CODEWITHSUNDEEP
pythoncurve-fittingdata-analysisnonlinear-optimization
Colt Bradley
Colt Bradley

Reputation: 1

lmfit for exponential data returns linear function

I'm working on fitting muon lifetime data to a curve to extract the mean lifetime using the lmfit function. The general process I'm using is to bin the 13,000 data points into 10 bins using the histogram function, calculating the uncertainty with the square root of the counts in each bin (it's an exponential model), then use the lmfit module to determine the best fit along with means and uncertainty. However, graphing the output of the model.fit() method returns this graph, where the red line is the fit (and obviously not the correct fit). Fit result output graph

I've looked online and can't find a solution to this, I'd really appreciate some help figuring out what's going on. Here's the code. 

import os
import numpy as np
import matplotlib.pyplot as plt
from numpy import sqrt, pi, exp, linspace
from lmfit import Model

class data():
    def __init__(self,file_name):
        times_dirty = sorted(np.genfromtxt(file_name, delimiter=' ',unpack=False)[:,0])
        self.times = []


    for i in range(len(times_dirty)):
            if times_dirty[i]<40000:
                self.times.append(times_dirty[i])
        self.counts = []
        self.binBounds = []
        self.uncertainties = []
        self.means = []

    def binData(self,k):
        self.counts, self.binBounds = np.histogram(self.times, bins=k)
        self.binBounds = self.binBounds[:-1]

    def calcStats(self):
        if len(self.counts)==0:
            print('Run binData function first')
        else:
            self.uncertainties = sqrt(self.counts)

    def plotData(self,fit):
        plt.errorbar(self.binBounds, self.counts, yerr=self.uncertainties, fmt='bo')
        plt.plot(self.binBounds, fit.init_fit, 'k--')
        plt.plot(self.binBounds, fit.best_fit, 'r')
        plt.show()

def decay(t, N, lamb, B):
    return N * lamb * exp(-lamb * t) +B

def main():
    muonEvents = data('C:\Users\Colt\Downloads\muon.data')
    muonEvents.binData(10)
    muonEvents.calcStats()
    mod = Model(decay)
    result = mod.fit(muonEvents.counts, t=muonEvents.binBounds, N=1, lamb=1, B = 1)
    muonEvents.plotData(result)
    print(result.fit_report())
    print (len(muonEvents.times))



if __name__ == "__main__":
    main()

Upvotes: 0

Views: 470

Answers (2)

M Newville
M Newville

Reputation: 7862

Just to build on James Phillips answer, I think the data you show in your graph imply values for N, lamb, and B that are very different from 1, 1, 1. Keep in mind that exp(-lamb*t) is essentially 0 for lamb = 1, and t> 100. So, if the algorithm starts at lamb=1 and varies that by a little bit to find a better value, it won't actually be able to see any difference in how well the model matches the data.

I would suggest trying to start with values that are more reasonable for the data you have, perhaps N=1.e6, lamb=1.e-4, and B=100.

As James suggested, having the variables have values on the order of 1 and putting in scale factors as necessary is often helpful in getting numerically stable solutions.

Upvotes: 0

James Phillips
James Phillips

Reputation: 4657

This might be a simple scaling problem. As a quick test, try dividing all raw data by a factor of 1000 (both X and Y) to see if changing the magnitude of the data has any effect.

Upvotes: 0

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