use ruv_fann::{SemanticCartanMatrix, RootVector, CartanAttention};

// Production-ready neural network with Cartan attention
pub struct ProductionSCMNetwork {
    layers: Vec<SemanticCartanMatrix>,
    attention_heads: Vec<CartanAttention>,
    optimizer: CartanOptimizer,
    metrics: PerformanceMetrics,
}

impl ProductionSCMNetwork {
    pub fn new(layer_sizes: &[usize], attention_heads: usize) -> Self {
        let layers = layer_sizes.windows(2)
            .map(|window| SemanticCartanMatrix::new(window[0], window[1]))
            .collect();
            
        let attention_heads = (0..attention_heads)
            .map(|_| CartanAttention::new(32, 8))
            .collect();
            
        Self {
            layers,
            attention_heads,
            optimizer: CartanOptimizer::adam(0.001),
            metrics: PerformanceMetrics::new(),
        }
    }
    
    pub fn forward(&mut self, input: &RootVector) -> RootVector {
        let mut x = input.clone();
        
        // Process through Cartan matrix layers
        for layer in &self.layers {
            x = layer.process(&x);
        }
        
        // Multi-head Cartan attention
        let attention_outputs: Vec<_> = self.attention_heads
            .iter()
            .map(|head| head.forward(&x))
            .collect();
            
        // Combine attention outputs using Cartan geometry
        self.combine_attention_outputs(&attention_outputs)
    }
    
    pub fn train(&mut self, dataset: &Dataset) -> TrainingResults {
        let mut results = TrainingResults::new();
        
        for epoch in 0..self.config.epochs {
            let mut epoch_loss = 0.0;
            
            for batch in dataset.batches(self.config.batch_size) {
                // Forward pass
                let predictions = batch.inputs
                    .iter()
                    .map(|input| self.forward(input))
                    .collect::<Vec<_>>();
                
                // Compute loss with Cartan-aware regularization
                let loss = self.compute_cartan_loss(&predictions, &batch.targets);
                epoch_loss += loss;
                
                // Backward pass with Cartan constraints
                self.backward_with_constraints(loss);
                
                // Update parameters preserving mathematical properties
                self.optimizer.step_constrained(&mut self.layers);
            }
            
            results.add_epoch(epoch, epoch_loss / dataset.len() as f32);
        }
        
        results
    }
}

impl SemanticCartanMatrix {
    /// Construct a Cartan matrix with mathematical guarantees
    pub fn construct_validated(root_system: RootSystem) -> Result<Self, CartanError> {
        let dimension = root_system.dimension();
        let mut matrix = CartanMatrix::zeros(dimension);
        
        // Build Cartan matrix from root system
        for i in 0..dimension {
            for j in 0..dimension {
                let root_i = root_system.simple_root(i);
                let root_j = root_system.simple_root(j);
                
                // Cartan matrix entry: A_ij = 2⟨αᵢ, αⱼ⟩ / ⟨αⱼ, αⱼ⟩
                let inner_product = root_i.inner_product(&root_j);
                let norm_squared = root_j.norm_squared();
                
                matrix[(i, j)] = 2.0 * inner_product / norm_squared;
            }
        }
        
        // Validate Cartan matrix properties
        Self::validate_cartan_properties(&matrix)?;
        
        Ok(Self { matrix, root_system })
    }
    
    /// Enforce mathematical constraints during training
    fn validate_cartan_properties(matrix: &CartanMatrix) -> Result<(), CartanError> {
        let n = matrix.nrows();
        
        // Check diagonal elements (must equal 2)
        for i in 0..n {
            if (matrix[(i, i)] - 2.0).abs() > 1e-10 {
                return Err(CartanError::InvalidDiagonal(i, matrix[(i, i)]));
            }
        }
        
        // Check off-diagonal elements (must be ≤ 0)
        for i in 0..n {
            for j in 0..n {
                if i != j && matrix[(i, j)] > 1e-10 {
                    return Err(CartanError::InvalidOffDiagonal(i, j, matrix[(i, j)]));
                }
            }
        }
        
        // Check positive definiteness of symmetrized matrix
        let symmetrized = Self::symmetrize_matrix(matrix);
        if !Self::is_positive_definite(&symmetrized) {
            return Err(CartanError::NotPositiveDefinite);
        }
        
        Ok(())
    }
}

#[derive(Debug, Clone)]
pub struct RootSystem {
    simple_roots: Vec<RootVector>,
    positive_roots: Vec<RootVector>,
    cartan_type: CartanType,
}

impl RootSystem {
    /// Create root system for specific Lie algebra types
    pub fn new(cartan_type: CartanType) -> Self {
        match cartan_type {
            CartanType::A(n) => Self::construct_type_a(n),
            CartanType::B(n) => Self::construct_type_b(n),
            CartanType::C(n) => Self::construct_type_c(n),
            CartanType::D(n) => Self::construct_type_d(n),
            CartanType::E(n) => Self::construct_exceptional_e(n),
            CartanType::F4 => Self::construct_f4(),
            CartanType::G2 => Self::construct_g2(),
        }
    }
    
    /// Construct A_n root system (sl_{n+1})
    fn construct_type_a(n: usize) -> Self {
        let mut simple_roots = Vec::new();
        
        // Simple roots: e_i - e_{i+1} for i = 1, ..., n
        for i in 0..n {
            let mut root = RootVector::zeros();
            root[i] = 1.0;
            root[i + 1] = -1.0;
            simple_roots.push(root);
        }
        
        // Generate all positive roots
        let positive_roots = Self::generate_positive_roots(&simple_roots);
        
        Self {
            simple_roots,
            positive_roots,
            cartan_type: CartanType::A(n),
        }
    }
    
    /// Generate positive roots from simple roots
    fn generate_positive_roots(simple_roots: &[RootVector]) -> Vec<RootVector> {
        let mut positive_roots = simple_roots.to_vec();
        let mut queue = simple_roots.to_vec();
        
        while let Some(root) = queue.pop() {
            for simple_root in simple_roots {
                let sum = &root + simple_root;
                
                // Check if sum is a valid root using root criteria
                if Self::is_valid_positive_root(&sum, simple_roots) {
                    if !positive_roots.contains(&sum) {
                        positive_roots.push(sum.clone());
                        queue.push(sum);
                    }
                }
            }
        }
        
        positive_roots
    }
}

#[derive(Debug, Clone, PartialEq)]
pub enum CartanType {
    A(usize), // sl_{n+1}
    B(usize), // so_{2n+1}
    C(usize), // sp_{2n}
    D(usize), // so_{2n}
    E(usize), // E_6, E_7, E_8
    F4,       // F_4
    G2,       // G_2
}

impl SemanticCartanMatrix {
    /// Backpropagation that preserves Cartan matrix structure
    pub fn backward_constrained(&mut self, gradient: &RootVector) -> RootVector {
        // Standard gradient computation
        let mut param_gradients = self.compute_parameter_gradients(gradient);
        
        // Project gradients to maintain Cartan constraints
        self.project_gradients_to_cartan_manifold(&mut param_gradients);
        
        // Apply orthogonalization to preserve root system structure
        self.orthogonalize_preserving_roots(&mut param_gradients);
        
        // Compute input gradient for backpropagation
        self.compute_input_gradient(&param_gradients)
    }
    
    fn project_gradients_to_cartan_manifold(&self, gradients: &mut CartanMatrix) {
        let n = gradients.nrows();
        
        // Project diagonal gradients (constrained to maintain diagonal = 2)
        for i in 0..n {
            // Diagonal elements have zero gradient to maintain constraint
            gradients[(i, i)] = 0.0;
        }
        
        // Project off-diagonal gradients to maintain non-positivity
        for i in 0..n {
            for j in 0..n {
                if i != j && self.matrix[(i, j)] > -1e-10 {
                    // At boundary, project gradient to feasible direction
                    gradients[(i, j)] = gradients[(i, j)].min(0.0);
                }
            }
        }
    }
    
    fn orthogonalize_preserving_roots(&mut self, gradients: &mut CartanMatrix) {
        // Modified Gram-Schmidt that preserves root system structure
        let root_space_projector = self.compute_root_space_projector();
        *gradients = &root_space_projector * gradients * &root_space_projector.transpose();
    }
}

pub struct CartanOptimizer {
    learning_rate: f32,
    momentum: f32,
    weight_decay: f32,
    constraint_penalty: f32,
    velocity: HashMap<String, CartanMatrix>,
}

impl CartanOptimizer {
    pub fn step_constrained(&mut self, matrices: &mut [SemanticCartanMatrix]) {
        for (idx, matrix) in matrices.iter_mut().enumerate() {
            let param_key = format!("matrix_{}", idx);
            
            // Get current gradients
            let gradients = matrix.get_gradients();
            
            // Apply momentum with Cartan manifold projection
            let velocity = self.velocity.entry(param_key).or_insert_with(|| CartanMatrix::zeros(gradients.nrows()));
            *velocity = self.momentum * &*velocity + (1.0 - self.momentum) * &gradients;
            
            // Riemannian gradient descent on Cartan manifold
            let riemannian_gradient = self.compute_riemannian_gradient(matrix, velocity);
            
            // Update parameters with constraint preservation
            matrix.update_constrained(&riemannian_gradient, self.learning_rate);
            
            // Apply regularization to maintain mathematical structure
            self.apply_cartan_regularization(matrix);
        }
    }
    
    fn compute_riemannian_gradient(&self, matrix: &SemanticCartanMatrix, euclidean_grad: &CartanMatrix) -> CartanMatrix {
        // Project Euclidean gradient to tangent space of Cartan manifold
        let tangent_projection = matrix.compute_tangent_projector();
        &tangent_projection * euclidean_grad
    }
    
    fn apply_cartan_regularization(&self, matrix: &mut SemanticCartanMatrix) {
        // Soft constraints to maintain Cartan properties
        let penalty = self.constraint_penalty;
        
        // Regularize towards diagonal = 2
        for i in 0..matrix.dimension() {
            let deviation = matrix.matrix[(i, i)] - 2.0;
            matrix.matrix[(i, i)] -= penalty * deviation;
        }
        
        // Regularize off-diagonal elements towards non-positive values
        for i in 0..matrix.dimension() {
            for j in 0..matrix.dimension() {
                if i != j && matrix.matrix[(i, j)] > 0.0 {
                    matrix.matrix[(i, j)] *= (1.0 - penalty);
                }
            }
        }
    }
}