Fix dipole discrepancy between channel and frequency path in SkyGenerator

[Copilot]

SkyGenerator produced different dipole maps depending on whether it was initialized with a channels argument or frequencies_ghz, because the frequency path unnecessarily routed the dipole through a map → alm → map round trip and applied Gaussian beam smoothing — neither of which the channel path did.

Changes

• _generate_dipole_frequencies(): Removed the estimate_alm + _apply_smoothing_and_windows_to_alm + pixelize_alm pipeline for the output_type == "map" case. The analytically-computed dipole map is now assigned directly, matching the channel path behavior in generate_solar_dipole(). For output_type == "alm", the alm conversion is retained but beam smoothing is removed.

• New test test_dipole_consistency_channel_vs_frequency: Asserts that channel-mode and frequency-mode dipole outputs are numerically identical (decimal=5).

# Previously: max absolute difference ~0.00020737
# After fix:
np.testing.assert_almost_equal(
    input_maps_ch.values,
    input_maps_freq.values[0],
    decimal=5,
)  # passes

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Original prompt

---

This section details on the original issue you should resolve

<issue_title>Dipole discrepancy in input_sky generation</issue_title>
<issue_description>Hello,

When defining input sky maps using a channel or using a frequency as argument, the dipole map is not exactly the same between the two cases.

Running the script below with make_dipole=False shows the maps are the same for the two cases, but when we set it to True, it is no longer the case and the max absolute difference (0.00020737) is quite high.

I tried to track it down and it seems to come from the map->alm->map operation (pixelize_alm() call in _generate_dipole_frequencies()) for the frequency case. This operation (and also the self._apply_smoothing_and_windows_to_alm()) is done only for the frequency-as-input case and not for the channel-as-input case. Maybe this is expected, in which case please close this issue.

Cheers,
Miguel

import litebird_sim as lbs
import numpy as np
from litebird_sim.input_sky import SkyGenerator

start_time = 0
time_span_s = 1 * 24 * 3600
nside = 64
fwhm_arcmin = 37.805193

imo_location = "schema.json"
imo = lbs.Imo(flatfile_location=imo_location)


channelinfo = lbs.FreqChannelInfo(
    bandcenter_ghz=140.0,
    channel="L4-140",
    bandwidth_ghz=1.0,
    fwhm_arcmin=fwhm_arcmin,
)


sky_params = lbs.SkyGenerationParams(
    make_cmb=True,
    seed_cmb=1234,
    output_type="map",
    make_dipole=False,
    make_fg=True,
    fg_models=["s0", "d0", "f1"],
    apply_beam=True,
    bandpass_integration=False,
    nside=nside,
    units="K_CMB",
)

gen_sky_ch = lbs.SkyGenerator(
    parameters=sky_params,
    channels=channelinfo,
)
input_maps_ch = gen_sky_ch.execute()["L4-140"]

gen_sky_freq = SkyGenerator(
    parameters=sky_params,
    frequencies_ghz=140.0,
    fwhm_rad=np.radians(fwhm_arcmin / 60.0),
)
input_maps_freq = gen_sky_freq.execute()

np.testing.assert_almost_equal(
    input_maps_ch.values,
    input_maps_freq.values[0],
    decimal=5,
    verbose=True,
)

```</issue_description>

## Comments on the Issue (you are @copilot in this section)

<comments>
</comments>

• Fixes Dipole discrepancy in input_sky generation #500

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