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Struct LU

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

LU decomposition with partial (row) pivoting.

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

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pub fn new( matrix: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>, ) -> LU<T, R, C>

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

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pub fn l( &self, ) -> Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>
where DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output>,

The lower triangular matrix of this decomposition.

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pub fn l_unpack( self, ) -> Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>
where DefaultAllocator: Reallocator<T, R, C, R, <R as DimMin<C>>::Output>,

The lower triangular matrix of this decomposition.

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pub fn u( &self, ) -> Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>
where DefaultAllocator: Allocator<T, <R as DimMin<C>>::Output, C>,

The upper triangular matrix of this decomposition.

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pub fn p(&self) -> &PermutationSequence<<R as DimMin<C>>::Output>

The row permutations of this decomposition.

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pub fn unpack( self, ) -> (PermutationSequence<<R as DimMin<C>>::Output>, Matrix<T, R, <R as DimMin<C>>::Output, <DefaultAllocator as Allocator<T, R, <R as DimMin<C>>::Output>>::Buffer>, Matrix<T, <R as DimMin<C>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimMin<C>>::Output, C>>::Buffer>)
where DefaultAllocator: Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<T, <R as DimMin<C>>::Output, C> + Reallocator<T, R, C, R, <R as DimMin<C>>::Output>,

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

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

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pub fn solve<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> Option<Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>>
where R2: Dim, C2: Dim, 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, C2, S2>(&self, b: &mut Matrix<T, R2, C2, S2>) -> bool
where R2: Dim, C2: Dim, 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<Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>>

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

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.

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

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

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

Performs copy-assignment from source. Read more
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impl<T, R, C> Debug for LU<T, R, C>
where T: Debug + ComplexField, R: Debug + DimMin<C>, C: Debug + Dim, DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize), <R as DimMin<C>>::Output>,

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

Formats the value using the given formatter. Read more
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impl<T, R, C> Copy for LU<T, R, C>
where T: ComplexField, R: DimMin<C>, C: Dim, DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize), <R as DimMin<C>>::Output>, Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>: Copy, PermutationSequence<<R as DimMin<C>>::Output>: 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> 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, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. Read more
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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<V> IntoPnt<V> for V

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fn into_pnt(self) -> V

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impl<V> IntoVec<V> for V

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fn into_vec(self) -> V

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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<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.