pycosmommf package¶

pycosmommf: A package for identifying structures in the cosmic web.

Submodules¶

pycosmommf.filter module¶

pycosmommf.filter.kspace_gaussian_filter(R_S, kv)¶

create a Gaussian filter in k-space.

Parameters:

R_S (float) – The smoothing scale.
kv (tuple) – The wavevectors in each dimension, each a 1D float np.ndarray.

Returns:

The filter in k-space.

Return type:

(3D float np.ndarray)

pycosmommf.filter.kspace_top_hat_filter(R_S, kv)¶

create a top-hat filter in k-space.

Parameters:

R_S (float) – The smoothing scale.
kv (tuple) – The wavevectors in each dimension.

Returns:

The filter in k-space.

Return type:

(3D float np.ndarray)

pycosmommf.filter.smooth_gauss(f, R_S, kv)¶

apply a Gaussian filter to a field f.

Parameters:

f (3D float np.ndarray) – The field to be smoothed.
R_S (float) – The smoothing scale in units of voxels.
kv (tuple) – The wavevectors in each dimension.

Returns:

The smoothed field.

Return type:

(3D float np.ndarray)

pycosmommf.filter.smooth_loggauss(f, R_S, kv)¶

apply a Gaussian filter to the log of a field f.

Parameters:

f (3D float np.ndarray) – The field to be smoothed.
R_S (float) – The smoothing scale in units of voxels.
kv (tuple) – The wavevectors in each dimension.

Returns:

The smoothed field.

Return type:

(3D float np.ndarray)

pycosmommf.filter.smooth_top_hat(f, R_S, kv)¶

apply a top-hat filter to a field f.

Parameters:

f (3D float np.ndarray) – The field to be smoothed.
R_S (float) – The smoothing scale in units of voxels.
kv (tuple) – The wavevectors in each dimension.

Returns:

The smoothed field.

Return type:

(3D float np.ndarray)

pycosmommf.filter.wavevectors3D(dims, box_size=(6.283185307179586, 6.283185307179586, 6.283185307179586))¶

Returns the wavevectors for a 3D grid of dimensions dims and box size box_size.

Parameters:

dims (tuple) – The dimensions of the grid (nx, ny, nz).
box_size (tuple, optional) – The size of the box in each dimension (Lx, Ly, Lz). Defaults to (2π, 2π, 2π).

Returns:

a tuple containing:

kx (np.ndarray): The wavevector in the x-direction.
ky (np.ndarray): The wavevector in the y-direction.
kz (np.ndarray): The wavevector in the z-direction.

Return type:

(tuple)

pycosmommf.hessian module¶

pycosmommf.hessian.fast_hessian_from_smoothed(f_Rn, R_S, kv)¶

Compute the hessian matrix of the smoothed field f_Rn.

Parameters:

f_Rn (3D float np.ndarray) – The smoothed field in real space.
R_S (float) – The smoothing scale in units of voxels.
kv (tuple) – The wavevectors in each dimension.

Returns:

The hessian matrix of the smoothed field. The shape is (nx, ny, nz, 6), where nx, ny, nz are the dimensions of f_Rn.

Return type:

(4D float np.ndarray)

pycosmommf.signatures module¶

pycosmommf.signatures.maximum_signature(Rs, density_cube, algorithm='NEXUSPLUS', eps=1e-16)¶

Compute the maximum signatures across all scales Rs.

Parameters:

Rs (list of float) – List of smoothing scales in units of voxels.
density_cube (3D float np.ndarray) – The 3D density field to analyze.
algorithm (str, optional) – The algorithm to use for smoothing. Can be either “NEXUS” or “NEXUSPLUS”. Defaults to “NEXUSPLUS”.
eps (float, optional) – Small value to avoid division by zero. Defaults to 1e-16.

Returns:

An array of signatures with shape (nx, ny, nz, 3), where nx, ny, nz are the dimensions of the input density_cube. The last dimension contains the signatures for clusters, filaments, and walls respectively.

Return type:

(4D float np.ndarray)

pycosmommf.signatures.signatures_from_hessian(hessian)¶

Function to calculate the signatures from a given hessian.

Parameters:

hessian (4D float np.ndarray) – The hessian matrix of the smoothed field, with shape (nx, ny, nz, 6).

Returns:

The signatures array with shape (nx, ny, nz, 3). Each signature corresponds to a different type of structure:

sigs[..., 0]: Cluster signature
sigs[..., 1]: Filament signature
sigs[..., 2]: Wall signature

Return type:

(4D float np.ndarray)

pycosmommf.tagging module¶

pycosmommf.tagging.calc_mass_change(sig_vec, density_vec, Smin, Smax)¶

Calculate the mass change curve for a given structure type.

Parameters:

sig_vec (1D float np.ndarray) – the signature values for a given structure type
density_vec (1D float np.ndarray) – the density values for a given structure type
Smin (float) – the minimum signature value
Smax (float) – the maximum signature value

Returns:

a tuple containing:

S (1D float np.ndarray): the signature values
ΔΜ_2 (1D float np.ndarray): the mass change curve

Return type:

(tuple)

pycosmommf.tagging.calc_structure_bools(density_cube, max_sigs, verbose_flag, clusbool=None, Smin=-3, Smax=2, overdensity_threshold=370)¶

Calculate the boolean filters for clusters, filaments, walls, and voids.

Parameters:

density_cube (3D float np.ndarray) – the (δ+1 = ρ/<ρ>) density_cube, this is NOT (δ = ρ/<ρ> - 1).
max_sigs (4D float np.ndarray) – the maximum signatures array from CosmoMMF.maximum_signature()
verbose_flag (bool) – a flag to allow the function to be more helpful and verbose.
clusbool (bool np.ndarray, optional) – the cluster boolean filter
Smin (float, optional) – the minimum signature value
Smax (float, optional) – the maximum signature value
overdensity_threshold (int, optional) – the overdensity parameter threshold for determining virialization

Returns:

a tuple containing:

clusbool (3D bool np.ndarray): the cluster boolean filter
filbool (3D bool np.ndarray): the filament boolean filter
wallbool (3D bool np.ndarray): the wall boolean filter
voidbool (3D bool np.ndarray): the void boolean filter
summary_data (dict): a dictionary returned only when verbose_flag = True, it contains the following keys:
- S_clus (1D float np.ndarray): the signature values for clusters
- f_vir_clus (1D float np.ndarray): the virialization fraction for clusters
- S_fil (1D float np.ndarray): the signature values for filaments
- dM2_fil (1D float np.ndarray): the mass change curve for filaments
- S_fil_thresh (float): the threshold value for filaments
- S_wall (1D float np.ndarray): the signature values for walls
- dM2_wall (1D float np.ndarray): the mass change curve for walls
- S_wall_thresh (float): the threshold value for walls
- mass_fractions (1D float np.ndarray): a list of mass fractions for clusters, filaments, walls, and voids
- volume_fractions (1D float np.ndarray): a list of volume fractions for clusters, filaments, walls, and voids

Return type:

(tuple)

pycosmommf.tagging.make_the_clusbool(delta, max_sigs, overdensity_threshold)¶

A function that creates a bool Filter which selects only the clusters in a given cosmological δ field. This function accomplishes this by finding a threshold value for 𝒮_cluster by looking at the change in virialization fraction as a function of 𝒮_cluster.

Parameters:

delta (3D float np.ndarray) – delta refers to the (δ = ρ / <ρ> - 1) field, this is NOT the (δ + 1 = ρ / <ρ>) field.
max_sigs (4D float np.ndarray) – the maximum signatures array from the maximum_signature() function.
verbose_flag (bool) – a flag to allow the function to be more helpful and verbose.
overdensity_threshold (float) – The overdensity parameter threshold for determining virialization. Commonly used values that are physically motivated can be 370, 200, or 500.

Returns:

a tuple containing:

clusbool (3D bool np.ndarray): a boolean filter that selects only the clusters in a given cosmological δ field.
S_th (float): the threshold value for 𝒮_cluster.
signature_thresholds (1D float np.ndarray): an array of threshold values for 𝒮_cluster.
virialized_fractions (1D float np.ndarray): an array of virialized fractions as a function of 𝒮_cluster.

Return type:

(tuple)

pycosmommf.utils module¶

pycosmommf.utils.cylinder(n, r)¶

Returns an nxnxn array with a cylinder in the center with radius r. All points within the radius are set to 10, the rest are set to 0.

Parameters:

n (int) – The size of the 3D array to create.
r (int) – The radius of the cylinder.

Returns:

An nxnxn array with a cylinder in the center.

Return type:

(3D float np.ndarray)

pycosmommf.utils.shrink(data, new_size)¶

A simple function to shrink a 3D array by summing over blocks of new_size.

Parameters:

data (3D float np.ndarray) – The input 3D array to be shrunk.
new_size (int) – The new size for each dimension after shrinking.

Returns:

The shrunk 3D array.

Return type:

(3D float np.ndarray)

pycosmommf.utils.sphere(n, r)¶

Returns an nxnxn array with a sphere in the center with radius r. All points within the radius are set to 10, the rest are set to 0.

Parameters:

n (int) – The size of the 3D array to create.
r (int) – The radius of the sphere.

Returns:

An nxnxn array with a sphere in the center.

Return type:

(3D float np.ndarray)

pycosmommf.utils.wall(n)¶

Builds a wall out of an nxnxn array. All values in the wall are set to 10. Other points are set to 0.

Parameters:: n (int) – The size of the 3D array to create.
Returns:: An nxnxn array with a wall in the center.
Return type:: (3D float np.ndarray)