Struct MultivariateNormal

pub struct MultivariateNormal<D>
where
    D: Dim,
    DefaultAllocator: Allocator<D> + Allocator<D, D>,
{ /* private fields */ }

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

Examples

use statrs::distribution::{MultivariateNormal, Continuous};
use nalgebra::{matrix, vector};
use statrs::statistics::{MeanN, VarianceN};

let mvn = MultivariateNormal::new_from_nalgebra(vector![0., 0.], matrix![1., 0.; 0., 1.]).unwrap();
assert_eq!(mvn.mean().unwrap(), vector![0., 0.]);
assert_eq!(mvn.variance().unwrap(), matrix![1., 0.; 0., 1.]);
assert_eq!(mvn.pdf(&vector![1.,  1.]), 0.05854983152431917);

Implementations

impl MultivariateNormal<Dyn>

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

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

impl<D> MultivariateNormal<D>

where D: DimMin<D, Output = D>, DefaultAllocator: Allocator<D> + Allocator<D, D>,

pub fn new_from_nalgebra( mean: OVector<f64, D>, cov: OMatrix<f64, D, D>, ) -> Result<Self, MultivariateNormalError>

Constructs a new multivariate normal distribution with a mean of mean and covariance matrix cov using nalgebra OVector and OMatrix instead of Vec<f64>

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<D> Clone for MultivariateNormal<D>

where D: Dim + Clone, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn clone(&self) -> MultivariateNormal<D>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<D> Continuous<&Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>, f64> for MultivariateNormal<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn pdf(&self, x: &OVector<f64, D>) -> 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: &OVector<f64, D>) -> f64

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

impl<D> Debug for MultivariateNormal<D>

where D: Dim + Debug, DefaultAllocator: Allocator<D> + Allocator<D, D>,

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

Formats the value using the given formatter.

impl<D> Display for MultivariateNormal<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

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

Formats the value using the given formatter.

impl<D> Distribution<Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>> for MultivariateNormal<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

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

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<D> Max<Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>> for MultivariateNormal<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn max(&self) -> OVector<f64, D>

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

impl<D> MeanN<Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>> for MultivariateNormal<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn mean(&self) -> Option<OVector<f64, D>>

Returns the mean of the normal distribution

Remarks

This is the same mean used to construct the distribution

impl<D> Min<Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>> for MultivariateNormal<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn min(&self) -> OVector<f64, D>

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

impl<D> Mode<Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>> for MultivariateNormal<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn mode(&self) -> OVector<f64, D>

Returns the mode of the multivariate normal distribution

Formula

μ

where μ is the mean

impl<D> PartialEq for MultivariateNormal<D>

where D: Dim + PartialEq, DefaultAllocator: Allocator<D> + Allocator<D, D>,

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl<D> VarianceN<Matrix<f64, D, D, <DefaultAllocator as Allocator<D, D>>::Buffer<f64>>> for MultivariateNormal<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn variance(&self) -> Option<OMatrix<f64, D, D>>

Returns the covariance matrix of the multivariate normal distribution

impl<D> StructuralPartialEq for MultivariateNormal<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,