LogNormalPowerBox

class powerbox.powerbox.LogNormalPowerBox(*args, **kwargs)

Bases: powerbox.powerbox.PowerBox

Calculate Log-Normal density fields with given power spectra.

See the documentation of PowerBox for a detailed explanation of the arguments, as this class has exactly the same arguments.

This class calculates an (over-)density field of arbitrary dimension given an input isotropic power spectrum. In this case, the field has a log-normal distribution of over-densities, always yielding a physically valid field.

Examples

To create a log-normal over-density field:

>>> from powerbox import LogNormalPowerBox
>>> lnpb = LogNormalPowerBox(100,lambda k : k**-7./5.,dim=2, boxlength=1.0)
>>> overdensities = lnpb.delta_x
>>> grid = lnpb.x
>>> radii = lnpb.r

To plot the overdensities:

>>> import matplotlib.pyplot as plt
>>> plt.imshow(pb.delta_x)

Compare the fields from a Gaussian and Lognormal realisation with the same power:

>>> lnpb = LogNormalPowerBox(300,lambda k : k**-7./5.,dim=2, boxlength=1.0)
>>> pb = PowerBox(300,lambda k : k**-7./5.,dim=2, boxlength=1.0)
>>> fig,ax = plt.subplots(2,1,sharex=True,sharey=True,figsize=(12,5))
>>> ax[0].imshow(lnpb.delta_x,aspect="equal",vmin=-1,vmax=lnpb.delta_x.max())
>>> ax[1].imshow(pb.delta_x,aspect="equal",vmin=-1,vmax = lnpb.delta_x.max())

To create and plot a discrete version of the field:

>>> positions = lnpb.create_discrete_sample(nbar=1000.0, # Number density in terms of boxlength units
>>>                                         randomise_in_cell=True)
>>> plt.scatter(positions[:,0],positions[:,1],s=2,alpha=0.5,lw=0)

Attributes Summary

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

Methods Summary

correlation_array()	The correlation function from the input power, on the grid
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 real-space over-density field, from the input power spectrum
gauss_hermitian()	A random array which has Gaussian magnitudes and Hermitian symmetry
gaussian_correlation_array()	The correlation function required for a Gaussian field to produce the input power on a lognormal field
gaussian_power_array()	The power spectrum required for a Gaussian field to produce the input power on a lognormal field
k()	The entire grid of wavenumber magitudes
power_array()	The Power Spectrum (volume normalised) at self.k

Attributes Documentation

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

Methods Documentation

correlation_array()

The correlation function from the input power, on the grid

create_discrete_sample(nbar, randomise_in_cell=True, min_at_zero=False, store_pos=False)

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.

Parameters:

nbar : float

Mean tracer density within the box.

randomise_in_cell : bool, optional

Whether to randomise the positions of the tracers within the cells, or put them at the grid-points (more efficient).

min_at_zero : bool, optional

Whether to make the lower corner of the box at the origin, otherwise the centre of the box is at the origin.

store_pos : bool, optional

Whether to store the sample of tracers as an instance variable tracer_positions.

Returns:

tracer_positions : float, array_like

(n, d)-array, with n the number of tracers and d the number of dimensions. Each row represents a single tracer’s co-ordinates.

delta_k()

A realisation of the delta_k, i.e. the gaussianised square root of the unitless power spectrum (i.e. the Fourier co-efficients)

delta_x()

The real-space over-density field, from the input power spectrum

gauss_hermitian()

A random array which has Gaussian magnitudes and Hermitian symmetry

gaussian_correlation_array()

The correlation function required for a Gaussian field to produce the input power on a lognormal field

gaussian_power_array()

The power spectrum required for a Gaussian field to produce the input power on a lognormal field

k()

The entire grid of wavenumber magitudes

power_array()

The Power Spectrum (volume normalised) at self.k