Opened 10 years ago

# improve piecewise plotting

Reported by: Owned by: kcrisman jason, was major sage-7.3 graphics piecewise wdj, jason, jondo, kcrisman, vbraun, slelievre, mkoeppe, eviatarbach, rws N/A #14801

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
```

### comment:1 Changed 10 years ago by kcrisman

• Description modified (diff)

### comment:2 Changed 9 years ago by kcrisman

• Description modified (diff)

### comment:3 Changed 9 years ago by kcrisman

• Description modified (diff)

### comment:4 Changed 9 years ago by kcrisman

• Description modified (diff)

### comment:5 Changed 9 years ago by kcrisman

• Description modified (diff)

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__`.

### comment:6 Changed 9 years ago by kcrisman

• Description modified (diff)

### comment:7 Changed 9 years ago by 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?

### comment:8 Changed 9 years ago by mjo

• Description modified (diff)

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

### comment:10 Changed 7 years ago by ppurka

• Dependencies set to #14801

### comment:11 Changed 4 years ago by mkoeppe

• Cc kcrisman vbraun slelievre mkoeppe eviatarbach rws added
• Description modified (diff)
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.