Dask Working Notes - Posts tagged array

Large SVDs

2020-05-13T00:00:00+00:00

We perform Singular Value Decomposition (SVD) calculations on large datasets.

We modify the computation both by using fully precise and approximate methods, and by using both CPUs and GPUs.

In the end we compute an approximate SVD of 200GB of simulated data and using a mutli-GPU machine in 15-20 seconds. Then we run this from a dataset stored in the cloud where we find that I/O is, predictably, a major bottleneck.

SVD - The simple case

Dask arrays contain a relatively sophisticated SVD algorithm that works in the tall-and-skinny or short-and-fat cases, but not so well in the roughly-square case. It works by taking QR decompositions of each block of the array, combining the R matrices, doing another smaller SVD on those, and then performing some matrix multiplication to get back to the full result. It’s numerically stable and decently fast, assuming that the intermediate R matrices of the QR decompositions mostly fit in memory.

The memory constraints here are that if you have an n by m tall and skinny array (n >> m) cut into k blocks then you need to have about m**2 * k space. This is true in many cases, including typical PCA machine learning workloads, where you have tabular data with a few columns (hundreds at most) and many rows.

It’s easy to use and quite robust.

import dask.array as da

x = da.random.random((10000000, 20))
x

	Array	Chunk
Bytes	1.60 GB	100.00 MB
Shape	(10000000, 20)	(625000, 20)
Count	16 Tasks	16 Chunks
Type	float64	numpy.ndarray

20 10000000

u, s, v = da.linalg.svd(x)

This works fine in the short and fat case too (when you have far more columns than rows) but we’re always going to assume that one of your dimensions is unchunked, and that the other dimension has chunks that are quite a bit longer, otherwise, things might not fit into memory.

Approximate SVD

If your dataset is large in both dimensions then the algorithm above won’t work as is. However, if you don’t need exact results, or if you only need a few of the components, then there are a number of excellent approximation algorithms.

Dask array has one of these approximation algorithms implemented in the da.linalg.svd_compressed function. And with it we can compute the approximate SVD of very large matrices.

We were recently working on a problem (explained below) and found that we were still running out of memory when dealing with this algorithm. There were two challenges that we ran into:

The algorithm requires multiple passes over the data, but the Dask task scheduler was keeping the input matrix in memory after it had been loaded once in order to avoid recomputation. Things still worked, but Dask had to move the data to disk and back repeatedly, which reduced performance significantly.

We resolved this by including explicit recomputation steps in the algorithm.
Related chunks of data would be loaded at different times, and so would need to stick around longer than necessary to wait for their associated chunks.

We resolved this by engaging task fusion as an optimization pass.

Before diving further into the technical solution we quickly provide the use case that was motivating this work.

Application - Genomics

Many studies are using genome sequencing to study genetic variation between different individuals within a species. These includes studies of human populations, but also other species such as mice, mosquitoes or disease-causing parasites. These studies will, in general, find a large number of sites in the genome sequence where individuals differ from each other. For example, humans have more than 100 million variable sites in the genome, and modern studies like the UK BioBank are working towards sequencing the genomes of 1 million individuals or more.

In diploid species like humans, mice or mosquitoes, each individual carries two genome sequences, one inherited from each parent. At each of the 100 million variable genome sites there will be two or more “alleles” that a single genome might carry. One way to think about this is via the Punnett square, which represents the different possible genotypes that one individual might carry at one of these variable sites:

In the above there are three possible genotypes: AA, Aa, and aa. For computational genomics, these genotypes can be encoded as 0, 1, or 2. In a study of a species with M genetic variants assayed in N individual samples, we can represent these genotypes as an (M x N) array of integers. For a modern human genetics study, the scale of this array might approach (100 million x 1 million). (Although in practice, the size of the first dimension (number of variants) can be reduced somewhat, by at least an order of magnitude, because many genetic variants will carry little information and/or be correlated with each other.)

These genetic differences are not random, but carry information about patterns of genetic similarity and shared ancestry between individuals, because of the way they have been inherited through many generations. A common task is to perform a dimensionality reduction analysis on these data, such as a principal components analysis (SVD), to identify genetic structure reflecting these differencies in degree of shared ancestry. This is an essential part of discovering genetic variants associated with different diseases, and for learning more about the genetic history of populations and species.

Reducing the time taken to compute an analysis such as SVD, like all science, allows for exploring larger datasets and testing more hypotheses in less time. Practically, this means not simply a fast SVD but an accelerated pipeline end-to-end, from data loading to analysis, to understanding.

We want to run an experiment in less time than it takes to make a cup of tea

Performant SVDs w/ Dask

Now that we have that scientific background, let’s transition back to talking about computation.

To stop Dask from holding onto the data we intentionally trigger computation as we build up the graph. This is a bit atypical in Dask calculations (we prefer to have as much of the computation at once before computing) but useful given the multiple-pass nature of this problem. This was a fairly easy change, and is available in dask/dask #5041.

Additionally, we found that it was helpful to turn on moderately wide task fusion.

import dask
dask.config.set({"optimization.fuse.ave-width": 5})

Then things work fine

We’re going to try this SVD on a few different choices of hardware including:

A MacBook Pro
A DGX-2, an NVIDIA worksation with 16 high-end GPUs and fast interconnect
A twenty-node cluster on AWS

Macbook Pro

We can happily perform an SVD on a 20GB array on a Macbook Pro

import dask.array as da

x = da.random.random(size=(1_000_000, 20_000), chunks=(20_000, 5_000))

u, s, v = da.linalg.svd_compressed(x, k=10, compute=True)
v.compute()

This call is no longer entirely lazy, and it recomputes x a couple times, but it works, and it works using only a few GB of RAM on a consumer laptop.

It takes around 2min 30s time to compute that on a laptop. That’s great! It was super easy to try out, didn’t require any special hardware or setup, and in many cases is fast enough. By working locally we can iterate quickly.

Now that things work, we can experiment with different hardware.

Adding GPUs (a 15 second SVD)

Disclaimer: one of the authors (Ben Zaitlen) works for NVIDIA

We can dramatically increase performance by using a multi-GPU machine. NVIDIA and other manufacturers now make machines with multiple GPUs co-located in the same physical box. In the following section, we will run the calculations on a DGX2, a machine with 16 GPUs and fast interconnect between the GPUs.

Below is almost the same code, running in significantly less same time but we make the following changes:

We increase the size of the array by a factor of 10x
We switch out NumPy for CuPy, a GPU NumPy implementation
We use a sixteen-GPU DGX-2 machine with NVLink interconnects between GPUs (NVLink will dramatically decrease transfer time between workers)

On A DGX2 we can calculate an SVD on a 200GB Dask array between 10 to 15 seconds.

The full notebook is here, but the relevant code snippets are below:

# Some GPU specific setup
from dask_cuda import LocalCluster

cluster = LocalCluster(...)
client = Client(cluster)

import cupy
import dask.array as da
rs = da.random.RandomState(RandomState=cupy.random.RandomState)

# Create the data and run the SVD as normal
x = rs.randint(0, 3, size=(10_000_000, 20_000),
               chunks=(20_000, 5_000), dtype="uint8")
x = x.persist()

u, s, v = da.linalg.svd_compressed(x, k=10, seed=rs)
v.compute()

To see this run, we recommend viewing this screencast:

Read dataset from Disk

While impressive, the computation above is mostly bound by generating random data and then performing matrix calculations. GPUs are good at both of these things.

In practice though, our input array won’t be randomly generated, it will be coming from some dataset stored on disk or increasingly more common, stored in the cloud. To make things more realistic we perform a similar calculation with data stored in a Zarr format in GCS

In this Zarr SVD example, we load a 25GB GCS backed data set onto a DGX2, run a few processing steps, then perform an SVD. The combination of preprocessing and SVD calculations ran in 18.7 sec and the data loading took 14.3 seconds.

Again, on a DGX2, from data loading to SVD we are running in time less than it would take to make a cup of tea. However, the data loading can be accelerated. From GCS we are reading into data into the main memory of the machine (host memory), uncompressing the zarr bits, then moving the data from host memory to the GPU (device memory). Passing data back and forth between host and device memory can significantly decrease performance. Reading directly into the GPU, bypassing host memory, would improve the overall pipeline.

And so we come back to a common lesson of high performance computing:

High performance computing isn’t about doing one thing exceedingly well, it’s about doing nothing poorly.

In this case GPUs made our computation fast enough that we now need to focus on other components of our system, notably disk bandwidth, and a direct reader for Zarr data to GPU memory.

Cloud

Diclaimer: one of the authors (Matthew Rocklin) works for Coiled Computing

We can also run this on the cloud with any number of frameworks. In this case we used the Coiled Cloud service to deploy on AWS

from coiled_cloud import Cloud, Cluster
cloud = Cloud()

cloud.create_cluster_type(
    organization="friends",
    name="genomics",
    worker_cpu=4,
    worker_memory="16 GiB",
    worker_environment={
        "OMP_NUM_THREADS": 1,
        "OPENBLAS_NUM_THREADS": 1,
        # "EXTRA_PIP_PACKAGES": "zarr"
    },
)

cluster = Cluster(
    organization="friends",
    typename="genomics",
    n_workers=20,
)

from dask.distributed import Client
client = Client(cluster)

# then proceed as normal

Using 20 machines with a total of 80 CPU cores on a dataset that was 10x larger than the MacBook pro example we were able to run in about the same amount of time. This shows near optimal scaling for this problem, which is nice to see given how complex the SVD calculation is.

A screencast of this problem is viewable here

Compression

One of the easiest ways for us to improve performance is to reduce the size of this data through compression. This data is highly compressible for two reasons:

The real-world data itself has structure and repetition (although the random play data does not)
We’re storing entries that take on only four values. We’re using eight-bit integers when we only needed two-bit integers

Let’s solve the second problem first.

Compression with bit twiddling

Ideally Numpy would have a two-bit integer datatype. Unfortunately it doesn’t, and this is hard because memory in computers is generally thought of in full bytes.

To work around this we can use bit arithmetic to shove four values into a single value Here are functions that do that, assuming that our array is square, and the last dimension is divisible by four.

import numpy as np

def compress(x: np.ndarray) -> np.ndarray:
    out = np.zeros_like(x, shape=(x.shape[0], x.shape[1] // 4))
    out += x[:, 0::4]
    out += x[:, 1::4] << 2
    out += x[:, 2::4] << 4
    out += x[:, 3::4] << 6
    return out


def decompress(out: np.ndarray) -> np.ndarray:
    back = np.zeros_like(out, shape=(out.shape[0], out.shape[1] * 4))
    back[:, 0::4] = out & 0b00000011
    back[:, 1::4] = (out & 0b00001100) >> 2
    back[:, 2::4] = (out & 0b00110000) >> 4
    back[:, 3::4] = (out & 0b11000000) >> 6
    return back

Then, we can use these functions along with Dask to store our data in a compressed state, but lazily decompress on-demand.

x = x.map_blocks(compress).persist().map_blocks(decompress)

That’s it. We compress each block our data and store that in memory. However the output variable that we have, x will decompress each chunk before we operate on it, so we don’t need to worry about handling compressed blocks.

Compression with Zarr

A slightly more general but probably less efficient route would be to compress our arrays with a proper compression library like Zarr.

The example below shows how we do this in practice.

import zarr
import numpy as np
from numcodecs import Blosc
compressor = Blosc(cname='lz4', clevel=3, shuffle=Blosc.BITSHUFFLE)


x = x.map_blocks(zarr.array, compressor=compressor).persist().map_blocks(np.array)

Additionally, if we’re using the dask-distributed scheduler then we want to make sure that the Blosc compression library doesn’t use additional threads. That way we don’t have parallel calls of a parallel library, which can cause some contention

def set_no_threads_blosc():
    """ Stop blosc from using multiple threads """
    import numcodecs
    numcodecs.blosc.use_threads = False

# Run on all workers
client.register_worker_plugin(set_no_threads_blosc)

This approach is more general, and probably a good trick to have up ones’ sleeve, but it also doesn’t work on GPUs, which in the end is why we ended up going with the bit-twiddling approach one section above, which uses API that was uniformly accessible within the Numpy and CuPy libraries.

Final Thoughts

In this post we did a few things, all around a single important problems in genomics.

We learned a bit of science
We translated a science problem into a computational problem, and in particular into a request to perform large singular value decompositions
We used a canned algorithm in dask.array that performed pretty well, assuming that we’re comfortable going over the array in a few passes
We then tried that algorithm on three architectures quickly
1. A Macbook Pro
2. A multi-GPU machine
3. A cluster in the cloud
Finally we talked about some tricks to pack more data into the same memory with compression

This problem was nice in that we got to dive deep into a technical science problem, and yet also try a bunch of architecture quickly to investigate hardware choices that we might make in the future.

We used several technologies here today, made by several different communities and companies. It was great to see how they all worked together seamlessly to provide a flexible-yet-consistent experience.

GPU Dask Arrays, first steps

2019-01-03T00:00:00+00:00

The following code creates and manipulates 2 TB of randomly generated data.

import dask.array as da

rs = da.random.RandomState()
x = rs.normal(10, 1, size=(500000, 500000), chunks=(10000, 10000))
(x + 1)[::2, ::2].sum().compute(scheduler='threads')

On a single CPU, this computation takes two hours.

On an eight-GPU single-node system this computation takes nineteen seconds.

Actually this computation isn’t that impressive. It’s a simple workload, for which most of the time is spent creating and destroying random data. The computation and communication patterns are simple, reflecting the simplicity commonly found in data processing workloads.

What is impressive is that we were able to create a distributed parallel GPU array quickly by composing these four existing libraries:

CuPy provides a partial implementation of Numpy on the GPU.
Dask Array provides chunked algorithms on top of Numpy-like libraries like Numpy and CuPy.

This enables us to operate on more data than we could fit in memory by operating on that data in chunks.
The Dask distributed task scheduler runs those algorithms in parallel, easily coordinating work across many CPU cores.
The Dask CUDA to extend Dask distributed with GPU support.

These tools already exist. We had to connect them together with a small amount of glue code and minor modifications. By mashing these tools together we can quickly build and switch between different architectures to explore what is best for our application.

For this example we relied on the following changes upstream:

Comparison among single/multi CPU/GPU

We can now easily run some experiments on different architectures. This is easy because …

We can switch between CPU and GPU by switching between Numpy and CuPy.
We can switch between single/multi-CPU-core and single/multi-GPU by switching between Dask’s different task schedulers.

These libraries allow us to quickly judge the costs of this computation for the following hardware choices:

Single-threaded CPU
Multi-threaded CPU with 40 cores (80 H/T)
Single-GPU
Multi-GPU on a single machine with 8 GPUs

We present code for these four choices below, but first, we present a table of results.

Results

Architecture	Time
Single CPU Core	2hr 39min
Forty CPU Cores	11min 30s
One GPU	1 min 37s
Eight GPUs	19s

Setup

import cupy
import dask.array as da

# generate chunked dask arrays of mamy numpy random arrays
rs = da.random.RandomState()
x = rs.normal(10, 1, size=(500000, 500000), chunks=(10000, 10000))

print(x.nbytes / 1e9)  # 2 TB
# 2000.0

CPU timing

(x + 1)[::2, ::2].sum().compute(scheduler='single-threaded')
(x + 1)[::2, ::2].sum().compute(scheduler='threads')

Single GPU timing

We switch from CPU to GPU by changing our data source to generate CuPy arrays rather than NumPy arrays. Everything else should more or less work the same without special handling for CuPy.

(This actually isn’t true yet, many things in dask.array will break for non-NumPy arrays, but we’re working on it actively both within Dask, within NumPy, and within the GPU array libraries. Regardless, everything in this example works fine.)

# generate chunked dask arrays of mamy cupy random arrays
rs = da.random.RandomState(RandomState=cupy.random.RandomState)  # <-- we specify cupy here
x = rs.normal(10, 1, size=(500000, 500000), chunks=(10000, 10000))

(x + 1)[::2, ::2].sum().compute(scheduler='single-threaded')

Multi GPU timing

from dask_cuda import LocalCUDACluster
from dask.distributed import Client

cluster = LocalCUDACluster()
client = Client(cluster)

(x + 1)[::2, ::2].sum().compute()

And again, here are the results:

Architecture	Time
Single CPU Core	2hr 39min
Forty CPU Cores	11min 30s
One GPU	1 min 37s
Eight GPUs	19s

First, this is my first time playing with an 40-core system. I was surprised to see that many cores. I was also pleased to see that Dask’s normal threaded scheduler happily saturates many cores.

Although later on it did dive down to around 5000-6000%, and if you do the math you’ll see that we’re not getting a 40x speedup. My guess is that performance would improve if we were to play with some mixture of threads and processes, like having ten processes with eight threads each.

The jump from the biggest multi-core CPU to a single GPU is still an order of magnitude though. The jump to multi-GPU is another order of magnitude, and brings the computation down to 19s, which is short enough that I’m willing to wait for it to finish before walking away from my computer.

Actually, it’s quite fun to watch on the dashboard (especially after you’ve been waiting for three hours for the sequential solution to run):

Conclusion

This computation was simple, but the range in architecture just explored was extensive. We swapped out the underlying architecture from CPU to GPU (which had an entirely different codebase) and tried both multi-core CPU parallelism as well as multi-GPU many-core parallelism.

We did this in less than twenty lines of code, making this experiment something that an undergraduate student or other novice could perform at home. We’re approaching a point where experimenting with multi-GPU systems is approachable to non-experts (at least for array computing).

Here is a notebook for the experiment above

Room for improvement

We can work to expand the computation above in a variety of directions. There is a ton of work we still have to do to make this reliable.

Use more complex array computing workloads

The Dask Array algorithms were designed first around Numpy. We’ve only recently started making them more generic to other kinds of arrays (like GPU arrays, sparse arrays, and so on). As a result there are still many bugs when exploring these non-Numpy workloads.

For example if you were to switch sum for mean in the computation above you would get an error because our mean computation contains an easy to fix error that assumes Numpy arrays exactly.
Use Pandas and cuDF instead of Numpy and CuPy

The cuDF library aims to reimplement the Pandas API on the GPU, much like how CuPy reimplements the NumPy API. Using Dask DataFrame with cuDF will require some work on both sides, but is quite doable.

I believe that there is plenty of low-hanging fruit here.
Improve and move LocalCUDACluster

The LocalCUDAClutster class used above is an experimental Cluster type that creates as many workers locally as you have GPUs, and assigns each worker to prefer a different GPU. This makes it easy for people to load balance across GPUs on a single-node system without thinking too much about it. This appears to be a common pain-point in the ecosystem today.

However, the LocalCUDACluster probably shouldn’t live in the dask/distributed repository (it seems too CUDA specific) so will probably move to some dask-cuda repository. Additionally there are still many questions about how to handle concurrency on top of GPUs, balancing between CPU cores and GPU cores, and so on.
Multi-node computation

There’s no reason that we couldn’t accelerate computations like these further by using multiple multi-GPU nodes. This is doable today with manual setup, but we should also improve the existing deployment solutions dask-kubernetes, dask-yarn, and dask-jobqueue, to make this easier for non-experts who want to use a cluster of multi-GPU resources.
Expense

The machine I ran this on is expensive. Well, it’s nowhere close to as expensive to own and operate as a traditional cluster that you would need for these kinds of results, but it’s still well beyond the price point of a hobbyist or student.

It would be useful to run this on a more budget system to get a sense of the tradeoffs on more reasonably priced systems. I should probably also learn more about provisioning GPUs on the cloud.

Come help!

If the work above sounds interesting to you then come help! There is a lot of low-hanging and high impact work to do.

If you’re interested in being paid to focus more on these topics, then consider applying for a job. The NVIDIA corporation is hiring around the use of Dask with GPUs.

Senior Library Software Engineer - RAPIDS

That’s a fairly generic posting. If you’re interested the posting doesn’t seem to fit then please apply anyway and we’ll tweak things.