powerbox.powerbox.PowerBox

class powerbox.powerbox.PowerBox(N, pk, dim=2, boxlength=1.0, ensure_physical=False, a=1.0, b=1.0, vol_normalised_power=True, seed=None)

An object which calculates and stores the real-space and fourier-space fields generated with a given power spectrum.

Parameters:

N : int

Number of grid-points on a side for the resulting box (equivalently, number of wavenumbers to use).

pk : func

A function of a single (vector) variable k, which is the isotropic power spectrum. The relationship of the k of which this is a function to the real-space co-ordinates is determined by the parameters a,b.

dim : int, default 2

Number of dimensions of resulting box.

boxlength : float, default 1.0

Length of the final signal on a side. This may have arbitrary units, so long as pk is a function of a variable which has the inverse units.

ensure_physical : bool, optional

Interpreting the power spectrum as a spectrum of density fluctuations, the minimum physical value of the real-space field, delta_x(), is -1. With ensure_physical set to True, delta_x() is clipped to return values >-1. If this is happening a lot, consider using a log-normal box.

a,b : float, optional

These define the Fourier convention used. See powerbox.dft for details. The defaults define the standard usage in cosmology (for example, as defined in Cosmological Physics, Peacock, 1999, pg. 496.). Standard numerical usage (eg. numpy) is (a,b) = (0,2pi).

vol_weighted_power : bool, optional

Whether the input power spectrum, pk, is volume-weighted. Default True because of standard cosmological usage.

Notes

A number of conventions need to be listed.

The conventions of using x for “real-space” and k for “fourier space” arise from cosmology, but this does not affect anything – x could just as well stand for “time domain” and k for “frequency domain”.

The important convention is the relationship between x and k, or in other words, whether k is interpreted as an angular frequency or ordinary frequency. By default, because of cosmological conventions, k is an angular frequency, so that the fourier transform integrand is delta_k*exp(-ikx). The conventions can be changed arbitrarily by setting the a,b parameters, in line with Mathematica’s definition.

The primary quantity of interest is delta_x, which is a zero-mean Gaussian field with a power spectrum equivalent to that which was input. Being zero-mean enables its direct interpretation as an overdensity field, and this interpretation is enforced in the make_discrete_sample method.

Examples

To create a 3-dimensional box of gaussian over-densities, with side length 1 Mpc, gridded equally into 100 bins, and where k=2pi/x, with a power-law power spectrum, simply use

>>> pb = PowerBox(100,lambda k : 0.1*k**-3., dim=3, boxlength=100.0)
>>> overdensities = pb.delta_x
>>> grid = pb.x
>>> radii = pb.r

To create a 2D turbulence structure, with arbitrary units, once can use

>>> import matplotlib.pyplot as plt
>>> pb = PowerBox(1000, lambda k : k**-7./5.)
>>> plt.imshow(pb.delta_x)

Methods

__init__(N, pk[, dim, boxlength, …])	x.__init__(…) initializes x; see help(type(x)) for signature
create_discrete_sample(nbar[, …])	Assuming that the real-space signal represents an over-density with respect to some mean, create a sample of tracers of the underlying density distribution.
delta_k()	A realisation of the delta_k, i.e.
delta_x()	The realised field in real-space from the input power spectrum
gauss_hermitian()	A random array which has Gaussian magnitudes and Hermitian symmetry
k()	The entire grid of wavenumber magitudes
power_array()	The Power Spectrum (volume normalised) at self.k

Attributes

kvec	The vector of wavenumbers along a side
r	The radial position of every point in the grid
x	The co-ordinates of the grid along a side