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corrcoef(x, y=None, rowvar=True, bias=<no value>, ddof=<no value>, *, dtype=None)

Please refer to the documentation for cov for more detail. The relationship between the correlation coefficient matrix, R, and the covariance matrix, :None:None:`C`, is

$$R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } }$$

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

Notes

Due to floating point rounding the resulting array may not be Hermitian, the diagonal elements may not be 1, and the elements may not satisfy the inequality abs(a) <= 1. The real and imaginary parts are clipped to the interval [-1, 1] in an attempt to improve on that situation but is not much help in the complex case.

This function accepts but discards arguments :None:None:`bias` and :None:None:`ddof`. This is for backwards compatibility with previous versions of this function. These arguments had no effect on the return values of the function and can be safely ignored in this and previous versions of numpy.

Parameters

x : array_like: A 1-D or 2-D array containing multiple variables and observations. Each row of x represents a variable, and each column a single observation of all those variables. Also see :None:None:`rowvar` below.
y : array_like, optional: An additional set of variables and observations. y has the same shape as x.
rowvar : bool, optional: If :None:None:`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 : _NoValue, optional: Has no effect, do not use.

deprecated
ddof : _NoValue, optional: Has no effect, do not use.

deprecated
dtype : data-type, optional: Data-type of the result. By default, the return data-type will have at least numpy.float64 precision.

versionadded

Returns

R : ndarray: The correlation coefficient matrix of the variables.

Return Pearson product-moment correlation coefficients.

Examples

In this example we generate two random arrays, xarr and yarr , and compute the row-wise and column-wise Pearson correlation coefficients, R . Since rowvar is true by default, we first find the row-wise Pearson correlation coefficients between the variables of xarr .

>>> import numpy as np
... rng = np.random.default_rng(seed=42)
... xarr = rng.random((3, 3))
... xarr
array([[0.77395605, 0.43887844, 0.85859792],
       [0.69736803, 0.09417735, 0.97562235],
       [0.7611397 , 0.78606431, 0.12811363]])

>>> R1 = np.corrcoef(xarr)
... R1
array([[ 1.        ,  0.99256089, -0.68080986],
       [ 0.99256089,  1.        , -0.76492172],
       [-0.68080986, -0.76492172,  1.        ]])

If we add another set of variables and observations yarr , we can compute the row-wise Pearson correlation coefficients between the variables in xarr and yarr .

>>> yarr = rng.random((3, 3))
... yarr
array([[0.45038594, 0.37079802, 0.92676499],
       [0.64386512, 0.82276161, 0.4434142 ],
       [0.22723872, 0.55458479, 0.06381726]])

>>> R2 = np.corrcoef(xarr, yarr)
... R2
array([[ 1.        ,  0.99256089, -0.68080986,  0.75008178, -0.934284  ,
        -0.99004057],
       [ 0.99256089,  1.        , -0.76492172,  0.82502011, -0.97074098,
        -0.99981569],
       [-0.68080986, -0.76492172,  1.        , -0.99507202,  0.89721355,
         0.77714685],
       [ 0.75008178,  0.82502011, -0.99507202,  1.        , -0.93657855,
        -0.83571711],
       [-0.934284  , -0.97074098,  0.89721355, -0.93657855,  1.        ,
         0.97517215],
       [-0.99004057, -0.99981569,  0.77714685, -0.83571711,  0.97517215,
         1.        ]])

Finally if we use the option rowvar=False , the columns are now being treated as the variables and we will find the column-wise Pearson correlation coefficients between variables in xarr and yarr .

>>> R3 = np.corrcoef(xarr, yarr, rowvar=False)
... R3
array([[ 1.        ,  0.77598074, -0.47458546, -0.75078643, -0.9665554 ,
         0.22423734],
       [ 0.77598074,  1.        , -0.92346708, -0.99923895, -0.58826587,
        -0.44069024],
       [-0.47458546, -0.92346708,  1.        ,  0.93773029,  0.23297648,
         0.75137473],
       [-0.75078643, -0.99923895,  0.93773029,  1.        ,  0.55627469,
         0.47536961],
       [-0.9665554 , -0.58826587,  0.23297648,  0.55627469,  1.        ,
        -0.46666491],
       [ 0.22423734, -0.44069024,  0.75137473,  0.47536961, -0.46666491,
         1.        ]])

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

pandas.core.window.rolling.Rolling.corr numpy.cov numpy.ma.extras.corrcoef pandas.core.window.expanding.Expanding.corr

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