faer 0.24.0

linear algebra library
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108

use crate::assert;
use crate::internal_prelude::*;
use linalg::matmul::triangular::BlockStructure;
pub fn reconstruct_scratch<I: Index, T: ComplexField>(
	dim: usize,
	par: Par,
) -> StackReq {
	_ = (dim, par);
	temp_mat_scratch::<T>(dim, dim)
}
#[track_caller]
pub fn reconstruct<I: Index, T: ComplexField>(
	out: MatMut<'_, T>,
	L: MatRef<'_, T>,
	perm: PermRef<'_, I>,
	par: Par,
	stack: &mut MemStack,
) {
	let mut out = out;
	let n = out.nrows();
	assert!(all(
		out.nrows() == n,
		out.ncols() == n,
		L.nrows() == n,
		L.ncols() == n,
	));
	let (mut tmp, _) = unsafe { temp_mat_uninit::<T, _, _>(n, n, stack) };
	let mut tmp = tmp.as_mat_mut();
	linalg::matmul::triangular::matmul(
		tmp.rb_mut(),
		BlockStructure::TriangularLower,
		Accum::Replace,
		L,
		BlockStructure::TriangularLower,
		L.adjoint(),
		BlockStructure::TriangularUpper,
		one(),
		par,
	);
	let p = perm.arrays().1;
	for j in 0..n {
		let jj = p[j].zx();
		for i in j..n {
			let ii = p[i].zx();
			if ii >= jj {
				out[(i, j)] = tmp[(ii, jj)].copy();
			} else {
				out[(i, j)] = tmp[(jj, ii)].conj();
			}
		}
	}
}
#[cfg(test)]
mod tests {
	use super::*;
	use crate::assert;
	use crate::stats::prelude::*;
	use crate::utils::approx::*;
	use dyn_stack::MemBuffer;
	use linalg::cholesky::llt_pivoting::*;
	#[test]
	fn test_reconstruct() {
		let rng = &mut StdRng::seed_from_u64(0);
		let n = 50;
		let A = CwiseMatDistribution {
			nrows: n,
			ncols: n,
			dist: ComplexDistribution::new(StandardNormal, StandardNormal),
		}
		.rand::<Mat<c64>>(rng);
		let A = &A * A.adjoint();
		let mut L = A.to_owned();
		let perm_fwd = &mut *vec![0usize; n];
		let perm_bwd = &mut *vec![0usize; n];
		let (_, perm) = factor::cholesky_in_place(
			L.as_mut(),
			perm_fwd,
			perm_bwd,
			Par::Seq,
			MemStack::new(&mut {
				MemBuffer::new(factor::cholesky_in_place_scratch::<usize, c64>(
					n,
					Par::Seq,
					default(),
				))
			}),
			default(),
		)
		.unwrap();
		let approx_eq = CwiseMat(ApproxEq::eps() * (n as f64));
		let mut A_rec = Mat::zeros(n, n);
		reconstruct::reconstruct(
			A_rec.as_mut(),
			L.as_ref(),
			perm,
			Par::Seq,
			MemStack::new(&mut MemBuffer::new(
				reconstruct::reconstruct_scratch::<usize, c64>(n, Par::Seq),
			)),
		);
		for j in 0..n {
			for i in 0..j {
				A_rec[(i, j)] = A_rec[(j, i)].conj();
			}
		}
		assert!(A_rec ~ A);
	}
}