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CAMB python convergence power spectrum code

  1. Jun 19, 2016 #1
    I'm trying to understand this python CAMB code: http://camb.readthedocs.io/en/latest/CAMBdemo.html
    Scroll down to In[29] and In[30] to see it.

    It's an integration over chi (comoving distance), yet scipy.integrate.quad is not called. It seems that the fun stuff happens in the last for-loop in In[30], where they use numpy.dot to take dot product of two arrays. What's going on here? The first array is Delta-Chi (see In[29]) and the second is simply the integrand. So how is this integration? Thanks
     
  2. jcsd
  3. Jun 19, 2016 #2
    I'v been messing around with this and found something interesting:

    Code (Python):
    from __future__ import division
    import numpy as np
    import matplotlib.pyplot as plt
    from scipy.integrate import quad

    xmax = 10
    N = 1000
    xx = np.linspace(0,xmax,N)

    dx = (xx[2:] - xx[:-2])/2
    xx = xx[1:-1]
    Nx = len(xx)
    yy1 = np.arange(0,Nx, dtype=np.float64)
    yy2 = []

    f = lambda z: z**3

    for ix, x in enumerate(xx):
        foo = np.linspace(min(xx),x,N-2)**3
        yy1[ix] = np.dot(dx, foo)
        yy2.append(quad(f,0,x)[0])

    plt.plot(xx,yy1,label='dot')
    plt.plot(xx,yy2,label='quad')
    If you run this script you'll find pretty good agreement between the integration via quad and integration using the dot product of dx and integrand. The value of N controls accuracy, with N>1000 not producing much noticeable difference. But why does this work? What is this method called thanks
     
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