issue with AXA optimization for catalogue cross-matches.

[AltieriBruno]

This part of the code (below) for the optimisation of the AXS crossmatches will not work for regions close to the equatorial poles, as for the window around ra the r (cross correlation radios) should be divided by cos(dec), otherwise the preselected region will be smaller than r along the right ascension axis as the distance along the right ascension is delta(ra)*cos(dec).

val join = if (useSMJOptim) df1.join(df2, df1("zone") === df2("zone") and (df1("ra") between(df2("ra") - r, df2("ra") + r))) else df1.join(df2, df1("zone") === df2("zone") and (df1("ra") between(df2("ra") - r, df2("ra") + r)) and (df1("dec") between(df2("dec") - r, df2("dec") + r)))

The current implementation leads to a loss of cross-correlated sources at high latitudes if optimisation in enabled.

[stargaser]

We see a drop in source density when using AXS to crossmatch AllWISE and Gaia DR2 in Galactic coordinates.

Here is sample code we ran on the epyc system, and the 2-D histogram.

allwise = axs_catalog.load("allwise_1am_dup")
gaia = axs_catalog.load("gaia_dr2_1am_dup")
allwise_gaia = (gaia.crossmatch(allwise).selectExpr(
           "ra", "dec", "source_id", "pmra", "pmdec", "parallax",
           "phot_g_mean_mag as G", "w1mpro", "w2mpro", "ecl_lon",
           "ecl_lat", "l", "b"))
image_histogram = allwise_gaia.histogram2d(
             allwise_gaia['l'], allwise_gaia['b'],
             360, 180, min1=0, max1=360, min2=-90, max2=90)
x,y,img = image_histogram
extent = (0, 360, -90, 90)
matplotlib.rcParams['figure.dpi'] = 150
plt.imshow(img.T, origin='lower', extent=extent,
      interpolation=None, vmax=0.2*np.max(img))
plt.xlabel("Galactic longitude [deg]")
plt.ylabel("Galactic latitude [deg]")
plt.title('Gaia DR2 xmatched with AllWISE')
plt.savefig('gaia_allwise_galactic.png');