Struct na::SVD

pub struct SVD<N, R, C> where
    C: Dim,
    N: ComplexField,
    R: DimMin<C>,
    DefaultAllocator: Allocator<N, <R as DimMin<C>>::Output, C>,
    DefaultAllocator: Allocator<N, R, <R as DimMin<C>>::Output>,
    DefaultAllocator: Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>,  {
    pub u: Option<Matrix<N, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<N, R, <R as DimMin<C>>::Output>>::Buffer>>,
    pub v_t: Option<Matrix<N, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<N, <R as DimMin<C>>::Output, C>>::Buffer>>,
    pub singular_values: Matrix<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1, <DefaultAllocator as Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>>::Buffer>,
}

Singular Value Decomposition of a general matrix.

Fields

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

The left-singular vectors U of this SVD.

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

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

singular_values: Matrix<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1, <DefaultAllocator as Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>>::Buffer>

The singular values of this SVD.

Implementations

impl<N, R, C> SVD<N, R, C> where
    C: Dim,
    N: ComplexField,
    R: DimMin<C>,
    <R as DimMin<C>>::Output: DimSub<U1>,
    DefaultAllocator: Allocator<N, R, C>,
    DefaultAllocator: Allocator<N, C, U1>,
    DefaultAllocator: Allocator<N, R, U1>,
    DefaultAllocator: Allocator<N, <<R as DimMin<C>>::Output as DimSub<U1>>::Output, U1>,
    DefaultAllocator: Allocator<N, <R as DimMin<C>>::Output, C>,
    DefaultAllocator: Allocator<N, R, <R as DimMin<C>>::Output>,
    DefaultAllocator: Allocator<N, <R as DimMin<C>>::Output, U1>,
    DefaultAllocator: Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>,
    DefaultAllocator: Allocator<<N as ComplexField>::RealField, <<R as DimMin<C>>::Output as DimSub<U1>>::Output, U1>, 

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

Computes the Singular Value Decomposition of matrix using implicit shift.

pub fn try_new(
    matrix: Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>,
    compute_u: bool,
    compute_v: bool,
    eps: <N as ComplexField>::RealField,
    max_niter: usize
) -> Option<SVD<N, 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: <N 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<N, R, C, <DefaultAllocator as Allocator<N, 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: <N as ComplexField>::RealField
) -> Result<Matrix<N, C, R, <DefaultAllocator as Allocator<N, C, R>>::Buffer>, &'static str> where
    DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>,
    eps: <N as ComplexField>::RealField
) -> Result<Matrix<N, C, C2, <DefaultAllocator as Allocator<N, C, C2>>::Buffer>, &'static str> where
    S2: Storage<N, R2, C2>,
    R2: Dim,
    C2: Dim,
    DefaultAllocator: Allocator<N, C, C2>,
    DefaultAllocator: Allocator<N, <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<N, R, C> Clone for SVD<N, R, C> where
    C: Clone + Dim,
    N: Clone + ComplexField,
    R: Clone + DimMin<C>,
    DefaultAllocator: Allocator<N, <R as DimMin<C>>::Output, C>,
    DefaultAllocator: Allocator<N, R, <R as DimMin<C>>::Output>,
    DefaultAllocator: Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>,
    <N as ComplexField>::RealField: Clone, 

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N, R, C> Debug for SVD<N, R, C> where
    C: Debug + Dim,
    N: Debug + ComplexField,
    R: Debug + DimMin<C>,
    DefaultAllocator: Allocator<N, <R as DimMin<C>>::Output, C>,
    DefaultAllocator: Allocator<N, R, <R as DimMin<C>>::Output>,
    DefaultAllocator: Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>,
    <N as ComplexField>::RealField: Debug, 

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

Formats the value using the given formatter.

impl<'de, N, R, C> Deserialize<'de> for SVD<N, R, C> where
    C: Dim,
    N: ComplexField,
    R: DimMin<C>,
    DefaultAllocator: Allocator<N, <R as DimMin<C>>::Output, C>,
    DefaultAllocator: Allocator<N, R, <R as DimMin<C>>::Output>,
    DefaultAllocator: Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>,
    DefaultAllocator: Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>,
    DefaultAllocator: Allocator<N, <R as DimMin<C>>::Output, C>,
    DefaultAllocator: Allocator<N, R, <R as DimMin<C>>::Output>,
    Matrix<N, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<N, R, <R as DimMin<C>>::Output>>::Buffer>: Deserialize<'de>,
    Matrix<N, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<N, <R as DimMin<C>>::Output, C>>::Buffer>: Deserialize<'de>,
    Matrix<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1, <DefaultAllocator as Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>>::Buffer>: Deserialize<'de>, 

pub fn deserialize<__D>(
    __deserializer: __D
) -> Result<SVD<N, R, C>, <__D as Deserializer<'de>>::Error> where
    __D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl<N, R, C> Serialize for SVD<N, R, C> where
    C: Dim,
    N: ComplexField,
    R: DimMin<C>,
    DefaultAllocator: Allocator<N, <R as DimMin<C>>::Output, C>,
    DefaultAllocator: Allocator<N, R, <R as DimMin<C>>::Output>,
    DefaultAllocator: Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>,
    DefaultAllocator: Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>,
    DefaultAllocator: Allocator<N, <R as DimMin<C>>::Output, C>,
    DefaultAllocator: Allocator<N, R, <R as DimMin<C>>::Output>,
    Matrix<N, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<N, R, <R as DimMin<C>>::Output>>::Buffer>: Serialize,
    Matrix<N, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<N, <R as DimMin<C>>::Output, C>>::Buffer>: Serialize,
    Matrix<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1, <DefaultAllocator as Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>>::Buffer>: Serialize, 

pub 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<N, R, C> Copy for SVD<N, R, C> where
    C: Dim,
    N: ComplexField,
    R: DimMin<C>,
    DefaultAllocator: Allocator<N, <R as DimMin<C>>::Output, C>,
    DefaultAllocator: Allocator<N, R, <R as DimMin<C>>::Output>,
    DefaultAllocator: Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>,
    Matrix<N, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<N, R, <R as DimMin<C>>::Output>>::Buffer>: Copy,
    Matrix<N, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<N, <R as DimMin<C>>::Output, C>>::Buffer>: Copy,
    Matrix<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1, <DefaultAllocator as Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1>>::Buffer>: Copy,