fast_distances/distances/
correlation.rs

1use ndarray::ArrayView1;
2use num::Float;
3
4/// Computes the Pearson correlation coefficient between two vectors `x` and `y`.
5///
6/// The Pearson correlation coefficient is defined as:
7///
8/// ..math::
9///     r = 1 - \frac{\sum (x_i - \mu_x) \cdot (y_i - \mu_y)}{\sqrt{\sum (x_i - \mu_x)^2} \cdot \sqrt{\sum (y_i - \mu_y)^2}}
10///
11/// # Arguments
12///
13/// * `x` - A 1D array representing the first vector.
14/// * `y` - A 1D array representing the second vector.
15///
16/// # Returns
17/// The Pearson correlation coefficient between the vectors `x` and `y`. A value of 1.0 means the vectors are perfectly correlated,
18/// and a value of 0.0 means no correlation.
19pub fn correlation<T>(x: &ArrayView1<T>, y: &ArrayView1<T>) -> T
20where
21    T: Float,
22{
23    let mut mu_x = T::zero();
24    let mut mu_y = T::zero();
25    let mut norm_x = T::zero();
26    let mut norm_y = T::zero();
27    let mut dot_product = T::zero();
28
29    // Compute the means (mu_x, mu_y)
30    for i in 0..x.len() {
31        mu_x = mu_x + x[i];
32        mu_y = mu_y + y[i];
33    }
34
35    mu_x = mu_x / T::from(x.len()).unwrap();
36    mu_y = mu_y / T::from(y.len()).unwrap();
37
38    // Compute the dot product and norms
39    for i in 0..x.len() {
40        let shifted_x = x[i] - mu_x;
41        let shifted_y = y[i] - mu_y;
42        norm_x = norm_x + shifted_x * shifted_x;
43        norm_y = norm_y + shifted_y * shifted_y;
44        dot_product = dot_product + shifted_x * shifted_y;
45    }
46
47    if norm_x.is_zero() && norm_y.is_zero() {
48        T::zero()
49    } else if dot_product.is_zero() {
50        T::one()
51    } else {
52        T::one() - (dot_product / (norm_x.sqrt() * norm_y.sqrt()))
53    }
54}
55
56#[cfg(test)]
57mod tests {
58    use super::*;
59    use ndarray::arr1;
60
61    #[test]
62    fn test_correlation_basic_f32() {
63        // Test with simple vectors using f32
64        let x = arr1(&[1.0_f32, 2.0, 3.0]);
65        let y = arr1(&[4.0_f32, 5.0, 6.0]);
66        let result = correlation(&x.view(), &y.view());
67        let expected_result = -1.1920929e-7;
68        assert_eq!(result, expected_result);
69    }
70
71    #[test]
72    fn test_correlation_zero_norm_f32() {
73        // Test with a zero vector using f32
74        let x = arr1(&[0.0_f32, 0.0, 0.0]);
75        let y = arr1(&[1.0_f32, 2.0, 3.0]);
76        let result = correlation(&x.view(), &y.view());
77        assert_eq!(result, 1.0_f32);
78    }
79
80    #[test]
81    fn test_correlation_zero_both_norm_f32() {
82        // Test with two zero vectors using f32
83        let x = arr1(&[0.0_f32, 0.0, 0.0]);
84        let y = arr1(&[0.0_f32, 0.0, 0.0]);
85        let result = correlation(&x.view(), &y.view());
86        assert_eq!(result, 0.0_f32);
87    }
88
89    #[test]
90    fn test_correlation_basic_f64() {
91        // Test with simple vectors using f64
92        let x = arr1(&[1.0_f64, 2.0, 3.0]);
93        let y = arr1(&[4.0_f64, 5.0, 6.0]);
94        let result = correlation(&x.view(), &y.view());
95        let expected_result = 2.220446049250313e-16;
96        assert_eq!(result, expected_result);
97    }
98
99    #[test]
100    fn test_correlation_zero_norm_f64() {
101        // Test with a zero vector using f64
102        let x = arr1(&[0.0_f64, 0.0, 0.0]);
103        let y = arr1(&[1.0_f64, 2.0, 3.0]);
104        let result = correlation(&x.view(), &y.view());
105        assert_eq!(result, 1.0_f64);
106    }
107
108    #[test]
109    fn test_correlation_zero_both_norm_f64() {
110        // Test with two zero vectors using f64
111        let x = arr1(&[0.0_f64, 0.0, 0.0]);
112        let y = arr1(&[0.0_f64, 0.0, 0.0]);
113        let result = correlation(&x.view(), &y.view());
114        assert_eq!(result, 0.0_f64);
115    }
116}
fast_distances/distances/correlation.rs

fast_distances/distances/
correlation.rs
