Counting and one-point PDFs

Counting filters an SFCField with one optional window and evaluates the continuous result at uniformly sampled box positions. The returned values can be used for count-in-cell PDFs, moments, environmental marks, and filtered-field diagnostics.

The complete Counting notebook compares the task and low-level interfaces and visualises the resulting one-point PDFs.

Minimal YAML

Counting:
   sfc_field: ./output/quijote8000_snap004_sfc.pkl
   random_count: 10000000
   seed: 42
   weight_normalization: catalog
   window:
      type: sphere
      len_args: {R: 20.0}
   threads: 8
   fout_path: ./output/quijote8000_snap004_counting_sph20.pkl

Run it from examples/:

python scripts/run_counting.py configs/param_counting.yaml

The result

import numpy as np
from pyhermes.io import CountingData

counts = CountingData(
    data_path="./output/quijote8000_snap004_counting_sph20.pkl"
)
print(counts.nx.shape)
print(np.mean(counts.nx), np.std(counts.nx))

CountingData.nx contains physical-unit field densities at the sampled positions. counting_info records the seed, sample count, window, input field, and normalisation. The random positions themselves are deterministic from those settings and are not stored separately.

Python task interface

from pyhermes.theory.counting import Counting

task = Counting()
task.sfc_field = "./output/quijote8000_snap004_sfc.pkl"
task.random_count = 300000
task.seed = 7
task.window = {"type": "gaussian", "len_args": {"R": 10.0}}
task.threads = 8
task.fout_path = "./output/counting_gaussian_R10.pkl"
result = task.run()

Low-level equivalent

When positions are scientifically meaningful rather than random, evaluate the field directly:

from pyhermes.io import SFCField, WindowFunc

D = SFCField(data_path="./output/quijote8000_snap004_sfc.pkl", threads=8)
W = WindowFunc(
    {"type": "sphere", "len_args": {"R": 20.0}},
    D.sfc_info,
    threads=8,
)
local_density = (D @ W).field_density_at_pos(
    halo_positions,
    value_unit="physical",
)

This is the route used to evaluate a local environment at each halo before constructing a marked field.

Choose the window deliberately

sphere

Literal count-in-sphere or top-hat-smoothed density.

gaussian

Smooth low-pass field without a hard boundary.

cubic or cylinder

Anisotropic finite-volume average.

cw, cws, gdw

Zero-mean localised fluctuation rather than a count density.

For a sphere of radius \(R\), a raw number field can be converted to an expected count by multiplying density by \(4\pi R^3/3\). With catalogue normalisation, remember that the field integrates to one; use its metadata and mean density rather than assuming a raw particle count.

MPI distribution

The filtered field is broadcast to all ranks. Each rank samples a disjoint deterministic subset of positions and rank 0 gathers the values. random_count is padded internally only when needed for an even rank distribution; the returned array is trimmed to the requested size.

Public tutorial

The rendered notebook compares task and low-level interfaces, constructs one-point PDFs, and contrasts low-pass and high-pass responses.