Struct lnkit::prelude::linalg::FullPivLU

pub struct FullPivLU<T, R, C> where
    C: Dim,
    T: ComplexField,
    R: DimMin<C>,
    DefaultAllocator: Allocator<T, R, C>,
    DefaultAllocator: Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1_usize>>,  { /* fields omitted */ }

LU decomposition with full row and column pivoting.

Implementations

impl<T, R, C> FullPivLU<T, R, C> where
    C: Dim,
    T: ComplexField,
    R: DimMin<C>,
    DefaultAllocator: Allocator<T, R, C>,
    DefaultAllocator: Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1_usize>>, 

pub fn new(
    matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>
) -> FullPivLU<T, R, C>

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
) -> Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer> where
    DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>, 

The lower triangular matrix of this decomposition.

pub fn u(
    &self
) -> Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer> where
    DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>, 

The upper triangular matrix of this decomposition.

pub fn p(&self) -> &PermutationSequence<<R as DimMin<C>>::Output>

The row permutations of this decomposition.

pub fn q(&self) -> &PermutationSequence<<R as DimMin<C>>::Output>

The column permutations of this decomposition.

pub fn unpack(
    self
) -> (PermutationSequence<<R as DimMin<C>>::Output>, Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>, Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>, PermutationSequence<<R as DimMin<C>>::Output>) where
    DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
    DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>, 

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

impl<T, D> FullPivLU<T, D, D> where
    T: ComplexField,
    D: DimMin<D, Output = D>,
    DefaultAllocator: Allocator<T, D, D>,
    DefaultAllocator: Allocator<(usize, usize), D, Const<1_usize>>, 

pub fn solve<R2, C2, S2>(
    &self,
    b: &Matrix<T, R2, C2, S2>
) -> Option<Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>> where
    R2: Dim,
    S2: Storage<T, R2, C2>,
    C2: Dim,
    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, C2, S2>(&self, b: &mut Matrix<T, R2, C2, S2>) -> bool where
    R2: Dim,
    S2: StorageMut<T, R2, C2>,
    C2: Dim,
    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<Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>>

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, R, C> Clone for FullPivLU<T, R, C> where
    C: Clone + Dim,
    T: Clone + ComplexField,
    R: Clone + DimMin<C>,
    DefaultAllocator: Allocator<T, R, C>,
    DefaultAllocator: Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1_usize>>, 

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T, R, C> Copy for FullPivLU<T, R, C> where
    C: Dim,
    T: ComplexField,
    R: DimMin<C>,
    DefaultAllocator: Allocator<T, R, C>,
    DefaultAllocator: Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1_usize>>,
    Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>: Copy,
    PermutationSequence<<R as DimMin<C>>::Output>: Copy, 

impl<T, R, C> Debug for FullPivLU<T, R, C> where
    C: Debug + Dim,
    T: Debug + ComplexField,
    R: Debug + DimMin<C>,
    DefaultAllocator: Allocator<T, R, C>,
    DefaultAllocator: Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1_usize>>, 

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

Formats the value using the given formatter.

impl<'de, T, R, C> Deserialize<'de> for FullPivLU<T, R, C> where
    C: Dim,
    T: ComplexField,
    R: DimMin<C>,
    DefaultAllocator: Allocator<T, R, C>,
    DefaultAllocator: Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1_usize>>,
    DefaultAllocator: Allocator<T, R, C>,
    DefaultAllocator: Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1_usize>>,
    Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>: Deserialize<'de>,
    PermutationSequence<<R as DimMin<C>>::Output>: Deserialize<'de>, 

pub fn deserialize<__D>(
    __deserializer: __D
) -> Result<FullPivLU<T, R, C>, <__D as Deserializer<'de>>::Error> where
    __D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl<T, R, C> Serialize for FullPivLU<T, R, C> where
    C: Dim,
    T: ComplexField,
    R: DimMin<C>,
    DefaultAllocator: Allocator<T, R, C>,
    DefaultAllocator: Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1_usize>>,
    DefaultAllocator: Allocator<T, R, C>,
    DefaultAllocator: Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1_usize>>,
    Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>: Serialize,
    PermutationSequence<<R as DimMin<C>>::Output>: Serialize, 

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

Serialize this value into the given Serde serializer.