Type Definition rstat::multivariate::normal::IsotropicNormal

type IsotropicNormal = MvNormal<Vector<f64>, f64>;

Multivariate Normal distribution with mean \(\bm{\mu}\) and isotropic covariance matrix \(\sigma^2\bm{I}\).

Methods

impl IsotropicNormal

pub fn isotropic<M: Into<Vector<f64>>>(
    mu: M,
    sigma2: f64
) -> Result<Self, Error>

Construct an \(n\)-dimensional IsotropicNormal distribution with mean \(\bm{\mu}\) and variance \(\sigma^2\bm{I}\).

Constraints

1. The variance term is positive real.

Examples

let dist = IsotropicNormal::isotropic(vec![0.0, 1.0], 1.0);

assert!(dist.is_ok());

pub fn isotropic_unchecked<M: Into<Vector<f64>>>(mu: M, sigma2: f64) -> Self

Construct an \(n\)-dimensional IsotropicNormal distribution with mean \(\bm{\mu}\) and variance \(\sigma^2\bm{I}\), without checking for correctness.

Examples

let dist = IsotropicNormal::isotropic_unchecked(vec![0.0, 1.0], 1.0);

pub fn homogeneous(n: usize, mu: f64, sigma2: f64) -> Result<Self, Error>

Construct an \(n\)-dimensional IsotropicNormal distribution with mean \(\mu\) and variance \(\sigma^2\) in each dimension.

Constraints

1. The dimensionality is a positive integer.

Examples

let dist = IsotropicNormal::homogeneous(2, 0.0, 1.0);

assert!(dist.is_ok());

pub fn homogeneous_unchecked(n: usize, mu: f64, sigma2: f64) -> Self

Construct an \(n\)-dimensional IsotropicNormal distribution with mean \(\mu\) and variance \(\sigma^2\) in each dimension, without checking for correctness.

Examples

let dist = IsotropicNormal::homogeneous_unchecked(2, 0.0, 1.0);

pub fn standard(n: usize) -> Result<Self, Error>

Construct an \(n\)-dimensional IsotropicNormal distribution with mean 0 and unit variance \(\sigma^2\) in each dimension.

Constraints

1. The dimensionality is a positive integer.

Examples

let dist = IsotropicNormal::standard(2);

assert!(dist.is_ok());

pub fn standard_unchecked(n: usize) -> Self

Construct an \(n\)-dimensional IsotropicNormal distribution with mean 0 and unit variance \(\sigma^2\) in each dimension, without checking for correctness.

Examples

let dist = IsotropicNormal::standard_unchecked(2);

Trait Implementations

impl ContinuousDistribution for IsotropicNormal

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

Evaluates the probability density function (PDF) at (x).

fn log_pdf(&self, x: &Sample<Self>) -> f64

Evaluates the log PDF at (x).

impl Distribution for IsotropicNormal

type Support = ProductSpace<Reals>

Support of sample elements.

type Params = IsotropicNormalParams

Parameter set uniquely defining the instance.

fn support(&self) -> ProductSpace<Reals>

Returns an instance of the support Space, Self::Support.

fn params(&self) -> Self::Params

Returns an instance of the distribution parameters, Self::Params.

fn cdf(&self, _: &Vec<f64>) -> Probability

Evaluates the cumulative distribution function (CDF) at (x).

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

Draw a random value from the distribution support.

fn into_support(self) -> Self::Support

Converts self into an instance of Self::Support.

fn into_params(self) -> Self::Params

Converts self into an instance of Self::Params.

fn ccdf(&self, x: &Sample<Self>) -> Probability

Evaluates the complementary CDF at (x).

fn log_cdf(&self, x: &Sample<Self>) -> f64

Evaluates the log CDF at (x), i.e. (\ln{F(x)}).

fn log_ccdf(&self, x: &Sample<Self>) -> f64

Evaluates the log complementary CDF at (x), i.e. (\ln{(1 - F(x))}).

fn sample_n<R: Rng + ?Sized>(&self, rng: &mut R, n: usize) -> Vec<Sample<Self>>

Draw n random value from the distribution support.

fn sample_iter<'a, R: Rng + ?Sized>(
    &'a self,
    rng: &'a mut R
) -> Sampler<'a, Self, R>

Draw an indefinite number of random values from the distribution support.

impl From<Params<ArrayBase<OwnedRepr<f64>, Dim<[usize; 1]>>, f64>> for IsotropicNormal

fn from(params: IsotropicNormalParams) -> IsotropicNormal

Performs the conversion.

impl Mahalanobis for IsotropicNormal

fn d_mahalanobis_squared(&self, x: &Vec<f64>) -> f64

Compute the squared Mahalanobis distance of sample (\boldsymbol{x}).

fn d_mahalanobis(&self, x: &Sample<Self>) -> f64

Compute the Mahalanobis distance of sample (\boldsymbol{x}).

impl MultivariateMoments for IsotropicNormal

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

Computes the vector of expected values of the distribution.

fn covariance(&self) -> Matrix<f64>

Computes the covariance matrix of the distribution.

fn variance(&self) -> Vector<f64>

Computes the vector of variances of the distribution.

fn correlation(&self) -> Matrix<f64>

Computes the correlation matrix of the distribution.