ndarray_linalg/krylov/
mgs.rs

1//! Modified Gram-Schmit orthogonalizer
2
3use super::*;
4use crate::{generate::*, inner::*, norm::Norm};
5
6/// Iterative orthogonalizer using modified Gram-Schmit procedure
7#[derive(Debug, Clone)]
8pub struct MGS<A: Scalar> {
9    /// Dimension of base space
10    dim: usize,
11
12    /// Basis of spanned space
13    q: Vec<Array1<A>>,
14
15    /// Tolerance
16    tol: A::Real,
17}
18
19impl<A: Scalar + Lapack> MGS<A> {
20    /// Create an empty orthogonalizer
21    pub fn new(dim: usize, tol: A::Real) -> Self {
22        Self {
23            dim,
24            q: Vec::new(),
25            tol,
26        }
27    }
28}
29
30impl<A: Scalar + Lapack> Orthogonalizer for MGS<A> {
31    type Elem = A;
32
33    fn dim(&self) -> usize {
34        self.dim
35    }
36
37    fn len(&self) -> usize {
38        self.q.len()
39    }
40
41    fn tolerance(&self) -> A::Real {
42        self.tol
43    }
44
45    fn decompose<S>(&self, a: &mut ArrayBase<S, Ix1>) -> Array1<A>
46    where
47        S: DataMut<Elem = A>,
48    {
49        assert_eq!(a.len(), self.dim());
50        let mut coef = Array1::zeros(self.len() + 1);
51        for i in 0..self.len() {
52            let q = &self.q[i];
53            let c = q.inner(a);
54            azip!((a in &mut *a, &q in q) *a -= c * q);
55            coef[i] = c;
56        }
57        let nrm = a.norm_l2();
58        coef[self.len()] = A::from_real(nrm);
59        coef
60    }
61
62    fn coeff<S>(&self, a: ArrayBase<S, Ix1>) -> Array1<A>
63    where
64        A: Lapack,
65        S: Data<Elem = A>,
66    {
67        let mut a = a.into_owned();
68        self.decompose(&mut a)
69    }
70
71    fn append<S>(&mut self, a: ArrayBase<S, Ix1>) -> AppendResult<A>
72    where
73        A: Lapack,
74        S: Data<Elem = A>,
75    {
76        let mut a = a.into_owned();
77        self.div_append(&mut a)
78    }
79
80    fn div_append<S>(&mut self, a: &mut ArrayBase<S, Ix1>) -> AppendResult<A>
81    where
82        A: Lapack,
83        S: DataMut<Elem = A>,
84    {
85        let coef = self.decompose(a);
86        let nrm = coef[coef.len() - 1].re();
87        if nrm < self.tol {
88            // Linearly dependent
89            return AppendResult::Dependent(coef);
90        }
91        azip!((a in &mut *a) *a /= A::from_real(nrm));
92        self.q.push(a.to_owned());
93        AppendResult::Added(coef)
94    }
95
96    fn get_q(&self) -> Q<A> {
97        hstack(&self.q).unwrap()
98    }
99}
100
101/// Online QR decomposition using modified Gram-Schmit algorithm
102pub fn mgs<A, S>(
103    iter: impl Iterator<Item = ArrayBase<S, Ix1>>,
104    dim: usize,
105    rtol: A::Real,
106    strategy: Strategy,
107) -> (Q<A>, R<A>)
108where
109    A: Scalar + Lapack,
110    S: Data<Elem = A>,
111{
112    let mgs = MGS::new(dim, rtol);
113    qr(iter, mgs, strategy)
114}
ndarray_linalg/krylov/mgs.rs

ndarray_linalg/krylov/
mgs.rs
