lmm 0.1.2

A language agnostic framework for emulating reality.
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

use crate::error::Result;

#[derive(Debug, Clone, PartialEq)]
pub struct Vector {
    pub data: Vec<f64>,
}

impl Vector {
    pub fn new(data: Vec<f64>) -> Self {
        Self { data }
    }

    pub fn dot(&self, other: &Self) -> f64 {
        self.data
            .iter()
            .zip(other.data.iter())
            .map(|(a, b)| a * b)
            .sum()
    }

    pub fn add(&self, other: &Self) -> Self {
        let data = self
            .data
            .iter()
            .zip(other.data.iter())
            .map(|(a, b)| a + b)
            .collect();
        Self { data }
    }

    pub fn scale(&self, factor: f64) -> Self {
        Self {
            data: self.data.iter().map(|x| x * factor).collect(),
        }
    }

    pub fn norm(&self) -> f64 {
        self.data.iter().map(|x| x * x).sum::<f64>().sqrt()
    }
}

#[derive(Debug, Clone, PartialEq)]
pub struct State {
    pub time: f64,
    pub variables: Vector,
}

pub trait MathematicalModel {
    fn evaluate(&self, state: &State) -> Result<Vector>;
}

#[derive(Debug, Clone)]
pub struct LinearModel {
    pub weights: Vector,
    pub bias: f64,
}

impl LinearModel {
    pub fn new(weights: Vec<f64>, bias: f64) -> Self {
        Self {
            weights: Vector::new(weights),
            bias,
        }
    }
}

impl MathematicalModel for LinearModel {
    fn evaluate(&self, state: &State) -> Result<Vector> {
        let prediction = self.weights.dot(&state.variables) + self.bias;
        Ok(Vector::new(vec![prediction]))
    }
}

#[derive(Debug, Clone)]
pub struct PolynomialModel {
    pub coeffs: Vec<f64>,
}

impl PolynomialModel {
    pub fn new(coeffs: Vec<f64>) -> Self {
        Self { coeffs }
    }

    pub fn evaluate_at(&self, x: f64) -> f64 {
        self.coeffs
            .iter()
            .enumerate()
            .map(|(i, &c)| c * x.powi(i as i32))
            .sum()
    }
}

impl MathematicalModel for PolynomialModel {
    fn evaluate(&self, state: &State) -> Result<Vector> {
        let x = state.variables.data.first().copied().unwrap_or(0.0);
        Ok(Vector::new(vec![self.evaluate_at(x)]))
    }
}

#[derive(Debug, Clone)]
pub struct FitResult {
    pub mse: f64,
    pub r_squared: f64,
}

impl FitResult {
    pub fn new(predictions: &[f64], targets: &[f64]) -> Self {
        if targets.is_empty() {
            return Self {
                mse: 0.0,
                r_squared: 0.0,
            };
        }
        let n = targets.len() as f64;
        let mse = predictions
            .iter()
            .zip(targets.iter())
            .map(|(p, t)| (p - t).powi(2))
            .sum::<f64>()
            / n;
        let mean_t: f64 = targets.iter().sum::<f64>() / n;
        let ss_tot: f64 = targets.iter().map(|t| (t - mean_t).powi(2)).sum();
        let ss_res: f64 = predictions
            .iter()
            .zip(targets.iter())
            .map(|(p, t)| (p - t).powi(2))
            .sum();
        let r_squared = if ss_tot == 0.0 {
            1.0
        } else {
            1.0 - ss_res / ss_tot
        };
        Self { mse, r_squared }
    }
}