Plot constraint violations of eoms with inequalities

[Peter230655]

I changed along the lines discussed in #488, which it should fix.
I tested every combination/permutation I could think of.

When subplots=True I changed the numbering of the eoms, now starting with Eq 0 (before Eq 1). Reason is that like this the user can easily see his eom_bounds key matching the label on the respective plot.

I disregard the case of one eom only.
I cannot imagine a situation that opty gets only one eom, and this eom has bounds.
Of course, easy to add if useful.
Update: I will add it to avoid exceptions.

[Peter230655]

Again, I tested all combinations I could think of.

[moorepants]

subplots should only be set to true or false by the user.

[moorepants]

Also "eom" is not a word.

[Peter230655]

subplots should only be set to true or false by the user.

If only one equation of motion is given, subplots really does not make sense.
I set it to True in the program to simplify the 'logical flow' if only one eom is given.

[Peter230655]

Also "eom" is not a word.

I changed this sentence to: If only one equation od motion is given and eom_bounds are given, the value of the equation of motion will be plotted.

[moorepants]

At the minimum, whether the output is an array of axes or a single axis matters also.

[Peter230655]

At the minimum, whether the output is an array of axes or a single axis matters also.

I believe this was taken care of earlier, It worked with my one-eom example, but I have to double check.
Update: it seems to work with one eom and no instance constraints.

[Neville-N]

I believe it would be clearer if the plot_constraint_violations function plotted only the violations, even when the subplots argument is set to True.

[Peter230655]

I don't want to beat a dead horse, but I just thought of this:
Say your are not very sure of the values of a, b in a < eom_i < b, so you make a good guess.
Say, it turns out that you selected a much too small, and b much too large. With the present method you could see this and adjust them.
Would this adjusting speed up opty \ Ipopt, as the search space becomes smaller`?
If this is true, it may be worth giving an additional optional keyword, if not I will change it as we discussed.
@moorepants: I do not want to be pushy, but I think, this plotting method is useful. If you want to release the next opty version before July or so, please let me know whether this thoguht above is uselful or not. Then I can finish it.
Thanks!

[Peter230655]

The violations of the inequality constraints are shown, as discussed during the recent hackathon.
I added an optional keyword show_range, default is False. If True and if subplots is True, its shows the range of the bounded eoms.
My reason:
Maybe in a < eom_i < b, a is set way too small, and b way too large. withshow_range == True this will be visible. Making a larger and b smaller reduces the size of the search space for Ipopt and may make it faster.
If this reasoning is wrong, the key word should be removed.

I tested it with one eom only, too (plot_betts_10_7). For the main tests I used plot_car_one_racecourse_smooth, where there are many eom_bounds available.