Struct nalgebra::linalg::SVD [−][src]
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
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>>,
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>>,
Computes the Singular Value Decomposition of matrix
using implicit shift.
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.
Computes the rank of the decomposed matrix, i.e., the number of singular values greater
than eps
.
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>,
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>,
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,
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,
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,
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,
impl<'de, T: ComplexField, R: DimMin<C>, C: Dim> Deserialize<'de> 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>>,
DefaultAllocator: Allocator<T::RealField, DimMinimum<R, C>> + Allocator<T, DimMinimum<R, C>, C> + Allocator<T, R, DimMinimum<R, C>>,
OMatrix<T, R, DimMinimum<R, C>>: Deserialize<'de>,
OMatrix<T, DimMinimum<R, C>, C>: Deserialize<'de>,
OVector<T::RealField, DimMinimum<R, C>>: Deserialize<'de>,
impl<'de, T: ComplexField, R: DimMin<C>, C: Dim> Deserialize<'de> 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>>,
DefaultAllocator: Allocator<T::RealField, DimMinimum<R, C>> + Allocator<T, DimMinimum<R, C>, C> + Allocator<T, R, DimMinimum<R, C>>,
OMatrix<T, R, DimMinimum<R, C>>: Deserialize<'de>,
OMatrix<T, DimMinimum<R, C>, C>: Deserialize<'de>,
OVector<T::RealField, DimMinimum<R, C>>: Deserialize<'de>,
fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where
__D: Deserializer<'de>,
fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where
__D: Deserializer<'de>,
Deserialize this value from the given Serde deserializer. Read more
impl<T: ComplexField, R: DimMin<C>, C: Dim> Serialize 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>>,
DefaultAllocator: Allocator<T::RealField, DimMinimum<R, C>> + Allocator<T, DimMinimum<R, C>, C> + Allocator<T, R, DimMinimum<R, C>>,
OMatrix<T, R, DimMinimum<R, C>>: Serialize,
OMatrix<T, DimMinimum<R, C>, C>: Serialize,
OVector<T::RealField, DimMinimum<R, C>>: Serialize,
impl<T: ComplexField, R: DimMin<C>, C: Dim> Serialize 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>>,
DefaultAllocator: Allocator<T::RealField, DimMinimum<R, C>> + Allocator<T, DimMinimum<R, C>, C> + Allocator<T, R, DimMinimum<R, C>>,
OMatrix<T, R, DimMinimum<R, C>>: Serialize,
OMatrix<T, DimMinimum<R, C>, C>: Serialize,
OVector<T::RealField, DimMinimum<R, C>>: Serialize,
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
impl<T, R, C> !RefUnwindSafe for SVD<T, R, C>
impl<T, R, C> !UnwindSafe for SVD<T, R, C>
Blanket Implementations
Mutably borrows from an owned value. Read more
The inverse inclusion map: attempts to construct self
from the equivalent element of its
superset. Read more
Checks if self
is actually part of its subset T
(and can be converted to it).
Use with care! Same as self.to_subset
but without any property checks. Always succeeds.
The inclusion map: converts self
to the equivalent element of its superset.