Struct rin::math::linalg::Schur

pub struct Schur<N, D> where
    N: ComplexField,
    D: Dim,
    DefaultAllocator: Allocator<N, D, D>,  { /* fields omitted */ }

Schur decomposition of a square matrix.

If this is a real matrix, this will be a RealField Schur decomposition.

Implementations

impl<N, D> Schur<N, D> where
    N: ComplexField,
    D: Dim + DimSub<U1>,
    DefaultAllocator: Allocator<N, D, <D as DimSub<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimSub<U1>>::Output, U1>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

pub fn new(
    m: Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
) -> Schur<N, D>

Computes the Schur decomposition of a square matrix.

pub fn try_new(
    m: Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>,
    eps: <N as ComplexField>::RealField,
    max_niter: usize
) -> Option<Schur<N, D>>

Attempts to compute the Schur decomposition of a square matrix.

If only eigenvalues are needed, it is more efficient to call the matrix method .eigenvalues() instead.

Arguments

• eps − tolerance used to determine when a value converged to 0.
• max_niter − maximum total number of iterations performed by the algorithm. If this number of iteration is exceeded, None is returned. If niter == 0, then the algorithm continues indefinitely until convergence.

pub fn unpack(
    self
) -> (Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>, Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>)

Retrieves the unitary matrix Q and the upper-quasitriangular matrix T such that the decomposed matrix equals Q * T * Q.transpose().

pub fn eigenvalues(
    &self
) -> Option<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

Computes the real eigenvalues of the decomposed matrix.

Return None if some eigenvalues are complex.

pub fn complex_eigenvalues(
    &self
) -> Matrix<Complex<N>, D, U1, <DefaultAllocator as Allocator<Complex<N>, D, U1>>::Buffer> where
    N: RealField,
    DefaultAllocator: Allocator<Complex<N>, D, U1>, 

Computes the complex eigenvalues of the decomposed matrix.

Trait Implementations

impl<N, D> Clone for Schur<N, D> where
    N: Clone + ComplexField,
    D: Clone + Dim,
    DefaultAllocator: Allocator<N, D, D>, 

pub fn clone(&self) -> Schur<N, D>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N, D> Debug for Schur<N, D> where
    N: Debug + ComplexField,
    D: Debug + Dim,
    DefaultAllocator: Allocator<N, D, D>, 

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

Formats the value using the given formatter.

impl<'de, N, D> Deserialize<'de> for Schur<N, D> where
    N: ComplexField,
    D: Dim,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, D>,
    Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>: Deserialize<'de>, 

pub fn deserialize<__D>(
    __deserializer: __D
) -> Result<Schur<N, D>, <__D as Deserializer<'de>>::Error> where
    __D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl<N, D> Serialize for Schur<N, D> where
    N: ComplexField,
    D: Dim,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, D>,
    Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>: 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.

impl<N, D> Copy for Schur<N, D> where
    N: ComplexField,
    D: Dim,
    DefaultAllocator: Allocator<N, D, D>,
    Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>: Copy,