numpy.corrcoef¶

numpy.
corrcoef
(x, y=None, rowvar=True, bias=<no value>, ddof=<no value>, *, dtype=None)[source]¶ Return Pearson productmoment correlation coefficients.
Please refer to the documentation for
cov
for more detail. The relationship between the correlation coefficient matrix, R, and the covariance matrix, C, isThe values of R are between 1 and 1, inclusive.
 Parameters
 xarray_like
A 1D or 2D 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.
 yarray_like, optional
An additional set of variables and observations. y has the same shape as x.
 rowvarbool, 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_NoValue, optional
Has no effect, do not use.
Deprecated since version 1.10.0.
 ddof_NoValue, optional
Has no effect, do not use.
Deprecated since version 1.10.0.
 dtypedatatype, optional
Datatype of the result. By default, the return datatype will have at least
numpy.float64
precision.New in version 1.20.
 Returns
 Rndarray
The correlation coefficient matrix of the variables.
See also
cov
Covariance matrix
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 bias and 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.
Examples
In this example we generate two random arrays,
xarr
andyarr
, and compute the rowwise and columnwise Pearson correlation coefficients,R
. Sincerowvar
is true by default, we first find the rowwise Pearson correlation coefficients between the variables ofxarr
.>>> 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 rowwise Pearson correlation coefficients between the variables inxarr
andyarr
.>>> 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 columnwise Pearson correlation coefficients between variables inxarr
andyarr
.>>> 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. ]])