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LBLT

nalgebra::linalg

Struct LBLT

pub struct LBLT<T: ComplexField, N: Dim>where
    DefaultAllocator: Allocator<N> + Allocator<N, N>,
{ /* private fields */ }

Expand description

Bunch–Kaufman LBL^H factorization of a Hermitian matrix with symmetric pivoting.

Implementations§

impl<T: Copy + ComplexField, N: Dim> LBLT<T, N>
where T::RealField: Copy, DefaultAllocator: Allocator<N> + Allocator<N, N>,

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

Compute the factorization of a complex Hermitian matrix using the Bunch-Kaufman block-diagonal pivoting method:

P A P^T = L * B * L^H

where P is the permutation induced by the pivot sequence, L is unit lower triangular in the permuted basis, and B is Hermitian block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This implementation follows the partial pivoting (Algorithm A) variant from Bunch & Kaufman (1977), which is also the basis for LAPACK’s ?sytrf/?hetrf routines.

pub fn l_permuted(&self) -> OMatrix<T, N, N>

Returns the permutation-aware factor P^T L.

This factor can be combined directly with d() to reconstruct the original matrix. In general P^T L is not lower triangular, even though L itself is unit lower triangular in the permuted basis.

pub fn d(&self) -> OMatrix<T, N, N>

The block diagonal matrix of this decomposition.

pub fn solve<M: Dim, S>( &self, b: &Matrix<T, N, M, S>, ) -> Option<OMatrix<T, N, M>>
where S: Storage<T, N, M>, DefaultAllocator: Allocator<N, M>,

Solves the linear system A * x = b using this factorization.

pub fn solve_mut<M: Dim>(&self, b: &mut OMatrix<T, N, M>) -> bool
where DefaultAllocator: Allocator<N, M>,

Solves the linear system A * x = b in place, overwriting b with the solution.

pub fn determinant(&self) -> T::RealField

Computes the determinant of the decomposed matrix.

Trait Implementations§

impl<T: Clone + ComplexField, N: Clone + Dim> Clone for LBLT<T, N>
where DefaultAllocator: Allocator<N> + Allocator<N, N>,

fn clone(&self) -> LBLT<T, N>

Returns a duplicate of the value. Read more

1.0.0 (const: unstable) · Source§

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

Performs copy-assignment from source. Read more

impl<T: Debug + ComplexField, N: Debug + Dim> Debug for LBLT<T, N>
where DefaultAllocator: Allocator<N> + Allocator<N, N>,

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

Formats the value using the given formatter. Read more

Auto Trait Implementations§

impl<T, N> !Freeze for LBLT<T, N>

impl<T, N> !RefUnwindSafe for LBLT<T, N>

impl<T, N> !Send for LBLT<T, N>

impl<T, N> !Sync for LBLT<T, N>

impl<T, N> !Unpin for LBLT<T, N>

impl<T, N> !UnsafeUnpin for LBLT<T, N>

impl<T, N> !UnwindSafe for LBLT<T, N>

Blanket Implementations§

impl<T> Any for T
where T: 'static + ?Sized,

fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

impl<T> Borrow<T> for T
where T: ?Sized,

fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more

impl<T> BorrowMut<T> for T
where T: ?Sized,

fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more

impl<T> CloneToUninit for T
where T: Clone,

unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)

Performs copy-assignment from self to dest. Read more

impl<T> From<T> for T

fn from(t: T) -> T

Returns the argument unchanged.

impl<T, W> HasTypeWitness<W> for T
where W: MakeTypeWitness<Arg = T>, T: ?Sized,

const WITNESS: W = W::MAKE

A constant of the type witness

impl<T> Identity for T
where T: ?Sized,

const TYPE_EQ: TypeEq<T, <T as Identity>::Type> = TypeEq::NEW

Proof that Self is the same type as Self::Type, provides methods for casting between Self and Self::Type.

type Type = T

The same type as Self, used to emulate type equality bounds (T == U) with associated type equality constraints (T: Identity<Type = U>).

impl<T, U> Into<U> for T
where U: From<T>,

fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

impl<T> Same for T

type Output = T

Should always be Self

impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).

fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.

fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.

impl<T> ToOwned for T
where T: Clone,

type Owned = T

The resulting type after obtaining ownership.

fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more

fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more

impl<T, U> TryFrom<U> for T
where U: Into<T>,

type Error = Infallible

The type returned in the event of a conversion error.

fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.

impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.

fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.