/usr/lib/python3/dist-packages/photutils/background/core.py is in python3-photutils 0.3-3.
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"""
This module defines background classes to estimate a scalar background
and background RMS from an array (which may be masked) of any dimension.
These classes were designed as part of an object-oriented interface for
the tools in the PSF subpackage.
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import abc
import numpy as np
from astropy.extern import six
from astropy.utils.misc import InheritDocstrings
from ..extern.sigma_clipping import sigma_clip
from ..extern.stats import mad_std, biweight_location, biweight_midvariance
__all__ = ['SigmaClip', 'BackgroundBase', 'BackgroundRMSBase',
'MeanBackground', 'MedianBackground', 'ModeEstimatorBackground',
'MMMBackground', 'SExtractorBackground',
'BiweightLocationBackground', 'StdBackgroundRMS',
'MADStdBackgroundRMS', 'BiweightMidvarianceBackgroundRMS']
def _masked_median(data, axis=None):
"""
Calculate the median of a (masked) array.
This function is necessary for a consistent interface across all
numpy versions. A bug was introduced in numpy v1.10 where
`numpy.ma.median` (with ``axis=None``) returns a single-valued
`~numpy.ma.MaskedArray` if the input data is a `~numpy.ndarray` or
if the data is a `~numpy.ma.MaskedArray`, but the mask is `False`
everywhere.
Parameters
----------
data : array-like
The input data.
axis : int or `None`, optional
The array axis along which the median is calculated. If
`None`, then the entire array is used.
Returns
-------
result : float or `~numpy.ma.MaskedArray`
The resulting median. If ``axis`` is `None`, then a float is
returned, otherwise a `~numpy.ma.MaskedArray` is returned.
"""
_median = np.ma.median(data, axis=axis)
if axis is None and np.ma.isMaskedArray(_median):
_median = _median.item()
return _median
class _ABCMetaAndInheritDocstrings(InheritDocstrings, abc.ABCMeta):
pass
class SigmaClip(object):
"""
Class to perform sigma clipping.
Parameters
----------
sigma : float, optional
The number of standard deviations to use for both the lower and
upper clipping limit. These limits are overridden by
``sigma_lower`` and ``sigma_upper``, if input. Defaults to 3.
sigma_lower : float or `None`, optional
The number of standard deviations to use as the lower bound for
the clipping limit. If `None` then the value of ``sigma`` is
used. Defaults to `None`.
sigma_upper : float or `None`, optional
The number of standard deviations to use as the upper bound for
the clipping limit. If `None` then the value of ``sigma`` is
used. Defaults to `None`.
iters : int or `None`, optional
The number of iterations to perform sigma clipping, or `None` to
clip until convergence is achieved (i.e., continue until the
last iteration clips nothing). Defaults to 5.
cenfunc : callable, optional
The function used to compute the center for the clipping. Must
be a callable that takes in a masked array and outputs the
central value. Defaults to the median (`numpy.ma.median`).
stdfunc : callable, optional
The function used to compute the standard deviation about the
center. Must be a callable that takes in a masked array and
outputs a width estimator. Masked (rejected) pixels are those
where::
deviation < (-sigma_lower * stdfunc(deviation))
deviation > (sigma_upper * stdfunc(deviation))
where::
deviation = data - cenfunc(data [,axis=int])
Defaults to the standard deviation (`numpy.std`).
"""
def __init__(self, sigma=3., sigma_lower=None, sigma_upper=None, iters=5,
cenfunc=np.ma.median, stdfunc=np.std):
self.sigma = sigma
self.sigma_lower = sigma_lower
self.sigma_upper = sigma_upper
self.iters = iters
self.cenfunc = np.ma.median
self.stdfunc = np.std
def __call__(self, data, axis=None, copy=True):
"""
Perform sigma clipping on the provided data.
Parameters
----------
data : array-like
The data to be sigma clipped.
axis : int or `None`, optional
If not `None`, clip along the given axis. For this case,
``axis`` will be passed on to ``cenfunc`` and ``stdfunc``,
which are expected to return an array with the axis
dimension removed (like the numpy functions). If `None`,
clip over all axes. Defaults to `None`.
copy : bool, optional
If `True`, the ``data`` array will be copied. If `False`,
the returned masked array data will contain the same array
as ``data``. Defaults to `True`.
Returns
-------
filtered_data : `numpy.ma.MaskedArray`
A masked array with the same shape as ``data`` input, where
the points rejected by the algorithm have been masked.
"""
return sigma_clip(data, sigma=self.sigma,
sigma_lower=self.sigma_lower,
sigma_upper=self.sigma_upper, iters=self.iters,
cenfunc=self.cenfunc, stdfunc=self.stdfunc,
axis=axis, copy=copy)
@six.add_metaclass(_ABCMetaAndInheritDocstrings)
class BackgroundBase(object):
"""
Base class for classes that estimate scalar background values.
Parameters
----------
sigma_clip : `SigmaClip` object, optional
A `SigmaClip` object that defines the sigma clipping parameters.
If `None` then no sigma clipping will be performed. The default
is to perform sigma clipping with ``sigma=3.`` and ``iters=5``.
"""
def __init__(self, sigma_clip=SigmaClip(sigma=3., iters=5)):
self.sigma_clip = sigma_clip
def __call__(self, data, axis=None):
return self.calc_background(data, axis=axis)
@abc.abstractmethod
def calc_background(self, data, axis=None):
"""
Calculate the background value.
Parameters
----------
data : array_like or `~numpy.ma.MaskedArray`
The array for which to calculate the background value.
axis : int or `None`, optional
The array axis along which the background is calculated. If
`None`, then the entire array is used.
Returns
-------
result : float or `~numpy.ma.MaskedArray`
The calculated background value. If ``axis`` is `None` then
a scalar will be returned, otherwise a
`~numpy.ma.MaskedArray` will be returned.
"""
@six.add_metaclass(_ABCMetaAndInheritDocstrings)
class BackgroundRMSBase(object):
"""
Base class for classes that estimate scalar background RMS values.
Parameters
----------
sigma_clip : `SigmaClip` object, optional
A `SigmaClip` object that defines the sigma clipping parameters.
If `None` then no sigma clipping will be performed. The default
is to perform sigma clipping with ``sigma=3.`` and ``iters=5``.
"""
def __init__(self, sigma_clip=SigmaClip(sigma=3., iters=5)):
self.sigma_clip = sigma_clip
def __call__(self, data, axis=None):
return self.calc_background_rms(data, axis=axis)
@abc.abstractmethod
def calc_background_rms(self, data, axis=None):
"""
Calculate the background RMS value.
Parameters
----------
data : array_like or `~numpy.ma.MaskedArray`
The array for which to calculate the background RMS value.
axis : int or `None`, optional
The array axis along which the background RMS is calculated.
If `None`, then the entire array is used.
Returns
-------
result : float or `~numpy.ma.MaskedArray`
The calculated background RMS value. If ``axis`` is `None`
then a scalar will be returned, otherwise a
`~numpy.ma.MaskedArray` will be returned.
"""
class MeanBackground(BackgroundBase):
"""
Class to calculate the background in an array as the (sigma-clipped)
mean.
Parameters
----------
sigma_clip : `SigmaClip` object, optional
A `SigmaClip` object that defines the sigma clipping parameters.
If `None` then no sigma clipping will be performed. The default
is to perform sigma clipping with ``sigma=3.`` and ``iters=5``.
Examples
--------
>>> from photutils import SigmaClip, MeanBackground
>>> data = np.arange(100)
>>> sigma_clip = SigmaClip(sigma=3.)
>>> bkg = MeanBackground(sigma_clip)
The background value can be calculated by using the
`calc_background` method, e.g.:
>>> bkg_value = bkg.calc_background(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
Alternatively, the background value can be calculated by calling the
class instance as a function, e.g.:
>>> bkg_value = bkg(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
"""
def calc_background(self, data, axis=None):
if self.sigma_clip is not None:
data = self.sigma_clip(data, axis=axis)
return np.ma.mean(data, axis=axis)
class MedianBackground(BackgroundBase):
"""
Class to calculate the background in an array as the (sigma-clipped)
median.
Parameters
----------
sigma_clip : `SigmaClip` object, optional
A `SigmaClip` object that defines the sigma clipping parameters.
If `None` then no sigma clipping will be performed. The default
is to perform sigma clipping with ``sigma=3.`` and ``iters=5``.
Examples
--------
>>> from photutils import SigmaClip, MedianBackground
>>> data = np.arange(100)
>>> sigma_clip = SigmaClip(sigma=3.)
>>> bkg = MedianBackground(sigma_clip)
The background value can be calculated by using the
`calc_background` method, e.g.:
>>> bkg_value = bkg.calc_background(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
Alternatively, the background value can be calculated by calling the
class instance as a function, e.g.:
>>> bkg_value = bkg(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
"""
def calc_background(self, data, axis=None):
if self.sigma_clip is not None:
data = self.sigma_clip(data, axis=axis)
return _masked_median(data, axis=axis)
class ModeEstimatorBackground(BackgroundBase):
"""
Class to calculate the background in an array using a mode estimator
of the form ``(median_factor * median) - (mean_factor * mean)``.
Parameters
----------
median_factor : float, optional
The multiplicative factor for the data median. Defaults to 3.
mean_factor : float, optional
The multiplicative factor for the data mean. Defaults to 2.
sigma_clip : `SigmaClip` object, optional
A `SigmaClip` object that defines the sigma clipping parameters.
If `None` then no sigma clipping will be performed. The default
is to perform sigma clipping with ``sigma=3.`` and ``iters=5``.
Examples
--------
>>> from photutils import SigmaClip, ModeEstimatorBackground
>>> data = np.arange(100)
>>> sigma_clip = SigmaClip(sigma=3.)
>>> bkg = ModeEstimatorBackground(median_factor=3., mean_factor=2.,
... sigma_clip=sigma_clip)
The background value can be calculated by using the
`calc_background` method, e.g.:
>>> bkg_value = bkg.calc_background(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
Alternatively, the background value can be calculated by calling the
class instance as a function, e.g.:
>>> bkg_value = bkg(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
"""
def __init__(self, median_factor=3., mean_factor=2., **kwargs):
super(ModeEstimatorBackground, self).__init__(**kwargs)
self.median_factor = median_factor
self.mean_factor = mean_factor
def calc_background(self, data, axis=None):
if self.sigma_clip is not None:
data = self.sigma_clip(data, axis=axis)
return ((self.median_factor * _masked_median(data, axis=axis)) -
(self.mean_factor * np.ma.mean(data, axis=axis)))
class MMMBackground(ModeEstimatorBackground):
"""
Class to calculate the background in an array using the DAOPHOT MMM
algorithm.
The background is calculated using a mode estimator of the form
``(3 * median) - (2 * mean)``.
Parameters
----------
sigma_clip : `SigmaClip` object, optional
A `SigmaClip` object that defines the sigma clipping parameters.
If `None` then no sigma clipping will be performed. The default
is to perform sigma clipping with ``sigma=3.`` and ``iters=5``.
Examples
--------
>>> from photutils import SigmaClip, MMMBackground
>>> data = np.arange(100)
>>> sigma_clip = SigmaClip(sigma=3.)
>>> bkg = MMMBackground(sigma_clip=sigma_clip)
The background value can be calculated by using the
`~photutils.background.core.ModeEstimatorBackground.calc_background`
method, e.g.:
>>> bkg_value = bkg.calc_background(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
Alternatively, the background value can be calculated by calling the
class instance as a function, e.g.:
>>> bkg_value = bkg(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
"""
def __init__(self, **kwargs):
kwargs['median_factor'] = 3.
kwargs['mean_factor'] = 2.
super(MMMBackground, self).__init__(**kwargs)
class SExtractorBackground(BackgroundBase):
"""
Class to calculate the background in an array using the
SExtractor algorithm.
The background is calculated using a mode estimator of the form
``(2.5 * median) - (1.5 * mean)``.
If ``(mean - median) / std > 0.3`` then the median is used instead.
Despite what the `SExtractor`_ User's Manual says, this is the
method it *always* uses.
.. _SExtractor: http://www.astromatic.net/software/sextractor
Parameters
----------
sigma_clip : `SigmaClip` object, optional
A `SigmaClip` object that defines the sigma clipping parameters.
If `None` then no sigma clipping will be performed. The default
is to perform sigma clipping with ``sigma=3.`` and ``iters=5``.
Examples
--------
>>> from photutils import SigmaClip, SExtractorBackground
>>> data = np.arange(100)
>>> sigma_clip = SigmaClip(sigma=3.)
>>> bkg = SExtractorBackground(sigma_clip)
The background value can be calculated by using the
`calc_background` method, e.g.:
>>> bkg_value = bkg.calc_background(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
Alternatively, the background value can be calculated by calling the
class instance as a function, e.g.:
>>> bkg_value = bkg(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
"""
def calc_background(self, data, axis=None):
if self.sigma_clip is not None:
data = self.sigma_clip(data, axis=axis)
_median = np.atleast_1d(_masked_median(data, axis=axis))
_mean = np.atleast_1d(np.ma.mean(data, axis=axis))
_std = np.atleast_1d(np.ma.std(data, axis=axis))
bkg = np.atleast_1d((2.5 * _median) - (1.5 * _mean))
bkg = np.ma.where(_std == 0, _mean, bkg)
idx = np.ma.where(_std != 0)
condition = (np.abs(_mean[idx] - _median[idx]) / _std[idx]) < 0.3
bkg[idx] = np.ma.where(condition, bkg[idx], _median[idx])
# np.ma.where always returns a masked array
if axis is None and np.ma.isMaskedArray(bkg):
bkg = bkg.item()
return bkg
class BiweightLocationBackground(BackgroundBase):
"""
Class to calculate the background in an array using the biweight
location.
Parameters
----------
c : float, optional
Tuning constant for the biweight estimator. Default value is
6.0.
M : float, optional
Initial guess for the biweight location. Default value is
`None`.
sigma_clip : `SigmaClip` object, optional
A `SigmaClip` object that defines the sigma clipping parameters.
If `None` then no sigma clipping will be performed. The default
is to perform sigma clipping with ``sigma=3.`` and ``iters=5``.
Examples
--------
>>> from photutils import SigmaClip, BiweightLocationBackground
>>> data = np.arange(100)
>>> sigma_clip = SigmaClip(sigma=3.)
>>> bkg = BiweightLocationBackground(sigma_clip=sigma_clip)
The background value can be calculated by using the
`calc_background` method, e.g.:
>>> bkg_value = bkg.calc_background(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
Alternatively, the background value can be calculated by calling the
class instance as a function, e.g.:
>>> bkg_value = bkg(data)
>>> print(bkg_value) # doctest: +FLOAT_CMP
49.5
"""
def __init__(self, c=6, M=None, **kwargs):
super(BiweightLocationBackground, self).__init__(**kwargs)
self.c = c
self.M = M
def calc_background(self, data, axis=None):
if self.sigma_clip is not None:
data = self.sigma_clip(data, axis=axis)
return biweight_location(data, c=self.c, M=self.M, axis=axis)
class StdBackgroundRMS(BackgroundRMSBase):
"""
Class to calculate the background RMS in an array as the
(sigma-clipped) standard deviation.
Parameters
----------
sigma_clip : `SigmaClip` object, optional
A `SigmaClip` object that defines the sigma clipping parameters.
If `None` then no sigma clipping will be performed. The default
is to perform sigma clipping with ``sigma=3.`` and ``iters=5``.
Examples
--------
>>> from photutils import SigmaClip, StdBackgroundRMS
>>> data = np.arange(100)
>>> sigma_clip = SigmaClip(sigma=3.)
>>> bkgrms = StdBackgroundRMS(sigma_clip)
The background RMS value can be calculated by using the
`calc_background_rms` method, e.g.:
>>> bkgrms_value = bkgrms.calc_background_rms(data)
>>> print(bkgrms_value) # doctest: +FLOAT_CMP
28.866070047722118
Alternatively, the background RMS value can be calculated by calling
the class instance as a function, e.g.:
>>> bkgrms_value = bkgrms(data)
>>> print(bkgrms_value) # doctest: +FLOAT_CMP
28.866070047722118
"""
def calc_background_rms(self, data, axis=None):
if self.sigma_clip is not None:
data = self.sigma_clip(data, axis=axis)
return np.ma.std(data, axis=axis)
class MADStdBackgroundRMS(BackgroundRMSBase):
"""
Class to calculate the background RMS in an array as using the
`median absolute deviation (MAD)
<http://en.wikipedia.org/wiki/Median_absolute_deviation>`_.
The standard deviation estimator is given by:
.. math::
\\sigma \\approx \\frac{{\\textrm{{MAD}}}}{{\Phi^{{-1}}(3/4)}}
\\approx 1.4826 \ \\textrm{{MAD}}
where :math:`\Phi^{{-1}}(P)` is the normal inverse cumulative
distribution function evaluated at probability :math:`P = 3/4`.
Parameters
----------
sigma_clip : `SigmaClip` object, optional
A `SigmaClip` object that defines the sigma clipping parameters.
If `None` then no sigma clipping will be performed. The default
is to perform sigma clipping with ``sigma=3.`` and ``iters=5``.
Examples
--------
>>> from photutils import SigmaClip, MADStdBackgroundRMS
>>> data = np.arange(100)
>>> sigma_clip = SigmaClip(sigma=3.)
>>> bkgrms = MADStdBackgroundRMS(sigma_clip)
The background RMS value can be calculated by using the
`calc_background_rms` method, e.g.:
>>> bkgrms_value = bkgrms.calc_background_rms(data)
>>> print(bkgrms_value) # doctest: +FLOAT_CMP
37.065055462640053
Alternatively, the background RMS value can be calculated by calling
the class instance as a function, e.g.:
>>> bkgrms_value = bkgrms(data)
>>> print(bkgrms_value) # doctest: +FLOAT_CMP
37.065055462640053
"""
def calc_background_rms(self, data, axis=None):
if self.sigma_clip is not None:
data = self.sigma_clip(data, axis=axis)
return mad_std(data, axis=axis)
class BiweightMidvarianceBackgroundRMS(BackgroundRMSBase):
"""
Class to calculate the background RMS in an array as the
(sigma-clipped) biweight midvariance.
Parameters
----------
c : float, optional
Tuning constant for the biweight estimator. Default value is
9.0.
M : float, optional
Initial guess for the biweight location. Default value is
`None`.
sigma_clip : `SigmaClip` object, optional
A `SigmaClip` object that defines the sigma clipping parameters.
If `None` then no sigma clipping will be performed. The default
is to perform sigma clipping with ``sigma=3.`` and ``iters=5``.
Examples
--------
>>> from photutils import SigmaClip, BiweightMidvarianceBackgroundRMS
>>> data = np.arange(100)
>>> sigma_clip = SigmaClip(sigma=3.)
>>> bkgrms = BiweightMidvarianceBackgroundRMS(sigma_clip=sigma_clip)
The background RMS value can be calculated by using the
`calc_background_rms` method, e.g.:
>>> bkgrms_value = bkgrms.calc_background_rms(data)
>>> print(bkgrms_value) # doctest: +FLOAT_CMP
30.094338485893392
Alternatively, the background RMS value can be calculated by calling
the class instance as a function, e.g.:
>>> bkgrms_value = bkgrms(data)
>>> print(bkgrms_value) # doctest: +FLOAT_CMP
30.094338485893392
"""
def __init__(self, c=9.0, M=None, **kwargs):
super(BiweightMidvarianceBackgroundRMS, self).__init__(**kwargs)
self.c = c
self.M = M
def calc_background_rms(self, data, axis=None):
if self.sigma_clip is not None:
data = self.sigma_clip(data, axis=axis)
return biweight_midvariance(data, c=self.c, M=self.M, axis=axis)
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