mindspore.ops.cov

mindspore.ops.cov(input, *, correction=1, fweights=None, aweights=None)

Return the covariance matrix of the input tensor, where the rows of the input tensor represent variables and the columns represent observations. The diagonal of the covariance matrix contains the variance of each variable in the input tensor, while the off-diagonal elements represent the covariance between pairs of variables. If the input is a 0-D or 1-D tensor, its variance is returned.

The unbiased sample covariance of the variables $a$ and $b$ is given by the following formula:

$${\text{cov}}_w(a,b)=\frac{\sum _{i=1}^N(a_i-\overline{a})(b_i-\overline{b})}{N-1}$$

where $\overline{a}$ and $\overline{b}$ are the simple means of the $a$ and $b$ respectively.

If fweights and/or aweights are provided, the unbiased weighted covariance is calculated, which is given by:

$${\text{cov}}_w(a,b)=\frac{\sum _{i=1}^N{w}_i(a_i-{\mu }_a^{\ast })(b_i-{\mu }_b^{\ast })}{\sum _{i=1}^N{w}_i-1}$$

where $w$ denotes fweights or aweights based on whichever is provided, or $w=fweights\times aweights$ if both are provided, and ${\mu }_x^{\ast }=\frac{\sum _{i=1}^N{w}_i{x}_i}{\sum _{i=1}^N{w}_i}$ is the weighted mean of the variable.

Warning

The values of fweights and aweights cannot be negative, and the negative weight scene result is undefined.

Note

Currently, complex number is not supported.

Parameters

input (Tensor) – The 0-D, 1-D or 2-D tensor.

Keyword Arguments

• correction (int, optional) – The difference between sample size and sample degrees of freedom. correction = 0 will return the simple average. Defaults to Bessel's correction, correction = 1 which returns the unbiased estimate, even if both fweights and aweights are specified.

• fweights (Tensor, optional) – 0D or 1D tensor containing integer frequency weight, indicating the number of repetition of each observation vector. Its numel must equal the number of columns of input. Ignored if None. Default None .

• aweights (Tensor, optional) – A scalar or 1D Tensor containing float observation weights represents the importance of each observation vector. The higher the importance, the greater the corresponding value. Its numel must equal the number of columns of input. Must have floating point dtype. Ignored if None. Default None .

Returns

Tensor

Supported Platforms:

Ascend GPU CPU

Examples

>>> import mindspore
>>> input = mindspore.tensor([[0., 5., 7.],
...                           [3., 5., 0.]])
>>> output = mindspore.ops.cov(input)
>>> print(output)
[[13.        -3.5      ]
 [-3.5        6.3333335]]
>>> output = mindspore.ops.cov(input, correction=0)
>>> print(output)
[[ 8.666667  -2.3333333]
 [-2.3333333  4.2222223]]
>>> fw = mindspore.tensor([5, 2, 4], dtype=mindspore.int64)
>>> aw = mindspore.tensor([0.4588, 0.9083, 0.7616], mindspore.float32)
>>> output = mindspore.ops.cov(input, fweights=fw, aweights=aw)
>>> print(output)
[[10.146146 -3.47241 ]
 [-3.47241   4.716825]]