powerbox 0.3.2

Create arbitrary boxes with isotropic power spectra

Make arbitrarily structured, arbitrary-dimension boxes.

powerbox is a pure-python code for creating density grids (or boxes) that have an arbitrary two-point distribution (i.e. power spectrum). Primary motivations for creating the code were the simple creation of lognormal mock galaxy distributions, but the methodology can be used for other applications.

Features

• Works in any number of dimensions.

• Really simple.

• Arbitrary isotropic power-spectra.

• Create Gaussian or Log-Normal fields

• Create discrete samples following the field, assuming it describes an over-density.

• Measure power spectra of output fields to ensure consistency.

• Seamlessly uses pyFFTW if available for ~double the speed.

Installation

Clone/Download then python setup.py install. Or just pip install powerbox.

Basic Usage

There are two useful classes: the basic PowerBox and one for log-normal fields: LogNormalPowerBox. You can import them like

from powerbox import PowerBox, LogNormalPowerBox

Once imported, to see all the options, just use help:

help(PowerBox)

For a basic 2D Gaussian field with a power-law power-spectrum, one can use the following:

pb = PowerBox(N=512,                     # Number of grid-points in the box
              dim=2,                     # 2D box
              pk = lambda k: 0.1*k**-2., # The power-spectrum
              boxlength = 1.0)           # Size of the box (sets the units of k in pk)
import matplotlib.pyplot as plt
plt.imshow(pb.delta_x)

Other attributes of the box can be accessed also – check them out with tab completion in an interpreter! The LogNormalPowerBox class is called in exactly the same way, but the resulting field has a log-normal pdf with the same power spectrum.

Just to be clear, for a more “realistic” example: a log-normal box (let’s say with 3 dimensions) with a power-spectrum given by cosmological density perturbations, can be created like this (this also uses the code hmf):

from hmf import MassFunction
from scipy.interpolate import InterpolatedUnivariateSpline as spline

# Set up a MassFunction instance to access its cosmological power-spectrum
mf = MassFunction(z=0)

# Generate a callable function that returns the cosmological power spectrum.
spl = spline(np.log(mf.k),np.log(mf.power),k=2)
power = lambda k : np.exp(spl(np.log(k))

# Create the power-box instance. The boxlength is in inverse units of the k of which pk is a function, i.e.
# Mpc/h in this case.
pb = LogNormalPowerBox(N=512, dim=3, pk = power, boxlength= 100.)

Now we can make a plot of a slice of the density field:

plt.imshow(pb.delta_x,extent=(0,100,0,100))
plt.colorbar()
plt.show()

And we can also compare the power-spectrum of the output field to the input power:

from powerbox import get_power

p_k, kbins = get_power(pb.delta_x,pb.boxlength)
plt.plot(mf.k,mf.power,label="Input Power")
plt.plot(kbins,p_k,label="Sampled Power')
plt.legend()
plt.show()

Furthermore, we can sample a set of discrete particles on the field, and plot their power spectrum

particles = pb.create_discrete_sample(nbar=1.0)
p_k_sample, kbins_sample = get_power(particles, pb.boxlength,N=pb.N)

plt.plot(mf.k,mf.power,label="Input Power")
plt.plot(kbins_sample,p_k_sample,label="Sampled Power Discrete")
plt.legend()
plt.show()

TODO

• At this point, log-normal transforms are done by back-and-forward FFTs on the grid, which could be slow for higher dimensions. Soon I will implement a more efficient way of doing this using numerical Hankel transforms.

• Some more tests might be nice.