On attempting to produce Automatic Peak Detection in Noisy Periodic and Quasi-Periodic Signals, by Felix Scholkmann, Jens Boss and Martin Wolf in Python, I've hit a stumbling block in the implementation.
Upon attempting to optimise, I've noticed that the nested for loops are creating a bottleneck in processing time (taking 115394 ms on average to complete).
Is there a more efficient means of constructing the nested for loop?
The parameter, signal, is a list of co-ordinates to which the algorithm will process which is of the form
s_time = range(1, len(signal)+1)
[fitPolynomial, fitError] = np.polyfit(s_time, signal, 1)
fitSignal = np.polyval([fitPolynomial, fitError], s_time)
dtrSignal = signal - fitSignal
N = len(dtrSignal)
L = math.ceil(N/2.0)-1
creation_start = time.time()
LSM = np.random.uniform(0, 2, size=(L, N))
creation_elapsedTime = time.time() - creation_start
print('LSM created in %s ms' % int(creation_elapsedTime * 1000))
loop_start = time.time()
for k in range(1, L):
for i in range(k+2, N-k+1):
if signal[i-1]>signal[i-k-1] and signal[i-1]>signal[i+k-1]:
LSM[k,i] = 0
loop_elapsedTime = time.time() - loop_start
print('Loop completed in %s ms' % int(loop_elapsedTime * 1000))
G = np.sum(LSM, axis=1)
l = min(enumerate(G), key=itemgetter(1))
MLSM = LSM[0:l]
S = np.std(MLSM, ddof=1)
found_indices = np.where(MLSM == ((S-1) == 0))
Here is a solution which uses only one loop
for k in range(1, L): mat=1-((signal[k+1:N-k]>signal[1:N-2*k]) & (signal[k+1:N-k]>signal[2*k+1:N])) LSM[k,k+2:N-k+1]*=mat
it's faster and seems do give the same solutions. You compare slices (as suggested by Ami Tavory), combine the comparisons with a
&, which gives a
True/False array; with
1-operation, you transform it to zeros and ones, the zeros corresponding to where the conditions are met. And lastly you multiply the row by the result.