# Licensed under a 3-clause BSD style license - see LICENSE.rst
import weakref
from abc import ABCMeta, abstractmethod
from copy import deepcopy
import numpy as np
# from astropy.utils.compat import ignored
from astropy import log
from astropy.units import Quantity, Unit, UnitConversionError
__all__ = [
"MissingDataAssociationException",
"IncompatibleUncertaintiesException",
"NDUncertainty",
"StdDevUncertainty",
"UnknownUncertainty",
"VarianceUncertainty",
"InverseVariance",
]
[docs]class IncompatibleUncertaintiesException(Exception):
"""This exception should be used to indicate cases in which uncertainties
with two different classes can not be propagated.
"""
[docs]class MissingDataAssociationException(Exception):
"""This exception should be used to indicate that an uncertainty instance
has not been associated with a parent `~astropy.nddata.NDData` object.
"""
[docs]class NDUncertainty(metaclass=ABCMeta):
"""This is the metaclass for uncertainty classes used with `NDData`.
Parameters
----------
array : any type, optional
The array or value (the parameter name is due to historical reasons) of
the uncertainty. `numpy.ndarray`, `~astropy.units.Quantity` or
`NDUncertainty` subclasses are recommended.
If the `array` is `list`-like or `numpy.ndarray`-like it will be cast
to a plain `numpy.ndarray`.
Default is ``None``.
unit : unit-like, optional
Unit for the uncertainty ``array``. Strings that can be converted to a
`~astropy.units.Unit` are allowed.
Default is ``None``.
copy : `bool`, optional
Indicates whether to save the `array` as a copy. ``True`` copies it
before saving, while ``False`` tries to save every parameter as
reference. Note however that it is not always possible to save the
input as reference.
Default is ``True``.
Raises
------
IncompatibleUncertaintiesException
If given another `NDUncertainty`-like class as ``array`` if their
``uncertainty_type`` is different.
"""
def __init__(self, array=None, copy=True, unit=None):
if isinstance(array, NDUncertainty):
# Given an NDUncertainty class or subclass check that the type
# is the same.
if array.uncertainty_type != self.uncertainty_type:
raise IncompatibleUncertaintiesException
# Check if two units are given and take the explicit one then.
if unit is not None and unit != array._unit:
# TODO : Clarify it (see NDData.init for same problem)?
log.info("overwriting Uncertainty's current unit with specified unit.")
elif array._unit is not None:
unit = array.unit
array = array.array
elif isinstance(array, Quantity):
# Check if two units are given and take the explicit one then.
if unit is not None and array.unit is not None and unit != array.unit:
log.info("overwriting Quantity's current unit with specified unit.")
elif array.unit is not None:
unit = array.unit
array = array.value
if unit is None:
self._unit = None
else:
self._unit = Unit(unit)
if copy:
array = deepcopy(array)
unit = deepcopy(unit)
self.array = array
self.parent_nddata = None # no associated NDData - until it is set!
@property
@abstractmethod
def uncertainty_type(self):
"""`str` : Short description of the type of uncertainty.
Defined as abstract property so subclasses *have* to override this.
"""
return None
@property
def supports_correlated(self):
"""`bool` : Supports uncertainty propagation with correlated \
uncertainties?
.. versionadded:: 1.2
"""
return False
@property
def array(self):
"""`numpy.ndarray` : the uncertainty's value."""
return self._array
@array.setter
def array(self, value):
if isinstance(value, (list, np.ndarray)):
value = np.array(value, subok=False, copy=False)
self._array = value
@property
def unit(self):
"""`~astropy.units.Unit` : The unit of the uncertainty, if any."""
return self._unit
@unit.setter
def unit(self, value):
"""
The unit should be set to a value consistent with the parent NDData
unit and the uncertainty type.
"""
if value is not None:
# Check the hidden attribute below, not the property. The property
# raises an exception if there is no parent_nddata.
if self._parent_nddata is not None:
parent_unit = self.parent_nddata.unit
try:
# Check for consistency with the unit of the parent_nddata
self._data_unit_to_uncertainty_unit(parent_unit).to(value)
except UnitConversionError:
raise UnitConversionError(
"Unit {} is incompatible with unit {} of parent nddata".format(
value, parent_unit
)
)
self._unit = Unit(value)
else:
self._unit = value
@property
def quantity(self):
"""
This uncertainty as an `~astropy.units.Quantity` object.
"""
return Quantity(self.array, self.unit, copy=False, dtype=self.array.dtype)
@property
def parent_nddata(self):
"""`NDData` : reference to `NDData` instance with this uncertainty.
In case the reference is not set uncertainty propagation will not be
possible since propagation might need the uncertain data besides the
uncertainty.
"""
no_parent_message = "uncertainty is not associated with an NDData object"
parent_lost_message = (
"the associated NDData object was deleted and cannot be accessed "
"anymore. You can prevent the NDData object from being deleted by "
"assigning it to a variable. If this happened after unpickling "
"make sure you pickle the parent not the uncertainty directly."
)
try:
parent = self._parent_nddata
except AttributeError:
raise MissingDataAssociationException(no_parent_message)
else:
if parent is None:
raise MissingDataAssociationException(no_parent_message)
else:
# The NDData is saved as weak reference so we must call it
# to get the object the reference points to. However because
# we have a weak reference here it's possible that the parent
# was deleted because its reference count dropped to zero.
if isinstance(self._parent_nddata, weakref.ref):
resolved_parent = self._parent_nddata()
if resolved_parent is None:
log.info(parent_lost_message)
return resolved_parent
else:
log.info("parent_nddata should be a weakref to an NDData object.")
return self._parent_nddata
@parent_nddata.setter
def parent_nddata(self, value):
if value is not None and not isinstance(value, weakref.ref):
# Save a weak reference on the uncertainty that points to this
# instance of NDData. Direct references should NOT be used:
# https://github.com/astropy/astropy/pull/4799#discussion_r61236832
value = weakref.ref(value)
# Set _parent_nddata here and access below with the property because value
# is a weakref
self._parent_nddata = value
# set uncertainty unit to that of the parent if it was not already set, unless initializing
# with empty parent (Value=None)
if value is not None:
parent_unit = self.parent_nddata.unit
if self.unit is None:
if parent_unit is None:
self.unit = None
else:
# Set the uncertainty's unit to the appropriate value
self.unit = self._data_unit_to_uncertainty_unit(parent_unit)
else:
# Check that units of uncertainty are compatible with those of
# the parent. If they are, no need to change units of the
# uncertainty or the data. If they are not, let the user know.
unit_from_data = self._data_unit_to_uncertainty_unit(parent_unit)
try:
unit_from_data.to(self.unit)
except UnitConversionError:
raise UnitConversionError(
"Unit {} of uncertainty "
"incompatible with unit {} of "
"data".format(self.unit, parent_unit)
)
@abstractmethod
def _data_unit_to_uncertainty_unit(self, value):
"""
Subclasses must override this property. It should take in a data unit
and return the correct unit for the uncertainty given the uncertainty
type.
"""
return None
def __repr__(self):
prefix = self.__class__.__name__ + "("
try:
body = np.array2string(self.array, separator=", ", prefix=prefix)
except AttributeError:
# In case it wasn't possible to use array2string
body = str(self.array)
return "".join([prefix, body, ")"])
def __getstate__(self):
# Because of the weak reference the class wouldn't be picklable.
try:
return self._array, self._unit, self.parent_nddata
except MissingDataAssociationException:
# In case there's no parent
return self._array, self._unit, None
def __setstate__(self, state):
if len(state) != 3:
raise TypeError("The state should contain 3 items.")
self._array = state[0]
self._unit = state[1]
parent = state[2]
if parent is not None:
parent = weakref.ref(parent)
self._parent_nddata = parent
def __getitem__(self, item):
"""Normal slicing on the array, keep the unit and return a reference."""
return self.__class__(self.array[item], unit=self.unit, copy=False)
[docs] def propagate(self, operation, other_nddata, result_data, correlation):
"""Calculate the resulting uncertainty given an operation on the data.
.. versionadded:: 1.2
Parameters
----------
operation : callable
The operation that is performed on the `NDData`. Supported are
`numpy.add`, `numpy.subtract`, `numpy.multiply` and
`numpy.true_divide` (or `numpy.divide`).
other_nddata : `NDData` instance
The second operand in the arithmetic operation.
result_data : `~astropy.units.Quantity` or ndarray
The result of the arithmetic operations on the data.
correlation : `numpy.ndarray` or number
The correlation (rho) is defined between the uncertainties in
sigma_AB = sigma_A * sigma_B * rho. A value of ``0`` means
uncorrelated operands.
Returns
-------
resulting_uncertainty : `NDUncertainty` instance
Another instance of the same `NDUncertainty` subclass containing
the uncertainty of the result.
Raises
------
ValueError
If the ``operation`` is not supported or if correlation is not zero
but the subclass does not support correlated uncertainties.
Notes
-----
First this method checks if a correlation is given and the subclass
implements propagation with correlated uncertainties.
Then the second uncertainty is converted (or an Exception is raised)
to the same class in order to do the propagation.
Then the appropriate propagation method is invoked and the result is
returned.
"""
# Check if the subclass supports correlation
if not self.supports_correlated:
if isinstance(correlation, np.ndarray) or correlation != 0:
raise ValueError(
"{} does not support uncertainty propagation"
" with correlation."
"".format(self.__class__.__name__)
)
# Get the other uncertainty (and convert it to a matching one)
other_uncert = self._convert_uncertainty(other_nddata.uncertainty)
if operation.__name__ == "add":
result = self._propagate_add(other_uncert, result_data, correlation)
elif operation.__name__ == "subtract":
result = self._propagate_subtract(other_uncert, result_data, correlation)
elif operation.__name__ == "multiply":
result = self._propagate_multiply(other_uncert, result_data, correlation)
elif operation.__name__ in ["true_divide", "divide"]:
result = self._propagate_divide(other_uncert, result_data, correlation)
else:
raise ValueError("unsupported operation")
return self.__class__(result, copy=False)
def _convert_uncertainty(self, other_uncert):
"""Checks if the uncertainties are compatible for propagation.
Checks if the other uncertainty is `NDUncertainty`-like and if so
verify that the uncertainty_type is equal. If the latter is not the
case try returning ``self.__class__(other_uncert)``.
Parameters
----------
other_uncert : `NDUncertainty` subclass
The other uncertainty.
Returns
-------
other_uncert : `NDUncertainty` subclass
but converted to a compatible `NDUncertainty` subclass if
possible and necessary.
Raises
------
IncompatibleUncertaintiesException:
If the other uncertainty cannot be converted to a compatible
`NDUncertainty` subclass.
"""
if isinstance(other_uncert, NDUncertainty):
if self.uncertainty_type == other_uncert.uncertainty_type:
return other_uncert
else:
return self.__class__(other_uncert)
else:
raise IncompatibleUncertaintiesException
@abstractmethod
def _propagate_add(self, other_uncert, result_data, correlation):
return None
@abstractmethod
def _propagate_subtract(self, other_uncert, result_data, correlation):
return None
@abstractmethod
def _propagate_multiply(self, other_uncert, result_data, correlation):
return None
@abstractmethod
def _propagate_divide(self, other_uncert, result_data, correlation):
return None
[docs] def represent_as(self, other_uncert):
"""Convert this uncertainty to a different uncertainty type.
Parameters
----------
other_uncert : `NDUncertainty` subclass
The `NDUncertainty` subclass to convert to.
Returns
-------
resulting_uncertainty : `NDUncertainty` instance
An instance of ``other_uncert`` subclass containing the uncertainty
converted to the new uncertainty type.
Raises
------
TypeError
If either the initial or final subclasses do not support
conversion, a `TypeError` is raised.
"""
as_variance = getattr(self, "_convert_to_variance", None)
if as_variance is None:
raise TypeError(
f"{type(self)} does not support conversion to another uncertainty type."
)
from_variance = getattr(other_uncert, "_convert_from_variance", None)
if from_variance is None:
raise TypeError(
f"{other_uncert.__name__} does not support conversion from "
"another uncertainty type."
)
return from_variance(as_variance())
[docs]class UnknownUncertainty(NDUncertainty):
"""This class implements any unknown uncertainty type.
The main purpose of having an unknown uncertainty class is to prevent
uncertainty propagation.
Parameters
----------
args, kwargs :
see `NDUncertainty`
"""
@property
def supports_correlated(self):
"""`False` : Uncertainty propagation is *not* possible for this class."""
return False
@property
def uncertainty_type(self):
"""``"unknown"`` : `UnknownUncertainty` implements any unknown \
uncertainty type.
"""
return "unknown"
def _data_unit_to_uncertainty_unit(self, value):
"""
No way to convert if uncertainty is unknown.
"""
return None
def _convert_uncertainty(self, other_uncert):
"""Raise an Exception because unknown uncertainty types cannot
implement propagation.
"""
msg = "Uncertainties of unknown type cannot be propagated."
raise IncompatibleUncertaintiesException(msg)
def _propagate_add(self, other_uncert, result_data, correlation):
"""Not possible for unknown uncertainty types."""
return None
def _propagate_subtract(self, other_uncert, result_data, correlation):
return None
def _propagate_multiply(self, other_uncert, result_data, correlation):
return None
def _propagate_divide(self, other_uncert, result_data, correlation):
return None
class _VariancePropagationMixin:
"""
Propagation of uncertainties for variances, also used to perform error
propagation for variance-like uncertainties (standard deviation and inverse
variance).
"""
def _propagate_add_sub(
self,
other_uncert,
result_data,
correlation,
subtract=False,
to_variance=lambda x: x,
from_variance=lambda x: x,
):
"""
Error propagation for addition or subtraction of variance or
variance-like uncertainties. Uncertainties are calculated using the
formulae for variance but can be used for uncertainty convertible to
a variance.
Parameters
----------
other_uncert : `~astropy.nddata.NDUncertainty` instance
The uncertainty, if any, of the other operand.
result_data : `~astropy.nddata.NDData` instance
The results of the operation on the data.
correlation : float or array-like
Correlation of the uncertainties.
subtract : bool, optional
If ``True``, propagate for subtraction, otherwise propagate for
addition.
to_variance : function, optional
Function that will transform the input uncertainties to variance.
The default assumes the uncertainty is the variance.
from_variance : function, optional
Function that will convert from variance to the input uncertainty.
The default assumes the uncertainty is the variance.
"""
if subtract:
correlation_sign = -1
else:
correlation_sign = 1
try:
result_unit_sq = result_data.unit**2
except AttributeError:
result_unit_sq = None
if other_uncert.array is not None:
# Formula: sigma**2 = dB
if other_uncert.unit is not None and result_unit_sq != to_variance(
other_uncert.unit
):
# If the other uncertainty has a unit and this unit differs
# from the unit of the result convert it to the results unit
other = (
to_variance(other_uncert.array << other_uncert.unit)
.to(result_unit_sq)
.value
)
else:
other = to_variance(other_uncert.array)
else:
other = 0
if self.array is not None:
# Formula: sigma**2 = dA
if (
self.unit is not None
and to_variance(self.unit) != self.parent_nddata.unit**2
):
# If the uncertainty has a different unit than the result we
# need to convert it to the results unit.
this = to_variance(self.array << self.unit).to(result_unit_sq).value
else:
this = to_variance(self.array)
else:
this = 0
# Formula: sigma**2 = dA + dB +/- 2*cor*sqrt(dA*dB)
# Formula: sigma**2 = sigma_other + sigma_self +/- 2*cor*sqrt(dA*dB)
# (sign depends on whether addition or subtraction)
# Determine the result depending on the correlation
if isinstance(correlation, np.ndarray) or correlation != 0:
corr = 2 * correlation * np.sqrt(this * other)
result = this + other + correlation_sign * corr
else:
result = this + other
return from_variance(result)
def _propagate_multiply_divide(
self,
other_uncert,
result_data,
correlation,
divide=False,
to_variance=lambda x: x,
from_variance=lambda x: x,
):
"""
Error propagation for multiplication or division of variance or
variance-like uncertainties. Uncertainties are calculated using the
formulae for variance but can be used for uncertainty convertible to
a variance.
Parameters
----------
other_uncert : `~astropy.nddata.NDUncertainty` instance
The uncertainty, if any, of the other operand.
result_data : `~astropy.nddata.NDData` instance
The results of the operation on the data.
correlation : float or array-like
Correlation of the uncertainties.
divide : bool, optional
If ``True``, propagate for division, otherwise propagate for
multiplication.
to_variance : function, optional
Function that will transform the input uncertainties to variance.
The default assumes the uncertainty is the variance.
from_variance : function, optional
Function that will convert from variance to the input uncertainty.
The default assumes the uncertainty is the variance.
"""
# For multiplication we don't need the result as quantity
if isinstance(result_data, Quantity):
result_data = result_data.value
if divide:
correlation_sign = -1
else:
correlation_sign = 1
if other_uncert.array is not None:
# We want the result to have a unit consistent with the parent, so
# we only need to convert the unit of the other uncertainty if it
# is different from its data's unit.
if (
other_uncert.unit
and to_variance(1 * other_uncert.unit)
!= ((1 * other_uncert.parent_nddata.unit) ** 2).unit
):
d_b = (
to_variance(other_uncert.array << other_uncert.unit)
.to((1 * other_uncert.parent_nddata.unit) ** 2)
.value
)
else:
d_b = to_variance(other_uncert.array)
# Formula: sigma**2 = |A|**2 * d_b
right = np.abs(self.parent_nddata.data**2 * d_b)
else:
right = 0
if self.array is not None:
# Just the reversed case
if (
self.unit
and to_variance(1 * self.unit)
!= ((1 * self.parent_nddata.unit) ** 2).unit
):
d_a = (
to_variance(self.array << self.unit)
.to((1 * self.parent_nddata.unit) ** 2)
.value
)
else:
d_a = to_variance(self.array)
# Formula: sigma**2 = |B|**2 * d_a
left = np.abs(other_uncert.parent_nddata.data**2 * d_a)
else:
left = 0
# Multiplication
#
# The fundamental formula is:
# sigma**2 = |AB|**2*(d_a/A**2+d_b/B**2+2*sqrt(d_a)/A*sqrt(d_b)/B*cor)
#
# This formula is not very handy since it generates NaNs for every
# zero in A and B. So we rewrite it:
#
# Multiplication Formula:
# sigma**2 = (d_a*B**2 + d_b*A**2 + (2 * cor * ABsqrt(dAdB)))
# sigma**2 = (left + right + (2 * cor * ABsqrt(dAdB)))
#
# Division
#
# The fundamental formula for division is:
# sigma**2 = |A/B|**2*(d_a/A**2+d_b/B**2-2*sqrt(d_a)/A*sqrt(d_b)/B*cor)
#
# As with multiplication, it is convenient to rewrite this to avoid
# nans where A is zero.
#
# Division formula (rewritten):
# sigma**2 = d_a/B**2 + (A/B)**2 * d_b/B**2
# - 2 * cor * A *sqrt(dAdB) / B**3
# sigma**2 = d_a/B**2 + (A/B)**2 * d_b/B**2
# - 2*cor * sqrt(d_a)/B**2 * sqrt(d_b) * A / B
# sigma**2 = multiplication formula/B**4 (and sign change in
# the correlation)
if isinstance(correlation, np.ndarray) or correlation != 0:
corr = (
2
* correlation
* np.sqrt(d_a * d_b)
* self.parent_nddata.data
* other_uncert.parent_nddata.data
)
else:
corr = 0
if divide:
return from_variance(
(left + right + correlation_sign * corr)
/ other_uncert.parent_nddata.data**4
)
else:
return from_variance(left + right + correlation_sign * corr)
[docs]class StdDevUncertainty(_VariancePropagationMixin, NDUncertainty):
"""Standard deviation uncertainty assuming first order gaussian error
propagation.
This class implements uncertainty propagation for ``addition``,
``subtraction``, ``multiplication`` and ``division`` with other instances
of `StdDevUncertainty`. The class can handle if the uncertainty has a
unit that differs from (but is convertible to) the parents `NDData` unit.
The unit of the resulting uncertainty will have the same unit as the
resulting data. Also support for correlation is possible but requires the
correlation as input. It cannot handle correlation determination itself.
Parameters
----------
args, kwargs :
see `NDUncertainty`
Examples
--------
`StdDevUncertainty` should always be associated with an `NDData`-like
instance, either by creating it during initialization::
>>> from astropy.nddata import NDData, StdDevUncertainty
>>> ndd = NDData([1,2,3], unit='m',
... uncertainty=StdDevUncertainty([0.1, 0.1, 0.1]))
>>> ndd.uncertainty # doctest: +FLOAT_CMP
StdDevUncertainty([0.1, 0.1, 0.1])
or by setting it manually on the `NDData` instance::
>>> ndd.uncertainty = StdDevUncertainty([0.2], unit='m', copy=True)
>>> ndd.uncertainty # doctest: +FLOAT_CMP
StdDevUncertainty([0.2])
the uncertainty ``array`` can also be set directly::
>>> ndd.uncertainty.array = 2
>>> ndd.uncertainty
StdDevUncertainty(2)
.. note::
The unit will not be displayed.
"""
@property
def supports_correlated(self):
"""`True` : `StdDevUncertainty` allows to propagate correlated \
uncertainties.
``correlation`` must be given, this class does not implement computing
it by itself.
"""
return True
@property
def uncertainty_type(self):
"""``"std"`` : `StdDevUncertainty` implements standard deviation."""
return "std"
def _convert_uncertainty(self, other_uncert):
if isinstance(other_uncert, StdDevUncertainty):
return other_uncert
else:
raise IncompatibleUncertaintiesException
def _propagate_add(self, other_uncert, result_data, correlation):
return super()._propagate_add_sub(
other_uncert,
result_data,
correlation,
subtract=False,
to_variance=np.square,
from_variance=np.sqrt,
)
def _propagate_subtract(self, other_uncert, result_data, correlation):
return super()._propagate_add_sub(
other_uncert,
result_data,
correlation,
subtract=True,
to_variance=np.square,
from_variance=np.sqrt,
)
def _propagate_multiply(self, other_uncert, result_data, correlation):
return super()._propagate_multiply_divide(
other_uncert,
result_data,
correlation,
divide=False,
to_variance=np.square,
from_variance=np.sqrt,
)
def _propagate_divide(self, other_uncert, result_data, correlation):
return super()._propagate_multiply_divide(
other_uncert,
result_data,
correlation,
divide=True,
to_variance=np.square,
from_variance=np.sqrt,
)
def _data_unit_to_uncertainty_unit(self, value):
return value
def _convert_to_variance(self):
new_array = None if self.array is None else self.array**2
new_unit = None if self.unit is None else self.unit**2
return VarianceUncertainty(new_array, unit=new_unit)
@classmethod
def _convert_from_variance(cls, var_uncert):
new_array = None if var_uncert.array is None else var_uncert.array ** (1 / 2)
new_unit = None if var_uncert.unit is None else var_uncert.unit ** (1 / 2)
return cls(new_array, unit=new_unit)
[docs]class VarianceUncertainty(_VariancePropagationMixin, NDUncertainty):
"""
Variance uncertainty assuming first order Gaussian error
propagation.
This class implements uncertainty propagation for ``addition``,
``subtraction``, ``multiplication`` and ``division`` with other instances
of `VarianceUncertainty`. The class can handle if the uncertainty has a
unit that differs from (but is convertible to) the parents `NDData` unit.
The unit of the resulting uncertainty will be the square of the unit of the
resulting data. Also support for correlation is possible but requires the
correlation as input. It cannot handle correlation determination itself.
Parameters
----------
args, kwargs :
see `NDUncertainty`
Examples
--------
Compare this example to that in `StdDevUncertainty`; the uncertainties
in the examples below are equivalent to the uncertainties in
`StdDevUncertainty`.
`VarianceUncertainty` should always be associated with an `NDData`-like
instance, either by creating it during initialization::
>>> from astropy.nddata import NDData, VarianceUncertainty
>>> ndd = NDData([1,2,3], unit='m',
... uncertainty=VarianceUncertainty([0.01, 0.01, 0.01]))
>>> ndd.uncertainty # doctest: +FLOAT_CMP
VarianceUncertainty([0.01, 0.01, 0.01])
or by setting it manually on the `NDData` instance::
>>> ndd.uncertainty = VarianceUncertainty([0.04], unit='m^2', copy=True)
>>> ndd.uncertainty # doctest: +FLOAT_CMP
VarianceUncertainty([0.04])
the uncertainty ``array`` can also be set directly::
>>> ndd.uncertainty.array = 4
>>> ndd.uncertainty
VarianceUncertainty(4)
.. note::
The unit will not be displayed.
"""
@property
def uncertainty_type(self):
"""``"var"`` : `VarianceUncertainty` implements variance."""
return "var"
@property
def supports_correlated(self):
"""`True` : `VarianceUncertainty` allows to propagate correlated \
uncertainties.
``correlation`` must be given, this class does not implement computing
it by itself.
"""
return True
def _propagate_add(self, other_uncert, result_data, correlation):
return super()._propagate_add_sub(
other_uncert, result_data, correlation, subtract=False
)
def _propagate_subtract(self, other_uncert, result_data, correlation):
return super()._propagate_add_sub(
other_uncert, result_data, correlation, subtract=True
)
def _propagate_multiply(self, other_uncert, result_data, correlation):
return super()._propagate_multiply_divide(
other_uncert, result_data, correlation, divide=False
)
def _propagate_divide(self, other_uncert, result_data, correlation):
return super()._propagate_multiply_divide(
other_uncert, result_data, correlation, divide=True
)
def _data_unit_to_uncertainty_unit(self, value):
return value**2
def _convert_to_variance(self):
return self
@classmethod
def _convert_from_variance(cls, var_uncert):
return var_uncert
def _inverse(x):
"""Just a simple inverse for use in the InverseVariance"""
return 1 / x
[docs]class InverseVariance(_VariancePropagationMixin, NDUncertainty):
"""
Inverse variance uncertainty assuming first order Gaussian error
propagation.
This class implements uncertainty propagation for ``addition``,
``subtraction``, ``multiplication`` and ``division`` with other instances
of `InverseVariance`. The class can handle if the uncertainty has a unit
that differs from (but is convertible to) the parents `NDData` unit. The
unit of the resulting uncertainty will the inverse square of the unit of
the resulting data. Also support for correlation is possible but requires
the correlation as input. It cannot handle correlation determination
itself.
Parameters
----------
args, kwargs :
see `NDUncertainty`
Examples
--------
Compare this example to that in `StdDevUncertainty`; the uncertainties
in the examples below are equivalent to the uncertainties in
`StdDevUncertainty`.
`InverseVariance` should always be associated with an `NDData`-like
instance, either by creating it during initialization::
>>> from astropy.nddata import NDData, InverseVariance
>>> ndd = NDData([1,2,3], unit='m',
... uncertainty=InverseVariance([100, 100, 100]))
>>> ndd.uncertainty # doctest: +FLOAT_CMP
InverseVariance([100, 100, 100])
or by setting it manually on the `NDData` instance::
>>> ndd.uncertainty = InverseVariance([25], unit='1/m^2', copy=True)
>>> ndd.uncertainty # doctest: +FLOAT_CMP
InverseVariance([25])
the uncertainty ``array`` can also be set directly::
>>> ndd.uncertainty.array = 0.25
>>> ndd.uncertainty
InverseVariance(0.25)
.. note::
The unit will not be displayed.
"""
@property
def uncertainty_type(self):
"""``"ivar"`` : `InverseVariance` implements inverse variance."""
return "ivar"
@property
def supports_correlated(self):
"""`True` : `InverseVariance` allows to propagate correlated \
uncertainties.
``correlation`` must be given, this class does not implement computing
it by itself.
"""
return True
def _propagate_add(self, other_uncert, result_data, correlation):
return super()._propagate_add_sub(
other_uncert,
result_data,
correlation,
subtract=False,
to_variance=_inverse,
from_variance=_inverse,
)
def _propagate_subtract(self, other_uncert, result_data, correlation):
return super()._propagate_add_sub(
other_uncert,
result_data,
correlation,
subtract=True,
to_variance=_inverse,
from_variance=_inverse,
)
def _propagate_multiply(self, other_uncert, result_data, correlation):
return super()._propagate_multiply_divide(
other_uncert,
result_data,
correlation,
divide=False,
to_variance=_inverse,
from_variance=_inverse,
)
def _propagate_divide(self, other_uncert, result_data, correlation):
return super()._propagate_multiply_divide(
other_uncert,
result_data,
correlation,
divide=True,
to_variance=_inverse,
from_variance=_inverse,
)
def _data_unit_to_uncertainty_unit(self, value):
return 1 / value**2
def _convert_to_variance(self):
new_array = None if self.array is None else 1 / self.array
new_unit = None if self.unit is None else 1 / self.unit
return VarianceUncertainty(new_array, unit=new_unit)
@classmethod
def _convert_from_variance(cls, var_uncert):
new_array = None if var_uncert.array is None else 1 / var_uncert.array
new_unit = None if var_uncert.unit is None else 1 / var_uncert.unit
return cls(new_array, unit=new_unit)