apex_solver/optimizer/

gauss_newton.rs

//! Gauss-Newton optimization algorithm implementation.
//!
//! The Gauss-Newton method is a fundamental iterative algorithm for solving nonlinear least squares problems
//! of the form:
//!
//! ```text
//! min f(x) = ½||r(x)||² = ½Σᵢ rᵢ(x)²
//! ```
//!
//! where `r: ℝⁿ → ℝᵐ` is the residual vector function.
//!
//! # Algorithm Overview
//!
//! The Gauss-Newton method solves the normal equations at each iteration:
//!
//! ```text
//! J^T·J·h = -J^T·r
//! ```
//!
//! where:
//! - `J` is the Jacobian matrix (m × n) of partial derivatives ∂rᵢ/∂xⱼ
//! - `r` is the residual vector (m × 1)
//! - `h` is the step vector (n × 1)
//!
//! The approximated Hessian `H ≈ J^T·J` replaces the true Hessian `∇²f = J^T·J + Σᵢ rᵢ·∇²rᵢ`,
//! which works well when residuals are small or nearly linear.
//!
//! ## Convergence Properties
//!
//! - **Quadratic convergence** near the solution when the Gauss-Newton approximation is valid
//! - **May diverge** if the initial guess is far from the optimum or the problem is ill-conditioned
//! - **No step size control** - always takes the full Newton step without damping
//!
//! ## When to Use
//!
//! Gauss-Newton is most effective when:
//! - The problem is well-conditioned with `J^T·J` having good numerical properties
//! - The initial parameter guess is close to the solution
//! - Fast convergence is prioritized over robustness
//! - Residuals at the solution are expected to be small
//!
//! For ill-conditioned problems or poor initial guesses, consider:
//! - [`LevenbergMarquardt`](crate::optimizer::LevenbergMarquardt) for adaptive damping
//! - [`DogLeg`](crate::optimizer::DogLeg) for trust region control
//!
//! # Implementation Features
//!
//! - **Sparse matrix support**: Efficient handling of large-scale problems via `faer` sparse library
//! - **Robust linear solvers**: Choice between Cholesky (fast) and QR (stable) factorizations
//! - **Jacobi scaling**: Optional diagonal preconditioning to improve conditioning
//! - **Manifold operations**: Support for optimization on Lie groups (SE2, SE3, SO2, SO3)
//! - **Comprehensive diagnostics**: Detailed convergence and performance summaries
//!
//! # Mathematical Background
//!
//! At each iteration k, the algorithm:
//!
//! 1. **Linearizes** the problem around current estimate xₖ: `r(xₖ + h) ≈ r(xₖ) + J(xₖ)·h`
//! 2. **Solves** the normal equations for step h: `J^T·J·h = -J^T·r`
//! 3. **Updates** parameters: `xₖ₊₁ = xₖ ⊕ h` (using manifold plus operation)
//! 4. **Checks** convergence criteria (cost, gradient, parameter change)
//!
//! The method terminates when cost change, gradient norm, or parameter update fall below
//! specified tolerances, or when maximum iterations are reached.
//!
//! # Examples
//!
//! ## Basic usage
//!
//! ```no_run
//! use apex_solver::optimizer::GaussNewton;
//! use apex_solver::core::problem::Problem;
//! use std::collections::HashMap;
//!
//! # fn main() -> Result<(), Box<dyn std::error::Error>> {
//! // Create optimization problem
//! let mut problem = Problem::new();
//! // ... add residual blocks (factors) to problem ...
//!
//! // Set up initial parameter values
//! let initial_values = HashMap::new();
//! // ... initialize parameters ...
//!
//! // Create solver with default configuration
//! let mut solver = GaussNewton::new();
//!
//! // Run optimization
//! let result = solver.optimize(&problem, &initial_values)?;
//! # Ok(())
//! # }
//! ```
//!
//! ## Advanced configuration
//!
//! ```no_run
//! use apex_solver::optimizer::gauss_newton::{GaussNewtonConfig, GaussNewton};
//! use apex_solver::linalg::LinearSolverType;
//!
//! # fn main() {
//! let config = GaussNewtonConfig::new()
//!     .with_max_iterations(100)
//!     .with_cost_tolerance(1e-8)
//!     .with_parameter_tolerance(1e-8)
//!     .with_gradient_tolerance(1e-10)
//!     .with_linear_solver_type(LinearSolverType::SparseQR)  // More stable
//!     .with_jacobi_scaling(true);  // Improve conditioning
//!
//! let mut solver = GaussNewton::with_config(config);
//! # }
//! ```
//!
//! # References
//!
//! - Nocedal, J. & Wright, S. (2006). *Numerical Optimization* (2nd ed.). Springer. Chapter 10.
//! - Madsen, K., Nielsen, H. B., & Tingleff, O. (2004). *Methods for Non-Linear Least Squares Problems* (2nd ed.).
//! - Björck, Å. (1996). *Numerical Methods for Least Squares Problems*. SIAM.

use crate::{core::problem, error, linalg, optimizer};
use apex_manifolds as manifold;

use faer::sparse;
use std::{collections, time};
use tracing::debug;

use crate::optimizer::IterationStats;

/// Configuration parameters for the Gauss-Newton optimizer.
///
/// Controls the behavior of the Gauss-Newton algorithm including convergence criteria,
/// linear solver selection, and numerical stability enhancements.
///
/// # Builder Pattern
///
/// All configuration options can be set using the builder pattern:
///
/// ```
/// use apex_solver::optimizer::gauss_newton::GaussNewtonConfig;
/// use apex_solver::linalg::LinearSolverType;
///
/// let config = GaussNewtonConfig::new()
///     .with_max_iterations(50)
///     .with_cost_tolerance(1e-6)
///     .with_linear_solver_type(LinearSolverType::SparseQR);
/// ```
///
/// # Convergence Criteria
///
/// The optimizer terminates when ANY of the following conditions is met:
///
/// - **Cost tolerance**: `|cost_k - cost_{k-1}| < cost_tolerance`
/// - **Parameter tolerance**: `||step|| < parameter_tolerance`
/// - **Gradient tolerance**: `||J^T·r|| < gradient_tolerance`
/// - **Maximum iterations**: `iteration >= max_iterations`
/// - **Timeout**: `elapsed_time >= timeout`
///
/// # See Also
///
/// - [`GaussNewton`] - The solver that uses this configuration
/// - [`LevenbergMarquardtConfig`](crate::optimizer::LevenbergMarquardtConfig) - For adaptive damping
/// - [`DogLegConfig`](crate::optimizer::DogLegConfig) - For trust region methods
#[derive(Clone)]
pub struct GaussNewtonConfig {
    /// Type of linear solver for the linear systems
    pub linear_solver_type: linalg::LinearSolverType,
    /// Maximum number of iterations
    pub max_iterations: usize,
    /// Convergence tolerance for cost function
    pub cost_tolerance: f64,
    /// Convergence tolerance for parameter updates
    pub parameter_tolerance: f64,
    /// Convergence tolerance for gradient norm
    pub gradient_tolerance: f64,
    /// Timeout duration
    pub timeout: Option<time::Duration>,
    /// Use Jacobi column scaling (preconditioning)
    ///
    /// When enabled, normalizes Jacobian columns by their L2 norm before solving.
    /// This can improve convergence for problems with mixed parameter scales
    /// (e.g., positions in meters + angles in radians) but adds ~5-10% overhead.
    ///
    /// Default: false (Gauss-Newton is typically used on well-conditioned problems)
    pub use_jacobi_scaling: bool,
    /// Small regularization to ensure J^T·J is positive definite
    ///
    /// Pure Gauss-Newton (λ=0) can fail when J^T·J is singular or near-singular.
    /// Adding a tiny diagonal regularization (e.g., 1e-10) ensures numerical stability
    /// while maintaining the fast convergence of Gauss-Newton.
    ///
    /// Default: 1e-10 (very small, practically identical to pure Gauss-Newton)
    pub min_diagonal: f64,

    /// Minimum objective function cutoff (optional early termination)
    ///
    /// If set, optimization terminates when cost falls below this threshold.
    /// Useful for early stopping when a "good enough" solution is acceptable.
    ///
    /// Default: None (disabled)
    pub min_cost_threshold: Option<f64>,

    /// Maximum condition number for Jacobian matrix (optional check)
    ///
    /// If set, the optimizer checks if condition_number(J^T*J) exceeds this
    /// threshold and terminates with IllConditionedJacobian status.
    /// Note: Computing condition number is expensive, so this is disabled by default.
    ///
    /// Default: None (disabled)
    pub max_condition_number: Option<f64>,

    /// Compute per-variable covariance matrices (uncertainty estimation)
    ///
    /// When enabled, computes covariance by inverting the Hessian matrix after
    /// convergence. The full covariance matrix is extracted into per-variable
    /// blocks stored in both Variable structs and optimier::SolverResult.
    ///
    /// Default: false (to avoid performance overhead)
    pub compute_covariances: bool,

    /// Enable real-time visualization (graphical debugging).
    ///
    /// When enabled, optimization progress is logged to a Rerun viewer.
    /// **Note:** Requires the `visualization` feature to be enabled in `Cargo.toml`.
    ///
    /// Default: false
    #[cfg(feature = "visualization")]
    pub enable_visualization: bool,
}

impl Default for GaussNewtonConfig {
    fn default() -> Self {
        Self {
            linear_solver_type: linalg::LinearSolverType::default(),
            // Ceres Solver default: 50 (changed from 100 for compatibility)
            max_iterations: 50,
            // Ceres Solver default: 1e-6 (changed from 1e-8 for compatibility)
            cost_tolerance: 1e-6,
            // Ceres Solver default: 1e-8 (unchanged)
            parameter_tolerance: 1e-8,
            // Ceres Solver default: 1e-10 (changed from 1e-8 for compatibility)
            gradient_tolerance: 1e-10,
            timeout: None,
            use_jacobi_scaling: false,
            min_diagonal: 1e-10,
            // New Ceres-compatible termination parameters
            min_cost_threshold: None,
            max_condition_number: None,
            compute_covariances: false,
            #[cfg(feature = "visualization")]
            enable_visualization: false,
        }
    }
}

impl GaussNewtonConfig {
    /// Create a new Gauss-Newton configuration with default values.
    pub fn new() -> Self {
        Self::default()
    }

    /// Set the linear solver type
    pub fn with_linear_solver_type(mut self, linear_solver_type: linalg::LinearSolverType) -> Self {
        self.linear_solver_type = linear_solver_type;
        self
    }

    /// Set the maximum number of iterations
    pub fn with_max_iterations(mut self, max_iterations: usize) -> Self {
        self.max_iterations = max_iterations;
        self
    }

    /// Set the cost tolerance
    pub fn with_cost_tolerance(mut self, cost_tolerance: f64) -> Self {
        self.cost_tolerance = cost_tolerance;
        self
    }

    /// Set the parameter tolerance
    pub fn with_parameter_tolerance(mut self, parameter_tolerance: f64) -> Self {
        self.parameter_tolerance = parameter_tolerance;
        self
    }

    /// Set the gradient tolerance
    pub fn with_gradient_tolerance(mut self, gradient_tolerance: f64) -> Self {
        self.gradient_tolerance = gradient_tolerance;
        self
    }

    /// Set the timeout duration
    pub fn with_timeout(mut self, timeout: time::Duration) -> Self {
        self.timeout = Some(timeout);
        self
    }

    /// Enable or disable Jacobi column scaling (preconditioning).
    ///
    /// When enabled, normalizes Jacobian columns by their L2 norm before solving.
    /// Can improve convergence for mixed-scale problems but adds ~5-10% overhead.
    pub fn with_jacobi_scaling(mut self, use_jacobi_scaling: bool) -> Self {
        self.use_jacobi_scaling = use_jacobi_scaling;
        self
    }

    /// Set the minimum diagonal regularization for numerical stability.
    ///
    /// A small value (e.g., 1e-10) ensures J^T·J is positive definite while
    /// maintaining the fast convergence of pure Gauss-Newton.
    pub fn with_min_diagonal(mut self, min_diagonal: f64) -> Self {
        self.min_diagonal = min_diagonal;
        self
    }

    /// Set minimum objective function cutoff for early termination.
    ///
    /// When set, optimization terminates with MinCostThresholdReached status
    /// if the cost falls below this threshold. Useful for early stopping when
    /// a "good enough" solution is acceptable.
    pub fn with_min_cost_threshold(mut self, min_cost: f64) -> Self {
        self.min_cost_threshold = Some(min_cost);
        self
    }

    /// Set maximum condition number for Jacobian matrix.
    ///
    /// If set, the optimizer checks if condition_number(J^T*J) exceeds this
    /// threshold and terminates with IllConditionedJacobian status.
    /// Note: Computing condition number is expensive, disabled by default.
    pub fn with_max_condition_number(mut self, max_cond: f64) -> Self {
        self.max_condition_number = Some(max_cond);
        self
    }

    /// Enable or disable covariance computation (uncertainty estimation).
    ///
    /// When enabled, computes the full covariance matrix by inverting the Hessian
    /// after convergence, then extracts per-variable covariance blocks.
    pub fn with_compute_covariances(mut self, compute_covariances: bool) -> Self {
        self.compute_covariances = compute_covariances;
        self
    }

    /// Enable real-time visualization.
    ///
    /// **Note:** Requires the `visualization` feature to be enabled in `Cargo.toml`.
    ///
    /// # Arguments
    ///
    /// * `enable` - Whether to enable visualization
    #[cfg(feature = "visualization")]
    pub fn with_visualization(mut self, enable: bool) -> Self {
        self.enable_visualization = enable;
        self
    }

    /// Print configuration parameters (info level logging)
    pub fn print_configuration(&self) {
        debug!(
            "\nConfiguration:\n  Solver:        Gauss-Newton\n  Linear solver: {:?}\n  Convergence Criteria:\n  Max iterations:      {}\n  Cost tolerance:      {:.2e}\n  Parameter tolerance: {:.2e}\n  Gradient tolerance:  {:.2e}\n  Timeout:             {:?}\n  Numerical Settings:\n  Jacobi scaling:      {}\n  Compute covariances: {}",
            self.linear_solver_type,
            self.max_iterations,
            self.cost_tolerance,
            self.parameter_tolerance,
            self.gradient_tolerance,
            self.timeout,
            if self.use_jacobi_scaling {
                "enabled"
            } else {
                "disabled"
            },
            if self.compute_covariances {
                "enabled"
            } else {
                "disabled"
            }
        );
    }
}

/// Result from step computation
struct StepResult {
    step: faer::Mat<f64>,
    gradient_norm: f64,
}

/// Result from cost evaluation
struct CostEvaluation {
    new_cost: f64,
    cost_reduction: f64,
}

/// Gauss-Newton solver for nonlinear least squares optimization.
///
/// Implements the classical Gauss-Newton algorithm which solves `J^T·J·h = -J^T·r` at each
/// iteration to find the step `h`. This provides fast quadratic convergence near the solution
/// but may diverge for poor initial guesses or ill-conditioned problems.
///
/// # Algorithm
///
/// At each iteration k:
/// 1. Compute residual `r(xₖ)` and Jacobian `J(xₖ)`
/// 2. Form normal equations: `(J^T·J)·h = -J^T·r`
/// 3. Solve for step `h` using Cholesky or QR factorization
/// 4. Update parameters: `xₖ₊₁ = xₖ ⊕ h` (manifold plus operation)
/// 5. Check convergence criteria
///
/// # Examples
///
/// ```no_run
/// use apex_solver::optimizer::GaussNewton;
/// use apex_solver::core::problem::Problem;
/// use std::collections::HashMap;
///
/// # fn main() -> Result<(), Box<dyn std::error::Error>> {
/// let mut problem = Problem::new();
/// // ... add factors to problem ...
///
/// let initial_values = HashMap::new();
/// // ... initialize parameters ...
///
/// let mut solver = GaussNewton::new();
/// let result = solver.optimize(&problem, &initial_values)?;
/// # Ok(())
/// # }
/// ```
///
/// # See Also
///
/// - [`GaussNewtonConfig`] - Configuration options
/// - [`LevenbergMarquardt`](crate::optimizer::LevenbergMarquardt) - For adaptive damping
/// - [`DogLeg`](crate::optimizer::DogLeg) - For trust region control
pub struct GaussNewton {
    config: GaussNewtonConfig,
    jacobi_scaling: Option<sparse::SparseColMat<usize, f64>>,
    observers: optimizer::OptObserverVec,
}

impl Default for GaussNewton {
    fn default() -> Self {
        Self::new()
    }
}

impl GaussNewton {
    /// Create a new Gauss-Newton solver with default configuration.
    pub fn new() -> Self {
        Self::with_config(GaussNewtonConfig::default())
    }

    /// Create a new Gauss-Newton solver with the given configuration.
    pub fn with_config(config: GaussNewtonConfig) -> Self {
        Self {
            config,
            jacobi_scaling: None,
            observers: optimizer::OptObserverVec::new(),
        }
    }

    /// Add an observer to the solver.
    ///
    /// Observers are notified at each iteration with the current variable values.
    /// This enables real-time visualization, logging, metrics collection, etc.
    ///
    /// # Examples
    ///
    /// ```no_run
    /// use apex_solver::optimizer::GaussNewton;
    /// # use apex_solver::optimizer::OptObserver;
    /// # use std::collections::HashMap;
    /// # use apex_solver::core::problem::VariableEnum;
    ///
    /// # struct MyObserver;
    /// # impl OptObserver for MyObserver {
    /// #     fn on_step(&self, _: &HashMap<String, VariableEnum>, _: usize) {}
    /// # }
    /// let mut solver = GaussNewton::new();
    /// solver.add_observer(MyObserver);
    /// ```
    pub fn add_observer(&mut self, observer: impl optimizer::OptObserver + 'static) {
        self.observers.add(observer);
    }

    /// Compute Gauss-Newton step by solving the normal equations
    fn compute_gauss_newton_step(
        &self,
        residuals: &faer::Mat<f64>,
        scaled_jacobian: &sparse::SparseColMat<usize, f64>,
        linear_solver: &mut Box<dyn linalg::SparseLinearSolver>,
    ) -> Option<StepResult> {
        // Solve the Gauss-Newton equation: J^T·J·Δx = -J^T·r
        // Use min_diagonal for numerical stability (tiny regularization)
        let residuals_owned = residuals.as_ref().to_owned();
        let scaled_step = linear_solver
            .solve_normal_equation(&residuals_owned, scaled_jacobian)
            .ok()?;

        // Get gradient from the solver (J^T * r)
        let gradient = linear_solver.get_gradient()?;
        // Compute gradient norm for convergence check
        let gradient_norm = gradient.norm_l2();

        // Apply inverse Jacobi scaling to get final step (if enabled)
        let step = if self.config.use_jacobi_scaling {
            let scaling = self.jacobi_scaling.as_ref()?;
            &scaled_step * scaling
        } else {
            scaled_step
        };

        Some(StepResult {
            step,
            gradient_norm,
        })
    }

    /// Apply step to parameters and evaluate new cost
    fn apply_step_and_evaluate_cost(
        &self,
        step_result: &StepResult,
        state: &mut optimizer::InitializedState,
        problem: &problem::Problem,
    ) -> error::ApexSolverResult<CostEvaluation> {
        // Apply parameter updates using manifold operations
        let _step_norm = optimizer::apply_parameter_step(
            &mut state.variables,
            step_result.step.as_ref(),
            &state.sorted_vars,
        );

        // Compute new cost (residual only, no Jacobian needed for step evaluation)
        let new_residual = problem.compute_residual_sparse(&state.variables)?;
        let new_cost = optimizer::compute_cost(&new_residual);

        // Compute cost reduction
        let cost_reduction = state.current_cost - new_cost;

        // Update current cost
        state.current_cost = new_cost;

        Ok(CostEvaluation {
            new_cost,
            cost_reduction,
        })
    }

    pub fn optimize(
        &mut self,
        problem: &problem::Problem,
        initial_params: &collections::HashMap<
            String,
            (manifold::ManifoldType, nalgebra::DVector<f64>),
        >,
    ) -> Result<
        optimizer::SolverResult<collections::HashMap<String, problem::VariableEnum>>,
        error::ApexSolverError,
    > {
        let start_time = time::Instant::now();
        let mut iteration = 0;
        let mut cost_evaluations = 1; // Initial cost evaluation
        let mut jacobian_evaluations = 0;

        // Initialize optimization state
        let mut state = optimizer::initialize_optimization_state(problem, initial_params)?;

        // Create linear solver
        let mut linear_solver = optimizer::create_linear_solver(&self.config.linear_solver_type);

        // Initialize summary tracking variables
        let mut max_gradient_norm: f64 = 0.0;
        let mut max_parameter_update_norm: f64 = 0.0;
        let mut total_cost_reduction = 0.0;
        let mut final_gradient_norm;
        let mut final_parameter_update_norm;

        // Initialize iteration statistics tracking
        let mut iteration_stats = Vec::with_capacity(self.config.max_iterations);
        let mut previous_cost = state.current_cost;

        // Print configuration and header if debug level is enabled
        if tracing::enabled!(tracing::Level::DEBUG) {
            self.config.print_configuration();
            IterationStats::print_header();
        }

        // Main optimization loop
        loop {
            let iter_start = time::Instant::now();
            // Evaluate residuals and Jacobian
            let (residuals, jacobian) = problem.compute_residual_and_jacobian_sparse(
                &state.variables,
                &state.variable_index_map,
                &state.symbolic_structure,
            )?;
            jacobian_evaluations += 1;

            // Process Jacobian (apply scaling if enabled)
            let scaled_jacobian = if self.config.use_jacobi_scaling {
                optimizer::process_jacobian(&jacobian, &mut self.jacobi_scaling, iteration)?
            } else {
                jacobian
            };

            // Compute Gauss-Newton step
            let step_result = match self.compute_gauss_newton_step(
                &residuals,
                &scaled_jacobian,
                &mut linear_solver,
            ) {
                Some(result) => result,
                None => {
                    return Err(optimizer::OptimizerError::LinearSolveFailed(
                        "Linear solver failed to solve Gauss-Newton system".to_string(),
                    )
                    .into());
                }
            };

            // Update tracking variables
            max_gradient_norm = max_gradient_norm.max(step_result.gradient_norm);
            final_gradient_norm = step_result.gradient_norm;
            let step_norm = step_result.step.norm_l2();
            max_parameter_update_norm = max_parameter_update_norm.max(step_norm);
            final_parameter_update_norm = step_norm;

            // Capture cost before applying step (for convergence check)
            let cost_before_step = state.current_cost;

            // Apply step and evaluate new cost
            let cost_eval = self.apply_step_and_evaluate_cost(&step_result, &mut state, problem)?;
            cost_evaluations += 1;
            total_cost_reduction += cost_eval.cost_reduction;

            // OPTIMIZATION: Only collect iteration statistics if debug level is enabled
            // This eliminates ~2-5ms overhead per iteration for non-debug optimization
            if tracing::enabled!(tracing::Level::DEBUG) {
                let iter_elapsed_ms = iter_start.elapsed().as_secs_f64() * 1000.0;
                let total_elapsed_ms = start_time.elapsed().as_secs_f64() * 1000.0;

                let stats = IterationStats {
                    iteration,
                    cost: state.current_cost,
                    cost_change: previous_cost - state.current_cost,
                    gradient_norm: step_result.gradient_norm,
                    step_norm,
                    tr_ratio: 0.0,  // Not used in Gauss-Newton
                    tr_radius: 0.0, // Not used in Gauss-Newton
                    ls_iter: 0,     // Direct solver (Cholesky) has no iterations
                    iter_time_ms: iter_elapsed_ms,
                    total_time_ms: total_elapsed_ms,
                    accepted: true, // Gauss-Newton always accepts steps
                };

                iteration_stats.push(stats.clone());
                stats.print_line();
            }

            previous_cost = state.current_cost;

            // Notify all observers with current state
            optimizer::notify_observers(
                &mut self.observers,
                &state.variables,
                iteration,
                state.current_cost,
                step_result.gradient_norm,
                None, // Gauss-Newton doesn't use damping
                step_norm,
                None, // Gauss-Newton doesn't use step quality
                linear_solver.as_ref(),
            );

            // Compute parameter norm for convergence check
            let parameter_norm = optimizer::compute_parameter_norm(&state.variables);

            // Check convergence using comprehensive termination criteria
            let elapsed = start_time.elapsed();
            if let Some(status) = optimizer::check_convergence(&optimizer::ConvergenceParams {
                iteration,
                current_cost: cost_before_step,
                new_cost: cost_eval.new_cost,
                parameter_norm,
                parameter_update_norm: step_norm,
                gradient_norm: step_result.gradient_norm,
                elapsed,
                step_accepted: true, // GN always accepts
                max_iterations: self.config.max_iterations,
                gradient_tolerance: self.config.gradient_tolerance,
                parameter_tolerance: self.config.parameter_tolerance,
                cost_tolerance: self.config.cost_tolerance,
                min_cost_threshold: self.config.min_cost_threshold,
                timeout: self.config.timeout,
                trust_region_radius: None,
                min_trust_region_radius: None,
            }) {
                // Print summary only if debug level is enabled
                if tracing::enabled!(tracing::Level::DEBUG) {
                    let summary = optimizer::create_optimizer_summary(
                        "Gauss-Newton",
                        state.initial_cost,
                        state.current_cost,
                        iteration + 1,
                        None,
                        None,
                        max_gradient_norm,
                        final_gradient_norm,
                        max_parameter_update_norm,
                        final_parameter_update_norm,
                        total_cost_reduction,
                        elapsed,
                        iteration_stats.clone(),
                        status.clone(),
                        None,
                        None,
                        None,
                    );
                    debug!("{}", summary);
                }

                // Compute covariances if enabled
                let covariances = if self.config.compute_covariances {
                    problem.compute_and_set_covariances(
                        &mut linear_solver,
                        &mut state.variables,
                        &state.variable_index_map,
                    )
                } else {
                    None
                };

                return Ok(optimizer::build_solver_result(
                    status,
                    iteration + 1,
                    state,
                    elapsed,
                    final_gradient_norm,
                    final_parameter_update_norm,
                    cost_evaluations,
                    jacobian_evaluations,
                    covariances,
                ));
            }

            iteration += 1;
        }
    }
}

impl optimizer::Solver for GaussNewton {
    type Config = GaussNewtonConfig;
    type Error = error::ApexSolverError;

    fn new() -> Self {
        Self::default()
    }

    fn optimize(
        &mut self,
        problem: &problem::Problem,
        initial_params: &std::collections::HashMap<
            String,
            (manifold::ManifoldType, nalgebra::DVector<f64>),
        >,
    ) -> Result<
        optimizer::SolverResult<std::collections::HashMap<String, problem::VariableEnum>>,
        Self::Error,
    > {
        self.optimize(problem, initial_params)
    }
}

#[cfg(test)]
mod tests {
    use crate::{core::problem, factors, optimizer};
    use apex_manifolds as manifold;
    use nalgebra::dvector;
    use std::collections;

    /// Custom Rosenbrock Factor 1: r1 = 10(x2 - x1²)
    /// Demonstrates extensibility - custom factors can be defined outside of factors.rs
    #[derive(Debug, Clone)]
    struct RosenbrockFactor1;

    impl factors::Factor for RosenbrockFactor1 {
        fn linearize(
            &self,
            params: &[nalgebra::DVector<f64>],
            compute_jacobian: bool,
        ) -> (nalgebra::DVector<f64>, Option<nalgebra::DMatrix<f64>>) {
            let x1 = params[0][0];
            let x2 = params[1][0];

            // Residual: r1 = 10(x2 - x1²)
            let residual = nalgebra::dvector![10.0 * (x2 - x1 * x1)];

            // Jacobian: ∂r1/∂x1 = -20*x1, ∂r1/∂x2 = 10
            let jacobian = if compute_jacobian {
                let mut jac = nalgebra::DMatrix::zeros(1, 2);
                jac[(0, 0)] = -20.0 * x1;
                jac[(0, 1)] = 10.0;
                Some(jac)
            } else {
                None
            };

            (residual, jacobian)
        }

        fn get_dimension(&self) -> usize {
            1
        }
    }

    /// Custom Rosenbrock Factor 2: r2 = 1 - x1
    /// Demonstrates extensibility - custom factors can be defined outside of factors.rs
    #[derive(Debug, Clone)]
    struct RosenbrockFactor2;

    impl factors::Factor for RosenbrockFactor2 {
        fn linearize(
            &self,
            params: &[nalgebra::DVector<f64>],
            compute_jacobian: bool,
        ) -> (nalgebra::DVector<f64>, Option<nalgebra::DMatrix<f64>>) {
            let x1 = params[0][0];

            // Residual: r2 = 1 - x1
            let residual = nalgebra::dvector![1.0 - x1];

            // Jacobian: ∂r2/∂x1 = -1
            let jacobian = if compute_jacobian {
                Some(nalgebra::DMatrix::from_element(1, 1, -1.0))
            } else {
                None
            };

            (residual, jacobian)
        }

        fn get_dimension(&self) -> usize {
            1
        }
    }

    #[test]
    fn test_rosenbrock_optimization() -> Result<(), Box<dyn std::error::Error>> {
        // Rosenbrock function test:
        // Minimize: r1² + r2² where
        //   r1 = 10(x2 - x1²)
        //   r2 = 1 - x1
        // Starting point: [-1.2, 1.0]
        // Expected minimum: [1.0, 1.0]

        let mut problem = problem::Problem::new();
        let mut initial_values = collections::HashMap::new();

        // Add variables using Rn manifold (Euclidean space)
        initial_values.insert(
            "x1".to_string(),
            (manifold::ManifoldType::RN, dvector![-1.2]),
        );
        initial_values.insert(
            "x2".to_string(),
            (manifold::ManifoldType::RN, dvector![1.0]),
        );

        // Add custom factors (demonstrates extensibility!)
        problem.add_residual_block(&["x1", "x2"], Box::new(RosenbrockFactor1), None);
        problem.add_residual_block(&["x1"], Box::new(RosenbrockFactor2), None);

        // Configure Gauss-Newton optimizer
        let config = optimizer::gauss_newton::GaussNewtonConfig::new()
            .with_max_iterations(100)
            .with_cost_tolerance(1e-8)
            .with_parameter_tolerance(1e-8)
            .with_gradient_tolerance(1e-10);

        let mut solver = optimizer::GaussNewton::with_config(config);
        let result = solver.optimize(&problem, &initial_values)?;

        // Extract final values
        let x1_final = result
            .parameters
            .get("x1")
            .ok_or("x1 not found")?
            .to_vector()[0];
        let x2_final = result
            .parameters
            .get("x2")
            .ok_or("x2 not found")?
            .to_vector()[0];

        // Verify convergence to [1.0, 1.0]
        assert!(
            matches!(
                result.status,
                optimizer::OptimizationStatus::Converged
                    | optimizer::OptimizationStatus::CostToleranceReached
                    | optimizer::OptimizationStatus::ParameterToleranceReached
                    | optimizer::OptimizationStatus::GradientToleranceReached
            ),
            "Optimization should converge"
        );
        assert!(
            (x1_final - 1.0).abs() < 1e-4,
            "x1 should converge to 1.0, got {}",
            x1_final
        );
        assert!(
            (x2_final - 1.0).abs() < 1e-4,
            "x2 should converge to 1.0, got {}",
            x2_final
        );
        assert!(
            result.final_cost < 1e-6,
            "Final cost should be near zero, got {}",
            result.final_cost
        );
        Ok(())
    }
}