matplotlib>=3.5
numpy>=1.21
scipy>=1.7
scikit-learn>=1.0
tqdm>=4.60

# Optional: enables GPU acceleration via CUDA. If CuPy is not installed,
# the script automatically falls back to the CPU (NumPy/SciPy) implementation.
# Install the wheel that matches your CUDA version, e.g.:
#   pip install cupy-cuda12x
# cupy-cuda12x