Function cov

numpy/lib/_function_base_impl.py:2688–2902

Estimate a covariance matrix, given data and weights. Covariance indicates the level to which two variables vary together. If we examine N-dimensional samples, :math:`X = [x_1, x_2, ..., x_N]^T`, then the covariance matrix element :math:`C_{ij}` is the covariance of :math:`x_i`

(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None,
        aweights=None, *, dtype=None)

@array_function_dispatch(_cov_dispatcher)
def cov(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None,
        aweights=None, *, dtype=None):
    """
    Estimate a covariance matrix, given data and weights.

    Covariance indicates the level to which two variables vary together.
    If we examine N-dimensional samples, :math:`X = [x_1, x_2, ..., x_N]^T`,
    then the covariance matrix element :math:`C_{ij}` is the covariance of
    :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance
    of :math:`x_i`.

    See the notes for an outline of the algorithm.

    Parameters
    ----------
    m : array_like
        A 1-D or 2-D array containing multiple variables and observations.
        Each row of `m` represents a variable, and each column a single
        observation of all those variables. Also see `rowvar` below.
    y : array_like, optional
        An additional set of variables and observations. `y` has the same form
        as that of `m`.
    rowvar : bool, optional
        If `rowvar` is True (default), then each row represents a
        variable, with observations in the columns. Otherwise, the relationship
        is transposed: each column represents a variable, while the rows
        contain observations.
    bias : bool, optional
        Default normalization (False) is by ``(N - 1)``, where ``N`` is the
        number of observations given (unbiased estimate). If `bias` is True,
        then normalization is by ``N``. These values can be overridden by using
        the keyword ``ddof`` in numpy versions >= 1.5.
    ddof : int, optional
        If not ``None`` the default value implied by `bias` is overridden.
        Note that ``ddof=1`` will return the unbiased estimate, even if both
        `fweights` and `aweights` are specified, and ``ddof=0`` will return
        the simple average. See the notes for the details. The default value
        is ``None``.
    fweights : array_like, int, optional
        1-D array of integer frequency weights; the number of times each
        observation vector should be repeated.
    aweights : array_like, optional
        1-D array of observation vector weights. These relative weights are
        typically large for observations considered "important" and smaller for
        observations considered less "important". If ``ddof=0`` the array of
        weights can be used to assign probabilities to observation vectors.
    dtype : data-type, optional
        Data-type of the result. By default, the return data-type will have
        at least `numpy.float64` precision.

        .. versionadded:: 1.20

    Returns
    -------
    out : ndarray
        The covariance matrix of the variables.

    See Also