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Fonction var - module numpy.matlib

Signature de la fonction var

def var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=<no value>, *, where=<no value>) 

Description

var.__doc__

    Compute the variance along the specified axis.

    Returns the variance of the array elements, a measure of the spread of a
    distribution.  The variance is computed for the flattened array by
    default, otherwise over the specified axis.

    Parameters
    ----------
    a : array_like
        Array containing numbers whose variance is desired.  If `a` is not an
        array, a conversion is attempted.
    axis : None or int or tuple of ints, optional
        Axis or axes along which the variance is computed.  The default is to
        compute the variance of the flattened array.

        .. versionadded:: 1.7.0

        If this is a tuple of ints, a variance is performed over multiple axes,
        instead of a single axis or all the axes as before.
    dtype : data-type, optional
        Type to use in computing the variance.  For arrays of integer type
        the default is `float64`; for arrays of float types it is the same as
        the array type.
    out : ndarray, optional
        Alternate output array in which to place the result.  It must have
        the same shape as the expected output, but the type is cast if
        necessary.
    ddof : int, optional
        "Delta Degrees of Freedom": the divisor used in the calculation is
        ``N - ddof``, where ``N`` represents the number of 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 input array.

        If the default value is passed, then `keepdims` will not be
        passed through to the `var` method of sub-classes of
        `ndarray`, however any non-default value will be.  If the
        sub-class' method does not implement `keepdims` any
        exceptions will be raised.

    where : array_like of bool, optional
        Elements to include in the variance. See `~numpy.ufunc.reduce` for
        details.

        .. versionadded:: 1.20.0

    Returns
    -------
    variance : ndarray, see dtype parameter above
        If ``out=None``, returns a new array containing the variance;
        otherwise, a reference to the output array is returned.

    See Also
    --------
    std, mean, nanmean, nanstd, nanvar
    :ref:`ufuncs-output-type`

    Notes
    -----
    The variance is the average of the squared deviations from the mean,
    i.e.,  ``var = mean(x)``, where ``x = abs(a - a.mean())**2``.

    The mean is typically 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 a hypothetical infinite population.
    ``ddof=0`` provides a maximum likelihood estimate of the variance for
    normally distributed variables.

    Note that for complex numbers, the absolute value is taken before
    squaring, so that the result is always real and nonnegative.

    For floating-point input, the variance 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
    --------
    >>> a = np.array([[1, 2], [3, 4]])
    >>> np.var(a)
    1.25
    >>> np.var(a, axis=0)
    array([1.,  1.])
    >>> np.var(a, axis=1)
    array([0.25,  0.25])

    In single precision, var() can be inaccurate:

    >>> a = np.zeros((2, 512*512), dtype=np.float32)
    >>> a[0, :] = 1.0
    >>> a[1, :] = 0.1
    >>> np.var(a)
    0.20250003

    Computing the variance in float64 is more accurate:

    >>> np.var(a, dtype=np.float64)
    0.20249999932944759 # may vary
    >>> ((1-0.55)**2 + (0.1-0.55)**2)/2
    0.2025

    Specifying a where argument:

    >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])
    >>> np.var(a)
    6.833333333333333 # may vary
    >>> np.var(a, where=[[True], [True], [False]])
    4.0