Struct LUFactorizedTridiagonal

pub struct LUFactorizedTridiagonal<A>
where
    A: Scalar,
{
    pub a: Tridiagonal<A>,
    pub du2: Vec<A>,
    pub ipiv: Vec<i32>,
    pub a_opnorm_one: <A as Scalar>::Real,
}

Represents the LU factorization of a tridiagonal matrix A as A = P*L*U.

Fields

a: Tridiagonal<A>

A tridiagonal matrix which consists of

• l : layout of raw matrix
• dl: (n-1) multipliers that define the matrix L.
• d : (n) diagonal elements of the upper triangular matrix U.
• du: (n-1) elements of the first super-diagonal of U.

du2: Vec<A>

(n-2) elements of the second super-diagonal of U.

ipiv: Vec<i32>

The pivot indices that define the permutation matrix P.

a_opnorm_one: <A as Scalar>::Real

Trait Implementations

impl<A> Clone for LUFactorizedTridiagonal<A>

where A: Clone + Scalar, <A as Scalar>::Real: Clone,

fn clone(&self) -> LUFactorizedTridiagonal<A>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<A> PartialEq for LUFactorizedTridiagonal<A>

where A: PartialEq + Scalar, <A as Scalar>::Real: PartialEq,

fn eq(&self, other: &LUFactorizedTridiagonal<A>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<A> ReciprocalConditionNumTridiagonal<A> for LUFactorizedTridiagonal<A>

where A: Scalar + Lapack,

fn rcond_tridiagonal(&self) -> Result<A::Real>

Estimates the reciprocal of the condition number of the tridiagonal matrix in 1-norm.

impl<A> ReciprocalConditionNumTridiagonalInto<A> for LUFactorizedTridiagonal<A>

where A: Scalar + Lapack,

fn rcond_tridiagonal_into(self) -> Result<A::Real>

Estimates the reciprocal of the condition number of the tridiagonal matrix in 1-norm.

impl<A> SolveTridiagonal<A, Dim<[usize; 1]>> for LUFactorizedTridiagonal<A>

where A: Scalar + Lapack,

fn solve_tridiagonal<S: Data<Elem = A>>( &self, b: &ArrayBase<S, Ix1>, ) -> Result<Array<A, Ix1>>

Solves a system of linear equations A * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

fn solve_tridiagonal_into<S: DataMut<Elem = A>>( &self, b: ArrayBase<S, Ix1>, ) -> Result<ArrayBase<S, Ix1>>

Solves a system of linear equations A * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

fn solve_t_tridiagonal<S: Data<Elem = A>>( &self, b: &ArrayBase<S, Ix1>, ) -> Result<Array<A, Ix1>>

Solves a system of linear equations A^T * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

fn solve_t_tridiagonal_into<S: DataMut<Elem = A>>( &self, b: ArrayBase<S, Ix1>, ) -> Result<ArrayBase<S, Ix1>>

Solves a system of linear equations A^T * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

fn solve_h_tridiagonal<S: Data<Elem = A>>( &self, b: &ArrayBase<S, Ix1>, ) -> Result<Array<A, Ix1>>

Solves a system of linear equations A^H * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

fn solve_h_tridiagonal_into<S: DataMut<Elem = A>>( &self, b: ArrayBase<S, Ix1>, ) -> Result<ArrayBase<S, Ix1>>

Solves a system of linear equations A^H * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

impl<A> SolveTridiagonal<A, Dim<[usize; 2]>> for LUFactorizedTridiagonal<A>

where A: Scalar + Lapack,

fn solve_tridiagonal<S: Data<Elem = A>>( &self, b: &ArrayBase<S, Ix2>, ) -> Result<Array<A, Ix2>>

Solves a system of linear equations A * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

fn solve_tridiagonal_into<S: DataMut<Elem = A>>( &self, b: ArrayBase<S, Ix2>, ) -> Result<ArrayBase<S, Ix2>>

Solves a system of linear equations A * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

fn solve_t_tridiagonal<S: Data<Elem = A>>( &self, b: &ArrayBase<S, Ix2>, ) -> Result<Array<A, Ix2>>

Solves a system of linear equations A^T * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

fn solve_t_tridiagonal_into<S: DataMut<Elem = A>>( &self, b: ArrayBase<S, Ix2>, ) -> Result<ArrayBase<S, Ix2>>

Solves a system of linear equations A^T * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

fn solve_h_tridiagonal<S: Data<Elem = A>>( &self, b: &ArrayBase<S, Ix2>, ) -> Result<Array<A, Ix2>>

Solves a system of linear equations A^H * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

fn solve_h_tridiagonal_into<S: DataMut<Elem = A>>( &self, b: ArrayBase<S, Ix2>, ) -> Result<ArrayBase<S, Ix2>>

Solves a system of linear equations A^H * x = b with tridiagonal matrix A, where A is self, b is the argument, and x is the successful result.

impl<A> SolveTridiagonalInplace<A, Dim<[usize; 2]>> for LUFactorizedTridiagonal<A>

where A: Scalar + Lapack,

fn solve_tridiagonal_inplace<'a, Sb>( &self, rhs: &'a mut ArrayBase<Sb, Ix2>, ) -> Result<&'a mut ArrayBase<Sb, Ix2>>

where Sb: DataMut<Elem = A>,

Solves a system of linear equations A * x = b tridiagonal matrix A, where A is self, b is the argument, and x is the successful result. The value of x is also assigned to the argument.

fn solve_t_tridiagonal_inplace<'a, Sb>( &self, rhs: &'a mut ArrayBase<Sb, Ix2>, ) -> Result<&'a mut ArrayBase<Sb, Ix2>>

where Sb: DataMut<Elem = A>,

Solves a system of linear equations A^T * x = b tridiagonal matrix A, where A is self, b is the argument, and x is the successful result. The value of x is also assigned to the argument.

fn solve_h_tridiagonal_inplace<'a, Sb>( &self, rhs: &'a mut ArrayBase<Sb, Ix2>, ) -> Result<&'a mut ArrayBase<Sb, Ix2>>

where Sb: DataMut<Elem = A>,

Solves a system of linear equations A^H * x = b tridiagonal matrix A, where A is self, b is the argument, and x is the successful result. The value of x is also assigned to the argument.

impl<A> StructuralPartialEq for LUFactorizedTridiagonal<A>

where A: Scalar,