Struct nalgebra::linalg::FullPivLU

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

LU decomposition with full row and column pivoting.

Implementations

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

pub fn new(matrix: MatrixMN<N, 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) -> MatrixMN<N, R, DimMinimum<R, C>> where
    DefaultAllocator: Allocator<N, R, DimMinimum<R, C>>, 

The lower triangular matrix of this decomposition.

pub fn u(&self) -> MatrixMN<N, DimMinimum<R, C>, C> where
    DefaultAllocator: Allocator<N, 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>>, MatrixMN<N, R, DimMinimum<R, C>>, MatrixMN<N, DimMinimum<R, C>, C>, PermutationSequence<DimMinimum<R, C>>) where
    DefaultAllocator: Allocator<N, R, DimMinimum<R, C>> + Allocator<N, DimMinimum<R, C>, C>, 

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

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

pub fn solve<R2: Dim, C2: Dim, S2>(
    &self,
    b: &Matrix<N, R2, C2, S2>
) -> Option<MatrixMN<N, R2, C2>> where
    S2: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R2, D>,
    DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>
) -> bool where
    S2: StorageMut<N, 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<MatrixN<N, 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) -> N

Computes the determinant of the decomposed matrix.

Trait Implementations

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

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

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

Formats the value using the given formatter.

impl<'de, N: ComplexField, R: DimMin<C>, C: Dim> Deserialize<'de> for FullPivLU<N, R, C> where
    DefaultAllocator: Allocator<N, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>,
    DefaultAllocator: Allocator<N, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>,
    MatrixMN<N, R, C>: Deserialize<'de>,
    PermutationSequence<DimMinimum<R, C>>: Deserialize<'de>, 

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where
    __D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl<N: ComplexField, R: DimMin<C>, C: Dim> Serialize for FullPivLU<N, R, C> where
    DefaultAllocator: Allocator<N, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>,
    DefaultAllocator: Allocator<N, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>,
    MatrixMN<N, R, C>: Serialize,
    PermutationSequence<DimMinimum<R, C>>: Serialize, 

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where
    __S: Serializer, 

Serialize this value into the given Serde serializer.

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