Struct nalgebra::linalg::Schur

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

Expand description

Schur decomposition of a square matrix.

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

Implementations

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impl<T: ComplexField, D: Dim> Schur<T, D> where
D: DimSub<U1>,
DefaultAllocator: Allocator<T, D, DimDiff<D, U1>> + Allocator<T, DimDiff<D, U1>> + Allocator<T, D, D> + Allocator<T, D>,

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pub fn new(m: OMatrix<T, D, D>) -> Self

Computes the Schur decomposition of a square matrix.

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pub fn try_new(
 m: OMatrix<T, D, D>,
 eps: T::RealField,
 max_niter: usize
) -> Option<Self>

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.

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pub fn unpack(self) -> (OMatrix<T, D, D>, OMatrix<T, D, D>)

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

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pub fn eigenvalues(&self) -> Option<OVector<T, D>>

Computes the real eigenvalues of the decomposed matrix.

Return None if some eigenvalues are complex.

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pub fn complex_eigenvalues(&self) -> OVector<NumComplex<T>, D> where
T: RealField,
DefaultAllocator: Allocator<NumComplex<T>, D>,

Computes the complex eigenvalues of the decomposed matrix.

Trait Implementations

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

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

Returns a copy of the value. Read more

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

Performs copy-assignment from source. Read more

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

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

Formats the value using the given formatter. Read more

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impl<'de, T: ComplexField, D: Dim> Deserialize<'de> for Schur<T, D> where
 DefaultAllocator: Allocator<T, D, D>,
 DefaultAllocator: Allocator<T, D, D>,
 OMatrix<T, D, D>: Deserialize<'de>,

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

Deserialize this value from the given Serde deserializer. Read more

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impl<T: ComplexField, D: Dim> Serialize for Schur<T, D> where
 DefaultAllocator: Allocator<T, D, D>,
 DefaultAllocator: Allocator<T, D, D>,
 OMatrix<T, D, D>: Serialize,

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

Serialize this value into the given Serde serializer. Read more

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impl<T: ComplexField, D: Dim> Copy for Schur<T, D> where
DefaultAllocator: Allocator<T, D, D>,
OMatrix<T, D, D>: Copy,

Auto Trait Implementations

impl<T, D> !RefUnwindSafe for Schur<T, D>

impl<T, D> !Send for Schur<T, D>

impl<T, D> !Sync for Schur<T, D>

impl<T, D> !Unpin for Schur<T, D>

impl<T, D> !UnwindSafe for Schur<T, D>

Blanket Implementations

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

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

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

const: unstable · source

fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more

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

const: unstable · source

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

Mutably borrows from an owned value. Read more

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impl<T> From<T> for T

const: unstable · source

fn from(t: T) -> T

Returns the argument unchanged.

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

const: unstable · source

fn into(self) -> U

Calls U::from(self).

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

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impl<T> Same<T> for T

type Output = T

Should always be Self

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

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

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

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fn is_in_subset(&self) -> bool

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

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fn to_subset_unchecked(&self) -> SS

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

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fn from_subset(element: &SS) -> SP

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

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

type Owned = T

The resulting type after obtaining ownership.

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fn to_owned(&self) -> T

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

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

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

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

type Error = Infallible

The type returned in the event of a conversion error.

const: unstable · source

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

Performs the conversion.

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

type Error = >::Error

The type returned in the event of a conversion error.

const: unstable · source

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

Performs the conversion.

Struct nalgebra::linalg::Schur

Implementations

impl<T: ComplexField, D: Dim> Schur<T, D> where D: DimSub<U1>, DefaultAllocator: Allocator<T, D, DimDiff<D, U1>> + Allocator<T, DimDiff<D, U1>> + Allocator<T, D, D> + Allocator<T, D>,

pub fn new(m: OMatrix<T, D, D>) -> Self

pub fn try_new( m: OMatrix<T, D, D>, eps: T::RealField, max_niter: usize) -> Option<Self>

Arguments

pub fn unpack(self) -> (OMatrix<T, D, D>, OMatrix<T, D, D>)

pub fn eigenvalues(&self) -> Option<OVector<T, D>>

pub fn complex_eigenvalues(&self) -> OVector<NumComplex<T>, D> where T: RealField, DefaultAllocator: Allocator<NumComplex<T>, D>,

Trait Implementations

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

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

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

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

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

impl<'de, T: ComplexField, D: Dim> Deserialize<'de> for Schur<T, D> where DefaultAllocator: Allocator<T, D, D>, DefaultAllocator: Allocator<T, D, D>, OMatrix<T, D, D>: Deserialize<'de>,

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

impl<T: ComplexField, D: Dim> Serialize for Schur<T, D> where DefaultAllocator: Allocator<T, D, D>, DefaultAllocator: Allocator<T, D, D>, OMatrix<T, D, D>: Serialize,

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

impl<T: ComplexField, D: Dim> Copy for Schur<T, D> where DefaultAllocator: Allocator<T, D, D>, OMatrix<T, D, D>: Copy,

Auto Trait Implementations

impl<T, D> !RefUnwindSafe for Schur<T, D>

impl<T, D> !Send for Schur<T, D>

impl<T, D> !Sync for Schur<T, D>

impl<T, D> !Unpin for Schur<T, D>

impl<T, D> !UnwindSafe for Schur<T, D>

Blanket Implementations

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

fn type_id(&self) -> TypeId

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

fn borrow(&self) -> &T

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

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

impl<T> From<T> for T

fn from(t: T) -> T

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

fn into(self) -> U

impl<T> Same<T> for T

type Output = T

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

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

fn is_in_subset(&self) -> bool

fn to_subset_unchecked(&self) -> SS

fn from_subset(element: &SS) -> SP

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

type Owned = T

fn to_owned(&self) -> T

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

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

type Error = Infallible

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

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

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

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

impl<T: ComplexField, D: Dim> Schur<T, D> where
D: DimSub<U1>,
DefaultAllocator: Allocator<T, D, DimDiff<D, U1>> + Allocator<T, DimDiff<D, U1>> + Allocator<T, D, D> + Allocator<T, D>,

pub fn try_new(
m: OMatrix<T, D, D>,
eps: T::RealField,
max_niter: usize
) -> Option<Self>

pub fn complex_eigenvalues(&self) -> OVector<NumComplex<T>, D> where
T: RealField,
DefaultAllocator: Allocator<NumComplex<T>, D>,

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

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

impl<'de, T: ComplexField, D: Dim> Deserialize<'de> for Schur<T, D> where
DefaultAllocator: Allocator<T, D, D>,
DefaultAllocator: Allocator<T, D, D>,
OMatrix<T, D, D>: Deserialize<'de>,

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

impl<T: ComplexField, D: Dim> Serialize for Schur<T, D> where
DefaultAllocator: Allocator<T, D, D>,
DefaultAllocator: Allocator<T, D, D>,
OMatrix<T, D, D>: Serialize,

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

impl<T: ComplexField, D: Dim> Copy for Schur<T, D> where
DefaultAllocator: Allocator<T, D, D>,
OMatrix<T, D, D>: Copy,

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

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

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

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

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

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

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

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