`scipy.stats._circstats:circvar`

source: build-install/usr/lib/python3.14/site-packages/scipy/stats/_circstats.py:411

Signature

def circvar(samples, high = 6.283185307179586, low = 0, axis = None, nan_policy = propagate, *, keepdims = False)

Summary

Compute the circular variance of a sample of angle observations.

Extended Summary

Given $n$ angle observations $x_{1}, \dots, x_{n}$ measured in radians, their circular variance is defined by (^[2], Eq. 2.3.3)

1 - \frac{1}{n} k = 1 \sum n e^{i x_{k}}

where $i$ is the imaginary unit and $∣ z ∣$ gives the length of the complex number $z$ . $∣ z ∣$ in the above expression is known as the mean resultant length.

Parameters

samples : array_like

Input array of angle observations. The value of a full angle is equal to (high - low).

high : float, optional

Upper boundary of the principal value of an angle. Default is 2*pi.

low : float, optional

Lower boundary of the principal value of an angle. Default is 0.

axis : int or None, default: None

If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If None, the input will be raveled before computing the statistic.

nan_policy : {'propagate', 'omit', 'raise'}

Defines how to handle input NaNs.

propagate: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.
omit: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output will be NaN.
raise: if a NaN is present, a ValueError will be raised.

nan_policy='raise' and nan_policy='omit' are not supported by lazy backends, and nan_policy='omit' is not compatible with MArray input. For multidimensional input, nan_policy='omit' is supported only by the NumPy backend. Instead, mask NaN values using MArray; and use the default nan_policy. See Notes for support information.

keepdims : bool, default: False

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 input array.

Returns

circvar : float

Circular variance. The returned value is in the range [0, 1], where 0 indicates no variance and 1 indicates large variance.

If the input array is empty, np.nan is returned.

Notes

In the limit of small angles, the circular variance is close to half the 'linear' variance if measured in radians.

Beginning in SciPy 1.9, np.matrix inputs (not recommended for new code) are converted to np.ndarray before the calculation is performed. In this case, the output will be a scalar or np.ndarray of appropriate shape rather than a 2D np.matrix. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or np.ndarray rather than a masked array with mask=False.

Examples

import numpy as np
from scipy.stats import circvar
import matplotlib.pyplot as plt
samples_1 = np.array([0.072, -0.158, 0.077, 0.108, 0.286,
                      0.133, -0.473, -0.001, -0.348, 0.131])
samples_2 = np.array([0.111, -0.879, 0.078, 0.733, 0.421,
                      0.104, -0.136, -0.867,  0.012,  0.105])
circvar_1 = circvar(samples_1)
circvar_2 = circvar(samples_2)

✓

Plot the samples.

fig, (left, right) = plt.subplots(ncols=2)

✓

for image in (left, right):
    image.plot(np.cos(np.linspace(0, 2*np.pi, 500)),
               np.sin(np.linspace(0, 2*np.pi, 500)),
               c='k')
    image.axis('equal')
    image.axis('off')
left.scatter(np.cos(samples_1), np.sin(samples_1), c='k', s=15)
left.set_title(f"circular variance: {np.round(circvar_1, 2)!r}")
right.scatter(np.cos(samples_2), np.sin(samples_2), c='k', s=15)
right.set_title(f"circular variance: {np.round(circvar_2, 2)!r}")

✗

Text(0.5, 1.0, 'circular variance: np.float64(0.11)')

plt.show()

✓

Aliases

scipy.stats.circvar