Struct MultivariateGaussian 

pub struct MultivariateGaussian<T: Real> { /* private fields */ }

A multivariate Gaussian distribution with mean vector μ, and covariance matrix Σ.

See: https://en.wikipedia.org/wiki/Multivariate_normal_distribution

Invariants

The mean Matrix must always be a column vector, and must be the same length as the covariance matrix.

Implementations

impl<T: Real> MultivariateGaussian<T>

pub fn new(mean: Matrix<T>, covariance: Matrix<T>) -> MultivariateGaussian<T>

Constructs a new multivariate Gaussian distribution from a Nx1 column vector of means and a NxN covariance matrix

This function does not check that the provided covariance matrix is actually a covariance matrix. If a square matrix that is not symmetric is supplied the Gaussian is not defined.

Panics

Panics if the covariance matrix is not square, or the column vector is not the same length as the covariance matrix size. Does not currently panic if the covariance matrix is not symmetric, but this could be checked in the future.

pub fn mean(&self) -> &Matrix<T>

The mean is a column vector of expected values in each dimension

pub fn covariance(&self) -> &Matrix<T>

The covariance matrix is a measure of how much values from each dimension vary from their expected value with respect to each other.

For a 2 dimensional multivariate Gaussian the covariance matrix could be the 2x2 identity matrix:

[
  1.0, 0.0
  0.0, 1.0
]

In which case the two dimensions are completely uncorrelated as C[0,1] = C[1,0] = 0.

impl<T: Real> MultivariateGaussian<T>

where for<'a> &'a T: RealRef<T>,

pub fn draw<I>(&self, source: &mut I, max_samples: usize) -> Option<Matrix<T>>

where I: Iterator<Item = T>,

Draws samples from this multivariate distribution, provided that the covariance matrix is positive definite.

For max_samples of M, sufficient random numbers from the source iterator in the uniformly distributed range [0, 1] inclusive, and this Gaussian’s dimensionality of N, returns an MxN matrix of drawn values.

The source iterator must have at least MxN random values if N is even, and Mx(N+1) random values if N is odd, or None will be returned.

Example of generating and feeding random numbers

If the covariance matrix is only positive semi definite, None is returned. You can check if a given covariance matrix is positive definite instead of just positive semi definite with the cholesky decomposition.

Trait Implementations

impl<T: Clone + Real> Clone for MultivariateGaussian<T>

fn clone(&self) -> MultivariateGaussian<T>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Debug + Real> Debug for MultivariateGaussian<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.