cosmocore.signal_kernels module

Pixel-space signal-matrix kernels for cosmological analysis.

Renamed from cosmocore.pixel (2026-05); see ADR-0002 follow-up (architecture backlog #5) for the rename rationale.

This module provides optimized functions for pixel-space computations in cosmological data analysis, including signal matrix calculations, pointing vector computations, and pixel masking operations. Many functions are optimized with Numba for performance.

Functions

count_nonzero_mask

Count non-zero pixels in a mask.

compute_pointings

Compute 3D pointing vectors for HEALPix pixels.

compute_00_contribution

Compute spin-0 x spin-0 field contributions to signal matrix.

compute_22_contribution

Compute spin-2 x spin-2 field contributions to signal matrix.

compute_02_contribution

Compute spin-0 x spin-2 field contributions to signal matrix.

compute_signal_matrix

Build the full signal covariance matrix.

derivative_step_00

Derivative computation for spin-0 x spin-0 correlations.

derivative_step_02

Derivative computation for spin-0 x spin-2 correlations.

derivative_step_22

Derivative computation for spin-2 x spin-2 correlations.

do_derivative_step

Execute derivative step for Fisher matrix calculations.

Notes

This module heavily uses Numba’s @njit decorator for performance optimization. The signal matrix calculations implement the full pixel-space likelihood for CMB analysis with proper handling of spin-0 (temperature) and spin-2 (polarization) fields.

References

[1]

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)

[2]

Kamionkowski, M., Kosowsky, A. & Stebbins, A. “Statistics of cosmic microwave background polarization” Phys. Rev. D 55, 7368 (1997)

[3]

Zaldarriaga, M. & Seljak, U. “All-sky analysis of polarization in the microwave background” Phys. Rev. D 55, 1830 (1997)

[4]

Ng, K.-W. & Liu, G.-C. “Correlation Functions of CMB Anisotropy and Polarization” Int. J. Mod. Phys. D 8, 61-83 (1999)

[5]

Challinor, A. et al. “All-sky convolution for polarimetry experiments” Phys. Rev. D 62, 123002 (2000)

cosmocore.signal_kernels.count_nonzero_mask(mask)

Count non-zero pixels in a 1D mask array.

Parameters:

mask (numpy.ndarray) – 1D array representing pixel mask values.

Returns:

Number of pixels with absolute value > 0.5.

Return type:

int

Notes

This function is optimized with Numba for performance in tight loops. Uses threshold of 0.5 to determine active pixels.

cosmocore.signal_kernels.compute_pointings(nside, npixs, point_vectors, theta_vectors, phi_vectors, active, ordering)

Compute 3D pointing vectors for active HEALPix pixels.

Parameters:

• nside (int) – HEALPix resolution parameter.

• npixs (list of int) – Number of active pixels for each field.

• point_vectors (tuple of numpy.ndarray) – Tuple of arrays to store pointing vectors for each field. Each array has shape (n_active, 3).

• theta_vectors (tuple of numpy.ndarray) – Tuple of arrays to store theta unit vectors for each field. Each array has shape (n_active).

• phi_vectors (tuple of numpy.ndarray) – Tuple of arrays to store phi unit vectors for each field. Each array has shape (n_active).

• active (numpy.ndarray or tuple) – Active pixel indices for each field.

• ordering (str) – HEALPix pixel ordering: "RING" or "NESTED".

Returns:

Updated pointing vectors with normalized 3D unit vectors.

Return type:

tuple of numpy.ndarray

Notes

Converts HEALPix pixel indices to 3D Cartesian unit vectors pointing to pixel centers. Used for spherical harmonic calculations and geometric operations.

cosmocore.signal_kernels.compute_00_contribution(cl, S_slice, vec1, vec2, legendre, mode)

Compute spin-0 x spin-0 field contribution to signal matrix.

Parameters:

• cl (numpy.ndarray) – Power spectrum coefficients for the field correlation.

• S_slice (numpy.ndarray) – 2D array slice of signal matrix to fill.

• vec1 (numpy.ndarray) – 3D pointing vectors for the two fields, shape (npix, 3).

• vec2 (numpy.ndarray) – 3D pointing vectors for the two fields, shape (npix, 3).

• legendre (numpy.ndarray) – Temporary array for Legendre polynomial computation.

• mode (int) – Computation mode (0 for symmetric, 1 for general).

Notes

Implements the pixel-space covariance for scalar fields (e.g., temperature). Uses Legendre polynomials to compute angular correlations.

The outer pixel loop uses prange for thread-level parallelism.

cosmocore.signal_kernels.compute_22_contribution(cl11, cl22, cl12, S_slice, vec1, vec2, legendre, f1, f2)

Compute spin-2 x spin-2 field contribution to signal matrix.

Parameters:

• cl11 (numpy.ndarray) – Power spectra for EE, BB, and EB correlations respectively.

• cl22 (numpy.ndarray) – Power spectra for EE, BB, and EB correlations respectively.

• cl12 (numpy.ndarray) – Power spectra for EE, BB, and EB correlations respectively.

• S_slice (numpy.ndarray) – 2D array slice of signal matrix to fill.

• vec1 (numpy.ndarray) – 3D pointing vectors for the two fields, shape (npix, 3).

• vec2 (numpy.ndarray) – 3D pointing vectors for the two fields, shape (npix, 3).

• legendre (numpy.ndarray) – Temporary array for Legendre polynomial computation.

• f1 (numpy.ndarray) – Temporary arrays for spin-2 harmonic functions.

• f2 (numpy.ndarray) – Temporary arrays for spin-2 harmonic functions.

Notes

Implements the pixel-space covariance for polarization fields with proper rotation handling. The outer pixel loop uses prange for parallelism.

cosmocore.signal_kernels.compute_02_contribution(cl12, cl13, S_slice, vec0, vec2, legendre)

Compute spin-0 x spin-2 field contribution to signal matrix.

Parameters:

• cl12 (numpy.ndarray) – Cross-power spectra for T-Q and T-U correlations respectively.

• cl13 (numpy.ndarray) – Cross-power spectra for T-Q and T-U correlations respectively.

• S_slice (numpy.ndarray) – 2D array slice of signal matrix to fill.

• vec0 (numpy.ndarray) – 3D pointing vectors for spin-0 field, shape (npix, 3).

• vec2 (numpy.ndarray) – 3D pointing vectors for spin-2 field, shape (npix, 3).

• legendre (numpy.ndarray) – Temporary array for Legendre polynomial computation.

Notes

Implements cross-correlations between temperature (spin-0) and polarization (spin-2) fields. The outer pixel loop uses prange for parallelism.

cosmocore.signal_kernels.compute_signal_matrix(S, lmax, fields)

Build the full signal covariance matrix for cosmological fields.

Parameters:

• S (numpy.ndarray) – 2D array to store the signal covariance matrix.

• lmax (int) – Maximum multipole for power spectrum computations.

• fields (FieldCollection) – Collection of cosmological fields with power spectra and pointing vectors.

Notes

Constructs the complete pixel-space signal covariance matrix by combining contributions from all field pairs. Handles different spin combinations: - Spin-0 x Spin-0: Temperature-like correlations - Spin-2 x Spin-2: Polarization-like correlations - Spin-0 x Spin-2: Temperature-polarization cross-correlations

The matrix structure accounts for proper field ordering and spin weights. Cross-correlations between different spin-2 fields are not yet implemented.

Raises:

NotImplementedError – If cross-correlation between different spin-2 fields is requested.

cosmocore.signal_kernels.derivative_step_00(S_slice, vec1, vec2, current_ell, legendre, mode)

Compute derivative step for spin-0 x spin-0 field correlations.

Parameters:

• S_slice (numpy.ndarray) – 2D array slice to store derivative contributions.

• vec1 (numpy.ndarray) – 3D pointing vectors for the two fields.

• vec2 (numpy.ndarray) – 3D pointing vectors for the two fields.

• current_ell (int) – Current multipole moment for the derivative calculation.

• legendre (numpy.ndarray) – Temporary array for Legendre polynomial computation.

• mode (int) – Computation mode (0 for symmetric, 1 for general).

Notes

Computes the derivative of the signal matrix with respect to power spectrum parameters for scalar field correlations. Used in Fisher matrix calculations.

cosmocore.signal_kernels.derivative_step_02(S_slice, vec0, vec2, current_ell, mode, legendre)

Compute derivative step for spin-0 x spin-2 field correlations.

Parameters:

• S_slice (numpy.ndarray) – 2D array slice to store derivative contributions.

• vec0 (numpy.ndarray) – 3D pointing vectors for the spin-0 field.

• vec2 (numpy.ndarray) – 3D pointing vectors for the spin-2 field.

• current_ell (int) – Current multipole moment for the derivative calculation.

• mode (int) – Computation mode (0 for T-Q, 1 for T-U correlations).

• legendre (numpy.ndarray) – Temporary array for Legendre polynomial computation.

Notes

Computes derivatives for temperature-polarization cross-correlations. Handles coordinate rotations and mode-dependent sign conventions. Used in Fisher matrix calculations for cross-spectrum parameters.

cosmocore.signal_kernels.derivative_step_22(S_slice, vec1, vec2, current_ell, mode, legendre, f1, f2)

Compute derivative step for spin-2 x spin-2 field correlations.

Parameters:

• S_slice (numpy.ndarray) – 2D array slice to store derivative contributions.

• vec1 (numpy.ndarray) – 3D pointing vectors for the two spin-2 fields.

• vec2 (numpy.ndarray) – 3D pointing vectors for the two spin-2 fields.

• current_ell (int) – Current multipole moment for the derivative calculation.

• mode (int) – Polarization mode (0 for EE, 1 for BB, 2 for EB).

• legendre (numpy.ndarray) – Temporary array for Legendre polynomial computation.

• f1 (numpy.ndarray) – Temporary arrays for spin-2 harmonic functions.

• f2 (numpy.ndarray) – Temporary arrays for spin-2 harmonic functions.

Notes

Computes derivatives for polarization-polarization correlations including proper E/B mode decomposition and coordinate rotations. Handles the three independent polarization power spectra: EE, BB, and EB.

cosmocore.signal_kernels.do_derivative_step(S, spectrum, npixs, spins, current_ell, fields)

Execute derivative step for Fisher matrix calculations.

Parameters:

• S (numpy.ndarray) – 2D signal matrix to fill with derivative contributions.

• spectrum (int) – Index of the power spectrum being differentiated.

• npixs (list of int) – Number of active pixels for each field (deprecated, use fields.n_active).

• spins (list of int) – Spin values for each field (deprecated, use fields.spin).

• current_ell (int) – Current multipole moment for the derivative calculation.

• fields (FieldCollection) – Collection of cosmological fields with power spectra and metadata.

Notes

Orchestrates the computation of signal matrix derivatives with respect to power spectrum parameters. Determines the appropriate field combinations and calls the corresponding derivative functions based on spin values.

Used in Fisher matrix calculations to compute parameter sensitivities. The function handles different field types and cross-correlations automatically.