numpy.cov — NumPy v1.13 Manual (original) (raw)

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

Estimate a covariance matrix, given data and weights.

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 freguency 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 : ndarray The covariance matrix of the variables.

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 freguency 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 : ndarray The covariance matrix of the variables.