document loss function to find the band gap

[basnijholt]

Many people have asked me how to do this.

I've recommended them to use the following loss function:

@adaptive.learner.learner1D.uses_nth_neighbors(0)
def abs_min_log_loss(xs, ys):
    from adaptive.learner.learner1D import default_loss
    ys = [np.log(np.abs(y).min()) for y in ys]
    return default_loss(xs, ys)

We should put this in the documentation somewhere.

[akhmerov]

What's the motivation for log, as opposed to any other monotonous function?

[basnijholt]

This makes small y-values more important.

[akhmerov]

But 1/abs(y).min() would make it even more important. I'm wondering why log specifically.

[jbweston]

when we say "band gap" here I guess we're making certain assumptions, e.g. system has direct gap, and valence and conduction bands are at y<0 and y>0 respectively.