Struct nalgebra::linalg::LU

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

Expand description

LU decomposition with partial (row) pivoting.

Implementations

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impl<T: ComplexField, R: DimMin<C>, C: Dim> LU<T, R, C> where
DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize ), 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<T, 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<T, 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<T, R, DimMinimum<R, C>> + Allocator<T, 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<T, D, D> + Allocator<(usize, usize ), 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<T, 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<T, R, C> + Allocator<(usize, usize ), 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<T, R, C> + Allocator<(usize, usize ), 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<T: ComplexField, R: DimMin<C>, C: Dim> Copy for LU<T, R, C> where
 DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize ), DimMinimum<R, C>>,
 OMatrix<T, R, C>: Copy,
 PermutationSequence<DimMinimum<R, C>>: Copy,

Auto Trait Implementations

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

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

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

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

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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pub fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

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impl<T> Borrow<T> for T where
T: ?Sized,

const: unstable · source

pub 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,

const: unstable · source

pub 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

pub fn from(t: T) -> T

Returns the argument unchanged.

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

const: unstable · source

pub 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

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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pub 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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pub 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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pub 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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pub 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,

type Owned = T

The resulting type after obtaining ownership.

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pub fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more

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pub fn clone_into(&self, target: &mut T)

🔬 This is a nightly-only experimental API. (toowned_clone_into)

Uses borrowed data to replace owned data, usually by cloning. Read more

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

type Error = Infallible

The type returned in the event of a conversion error.

const: unstable · source

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

Performs the conversion.

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impl<T, U> TryInto for T where
U: TryFrom<T>,

type Error = >::Error

The type returned in the event of a conversion error.

const: unstable · source

pub fn try_into(self) -> Result<U, >::Error>

Performs the conversion.

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impl<V, T> VZip<V> for T where
V: MultiLane<T>,

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Struct nalgebra::linalg::LU

Implementations

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

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

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

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

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

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

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

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

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<T, R2, C2>,

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>,

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

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

pub fn determinant(&self) -> T

pub fn is_invertible(&self) -> bool

Trait Implementations

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

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

fn clone_from(&mut self, source: &Self)

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

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

impl<T: ComplexField, R: DimMin<C>, C: Dim> Copy for LU<T, R, C> where DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>, OMatrix<T, R, C>: Copy, PermutationSequence<DimMinimum<R, C>>: Copy,

Auto Trait Implementations

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

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

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

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

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

Blanket Implementations

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

pub fn type_id(&self) -> TypeId

impl<T> Borrow<T> for T where T: ?Sized,

pub fn borrow(&self) -> &T

impl<T> BorrowMut<T> for T where T: ?Sized,

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

impl<T> From<T> for T

pub fn from(t: T) -> T

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

pub fn into(self) -> U

impl<T> Same<T> for T

type Output = T

impl<SS, SP> SupersetOf<SS> for SP where SS: SubsetOf<SP>,

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

pub fn is_in_subset(&self) -> bool

pub fn to_subset_unchecked(&self) -> SS

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

impl<T> ToOwned for T where T: Clone,

type Owned = T

pub fn to_owned(&self) -> T

pub fn clone_into(&self, target: &mut T)

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

type Error = Infallible

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

impl<T, U> TryInto<U> for T where U: TryFrom<T>,

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

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

impl<V, T> VZip<V> for T where V: MultiLane<T>,

pub fn vzip(self) -> V

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

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

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

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

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

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

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<T, R2, C2>,

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>,

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

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

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

impl<T: ComplexField, R: DimMin<C>, C: Dim> Copy for LU<T, R, C> where
DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize ), DimMinimum<R, C>>,
OMatrix<T, R, C>: Copy,
PermutationSequence<DimMinimum<R, C>>: Copy,

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

impl<T> Borrow<T> for T where
T: ?Sized,

impl<T> BorrowMut<T> for T where
T: ?Sized,

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

impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,

impl<T> ToOwned for T where
T: Clone,

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

impl<T, U> TryInto<U> for T where
U: TryFrom<T>,

impl<V, T> VZip<V> for T where
V: MultiLane<T>,