Struct Qr 

pub struct Qr<T> { /* private fields */ }

The QR decomposition A = Q·R of an m × n matrix by Householder reflections: Q of m × min(m, n) with orthonormal columns (unitary for complex elements), R of min(m, n) × n upper triangular with a real diagonal. From Matrix::qr.

Examples

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

let a: Matrix<f64> = Matrix::from_rows(&[[3.0, 1.0], [4.0, 2.0]]);
let qr = a.qr();
let (q, r) = (qr.q(), qr.r());
assert!((&q * &r - &a).as_slice().iter().all(|x| x.abs() < 1e-15));
assert!((&q.transpose() * &q - Matrix::identity(2)).as_slice().iter().all(|x| x.abs() < 1e-15));
assert!((r[(0, 0)].abs() - 5.0).abs() < 1e-15);

Implementations

impl<T: Scalar> Qr<T>

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

Q, m × min(m, n), with orthonormal columns.

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

The whole m × m unitary Q, whose first min(m, n) columns are q.

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

R, min(m, n) × n, upper triangular.

pub fn solve(&self, b: &Matrix<T>) -> Option<Matrix<T>>

The X of the least squares, which makes ‖A·X - B‖ the smallest, for m ≥ n: the solution of R·X = Q*·B, or None when a diagonal element of R is zero, the columns of A dependent. For a square matrix it solves A·X = B.

Panics

Panics if the matrix has fewer rows than columns, or B not as many rows as it.

Trait Implementations

impl<T: Clone> Clone for Qr<T>

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> Debug for Qr<T>

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

Formats the value using the given formatter.