1881 lines
64 KiB
Python
1881 lines
64 KiB
Python
"""
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Functions that ignore NaN.
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Functions
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---------
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- `nanmin` -- minimum non-NaN value
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- `nanmax` -- maximum non-NaN value
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- `nanargmin` -- index of minimum non-NaN value
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- `nanargmax` -- index of maximum non-NaN value
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- `nansum` -- sum of non-NaN values
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- `nanprod` -- product of non-NaN values
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- `nancumsum` -- cumulative sum of non-NaN values
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- `nancumprod` -- cumulative product of non-NaN values
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- `nanmean` -- mean of non-NaN values
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- `nanvar` -- variance of non-NaN values
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- `nanstd` -- standard deviation of non-NaN values
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- `nanmedian` -- median of non-NaN values
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- `nanquantile` -- qth quantile of non-NaN values
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- `nanpercentile` -- qth percentile of non-NaN values
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"""
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import functools
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import warnings
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import numpy as np
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from numpy.lib import function_base
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from numpy.core import overrides
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array_function_dispatch = functools.partial(
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overrides.array_function_dispatch, module='numpy')
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__all__ = [
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'nansum', 'nanmax', 'nanmin', 'nanargmax', 'nanargmin', 'nanmean',
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'nanmedian', 'nanpercentile', 'nanvar', 'nanstd', 'nanprod',
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'nancumsum', 'nancumprod', 'nanquantile'
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]
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def _nan_mask(a, out=None):
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"""
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Parameters
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----------
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a : array-like
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Input array with at least 1 dimension.
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out : ndarray, optional
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Alternate output array in which to place the result. The default
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is ``None``; if provided, it must have the same shape as the
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expected output and will prevent the allocation of a new array.
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Returns
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-------
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y : bool ndarray or True
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A bool array where ``np.nan`` positions are marked with ``False``
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and other positions are marked with ``True``. If the type of ``a``
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is such that it can't possibly contain ``np.nan``, returns ``True``.
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"""
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# we assume that a is an array for this private function
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if a.dtype.kind not in 'fc':
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return True
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y = np.isnan(a, out=out)
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y = np.invert(y, out=y)
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return y
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def _replace_nan(a, val):
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"""
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If `a` is of inexact type, make a copy of `a`, replace NaNs with
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the `val` value, and return the copy together with a boolean mask
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marking the locations where NaNs were present. If `a` is not of
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inexact type, do nothing and return `a` together with a mask of None.
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Note that scalars will end up as array scalars, which is important
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for using the result as the value of the out argument in some
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operations.
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Parameters
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----------
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a : array-like
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Input array.
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val : float
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NaN values are set to val before doing the operation.
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Returns
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-------
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y : ndarray
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If `a` is of inexact type, return a copy of `a` with the NaNs
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replaced by the fill value, otherwise return `a`.
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mask: {bool, None}
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If `a` is of inexact type, return a boolean mask marking locations of
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NaNs, otherwise return None.
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"""
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a = np.asanyarray(a)
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if a.dtype == np.object_:
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# object arrays do not support `isnan` (gh-9009), so make a guess
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mask = np.not_equal(a, a, dtype=bool)
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elif issubclass(a.dtype.type, np.inexact):
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mask = np.isnan(a)
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else:
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mask = None
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if mask is not None:
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a = np.array(a, subok=True, copy=True)
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np.copyto(a, val, where=mask)
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return a, mask
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def _copyto(a, val, mask):
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"""
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Replace values in `a` with NaN where `mask` is True. This differs from
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copyto in that it will deal with the case where `a` is a numpy scalar.
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Parameters
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----------
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a : ndarray or numpy scalar
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Array or numpy scalar some of whose values are to be replaced
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by val.
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val : numpy scalar
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Value used a replacement.
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mask : ndarray, scalar
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Boolean array. Where True the corresponding element of `a` is
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replaced by `val`. Broadcasts.
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Returns
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-------
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res : ndarray, scalar
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Array with elements replaced or scalar `val`.
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"""
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if isinstance(a, np.ndarray):
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np.copyto(a, val, where=mask, casting='unsafe')
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else:
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a = a.dtype.type(val)
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return a
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def _remove_nan_1d(arr1d, overwrite_input=False):
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"""
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Equivalent to arr1d[~arr1d.isnan()], but in a different order
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Presumably faster as it incurs fewer copies
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Parameters
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----------
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arr1d : ndarray
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Array to remove nans from
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overwrite_input : bool
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True if `arr1d` can be modified in place
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Returns
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-------
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res : ndarray
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Array with nan elements removed
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overwrite_input : bool
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True if `res` can be modified in place, given the constraint on the
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input
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"""
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if arr1d.dtype == object:
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# object arrays do not support `isnan` (gh-9009), so make a guess
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c = np.not_equal(arr1d, arr1d, dtype=bool)
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else:
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c = np.isnan(arr1d)
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s = np.nonzero(c)[0]
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if s.size == arr1d.size:
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warnings.warn("All-NaN slice encountered", RuntimeWarning,
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stacklevel=5)
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return arr1d[:0], True
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elif s.size == 0:
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return arr1d, overwrite_input
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else:
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if not overwrite_input:
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arr1d = arr1d.copy()
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# select non-nans at end of array
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enonan = arr1d[-s.size:][~c[-s.size:]]
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# fill nans in beginning of array with non-nans of end
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arr1d[s[:enonan.size]] = enonan
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return arr1d[:-s.size], True
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def _divide_by_count(a, b, out=None):
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"""
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Compute a/b ignoring invalid results. If `a` is an array the division
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is done in place. If `a` is a scalar, then its type is preserved in the
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output. If out is None, then a is used instead so that the division
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is in place. Note that this is only called with `a` an inexact type.
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Parameters
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----------
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a : {ndarray, numpy scalar}
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Numerator. Expected to be of inexact type but not checked.
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b : {ndarray, numpy scalar}
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Denominator.
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out : ndarray, optional
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Alternate output array in which to place the result. The default
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is ``None``; if provided, it must have the same shape as the
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expected output, but the type will be cast if necessary.
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Returns
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-------
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ret : {ndarray, numpy scalar}
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The return value is a/b. If `a` was an ndarray the division is done
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in place. If `a` is a numpy scalar, the division preserves its type.
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"""
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with np.errstate(invalid='ignore', divide='ignore'):
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if isinstance(a, np.ndarray):
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if out is None:
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return np.divide(a, b, out=a, casting='unsafe')
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else:
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return np.divide(a, b, out=out, casting='unsafe')
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else:
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if out is None:
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# Precaution against reduced object arrays
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try:
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return a.dtype.type(a / b)
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except AttributeError:
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return a / b
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else:
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# This is questionable, but currently a numpy scalar can
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# be output to a zero dimensional array.
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return np.divide(a, b, out=out, casting='unsafe')
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def _nanmin_dispatcher(a, axis=None, out=None, keepdims=None,
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initial=None, where=None):
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return (a, out)
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@array_function_dispatch(_nanmin_dispatcher)
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def nanmin(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
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where=np._NoValue):
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"""
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Return minimum of an array or minimum along an axis, ignoring any NaNs.
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When all-NaN slices are encountered a ``RuntimeWarning`` is raised and
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Nan is returned for that slice.
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Parameters
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----------
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a : array_like
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Array containing numbers whose minimum is desired. If `a` is not an
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array, a conversion is attempted.
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axis : {int, tuple of int, None}, optional
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Axis or axes along which the minimum is computed. The default is to compute
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the minimum of the flattened array.
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out : ndarray, optional
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Alternate output array in which to place the result. The default
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is ``None``; if provided, it must have the same shape as the
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expected output, but the type will be cast if necessary. See
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:ref:`ufuncs-output-type` for more details.
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.. versionadded:: 1.8.0
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keepdims : bool, optional
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If this is set to True, the axes which are reduced are left
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in the result as dimensions with size one. With this option,
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the result will broadcast correctly against the original `a`.
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If the value is anything but the default, then
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`keepdims` will be passed through to the `min` method
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of sub-classes of `ndarray`. If the sub-classes methods
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does not implement `keepdims` any exceptions will be raised.
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.. versionadded:: 1.8.0
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initial : scalar, optional
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The maximum value of an output element. Must be present to allow
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computation on empty slice. See `~numpy.ufunc.reduce` for details.
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.. versionadded:: 1.22.0
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where : array_like of bool, optional
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Elements to compare for the minimum. See `~numpy.ufunc.reduce`
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for details.
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.. versionadded:: 1.22.0
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Returns
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-------
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nanmin : ndarray
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An array with the same shape as `a`, with the specified axis
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removed. If `a` is a 0-d array, or if axis is None, an ndarray
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scalar is returned. The same dtype as `a` is returned.
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See Also
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--------
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nanmax :
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The maximum value of an array along a given axis, ignoring any NaNs.
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amin :
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The minimum value of an array along a given axis, propagating any NaNs.
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fmin :
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Element-wise minimum of two arrays, ignoring any NaNs.
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minimum :
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Element-wise minimum of two arrays, propagating any NaNs.
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isnan :
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Shows which elements are Not a Number (NaN).
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isfinite:
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Shows which elements are neither NaN nor infinity.
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amax, fmax, maximum
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Notes
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-----
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NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
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(IEEE 754). This means that Not a Number is not equivalent to infinity.
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Positive infinity is treated as a very large number and negative
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infinity is treated as a very small (i.e. negative) number.
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If the input has a integer type the function is equivalent to np.min.
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Examples
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--------
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>>> a = np.array([[1, 2], [3, np.nan]])
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>>> np.nanmin(a)
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1.0
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>>> np.nanmin(a, axis=0)
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array([1., 2.])
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>>> np.nanmin(a, axis=1)
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array([1., 3.])
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When positive infinity and negative infinity are present:
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>>> np.nanmin([1, 2, np.nan, np.inf])
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1.0
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>>> np.nanmin([1, 2, np.nan, np.NINF])
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-inf
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"""
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kwargs = {}
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if keepdims is not np._NoValue:
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kwargs['keepdims'] = keepdims
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if initial is not np._NoValue:
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kwargs['initial'] = initial
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if where is not np._NoValue:
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kwargs['where'] = where
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|
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if type(a) is np.ndarray and a.dtype != np.object_:
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# Fast, but not safe for subclasses of ndarray, or object arrays,
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# which do not implement isnan (gh-9009), or fmin correctly (gh-8975)
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res = np.fmin.reduce(a, axis=axis, out=out, **kwargs)
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if np.isnan(res).any():
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warnings.warn("All-NaN slice encountered", RuntimeWarning,
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stacklevel=3)
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else:
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# Slow, but safe for subclasses of ndarray
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a, mask = _replace_nan(a, +np.inf)
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res = np.amin(a, axis=axis, out=out, **kwargs)
|
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if mask is None:
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return res
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|
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# Check for all-NaN axis
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kwargs.pop("initial", None)
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mask = np.all(mask, axis=axis, **kwargs)
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if np.any(mask):
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res = _copyto(res, np.nan, mask)
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warnings.warn("All-NaN axis encountered", RuntimeWarning,
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stacklevel=3)
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return res
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|
|
|
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def _nanmax_dispatcher(a, axis=None, out=None, keepdims=None,
|
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initial=None, where=None):
|
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return (a, out)
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|
|
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@array_function_dispatch(_nanmax_dispatcher)
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def nanmax(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
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where=np._NoValue):
|
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"""
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|
Return the maximum of an array or maximum along an axis, ignoring any
|
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NaNs. When all-NaN slices are encountered a ``RuntimeWarning`` is
|
|
raised and NaN is returned for that slice.
|
|
|
|
Parameters
|
|
----------
|
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a : array_like
|
|
Array containing numbers whose maximum is desired. If `a` is not an
|
|
array, a conversion is attempted.
|
|
axis : {int, tuple of int, None}, optional
|
|
Axis or axes along which the maximum is computed. The default is to compute
|
|
the maximum of the flattened array.
|
|
out : ndarray, optional
|
|
Alternate output array in which to place the result. The default
|
|
is ``None``; if provided, it must have the same shape as the
|
|
expected output, but the type will be cast if necessary. See
|
|
:ref:`ufuncs-output-type` for more details.
|
|
|
|
.. versionadded:: 1.8.0
|
|
keepdims : bool, optional
|
|
If this is set to True, the axes which are reduced are left
|
|
in the result as dimensions with size one. With this option,
|
|
the result will broadcast correctly against the original `a`.
|
|
|
|
If the value is anything but the default, then
|
|
`keepdims` will be passed through to the `max` method
|
|
of sub-classes of `ndarray`. If the sub-classes methods
|
|
does not implement `keepdims` any exceptions will be raised.
|
|
|
|
.. versionadded:: 1.8.0
|
|
initial : scalar, optional
|
|
The minimum value of an output element. Must be present to allow
|
|
computation on empty slice. See `~numpy.ufunc.reduce` for details.
|
|
|
|
.. versionadded:: 1.22.0
|
|
where : array_like of bool, optional
|
|
Elements to compare for the maximum. See `~numpy.ufunc.reduce`
|
|
for details.
|
|
|
|
.. versionadded:: 1.22.0
|
|
|
|
Returns
|
|
-------
|
|
nanmax : ndarray
|
|
An array with the same shape as `a`, with the specified axis removed.
|
|
If `a` is a 0-d array, or if axis is None, an ndarray scalar is
|
|
returned. The same dtype as `a` is returned.
|
|
|
|
See Also
|
|
--------
|
|
nanmin :
|
|
The minimum value of an array along a given axis, ignoring any NaNs.
|
|
amax :
|
|
The maximum value of an array along a given axis, propagating any NaNs.
|
|
fmax :
|
|
Element-wise maximum of two arrays, ignoring any NaNs.
|
|
maximum :
|
|
Element-wise maximum of two arrays, propagating any NaNs.
|
|
isnan :
|
|
Shows which elements are Not a Number (NaN).
|
|
isfinite:
|
|
Shows which elements are neither NaN nor infinity.
|
|
|
|
amin, fmin, minimum
|
|
|
|
Notes
|
|
-----
|
|
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
|
|
(IEEE 754). This means that Not a Number is not equivalent to infinity.
|
|
Positive infinity is treated as a very large number and negative
|
|
infinity is treated as a very small (i.e. negative) number.
|
|
|
|
If the input has a integer type the function is equivalent to np.max.
|
|
|
|
Examples
|
|
--------
|
|
>>> a = np.array([[1, 2], [3, np.nan]])
|
|
>>> np.nanmax(a)
|
|
3.0
|
|
>>> np.nanmax(a, axis=0)
|
|
array([3., 2.])
|
|
>>> np.nanmax(a, axis=1)
|
|
array([2., 3.])
|
|
|
|
When positive infinity and negative infinity are present:
|
|
|
|
>>> np.nanmax([1, 2, np.nan, np.NINF])
|
|
2.0
|
|
>>> np.nanmax([1, 2, np.nan, np.inf])
|
|
inf
|
|
|
|
"""
|
|
kwargs = {}
|
|
if keepdims is not np._NoValue:
|
|
kwargs['keepdims'] = keepdims
|
|
if initial is not np._NoValue:
|
|
kwargs['initial'] = initial
|
|
if where is not np._NoValue:
|
|
kwargs['where'] = where
|
|
|
|
if type(a) is np.ndarray and a.dtype != np.object_:
|
|
# Fast, but not safe for subclasses of ndarray, or object arrays,
|
|
# which do not implement isnan (gh-9009), or fmax correctly (gh-8975)
|
|
res = np.fmax.reduce(a, axis=axis, out=out, **kwargs)
|
|
if np.isnan(res).any():
|
|
warnings.warn("All-NaN slice encountered", RuntimeWarning,
|
|
stacklevel=3)
|
|
else:
|
|
# Slow, but safe for subclasses of ndarray
|
|
a, mask = _replace_nan(a, -np.inf)
|
|
res = np.amax(a, axis=axis, out=out, **kwargs)
|
|
if mask is None:
|
|
return res
|
|
|
|
# Check for all-NaN axis
|
|
kwargs.pop("initial", None)
|
|
mask = np.all(mask, axis=axis, **kwargs)
|
|
if np.any(mask):
|
|
res = _copyto(res, np.nan, mask)
|
|
warnings.warn("All-NaN axis encountered", RuntimeWarning,
|
|
stacklevel=3)
|
|
return res
|
|
|
|
|
|
def _nanargmin_dispatcher(a, axis=None, out=None, *, keepdims=None):
|
|
return (a,)
|
|
|
|
|
|
@array_function_dispatch(_nanargmin_dispatcher)
|
|
def nanargmin(a, axis=None, out=None, *, keepdims=np._NoValue):
|
|
"""
|
|
Return the indices of the minimum values in the specified axis ignoring
|
|
NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the results
|
|
cannot be trusted if a slice contains only NaNs and Infs.
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Input data.
|
|
axis : int, optional
|
|
Axis along which to operate. By default flattened input is used.
|
|
out : array, optional
|
|
If provided, the result will be inserted into this array. It should
|
|
be of the appropriate shape and dtype.
|
|
|
|
.. versionadded:: 1.22.0
|
|
keepdims : bool, optional
|
|
If this is set to True, the axes which are reduced are left
|
|
in the result as dimensions with size one. With this option,
|
|
the result will broadcast correctly against the array.
|
|
|
|
.. versionadded:: 1.22.0
|
|
|
|
Returns
|
|
-------
|
|
index_array : ndarray
|
|
An array of indices or a single index value.
|
|
|
|
See Also
|
|
--------
|
|
argmin, nanargmax
|
|
|
|
Examples
|
|
--------
|
|
>>> a = np.array([[np.nan, 4], [2, 3]])
|
|
>>> np.argmin(a)
|
|
0
|
|
>>> np.nanargmin(a)
|
|
2
|
|
>>> np.nanargmin(a, axis=0)
|
|
array([1, 1])
|
|
>>> np.nanargmin(a, axis=1)
|
|
array([1, 0])
|
|
|
|
"""
|
|
a, mask = _replace_nan(a, np.inf)
|
|
if mask is not None:
|
|
mask = np.all(mask, axis=axis)
|
|
if np.any(mask):
|
|
raise ValueError("All-NaN slice encountered")
|
|
res = np.argmin(a, axis=axis, out=out, keepdims=keepdims)
|
|
return res
|
|
|
|
|
|
def _nanargmax_dispatcher(a, axis=None, out=None, *, keepdims=None):
|
|
return (a,)
|
|
|
|
|
|
@array_function_dispatch(_nanargmax_dispatcher)
|
|
def nanargmax(a, axis=None, out=None, *, keepdims=np._NoValue):
|
|
"""
|
|
Return the indices of the maximum values in the specified axis ignoring
|
|
NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the
|
|
results cannot be trusted if a slice contains only NaNs and -Infs.
|
|
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Input data.
|
|
axis : int, optional
|
|
Axis along which to operate. By default flattened input is used.
|
|
out : array, optional
|
|
If provided, the result will be inserted into this array. It should
|
|
be of the appropriate shape and dtype.
|
|
|
|
.. versionadded:: 1.22.0
|
|
keepdims : bool, optional
|
|
If this is set to True, the axes which are reduced are left
|
|
in the result as dimensions with size one. With this option,
|
|
the result will broadcast correctly against the array.
|
|
|
|
.. versionadded:: 1.22.0
|
|
|
|
Returns
|
|
-------
|
|
index_array : ndarray
|
|
An array of indices or a single index value.
|
|
|
|
See Also
|
|
--------
|
|
argmax, nanargmin
|
|
|
|
Examples
|
|
--------
|
|
>>> a = np.array([[np.nan, 4], [2, 3]])
|
|
>>> np.argmax(a)
|
|
0
|
|
>>> np.nanargmax(a)
|
|
1
|
|
>>> np.nanargmax(a, axis=0)
|
|
array([1, 0])
|
|
>>> np.nanargmax(a, axis=1)
|
|
array([1, 1])
|
|
|
|
"""
|
|
a, mask = _replace_nan(a, -np.inf)
|
|
if mask is not None:
|
|
mask = np.all(mask, axis=axis)
|
|
if np.any(mask):
|
|
raise ValueError("All-NaN slice encountered")
|
|
res = np.argmax(a, axis=axis, out=out, keepdims=keepdims)
|
|
return res
|
|
|
|
|
|
def _nansum_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
|
|
initial=None, where=None):
|
|
return (a, out)
|
|
|
|
|
|
@array_function_dispatch(_nansum_dispatcher)
|
|
def nansum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
|
|
initial=np._NoValue, where=np._NoValue):
|
|
"""
|
|
Return the sum of array elements over a given axis treating Not a
|
|
Numbers (NaNs) as zero.
|
|
|
|
In NumPy versions <= 1.9.0 Nan is returned for slices that are all-NaN or
|
|
empty. In later versions zero is returned.
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Array containing numbers whose sum is desired. If `a` is not an
|
|
array, a conversion is attempted.
|
|
axis : {int, tuple of int, None}, optional
|
|
Axis or axes along which the sum is computed. The default is to compute the
|
|
sum of the flattened array.
|
|
dtype : data-type, optional
|
|
The type of the returned array and of the accumulator in which the
|
|
elements are summed. By default, the dtype of `a` is used. An
|
|
exception is when `a` has an integer type with less precision than
|
|
the platform (u)intp. In that case, the default will be either
|
|
(u)int32 or (u)int64 depending on whether the platform is 32 or 64
|
|
bits. For inexact inputs, dtype must be inexact.
|
|
|
|
.. versionadded:: 1.8.0
|
|
out : ndarray, optional
|
|
Alternate output array in which to place the result. The default
|
|
is ``None``. If provided, it must have the same shape as the
|
|
expected output, but the type will be cast if necessary. See
|
|
:ref:`ufuncs-output-type` for more details. The casting of NaN to integer
|
|
can yield unexpected results.
|
|
|
|
.. versionadded:: 1.8.0
|
|
keepdims : bool, optional
|
|
If this is set to True, the axes which are reduced are left
|
|
in the result as dimensions with size one. With this option,
|
|
the result will broadcast correctly against the original `a`.
|
|
|
|
|
|
If the value is anything but the default, then
|
|
`keepdims` will be passed through to the `mean` or `sum` methods
|
|
of sub-classes of `ndarray`. If the sub-classes methods
|
|
does not implement `keepdims` any exceptions will be raised.
|
|
|
|
.. versionadded:: 1.8.0
|
|
initial : scalar, optional
|
|
Starting value for the sum. See `~numpy.ufunc.reduce` for details.
|
|
|
|
.. versionadded:: 1.22.0
|
|
where : array_like of bool, optional
|
|
Elements to include in the sum. See `~numpy.ufunc.reduce` for details.
|
|
|
|
.. versionadded:: 1.22.0
|
|
|
|
Returns
|
|
-------
|
|
nansum : ndarray.
|
|
A new array holding the result is returned unless `out` is
|
|
specified, in which it is returned. The result has the same
|
|
size as `a`, and the same shape as `a` if `axis` is not None
|
|
or `a` is a 1-d array.
|
|
|
|
See Also
|
|
--------
|
|
numpy.sum : Sum across array propagating NaNs.
|
|
isnan : Show which elements are NaN.
|
|
isfinite : Show which elements are not NaN or +/-inf.
|
|
|
|
Notes
|
|
-----
|
|
If both positive and negative infinity are present, the sum will be Not
|
|
A Number (NaN).
|
|
|
|
Examples
|
|
--------
|
|
>>> np.nansum(1)
|
|
1
|
|
>>> np.nansum([1])
|
|
1
|
|
>>> np.nansum([1, np.nan])
|
|
1.0
|
|
>>> a = np.array([[1, 1], [1, np.nan]])
|
|
>>> np.nansum(a)
|
|
3.0
|
|
>>> np.nansum(a, axis=0)
|
|
array([2., 1.])
|
|
>>> np.nansum([1, np.nan, np.inf])
|
|
inf
|
|
>>> np.nansum([1, np.nan, np.NINF])
|
|
-inf
|
|
>>> from numpy.testing import suppress_warnings
|
|
>>> with suppress_warnings() as sup:
|
|
... sup.filter(RuntimeWarning)
|
|
... np.nansum([1, np.nan, np.inf, -np.inf]) # both +/- infinity present
|
|
nan
|
|
|
|
"""
|
|
a, mask = _replace_nan(a, 0)
|
|
return np.sum(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
|
|
initial=initial, where=where)
|
|
|
|
|
|
def _nanprod_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
|
|
initial=None, where=None):
|
|
return (a, out)
|
|
|
|
|
|
@array_function_dispatch(_nanprod_dispatcher)
|
|
def nanprod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
|
|
initial=np._NoValue, where=np._NoValue):
|
|
"""
|
|
Return the product of array elements over a given axis treating Not a
|
|
Numbers (NaNs) as ones.
|
|
|
|
One is returned for slices that are all-NaN or empty.
|
|
|
|
.. versionadded:: 1.10.0
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Array containing numbers whose product is desired. If `a` is not an
|
|
array, a conversion is attempted.
|
|
axis : {int, tuple of int, None}, optional
|
|
Axis or axes along which the product is computed. The default is to compute
|
|
the product of the flattened array.
|
|
dtype : data-type, optional
|
|
The type of the returned array and of the accumulator in which the
|
|
elements are summed. By default, the dtype of `a` is used. An
|
|
exception is when `a` has an integer type with less precision than
|
|
the platform (u)intp. In that case, the default will be either
|
|
(u)int32 or (u)int64 depending on whether the platform is 32 or 64
|
|
bits. For inexact inputs, dtype must be inexact.
|
|
out : ndarray, optional
|
|
Alternate output array in which to place the result. The default
|
|
is ``None``. If provided, it must have the same shape as the
|
|
expected output, but the type will be cast if necessary. See
|
|
:ref:`ufuncs-output-type` for more details. The casting of NaN to integer
|
|
can yield unexpected results.
|
|
keepdims : bool, optional
|
|
If True, the axes which are reduced are left in the result as
|
|
dimensions with size one. With this option, the result will
|
|
broadcast correctly against the original `arr`.
|
|
initial : scalar, optional
|
|
The starting value for this product. See `~numpy.ufunc.reduce`
|
|
for details.
|
|
|
|
.. versionadded:: 1.22.0
|
|
where : array_like of bool, optional
|
|
Elements to include in the product. See `~numpy.ufunc.reduce`
|
|
for details.
|
|
|
|
.. versionadded:: 1.22.0
|
|
|
|
Returns
|
|
-------
|
|
nanprod : ndarray
|
|
A new array holding the result is returned unless `out` is
|
|
specified, in which case it is returned.
|
|
|
|
See Also
|
|
--------
|
|
numpy.prod : Product across array propagating NaNs.
|
|
isnan : Show which elements are NaN.
|
|
|
|
Examples
|
|
--------
|
|
>>> np.nanprod(1)
|
|
1
|
|
>>> np.nanprod([1])
|
|
1
|
|
>>> np.nanprod([1, np.nan])
|
|
1.0
|
|
>>> a = np.array([[1, 2], [3, np.nan]])
|
|
>>> np.nanprod(a)
|
|
6.0
|
|
>>> np.nanprod(a, axis=0)
|
|
array([3., 2.])
|
|
|
|
"""
|
|
a, mask = _replace_nan(a, 1)
|
|
return np.prod(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
|
|
initial=initial, where=where)
|
|
|
|
|
|
def _nancumsum_dispatcher(a, axis=None, dtype=None, out=None):
|
|
return (a, out)
|
|
|
|
|
|
@array_function_dispatch(_nancumsum_dispatcher)
|
|
def nancumsum(a, axis=None, dtype=None, out=None):
|
|
"""
|
|
Return the cumulative sum of array elements over a given axis treating Not a
|
|
Numbers (NaNs) as zero. The cumulative sum does not change when NaNs are
|
|
encountered and leading NaNs are replaced by zeros.
|
|
|
|
Zeros are returned for slices that are all-NaN or empty.
|
|
|
|
.. versionadded:: 1.12.0
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Input array.
|
|
axis : int, optional
|
|
Axis along which the cumulative sum is computed. The default
|
|
(None) is to compute the cumsum over the flattened array.
|
|
dtype : dtype, optional
|
|
Type of the returned array and of the accumulator in which the
|
|
elements are summed. If `dtype` is not specified, it defaults
|
|
to the dtype of `a`, unless `a` has an integer dtype with a
|
|
precision less than that of the default platform integer. In
|
|
that case, the default platform integer is used.
|
|
out : ndarray, optional
|
|
Alternative output array in which to place the result. It must
|
|
have the same shape and buffer length as the expected output
|
|
but the type will be cast if necessary. See :ref:`ufuncs-output-type` for
|
|
more details.
|
|
|
|
Returns
|
|
-------
|
|
nancumsum : ndarray.
|
|
A new array holding the result is returned unless `out` is
|
|
specified, in which it is returned. The result has the same
|
|
size as `a`, and the same shape as `a` if `axis` is not None
|
|
or `a` is a 1-d array.
|
|
|
|
See Also
|
|
--------
|
|
numpy.cumsum : Cumulative sum across array propagating NaNs.
|
|
isnan : Show which elements are NaN.
|
|
|
|
Examples
|
|
--------
|
|
>>> np.nancumsum(1)
|
|
array([1])
|
|
>>> np.nancumsum([1])
|
|
array([1])
|
|
>>> np.nancumsum([1, np.nan])
|
|
array([1., 1.])
|
|
>>> a = np.array([[1, 2], [3, np.nan]])
|
|
>>> np.nancumsum(a)
|
|
array([1., 3., 6., 6.])
|
|
>>> np.nancumsum(a, axis=0)
|
|
array([[1., 2.],
|
|
[4., 2.]])
|
|
>>> np.nancumsum(a, axis=1)
|
|
array([[1., 3.],
|
|
[3., 3.]])
|
|
|
|
"""
|
|
a, mask = _replace_nan(a, 0)
|
|
return np.cumsum(a, axis=axis, dtype=dtype, out=out)
|
|
|
|
|
|
def _nancumprod_dispatcher(a, axis=None, dtype=None, out=None):
|
|
return (a, out)
|
|
|
|
|
|
@array_function_dispatch(_nancumprod_dispatcher)
|
|
def nancumprod(a, axis=None, dtype=None, out=None):
|
|
"""
|
|
Return the cumulative product of array elements over a given axis treating Not a
|
|
Numbers (NaNs) as one. The cumulative product does not change when NaNs are
|
|
encountered and leading NaNs are replaced by ones.
|
|
|
|
Ones are returned for slices that are all-NaN or empty.
|
|
|
|
.. versionadded:: 1.12.0
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Input array.
|
|
axis : int, optional
|
|
Axis along which the cumulative product is computed. By default
|
|
the input is flattened.
|
|
dtype : dtype, optional
|
|
Type of the returned array, as well as of the accumulator in which
|
|
the elements are multiplied. If *dtype* is not specified, it
|
|
defaults to the dtype of `a`, unless `a` has an integer dtype with
|
|
a precision less than that of the default platform integer. In
|
|
that case, the default platform integer is used instead.
|
|
out : ndarray, optional
|
|
Alternative output array in which to place the result. It must
|
|
have the same shape and buffer length as the expected output
|
|
but the type of the resulting values will be cast if necessary.
|
|
|
|
Returns
|
|
-------
|
|
nancumprod : ndarray
|
|
A new array holding the result is returned unless `out` is
|
|
specified, in which case it is returned.
|
|
|
|
See Also
|
|
--------
|
|
numpy.cumprod : Cumulative product across array propagating NaNs.
|
|
isnan : Show which elements are NaN.
|
|
|
|
Examples
|
|
--------
|
|
>>> np.nancumprod(1)
|
|
array([1])
|
|
>>> np.nancumprod([1])
|
|
array([1])
|
|
>>> np.nancumprod([1, np.nan])
|
|
array([1., 1.])
|
|
>>> a = np.array([[1, 2], [3, np.nan]])
|
|
>>> np.nancumprod(a)
|
|
array([1., 2., 6., 6.])
|
|
>>> np.nancumprod(a, axis=0)
|
|
array([[1., 2.],
|
|
[3., 2.]])
|
|
>>> np.nancumprod(a, axis=1)
|
|
array([[1., 2.],
|
|
[3., 3.]])
|
|
|
|
"""
|
|
a, mask = _replace_nan(a, 1)
|
|
return np.cumprod(a, axis=axis, dtype=dtype, out=out)
|
|
|
|
|
|
def _nanmean_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
|
|
*, where=None):
|
|
return (a, out)
|
|
|
|
|
|
@array_function_dispatch(_nanmean_dispatcher)
|
|
def nanmean(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
|
|
*, where=np._NoValue):
|
|
"""
|
|
Compute the arithmetic mean along the specified axis, ignoring NaNs.
|
|
|
|
Returns the average of the array elements. The average is taken over
|
|
the flattened array by default, otherwise over the specified axis.
|
|
`float64` intermediate and return values are used for integer inputs.
|
|
|
|
For all-NaN slices, NaN is returned and a `RuntimeWarning` is raised.
|
|
|
|
.. versionadded:: 1.8.0
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Array containing numbers whose mean is desired. If `a` is not an
|
|
array, a conversion is attempted.
|
|
axis : {int, tuple of int, None}, optional
|
|
Axis or axes along which the means are computed. The default is to compute
|
|
the mean of the flattened array.
|
|
dtype : data-type, optional
|
|
Type to use in computing the mean. For integer inputs, the default
|
|
is `float64`; for inexact inputs, it is the same as the input
|
|
dtype.
|
|
out : ndarray, optional
|
|
Alternate output array in which to place the result. The default
|
|
is ``None``; if provided, it must have the same shape as the
|
|
expected output, but the type will be cast if necessary. See
|
|
:ref:`ufuncs-output-type` for more details.
|
|
keepdims : bool, optional
|
|
If this is set to True, the axes which are reduced are left
|
|
in the result as dimensions with size one. With this option,
|
|
the result will broadcast correctly against the original `a`.
|
|
|
|
If the value is anything but the default, then
|
|
`keepdims` will be passed through to the `mean` or `sum` methods
|
|
of sub-classes of `ndarray`. If the sub-classes methods
|
|
does not implement `keepdims` any exceptions will be raised.
|
|
where : array_like of bool, optional
|
|
Elements to include in the mean. See `~numpy.ufunc.reduce` for details.
|
|
|
|
.. versionadded:: 1.22.0
|
|
|
|
Returns
|
|
-------
|
|
m : ndarray, see dtype parameter above
|
|
If `out=None`, returns a new array containing the mean values,
|
|
otherwise a reference to the output array is returned. Nan is
|
|
returned for slices that contain only NaNs.
|
|
|
|
See Also
|
|
--------
|
|
average : Weighted average
|
|
mean : Arithmetic mean taken while not ignoring NaNs
|
|
var, nanvar
|
|
|
|
Notes
|
|
-----
|
|
The arithmetic mean is the sum of the non-NaN elements along the axis
|
|
divided by the number of non-NaN elements.
|
|
|
|
Note that for floating-point input, the mean is computed using the same
|
|
precision the input has. Depending on the input data, this can cause
|
|
the results to be inaccurate, especially for `float32`. Specifying a
|
|
higher-precision accumulator using the `dtype` keyword can alleviate
|
|
this issue.
|
|
|
|
Examples
|
|
--------
|
|
>>> a = np.array([[1, np.nan], [3, 4]])
|
|
>>> np.nanmean(a)
|
|
2.6666666666666665
|
|
>>> np.nanmean(a, axis=0)
|
|
array([2., 4.])
|
|
>>> np.nanmean(a, axis=1)
|
|
array([1., 3.5]) # may vary
|
|
|
|
"""
|
|
arr, mask = _replace_nan(a, 0)
|
|
if mask is None:
|
|
return np.mean(arr, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
|
|
where=where)
|
|
|
|
if dtype is not None:
|
|
dtype = np.dtype(dtype)
|
|
if dtype is not None and not issubclass(dtype.type, np.inexact):
|
|
raise TypeError("If a is inexact, then dtype must be inexact")
|
|
if out is not None and not issubclass(out.dtype.type, np.inexact):
|
|
raise TypeError("If a is inexact, then out must be inexact")
|
|
|
|
cnt = np.sum(~mask, axis=axis, dtype=np.intp, keepdims=keepdims,
|
|
where=where)
|
|
tot = np.sum(arr, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
|
|
where=where)
|
|
avg = _divide_by_count(tot, cnt, out=out)
|
|
|
|
isbad = (cnt == 0)
|
|
if isbad.any():
|
|
warnings.warn("Mean of empty slice", RuntimeWarning, stacklevel=3)
|
|
# NaN is the only possible bad value, so no further
|
|
# action is needed to handle bad results.
|
|
return avg
|
|
|
|
|
|
def _nanmedian1d(arr1d, overwrite_input=False):
|
|
"""
|
|
Private function for rank 1 arrays. Compute the median ignoring NaNs.
|
|
See nanmedian for parameter usage
|
|
"""
|
|
arr1d_parsed, overwrite_input = _remove_nan_1d(
|
|
arr1d, overwrite_input=overwrite_input,
|
|
)
|
|
|
|
if arr1d_parsed.size == 0:
|
|
# Ensure that a nan-esque scalar of the appropriate type (and unit)
|
|
# is returned for `timedelta64` and `complexfloating`
|
|
return arr1d[-1]
|
|
|
|
return np.median(arr1d_parsed, overwrite_input=overwrite_input)
|
|
|
|
|
|
def _nanmedian(a, axis=None, out=None, overwrite_input=False):
|
|
"""
|
|
Private function that doesn't support extended axis or keepdims.
|
|
These methods are extended to this function using _ureduce
|
|
See nanmedian for parameter usage
|
|
|
|
"""
|
|
if axis is None or a.ndim == 1:
|
|
part = a.ravel()
|
|
if out is None:
|
|
return _nanmedian1d(part, overwrite_input)
|
|
else:
|
|
out[...] = _nanmedian1d(part, overwrite_input)
|
|
return out
|
|
else:
|
|
# for small medians use sort + indexing which is still faster than
|
|
# apply_along_axis
|
|
# benchmarked with shuffled (50, 50, x) containing a few NaN
|
|
if a.shape[axis] < 600:
|
|
return _nanmedian_small(a, axis, out, overwrite_input)
|
|
result = np.apply_along_axis(_nanmedian1d, axis, a, overwrite_input)
|
|
if out is not None:
|
|
out[...] = result
|
|
return result
|
|
|
|
|
|
def _nanmedian_small(a, axis=None, out=None, overwrite_input=False):
|
|
"""
|
|
sort + indexing median, faster for small medians along multiple
|
|
dimensions due to the high overhead of apply_along_axis
|
|
|
|
see nanmedian for parameter usage
|
|
"""
|
|
a = np.ma.masked_array(a, np.isnan(a))
|
|
m = np.ma.median(a, axis=axis, overwrite_input=overwrite_input)
|
|
for i in range(np.count_nonzero(m.mask.ravel())):
|
|
warnings.warn("All-NaN slice encountered", RuntimeWarning,
|
|
stacklevel=4)
|
|
|
|
fill_value = np.timedelta64("NaT") if m.dtype.kind == "m" else np.nan
|
|
if out is not None:
|
|
out[...] = m.filled(fill_value)
|
|
return out
|
|
return m.filled(fill_value)
|
|
|
|
|
|
def _nanmedian_dispatcher(
|
|
a, axis=None, out=None, overwrite_input=None, keepdims=None):
|
|
return (a, out)
|
|
|
|
|
|
@array_function_dispatch(_nanmedian_dispatcher)
|
|
def nanmedian(a, axis=None, out=None, overwrite_input=False, keepdims=np._NoValue):
|
|
"""
|
|
Compute the median along the specified axis, while ignoring NaNs.
|
|
|
|
Returns the median of the array elements.
|
|
|
|
.. versionadded:: 1.9.0
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Input array or object that can be converted to an array.
|
|
axis : {int, sequence of int, None}, optional
|
|
Axis or axes along which the medians are computed. The default
|
|
is to compute the median along a flattened version of the array.
|
|
A sequence of axes is supported since version 1.9.0.
|
|
out : ndarray, optional
|
|
Alternative output array in which to place the result. It must
|
|
have the same shape and buffer length as the expected output,
|
|
but the type (of the output) will be cast if necessary.
|
|
overwrite_input : bool, optional
|
|
If True, then allow use of memory of input array `a` for
|
|
calculations. The input array will be modified by the call to
|
|
`median`. This will save memory when you do not need to preserve
|
|
the contents of the input array. Treat the input as undefined,
|
|
but it will probably be fully or partially sorted. Default is
|
|
False. If `overwrite_input` is ``True`` and `a` is not already an
|
|
`ndarray`, an error will be raised.
|
|
keepdims : bool, optional
|
|
If this is set to True, the axes which are reduced are left
|
|
in the result as dimensions with size one. With this option,
|
|
the result will broadcast correctly against the original `a`.
|
|
|
|
If this is anything but the default value it will be passed
|
|
through (in the special case of an empty array) to the
|
|
`mean` function of the underlying array. If the array is
|
|
a sub-class and `mean` does not have the kwarg `keepdims` this
|
|
will raise a RuntimeError.
|
|
|
|
Returns
|
|
-------
|
|
median : ndarray
|
|
A new array holding the result. If the input contains integers
|
|
or floats smaller than ``float64``, then the output data-type is
|
|
``np.float64``. Otherwise, the data-type of the output is the
|
|
same as that of the input. If `out` is specified, that array is
|
|
returned instead.
|
|
|
|
See Also
|
|
--------
|
|
mean, median, percentile
|
|
|
|
Notes
|
|
-----
|
|
Given a vector ``V`` of length ``N``, the median of ``V`` is the
|
|
middle value of a sorted copy of ``V``, ``V_sorted`` - i.e.,
|
|
``V_sorted[(N-1)/2]``, when ``N`` is odd and the average of the two
|
|
middle values of ``V_sorted`` when ``N`` is even.
|
|
|
|
Examples
|
|
--------
|
|
>>> a = np.array([[10.0, 7, 4], [3, 2, 1]])
|
|
>>> a[0, 1] = np.nan
|
|
>>> a
|
|
array([[10., nan, 4.],
|
|
[ 3., 2., 1.]])
|
|
>>> np.median(a)
|
|
nan
|
|
>>> np.nanmedian(a)
|
|
3.0
|
|
>>> np.nanmedian(a, axis=0)
|
|
array([6.5, 2. , 2.5])
|
|
>>> np.median(a, axis=1)
|
|
array([nan, 2.])
|
|
>>> b = a.copy()
|
|
>>> np.nanmedian(b, axis=1, overwrite_input=True)
|
|
array([7., 2.])
|
|
>>> assert not np.all(a==b)
|
|
>>> b = a.copy()
|
|
>>> np.nanmedian(b, axis=None, overwrite_input=True)
|
|
3.0
|
|
>>> assert not np.all(a==b)
|
|
|
|
"""
|
|
a = np.asanyarray(a)
|
|
# apply_along_axis in _nanmedian doesn't handle empty arrays well,
|
|
# so deal them upfront
|
|
if a.size == 0:
|
|
return np.nanmean(a, axis, out=out, keepdims=keepdims)
|
|
|
|
return function_base._ureduce(a, func=_nanmedian, keepdims=keepdims,
|
|
axis=axis, out=out,
|
|
overwrite_input=overwrite_input)
|
|
|
|
|
|
def _nanpercentile_dispatcher(
|
|
a, q, axis=None, out=None, overwrite_input=None,
|
|
method=None, keepdims=None, *, interpolation=None):
|
|
return (a, q, out)
|
|
|
|
|
|
@array_function_dispatch(_nanpercentile_dispatcher)
|
|
def nanpercentile(
|
|
a,
|
|
q,
|
|
axis=None,
|
|
out=None,
|
|
overwrite_input=False,
|
|
method="linear",
|
|
keepdims=np._NoValue,
|
|
*,
|
|
interpolation=None,
|
|
):
|
|
"""
|
|
Compute the qth percentile of the data along the specified axis,
|
|
while ignoring nan values.
|
|
|
|
Returns the qth percentile(s) of the array elements.
|
|
|
|
.. versionadded:: 1.9.0
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Input array or object that can be converted to an array, containing
|
|
nan values to be ignored.
|
|
q : array_like of float
|
|
Percentile or sequence of percentiles to compute, which must be
|
|
between 0 and 100 inclusive.
|
|
axis : {int, tuple of int, None}, optional
|
|
Axis or axes along which the percentiles are computed. The default
|
|
is to compute the percentile(s) along a flattened version of the
|
|
array.
|
|
out : ndarray, optional
|
|
Alternative output array in which to place the result. It must have
|
|
the same shape and buffer length as the expected output, but the
|
|
type (of the output) will be cast if necessary.
|
|
overwrite_input : bool, optional
|
|
If True, then allow the input array `a` to be modified by
|
|
intermediate calculations, to save memory. In this case, the
|
|
contents of the input `a` after this function completes is
|
|
undefined.
|
|
method : str, optional
|
|
This parameter specifies the method to use for estimating the
|
|
percentile. There are many different methods, some unique to NumPy.
|
|
See the notes for explanation. The options sorted by their R type
|
|
as summarized in the H&F paper [1]_ are:
|
|
|
|
1. 'inverted_cdf'
|
|
2. 'averaged_inverted_cdf'
|
|
3. 'closest_observation'
|
|
4. 'interpolated_inverted_cdf'
|
|
5. 'hazen'
|
|
6. 'weibull'
|
|
7. 'linear' (default)
|
|
8. 'median_unbiased'
|
|
9. 'normal_unbiased'
|
|
|
|
The first three methods are discontinuous. NumPy further defines the
|
|
following discontinuous variations of the default 'linear' (7.) option:
|
|
|
|
* 'lower'
|
|
* 'higher',
|
|
* 'midpoint'
|
|
* 'nearest'
|
|
|
|
.. versionchanged:: 1.22.0
|
|
This argument was previously called "interpolation" and only
|
|
offered the "linear" default and last four options.
|
|
|
|
keepdims : bool, optional
|
|
If this is set to True, the axes which are reduced are left in
|
|
the result as dimensions with size one. With this option, the
|
|
result will broadcast correctly against the original array `a`.
|
|
|
|
If this is anything but the default value it will be passed
|
|
through (in the special case of an empty array) to the
|
|
`mean` function of the underlying array. If the array is
|
|
a sub-class and `mean` does not have the kwarg `keepdims` this
|
|
will raise a RuntimeError.
|
|
|
|
interpolation : str, optional
|
|
Deprecated name for the method keyword argument.
|
|
|
|
.. deprecated:: 1.22.0
|
|
|
|
Returns
|
|
-------
|
|
percentile : scalar or ndarray
|
|
If `q` is a single percentile and `axis=None`, then the result
|
|
is a scalar. If multiple percentiles are given, first axis of
|
|
the result corresponds to the percentiles. The other axes are
|
|
the axes that remain after the reduction of `a`. If the input
|
|
contains integers or floats smaller than ``float64``, the output
|
|
data-type is ``float64``. Otherwise, the output data-type is the
|
|
same as that of the input. If `out` is specified, that array is
|
|
returned instead.
|
|
|
|
See Also
|
|
--------
|
|
nanmean
|
|
nanmedian : equivalent to ``nanpercentile(..., 50)``
|
|
percentile, median, mean
|
|
nanquantile : equivalent to nanpercentile, except q in range [0, 1].
|
|
|
|
Notes
|
|
-----
|
|
For more information please see `numpy.percentile`
|
|
|
|
Examples
|
|
--------
|
|
>>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
|
|
>>> a[0][1] = np.nan
|
|
>>> a
|
|
array([[10., nan, 4.],
|
|
[ 3., 2., 1.]])
|
|
>>> np.percentile(a, 50)
|
|
nan
|
|
>>> np.nanpercentile(a, 50)
|
|
3.0
|
|
>>> np.nanpercentile(a, 50, axis=0)
|
|
array([6.5, 2. , 2.5])
|
|
>>> np.nanpercentile(a, 50, axis=1, keepdims=True)
|
|
array([[7.],
|
|
[2.]])
|
|
>>> m = np.nanpercentile(a, 50, axis=0)
|
|
>>> out = np.zeros_like(m)
|
|
>>> np.nanpercentile(a, 50, axis=0, out=out)
|
|
array([6.5, 2. , 2.5])
|
|
>>> m
|
|
array([6.5, 2. , 2.5])
|
|
|
|
>>> b = a.copy()
|
|
>>> np.nanpercentile(b, 50, axis=1, overwrite_input=True)
|
|
array([7., 2.])
|
|
>>> assert not np.all(a==b)
|
|
|
|
References
|
|
----------
|
|
.. [1] R. J. Hyndman and Y. Fan,
|
|
"Sample quantiles in statistical packages,"
|
|
The American Statistician, 50(4), pp. 361-365, 1996
|
|
|
|
"""
|
|
if interpolation is not None:
|
|
method = function_base._check_interpolation_as_method(
|
|
method, interpolation, "nanpercentile")
|
|
|
|
a = np.asanyarray(a)
|
|
q = np.true_divide(q, 100.0)
|
|
# undo any decay that the ufunc performed (see gh-13105)
|
|
q = np.asanyarray(q)
|
|
if not function_base._quantile_is_valid(q):
|
|
raise ValueError("Percentiles must be in the range [0, 100]")
|
|
return _nanquantile_unchecked(
|
|
a, q, axis, out, overwrite_input, method, keepdims)
|
|
|
|
|
|
def _nanquantile_dispatcher(a, q, axis=None, out=None, overwrite_input=None,
|
|
method=None, keepdims=None, *, interpolation=None):
|
|
return (a, q, out)
|
|
|
|
|
|
@array_function_dispatch(_nanquantile_dispatcher)
|
|
def nanquantile(
|
|
a,
|
|
q,
|
|
axis=None,
|
|
out=None,
|
|
overwrite_input=False,
|
|
method="linear",
|
|
keepdims=np._NoValue,
|
|
*,
|
|
interpolation=None,
|
|
):
|
|
"""
|
|
Compute the qth quantile of the data along the specified axis,
|
|
while ignoring nan values.
|
|
Returns the qth quantile(s) of the array elements.
|
|
|
|
.. versionadded:: 1.15.0
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Input array or object that can be converted to an array, containing
|
|
nan values to be ignored
|
|
q : array_like of float
|
|
Quantile or sequence of quantiles to compute, which must be between
|
|
0 and 1 inclusive.
|
|
axis : {int, tuple of int, None}, optional
|
|
Axis or axes along which the quantiles are computed. The
|
|
default is to compute the quantile(s) along a flattened
|
|
version of the array.
|
|
out : ndarray, optional
|
|
Alternative output array in which to place the result. It must
|
|
have the same shape and buffer length as the expected output,
|
|
but the type (of the output) will be cast if necessary.
|
|
overwrite_input : bool, optional
|
|
If True, then allow the input array `a` to be modified by intermediate
|
|
calculations, to save memory. In this case, the contents of the input
|
|
`a` after this function completes is undefined.
|
|
method : str, optional
|
|
This parameter specifies the method to use for estimating the
|
|
quantile. There are many different methods, some unique to NumPy.
|
|
See the notes for explanation. The options sorted by their R type
|
|
as summarized in the H&F paper [1]_ are:
|
|
|
|
1. 'inverted_cdf'
|
|
2. 'averaged_inverted_cdf'
|
|
3. 'closest_observation'
|
|
4. 'interpolated_inverted_cdf'
|
|
5. 'hazen'
|
|
6. 'weibull'
|
|
7. 'linear' (default)
|
|
8. 'median_unbiased'
|
|
9. 'normal_unbiased'
|
|
|
|
The first three methods are discontinuous. NumPy further defines the
|
|
following discontinuous variations of the default 'linear' (7.) option:
|
|
|
|
* 'lower'
|
|
* 'higher',
|
|
* 'midpoint'
|
|
* 'nearest'
|
|
|
|
.. versionchanged:: 1.22.0
|
|
This argument was previously called "interpolation" and only
|
|
offered the "linear" default and last four options.
|
|
|
|
keepdims : bool, optional
|
|
If this is set to True, the axes which are reduced are left in
|
|
the result as dimensions with size one. With this option, the
|
|
result will broadcast correctly against the original array `a`.
|
|
|
|
If this is anything but the default value it will be passed
|
|
through (in the special case of an empty array) to the
|
|
`mean` function of the underlying array. If the array is
|
|
a sub-class and `mean` does not have the kwarg `keepdims` this
|
|
will raise a RuntimeError.
|
|
|
|
interpolation : str, optional
|
|
Deprecated name for the method keyword argument.
|
|
|
|
.. deprecated:: 1.22.0
|
|
|
|
Returns
|
|
-------
|
|
quantile : scalar or ndarray
|
|
If `q` is a single percentile and `axis=None`, then the result
|
|
is a scalar. If multiple quantiles are given, first axis of
|
|
the result corresponds to the quantiles. The other axes are
|
|
the axes that remain after the reduction of `a`. If the input
|
|
contains integers or floats smaller than ``float64``, the output
|
|
data-type is ``float64``. Otherwise, the output data-type is the
|
|
same as that of the input. If `out` is specified, that array is
|
|
returned instead.
|
|
|
|
See Also
|
|
--------
|
|
quantile
|
|
nanmean, nanmedian
|
|
nanmedian : equivalent to ``nanquantile(..., 0.5)``
|
|
nanpercentile : same as nanquantile, but with q in the range [0, 100].
|
|
|
|
Notes
|
|
-----
|
|
For more information please see `numpy.quantile`
|
|
|
|
Examples
|
|
--------
|
|
>>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
|
|
>>> a[0][1] = np.nan
|
|
>>> a
|
|
array([[10., nan, 4.],
|
|
[ 3., 2., 1.]])
|
|
>>> np.quantile(a, 0.5)
|
|
nan
|
|
>>> np.nanquantile(a, 0.5)
|
|
3.0
|
|
>>> np.nanquantile(a, 0.5, axis=0)
|
|
array([6.5, 2. , 2.5])
|
|
>>> np.nanquantile(a, 0.5, axis=1, keepdims=True)
|
|
array([[7.],
|
|
[2.]])
|
|
>>> m = np.nanquantile(a, 0.5, axis=0)
|
|
>>> out = np.zeros_like(m)
|
|
>>> np.nanquantile(a, 0.5, axis=0, out=out)
|
|
array([6.5, 2. , 2.5])
|
|
>>> m
|
|
array([6.5, 2. , 2.5])
|
|
>>> b = a.copy()
|
|
>>> np.nanquantile(b, 0.5, axis=1, overwrite_input=True)
|
|
array([7., 2.])
|
|
>>> assert not np.all(a==b)
|
|
|
|
References
|
|
----------
|
|
.. [1] R. J. Hyndman and Y. Fan,
|
|
"Sample quantiles in statistical packages,"
|
|
The American Statistician, 50(4), pp. 361-365, 1996
|
|
|
|
"""
|
|
if interpolation is not None:
|
|
method = function_base._check_interpolation_as_method(
|
|
method, interpolation, "nanquantile")
|
|
|
|
a = np.asanyarray(a)
|
|
q = np.asanyarray(q)
|
|
if not function_base._quantile_is_valid(q):
|
|
raise ValueError("Quantiles must be in the range [0, 1]")
|
|
return _nanquantile_unchecked(
|
|
a, q, axis, out, overwrite_input, method, keepdims)
|
|
|
|
|
|
def _nanquantile_unchecked(
|
|
a,
|
|
q,
|
|
axis=None,
|
|
out=None,
|
|
overwrite_input=False,
|
|
method="linear",
|
|
keepdims=np._NoValue,
|
|
):
|
|
"""Assumes that q is in [0, 1], and is an ndarray"""
|
|
# apply_along_axis in _nanpercentile doesn't handle empty arrays well,
|
|
# so deal them upfront
|
|
if a.size == 0:
|
|
return np.nanmean(a, axis, out=out, keepdims=keepdims)
|
|
return function_base._ureduce(a,
|
|
func=_nanquantile_ureduce_func,
|
|
q=q,
|
|
keepdims=keepdims,
|
|
axis=axis,
|
|
out=out,
|
|
overwrite_input=overwrite_input,
|
|
method=method)
|
|
|
|
|
|
def _nanquantile_ureduce_func(a, q, axis=None, out=None, overwrite_input=False,
|
|
method="linear"):
|
|
"""
|
|
Private function that doesn't support extended axis or keepdims.
|
|
These methods are extended to this function using _ureduce
|
|
See nanpercentile for parameter usage
|
|
"""
|
|
if axis is None or a.ndim == 1:
|
|
part = a.ravel()
|
|
result = _nanquantile_1d(part, q, overwrite_input, method)
|
|
else:
|
|
result = np.apply_along_axis(_nanquantile_1d, axis, a, q,
|
|
overwrite_input, method)
|
|
# apply_along_axis fills in collapsed axis with results.
|
|
# Move that axis to the beginning to match percentile's
|
|
# convention.
|
|
if q.ndim != 0:
|
|
result = np.moveaxis(result, axis, 0)
|
|
|
|
if out is not None:
|
|
out[...] = result
|
|
return result
|
|
|
|
|
|
def _nanquantile_1d(arr1d, q, overwrite_input=False, method="linear"):
|
|
"""
|
|
Private function for rank 1 arrays. Compute quantile ignoring NaNs.
|
|
See nanpercentile for parameter usage
|
|
"""
|
|
arr1d, overwrite_input = _remove_nan_1d(arr1d,
|
|
overwrite_input=overwrite_input)
|
|
if arr1d.size == 0:
|
|
# convert to scalar
|
|
return np.full(q.shape, np.nan, dtype=arr1d.dtype)[()]
|
|
|
|
return function_base._quantile_unchecked(
|
|
arr1d, q, overwrite_input=overwrite_input, method=method)
|
|
|
|
|
|
def _nanvar_dispatcher(a, axis=None, dtype=None, out=None, ddof=None,
|
|
keepdims=None, *, where=None):
|
|
return (a, out)
|
|
|
|
|
|
@array_function_dispatch(_nanvar_dispatcher)
|
|
def nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue,
|
|
*, where=np._NoValue):
|
|
"""
|
|
Compute the variance along the specified axis, while ignoring NaNs.
|
|
|
|
Returns the variance of the array elements, a measure of the spread of
|
|
a distribution. The variance is computed for the flattened array by
|
|
default, otherwise over the specified axis.
|
|
|
|
For all-NaN slices or slices with zero degrees of freedom, NaN is
|
|
returned and a `RuntimeWarning` is raised.
|
|
|
|
.. versionadded:: 1.8.0
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Array containing numbers whose variance is desired. If `a` is not an
|
|
array, a conversion is attempted.
|
|
axis : {int, tuple of int, None}, optional
|
|
Axis or axes along which the variance is computed. The default is to compute
|
|
the variance of the flattened array.
|
|
dtype : data-type, optional
|
|
Type to use in computing the variance. For arrays of integer type
|
|
the default is `float64`; for arrays of float types it is the same as
|
|
the array type.
|
|
out : ndarray, optional
|
|
Alternate output array in which to place the result. It must have
|
|
the same shape as the expected output, but the type is cast if
|
|
necessary.
|
|
ddof : int, optional
|
|
"Delta Degrees of Freedom": the divisor used in the calculation is
|
|
``N - ddof``, where ``N`` represents the number of non-NaN
|
|
elements. By default `ddof` is zero.
|
|
keepdims : bool, optional
|
|
If this is set to True, the axes which are reduced are left
|
|
in the result as dimensions with size one. With this option,
|
|
the result will broadcast correctly against the original `a`.
|
|
where : array_like of bool, optional
|
|
Elements to include in the variance. See `~numpy.ufunc.reduce` for
|
|
details.
|
|
|
|
.. versionadded:: 1.22.0
|
|
|
|
Returns
|
|
-------
|
|
variance : ndarray, see dtype parameter above
|
|
If `out` is None, return a new array containing the variance,
|
|
otherwise return a reference to the output array. If ddof is >= the
|
|
number of non-NaN elements in a slice or the slice contains only
|
|
NaNs, then the result for that slice is NaN.
|
|
|
|
See Also
|
|
--------
|
|
std : Standard deviation
|
|
mean : Average
|
|
var : Variance while not ignoring NaNs
|
|
nanstd, nanmean
|
|
:ref:`ufuncs-output-type`
|
|
|
|
Notes
|
|
-----
|
|
The variance is the average of the squared deviations from the mean,
|
|
i.e., ``var = mean(abs(x - x.mean())**2)``.
|
|
|
|
The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``.
|
|
If, however, `ddof` is specified, the divisor ``N - ddof`` is used
|
|
instead. In standard statistical practice, ``ddof=1`` provides an
|
|
unbiased estimator of the variance of a hypothetical infinite
|
|
population. ``ddof=0`` provides a maximum likelihood estimate of the
|
|
variance for normally distributed variables.
|
|
|
|
Note that for complex numbers, the absolute value is taken before
|
|
squaring, so that the result is always real and nonnegative.
|
|
|
|
For floating-point input, the variance is computed using the same
|
|
precision the input has. Depending on the input data, this can cause
|
|
the results to be inaccurate, especially for `float32` (see example
|
|
below). Specifying a higher-accuracy accumulator using the ``dtype``
|
|
keyword can alleviate this issue.
|
|
|
|
For this function to work on sub-classes of ndarray, they must define
|
|
`sum` with the kwarg `keepdims`
|
|
|
|
Examples
|
|
--------
|
|
>>> a = np.array([[1, np.nan], [3, 4]])
|
|
>>> np.nanvar(a)
|
|
1.5555555555555554
|
|
>>> np.nanvar(a, axis=0)
|
|
array([1., 0.])
|
|
>>> np.nanvar(a, axis=1)
|
|
array([0., 0.25]) # may vary
|
|
|
|
"""
|
|
arr, mask = _replace_nan(a, 0)
|
|
if mask is None:
|
|
return np.var(arr, axis=axis, dtype=dtype, out=out, ddof=ddof,
|
|
keepdims=keepdims, where=where)
|
|
|
|
if dtype is not None:
|
|
dtype = np.dtype(dtype)
|
|
if dtype is not None and not issubclass(dtype.type, np.inexact):
|
|
raise TypeError("If a is inexact, then dtype must be inexact")
|
|
if out is not None and not issubclass(out.dtype.type, np.inexact):
|
|
raise TypeError("If a is inexact, then out must be inexact")
|
|
|
|
# Compute mean
|
|
if type(arr) is np.matrix:
|
|
_keepdims = np._NoValue
|
|
else:
|
|
_keepdims = True
|
|
# we need to special case matrix for reverse compatibility
|
|
# in order for this to work, these sums need to be called with
|
|
# keepdims=True, however matrix now raises an error in this case, but
|
|
# the reason that it drops the keepdims kwarg is to force keepdims=True
|
|
# so this used to work by serendipity.
|
|
cnt = np.sum(~mask, axis=axis, dtype=np.intp, keepdims=_keepdims,
|
|
where=where)
|
|
avg = np.sum(arr, axis=axis, dtype=dtype, keepdims=_keepdims, where=where)
|
|
avg = _divide_by_count(avg, cnt)
|
|
|
|
# Compute squared deviation from mean.
|
|
np.subtract(arr, avg, out=arr, casting='unsafe', where=where)
|
|
arr = _copyto(arr, 0, mask)
|
|
if issubclass(arr.dtype.type, np.complexfloating):
|
|
sqr = np.multiply(arr, arr.conj(), out=arr, where=where).real
|
|
else:
|
|
sqr = np.multiply(arr, arr, out=arr, where=where)
|
|
|
|
# Compute variance.
|
|
var = np.sum(sqr, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
|
|
where=where)
|
|
|
|
# Precaution against reduced object arrays
|
|
try:
|
|
var_ndim = var.ndim
|
|
except AttributeError:
|
|
var_ndim = np.ndim(var)
|
|
if var_ndim < cnt.ndim:
|
|
# Subclasses of ndarray may ignore keepdims, so check here.
|
|
cnt = cnt.squeeze(axis)
|
|
dof = cnt - ddof
|
|
var = _divide_by_count(var, dof)
|
|
|
|
isbad = (dof <= 0)
|
|
if np.any(isbad):
|
|
warnings.warn("Degrees of freedom <= 0 for slice.", RuntimeWarning,
|
|
stacklevel=3)
|
|
# NaN, inf, or negative numbers are all possible bad
|
|
# values, so explicitly replace them with NaN.
|
|
var = _copyto(var, np.nan, isbad)
|
|
return var
|
|
|
|
|
|
def _nanstd_dispatcher(a, axis=None, dtype=None, out=None, ddof=None,
|
|
keepdims=None, *, where=None):
|
|
return (a, out)
|
|
|
|
|
|
@array_function_dispatch(_nanstd_dispatcher)
|
|
def nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue,
|
|
*, where=np._NoValue):
|
|
"""
|
|
Compute the standard deviation along the specified axis, while
|
|
ignoring NaNs.
|
|
|
|
Returns the standard deviation, a measure of the spread of a
|
|
distribution, of the non-NaN array elements. The standard deviation is
|
|
computed for the flattened array by default, otherwise over the
|
|
specified axis.
|
|
|
|
For all-NaN slices or slices with zero degrees of freedom, NaN is
|
|
returned and a `RuntimeWarning` is raised.
|
|
|
|
.. versionadded:: 1.8.0
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Calculate the standard deviation of the non-NaN values.
|
|
axis : {int, tuple of int, None}, optional
|
|
Axis or axes along which the standard deviation is computed. The default is
|
|
to compute the standard deviation of the flattened array.
|
|
dtype : dtype, optional
|
|
Type to use in computing the standard deviation. For arrays of
|
|
integer type the default is float64, for arrays of float types it
|
|
is the same as the array type.
|
|
out : ndarray, optional
|
|
Alternative output array in which to place the result. It must have
|
|
the same shape as the expected output but the type (of the
|
|
calculated values) will be cast if necessary.
|
|
ddof : int, optional
|
|
Means Delta Degrees of Freedom. The divisor used in calculations
|
|
is ``N - ddof``, where ``N`` represents the number of non-NaN
|
|
elements. By default `ddof` is zero.
|
|
|
|
keepdims : bool, optional
|
|
If this is set to True, the axes which are reduced are left
|
|
in the result as dimensions with size one. With this option,
|
|
the result will broadcast correctly against the original `a`.
|
|
|
|
If this value is anything but the default it is passed through
|
|
as-is to the relevant functions of the sub-classes. If these
|
|
functions do not have a `keepdims` kwarg, a RuntimeError will
|
|
be raised.
|
|
where : array_like of bool, optional
|
|
Elements to include in the standard deviation.
|
|
See `~numpy.ufunc.reduce` for details.
|
|
|
|
.. versionadded:: 1.22.0
|
|
|
|
Returns
|
|
-------
|
|
standard_deviation : ndarray, see dtype parameter above.
|
|
If `out` is None, return a new array containing the standard
|
|
deviation, otherwise return a reference to the output array. If
|
|
ddof is >= the number of non-NaN elements in a slice or the slice
|
|
contains only NaNs, then the result for that slice is NaN.
|
|
|
|
See Also
|
|
--------
|
|
var, mean, std
|
|
nanvar, nanmean
|
|
:ref:`ufuncs-output-type`
|
|
|
|
Notes
|
|
-----
|
|
The standard deviation is the square root of the average of the squared
|
|
deviations from the mean: ``std = sqrt(mean(abs(x - x.mean())**2))``.
|
|
|
|
The average squared deviation is normally calculated as
|
|
``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is
|
|
specified, the divisor ``N - ddof`` is used instead. In standard
|
|
statistical practice, ``ddof=1`` provides an unbiased estimator of the
|
|
variance of the infinite population. ``ddof=0`` provides a maximum
|
|
likelihood estimate of the variance for normally distributed variables.
|
|
The standard deviation computed in this function is the square root of
|
|
the estimated variance, so even with ``ddof=1``, it will not be an
|
|
unbiased estimate of the standard deviation per se.
|
|
|
|
Note that, for complex numbers, `std` takes the absolute value before
|
|
squaring, so that the result is always real and nonnegative.
|
|
|
|
For floating-point input, the *std* is computed using the same
|
|
precision the input has. Depending on the input data, this can cause
|
|
the results to be inaccurate, especially for float32 (see example
|
|
below). Specifying a higher-accuracy accumulator using the `dtype`
|
|
keyword can alleviate this issue.
|
|
|
|
Examples
|
|
--------
|
|
>>> a = np.array([[1, np.nan], [3, 4]])
|
|
>>> np.nanstd(a)
|
|
1.247219128924647
|
|
>>> np.nanstd(a, axis=0)
|
|
array([1., 0.])
|
|
>>> np.nanstd(a, axis=1)
|
|
array([0., 0.5]) # may vary
|
|
|
|
"""
|
|
var = nanvar(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
|
|
keepdims=keepdims, where=where)
|
|
if isinstance(var, np.ndarray):
|
|
std = np.sqrt(var, out=var)
|
|
elif hasattr(var, 'dtype'):
|
|
std = var.dtype.type(np.sqrt(var))
|
|
else:
|
|
std = np.sqrt(var)
|
|
return std
|