I have a performance question about two bits of code. One is implemented in python and one in MATLAB. The code calculates the sample entropy of a time series (which sounds complicated but is basically a bunch of for loops).
I am running both implementations on relatively large time series (~95k+ samples) depending on the time series. The MATLAB implementation finishes the calculation in ~45 sec to 1 min. The python one basically never finishes. I threw tqdm over the python for loops and the upper loop was only moving at about ~1.85s/it which gives 50+ hours as a estimated completion time (I've let it run for 15+ mins and the iteration count was pretty consistent).
Example inputs and runtimes:
MATLAB (~ 52 sec):
a = rand(1, 95000)
sampenc(a, 4, 0.1 * std(a))
Python (currently 5 mins in with 49 hours estimated):
import numpy as np
a = np.random.rand(1, 95000)[0]
sample_entropy(a, 4, 0.1 * np.std(a))
Python Implementation:
# https://github.com/nikdon/pyEntropy
def sample_entropy(time_series, sample_length, tolerance=None):
"""Calculate and return Sample Entropy of the given time series.
Distance between two vectors defined as Euclidean distance and can
be changed in future releases
Args:
time_series: Vector or string of the sample data
sample_length: Number of sequential points of the time series
tolerance: Tolerance (default = 0.1...0.2 * std(time_series))
Returns:
Vector containing Sample Entropy (float)
References:
[1] http://en.wikipedia.org/wiki/Sample_Entropy
[2] http://physionet.incor.usp.br/physiotools/sampen/
[3] Madalena Costa, Ary Goldberger, CK Peng. Multiscale entropy analysis
of biological signals
"""
if tolerance is None:
tolerance = 0.1 * np.std(time_series)
n = len(time_series)
prev = np.zeros(n)
curr = np.zeros(n)
A = np.zeros((sample_length, 1)) # number of matches for m = [1,...,template_length - 1]
B = np.zeros((sample_length, 1)) # number of matches for m = [1,...,template_length]
for i in range(n - 1):
nj = n - i - 1
ts1 = time_series[i]
for jj in range(nj):
j = jj + i + 1
if abs(time_series[j] - ts1) < tolerance: # distance between two vectors
curr[jj] = prev[jj] + 1
temp_ts_length = min(sample_length, curr[jj])
for m in range(int(temp_ts_length)):
A[m] += 1
if j < n - 1:
B[m] += 1
else:
curr[jj] = 0
for j in range(nj):
prev[j] = curr[j]
N = n * (n - 1) / 2
B = np.vstack(([N], B[:sample_length - 1]))
similarity_ratio = A / B
se = - np.log(similarity_ratio)
se = np.reshape(se, -1)
return se
MATLAB Implementation:
function [e,A,B]=sampenc(y,M,r);
%function [e,A,B]=sampenc(y,M,r);
%
%Input
%
%y input data
%M maximum template length
%r matching tolerance
%
%Output
%
%e sample entropy estimates for m=0,1,...,M-1
%A number of matches for m=1,...,M
%B number of matches for m=0,...,M-1 excluding last point
n=length(y);
lastrun=zeros(1,n);
run=zeros(1,n);
A=zeros(M,1);
B=zeros(M,1);
p=zeros(M,1);
e=zeros(M,1);
for i=1:(n-1)
nj=n-i;
y1=y(i);
for jj=1:nj
j=jj+i;
if abs(y(j)-y1)<r
run(jj)=lastrun(jj)+1;
M1=min(M,run(jj));
for m=1:M1
A(m)=A(m)+1;
if j<n
B(m)=B(m)+1;
end
end
else
run(jj)=0;
end
end
for j=1:nj
lastrun(j)=run(j);
end
end
N=n*(n-1)/2;
B=[N;B(1:(M-1))];
p=A./B;
e=-log(p);
I've also tried a few other python implementations and all of them have the same slow result: vectorized-sample-entropy
Wikipedia sample entropy implementation
I don't think computer issue as it runs relativity fast in MATLAB.
As far as I can tell, implementation-wise both sets of code are the same. I have no idea why the python implementations are so slow. I would understand a difference of a few seconds but not such a large discrepancy. Let me know your thoughts on why this is or suggestions on how to improve the python versions.
BTW: I'm using Python 3.6.5 with numpy 1.14.5 and MATLAB R2018a.
