pub struct SVD<T, R, C>where
T: ComplexField,
R: DimMin<C>,
C: Dim,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>,{
pub u: Option<Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>>,
pub v_t: Option<Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>>,
pub singular_values: Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>>::Buffer>,
}
Expand description
Singular Value Decomposition of a general matrix.
Fields§
§u: Option<Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>>
The left-singular vectors U
of this SVD.
v_t: Option<Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>>
The right-singular vectors V^t
of this SVD.
singular_values: Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>>::Buffer>
The singular values of this SVD.
Implementations§
source§impl<T, R, C> SVD<T, R, C>where
T: ComplexField,
R: DimMin<C>,
C: Dim,
<R as DimMin<C>>::Output: DimSub<Const<1>>,
DefaultAllocator: Allocator<T, R, C> + Allocator<T, C, Const<1>> + Allocator<T, R, Const<1>> + Allocator<T, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>> + Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>>,
impl<T, R, C> SVD<T, R, C>where T: ComplexField, R: DimMin<C>, C: Dim, <R as DimMin<C>>::Output: DimSub<Const<1>>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, C, Const<1>> + Allocator<T, R, Const<1>> + Allocator<T, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>> + Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>>,
sourcepub fn new_unordered(
matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>,
compute_u: bool,
compute_v: bool
) -> SVD<T, R, C>
pub fn new_unordered( matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>, compute_u: bool, compute_v: bool ) -> SVD<T, R, C>
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.
sourcepub fn try_new_unordered(
matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>,
compute_u: bool,
compute_v: bool,
eps: <T as ComplexField>::RealField,
max_niter: usize
) -> Option<SVD<T, R, C>>
pub fn try_new_unordered( matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>, compute_u: bool, compute_v: bool, eps: <T as ComplexField>::RealField, max_niter: usize ) -> Option<SVD<T, R, C>>
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 totrue
to enable the computation of left-singular vectors.compute_v
− set this totrue
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. Ifniter == 0
, then the algorithm continues indefinitely until convergence.
sourcepub fn rank(&self, eps: <T as ComplexField>::RealField) -> usize
pub fn rank(&self, eps: <T as ComplexField>::RealField) -> usize
Computes the rank of the decomposed matrix, i.e., the number of singular values greater
than eps
.
sourcepub fn recompose(
self
) -> Result<Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>, &'static str>
pub fn recompose( self ) -> Result<Matrix<T, R, C, <DefaultAllocator as Allocator<T, 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.
sourcepub fn pseudo_inverse(
self,
eps: <T as ComplexField>::RealField
) -> Result<Matrix<T, C, R, <DefaultAllocator as Allocator<T, C, R>>::Buffer>, &'static str>where
DefaultAllocator: Allocator<T, C, R>,
pub fn pseudo_inverse( self, eps: <T as ComplexField>::RealField ) -> Result<Matrix<T, C, R, <DefaultAllocator as Allocator<T, C, R>>::Buffer>, &'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.
sourcepub fn solve<R2, C2, S2>(
&self,
b: &Matrix<T, R2, C2, S2>,
eps: <T as ComplexField>::RealField
) -> Result<Matrix<T, C, C2, <DefaultAllocator as Allocator<T, C, C2>>::Buffer>, &'static str>where
R2: Dim,
C2: Dim,
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, C, C2> + Allocator<T, <R as DimMin<C>>::Output, C2>,
ShapeConstraint: SameNumberOfRows<R, R2>,
pub fn solve<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2>, eps: <T as ComplexField>::RealField ) -> Result<Matrix<T, C, C2, <DefaultAllocator as Allocator<T, C, C2>>::Buffer>, &'static str>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, C, C2> + Allocator<T, <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.
sourcepub fn to_polar(
&self
) -> Option<(Matrix<T, R, R, <DefaultAllocator as Allocator<T, R, R>>::Buffer>, Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>)>where
DefaultAllocator: Allocator<T, R, C> + Allocator<T, <R as DimMin<C>>::Output, R> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<T, R, R> + Allocator<T, <R as DimMin<C>>::Output, <R as DimMin<C>>::Output>,
pub fn to_polar( &self ) -> Option<(Matrix<T, R, R, <DefaultAllocator as Allocator<T, R, R>>::Buffer>, Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>)>where DefaultAllocator: Allocator<T, R, C> + Allocator<T, <R as DimMin<C>>::Output, R> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<T, R, R> + Allocator<T, <R as DimMin<C>>::Output, <R as DimMin<C>>::Output>,
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
source§impl<T, R, C> SVD<T, R, C>where
T: ComplexField,
R: DimMin<C>,
C: Dim,
<R as DimMin<C>>::Output: DimSub<Const<1>>,
DefaultAllocator: Allocator<T, R, C> + Allocator<T, C, Const<1>> + Allocator<T, R, Const<1>> + Allocator<T, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>> + Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>> + Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1>> + Allocator<(<T as ComplexField>::RealField, usize), <R as DimMin<C>>::Output, Const<1>>,
impl<T, R, C> SVD<T, R, C>where T: ComplexField, R: DimMin<C>, C: Dim, <R as DimMin<C>>::Output: DimSub<Const<1>>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, C, Const<1>> + Allocator<T, R, Const<1>> + Allocator<T, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>> + Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>> + Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1>> + Allocator<(<T as ComplexField>::RealField, usize), <R as DimMin<C>>::Output, Const<1>>,
sourcepub fn new(
matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>,
compute_u: bool,
compute_v: bool
) -> SVD<T, R, C>
pub fn new( matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>, compute_u: bool, compute_v: bool ) -> SVD<T, R, C>
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
.
sourcepub fn try_new(
matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>,
compute_u: bool,
compute_v: bool,
eps: <T as ComplexField>::RealField,
max_niter: usize
) -> Option<SVD<T, R, C>>
pub fn try_new( matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>, compute_u: bool, compute_v: bool, eps: <T as ComplexField>::RealField, max_niter: usize ) -> Option<SVD<T, R, C>>
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 totrue
to enable the computation of left-singular vectors.compute_v
− set this totrue
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. Ifniter == 0
, then the algorithm continues indefinitely until convergence.
sourcepub fn sort_by_singular_values(&mut self)
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_unordered
were used and the specific sorting is required afterward.
Trait Implementations§
source§impl<T, R, C> Clone for SVD<T, R, C>where
T: Clone + ComplexField,
R: Clone + DimMin<C>,
C: Clone + Dim,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>,
<T as ComplexField>::RealField: Clone,
impl<T, R, C> Clone for SVD<T, R, C>where T: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim, DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>, <T as ComplexField>::RealField: Clone,
source§impl<T, R, C> Debug for SVD<T, R, C>where
T: Debug + ComplexField,
R: Debug + DimMin<C>,
C: Debug + Dim,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>,
<T as ComplexField>::RealField: Debug,
impl<T, R, C> Debug for SVD<T, R, C>where T: Debug + ComplexField, R: Debug + DimMin<C>, C: Debug + Dim, DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>, <T as ComplexField>::RealField: Debug,
impl<T, R, C> Copy for SVD<T, R, C>where T: ComplexField, R: DimMin<C>, C: Dim, DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>, Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>: Copy, Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>: Copy, Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>>::Buffer>: Copy,
Auto Trait Implementations§
impl<T, R, C> !RefUnwindSafe for SVD<T, R, C>
impl<T, R, C> !Send for SVD<T, R, C>
impl<T, R, C> !Sync for SVD<T, R, C>
impl<T, R, C> !Unpin for SVD<T, R, C>
impl<T, R, C> !UnwindSafe for SVD<T, R, C>
Blanket Implementations§
source§impl<T> BorrowMut<T> for Twhere
T: ?Sized,
impl<T> BorrowMut<T> for Twhere T: ?Sized,
source§fn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
source§impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,
impl<SS, SP> SupersetOf<SS> for SPwhere SS: SubsetOf<SP>,
source§fn to_subset(&self) -> Option<SS>
fn to_subset(&self) -> Option<SS>
self
from the equivalent element of its
superset. Read moresource§fn is_in_subset(&self) -> bool
fn is_in_subset(&self) -> bool
self
is actually part of its subset T
(and can be converted to it).source§fn to_subset_unchecked(&self) -> SS
fn to_subset_unchecked(&self) -> SS
self.to_subset
but without any property checks. Always succeeds.source§fn from_subset(element: &SS) -> SP
fn from_subset(element: &SS) -> SP
self
to the equivalent element of its superset.