How I Got a 327x Speedup Of Some Python Code
I don't usually post code stuff on this blog, but I had some fun working on this and I wanted to share!
My colleague, Abhi, is processing data from an instrument collecting actual data from the real world (you should know that this is something I have never done!) and is having some problems with how long his analysis is taking. In particular, it is taking him longer than a day to analyze a day's worth of data, which is clearly an unacceptable rate of progress. One step in his analysis is to take the data from all ~30,000 frequency channels of the instrument, and calculate an average across a moving window 1,000 entries long. For example, if I had the list:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
and I wanted to find the average over a window of length three, I'd get:
[1, 2, 3, 4, 5, 6, 7, 8]
Notice that I started by averaging [0, 1, 2]=>1, as this is the first way to come up with a window of three values. Similarly, the last entry is [7, 8, 9]=>8. Here is a simplified version of how Ahbi was doing it (all of the code snippets shown here are also available [here][1]):
def avg0(arr, l):
# arr - the list of values
# l - the length of the window to average over
new = []
for i in range(arr.size - l + 1):
s = 0
for j in range(i, l + i):
s += j
new.append(s / l)
return new
This function is correct, but when we time this simple function (using an IPython Magic) we get:
# a is [0, 1, 2, ..., 29997, 29998, 29999]
a = np.arange(30000)
%timeit avg0(a, 1000)
1 loops, best of 3: 3.19 s per loop
Which isn't so horrible in the absolute sense -- 3 seconds isn't that long compared to how much time we all waste per day. However, I neglected to mention above that Abhi must do this averaging for nearly 9,000 chunks of data per collecting day. This means that this averaging step alone takes about 8 hours of processing time per day of collected data. This is clearly taking too long!
The next thing I tried is to take advantage of Numpy, which is a Python package that enables much faster numerical analysis than with vanilla Python. In this function I'm essentially doing the same thing as above, but using Numpy methods, including pre-allocating space, summing values using the accelerated Numpy .sum() function, and using the xrange() iterator, which is somewhat faster than plain range():
def avg1(arr, l):
new = np.empty(arr.size - l + 1, dtype=arr.dtype)
for i in xrange(arr.size - l + 1):
new[i] = arr[i:l+i].sum() / l
return new
This provides a healthy speed up of about a factor of eight:
%timeit avg1(a, 1000)
1 loops, best of 3: 405 ms per loop
But this still isn't fast enough; we've gone from 8 hours to just under an hour. We'd like to run this analysis in at most a few minutes. Below is an improved method that takes advantage of a queue, which is a programming construct that allows you to efficiently keep track of values you've seen before.
def avg2(arr, l):
new = np.empty(arr.size - l + 1, dtype=arr.dtype)
d = deque()
s = 0
i = 0
for value in arr:
d.append(value)
s += value
if len(d) == l:
new[i] = s / l
i += 1
elif len(d) > l:
s -= d.popleft()
new[i] = s / l
i += 1
return new
And here we can see that we've cut our time down by another factor of 4:
%timeit avg2(a, 1000)
10 loops, best of 3: 114 ms per loop
This means that from 8 hours we're now down to roughly 13 minutes. Getting better, but still not great. What else can we try? I've been looking for an excuse to try out Numba, which is a tool that is supposed to help speed up numerical analysis in Python, so I decided to give it a shot. What makes Numba attractive is that with a single additional line, Numba can take a function and dramatically speed it up by seamlessly converting it into C and compiling it when needed. So let's try this on the first averaging function:
@jit(argtypes=[int32[:], int32], restype=int32[:])
def avg0_numba(arr, l):
new = []
for i in range(arr.size - l + 1):
s = 0
for j in range(i, l + i):
s += j
new.append(s / l)
return np.array(new)
In the line beginning with @jit, all I have to do is describe the input and the output types, and it handles the rest. And here's the result:
%timeit avg0_numba(a, 1000)
10 loops, best of 3: 21.6 ms per loop
What is incredible here is that not only is this roughly 5 times faster than the queue method above, it's a ridiculous 147 times faster than the original method and only one line has been added. We've now reduced 8 hours to about 4 minutes. Not bad!
Let's try this on the second averaging method, which if you recall, was substantially better than the original method:
@jit(argtypes=[int32[:], int32], restype=int32[:])
def avg1_numba(arr, l):
new = np.empty(arr.size - l + 1, dtype=arr.dtype)
for i in xrange(arr.size - l + 1):
new[i] = arr[i:l+i].sum() / l
return new
%timeit avg1_numba(a, 1000)
1 loops, best of 3: 688 ms per loop
That's interesting! For some reason I don't understand, this is actually slower than the un-optimized version of avg1. Let's see if Numba can speed up the queue method:
@jit(argtypes=[int32[:], int32], restype=int32[:])
def avg2_numba(arr, l):
new = np.empty(arr.size - l + 1, dtype=arr.dtype)
d = deque()
s = 0
i = 0
for value in arr:
d.append(value)
s += value
if len(d) == l:
new[i] = s / l
i += 1
elif len(d) > l:
s -= d.popleft()
new[i] = s / l
i += 1
return new
%timeit avg2_numba(a, 1000)
10 loops, best of 3: 77.5 ms per loop
This is somewhat better than before, but still not as fast as avg0_numba, which comes in at roughly 20ms. But what if I really try hard to optimize the queue method by using only Numpy arrays?
@jit(argtypes=[int32[:], int32], restype=int32[:])
def avg2_numba2(arr, l):
new = np.empty(arr.size - l + 1, dtype=arr.dtype)
d = np.empty(l + 1, dtype=arr.dtype)
s = 0
i = 0
left = 0
right = 0
full = False
for j in xrange(arr.size):
d[right] = arr[j]
s += arr[j]
right = (right + 1) % (l+1)
if not full and right == l:
new[i] = s / l
i += 1
full = True
elif full:
s -= d[left]
left = (left + 1) % (l+1)
new[i] = s / l
i += 1
return new
%timeit avg2_numba2(a, 1000)
100 loops, best of 3: 9.77 ms per loop
A ha! That's even faster, and our 3.19s are now down to 9.77ms, an improvement of 327 times. The original 8 hours are now reduced to less than two minutes. I hope you've enjoyed this as much as I have!
Update:
After chatting with a couple of my colleagues, this appears to be the fastest way to do this kind of operation:
from scipy.signal import fftconvolve
import numpy as np
a = np.arange(30000)
b = np.ones(1000) / 1000.
%timeit fftconvolve(a, b, 'valid')
100 loops, best of 3: 6.25 ms per loop
Working Conditions
Of late, there has been a great deal of construction in and around my office. Beginning two weeks ago my office cluster has been repainted, doors refinished, window shades replaced, some carpet has been replaced, and some wires and pipes have been installed and moved. There is still some more work to be done.
Beginning yesterday, and continuing for the next four to six weeks, the scoreboards for the stadium are being replaced. Pictured above is a crane removing pieces of the old one (notice the asymmetry in solid black/shaded regions). This crane is more or less just outside my window, which, as you can imagine, is kind of neat for the first five minutes, and then gets tiresome and annoying after that. The construction has also closed off large amount of space in front of the offices which is inconvenient for us, and they even cut down two perfectly healthy trees, presumably to make space for the crane (insert tree-sitter joke here).
As a matter of fact, the conduit carrying the control wires for the new scoreboards passes by my office. The next time Stanfurd plays the Buffs, don't be surprised if - wait, I'm saying too much.
more ...CU Janus Supercomputer
Last night I had the opportunity to tour the supercomputer recently built here at CU named "Janus" that I've been using. It is a 16,000-core Dell cluster using 6-core Intel processors running RedHat Linux. It was built in an interesting way. Instead of building a machine room in a building and then filling it with cooling ducts, pipes, and power connections, the machine room is made up of standard shipping containers that had all those connections in place, similar to a pre-fab house. These were shipped from the factory (in Canada, I think) on trucks, and then dropped next to each other in a parking lot behind a campus building. Unfortunately, because it was nighttime, I don't have a good picture of the outside.
Below are some pictures I took of Janus.
The machine racks. The door encloses the ‘hot' side of the machines, where the air is sucked to the heat exchangers.
The cooling system.
The blinky and hot end of the machines. Lots of wires!
A close up of the back of a compute node. Notice that they have serial ports, which are based on a 40+ year old standard. At least they have USB ports, too.
It was using 415 kW of power. I think it can go much higher than that when the machine is under heavy load on a hot day.
more ...
