Find multiple max in a data (plot)

Question

I have a list with Y values. If I plot it I get this:

There are three dominant peaks visible.

Question: Is there a way, in Python, to find the n-th most dominant spikes in a data list and print their x-position (in the list)?

I need to take into account spikes with very small distance to each other. For example the first left big spike is actually a double spike (it is the sodium double line from a daylight spectra).

Answer 1

EDIT

I deleted everything. Use this two new methods:

def FindMax( listOfY , indexes, numOfMax):
    'This method finds the maximum values in the list of peaks'
    listMax = []
    xList = []
    reconstructedList = []
    for c in range(0,numOfMax):
        listMax.append(max(listOfY))
        index = listOfY.index(max(listOfY))
        xList.append(indexes[index])
        listOfY.pop(index)
    return listMax, xList

def FindPeaks(listY):
    'This method finds the peaks from the list with the Y values'
    peaks = []
    indexes = []
    count = 0
    m2 = 0 #Old slope: starts with 0
    for value in range(1,len(listY)):
        m1 = listY[value] - listY[value-1] #New slope
        if( m2 > 0 and m1 < 0 ):
            peaks.append(listY[value-1])
            indexes.append( value-1 )
        m2 = m1 #Old slope is assigned
    return peaks, indexes

#Test
list = [1,3,55,5,76,26,77,88,4,96,1,5,2,7,3,100,100,100,76,25]
peaksList = FindPeaks(list) #List: (['peaks'],['indexes'])
print ("List: " , list)
print ("Peaks list: ",peaksList[0])
print ("Peaks indexes: ",peaksList[1])
maxList = FindMax(peaksList[0],peaksList[1],3)  
print ("Max: ", maxList[0])
print ("Max indexes: ", maxList[1])
peaksList = FindPeaks(list)
print ("Peaks: ",peaksList)

FindPeaks() method will use your list with the Y values as argument and won't modify it, it also returns a 2D list, where the first index of that list is the peaks list, and second list their index in "list". After that, the peaksList[0], peaksList1, and the number of max peaks you want are passed as argument to the method FindMax(), returning a 2D list. This new list has in the index '0' a list containing the maximum peaks, in descending order, at the index '1' of peaksList are the indexes where you find them at List 'list', which is your inicial list.

Below the comment #Test you can find all the tests I ran. As you can see this method can't detect flat peaks, but you could pass as an argument to the method FindMax() the whole list, with all the arguments described above as well and you will get all the values in the flat peak, which will look as a sequence of the same value ( [...',100,100,100'...] ). But the method FindPeaks() will be usefull when finding all other peaks (not flat peaks as I described), so in the case you have a flat peak this method won't return it.

Output command-line window

I hope you find this useful for you.

Answer 2

I ran into the same problem when making a stats library which you can find on my github, but to answer your question; Make a dictionary with the X values as keys and the Y values as Values. Find the Key with the max value using:

max(dict, key=dict.get)

You can use this as an index of the dictionary to get the value of that key. What you want to do is initialize a new dictionary just in case other keys share the same max value:

new_dict = {max(dict, key=dict.get):dict[max(dict, key=dict.get)]}

Lastly, iterate through the dictionary by key, value pair, updating your new dictionary with any key, value pair where the value is equal to the value of your initial max key, value pair:

def mode(list):
    list = sorted(list)
    dict = {}

    '''iterates through list and gives key value pair
    key being the instance in the list, value being 
    number of times that instance appears in the list'''
    for i in list:
        #n will be the indicator of the frequency i shows up
        n = 0
        for e in list:
            if e == i:
                #n increases by one every time i shows up in the list again
                n+=1
        dict.update({i:n})

    '''initial list of max key, value pair. Will update if another key 
    shares same max value'''
    new_dict = {max(dict, key=dict.get):dict[max(dict, key=dict.get)]}

    for key, value in dict.iteritems():
    '''if value of instance == value of key, value pair in new_dict, it 
    shares the max value so add to new dictionary''''
        if value == new_dict.get(new_dict.keys()[0]):
            new_dict.update({key:value})

    return new_dict