var

Calculates the variance of the input array x.

Parameters:

Name	Type	Description	Default
x		input array of a real-valued floating-point data type.	required
axis		axis or axes along which variances are computed. By default, the variance is computed over the entire array. If a tuple of integers, variances are computed over multiple axes. Default: None.	None
correction		degrees of freedom adjustment. Setting this parameter to a value other than 0 has the effect of adjusting the divisor during the calculation of the variance according to N-c where N corresponds to the total number of elements over which the variance is computed and c corresponds to the provided degrees of freedom adjustment. When computing the variance of a population, setting this parameter to 0 is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the unbiased sample variance, setting this parameter to 1 is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction). Default: 0.	0.0
keepdims		if True, the reduced axes are included in the result as singleton dimensions, and, accordingly, the result is compatible with the input array. Otherwise, if False, the reduced axes (dimensions) are not included in the result. Default: False.	False

Returns:

Name	Type	Description
out	array	if the variance was computed over the entire array, a zero-dimensional array containing the variance; otherwise, a non-zero-dimensional array containing the variances. The returned array must have the same data type as x.

Special Cases

Let N equal the number of elements over which to compute the variance.

• If N - correction is less than or equal to 0, the variance is NaN.
• If x_i is NaN, the variance is NaN (i.e., NaN values propagate).

Examples:

>>> a = sparse.COO.from_numpy(np.array([[0, 2], [-1, 1]]))
>>> o = sparse.var(a, axis=1)
>>> o.todense()
array([1., 1.])

Source code in sparse/numba_backend/_common.py

def var(x, /, *, axis=None, correction=0.0, keepdims=False):
    """
    Calculates the variance of the input array ``x``.

    Parameters
    ----------
    x: array
        input array of a real-valued floating-point data type.
    axis: Optional[Union[int, Tuple[int, ...]]]
        axis or axes along which variances are computed.
        By default, the variance is computed over the entire array.
        If a tuple of integers, variances are computed over multiple axes. Default: ``None``.
    correction: Union[int, float]
        degrees of freedom adjustment. Setting this parameter to a value other than ``0``
        has the effect of adjusting the divisor during the calculation of the variance according to ``N-c``
        where ``N`` corresponds to the total number of elements over which the variance is computed and ``c``
        corresponds to the provided degrees of freedom adjustment.
        When computing the variance of a population, setting this parameter to ``0`` is the standard choice
        (i.e., the provided array contains data constituting an entire population).
        When computing the unbiased sample variance, setting this parameter to ``1`` is the standard choice
        (i.e., the provided array contains data sampled from a larger population; this is commonly referred
        to as Bessel's correction). Default: ``0``.
    keepdims: bool
        if ``True``, the reduced axes are included in the result as singleton dimensions, and,
        accordingly, the result is compatible with the input array.
        Otherwise, if ``False``, the reduced axes (dimensions) are not included in the result. Default: ``False``.

    Returns
    -------
    out: array
        if the variance was computed over the entire array, a zero-dimensional array containing the variance;
        otherwise, a non-zero-dimensional array containing the variances.
        The returned array must have the same data type as ``x``.

    Special Cases
    -------------
    Let ``N`` equal the number of elements over which to compute the variance.

    -   If ``N - correction`` is less than or equal to ``0``, the variance is ``NaN``.
    -   If ``x_i`` is ``NaN``, the variance is ``NaN`` (i.e., ``NaN`` values propagate).

    Examples
    --------
    >>> a = sparse.COO.from_numpy(np.array([[0, 2], [-1, 1]]))
    >>> o = sparse.var(a, axis=1)
    >>> o.todense()
    array([1., 1.])
    """
    return x.var(axis=axis, ddof=correction, keepdims=keepdims)