`numpy:corrcoef`

source: /numpy/lib/_function_base_impl.py:2897

Signature

def corrcoef(x, y = None, rowvar = True, *, dtype = None)

Summary

Return Pearson product-moment correlation coefficients.

Extended Summary

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

R_{ij} = \frac{C _{ij}}{C _{ii} C _{j j}}

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

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 rowvar below.
y : array_like, optional: An additional set of variables and observations. y has the same shape as x.
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.
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

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

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.

Examples

import numpy as np

✓

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
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
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.        ]])

Aliases

numpy.corrcoef