rscm-core 0.2.3

Core traits and functionalities for the creation of reduced-complexity climate models
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

use crate::errors::RSCMResult;
use crate::interpolate::strategies::{find_segment, Interp1DStrategy, SegmentOptions};
use num::Float;
use numpy::ndarray::{s, ArrayBase, Data};
use numpy::Ix1;
use std::cmp::min;

/// LinearSpline 1D interpolation
///
/// The interpolated value is
/// derived from a linear interpolation of the two points
/// to either side of time_target.
///
/// The resulting curve is therefore only zero-order continuous.
#[derive(Clone)]
pub struct LinearSplineStrategy {
    extrapolate: bool,
}

impl LinearSplineStrategy {
    pub fn new(extrapolate: bool) -> Self {
        Self { extrapolate }
    }
}

impl<At, Ay> Interp1DStrategy<At, Ay> for LinearSplineStrategy
where
    At: Data,
    At::Elem: Float,
    Ay: Data,
    Ay::Elem: Float + From<At::Elem>,
{
    fn interpolate(
        &self,
        time: &ArrayBase<At, Ix1>,
        y: &ArrayBase<Ay, Ix1>,
        time_target: At::Elem,
    ) -> RSCMResult<Ay::Elem> {
        let segment_info = find_segment(
            time_target,
            // Trim off the last bound as it isn't needed for linear extrapolation
            &time.slice(s![..time.len() - 1]),
            self.extrapolate,
        );

        let (segment_options, end_segment_idx) = match segment_info {
            Ok(info) => info,
            Err(e) => return Err(e),
        };
        // Clip the index to exclude the last bound
        let end_segment_idx = min(end_segment_idx, y.len() - 1);

        if segment_options == SegmentOptions::OnBoundary {
            // Fast return
            return Ok(y[end_segment_idx]);
        }

        let (time1, time2, y1, y2) = match segment_options {
            SegmentOptions::ExtrapolateBackward => {
                // Use first two points
                let time1 = time[0];
                let y1 = y[0];

                let time2 = time[1];
                let y2 = y[1];

                (time1, time2, y1, y2)
            }
            SegmentOptions::ExtrapolateForward => {
                assert!(y.len() >= 2);
                // Use last two points (excludes the influence of the bound of the last value
                let time1 = time[y.len() - 2];
                let y1 = y[y.len() - 2];

                let time2 = time[y.len() - 1];
                let y2 = y[y.len() - 1];

                (time1, time2, y1, y2)
            }
            SegmentOptions::InSegment | SegmentOptions::OnBoundary => {
                // Use points surrounding time_target
                let time1 = time[end_segment_idx - 1];
                let y1 = y[end_segment_idx - 1];

                let time2 = time[end_segment_idx];
                let y2 = y[end_segment_idx];

                (time1, time2, y1, y2)
            }
        };

        let time1: Ay::Elem = time1.into();
        let time2: Ay::Elem = time2.into();
        let time_target: Ay::Elem = time_target.into();

        let m = (y2 - y1) / (time2 - time1);

        Ok(m * (time_target - time1) + y1)
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use is_close::is_close;
    use numpy::array;
    use std::iter::zip;

    #[test]
    fn test_linear() {
        let time = array![0.0, 0.5, 1.0, 1.5];
        let y = array![5.0, 8.0, 9.0];

        let target = vec![0.0, 0.25, 0.5, 0.75, 1.0];
        let exps = vec![5.0, 6.5, 8.0, 8.5, 9.0];

        let strategy = LinearSplineStrategy::new(false);

        zip(target.into_iter(), exps.into_iter()).for_each(|(t, e)| {
            println!("target={}, expected={}", t, e);
            assert!(is_close!(strategy.interpolate(&time, &y, t).unwrap(), e));
        })
    }

    #[test]
    fn test_linear_extrapolation_error() {
        let time = array![0.0, 1.0];
        let y = array![5.0];

        let target = vec![-1.0, -0.01, 1.01, 1.2];

        let strategy = LinearSplineStrategy::new(false);

        target.into_iter().for_each(|t| {
            println!("target={t}");
            let res = strategy.interpolate(&time, &y, t);
            assert!(res.is_err());

            let err = res.err().unwrap();
            assert!(err.to_string().starts_with("Extrapolation is not allowed"))
        })
    }

    #[test]
    fn test_linear_extrapolation() {
        let time = array![0.0, 0.5, 1.0, 1.5];
        let y = array![5.0, 8.0, 9.0];

        let target = vec![1.5, 2.0];
        let exps = vec![10.0, 11.0];

        let strategy = LinearSplineStrategy::new(true);

        zip(target.into_iter(), exps.into_iter()).for_each(|(t, e)| {
            let res = strategy.interpolate(&time, &y, t).unwrap();
            println!("target={}, expected={}, found={}", t, e, res);
            assert!(is_close!(res, e));
        })
    }
}