Function matmul_with_conj

pub fn matmul_with_conj<E>(
    acc: impl As2DMut<E>,
    acc_structure: BlockStructure,
    lhs: impl As2D<E>,
    lhs_structure: BlockStructure,
    conj_lhs: Conj,
    rhs: impl As2D<E>,
    rhs_structure: BlockStructure,
    conj_rhs: Conj,
    alpha: Option<E>,
    beta: E,
    parallelism: Parallelism<'_>,
)
where
    E: ComplexField,

Computes the matrix product [alpha * acc] + beta * lhs * rhs (while optionally conjugating either or both of the input matrices) and stores the result in acc.

Performs the operation:

• acc = beta * Op_lhs(lhs) * Op_rhs(rhs) if alpha is None (in this case, the preexisting values in acc are not read, so it is allowed to be a view over uninitialized values if E: Copy),
• acc = alpha * acc + beta * Op_lhs(lhs) * Op_rhs(rhs) if alpha is Some(_),

The left hand side and right hand side may be interpreted as triangular depending on the given corresponding matrix structure.

For the destination matrix, the result is:

• fully computed if the structure is rectangular,
• only the triangular half (including the diagonal) is computed if the structure is triangular,
• only the strict triangular half (excluding the diagonal) is computed if the structure is strictly triangular or unit triangular.

Op_lhs is the identity if conj_lhs is Conj::No, and the conjugation operation if it is Conj::Yes.
Op_rhs is the identity if conj_rhs is Conj::No, and the conjugation operation if it is Conj::Yes.

Panics

Panics if the matrix dimensions are not compatible for matrix multiplication.
i.e.

• acc.nrows() == lhs.nrows()
• acc.ncols() == rhs.ncols()
• lhs.ncols() == rhs.nrows()

Additionally, matrices that are marked as triangular must be square, i.e., they must have the same number of rows and columns.

Example

use faer::{
    linalg::matmul::triangular::{matmul_with_conj, BlockStructure},
    mat, unzipped, zipped, Conj, Mat, Parallelism,
};

let lhs = mat![[0.0, 2.0], [1.0, 3.0]];
let rhs = mat![[4.0, 6.0], [5.0, 7.0]];

let mut acc = Mat::<f64>::zeros(2, 2);
let target = mat![
    [
        2.5 * (lhs.read(0, 0) * rhs.read(0, 0) + lhs.read(0, 1) * rhs.read(1, 0)),
        0.0,
    ],
    [
        2.5 * (lhs.read(1, 0) * rhs.read(0, 0) + lhs.read(1, 1) * rhs.read(1, 0)),
        2.5 * (lhs.read(1, 0) * rhs.read(0, 1) + lhs.read(1, 1) * rhs.read(1, 1)),
    ],
];

matmul_with_conj(
    acc.as_mut(),
    BlockStructure::TriangularLower,
    lhs.as_ref(),
    BlockStructure::Rectangular,
    Conj::No,
    rhs.as_ref(),
    BlockStructure::Rectangular,
    Conj::No,
    None,
    2.5,
    Parallelism::None,
);

zipped!(acc.as_ref(), target.as_ref())
    .for_each(|unzipped!(acc, target)| assert!((acc.read() - target.read()).abs() < 1e-10));