# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Function Units and Quantities."""
from abc import ABCMeta, abstractmethod
import numpy as np
from astropy.units import (
Quantity,
Unit,
UnitBase,
UnitConversionError,
UnitsError,
UnitTypeError,
dimensionless_unscaled,
)
__all__ = ["FunctionUnitBase", "FunctionQuantity"]
SUPPORTED_UFUNCS = {
getattr(np.core.umath, ufunc)
for ufunc in (
"isfinite",
"isinf",
"isnan",
"sign",
"signbit",
"rint",
"floor",
"ceil",
"trunc",
"_ones_like",
"ones_like",
"positive",
)
if hasattr(np.core.umath, ufunc)
}
# TODO: the following could work if helper changed relative to Quantity:
# - spacing should return dimensionless, not same unit
# - negative should negate unit too,
# - add, subtract, comparisons can work if units added/subtracted
SUPPORTED_FUNCTIONS = {
getattr(np, function)
for function in ("clip", "trace", "mean", "min", "max", "round")
}
# subclassing UnitBase or CompositeUnit was found to be problematic, requiring
# a large number of overrides. Hence, define new class.
[docs]class FunctionUnitBase(metaclass=ABCMeta):
"""Abstract base class for function units.
Function units are functions containing a physical unit, such as dB(mW).
Most of the arithmetic operations on function units are defined in this
base class.
While instantiation is defined, this class should not be used directly.
Rather, subclasses should be used that override the abstract properties
`_default_function_unit` and `_quantity_class`, and the abstract methods
`from_physical`, and `to_physical`.
Parameters
----------
physical_unit : `~astropy.units.Unit` or `string`
Unit that is encapsulated within the function unit.
If not given, dimensionless.
function_unit : `~astropy.units.Unit` or `string`
By default, the same as the function unit set by the subclass.
"""
# ↓↓↓ the following four need to be set by subclasses
# Make this a property so we can ensure subclasses define it.
@property
@abstractmethod
def _default_function_unit(self):
"""Default function unit corresponding to the function.
This property should be overridden by subclasses, with, e.g.,
`~astropy.unit.MagUnit` returning `~astropy.unit.mag`.
"""
# This has to be a property because the function quantity will not be
# known at unit definition time, as it gets defined after.
@property
@abstractmethod
def _quantity_class(self):
"""Function quantity class corresponding to this function unit.
This property should be overridden by subclasses, with, e.g.,
`~astropy.unit.MagUnit` returning `~astropy.unit.Magnitude`.
"""
[docs] @abstractmethod
def from_physical(self, x):
"""Transformation from value in physical to value in function units.
This method should be overridden by subclasses. It is used to
provide automatic transformations using an equivalency.
"""
[docs] @abstractmethod
def to_physical(self, x):
"""Transformation from value in function to value in physical units.
This method should be overridden by subclasses. It is used to
provide automatic transformations using an equivalency.
"""
# ↑↑↑ the above four need to be set by subclasses
# have priority over arrays, regular units, and regular quantities
__array_priority__ = 30000
def __init__(self, physical_unit=None, function_unit=None):
if physical_unit is None:
physical_unit = dimensionless_unscaled
else:
physical_unit = Unit(physical_unit)
if not isinstance(physical_unit, UnitBase) or physical_unit.is_equivalent(
self._default_function_unit
):
raise UnitConversionError(f"{physical_unit} is not a physical unit.")
if function_unit is None:
function_unit = self._default_function_unit
else:
# any function unit should be equivalent to subclass default
function_unit = Unit(getattr(function_unit, "function_unit", function_unit))
if not function_unit.is_equivalent(self._default_function_unit):
raise UnitConversionError(
f"Cannot initialize '{self.__class__.__name__}' instance with "
f"function unit '{function_unit}', as it is not equivalent to "
f"default function unit '{self._default_function_unit}'."
)
self._physical_unit = physical_unit
self._function_unit = function_unit
def _copy(self, physical_unit=None):
"""Copy oneself, possibly with a different physical unit."""
if physical_unit is None:
physical_unit = self.physical_unit
return self.__class__(physical_unit, self.function_unit)
@property
def physical_unit(self):
return self._physical_unit
@property
def function_unit(self):
return self._function_unit
@property
def equivalencies(self):
"""List of equivalencies between function and physical units.
Uses the `from_physical` and `to_physical` methods.
"""
return [(self, self.physical_unit, self.to_physical, self.from_physical)]
# ↓↓↓ properties/methods required to behave like a unit
[docs] def decompose(self, bases=set()):
"""Copy the current unit with the physical unit decomposed.
For details, see `~astropy.units.UnitBase.decompose`.
"""
return self._copy(self.physical_unit.decompose(bases))
@property
def si(self):
"""Copy the current function unit with the physical unit in SI."""
return self._copy(self.physical_unit.si)
@property
def cgs(self):
"""Copy the current function unit with the physical unit in CGS."""
return self._copy(self.physical_unit.cgs)
def _get_physical_type_id(self):
"""Get physical type corresponding to physical unit."""
return self.physical_unit._get_physical_type_id()
@property
def physical_type(self):
"""Return the physical type of the physical unit (e.g., 'length')."""
return self.physical_unit.physical_type
[docs] def is_equivalent(self, other, equivalencies=[]):
"""
Returns `True` if this unit is equivalent to ``other``.
Parameters
----------
other : `~astropy.units.Unit`, string, 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:`astropy:unit_equivalencies`.
This list is in addition to the built-in equivalencies between the
function unit and the physical one, as well as possible global
defaults set by, e.g., `~astropy.units.set_enabled_equivalencies`.
Use `None` to turn off any global equivalencies.
Returns
-------
bool
"""
if isinstance(other, tuple):
return any(self.is_equivalent(u, equivalencies) for u in other)
other_physical_unit = getattr(
other,
"physical_unit",
(
dimensionless_unscaled
if self.function_unit.is_equivalent(other)
else other
),
)
return self.physical_unit.is_equivalent(other_physical_unit, equivalencies)
[docs] def to(self, other, value=1.0, equivalencies=[]):
"""
Return the converted values in the specified unit.
Parameters
----------
other : `~astropy.units.Unit`, `~astropy.units.FunctionUnitBase`, or str
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:`astropy:unit_equivalencies`.
This list is in meant to treat only equivalencies between different
physical units; the built-in equivalency between the function
unit and the physical one is automatically taken into account.
Returns
-------
values : scalar or array
Converted value(s). Input value sequences are returned as
numpy arrays.
Raises
------
`~astropy.units.UnitsError`
If units are inconsistent.
"""
# conversion to one's own physical unit should be fastest
if other is self.physical_unit:
return self.to_physical(value)
other_function_unit = getattr(other, "function_unit", other)
if self.function_unit.is_equivalent(other_function_unit):
# when other is an equivalent function unit:
# first convert physical units to other's physical units
other_physical_unit = getattr(
other, "physical_unit", dimensionless_unscaled
)
if self.physical_unit != other_physical_unit:
value_other_physical = self.physical_unit.to(
other_physical_unit, self.to_physical(value), equivalencies
)
# make function unit again, in own system
value = self.from_physical(value_other_physical)
# convert possible difference in function unit (e.g., dex->dB)
return self.function_unit.to(other_function_unit, value)
else:
try:
# when other is not a function unit
return self.physical_unit.to(
other, self.to_physical(value), equivalencies
)
except UnitConversionError as e:
if self.function_unit == Unit("mag"):
# One can get to raw magnitudes via math that strips the dimensions off.
# Include extra information in the exception to remind users of this.
msg = "Did you perhaps subtract magnitudes so the unit got lost?"
e.args += (msg,)
raise e
else:
raise
[docs] def is_unity(self):
return False
def __eq__(self, other):
return self.physical_unit == getattr(
other, "physical_unit", dimensionless_unscaled
) and self.function_unit == getattr(other, "function_unit", other)
def __ne__(self, other):
return not self.__eq__(other)
def __rlshift__(self, other):
"""Unit conversion operator ``<<``"""
try:
return self._quantity_class(other, self, copy=False, subok=True)
except Exception:
return NotImplemented
def __mul__(self, other):
if isinstance(other, (str, UnitBase, FunctionUnitBase)):
if self.physical_unit == dimensionless_unscaled:
# If dimensionless, drop back to normal unit and retry.
return self.function_unit * other
else:
raise UnitsError(
"Cannot multiply a function unit with a physical dimension "
"with any unit."
)
else:
# Anything not like a unit, try initialising as a function quantity.
try:
return self._quantity_class(other, unit=self)
except Exception:
return NotImplemented
def __rmul__(self, other):
return self.__mul__(other)
def __truediv__(self, other):
if isinstance(other, (str, UnitBase, FunctionUnitBase)):
if self.physical_unit == dimensionless_unscaled:
# If dimensionless, drop back to normal unit and retry.
return self.function_unit / other
else:
raise UnitsError(
"Cannot divide a function unit with a physical dimension "
"by any unit."
)
else:
# Anything not like a unit, try initialising as a function quantity.
try:
return self._quantity_class(1.0 / other, unit=self)
except Exception:
return NotImplemented
def __rtruediv__(self, other):
if isinstance(other, (str, UnitBase, FunctionUnitBase)):
if self.physical_unit == dimensionless_unscaled:
# If dimensionless, drop back to normal unit and retry.
return other / self.function_unit
else:
raise UnitsError(
"Cannot divide a function unit with a physical dimension "
"into any unit"
)
else:
# Don't know what to do with anything not like a unit.
return NotImplemented
def __pow__(self, power):
if power == 0:
return dimensionless_unscaled
elif power == 1:
return self._copy()
if self.physical_unit == dimensionless_unscaled:
return self.function_unit**power
raise UnitsError(
"Cannot raise a function unit with a physical dimension "
"to any power but 0 or 1."
)
def __pos__(self):
return self._copy()
[docs] def to_string(self, format="generic"):
"""
Output the unit in the given format as a string.
The physical unit is appended, within parentheses, to the function
unit, as in "dB(mW)", with both units set using the given format
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.
"""
if format not in ("generic", "unscaled", "latex", "latex_inline"):
raise ValueError(
f"Function units cannot be written in {format} "
"format. Only 'generic', 'unscaled', 'latex' and "
"'latex_inline' are supported."
)
self_str = self.function_unit.to_string(format)
pu_str = self.physical_unit.to_string(format)
if pu_str == "":
pu_str = "1"
if format.startswith("latex"):
# need to strip leading and trailing "$"
self_str += rf"$\mathrm{{\left( {pu_str[1:-1]} \right)}}$"
else:
self_str += f"({pu_str})"
return self_str
def __str__(self):
"""Return string representation for unit."""
self_str = str(self.function_unit)
pu_str = str(self.physical_unit)
if pu_str:
self_str += f"({pu_str})"
return self_str
def __repr__(self):
# By default, try to give a representation using `Unit(<string>)`,
# with string such that parsing it would give the correct FunctionUnit.
if callable(self.function_unit):
return f'Unit("{self.to_string()}")'
else:
return '{}("{}"{})'.format(
self.__class__.__name__,
self.physical_unit,
""
if self.function_unit is self._default_function_unit
else f', unit="{self.function_unit}"',
)
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 self.to_string("latex")
def __hash__(self):
return hash((self.function_unit, self.physical_unit))
[docs]class FunctionQuantity(Quantity):
"""A representation of a (scaled) function of a number with a unit.
Function quantities are quantities whose units are functions containing a
physical unit, such as dB(mW). Most of the arithmetic operations on
function quantities are defined in this base class.
While instantiation is also defined here, this class should not be
instantiated directly. Rather, subclasses should be made which have
``_unit_class`` pointing back to the corresponding function unit class.
Parameters
----------
value : number, quantity-like, or sequence thereof
The numerical value of the function quantity. If a number or
a `~astropy.units.Quantity` with a function unit, it will be converted
to ``unit`` and the physical unit will be inferred from ``unit``.
If a `~astropy.units.Quantity` with just a physical unit, it will
converted to the function unit, after, if necessary, converting it to
the physical unit inferred from ``unit``.
unit : str, `~astropy.units.UnitBase`, or `~astropy.units.FunctionUnitBase`, optional
For an `~astropy.units.FunctionUnitBase` instance, the
physical unit will be taken from it; for other input, it will be
inferred from ``value``. By default, ``unit`` is set by the subclass.
dtype : `~numpy.dtype`, optional
The dtype of the resulting Numpy array or scalar that will
hold the value. If not provided, it is determined from the input,
except that any input that cannot represent float (integer and bool)
is converted to float.
copy : bool, optional
If `True` (default), then the value is copied. Otherwise, a copy will
only be made if ``__array__`` returns a copy, if value is a nested
sequence, or if a copy is needed to satisfy an explicitly given
``dtype``. (The `False` option is intended mostly for internal use,
to speed up initialization where a copy is known to have been made.
Use with care.)
order : {'C', 'F', 'A'}, optional
Specify the order of the array. As in `~numpy.array`. Ignored
if the input does not need to be converted and ``copy=False``.
subok : bool, optional
If `False` (default), the returned array will be forced to be of the
class used. Otherwise, subclasses will be passed through.
ndmin : int, optional
Specifies the minimum number of dimensions that the resulting array
should have. Ones will be pre-pended to the shape as needed to meet
this requirement. This parameter is ignored if the input is a
`~astropy.units.Quantity` and ``copy=False``.
Raises
------
TypeError
If the value provided is not a Python numeric type.
TypeError
If the unit provided is not a `~astropy.units.FunctionUnitBase`
or `~astropy.units.Unit` object, or a parseable string unit.
"""
_unit_class = None
"""Default `~astropy.units.FunctionUnitBase` subclass.
This should be overridden by subclasses.
"""
# Ensure priority over ndarray, regular Unit & Quantity, and FunctionUnit.
__array_priority__ = 40000
# Define functions that work on FunctionQuantity.
_supported_ufuncs = SUPPORTED_UFUNCS
_supported_functions = SUPPORTED_FUNCTIONS
def __new__(
cls,
value,
unit=None,
dtype=np.inexact,
copy=True,
order=None,
subok=False,
ndmin=0,
):
if unit is not None:
# Convert possible string input to a (function) unit.
unit = Unit(unit)
if not isinstance(unit, FunctionUnitBase):
# By default, use value's physical unit.
value_unit = getattr(value, "unit", None)
if value_unit is None:
# if iterable, see if first item has a unit
# (mixed lists fail in super call below).
try:
value_unit = getattr(value[0], "unit")
except Exception:
pass
physical_unit = getattr(value_unit, "physical_unit", value_unit)
unit = cls._unit_class(physical_unit, function_unit=unit)
# initialise!
return super().__new__(
cls,
value,
unit,
dtype=dtype,
copy=copy,
order=order,
subok=subok,
ndmin=ndmin,
)
# ↓↓↓ properties not found in Quantity
@property
def physical(self):
"""The physical quantity corresponding the function one."""
return self.to(self.unit.physical_unit)
@property
def _function_view(self):
"""View as Quantity with function unit, dropping the physical unit.
Use `~astropy.units.quantity.Quantity.value` for just the value.
"""
return self._new_view(unit=self.unit.function_unit)
# ↓↓↓ methods overridden to change the behavior
@property
def si(self):
"""Return a copy with the physical unit in SI units."""
return self.__class__(self.physical.si)
@property
def cgs(self):
"""Return a copy with the physical unit in CGS units."""
return self.__class__(self.physical.cgs)
[docs] def decompose(self, bases=[]):
"""Generate a new instance with the physical unit decomposed.
For details, see `~astropy.units.Quantity.decompose`.
"""
return self.__class__(self.physical.decompose(bases))
# ↓↓↓ methods overridden to add additional behavior
def __quantity_subclass__(self, unit):
if isinstance(unit, FunctionUnitBase):
return self.__class__, True
else:
return super().__quantity_subclass__(unit)[0], False
def _set_unit(self, unit):
if not isinstance(unit, self._unit_class):
# Have to take care of, e.g., (10*u.mag).view(u.Magnitude)
try:
# "or 'nonsense'" ensures `None` breaks, just in case.
unit = self._unit_class(function_unit=unit or "nonsense")
except Exception:
raise UnitTypeError(
f"{type(self).__name__} instances require"
f" {self._unit_class.__name__} function units, so cannot set it to"
f" '{unit}'."
)
self._unit = unit
def __array_ufunc__(self, function, method, *inputs, **kwargs):
# TODO: it would be more logical to have this in Quantity already,
# instead of in UFUNC_HELPERS, where it cannot be overridden.
# And really it should just return NotImplemented, since possibly
# another argument might know what to do.
if function not in self._supported_ufuncs:
raise UnitTypeError(
f"Cannot use ufunc '{function.__name__}' with function quantities"
)
return super().__array_ufunc__(function, method, *inputs, **kwargs)
def _maybe_new_view(self, result):
"""View as function quantity if the unit is unchanged.
Used for the case that self.unit.physical_unit is dimensionless,
where multiplication and division is done using the Quantity
equivalent, to transform them back to a FunctionQuantity if possible.
"""
if isinstance(result, Quantity) and result.unit == self.unit:
return self._new_view(result)
else:
return result
# ↓↓↓ methods overridden to change behavior
def __mul__(self, other):
if self.unit.physical_unit == dimensionless_unscaled:
return self._maybe_new_view(self._function_view * other)
raise UnitTypeError(
"Cannot multiply function quantities which are not dimensionless "
"with anything."
)
def __truediv__(self, other):
if self.unit.physical_unit == dimensionless_unscaled:
return self._maybe_new_view(self._function_view / other)
raise UnitTypeError(
"Cannot divide function quantities which are not dimensionless by anything."
)
def __rtruediv__(self, other):
if self.unit.physical_unit == dimensionless_unscaled:
return self._maybe_new_view(self._function_view.__rtruediv__(other))
raise UnitTypeError(
"Cannot divide function quantities which are not dimensionless "
"into anything."
)
def _comparison(self, other, comparison_func):
"""Do a comparison between self and other, raising UnitsError when
other cannot be converted to self because it has different physical
unit, and returning NotImplemented when there are other errors."""
try:
# will raise a UnitsError if physical units not equivalent
other_in_own_unit = self._to_own_unit(other, check_precision=False)
except UnitsError as exc:
if self.unit.physical_unit != dimensionless_unscaled:
raise exc
try:
other_in_own_unit = self._function_view._to_own_unit(
other, check_precision=False
)
except Exception:
raise exc
except Exception:
return NotImplemented
return comparison_func(other_in_own_unit)
def __eq__(self, other):
try:
return self._comparison(other, self.value.__eq__)
except UnitsError:
return False
def __ne__(self, other):
try:
return self._comparison(other, self.value.__ne__)
except UnitsError:
return True
def __gt__(self, other):
return self._comparison(other, self.value.__gt__)
def __ge__(self, other):
return self._comparison(other, self.value.__ge__)
def __lt__(self, other):
return self._comparison(other, self.value.__lt__)
def __le__(self, other):
return self._comparison(other, self.value.__le__)
def __lshift__(self, other):
"""Unit conversion operator `<<`"""
try:
other = Unit(other, parse_strict="silent")
except UnitTypeError:
return NotImplemented
return self.__class__(self, other, copy=False, subok=True)
# Ensure Quantity methods are used only if they make sense.
def _wrap_function(self, function, *args, **kwargs):
if function in self._supported_functions:
return super()._wrap_function(function, *args, **kwargs)
# For dimensionless, we can convert to regular quantities.
if all(
arg.unit.physical_unit == dimensionless_unscaled
for arg in (self,) + args
if (hasattr(arg, "unit") and hasattr(arg.unit, "physical_unit"))
):
args = tuple(getattr(arg, "_function_view", arg) for arg in args)
return self._function_view._wrap_function(function, *args, **kwargs)
raise TypeError(
f"Cannot use method that uses function '{function.__name__}' with "
"function quantities that are not dimensionless."
)
# Override functions that are supported but do not use _wrap_function
# in Quantity.
[docs] def max(self, axis=None, out=None, keepdims=False):
return self._wrap_function(np.max, axis, out=out, keepdims=keepdims)
[docs] def min(self, axis=None, out=None, keepdims=False):
return self._wrap_function(np.min, axis, out=out, keepdims=keepdims)
[docs] def sum(self, axis=None, dtype=None, out=None, keepdims=False):
return self._wrap_function(np.sum, axis, dtype, out=out, keepdims=keepdims)
[docs] def cumsum(self, axis=None, dtype=None, out=None):
return self._wrap_function(np.cumsum, axis, dtype, out=out)
[docs] def clip(self, a_min, a_max, out=None):
return self._wrap_function(
np.clip, self._to_own_unit(a_min), self._to_own_unit(a_max), out=out
)