Struct nalgebra::linalg::Bidiagonal

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 */ }

The bidiagonalization of a general matrix.

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

Computes the Bidiagonal decomposition using householder reflections.

pub fn is_upper_diagonal(&self) -> bool

Indicates whether this decomposition contains an upper-diagonal matrix.

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.

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.

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.

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.

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.

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

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>

Returns a copy of the value.

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

Performs copy-assignment from source.

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

Formats the value using the given formatter.

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,