# 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.stats.funcs import mad_std 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) def _nanmadstd(array, axis=None): """mad_std function that ignores NaNs by default.""" return mad_std(array, axis=axis, ignore_nan=True) 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 < center - (sigma_lower * std) data > center + (sigma_upper * std) where:: center = cenfunc(data [, axis=]) std = stdfunc(data [, axis=]) 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. The equivalent settings to `scipy.stats.sigmaclip` are:: sigclip = SigmaClip(sigma=4., cenfunc='mean', maxiters=None) sigclip(data, axis=None, masked=False, return_bounds=True) 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 it must have 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 it must have an ``axis`` keyword to return an array with axis dimension(s) removed. The default is ``'std'``. grow : float or `False`, optional Radius within which to mask the neighbouring pixels of those that 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. See Also -------- sigma_clip, sigma_clipped_stats 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 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._min_value = np.nan self._max_value = np.nan self._niterations = 0 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 self._binary_dilation = 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, repr(self.cenfunc), repr(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}: {repr(getattr(self, attr))}') return '\n'.join(lines) @staticmethod def _parse_cenfunc(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 @staticmethod def _parse_stdfunc(stdfunc): if isinstance(stdfunc, str): if stdfunc == 'std': if HAS_BOTTLENECK: stdfunc = _nanstd else: stdfunc = np.nanstd # pragma: no cover elif stdfunc == 'mad_std': stdfunc = _nanmadstd 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, masked=True, return_bounds=False, 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) mask = ~np.isfinite(data_reshaped) if np.any(mask): warnings.warn('Input data contains invalid values (NaNs or ' 'infs), which were automatically clipped.', AstropyUserWarning) if isinstance(data_reshaped, np.ma.MaskedArray): mask |= data_reshaped.mask data = data.view(np.ndarray) data_reshaped = data_reshaped.view(np.ndarray) mask = np.broadcast_to(mask, data_reshaped.shape).copy() bound_lo, bound_hi = _sigma_clip_fast( data_reshaped, mask, self.cenfunc == 'median', self.stdfunc == 'mad_std', -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. mask = mask.reshape(transposed_shape) mask = mask.transpose(tuple(transposed_axes.index(ax) for ax in range(data.ndim))) if masked: result = np.ma.array(data, mask=mask, copy=copy) else: if copy: result = data.astype(float, copy=True) else: result = data result[mask] = np.nan 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 def _sigmaclip_noaxis(self, data, masked=True, return_bounds=False, copy=True): """ Sigma clip 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 if isinstance(filtered_data, np.ma.MaskedArray): filtered_data = filtered_data.data[~filtered_data.mask] # remove invalid values good_mask = np.isfinite(filtered_data) if np.any(~good_mask): filtered_data = filtered_data[good_mask] 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 if masked: # return a masked array and optional bounds filtered_data = np.ma.masked_invalid(data, copy=copy) # update the mask in place, ignoring RuntimeWarnings for # comparisons with NaN data values with np.errstate(invalid='ignore'): filtered_data.mask |= np.logical_or(data < self._min_value, data > self._max_value) if return_bounds: return filtered_data, self._min_value, self._max_value else: return filtered_data def _sigmaclip_withaxis(self, data, axis=None, masked=True, 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 bad_mask = ~np.isfinite(filtered_data) if np.any(bad_mask): filtered_data[bad_mask] = np.nan warnings.warn('Input data contains invalid values (NaNs or ' 'infs), which were automatically clipped.', AstropyUserWarning) # remove masked values and convert to plain ndarray if isinstance(filtered_data, np.ma.MaskedArray): filtered_data = np.ma.masked_invalid(filtered_data).astype(float) 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: # 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 indices outside the growth radius, so masked # points won't "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: new_mask = self._binary_dilation(new_mask, kernel) filtered_data[new_mask] = np.nan nchanged = np.count_nonzero(new_mask) del new_mask self._niterations = iteration if masked: # create an output masked array if copy: filtered_data = np.ma.MaskedArray(data, ~np.isfinite(filtered_data), copy=True) else: # ignore RuntimeWarnings for comparisons with NaN data values with np.errstate(invalid='ignore'): out = np.ma.masked_invalid(data, copy=False) filtered_data = np.ma.masked_where(np.logical_or( 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 def __call__(self, data, axis=None, masked=True, return_bounds=False, copy=True): """ Perform sigma clipping on the provided data. Parameters ---------- data : array-like or `~numpy.ma.MaskedArray` 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`. masked : bool, optional If `True`, then a `~numpy.ma.MaskedArray` is returned, where the mask is `True` for clipped values. If `False`, then a `~numpy.ndarray` is 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 `False` and ``masked=True``, then the returned masked array 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 If ``masked=True``, then a `~numpy.ma.MaskedArray` is 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. If ``return_bounds=True``, then in addition to the masked 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: if masked: result = np.ma.MaskedArray(data) else: result = data if return_bounds: return result, self._min_value, self._max_value else: return result if isinstance(data, np.ma.MaskedArray) and data.mask.all(): if masked: result = data else: result = np.full(data.shape, np.nan) if return_bounds: return result, self._min_value, self._max_value else: return result # Shortcut for common cases where a fast C implementation can be # used. if (self.cenfunc in ('mean', 'median') and self.stdfunc in ('std', 'mad_std') and axis is not None and not self.grow): return self._sigmaclip_fast(data, axis=axis, masked=masked, 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 self._sigmaclip_noaxis(data, masked=masked, return_bounds=return_bounds, copy=copy) else: return self._sigmaclip_withaxis(data, axis=axis, masked=masked, return_bounds=return_bounds, copy=copy) def sigma_clip(data, sigma=3, sigma_lower=None, sigma_upper=None, maxiters=5, cenfunc='median', stdfunc='std', axis=None, masked=True, 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 < center - (sigma_lower * std) data > center + (sigma_upper * std) where:: center = cenfunc(data [, axis=]) std = stdfunc(data [, axis=]) 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. The equivalent settings to `scipy.stats.sigmaclip` are:: sigma_clip(sigma=4., cenfunc='mean', maxiters=None, axis=None, ... masked=False, return_bounds=True) Parameters ---------- data : array-like or `~numpy.ma.MaskedArray` 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 it must have 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 it must have 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`. masked : bool, optional 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 `False` and ``masked=True``, then the returned masked array 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 Radius within which to mask the neighbouring pixels of those that 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 If ``masked=True``, then a `~numpy.ma.MaskedArray` is 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. If ``return_bounds=True``, then in addition to the masked 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. See Also -------- SigmaClip, sigma_clipped_stats 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 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, ... cenfunc=mean, masked=False, copy=False) 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 sigclip(data, axis=axis, masked=masked, return_bounds=return_bounds, copy=copy) def sigma_clipped_stats(data, mask=None, mask_value=None, sigma=3.0, 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-like or `~numpy.ma.MaskedArray` Data array or object that can be converted to an array. mask : `numpy.ndarray` (bool), optional 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. mask_value : float, optional A data value (e.g., ``0.0``) that is ignored when computing the statistics. ``mask_value`` will be masked in addition to any input ``mask``. 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 it must have 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 it must have 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 Radius within which to mask the neighbouring pixels of those that 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. See Also -------- SigmaClip, sigma_clip """ if mask is not None: data = np.ma.MaskedArray(data, mask) if mask_value is not None: data = np.ma.masked_values(data, mask_value) if isinstance(data, np.ma.MaskedArray) and data.mask.all(): return np.ma.masked, np.ma.masked, np.ma.masked 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