Struct statrs::distribution::MultivariateNormal

pub struct MultivariateNormal { /* private fields */ }

Implements the Multivariate Normal distribution using the “nalgebra” crate for matrix operations

Examples

use statrs::distribution::{MultivariateNormal, Continuous};
use nalgebra::{DVector, DMatrix};
use statrs::statistics::{MeanN, VarianceN};

let mvn = MultivariateNormal::new(vec![0., 0.], vec![1., 0., 0., 1.]).unwrap();
assert_eq!(mvn.mean().unwrap(), DVector::from_vec(vec![0., 0.]));
assert_eq!(mvn.variance().unwrap(), DMatrix::from_vec(2, 2, vec![1., 0., 0., 1.]));
assert_eq!(mvn.pdf(&DVector::from_vec(vec![1.,  1.])), 0.05854983152431917);

Implementations

impl MultivariateNormal

pub fn new(mean: Vec<f64>, cov: Vec<f64>) -> Result<Self>

Constructs a new multivariate normal distribution with a mean of mean and covariance matrix cov

Errors

Returns an error if the given covariance matrix is not symmetric or positive-definite

pub fn entropy(&self) -> Option<f64>

Returns the entropy of the multivariate normal distribution

Formula

(1 / 2) * ln(det(2 * π * e * Σ))

where Σ is the covariance matrix and det is the determinant

Trait Implementations

impl Clone for MultivariateNormal

fn clone(&self) -> MultivariateNormal

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<'a> Continuous<&'a Matrix<f64, Dynamic, Const<1>, VecStorage<f64, Dynamic, Const<1>>>, f64> for MultivariateNormal

fn pdf(&self, x: &'a DVector<f64>) -> f64

Calculates the probability density function for the multivariate normal distribution at x

Formula

(2 * π) ^ (-k / 2) * det(Σ) ^ (1 / 2) * e ^ ( -(1 / 2) * transpose(x - μ) * inv(Σ) * (x - μ))

where μ is the mean, inv(Σ) is the precision matrix, det(Σ) is the determinant of the covariance matrix, and k is the dimension of the distribution

fn ln_pdf(&self, x: &'a DVector<f64>) -> f64

Calculates the log probability density function for the multivariate normal distribution at x. Equivalent to pdf(x).ln().

impl Debug for MultivariateNormal

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

Formats the value using the given formatter.

impl Distribution<Matrix<f64, Dynamic, Const<1>, VecStorage<f64, Dynamic, Const<1>>>> for MultivariateNormal

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> DVector<f64>

Samples from the multivariate normal distribution

Formula

L * Z + μ

where L is the Cholesky decomposition of the covariance matrix, Z is a vector of normally distributed random variables, and μ is the mean vector

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl Max<Matrix<f64, Dynamic, Const<1>, VecStorage<f64, Dynamic, Const<1>>>> for MultivariateNormal

fn max(&self) -> DVector<f64>

Returns the maximum value in the domain of the multivariate normal distribution represented by a real vector

impl MeanN<Matrix<f64, Dynamic, Const<1>, VecStorage<f64, Dynamic, Const<1>>>> for MultivariateNormal

fn mean(&self) -> Option<DVector<f64>>

Returns the mean of the normal distribution

Remarks

This is the same mean used to construct the distribution

impl Min<Matrix<f64, Dynamic, Const<1>, VecStorage<f64, Dynamic, Const<1>>>> for MultivariateNormal

fn min(&self) -> DVector<f64>

Returns the minimum value in the domain of the multivariate normal distribution represented by a real vector

impl Mode<Matrix<f64, Dynamic, Const<1>, VecStorage<f64, Dynamic, Const<1>>>> for MultivariateNormal

fn mode(&self) -> DVector<f64>

Returns the mode of the multivariate normal distribution

Formula

μ

where μ is the mean

impl PartialEq<MultivariateNormal> for MultivariateNormal

fn eq(&self, other: &MultivariateNormal) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl VarianceN<Matrix<f64, Dynamic, Dynamic, VecStorage<f64, Dynamic, Dynamic>>> for MultivariateNormal

fn variance(&self) -> Option<DMatrix<f64>>

Returns the covariance matrix of the multivariate normal distribution

impl StructuralPartialEq for MultivariateNormal