Expected round-trip error?

[mcgibbon]

When I run the test specified in tests/test_harmonic_transform.py, I get RMS: 0.004188947245384965, Max: 0.08884372968086218. Subsequent re-runs give slightly lower values bit still > 0.002, 0.04. These errors seem fairly large to me (especially the maximum error). Are values in this range expected?

I generate random data on the physical grid and round-trip that, errors are quite a lot larger than I expected, given how uniform the healpix grid is. This test gives RMS: 0.8145438432693481, Max: 3.090202808380127:

def test_sht_round_trip_real_space():
    device = get_device()
    nside = 32
    npix = 12 * nside**2

    quad_weights = "ring"
    lmax = 2 * nside + 1
    mmax = lmax

    sht = SHT(nside, lmax=lmax, mmax=mmax, quad_weights=quad_weights)
    isht = iSHT(nside, lmax=lmax, mmax=mmax)

    signal_ori = torch.randn(npix, dtype=torch.float32).to(device)

    signal_back = isht(sht(signal_ori))
    diff = signal_ori - signal_back
    rms = torch.sqrt((diff.abs().pow(2)).mean())
    max_value = torch.max(diff.abs())

    print(f"RMS: {rms}, Max: {max_value}")
    torch.testing.assert_close(signal_ori, signal_back)

Is this also expected? These errors are comparable to what I get with the torch-harmonics SHT on a lat-lon domain, which is extremely oversampled in the poles compared with a healpix grid.