# jax.numpy.cov¶

jax.numpy.cov(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None, aweights=None)[source]

Estimate a covariance matrix, given data and weights.

LAX-backend implementation of cov().

Original docstring below.

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

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.

New in version 1.5.

• fweights (array_like, int, optional) –

1-D array of integer frequency weights; the number of times each observation vector should be repeated.

New in version 1.10.

• 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.

New in version 1.10.

Returns

out – The covariance matrix of the variables.

Return type

ndarray