Struct ndarray_linalg::tridiagonal::LUFactorizedTridiagonal

pub struct LUFactorizedTridiagonal<A: Scalar> {
    pub a: Tridiagonal<A>,
    pub du2: Vec<A>,
    pub anom: A::Real,
    pub ipiv: Pivot,
}

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.

anom: A::Real

1-norm of raw matrix (used in .rcond_tridiagonal()).

ipiv: Pivot

The pivot indices that define the permutation matrix P.

Trait Implementations

impl<A: Clone + Scalar> Clone for LUFactorizedTridiagonal<A> where
    A::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> 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.