README.md

LQ Matrix Backpropagation Algorithm Implementation

TensorFlow implementation of differentiable LQ matrix decomposition for square, wide and deep tensors. This is in addition to the differentiable decompositions implemented by the authors in TensorFlow Core, PyTorch, and MXNet (and part of the official distributions).

To Cite [Update: oral presentation in the 8th International Conferance on Algorithmic Differentation (AD2024)]

If you use this implementation in your research please cite (QR and LQ Decomposition Matrix Backpropagation Algorithms for Square, Wide, and Deep - Real or Complex - Matrices and Their Software Implementation)[https://arxiv.org/pdf/2009.10071.pdf]:

@article{roberts2020qr,
  title={QR and LQ Decomposition Matrix Backpropagation Algorithms for Square, Wide, and Deep - Real or Complex - Matrices and Their Software Implementation},
  author={Roberts, Denisa AO and Roberts, Lucas R},
  journal={arXiv preprint arXiv:2009.10071},
  year={2020}
}

To Use

Requirements: tf >v1; Python > 3.6.

Recommended: install Anaconda. 
Create a tensorflow environment.


# tf cpu only; v2 by default at this time.

conda create -n tf tensorflow
conda activate tf
# conda install numpy
git clone https://github.com/D-Roberts/lq-backprop.git
cd lq-backprop

# to run tests
conda install nose # new terminal may be necessary
nosetests -v test_lq_op_grad.py 

# to use

# Example:

import tensorflow as tf 
import numpy as np 
from lq_op_grad import lq, LqGrad

np.random.seed(42)
a_np = np.random.uniform(-1, 1, (3, 2)).astype(np.float32)
a = tf.convert_to_tensor(a_np)
l, q = lq(a)
grad = LqGrad(a, l, q, tf.ones_like(l), tf.ones_like(q))
print(grad)