kneed 1.0.0

Pure rust implementation of Knee-point detection
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

#![allow(dead_code)]

use crate::knee_locator::{ValidCurve, ValidDirection};

type Shape = (ValidDirection, ValidCurve);

/// Detect the direction and curve type of the line.
fn find_shape(x: &[f64], y: &[f64]) -> Shape {
    assert_eq!(x.len(), y.len(), "x and y must have the same length");

    // Perform polynomial fitting
    let n = x.len() as f64;
    let sum_x: f64 = x.iter().sum();
    let sum_y: f64 = y.iter().sum();
    let sum_xy: f64 = x.iter().zip(y.iter()).map(|(&xi, &yi)| xi * yi).sum();
    let sum_xx: f64 = x.iter().map(|&xi| xi * xi).sum();

    let slope = (n * sum_xy - sum_x * sum_y) / (n * sum_xx - sum_x * sum_x);
    let intercept = (sum_y - slope * sum_x) / n;

    // Calculate indices for the middle 60% of the data
    let x1 = (x.len() as f64 * 0.2) as usize;
    let x2 = (x.len() as f64 * 0.8) as usize;

    // Calculate q
    let middle_x = &x[x1..x2];
    let middle_y = &y[x1..x2];
    let middle_y_mean: f64 = middle_y.iter().sum::<f64>() / middle_y.len() as f64;
    let middle_fitted_y_mean: f64 = middle_x
        .iter()
        .map(|&xi| xi * slope + intercept)
        .sum::<f64>()
        / middle_x.len() as f64;
    let q = middle_y_mean - middle_fitted_y_mean;

    // Use a small epsilon value to handle floating-point imprecision
    const EPSILON: f64 = 1e-10;

    // Determine direction and curve type
    if slope.abs() < EPSILON {
        // If slope is very close to zero, classify as decreasing and convex
        (ValidDirection::Decreasing, ValidCurve::Convex)
    } else if slope > 0.0 {
        if q >= 0.0 {
            (ValidDirection::Increasing, ValidCurve::Concave)
        } else {
            (ValidDirection::Increasing, ValidCurve::Convex)
        }
    } else if q > 0.0 {
        (ValidDirection::Decreasing, ValidCurve::Concave)
    } else {
        (ValidDirection::Decreasing, ValidCurve::Convex)
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    #[cfg(feature = "testing")]
    use crate::data_generator::DataGenerator;
    use crate::knee_locator::{ValidCurve, ValidDirection};

    #[test]
    fn test_curve_and_direction() {
        // Test case 1
        let x1 = vec![1.0, 2.0, 3.0, 4.0, 5.0];
        let y1 = vec![1.0, 3.0, 6.0, 10.0, 15.0];
        assert_eq!(
            find_shape(&x1, &y1),
            (ValidDirection::Increasing, ValidCurve::Convex)
        );

        // Test case 2
        let x2 = vec![1.0, 2.0, 3.0, 4.0, 5.0];
        let y2 = vec![1.0, 1.5, 1.8, 1.9, 2.0];
        assert_eq!(
            find_shape(&x2, &y2),
            (ValidDirection::Increasing, ValidCurve::Concave)
        );

        // Test case 3
        let x3 = vec![1.0, 2.0, 3.0, 4.0, 5.0];
        let y3 = vec![15.0, 10.0, 6.0, 3.0, 1.0];
        assert_eq!(
            find_shape(&x3, &y3),
            (ValidDirection::Decreasing, ValidCurve::Convex)
        );

        // Test case 4
        let x4 = vec![1.0, 2.0, 3.0, 4.0, 5.0];
        let y4 = vec![2.0, 1.9, 1.8, 1.5, 1.0];
        assert_eq!(
            find_shape(&x4, &y4),
            (ValidDirection::Decreasing, ValidCurve::Concave)
        );

        // Test case 5
        let x5 = vec![1.0, 2.0, 3.0, 4.0, 5.0];
        let y5 = vec![1.0, 2.0, 3.0, 4.0, 5.0];
        assert_eq!(
            find_shape(&x5, &y5),
            (ValidDirection::Increasing, ValidCurve::Concave)
        );

        // Test case 6
        let x6 = vec![1.0, 2.0, 3.0, 4.0, 5.0];
        let y6 = vec![5.0, 4.0, 3.0, 2.0, 1.0];
        assert_eq!(
            find_shape(&x6, &y6),
            (ValidDirection::Decreasing, ValidCurve::Convex)
        );

        // Test case 7
        let x7 = vec![1.0, 2.0, 3.0, 4.0, 5.0];
        let y7 = vec![2.0, 2.0, 2.0, 2.0, 2.0];
        assert_eq!(
            find_shape(&x7, &y7),
            (ValidDirection::Decreasing, ValidCurve::Convex)
        );

        // Test case 8
        let x8 = vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0];
        let y8 = vec![1.1, 1.0, 1.2, 1.3, 1.25, 1.4, 1.5, 1.6, 1.7, 1.8];
        assert_eq!(
            find_shape(&x8, &y8),
            (ValidDirection::Increasing, ValidCurve::Convex)
        );
    }

    #[test]
    fn test_find_shape() {
        let (x, y) = DataGenerator::concave_increasing();
        assert_eq!(
            find_shape(&x, &y),
            (ValidDirection::Increasing, ValidCurve::Concave)
        );

        let (x, y) = DataGenerator::concave_decreasing();
        assert_eq!(
            find_shape(&x, &y),
            (ValidDirection::Decreasing, ValidCurve::Concave)
        );

        let (x, y) = DataGenerator::convex_increasing();
        assert_eq!(
            find_shape(&x, &y),
            (ValidDirection::Increasing, ValidCurve::Convex)
        );

        let (x, y) = DataGenerator::convex_decreasing();
        assert_eq!(
            find_shape(&x, &y),
            (ValidDirection::Decreasing, ValidCurve::Convex)
        );
    }
}