totsu_core 0.1.1

A first-order conic linear program solver for convex optimization.
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
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156

//! Linear operator

use crate::solver::LinAlg;

/// Linear operator trait.
/// 
/// <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
/// <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
/// 
/// Expresses a linear operator \\(K: \mathbb{R}^n \to \mathbb{R}^m\\) (or a matrix \\(K \in \mathbb{R}^{m \times n}\\)).
pub trait Operator<L: LinAlg>
{
    /// Size of \\(K\\).
    /// 
    /// Returns a tuple of \\(m\\) and \\(n\\).
    fn size(&self) -> (usize, usize);

    /// Calculate \\(\alpha K x + \beta y\\).
    /// 
    /// * `alpha` is a scalar \\(\alpha\\).
    /// * `x` is a vector \\(x\\).
    ///   The length of `x` shall be \\(n\\).
    /// * `beta` is a scalar \\(\beta\\).
    /// * `y` is a vector \\(y\\) before entry,
    ///   \\(\alpha K x + \beta y\\) on exit.
    ///   The length of `y` shall be \\(m\\).
    fn op(&self, alpha: L::F, x: &L::Sl, beta: L::F, y: &mut L::Sl);

    /// Calculate \\(\alpha K^T x + \beta y\\).
    /// 
    /// * `alpha` is a scalar \\(\alpha\\).
    /// * `x` is a vector \\(x\\).
    ///   The length of `x` shall be \\(m\\).
    /// * `beta` is a scalar \\(\beta\\).
    /// * `y` is a vector \\(y\\) before entry,
    ///   \\(\alpha K^T x + \beta y\\) on exit.
    ///   The length of `y` shall be \\(n\\).
    /// 
    /// The calculation shall be equivalent to the general reference implementation shown below.
    /// ```
    /// # use num_traits::{Zero, One};
    /// # use totsu_core::solver::{SliceLike, Operator};
    /// # use totsu_core::{LinAlgEx, splitm, splitm_mut};
    /// # struct OpRef<L>(std::marker::PhantomData<L>);
    /// impl<L: LinAlgEx> Operator<L> for OpRef<L>
    /// {
    /// #   fn size(&self) -> (usize, usize) {(0, 0)}
    /// #   fn op(&self, alpha: L::F, x: &L::Sl, beta: L::F, y: &mut L::Sl) {}
    /// #   fn absadd_cols(&self, tau: &mut L::Sl) {}
    /// #   fn absadd_rows(&self, sigma: &mut L::Sl) {}
    ///     fn trans_op(&self, alpha: L::F, x: &L::Sl, beta: L::F, y: &mut L::Sl)
    ///     {
    ///         let f0 = L::F::zero();
    ///         let f1 = L::F::one();
    ///         let (m, n) = self.size();
    /// 
    ///         let mut col_v = std::vec![f0; m];
    ///         let mut row_v = std::vec![f0; n];
    ///         let mut col = L::Sl::new_mut(&mut col_v);
    ///         let mut row = L::Sl::new_mut(&mut row_v);
    /// 
    ///         for c in 0.. n {
    ///             row.set(c, f1);
    ///             self.op(f1, &row, f0, &mut col);
    ///             row.set(c, f0);
    /// 
    ///             splitm_mut!(y, (_y_done; c), (yc; 1));
    ///             L::transform_ge(true, m, 1, alpha, &col, x, beta, &mut yc);
    ///         }
    ///     }
    /// }
    /// ```
    fn trans_op(&self, alpha: L::F, x: &L::Sl, beta: L::F, y: &mut L::Sl);

    /// Calculate \\(\left[ \tau_j + \sum_{i=0}^{m-1}|K_{ij}| \right]_{j=0,...,n-1}\\).
    /// 
    /// * `tau` is a vector \\(\tau\\) before entry,
    ///   \\(\left[ \tau_j + \sum_{i=0}^{m-1}|K_{ij}| \right]_{j=0,...,n-1}\\) on exit.
    ///   The length of `tau` shall be \\(n\\).
    /// 
    /// The calculation shall be equivalent to the general reference implementation shown below.
    /// ```
    /// # use num_traits::{Zero, One};
    /// # use totsu_core::solver::{SliceLike, LinAlg, Operator};
    /// # struct OpRef<L>(std::marker::PhantomData<L>);
    /// impl<L: LinAlg> Operator<L> for OpRef<L>
    /// {
    /// #   fn size(&self) -> (usize, usize) {(0, 0)}
    /// #   fn op(&self, alpha: L::F, x: &L::Sl, beta: L::F, y: &mut L::Sl) {}
    /// #   fn trans_op(&self, alpha: L::F, x: &L::Sl, beta: L::F, y: &mut L::Sl) {}
    /// #   fn absadd_rows(&self, sigma: &mut L::Sl) {}
    ///     fn absadd_cols(&self, tau: &mut L::Sl)
    ///     {
    ///         let f0 = L::F::zero();
    ///         let f1 = L::F::one();
    ///         let (m, n) = self.size();
    /// 
    ///         let mut col_v = std::vec![f0; m];
    ///         let mut row_v = std::vec![f0; n];
    ///         let mut col = L::Sl::new_mut(&mut col_v);
    ///         let mut row = L::Sl::new_mut(&mut row_v);
    /// 
    ///         for c in 0.. tau.len() {
    ///             row.set(c, f1);
    ///             self.op(f1, &row, f0, &mut col);
    ///             row.set(c, f0);
    /// 
    ///             let val_tau = tau.get(c) + L::abssum(&col, 1);
    ///             tau.set(c, val_tau);
    ///         }
    ///     }
    /// }
    /// ```
    fn absadd_cols(&self, tau: &mut L::Sl);

    /// Calculate \\(\left[ \sigma_i + \sum_{j=0}^{n-1}|K_{ij}| \right]_{i=0,...,m-1}\\).
    /// 
    /// * `sigma` is a vector \\(\sigma\\) before entry,
    ///   \\(\left[ \sigma_i + \sum_{j=0}^{n-1}|K_{ij}| \right]_{i=0,...,m-1}\\) on exit.
    ///   The length of `sigma` shall be \\(m\\).
    /// 
    /// The calculation shall be equivalent to the general reference implementation shown below.
    /// ```
    /// # use num_traits::{Zero, One};
    /// # use totsu_core::solver::{SliceLike, LinAlg, Operator};
    /// # struct OpRef<L>(std::marker::PhantomData<L>);
    /// impl<L: LinAlg> Operator<L> for OpRef<L>
    /// {
    /// #   fn size(&self) -> (usize, usize) {(0, 0)}
    /// #   fn op(&self, alpha: L::F, x: &L::Sl, beta: L::F, y: &mut L::Sl) {}
    /// #   fn trans_op(&self, alpha: L::F, x: &L::Sl, beta: L::F, y: &mut L::Sl) {}
    /// #   fn absadd_cols(&self, tau: &mut L::Sl) {}
    ///     fn absadd_rows(&self, sigma: &mut L::Sl)
    ///     {
    ///         let f0 = L::F::zero();
    ///         let f1 = L::F::one();
    ///         let (m, n) = self.size();
    /// 
    ///         let mut col_v = std::vec![f0; m];
    ///         let mut row_v = std::vec![f0; n];
    ///         let mut col = L::Sl::new_mut(&mut col_v);
    ///         let mut row = L::Sl::new_mut(&mut row_v);
    /// 
    ///         for r in 0.. sigma.len() {
    ///             col.set(r, f1);
    ///             self.trans_op(f1, &col, f0, &mut row);
    ///             col.set(r, f0);
    /// 
    ///             let val_sigma = sigma.get(r) + L::abssum(&row, 1);
    ///             sigma.set(r, val_sigma);
    ///         }
    ///     }
    /// }
    /// ```
    fn absadd_rows(&self, sigma: &mut L::Sl);
}