Melvin Alvarez
153 lines
3.1 KiB
Markdown
153 lines
3.1 KiB
Markdown
# Examples
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This page lists all available examples and tutorials for OptimizR.
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## Jupyter Notebooks
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All notebooks are located in the [examples/](https://github.com/ThotDjehuty/optimiz-r/tree/main/examples) directory.
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### 1. Differential Evolution
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**File**: `01_differential_evolution_tutorial.ipynb`
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Learn how to use the Differential Evolution optimizer:
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- Basic optimization problems (Rosenbrock, Rastrigin, Ackley)
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- Strategy comparison (rand/1, best/1, current-to-best/1)
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- Parameter tuning (F, CR, population size)
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- Convergence analysis and visualization
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### 2. Mean Field Games
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**File**: `02_mean_field_games_tutorial.ipynb`
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Solve 1D Mean Field Games:
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- HJB-Fokker-Planck coupling
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- Agent population dynamics
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- Nash equilibrium computation
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- 3D visualization (time × space × density)
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### 3. Hidden Markov Models
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**File**: `03_hmm_tutorial.ipynb`
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Train and apply HMMs:
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- Baum-Welch training algorithm
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- Viterbi decoding
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- Gaussian emission models
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- Real-world applications (regime detection, speech recognition)
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### 4. MCMC Sampling
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**File**: `04_mcmc_tutorial.ipynb`
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Bayesian inference with Metropolis-Hastings:
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- Sampling from complex distributions
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- Adaptive proposal tuning
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- Convergence diagnostics
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- Posterior analysis
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### 5. Sparse Optimization
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**File**: `05_sparse_optimization_tutorial.ipynb`
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Sparse methods for high-dimensional data:
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- Sparse PCA
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- Elastic Net
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- ADMM solver
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- Feature selection
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### 6. Optimal Control
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**File**: `06_optimal_control_tutorial.ipynb`
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Solve HJB equations:
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- Regime-switching jump diffusions (MRSJD)
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- Optimal stopping problems
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- Dynamic programming
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- Financial applications
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### 7. Risk Metrics
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**File**: `07_risk_metrics_tutorial.ipynb`
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Time series analysis:
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- Hurst exponent estimation
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- Half-life calculation
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- Mean reversion testing
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- Trading signal generation
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## Python Scripts
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Quick examples for copy-paste usage:
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### Optimize Rosenbrock Function
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```python
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import numpy as np
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from optimizr import DifferentialEvolution
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def rosenbrock(x):
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return sum(100.0 * (x[1:] - x[:-1]**2)**2 + (1 - x[:-1])**2)
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de = DifferentialEvolution(bounds=[(-5, 5)] * 10)
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result = de.optimize(rosenbrock, max_iterations=200)
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print(f"Minimum: {result.best_fitness}")
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```
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### Train HMM on Data
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```python
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import numpy as np
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from optimizr import HMMGaussian
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# Load your data
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observations = np.load("data.npy")
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# Train model
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hmm = HMMGaussian(n_states=3)
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hmm.fit(observations)
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# Predict states
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states = hmm.decode(observations)
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```
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### MCMC Sampling
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```python
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import numpy as np
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from optimizr import MetropolisHastings
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def log_posterior(x):
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return -0.5 * np.sum((x - 2)**2)
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sampler = MetropolisHastings(log_posterior, initial_state=np.zeros(5))
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samples = sampler.sample(n_samples=10000)
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```
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## Running Examples
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To run notebooks:
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```bash
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cd examples/
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jupyter notebook
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```
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To run Python scripts:
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```bash
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python examples/basic_optimization.py
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```
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## Contribute Examples
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Have a cool use case? Contribute your example:
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1. Fork the [repository](https://github.com/ThotDjehuty/optimiz-r)
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2. Add your notebook to `examples/`
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3. Ensure it runs without errors
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4. Submit a pull request
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See [Contributing Guide](contributing.md) for details.
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