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NumPy | cov method

schedule Aug 12, 2023
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Numpy's cov(~) method computes the covariance given two arrays.

Parameters

1. x | array-like

Each row represents a separate column data (i.e. a variable). See the example below for clarification.

2. y | array-like | optional

Instead of specifying your dataset as a new row in x, you can just specify it as y.

3. rowvar | boolean | optional

If True, then each row in x represents a variable. If False, then each column in x represents a variable. By default, rowvar=True.

4. bias | boolean | optional

Whether to compute the biased estimate of the covariance, or the unbiased one. By default, bias=False (sample covariance).

5. ddof | int | optional

The delta degree of freedom. This can be used to modify the denominator in the front:

$$\frac{1}{N\color{blue}{-ddof}}\sum_{i=0}^{N}\left(x_i-\bar{x}^2\right)$$

By default, ddof=0.

6. fweights | array-like | optional

The number of times each observation should be repeated. See example below for clarification.

7. aweights | array-like | optional

A 1D array of weights placed on each observation. The higher the weight, the more important the observation is.

Return value

If one variable is given, then the a scalar is returned. Otherwise, a Numpy array is returned.

Examples

Computing sample covariance

np.cov([2,3,5,6], [3,5,8,12])
array([[ 3.33333333, 7. ],
[ 7. , 15.33333333]])

This is exactly the same as specifying a 2D array:

np.cov([[2,3,5,6], [3,5,8,12]])
array([[ 3.33333333, 7. ],
[ 7. , 15.33333333]])

Computing population covariance

np.cov([2,3,5,6], [3,5,8,12], ddof=0)
array([[ 2.5 , 5.25],
[ 5.25, 11.5 ]])

You could also set bias=True:

np.cov([2,3,5,6], [3,5,8,12], bias=True)
array([[ 2.5 , 5.25],
[ 5.25, 11.5 ]])

Repeating values using fweights

np.cov([2,3,5,6], [3,5,8,12], fweights=[2,1,1,1])
array([[ 3.3 , 6.85],
[ 6.85, 14.7 ]])

This is exactly the same as the following:

np.cov([2,2,3,5,6], [3,3,5,8,12])
array([[ 3.3 , 6.85],
[ 6.85, 14.7 ]])

That is, the first value of each array was repeated twice, as specified by fweights.

robocat
Published by Isshin Inada
Edited by 0 others
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