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
109
110
111
112
113
114
115
116
117
118
119
120

use crate::assert;
use crate::internal_prelude::*;
use linalg::matmul::triangular::BlockStructure;
pub fn inverse_scratch<I: Index, T: ComplexField>(
	dim: usize,
	par: Par,
) -> StackReq {
	_ = par;
	temp_mat_scratch::<T>(dim, dim)
}
#[track_caller]
pub fn inverse<I: Index, T: ComplexField>(
	out: MatMut<'_, T>,
	L: MatRef<'_, T>,
	U: MatRef<'_, T>,
	row_perm: PermRef<'_, I>,
	col_perm: PermRef<'_, I>,
	par: Par,
	stack: &mut MemStack,
) {
	let n = L.ncols();
	assert!(all(
		L.nrows() == n,
		L.ncols() == n,
		U.nrows() == n,
		U.ncols() == n,
		out.nrows() == n,
		out.ncols() == n,
		row_perm.len() == n,
	));
	let (mut tmp, _) = unsafe { temp_mat_uninit::<T, _, _>(n, n, stack) };
	let mut tmp = tmp.as_mat_mut();
	let mut out = out;
	linalg::triangular_inverse::invert_unit_lower_triangular(
		out.rb_mut(),
		L,
		par,
	);
	linalg::triangular_inverse::invert_upper_triangular(out.rb_mut(), U, par);
	linalg::matmul::triangular::matmul(
		tmp.rb_mut(),
		BlockStructure::Rectangular,
		Accum::Replace,
		out.rb(),
		BlockStructure::TriangularUpper,
		out.rb(),
		BlockStructure::UnitTriangularLower,
		one(),
		par,
	);
	with_dim!(N, n);
	let (row_perm, col_perm) = (
		col_perm.as_shape(N).bound_arrays().1,
		row_perm.as_shape(N).bound_arrays().1,
	);
	let tmp = tmp.rb().as_shape(N, N);
	let mut out = out.rb_mut().as_shape_mut(N, N);
	for j in N.indices() {
		for i in N.indices() {
			out[(i, j)] = tmp[(row_perm[i].zx(), col_perm[j].zx())].clone();
		}
	}
}
#[cfg(test)]
mod tests {
	use super::*;
	use crate::assert;
	use crate::stats::prelude::*;
	use crate::utils::approx::*;
	use dyn_stack::MemBuffer;
	use linalg::lu::full_pivoting::*;
	#[test]
	fn test_inverse() {
		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 mut LU = A.to_owned();
		let row_perm_fwd = &mut *vec![0usize; n];
		let row_perm_bwd = &mut *vec![0usize; n];
		let col_perm_fwd = &mut *vec![0usize; n];
		let col_perm_bwd = &mut *vec![0usize; n];
		let (_, row_perm, col_perm) = factor::lu_in_place(
			LU.as_mut(),
			row_perm_fwd,
			row_perm_bwd,
			col_perm_fwd,
			col_perm_bwd,
			Par::Seq,
			MemStack::new(&mut {
				MemBuffer::new(factor::lu_in_place_scratch::<usize, c64>(
					n,
					n,
					Par::Seq,
					default(),
				))
			}),
			default(),
		);
		let approx_eq = CwiseMat(ApproxEq::eps() * (n as f64));
		let mut A_inv = Mat::zeros(n, n);
		inverse::inverse(
			A_inv.as_mut(),
			LU.as_ref(),
			LU.as_ref(),
			row_perm,
			col_perm,
			Par::Seq,
			MemStack::new(&mut MemBuffer::new(inverse::inverse_scratch::<
				usize,
				c64,
			>(n, Par::Seq))),
		);
		assert!(& A_inv * & A ~ Mat::identity(n, n));
	}
}