def harmonic_ilc_alm(components, instrument, alms, lbins=None, fsky=None):
""" Internal Linear Combination of alms
Parameters
----------
components: list or tuple of lists
`Components` of the mixing matrix. They must have no free parameter.
instrument:
Object that provides the following as a key or an attribute.
- **frequency**
It can be anything that is convertible to a float numpy array.
alms: ndarray
Data vector to be separated. Shape ``(n_freq, ..., lm)``.
``...`` can be 1, 3 or absent. The ILC weights are computed
independently for each of its indices.
lbins: array
It stores the edges of the bins that will have the same ILC weights.
If a multipole is not in a bin but is the alms, an independent bin
will be assigned to it
fsky: array
If provided the output power spectra are corrected for this factor
Returns
-------
result : dict
It includes
- **W**: *(ndarray)* - ILC weights for each component and possibly
each index of the `...` dimension in the alms.
- **s**: *(ndarray)* - Alms of the cleaned components
- **cl_in**: *(ndarray)* - Spectra of the input alm
- **cl_out**: *(ndarray)* - Spectra of the output alm
- **fsky**: *(ndarray)* - The input fsky used to correct the cls
"""
cl_in = np.array([hp.alm2cl(alm) for alm in alms])
mm = MixingMatrix(*components)
A = mm.eval(instrument.frequency)
cov = _empirical_harmonic_covariance(alms)
if lbins is not None:
for lmin, lmax in zip(lbins[:-1], lbins[1:]):
# Average the covariances in the bin
lmax = min(lmax, cov.shape[-1])
dof = 2 * np.arange(lmin, lmax) + 1
cov[..., lmin:lmax] = ((dof / dof.sum() *
cov[..., lmin:lmax]).sum(-1))[...,
np.newaxis]
cov = _regularized_inverse(cov.swapaxes(-1, -3))
ilc_filter = np.linalg.inv(A.T @ cov @ A) @ A.T @ cov
del cov, dof
res = OptimizeResult()
res.s = _apply_harmonic_W(ilc_filter, alms)
# Craft output
cl_out = np.array([hp.alm2cl(alm) for alm in res.s])
res.cl_in = cl_in
res.cl_out = cl_out
if fsky:
res.cl_in /= fsky
res.cl_out /= fsky
res.fsky = fsky
res.W = ilc_filter
return res
