cosmocore 1.0.0rc2

CosmoCore: common algebra for harmonic-pixel handling.

CosmoCore

CosmoCore Documentation | API Reference | Main Documentation

CosmoCore is the foundational package of CosmoForge, providing core functionality for the analysis of spin-0 and spin-2 fields on the sphere, including field management, computation basis methods, matrix operations, I/O utilities, and spherical harmonic operations.

Overview

CosmoCore serves as the base layer for all cosmological computations in CosmoForge. It provides:

• Field Management: Scalar (spin-0) and tensor (spin-2) field handling with HEALPix integration
• Basis: Harmonic and pixel computation basis for Fisher matrix computation, with multi-field and spin-2 support
• Matrix Operations: Optimized LAPACK-based linear algebra with Numba acceleration
• Harmonic Analysis: Power spectrum management, beam handling, and spherical harmonic transforms
• Pixel Operations: Signal matrix computation and HEALPix pixel-based operations
• I/O Utilities: Reading and writing of cosmological data formats

Key Components

Computation Basis

Two computation basis methods for efficient Fisher matrix and QML estimation:

• HarmonicBasis (Tegmark-like): Direct transformation to harmonic space (n_pix -> n_modes). Fast when n_modes << n_pix. Supports optional m-block compression (compress=True) that approximates K as block-diagonal in azimuthal number m, giving ~lmax^2 speedup.
• PixelBasis (Gjerlow-like): Pixel-space projector with eigenvalue truncation (n_pix -> n_kept). Supports multiple basis choices and per-field threshold tuning.
• create_computation_basis: Factory function for creating basis instances by name.

Both methods support:

• Multi-field: Multiple components with independent sky coverage and noise
• Spin-2 polarization: E/B mode decomposition with spin-weighted spherical harmonics
• Per-field eigenspectrum inspection: compute_eigenspectrum_per_field() for choosing eigenmode thresholds, with E/B breakdown for spin-2 fields
• Visualization: plot_eigenvalue_spectrum() and plot_eigenvalue_comparison() with per-component subplots

Fields

• ScalarField: Spin-0 field implementation (e.g. CMB temperature, convergence)
• PolarizationField: Spin-2 field implementation (e.g. CMB polarization, cosmic shear)
• FieldCollection: Container for managing multiple fields
• create_field: Factory function for field creation

Managers

• SpectraManager: Power spectrum handling and normalization
• BeamManager: Instrumental beam function management

Binning

• Bins: Multipole binning specification for bandpower estimation. Supports uniform bins (Bins.fromdeltal) and custom non-uniform bins. Both bounds are inclusive. Used by QUBE for binned QML estimation.

Mathematical Operations

• Legendre Polynomials: legendre_00, legendre_02, legendre_22, legendre_plm
• Matrix Operations: matrix_mult, matrix_inverse_symm, matrix_trace, matrix_slogdet_symm
• Harmonic Transforms: cl_to_vec, vec_to_cl
• Wigner d-matrices: Spin-weighted harmonic basis functions
• SMW Formula: Sherman-Morrison-Woodbury compressed inverse and log-determinant

Core

• Core: Base class for cosmological analysis pipelines
• InputParams: Parameter file management
• CosmoLogger / Timer: Logging and profiling utilities

Installation

CosmoCore is automatically installed as part of CosmoForge:

pip install -e /path/to/CosmoForge

Usage

Computation Basis Workflow

from cosmocore.basis import PixelBasis
import numpy as np

# Set up pixel basis
ppc = PixelBasis(N, N_inv, theta, phi, lmax=100)
ppc.setup()

# Inspect per-field eigenspectra to choose thresholds
fig, axes = ppc.plot_eigenvalue_spectrum(basis="noise_weighted")

# Apply eigenmode truncation with chosen threshold
ppc.apply_compression(epsilon=1e-4, basis="noise_weighted")

# Compute Fisher matrix
fisher = ppc.compute_fisher_matrix(C_ell)

Multi-Field with Spin-2 Polarization

from cosmocore.basis import PixelBasis

# T (spin-0) + QU (spin-2) setup
ppc = PixelBasis(
    N, N_inv,
    theta=(theta_t, theta_p),
    phi=(phi_t, phi_p),
    lmax=100,
    spins=[0, 2],
)
ppc.setup()

# Per-field eigenspectrum with E/B breakdown
spectra = ppc.compute_eigenspectrum_per_field(basis="noise_weighted")
for entry in spectra:
    print(f"{entry['label']}: {len(entry['eigenvalues'])} modes")

# Per-field thresholds (scalar for T, E/B tuple for polarization)
ppc.apply_compression(epsilon=[1e-4, (1e-4, 1e-3)])

# Multi-field Fisher matrix
fisher = ppc.compute_fisher_matrix(C_ell_dict, spectra_list)

Field Creation

from cosmocore import create_field, FieldCollection

# Create temperature field
temp_field = create_field(
    spin=0, nside=32, lmax=64,
    mask=mask_array, labels="T"
)

# Create polarization field
pol_field = create_field(
    spin=2, nside=32, lmax=64,
    mask=mask_array, labels=["E", "B"]
)

# Create field collection
collection = FieldCollection(params, [temp_field, pol_field])

Power Spectrum Management

from cosmocore import SpectraManager, BeamManager

spectra_mgr = SpectraManager(fields)
beam_mgr = BeamManager(fields)

spectra_mgr.set_cls_from_file("fiducial_cls.txt", params)
beam_mgr.apply_smoothing(spectra_mgr)

Matrix Operations

from cosmocore import matrix_mult, matrix_inverse_symm, matrix_trace

C = matrix_mult(A, B)
inv_A = matrix_inverse_symm(A)
tr_AB = matrix_trace(A, B)

Configuration

CosmoCore uses parameter files for configuration:

# Field configuration
nside: 32
lmax: 64
spins: [0, 2]  # Temperature and polarization
labels: ["T", "E", "B"]

# I/O configuration
maskfile: "data/mask.fits"
inputclfile: "data/fiducial_cls.txt"
input_convention: Dl  # "Cl" (default) or "Dl" for input files
output_convention: Cl  # "Cl" (default) or "Dl" for QML output
covmatfile1: "data/noise_cov.bin"

# Beam configuration
smoothing_type: gaussian
fwhmarcmin: 5.0
beam_file: "data/beam.fits"

Architecture

cosmocore/
├── __init__.py              # Public API
├── core.py                  # Core base class
├── fields.py                # Field implementations (Scalar, Polarization)
├── settings.py              # Parameter management
├── harmonic.py              # Power spectrum and beam managers
├── pixel.py                 # Pixel-based signal matrix operations
├── in_out.py                # I/O utilities
├── logger.py                # Logging and timing
├── basics/                  # Mathematical primitives
│   ├── linalg.py            #   Matrix operations (mult, inverse, trace)
│   ├── legendre.py          #   Legendre polynomial evaluation
│   ├── wigner.py            #   Wigner d-matrices for spin-2
│   ├── geometry.py          #   Rotation angles and coordinate transforms
│   ├── indexing.py          #   Spectrum index utilities
│   └── smw.py               #   Sherman-Morrison-Woodbury formula
└── basis/             # Computation basis for Fisher/QML
    ├── base.py              #   Abstract base class and SMW types
    ├── harmonic_basis.py    #   Harmonic basis builder (V operator, Lambda)
    ├── harmonic.py          #   HarmonicBasis (Tegmark-like)
    └── pixel.py             #   PixelBasis (Gjerlow-like)

Performance Features

Numba Acceleration

Critical functions use Numba JIT compilation for near-C performance:

@njit(cache=True)
def legendre_unified(cos_theta, lmax, pl_00, pl_02, pl_22):
    ...

Memory Optimization

• In-place operations and pre-allocated buffers for hot paths
• Efficient memory layouts (Fortran-order for LAPACK calls)
• SMW formula avoids forming full n_pix x n_pix inverses

Vectorized Operations

• NumPy/BLAS vectorization for matrix operations
• Precomputed derivative diagonals for O(l^2) Fisher computation
• Block-diagonal structure exploited for multi-field computation
• M-block compression: block-diagonal K in azimuthal number m for ~lmax^2 speedup
• Field block-diagonal K: automatic detection and exploitation when fields are independent

Testing

Run CosmoCore tests:

uv run pytest src/cosmoforge.cosmocore/tests/

Dependencies

• NumPy: Numerical computations
• SciPy: Scientific computing (LAPACK wrappers)
• Numba: JIT compilation
• Matplotlib: Eigenspectrum visualization
• HEALPix: Pixelization (via healpy)

Documentation

• Core Module - Main Core class and pipeline
• Fields Module - Field management and HEALPix
• Basics Module - Mathematical utilities
• Harmonic Module - Power spectrum and beams
• I/O Module - Data input/output

References

• Tegmark, M. "How to measure CMB power spectra without losing information" Phys. Rev. D 55, 5895 (1997)
• Gjerlow, E. et al. "Component separation for the CMB with a low-resolution analysis" A&A 629, A51 (2019)
• Gorski, K.M. et al. "HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere" Astrophys. J. 622, 759-771 (2005)