Trait lax::solve::SolveImpl

pub trait SolveImpl: Scalar {
    fn solve(
        l: MatrixLayout,
        t: Transpose,
        a: &[Self],
        p: &Pivot,
        b: &mut [Self]
    ) -> Result<()>;
}

Helper trait to abstract *getrs LAPACK routines for implementing Lapack::solve

If the array has C layout, then it needs to be handled specially, since LAPACK expects a Fortran-layout array. Reinterpreting a C layout array as Fortran layout is equivalent to transposing it. So, we can handle the “no transpose” and “transpose” cases by swapping to “transpose” or “no transpose”, respectively. For the “Hermite” case, we can take advantage of the following:

$$ \begin{align*} A^H x &= b \\ \Leftrightarrow \overline{A^T} x &= b \\ \Leftrightarrow \overline{\overline{A^T} x} &= \overline{b} \\ \Leftrightarrow \overline{\overline{A^T}} \overline{x} &= \overline{b} \\ \Leftrightarrow A^T \overline{x} &= \overline{b} \end{align*} $$

So, we can handle this case by switching to “no transpose” (which is equivalent to transposing the array since it will be reinterpreted as Fortran layout) and applying the elementwise conjugate to x and b.

Required Methods

fn solve(
    l: MatrixLayout,
    t: Transpose,
    a: &[Self],
    p: &Pivot,
    b: &mut [Self]
) -> Result<()>

LAPACK correspondance

f32	f64	c32	c64
sgetrs	dgetrs	cgetrs	zgetrs

Implementations on Foreign Types

impl SolveImpl for f64

fn solve(
    l: MatrixLayout,
    t: Transpose,
    a: &[Self],
    ipiv: &Pivot,
    b: &mut [Self]
) -> Result<()>

impl SolveImpl for f32

fn solve(
    l: MatrixLayout,
    t: Transpose,
    a: &[Self],
    ipiv: &Pivot,
    b: &mut [Self]
) -> Result<()>

impl SolveImpl for c64

fn solve(
    l: MatrixLayout,
    t: Transpose,
    a: &[Self],
    ipiv: &Pivot,
    b: &mut [Self]
) -> Result<()>

impl SolveImpl for c32

fn solve(
    l: MatrixLayout,
    t: Transpose,
    a: &[Self],
    ipiv: &Pivot,
    b: &mut [Self]
) -> Result<()>

Implementors