):
return self.name
def is_unity(self):
return False
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, namespace=None,
doc=None, parse_strict='raise'):
# Short-circuit if we're already a unit
if hasattr(s, '_get_physical_type_id'):
return s
# turn possible Quantity input for s or represents into a Unit
from .quantity import Quantity
if isinstance(represents, Quantity):
if is_effectively_unity(represents.value):
represents = represents.unit
else:
represents = CompositeUnit(represents.value *
represents.unit.scale,
bases=represents.unit.bases,
powers=represents.unit.powers,
_error_check=False)
if isinstance(s, Quantity):
if is_effectively_unity(s.value):
s = s.unit
else:
s = CompositeUnit(s.value * s.unit.scale,
bases=s.unit.bases,
powers=s.unit.powers,
_error_check=False)
# now decide what we really need to do; define derived Unit?
if isinstance(represents, UnitBase):
# This has the effect of calling the real __new__ and
# __init__ on the Unit class.
return super().__call__(
s, represents, format=format, namespace=namespace, doc=doc)
# or interpret a Quantity (now became unit), string or number?
if isinstance(s, UnitBase):
return s
elif isinstance(s, (bytes, str)):
if len(s.strip()) == 0:
# Return the NULL unit
return dimensionless_unscaled
if format is None:
format = unit_format.Generic
f = unit_format.get_format(format)
if isinstance(s, bytes):
s = s.decode('ascii')
try:
return f.parse(s)
except Exception as e:
if parse_strict == 'silent':
pass
else:
# Deliberately not issubclass here. Subclasses
# should use their name.
if f is not unit_format.Generic:
format_clause = f.name + ' '
else:
format_clause = ''
msg = ("'{}' did not parse as {}unit: {} "
"If this is meant to be a custom unit, "
"define it with 'u.def_unit'. To have it "
"recognized inside a file reader or other code, "
"enable it with 'u.add_enabled_units'. "
"For details, see "
"https://docs.astropy.org/en/latest/units/combining_and_defining.html"
.format(s, format_clause, str(e)))
if parse_strict == 'raise':
raise ValueError(msg)
elif parse_strict == 'warn':
warnings.warn(msg, UnitsWarning)
else:
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, [], [], _error_check=False)
elif s is None:
raise TypeError("None is not a valid Unit")
else:
raise TypeError(f"{s} can not be converted to a Unit")
class Unit(NamedUnit, metaclass=_UnitMetaClass):
"""
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 no arguments::
Unit()
Returns the dimensionless unit.
- The last form, which creates a new `Unit` is described in detail
below.
See also: https://docs.astropy.org/en/stable/units/
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.
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'}
namespace : dict, optional
When provided, inject the unit (and all of its aliases) into
the given namespace.
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, represents=None, doc=None,
format=None, namespace=None):
represents = Unit(represents)
self._represents = represents
NamedUnit.__init__(self, st, namespace=namespace, doc=doc,
format=format)
@property
def represents(self):
"""The unit that this named unit represents."""
return self._represents
def decompose(self, bases=set()):
return self._represents.decompose(bases=bases)
def is_unity(self):
return self._represents.is_unity()
def __hash__(self):
if self._hash is None:
self._hash = hash((self.name, self._represents))
return self._hash
@classmethod
def _from_physical_type_id(cls, physical_type_id):
# get string bases and powers from the ID tuple
bases = [cls(base) for base, _ in physical_type_id]
powers = [power for _, power in physical_type_id]
if len(physical_type_id) == 1 and powers[0] == 1:
unit = bases[0]
else:
unit = CompositeUnit(1, bases, powers,
_error_check=False)
return unit
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`.
"""
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.
"""
_decomposed_cache = None
def __init__(self, scale, bases, powers, decompose=False,
decompose_bases=set(), _error_check=True):
# There are many cases internal to astropy.units where we
# already know that all the bases are Unit objects, and the
# powers have been validated. In those cases, we can skip the
# error checking for performance reasons. When the private
# kwarg `_error_check` is False, the error checking is turned
# off.
if _error_check:
for base in bases:
if not isinstance(base, UnitBase):
raise TypeError(
"bases must be sequence of UnitBase instances")
powers = [validate_power(p) for p in powers]
if not decompose and len(bases) == 1 and powers[0] >= 0:
# Short-cut; with one unit there's nothing to expand and gather,
# as that has happened already when creating the unit. But do only
# positive powers, since for negative powers we need to re-sort.
unit = bases[0]
power = powers[0]
if power == 1:
scale *= unit.scale
self._bases = unit.bases
self._powers = unit.powers
elif power == 0:
self._bases = []
self._powers = []
else:
scale *= unit.scale ** power
self._bases = unit.bases
self._powers = [operator.mul(*resolve_fractions(p, power))
for p in unit.powers]
self._scale = sanitize_scale(scale)
else:
# Regular case: use inputs as preliminary scale, bases, and powers,
# then "expand and gather" identical bases, sanitize the scale, &c.
self._scale = scale
self._bases = bases
self._powers = powers
self._expand_and_gather(decompose=decompose,
bases=decompose_bases)
def __repr__(self):
if len(self._bases):
return super().__repr__()
else:
if self._scale != 1.0:
return f'Unit(dimensionless with a scale of {self._scale})'
else:
return 'Unit(dimensionless)'
@property
def scale(self):
"""
Return the scale of the composite unit.
"""
return self._scale
@property
def bases(self):
"""
Return the bases of the composite unit.
"""
return self._bases
@property
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 bases and unit not in bases:
for base in bases:
try:
scale *= unit._to(base) ** power
except UnitsError:
pass
else:
unit = base
break
if unit in new_parts:
a, b = resolve_fractions(new_parts[unit], power)
new_parts[unit] = a + b
else:
new_parts[unit] = power
return scale
new_parts = {}
scale = self._scale
for b, p in zip(self._bases, self._powers):
if decompose and 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):
a, b = resolve_fractions(p_sub, p)
scale = add_unit(b_sub, a * b, 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], getattr(x[0], 'name', '')))
self._bases = [x[0] for x in new_parts]
self._powers = [x[1] for x in new_parts]
self._scale = sanitize_scale(scale)
def __copy__(self):
"""
For compatibility with python copy module.
"""
return CompositeUnit(self._scale, self._bases[:], self._powers[:])
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, decompose=True,
decompose_bases=bases)
if len(bases) == 0:
self._decomposed_cache = x
return x
def is_unity(self):
unit = self.decompose()
return len(unit.bases) == 0 and unit.scale == 1.0
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)
]
binary_prefixes = [
(['Ki'], ['kibi'], 2. ** 10),
(['Mi'], ['mebi'], 2. ** 20),
(['Gi'], ['gibi'], 2. ** 30),
(['Ti'], ['tebi'], 2. ** 40),
(['Pi'], ['pebi'], 2. ** 50),
(['Ei'], ['exbi'], 2. ** 60)
]
def _add_prefixes(u, excludes=[], namespace=None, prefixes=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.
namespace : dict, optional
When provided, inject the unit (and all of its aliases) into
the given namespace dictionary.
prefixes : list, optional
When provided, it is a list of prefix definitions of the form:
(short_names, long_tables, factor)
"""
if prefixes is True:
prefixes = si_prefixes
elif prefixes is False:
prefixes = []
for short, full, factor in prefixes:
names = []
format = {}
for prefix in short:
if prefix in excludes:
continue
for alias in u.short_names:
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'] = '\N{MICRO SIGN}' + u.get_format_name('unicode')
for key, val in u._format.items():
format.setdefault(key, prefix + val)
for prefix in full:
if prefix in excludes:
continue
for alias in u.long_names:
names.append(prefix + alias)
if len(names):
PrefixUnit(names, CompositeUnit(factor, [u], [1],
_error_check=False),
namespace=namespace, format=format)
def def_unit(s, represents=None, doc=None, format=None, prefixes=False,
exclude_prefixes=[], namespace=None):
"""
Factory function for defining new units.
Parameters
----------
s : 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.
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 or list, 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. When a list, it is a list of
prefix definitions of the form:
(short_names, long_tables, factor)
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"]``.
namespace : dict, optional
When provided, inject the unit (and all of its aliases and
prefixes), into the given namespace dictionary.
Returns
-------
unit : `~astropy.units.UnitBase`
The newly-defined unit, or a matching unit that was already
defined.
"""
if represents is not None:
result = Unit(s, represents, namespace=namespace, doc=doc,
format=format)
else:
result = IrreducibleUnit(
s, namespace=namespace, doc=doc, format=format)
if prefixes:
_add_prefixes(result, excludes=exclude_prefixes, namespace=namespace,
prefixes=prefixes)
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, (np.ndarray, float, int, complex)):
return value
avalue = np.array(value)
if avalue.dtype.kind not in ['i', 'f', 'c']:
raise ValueError("Value not scalar compatible or convertible to "
"an int, float, or complex array")
return avalue
def unit_scale_converter(val):
"""Function that just multiplies the value by unity.
This is a separate function so it can be recognized and
discarded in unit conversion.
"""
return 1. * _condition_arg(val)
dimensionless_unscaled = CompositeUnit(1, [], [], _error_check=False)
# Abbreviation of the above, see #1980
one = dimensionless_unscaled
# Maintain error in old location for backward compatibility
# TODO: Is this still needed? Should there be a deprecation warning?
unit_format.fits.UnitScaleError = UnitScaleError