nalgebra::linalg

Struct LU

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pub struct LU<T: ComplexField, R: DimMin<C>, C: Dim>
where
    DefaultAllocator: Allocator<R, C> + Allocator<DimMinimum<R, C>>,
{ /* private fields */ }
Expand description

LU decomposition with partial (row) pivoting.

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impl<T: ComplexField, R: DimMin<C>, C: Dim> LU<T, R, C>
where DefaultAllocator: Allocator<R, C> + Allocator<DimMinimum<R, C>>,

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pub fn new(matrix: OMatrix<T, R, C>) -> Self

Computes the LU decomposition with partial (row) pivoting of matrix.

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pub fn l(&self) -> OMatrix<T, R, DimMinimum<R, C>>
where DefaultAllocator: Allocator<R, DimMinimum<R, C>>,

The lower triangular matrix of this decomposition.

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pub fn l_unpack(self) -> OMatrix<T, R, DimMinimum<R, C>>
where DefaultAllocator: Reallocator<T, R, C, R, DimMinimum<R, C>>,

The lower triangular matrix of this decomposition.

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pub fn u(&self) -> OMatrix<T, DimMinimum<R, C>, C>
where DefaultAllocator: Allocator<DimMinimum<R, C>, C>,

The upper triangular matrix of this decomposition.

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pub fn p(&self) -> &PermutationSequence<DimMinimum<R, C>>

The row permutations of this decomposition.

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pub fn unpack( self, ) -> (PermutationSequence<DimMinimum<R, C>>, OMatrix<T, R, DimMinimum<R, C>>, OMatrix<T, DimMinimum<R, C>, C>)
where DefaultAllocator: Allocator<R, DimMinimum<R, C>> + Allocator<DimMinimum<R, C>, C> + Reallocator<T, R, C, R, DimMinimum<R, C>>,

The row permutations and two triangular matrices of this decomposition: (P, L, U).

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impl<T: ComplexField, D: DimMin<D, Output = D>> LU<T, D, D>
where DefaultAllocator: Allocator<D, D> + Allocator<D>,

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

Solves the linear system self * x = b, where x is the unknown to be determined.

Returns None if self is not invertible.

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pub fn solve_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, ) -> bool
where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self * x = b, where x is the unknown to be determined.

If the decomposed matrix is not invertible, this returns false and its input b may be overwritten with garbage.

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pub fn try_inverse(&self) -> Option<OMatrix<T, D, D>>

Computes the inverse of the decomposed matrix.

Returns None if the matrix is not invertible.

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pub fn try_inverse_to<S2: StorageMut<T, D, D>>( &self, out: &mut Matrix<T, D, D, S2>, ) -> bool

Computes the inverse of the decomposed matrix and outputs the result to out.

If the decomposed matrix is not invertible, this returns false and out may be overwritten with garbage.

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pub fn determinant(&self) -> T

Computes the determinant of the decomposed matrix.

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pub fn is_invertible(&self) -> bool

Indicates if the decomposed matrix is invertible.

Trait Implementations§

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impl<T: Clone + ComplexField, R: Clone + DimMin<C>, C: Clone + Dim> Clone for LU<T, R, C>
where DefaultAllocator: Allocator<R, C> + Allocator<DimMinimum<R, C>>,

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fn clone(&self) -> LU<T, R, C>

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 + ComplexField, R: Debug + DimMin<C>, C: Debug + Dim> Debug for LU<T, R, C>
where DefaultAllocator: Allocator<R, C> + Allocator<DimMinimum<R, C>>,

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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<'de, T: ComplexField, R: DimMin<C>, C: Dim> Deserialize<'de> for LU<T, R, C>
where DefaultAllocator: Allocator<R, C> + Allocator<DimMinimum<R, C>>, OMatrix<T, R, C>: Deserialize<'de>, PermutationSequence<DimMinimum<R, C>>: Deserialize<'de>,

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fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>
where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer. Read more
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impl<T: ComplexField, R: DimMin<C>, C: Dim> Serialize for LU<T, R, C>
where DefaultAllocator: Allocator<R, C> + Allocator<DimMinimum<R, C>>, OMatrix<T, R, C>: Serialize, PermutationSequence<DimMinimum<R, C>>: Serialize,

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fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>
where __S: Serializer,

Serialize this value into the given Serde serializer. Read more
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impl<T: ComplexField, R: DimMin<C>, C: Dim> Copy for LU<T, R, C>
where DefaultAllocator: Allocator<R, C> + Allocator<DimMinimum<R, C>>, OMatrix<T, R, C>: Copy, PermutationSequence<DimMinimum<R, C>>: Copy,

Auto Trait Implementations§

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impl<T, R, C> !Freeze for LU<T, R, C>

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impl<T, R, C> !RefUnwindSafe for LU<T, R, C>

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impl<T, R, C> !Send for LU<T, R, C>

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impl<T, R, C> !Sync for LU<T, R, C>

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impl<T, R, C> !Unpin for LU<T, R, C>

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impl<T, R, C> !UnwindSafe for LU<T, R, C>

Blanket Implementations§

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impl<T> Any for T
where 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> ArchivePointee for T

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type ArchivedMetadata = ()

The archived version of the pointer metadata for this type.
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fn pointer_metadata( _: &<T as ArchivePointee>::ArchivedMetadata, ) -> <T as Pointee>::Metadata

Converts some archived metadata to the pointer metadata for itself.
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

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

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

Mutably borrows from an owned value. Read more
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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dst: *mut T)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dst. Read more
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impl<F, W, T, D> Deserialize<With<T, W>, D> for F
where W: DeserializeWith<F, T, D>, D: Fallible + ?Sized, F: ?Sized,

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fn deserialize( &self, deserializer: &mut D, ) -> Result<With<T, W>, <D as Fallible>::Error>

Deserializes using the given deserializer
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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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> IntoEither for T

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fn into_either(self, into_left: bool) -> Either<Self, Self>

Converts self into a Left variant of Either<Self, Self> if into_left is true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
where F: FnOnce(&Self) -> bool,

Converts self into a Left variant of Either<Self, Self> if into_left(&self) returns true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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impl<T> LayoutRaw for T

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fn layout_raw(_: <T as Pointee>::Metadata) -> Result<Layout, LayoutError>

Gets the layout of the type.
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impl<T> Pointable for T

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const ALIGN: usize = _

The alignment of pointer.
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type Init = T

The type for initializers.
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unsafe fn init(init: <T as Pointable>::Init) -> usize

Initializes a with the given initializer. Read more
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unsafe fn deref<'a>(ptr: usize) -> &'a T

Dereferences the given pointer. Read more
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unsafe fn deref_mut<'a>(ptr: usize) -> &'a mut T

Mutably dereferences the given pointer. Read more
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unsafe fn drop(ptr: usize)

Drops the object pointed to by the given pointer. Read more
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impl<T> Pointee for T

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type Metadata = ()

The type for metadata in pointers and references to Self.
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impl<T> Same for T

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type Output = T

Should always be Self
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impl<SS, SP> SupersetOf<SS> for SP
where 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<SS, SP> SupersetOf<SS> for SP
where 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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unsafe 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 T
where 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 T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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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 T
where U: TryFrom<T>,

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

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<V, T> VZip<V> for T
where V: MultiLane<T>,

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fn vzip(self) -> V

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impl<T> DeserializeOwned for T
where T: for<'de> Deserialize<'de>,