```
pub struct Cholesky<T: SimdComplexField, D: Dim>where
DefaultAllocator: Allocator<T, D, D>,{ /* private fields */ }
```

## Expand description

The Cholesky decomposition of a symmetric-definite-positive matrix.

## Implementations§

source§### impl<T: SimdComplexField, D: Dim> Cholesky<T, D>where
DefaultAllocator: Allocator<T, D, D>,

### impl<T: SimdComplexField, D: Dim> Cholesky<T, D>where
DefaultAllocator: Allocator<T, D, D>,

source#### pub fn new_unchecked(matrix: OMatrix<T, D, D>) -> Self

#### pub fn new_unchecked(matrix: OMatrix<T, D, D>) -> Self

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.)

source#### pub fn pack_dirty(matrix: OMatrix<T, D, D>) -> Self

#### pub fn pack_dirty(matrix: OMatrix<T, D, D>) -> Self

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.

source#### pub fn unpack(self) -> OMatrix<T, D, D>

#### pub fn unpack(self) -> OMatrix<T, D, D>

Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly upper-triangular part filled with zeros.

source#### pub fn unpack_dirty(self) -> OMatrix<T, D, D>

#### pub fn unpack_dirty(self) -> OMatrix<T, D, D>

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.

source#### pub fn l(&self) -> OMatrix<T, D, D>

#### pub fn l(&self) -> OMatrix<T, D, D>

Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly uppen-triangular part filled with zeros.

source#### pub fn l_dirty(&self) -> &OMatrix<T, D, D>

#### pub fn l_dirty(&self) -> &OMatrix<T, D, D>

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.

source#### pub fn solve_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<T, R2, C2, S2>)

#### pub fn solve_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<T, R2, C2, S2>)

Solves the system `self * x = b`

where `self`

is the decomposed matrix and `x`

the unknown.

The result is stored on `b`

.

source#### pub fn solve<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2>where
S2: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,

#### pub fn solve<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>
) -> OMatrix<T, R2, C2>where
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.

source#### pub fn determinant(&self) -> T::SimdRealField

#### pub fn determinant(&self) -> T::SimdRealField

Computes the determinant of the decomposed matrix.

source#### pub fn ln_determinant(&self) -> T::SimdRealField

#### pub fn ln_determinant(&self) -> T::SimdRealField

Computes the natural logarithm of determinant of the decomposed matrix.

This method is more robust than `.determinant()`

to very small or very
large determinants since it returns the natural logarithm of the
determinant rather than the determinant itself.

source§### impl<T: ComplexField, D: Dim> Cholesky<T, D>where
DefaultAllocator: Allocator<T, D, D>,

### impl<T: ComplexField, D: Dim> Cholesky<T, D>where
DefaultAllocator: Allocator<T, D, D>,

source#### pub fn new(matrix: OMatrix<T, D, D>) -> Option<Self>

#### pub fn new(matrix: OMatrix<T, D, D>) -> Option<Self>

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.

source#### pub fn new_with_substitute(
matrix: OMatrix<T, D, D>,
substitute: T
) -> Option<Self>

#### pub fn new_with_substitute( matrix: OMatrix<T, D, D>, substitute: T ) -> Option<Self>

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.

source#### pub fn rank_one_update<R2: Dim, S2>(
&mut self,
x: &Vector<T, R2, S2>,
sigma: T::RealField
)where
S2: Storage<T, R2, U1>,
DefaultAllocator: Allocator<T, R2, U1>,
ShapeConstraint: SameNumberOfRows<R2, D>,

#### pub fn rank_one_update<R2: Dim, S2>(
&mut self,
x: &Vector<T, R2, S2>,
sigma: T::RealField
)where
S2: Storage<T, R2, U1>,
DefaultAllocator: Allocator<T, 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())`

.

source#### pub fn insert_column<R2, S2>(
&self,
j: usize,
col: Vector<T, R2, S2>
) -> Cholesky<T, DimSum<D, U1>>

#### pub fn insert_column<R2, S2>( &self, j: usize, col: Vector<T, R2, S2> ) -> Cholesky<T, DimSum<D, U1>>

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.

## Trait Implementations§

source§### impl<T: Clone + SimdComplexField, D: Clone + Dim> Clone for Cholesky<T, D>where
DefaultAllocator: Allocator<T, D, D>,

### impl<T: Clone + SimdComplexField, D: Clone + Dim> Clone for Cholesky<T, D>where
DefaultAllocator: Allocator<T, D, D>,

source§### impl<T: Debug + SimdComplexField, D: Debug + Dim> Debug for Cholesky<T, D>where
DefaultAllocator: Allocator<T, D, D>,

### impl<T: Debug + SimdComplexField, D: Debug + Dim> Debug for Cholesky<T, D>where
DefaultAllocator: Allocator<T, D, D>,

### impl<T: SimdComplexField, D: Dim> Copy for Cholesky<T, D>

## 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§

source§### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

source§#### fn borrow_mut(&mut self) -> &mut T

#### fn borrow_mut(&mut self) -> &mut T

source§### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

source§#### fn to_subset(&self) -> Option<SS>

#### fn to_subset(&self) -> Option<SS>

`self`

from the equivalent element of its
superset. Read moresource§#### fn is_in_subset(&self) -> bool

#### fn is_in_subset(&self) -> bool

`self`

is actually part of its subset `T`

(and can be converted to it).source§#### fn to_subset_unchecked(&self) -> SS

#### fn to_subset_unchecked(&self) -> SS

`self.to_subset`

but without any property checks. Always succeeds.source§#### fn from_subset(element: &SS) -> SP

#### fn from_subset(element: &SS) -> SP

`self`

to the equivalent element of its superset.