improve piecewise plotting

[kcrisman]

Until we actually totally rewrite piecewise functions (done in #14801), we should improve some things.

For concreteness, here is one thing that should work but doesn't. I'm sure there are more - add to this list, and then whatever isn't fixed in this ticket can be moved to another ticket. I just want to make sure they're listed in one place, not ten tickets.

List:

• plotting more than one

  sage: f = Piecewise([[(0,1),x^3], [(1,2),x^2]], x)
  sage: plot([f,x^3],(x,0,2))
  

  A very similar example was at ​this ask.sagemath.org post:

  sage: f = Piecewise([[(-2,1),1],[(1,4),x]])
  sage: g =  Piecewise([[(-2,1),1],[(1,4),2*x]])
  sage: plot([f,g])
  AttributeError: PiecewisePolynomial instance has no attribute '__float__'
  

Both examples work in the new piecewise (#14801):

sage: f = piecewise([[(0,1),x^3], [(1,2),x^2]], var=x)
sage: plot([f,x^3],(x,0,2))

sage: f = piecewise([[(-2,1),1],[(1,4),x]])
sage: g =  piecewise([[(-2,1),1],[(1,4),2*x]])
sage: plot([f,g], xmin=-3, xmax=5)

• plotting a product of a piecewise with a symbolic (well, the problem is multiplying the two, but still worth putting here - see ​this sage-support thread)

fixed in new piecewise

• Maybe unify with plot_step_function, which currently is sort of its own thing?
• In this example:

  sage: zero_func(x)=0
  sage: g = Piecewise([[(-1000,1),zero_func],[(1,1000),(x-1)^3]],x)
  sage: G = g.plot()
  sage: G.show(xmin=-5,xmax=5,ymax=100)
  sage: g(1)
  0
  

  • You can use oo (infinity) for endpoints, but then the plot code for Piecewise gets screwed up.
  • You can try putting in zero instead of defining this new zero function, but then g(1) and g(-1) etc. won't work.
  • You can try using extend_by_zero to make the zero part, but it gives the same problem.
  • You can plot without xmin and xmax, but that gives the whole function.
  • You can plot without ymax, but that gives the range further out than you want.
  • You can try plot(g), but that turns out to uncover a very strange error that may or may not be a bug.

In new piecewise (#14801) 0 is no longer in the domain (open intervals?); and there is now support for unbounded intervals.

sage: zero_func(x)=0
sage: g = piecewise([[(-1000,1),zero_func],[(1,1000),(x-1)^3]])
sage: G = g.plot()
sage: G.show(xmin=-5,xmax=5,ymax=100)
Launched png viewer for Graphics object consisting of 1 graphics primitive
sage: g(1)
ValueError: point 1 is not in the domain

See also #1773.

[kcrisman]

Regarding the first item (can't plot two of them), It probably wouldn't even be that hard to fix. The problem is that setup_for_eval_on_grid wants to use fast_float but Piecewise guys don't have that, or more precisely don't have __float__.

[kcrisman]

From DSM on ​this ask.sagemath.org question:

# monkeypatch legend duplication of trac #11225
def fix_piecewise(fn):
    import types
    def fixed_plot(self, *args, **kwargs): 
        from sage.plot.all import plot
        return sum([plot(f, a, b, *args, **(dict((k,v) for k,v in kwargs.items() if i == 0 or k != 'legend_label')))
                    for i, ((a,b),f) in enumerate(self.list())])
    def fn2(*args, **kwargs):
        ans = fn(*args, **kwargs)
        ans.plot = types.MethodType(fixed_plot, ans)
        return ans
    return fn2

Piecewise = fix_piecewise(Piecewise)

Nice protopatch, perhaps?

[mjo]

I removed the last bullet point and created #12651 where I'll post a patch with dsm's fix.

[mkoeppe]

Updated description for new piecewise (#14801). Didn't check the xmin/xmax etc. behavior that is mentioned in the description.

This can probably be closed when the old Piecewise (now deprecated) is removed completely.