mbd 0.1.1

Rust implementation of the modified band depth that also compiles to WASM.
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

mod utils;

use wasm_bindgen::prelude::*;

// When the `wee_alloc` feature is enabled, use `wee_alloc` as the global
// allocator.
#[cfg(feature = "wee_alloc")]
#[global_allocator]
static ALLOC: wee_alloc::WeeAlloc = wee_alloc::WeeAlloc::INIT;

#[wasm_bindgen]
#[derive(Debug, PartialEq)]
pub struct ModifiedBandDepth {
    num_samples: usize,
    num_timepoints: usize,
    sorted_matrix: Vec<f32>, // column major
}

#[wasm_bindgen]
impl ModifiedBandDepth {
    /// Constructs the modified band depth from a contiguous row-major `data_matrix`.
    /// This means that each row of the matrix represents one functional.
    pub fn from_data_matrix(rows: usize, timepoints: usize, data_matrix: &[f32]) -> Self {
        let mut sorted_matrix = Vec::with_capacity(rows * timepoints);
        for j in 0..timepoints {
            for i in 0..rows {
                sorted_matrix.push(data_matrix[i * timepoints + j]);
            }
            sorted_matrix
                .chunks_mut(rows)
                .for_each(|c| c.sort_by(|a, b| a.partial_cmp(b).unwrap()));
        }
        Self {
            num_samples: rows,
            num_timepoints: timepoints,
            sorted_matrix,
        }
    }

    /// Computes the modified band depth for a given `sample`.
    ///
    /// # Example
    /// ```
    /// let data_matrix = [
    ///     4.0, 5.0, 6.0,
    ///     1.0, 2.0, 3.0
    /// ];
    /// let mbd = mbd::ModifiedBandDepth::from_data_matrix(2, 3, &data_matrix);
    /// assert_eq!(mbd.query(&[2.0, 3.0, 4.0]), 1.0);
    /// assert_eq!(mbd.query(&[5.0, 6.0, 7.0]), 0.0);
    /// ```
    pub fn query(&self, sample: &[f32]) -> f32 {
        debug_assert_eq!(sample.len(), self.num_timepoints);
        let mut count = 0;
        for (sorted_ys, &v) in self
            .sorted_matrix
            .chunks(self.num_samples)
            .zip(sample.iter())
        {
            let (lt, eq, gt) = partition(sorted_ys, v);
            count += lt * eq + eq * gt + lt * gt + binomial_choose_2(eq);
        }
        count as f32 / (self.num_timepoints * binomial_choose_2(self.num_samples)) as f32
    }
}

impl ModifiedBandDepth {
    /// Constructs the modified band depth from a set of `functionals`.
    pub fn from_samples(functionals: &[Vec<f32>]) -> Self {
        let num_samples = functionals.len();
        let num_timepoints = functionals.first().unwrap().len();
        let mut data_matrix = Vec::with_capacity(num_samples * num_timepoints);
        for x in 0..num_timepoints {
            for f in functionals {
                data_matrix.push(f[x]);
            }
            data_matrix
                .chunks_mut(num_samples)
                .for_each(|c| c.sort_by(|a, b| a.partial_cmp(b).unwrap()));
        }
        Self {
            num_samples,
            num_timepoints,
            sorted_matrix: data_matrix,
        }
    }
}

/// Computes the number of two-bands
fn binomial_choose_2(from: usize) -> usize {
    match from >= 2 {
        true => ((from * from) - from) / 2,
        false => 0,
    }
}

/// Counts how many elements are `(smaller, equal, larger)` to x
fn partition(sorted_ys: &[f32], x: f32) -> (usize, usize, usize) {
    let lt = sorted_ys.partition_point(|&y| y < x);
    let eq = sorted_ys[lt..].partition_point(|&y| y <= x);
    let gt = sorted_ys.len() - lt - eq;
    (lt, eq, gt)
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_binomial_choose_2() {
        assert_eq!(binomial_choose_2(5), 10);
        assert_eq!(binomial_choose_2(2), 1);
        assert_eq!(binomial_choose_2(3), 3);
        assert_eq!(binomial_choose_2(10_000), 49_995_000);
        assert_eq!(binomial_choose_2(10_001), 50_005_000);
    }

    #[test]
    fn test_partition() {
        let seq = [1.0, 1.0, 2.0, 3.0, 4.0, 4.0, 4.0, 5.0, 8.0, 9.0];
        assert_eq!(partition(&seq, 0.0), (0, 0, 10));
        assert_eq!(partition(&seq, 1.0), (0, 2, 8));
        assert_eq!(partition(&seq, 2.0), (2, 1, 7));
        assert_eq!(partition(&seq, 3.0), (3, 1, 6));
        assert_eq!(partition(&seq, 4.0), (4, 3, 3));
        assert_eq!(partition(&seq, 5.0), (7, 1, 2));
        assert_eq!(partition(&seq, 6.0), (8, 0, 2));
        assert_eq!(partition(&seq, 7.0), (8, 0, 2));
        assert_eq!(partition(&seq, 8.0), (8, 1, 1));
        assert_eq!(partition(&seq, 9.0), (9, 1, 0));
        assert_eq!(partition(&seq, 10.0), (10, 0, 0));
    }

    #[test]
    fn test_from_samples() {
        let data = vec![vec![4.0, 5.0, 6.0], vec![1.0, 2.0, 3.0]];
        let mbd = ModifiedBandDepth::from_samples(&data);
        assert_eq!(
            mbd,
            ModifiedBandDepth {
                num_samples: 2,
                num_timepoints: 3,
                sorted_matrix: vec![1.0, 4.0, 2.0, 5.0, 3.0, 6.0],
            }
        );
    }

    #[test]
    fn test_fully_contained() {
        let data = vec![vec![4.0, 5.0, 6.0], vec![1.0, 2.0, 3.0]];
        let mbd = ModifiedBandDepth::from_samples(&data);
        assert_eq!(mbd.query(&[2.0, 3.0, 4.0]), 1.0);
    }
}