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An algorithm that approximates an orthogonal matrix with few-factor Givens factorization.
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Approximating Orthogonal Matrices with Effective Givens Factorization

This is an implementation of the algorithms analyzed in our ICML 2019 paper:

Approximating Orthogonal Matrices with Effective Givens Factorization (Thomas Frerix, Joan Bruna; ICML 2019)

The core algorithm is written in C++/CUDA and interfaces with python through pybind11.


  1. Make sure you have a running Python 3 (tested with Python 3.7) ecosytem, e.g. through conda, and an Nvidia GPU (tested with CUDA 9.0 on a Titan X).
  2. Install the python dependencies via pip install -r pip_requirements.txt.
  3. Install CUB (tested with 1.8.0) and Eigen3 (tested with 3.2).
  4. Specify the environment variables CUB_INCLUDE_DIR to the CUB library and PYBIND_INDLUDE_DIR to the python library path of your installation that includes pybind11 (installed as a python package).
  5. Run cmake . and make to compile the code.
  6. Run the end-to-end tests by calling pytest -v -s.


The file contains an example of factorizing an orthogonal matrix with various algorithms, which are explained and discussed in the paper.

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