## 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 C_{ij} 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)

Parameters:

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: **

- Python3

`# 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` `(` `"Covariance matrix of x:\n"` `, np.cov(x))` |

**Output:**

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

**Example #2: **

- Python3

`# 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))` |

**Output:**

[[ 2.03629167 0.9313 ] [ 0.9313 0.4498 ]]

**Example #3: **

- Python3

`# 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))` |

**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]]

Last Updated on March 1, 2022 by admin