Struct bevy_rapier3d::prelude::nalgebra::Cholesky [−][src]
pub struct Cholesky<T, D> where
T: SimdComplexField,
D: Dim,
DefaultAllocator: Allocator<T, D, D>, { /* fields omitted */ }
Expand description
The Cholesky decomposition of a symmetric-definite-positive matrix.
Implementations
impl<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>,
pub 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.)
pub 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.
Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly upper-triangular part filled with zeros.
pub 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.
Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly uppen-triangular part filled with zeros.
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<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
.
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>,
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.
Computes the inverse of the decomposed matrix.
Computes the determinant of the decomposed matrix.
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 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.
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>,
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())
.
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>,
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.
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<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>,
impl<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> !UnwindSafe for Cholesky<T, D>
Blanket Implementations
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T: Any,
impl<T> Downcast for T where
T: Any,
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) to Box<dyn Any>
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into Box<ConcreteType>
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implements Trait
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pub fn into_any_rc(self: Rc<T>) -> Rc<dyn Any + 'static>
pub fn into_any_rc(self: Rc<T>) -> Rc<dyn Any + 'static>
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(where Trait: Downcast
) to Rc<Any>
. Rc<Any>
can then be
further downcast
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(where Trait: Downcast
) to &Any
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pub fn as_any_mut(&mut self) -> &mut (dyn Any + 'static)
pub fn as_any_mut(&mut self) -> &mut (dyn Any + 'static)
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) to &Any
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The inverse inclusion map: attempts to construct self
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pub fn is_in_subset(&self) -> bool
pub fn is_in_subset(&self) -> bool
Checks if self
is actually part of its subset T
(and can be converted to it).
pub fn to_subset_unchecked(&self) -> SS
pub fn to_subset_unchecked(&self) -> SS
Use with care! Same as self.to_subset
but without any property checks. Always succeeds.
pub fn from_subset(element: &SS) -> SP
pub fn from_subset(element: &SS) -> SP
The inclusion map: converts self
to the equivalent element of its superset.
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Attaches the provided Subscriber
to this type, returning a
WithDispatch
wrapper. Read more
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