mc64 0.1.1

Sparse matrix scalings
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
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243

use crate::tests::{gen_random_sym, gen_random_unsym, MatrixType};
use crate::{hungarian_scale_sym, hungarian_scale_unsym, HungarianInform, HungarianOptions};
use spral::random::{random_integer, INITIAL_SEED};

/// Test [hungarian_scaling_sym] with random matrices.
#[test]
fn test_hungarian_sym_random() {
    const MAX_N: usize = 1000;
    const MAX_NZ: usize = 1_000_000;
    const N_PROB: usize = 100;
    const ERR_TOL: f64 = 1e-10;

    let mut a = MatrixType {
        n: 0,
        m: 0,
        ptr: vec![0; MAX_N + 1],
        row: vec![0; 2 * MAX_NZ],
        val: vec![0.0; 2 * MAX_NZ],
    };
    let mut scaling = vec![0.0; MAX_N];
    let mut match_result = vec![0; MAX_N];
    let mut rmax = vec![0.0; MAX_N];
    let mut cnt = vec![0; MAX_N];

    let options = HungarianOptions::default();
    let mut inform = HungarianInform::default();

    let mut state = INITIAL_SEED;

    for prblm in 1..=N_PROB {
        // Generate parameters
        a.n = random_integer(&mut state, MAX_N);
        if prblm < 21 {
            a.n = prblm;
        } // check very small problems
        let mut i = a.n.pow(2) / 10 - a.n;
        i = usize::max(0, i);
        let nza = a.n + random_integer(&mut state, i);

        print!(" - no. {} n = {} nza = {}...", prblm, a.n, nza);

        assert!(
            a.n <= MAX_N,
            "bad random matrix: n = {} > max_n = {}",
            a.n,
            MAX_N
        );
        assert!(
            nza <= MAX_NZ,
            "bad random matrix: nza = {} > max_nz = {}",
            nza,
            MAX_NZ
        );

        gen_random_sym(&mut a, nza, &mut state, None);

        // Call scaling
        hungarian_scale_sym(
            a.n,
            &a.ptr,
            &a.row,
            &a.val,
            &mut scaling,
            &options,
            &mut inform,
            Some(&mut match_result),
        );
        assert!(inform.flag >= 0, "returned inform.flag = {}", inform.flag);

        // Ensure each row and column are matched
        cnt.fill(0);
        for i in 0..a.n {
            let j = match_result[i] as usize;
            assert!(j != 0 && j <= a.n, "match({}) = {}", i, j); // TODO: C
            cnt[j - 1] += 1;
            // TODO: check a.row[]
            if !a.row[a.ptr[j - 1]..a.ptr[j]].iter().any(|&k| k == i + 1)
                && !a.row[a.ptr[i]..a.ptr[i + 1]].iter().any(|&k| k == j)
            {
                panic!("matched on ({},{}) but no such entry", i + 1, j);
            }
        }
        assert!(!cnt.iter().any(|&c| c != 1), "mismatched row");

        // Ensure all scaled entries are <= 1.0 and each row/col has an entry at 1
        rmax.fill(0.0);
        for i in 0..a.n {
            let mut cmax = 0.0;
            for j in a.ptr[i]..a.ptr[i + 1] {
                let v = (scaling[i] * a.val[j] * scaling[a.row[j] - 1]).abs();
                if v >= 1.0 + ERR_TOL {
                    panic!("scaled entry = {:.4e}", v);
                }
                cmax = f64::max(cmax, v);
                rmax[a.row[j] - 1] = f64::max(rmax[a.row[j] - 1], v);
            }
            rmax[i] = f64::max(rmax[i], cmax);
        }

        for (i, &r) in rmax.iter().enumerate().take(a.n) {
            if r < 1.0 - ERR_TOL {
                panic!("rmax({}) = {:.4e}", i + 1, r);
            }
        }
    }
}

/// Test [hungarian_scaling_unsym] with random matrices.
#[test]
fn test_hungarian_unsym_random() {
    const MAX_N: usize = 1000;
    const MAX_NZ: usize = 1_000_000;
    const N_PROB: usize = 100;
    const ERR_TOL: f64 = 1e-10;

    let mut a = MatrixType {
        n: 0,
        m: 0,
        ptr: vec![0; MAX_N + 1],
        row: vec![0; 2 * MAX_NZ],
        val: vec![0.0; 2 * MAX_NZ],
    };
    let mut rscaling = vec![0.0; MAX_N];
    let mut cscaling = vec![0.0; MAX_N];
    let mut match_result = vec![0; MAX_N];
    let mut rmax = vec![0.0; MAX_N];
    let mut cnt = vec![0; MAX_N];

    let options = HungarianOptions::default();
    let mut inform = HungarianInform::default();

    let mut state = INITIAL_SEED;

    for prblm in 1..=N_PROB {
        // Generate parameters
        a.n = random_integer(&mut state, MAX_N);
        a.m = random_integer(&mut state, MAX_N);
        if random_integer(&mut state, 2) == 1 {
            a.m = a.n; // 50% chance of unsym vs rect
        }
        if prblm < 21 {
            a.n = prblm; // check very small problems
            a.m = prblm;
        }
        let mut i = a.m * a.n / 2 - usize::max(a.m, a.n);
        i = usize::max(0, i);
        let nza = usize::max(a.m, a.n) + random_integer(&mut state, i);

        print!(" - no. {} m = {} n = {} nza = {}...", prblm, a.m, a.n, nza);

        assert!(
            a.n <= MAX_N,
            "bad random matrix: n = {} > max_n = {}",
            a.n,
            MAX_N
        );
        assert!(
            a.m <= MAX_N,
            "bad random matrix: m = {} > max_n = {}",
            a.m,
            MAX_N
        );
        assert!(
            nza <= MAX_NZ,
            "bad random matrix: nza = {} > max_nz = {}",
            nza,
            MAX_NZ
        );

        gen_random_unsym(&mut a, nza, &mut state);

        // Call scaling
        hungarian_scale_unsym(
            a.m,
            a.n,
            &a.ptr,
            &a.row,
            &a.val,
            &mut rscaling,
            &mut cscaling,
            &options,
            &mut inform,
            Some(&mut match_result),
        );
        assert!(inform.flag >= 0, "returned inform.flag = {}", inform.flag);

        // Ensure each row and column are matched [and on an entry that exists]
        let mut nmatch = 0;
        cnt.fill(0);
        for i in 0..a.m {
            let j = match_result[i] as usize;
            assert!(j != 0 && j <= a.n, "match({}) = {}", i, j); // TODO: C
            if j != 0 {
                cnt[j - 1] += 1;
                nmatch += 1;
                // TODO: check range
                if !a.row[a.ptr[j - 1]..a.ptr[j]].iter().any(|&k| k == i + 1) {
                    panic!("matched on ({},{}) but no such entry", i + 1, j);
                }
            }
        }
        if nmatch != usize::min(a.m, a.n) {
            panic!("Only matched {} in {}x{} matrix", nmatch, a.m, a.n);
        }
        if cnt.iter().take(a.m).any(|&c| c > 1) {
            panic!("mismatched row");
        }

        // Ensure all scaled entries are <= 1.0 and each row/col has an entry at 1
        rmax.fill(0.0);
        for i in 0..a.n {
            let mut cmax = 0.0;
            for j in a.ptr[i]..a.ptr[i + 1] {
                let v = (cscaling[i] * a.val[j] * rscaling[a.row[j] - 1]).abs();
                if v >= 1.0 + ERR_TOL {
                    panic!("scaled entry = {:.4e}", v);
                }
                cmax = f64::max(cmax, v);
                rmax[a.row[j] - 1] = f64::max(rmax[a.row[j] - 1], v);
            }
            if cmax < 1.0 - ERR_TOL && a.ptr[i] != a.ptr[i + 1] {
                panic!("cmax({}) = {:.4e}", i + 1, cmax);
            }
        }

        for i in 0..a.m {
            if rmax[i] < 1.0 - ERR_TOL {
                // Check non-empty row before we complain
                let rcnt = (0..a.n)
                    .map(|j| {
                        a.row[a.ptr[j]..a.ptr[j + 1]]
                            .iter()
                            .filter(|&&k| a.row[k] == i + 1)
                            .count()
                    })
                    .sum::<usize>();
                if rcnt > 0 {
                    panic!("rmax({}) = {:.4e}", i + 1, rmax[i]);
                }
            }
        }
    }
}