numpy.corrcoef(x, y=None, rowvar=1, bias=0, ddof=None)[source]

Return correlation coefficients.

Please refer to the documentation for cov for more detail. The relationship between the correlation coefficient matrix, P, and the covariance matrix, C, is

P_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } }

The values of P are between -1 and 1, inclusive.


x : 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 shape as m.

rowvar : int, optional

If rowvar is non-zero (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 : int, optional

Default normalization is by (N - 1), where N is the number of observations (unbiased estimate). If bias is 1, then normalization is by N. These values can be overridden by using the keyword ddof in numpy versions >= 1.5.

ddof : {None, int}, optional

New in version 1.5.

If not None normalization is by (N - ddof), where N is the number of observations; this overrides the value implied by bias. The default value is None.


out : ndarray

The correlation coefficient matrix of the variables.

See also

Covariance matrix

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