find a list of peaks and valleys in xy points sequence

peakdet.py

import numbers
import math
from collections.abc import Iterable


def peakdet(v, delta, x=None, xinit=1, original=False):
	"""
	this code was kindly provided  by it's original developer.
	# Eli Billauer, 3.4.05 (Explicitly not copyrighted).
	my humble additions were aimed to catch more peaks and values, 
	in the following 2 cases:
	* record the first extreme when it is a minimum. 
	  since lookformax is initially true, the original misses this case.
	* record the last extreme. the original missed it, 
	  as being last is not being followed, 
	  especially not by a direction breaking value.
	my aim is to lessen the memory commitment, and provide iterables as input.
	the original functionality may be obtained by using the 'original' parameter.
	
	this is the original doc:
	#PEAKDET Detect peaks in a vector
	# [MAXTAB, MINTAB] = PEAKDET(V, DELTA) finds the local
	# maxima and minima ("peaks") in the vector V.
	# MAXTAB and MINTAB consists of two columns. Column 1
	# contains indices in V, and column 2 the found values.
	#
	# With [MAXTAB, MINTAB] = PEAKDET(V, DELTA, X) the indices
	# in MAXTAB and MINTAB are replaced with the corresponding
	# X-values.
	#
	# A point is considered a maximum peak if it has the maximal
	# value, and was preceded (to the left) by a value lower by
	# DELTA.
	
	# Eli Billauer, 3.4.05 (Explicitly not copyrighted).
	# This function is released to the public domain; Any use is allowed.
	"""
	
	def infinite_sequence(init):
		num = init
		while True:
			yield num
			num += 1
	
	maxtab = []
	mintab = []
	
	if not isinstance(v, Iterable):
		raise Exception('values should be iterable')
	
	if not x:
		x = infinite_sequence(xinit)
	elif isinstance(x, Iterable):
		x = iter(x)
	else:
		raise Exception('if given, x values should be iterable')
	
	if not (isinstance(delta, numbers.Number) and delta > 0):
		raise Exception('Input argument DELTA must be a positive number')
	
	mn = math.inf; mx = -math.inf;
	mnpos = math.nan; mxpos = math.nan;
	
	lookformax = 1
	firstmn = True
	lastmn = None
	lastmx = None
	
	for this in v:
		thispos = next(x)
		
		if this > mx:
			mx = this; mxpos = thispos;
			if mx >= mn+delta and not original:
				if firstmn:
					# as lookformax is initially true, 
					# the min that precedes the first max
					# will be ignored
					mintab.append((mnpos, mn));
					firstmn = False
					lastmn = None
				lastmx = (mxpos, mx)
		if this < mn:
			mn = this; mnpos = thispos;
			if mn <= mx+delta:
				lastmn = (mnpos, mn)
		
		if lookformax:
			if this < mx-delta:
				maxtab.append((mxpos, mx));
				mn = this; mnpos = thispos;
				lookformax = 0;
				lastmx = None
		else:
			if this > mn+delta:
				mintab.append((mnpos, mn));
				firstmn = False
				mx = this; mxpos = thispos;
				lookformax = 1;
				lastmn = None
		
	# if there was no change >= delta after the last mn/mx, that 
	# are here only if they moved by delta from the point before them
	if not original:
		if lastmx:
			maxtab.append(lastmx);
		if lastmn:
			mintab.append(lastmn);
	
	return maxtab, mintab


import matplotlib.pyplot as plt
from operator import itemgetter

def split_tab(tab):
	x, y = list(), list()
	for row in tab:
		x.append(row[0])
		y.append(row[1])
	return x, y

def show(inputs, delta, original=False, scale=1, subplt=None):
	
	whole = False
	if subplt is None:
		subplt = plt
		whole = True
	
	inputs = [(c, value * scale) for c, value in enumerate(inputs, start=1)]
	x, v = split_tab(inputs)
	maxtab, mintab = peakdet(v, delta, x, original=original)
	
	print('inputs:', inputs)
	print('maxtab:', maxtab)
	print('mintab:', mintab)
	
	subplt.plot(x, v, 'b-', label='inputs')
	
	if whole:
		subplt.xticks(x, x)
		subplt.yticks(v, v)
	else:
		subplt.set_xticks(x, x, minor=False)
		subplt.set_yticks(v, v, minor=False)
	
	x, v = split_tab(sorted(mintab + maxtab, key=itemgetter(0)))
	subplt.plot(x, v, 'co-.', label='evt')
	
	x, v = split_tab(maxtab)
	subplt.plot(x, v, 'g+', label='peaks')
	
	x, v = split_tab(mintab)
	subplt.plot(x, v, 'r+', label='valleys')
	
	subplt.plot([], [], 'yo', label='delta=%g' % delta)
	
	if original:
		subplt.plot([], [], 'yo', label='original')
	
	if whole:
		subplt.title('peaks & valleys')
		subplt.ylabel('value')
		subplt.xlabel('index')
	else:
		subplt.set_title('peaks & valleys')
		subplt.set_ylabel('value')
		subplt.set_xlabel('index')
	subplt.grid()
	subplt.legend(loc='best')

def show_compare(inputs, delta):
	fig, axs = plt.subplots(2, 2)
	show(inputs, delta, original=False, scale=1, subplt=axs[0, 0])
	show(inputs, delta, original=False, scale=-1, subplt=axs[0, 1])
	show(inputs, delta, original=True, scale=1, subplt=axs[1, 0])
	show(inputs, delta, original=True, scale=-1, subplt=axs[1, 1])
	
	# Hide x labels and tick labels for top plots and y ticks for right plots.
	for ax in axs.flat:
		ax.label_outer()

def main():
	
	inputs = [
		2.0, 1.0, 2.0, 3.0, 2.0, 1.0, 0.0, 2.0, 4.0, 6.0, 8.0, 
		12.0, 11.0, 10.0, 11.0, 9.0, 7.0, 5.0, 3.0, 2.0, 1.0
	]
	delta = 1.5
	
	#show(inputs, delta)
	show_compare(inputs, delta)
	plt.show()

if __name__ == '__main__':
	main()