Creates a multivariate normal (also called Gaussian) distribution parameterized by a mean vector and a covariance matrix.
Usage
distr_multivariate_normal(
loc,
covariance_matrix = NULL,
precision_matrix = NULL,
scale_tril = NULL,
validate_args = NULL
)Arguments
- loc
(Tensor): mean of the distribution
- covariance_matrix
(Tensor): positive-definite covariance matrix
- precision_matrix
(Tensor): positive-definite precision matrix
- scale_tril
(Tensor): lower-triangular factor of covariance, with positive-valued diagonal
- validate_args
Bool wether to validate the arguments or not.
Details
The multivariate normal distribution can be parameterized either in terms of a positive definite covariance matrix \(\mathbf{\Sigma}\) or a positive definite precision matrix \(\mathbf{\Sigma}^{-1}\) or a lower-triangular matrix \(\mathbf{L}\) with positive-valued diagonal entries, such that \(\mathbf{\Sigma} = \mathbf{L}\mathbf{L}^\top\). This triangular matrix can be obtained via e.g. Cholesky decomposition of the covariance.
Note
Only one of covariance_matrix or precision_matrix or
scale_tril can be specified.
Using scale_tril will be more efficient: all computations internally
are based on scale_tril. If covariance_matrix or
precision_matrix is passed instead, it is only used to compute
the corresponding lower triangular matrices using a Cholesky decomposition.
See also
Distribution for details on the available methods.
Other distributions:
distr_bernoulli(),
distr_chi2(),
distr_gamma(),
distr_normal(),
distr_poisson()
Examples
if (torch_is_installed()) {
m <- distr_multivariate_normal(torch_zeros(2), torch_eye(2))
m$sample() # normally distributed with mean=`[0,0]` and covariance_matrix=`I`
}
#> torch_tensor
#> 0.2418
#> 1.1116
#> [ CPUFloatType{2} ]