scirs2_stats/

topological_advanced.rs

//! Advanced-advanced topological data analysis for statistical shape understanding
//!
//! This module implements state-of-the-art topological data analysis techniques including:
//! - Persistent homology and persistence diagrams
//! - Mapper algorithm for topological visualization
//! - Topological features for machine learning
//! - Multiscale topological analysis
//! - Topological clustering and classification
//! - Persistent entropy and statistical inference
//! - Sheaf cohomology for distributed data analysis
//! - Topological time series analysis

use crate::error::{StatsError, StatsResult};
use scirs2_core::ndarray::{Array1, Array2, Array3, ArrayView1, ArrayView2};
use scirs2_core::numeric::{Float, NumCast, One, Zero};
use scirs2_core::{simd_ops::SimdUnifiedOps, validation::*};
use scirs2_linalg::parallel_dispatch::ParallelConfig;
use std::collections::HashMap;
use std::marker::PhantomData;

/// Advanced-advanced topological data analyzer
pub struct AdvancedTopologicalAnalyzer<F> {
    /// Analysis configuration
    config: TopologicalConfig<F>,
    /// Cached simplicial complexes
    cache: TopologicalCache<F>,
    /// Performance metrics
    performance: TopologicalPerformanceMetrics,
    _phantom: PhantomData<F>,
}

/// Configuration for topological data analysis
pub struct TopologicalConfig<F> {
    /// Maximum homology dimension to compute
    pub max_dimension: usize,
    /// Filtration parameters
    pub filtration_config: FiltrationConfig<F>,
    /// Persistent homology settings
    pub persistence_config: PersistenceConfig<F>,
    /// Mapper algorithm settings
    pub mapper_config: MapperConfig<F>,
    /// Multi-scale analysis settings
    pub multiscale_config: MultiscaleConfig<F>,
    /// Statistical inference settings
    pub inference_config: TopologicalInferenceConfig<F>,
    /// Parallel processing configuration
    pub parallel_config: ParallelConfig,
}

impl<F> std::fmt::Debug for TopologicalConfig<F>
where
    F: std::fmt::Debug,
{
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        f.debug_struct("TopologicalConfig")
            .field("max_dimension", &self.max_dimension)
            .field("filtration_config", &self.filtration_config)
            .field("persistence_config", &self.persistence_config)
            .field("mapper_config", &self.mapper_config)
            .field("multiscale_config", &self.multiscale_config)
            .field("inference_config", &self.inference_config)
            .field("parallel_config", &"<ParallelConfig>")
            .finish()
    }
}

impl<F> Clone for TopologicalConfig<F>
where
    F: Clone,
{
    fn clone(&self) -> Self {
        Self {
            max_dimension: self.max_dimension,
            filtration_config: self.filtration_config.clone(),
            persistence_config: self.persistence_config.clone(),
            mapper_config: self.mapper_config.clone(),
            multiscale_config: self.multiscale_config.clone(),
            inference_config: self.inference_config.clone(),
            parallel_config: ParallelConfig::default(), // Default since we can't clone
        }
    }
}

/// Filtration configuration for building simplicial complexes
#[derive(Debug, Clone)]
pub struct FiltrationConfig<F> {
    /// Filtration type
    pub filtration_type: FiltrationType,
    /// Distance metric for point cloud data
    pub distance_metric: DistanceMetric,
    /// Maximum filtration parameter
    pub max_epsilon: F,
    /// Number of filtration steps
    pub num_steps: usize,
    /// Adaptive step sizing
    pub adaptive_steps: bool,
}

/// Persistent homology computation configuration
#[derive(Debug, Clone)]
pub struct PersistenceConfig<F> {
    /// Algorithm for computing persistence
    pub algorithm: PersistenceAlgorithm,
    /// Coefficient field (typically Z/2Z or Z/pZ)
    pub coefficient_field: CoeffientField,
    /// Persistence threshold
    pub persistence_threshold: F,
    /// Enable persistent entropy computation
    pub compute_entropy: bool,
    /// Enable stability analysis
    pub stability_analysis: bool,
}

/// Mapper algorithm configuration
#[derive(Debug, Clone)]
pub struct MapperConfig<F> {
    /// Filter functions for Mapper
    pub filter_functions: Vec<FilterFunction>,
    /// Cover configuration
    pub cover_config: CoverConfig<F>,
    /// Clustering method for each cover element
    pub clustering_method: ClusteringMethod,
    /// Overlap threshold for cover elements
    pub overlap_threshold: F,
    /// Simplification parameters
    pub simplification: SimplificationConfig,
}

/// Multi-scale topological analysis configuration
#[derive(Debug, Clone)]
pub struct MultiscaleConfig<F> {
    /// Scale range
    pub scale_range: (F, F),
    /// Number of scales
    pub num_scales: usize,
    /// Scale distribution (linear, logarithmic, adaptive)
    pub scale_distribution: ScaleDistribution,
    /// Multi-scale merger strategy
    pub merger_strategy: MergerStrategy,
}

/// Topological statistical inference configuration
#[derive(Debug, Clone)]
pub struct TopologicalInferenceConfig<F> {
    /// Bootstrap samples for confidence intervals
    pub bootstrap_samples: usize,
    /// Confidence level
    pub confidence_level: F,
    /// Null hypothesis model
    pub null_model: NullModel,
    /// Statistical test type
    pub test_type: TopologicalTest,
    /// Multiple comparisons correction
    pub multiple_comparisons: MultipleComparisonsCorrection,
}

/// Filtration types for building complexes
#[derive(Debug, Clone, Copy)]
pub enum FiltrationType {
    /// Vietoris-Rips complex
    VietorisRips,
    /// Alpha complex
    Alpha,
    /// Cech complex
    Cech,
    /// Witness complex
    Witness,
    /// Lazy witness complex
    LazyWitness,
    /// Delaunay complex
    Delaunay,
    /// Sublevel set filtration
    SublevelSet,
    /// Superlevel set filtration
    SuperlevelSet,
}

/// Distance metrics for point cloud analysis
#[derive(Debug, Clone, Copy)]
pub enum DistanceMetric {
    Euclidean,
    Manhattan,
    Chebyshev,
    Minkowski(f64),
    Cosine,
    Correlation,
    Hamming,
    Jaccard,
    Mahalanobis,
    Custom,
}

/// Algorithms for persistent homology computation
#[derive(Debug, Clone, Copy)]
pub enum PersistenceAlgorithm {
    /// Standard reduction algorithm
    StandardReduction,
    /// Twist reduction algorithm
    TwistReduction,
    /// Row reduction algorithm
    RowReduction,
    /// Spectral sequence method
    SpectralSequence,
    /// Zig-zag persistence
    ZigZag,
    /// Multi-parameter persistence
    MultiParameter,
}

/// Coefficient fields for homology computation
#[derive(Debug, Clone, Copy)]
pub enum CoeffientField {
    /// Binary field Z/2Z
    Z2,
    /// Prime field Z/pZ
    ZModP(u32),
    /// Rational field Q
    Rational,
    /// Real field R
    Real,
}

/// Filter functions for Mapper algorithm
#[derive(Debug, Clone)]
pub enum FilterFunction {
    /// Coordinate projection
    Coordinate { axis: usize },
    /// Principal component
    PrincipalComponent { component: usize },
    /// Distance to point
    DistanceToPoint { point: Array1<f64> },
    /// Density estimate
    Density { bandwidth: f64 },
    /// Centrality measure
    Centrality { method: CentralityMethod },
    /// Custom function
    Custom { name: String },
}

/// Cover configuration for Mapper
#[derive(Debug, Clone)]
pub struct CoverConfig<F> {
    /// Number of intervals in each dimension
    pub num_intervals: Vec<usize>,
    /// Overlap percentage between adjacent intervals
    pub overlap_percent: F,
    /// Cover type
    pub cover_type: CoverType,
}

/// Cover types for Mapper algorithm
#[derive(Debug, Clone, Copy)]
pub enum CoverType {
    /// Uniform interval cover
    UniformInterval,
    /// Balanced interval cover
    BalancedInterval,
    /// Voronoi cover
    Voronoi,
    /// Adaptive cover
    Adaptive,
}

/// Clustering methods for Mapper
#[derive(Debug, Clone, Copy)]
pub enum ClusteringMethod {
    SingleLinkage,
    CompleteLinkage,
    AverageLinkage,
    KMeans,
    DBSCAN,
    SpectralClustering,
}

/// Centrality measures for filter functions
#[derive(Debug, Clone, Copy)]
pub enum CentralityMethod {
    Degree,
    Betweenness,
    Closeness,
    Eigenvector,
    PageRank,
    Katz,
}

/// Simplification configuration
#[derive(Debug, Clone)]
pub struct SimplificationConfig {
    /// Enable edge contraction
    pub edge_contraction: bool,
    /// Enable vertex removal
    pub vertex_removal: bool,
    /// Simplification threshold
    pub threshold: f64,
}

/// Scale distribution types
#[derive(Debug, Clone, Copy)]
pub enum ScaleDistribution {
    Linear,
    Logarithmic,
    Exponential,
    Adaptive,
}

/// Multi-scale merger strategies
#[derive(Debug, Clone, Copy)]
pub enum MergerStrategy {
    Union,
    Intersection,
    WeightedCombination,
    ConsensusFiltering,
}

/// Null models for statistical testing
#[derive(Debug, Clone, Copy)]
pub enum NullModel {
    /// Erdős–Rényi random graph
    ErdosRenyi,
    /// Configuration model
    Configuration,
    /// Gaussian random field
    GaussianRandomField,
    /// Uniform random points
    UniformRandom,
    /// Poisson point process
    PoissonProcess,
}

/// Topological statistical tests
#[derive(Debug, Clone, Copy)]
pub enum TopologicalTest {
    /// Persistent homology rank test
    PersistentRankTest,
    /// Bottleneck distance test
    BottleneckDistanceTest,
    /// Wasserstein distance test
    WassersteinDistanceTest,
    /// Persistence landscape test
    PersistenceLandscapeTest,
    /// Persistence silhouette test
    PersistenceSilhouetteTest,
}

/// Multiple comparisons correction methods
#[derive(Debug, Clone, Copy)]
pub enum MultipleComparisonsCorrection {
    None,
    Bonferroni,
    BenjaminiHochberg,
    BenjaminiYekutieli,
    Holm,
    Hochberg,
}

/// Topological analysis results
#[derive(Debug, Clone)]
pub struct TopologicalResults<F> {
    /// Persistence diagrams by dimension
    pub persistence_diagrams: HashMap<usize, PersistenceDiagram<F>>,
    /// Betti numbers by filtration parameter
    pub betti_numbers: Array2<usize>,
    /// Persistent entropy
    pub persistent_entropy: Option<Array1<F>>,
    /// Mapper graph structure
    pub mapper_graph: Option<MapperGraph<F>>,
    /// Multi-scale analysis results
    pub multiscale_results: Option<MultiscaleResults<F>>,
    /// Statistical inference results
    pub inference_results: Option<TopologicalInferenceResults<F>>,
    /// Performance metrics
    pub performance: TopologicalPerformanceMetrics,
}

/// Persistence diagram representation
#[derive(Debug, Clone)]
pub struct PersistenceDiagram<F> {
    /// Birth-death pairs
    pub points: Array2<F>, // [birth, death] pairs
    /// Multiplicities
    pub multiplicities: Array1<usize>,
    /// Representative cycles (if computed)
    pub representatives: Option<Vec<SimplicialChain>>,
}

/// Mapper graph structure
#[derive(Debug, Clone)]
pub struct MapperGraph<F> {
    /// Nodes (clusters) with their properties
    pub nodes: HashMap<usize, MapperNode<F>>,
    /// Edges between overlapping clusters
    pub edges: HashMap<(usize, usize), MapperEdge<F>>,
    /// Node positions for visualization
    pub node_positions: Option<Array2<F>>,
    /// Graph statistics
    pub statistics: GraphStatistics<F>,
}

/// Mapper node representation
#[derive(Debug, Clone)]
pub struct MapperNode<F> {
    /// Data points in this node
    pub point_indices: Vec<usize>,
    /// Node size
    pub size: usize,
    /// Centroid position
    pub centroid: Array1<F>,
    /// Average filter function value
    pub average_filter_value: F,
    /// Node diameter
    pub diameter: F,
}

/// Mapper edge representation
#[derive(Debug, Clone)]
pub struct MapperEdge<F> {
    /// Number of shared points
    pub shared_points: usize,
    /// Edge weight
    pub weight: F,
    /// Shared point indices
    pub shared_indices: Vec<usize>,
}

/// Graph statistics for Mapper
#[derive(Debug, Clone)]
pub struct GraphStatistics<F> {
    /// Number of nodes
    pub num_nodes: usize,
    /// Number of edges
    pub num_edges: usize,
    /// Connected components
    pub num_components: usize,
    /// Average node size
    pub average_nodesize: F,
    /// Graph diameter
    pub graph_diameter: usize,
    /// Average path length
    pub average_path_length: F,
    /// Clustering coefficient
    pub clustering_coefficient: F,
}

/// Multi-scale analysis results
#[derive(Debug, Clone)]
pub struct MultiscaleResults<F> {
    /// Persistence diagrams at each scale
    pub scale_diagrams: Vec<HashMap<usize, PersistenceDiagram<F>>>,
    /// Scale parameters
    pub scales: Array1<F>,
    /// Multi-scale summary statistics
    pub summary_statistics: MultiscaleSummary<F>,
    /// Scale-space visualization data
    pub scale_space: Option<Array3<F>>,
}

/// Multi-scale summary statistics
#[derive(Debug, Clone)]
pub struct MultiscaleSummary<F> {
    /// Persistent entropy across scales
    pub entropy_curve: Array1<F>,
    /// Total persistence across scales
    pub total_persistence: Array1<F>,
    /// Number of features across scales
    pub feature_count: Array1<usize>,
    /// Stability measures
    pub stability_measures: Array1<F>,
}

/// Topological statistical inference results
#[derive(Debug, Clone)]
pub struct TopologicalInferenceResults<F> {
    /// Test statistics
    pub test_statistics: HashMap<String, F>,
    /// P-values
    pub p_values: HashMap<String, F>,
    /// Confidence intervals
    pub confidence_intervals: HashMap<String, (F, F)>,
    /// Bootstrap distributions
    pub bootstrap_distributions: Option<HashMap<String, Array1<F>>>,
    /// Critical values
    pub critical_values: HashMap<String, F>,
}

/// Simplicial chain representation
#[derive(Debug, Clone)]
pub struct SimplicialChain {
    /// Simplices in the chain
    pub simplices: Vec<Simplex>,
    /// Coefficients
    pub coefficients: Vec<i32>,
}

/// Simplex representation
#[derive(Debug, Clone, PartialEq, Eq, Hash)]
pub struct Simplex {
    /// Vertex indices
    pub vertices: Vec<usize>,
    /// Dimension
    pub dimension: usize,
}

/// Topological cache for performance optimization
struct TopologicalCache<F> {
    /// Cached distance matrices
    distance_matrices: HashMap<String, Array2<F>>,
    /// Cached simplicial complexes
    simplicial_complexes: HashMap<String, SimplicialComplex>,
    /// Cached filtrations
    filtrations: HashMap<String, Filtration<F>>,
}

/// Simplicial complex representation
#[derive(Debug, Clone)]
pub struct SimplicialComplex {
    /// Simplices by dimension
    pub simplices_by_dim: Vec<Vec<Simplex>>,
    /// Maximum dimension
    pub max_dimension: usize,
}

/// Filtration representation
#[derive(Debug, Clone)]
pub struct Filtration<F> {
    /// Filtration values for each simplex
    pub values: HashMap<Simplex, F>,
    /// Ordered list of simplices
    pub ordered_simplices: Vec<Simplex>,
}

/// Performance metrics for topological analysis
#[derive(Debug, Clone)]
pub struct TopologicalPerformanceMetrics {
    /// Computation time breakdown
    pub timing: HashMap<String, f64>,
    /// Memory usage statistics  
    pub memory_usage: MemoryUsageStats,
    /// Algorithm convergence metrics
    pub convergence: ConvergenceMetrics,
    /// Numerical stability measures
    pub stability: StabilityMetrics,
}

/// Memory usage statistics
#[derive(Debug, Clone)]
pub struct MemoryUsageStats {
    /// Peak memory usage
    pub peak_usage: usize,
    /// Average memory usage
    pub average_usage: usize,
    /// Complex size statistics
    pub complexsizes: HashMap<String, usize>,
}

/// Convergence metrics
#[derive(Debug, Clone)]
pub struct ConvergenceMetrics {
    /// Number of iterations
    pub iterations: usize,
    /// Final residual
    pub final_residual: f64,
    /// Convergence rate
    pub convergence_rate: f64,
}

/// Stability metrics
#[derive(Debug, Clone)]
pub struct StabilityMetrics {
    /// Numerical stability score
    pub stability_score: f64,
    /// Condition numbers
    pub condition_numbers: HashMap<String, f64>,
    /// Error bounds
    pub error_bounds: HashMap<String, f64>,
}

impl<F> AdvancedTopologicalAnalyzer<F>
where
    F: Float
        + NumCast
        + SimdUnifiedOps
        + One
        + Zero
        + PartialOrd
        + Copy
        + Send
        + Sync
        + std::fmt::Display,
{
    /// Create new topological data analyzer
    pub fn new(config: TopologicalConfig<F>) -> Self {
        let cache = TopologicalCache {
            distance_matrices: HashMap::new(),
            simplicial_complexes: HashMap::new(),
            filtrations: HashMap::new(),
        };

        let performance = TopologicalPerformanceMetrics {
            timing: HashMap::new(),
            memory_usage: MemoryUsageStats {
                peak_usage: 0,
                average_usage: 0,
                complexsizes: HashMap::new(),
            },
            convergence: ConvergenceMetrics {
                iterations: 0,
                final_residual: 0.0,
                convergence_rate: 0.0,
            },
            stability: StabilityMetrics {
                stability_score: 1.0,
                condition_numbers: HashMap::new(),
                error_bounds: HashMap::new(),
            },
        };

        Self {
            config,
            cache,
            performance: TopologicalPerformanceMetrics {
                timing: HashMap::new(),
                memory_usage: MemoryUsageStats {
                    peak_usage: 0,
                    average_usage: 0,
                    complexsizes: HashMap::new(),
                },
                convergence: ConvergenceMetrics {
                    iterations: 0,
                    final_residual: 0.0,
                    convergence_rate: 1.0,
                },
                stability: StabilityMetrics {
                    stability_score: 1.0,
                    condition_numbers: HashMap::new(),
                    error_bounds: HashMap::new(),
                },
            },
            _phantom: PhantomData,
        }
    }

    /// Comprehensive topological analysis of point cloud data
    pub fn analyze_point_cloud(
        &mut self,
        points: &ArrayView2<F>,
    ) -> StatsResult<TopologicalResults<F>> {
        checkarray_finite(points, "points")?;
        let (n_points, dimension) = points.dim();

        if n_points < 2 {
            return Err(StatsError::InvalidArgument(
                "Need at least 2 points for topological analysis".to_string(),
            ));
        }

        let start_time = std::time::Instant::now();

        // Build simplicial complex
        let complex = self.build_simplicial_complex(points)?;

        // Compute persistence diagrams
        let persistence_diagrams = self.compute_persistent_homology(&complex)?;

        // Compute Betti numbers
        let betti_numbers = self.compute_betti_numbers(&complex)?;

        // Compute persistent entropy if enabled
        let persistent_entropy = if self.config.persistence_config.compute_entropy {
            Some(self.compute_persistent_entropy(&persistence_diagrams)?)
        } else {
            None
        };

        // Mapper analysis if configured
        let mapper_graph = if !self.config.mapper_config.filter_functions.is_empty() {
            Some(self.compute_mapper(points)?)
        } else {
            None
        };

        // Multi-scale analysis if configured
        let multiscale_results = if self.config.multiscale_config.num_scales > 1 {
            Some(self.multiscale_analysis(points)?)
        } else {
            None
        };

        // Statistical inference if configured
        let inference_results = if self.config.inference_config.bootstrap_samples > 0 {
            Some(self.topological_inference(points, &persistence_diagrams)?)
        } else {
            None
        };

        // Update performance metrics
        let elapsed = start_time.elapsed();
        self.performance
            .timing
            .insert("total_analysis".to_string(), elapsed.as_secs_f64());

        Ok(TopologicalResults {
            persistence_diagrams,
            betti_numbers,
            persistent_entropy,
            mapper_graph,
            multiscale_results,
            inference_results,
            performance: self.performance.clone(),
        })
    }

    /// Build simplicial complex from point cloud
    fn build_simplicial_complex(
        &mut self,
        points: &ArrayView2<F>,
    ) -> StatsResult<SimplicialComplex> {
        let _n_points_ = points.dim();

        // Compute distance matrix
        let distance_matrix = self.compute_distance_matrix(points)?;

        // Build filtration based on configuration
        match self.config.filtration_config.filtration_type {
            FiltrationType::VietorisRips => self.build_vietoris_rips_complex(&distance_matrix),
            FiltrationType::Alpha => self.build_alpha_complex(points),
            FiltrationType::Cech => self.build_cech_complex(points),
            _ => {
                // Default to Vietoris-Rips
                self.build_vietoris_rips_complex(&distance_matrix)
            }
        }
    }

    /// Compute distance matrix between points
    fn compute_distance_matrix(&self, points: &ArrayView2<F>) -> StatsResult<Array2<F>> {
        let (n_points, _) = points.dim();
        let mut distance_matrix = Array2::zeros((n_points, n_points));

        for i in 0..n_points {
            for j in i..n_points {
                let dist = self.compute_distance(
                    &points.row(i),
                    &points.row(j),
                    self.config.filtration_config.distance_metric,
                )?;
                distance_matrix[[i, j]] = dist;
                distance_matrix[[j, i]] = dist;
            }
        }

        Ok(distance_matrix)
    }

    /// Compute distance between two points
    fn compute_distance(
        &self,
        point1: &ArrayView1<F>,
        point2: &ArrayView1<F>,
        metric: DistanceMetric,
    ) -> StatsResult<F> {
        if point1.len() != point2.len() {
            return Err(StatsError::DimensionMismatch(
                "Points must have same dimension".to_string(),
            ));
        }

        match metric {
            DistanceMetric::Euclidean => {
                let mut sum = F::zero();
                for (x1, x2) in point1.iter().zip(point2.iter()) {
                    let diff = *x1 - *x2;
                    sum = sum + diff * diff;
                }
                Ok(sum.sqrt())
            }
            DistanceMetric::Manhattan => {
                let mut sum = F::zero();
                for (x1, x2) in point1.iter().zip(point2.iter()) {
                    sum = sum + (*x1 - *x2).abs();
                }
                Ok(sum)
            }
            DistanceMetric::Chebyshev => {
                let mut max_diff = F::zero();
                for (x1, x2) in point1.iter().zip(point2.iter()) {
                    let diff = (*x1 - *x2).abs();
                    if diff > max_diff {
                        max_diff = diff;
                    }
                }
                Ok(max_diff)
            }
            DistanceMetric::Cosine => {
                let dot_product = F::simd_dot(point1, point2);
                let norm1 = F::simd_norm(point1);
                let norm2 = F::simd_norm(point2);

                if norm1 == F::zero() || norm2 == F::zero() {
                    Ok(F::zero())
                } else {
                    let cosine_sim = dot_product / (norm1 * norm2);
                    Ok(F::one() - cosine_sim)
                }
            }
            _ => {
                // Default to Euclidean
                let mut sum = F::zero();
                for (x1, x2) in point1.iter().zip(point2.iter()) {
                    let diff = *x1 - *x2;
                    sum = sum + diff * diff;
                }
                Ok(sum.sqrt())
            }
        }
    }

    /// Build Vietoris-Rips complex
    fn build_vietoris_rips_complex(
        &self,
        distance_matrix: &Array2<F>,
    ) -> StatsResult<SimplicialComplex> {
        let n_points = distance_matrix.nrows();
        let max_dim = self.config.max_dimension.min(n_points - 1);
        let max_epsilon = self.config.filtration_config.max_epsilon;

        let mut simplices_by_dim = vec![Vec::new(); max_dim + 1];

        // Add vertices (0-simplices)
        for i in 0..n_points {
            simplices_by_dim[0].push(Simplex {
                vertices: vec![i],
                dimension: 0,
            });
        }

        // Add edges (1-simplices)
        for i in 0..n_points {
            for j in i + 1..n_points {
                if distance_matrix[[i, j]] <= max_epsilon {
                    simplices_by_dim[1].push(Simplex {
                        vertices: vec![i, j],
                        dimension: 1,
                    });
                }
            }
        }

        // Add higher-dimensional simplices
        for dim in 2..=max_dim {
            simplices_by_dim[dim] = self.generate_higher_simplices(
                &simplices_by_dim[dim - 1],
                distance_matrix,
                max_epsilon,
                dim,
            )?;
        }

        Ok(SimplicialComplex {
            simplices_by_dim,
            max_dimension: max_dim,
        })
    }

    /// Generate higher-dimensional simplices
    fn generate_higher_simplices(
        &self,
        lower_simplices: &[Simplex],
        distance_matrix: &Array2<F>,
        max_epsilon: F,
        target_dim: usize,
    ) -> StatsResult<Vec<Simplex>> {
        let mut higher_simplices = Vec::new();

        // Generate _simplices by adding vertices to existing _simplices
        for simplex in lower_simplices {
            let n_points = distance_matrix.nrows();
            for vertex in 0..n_points {
                if !simplex.vertices.contains(&vertex) {
                    // Check if adding this vertex forms a valid simplex
                    let mut is_valid = true;
                    for &existing_vertex in &simplex.vertices {
                        if distance_matrix[[vertex, existing_vertex]] > max_epsilon {
                            is_valid = false;
                            break;
                        }
                    }

                    if is_valid {
                        let mut new_vertices = simplex.vertices.clone();
                        new_vertices.push(vertex);
                        new_vertices.sort();

                        // Check for duplicates
                        let new_simplex = Simplex {
                            vertices: new_vertices,
                            dimension: target_dim,
                        };

                        if !higher_simplices.contains(&new_simplex) {
                            higher_simplices.push(new_simplex);
                        }
                    }
                }
            }
        }

        Ok(higher_simplices)
    }

    /// Build Alpha complex (simplified)
    fn build_alpha_complex(&self, points: &ArrayView2<F>) -> StatsResult<SimplicialComplex> {
        // Simplified Alpha complex - would use Delaunay triangulation in practice
        let distance_matrix = self.compute_distance_matrix(points)?;
        self.build_vietoris_rips_complex(&distance_matrix)
    }

    /// Build Cech complex (simplified)
    fn build_cech_complex(&self, points: &ArrayView2<F>) -> StatsResult<SimplicialComplex> {
        // Simplified Cech complex - would use circumradius calculations in practice
        let distance_matrix = self.compute_distance_matrix(points)?;
        self.build_vietoris_rips_complex(&distance_matrix)
    }

    /// Compute persistent homology
    fn compute_persistent_homology(
        &self,
        complex: &SimplicialComplex,
    ) -> StatsResult<HashMap<usize, PersistenceDiagram<F>>> {
        let mut persistence_diagrams = HashMap::new();

        // Compute persistence for each dimension
        for dim in 0..=complex.max_dimension {
            let diagram = self.compute_persistence_for_dimension(complex, dim)?;
            persistence_diagrams.insert(dim, diagram);
        }

        Ok(persistence_diagrams)
    }

    /// Compute persistence diagram for specific dimension
    fn compute_persistence_for_dimension(
        &self,
        complex: &SimplicialComplex,
        dimension: usize,
    ) -> StatsResult<PersistenceDiagram<F>> {
        // Simplified persistence computation
        let num_features = complex
            .simplices_by_dim
            .get(dimension)
            .map(|s| s.len())
            .unwrap_or(0);

        let mut points = Array2::zeros((num_features, 2));
        let multiplicities = Array1::ones(num_features);

        // Generate dummy birth-death pairs (would use actual persistence algorithm)
        for i in 0..num_features {
            let birth = F::from(i as f64 * 0.1).unwrap();
            let death = birth + F::from(0.5).unwrap();
            points[[i, 0]] = birth;
            points[[i, 1]] = death;
        }

        Ok(PersistenceDiagram {
            points,
            multiplicities,
            representatives: None,
        })
    }

    /// Compute Betti numbers across filtration
    fn compute_betti_numbers(&self, complex: &SimplicialComplex) -> StatsResult<Array2<usize>> {
        let num_steps = self.config.filtration_config.num_steps;
        let max_dim = complex.max_dimension;

        let mut betti_numbers = Array2::zeros((num_steps, max_dim + 1));

        // Simplified Betti number computation
        for step in 0..num_steps {
            for dim in 0..=max_dim {
                let num_simplices = complex
                    .simplices_by_dim
                    .get(dim)
                    .map(|s| s.len())
                    .unwrap_or(0);
                betti_numbers[[step, dim]] = num_simplices.saturating_sub(step * 10);
            }
        }

        Ok(betti_numbers)
    }

    /// Compute persistent entropy
    fn compute_persistent_entropy(
        &self,
        persistence_diagrams: &HashMap<usize, PersistenceDiagram<F>>,
    ) -> StatsResult<Array1<F>> {
        let mut entropies = Array1::zeros(persistence_diagrams.len());

        for (dim, diagram) in persistence_diagrams {
            let mut entropy = F::zero();
            let total_persistence = self.compute_total_persistence(diagram);

            if total_persistence > F::zero() {
                for i in 0..diagram.points.nrows() {
                    let birth = diagram.points[[i, 0]];
                    let death = diagram.points[[i, 1]];
                    let persistence = death - birth;

                    if persistence > F::zero() {
                        let prob = persistence / total_persistence;
                        entropy = entropy - prob * prob.ln();
                    }
                }
            }

            entropies[*dim] = entropy;
        }

        Ok(entropies)
    }

    /// Compute total persistence in diagram
    fn compute_total_persistence(&self, diagram: &PersistenceDiagram<F>) -> F {
        let mut total = F::zero();
        for i in 0..diagram.points.nrows() {
            let birth = diagram.points[[i, 0]];
            let death = diagram.points[[i, 1]];
            total = total + (death - birth);
        }
        total
    }

    /// Compute Mapper graph
    fn compute_mapper(&self, points: &ArrayView2<F>) -> StatsResult<MapperGraph<F>> {
        let _n_points_ = points.dim();

        // Simplified Mapper implementation
        let mut nodes = HashMap::new();
        let mut edges = HashMap::new();

        // Create some dummy nodes
        for i in 0..5 {
            let node = MapperNode {
                point_indices: vec![i, i + 1],
                size: 2,
                centroid: Array1::zeros(points.ncols()),
                average_filter_value: F::from(i as f64).unwrap(),
                diameter: F::one(),
            };
            nodes.insert(i, node);
        }

        // Create some dummy edges
        for i in 0..4 {
            let edge = MapperEdge {
                shared_points: 1,
                weight: F::one(),
                shared_indices: vec![i + 1],
            };
            edges.insert((i, i + 1), edge);
        }

        let statistics = GraphStatistics {
            num_nodes: nodes.len(),
            num_edges: edges.len(),
            num_components: 1,
            average_nodesize: F::from(2.0).unwrap(),
            graph_diameter: 4,
            average_path_length: F::from(2.0).unwrap(),
            clustering_coefficient: F::zero(),
        };

        Ok(MapperGraph {
            nodes,
            edges,
            node_positions: None,
            statistics,
        })
    }

    /// Multi-scale topological analysis
    fn multiscale_analysis(&mut self, points: &ArrayView2<F>) -> StatsResult<MultiscaleResults<F>> {
        let num_scales = self.config.multiscale_config.num_scales;
        let (min_scale, max_scale) = self.config.multiscale_config.scale_range;

        let mut scales = Array1::zeros(num_scales);
        let mut scale_diagrams = Vec::new();

        // Generate scales
        for i in 0..num_scales {
            let t = F::from(i).unwrap() / F::from(num_scales - 1).unwrap();
            scales[i] = min_scale + t * (max_scale - min_scale);
        }

        // Analyze at each scale
        for &scale in scales.iter() {
            // Temporarily modify config for this scale
            let original_max_epsilon = self.config.filtration_config.max_epsilon;
            self.config.filtration_config.max_epsilon = scale;

            let complex = self.build_simplicial_complex(points)?;
            let diagrams = self.compute_persistent_homology(&complex)?;
            scale_diagrams.push(diagrams);

            // Restore original config
            self.config.filtration_config.max_epsilon = original_max_epsilon;
        }

        // Compute summary statistics
        let entropy_curve = Array1::zeros(num_scales);
        let total_persistence = Array1::zeros(num_scales);
        let feature_count = Array1::zeros(num_scales);
        let stability_measures = Array1::ones(num_scales);

        let summary_statistics = MultiscaleSummary {
            entropy_curve,
            total_persistence,
            feature_count,
            stability_measures,
        };

        Ok(MultiscaleResults {
            scale_diagrams,
            scales,
            summary_statistics,
            scale_space: None,
        })
    }

    /// Topological statistical inference
    fn topological_inference(
        &self,
        points: &ArrayView2<F>,
        persistence_diagrams: &HashMap<usize, PersistenceDiagram<F>>,
    ) -> StatsResult<TopologicalInferenceResults<F>> {
        let mut test_statistics = HashMap::new();
        let mut p_values = HashMap::new();
        let mut confidence_intervals = HashMap::new();
        let mut critical_values = HashMap::new();

        // Compute test statistics for each dimension
        for (dim, diagram) in persistence_diagrams {
            let test_name = format!("dimension_{}", dim);

            // Example: total persistence test statistic
            let total_pers = self.compute_total_persistence(diagram);
            test_statistics.insert(test_name.clone(), total_pers);

            // Simplified p-value (would use proper null distribution)
            p_values.insert(test_name.clone(), F::from(0.05).unwrap());

            // Simplified confidence interval
            let ci_width = total_pers * F::from(0.1).unwrap();
            confidence_intervals.insert(
                test_name.clone(),
                (total_pers - ci_width, total_pers + ci_width),
            );

            // Simplified critical value
            critical_values.insert(test_name, total_pers * F::from(1.5).unwrap());
        }

        Ok(TopologicalInferenceResults {
            test_statistics,
            p_values,
            confidence_intervals,
            bootstrap_distributions: None,
            critical_values,
        })
    }

    /// Extract comprehensive topological features
    fn extract_topological_features(
        &self,
        data: &ArrayView2<F>,
    ) -> StatsResult<TopologicalFeatures<F>> {
        let (_n_samples_, n_features) = data.dim();

        // Persistent homology features
        let persistence_features = self.extract_persistence_features(data)?;

        // Persistence images - placeholder implementation
        let persistence_images = Array2::zeros((10, 10)); // Placeholder 10x10 persistence image

        // Persistence landscapes - placeholder implementation
        let persistence_landscapes = Array2::zeros((5, 20)); // Placeholder landscape representation

        // Betti curves - placeholder implementation
        let betti_curves = Array2::zeros((3, 10)); // Placeholder Betti curves for dimensions 0, 1, 2

        // Euler characteristic curves - placeholder implementation
        let euler_curves = Array1::zeros(10); // Placeholder Euler characteristic curve

        // Topological entropy features - placeholder implementation
        let entropy_features = TopologicalEntropyFeatures {
            persistent_entropy: F::from(1.0).unwrap(),
            weighted_entropy: F::from(0.8).unwrap(),
            multiscale_entropy: Array1::ones(5),
            complexity: F::from(0.6).unwrap(),
        };

        Ok(TopologicalFeatures {
            persistence_features,
            persistence_images,
            persistence_landscapes,
            betti_curves,
            euler_curves,
            entropy_features,
            dimensionality: n_features,
        })
    }

    /// Extract persistence features from data
    fn extract_persistence_features(
        &self,
        data: &ArrayView2<F>,
    ) -> StatsResult<Vec<PersistenceFeature<F>>> {
        // Compute filtration at multiple scales
        let mut features = Vec::new();
        let num_scales = 10;

        for scale_idx in 0..num_scales {
            let scale = F::from(scale_idx as f64 / num_scales as f64).unwrap();
            let epsilon = self.config.filtration_config.max_epsilon * scale;

            // Build complex at this scale
            let analyzer = AdvancedTopologicalAnalyzer::new(self.config.clone());
            let distance_matrix = analyzer.compute_distance_matrix(data)?;
            let complex =
                self.build_vietoris_rips_complex_with_epsilon(&distance_matrix, epsilon)?;

            // Compute persistence
            let diagrams = analyzer.compute_persistent_homology(&complex)?;

            // Extract features from diagrams
            for (dim, diagram) in diagrams {
                for i in 0..diagram.points.nrows() {
                    let birth = diagram.points[[i, 0]];
                    let death = diagram.points[[i, 1]];
                    features.push(PersistenceFeature {
                        birth,
                        death,
                        persistence: death - birth,
                        dimension: dim,
                        scale: epsilon,
                        midlife: (birth + death) / F::from(2.0).unwrap(),
                    });
                }
            }
        }

        Ok(features)
    }

    /// Build Vietoris-Rips complex with specific epsilon
    fn build_vietoris_rips_complex_with_epsilon(
        &self,
        distance_matrix: &Array2<F>,
        epsilon: F,
    ) -> StatsResult<SimplicialComplex> {
        let n_points = distance_matrix.nrows();
        let mut simplices_by_dim = vec![Vec::new(); self.config.max_dimension + 1];

        // Add vertices (0-simplices)
        for i in 0..n_points {
            simplices_by_dim[0].push(Simplex {
                vertices: vec![i],
                dimension: 0,
            });
        }

        // Add edges (1-simplices)
        for i in 0..n_points {
            for j in (i + 1)..n_points {
                if distance_matrix[[i, j]] <= epsilon {
                    simplices_by_dim[1].push(Simplex {
                        vertices: vec![i, j],
                        dimension: 1,
                    });
                }
            }
        }

        // Add higher-dimensional simplices
        for dim in 2..=self.config.max_dimension {
            if dim - 1 < simplices_by_dim.len() && !simplices_by_dim[dim - 1].is_empty() {
                simplices_by_dim[dim] = self.generate_higher_simplices(
                    &simplices_by_dim[dim - 1],
                    distance_matrix,
                    epsilon,
                    dim,
                )?;
            }
        }

        Ok(SimplicialComplex {
            simplices_by_dim,
            max_dimension: self.config.max_dimension,
        })
    }

    /// Get configuration
    pub fn get_config(&self) -> &TopologicalConfig<F> {
        &self.config
    }

    /// Update configuration
    pub fn update_config(&mut self, config: TopologicalConfig<F>) {
        self.config = config;
    }
}

impl<F> Default for TopologicalConfig<F>
where
    F: Float + NumCast + Copy + std::fmt::Display + SimdUnifiedOps + Send + Sync,
{
    fn default() -> Self {
        Self {
            max_dimension: 2,
            filtration_config: FiltrationConfig {
                filtration_type: FiltrationType::VietorisRips,
                distance_metric: DistanceMetric::Euclidean,
                max_epsilon: F::from(1.0).unwrap(),
                num_steps: 100,
                adaptive_steps: false,
            },
            persistence_config: PersistenceConfig {
                algorithm: PersistenceAlgorithm::StandardReduction,
                coefficient_field: CoeffientField::Z2,
                persistence_threshold: F::from(0.01).unwrap(),
                compute_entropy: true,
                stability_analysis: false,
            },
            mapper_config: MapperConfig {
                filter_functions: Vec::new(),
                cover_config: CoverConfig {
                    num_intervals: vec![10],
                    overlap_percent: F::from(0.3).unwrap(),
                    cover_type: CoverType::UniformInterval,
                },
                clustering_method: ClusteringMethod::SingleLinkage,
                overlap_threshold: F::from(0.1).unwrap(),
                simplification: SimplificationConfig {
                    edge_contraction: false,
                    vertex_removal: false,
                    threshold: 0.01,
                },
            },
            multiscale_config: MultiscaleConfig {
                scale_range: (F::from(0.1).unwrap(), F::from(2.0).unwrap()),
                num_scales: 10,
                scale_distribution: ScaleDistribution::Linear,
                merger_strategy: MergerStrategy::Union,
            },
            inference_config: TopologicalInferenceConfig {
                bootstrap_samples: 0,
                confidence_level: F::from(0.95).unwrap(),
                null_model: NullModel::UniformRandom,
                test_type: TopologicalTest::PersistentRankTest,
                multiple_comparisons: MultipleComparisonsCorrection::BenjaminiHochberg,
            },
            parallel_config: ParallelConfig::default(),
        }
    }
}

impl<F> TopologicalConfig<F>
where
    F: Float + NumCast + Copy + std::fmt::Display + SimdUnifiedOps + Send + Sync,
{
    /// Advanced-advanced topological machine learning with persistent features
    pub fn topological_machine_learning(
        &mut self,
        data: &ArrayView2<F>,
        _labels: Option<&ArrayView1<F>>,
    ) -> StatsResult<TopologicalMLResult<F>> {
        // Extract topological features for machine learning
        let topological_features = (*self).extract_topological_features(data)?;

        // Create simplified feature matrix from topological features
        let feature_matrix = Array2::zeros((data.nrows(), 10)); // Simplified feature representation

        // Compute distance matrix for ML
        let analyzer = AdvancedTopologicalAnalyzer::new(self.clone());
        let kernel_matrix = analyzer.compute_distance_matrix(&feature_matrix.view())?;

        // Simplified ML results for now
        let prediction_result = None; // Placeholder for future implementation

        // Create proper clustering result
        let clustering_result = TopologicalClusteringResult {
            cluster_labels: Array1::zeros(data.nrows()),
            cluster_centers: Array2::zeros((3, data.ncols())), // Assume 3 clusters
            silhouette_score: F::from(0.5).unwrap(),
            inertia: F::from(1.0).unwrap(),
        };

        let feature_importance = Array1::ones(feature_matrix.ncols()); // Placeholder importance

        // Create topological signatures from the features
        let signatures = TopologicalSignatures {
            image_signature: topological_features
                .persistence_images
                .iter()
                .cloned()
                .collect(),
            landscape_signature: topological_features
                .persistence_landscapes
                .iter()
                .cloned()
                .collect(),
            betti_statistics: topological_features.betti_curves.iter().cloned().collect(),
            euler_statistics: topological_features.euler_curves.iter().cloned().collect(),
            entropy_vector: vec![topological_features.entropy_features.persistent_entropy],
        };

        Ok(TopologicalMLResult {
            topological_features: feature_matrix,
            kernel_matrix,
            signatures,
            prediction_result,
            clustering_result,
            feature_importance,
            stability_score: F::from(0.95).unwrap(), // Placeholder stability score
        })
    }

    /// Extract comprehensive topological features
    fn extract_topological_features(
        &self,
        data: &ArrayView2<F>,
    ) -> StatsResult<TopologicalFeatures<F>> {
        let (_n_samples_, n_features) = data.dim();

        // Persistent homology features
        let persistence_features = self.extract_persistence_features(data)?;

        // Persistence images - placeholder implementation
        let persistence_images = Array2::zeros((10, 10)); // Placeholder 10x10 persistence image

        // Persistence landscapes - placeholder implementation
        let persistence_landscapes = Array2::zeros((5, 20)); // Placeholder landscape representation

        // Betti curves - placeholder implementation
        let betti_curves = Array2::zeros((3, 10)); // Placeholder Betti curves for dimensions 0, 1, 2

        // Euler characteristic curves - placeholder implementation
        let euler_curves = Array1::zeros(10); // Placeholder Euler characteristic curve

        // Topological entropy features - placeholder implementation
        let entropy_features = TopologicalEntropyFeatures {
            persistent_entropy: F::from(1.0).unwrap(),
            weighted_entropy: F::from(0.8).unwrap(),
            multiscale_entropy: Array1::ones(5),
            complexity: F::from(0.6).unwrap(),
        };

        Ok(TopologicalFeatures {
            persistence_features,
            persistence_images,
            persistence_landscapes,
            betti_curves,
            euler_curves,
            entropy_features,
            dimensionality: n_features,
        })
    }

    /// Extract persistence features from data
    fn extract_persistence_features(
        &self,
        data: &ArrayView2<F>,
    ) -> StatsResult<Vec<PersistenceFeature<F>>> {
        // Compute filtration at multiple scales
        let mut features = Vec::new();
        let num_scales = 10;

        for scale_idx in 0..num_scales {
            let scale = F::from(scale_idx as f64 / num_scales as f64).unwrap();
            let epsilon = self.filtration_config.max_epsilon * scale;

            // Build complex at this scale
            let analyzer = AdvancedTopologicalAnalyzer::new(self.clone());
            let distance_matrix = analyzer.compute_distance_matrix(data)?;
            let complex =
                self.build_vietoris_rips_complex_with_epsilon(&distance_matrix, epsilon)?;

            // Compute persistence
            let diagrams = analyzer.compute_persistent_homology(&complex)?;

            // Extract features from diagrams
            for (dim, diagram) in diagrams {
                for i in 0..diagram.points.nrows() {
                    let birth = diagram.points[[i, 0]];
                    let death = diagram.points[[i, 1]];
                    features.push(PersistenceFeature {
                        birth,
                        death,
                        persistence: death - birth,
                        dimension: dim,
                        scale: epsilon,
                        midlife: (birth + death) / F::from(2.0).unwrap(),
                    });
                }
            }
        }

        Ok(features)
    }

    /// Build Vietoris-Rips complex with specific epsilon
    fn build_vietoris_rips_complex_with_epsilon(
        &self,
        distance_matrix: &Array2<F>,
        epsilon: F,
    ) -> StatsResult<SimplicialComplex> {
        let n_points = distance_matrix.nrows();
        let mut simplices_by_dim = vec![Vec::new(); self.max_dimension + 1];

        // Add vertices (0-simplices)
        for i in 0..n_points {
            simplices_by_dim[0].push(Simplex {
                vertices: vec![i],
                dimension: 0,
            });
        }

        // Add edges (1-simplices)
        for i in 0..n_points {
            for j in (i + 1)..n_points {
                if distance_matrix[[i, j]] <= epsilon {
                    simplices_by_dim[1].push(Simplex {
                        vertices: vec![i, j],
                        dimension: 1,
                    });
                }
            }
        }

        // Add higher-dimensional simplices
        for dim in 2..=self.max_dimension {
            if dim - 1 < simplices_by_dim.len() && !simplices_by_dim[dim - 1].is_empty() {
                let analyzer = AdvancedTopologicalAnalyzer::new(self.clone());
                simplices_by_dim[dim] = analyzer.generate_higher_simplices(
                    &simplices_by_dim[dim - 1],
                    distance_matrix,
                    epsilon,
                    dim,
                )?;
            }
        }

        Ok(SimplicialComplex {
            simplices_by_dim,
            max_dimension: self.max_dimension,
        })
    }

    /// Compute persistence images for vectorization
    fn compute_persistence_images(
        &self,
        features: &[PersistenceFeature<F>],
    ) -> StatsResult<Array2<F>> {
        let resolution = 20; // 20x20 image
        let mut image = Array2::zeros((resolution, resolution));

        // Find bounds for normalization
        let max_birth = features
            .iter()
            .map(|f| f.birth)
            .fold(F::zero(), |a, b| if a > b { a } else { b });
        let max_death = features
            .iter()
            .map(|f| f.death)
            .fold(F::zero(), |a, b| if a > b { a } else { b });

        let max_val = if max_death > max_birth {
            max_death
        } else {
            max_birth
        };

        if max_val > F::zero() {
            // Gaussian kernel parameters
            let sigma = F::from(0.1).unwrap() * max_val;
            let sigma_sq = sigma * sigma;

            for feature in features {
                // Map to image coordinates
                let _birth_coord = (feature.birth / max_val * F::from(resolution as f64).unwrap())
                    .to_usize()
                    .unwrap_or(0)
                    .min(resolution - 1);
                let _death_coord = (feature.death / max_val * F::from(resolution as f64).unwrap())
                    .to_usize()
                    .unwrap_or(0)
                    .min(resolution - 1);

                // Add Gaussian kernel centered at (birth, death)
                for i in 0..resolution {
                    for j in 0..resolution {
                        let x = F::from(i as f64).unwrap() / F::from(resolution as f64).unwrap()
                            * max_val;
                        let y = F::from(j as f64).unwrap() / F::from(resolution as f64).unwrap()
                            * max_val;

                        let dist_sq = (x - feature.birth) * (x - feature.birth)
                            + (y - feature.death) * (y - feature.death);
                        let weight = (-dist_sq / sigma_sq).exp() * feature.persistence;

                        image[[i, j]] = image[[i, j]] + weight;
                    }
                }
            }
        }

        Ok(image)
    }

    /// Compute persistence landscapes
    fn compute_persistence_landscapes(
        &self,
        features: &[PersistenceFeature<F>],
    ) -> StatsResult<Array2<F>> {
        let num_points = 100;
        let num_landscapes = 5;
        let mut landscapes = Array2::zeros((num_landscapes, num_points));

        if features.is_empty() {
            return Ok(landscapes);
        }

        // Find parameter range
        let min_birth = features
            .iter()
            .map(|f| f.birth)
            .fold(F::infinity(), |a, b| if a < b { a } else { b });
        let max_death = features
            .iter()
            .map(|f| f.death)
            .fold(F::neg_infinity(), |a, b| if a > b { a } else { b });

        let range = max_death - min_birth;
        if range <= F::zero() {
            return Ok(landscapes);
        }

        for point_idx in 0..num_points {
            let t = min_birth
                + F::from(point_idx as f64).unwrap() / F::from(num_points as f64).unwrap() * range;

            // Compute landscape functions at parameter t
            let mut values = Vec::new();

            for feature in features {
                if t >= feature.birth && t <= feature.death {
                    let value = if t <= (feature.birth + feature.death) / F::from(2.0).unwrap() {
                        t - feature.birth
                    } else {
                        feature.death - t
                    };
                    values.push(value);
                }
            }

            // Sort values in descending order
            values.sort_by(|a, b| b.partial_cmp(a).unwrap_or(std::cmp::Ordering::Equal));

            // Fill landscape levels
            for landscape_idx in 0..num_landscapes {
                if landscape_idx < values.len() {
                    landscapes[[landscape_idx, point_idx]] = values[landscape_idx];
                }
            }
        }

        Ok(landscapes)
    }

    /// Compute Betti curves
    fn compute_betti_curves(&self, features: &[PersistenceFeature<F>]) -> StatsResult<Array2<F>> {
        let num_points = 100;
        let max_dim = 3;
        let mut betti_curves = Array2::zeros((max_dim, num_points));

        if features.is_empty() {
            return Ok(betti_curves);
        }

        // Find parameter range
        let min_val = features
            .iter()
            .map(|f| f.birth)
            .fold(F::infinity(), |a, b| if a < b { a } else { b });
        let max_val = features
            .iter()
            .map(|f| f.death)
            .fold(F::neg_infinity(), |a, b| if a > b { a } else { b });

        let range = max_val - min_val;
        if range <= F::zero() {
            return Ok(betti_curves);
        }

        for point_idx in 0..num_points {
            let t = min_val
                + F::from(point_idx as f64).unwrap() / F::from(num_points as f64).unwrap() * range;

            // Count active features for each dimension
            for dim in 0..max_dim {
                let count = features
                    .iter()
                    .filter(|f| f.dimension == dim && f.birth <= t && t < f.death)
                    .count();

                betti_curves[[dim, point_idx]] = F::from(count).unwrap();
            }
        }

        Ok(betti_curves)
    }

    /// Compute Euler characteristic curves
    fn compute_euler_characteristic_curves(
        &self,
        features: &[PersistenceFeature<F>],
    ) -> StatsResult<Array1<F>> {
        let num_points = 100;
        let mut euler_curve = Array1::zeros(num_points);

        if features.is_empty() {
            return Ok(euler_curve);
        }

        // Find parameter range
        let min_val = features
            .iter()
            .map(|f| f.birth)
            .fold(F::infinity(), |a, b| if a < b { a } else { b });
        let max_val = features
            .iter()
            .map(|f| f.death)
            .fold(F::neg_infinity(), |a, b| if a > b { a } else { b });

        let range = max_val - min_val;
        if range <= F::zero() {
            return Ok(euler_curve);
        }

        for point_idx in 0..num_points {
            let t = min_val
                + F::from(point_idx as f64).unwrap() / F::from(num_points as f64).unwrap() * range;

            // Compute Euler characteristic: χ = Σ(-1)^i * β_i
            let mut euler_char = F::zero();

            for dim in 0..=3 {
                let betti_number = features
                    .iter()
                    .filter(|f| f.dimension == dim && f.birth <= t && t < f.death)
                    .count();

                let sign = if dim % 2 == 0 { F::one() } else { -F::one() };
                euler_char = euler_char + sign * F::from(betti_number).unwrap();
            }

            euler_curve[point_idx] = euler_char;
        }

        Ok(euler_curve)
    }

    /// Compute topological entropy features
    fn compute_topological_entropy_features(
        &self,
        features: &[PersistenceFeature<F>],
    ) -> StatsResult<TopologicalEntropyFeatures<F>> {
        // Persistent entropy
        let persistent_entropy = self.compute_persistent_entropy(features)?;

        // Persistence-weighted entropy
        let weighted_entropy = self.compute_persistence_weighted_entropy(features)?;

        // Multi-scale entropy
        let multiscale_entropy = self.compute_multiscale_topological_entropy(features)?;

        // Topological complexity
        let complexity = self.compute_topological_complexity(features)?;

        Ok(TopologicalEntropyFeatures {
            persistent_entropy,
            weighted_entropy,
            multiscale_entropy,
            complexity,
        })
    }

    /// Compute persistent entropy
    fn compute_persistent_entropy(&self, features: &[PersistenceFeature<F>]) -> StatsResult<F> {
        if features.is_empty() {
            return Ok(F::zero());
        }

        // Normalize persistence values
        let total_persistence = features
            .iter()
            .map(|f| f.persistence)
            .fold(F::zero(), |acc, p| acc + p);

        if total_persistence <= F::zero() {
            return Ok(F::zero());
        }

        // Compute Shannon entropy of persistence distribution
        let mut entropy = F::zero();
        for feature in features {
            if feature.persistence > F::zero() {
                let prob = feature.persistence / total_persistence;
                entropy = entropy - prob * prob.ln();
            }
        }

        Ok(entropy)
    }

    /// Compute persistence-weighted entropy
    fn compute_persistence_weighted_entropy(
        &self,
        features: &[PersistenceFeature<F>],
    ) -> StatsResult<F> {
        if features.is_empty() {
            return Ok(F::zero());
        }

        let mut weighted_entropy = F::zero();
        let total_weight = features
            .iter()
            .map(|f| f.persistence * f.persistence)
            .fold(F::zero(), |acc, w| acc + w);

        if total_weight > F::zero() {
            for feature in features {
                let weight = (feature.persistence * feature.persistence) / total_weight;
                if weight > F::zero() {
                    weighted_entropy = weighted_entropy - weight * weight.ln();
                }
            }
        }

        Ok(weighted_entropy)
    }

    /// Compute multi-scale topological entropy
    fn compute_multiscale_topological_entropy(
        &self,
        features: &[PersistenceFeature<F>],
    ) -> StatsResult<Array1<F>> {
        let num_scales = 5;
        let mut multiscale_entropy = Array1::zeros(num_scales);

        for scale_idx in 0..num_scales {
            let scale_threshold = F::from((scale_idx + 1) as f64 / num_scales as f64).unwrap();

            // Filter features by scale
            let filtered_features: Vec<_> = features
                .iter()
                .filter(|f| f.persistence >= scale_threshold * f.death)
                .cloned()
                .collect();

            multiscale_entropy[scale_idx] = self.compute_persistent_entropy(&filtered_features)?;
        }

        Ok(multiscale_entropy)
    }

    /// Compute topological complexity
    fn compute_topological_complexity(&self, features: &[PersistenceFeature<F>]) -> StatsResult<F> {
        if features.is_empty() {
            return Ok(F::zero());
        }

        // Combine multiple complexity measures
        let entropy = self.compute_persistent_entropy(features)?;
        let num_features = F::from(features.len()).unwrap();
        let avg_persistence = features
            .iter()
            .map(|f| f.persistence)
            .fold(F::zero(), |acc, p| acc + p)
            / num_features;

        // Weighted complexity score
        let complexity = entropy * num_features.ln() * avg_persistence;

        Ok(complexity)
    }

    /// Compute topological signatures
    fn compute_topological_signatures(
        &self,
        features: &TopologicalFeatures<F>,
    ) -> StatsResult<TopologicalSignatures<F>> {
        // Flatten persistence images
        let image_signature = features.persistence_images.as_slice().unwrap().to_vec();

        // Flatten persistence landscapes
        let landscape_signature = features.persistence_landscapes.as_slice().unwrap().to_vec();

        // Statistics from Betti curves
        let betti_statistics = self.compute_curve_statistics(&features.betti_curves)?;

        // Statistics from Euler curves
        let euler_statistics = self.compute_curve_statistics_1d(&features.euler_curves)?;

        // Entropy features
        let entropy_vector = vec![
            features.entropy_features.persistent_entropy,
            features.entropy_features.weighted_entropy,
            features.entropy_features.complexity,
        ];

        Ok(TopologicalSignatures {
            image_signature,
            landscape_signature,
            betti_statistics,
            euler_statistics,
            entropy_vector,
        })
    }

    /// Compute statistics from 2D curves
    fn compute_curve_statistics(&self, curves: &Array2<F>) -> StatsResult<Vec<F>> {
        let mut statistics = Vec::new();

        let (num_curves, num_points) = curves.dim();

        for curve_idx in 0..num_curves {
            let curve = curves.row(curve_idx);

            // Basic statistics
            let mean = curve.sum() / F::from(num_points).unwrap();
            let variance = curve
                .iter()
                .map(|&x| (x - mean) * (x - mean))
                .fold(F::zero(), |acc, x| acc + x)
                / F::from(num_points).unwrap();
            let std_dev = variance.sqrt();

            // Extrema
            let min_val = curve
                .iter()
                .fold(F::infinity(), |a, &b| if a < b { a } else { b });
            let max_val = curve
                .iter()
                .fold(F::neg_infinity(), |a, &b| if a > b { a } else { b });

            // Integral (area under curve)
            let integral = curve.sum() / F::from(num_points).unwrap();

            statistics.extend_from_slice(&[mean, std_dev, min_val, max_val, integral]);
        }

        Ok(statistics)
    }

    /// Compute statistics from 1D curves
    fn compute_curve_statistics_1d(&self, curve: &Array1<F>) -> StatsResult<Vec<F>> {
        let num_points = curve.len();

        if num_points == 0 {
            return Ok(vec![F::zero(); 5]);
        }

        // Basic statistics
        let mean = curve.sum() / F::from(num_points).unwrap();
        let variance = curve
            .iter()
            .map(|&x| (x - mean) * (x - mean))
            .fold(F::zero(), |acc, x| acc + x)
            / F::from(num_points).unwrap();
        let std_dev = variance.sqrt();

        // Extrema
        let min_val = curve
            .iter()
            .fold(F::infinity(), |a, &b| if a < b { a } else { b });
        let max_val = curve
            .iter()
            .fold(F::neg_infinity(), |a, &b| if a > b { a } else { b });

        Ok(vec![mean, std_dev, min_val, max_val, curve.sum()])
    }

    /// Encode persistent features for machine learning
    fn encode_persistent_features(
        &self,
        signatures: &TopologicalSignatures<F>,
    ) -> StatsResult<Array2<F>> {
        // Combine all signature vectors into feature matrix
        let mut all_features = Vec::new();

        all_features.extend_from_slice(&signatures.image_signature);
        all_features.extend_from_slice(&signatures.landscape_signature);
        all_features.extend_from_slice(&signatures.betti_statistics);
        all_features.extend_from_slice(&signatures.euler_statistics);
        all_features.extend_from_slice(&signatures.entropy_vector);

        // Create feature matrix (1 sample, n_features)
        let n_features = all_features.len();
        let mut feature_matrix = Array2::zeros((1, n_features));

        for (i, &feature) in all_features.iter().enumerate() {
            feature_matrix[[0, i]] = feature;
        }

        Ok(feature_matrix)
    }

    /// Compute topological kernel matrix
    fn compute_topological_kernel_matrix(&self, features: &Array2<F>) -> StatsResult<Array2<F>> {
        let (n_samples_, n_features) = features.dim();
        let mut kernel_matrix = Array2::zeros((n_samples_, n_samples_));

        // Gaussian RBF kernel with topological distance
        let sigma = F::from(1.0).unwrap();
        let sigma_sq = sigma * sigma;

        for i in 0..n_samples_ {
            for j in 0..n_samples_ {
                let mut dist_sq = F::zero();

                for k in 0..n_features {
                    let diff = features[[i, k]] - features[[j, k]];
                    dist_sq = dist_sq + diff * diff;
                }

                kernel_matrix[[i, j]] = (-dist_sq / sigma_sq).exp();
            }
        }

        Ok(kernel_matrix)
    }

    /// Topological classification
    fn topological_classification(
        &self,
        features: &Array2<F>,
        labels: &ArrayView1<F>,
        kernel_matrix: &Array2<F>,
    ) -> StatsResult<TopologicalPredictionResult<F>> {
        let n_samples_ = features.nrows();

        // Simplified topological SVM using kernel _matrix
        let mut predictions = Array1::zeros(n_samples_);
        let mut confidence_scores = Array1::zeros(n_samples_);

        // Simple nearest neighbor classification using topological kernel
        for i in 0..n_samples_ {
            let mut best_similarity = F::zero();
            let mut predicted_label = labels[0];

            for j in 0..n_samples_ {
                if i != j && kernel_matrix[[i, j]] > best_similarity {
                    best_similarity = kernel_matrix[[i, j]];
                    predicted_label = labels[j];
                }
            }

            predictions[i] = predicted_label;
            confidence_scores[i] = best_similarity;
        }

        // Compute accuracy
        let correct_predictions: usize = predictions
            .iter()
            .zip(labels.iter())
            .map(|(&pred, &true_label)| {
                if (pred - true_label).abs() < F::from(0.5).unwrap() {
                    1
                } else {
                    0
                }
            })
            .sum();

        let accuracy = F::from(correct_predictions as f64 / n_samples_ as f64).unwrap();

        Ok(TopologicalPredictionResult {
            predictions,
            confidence_scores,
            accuracy,
            feature_weights: Array1::ones(features.ncols()),
        })
    }

    /// Topological clustering
    fn topological_clustering(
        &self,
        features: &Array2<F>,
    ) -> StatsResult<TopologicalClusteringResult<F>> {
        let n_samples_ = features.nrows();
        let num_clusters = 3; // Simplified to 3 clusters

        // Simple k-means clustering on topological features
        let mut cluster_labels = Array1::zeros(n_samples_);
        let mut cluster_centers = Array2::zeros((num_clusters, features.ncols()));

        // Initialize centers randomly
        for i in 0..num_clusters {
            for j in 0..features.ncols() {
                cluster_centers[[i, j]] = F::from(i as f64 / num_clusters as f64).unwrap();
            }
        }

        // Simple assignment based on distance to centers
        for i in 0..n_samples_ {
            let mut best_distance = F::infinity();
            let mut best_cluster = 0;

            for cluster in 0..num_clusters {
                let mut distance = F::zero();
                for j in 0..features.ncols() {
                    let diff = features[[i, j]] - cluster_centers[[cluster, j]];
                    distance = distance + diff * diff;
                }

                if distance < best_distance {
                    best_distance = distance;
                    best_cluster = cluster;
                }
            }

            cluster_labels[i] = F::from(best_cluster).unwrap();
        }

        // Compute clustering quality (simplified silhouette score)
        let silhouette_score = F::from(0.7).unwrap(); // Placeholder

        Ok(TopologicalClusteringResult {
            cluster_labels,
            cluster_centers,
            silhouette_score,
            inertia: F::from(100.0).unwrap(),
        })
    }

    /// Analyze topological feature importance
    fn analyze_topological_feature_importance(
        &self,
        features: &Array2<F>,
        labels: Option<&ArrayView1<F>>,
    ) -> StatsResult<Array1<F>> {
        let (_, n_features) = features.dim();
        let mut importance_scores = Array1::zeros(n_features);

        if let Some(labels) = labels {
            // Compute feature importance based on correlation with labels
            for j in 0..n_features {
                let feature_col = features.column(j);
                let correlation = self.compute_correlation(&feature_col, labels)?;
                importance_scores[j] = correlation.abs();
            }
        } else {
            // Compute feature importance based on variance
            for j in 0..n_features {
                let feature_col = features.column(j);
                let mean = feature_col.sum() / F::from(feature_col.len()).unwrap();
                let variance = feature_col
                    .iter()
                    .map(|&x| (x - mean) * (x - mean))
                    .fold(F::zero(), |acc, x| acc + x)
                    / F::from(feature_col.len()).unwrap();

                importance_scores[j] = variance;
            }
        }

        Ok(importance_scores)
    }

    /// Compute correlation between two arrays
    fn compute_correlation(&self, x: &ArrayView1<F>, y: &ArrayView1<F>) -> StatsResult<F> {
        let n = x.len();
        if n != y.len() || n == 0 {
            return Ok(F::zero());
        }

        let n_f = F::from(n).unwrap();
        let mean_x = x.sum() / n_f;
        let mean_y = y.sum() / n_f;

        let mut num = F::zero();
        let mut den_x = F::zero();
        let mut den_y = F::zero();

        for i in 0..n {
            let dx = x[i] - mean_x;
            let dy = y[i] - mean_y;

            num = num + dx * dy;
            den_x = den_x + dx * dx;
            den_y = den_y + dy * dy;
        }

        let denominator = (den_x * den_y).sqrt();
        if denominator > F::zero() {
            Ok(num / denominator)
        } else {
            Ok(F::zero())
        }
    }

    /// Compute topological stability score
    fn compute_topological_stability(
        &self,
        signatures: &TopologicalSignatures<F>,
    ) -> StatsResult<F> {
        // Simplified stability score based on signature consistency
        let image_norm = signatures
            .image_signature
            .iter()
            .map(|&x| x * x)
            .fold(F::zero(), |acc, x| acc + x)
            .sqrt();

        let landscape_norm = signatures
            .landscape_signature
            .iter()
            .map(|&x| x * x)
            .fold(F::zero(), |acc, x| acc + x)
            .sqrt();

        let entropy_norm = signatures
            .entropy_vector
            .iter()
            .map(|&x| x * x)
            .fold(F::zero(), |acc, x| acc + x)
            .sqrt();

        // Combine norms as stability measure
        let stability = (image_norm + landscape_norm + entropy_norm) / F::from(3.0).unwrap();

        Ok(stability)
    }

    /// Get configuration
    pub fn get_config(&self) -> &TopologicalConfig<F> {
        self
    }

    /// Update configuration
    pub fn update_config(&mut self, config: TopologicalConfig<F>) {
        *self = config;
    }
}

/// Persistence feature for machine learning
#[derive(Debug, Clone)]
pub struct PersistenceFeature<F> {
    pub birth: F,
    pub death: F,
    pub persistence: F,
    pub dimension: usize,
    pub scale: F,
    pub midlife: F,
}

/// Comprehensive topological features
#[derive(Debug, Clone)]
pub struct TopologicalFeatures<F> {
    pub persistence_features: Vec<PersistenceFeature<F>>,
    pub persistence_images: Array2<F>,
    pub persistence_landscapes: Array2<F>,
    pub betti_curves: Array2<F>,
    pub euler_curves: Array1<F>,
    pub entropy_features: TopologicalEntropyFeatures<F>,
    pub dimensionality: usize,
}

/// Topological entropy features
#[derive(Debug, Clone)]
pub struct TopologicalEntropyFeatures<F> {
    pub persistent_entropy: F,
    pub weighted_entropy: F,
    pub multiscale_entropy: Array1<F>,
    pub complexity: F,
}

/// Topological signatures for ML
#[derive(Debug, Clone)]
pub struct TopologicalSignatures<F> {
    pub image_signature: Vec<F>,
    pub landscape_signature: Vec<F>,
    pub betti_statistics: Vec<F>,
    pub euler_statistics: Vec<F>,
    pub entropy_vector: Vec<F>,
}

/// Results from topological machine learning
#[derive(Debug, Clone)]
pub struct TopologicalMLResult<F> {
    pub topological_features: Array2<F>,
    pub kernel_matrix: Array2<F>,
    pub signatures: TopologicalSignatures<F>,
    pub prediction_result: Option<TopologicalPredictionResult<F>>,
    pub clustering_result: TopologicalClusteringResult<F>,
    pub feature_importance: Array1<F>,
    pub stability_score: F,
}

/// Results from topological prediction
#[derive(Debug, Clone)]
pub struct TopologicalPredictionResult<F> {
    pub predictions: Array1<F>,
    pub confidence_scores: Array1<F>,
    pub accuracy: F,
    pub feature_weights: Array1<F>,
}

/// Results from topological clustering
#[derive(Debug, Clone)]
pub struct TopologicalClusteringResult<F> {
    pub cluster_labels: Array1<F>,
    pub cluster_centers: Array2<F>,
    pub silhouette_score: F,
    pub inertia: F,
}

#[cfg(test)]
mod tests {
    use super::*;
    use scirs2_core::ndarray::array;

    #[test]
    fn test_topological_analyzer_creation() {
        let config = TopologicalConfig::default();
        let analyzer = AdvancedTopologicalAnalyzer::<f64>::new(config);

        assert_eq!(analyzer.config.max_dimension, 2);
        assert_eq!(analyzer.config.filtration_config.num_steps, 100);
    }

    #[test]
    fn test_distance_computation() {
        let config = TopologicalConfig::default();
        let analyzer = AdvancedTopologicalAnalyzer::<f64>::new(config);

        let p1 = array![0.0, 0.0];
        let p2 = array![3.0, 4.0];

        let dist = analyzer
            .compute_distance(&p1.view(), &p2.view(), DistanceMetric::Euclidean)
            .unwrap();

        assert!((dist - 5.0).abs() < 1e-10);
    }

    #[test]
    fn test_point_cloud_analysis() {
        let config = TopologicalConfig::default();
        let mut analyzer = AdvancedTopologicalAnalyzer::<f64>::new(config);

        // Simple 2D point cloud
        let points = array![[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0], [0.5, 0.5]];

        let result = analyzer.analyze_point_cloud(&points.view()).unwrap();

        assert!(!result.persistence_diagrams.is_empty());
        assert!(result.betti_numbers.nrows() > 0);
        assert!(result.performance.timing.contains_key("total_analysis"));
    }

    #[test]
    fn test_simplicial_complex_construction() {
        let config = TopologicalConfig::default();
        let mut analyzer = AdvancedTopologicalAnalyzer::<f64>::new(config);

        let points = array![[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]];

        let complex = analyzer.build_simplicial_complex(&points.view()).unwrap();

        assert_eq!(complex.simplices_by_dim[0].len(), 3); // 3 vertices
        assert!(complex.simplices_by_dim[1].len() > 0); // Some edges
    }

    #[test]
    fn test_persistence_computation() {
        let config = TopologicalConfig::default();
        let analyzer = AdvancedTopologicalAnalyzer::<f64>::new(config);

        let complex = SimplicialComplex {
            simplices_by_dim: vec![
                vec![
                    Simplex {
                        vertices: vec![0],
                        dimension: 0,
                    },
                    Simplex {
                        vertices: vec![1],
                        dimension: 0,
                    },
                    Simplex {
                        vertices: vec![2],
                        dimension: 0,
                    },
                ],
                vec![
                    Simplex {
                        vertices: vec![0, 1],
                        dimension: 1,
                    },
                    Simplex {
                        vertices: vec![1, 2],
                        dimension: 1,
                    },
                ],
            ],
            max_dimension: 1,
        };

        let diagrams = analyzer.compute_persistent_homology(&complex).unwrap();

        assert!(diagrams.contains_key(&0)); // H_0
        assert!(diagrams.contains_key(&1)); // H_1
    }
}