# Source code for astropy.nddata.mixins.ndarithmetic

```
# Licensed under a 3-clause BSD style license - see LICENSE.rst
# This module implements the Arithmetic mixin to the NDData class.
import warnings
from copy import deepcopy
import numpy as np
from astropy.nddata.nduncertainty import NDUncertainty
from astropy.units import dimensionless_unscaled
from astropy.utils import format_doc, sharedmethod
from astropy.utils.exceptions import AstropyUserWarning
from astropy.utils.masked import Masked
__all__ = ["NDArithmeticMixin"]
# Global so it doesn't pollute the class dict unnecessarily:
# Docstring templates for add, subtract, multiply, divide methods.
_arit_doc = """
Performs {name} by evaluating ``self`` {op} ``operand``.
Parameters
----------
operand, operand2 : `NDData`-like instance
If ``operand2`` is ``None`` or not given it will perform the operation
``self`` {op} ``operand``.
If ``operand2`` is given it will perform ``operand`` {op} ``operand2``.
If the method was called on a class rather than on the instance
``operand2`` must be given.
propagate_uncertainties : `bool` or ``None``, optional
If ``None`` the result will have no uncertainty. If ``False`` the
result will have a copied version of the first operand that has an
uncertainty. If ``True`` the result will have a correctly propagated
uncertainty from the uncertainties of the operands but this assumes
that the uncertainties are `NDUncertainty`-like. Default is ``True``.
.. versionchanged:: 1.2
This parameter must be given as keyword-parameter. Using it as
positional parameter is deprecated.
``None`` was added as valid parameter value.
handle_mask : callable, ``'first_found'`` or ``None``, optional
If ``None`` the result will have no mask. If ``'first_found'`` the
result will have a copied version of the first operand that has a
mask). If it is a callable then the specified callable must
create the results ``mask`` and if necessary provide a copy.
Default is `numpy.logical_or`.
.. versionadded:: 1.2
handle_meta : callable, ``'first_found'`` or ``None``, optional
If ``None`` the result will have no meta. If ``'first_found'`` the
result will have a copied version of the first operand that has a
(not empty) meta. If it is a callable then the specified callable must
create the results ``meta`` and if necessary provide a copy.
Default is ``None``.
.. versionadded:: 1.2
compare_wcs : callable, ``'first_found'`` or ``None``, optional
If ``None`` the result will have no wcs and no comparison between
the wcs of the operands is made. If ``'first_found'`` the
result will have a copied version of the first operand that has a
wcs. If it is a callable then the specified callable must
compare the ``wcs``. The resulting ``wcs`` will be like if ``False``
was given otherwise it raises a ``ValueError`` if the comparison was
not successful. Default is ``'first_found'``.
.. versionadded:: 1.2
uncertainty_correlation : number or `~numpy.ndarray`, optional
The correlation between the two operands is used for correct error
propagation for correlated data as given in:
https://en.wikipedia.org/wiki/Propagation_of_uncertainty#Example_formulas
Default is 0.
.. versionadded:: 1.2
kwargs :
Any other parameter that should be passed to the callables used.
Returns
-------
result : `~astropy.nddata.NDData`-like
The resulting dataset
Notes
-----
If a ``callable`` is used for ``mask``, ``wcs`` or ``meta`` the
callable must accept the corresponding attributes as first two
parameters. If the callable also needs additional parameters these can be
defined as ``kwargs`` and must start with ``"wcs_"`` (for wcs callable) or
``"meta_"`` (for meta callable). This startstring is removed before the
callable is called.
``"first_found"`` can also be abbreviated with ``"ff"``.
"""
[docs]
class NDArithmeticMixin:
"""
Mixin class to add arithmetic to an NDData object.
When subclassing, be sure to list the superclasses in the correct order
so that the subclass sees NDData as the main superclass. See
`~astropy.nddata.NDDataArray` for an example.
Notes
-----
This class only aims at covering the most common cases so there are certain
restrictions on the saved attributes::
- ``uncertainty`` : has to be something that has a `NDUncertainty`-like
interface for uncertainty propagation
- ``mask`` : has to be something that can be used by a bitwise ``or``
operation.
- ``wcs`` : has to implement a way of comparing with ``=`` to allow
the operation.
But there is a workaround that allows to disable handling a specific
attribute and to simply set the results attribute to ``None`` or to
copy the existing attribute (and neglecting the other).
For example for uncertainties not representing an `NDUncertainty`-like
interface you can alter the ``propagate_uncertainties`` parameter in
:meth:`NDArithmeticMixin.add`. ``None`` means that the result will have no
uncertainty, ``False`` means it takes the uncertainty of the first operand
(if this does not exist from the second operand) as the result's
uncertainty. This behavior is also explained in the docstring for the
different arithmetic operations.
Decomposing the units is not attempted, mainly due to the internal mechanics
of `~astropy.units.Quantity`, so the resulting data might have units like
``km/m`` if you divided for example 100km by 5m. So this Mixin has adopted
this behavior.
Examples
--------
Using this Mixin with `~astropy.nddata.NDData`:
>>> from astropy.nddata import NDData, NDArithmeticMixin
>>> class NDDataWithMath(NDArithmeticMixin, NDData):
... pass
Using it with one operand on an instance::
>>> ndd = NDDataWithMath(100)
>>> ndd.add(20)
NDDataWithMath(120)
Using it with two operand on an instance::
>>> ndd = NDDataWithMath(-4)
>>> ndd.divide(1, ndd)
NDDataWithMath(-0.25)
Using it as classmethod requires two operands::
>>> NDDataWithMath.subtract(5, 4)
NDDataWithMath(1)
"""
def _arithmetic(
self,
operation,
operand,
propagate_uncertainties=True,
handle_mask=np.logical_or,
handle_meta=None,
uncertainty_correlation=0,
compare_wcs="first_found",
operation_ignores_mask=False,
axis=None,
**kwds,
):
"""
Base method which calculates the result of the arithmetic operation.
This method determines the result of the arithmetic operation on the
``data`` including their units and then forwards to other methods
to calculate the other properties for the result (like uncertainty).
Parameters
----------
operation : callable
The operation that is performed on the `NDData`. Supported are
`numpy.add`, `numpy.subtract`, `numpy.multiply` and
`numpy.true_divide`.
operand : same type (class) as self
see :meth:`NDArithmeticMixin.add`
propagate_uncertainties : `bool` or ``None``, optional
see :meth:`NDArithmeticMixin.add`
handle_mask : callable, ``'first_found'`` or ``None``, optional
see :meth:`NDArithmeticMixin.add`
handle_meta : callable, ``'first_found'`` or ``None``, optional
see :meth:`NDArithmeticMixin.add`
compare_wcs : callable, ``'first_found'`` or ``None``, optional
see :meth:`NDArithmeticMixin.add`
uncertainty_correlation : ``Number`` or `~numpy.ndarray`, optional
see :meth:`NDArithmeticMixin.add`
operation_ignores_mask : bool, optional
When True, masked values will be excluded from operations;
otherwise the operation will be performed on all values,
including masked ones.
axis : int or tuple of ints, optional
axis or axes over which to perform collapse operations like min, max, sum or mean.
kwargs :
Any other parameter that should be passed to the
different :meth:`NDArithmeticMixin._arithmetic_mask` (or wcs, ...)
methods.
Returns
-------
result : ndarray or `~astropy.units.Quantity`
The resulting data as array (in case both operands were without
unit) or as quantity if at least one had a unit.
kwargs : `dict`
The kwargs should contain all the other attributes (besides data
and unit) needed to create a new instance for the result. Creating
the new instance is up to the calling method, for example
:meth:`NDArithmeticMixin.add`.
"""
# Find the appropriate keywords for the appropriate method (not sure
# if data and uncertainty are ever used ...)
kwds2 = {"mask": {}, "meta": {}, "wcs": {}, "data": {}, "uncertainty": {}}
for i in kwds:
splitted = i.split("_", 1)
try:
kwds2[splitted[0]][splitted[1]] = kwds[i]
except KeyError:
raise KeyError(f"Unknown prefix {splitted[0]} for parameter {i}")
kwargs = {}
# First check that the WCS allows the arithmetic operation
if compare_wcs is None:
kwargs["wcs"] = None
elif compare_wcs in ["ff", "first_found"]:
if self.wcs is None and hasattr(operand, "wcs"):
kwargs["wcs"] = deepcopy(operand.wcs)
else:
kwargs["wcs"] = deepcopy(self.wcs)
else:
kwargs["wcs"] = self._arithmetic_wcs(
operation, operand, compare_wcs, **kwds2["wcs"]
)
# collapse operations on masked quantities/arrays which are supported by
# the astropy.utils.masked or np.ma modules should use those modules to
# do the arithmetic on the data and propagate masks.
use_masked_arith = operand is None and self.mask is not None
if use_masked_arith:
# if we're *including* masked values in the operation,
# use the astropy Masked module:
if not operation_ignores_mask:
# call the numpy operation on a Masked NDDataArray
# representation of the nddata, with units when available:
if self.unit is not None and not hasattr(self.data, "unit"):
masked_input = Masked(self.data << self.unit, mask=self.mask)
else:
masked_input = Masked(self.data, mask=self.mask)
# if we're *excluding* masked values in the operation,
# we use the numpy.ma module:
else:
masked_input = np.ma.masked_array(self.data, self.mask)
result = operation(masked_input, axis=axis)
# since result may be e.g. a float if operation is a sum over all axes,
# let's ensure that result is a masked array, since we'll assume this later:
if not hasattr(result, "mask"):
result = np.ma.masked_array(
result, mask=np.zeros_like(result, dtype=bool)
)
else:
# Then calculate the resulting data (which can but needs not be a
# quantity)
result = self._arithmetic_data(
operation, operand, axis=axis, **kwds2["data"]
)
# preserve original units
if not hasattr(result, "unit") and hasattr(self, "unit"):
kwargs["unit"] = self.unit
# Determine the other properties
if propagate_uncertainties is None:
kwargs["uncertainty"] = None
elif not propagate_uncertainties:
if self.uncertainty is None:
kwargs["uncertainty"] = deepcopy(operand.uncertainty)
else:
kwargs["uncertainty"] = deepcopy(self.uncertainty)
else:
kwargs["uncertainty"] = self._arithmetic_uncertainty(
operation,
operand,
result,
uncertainty_correlation,
axis=axis,
**kwds2["uncertainty"],
)
# If both are None, there is nothing to do.
if self.psf is not None or (operand is not None and operand.psf is not None):
warnings.warn(
f"Not setting psf attribute during {operation.__name__}.",
AstropyUserWarning,
)
if handle_mask is None:
pass
elif hasattr(result, "mask"):
# if numpy.ma or astropy.utils.masked is being used, the constructor
# will pick up the mask from the masked object:
kwargs["mask"] = None
elif handle_mask in ["ff", "first_found"]:
if self.mask is None:
kwargs["mask"] = deepcopy(operand.mask)
else:
kwargs["mask"] = deepcopy(self.mask)
else:
kwargs["mask"] = self._arithmetic_mask(
operation, operand, handle_mask, axis=axis, **kwds2["mask"]
)
if handle_meta is None:
kwargs["meta"] = None
elif handle_meta in ["ff", "first_found"]:
if not self.meta:
kwargs["meta"] = deepcopy(operand.meta)
else:
kwargs["meta"] = deepcopy(self.meta)
else:
kwargs["meta"] = self._arithmetic_meta(
operation, operand, handle_meta, **kwds2["meta"]
)
# Wrap the individual results into a new instance of the same class.
return result, kwargs
def _arithmetic_data(self, operation, operand, **kwds):
"""
Calculate the resulting data.
Parameters
----------
operation : callable
see `NDArithmeticMixin._arithmetic` parameter description.
operand : `NDData`-like instance
The second operand wrapped in an instance of the same class as
self.
kwds :
Additional parameters.
Returns
-------
result_data : ndarray or `~astropy.units.Quantity`
If both operands had no unit the resulting data is a simple numpy
array, but if any of the operands had a unit the return is a
Quantity.
"""
# Do the calculation with or without units
if self.unit is None and hasattr(operand, "data"):
if hasattr(operand, "unit") and operand.unit is None:
result = operation(self.data, operand.data)
else:
result = operation(
self.data << dimensionless_unscaled, operand.data << operand.unit
)
elif hasattr(operand, "unit"):
if operand.unit is not None:
result = operation(self.data << self.unit, operand.data << operand.unit)
else:
result = operation(
self.data << self.unit, operand.data << dimensionless_unscaled
)
elif operand is not None:
result = operation(self.data << self.unit, operand.data << operand.unit)
else:
result = operation(self.data, axis=kwds["axis"])
return result
def _arithmetic_uncertainty(self, operation, operand, result, correlation, **kwds):
"""
Calculate the resulting uncertainty.
Parameters
----------
operation : callable
see :meth:`NDArithmeticMixin._arithmetic` parameter description.
operand : `NDData`-like instance
The second operand wrapped in an instance of the same class as
self.
result : `~astropy.units.Quantity` or `~numpy.ndarray`
The result of :meth:`NDArithmeticMixin._arithmetic_data`.
correlation : number or `~numpy.ndarray`
see :meth:`NDArithmeticMixin.add` parameter description.
kwds :
Additional parameters.
Returns
-------
result_uncertainty : `NDUncertainty` subclass instance or None
The resulting uncertainty already saved in the same `NDUncertainty`
subclass that ``self`` had (or ``operand`` if self had no
uncertainty). ``None`` only if both had no uncertainty.
"""
# Make sure these uncertainties are NDUncertainties so this kind of
# propagation is possible.
if self.uncertainty is not None and not isinstance(
self.uncertainty, NDUncertainty
):
raise TypeError(
"Uncertainty propagation is only defined for "
"subclasses of NDUncertainty."
)
if (
operand is not None
and operand.uncertainty is not None
and not isinstance(operand.uncertainty, NDUncertainty)
):
raise TypeError(
"Uncertainty propagation is only defined for "
"subclasses of NDUncertainty."
)
# Now do the uncertainty propagation
# TODO: There is no enforced requirement that actually forbids the
# uncertainty to have negative entries but with correlation the
# sign of the uncertainty DOES matter.
if self.uncertainty is None and (
not hasattr(operand, "uncertainty") or operand.uncertainty is None
):
# Neither has uncertainties so the result should have none.
return None
elif self.uncertainty is None:
# Create a temporary uncertainty to allow uncertainty propagation
# to yield the correct results. (issue #4152)
self.uncertainty = operand.uncertainty.__class__(None)
result_uncert = self.uncertainty.propagate(
operation, operand, result, correlation
)
# Delete the temporary uncertainty again.
self.uncertainty = None
return result_uncert
elif operand is not None and operand.uncertainty is None:
# As with self.uncertainty is None but the other way around.
operand.uncertainty = self.uncertainty.__class__(None)
result_uncert = self.uncertainty.propagate(
operation, operand, result, correlation
)
operand.uncertainty = None
return result_uncert
else:
# Both have uncertainties so just propagate.
# only supply the axis kwarg if one has been specified for a collapsing operation
axis_kwarg = dict(axis=kwds["axis"]) if "axis" in kwds else dict()
return self.uncertainty.propagate(
operation, operand, result, correlation, **axis_kwarg
)
def _arithmetic_mask(self, operation, operand, handle_mask, axis=None, **kwds):
"""
Calculate the resulting mask.
This is implemented as the piecewise ``or`` operation if both have a
mask.
Parameters
----------
operation : callable
see :meth:`NDArithmeticMixin._arithmetic` parameter description.
By default, the ``operation`` will be ignored.
operand : `NDData`-like instance
The second operand wrapped in an instance of the same class as
self.
handle_mask : callable
see :meth:`NDArithmeticMixin.add`
kwds :
Additional parameters given to ``handle_mask``.
Returns
-------
result_mask : any type
If only one mask was present this mask is returned.
If neither had a mask ``None`` is returned. Otherwise
``handle_mask`` must create (and copy) the returned mask.
"""
# If only one mask is present we need not bother about any type checks
if (
self.mask is None and operand is not None and operand.mask is None
) or handle_mask is None:
return None
elif self.mask is None and operand is not None:
# Make a copy so there is no reference in the result.
return deepcopy(operand.mask)
elif operand is None or getattr(operand, "mask", None) is None:
# first condition lets through masks within collapse operations,
# second lets through masks when doing arithmetic on an
# operand without a mask:
return deepcopy(self.mask)
else:
# Now let's calculate the resulting mask (operation enforces copy)
return handle_mask(self.mask, operand.mask, **kwds)
def _arithmetic_wcs(self, operation, operand, compare_wcs, **kwds):
"""
Calculate the resulting wcs.
There is actually no calculation involved but it is a good place to
compare wcs information of both operands. This is currently not working
properly with `~astropy.wcs.WCS` (which is the suggested class for
storing as wcs property) but it will not break it neither.
Parameters
----------
operation : callable
see :meth:`NDArithmeticMixin._arithmetic` parameter description.
By default, the ``operation`` will be ignored.
operand : `NDData` instance or subclass
The second operand wrapped in an instance of the same class as
self.
compare_wcs : callable
see :meth:`NDArithmeticMixin.add` parameter description.
kwds :
Additional parameters given to ``compare_wcs``.
Raises
------
ValueError
If ``compare_wcs`` returns ``False``.
Returns
-------
result_wcs : any type
The ``wcs`` of the first operand is returned.
"""
# ok, not really arithmetic but we need to check which wcs makes sense
# for the result and this is an ideal place to compare the two WCS,
# too.
# I'll assume that the comparison returned None or False in case they
# are not equal.
if not compare_wcs(self.wcs, operand.wcs, **kwds):
raise ValueError("WCS are not equal.")
return deepcopy(self.wcs)
def _arithmetic_meta(self, operation, operand, handle_meta, **kwds):
"""
Calculate the resulting meta.
Parameters
----------
operation : callable
see :meth:`NDArithmeticMixin._arithmetic` parameter description.
By default, the ``operation`` will be ignored.
operand : `NDData`-like instance
The second operand wrapped in an instance of the same class as
self.
handle_meta : callable
see :meth:`NDArithmeticMixin.add`
kwds :
Additional parameters given to ``handle_meta``.
Returns
-------
result_meta : any type
The result of ``handle_meta``.
"""
# Just return what handle_meta does with both of the metas.
return handle_meta(self.meta, operand.meta, **kwds)
[docs]
@sharedmethod
@format_doc(_arit_doc, name="addition", op="+")
def add(self, operand, operand2=None, **kwargs):
return self._prepare_then_do_arithmetic(np.add, operand, operand2, **kwargs)
[docs]
@sharedmethod
@format_doc(_arit_doc, name="subtraction", op="-")
def subtract(self, operand, operand2=None, **kwargs):
return self._prepare_then_do_arithmetic(
np.subtract, operand, operand2, **kwargs
)
[docs]
@sharedmethod
@format_doc(_arit_doc, name="multiplication", op="*")
def multiply(self, operand, operand2=None, **kwargs):
return self._prepare_then_do_arithmetic(
np.multiply, operand, operand2, **kwargs
)
[docs]
@sharedmethod
@format_doc(_arit_doc, name="division", op="/")
def divide(self, operand, operand2=None, **kwargs):
return self._prepare_then_do_arithmetic(
np.true_divide, operand, operand2, **kwargs
)
[docs]
@sharedmethod
def sum(self, **kwargs):
return self._prepare_then_do_arithmetic(np.sum, **kwargs)
[docs]
@sharedmethod
def mean(self, **kwargs):
return self._prepare_then_do_arithmetic(np.mean, **kwargs)
[docs]
@sharedmethod
def min(self, **kwargs):
# use the provided propagate_uncertainties if available, otherwise default is False:
propagate_uncertainties = kwargs.pop("propagate_uncertainties", None)
return self._prepare_then_do_arithmetic(
np.min, propagate_uncertainties=propagate_uncertainties, **kwargs
)
[docs]
@sharedmethod
def max(self, **kwargs):
# use the provided propagate_uncertainties if available, otherwise default is False:
propagate_uncertainties = kwargs.pop("propagate_uncertainties", None)
return self._prepare_then_do_arithmetic(
np.max, propagate_uncertainties=propagate_uncertainties, **kwargs
)
@sharedmethod
def _prepare_then_do_arithmetic(
self_or_cls, operation, operand=None, operand2=None, **kwargs
):
"""Intermediate method called by public arithmetic (i.e. ``add``)
before the processing method (``_arithmetic``) is invoked.
.. warning::
Do not override this method in subclasses.
This method checks if it was called as instance or as class method and
then wraps the operands and the result from ``_arithmetic`` in the
appropriate subclass.
Parameters
----------
self_or_cls : instance or class
``sharedmethod`` behaves like a normal method if called on the
instance (then this parameter is ``self``) but like a classmethod
when called on the class (then this parameter is ``cls``).
operations : callable
The operation (normally a numpy-ufunc) that represents the
appropriate action.
operand, operand2, kwargs :
See for example ``add``.
Result
------
result : `~astropy.nddata.NDData`-like
Depending how this method was called either ``self_or_cls``
(called on class) or ``self_or_cls.__class__`` (called on instance)
is the NDData-subclass that is used as wrapper for the result.
"""
# DO NOT OVERRIDE THIS METHOD IN SUBCLASSES.
if isinstance(self_or_cls, NDArithmeticMixin):
# True means it was called on the instance, so self_or_cls is
# a reference to self
cls = self_or_cls.__class__
if operand2 is None:
# Only one operand was given. Set operand2 to operand and
# operand to self so that we call the appropriate method of the
# operand.
operand2 = operand
operand = self_or_cls
else:
# Convert the first operand to the class of this method.
# This is important so that always the correct _arithmetics is
# called later that method.
operand = cls(operand)
else:
# It was used as classmethod so self_or_cls represents the cls
cls = self_or_cls
# It was called on the class so we expect two operands!
if operand2 is None:
raise TypeError(
"operand2 must be given when the method isn't "
"called on an instance."
)
# Convert to this class. See above comment why.
operand = cls(operand)
# At this point operand, operand2, kwargs and cls are determined.
if operand2 is not None and not issubclass(
operand2.__class__, NDArithmeticMixin
):
# Let's try to convert operand2 to the class of operand to allow for
# arithmetic operations with numbers, lists, numpy arrays, numpy masked
# arrays, astropy quantities, masked quantities and of other subclasses
# of NDData.
operand2 = cls(operand2)
# Now call the _arithmetics method to do the arithmetic.
result, init_kwds = operand._arithmetic(operation, operand2, **kwargs)
elif issubclass(operand2.__class__, NDArithmeticMixin):
# calling as class method:
result, init_kwds = cls._arithmetic(
operand,
operation,
operand2,
**kwargs,
)
else:
# otherwise call the _arithmetic method on self for a collapse operation:
# for collapse operations, use astropy.utils.masked rather than handle_mask
result, init_kwds = self_or_cls._arithmetic(
operation,
operand2,
**kwargs,
)
# Return a new class based on the result
return cls(result, **init_kwds)
```