sys_mapping.power_spectrum
==========================

Harmonic-space systematic mitigation via pseudo-:math:`C_\ell` estimators.

**Inputs:** Full-sky HEALPix overdensity map, survey mask, template maps,
and estimated contamination amplitudes.

**Outputs:** Pseudo-:math:`C_\ell` arrays (shape ``(lmax+1,)``), bias
corrections, and mode-projected power spectra.

The pipeline is:

1. :func:`~sys_mapping.power_spectrum.measure_pseudo_cl` — apply mask and
   call ``healpy.anafast``.
2. :func:`~sys_mapping.power_spectrum.subtract_template_cl` — subtract
   :math:`\sum_i \hat\alpha_i \hat C_\ell^{t_i}`.
3. :func:`~sys_mapping.power_spectrum.harmonic_bias` — compute the residual
   bias :math:`b_\ell = -n/(2\ell+1)`.
4. :func:`~sys_mapping.power_spectrum.mode_projection_bias` — apply BMP or
   EMP deprojection.

**Key papers:**
`Elsner et al. 2016 <https://ui.adsabs.harvard.edu/abs/2016MNRAS.456.2095E/abstract>`_;
`Elsner et al. 2017 <https://ui.adsabs.harvard.edu/abs/2017MNRAS.465.1847E/abstract>`_;
`Leistedt & Peiris 2014 <https://ui.adsabs.harvard.edu/abs/2014MNRAS.444....2L/abstract>`_ — see also :doc:`../methods`.

.. automodule:: sys_mapping.power_spectrum
   :members:
   :show-inheritance: