Fix non-unit direction vectors

[hagenw]

This tries to fix #20 and #28.

I renamed util.normal_vector() to util.normalize_vector() as proposed in #28 and used it for every single dimensional direction vector n. The field plotted in #20 looks now correct with this.

I'm still not happy with the naming, which I will discuss directly in #28 and there is the problem how to handle several unit vectors at once like n0 = util.asarray_of_rows(n0).

[mgeier]

Any objections?
If not, LGTM!

[hagenw]

Just a reminder, the fix is not done for n0 = util.asarray_of_rows(n0) as I didn't know what is the best way to apply it there. With a loop? Can someone help out with this?

[mgeier]

If this would be needed only once, you could do something like:

n0 = util.asarray_of_rows(n0)
n0 = np.row_stack([util.normalize_vector(n) for n in n0])

But since we need this several times, we should make a function.

Should we include this into util.normalize_vector()?
We could do a simple np.asarray() and then do different things for one and two-dimensional arrays.
This could be used like util.normalize_vector(util.asarray_of_rows(n0))

Or should we make a new function util.asarray_of_normalized_rows()?
This has the problem of #28, could be both types of "normalization".

In a separate function, you could use something like this:

# make sure x is a 2-dimensional array
x / np.linalg.norm(x, axis=1, keepdims=True)

However, note that the keepdims argument is only available since NumPy 1.10.0 (see https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.norm.html).

This should do the same thing and also work for older versions:

# make sure x is a 2-dimensional array
x / np.linalg.norm(x, axis=1).reshape(-1, 1)

[mgeier]

PS: if we include this in util.normalize_vector(), it will lose its squeezing ability.
This means we would have to use util.normalize_vector(util.asarray_1d(n)) in many cases.

Which would be a bit longer, but it would actually be more explicit, which generally is a good thing.

Another problem: we would have to decide between normalize_vector() and normalize_vectors().

BTW, if we decide for some fundamental changes along the lines of #36, we'll have to change those functions again.

[mgeier]

PPS: We can also implement this later, we should just create a new issue as a reminder.

[hagenw]

At the beginning I was also thinking of two functions similar to the asarray once, e.g.

util.asdirection()
util.asdirections()

But maybe it is better to have to use it in an explicit way?

util.normalize_vector(util.asarray_1d(n))
util.normalize_vector(util.asarray_of_rows(n))

[mgeier]

I would suggest to merge this PR as is and postpone further changes until we see how our understanding of a "direction" evolves.

[hagenw]

Fine with me, I created an issue for the remaining TODO of this PR.