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