Struct nalgebra::linalg::Bidiagonal

pub struct Bidiagonal<N: ComplexField, 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>>,  { /* fields omitted */ }

The bidiagonalization of a general matrix.

Implementations

impl<N: ComplexField, 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>>, 

pub fn new(matrix: MatrixMN<N, 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
) -> (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>, 

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>>, 

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>>, 

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>, 

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

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

The diagonal part of this decomposed matrix.

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

The off-diagonal part of this decomposed matrix.

Trait Implementations

impl<N: Clone + ComplexField, 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>>, 

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: Debug + ComplexField, 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>>, 

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

Formats the value using the given formatter.

impl<'de, N: ComplexField, R: DimMin<C>, C: Dim> Deserialize<'de> 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>>,
    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>: Deserialize<'de>,
    VectorN<N, DimMinimum<R, C>>: Deserialize<'de>,
    VectorN<N, DimDiff<DimMinimum<R, C>, U1>>: Deserialize<'de>, 

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

Deserialize this value from the given Serde deserializer.

impl<N: ComplexField, R: DimMin<C>, C: Dim> Serialize 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>>,
    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>: Serialize,
    VectorN<N, DimMinimum<R, C>>: Serialize,
    VectorN<N, DimDiff<DimMinimum<R, C>, U1>>: Serialize, 

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

Serialize this value into the given Serde serializer.

impl<N: ComplexField, 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,