Python | numpy.cov() function

Covariance provides the a measure of strength of correlation between two variable or more set of variables. The covariance matrix element Cij is the covariance of xi and xj. The element Cii is the variance of xi.

  • If COV(xi, xj) = 0 then variables are uncorrelated
  • If COV(xi, xj) > 0 then variables positively correlated
  • If COV(xi, xj) > < 0 then variables negatively correlated

Syntax: numpy.cov(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None, aweights=None)

Parametrs:
m : [array_like] A 1D or 2D variables. variables are columns
y : [array_like] It 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:
bias : Default normalization is False. If bias is True it normalize the data points.
ddof : 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.
fweights : fweight is 1-D array of integer frequency weights
aweights : aweight is 1-D array of observation vector weights.



Returns: It returns ndarray covariance matrix

Example #1:

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# Python code to demonstrate the 
# use of numpy.cov
import numpy as np
  
x = np.array([[0, 3, 4], [1, 2, 4], [3, 4, 5]])
  
print("Shape of array:\n", np.shape(x))
  
print("Covarinace matrix of x:\n", np.cov(x))

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Output:

Shape of array:
 (3, 3)
Covarinace matrix of x:
 [[ 4.33333333  2.83333333  2.        ]
 [ 2.83333333  2.33333333  1.5       ]
 [ 2.          1.5         1.        ]]

Example #2:

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# Python code to demonstrate the 
# use of numpy.cov
import numpy as np
  
x = [1.23, 2.12, 3.34, 4.5]
  
y = [2.56, 2.89, 3.76, 3.95]
  
# find out covariance with respect  columns
cov_mat = np.stack((x, y), axis = 0
  
print(np.cov(cov_mat))

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Output:

[[ 2.03629167  0.9313    ]
 [ 0.9313      0.4498    ]]

Example #3:

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# Python code to demonstrate the 
# use of numpy.cov
import numpy as np
  
x = [1.23, 2.12, 3.34, 4.5]
  
y = [2.56, 2.89, 3.76, 3.95]
  
# find out covariance with respect  rows
cov_mat = np.stack((x, y), axis = 1
  
print("shape of matrix x and y:", np.shape(cov_mat))
  
print("shape of covariance matrix:", np.shape(np.cov(cov_mat)))
  
print(np.cov(cov_mat))

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Output:

shape of matrix x and y: (4, 2)
shape of covariance matrix: (4, 4)
[[ 0.88445  0.51205  0.2793  -0.36575]
 [ 0.51205  0.29645  0.1617  -0.21175]
 [ 0.2793   0.1617   0.0882  -0.1155 ]
 [-0.36575 -0.21175 -0.1155   0.15125]]


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