# Source code for astropy.stats.sigma_clipping

```# Licensed under a 3-clause BSD style license - see LICENSE.rst

import warnings

import numpy as np
from numpy.core.multiarray import normalize_axis_index

from astropy.units import Quantity
from astropy.utils import isiterable
from astropy.utils.exceptions import AstropyUserWarning
from astropy.stats._fast_sigma_clip import _sigma_clip_fast
from astropy.utils.compat.optional_deps import HAS_BOTTLENECK

if HAS_BOTTLENECK:
import bottleneck

__all__ = ['SigmaClip', 'sigma_clip', 'sigma_clipped_stats']

def _move_tuple_axes_first(array, axis):
"""
Bottleneck can only take integer axis, not tuple, so this function
takes all the axes to be operated on and combines them into the
first dimension of the array so that we can then use axis=0
"""

# Figure out how many axes we are operating over
naxis = len(axis)

# Add remaining axes to the axis tuple
axis += tuple(i for i in range(array.ndim) if i not in axis)

# The new position of each axis is just in order
destination = tuple(range(array.ndim))

# Reorder the array so that the axes being operated on are at the beginning
array_new = np.moveaxis(array, axis, destination)

# Collapse the dimensions being operated on into a single dimension so that
# we can then use axis=0 with the bottleneck functions
array_new = array_new.reshape((-1,) + array_new.shape[naxis:])

return array_new

def _nanmean(array, axis=None):
"""Bottleneck nanmean function that handle tuple axis."""

if isinstance(axis, tuple):
array = _move_tuple_axes_first(array, axis=axis)
axis = 0

if isinstance(array, Quantity):
return array.__array_wrap__(bottleneck.nanmean(array, axis=axis))
else:
return bottleneck.nanmean(array, axis=axis)

def _nanmedian(array, axis=None):
"""Bottleneck nanmedian function that handle tuple axis."""

if isinstance(axis, tuple):
array = _move_tuple_axes_first(array, axis=axis)
axis = 0

if isinstance(array, Quantity):
return array.__array_wrap__(bottleneck.nanmedian(array, axis=axis))
else:
return bottleneck.nanmedian(array, axis=axis)

def _nanstd(array, axis=None, ddof=0):
"""Bottleneck nanstd function that handle tuple axis."""

if isinstance(axis, tuple):
array = _move_tuple_axes_first(array, axis=axis)
axis = 0

if isinstance(array, Quantity):
return array.__array_wrap__(bottleneck.nanstd(array, axis=axis,
ddof=ddof))
else:
return bottleneck.nanstd(array, axis=axis, ddof=ddof)

"""mad_std function that ignores NaNs by default."""

[docs]class SigmaClip:
"""
Class to perform sigma clipping.

The data will be iterated over, each time rejecting values that are
less or more than a specified number of standard deviations from a
center value.

Clipped (rejected) pixels are those where::

data < cenfunc(data [,axis=int]) - (sigma_lower * stdfunc(data [,axis=int]))
data > cenfunc(data [,axis=int]) + (sigma_upper * stdfunc(data [,axis=int]))

Invalid data values (i.e., NaN or inf) are automatically clipped.

For a functional interface to sigma clipping, see
:func:`sigma_clip`.

.. note::
`scipy.stats.sigmaclip`
provides a subset of the functionality in this class.  Also, its
input data cannot be a masked array and it does not handle data
that contains invalid values (i.e., NaN or inf).  Also note that
it uses the mean as the centering function.

If your data is a `~numpy.ndarray` with no invalid values and
you want to use the mean as the centering function with
``axis=None`` and iterate to convergence, then
`scipy.stats.sigmaclip` is ~25-30% faster than the equivalent
settings here (``s = SigmaClip(cenfunc='mean', maxiters=None);
s(data, axis=None)``).

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.  The default is
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.  The default is `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.  The default is `None`.

maxiters : int or None, optional
The maximum number of sigma-clipping iterations to perform or
`None` to clip until convergence is achieved (i.e., iterate
until the last iteration clips nothing).  If convergence is
achieved prior to ``maxiters`` iterations, the clipping
iterations will stop.  The default is 5.

cenfunc : {'median', 'mean'} or callable, optional
The statistic or callable function/object used to compute the
center value for the clipping. If using a callable function/object and
the ``axis`` keyword is used, then it must be able to ignore
NaNs (e.g., `numpy.nanmean`) and has an ``axis`` keyword to return an
array with axis dimension(s) removed.  The default is ``'median'``.

stdfunc : {'std', 'mad_std'} or callable, optional
The statistic or callable function/object used to compute the
standard deviation about the center value. If using a callable
function/object and the ``axis`` keyword is used, then it must
be able to ignore NaNs (e.g., `numpy.nanstd`) and has
an ``axis`` keyword to return an array with axis dimension(s)
removed.  The default is ``'std'``.

grow : float or `False`, optional
fall outwith the clipping limits (only applied along ``axis``, if
specified). As an example, for a 2D image a value of 1 will mask the
nearest pixels in a cross pattern around each deviant pixel, while
1.5 will also reject the nearest diagonal neighbours and so on.

Notes
-----

The best performance will typically be obtained by setting ``cenfunc`` and
``stdfunc`` to one of the built-in functions specified as as string. If one of
the options is set to a string while the other has a custom callable, you may in some
cases see better performance if you have the `bottleneck`_ package installed.

.. _bottleneck:  https://github.com/pydata/bottleneck

--------
sigma_clip, sigma_clipped_stats

Examples
--------
This example uses a data array of random variates from a Gaussian
distribution.  We clip all points that are more than 2 sample
standard deviations from the median.  The result is a masked array,
where the mask is `True` for clipped data::

>>> from astropy.stats import SigmaClip
>>> from numpy.random import randn
>>> randvar = randn(10000)
>>> sigclip = SigmaClip(sigma=2, maxiters=5)
>>> filtered_data = sigclip(randvar)

This example clips all points that are more than 3 sigma relative to
the sample *mean*, clips until convergence, returns an unmasked
`~numpy.ndarray`, and modifies the data in-place::

>>> from astropy.stats import SigmaClip
>>> from numpy.random import randn
>>> from numpy import mean
>>> randvar = randn(10000)
>>> sigclip = SigmaClip(sigma=3, maxiters=None, cenfunc='mean')
>>> filtered_data = sigclip(randvar, masked=False, copy=False)

This example sigma clips along one axis::

>>> from astropy.stats import SigmaClip
>>> from numpy.random import normal
>>> from numpy import arange, diag, ones
>>> data = arange(5) + normal(0., 0.05, (5, 5)) + diag(ones(5))
>>> sigclip = SigmaClip(sigma=2.3)
>>> filtered_data = sigclip(data, axis=0)

Note that along the other axis, no points would be clipped, as the
standard deviation is higher.
"""

def __init__(self, sigma=3., sigma_lower=None, sigma_upper=None,
maxiters=5, cenfunc='median', stdfunc='std', grow=False):

self.sigma = sigma
self.sigma_lower = sigma_lower or sigma
self.sigma_upper = sigma_upper or sigma
self.maxiters = maxiters or np.inf
self.cenfunc = cenfunc
self.stdfunc = stdfunc
self._cenfunc_parsed = self._parse_cenfunc(cenfunc)
self._stdfunc_parsed = self._parse_stdfunc(stdfunc)
self.grow = grow

# This just checks that SciPy is available, to avoid failing later
# than necessary if __call__ needs it:
if self.grow:
from scipy.ndimage import binary_dilation

def __repr__(self):
return ('SigmaClip(sigma={}, sigma_lower={}, sigma_upper={}, '
'maxiters={}, cenfunc={}, stdfunc={}, grow={})'
.format(self.sigma, self.sigma_lower, self.sigma_upper,
self.maxiters, self.cenfunc, self.stdfunc, self.grow))

def __str__(self):
lines = ['<' + self.__class__.__name__ + '>']
attrs = ['sigma', 'sigma_lower', 'sigma_upper', 'maxiters', 'cenfunc',
'stdfunc', 'grow']
for attr in attrs:
lines.append(f'    {attr}: {getattr(self, attr)}')
return '\n'.join(lines)

def _parse_cenfunc(self, cenfunc):
if isinstance(cenfunc, str):
if cenfunc == 'median':
if HAS_BOTTLENECK:
cenfunc = _nanmedian
else:
cenfunc = np.nanmedian  # pragma: no cover

elif cenfunc == 'mean':
if HAS_BOTTLENECK:
cenfunc = _nanmean
else:
cenfunc = np.nanmean  # pragma: no cover

else:
raise ValueError(f'{cenfunc} is an invalid cenfunc.')

return cenfunc

def _parse_stdfunc(self, stdfunc):
if isinstance(stdfunc, str):
if stdfunc == 'std':
if HAS_BOTTLENECK:
stdfunc = _nanstd
else:
stdfunc = np.nanstd  # pragma: no cover
else:
raise ValueError(f'{stdfunc} is an invalid stdfunc.')

return stdfunc

def _compute_bounds(self, data, axis=None):
# ignore RuntimeWarning if the array (or along an axis) has only
# NaNs
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=RuntimeWarning)
self._max_value = self._cenfunc_parsed(data, axis=axis)
std = self._stdfunc_parsed(data, axis=axis)
self._min_value = self._max_value - (std * self.sigma_lower)
self._max_value += std * self.sigma_upper

def _sigmaclip_fast(self, data, axis=None,
copy=True):
"""
Fast C implementation for simple use cases
"""

if isinstance(data, Quantity):
data, unit = data.value, data.unit
else:
unit = None

if copy is False and masked is False and data.dtype.kind != 'f':
raise Exception("cannot mask non-floating-point array with NaN "
"values, set copy=True or masked=True to avoid "
"this.")

if axis is None:
axis = -1 if data.ndim == 1 else tuple(range(data.ndim))

if not isiterable(axis):
axis = normalize_axis_index(axis, data.ndim)
data_reshaped = data
transposed_shape = None
else:
# The gufunc implementation does not handle non-scalar axis
# so we combine the dimensions together as the last
# dimension and set axis=-1
axis = tuple(normalize_axis_index(ax, data.ndim) for ax in axis)
transposed_axes = tuple(ax for ax in range(data.ndim)
if ax not in axis) + axis
data_transposed = data.transpose(transposed_axes)
transposed_shape = data_transposed.shape
data_reshaped = data_transposed.reshape(
transposed_shape[:data.ndim - len(axis)] + (-1,))
axis = -1

if data_reshaped.dtype.kind != 'f' or data_reshaped.dtype.itemsize > 8:
data_reshaped = data_reshaped.astype(float)

warnings.warn('Input data contains invalid values (NaNs or '
'infs), which were automatically clipped.',
AstropyUserWarning)

data = data.view(np.ndarray)
data_reshaped = data_reshaped.view(np.ndarray)

self.cenfunc == 'median',
-1 if np.isinf(self.maxiters) else self.maxiters,
self.sigma_lower, self.sigma_upper, axis=axis)

with np.errstate(invalid='ignore'):
mask |= data_reshaped < np.expand_dims(bound_lo, axis)
mask |= data_reshaped > np.expand_dims(bound_hi, axis)

if transposed_shape is not None:
# Get mask in shape of data.
for ax in range(data.ndim)))

else:
if copy:
result = data.astype(float, copy=True)
else:
result = data

if unit is not None:
result = result << unit
bound_lo = bound_lo << unit
bound_hi = bound_hi << unit

if return_bounds:
return result, bound_lo, bound_hi
else:
return result

copy=True):
"""
Sigma clip the data when ``axis`` is None and ``grow`` is not >0.

In this simple case, we remove clipped elements from the
flattened array during each iteration.
"""

filtered_data = data.ravel()

# remove masked values and convert to ndarray

# remove invalid values
warnings.warn('Input data contains invalid values (NaNs or '
'infs), which were automatically clipped.',
AstropyUserWarning)

nchanged = 1
iteration = 0
while nchanged != 0 and (iteration < self.maxiters):
iteration += 1
size = filtered_data.size
self._compute_bounds(filtered_data, axis=None)
filtered_data = filtered_data[(filtered_data >= self._min_value) &
(filtered_data <= self._max_value)]
nchanged = size - filtered_data.size

self._niterations = iteration

# return a masked array and optional bounds

# update the mask in place, ignoring RuntimeWarnings for
# comparisons with NaN data values
with np.errstate(invalid='ignore'):
data > self._max_value)

if return_bounds:
return filtered_data, self._min_value, self._max_value
else:
return filtered_data

return_bounds=False, copy=True):
"""
Sigma clip the data when ``axis`` or ``grow`` is specified.

In this case, we replace clipped values with NaNs as placeholder
values.
"""

# float array type is needed to insert nans into the array
filtered_data = data.astype(float)    # also makes a copy

# remove invalid values
warnings.warn('Input data contains invalid values (NaNs or '
'infs), which were automatically clipped.',
AstropyUserWarning)

# remove masked values and convert to plain ndarray
filtered_data = filtered_data.filled(np.nan)

if axis is not None:
# convert negative axis/axes
if not isiterable(axis):
axis = (axis,)
axis = tuple(filtered_data.ndim + n if n < 0 else n for n in axis)

# define the shape of min/max arrays so that they can be broadcast
# with the data
mshape = tuple(1 if dim in axis else size
for dim, size in enumerate(filtered_data.shape))

if self.grow:
from scipy.ndimage import binary_dilation

# Construct a growth kernel from the specified radius in pixels
# (consider caching this for re-use by subsequent calls?):
cenidx = int(self.grow)
size = 2 * cenidx + 1
indices = np.mgrid[(slice(0, size),) * data.ndim]
if axis is not None:
for n, dim in enumerate(indices):
# For any axes that we're not clipping over, set their
# "grow" in that dimension:
if n not in axis:
dim[dim != cenidx] = size
kernel = sum(((idx - cenidx)**2 for idx in indices)) <= self.grow**2
del indices

nchanged = 1
iteration = 0
while nchanged != 0 and (iteration < self.maxiters):
iteration += 1
self._compute_bounds(filtered_data, axis=axis)
if not np.isscalar(self._min_value):
self._min_value = self._min_value.reshape(mshape)
self._max_value = self._max_value.reshape(mshape)

with np.errstate(invalid='ignore'):
# Since these comparisons are always False for NaNs, the
# resulting mask contains only newly-rejected pixels and we
# can dilate it without growing masked pixels more than once.
new_mask = ((filtered_data < self._min_value) |
(filtered_data > self._max_value))
if self.grow:

self._niterations = iteration

# create an output masked array
if copy:
~np.isfinite(filtered_data),
copy=True)
else:
# ignore RuntimeWarnings for comparisons with NaN data values
with np.errstate(invalid='ignore'):

out < self._min_value, out > self._max_value),
out, copy=False)

if return_bounds:
return filtered_data, self._min_value, self._max_value
else:
return filtered_data

[docs]    def __call__(self, data, axis=None, masked=True, return_bounds=False,
copy=True):
"""
Perform sigma clipping on the provided data.

Parameters
----------
The data to be sigma clipped.

axis : None or int or tuple of int, optional
The axis or axes along which to sigma clip the data.  If `None`,
then the flattened data will be used.  ``axis`` is passed
to the ``cenfunc`` and ``stdfunc``.  The default is `None`.

If `True`, then a `~numpy.ma.MaskedArray` is returned, where
the mask is `True` for clipped values.  If `False`, then a
`~numpy.ndarray` and the minimum and maximum clipping
thresholds are returned.  The default is `True`.

return_bounds : bool, optional
If `True`, then the minimum and maximum clipping bounds are
also returned.

copy : bool, optional
If `True`, then the ``data`` array will be copied.  If
data will contain the same array as the input ``data`` (if
``data`` is a `~numpy.ndarray` or `~numpy.ma.MaskedArray`).
If `False` and ``masked=False``, the input data is modified
in-place. The default is `True`.

Returns
-------
result : array-like
returned, where the mask is `True` for clipped values and
where the input mask was `True`.

If ``masked=False``, then a `~numpy.ndarray` is returned.

array or array above, the minimum and maximum clipping
bounds are returned.

If ``masked=False`` and ``axis=None``, then the output array
is a flattened 1D `~numpy.ndarray` where the clipped values
have been removed.  If ``return_bounds=True`` then the
returned minimum and maximum thresholds are scalars.

If ``masked=False`` and ``axis`` is specified, then the
output `~numpy.ndarray` will have the same shape as the
input ``data`` and contain ``np.nan`` where values were
clipped.  If the input ``data`` was a masked array, then the
output `~numpy.ndarray` will also contain ``np.nan`` where
the input mask was `True`.  If ``return_bounds=True`` then
the returned minimum and maximum clipping thresholds will be
be `~numpy.ndarray`\\s.
"""

data = np.asanyarray(data)

if data.size == 0:
return data

return data
else:
return np.ma.filled(data.astype(float), fill_value=np.nan)

# Shortcut for common cases where a fast C implementation can be used.
if (self.cenfunc in ('mean', 'median') and
axis is not None and not self.grow):
return_bounds=return_bounds,
copy=copy)

# These two cases are treated separately because when ``axis=None``
# we can simply remove clipped values from the array.  This is not
# possible when ``axis`` or ``grow`` is specified.
if axis is None and not self.grow:
return_bounds=return_bounds,
copy=copy)
else:
return_bounds=return_bounds,
copy=copy)

[docs]def sigma_clip(data, sigma=3, sigma_lower=None, sigma_upper=None, maxiters=5,
return_bounds=False, copy=True, grow=False):
"""
Perform sigma-clipping on the provided data.

The data will be iterated over, each time rejecting values that are
less or more than a specified number of standard deviations from a
center value.

Clipped (rejected) pixels are those where::

data < cenfunc(data [,axis=int]) - (sigma_lower * stdfunc(data [,axis=int]))
data > cenfunc(data [,axis=int]) + (sigma_upper * stdfunc(data [,axis=int]))

Invalid data values (i.e., NaN or inf) are automatically clipped.

For an object-oriented interface to sigma clipping, see
:class:`SigmaClip`.

.. note::
`scipy.stats.sigmaclip`
provides a subset of the functionality in this class.  Also, its
input data cannot be a masked array and it does not handle data
that contains invalid values (i.e., NaN or inf).  Also note that
it uses the mean as the centering function.

If your data is a `~numpy.ndarray` with no invalid values and
you want to use the mean as the centering function with
``axis=None`` and iterate to convergence, then
`scipy.stats.sigmaclip` is ~25-30% faster than the equivalent
settings here (``sigma_clip(data, cenfunc='mean', maxiters=None,
axis=None)``).

Parameters
----------
The data to be sigma clipped.

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.  The default is
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.  The default is `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.  The default is `None`.

maxiters : int or None, optional
The maximum number of sigma-clipping iterations to perform or
`None` to clip until convergence is achieved (i.e., iterate
until the last iteration clips nothing).  If convergence is
achieved prior to ``maxiters`` iterations, the clipping
iterations will stop.  The default is 5.

cenfunc : {'median', 'mean'} or callable, optional
The statistic or callable function/object used to compute the
center value for the clipping. If using a callable function/object and
the ``axis`` keyword is used, then it must be able to ignore
NaNs (e.g., `numpy.nanmean`) and has an ``axis`` keyword to return an
array with axis dimension(s) removed.  The default is ``'median'``.

stdfunc : {'std', 'mad_std'} or callable, optional
The statistic or callable function/object used to compute the
standard deviation about the center value. If using a callable
function/object and the ``axis`` keyword is used, then it must
be able to ignore NaNs (e.g., `numpy.nanstd`) and has
an ``axis`` keyword to return an array with axis dimension(s)
removed.  The default is ``'std'``.

axis : None or int or tuple of int, optional
The axis or axes along which to sigma clip the data.  If `None`,
then the flattened data will be used.  ``axis`` is passed to the
``cenfunc`` and ``stdfunc``.  The default is `None`.

If `True`, then a `~numpy.ma.MaskedArray` is returned, where the
mask is `True` for clipped values.  If `False`, then a
`~numpy.ndarray` and the minimum and maximum clipping thresholds
are returned.  The default is `True`.

return_bounds : bool, optional
If `True`, then the minimum and maximum clipping bounds are also
returned.

copy : bool, optional
If `True`, then the ``data`` array will be copied.  If
data will contain the same array as the input ``data`` (if
``data`` is a `~numpy.ndarray` or `~numpy.ma.MaskedArray`).
If `False` and ``masked=False``, the input data is modified
in-place. The default is `True`.

grow : float or `False`, optional
fall outwith the clipping limits (only applied along ``axis``, if
specified). As an example, for a 2D image a value of 1 will mask the
nearest pixels in a cross pattern around each deviant pixel, while
1.5 will also reject the nearest diagonal neighbours and so on.

Returns
-------
result : array-like
where the mask is `True` for clipped values and where the input

If ``masked=False``, then a `~numpy.ndarray` is returned.

or array above, the minimum and maximum clipping bounds are
returned.

If ``masked=False`` and ``axis=None``, then the output array is
a flattened 1D `~numpy.ndarray` where the clipped values have
been removed.  If ``return_bounds=True`` then the returned
minimum and maximum thresholds are scalars.

If ``masked=False`` and ``axis`` is specified, then the output
`~numpy.ndarray` will have the same shape as the input ``data``
and contain ``np.nan`` where values were clipped.  If the input
``data`` was a masked array, then the output `~numpy.ndarray`
will also contain ``np.nan`` where the input mask was `True`.
If ``return_bounds=True`` then the returned minimum and maximum
clipping thresholds will be be `~numpy.ndarray`\\s.

Notes
-----

The best performance will typically be obtained by setting ``cenfunc`` and
``stdfunc`` to one of the built-in functions specified as as string. If one of
the options is set to a string while the other has a custom callable, you may in some
cases see better performance if you have the `bottleneck`_ package installed.

.. _bottleneck:  https://github.com/pydata/bottleneck

--------
SigmaClip, sigma_clipped_stats

Examples
--------
This example uses a data array of random variates from a Gaussian
distribution.  We clip all points that are more than 2 sample
standard deviations from the median.  The result is a masked array,
where the mask is `True` for clipped data::

>>> from astropy.stats import sigma_clip
>>> from numpy.random import randn
>>> randvar = randn(10000)
>>> filtered_data = sigma_clip(randvar, sigma=2, maxiters=5)

This example clips all points that are more than 3 sigma relative to
the sample *mean*, clips until convergence, returns an unmasked
`~numpy.ndarray`, and does not copy the data::

>>> from astropy.stats import sigma_clip
>>> from numpy.random import randn
>>> from numpy import mean
>>> randvar = randn(10000)
>>> filtered_data = sigma_clip(randvar, sigma=3, maxiters=None,

This example sigma clips along one axis::

>>> from astropy.stats import sigma_clip
>>> from numpy.random import normal
>>> from numpy import arange, diag, ones
>>> data = arange(5) + normal(0., 0.05, (5, 5)) + diag(ones(5))
>>> filtered_data = sigma_clip(data, sigma=2.3, axis=0)

Note that along the other axis, no points would be clipped, as the
standard deviation is higher.
"""

sigclip = SigmaClip(sigma=sigma, sigma_lower=sigma_lower,
sigma_upper=sigma_upper, maxiters=maxiters,
cenfunc=cenfunc, stdfunc=stdfunc, grow=grow)

return_bounds=return_bounds, copy=copy)

sigma_lower=None, sigma_upper=None, maxiters=5,
cenfunc='median', stdfunc='std', std_ddof=0,
axis=None, grow=False):
"""
Calculate sigma-clipped statistics on the provided data.

Parameters
----------
Data array or object that can be converted to an array.

A boolean mask with the same shape as ``data``, where a `True`
value indicates the corresponding element of ``data`` is masked.
Masked pixels are excluded when computing the statistics.

A data value (e.g., ``0.0``) that is ignored when computing the

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.  The default is
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.  The default is `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.  The default is `None`.

maxiters : int or None, optional
The maximum number of sigma-clipping iterations to perform or
`None` to clip until convergence is achieved (i.e., iterate
until the last iteration clips nothing).  If convergence is
achieved prior to ``maxiters`` iterations, the clipping
iterations will stop.  The default is 5.

cenfunc : {'median', 'mean'} or callable, optional
The statistic or callable function/object used to compute the
center value for the clipping. If using a callable function/object and
the ``axis`` keyword is used, then it must be able to ignore
NaNs (e.g., `numpy.nanmean`) and has an ``axis`` keyword to return an
array with axis dimension(s) removed.  The default is ``'median'``.

stdfunc : {'std', 'mad_std'} or callable, optional
The statistic or callable function/object used to compute the
standard deviation about the center value. If using a callable
function/object and the ``axis`` keyword is used, then it must
be able to ignore NaNs (e.g., `numpy.nanstd`) and has
an ``axis`` keyword to return an array with axis dimension(s)
removed.  The default is ``'std'``.

std_ddof : int, optional
The delta degrees of freedom for the standard deviation
calculation.  The divisor used in the calculation is ``N -
std_ddof``, where ``N`` represents the number of elements.  The
default is 0.

axis : None or int or tuple of int, optional
The axis or axes along which to sigma clip the data.  If `None`,
then the flattened data will be used.  ``axis`` is passed
to the ``cenfunc`` and ``stdfunc``.  The default is `None`.

grow : float or `False`, optional
fall outwith the clipping limits (only applied along ``axis``, if
specified). As an example, for a 2D image a value of 1 will mask the
nearest pixels in a cross pattern around each deviant pixel, while
1.5 will also reject the nearest diagonal neighbours and so on.

Notes
-----

The best performance will typically be obtained by setting ``cenfunc`` and
``stdfunc`` to one of the built-in functions specified as as string. If one of
the options is set to a string while the other has a custom callable, you may in some
cases see better performance if you have the `bottleneck`_ package installed.

.. _bottleneck:  https://github.com/pydata/bottleneck

Returns
-------
mean, median, stddev : float
The mean, median, and standard deviation of the sigma-clipped
data.

--------
SigmaClip, sigma_clip
"""

sigclip = SigmaClip(sigma=sigma, sigma_lower=sigma_lower,
sigma_upper=sigma_upper, maxiters=maxiters,
cenfunc=cenfunc, stdfunc=stdfunc, grow=grow)
data_clipped = sigclip(data, axis=axis, masked=False, return_bounds=False,
copy=True)

if HAS_BOTTLENECK:
mean = _nanmean(data_clipped, axis=axis)
median = _nanmedian(data_clipped, axis=axis)
std = _nanstd(data_clipped, ddof=std_ddof, axis=axis)
else:  # pragma: no cover
mean = np.nanmean(data_clipped, axis=axis)
median = np.nanmedian(data_clipped, axis=axis)
std = np.nanstd(data_clipped, ddof=std_ddof, axis=axis)

return mean, median, std
```