Struct na::SVD[][src]

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>, 
[src]

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>
[src]

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>>
[src]

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[src]

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>
[src]

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>, 
[src]

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>, 
[src]

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
[src]

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
[src]

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>, 
[src]

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
[src]

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
[src]

Auto Trait Implementations

impl<N, R, C> !RefUnwindSafe for SVD<N, R, C>

impl<N, R, C> !Send for SVD<N, R, C>

impl<N, R, C> !Sync for SVD<N, R, C>

impl<N, R, C> !Unpin for SVD<N, R, C>

impl<N, R, C> !UnwindSafe for SVD<N, R, C>

Blanket Implementations

impl<T> Any for T where
    T: 'static + ?Sized
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impl<T> Borrow<T> for T where
    T: ?Sized
[src]

impl<T> BorrowMut<T> for T where
    T: ?Sized
[src]

impl<T> From<T> for T[src]

impl<T, U> Into<U> for T where
    U: From<T>, 
[src]

impl<V> IntoPnt<V> for V[src]

impl<V> IntoVec<V> for V[src]

impl<T> Same<T> for T[src]

type Output = T

Should always be Self

impl<SS, SP> SupersetOf<SS> for SP where
    SS: SubsetOf<SP>, 
[src]

impl<T> ToOwned for T where
    T: Clone
[src]

type Owned = T

The resulting type after obtaining ownership.

impl<T, U> TryFrom<U> for T where
    U: Into<T>, 
[src]

type Error = Infallible

The type returned in the event of a conversion error.

impl<T, U> TryInto<U> for T where
    U: TryFrom<T>, 
[src]

type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.

impl<V, T> VZip<V> for T where
    V: MultiLane<T>, 
[src]