"argument must be a callable function" when using scipy.integrate.quad

Question

I've written some code that enables me to take data from DICOM files and separate the data into the individual FID signals.

from pylab import *
import dicom
import numpy as np
import scipy as sp

plan=dicom.read_file("1.3.46.670589.11.38085.5.22.3.1.4792.2013050818105496124")
all_points = array(plan.SpectroscopyData)
cmplx_data = all_points[0::2] -1j*all_points[1::2]
frames = int(plan.NumberOfFrames)
fid_pts = len(cmplx_data)/frames
del_t = plan.AcquisitionDuration / (frames * fid_pts)

fid_list = []
for fidN in arange(frames):
    offset = fidN * fid_pts 
    current_fid = cmplx_data[offset:offset+fid_pts]
    fid_list.append(current_fid)

I'd now like to quantify some of this data so, after applying a Fourier transform and shift I've tried to use Scipy's quad function and encountered the following error:

spec = fftshift(fft(fid_list[0])))
sp.integrate.quad(spec, 660.0, 700.0)



error                                     Traceback (most recent call last)
/home/dominicc/Experiments/In Vitro/Glu, Cr/Phantom 1: 10mM Cr, 5mM Glu/WIP_SV_PRESS_ME_128TEs_5ms_spacing_1828/<ipython-input-107-17cb50e45927> in <module>()
----> 1 sp.integrate.quad(fid, 660.0, 700.0)

/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.pyc in quad(func, a, b, args, full_output, epsabs, epsrel, limit, points, weight, wvar, wopts, maxp1, limlst)
243     if type(args) != type(()): args = (args,)
244     if (weight is None):
--> 245         retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points)
246     else:
247         retval = _quad_weight(func,a,b,args,full_output,epsabs,epsrel,limlst,limit,maxp1,weight,wvar,wopts)

/usr/lib/python2.7/dist-packages/scipy/integrate/quadpack.pyc in _quad(func, a, b, args, full_output, epsabs, epsrel, limit, points)
307     if points is None:
308         if infbounds == 0:
--> 309             return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit)
310         else:
311             return _quadpack._qagie(func,bound,infbounds,args,full_output,epsabs,epsrel,limit)

error: First argument must be a callable function.

Could somebody please suggest a way to make this object callable? I'm still not particularly clear after reading What is a "callable" in Python?. After reading that I tried

def fid():
    spec = fftshift(fft(fid_list[0])) 
    return spec

Which returned the same error.

Any help would be greatly appreciated, thanks.

Shouldn't it be a function that takes an argument? How else can it be integrated? — Lev Levitsky, May 09 '13 at 13:42
This question makes no sense. You cannot use `scipy.integrate.quad` to integrate an array. It integrates a *function* which takes an argument (like `sin(x)` for example). Use something like `scipy.integrate.simps` for integrating an array of function values. — talonmies, May 09 '13 at 13:44

Eric O Lebigot · Accepted Answer · 2013-05-10T01:38:52.460

Since you are integrating a function defined only on a grid (i.e., an array of numbers), you need to use one of the routines from "Integration, given fixed samples".

In fact, the first argument of quad() must be a function, something you can call (a "callable"). For instance, you can do:

>>> from scipy.integrate import quad
>>> def f(x):
...     return x**2
... 
>>> quad(f, 0, 1)
(0.33333333333333337, 3.700743415417189e-15)

This can be done instead by sampling f():

>>> from scipy.integrate import simps
>>> x_grid = numpy.linspace(0, 1, 101)  # 101 numbers between 0 and 1
>>> simps(x_grid**2, dx=x_grid[1]-x_grid[0])  # x_grid**2 is an *array*.  dx=0.01 between x_grid values
0.33333333333333337

Your situation is like in this second example: you integrate a sampled function, so it is natural to use one or cumtrapz(), simps() or romb().

"argument must be a callable function" when using scipy.integrate.quad

1 Answers1