Covariance provides a measure of the strength of the correlation between two or more variables. An element of the covariance matrix C ij is the covariance of xi and xj. The element Cii is the variance of xi.
- If COV (xi, xj) = 0, then the variables are uncorrelated
- If COV (xi, xj)" 0, then the variables are positively correlated
- If COV (xi, xj)" "0, variables are negatively correlated
Syntax: numpy.cov (m, y = None, rowvar = True, bias = False, ddof = None, fweights = None, aweights = None)
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:
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 No. 2:
[[2.03629167 0.9313] [0.9313 0.4498]]
Example # 3 :
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]]