Pytorch Batched SVD

Introduction

A 100x faster SVD for PyTorch including forward and backward function.

Performance:

matrix size	torch_batch_svd.svd	torch.svd
(10000, 9, 9)	0.043 s	19.352 s
(20000, 9, 9)	0.073 s	34.578 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.

Get Started

Requirements

• Pytorch >= 1.0

• CUDA 9.0/10.2 (should work with 10.0/10.1 too)

• Tested in Pytorch 1.4 & 1.5, with CUDA 10.2

Install

export CUDA_HOME=/your/cuda/home/directory/
python setup.py install

Test

cd tests
python test.py

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.

Example

See test.py and introduction.

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