TypeError: 'numpy.ndarray' object is not callable in scipy.optimize leastsq

Question

I'm new to Python and, for work reason, I'm trying to write a Python code capable to read three files containing float (x,y) data (let's say x1,y1; x2,y2; x3,y3) and combine two of the arrays (y1 and y2) with a linear combination to approach the third (y3) as closely as possible. Moreover, x1 and x2 are identical, whereas x3 is different, so I interpolate x3 and y3 using x1. I'm working on Idle on Mac OSX, and Python 2.7. Here's my code:

import numpy as np
import matplotlib.pyplot as plt
import Tkinter as tk
import tkFileDialog
from scipy.optimize import leastsq

root1 = tk.Tk()
root1.geometry() #window centered on desktop?
root1.withdraw() #the main app window doesn't remain in the background
filename1 = tkFileDialog.askopenfilename(parent=root1, title="Ouvrir le spectre n° 1",
    filetypes=[('dat files', '.dat'), ('all files', '.*')],
    initialdir="/Users//Science/Manips/2011_10_05_Nb_W/")
filename2 = tkFileDialog.askopenfilename(parent=root1,title="Ouvrir le spectre n° 2",
    filetypes=[('dat files', '.dat'), ('all files', '.*')],
    initialdir="/Users/Science/Manips/2011_10_05_Nb_W/")
filenameexp = tkFileDialog.askopenfilename(parent=root1, title="Ouvrir le spectre exp",
    filetypes=[('txt files', '.txt'), ('all files', '.*')],
    initialdir="/Users/Science/Manips/2011_10_05_Nb_W/spectres_exp")

print 'Fichiers choisis = '
print filename1
print filename2
print filenameexp

energy1, spectrum1 = np.loadtxt(filename1, delimiter='   ', usecols=(0, 1),
                            unpack=True, skiprows=0)
energy2, spectrum2 = np.loadtxt(filename2, delimiter='   ', usecols=(0, 1),
                            unpack=True, skiprows=0)
energyexp, spectrumexp = np.loadtxt(filenameexp, delimiter='\t', usecols=(0, 1),
                            unpack=True, skiprows=0)

#Interpolating experimental energy grid on theoretical energy grid
sp_exp_int = np.interp(energy1, energyexp, spectrumexp)

#guess contains the first guess of the parameters 
guess=[1.0,1.0]
spec_theo = guess[0] * spectrum1 + guess[1] * spectrum2

# ErrorFunc is the difference between the "fit" and the y experimental data
ErrorFunc = spec_theo - sp_exp_int
# leastsq finds the set of parameters in the tuple tpl that minimizes
# ErrorFunc=yfit-yExperimental
tplFinal, success = leastsq(ErrorFunc, guess[:], args=(energy1, sp_exp_int))
print "best choice = ", tplFinal

fig, ax1 = plt.subplots()
theory = ax1.plot(energy1, spec_theo, 'b-', label='Theory')
ax1.set_xlabel('Energy (eV)')
# Make the y-axis label and match the line color.
ax1.set_ylabel('Theory', color='b')

ax2 = ax1.twinx()
experiment = ax2.plot(energy1, sp_exp_int, 'r-', label='Experiment')
ax2.set_ylabel('Experiment', color='r', rotation=-90, labelpad=15)

#one legend for all axes
lns = theory + experiment
labs = [l.get_label() for l in lns]
ax1.legend(lns, labs, loc=0)

plt.show()

When I try to run the code I get:

Traceback (most recent call last):
 File "/Users/Science/Manips/2011_05_Nb_W/Mars2016/comblin_leastsquares.py", line 79, in <module>
tplFinal, success = leastsq(ErrorFunc, guess[:], args=(energy1, sp_exp_int))
File   "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site- packages/scipy/optimize/minpack.py", line 377, in leastsq
shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
File "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/scipy/optimize/minpack.py", line 26, in _check_func
res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
TypeError: 'numpy.ndarray' object is not callable

I understand that something is wrong with my leastsq usage, but I really can't figure out what it could be, my knowledge of Python is clearly insufficient. Can someone help me ?

Answer 1

Just in case it could help other people, I've made the code work with:

<same code as in my question>
#guess contains the first guess of the parameters 
guess=[1.0,1.0]

# error_func is the difference between the "fit" and the y experimental data
#error_func = spec_theo - sp_exp_int
def error_func(coeff, sp1, sp2, y):
    return (coeff[0] * sp1 + coeff[1] * sp2) - y

# leastsq finds the set of parameters in the tuple tpl that minimizes
# error_func=yfit-yExperimental
guess_fin, success = leastsq(error_func, guess[:], args=(spectrum1, \
                            spectrum2, sp_exp_int))
print 'best choice = ', guess_fin
print 'success = ', success

spec_theo = guess_fin[0] * spectrum1 + guess_fin[1] * spectrum2

fig, ax1 = plt.subplots()
...

Thanks Bakuriu!

Answer 2

The error clearly states what's wrong: you are passing an array instead of a function/callable. In fact the leastsq documentation states that the first argument should be a callable.

You are passing ErrorFunc as first argument but this is not a function nor a callable. It's an array. (It may represent a function, but it isn't in the format required by leastsq).

So you have to follow the description for the argument:

should take at least one (possibly length N vector) argument and returns M floating point numbers. It must not return NaNs or fitting might fail.

So replace ErrorFunc with a callable that given the input returns the error as floats. Basically you should have:

def error_func(input):
    return input - data

Where data is your experimental data andinput is the value of the fitting that scipy is doing. It needs a callable because it will perform more iterations and for each iteration it has to compute the error in order to fit the data.

^{Obviously change error_func to match what you are doing, that is only to give the idea of what is expected by leastsq.}