Finding very high multiple peak element leaving the rest low peaks

Question

I have a bunch of values stored in an array, I need to find the very highest peak. I tried using this code:

arr=["values"]
n=len(arr)
if arr == []:
print (pos)
Diff = []
for i in range(0,n-1):
    if arr[i]< arr[i+1]:
       Diff.append(1)
    elif arr[i] == arr[i+1]:
       Diff.append(0)
    if arr[i] > arr[i+1]:
       Diff.append(-1)
pos = []
peaks = []
j = 0
for i in range(0,n-2):
   if Diff[i] == 1 and Diff[i+1] == -1:
     pos.append(i+1)
     peaks.append(arr[i+1])
   if Diff[i] == 1 and Diff[i+1] == 0:
     if Diff[i+1:] == [Diff[i+1]]:
        break
     j = i+1
     while(Diff[j] == 0 and j < n-2):
        j = j+1
     if Diff[j] == -1:
        pos.append(i+1)
        peaks.append(arr[i+1])
print (pos)
print (peaks)

But what I get is all the peaks, I am trying to solve to get the highest peak alone.

The data i have is:

A=['5662', '5660', '5658', '5658', '5658', '5658', '5655', '5653', '5655', '5660', '5664', '5664', '5662', '5655', '5655', '5655', '5658', '5664', '5674', '5685', '5694', '5699', '5701', '5704', '5706', '5708', '5704', '5701', '5704', '5708', '5713', '5720', '5720', '5724', '5733', '5745', '5761', '5777', '5798', '5819', '5832', '5842', '5846', '5851', '5858', '5862', '5865', '5869', '5874', '5874', '5867', '5855', '5851', '5855', '5865', '5874', '5878', '5883', '5888', '5892', '5897', '5899', '5901', '5901', '5904', '5899', '5894', '5890', '5894', '5899', '5904', '5904', '5894', '5881', '5860', '5839', '5823', '5814', '5809', '5805', '5798', '5791', '5786', '5782', '5779', '5777', '5775', '5773', '5775', '5777', '5779', '5779', '5773', '5763', '5752', '5745', '5740', '5738', '5729', '5717', '5701', '5687', '5678', '5674', '5664', '5653', '5646', '5646', '5651', '5655', '5655', '5653', '5651', '5646', '5646', '5646', '5648', '5653', '5653', '5653', '5653', '5655', '5662', '5664', '5660', '5651', '5648', '5651', '5658', '5662', '5662', '5660', '5658', '5653', '5648', '5648', '5653', '5658', '5658', '5658', '5658', '5662', '5667', '5664', '5658', '5651', '5653', '5655', '5658', '5660', '5662', '5664', '5664', '5660', '5655', '5658', '5664', '5667', '5667', '5664', '5667', '5669', '5669', '5664', '5660', '5658', '5660', '5662', '5664', '5669', '5674', '5674', '5669', '5664', '5662', '5660', '5660', '5658', '5658', '5662', '5669', '5671', '5669', '5662', '5660', '5660', '5664', '5664', '5667', '5667', '5667', '5664', '5660', '5660', '5662', '5664', '5664', '5664', '5667', '5671', '5676', '5674', '5669', '5667', '5664', '5662', '5660', '5662', '5667', '5671', '5674', '5671', '5669', '5669', '5671', '5671', '5669', '5667', '5669', '5674', '5676', '5678', '5676', '5674', '5669', '5669', '5671', '5676', '5678', '5676', '5676', '5676', '5674', '5674', '5669', '5667', '5667', '5669', '5674', '5676', '5676', '5676', '5676', '5671', '5669', '5667', '5667', '5671', '5676', '5676', '5674', '5674', '5676', '5678', '5678', '5674', '5671', '5674', '5678', '5681', '5683', '5683', '5681', '5678', '5674', '5671', '5676', '5681', '5685', '5685', '5683', '5683', '5685', '5683', '5678', '5671', '5671', '5674', '5681', '5683', '5683', '5685', '5694', '5701', '5706', '5706', '5708', '5713', '5720', '5727', '5729', '5733', '5731', '5724', '5717', '5715', '5717', '5724', '5727', '5727', '5727', '5727', '5727', '5724', '5720', '5713', '5713', '5715', '5715', '5713', '5708', '5701', '5694', '5687', '5681', '5676', '5678', '5681', '5681', '5676', '5674', '5676', '5681', '5678', '5674', '5669', '5671', '5676', '5683', '5683', '5685', '5685', '5683', '5678', '5674', '5676', '5681', '5687', '5687', '5683', '5678', '5676', '5681', '5683', '5685', '5685', '5683', '5681', '5681', '5678', '5681', '5678', '5678', '5681', '5690', '5708', '5736', '5766', '5798', '5830', '5871', '5924', '5984', '6044', '6106', '6175', '6262', '6359', '6456', '6543', '6614', '6667', '6688', '6663', '6589', '6488', '6382', '6281', '6175', '6060', '5943', '5839', '5763', '5708', '5660', '5623', '5602', '5602', '5609', '5612', '5612', '5612', '5616', '5625', '5635', '5641', '5648', '5655', '5660', '5664', '5664', '5662', '5662', '5664', '5664', '5667', '5664', '5662', '5662', '5667', '5671', '5676', '5671', '5662', '5658', '5662', '5671', '5676', '5676', '5671', '5669', '5671', '5671', '5671', '5664', '5660', '5660', '5667', '5674', '5681', '5681', '5681', '5681', '5685', '5692', '5697', '5701', '5704', '5708', '5715', '5717', '5715', '5715', '5715', '5713', '5710', '5710', '5717', '5733', '5750', '5761', '5773', '5786', '5805', '5823', '5837', '5846', '5853', '5865', '5876', '5883', '5885', '5885', '5883', '5876', '5869', '5865', '5862', '5871', '5881', '5888', '5894', '5897', '5899', '5901', '5901', '5904', '5906', '5908', '5911', '5911', '5908', '5908', '5908', '5904', '5899', '5897', '5897', '5897', '5888', '5869', '5846', '5828', '5816', '5812', '5805', '5798', '5793', '5796', '5796', '5796', '5796', '5793', '5789', '5786', '5782', '5779', '5779', '5775', '5768', '5759', '5754', '5747', '5738', '5720', '5699', '5685', '5678', '5681', '5681', '5678', '5671', '5667', '5664', '5660', '5658', '5660', '5667', '5671', '5671', '5669', '5669', '5669', '5667', '5664', '5658', '5658', '5662', '5664', '5664', '5664', '5664', '5664', '5662', '5658', '5658', '5660', '5667', '5669', '5667', '5662', '5662', '5664', '5669', '5667', '5660', '5658', '5660', '5667', '5674', '5676', '5676', '5671', '5664', '5658', '5658', '5664', '5671', '5674', '5671', '5669', '5667', '5667', '5664', '5664', '5662', '5662', '5667', '5669', '5676', '5676', '5674', '5671', '5669', '5671', '5674', '5671', '5667', '5667', '5671', '5678', '5681', '5676', '5669', '5667', '5669', '5671', '5674', '5676', '5678', '5681', '5681', '5676', '5671', '5669', '5671', '5674', '5676', '5676', '5681', '5683', '5685', '5685', '5683', '5676', '5671', '5671', '5674', '5681', '5683', '5681', '5678', '5674', '5674', '5674', '5676', '5678', '5678', '5678', '5678', '5681', '5685', '5685', '5681', '5674', '5669', '5671', '5676', '5681', '5683', '5681', '5681', '5678', '5676', '5674', '5676', '5678', '5678', '5678', '5678', '5681', '5683', '5681', '5676', '5669', '5671', '5676', '5681', '5681', '5683', '5683', '5685', '5685', '5683', '5681', '5681', '5683', '5685', '5685', '5683', '5685', '5685', '5683', '5678', '5676', '5681', '5685', '5687', '5685', '5687', '5690', '5690', '5687', '5683', '5678', '5678', '5678', '5681', '5683', '5687', '5692', '5690', '5683', '5674', '5674', '5683', '5694', '5704', '5710', '5715', '5722', '5727', '5729', '5729', '5727', '5727', '5727', '5727', '5729', '5733', '5736', '5736', '5731', '5727', '5727', '5729', '5733', '5731', '5729', '5729', '5733', '5736', '5733', '5724', '5713', '5706', '5701', '5699', '5694', '5692', '5690', '5690', '5687', '5685', '5685', '5685', '5685', '5685', '5685', '5687', '5687', '5690', '5685', '5678', '5669', '5667', '5669', '5678', '5687', '5692', '5694', '5690', '5685', '5683', '5683', '5685', '5683', '5681', '5681', '5683', '5690', '5692', '5692', '5687', '5683', '5676', '5676', '5681', '5692', '5706', '5722', '5745', '5768', '5798', '5828', '5867', '5917', '5977', '6042', '6108', '6187', '6276', '6377', '6469', '6548', '6607', '6658', '6688', '6679', '6617', '6513', '6396', '6285', '6173', '6058', '5940', '5842', '5768', '5717', '5678', '5646', '5621', '5612', '5607', '5605', '5605', '5609', '5623', '5637', '5646', '5653', '5658', '5664', '5667', '5667', '5664', '5660', '5662', '5664', '5671', '5674', '5674', '5671', '5667', '5664', '5667', '5669', '5671', '5674', '5676', '5676', '5676', '5674', '5671', '5674', '5674', '5671', '5667', '5667', '5676', '5683', '5685', '5676', '5669', '5671', '5681', '5685', '5685', '5685', '5692', '5708', '5720', '5722', '5717', '5713', '5717', '5722', '5724', '5724', '5727', '5731', '5731', '5729', '5731', '5743', '5759', '5779', '5791', '5805', '5823', '5844', '5860', '5867', '5862', '5860', '5865', '5876', '5890', '5894', '5892', '5883', '5876', '5874', '5876', '5883', '5892', '5899', '5906', '5908', '5911', '5913', '5915', '5917', '5915', '5908', '5904', '5908', '5917', '5924', '5924', '5915', '5911', '5906', '5901', '5885', '5862', '5839', '5825', '5816', '5812', '5807', '5805', '5802', '5798', '5793', '5791', '5793', '5798', '5800', '5798', '5793', '5791', '5786', '5777', '5768', '5761', '5759', '5754', '5743', '5729', '5717', '5708', '5697', '5681', '5669', '5667', '5671', '5674', '5671', '5671', '5671', '5674', '5671', '5667', '5662', '5664', '5667', '5667', '5664', '5667', '5674', '5678', '5674', '5664', '5660', '5660', '5664', '5667', '5667', '5667', '5669', '5674', '5671', '5667', '5664', '5667', '5671', '5674', '5674', '5674', '5676', '5681', '5676', '5671', '5664', '5667', '5674', '5676', '5674', '5671', '5671', '5678', '5683', '5678', '5667', '5662', '5669', '5678', '5681', '5676', '5674', '5676', '5678', '5674', '5667', '5664', '5669', '5678', '5681', '5676', '5674', '5674', '5678', '5678', '5676', '5671', '5676', '5681', '5683', '5683', '5678', '5676', '5674', '5671', '5669', '5669', '5667', '5669', '5669', '5671', '5676', '5681', '5681', '5678', '5671', '5669', '5671', '5676', '5681', '5685', '5681', '5676', '5671', '5671', '5674', '5681', '5681', '5681', '5678', '5683', '5690', '5692', '5687', '5678', '5669', '5722', '5729', '5733', '5738', '5740', '5738', '5736', '5733', '5736', '5738', '5745', '5747', '5747', '5745', '5740', '5738', '5733', '5733', '5736', '5743', '5750', '5752', '5745', '5736', '5724', '5717', '5713', '5706', '5699', '5694', '5690', '5692', '5694', '5697', '5697', '5692', '5687', '5683', '5683', '5687', '5692', '5694', '5694', '5692', '5690', '5685', '5685', '5685', '5690', '5694', '5697', '5699', '5701', '5701', '5697', '5692', '5685', '5683', '5690', '5694', '5699', '5699', '5699', '5701', '5699', '5692', '5683', '5678', '5685', '5701', '5722', '5745', '5773', '5802', '5832', '5867', '5913', '5968', '6035', '6104', '6177', '6262', '6359', '6458', '6543', '6610', '6658', '6686', '6679', '6624', '6529', '6419', '6313', '6205', '6090', '5968', '5860', '5779', '5727', '5687', '5653', '5625', '5614', '5618', '5623', '5621', '5616', '5618', '5632', '5651', '5662', '5669', '5671', '5671', '5671', '5676', '5678', '5681', '5678', '5674', '5676', '5681', '5687', '5690', '5687', '5683', '5676', '5669', '5669', '5674', '5681', '5687', '5690', '5685', '5681', '5678', '5678', '5678', '5674', '5674', '5676', '5681', '5683', '5683', '5678', '5681', '5683', '5685', '5690', '5701', '5713', '5724', '5729', '5729', '5729', '5727', '5729', '5729', '5729', '5729', '5731', '5733', '5740', '5752', '5761', '5768', '5773', '5784', '5802', '5828', '5848', '5862', '5867', '5871', '5876', '5883', '5888', '5888', '5888', '5885', '5883', '5881', '5878', '5881', '5885', '5894', '5901', '5906', '5911', '5911', '5915', '5917', '5922', '5922', '5920', '5915', '5911', '5911', '5913', '5915', '5920', '5920', '5920', '5911', '5892', '5869', '5848', '5835', '5828', '5823', '5819', '5812', '5807', '5805', '5802', '5802', '5800', '5796', '5791', '5791', '5796', '5800', '5800', '5789', '5773', '5763', '5761', '5763', '5759', '5743', '5724', '5706', '5699', '5697', '5692', '5685', '5676', '5669', '5667', '5669', '5674', '5681', '5685', '5685', '5683', '5678', '5674', '5669', '5669', '5671', '5674', '5674', '5674', '5671', '5671', '5669', '5667', '5667', '5667', '5671', '5678', '5681', '5681', '5678', '5674', '5671', '5667', '5669', '5671', '5676', '5676', '5676', '5676', '5681', '5685', '5683', '5676', '5669', '5669', '5678', '5687', '5690', '5687', '5683', '5678', '5678', '5678', '5683', '5685', '5683', '5681', '5681', '5683', '5687', '5690', '5685', '5678', '5676', '5676', '5678', '5683', '5687', '5687', '5685', '5681', '5676', '5676', '5678', '5681', '5681', '5678', '5681', '5687', '5690', '5685', '5676', '5671', '5674', '5678', '5683', '5683', '5683', '5685', '5687', '5685', '5681', '5676', '5678', '5683', '5685', '5683', '5683', '5687', '5692', '5692', '5687', '5681', '5681', '5685', '5690', '5692', '5690', '5687', '5687', '5687', '5685', '5683', '5681', '5683', '5685', '5687', '5687', '5690', '5690', '5685', '5681', '5678', '5681', '5685', '5687', '5687', '5687', '5690', '5692', '5692', '5690', '5685', '5681', '5681', '5681', '5685', '5690', '5692', '5694', '5690', '5685', '5683', '5685', '5692', '5694', '5694', '5694', '5694', '5697', '5694', '5690', '5685', '5685', '5687', '5690', '5692', '5694', '5697', '5694', '5692', '5687', '5685', '5685', '5687', '5692', '5692', '5692', '5694', '5694', '5694', '5692', '5690', '5687', '5687', '5690', '5694', '5706', '5715', '5720', '5717', '5715', '5717', '5722', '5729', '5733', '5733', '5733', '5738', '5740', '5738', '5733', '5731', '5733', '5736', '5738', '5740', '5743', '5747', '5747', '5743', '5736', '5733', '5738', '5738', '5729', '5717', '5708', '5708', '5713', '5706', '5694', '5685', '5683', '5690', '5697', '5697', '5694', '5690', '5690', '5690', '5690', '5690', '5687', '5690', '5690', '5690', '5692', '5694', '5694', '5692', '5692', '5690', '5687', '5687', '5692', '5697', '5701', '5697', '5692', '5690', '5692', '5697', '5697', '5694', '5694', '5697', '5699', '5699', '5699', '5706', '5722', '5740', '5761', '5786', '5819', '5860', '5911', '5966', '6026', '6088', '6157', '6237', '6331', '6428', '6520', '6596', '6653', '6690', '6688', '6640', '6550', '6440', '6329', '6226', '6118', '6005', '5894', '5805', '5743', '5697', '5658', '5625', '5609', '5607', '5609', '5614', '5621', '5632', '5641', '5646', '5646', '5651', '5662', '5676', '5681', '5678', '5676', '5678', '5683', '5681', '5676', '5671', '5674', '5676', '5678', '5676', '5676', '5678', '5681', '5678', '5674', '5674', '5678', '5683', '5681', '5678', '5678', '5681', '5683', '5681', '5674', '5671', '5676', '5685', '5687', '5690', '5690', '5694', '5701', '5704', '5704', '5708', '5717', '5727', '5729', '5727', '5724', '5729', '5736', '5736', '5729', '5722', '5724', '5736', 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'5667', '5667', '5674', '5683', '5685', '5678', '5676', '5678', '5683', '5683', '5676', '5671', '5671', '5676', '5683', '5687', '5690', '5687', '5685', '5681', '5676', '5676', '5678', '5678', '5678', '5681', '5685', '5690', '5690', '5683', '5678', '5674', '5676', '5683', '5687', '5692', '5692', '5690', '5687', '5683', '5681', '5681', '5683', '5683', '5683', '5683', '5685', '5687', '5687', '5683', '5676', '5676', '5678', '5685', '5690', '5690', '5690', '5687', '5685', '5683', '5683', '5685', '5685', '5690', '5690', '5690', '5692', '5694', '5694', '5694', '5690', '5685', '5685', '5687', '5690', '5692', '5690', '5685', '5683', '5683', '5683', '5685', '5685', '5685', '5687', '5692', '5694', '5697', '5699', '5697', '5692', '5687', '5687', '5692', '5697', '5699', '5697', '5692', '5692', '5697', '5697', '5692', '5685', '5683', '5690', '5699', '5706', '5704', '5697', '5690', '5685', '5683', '5685', '5690', '5694', '5694', '5692', '5692', '5697', '5706', '5710', , '5860', '5862', '5865', '5869', '5878', '5888', '5892', '5892', '5890', '5883', '5878', '5874', '5876', '5883', '5890', '5899']

Kindly help.

Answer 1

First, convert your list of strings to a numpy array or pandas Series:

import pandas as pd
s = pd.Series(A).astype(int)

Secondly, identify all extreme values (e.g. those in the extreme 1% of the distribution), then finally get the maximum value by consecutive values (peaks). We can easily identify the consecutive groups with more_itertools.consecutive_groups:

from more_itertools import consecutive_groups

grp_peaks = consecutive_groups(s[s >= s.quantile(.99)].index)
max_peaks = [s[grp].idxmax() for grp in grp_peaks]
print(s[max_peaks])

Output:

372     6688
787     6688
1132    6686
1547    6690
1963    6690
2378    6686
2793    6695
dtype: int64

Data visualization:

import matplotlib.pyplot as plt
plt.figure(figsize=(12,8))
plt.plot(s, marker='o')

# Set a line delimiting the extreme 1% values of the distribution
plt.axhline(y=s.quantile(.99), color='r', linestyle='--')

# Identify the maximum value per peak
plt.plot(s[max_peaks], color='r', marker='o', linestyle='None')

plt.show()

---

An approach to reproduce the results above without importing any libraries:

# Convert list of strings to integers and get respective indexes
A = list(map(int, A))
idx = range(len(A))

# Calculate empirical p-values to get the peaks
pval = [1 - sum([i >= j for j in A]) / (len(A)+1) for i in A]

# Identify extreme values (peaks)
stat_pval = [idx for idx,p in enumerate(pval) if p <= 0.01]

# Identify consecutive indexes in target
grps = []
consec_idx = []
stat_pval.append(stat_pval[-1]+2)

for i in range(len(stat_pval)-1):
    if stat_pval[i] == stat_pval[i+1]-1:
        consec_idx.append(stat_pval[i])
    else:
        consec_idx.append(stat_pval[i])
        grps.append(consec_idx)
        consec_idx = []

del consec_idx
del stat_pval[-1]

# Then, identify the maximum value per peak:
[max(A[grp[0]:grp[-1]+1]) for grp in grps]

[6688, 6688, 6686, 6690, 6690, 6686, 6695]

Alternatively, if you wanna print both maximum values per peak, as well as their index:

idx_and_max_per_peak = []
for grp in grps:
    peak = A[grp[0]:grp[-1]+1]
    peak_max = max(peak)
    idx_and_max_per_peak.extend([(grp[i], value) for i,value in enumerate(peak) if value==peak_max])

Output of idx_and_max_per_peak:

[(372, 6688),
 (787, 6688),
 (1132, 6686),
 (1547, 6690),
 (1963, 6690),
 (2378, 6686),
 (2793, 6695)]