Struct Svd 

pub struct Svd<T: Scalar> { /* private fields */ }

The singular value decomposition A = U·Σ·V* of an m × n matrix, k = min(m, n): U of m × k and V of n × k with orthonormal columns, Σ the diagonal of the singular values, real, not negative, in descending order. From Matrix::svd.

Examples

use a::math::matrix::Matrix;

let a: Matrix<f64> = Matrix::from_rows(&[[3.0, 0.0], [4.0, 5.0]]);
let svd = a.svd();
let s = svd.singular_values();
assert!((s[0] - 45f64.sqrt()).abs() < 1e-14 && (s[1] - 5f64.sqrt()).abs() < 1e-14);
let sigma = Matrix::from_diagonal(s);
let back = &(&svd.u() * &sigma) * &svd.v().transpose();
assert!((&back - &a).as_slice().iter().all(|x| x.abs() < 1e-14));

Implementations

impl<T: Scalar> Svd<T>

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

U, m × min(m, n), the left singular vectors as orthonormal columns.

pub fn singular_values(&self) -> &[T::Real]

The singular values, real, not negative, in descending order.

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

V, n × min(m, n), the right singular vectors as orthonormal columns.

Trait Implementations

impl<T: Clone + Scalar> Clone for Svd<T>

where T::Real: Clone,

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Debug + Scalar> Debug for Svd<T>

where T::Real: Debug,

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

Formats the value using the given formatter.