Struct oxygengine_physics_2d::prelude::nalgebra::SVD

pub struct SVD<T, R, C>where
    T: ComplexField,
    R: DimMin<C>,
    C: Dim,
    DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>,{
    pub u: Option<Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>>,
    pub v_t: Option<Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>>,
    pub singular_values: Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>>::Buffer>,
}

Singular Value Decomposition of a general matrix.

Fields

u: Option<Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>>

The left-singular vectors U of this SVD.

v_t: Option<Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>>

The right-singular vectors V^t of this SVD.

singular_values: Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>>::Buffer>

The singular values of this SVD.

Implementations

impl<T, R, C> SVD<T, R, C>where T: ComplexField, R: DimMin<C>, C: Dim, <R as DimMin<C>>::Output: DimSub<Const<1>>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, C, Const<1>> + Allocator<T, R, Const<1>> + Allocator<T, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>> + Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>>,

pub fn new( matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>, compute_u: bool, compute_v: bool ) -> SVD<T, R, C>

Computes the Singular Value Decomposition of matrix using implicit shift.

pub fn try_new( matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>, compute_u: bool, compute_v: bool, eps: <T as ComplexField>::RealField, max_niter: usize ) -> Option<SVD<T, R, C>>

Attempts to compute the Singular Value Decomposition of matrix using implicit shift.

Arguments

• compute_u − set this to true to enable the computation of left-singular vectors.
• compute_v − set this to true to enable the computation of right-singular vectors.
• eps − tolerance used to determine when a value converged to 0.
• max_niter − maximum total number of iterations performed by the algorithm. If this number of iteration is exceeded, None is returned. If niter == 0, then the algorithm continues indefinitely until convergence.

pub fn rank(&self, eps: <T as ComplexField>::RealField) -> usize

Computes the rank of the decomposed matrix, i.e., the number of singular values greater than eps.

pub fn recompose( self ) -> Result<Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>, &'static str>

Rebuild the original matrix.

This is useful if some of the singular values have been manually modified. Returns Err if the right- and left- singular vectors have not been computed at construction-time.

pub fn pseudo_inverse( self, eps: <T as ComplexField>::RealField ) -> Result<Matrix<T, C, R, <DefaultAllocator as Allocator<T, C, R>>::Buffer>, &'static str>where DefaultAllocator: Allocator<T, C, R>,

Computes the pseudo-inverse of the decomposed matrix.

Any singular value smaller than eps is assumed to be zero. Returns Err if the right- and left- singular vectors have not been computed at construction-time.

pub fn solve<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2>, eps: <T as ComplexField>::RealField ) -> Result<Matrix<T, C, C2, <DefaultAllocator as Allocator<T, C, C2>>::Buffer>, &'static str>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, C, C2> + Allocator<T, <R as DimMin<C>>::Output, C2>, ShapeConstraint: SameNumberOfRows<R, R2>,

Solves the system self * x = b where self is the decomposed matrix and x the unknown.

Any singular value smaller than eps is assumed to be zero. Returns Err if the singular vectors U and V have not been computed.

Trait Implementations

impl<T, R, C> Clone for SVD<T, R, C>where T: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim, DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>, <T as ComplexField>::RealField: Clone,

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T, R, C> Debug for SVD<T, R, C>where T: Debug + ComplexField, R: Debug + DimMin<C>, C: Debug + Dim, DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>, <T as ComplexField>::RealField: Debug,

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

Formats the value using the given formatter.

impl<'de, T, R, C> Deserialize<'de> for SVD<T, R, C>where T: ComplexField, R: DimMin<C>, C: Dim, DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>, Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>: Deserialize<'de>, Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>: Deserialize<'de>, Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>>::Buffer>: Deserialize<'de>,

fn deserialize<__D>( __deserializer: __D ) -> Result<SVD<T, R, C>, <__D as Deserializer<'de>>::Error>where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<T, R, C> Serialize for SVD<T, R, C>where T: ComplexField, R: DimMin<C>, C: Dim, DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>, Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>: Serialize, Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>: Serialize, Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>>::Buffer>: Serialize,

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

Serialize this value into the given Serde serializer.

impl<T, R, C> Copy for SVD<T, R, C>where T: ComplexField, R: DimMin<C>, C: Dim, DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>, Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>: Copy, Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>: Copy, Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>>::Buffer>: Copy,