pub struct Cholesky<T, D> where
T: SimdComplexField,
D: Dim,
DefaultAllocator: Allocator<T, D, D>, { /* private fields */ }
Expand description
The Cholesky decomposition of a symmetric-definite-positive matrix.
Implementations
sourceimpl<T, D> Cholesky<T, D> where
T: SimdComplexField,
D: Dim,
DefaultAllocator: Allocator<T, D, D>,
impl<T, D> Cholesky<T, D> where
T: SimdComplexField,
D: Dim,
DefaultAllocator: Allocator<T, D, D>,
sourcepub fn new_unchecked(
matrix: Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
) -> Cholesky<T, D>
pub fn new_unchecked(
matrix: Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
) -> Cholesky<T, D>
Computes the Cholesky decomposition of matrix
without checking that the matrix is definite-positive.
If the input matrix is not definite-positive, the decomposition may contain trash values (Inf, NaN, etc.)
sourcepub fn pack_dirty(
matrix: Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
) -> Cholesky<T, D>
pub fn pack_dirty(
matrix: Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
) -> Cholesky<T, D>
Uses the given matrix as-is without any checks or modifications as the Cholesky decomposition.
It is up to the user to ensure all invariants hold.
sourcepub fn unpack(
self
) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
pub fn unpack(
self
) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly upper-triangular part filled with zeros.
sourcepub fn unpack_dirty(
self
) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
pub fn unpack_dirty(
self
) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
Retrieves the lower-triangular factor of the Cholesky decomposition, without zeroing-out its strict upper-triangular part.
The values of the strict upper-triangular part are garbage and should be ignored by further computations.
sourcepub fn l(
&self
) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
pub fn l(
&self
) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly uppen-triangular part filled with zeros.
sourcepub fn l_dirty(
&self
) -> &Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
pub fn l_dirty(
&self
) -> &Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
Retrieves the lower-triangular factor of the Cholesky decomposition, without zeroing-out its strict upper-triangular part.
This is an allocation-less version of self.l()
. The values of the strict upper-triangular
part are garbage and should be ignored by further computations.
sourcepub fn solve_mut<R2, C2, S2>(&self, b: &mut Matrix<T, R2, C2, S2>) where
R2: Dim,
C2: Dim,
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve_mut<R2, C2, S2>(&self, b: &mut Matrix<T, R2, C2, S2>) where
R2: Dim,
C2: Dim,
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Solves the system self * x = b
where self
is the decomposed matrix and x
the unknown.
The result is stored on b
.
sourcepub fn solve<R2, C2, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer> where
R2: Dim,
C2: Dim,
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn solve<R2, C2, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer> where
R2: Dim,
C2: Dim,
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Returns the solution of the system self * x = b
where self
is the decomposed matrix and
x
the unknown.
sourcepub fn inverse(
&self
) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
pub fn inverse(
&self
) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
Computes the inverse of the decomposed matrix.
sourcepub fn determinant(&self) -> <T as SimdComplexField>::SimdRealField
pub fn determinant(&self) -> <T as SimdComplexField>::SimdRealField
Computes the determinant of the decomposed matrix.
sourceimpl<T, D> Cholesky<T, D> where
T: ComplexField,
D: Dim,
DefaultAllocator: Allocator<T, D, D>,
impl<T, D> Cholesky<T, D> where
T: ComplexField,
D: Dim,
DefaultAllocator: Allocator<T, D, D>,
sourcepub fn new(
matrix: Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
) -> Option<Cholesky<T, D>>
pub fn new(
matrix: Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
) -> Option<Cholesky<T, D>>
Attempts to compute the Cholesky decomposition of matrix
.
Returns None
if the input matrix is not definite-positive. The input matrix is assumed
to be symmetric and only the lower-triangular part is read.
sourcepub fn new_with_substitute(
matrix: Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>,
substitute: T
) -> Option<Cholesky<T, D>>
pub fn new_with_substitute(
matrix: Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>,
substitute: T
) -> Option<Cholesky<T, D>>
Attempts to approximate the Cholesky decomposition of matrix
by
replacing non-positive values on the diagonals during the decomposition
with the given substitute
.
try_sqrt
will be applied to the substitute
when it has to be used.
If your input matrix results only in positive values on the diagonals
during the decomposition, substitute
is unused and the result is just
the same as if you used new
.
This method allows to compensate for matrices with very small or even
negative values due to numerical errors but necessarily results in only
an approximation: it is basically a hack. If you don’t specifically need
Cholesky, it may be better to consider alternatives like the
LU
decomposition/factorization.
sourcepub fn rank_one_update<R2, S2>(
&mut self,
x: &Matrix<T, R2, Const<1_usize>, S2>,
sigma: <T as ComplexField>::RealField
) where
R2: Dim,
S2: Storage<T, R2, Const<1_usize>>,
DefaultAllocator: Allocator<T, R2, Const<1_usize>>,
ShapeConstraint: SameNumberOfRows<R2, D>,
pub fn rank_one_update<R2, S2>(
&mut self,
x: &Matrix<T, R2, Const<1_usize>, S2>,
sigma: <T as ComplexField>::RealField
) where
R2: Dim,
S2: Storage<T, R2, Const<1_usize>>,
DefaultAllocator: Allocator<T, R2, Const<1_usize>>,
ShapeConstraint: SameNumberOfRows<R2, D>,
Given the Cholesky decomposition of a matrix M
, a scalar sigma
and a vector v
,
performs a rank one update such that we end up with the decomposition of M + sigma * (v * v.adjoint())
.
sourcepub fn insert_column<R2, S2>(
&self,
j: usize,
col: Matrix<T, R2, Const<1_usize>, S2>
) -> Cholesky<T, <D as DimAdd<Const<1_usize>>>::Output> where
D: DimAdd<Const<1_usize>>,
R2: Dim,
S2: Storage<T, R2, Const<1_usize>>,
DefaultAllocator: Allocator<T, <D as DimAdd<Const<1_usize>>>::Output, <D as DimAdd<Const<1_usize>>>::Output>,
DefaultAllocator: Allocator<T, R2, Const<1_usize>>,
ShapeConstraint: SameNumberOfRows<R2, <D as DimAdd<Const<1_usize>>>::Output>,
pub fn insert_column<R2, S2>(
&self,
j: usize,
col: Matrix<T, R2, Const<1_usize>, S2>
) -> Cholesky<T, <D as DimAdd<Const<1_usize>>>::Output> where
D: DimAdd<Const<1_usize>>,
R2: Dim,
S2: Storage<T, R2, Const<1_usize>>,
DefaultAllocator: Allocator<T, <D as DimAdd<Const<1_usize>>>::Output, <D as DimAdd<Const<1_usize>>>::Output>,
DefaultAllocator: Allocator<T, R2, Const<1_usize>>,
ShapeConstraint: SameNumberOfRows<R2, <D as DimAdd<Const<1_usize>>>::Output>,
Updates the decomposition such that we get the decomposition of a matrix with the given column col
in the j
th position.
Since the matrix is square, an identical row will be added in the j
th row.
sourcepub fn remove_column(
&self,
j: usize
) -> Cholesky<T, <D as DimSub<Const<1_usize>>>::Output> where
D: DimSub<Const<1_usize>>,
DefaultAllocator: Allocator<T, <D as DimSub<Const<1_usize>>>::Output, <D as DimSub<Const<1_usize>>>::Output>,
DefaultAllocator: Allocator<T, D, Const<1_usize>>,
pub fn remove_column(
&self,
j: usize
) -> Cholesky<T, <D as DimSub<Const<1_usize>>>::Output> where
D: DimSub<Const<1_usize>>,
DefaultAllocator: Allocator<T, <D as DimSub<Const<1_usize>>>::Output, <D as DimSub<Const<1_usize>>>::Output>,
DefaultAllocator: Allocator<T, D, Const<1_usize>>,
Updates the decomposition such that we get the decomposition of the factored matrix with its j
th column removed.
Since the matrix is square, the j
th row will also be removed.
Trait Implementations
sourceimpl<T, D> Clone for Cholesky<T, D> where
T: Clone + SimdComplexField,
D: Clone + Dim,
DefaultAllocator: Allocator<T, D, D>,
impl<T, D> Clone for Cholesky<T, D> where
T: Clone + SimdComplexField,
D: Clone + Dim,
DefaultAllocator: Allocator<T, D, D>,
sourceimpl<T, D> Debug for Cholesky<T, D> where
T: Debug + SimdComplexField,
D: Debug + Dim,
DefaultAllocator: Allocator<T, D, D>,
impl<T, D> Debug for Cholesky<T, D> where
T: Debug + SimdComplexField,
D: Debug + Dim,
DefaultAllocator: Allocator<T, D, D>,
impl<T, D> Copy for Cholesky<T, D> where
T: SimdComplexField,
D: Dim,
DefaultAllocator: Allocator<T, D, D>,
Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>: Copy,
Auto Trait Implementations
impl<T, D> !RefUnwindSafe for Cholesky<T, D>
impl<T, D> !Send for Cholesky<T, D>
impl<T, D> !Sync for Cholesky<T, D>
impl<T, D> !Unpin for Cholesky<T, D>
impl<T, D> !UnwindSafe for Cholesky<T, D>
Blanket Implementations
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more
sourceimpl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,
impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,
sourcefn to_subset(&self) -> Option<SS>
fn to_subset(&self) -> Option<SS>
The inverse inclusion map: attempts to construct self
from the equivalent element of its
superset. Read more
sourcefn is_in_subset(&self) -> bool
fn is_in_subset(&self) -> bool
Checks if self
is actually part of its subset T
(and can be converted to it).
sourcefn to_subset_unchecked(&self) -> SS
fn to_subset_unchecked(&self) -> SS
Use with care! Same as self.to_subset
but without any property checks. Always succeeds.
sourcefn from_subset(element: &SS) -> SP
fn from_subset(element: &SS) -> SP
The inclusion map: converts self
to the equivalent element of its superset.
sourceimpl<T> ToOwned for T where
T: Clone,
impl<T> ToOwned for T where
T: Clone,
type Owned = T
type Owned = T
The resulting type after obtaining ownership.
sourcefn clone_into(&self, target: &mut T)
fn clone_into(&self, target: &mut T)
toowned_clone_into
)Uses borrowed data to replace owned data, usually by cloning. Read more