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 (Piecewise functions done right #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.

Depends on #14801

CC: @wdjoyner @jasongrout @jondo @kcrisman @vbraun @slel @mkoeppe @eviatarbach @rwst

Component: graphics

Keywords: piecewise

Issue created by migration from https://trac.sagemath.org/ticket/11225

[kcrisman]

Description changed:

--- 
+++ 
@@ -1,10 +1,12 @@
-Until we actual totally rewrite piecewise functions, we should improve some things.
+Until we actually totally rewrite piecewise functions, 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))
 ```
-
+* Maybe unify with `plot_step_function`, which currently is sort of its own thing?

[kcrisman]

Description changed:

--- 
+++ 
@@ -10,3 +10,19 @@
 sage: plot([f,x^3],(x,0,2))
 ```
 * 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.

[kcrisman]

Description changed:

--- 
+++ 
@@ -9,6 +9,7 @@
 sage: f = Piecewise([[(0,1),x^3], [(1,2),x^2]], x)
 sage: plot([f,x^3],(x,0,2))
 ```
+* 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](http://groups.google.com/group/sage-support/browse_thread/thread/7357d08529de32dd))
 * Maybe unify with `plot_step_function`, which currently is sort of its own thing?
 * In this example:
 

[kcrisman]

Description changed:

--- 
+++ 
@@ -27,3 +27,7 @@
 * 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.
+
+
+See also #1773.
+

[kcrisman]

comment:5

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]

Description changed:

--- 
+++ 
@@ -8,6 +8,14 @@
 ```
 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](http://ask.sagemath.org/question/868/two-piecewise-defined-functions-in-one-plot):
+
+```
+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__'
 ```
 * 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](http://groups.google.com/group/sage-support/browse_thread/thread/7357d08529de32dd))
 * Maybe unify with `plot_step_function`, which currently is sort of its own thing?

[kcrisman]

Description changed:

--- 
+++ 
@@ -35,7 +35,7 @@
 * 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.
-
+* Most keywords are passed on to all component functions, but that is the wrong thing to do for legends.  See [this ask.sagemath.org question](http://ask.sagemath.org/question/925/piecewise-functions-and-legend-label).
 
 See also #1773.
 

[kcrisman]

comment:7

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?

[orlitzky]

Description changed:

--- 
+++ 
@@ -35,7 +35,6 @@
 * 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.
-* Most keywords are passed on to all component functions, but that is the wrong thing to do for legends.  See [this ask.sagemath.org question](http://ask.sagemath.org/question/925/piecewise-functions-and-legend-label).
 
 See also #1773.
 

[orlitzky]

comment:8

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