Issue with halo/sky drawing plot in chapter 5.

[CamDavidsonPilon]

Brought to me attention by Gabriel Kronberger:

I'm almost sure that your draw_sky routine has a bug. This is apparent in one-halo sky (7) because the nearest galaxies are not elongated tangentially but instead point into the direction of the halo. Comparing your picture with my outputs some galaxies are shown correctly while others are elongated in the wrong direction. This indicates that there might by a problem with the calculation of the angle using arctan / atan2. I checked your code but can't point the finger at the bug, because I'm not familiar with the ellipse command, does it handle negative angles correctly?

If it helps I used linear transformations for the graphical output in C#

        m.Translate(x, y]);
        m.Rotate(45);
        m.Scale(1f + Math.Max(0, e2[i]), 1.0f - Math.Min(e2[i], 0));
        m.Rotate(-45);
        m.Scale(1f + Math.Max(0, e1[i]), 1.0f - Math.Min(e1[i], 0));
        graphics.Transform = m;
        graphics.FillEllipse(Brushes.Black, -2f, -2f, 4f, 4f);

A main issue is the strange reference system for e1 and e2.
One thing you can try is to check skys that have one very pronounced halo (e.g. 3). For comparison I attached my visualization of training sky number 3.

[CamDavidsonPilon]

pinging @vgoklani as my code was adapted from his. Maybe he can assist?

[CamDavidsonPilon]

Fixed, small indexing error