Struct nalgebra::linalg::FullPivLU

pub struct FullPivLU<T: ComplexField, R: DimMin<C>, C: Dim>where
    DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>,{ /* private fields */ }

LU decomposition with full row and column pivoting.

Implementations

impl<T: ComplexField, R: DimMin<C>, C: Dim> FullPivLU<T, R, C>where
    DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>,

pub fn new(matrix: OMatrix<T, R, C>) -> Self

Computes the LU decomposition with full pivoting of matrix.

This effectively computes P, L, U, Q such that P * matrix * Q = LU.

pub fn l(&self) -> OMatrix<T, R, DimMinimum<R, C>>where
    DefaultAllocator: Allocator<T, R, DimMinimum<R, C>>,

The lower triangular matrix of this decomposition.

pub fn u(&self) -> OMatrix<T, DimMinimum<R, C>, C>where
    DefaultAllocator: Allocator<T, DimMinimum<R, C>, C>,

The upper triangular matrix of this decomposition.

pub fn p(&self) -> &PermutationSequence<DimMinimum<R, C>>

The row permutations of this decomposition.

pub fn q(&self) -> &PermutationSequence<DimMinimum<R, C>>

The column permutations of this decomposition.

pub fn unpack(
    self
) -> (PermutationSequence<DimMinimum<R, C>>, OMatrix<T, R, DimMinimum<R, C>>, OMatrix<T, DimMinimum<R, C>, C>, PermutationSequence<DimMinimum<R, C>>)where
    DefaultAllocator: Allocator<T, R, DimMinimum<R, C>> + Allocator<T, DimMinimum<R, C>, C>,

The two matrices of this decomposition and the row and column permutations: (P, L, U, Q).

impl<T: ComplexField, D: DimMin<D, Output = D>> FullPivLU<T, D, D>where
    DefaultAllocator: Allocator<T, D, D> + Allocator<(usize, usize), D>,

pub fn solve<R2: Dim, C2: Dim, S2>(
    &self,
    b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>>where
    S2: Storage<T, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R2, D>,
    DefaultAllocator: Allocator<T, R2, C2>,

Solves the linear system self * x = b, where x is the unknown to be determined.

Returns None if the decomposed matrix is not invertible.

pub fn solve_mut<R2: Dim, C2: Dim, S2>(
    &self,
    b: &mut Matrix<T, R2, C2, S2>
) -> boolwhere
    S2: StorageMut<T, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self * x = b, where x is the unknown to be determined.

If the decomposed matrix is not invertible, this returns false and its input b may be overwritten with garbage.

pub fn try_inverse(&self) -> Option<OMatrix<T, D, D>>

Computes the inverse of the decomposed matrix.

Returns None if the decomposed matrix is not invertible.

pub fn is_invertible(&self) -> bool

Indicates if the decomposed matrix is invertible.

pub fn determinant(&self) -> T

Computes the determinant of the decomposed matrix.

Trait Implementations

impl<T: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim> Clone for FullPivLU<T, R, C>where
    DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>,

fn clone(&self) -> FullPivLU<T, R, C>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug + ComplexField, R: Debug + DimMin<C>, C: Debug + Dim> Debug for FullPivLU<T, R, C>where
    DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>,

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

Formats the value using the given formatter.

impl<T: ComplexField, R: DimMin<C>, C: Dim> Copy for FullPivLU<T, R, C>where
    DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>,
    OMatrix<T, R, C>: Copy,
    PermutationSequence<DimMinimum<R, C>>: Copy,