[−][src]Struct oxygengine_physics_2d::prelude::nalgebra::Cholesky
The Cholesky decomposition of a symmetric-definite-positive matrix.
Implementations
impl<N, D> Cholesky<N, D> where
D: Dim,
N: SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
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D: Dim,
N: SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
pub fn new_unchecked(
matrix: Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
) -> Cholesky<N, D>
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matrix: Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
) -> Cholesky<N, 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.)
pub fn unpack(
self
) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
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self
) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly upper-triangular part filled with zeros.
pub fn unpack_dirty(
self
) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
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self
) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, 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.
pub fn l(
&self
) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
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&self
) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly uppen-triangular part filled with zeros.
pub fn l_dirty(
&self
) -> &Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
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&self
) -> &Matrix<N, D, D, <DefaultAllocator as Allocator<N, 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.
pub fn solve_mut<R2, C2, S2>(&self, b: &mut Matrix<N, R2, C2, S2>) where
C2: Dim,
R2: Dim,
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
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C2: Dim,
R2: Dim,
S2: StorageMut<N, 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
.
pub fn solve<R2, C2, S2>(
&self,
b: &Matrix<N, R2, C2, S2>
) -> Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer> where
C2: Dim,
R2: Dim,
S2: Storage<N, R2, C2>,
DefaultAllocator: Allocator<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
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&self,
b: &Matrix<N, R2, C2, S2>
) -> Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer> where
C2: Dim,
R2: Dim,
S2: Storage<N, R2, C2>,
DefaultAllocator: Allocator<N, 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.
pub fn inverse(
&self
) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
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&self
) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
Computes the inverse of the decomposed matrix.
impl<N, D> Cholesky<N, D> where
D: Dim,
N: ComplexField,
DefaultAllocator: Allocator<N, D, D>,
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D: Dim,
N: ComplexField,
DefaultAllocator: Allocator<N, D, D>,
pub fn new(
matrix: Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
) -> Option<Cholesky<N, D>>
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matrix: Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
) -> Option<Cholesky<N, 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.
pub fn rank_one_update<R2, S2>(
&mut self,
x: &Matrix<N, R2, U1, S2>,
sigma: <N as ComplexField>::RealField
) where
R2: Dim,
S2: Storage<N, R2, U1>,
DefaultAllocator: Allocator<N, R2, U1>,
ShapeConstraint: SameNumberOfRows<R2, D>,
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&mut self,
x: &Matrix<N, R2, U1, S2>,
sigma: <N as ComplexField>::RealField
) where
R2: Dim,
S2: Storage<N, R2, U1>,
DefaultAllocator: Allocator<N, R2, U1>,
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())
.
pub fn insert_column<R2, S2>(
&self,
j: usize,
col: Matrix<N, R2, U1, S2>
) -> Cholesky<N, <D as DimAdd<U1>>::Output> where
D: DimAdd<U1>,
R2: Dim,
S2: Storage<N, R2, U1>,
DefaultAllocator: Allocator<N, <D as DimAdd<U1>>::Output, <D as DimAdd<U1>>::Output>,
DefaultAllocator: Allocator<N, R2, U1>,
ShapeConstraint: SameNumberOfRows<R2, <D as DimAdd<U1>>::Output>,
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&self,
j: usize,
col: Matrix<N, R2, U1, S2>
) -> Cholesky<N, <D as DimAdd<U1>>::Output> where
D: DimAdd<U1>,
R2: Dim,
S2: Storage<N, R2, U1>,
DefaultAllocator: Allocator<N, <D as DimAdd<U1>>::Output, <D as DimAdd<U1>>::Output>,
DefaultAllocator: Allocator<N, R2, U1>,
ShapeConstraint: SameNumberOfRows<R2, <D as DimAdd<U1>>::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.
pub fn remove_column(&self, j: usize) -> Cholesky<N, <D as DimSub<U1>>::Output> where
D: DimSub<U1>,
DefaultAllocator: Allocator<N, <D as DimSub<U1>>::Output, <D as DimSub<U1>>::Output>,
DefaultAllocator: Allocator<N, D, U1>,
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D: DimSub<U1>,
DefaultAllocator: Allocator<N, <D as DimSub<U1>>::Output, <D as DimSub<U1>>::Output>,
DefaultAllocator: Allocator<N, D, U1>,
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
impl<N, D> Clone for Cholesky<N, D> where
D: Dim + Clone,
N: Clone + SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
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D: Dim + Clone,
N: Clone + SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
impl<N, D> Copy for Cholesky<N, D> where
D: Dim,
N: SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>: Copy,
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D: Dim,
N: SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>: Copy,
impl<N, D> Debug for Cholesky<N, D> where
D: Dim + Debug,
N: Debug + SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
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D: Dim + Debug,
N: Debug + SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
impl<'de, N, D> Deserialize<'de> for Cholesky<N, D> where
D: Dim,
N: SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
DefaultAllocator: Allocator<N, D, U1>,
Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>: Deserialize<'de>,
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D: Dim,
N: SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
DefaultAllocator: Allocator<N, D, U1>,
Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>: Deserialize<'de>,
fn deserialize<__D>(
__deserializer: __D
) -> Result<Cholesky<N, D>, <__D as Deserializer<'de>>::Error> where
__D: Deserializer<'de>,
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__deserializer: __D
) -> Result<Cholesky<N, D>, <__D as Deserializer<'de>>::Error> where
__D: Deserializer<'de>,
impl<N, D> Serialize for Cholesky<N, D> where
D: Dim,
N: SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
DefaultAllocator: Allocator<N, D, U1>,
Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>: Serialize,
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D: Dim,
N: SimdComplexField,
DefaultAllocator: Allocator<N, D, D>,
DefaultAllocator: Allocator<N, D, U1>,
Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>: Serialize,
fn serialize<__S>(
&self,
__serializer: __S
) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error> where
__S: Serializer,
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&self,
__serializer: __S
) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error> where
__S: Serializer,
Auto Trait Implementations
impl<N, D> !RefUnwindSafe for Cholesky<N, D>
impl<N, D> !Send for Cholesky<N, D>
impl<N, D> !Sync for Cholesky<N, D>
impl<N, D> !Unpin for Cholesky<N, D>
impl<N, D> !UnwindSafe for Cholesky<N, D>
Blanket Implementations
impl<T> Any for T where
T: 'static + ?Sized,
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T: 'static + ?Sized,
impl<T> Any for T where
T: Any,
T: Any,
fn get_type_id(&self) -> TypeId
impl<T> Borrow<T> for T where
T: ?Sized,
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T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
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T: ?Sized,
fn borrow_mut(&mut self) -> &mut T
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impl<T> Downcast for T where
T: Any,
T: Any,
fn into_any(self: Box<T>) -> Box<dyn Any + 'static>
fn into_any_rc(self: Rc<T>) -> Rc<dyn Any + 'static>
fn as_any(&self) -> &(dyn Any + 'static)
fn as_any_mut(&mut self) -> &mut (dyn Any + 'static)
impl<T> From<T> for T
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impl<T, U> Into<U> for T where
U: From<T>,
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U: From<T>,
impl<T> Resource for T where
T: Any,
T: Any,
impl<T> Same<T> for T
type Output = T
Should always be Self
impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,
SS: SubsetOf<SP>,
fn to_subset(&self) -> Option<SS>
fn is_in_subset(&self) -> bool
fn to_subset_unchecked(&self) -> SS
fn from_subset(element: &SS) -> SP
impl<T> ToOwned for T where
T: Clone,
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T: Clone,
type Owned = T
The resulting type after obtaining ownership.
fn to_owned(&self) -> T
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fn clone_into(&self, target: &mut T)
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impl<T, U> TryFrom<U> for T where
U: Into<T>,
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U: Into<T>,
type Error = Infallible
The type returned in the event of a conversion error.
fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>
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impl<T, U> TryInto<U> for T where
U: TryFrom<T>,
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U: TryFrom<T>,
type Error = <U as TryFrom<T>>::Error
The type returned in the event of a conversion error.
fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>
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impl<V, T> VZip<V> for T where
V: MultiLane<T>,
V: MultiLane<T>,