A linear memory CUDA algorithm for solving Time Warp Edit Distance.
This is a novel parallel implementation of Time Warp Edit Distance.
The original algorithm was described by Marteau in:
Time Warp Edit Distance with Stiffness Adjustment for Time Series Matching (2009).
A variant of the code from that paper is included in
reference_implementation, and was used to compare results. There is
also a wiki
page.
The original TWED algorithm is O(n^2) in time and space. This
algorithm is roughly O(n * n/p) in time for p (CUDA) cores. Most
importantly, cuTWED is linear in memory, using storage for roughly
6*nA + 6*nB elements.
In the process of understanding the dynamic program data dependencies in
order to parallelize towards the CUDA architecture, I devised a method
with improved memory access patterns and the ability to massively
parallelize over large problems. This is accomplished by a procession of
a three diagonal band moving across the dynamic program matrix in
nA+nB-1 steps. No O(n^2) matrix is required anywhere. Note, this
is not an approximation method. The full and complete TWED dynamic
program computation occurs with linear storage.
The code is provided in a library that has methods for double and
float precision. It admits input time series in R^N as arrays of
N-dimensional arrays in C-order (time is the slow moving axis).
For typical problems computable by the original TWED implementation, utilizing cuTWED and thousands of CUDA cores achieves great speedups. For common problems speedups are one to two orders of magnitude, capable of achieving 200x acceleration on a P100 GPUs in doubles. More so, the linear memory footprint allows for the computation of previously intractable problems. Large problems, large systems of inputs can be computed much more effectively now.
Some speed comparisons and a more formal paper will follow.
Marteau's original code with a some minor changes has been included in
this package. It is built both as a C library and part of the Python
package cuTWED.ctwed. The minor changes are an extra argument
dimension to admit R^N inputs, and more common handling of norm
(nth-root). These modications were made to facilitate refence testing
cuTWED and also make the original code more general.
ctwed is also included for users without a CUDA card who find other
implementations too slow.
For many users the prepackaged (linux) Python distribution is the simplest way to get the code. If you have CUDA10/11 and a Python 3.6+ manylinux compatible installation you can try the prepackged wheels with:
pip install cuTWED
For other situations, or users seeking maximum performance, instructions follow for building the core CUDA libray, installing, and building the Python bindings from source.
For the CUDA code you will need NVCC, a CUDA capable card and CMake. Otherwise, the CUDA code has no dependencies.
If you do not have CMake or it is too old, a lot of people just pip
install it pip install cmake>=3.11. Otherwise you'll need to
refer to their (Kitware) docs for your situation.
For the Python binding pip manages the specific depends and
installation of the Python interface after you have built the main CUDA
C library. Generally requires numpy, pycuda, and cffi. I
recommend you use virtualenv or conda to manage Python.
Building has two stages. First the CUDA C library is built and installed. Second the Python bindings (if desired) are built on top of that.
The CUDA C library may be permanently installed to your system, in a standard fashion, with some customization via CMake. Alternatively a manual local install option is described below.
Note you may customize the call to cmake below with flags like
-DCMAKE_INSTALL_PREFIX=/opt/, or other flags you might require.
# git a copy of the source code git clone https://github.com/garrettwrong/cuTWED cd cuTWED # setup a build area mkdir build cd build cmake ../ # configures/generates makefiles # make make -j # builds the software
This should create several files in the build directory including
libcuTWED.so, *.h headers, and some other stuff. To install to
your system permanently (may require sudo):
make install
If you would rather just want to temporarily have the library available on your linux machine you can just use the LD path. This makes no changes to your system outside the repo and this shell process. Assuming you are still in your build directory, add the library to your path. Users may decide to add a similar line permanently to their .bashrc or equivalent.
export LD_LIBRARY_PATH=$PWD:$LD_LIBRARY_PATH
Once you have the CUDA C library readied, we can use pip for the
Python bindings. From the root of the git repo:
pip install .
If you are planning to edit the code, you might prefer pip install in local editable mode instead.
pip install -e .
Assuming you have built both the CUDA library and the Python bindings, you can run the unit test suite:
pytest
For developers there is a whole mess of configured tests which you can run with:
tox --skip-missing-interpreters
I hope to improve this soon, but there are a lot of complication running hybrid codes with free CI tools, and also packaging properly with Python etc that need to be worked through. Some are most easily addressed by using a managed CI host, but this is non free.... I suspect this is largely why you do not see a plethera of free high performance hybrid codes... perhaps a future project...
In C/C++ you should be able to include "cuTWED.h" and link with the
shared library libcuTWED.so. This is what I do in test.x. The
public methods are extern C mangled and should be usable from both C and
C++ without issue.
Float (32bit) versions of all the public methods are included in the
shared library. They simply have an f appended, for example,
twedf is the float version of twed. You may choose which one is
suitable for your application. I use floats in testf.x.
There are currently two main ways to invoke the cuTWED alogorithm,
twed and twed_dev. First twed is the most common way, where
you pass C arrays on the host, and the library manages device memory and
transfers for you.
Alternatively, if you are already managing GPU memory, you may use
twed_dev which expects pointers to memory that resides on the gpu. I
have also provided malloc, copy, and free helpers in case it makes sense
to reuse memory. See cuTWED.h. All logic and size checks for such
advanced cases are expected to be owned by the user.
There is an additional batch method. Until I have a chance to write up
better documentation, you may find example use in test_batch,
test_batch_dev, and a small but respectable ML batch problem set in
test_synthetic_validation.py.
I have included a Jupyter Notebook which demonstrates validation using the UCI Pseudo Periodic Synthetic Time Series Data Set. This is a much larger dataset.
Future plans include optimization and multi-gpu options for large batches..
from cuTWED import twed
For Python I have included basic pip installable Python bindings. I use
it in tests/test_basic.py. If you are curious, these are implemented
by a cffi backend which parses the C header. which is built for you
by setuptools. The main Python interface is in cuTWED.py. This
requires that you have built the library, and have it installed in a
location known to the system or available in your LD_LIBRARY_PATH.
I have also wrapped up the GPU only memory methods in Python, using
PyCUDA gpuarrays. Examples in double and single precision are in
tests/test_basic_dev.py.
from cuTWED import twed_dev
The batch interfaces are twed_batch and twed_batch_dev
respectively. Currently it is doing a barbaric synchonization. I have a
branch using streams with events, but I need to validate it is robust
before I push it. That gives back about another 20% in batch mode
afaict.
If you want to run Marteau's C code from Python you can try ctwed.
For (very) small problems you may find his original C code is faster.
This software is early in its life cycle. The following are known issues:
- Portability, I expect you have linux at this time.
- I have not had time to profile or optimize it, there are things I know to have improvements.
If you find an issue or bug with the code, please submit an issue. More details about this can be found in the contributing document.
GPLv3
Copyright 2020 Garrett Wright, Gestalt Group LLC