Struct nalgebra::linalg::Bidiagonal

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pub struct Bidiagonal<T: ComplexField, R: DimMin<C>, C: Dim> where
    DimMinimum<R, C>: DimSub<U1>,
    DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,  { /* private fields */ }

Expand description

The bidiagonalization of a general matrix.

Implementations

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impl<T: ComplexField, R: DimMin<C>, C: Dim> Bidiagonal<T, R, C> where
DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<T, R, C> + Allocator<T, C> + Allocator<T, R> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,

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

Computes the Bidiagonal decomposition using householder reflections.

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pub fn is_upper_diagonal(&self) -> bool

Indicates whether this decomposition contains an upper-diagonal matrix.

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

Unpacks this decomposition into its three matrix factors (U, D, V^t).

The decomposed matrix M is equal to U * D * V^t.

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

Retrieves the upper trapezoidal submatrix R of this decomposition.

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

Computes the orthogonal matrix U of this U * D * V decomposition.

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

Computes the orthogonal matrix V_t of this U * D * V_t decomposition.

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pub fn diagonal(&self) -> OVector<T::RealField, DimMinimum<R, C>> where
DefaultAllocator: Allocator<T::RealField, DimMinimum<R, C>>,

The diagonal part of this decomposed matrix.

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pub fn off_diagonal(
&self
) -> OVector<T::RealField, DimDiff<DimMinimum<R, C>, U1>> where
DefaultAllocator: Allocator<T::RealField, DimDiff<DimMinimum<R, C>, U1>>,

The off-diagonal part of this decomposed matrix.

Trait Implementations

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impl<T: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim> Clone for Bidiagonal<T, R, C> where
DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,

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fn clone(&self) -> Bidiagonal<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 Bidiagonal<T, R, C> where
DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,

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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 Bidiagonal<T, R, C> where
 DimMinimum<R, C>: DimSub<U1>,
 DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,
 DimMinimum<R, C>: DimSub<U1>,
 DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,
 OMatrix<T, R, C>: Deserialize<'de>,
 OVector<T, DimMinimum<R, C>>: Deserialize<'de>,
 OVector<T, DimDiff<DimMinimum<R, C>, U1>>: 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 Bidiagonal<T, R, C> where
 DimMinimum<R, C>: DimSub<U1>,
 DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,
 DimMinimum<R, C>: DimSub<U1>,
 DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,
 OMatrix<T, R, C>: Serialize,
 OVector<T, DimMinimum<R, C>>: Serialize,
 OVector<T, DimDiff<DimMinimum<R, C>, U1>>: 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 Bidiagonal<T, R, C> where
 DimMinimum<R, C>: DimSub<U1>,
 DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,
 OMatrix<T, R, C>: Copy,
 OVector<T, DimMinimum<R, C>>: Copy,
 OVector<T, DimDiff<DimMinimum<R, C>, U1>>: Copy,

Auto Trait Implementations

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

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

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

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

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

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::Bidiagonal

Implementations

impl<T: ComplexField, R: DimMin<C>, C: Dim> Bidiagonal<T, R, C> where DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, C> + Allocator<T, R> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,

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

pub fn is_upper_diagonal(&self) -> bool

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

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

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

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

pub fn diagonal(&self) -> OVector<T::RealField, DimMinimum<R, C>> where DefaultAllocator: Allocator<T::RealField, DimMinimum<R, C>>,

pub fn off_diagonal( &self) -> OVector<T::RealField, DimDiff<DimMinimum<R, C>, U1>> where DefaultAllocator: Allocator<T::RealField, DimDiff<DimMinimum<R, C>, U1>>,

Trait Implementations

impl<T: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim> Clone for Bidiagonal<T, R, C> where DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,

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

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

impl<T: Debug + ComplexField, R: Debug + DimMin<C>, C: Debug + Dim> Debug for Bidiagonal<T, R, C> where DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,

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

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

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

Auto Trait Implementations

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

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

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

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

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

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, R: DimMin<C>, C: Dim> Bidiagonal<T, R, C> where
DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<T, R, C> + Allocator<T, C> + Allocator<T, R> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,

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

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

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

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

pub fn diagonal(&self) -> OVector<T::RealField, DimMinimum<R, C>> where
DefaultAllocator: Allocator<T::RealField, DimMinimum<R, C>>,

pub fn off_diagonal(
&self
) -> OVector<T::RealField, DimDiff<DimMinimum<R, C>, U1>> where
DefaultAllocator: Allocator<T::RealField, DimDiff<DimMinimum<R, C>, U1>>,

impl<T: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim> Clone for Bidiagonal<T, R, C> where
DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,

impl<T: Debug + ComplexField, R: Debug + DimMin<C>, C: Debug + Dim> Debug for Bidiagonal<T, R, C> where
DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>>,

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

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

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>,