129 lines
4.5 KiB
Python
129 lines
4.5 KiB
Python
import numpy as np
|
|
|
|
from scipy._lib._util import _get_nan
|
|
from scipy._lib._array_api import array_namespace, xp_copysign
|
|
|
|
from ._axis_nan_policy import _axis_nan_policy_factory
|
|
|
|
|
|
@_axis_nan_policy_factory(
|
|
lambda x: x, n_outputs=1, result_to_tuple=lambda x: (x,)
|
|
)
|
|
def variation(a, axis=0, nan_policy='propagate', ddof=0, *, keepdims=False):
|
|
"""
|
|
Compute the coefficient of variation.
|
|
|
|
The coefficient of variation is the standard deviation divided by the
|
|
mean. This function is equivalent to::
|
|
|
|
np.std(x, axis=axis, ddof=ddof) / np.mean(x)
|
|
|
|
The default for ``ddof`` is 0, but many definitions of the coefficient
|
|
of variation use the square root of the unbiased sample variance
|
|
for the sample standard deviation, which corresponds to ``ddof=1``.
|
|
|
|
The function does not take the absolute value of the mean of the data,
|
|
so the return value is negative if the mean is negative.
|
|
|
|
Parameters
|
|
----------
|
|
a : array_like
|
|
Input array.
|
|
axis : int or None, optional
|
|
Axis along which to calculate the coefficient of variation.
|
|
Default is 0. If None, compute over the whole array `a`.
|
|
nan_policy : {'propagate', 'raise', 'omit'}, optional
|
|
Defines how to handle when input contains ``nan``.
|
|
The following options are available:
|
|
|
|
* 'propagate': return ``nan``
|
|
* 'raise': raise an exception
|
|
* 'omit': perform the calculation with ``nan`` values omitted
|
|
|
|
The default is 'propagate'.
|
|
ddof : int, optional
|
|
Gives the "Delta Degrees Of Freedom" used when computing the
|
|
standard deviation. The divisor used in the calculation of the
|
|
standard deviation is ``N - ddof``, where ``N`` is the number of
|
|
elements. `ddof` must be less than ``N``; if it isn't, the result
|
|
will be ``nan`` or ``inf``, depending on ``N`` and the values in
|
|
the array. By default `ddof` is zero for backwards compatibility,
|
|
but it is recommended to use ``ddof=1`` to ensure that the sample
|
|
standard deviation is computed as the square root of the unbiased
|
|
sample variance.
|
|
|
|
Returns
|
|
-------
|
|
variation : ndarray
|
|
The calculated variation along the requested axis.
|
|
|
|
Notes
|
|
-----
|
|
There are several edge cases that are handled without generating a
|
|
warning:
|
|
|
|
* If both the mean and the standard deviation are zero, ``nan``
|
|
is returned.
|
|
* If the mean is zero and the standard deviation is nonzero, ``inf``
|
|
is returned.
|
|
* If the input has length zero (either because the array has zero
|
|
length, or all the input values are ``nan`` and ``nan_policy`` is
|
|
``'omit'``), ``nan`` is returned.
|
|
* If the input contains ``inf``, ``nan`` is returned.
|
|
|
|
References
|
|
----------
|
|
.. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
|
|
Probability and Statistics Tables and Formulae. Chapman & Hall: New
|
|
York. 2000.
|
|
|
|
Examples
|
|
--------
|
|
>>> import numpy as np
|
|
>>> from scipy.stats import variation
|
|
>>> variation([1, 2, 3, 4, 5], ddof=1)
|
|
0.5270462766947299
|
|
|
|
Compute the variation along a given dimension of an array that contains
|
|
a few ``nan`` values:
|
|
|
|
>>> x = np.array([[ 10.0, np.nan, 11.0, 19.0, 23.0, 29.0, 98.0],
|
|
... [ 29.0, 30.0, 32.0, 33.0, 35.0, 56.0, 57.0],
|
|
... [np.nan, np.nan, 12.0, 13.0, 16.0, 16.0, 17.0]])
|
|
>>> variation(x, axis=1, ddof=1, nan_policy='omit')
|
|
array([1.05109361, 0.31428986, 0.146483 ])
|
|
|
|
"""
|
|
xp = array_namespace(a)
|
|
a = xp.asarray(a)
|
|
# `nan_policy` and `keepdims` are handled by `_axis_nan_policy`
|
|
# `axis=None` is only handled for NumPy backend
|
|
if axis is None:
|
|
a = xp.reshape(a, (-1,))
|
|
axis = 0
|
|
|
|
n = a.shape[axis]
|
|
NaN = _get_nan(a)
|
|
|
|
if a.size == 0 or ddof > n:
|
|
# Handle as a special case to avoid spurious warnings.
|
|
# The return values, if any, are all nan.
|
|
shp = list(a.shape)
|
|
shp.pop(axis)
|
|
result = xp.full(shp, fill_value=NaN)
|
|
return result[()] if result.ndim == 0 else result
|
|
|
|
mean_a = xp.mean(a, axis=axis)
|
|
|
|
if ddof == n:
|
|
# Another special case. Result is either inf or nan.
|
|
std_a = xp.std(a, axis=axis, correction=0)
|
|
result = xp.where(std_a > 0, xp_copysign(xp.asarray(xp.inf), mean_a), NaN)
|
|
return result[()] if result.ndim == 0 else result
|
|
|
|
with np.errstate(divide='ignore', invalid='ignore'):
|
|
std_a = xp.std(a, axis=axis, correction=ddof)
|
|
result = std_a / mean_a
|
|
|
|
return result[()] if result.ndim == 0 else result
|