Skip to main content

Create arbitrary boxes with isotropic power spectra

Project description

https://coveralls.io/repos/github/steven-murray/powerbox/badge.svg?branch=master https://img.shields.io/pypi/v/powerbox.svg https://travis-ci.org/steven-murray/powerbox.svg?branch=master

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.

Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

powerbox-0.3.2.tar.gz (8.2 kB view hashes)

Uploaded Source

Built Distribution

powerbox-0.3.2-py2-none-any.whl (10.9 kB view hashes)

Uploaded Python 2

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page