nalgebra::linalg

Struct FullPivLU

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

LU decomposition with full row and column pivoting.

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impl<T: ComplexField, R: DimMin<C>, C: Dim> FullPivLU<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 full pivoting of matrix.

This effectively computes P, L, U, Q such that P * matrix * Q = LU.

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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 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 q(&self) -> &PermutationSequence<DimMinimum<R, C>>

The column 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>, PermutationSequence<DimMinimum<R, C>>)
where DefaultAllocator: Allocator<R, DimMinimum<R, C>> + Allocator<DimMinimum<R, C>, C>,

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

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impl<T: ComplexField, D: DimMin<D, Output = D>> FullPivLU<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 the decomposed matrix 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 decomposed matrix is not invertible.

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pub fn is_invertible(&self) -> bool

Indicates if the decomposed matrix is invertible.

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pub fn determinant(&self) -> T

Computes the determinant of the decomposed matrix.

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

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

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

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

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

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

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

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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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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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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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const ALIGN: usize = _

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unsafe fn init(init: <T as Pointable>::Init) -> usize

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unsafe fn drop(ptr: usize)

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The type for metadata in pointers and references to Self.
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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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type Error = Infallible

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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

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Performs the conversion.
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impl<V, T> VZip<V> for T
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fn vzip(self) -> V

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