faer-cholesky 0.9.0

Basic linear algebra routines
Documentation 
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use assert2::assert;
use dyn_stack::{DynStack, SizeOverflow, StackReq};
use faer_core::{
    inverse::invert_lower_triangular,
    mul::triangular::{self, BlockStructure},
    temp_mat_req, temp_mat_uninit, ComplexField, Entity, MatMut, MatRef, Parallelism,
};
use reborrow::*;

fn invert_lower_impl<E: ComplexField>(
    dst: MatMut<'_, E>,
    cholesky_factor: Option<MatRef<'_, E>>,
    parallelism: Parallelism,
    stack: DynStack,
) {
    // (L L.*).inv() = L.inv().* L.inv()
    //
    let cholesky_factor = match cholesky_factor {
        Some(cholesky_factor) => cholesky_factor,
        None => dst.rb(),
    };
    let n = cholesky_factor.nrows();

    let (mut tmp, _) = unsafe { temp_mat_uninit::<E>(n, n, stack) };
    let mut tmp = tmp.as_mut();

    invert_lower_triangular(tmp.rb_mut(), cholesky_factor, parallelism);

    triangular::matmul(
        dst,
        BlockStructure::TriangularLower,
        tmp.rb().adjoint(),
        BlockStructure::TriangularUpper,
        tmp.rb(),
        BlockStructure::TriangularLower,
        None,
        E::one(),
        parallelism,
    );
}

/// Computes the size and alignment of required workspace for computing the lower triangular part
/// of the inverse of a matrix out of place, given the Cholesky
/// decomposition.
pub fn invert_lower_req<E: Entity>(
    dimension: usize,
    parallelism: Parallelism,
) -> Result<StackReq, SizeOverflow> {
    let _ = parallelism;
    temp_mat_req::<E>(dimension, dimension)
}

/// Computes the size and alignment of required workspace for computing the lower triangular part
/// of the inverse of a matrix, given its Cholesky decomposition.
pub fn invert_lower_in_place_req<E: Entity>(
    dimension: usize,
    parallelism: Parallelism,
) -> Result<StackReq, SizeOverflow> {
    invert_lower_req::<E>(dimension, parallelism)
}

/// Computes the lower triangular part of the inverse of a matrix, given its Cholesky
/// decomposition, and stores the result in `cholesky_factor`.
///
/// # Panics
///
/// - Panics if `cholesky_factor` is not a square matrix.
/// - Panics if the provided memory in `stack` is insufficient.
#[track_caller]
pub fn invert_lower_in_place<E: ComplexField>(
    cholesky_factor: MatMut<'_, E>,
    parallelism: Parallelism,
    stack: DynStack,
) {
    assert!(cholesky_factor.nrows() == cholesky_factor.ncols());
    invert_lower_impl(cholesky_factor, None, parallelism, stack);
}

/// Computes the inverse of a matrix, given its partial pivoting LU decomposition,
/// and stores the result in `lu_factors`.
///
/// # Panics
///
/// - Panics if `cholesky_factor` is not a square matrix.
/// - Panics if the destination shape doesn't match the shape of the matrix.
/// - Panics if the provided memory in `stack` is insufficient.
#[track_caller]
pub fn invert_lower<E: ComplexField>(
    dst: MatMut<'_, E>,
    cholesky_factor: MatRef<'_, E>,
    parallelism: Parallelism,
    stack: DynStack,
) {
    assert!(cholesky_factor.nrows() == cholesky_factor.ncols());
    assert!((dst.nrows(), dst.ncols()) == (cholesky_factor.nrows(), cholesky_factor.ncols()));
    invert_lower_impl(dst, Some(cholesky_factor), parallelism, stack);
}