Struct nalgebra::linalg::Bidiagonal
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pub struct Bidiagonal<N: Real, R: DimMin<C>, C: Dim> where
DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>> + Allocator<N, DimDiff<DimMinimum<R, C>, U1>>, { pub diagonal: VectorN<N, DimMinimum<R, C>>, pub off_diagonal: VectorN<N, DimDiff<DimMinimum<R, C>, U1>>, // some fields omitted }
The bidiagonalization of a general matrix.
Fields
diagonal: VectorN<N, DimMinimum<R, C>>
The diagonal elements of the decomposed matrix.
off_diagonal: VectorN<N, DimDiff<DimMinimum<R, C>, U1>>
The off-diagonal elements of the decomposed matrix.
Methods
impl<N: Real, R: DimMin<C>, C: Dim> Bidiagonal<N, R, C> where
DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<N, R, C> + Allocator<N, C> + Allocator<N, R> + Allocator<N, DimMinimum<R, C>> + Allocator<N, DimDiff<DimMinimum<R, C>, U1>>,
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DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<N, R, C> + Allocator<N, C> + Allocator<N, R> + Allocator<N, DimMinimum<R, C>> + Allocator<N, DimDiff<DimMinimum<R, C>, U1>>,
pub fn new(matrix: MatrixMN<N, R, C>) -> Self
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Computes the Bidiagonal decomposition using householder reflections.
pub fn is_upper_diagonal(&self) -> bool
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Indicates whether this decomposition contains an upper-diagonal matrix.
pub fn unpack(
self
) -> (MatrixMN<N, R, DimMinimum<R, C>>, MatrixN<N, DimMinimum<R, C>>, MatrixMN<N, DimMinimum<R, C>, C>) where
DefaultAllocator: Allocator<N, DimMinimum<R, C>, DimMinimum<R, C>> + Allocator<N, R, DimMinimum<R, C>> + Allocator<N, DimMinimum<R, C>, C>,
DimMinimum<R, C>: DimMin<DimMinimum<R, C>, Output = DimMinimum<R, C>>,
ShapeConstraint: DimEq<Dynamic, DimDiff<DimMinimum<R, C>, U1>>,
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self
) -> (MatrixMN<N, R, DimMinimum<R, C>>, MatrixN<N, DimMinimum<R, C>>, MatrixMN<N, DimMinimum<R, C>, C>) where
DefaultAllocator: Allocator<N, DimMinimum<R, C>, DimMinimum<R, C>> + Allocator<N, R, DimMinimum<R, C>> + Allocator<N, DimMinimum<R, C>, C>,
DimMinimum<R, C>: DimMin<DimMinimum<R, C>, Output = DimMinimum<R, C>>,
ShapeConstraint: DimEq<Dynamic, DimDiff<DimMinimum<R, C>, U1>>,
Unpacks this decomposition into its three matrix factors (U, D, V^t)
.
The decomposed matrix M
is equal to U * D * V^t
.
pub fn d(&self) -> MatrixN<N, DimMinimum<R, C>> where
DefaultAllocator: Allocator<N, DimMinimum<R, C>, DimMinimum<R, C>>,
DimMinimum<R, C>: DimMin<DimMinimum<R, C>, Output = DimMinimum<R, C>>,
ShapeConstraint: DimEq<Dynamic, DimDiff<DimMinimum<R, C>, U1>>,
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DefaultAllocator: Allocator<N, DimMinimum<R, C>, DimMinimum<R, C>>,
DimMinimum<R, C>: DimMin<DimMinimum<R, C>, Output = DimMinimum<R, C>>,
ShapeConstraint: DimEq<Dynamic, DimDiff<DimMinimum<R, C>, U1>>,
Retrieves the upper trapezoidal submatrix R
of this decomposition.
pub fn u(&self) -> MatrixMN<N, R, DimMinimum<R, C>> where
DefaultAllocator: Allocator<N, R, DimMinimum<R, C>>,
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DefaultAllocator: Allocator<N, R, DimMinimum<R, C>>,
Computes the orthogonal matrix U
of this U * D * V
decomposition.
pub fn v_t(&self) -> MatrixMN<N, DimMinimum<R, C>, C> where
DefaultAllocator: Allocator<N, DimMinimum<R, C>, C>,
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DefaultAllocator: Allocator<N, DimMinimum<R, C>, C>,
Computes the orthogonal matrix V
of this U * D * V
decomposition.
pub fn diagonal(&self) -> &VectorN<N, DimMinimum<R, C>>
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The diagonal part of this decomposed matrix.
pub fn off_diagonal(&self) -> &VectorN<N, DimDiff<DimMinimum<R, C>, U1>>
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The off-diagonal part of this decomposed matrix.
Trait Implementations
impl<N: Clone + Real, R: Clone + DimMin<C>, C: Clone + Dim> Clone for Bidiagonal<N, R, C> where
DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>> + Allocator<N, DimDiff<DimMinimum<R, C>, U1>>,
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DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>> + Allocator<N, DimDiff<DimMinimum<R, C>, U1>>,
fn clone(&self) -> Bidiagonal<N, R, C>
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Returns a copy of the value. Read more
fn clone_from(&mut self, source: &Self)
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Performs copy-assignment from source
. Read more
impl<N: Debug + Real, R: Debug + DimMin<C>, C: Debug + Dim> Debug for Bidiagonal<N, R, C> where
DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>> + Allocator<N, DimDiff<DimMinimum<R, C>, U1>>,
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DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>> + Allocator<N, DimDiff<DimMinimum<R, C>, U1>>,
fn fmt(&self, __arg_0: &mut Formatter) -> Result
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Formats the value using the given formatter. Read more
impl<N: Real, R: DimMin<C>, C: Dim> Copy for Bidiagonal<N, R, C> where
DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>> + Allocator<N, DimDiff<DimMinimum<R, C>, U1>>,
MatrixMN<N, R, C>: Copy,
VectorN<N, DimMinimum<R, C>>: Copy,
VectorN<N, DimDiff<DimMinimum<R, C>, U1>>: Copy,
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DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>> + Allocator<N, DimDiff<DimMinimum<R, C>, U1>>,
MatrixMN<N, R, C>: Copy,
VectorN<N, DimMinimum<R, C>>: Copy,
VectorN<N, DimDiff<DimMinimum<R, C>, U1>>: Copy,