Struct nalgebra::linalg::QR

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pub struct QR<T: ComplexField, R: DimMin<C>, C: Dim>where
    DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,{ /* private fields */ }

Expand description

The QR decomposition of a general matrix.

Implementations

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impl<T: ComplexField, R: DimMin<C>, C: Dim> QR<T, R, C>where
DefaultAllocator: Allocator<T, R, C> + Allocator<T, R> + Allocator<T, DimMinimum<R, C>>,

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

Computes the QR decomposition using householder reflections.

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pub fn r(&self) -> OMatrix<T, DimMinimum<R, C>, C>where
DefaultAllocator: Allocator<T, DimMinimum<R, C>, C>,

Retrieves the upper trapezoidal submatrix R of this decomposition.

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pub fn unpack_r(self) -> OMatrix<T, DimMinimum<R, C>, C>where
DefaultAllocator: Reallocator<T, R, C, DimMinimum<R, C>, C>,

Retrieves the upper trapezoidal submatrix R of this decomposition.

This is usually faster than r but consumes self.

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pub fn q(&self) -> OMatrix<T, R, DimMinimum<R, C>>where
DefaultAllocator: Allocator<T, R, DimMinimum<R, C>>,

Computes the orthogonal matrix Q of this decomposition.

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pub fn unpack(
 self
) -> (OMatrix<T, R, DimMinimum<R, C>>, OMatrix<T, DimMinimum<R, C>, C>)where
 DimMinimum<R, C>: DimMin<C, Output = DimMinimum<R, C>>,
 DefaultAllocator: Allocator<T, R, DimMinimum<R, C>> + Reallocator<T, R, C, DimMinimum<R, C>, C>,

Unpacks this decomposition into its two matrix factors.

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pub fn q_tr_mul<R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<T, R2, C2, S2>)where
S2: StorageMut<T, R2, C2>,

Multiplies the provided matrix by the transpose of the Q matrix of this decomposition.

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impl<T: ComplexField, D: DimMin<D, Output = D>> QR<T, D, D>where
DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,

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pub fn solve<R2: Dim, C2: Dim, S2>(
 &self,
 b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>>where
 S2: Storage<T, R2, C2>,
 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 self is not invertible.

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pub fn solve_mut<R2: Dim, C2: Dim, S2>(
 &self,
 b: &mut Matrix<T, R2, C2, S2>
) -> boolwhere
 S2: StorageMut<T, 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 is overwritten with garbage.

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pub fn try_inverse(&self) -> Option<OMatrix<T, D, D>>

Computes the inverse of the decomposed matrix.

Returns None if the decomposed matrix is not invertible.

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pub fn is_invertible(&self) -> bool

Indicates if the decomposed matrix is invertible.

Trait Implementations

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impl<T: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim> Clone for QR<T, R, C>where
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,

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

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, R: Debug + DimMin<C>, C: Debug + Dim> Debug for QR<T, R, C>where
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,

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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, R: DimMin<C>, C: Dim> Deserialize<'de> for QR<T, R, C>where
 DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,
 DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,
 OMatrix<T, R, C>: Deserialize<'de>,
 OVector<T, DimMinimum<R, C>>: 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, R: DimMin<C>, C: Dim> Serialize for QR<T, R, C>where
 DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,
 DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,
 OMatrix<T, R, C>: Serialize,
 OVector<T, DimMinimum<R, C>>: 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, R: DimMin<C>, C: Dim> Copy for QR<T, R, C>where
 DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,
 OMatrix<T, R, C>: Copy,
 OVector<T, DimMinimum<R, C>>: Copy,

Auto Trait Implementations

impl<T, R, C> !RefUnwindSafe for QR<T, R, C>

impl<T, R, C> !Send for QR<T, R, C>

impl<T, R, C> !Sync for QR<T, R, C>

impl<T, R, C> !Unpin for QR<T, R, C>

impl<T, R, C> !UnwindSafe for QR<T, R, C>

Blanket Implementations

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impl<T> Any for Twhere
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> ArchivePointee for T

type ArchivedMetadata = ()

The archived version of the pointer metadata for this type.

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fn pointer_metadata(
&<T as ArchivePointee>::ArchivedMetadata
) -> <T as Pointee>::Metadata

Converts some archived metadata to the pointer metadata for itself.

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impl<T> Borrow<T> for Twhere
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 Twhere
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<F, W, T, D> Deserialize<With<T, W>, D> for Fwhere
 W: DeserializeWith<F, T, D>,
 D: Fallible + ?Sized,
 F: ?Sized,

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fn deserialize(
&self,
deserializer: &mut D
) -> Result<With<T, W>, <D as Fallible>::Error>

Deserializes using the given deserializer

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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 Twhere
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.

impl<T> Pointee for T

type Metadata = ()

The type for metadata in pointers and references to Self.

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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 SPwhere
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<SS, SP> SupersetOf<SS> for SPwhere
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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unsafe 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 Twhere
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 Twhere
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 Twhere
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::QR

Implementations

impl<T: ComplexField, R: DimMin<C>, C: Dim> QR<T, R, C>where DefaultAllocator: Allocator<T, R, C> + Allocator<T, R> + Allocator<T, DimMinimum<R, C>>,

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

pub fn r(&self) -> OMatrix<T, DimMinimum<R, C>, C>where DefaultAllocator: Allocator<T, DimMinimum<R, C>, C>,

pub fn unpack_r(self) -> OMatrix<T, DimMinimum<R, C>, C>where DefaultAllocator: Reallocator<T, R, C, DimMinimum<R, C>, C>,

pub fn q(&self) -> OMatrix<T, R, DimMinimum<R, C>>where DefaultAllocator: Allocator<T, R, DimMinimum<R, C>>,

pub fn unpack( self) -> (OMatrix<T, R, DimMinimum<R, C>>, OMatrix<T, DimMinimum<R, C>, C>)where DimMinimum<R, C>: DimMin<C, Output = DimMinimum<R, C>>, DefaultAllocator: Allocator<T, R, DimMinimum<R, C>> + Reallocator<T, R, C, DimMinimum<R, C>, C>,

pub fn q_tr_mul<R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<T, R2, C2, S2>)where S2: StorageMut<T, R2, C2>,

impl<T: ComplexField, D: DimMin<D, Output = D>> QR<T, D, D>where DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,

pub fn solve<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>) -> Option<OMatrix<T, R2, C2>>where S2: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>, DefaultAllocator: Allocator<T, R2, C2>,

pub fn solve_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>) -> boolwhere S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

pub fn try_inverse(&self) -> Option<OMatrix<T, D, D>>

pub fn is_invertible(&self) -> bool

Trait Implementations

impl<T: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim> Clone for QR<T, R, C>where DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,

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

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

impl<T: Debug + ComplexField, R: Debug + DimMin<C>, C: Debug + Dim> Debug for QR<T, R, C>where DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,

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

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

impl<T: ComplexField, R: DimMin<C>, C: Dim> Serialize for QR<T, R, C>where DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>, OMatrix<T, R, C>: Serialize, OVector<T, DimMinimum<R, C>>: Serialize,

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

impl<T: ComplexField, R: DimMin<C>, C: Dim> Copy for QR<T, R, C>where DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>, OMatrix<T, R, C>: Copy, OVector<T, DimMinimum<R, C>>: Copy,

Auto Trait Implementations

impl<T, R, C> !RefUnwindSafe for QR<T, R, C>

impl<T, R, C> !Send for QR<T, R, C>

impl<T, R, C> !Sync for QR<T, R, C>

impl<T, R, C> !Unpin for QR<T, R, C>

impl<T, R, C> !UnwindSafe for QR<T, R, C>

Blanket Implementations

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

fn type_id(&self) -> TypeId

impl<T> ArchivePointee for T

type ArchivedMetadata = ()

fn pointer_metadata( &<T as ArchivePointee>::ArchivedMetadata) -> <T as Pointee>::Metadata

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

fn borrow(&self) -> &T

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

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

impl<F, W, T, D> Deserialize<With<T, W>, D> for Fwhere W: DeserializeWith<F, T, D>, D: Fallible + ?Sized, F: ?Sized,

fn deserialize( &self, deserializer: &mut D) -> Result<With<T, W>, <D as Fallible>::Error>

impl<T> From<T> for T

fn from(t: T) -> T

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

fn into(self) -> U

impl<T> Pointee for T

type Metadata = ()

impl<T> Same<T> for T

type Output = T

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

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

fn is_in_subset(&self) -> bool

unsafe fn to_subset_unchecked(&self) -> SS

fn from_subset(element: &SS) -> SP

impl<T> ToOwned for Twhere T: Clone,

type Owned = T

fn to_owned(&self) -> T

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

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

type Error = Infallible

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

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

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

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

impl<V, T> VZip<V> for Twhere V: MultiLane<T>,

fn vzip(self) -> V

impl<T: ComplexField, R: DimMin<C>, C: Dim> QR<T, R, C>where
DefaultAllocator: Allocator<T, R, C> + Allocator<T, R> + Allocator<T, DimMinimum<R, C>>,

pub fn r(&self) -> OMatrix<T, DimMinimum<R, C>, C>where
DefaultAllocator: Allocator<T, DimMinimum<R, C>, C>,

pub fn unpack_r(self) -> OMatrix<T, DimMinimum<R, C>, C>where
DefaultAllocator: Reallocator<T, R, C, DimMinimum<R, C>, C>,

pub fn q(&self) -> OMatrix<T, R, DimMinimum<R, C>>where
DefaultAllocator: Allocator<T, R, DimMinimum<R, C>>,

pub fn unpack(
self
) -> (OMatrix<T, R, DimMinimum<R, C>>, OMatrix<T, DimMinimum<R, C>, C>)where
DimMinimum<R, C>: DimMin<C, Output = DimMinimum<R, C>>,
DefaultAllocator: Allocator<T, R, DimMinimum<R, C>> + Reallocator<T, R, C, DimMinimum<R, C>, C>,

pub fn q_tr_mul<R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<T, R2, C2, S2>)where
S2: StorageMut<T, R2, C2>,

impl<T: ComplexField, D: DimMin<D, Output = D>> QR<T, D, D>where
DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,

pub fn solve<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Option<OMatrix<T, R2, C2>>where
S2: Storage<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
DefaultAllocator: Allocator<T, R2, C2>,

pub fn solve_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>
) -> boolwhere
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,

impl<T: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim> Clone for QR<T, R, C>where
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,

impl<T: Debug + ComplexField, R: Debug + DimMin<C>, C: Debug + Dim> Debug for QR<T, R, C>where
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,

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

impl<T: ComplexField, R: DimMin<C>, C: Dim> Serialize for QR<T, R, C>where
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,
OMatrix<T, R, C>: Serialize,
OVector<T, DimMinimum<R, C>>: Serialize,

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

impl<T: ComplexField, R: DimMin<C>, C: Dim> Copy for QR<T, R, C>where
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>>,
OMatrix<T, R, C>: Copy,
OVector<T, DimMinimum<R, C>>: Copy,

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

fn pointer_metadata(
&<T as ArchivePointee>::ArchivedMetadata
) -> <T as Pointee>::Metadata

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

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

impl<F, W, T, D> Deserialize<With<T, W>, D> for Fwhere
W: DeserializeWith<F, T, D>,
D: Fallible + ?Sized,
F: ?Sized,

fn deserialize(
&self,
deserializer: &mut D
) -> Result<With<T, W>, <D as Fallible>::Error>

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

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

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

impl<T> ToOwned for Twhere
T: Clone,

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

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

impl<V, T> VZip<V> for Twhere
V: MultiLane<T>,