avila-clustering 0.1.0

//! Manifold-related computations for clustering

use crate::{ClusteringError, Result};
use ndarray::ArrayView1;

pub use crate::metrics::distance::Manifold;

/// Compute Christoffel symbols for a given manifold
pub fn christoffel_symbols(
    manifold: &Manifold,
    point: &ArrayView1<f64>,
) -> Result<Vec<Vec<Vec<f64>>>> {
    // TODO: Implement Christoffel symbol computation
    // Needed for geodesic calculations in curved spacetime
    unimplemented!("christoffel_symbols")
}

/// Compute metric tensor at a point
pub fn metric_tensor(manifold: &Manifold, point: &ArrayView1<f64>) -> Result<Vec<Vec<f64>>> {
    match manifold {
        Manifold::Schwarzschild { mass } => {
            // TODO: Implement Schwarzschild metric tensor
            // ds² = -(1 - 2M/r)dt² + (1 - 2M/r)⁻¹dr² + r²dΩ²
            unimplemented!("Schwarzschild metric tensor")
        }
        Manifold::Kerr { mass, spin } => {
            // TODO: Implement Kerr metric tensor
            unimplemented!("Kerr metric tensor")
        }
        Manifold::Euclidean => {
            // Flat metric: diag(1, 1, 1, ...)
            let dim = point.len();
            let mut tensor = vec![vec![0.0; dim]; dim];
            for i in 0..dim {
                tensor[i][i] = 1.0;
            }
            Ok(tensor)
        }
    }
}

/// Solve geodesic equation to find shortest path on manifold
pub fn geodesic_path(
    manifold: &Manifold,
    start: &ArrayView1<f64>,
    end: &ArrayView1<f64>,
) -> Result<Vec<Vec<f64>>> {
    // TODO: Implement geodesic path computation
    // Solve: d²x^μ/dτ² + Γ^μ_νρ (dx^ν/dτ)(dx^ρ/dτ) = 0
    unimplemented!("geodesic_path")
}

/// Compute Ricci scalar (curvature) at a point
pub fn ricci_scalar(manifold: &Manifold, point: &ArrayView1<f64>) -> Result<f64> {
    // TODO: Implement Ricci scalar computation
    // Useful for understanding local curvature effects on clustering
    unimplemented!("ricci_scalar")
}