sklears-manifold 0.1.2

//! Riemannian manifold processing algorithms
//!
//! This module provides tools for working with Riemannian manifolds, including:
//! - **Geodesic computation**: Computing shortest paths on manifolds
//! - **Parallel transport**: Moving vectors along geodesics while preserving geometric properties
//! - **Curvature estimation**: Computing Gaussian and mean curvature
//! - **Riemannian optimization**: Optimization methods that respect manifold structure
//!
//! Riemannian manifolds are smooth manifolds equipped with a Riemannian metric,
//! which allows measurement of distances, angles, and curvature.

use scirs2_core::ndarray::{Array1, Array2, ArrayView1, ArrayView2, Axis};
use sklears_core::{
    error::{Result as SklResult, SklearsError},
    traits::{Estimator, Fit, Transform, Untrained},
    types::Float,
};

/// Riemannian manifold representation with geodesic computation capabilities
///
/// # Parameters
///
/// * `n_neighbors` - Number of neighbors for local metric estimation
/// * `metric_type` - Type of metric to use ("euclidean", "geodesic")
/// * `geodesic_method` - Method for geodesic computation ("dijkstra", "floyd_warshall")
/// * `parallel_transport_method` - Method for parallel transport ("schild_ladder", "pole_ladder")
///
/// # Examples
///
/// ```
/// use sklears_manifold::riemannian::RiemannianManifold;
/// use sklears_core::traits::{Transform, Fit};
/// use scirs2_core::ndarray::{array, Array1, ArrayView1, ArrayView2};
///
/// let data = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0], [7.0, 8.0]];
/// let manifold = RiemannianManifold::builder()
///     .n_neighbors(3)
///     .metric_type("geodesic")
///     .build();
/// let fitted = manifold.fit(&data.view(), &()).unwrap();
/// ```
#[derive(Debug, Clone)]
pub struct RiemannianManifold<S = Untrained> {
    n_neighbors: usize,
    metric_type: String,
    geodesic_method: String,
    parallel_transport_method: String,
    curvature_estimation_radius: Float,
    state: S,
}

/// Trained state for RiemannianManifold
#[derive(Debug, Clone)]
pub struct RiemannianManifoldTrained {
    /// metric_tensor
    pub metric_tensor: Array2<Float>,
    /// geodesic_distances
    pub geodesic_distances: Array2<Float>,
    /// christoffel_symbols
    pub christoffel_symbols: Array2<Float>,
    /// gaussian_curvature
    pub gaussian_curvature: Array1<Float>,
    /// mean_curvature
    pub mean_curvature: Array1<Float>,
    /// data_points
    pub data_points: Array2<Float>,
    /// n_neighbors
    pub n_neighbors: usize,
}

impl Default for RiemannianManifold<Untrained> {
    fn default() -> Self {
        Self::new()
    }
}

impl RiemannianManifold<Untrained> {
    /// Create a new RiemannianManifold builder
    pub fn builder() -> RiemannianManifoldBuilder {
        RiemannianManifoldBuilder::new()
    }

    /// Create a RiemannianManifold with default parameters
    pub fn new() -> Self {
        Self {
            n_neighbors: 5,
            metric_type: "euclidean".to_string(),
            geodesic_method: "dijkstra".to_string(),
            parallel_transport_method: "schild_ladder".to_string(),
            curvature_estimation_radius: 1.0,
            state: Untrained,
        }
    }
}

/// Builder for RiemannianManifold
#[derive(Debug)]
pub struct RiemannianManifoldBuilder {
    n_neighbors: usize,
    metric_type: String,
    geodesic_method: String,
    parallel_transport_method: String,
    curvature_estimation_radius: Float,
}

impl RiemannianManifoldBuilder {
    fn new() -> Self {
        Self {
            n_neighbors: 5,
            metric_type: "euclidean".to_string(),
            geodesic_method: "dijkstra".to_string(),
            parallel_transport_method: "schild_ladder".to_string(),
            curvature_estimation_radius: 1.0,
        }
    }

    /// Set number of neighbors for local metric estimation
    pub fn n_neighbors(mut self, n_neighbors: usize) -> Self {
        self.n_neighbors = n_neighbors;
        self
    }

    /// Set metric type ("euclidean", "geodesic")
    pub fn metric_type(mut self, metric_type: &str) -> Self {
        self.metric_type = metric_type.to_string();
        self
    }

    /// Set geodesic computation method ("dijkstra", "floyd_warshall")
    pub fn geodesic_method(mut self, method: &str) -> Self {
        self.geodesic_method = method.to_string();
        self
    }

    /// Set parallel transport method ("schild_ladder", "pole_ladder")
    pub fn parallel_transport_method(mut self, method: &str) -> Self {
        self.parallel_transport_method = method.to_string();
        self
    }

    /// Set radius for curvature estimation
    pub fn curvature_estimation_radius(mut self, radius: Float) -> Self {
        self.curvature_estimation_radius = radius;
        self
    }

    /// Build the RiemannianManifold
    pub fn build(self) -> RiemannianManifold<Untrained> {
        RiemannianManifold {
            n_neighbors: self.n_neighbors,
            metric_type: self.metric_type,
            geodesic_method: self.geodesic_method,
            parallel_transport_method: self.parallel_transport_method,
            curvature_estimation_radius: self.curvature_estimation_radius,
            state: Untrained,
        }
    }
}

impl Estimator for RiemannianManifold<Untrained> {
    type Config = ();
    type Error = SklearsError;
    type Float = Float;

    fn config(&self) -> &Self::Config {
        &()
    }
}

impl Fit<ArrayView2<'_, Float>, ()> for RiemannianManifold<Untrained> {
    type Fitted = RiemannianManifold<RiemannianManifoldTrained>;

    fn fit(self, x: &ArrayView2<'_, Float>, _y: &()) -> SklResult<Self::Fitted> {
        let (n_samples, _n_features) = x.dim();

        if n_samples < self.n_neighbors {
            return Err(SklearsError::InvalidInput(format!(
                "Number of samples ({}) must be >= n_neighbors ({})",
                n_samples, self.n_neighbors
            )));
        }

        // Compute local metric tensor
        let metric_tensor = compute_metric_tensor(x, self.n_neighbors)?;

        // Compute geodesic distances
        let geodesic_distances = match self.geodesic_method.as_str() {
            "dijkstra" => compute_geodesic_distances_dijkstra(x, self.n_neighbors)?,
            "floyd_warshall" => compute_geodesic_distances_floyd_warshall(x, self.n_neighbors)?,
            _ => {
                return Err(SklearsError::InvalidInput(format!(
                    "Unknown geodesic method: {}",
                    self.geodesic_method
                )))
            }
        };

        // Compute Christoffel symbols for the connection
        let christoffel_symbols = compute_christoffel_symbols(&metric_tensor)?;

        // Estimate curvature
        let (gaussian_curvature, mean_curvature) =
            estimate_curvature(x, self.n_neighbors, self.curvature_estimation_radius)?;

        let trained_state = RiemannianManifoldTrained {
            metric_tensor,
            geodesic_distances,
            christoffel_symbols,
            gaussian_curvature,
            mean_curvature,
            data_points: x.to_owned(),
            n_neighbors: self.n_neighbors,
        };

        Ok(RiemannianManifold {
            n_neighbors: self.n_neighbors,
            metric_type: self.metric_type,
            geodesic_method: self.geodesic_method,
            parallel_transport_method: self.parallel_transport_method,
            curvature_estimation_radius: self.curvature_estimation_radius,
            state: trained_state,
        })
    }
}

impl Transform<ArrayView2<'_, Float>, Array2<Float>>
    for RiemannianManifold<RiemannianManifoldTrained>
{
    fn transform(&self, x: &ArrayView2<'_, Float>) -> SklResult<Array2<Float>> {
        // For new points, compute their geodesic distances to training points
        let n_new = x.nrows();
        let n_train = self.state.data_points.nrows();
        let mut result = Array2::zeros((n_new, n_train));

        for i in 0..n_new {
            for j in 0..n_train {
                let dist = compute_geodesic_distance_between_points(
                    &x.row(i),
                    &self.state.data_points.row(j),
                    &self.state.metric_tensor,
                )?;
                result[(i, j)] = dist;
            }
        }

        Ok(result)
    }
}

impl RiemannianManifold<RiemannianManifoldTrained> {
    /// Compute parallel transport of a vector along a geodesic
    pub fn parallel_transport(
        &self,
        vector: &ArrayView1<Float>,
        start_point: &ArrayView1<Float>,
        end_point: &ArrayView1<Float>,
    ) -> SklResult<Array1<Float>> {
        match self.parallel_transport_method.as_str() {
            "schild_ladder" => parallel_transport_schild_ladder(
                vector,
                start_point,
                end_point,
                &self.state.christoffel_symbols,
            ),
            "pole_ladder" => parallel_transport_pole_ladder(
                vector,
                start_point,
                end_point,
                &self.state.christoffel_symbols,
            ),
            _ => Err(SklearsError::InvalidInput(format!(
                "Unknown parallel transport method: {}",
                self.parallel_transport_method
            ))),
        }
    }

    /// Compute the exponential map at a point
    pub fn exponential_map(
        &self,
        base_point: &ArrayView1<Float>,
        tangent_vector: &ArrayView1<Float>,
    ) -> SklResult<Array1<Float>> {
        exponential_map(base_point, tangent_vector, &self.state.christoffel_symbols)
    }

    /// Compute the logarithmic map at a point  
    pub fn logarithmic_map(
        &self,
        base_point: &ArrayView1<Float>,
        target_point: &ArrayView1<Float>,
    ) -> SklResult<Array1<Float>> {
        logarithmic_map(base_point, target_point, &self.state.christoffel_symbols)
    }

    /// Get the Gaussian curvature at data points
    pub fn gaussian_curvature(&self) -> &Array1<Float> {
        &self.state.gaussian_curvature
    }

    /// Get the mean curvature at data points
    pub fn mean_curvature(&self) -> &Array1<Float> {
        &self.state.mean_curvature
    }

    /// Get the metric tensor
    pub fn metric_tensor(&self) -> &Array2<Float> {
        &self.state.metric_tensor
    }

    /// Get geodesic distances between training points
    pub fn geodesic_distances(&self) -> &Array2<Float> {
        &self.state.geodesic_distances
    }
}

// Helper functions for Riemannian computations

/// Compute local metric tensor using neighborhood information
fn compute_metric_tensor(
    x: &ArrayView2<'_, Float>,
    n_neighbors: usize,
) -> SklResult<Array2<Float>> {
    let (n_samples, n_features) = x.dim();
    let mut metric = Array2::zeros((n_features, n_features));

    // Use local PCA to estimate the metric tensor
    for i in 0..n_samples {
        let point = x.row(i);

        // Find k nearest neighbors
        let mut distances: Vec<(Float, usize)> = Vec::new();
        for j in 0..n_samples {
            if i != j {
                let dist = (&x.row(j) - &point).mapv(|x| x * x).sum().sqrt();
                distances.push((dist, j));
            }
        }
        distances.sort_by(|a, b| a.0.partial_cmp(&b.0).expect("operation should succeed"));

        let neighbors: Vec<usize> = distances
            .iter()
            .take(n_neighbors.min(n_samples - 1))
            .map(|(_, idx)| *idx)
            .collect();

        // Compute local covariance matrix
        let mut local_data = Array2::zeros((neighbors.len(), n_features));
        for (k, &neighbor_idx) in neighbors.iter().enumerate() {
            let diff = &x.row(neighbor_idx) - &point;
            local_data.row_mut(k).assign(&diff);
        }

        // Compute covariance matrix
        let mean = local_data
            .mean_axis(Axis(0))
            .expect("operation should succeed");
        let centered_data = &local_data - &mean;
        let cov = centered_data.t().dot(&centered_data) / (neighbors.len() as Float - 1.0);

        metric = metric + cov;
    }

    // Average over all points
    metric /= n_samples as Float;

    // Ensure positive definiteness by adding small regularization
    for i in 0..n_features {
        metric[(i, i)] += 1e-6;
    }

    Ok(metric)
}

/// Compute geodesic distances using Dijkstra's algorithm
fn compute_geodesic_distances_dijkstra(
    x: &ArrayView2<'_, Float>,
    n_neighbors: usize,
) -> SklResult<Array2<Float>> {
    let n_samples = x.nrows();
    let mut distances = Array2::from_elem((n_samples, n_samples), Float::INFINITY);

    // Set diagonal to zero
    for i in 0..n_samples {
        distances[(i, i)] = 0.0;
    }

    // Build neighborhood graph
    for i in 0..n_samples {
        let point = x.row(i);

        // Find k nearest neighbors
        let mut neighbor_distances: Vec<(Float, usize)> = Vec::new();
        for j in 0..n_samples {
            if i != j {
                let dist = (&x.row(j) - &point).mapv(|x| x * x).sum().sqrt();
                neighbor_distances.push((dist, j));
            }
        }
        neighbor_distances.sort_by(|a, b| a.0.partial_cmp(&b.0).expect("operation should succeed"));

        // Add edges to k nearest neighbors
        for &(dist, j) in neighbor_distances
            .iter()
            .take(n_neighbors.min(n_samples - 1))
        {
            distances[(i, j)] = dist;
            distances[(j, i)] = dist; // Make symmetric
        }
    }

    // Apply Dijkstra's algorithm from each point
    for start in 0..n_samples {
        let mut dist = vec![Float::INFINITY; n_samples];
        let mut visited = vec![false; n_samples];
        dist[start] = 0.0;

        for _ in 0..n_samples {
            // Find unvisited vertex with minimum distance
            let mut min_dist = Float::INFINITY;
            let mut min_vertex = 0;
            for v in 0..n_samples {
                if !visited[v] && dist[v] < min_dist {
                    min_dist = dist[v];
                    min_vertex = v;
                }
            }

            visited[min_vertex] = true;

            // Update distances to neighbors
            for neighbor in 0..n_samples {
                if !visited[neighbor] && distances[(min_vertex, neighbor)] != Float::INFINITY {
                    let new_dist = dist[min_vertex] + distances[(min_vertex, neighbor)];
                    if new_dist < dist[neighbor] {
                        dist[neighbor] = new_dist;
                    }
                }
            }
        }

        // Store computed distances
        for end in 0..n_samples {
            distances[(start, end)] = dist[end];
        }
    }

    Ok(distances)
}

/// Compute geodesic distances using Floyd-Warshall algorithm
fn compute_geodesic_distances_floyd_warshall(
    x: &ArrayView2<'_, Float>,
    n_neighbors: usize,
) -> SklResult<Array2<Float>> {
    let n_samples = x.nrows();
    let mut distances = Array2::from_elem((n_samples, n_samples), Float::INFINITY);

    // Set diagonal to zero
    for i in 0..n_samples {
        distances[(i, i)] = 0.0;
    }

    // Build neighborhood graph
    for i in 0..n_samples {
        let point = x.row(i);

        // Find k nearest neighbors
        let mut neighbor_distances: Vec<(Float, usize)> = Vec::new();
        for j in 0..n_samples {
            if i != j {
                let dist = (&x.row(j) - &point).mapv(|x| x * x).sum().sqrt();
                neighbor_distances.push((dist, j));
            }
        }
        neighbor_distances.sort_by(|a, b| a.0.partial_cmp(&b.0).expect("operation should succeed"));

        // Add edges to k nearest neighbors
        for &(dist, j) in neighbor_distances
            .iter()
            .take(n_neighbors.min(n_samples - 1))
        {
            distances[(i, j)] = dist;
            distances[(j, i)] = dist; // Make symmetric
        }
    }

    // Floyd-Warshall algorithm
    for k in 0..n_samples {
        for i in 0..n_samples {
            for j in 0..n_samples {
                if distances[(i, k)] != Float::INFINITY && distances[(k, j)] != Float::INFINITY {
                    let new_dist = distances[(i, k)] + distances[(k, j)];
                    if new_dist < distances[(i, j)] {
                        distances[(i, j)] = new_dist;
                    }
                }
            }
        }
    }

    Ok(distances)
}

/// Compute Christoffel symbols from metric tensor
fn compute_christoffel_symbols(metric: &Array2<Float>) -> SklResult<Array2<Float>> {
    let n = metric.nrows();
    let christoffel = Array2::zeros((n * n, n));

    // For a constant metric tensor, Christoffel symbols are zero
    // In practice, we would need metric derivatives for the full computation
    // This is a simplified version for demonstration

    // Γᵢⱼᵏ = ½ gᵏˡ (∂gᵢˡ/∂xʲ + ∂gⱼˡ/∂xᵢ - ∂gᵢⱼ/∂xˡ)
    // For constant metric, all derivatives are zero

    Ok(christoffel)
}

/// Estimate Gaussian and mean curvature at data points
fn estimate_curvature(
    x: &ArrayView2<'_, Float>,
    n_neighbors: usize,
    radius: Float,
) -> SklResult<(Array1<Float>, Array1<Float>)> {
    let n_samples = x.nrows();
    let mut gaussian_curvature = Array1::zeros(n_samples);
    let mut mean_curvature = Array1::zeros(n_samples);

    for i in 0..n_samples {
        let point = x.row(i);

        // Find neighbors within radius
        let mut neighbors = Vec::new();
        for j in 0..n_samples {
            if i != j {
                let dist = (&x.row(j) - &point).mapv(|x| x * x).sum().sqrt();
                if dist <= radius {
                    neighbors.push(j);
                }
            }
        }

        if neighbors.len() >= n_neighbors {
            // Estimate curvature using local surface fitting
            // This is a simplified estimation
            let local_variance = estimate_local_variance(x, i, &neighbors);
            gaussian_curvature[i] = 1.0 / (1.0 + local_variance);
            mean_curvature[i] = local_variance.sqrt();
        }
    }

    Ok((gaussian_curvature, mean_curvature))
}

/// Estimate local variance for curvature computation
fn estimate_local_variance(
    x: &ArrayView2<'_, Float>,
    center_idx: usize,
    neighbors: &[usize],
) -> Float {
    let center = x.row(center_idx);
    let mut variance = 0.0;

    for &neighbor_idx in neighbors {
        let diff = &x.row(neighbor_idx) - &center;
        variance += diff.mapv(|x| x * x).sum();
    }

    if !neighbors.is_empty() {
        variance / neighbors.len() as Float
    } else {
        0.0
    }
}

/// Compute geodesic distance between two specific points
fn compute_geodesic_distance_between_points(
    point1: &ArrayView1<Float>,
    point2: &ArrayView1<Float>,
    metric: &Array2<Float>,
) -> SklResult<Float> {
    let diff = point2 - point1;
    let dist_squared = diff.dot(&metric.dot(&diff));
    Ok(dist_squared.sqrt())
}

/// Parallel transport using Schild's ladder construction
fn parallel_transport_schild_ladder(
    vector: &ArrayView1<Float>,
    _start_point: &ArrayView1<Float>,
    _end_point: &ArrayView1<Float>,
    _christoffel: &Array2<Float>,
) -> SklResult<Array1<Float>> {
    // Simplified parallel transport - in practice this would use the geodesic equation
    // and Christoffel symbols for accurate parallel transport

    // For now, return the vector unchanged (valid for flat spaces)
    Ok(vector.to_owned())
}

/// Parallel transport using pole ladder construction  
fn parallel_transport_pole_ladder(
    vector: &ArrayView1<Float>,
    _start_point: &ArrayView1<Float>,
    _end_point: &ArrayView1<Float>,
    _christoffel: &Array2<Float>,
) -> SklResult<Array1<Float>> {
    // Simplified parallel transport - pole ladder is more accurate than Schild's ladder
    // For now, return the vector unchanged (valid for flat spaces)
    Ok(vector.to_owned())
}

/// Exponential map: map tangent vector to manifold point
fn exponential_map(
    base_point: &ArrayView1<Float>,
    tangent_vector: &ArrayView1<Float>,
    _christoffel: &Array2<Float>,
) -> SklResult<Array1<Float>> {
    // Simplified exponential map for flat space
    Ok(base_point + tangent_vector)
}

/// Logarithmic map: map manifold point to tangent vector
fn logarithmic_map(
    base_point: &ArrayView1<Float>,
    target_point: &ArrayView1<Float>,
    _christoffel: &Array2<Float>,
) -> SklResult<Array1<Float>> {
    // Simplified logarithmic map for flat space
    Ok(target_point - base_point)
}