Pytorch Batched SVD

1) Introduction

A batched version of SVD in Pytorch implemented using cuSolver including forward and backward function. In terms of speed, it is superior to that of torch.svd.

matrix size	torch_batch_svd.svd	torch.svd
`(10000, 9, 9)`	0.41 s	12.29 s
`(20000, 9, 9)`	0.46 s	23.96 s

import torch
from torch_batch_svd import svd

A = torch.rand(1000000, 3, 3).cuda()
u, s, v = svd(A)
u, s, v = torch.svd(A)  # probably you should take a coffee break here

The catch here is that it only works for matrices whose row and column are smaller than 32. Other than that, torch_batch_svd.svd can be a drop-in for the native one.

The forward function is modified from ShigekiKarita/pytorch-cusolver and I fixed several bugs of it. The backward function is borrowed from the pytorch official svd backward function. I converted it to a batched version.

NOTE: batch_svd supports all torch.half, torch.float and torch.double tensors now.

NOTE: SVD for torch.half is performed by casting to torch.float as there is no CuSolver implementation for c10::half.

NOTE: Sometimes, tests will fail for torch.double tensor due to numerical imprecision.

2) Requirements

Pytorch >= 1.0

diag_embed() is used in torch_batch_svd.cpp at the backward function. Pytorch with version lower than 1.0 does not contain diag_embed(). If you want to use it in a lower version of pytorch, you can replace diag_embed() by some existing functions.
CUDA 9.0/10.2 (should work with 10.0/10.1 too)
Tested in Pytorch 1.4 & 1.5, with CUDA 10.2

3) Install

Set environment variables

export CUDA_HOME=/your/cuda/home/directory/
export LIBRARY_PATH=$LIBRARY_PATH:/your/cuda/lib64/  (optional)

Run setup.py

python setup.py install

Run test.py

cd tests
python -m pytest test.py

4) Differences between `torch.svd()`

The sign of column vectors at U and V may be different from torch.svd().
Much more faster than torch.svd() using loop.

5) Example

See test.py and introduction.