Find when the values of a pandas.Series change by at least x

I don't know if I am understanding you correctly, but here is how I interpreted the problem:

import pandas as pdimport numpy as np# Our series of data.data = pd.DataFrame(np.random.rand(10), columns = ['value'])# The threshold.threshold = .33# For each point t, grab t - 1. data['value_shifted'] = data['value'].shift(1)# Absolute difference of t and t - 1.data['abs_change'] = abs(data['value'] - data['value_shifted'])# Test against the threshold.data['change_exceeds_threshold'] = np.where(data['abs_change'] > threshold, 1, 0)print(data)

Giving:

      value  value_shifted  abs_change  change_exceeds_threshold0  0.005382            NaN         NaN                         01  0.060954       0.005382    0.055573                         02  0.090456       0.060954    0.029502                         03  0.603118       0.090456    0.512661                         14  0.178681       0.603118    0.424436                         15  0.597814       0.178681    0.419133                         16  0.976092       0.597814    0.378278                         17  0.660010       0.976092    0.316082                         08  0.805768       0.660010    0.145758                         09  0.698369       0.805768    0.107400                         0

I don't think the pseudo code can be vectorized because the next state of s* is dependent on the last state. There's a pure python solution (1 iteration):

import randomimport pandas as pds = [random.randint(0,100) for _ in range(100)]res = [] # record changesthres = 20ss = s[0]for i in range(len(s)):    if abs(s[i] - ss) > thres:        ss = s[i]        res.append([i, s[i]])df = pd.DataFrame(res, columns=['value'])

I think there's no way to run faster than O(N) in this case.