Struct lnkit::prelude::linalg::SVD [−][src]
pub struct SVD<T, R, C> where
C: Dim,
T: ComplexField,
R: DimMin<C>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>, { 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_usize>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>>::Buffer>, }
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_usize>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>>::Buffer>
The singular values of this SVD.
Implementations
impl<T, R, C> SVD<T, R, C> where
C: Dim,
T: ComplexField,
R: DimMin<C>,
<R as DimMin<C>>::Output: DimSub<Const<1_usize>>,
DefaultAllocator: Allocator<T, R, C>,
DefaultAllocator: Allocator<T, C, Const<1_usize>>,
DefaultAllocator: Allocator<T, R, Const<1_usize>>,
DefaultAllocator: Allocator<T, <<R as DimMin<C>>::Output as DimSub<Const<1_usize>>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <<R as DimMin<C>>::Output as DimSub<Const<1_usize>>>::Output, Const<1_usize>>,
[src]
impl<T, R, C> SVD<T, R, C> where
C: Dim,
T: ComplexField,
R: DimMin<C>,
<R as DimMin<C>>::Output: DimSub<Const<1_usize>>,
DefaultAllocator: Allocator<T, R, C>,
DefaultAllocator: Allocator<T, C, Const<1_usize>>,
DefaultAllocator: Allocator<T, R, Const<1_usize>>,
DefaultAllocator: Allocator<T, <<R as DimMin<C>>::Output as DimSub<Const<1_usize>>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <<R as DimMin<C>>::Output as DimSub<Const<1_usize>>>::Output, Const<1_usize>>,
[src]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>
[src]
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.
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>>
[src]
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.
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.
pub fn rank(&self, eps: <T 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<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>, &'static str>
[src]
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.
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>,
[src]
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.
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,
S2: Storage<T, R2, C2>,
C2: Dim,
DefaultAllocator: Allocator<T, C, C2>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C2>,
ShapeConstraint: SameNumberOfRows<R, R2>,
[src]
&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,
S2: Storage<T, R2, C2>,
C2: Dim,
DefaultAllocator: Allocator<T, C, C2>,
DefaultAllocator: 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.
Trait Implementations
impl<T, R, C> Clone for SVD<T, R, C> where
C: Clone + Dim,
T: Clone + ComplexField,
R: Clone + DimMin<C>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
<T as ComplexField>::RealField: Clone,
[src]
impl<T, R, C> Clone for SVD<T, R, C> where
C: Clone + Dim,
T: Clone + ComplexField,
R: Clone + DimMin<C>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
<T as ComplexField>::RealField: Clone,
[src]impl<T, R, C> Copy for SVD<T, R, C> where
C: Dim,
T: ComplexField,
R: DimMin<C>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
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_usize>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>>::Buffer>: Copy,
[src]
impl<T, R, C> Copy for SVD<T, R, C> where
C: Dim,
T: ComplexField,
R: DimMin<C>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
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_usize>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>>::Buffer>: Copy,
[src]impl<T, R, C> Debug for SVD<T, R, C> where
C: Debug + Dim,
T: Debug + ComplexField,
R: Debug + DimMin<C>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
<T as ComplexField>::RealField: Debug,
[src]
impl<T, R, C> Debug for SVD<T, R, C> where
C: Debug + Dim,
T: Debug + ComplexField,
R: Debug + DimMin<C>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
<T as ComplexField>::RealField: Debug,
[src]impl<'de, T, R, C> Deserialize<'de> for SVD<T, R, C> where
C: Dim,
T: ComplexField,
R: DimMin<C>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>: Deserialize<'de>,
Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>: Deserialize<'de>,
Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>>::Buffer>: Deserialize<'de>,
[src]
impl<'de, T, R, C> Deserialize<'de> for SVD<T, R, C> where
C: Dim,
T: ComplexField,
R: DimMin<C>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>: Deserialize<'de>,
Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>: Deserialize<'de>,
Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>>::Buffer>: Deserialize<'de>,
[src]pub fn deserialize<__D>(
__deserializer: __D
) -> Result<SVD<T, R, C>, <__D as Deserializer<'de>>::Error> where
__D: Deserializer<'de>,
[src]
__deserializer: __D
) -> Result<SVD<T, R, C>, <__D as Deserializer<'de>>::Error> where
__D: Deserializer<'de>,
impl<T, R, C> Serialize for SVD<T, R, C> where
C: Dim,
T: ComplexField,
R: DimMin<C>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>: Serialize,
Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>: Serialize,
Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>>::Buffer>: Serialize,
[src]
impl<T, R, C> Serialize for SVD<T, R, C> where
C: Dim,
T: ComplexField,
R: DimMin<C>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>,
DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,
DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,
Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>: Serialize,
Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>: Serialize,
Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1_usize>>>::Buffer>: Serialize,
[src]pub fn serialize<__S>(
&self,
__serializer: __S
) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error> where
__S: Serializer,
[src]
&self,
__serializer: __S
) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error> where
__S: Serializer,
Auto Trait Implementations
impl<T, R, C> !RefUnwindSafe for SVD<T, R, C>
impl<T, R, C> !RefUnwindSafe for SVD<T, R, C>
impl<T, R, C> !UnwindSafe for SVD<T, R, C>
impl<T, R, C> !UnwindSafe for SVD<T, R, C>
Blanket Implementations
impl<T, U> Cast<U> for T where
U: FromCast<T>,
impl<T, U> Cast<U> for T where
U: FromCast<T>,
pub fn cast(self) -> U
impl<T> Downcast for T where
T: Any,
impl<T> Downcast for T where
T: Any,
impl<T> FromBits<T> for T
impl<T> FromBits<T> for T
pub fn from_bits(t: T) -> T
impl<T> FromCast<T> for T
impl<T> FromCast<T> for T
pub fn from_cast(t: T) -> T
impl<T, U> IntoBits<U> for T where
U: FromBits<T>,
impl<T, U> IntoBits<U> for T where
U: FromBits<T>,
pub fn into_bits(self) -> U
impl<T> Same<T> for T
impl<T> Same<T> for T
type Output = T
Should always be Self
impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,
impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,
pub fn to_subset(&self) -> Option<SS>
pub fn is_in_subset(&self) -> bool
pub fn to_subset_unchecked(&self) -> SS
pub fn from_subset(element: &SS) -> SP
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,