SVD in nalgebra::linalg - Rust
Description: Singular Value Decomposition of a general matrix.
Keywords: rust, rustlang, rust-lang, SVD

# 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.

## Trait Implementations§

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### 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,

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

Returns a copy of the value. Read more
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#### fn clone_from(&mut self, source: &Self)

Performs copy-assignment from `source`. Read more
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### 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,

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

Formats the value using the given formatter. Read more
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### 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,

## Auto Trait Implementations§

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### impl<T, R, C> !RefUnwindSafe for SVD<T, R, C>

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### impl<T, R, C> !Send for SVD<T, R, C>

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### impl<T, R, C> !Sync for SVD<T, R, C>

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### impl<T, R, C> !Unpin for SVD<T, R, C>

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### impl<T, R, C> !UnwindSafe for SVD<T, R, C>

## Blanket Implementations§

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### impl<T> Any for Twhere
T: 'static + ?Sized,

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#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
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### impl<T> Borrow<T> for Twhere
T: ?Sized,

const: unstable · source§

#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

const: unstable · source§

#### fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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### impl<T> From<T> for T

const: unstable · source§

#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for Twhere
U: From<T>,

const: unstable · source§

#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

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### impl<T> Same<T> for T

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#### type Output = T

Should always be `Self`
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### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

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#### fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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#### fn is_in_subset(&self) -> bool

Checks if `self` is actually part of its subset `T` (and can be converted to it).
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#### fn to_subset_unchecked(&self) -> SS

Use with care! Same as `self.to_subset` but without any property checks. Always succeeds.
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#### fn from_subset(element: &SS) -> SP

The inclusion map: converts `self` to the equivalent element of its superset.
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### impl<T> ToOwned for Twhere
T: Clone,

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#### type Owned = T

The resulting type after obtaining ownership.
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#### fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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#### fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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### impl<T, U> TryFrom<U> for Twhere
U: Into<T>,

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#### type Error = Infallible

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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### impl<T, U> TryInto<U> for Twhere
U: TryFrom<T>,

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

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.