Cholesky in nalgebra::linalg - Rust
Description: The Cholesky decomposition of a symmetric-definite-positive matrix.
Keywords: rust, rustlang, rust-lang, Cholesky

# Struct nalgebra::linalg::Cholesky

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    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§

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

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#### 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.)

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#### 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.

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#### 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.

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#### 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.

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#### 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.

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#### 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.

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

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#### 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.

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

Computes the inverse of the decomposed matrix.

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

Computes the determinant of the decomposed matrix.

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#### 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.

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

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#### 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.

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#### 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.

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#### 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())`.

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#### pub fn insert_column<R2, S2>(
&self,
j: usize,
col: Vector<T, R2, S2>
) -> Cholesky<T, DimSum<D, U1>>where
D: DimAdd<U1>,
R2: Dim,
S2: Storage<T, R2, U1>,
DefaultAllocator: Allocator<T, DimSum<D, U1>, DimSum<D, U1>> + Allocator<T, R2>,
ShapeConstraint: SameNumberOfRows<R2, 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.

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#### pub fn remove_column(&self, j: usize) -> Cholesky<T, DimDiff<D, U1>>where
D: DimSub<U1>,
DefaultAllocator: Allocator<T, DimDiff<D, U1>, DimDiff<D, U1>> + Allocator<T, D>,

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§

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

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#### fn clone(&self) -> Cholesky<T, D>

Returns a copy of the value. Read more
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#### fn clone_from(&mut self, source: &Self)

Performs copy-assignment from `source`. Read more
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### impl<T: Debug + SimdComplexField, D: Debug + Dim> Debug for Cholesky<T, D>where
DefaultAllocator: Allocator<T, D, D>,

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#### fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter. Read more
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### impl<T: SimdComplexField, D: Dim> Copy for Cholesky<T, D>where
DefaultAllocator: Allocator<T, D, D>,
OMatrix<T, D, D>: Copy,

## Auto Trait Implementations§

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### impl<T, D> !RefUnwindSafe for Cholesky<T, D>

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### impl<T, D> !Send for Cholesky<T, D>

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### impl<T, D> !Sync for Cholesky<T, D>

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### impl<T, D> !Unpin for Cholesky<T, D>

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### impl<T, D> !UnwindSafe for Cholesky<T, D>

## Blanket Implementations§

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### impl<T> Any for Twhere
T: 'static + ?Sized,

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#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
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### impl<T> Borrow<T> for Twhere
T: ?Sized,

const: unstable · source§

#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

const: unstable · source§

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

Mutably borrows from an owned value. Read more
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### impl<T> From<T> for T

const: unstable · source§

#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for Twhere
U: From<T>,

const: unstable · source§

#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

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### impl<T> Same<T> for T

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#### type Output = T

Should always be `Self`
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### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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#### fn is_in_subset(&self) -> bool

Checks if `self` is actually part of its subset `T` (and can be converted to it).
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#### fn to_subset_unchecked(&self) -> SS

Use with care! Same as `self.to_subset` but without any property checks. Always succeeds.
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#### fn from_subset(element: &SS) -> SP

The inclusion map: converts `self` to the equivalent element of its superset.
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### impl<T> ToOwned for Twhere
T: Clone,

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#### type Owned = T

The resulting type after obtaining ownership.
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#### fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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#### fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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### impl<T, U> TryFrom<U> for Twhere
U: Into<T>,

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#### type Error = Infallible

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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### impl<T, U> TryInto<U> for Twhere
U: TryFrom<T>,

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#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.