# nbodykit.source.mesh.catalog¶

Functions

 CompensateCIC(w, v) Return the Fourier-space kernel that accounts for the convolution of the gridded field with the CIC window function in configuration space Return the Fourier-space kernel that accounts for the convolution of the gridded field with the CIC window function in configuration space, as well as the approximate aliasing correction to the first order CompensatePCS(w, v) Return the Fourier-space kernel that accounts for the convolution of the gridded field with the PCS window function in configuration space. Return the Fourier-space kernel that accounts for the convolution of the gridded field with the PCS window function in configuration space, as well as the approximate aliasing correction to first order CompensateTSC(w, v) Return the Fourier-space kernel that accounts for the convolution of the gridded field with the TSC window function in configuration space. Return the Fourier-space kernel that accounts for the convolution of the gridded field with the TSC window function in configuration space, as well as the approximate aliasing correction to the first order get_compensation(interlaced, resampler) Return the compensation function, which corrects for the windowing kernel.

Classes

 CatalogMesh(source, Nmesh, BoxSize, Position) A mesh generated by resampling a Catalog with the given parameters.
class nbodykit.source.mesh.catalog.CatalogMesh(source, Nmesh, BoxSize, Position, dtype='f4', resampler='cic', compensated=False, interlaced=False, Value=None, Selection=None, Weight=None, **kwargs)[source]

A mesh generated by resampling a Catalog with the given parameters.

The original CatalogSource object is stored as the base attribute.

Parameters
• source (CatalogSource) – the input catalog that we are viewing as a mesh

• BoxSize – the size of the box

• Nmesh (int, 3-vector) – the number of cells per mesh side

• dtype (str) – the data type of the values stored on mesh

• Weight (array_like, Column, None) – column that specifies the weight value for each particle in the source to use when gridding

• Value (array_like, Column, None) – column that specifies the field value for each particle; the mesh stores a weighted average of this column

• Selection (array_like, Column, None) – column that selects the subset of particles to grid to the mesh

• Position (array_like, Column, None) – column in source specifying the position coordinates; default is Position

• interlaced (bool, optional) – use the interlacing technique of Sefusatti et al. 2015 to reduce the effects of aliasing on Fourier space quantities computed from the mesh

• compensated (bool, optional) – whether to correct for the window introduced by the grid interpolation scheme

• window (str, optional) – the string specifying which window interpolation scheme to use; see pmesh.window.methods

‘Weight’, ‘Value’, ‘Selection’, ‘Position’ are items of the collection that can be reassigned after the creation of the object.

Attributes
actions

The actions to apply to the interpolated density field, optionally included the compensation correction.

attrs

A dictionary storing relevant meta-data about the CatalogSource.

compensated

Boolean flag to indicate whether to correct for the windowing kernel introduced when interpolating the discrete particles to a continuous field.

interlaced

Whether to use interlacing when interpolating the density field.

resampler

String specifying the name of the interpolation kernel when gridding the density field.

window

Methods

 apply(func[, kind, mode]) Return a view of the mesh, with actions updated to apply the specified function, either in Fourier space or configuration space, based on mode compute([mode, Nmesh]) Compute / Fetch the mesh object into memory as a RealField or ComplexField object. preview([axes, Nmesh, root]) Gather the mesh into as a numpy array, with (reduced) resolution. save(output[, dataset, mode]) Save the mesh as a BigFileMesh on disk, either in real or complex space. to_complex_field([out]) Convert the mesh source to the Fourier-space field, returning a pmesh.pm.ComplexField object. to_field([mode, out]) Return the mesh as a pmesh Field object, either in Fourier space or configuration space, based on mode. to_real_field([out, normalize]) Paint the density field, by interpolating the position column on to the mesh. Return a “view” of the MeshSource, in the spirit of numpy’s ndarray view.
 paint
__finalize__(other)

Finalize the creation of a MeshSource object by copying over attributes from a second MeshSource.

Parameters

other (MeshSource) – the second MeshSource to copy over attributes from

__len__()

Length of a mesh source is zero

property actions

The actions to apply to the interpolated density field, optionally included the compensation correction.

apply(func, kind='wavenumber', mode='complex')

Return a view of the mesh, with actions updated to apply the specified function, either in Fourier space or configuration space, based on mode

Parameters
• func (callable or a MeshFilter object) – func(x, y) where x is a list of r (k) values that broadcasts into a full array, when mode is ‘real’ (‘complex’); the value of x depends on kind. y is the value of the mesh field on the corresponding locations.

• kind (string, optional) –

if a MeshFilter object is given as func, this is ignored. The kind of value in x.

• When mode is ‘complex’:

• ’wavenumber’ means wavenumber from [- 2 pi / L * N / 2, 2 pi / L * N / 2).

• ’circular’ means circular frequency from [- pi, pi).

• ’index’ means [0, Nmesh )

• When mode is ‘real’:

• ’relative’ means distance from [-0.5 Boxsize, 0.5 BoxSize).

• ’index’ means [0, Nmesh )

• mode ('complex' or 'real', optional) – if a MeshFilter object is given as func, this is ignored. whether to apply the function to the mesh in configuration space or Fourier space

Returns

a view of the mesh object with the actions attribute updated to include the new action

Return type

MeshSource

property attrs

A dictionary storing relevant meta-data about the CatalogSource.

property compensated

Boolean flag to indicate whether to correct for the windowing kernel introduced when interpolating the discrete particles to a continuous field.

See the documentation for further details.

compute(mode='real', Nmesh=None)

Compute / Fetch the mesh object into memory as a RealField or ComplexField object.

property interlaced

Whether to use interlacing when interpolating the density field. See the documentation for further details.

See also: Section 3.1 of Sefusatti et al. 2015

preview(axes=None, Nmesh=None, root=0)

Gather the mesh into as a numpy array, with (reduced) resolution. The result is broadcast to all ranks, so this uses $$\mathrm{Nmesh}^3$$ per rank.

Parameters
• Nmesh (int, array_like) – The desired Nmesh of the result. Be aware this function allocates memory to hold a full Nmesh on each rank.

• axes (int, array_like) – The axes to project the preview onto., e.g. (0, 1)

• root (int, optional) – the rank number to treat as root when gathering to a single rank

Returns

out – An numpy array holding the real density field.

Return type

array_like

property resampler

String specifying the name of the interpolation kernel when gridding the density field.

See the documentation for further details.

Note

Valid values must be in pmesh.resampler.methods

save(output, dataset='Field', mode='real')

Save the mesh as a BigFileMesh on disk, either in real or complex space.

Parameters
• output (str) – name of the bigfile file

• dataset (str, optional) – name of the bigfile data set where the field is stored

• mode (str, optional) – real or complex; the form of the field to store

to_complex_field(out=None)

Convert the mesh source to the Fourier-space field, returning a pmesh.pm.ComplexField object.

Not implemented in the base class, unless object is a view.

to_field(mode='real', out=None)

Return the mesh as a pmesh Field object, either in Fourier space or configuration space, based on mode.

This will call to_real_field() or to_complex_field() based on mode.

Parameters

mode ('real' or 'complex') – the return type of the field

Returns

either a RealField of ComplexField, storing the value of the field on the mesh

Return type

RealField, ComplexField

to_real_field(out=None, normalize=True)[source]

Paint the density field, by interpolating the position column on to the mesh.

This computes the following meta-data attributes in the process of painting, returned in the attrs attributes of the returned RealField object:

• Nint

the (unweighted) total number of objects painted to the mesh

• Wfloat

the weighted number of total objects, equal to the collective sum of the ‘weight’ column

• shotnoisefloat

the Poisson shot noise, equal to the volume divided by N

• num_per_cellfloat

the mean number of weighted objects per cell

Note

The density field on the mesh is normalized as $$1+\delta$$, such that the collective mean of the field is unity.

See the documentation on painting for more details on painting catalogs to a mesh.

Returns

real – the painted real field; this has a attrs dict storing meta-data

Return type

pmesh.pm.RealField

view()

Return a “view” of the MeshSource, in the spirit of numpy’s ndarray view.

This returns a new MeshSource whose memory is owned by self.

Note that for CatalogMesh objects, this is overidden by the CatalogSource.view function.

nbodykit.source.mesh.catalog.CompensateCIC(w, v)[source]

Return the Fourier-space kernel that accounts for the convolution of the gridded field with the CIC window function in configuration space

Note

see equation 18 (with p=2) of Jing et al 2005

Parameters
• w (list of arrays) – the list of “circular” coordinate arrays, ranging from $$[-\pi, \pi)$$.

• v (array_like) – the field array

nbodykit.source.mesh.catalog.CompensateCICShotnoise(w, v)[source]

Return the Fourier-space kernel that accounts for the convolution of the gridded field with the CIC window function in configuration space, as well as the approximate aliasing correction to the first order

Note

see equation 20 of Jing et al 2005

Parameters
• w (list of arrays) – the list of “circular” coordinate arrays, ranging from $$[-\pi, \pi)$$.

• v (array_like) – the field array

nbodykit.source.mesh.catalog.CompensatePCS(w, v)[source]

Return the Fourier-space kernel that accounts for the convolution of the gridded field with the PCS window function in configuration space.

Note

see equation 18 (with p=4) of Jing et al 2005

Parameters
• w (list of arrays) – the list of “circular” coordinate arrays, ranging from $$[-\pi, \pi)$$.

• v (array_like) – the field array

nbodykit.source.mesh.catalog.CompensatePCSShotnoise(w, v)[source]

Return the Fourier-space kernel that accounts for the convolution of the gridded field with the PCS window function in configuration space, as well as the approximate aliasing correction to first order

Note

YF: I derived this by fitting the result to s ** 3 according to the form given in equation 20 of Jing et al. It must be possible to derive this manually.

Parameters
• w (list of arrays) – the list of “circular” coordinate arrays, ranging from $$[-\pi, \pi)$$.

• v (array_like) – the field array

nbodykit.source.mesh.catalog.CompensateTSC(w, v)[source]

Return the Fourier-space kernel that accounts for the convolution of the gridded field with the TSC window function in configuration space.

Note

see equation 18 (with p=3) of Jing et al 2005

Parameters
• w (list of arrays) – the list of “circular” coordinate arrays, ranging from $$[-\pi, \pi)$$.

• v (array_like) – the field array

nbodykit.source.mesh.catalog.CompensateTSCShotnoise(w, v)[source]

Return the Fourier-space kernel that accounts for the convolution of the gridded field with the TSC window function in configuration space, as well as the approximate aliasing correction to the first order

Note

see equation 20 of Jing et al 2005

Parameters
• w (list of arrays) – the list of “circular” coordinate arrays, ranging from $$[-\pi, \pi)$$.

• v (array_like) – the field array

nbodykit.source.mesh.catalog.get_compensation(interlaced, resampler)[source]

Return the compensation function, which corrects for the windowing kernel.

The compensation function is computed as: