Struct MultivariateNormal 

pub struct MultivariateNormal {
    pub mean: Array1<f64>,
    pub cov: Array2<f64>,
    pub dim: usize,
    /* private fields */
}

Multivariate Normal distribution structure

Fields

mean: Array1<f64>

Mean vector

cov: Array2<f64>

Covariance matrix

dim: usize

Dimensionality of the distribution

Implementations

impl MultivariateNormal

pub fn new<D1, D2>( mean: ArrayBase<D1, Ix1>, cov: ArrayBase<D2, Ix2>, ) -> StatsResult<Self>

where D1: Data<Elem = f64>, D2: Data<Elem = f64>,

Create a new multivariate normal distribution with given mean vector and covariance matrix

Arguments

• mean - Mean vector (k-dimensional)
• cov - Covariance matrix (k x k, symmetric positive-definite)

Returns

• A new MultivariateNormal distribution instance

Examples

use scirs2_core::ndarray::{array, Array1, Array2};
use scirs2_stats::distributions::multivariate::normal::MultivariateNormal;

// Create a 2D multivariate normal distribution
let mean = array![0.0, 0.0];
let cov = array![[1.0, 0.5], [0.5, 2.0]];
let mvn = MultivariateNormal::new(mean, cov).expect("Operation failed");

pub fn pdf<D>(&self, x: &ArrayBase<D, Ix1>) -> f64

where D: Data<Elem = f64>,

Calculate the probability density function (PDF) at a given point

Arguments

• x - The point at which to evaluate the PDF

Returns

• The value of the PDF at the given point

Examples

use scirs2_core::ndarray::array;
use scirs2_stats::distributions::multivariate::normal::MultivariateNormal;

let mean = array![0.0, 0.0];
let cov = array![[1.0, 0.0], [0.0, 1.0]];
let mvn = MultivariateNormal::new(mean, cov).expect("Operation failed");

// PDF at origin for a standard 2D normal should be 1/(2π)
let pdf_at_origin = mvn.pdf(&array![0.0, 0.0]);
assert!((pdf_at_origin - 0.15915494).abs() < 1e-7); // 1/(2π) ≈ 0.15915494

pub fn rvs(&self, size: usize) -> StatsResult<Array2<f64>>

Generate random samples from the distribution

Arguments

• size - Number of samples to generate

Returns

• Matrix where each row is a random sample

Examples

use scirs2_core::ndarray::array;
use scirs2_stats::distributions::multivariate::normal::MultivariateNormal;

let mean = array![0.0, 0.0];
let cov = array![[1.0, 0.5], [0.5, 2.0]];
let mvn = MultivariateNormal::new(mean, cov).expect("Operation failed");

let samples = mvn.rvs(100).expect("Operation failed");
assert_eq!(samples.shape(), &[100, 2]);

pub fn rvs_single(&self) -> StatsResult<Array1<f64>>

Generate a single random sample from the distribution

Returns

• Vector representing a single sample

Examples

use scirs2_core::ndarray::array;
use scirs2_stats::distributions::multivariate::normal::MultivariateNormal;

let mean = array![0.0, 0.0];
let cov = array![[1.0, 0.5], [0.5, 2.0]];
let mvn = MultivariateNormal::new(mean, cov).expect("Operation failed");

let sample = mvn.rvs_single().expect("Operation failed");
assert_eq!(sample.len(), 2);

pub fn logpdf<D>(&self, x: &ArrayBase<D, Ix1>) -> f64

where D: Data<Elem = f64>,

Calculate the log probability density function (log PDF) at a given point

Arguments

• x - The point at which to evaluate the log PDF

Returns

• The value of the log PDF at the given point

Examples

use scirs2_core::ndarray::array;
use scirs2_stats::distributions::multivariate::normal::MultivariateNormal;

let mean = array![0.0, 0.0];
let cov = array![[1.0, 0.0], [0.0, 1.0]];
let mvn = MultivariateNormal::new(mean, cov).expect("Operation failed");

let log_pdf = mvn.logpdf(&array![0.0, 0.0]);
assert!((log_pdf - (-1.8378770664093453)).abs() < 1e-7); // ln(1/(2π)) ≈ -1.837877

pub fn dim(&self) -> usize

Get the dimension of the distribution

pub fn cov(&self) -> ArrayView2<'_, f64>

Get the covariance matrix of the distribution

pub fn mean(&self) -> ArrayView1<'_, f64>

Get the mean vector of the distribution

Trait Implementations

impl Clone for MultivariateNormal

fn clone(&self) -> MultivariateNormal

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for MultivariateNormal

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

Formats the value using the given formatter.

impl Distribution<f64> for MultivariateNormal

fn mean(&self) -> f64

Mean (expected value) of the distribution

fn var(&self) -> f64

Variance of the distribution

fn std(&self) -> f64

Standard deviation of the distribution

fn rvs(&self, size: usize) -> StatsResult<Array1<f64>>

Generate random samples from the distribution

fn entropy(&self) -> f64

Entropy of the distribution

fn rvs_array(&self, shape: &[usize]) -> StatsResult<ArrayD<F>>

Generate random samples with a user-specified output shape.

impl MultivariateDistribution<f64> for MultivariateNormal

fn pdf(&self, x: &Array1<f64>) -> f64

Probability density function for multivariate distributions

fn rvs(&self, size: usize) -> StatsResult<Array2<f64>>

Generate random samples from the multivariate distribution

fn mean(&self) -> Array1<f64>

Mean vector of the distribution

fn cov(&self) -> Array2<f64>

Covariance matrix of the distribution

fn dim(&self) -> usize

Dimensionality of the distribution

fn logpdf(&self, x: &Array1<f64>) -> f64

Log probability density function for multivariate distributions

fn rvs_single(&self) -> StatsResult<Vec<f64>>

Generate a single random sample from the multivariate distribution

impl SampleableDistribution<ArrayBase<OwnedRepr<f64>, Dim<[usize; 1]>>> for MultivariateNormal

Implementation of SampleableDistribution for MultivariateNormal

fn rvs(&self, size: usize) -> StatsResult<Vec<Array1<f64>>>

Generate random samples from the distribution