Scientific Modeling Cheatsheet

A comprehensive quick reference guide comparing MATLAB, Python, and Julia for scientific computing and modeling tasks.

View the Cheatsheet

📚 Overview

This cheatsheet provides side-by-side comparisons of common scientific computing operations across three major platforms:

• MATLAB - The traditional choice for engineering and scientific computing
• Scilab - Open source software for numerical computation sharing many features and language idioms with MATLAB
• Python - Using NumPy, SciPy, PyTorch, and SymPy for scientific computing
• Julia - Modern high-performance scientific computing with unified ecosystem

Topics Covered

Basic Operations

• Vector/Matrix creation and manipulation
• Linear algebra operations (eigenvalues, decompositions)
• Array indexing and slicing
• Mathematical operations

Scientific Computing

• Differential Equations

  • ODEs (Ordinary Differential Equations)
  • DAEs (Differential-Algebraic Equations)
  • Mass matrix formulations
  • Stiff systems

• Nonlinear Solving

  • Root finding
  • Systems of nonlinear equations

• Optimization

  • Unconstrained optimization
  • Gradient-based methods

• Automatic Differentiation

  • Forward mode
  • Reverse mode (gradients)
  • Comparison of different AD systems

• Symbolic Computing

  • Symbolic math operations
  • Code generation from symbolic expressions

• Component-Based Modeling

  • System definition
  • Automatic simplification and index reduction
  • Acausal component modeling

• Numerical Integration

  • Quadrature methods
  • Adaptive integration

⚠️ Important Notes

Python Ecosystem Fragmentation

The Python scientific computing ecosystem has compatibility issues between different libraries:

• SymPy symbolic objects are incompatible with NumPy arrays and PyTorch tensors
• PyTorch, TensorFlow, and JAX use incompatible array types
• SciPy lacks native DAE support (use Assimulo or CasADi for DAEs)
• Each automatic differentiation system is isolated from others

Julia Unified Ecosystem

Julia provides a more unified experience:

• ModelingToolkit integrates with all DifferentialEquations.jl solvers
• Automatic differentiation works seamlessly across packages
• Symbolic and numeric computing can be mixed naturally

🧪 Testing

Test scripts are available in the test/ directory:

• test_julia_examples.jl - Tests all Julia code examples
• test_python_examples.py - Tests all Python code examples

🤝 Contributing

Contributions are welcome! Please feel free to submit pull requests with:

• Additional examples
• Corrections or improvements
• New topics relevant to scientific computing

🔗 Resources

• Julia Documentation
• DifferentialEquations.jl
• ModelingToolkit.jl
• NumPy Documentation
• SciPy Documentation
• PyTorch Documentation
• MATLAB Documentation
• Scilab Documentation