nalgebra_lapack

Struct LU

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

LU decomposition with partial pivoting.

This decomposes a matrix M with m rows and n columns into three parts:

  • L which is a m × min(m, n) lower-triangular matrix.
  • U which is a min(m, n) × n upper-triangular matrix.
  • P which is a m * m permutation matrix.

Those are such that M == P * L * U.

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

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pub fn new(m: 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>>

Gets the lower-triangular matrix part of the decomposition.

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

Gets the upper-triangular matrix part of the decomposition.

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pub fn p(&self) -> OMatrix<T, R, R>

Gets the row permutation matrix of this decomposition.

Computing the permutation matrix explicitly is costly and usually not necessary. To permute rows of a matrix or vector, use the method self.permute(...) instead.

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pub fn permutation_indices(&self) -> &OVector<i32, DimMinimum<R, C>>

Gets the LAPACK permutation indices.

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pub fn permute<C2: Dim>(&self, rhs: &mut OMatrix<T, R, C2>)
where DefaultAllocator: Allocator<R, C2>,

Applies the permutation matrix to a given matrix or vector in-place.

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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>, DefaultAllocator: Allocator<R2, C2> + Allocator<R2>,

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

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

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

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

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

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pub fn solve_mut<R2: Dim, C2: Dim>(&self, b: &mut OMatrix<T, R2, C2>) -> bool
where DefaultAllocator: Allocator<R2, C2> + Allocator<R2>,

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

Returns false if no solution was found (the decomposed matrix is singular).

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pub fn solve_transpose_mut<R2: Dim, C2: Dim>( &self, b: &mut OMatrix<T, R2, C2>, ) -> bool
where DefaultAllocator: Allocator<R2, C2> + Allocator<R2>,

Solves in-place the linear system self.transpose() * x = b, where x is the unknown to be determined.

Returns false if no solution was found (the decomposed matrix is singular).

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pub fn solve_adjoint_mut<R2: Dim, C2: Dim>( &self, b: &mut OMatrix<T, R2, C2>, ) -> bool
where DefaultAllocator: Allocator<R2, C2> + Allocator<R2>,

Solves in-place the linear system self.adjoint() * x = b, where x is the unknown to be determined.

Returns false if no solution was found (the decomposed matrix is singular).

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impl<T, D> LU<T, D, D>
where T: Zero + One + LUScalar, D: DimMin<D, Output = D> + Dim, DefaultAllocator: Allocator<D, D> + Allocator<D>,

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

Computes the inverse of the decomposed matrix.

Trait Implementations§

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

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

Returns a duplicate 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 + Scalar, R: Debug + DimMin<C>, C: Debug + Dim> Debug for LU<T, R, C>
where DefaultAllocator: Allocator<DimMinimum<R, C>> + Allocator<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: Scalar + Copy, 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, OVector<i32, 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> 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<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.