Struct nalgebra::linalg::SVD

pub struct SVD<T: ComplexField, R: DimMin<C>, C: Dim>where
    DefaultAllocator: Allocator<T, DimMinimum<R, C>, C> + Allocator<T, R, DimMinimum<R, C>> + Allocator<T::RealField, DimMinimum<R, C>>,{
    pub u: Option<OMatrix<T, R, DimMinimum<R, C>>>,
    pub v_t: Option<OMatrix<T, DimMinimum<R, C>, C>>,
    pub singular_values: OVector<T::RealField, DimMinimum<R, C>>,
}

Singular Value Decomposition of a general matrix.

Fields

u: Option<OMatrix<T, R, DimMinimum<R, C>>>

The left-singular vectors U of this SVD.

v_t: Option<OMatrix<T, DimMinimum<R, C>, C>>

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

singular_values: OVector<T::RealField, DimMinimum<R, C>>

The singular values of this SVD.

Implementations

impl<T: ComplexField, R: DimMin<C>, C: Dim> SVD<T, R, C>where
    DimMinimum<R, C>: DimSub<U1>,
    DefaultAllocator: Allocator<T, R, C> + Allocator<T, C> + Allocator<T, R> + Allocator<T, DimDiff<DimMinimum<R, C>, U1>> + Allocator<T, DimMinimum<R, C>, C> + Allocator<T, R, DimMinimum<R, C>> + Allocator<T, DimMinimum<R, C>> + Allocator<T::RealField, DimMinimum<R, C>> + Allocator<T::RealField, DimDiff<DimMinimum<R, C>, U1>>,

pub fn new(matrix: OMatrix<T, R, C>, compute_u: bool, compute_v: bool) -> Self

Computes the Singular Value Decomposition of matrix using implicit shift.

pub fn try_new(
    matrix: OMatrix<T, R, C>,
    compute_u: bool,
    compute_v: bool,
    eps: T::RealField,
    max_niter: usize
) -> Option<Self>

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::RealField) -> usize

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

pub fn recompose(self) -> Result<OMatrix<T, R, C>, &'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::RealField
) -> Result<OMatrix<T, C, R>, &'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: Dim, C2: Dim, S2>(
    &self,
    b: &Matrix<T, R2, C2, S2>,
    eps: T::RealField
) -> Result<OMatrix<T, C, C2>, &'static str>where
    S2: Storage<T, R2, C2>,
    DefaultAllocator: Allocator<T, C, C2> + Allocator<T, DimMinimum<R, C>, 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: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim> Clone for SVD<T, R, C>where
    DefaultAllocator: Allocator<T, DimMinimum<R, C>, C> + Allocator<T, R, DimMinimum<R, C>> + Allocator<T::RealField, DimMinimum<R, C>>,
    T::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: Debug + ComplexField, R: Debug + DimMin<C>, C: Debug + Dim> Debug for SVD<T, R, C>where
    DefaultAllocator: Allocator<T, DimMinimum<R, C>, C> + Allocator<T, R, DimMinimum<R, C>> + Allocator<T::RealField, DimMinimum<R, C>>,
    T::RealField: Debug,

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

Formats the value using the given formatter.

impl<T: ComplexField, R: DimMin<C>, C: Dim> Copy for SVD<T, R, C>where
    DefaultAllocator: Allocator<T, DimMinimum<R, C>, C> + Allocator<T, R, DimMinimum<R, C>> + Allocator<T::RealField, DimMinimum<R, C>>,
    OMatrix<T, R, DimMinimum<R, C>>: Copy,
    OMatrix<T, DimMinimum<R, C>, C>: Copy,
    OVector<T::RealField, DimMinimum<R, C>>: Copy,