Struct nalgebra::linalg::SVD

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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>>,
}

Expand description

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§

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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>>,

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

Computes the Singular Value Decomposition of matrix using implicit shift. The singular values are not guaranteed to be sorted in any particular order. If a descending order is required, consider using new instead.

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pub fn try_new_unordered(
 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. The singular values are not guaranteed to be sorted in any particular order. If a descending order is required, consider using try_new instead.

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.

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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.

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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.

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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.

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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.

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pub fn to_polar(&self) -> Option<(OMatrix<T, R, R>, OMatrix<T, R, C>)>where
DefaultAllocator: Allocator<T, R, C> + Allocator<T, DimMinimum<R, C>, R> + Allocator<T, DimMinimum<R, C>> + Allocator<T, R, R> + Allocator<T, DimMinimum<R, C>, DimMinimum<R, C>>,

converts SVD results to Polar decomposition form of the original Matrix: A = P' * U.

The polar decomposition used here is Left Polar Decomposition (or Reverse Polar Decomposition) Returns None if the singular vectors of the SVD haven’t been calculated

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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>> + Allocator<(usize, usize), DimMinimum<R, C>> + Allocator<(T::RealField, usize), DimMinimum<R, C>>,

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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. The singular values are guaranteed to be sorted in descending order. If this order is not required consider using new_unordered.

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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. The singular values are guaranteed to be sorted in descending order. If this order is not required consider using try_new_unordered.

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.

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pub fn sort_by_singular_values(&mut self)

Sort the estimated components of the SVD by its singular values in descending order. Such an ordering is often implicitly required when the decompositions are used for estimation or fitting purposes. Using this function is only required if new_unordered or try_new_unorderd were used and the specific sorting is required afterward.