nbodykit.algorithms.fftpower¶
Functions

Project a 3D statistic on to the specified basis. 
Classes

Base class provides functions for periodic FFT based Power spectrum code. 

Algorithm to compute the 1d or 2d power spectrum and/or multipoles in a periodic box, using a Fast Fourier Transform (FFT). 

The power spectrum of a field in a periodic box, projected over certain axes. 

class
nbodykit.algorithms.fftpower.
FFTBase
(first, second, Nmesh, BoxSize)[source]¶ Base class provides functions for periodic FFT based Power spectrum code.
 Parameters
first (CatalogSource) – the first catalog source
second (CatalogSource, None) – the second source, or None for autocorrelations
Nmesh (int, 3vector) – the number of cells per mesh size
BoxSize (3vector) – the size of the box
Methods
load
(output[, comm])Load a saved result.
save
(self, output)Save the result to disk.

class
nbodykit.algorithms.fftpower.
FFTPower
(first, mode, Nmesh=None, BoxSize=None, second=None, los=[0, 0, 1], Nmu=5, dk=None, kmin=0.0, kmax=None, poles=[])[source]¶ Algorithm to compute the 1d or 2d power spectrum and/or multipoles in a periodic box, using a Fast Fourier Transform (FFT).
This computes the power spectrum as the square of the Fourier modes of the density field, which are computed via a FFT.
Results are computed when the object is inititalized. See the documenation of
run()
for the attributes storing the results.Note
A full tutorial on the class is available in the documentation here.
 Parameters
first (CatalogSource, MeshSource) – the source for the first field; if a CatalogSource is provided, it is automatically converted to MeshSource using the default painting parameters (via
to_mesh()
)mode ({'1d', '2d'}) – compute either 1d or 2d power spectra
Nmesh (int, optional) – the number of cells per side in the particle mesh used to paint the source
BoxSize (int, 3vector, optional) – the size of the box
second (CatalogSource, MeshSource, optional) – the second source for crosscorrelations
los (array_like , optional) – the direction to use as the lineofsight; must be a unit vector
Nmu (int, optional) – the number of mu bins to use from \(\mu=[0,1]\); if mode = 1d, then
Nmu
is set to 1dk (float, optional) – the linear spacing of
k
bins to use; if not provided, the fundamental mode of the box is used; if dk=0 is set, use fine bins such that the modes contributing to the bin has identical modulus.kmin (float, optional) – the lower edge of the first
k
bin to usekmin – the upper limit of the last
k
bin to use (not exact)poles (list of int, optional) – a list of multipole numbers
ell
to compute \(P_\ell(k)\) from \(P(k,\mu)\)
Methods
load
(output[, comm])Load a saved result.
run
(self)Compute the power spectrum in a periodic box, using FFTs.
save
(self, output)Save the result to disk.

classmethod
load
(output, comm=None)¶ Load a saved result. The result has been saved to disk with
save()
.

run
(self)[source]¶ Compute the power spectrum in a periodic box, using FFTs.
 Returns
power (
BinnedStatistic
) – a BinnedStatistic object that holds the measured \(P(k)\) or \(P(k,\mu)\). It stores the following variables: k :
the mean value for each
k
bin
 mu
mode=2d
only the mean value for each
mu
bin
 mu
 power :
complex array storing the real and imaginary components of the power
 modes :
the number of Fourier modes averaged together in each bin
poles (
BinnedStatistic
orNone
) – a BinnedStatistic object to hold the multipole results \(P_\ell(k)\); if no multipoles were requested by the user, this isNone
. It stores the following variables: k :
the mean value for each
k
bin
 power_L :
complex array storing the real and imaginary components for the \(\ell=L\) multipole
 modes :
the number of Fourier modes averaged together in each bin
power.attrs, poles.attrs (dict) – dictionary of metadata; in addition to storing the input parameters, it includes the following fields computed during the algorithm execution:
 shotnoisefloat
the power Poisson shot noise, equal to \(V/N\), where \(V\) is the volume of the box and N is the total number of objects; if a crosscorrelation is computed, this will be equal to zero
 N1int
the total number of objects in the first source
 N2int
the total number of objects in the second source

save
(self, output)¶ Save the result to disk. The format is currently JSON.

class
nbodykit.algorithms.fftpower.
ProjectedFFTPower
(first, Nmesh=None, BoxSize=None, second=None, axes=(0, 1), dk=None, kmin=0.0)[source]¶ The power spectrum of a field in a periodic box, projected over certain axes.
This is not really always physically meaningful, but convenient for making sense of LymanAlpha forest or lensing maps.
This is usually called the 1d power spectrum or 2d power spectrum.
Results are computed when the object is inititalized. See the documenation of
run()
for the attributes storing the results. Parameters
first (CatalogSource, MeshSource) – the source for the first field; if a CatalogSource is provided, it is automatically converted to MeshSource using the default painting parameters (via
to_mesh()
)Nmesh (int, optional) – the number of cells per side in the particle mesh used to paint the source
BoxSize (int, 3vector, optional) – the size of the box
second (CatalogSource, MeshSource, optional) – the second source for crosscorrelations
axes (tuple) – axes to measure the power on. The axes not in the list will be averaged out. For example:  (0, 1) : project to x,y and measure power  (0) : project to x and measure power.
dk (float, optional) – the linear spacing of
k
bins to use; if not provided, the fundamental mode of the box is usedkmin (float, optional) – the lower edge of the first
k
bin to use
Methods
load
(output[, comm])Load a saved result.
run
(self)Run the algorithm.
save
(self, output)Save the result to disk.

classmethod
load
(output, comm=None)¶ Load a saved result. The result has been saved to disk with
save()
.

run
(self)[source]¶ Run the algorithm. This attaches the following attributes to the class:

edges
¶ the edges of the wavenumber bins
 Type
array_like

power
¶ a BinnedStatistic object that holds the projected power. It stores the following variables:
 k :
the mean value for each
k
bin
 power :
complex array holding the real and imaginary components of the projected power
 modes :
the number of Fourier modes averaged together in each bin
 Type


save
(self, output)¶ Save the result to disk. The format is currently JSON.

nbodykit.algorithms.fftpower.
project_to_basis
(y3d, edges, los=[0, 0, 1], poles=[])[source]¶ Project a 3D statistic on to the specified basis. The basis will be one of:
2D (x, mu) bins: mu is the cosine of the angle to the lineofsight
2D (x, ell) bins: ell is the multipole number, which specifies the Legendre polynomial when weighting different mu bins
Note
The 2D (x, mu) bins will be computed only if poles is specified. See return types for further details.
Notes
the mu range extends from 0.0 to 1.0
the mu bins are halfinclusive halfexclusive, except the last bin is inclusive on both ends (to include mu = 1.0)
 Parameters
y3d (RealField or ComplexField) – the 3D array holding the statistic to be projected to the specified basis
edges (list of arrays, (2,)) – list of arrays specifying the edges of the desired x bins and mu bins
los (array_like,) – the lineofsight direction to use, which mu is defined with respect to; default is [0, 0, 1] for z.
poles (list of int, optional) – if provided, a list of integers specifying multipole numbers to project the 2d (x, mu) bins on to
hermitian_symmetric (bool, optional) – Whether the input array y3d is Hermitiansymmetric, i.e., the negative frequency terms are just the complex conjugates of the corresponding positivefrequency terms; if
True
, the positive frequency terms will be explicitly doublecounted to account for this symmetry
 Returns
result (tuple) – the 2D binned results; a tuple of
(xmean_2d, mumean_2d, y2d, N_2d)
, where: xmean_2darray_like, (Nx, Nmu)
the mean x value in each 2D bin
 mumean_2darray_like, (Nx, Nmu)
the mean mu value in each 2D bin
 y2darray_like, (Nx, Nmu)
the mean y3d value in each 2D bin
 N_2darray_like, (Nx, Nmu)
the number of values averaged in each 2D bin
pole_result (tuple or None) – the multipole results; if poles supplied it is a tuple of
(xmean_1d, poles, N_1d)
, where: xmean_1darray_like, (Nx,)
the mean x value in each 1D multipole bin
 polesarray_like, (Nell, Nx)
the mean multipoles value in each 1D bin
 N_1darray_like, (Nx,)
the number of values averaged in each 1D bin