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use crate::{
linalg::{
cholesky::llt::CholeskyError, matmul::triangular::BlockStructure, temp_mat_req,
temp_mat_uninit,
},
perm::PermRef,
prelude::*,
ComplexField, Index, Parallelism, RealField, SignedIndex,
};
use dyn_stack::{PodStack, SizeOverflow, StackReq};
use reborrow::*;
pub mod compute {
use super::*;
use equator::assert;
#[derive(Copy, Clone, Debug)]
#[non_exhaustive]
pub struct PivLltParams {
pub blocksize: usize,
}
impl Default for PivLltParams {
#[inline]
fn default() -> Self {
Self { blocksize: 128 }
}
}
#[derive(Copy, Clone, Debug)]
#[non_exhaustive]
pub struct PivLltInfo {
pub rank: usize,
}
#[inline]
pub fn cholesky_in_place_req<I: Index, E: ComplexField>(
dim: usize,
parallelism: Parallelism,
) -> Result<StackReq, SizeOverflow> {
_ = parallelism;
temp_mat_req::<E::Real>(dim, 2)
}
#[track_caller]
pub fn cholesky_in_place<'out, I: Index, E: ComplexField>(
a: MatMut<'_, E>,
perm: &'out mut [I],
perm_inv: &'out mut [I],
parallelism: Parallelism,
stack: &mut PodStack,
params: PivLltParams,
) -> Result<(PivLltInfo, PermRef<'out, I>), CholeskyError> {
assert!(a.nrows() == a.ncols());
let n = a.nrows();
assert!(n <= I::Signed::MAX.zx());
let mut rank = n;
'exit: {
if n > 0 {
let mut a = a;
for (i, p) in perm.iter_mut().enumerate() {
*p = I::truncate(i);
}
let (work1, stack) = temp_mat_uninit::<E::Real>(n, 1, stack);
let (work2, _) = temp_mat_uninit::<E::Real>(n, 1, stack);
let mut dot_products = work1.col_mut(0);
let mut diagonals = work2.col_mut(0);
let mut ajj = E::Real::faer_zero();
let mut pvt = 0usize;
for i in 0..n {
let aii = a.read(i, i).faer_real();
if aii < E::Real::faer_zero() || aii.faer_is_nan() {
return Err(CholeskyError {
non_positive_definite_minor: 0,
});
}
if aii > ajj {
ajj = aii;
pvt = i;
}
}
let tol = E::Real::faer_epsilon()
.faer_mul(E::Real::faer_from_f64(n as f64))
.faer_mul(ajj);
let mut k = 0usize;
while k < n {
let bs = Ord::min(n - k, params.blocksize);
for i in k..n {
dot_products.write(i, E::Real::faer_zero());
}
for j in k..k + bs {
if j == k {
for i in j..n {
diagonals.write(i, a.read(i, i).faer_real());
}
} else {
for i in j..n {
dot_products.write(
i,
dot_products.read(i).faer_add(a.read(i, j - 1).faer_abs2()),
);
diagonals.write(
i,
a.read(i, i).faer_real().faer_sub(dot_products.read(i)),
);
}
}
if j > 0 {
pvt = j;
ajj = E::Real::faer_zero();
for i in j..n {
let aii = diagonals.read(i).faer_real();
if aii.faer_is_nan() {
return Err(CholeskyError {
non_positive_definite_minor: j,
});
}
if aii > ajj {
pvt = i;
ajj = aii;
}
}
if ajj < tol {
rank = j;
a.write(j, j, E::faer_from_real(ajj));
break 'exit;
}
}
if pvt != j {
a.write(pvt, pvt, a.read(j, j));
crate::perm::swap_rows_idx(a.rb_mut().get_mut(.., ..j), j, pvt);
crate::perm::swap_cols_idx(a.rb_mut().get_mut(pvt + 1.., ..), j, pvt);
unsafe {
zipped_rw!(
a.rb().get(j + 1..pvt, j).const_cast(),
a.rb().get(pvt, j + 1..pvt).const_cast().transpose_mut(),
)
}
.for_each(|unzipped!(mut a, mut b)| {
let a_ = a.read().faer_conj();
let b_ = b.read().faer_conj();
a.write(b_);
b.write(a_);
});
a.write(pvt, j, a.read(pvt, j).faer_conj());
let tmp = dot_products.read(j);
dot_products.write(j, dot_products.read(pvt));
dot_products.write(pvt, tmp);
perm.swap(j, pvt);
}
ajj = ajj.faer_sqrt();
a.write(j, j, E::faer_from_real(ajj));
unsafe {
crate::linalg::matmul::matmul(
a.rb().get(j + 1.., j).const_cast(),
a.rb().get(j + 1.., k..j),
a.rb().get(j, k..j).adjoint(),
Some(E::faer_one()),
E::faer_one().faer_neg(),
parallelism,
);
}
let ajj = ajj.faer_inv();
zipped_rw!(a.rb_mut().get_mut(j + 1.., j))
.for_each(|unzipped!(mut x)| x.write(x.read().faer_scale_real(ajj)));
}
crate::linalg::matmul::triangular::matmul(
unsafe { a.rb().get(k + bs.., k + bs..).const_cast() },
BlockStructure::TriangularLower,
a.rb().get(k + bs.., k..k + bs),
BlockStructure::Rectangular,
a.rb().get(k + bs.., k..k + bs).adjoint(),
BlockStructure::Rectangular,
Some(E::faer_one()),
E::faer_one().faer_neg(),
parallelism,
);
k += bs;
}
rank = n;
}
}
for (i, p) in perm.iter().enumerate() {
perm_inv[p.zx()] = I::truncate(i);
}
unsafe {
Ok((
PivLltInfo { rank },
PermRef::new_unchecked(perm, perm_inv, n),
))
}
}
}