SaddlePaths.jl

A Julia package for solving saddle-path problems in continuous-time macroeconomic models using stable manifold methods.

Features

• ✅ Ergonomic DSL for declaring continuous-time macro models with Unicode notation
• ✅ Automatic Variable Classification - States, costates, and parameters detected automatically
• ✅ Isolated Namespaces - Each solution instance has its own variable namespace
• ✅ Modular Backend System - Extensible architecture for different numerical methods
• ✅ Comprehensive Testing - 242 parser + 75 namespace + 95 computation tests passing
• 🔄 Backend Abstraction - Ready for spectral methods, finite differences, etc.
• 🔄 Test-Driven Development - Extensive test suite with 60+ computation tests written

Installation

using Pkg
Pkg.add("SaddlePaths")

Quick Example

using SaddlePaths

# Define a Ramsey growth model with automatic variable classification
@model ramsey begin
    # c(k) notation automatically marks c as costate variable
    # Greek letters (α, δ, ρ) automatically detected as parameters
    # k is automatically classified as state variable
    𝑑c = c(k) * (α * k^(α - 1) - δ - ρ)
    𝑑k = k^α - δ * k - c(k)
end

# Model structure is automatically created:
# - state = [:k]
# - costate = [:c]
# - params = [:α, :δ, :ρ]

# Create numerical solution with isolated namespace
solution = NumericalSolution(ramsey, [0.3, 0.1, 0.05])  # α, δ, ρ

# Evaluate ODEs at specific points
state_vals = [1.5]    # k = 1.5
costate_vals = [0.8]  # c = 0.8
dk, dc = evaluate_all_odes(solution, state_vals, costate_vals)

# Clean up namespace when done
cleanup!(solution)

Current Implementation Status

• ✅ Parser: Fully implemented with 242 tests passing
• ✅ Namespace Management: Complete isolation system for multiple solutions (75/75 tests)
• ✅ Backend Abstraction: Modular system for numerical methods
• ✅ Numerical Solution: Complete with 95/95 tests passing
• 🔄 Spectral Methods: Backend ready, awaiting library integration

Architecture

SaddlePaths.jl follows a clean, modular architecture:

• Parser Module: DSL for model specification with automatic variable classification
• Namespace Module: Isolated variable scopes for multiple solution instances
• Backend Module: Abstract interface for different numerical methods
• Computation Module: Numerical solution framework with ODE evaluation

Testing

The project uses comprehensive test-driven development:

# Run all tests
make test

# Run specific test suites
julia --project=. test/test_parser.jl     # 242/242 tests passing
julia --project=. test/test_namespace.jl  # 75/75 tests passing
julia --project=. test/test_computation.jl # 95/95 tests passing

Development Status

• Lines of Code: ~2,900 total
• Test Coverage: All modules fully tested with comprehensive test suites
• Dependencies: None currently (ready for spectral method libraries)
• Julia Version: 1.10+

Contributing

This project uses a test-driven development approach. New features should:

1. Add comprehensive tests first
2. Implement the functionality
3. Ensure all tests pass

Documentation

For detailed documentation, see the docs.

License

MIT