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from ..arithmetic.sqrt import sqrt
from .nanvar import nanvar
[docs]def nanstd(
a, axis=None, dtype=None, out=None, ddof=0, keepdims=None, combine_size=None
):
"""
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 tensor elements. The standard deviation is
computed for the flattened tensor 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.
Parameters
----------
a : array_like
Calculate the standard deviation of the non-NaN values.
axis : int, optional
Axis along which the standard deviation is computed. The default is
to compute the standard deviation of the flattened tensor.
dtype : dtype, optional
Type to use in computing the standard deviation. For tensors of
integer type the default is float64, for tensors of float types it
is the same as the tensor type.
out : Tensor, optional
Alternative output tensor 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.
combine_size: int, optional
The number of chunks to combine.
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 tensor. 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
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
--------
>>> import mars.tensor as mt
>>> a = mt.array([[1, mt.nan], [3, 4]])
>>> mt.nanstd(a).execute()
1.247219128924647
>>> mt.nanstd(a, axis=0).execute()
array([ 1., 0.])
>>> mt.nanstd(a, axis=1).execute()
array([ 0., 0.5])
"""
ret = sqrt(
nanvar(
a,
axis=axis,
dtype=dtype,
out=out,
ddof=ddof,
keepdims=keepdims,
combine_size=combine_size,
)
)
if dtype is not None and ret.dtype != dtype:
ret = ret.astype(dtype)
return ret