A quick closed-form solution for volumetric 3x3 matrices Eigen-Decomposition with Pytorch.

# Torch Vectorized

Batched and vectorized operations on volume of 3x3 symmetric matrices with Pytorch. The current Pytorch's implementation of batch eigen-decomposition is very slow when dealing with huge number of small matrices (e.g. 500k x 3x3). This library offers some basic functions like vSymEig, vExpm and vLogm for fast computation (>250x faster) of huge number of small matrices with Pytorch using an analytical solution.

## vSymEig

A quick closed-form solution for volumetric 3x3 matrices Eigen-Decomposition with Pytorch. Solves Eigen-Decomposition of data with shape Bx9xDxHxW, where B is the batch size, 9 is the flattened 3x3 symmetric matrices, D is the depth, H is the Height, W is the width. The goal is to accelerate the Eigen-Decomposition of multiple (>500k) small matrices (3x3) on GPU with Pytorch using an analytical solution.

## vExpm

Based on vSymEig, computes the matrix exponential for batch of volumetric 3x3 matrices.

## vLogm

Based on vSymEig, computes the matrix logarithm for batch of volumetric 3x3 matrices.

## Install me

pip install torch-vectorized

## How to use

import torch
from torchvectorized.utils import sym
from torchvectorized.vlinalg import vSymEig

# Random batch of volumetric 3x3 symmetric matrices of size 16x9x32x32x32
input = sym(torch.rand(16, 9, 32, 32, 32))

# Output eig_vals with size: 16x3x32x32x32 and eig_vecs with size 16,3,3,32,32,32
eig_vals, eig_vecs = vSymEig(input, eigenvectors=True)


## Contributing

#### How to contribute ?

• Create a branch by feature and/or bug fix
• Get the code
• Commit and push
• Create a pull request

#### Branch naming

##### Feature branch

feature/ [Short feature description] [Issue number]

##### Bug branch

fix/ [Short fix description] [Issue number]

#### Commits syntax:

+ Added [Short Description] [Issue Number]

##### Deleting code:

- Deleted [Short Description] [Issue Number]

##### Modifying code:

* Changed [Short Description] [Issue Number]

##### Merging code:

Y Merged [Short Description] [Issue Number]

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