Struct Lu 

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

The LU decomposition P·A = L·U of an m × n matrix, by Gaussian elimination with partial pivoting: P a permutation, L of m × min(m, n) lower triangular with ones on its diagonal, U of min(m, n) × n upper triangular. From Matrix::lu.

Examples

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

let a = Matrix::from_rows(&[[2.0, 1.0], [4.0, 3.0]]);
let lu = a.lu();
// The larger first column's element is the pivot: the rows are swapped.
assert_eq!(lu.permutation(), [1, 0]);
assert_eq!(lu.l(), Matrix::from_rows(&[[1.0, 0.0], [0.5, 1.0]]));
assert_eq!(lu.u(), Matrix::from_rows(&[[4.0, 3.0], [0.0, -0.5]]));
assert_eq!(&lu.p() * &a, &lu.l() * &lu.u());
assert_eq!(lu.det(), 2.0);
let x = lu.solve(&Matrix::from_rows(&[[3.0], [7.0]])).unwrap();
assert_eq!(x, Matrix::from_rows(&[[1.0], [1.0]]));

Implementations

impl<T: Scalar> Lu<T>

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

L, m × min(m, n), lower triangular with ones on the diagonal.

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

U, min(m, n) × n, upper triangular.

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

P, the m × m permutation matrix with P·A = L·U.

pub fn permutation(&self) -> &[usize]

The permutation: row i of P·A is row permutation()[i] of A.

pub fn is_singular(&self) -> bool

Whether a pivot is zero, which for a square matrix makes it singular.

pub fn det(&self) -> T

The determinant of the square matrix: the product of the pivots, negated for an odd permutation.

Panics

Panics if the matrix is not square.

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

The solution X of A·X = B for the square matrix, or None when it is singular.

Panics

Panics if the matrix is not square, or B has not as many rows.

pub fn inverse(&self) -> Option<Matrix<T>>

The inverse of the square matrix, or None when it is singular.

Panics

Panics if the matrix is not square.

Trait Implementations

impl<T: Clone> Clone for Lu<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 Lu<T>

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

Formats the value using the given formatter.