ΩID

ΩID is a Python package for calculating the integrated information decomposition (ΦID) of time series data. It is designed for high-performance computing, with optional GPU acceleration via CuPy.

Features

• Backend Agnostic: Seamlessly switch between CPU (NumPy) and GPU (CuPy) for computation.
• High Performance: Vectorized operations and Numba-optimized functions for significant speedups.
• Numerical Integrity: Results are numerically consistent with the original phyid implementation within single/double precision tolerances.
• Multivariate Decomposition: Supports decomposition of systems with multiple source and target variables using the Doublet Lattice approximation.

Installation

ΩID is available on PyPI. You can install it with pip or uv pip.

Standard Installation (CPU only)

pip install omegaid

With GPU support

To install ΩID with GPU support, you need to have a CUDA-enabled GPU and the CUDA toolkit installed. Choose the command that matches your CUDA version.

For CUDA 12.x:

pip install "omegaid[cuda-12x]"

For CUDA 11.x:

pip install "omegaid[cuda-11x]"

Usage

Selecting the Backend

You can select the computation backend by setting the OMEGAID_BACKEND environment variable before running your Python script.

• For NumPy (default):

  export OMEGAID_BACKEND=numpy
  

• For CuPy:

  export OMEGAID_BACKEND=cupy
  

If the variable is not set, OmegaID will default to using NumPy.

Example

Here is a simple example of how to use omegaid to calculate the Phi-ID decomposition for a multivariate system.

import numpy as np
from omegaid.core.decomposition import calc_phiid_multivariate
from omegaid.utils.backend import set_backend

# For programmatic control, you can also use set_backend
# set_backend('cupy') 

# Generate some random time series data (4 sources, 2 targets)
n_sources = 4
n_targets = 2
n_samples = 10000
tau = 1
sources = np.random.randn(n_sources, n_samples)
targets = np.random.randn(n_targets, n_samples)

# Calculate Phi-ID using the Doublet Lattice approximation
atoms_res, _ = calc_phiid_multivariate(sources, targets, tau)

# Print a synergistic atom, e.g., between source 0 and target 1
print("Synergy (s0, t1):", atoms_res.get((0, 1), "N/A"))

Performance

The package has been benchmarked for various systems. The results below show the performance against the original phyid (where applicable) and between CPU/GPU backends.

The results demonstrate that for more complex multivariate systems (e.g., 4x2 and 4x4), the CuPy backend provides a consistent and significant performance advantage due to the fully vectorized implementation. For simpler 2x2 systems, the Numba-optimized NumPy backend remains highly competitive.

License

This project is licensed under the BSD 3-Clause License.