torch.cov¶
- torch.cov(input, *, correction=1, fweights=None, aweights=None) Tensor ¶
Estimates the covariance matrix of the variables given by the
input
matrix, where rows are the variables and columns are the observations.A covariance matrix is a square matrix giving the covariance of each pair of variables. The diagonal contains the variance of each variable (covariance of a variable with itself). By definition, if
input
represents a single variable (Scalar or 1D) then its variance is returned.The sample covariance of the variables $x$ and $y$ is given by:
$\text{cov}(x,y) = \frac{\sum^{N}_{i = 1}(x_{i} - \bar{x})(y_{i} - \bar{y})}{\max(0,~N~-~\delta N)}$where $\bar{x}$ and $\bar{y}$ are the simple means of the $x$ and $y$ respectively, and $\delta N$ is the
correction
.If
fweights
and/oraweights
are provided, the weighted covariance is calculated, which is given by:$\text{cov}_w(x,y) = \frac{\sum^{N}_{i = 1}w_i(x_{i} - \mu_x^*)(y_{i} - \mu_y^*)} {\max(0,~\sum^{N}_{i = 1}w_i~-~\frac{\sum^{N}_{i = 1}w_ia_i}{\sum^{N}_{i = 1}w_i}~\delta N)}$where $w$ denotes
fweights
oraweights
(f
anda
for brevity) based on whichever is provided, or $w = f \times a$ if both are provided, and $\mu_x^* = \frac{\sum^{N}_{i = 1}w_ix_{i} }{\sum^{N}_{i = 1}w_i}$ is the weighted mean of the variable. If not provided,f
and/ora
can be seen as a $\mathbb{1}$ vector of appropriate size.- Parameters
input (Tensor) – A 2D matrix containing multiple variables and observations, or a Scalar or 1D vector representing a single variable.
- Keyword Arguments
correction (int, optional) – difference between the sample size and sample degrees of freedom. Defaults to Bessel’s correction,
correction = 1
which returns the unbiased estimate, even if bothfweights
andaweights
are specified.correction = 0
will return the simple average. Defaults to1
.fweights (tensor, optional) – A Scalar or 1D tensor of observation vector frequencies representing the number of times each observation should be repeated. Its numel must equal the number of columns of
input
. Must have integral dtype. Ignored ifNone
. Defaults toNone
.aweights (tensor, optional) – A Scalar or 1D array of observation vector weights. These relative weights are typically large for observations considered “important” and smaller for observations considered less “important”. Its numel must equal the number of columns of
input
. Must have floating point dtype. Ignored ifNone
. Defaults toNone
.
- Returns
(Tensor) The covariance matrix of the variables.
See also
torch.corrcoef()
normalized covariance matrix.- Example::
>>> x = torch.tensor([[0, 2], [1, 1], [2, 0]]).T >>> x tensor([[0, 1, 2], [2, 1, 0]]) >>> torch.cov(x) tensor([[ 1., -1.], [-1., 1.]]) >>> torch.cov(x, correction=0) tensor([[ 0.6667, -0.6667], [-0.6667, 0.6667]]) >>> fw = torch.randint(1, 10, (3,)) >>> fw tensor([1, 6, 9]) >>> aw = torch.rand(3) >>> aw tensor([0.4282, 0.0255, 0.4144]) >>> torch.cov(x, fweights=fw, aweights=aw) tensor([[ 0.4169, -0.4169], [-0.4169, 0.4169]])