python 2.7 - Trying to fit a sine function to phased light curve

Question

import numpy as np
import matplotlib.pyplot as plt
from lmfit import Model,Parameters


f2= "KELT_N16_lc_006261_V01_west_tfa.dat"    
t2="TIMES"   # file name

NewData2 = np.loadtxt(t2, dtype=float, unpack=True)
NewData = np.loadtxt(f2,dtype=float, unpack=True, usecols=(1,))

flux = NewData   
time= NewData2

new_flux=np.hstack([flux,flux])

# fold
period = 2.0232               # period (must be known already!)

foldTimes = ((time)/ period)  # divide by period to convert to phase
foldTimes = foldTimes % 1   # take fractional part of phase only (i.e. discard whole number part)


new_phase=np.hstack([foldTimes+1,foldTimes])

print len(new_flux)
print len(new_phase)


def Wave(x, new_flux,new_phase):
    wave = new_flux*np.sin(new_phase+x)
    return wave
model = Model(Wave)
print "Independent Vars:", model.independent_vars
print "Parameters:",model.param_names
p = Parameters()
p.add_many(('new_flux',13.42, True, None, None, None) )   
p.add_many(('new_phase',0,True, None, None, None) )   

result=model.fit(new_flux,x=new_phase,params=p,weights= None)


plt.scatter(new_phase,new_flux,marker='o',edgecolors='none',color='blue',s=5.0, label="Period: 2.0232  days")   
plt.ylim([13.42,13.54])
plt.xlim(0,2)
plt.gca().invert_yaxis()
plt.title('HD 240121 Light Curve with BJD Correction')
plt.ylabel('KELT Instrumental Magnitude')
plt.xlabel('Phase')
legend = plt.legend(loc='lower right', shadow=True)
plt.scatter(new_phase,result.best_fit,label="One Oscillation Fit", color='red',s=60.0)
plt.savefig('NewEpoch.png')
print result.fit_report()

I am trying to fit a sine function to phased light curve data for a research project. However, I am unsure as to where I am going wrong, and I believe it lays in my parameters. It appears that the fit has an amplitude that is too high, and a period that is too long. Any help would be appreciated. Thank you!

This is what the graph looks like now (Attempt at fitting a sine function to my dataset):

Answer 1

A couple of comments/suggestions:

First, it is almost certainly better to replace

p = Parameters()
p.add_many(('new_flux',13.42, True, None, None, None) )
p.add_many(('new_phase',0,True, None, None, None) )

with

p = Parameters()
p.add('new_flux', value=13.42, vary=True)
p.add('new_phase', value=0, vary=True)

Second, your model does not include a DC offset, but your data clearly has one. The offset is approximately 13.4 and the amplitude of the sine wave is approximately 0.05. While you're at it, you probably want to include a scale the phase as a well as an offset, so that the model is

offset + amplitude * sin(scale*x + phase_shift)

You don't necessarily have to vary all of those, but making your model more general will allow to see how the phase shift and scale are correlated -- given the noise level in your data, that might be important.

With the more general model, you can try a few sets of parameter values, using model.eval() to evaluate a model with a set of Parameters. Once you have a better model and reasonable starting points, you should get a reasonable fit.