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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,75 @@ | ||
| use ndarray::Array2; | ||
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| /// Kendall's tau matrix for a given data matrix | ||
| pub fn kendall_tau(data: &Array2<f64>) -> Array2<f64> { | ||
| let cols = data.ncols(); | ||
| let mut tau_matrix = Array2::<f64>::zeros((cols, cols)); | ||
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| for i in 0..cols { | ||
| for j in i..cols { | ||
| let col_i = data.column(i); | ||
| let col_j = data.column(j); | ||
| let mut concordant = 0; | ||
| let mut discordant = 0; | ||
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| for k in 0..col_i.len() { | ||
| for l in (k + 1)..col_i.len() { | ||
| let x_diff = col_i[k] - col_i[l]; | ||
| let y_diff = col_j[k] - col_j[l]; | ||
| let sign = x_diff * y_diff; | ||
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| if sign > 0.0 { | ||
| concordant += 1; | ||
| } else if sign < 0.0 { | ||
| discordant += 1; | ||
| } | ||
| } | ||
| } | ||
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| let total_pairs = (col_i.len() * (col_i.len() - 1)) / 2; | ||
| let tau = (concordant as f64 - discordant as f64) / total_pairs as f64; | ||
| tau_matrix[[i, j]] = tau; | ||
| tau_matrix[[j, i]] = tau; | ||
| } | ||
| } | ||
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| tau_matrix | ||
| } | ||
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| fn spearman_correlation(data: &Array2<f64>) -> Array2<f64> { | ||
| let cols = data.ncols(); | ||
| let mut rho_matrix = Array2::<f64>::zeros((cols, cols)); | ||
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| for i in 0..cols { | ||
| for j in i..cols { | ||
| let col_i = data.column(i); | ||
| let col_j = data.column(j); | ||
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| let mean_i = col_i.sum() / col_i.len() as f64; | ||
| let mean_j = col_j.sum() / col_j.len() as f64; | ||
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| let numerator: f64 = col_i | ||
| .iter() | ||
| .zip(col_j.iter()) | ||
| .map(|(&xi, &yi)| (xi - mean_i) * (yi - mean_j)) | ||
| .sum(); | ||
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| let denominator_i = col_i | ||
| .iter() | ||
| .map(|&xi| (xi - mean_i).powi(2)) | ||
| .sum::<f64>() | ||
| .sqrt(); | ||
| let denominator_j = col_j | ||
| .iter() | ||
| .map(|&yi| (yi - mean_j).powi(2)) | ||
| .sum::<f64>() | ||
| .sqrt(); | ||
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| let rho = numerator / (denominator_i * denominator_j); | ||
| rho_matrix[[i, j]] = rho; | ||
| rho_matrix[[j, i]] = rho; // Szimmetrikus mátrix | ||
| } | ||
| } | ||
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| rho_matrix | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,89 @@ | ||
| use ndarray::{Array1, Array2}; | ||
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| /// Empirical copula (2D) - rank-based transformation | ||
| #[derive(Clone, Debug)] | ||
| pub struct EmpiricalCopula2D { | ||
| /// The rank-transformed data (N x 2), each row in [0,1]^2 | ||
| pub rank_data: Array2<f64>, | ||
| } | ||
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| impl EmpiricalCopula2D { | ||
| /// Create an EmpiricalCopula2D from two 1D arrays (`x` and `y`) of equal length. | ||
| /// This performs a rank-based transform: for each sample i, | ||
| /// sx[i] = rank_of_x[i] / n | ||
| /// sy[i] = rank_of_y[i] / n | ||
| /// and stores the resulting points in [0,1]^2. | ||
| pub fn new_from_two_series(x: &Array1<f64>, y: &Array1<f64>) -> Self { | ||
| assert_eq!(x.len(), y.len(), "x and y must have the same length!"); | ||
| let n = x.len(); | ||
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| // Convert to Vec for easier sorting with indices | ||
| let mut xv: Vec<(f64, usize)> = x.iter().enumerate().map(|(i, &val)| (val, i)).collect(); | ||
| let mut yv: Vec<(f64, usize)> = y.iter().enumerate().map(|(i, &val)| (val, i)).collect(); | ||
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| // Sort by the actual float value | ||
| xv.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap_or(std::cmp::Ordering::Equal)); | ||
| yv.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap_or(std::cmp::Ordering::Equal)); | ||
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| // After sorting, xv[k] = (value, original_index). | ||
| // The rank of that original index is k. | ||
| let mut rank_x = vec![0.0; n]; | ||
| let mut rank_y = vec![0.0; n]; | ||
| for (rank, &(_val, orig_i)) in xv.iter().enumerate() { | ||
| rank_x[orig_i] = rank as f64; // rank in [0..n-1] | ||
| } | ||
| for (rank, &(_val, orig_i)) in yv.iter().enumerate() { | ||
| rank_y[orig_i] = rank as f64; | ||
| } | ||
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| // Normalize ranks to [0,1]. | ||
| for i in 0..n { | ||
| rank_x[i] /= n as f64; | ||
| rank_y[i] /= n as f64; | ||
| } | ||
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| // Build final (n x 2) array | ||
| let mut rank_data = Array2::<f64>::zeros((n, 2)); | ||
| for i in 0..n { | ||
| rank_data[[i, 0]] = rank_x[i]; | ||
| rank_data[[i, 1]] = rank_y[i]; | ||
| } | ||
| EmpiricalCopula2D { rank_data } | ||
| } | ||
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| fn sample(&self, _n: usize) -> Array2<f64> { | ||
| self.rank_data.clone() | ||
| } | ||
| } | ||
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| #[cfg(test)] | ||
| mod tests { | ||
| use ndarray::Array1; | ||
| use rand::thread_rng; | ||
| use rand_distr::{Distribution, Uniform}; | ||
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| use crate::{stats::copula::plot_copula_samples, stochastic::N}; | ||
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| use super::EmpiricalCopula2D; | ||
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| #[test] | ||
| fn test_empirical_copula() { | ||
| let mut rng = thread_rng(); | ||
| let uniform = Uniform::new(0.0, 1.0); | ||
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| let len_data = 500; | ||
| let mut x = Array1::<f64>::zeros(len_data); | ||
| let mut y = Array1::<f64>::zeros(len_data); | ||
| for i in 0..len_data { | ||
| let xv = uniform.sample(&mut rng); | ||
| // Introduce some linear correlation | ||
| let yv = 0.3 * uniform.sample(&mut rng) + 0.7 * xv; | ||
| x[i] = xv; | ||
| y[i] = yv.clamp(0.0, 1.0); | ||
| } | ||
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| let empirical = EmpiricalCopula2D::new_from_two_series(&x, &y); | ||
| let emp_samples = empirical.sample(N); | ||
| plot_copula_samples(&emp_samples, "Empirical Copula (2D) - Rank-based data"); | ||
| } | ||
| } |