doctest proper handling of domain in evalf functions

[tkluck]

Previous description of ticket:

---

Plotting currently fails when plotting a symbolic function that evaluates to complex values:

sage: def evalf_func(self,x,parent=None):
....:     return parent(I*x) if parent!=None else I*x
....: 
sage: f = function('f', evalf_func=evalf_func)
sage: plot(abs(f(x)),0,5)
verbose 0 (2392: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 199 points.
verbose 0 (2392: plot.py, generate_plot_points) Last error message: 'unable to simplify to float approximation'

This is because plot uses fast_float, and fast_float cannot deal with the intermediate complex value.

The attached patch first changes these things:

• it adds a method to class Function that allows one to see what output range is to be expected for a given input range. By default, it will return a complex field.
• it overrides this method for builtin functions, which return floats for float input
• this is then used by fast_float to throw an exception if complex values are to be expected

This exception will cause plot to fall back to fast_callable instead of fast_float. However, fast_callable needs patching too:

• it now uses the _evalf_ method when available instead of just __call__. Otherwise, plot will try to coerce the result to float, which also cannot deal with complex intermediate values.

An alternative to this step would be to fix float coercion, which I haven't looked into.

[tkluck]

There's some issues with the patch as it is, please wait with reviewing.

[tkluck]

The _002.patch solves the issues I mentioned. Setting status back to "needs review".

[tkluck]

Added an attachment containing the two patches together, with a proper filename containing the trac number.

[chapoton]

for the bot:

apply trac_13355_plot_with_complex_intermediates.patch

[chapoton]

one failing doctest, see bot report

[tkluck]

This should fix the doctest problem.

Apply trac_13355_plot_with_complex_intermediates.patch

[vdelecroix]

Hello,

I don't understand your example. You did not even defined f, how do you want to plot it? It has nothing to do with complex values

sage: def evalf_func(self,x,parent=None):
....:     return parent(I*x) if parent!=None else I*x
....: 
sage: f = function('f', evalf_func=evalf_func)
sage: float(f(3))
Traceback (most recent call last)
...
TypeError: unable to simplify to float approximation

Could you be more explicit about the problem you intend to solve ?

[tkluck]

Thanks for looking at this!

Replying to vdelecroix:

I don't understand your example. You define f to take complex values, how do you want to plot it as a real function?

My example was

sage: plot(abs(f(x)),0,5)

Note the abs.

Now the point is that

sage: abs(f(3))
abs(f(3))
sage: float(abs(f(3)))
3.0

both work, but plotting doesn't:

plot(abs(f(x)),x,0,10)
verbose 0 (2430: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 199 points.
verbose 0 (2430: plot.py, generate_plot_points) Last error message: 'unable to simplify to float approximation'

The reason is that there is an optimization to use fast_callable for calculating plot points. The current implementation assumes that all intermediate values are floats, whereas we can still make a real plot when the argument to abs is complex. This patch should fix that.

Is this any clearer? It would be great if you could test/review the patch!

[vdelecroix]

Replying to tkluck:

Is this any clearer?

I see. Sorry for my too fast lecture and thanks for the clarification!

It would be great if you could test/review the patch!

It was my intention ;-)

[eviatarbach]

#15030 fixes the same issue in a different (and I think simpler) way. I tried your example and it works with the #15030 patch as well.

I also think this is a significant issue; you can't even plot functions like abs(log(x)) properly. tkluck, it would be great if you could look at my patch and if you think it's a better solution review it.

[kcrisman]

Note that #15030 was apparently merged.

Also, anyone know how this impacts 3d plots?

[kcrisman]

One thing that could be done here is if there are any significant/useful examples on this ticket that weren't added in #15030, they could be added here...

[rws]

I have extracted the doctests from the patch and changed the description accordingly. However, some doctests fail.

sage -t --long src/sage/ext/fast_callable.pyx
**********************************************************************
File "src/sage/ext/fast_callable.pyx", line 397, in sage.ext.fast_callable.?
Failed example:
    fc(3,4)
Expected:
    12
Got:
    f(3, 4)
**********************************************************************
File "src/sage/ext/fast_callable.pyx", line 405, in sage.ext.fast_callable.?
Failed example:
    fc(3,4)
Expected:
    12*I
Got:
    g(3, 4)
**********************************************************************
1 item had failures:
   2 of  47 in sage.ext.fast_callable.?
    [586 tests, 2 failures, 3.54 s]
----------------------------------------------------------------------
sage -t --long src/sage/ext/fast_callable.pyx  # 2 doctests failed
----------------------------------------------------------------------

---

New commits:

​23e82c2

13355: handle domain properly in evalf functions (doctests)

[kcrisman]

Hmm, these doctests look strange to me anyway.

parent!=None

should be

parent is not None

I think. The failures are actually probably features, not bugs, since f and g are symbolic functions, which are now not automatically evaluated, if that makes sense...

[rws]

Yes. So change the doctests or abandon them?

[kcrisman]

If you agree that this is proper behavior, then we might as well change them. Also, the plot one is definitely useful.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​66aa509	Merge branch 'develop' into t/13355/plot_fails_if_a_function_implicitly_needs_complex_intermediate_values
​65675e8	13355 reviewer's patch: fix doctests, typos, PEP8

[rws]

But then, somehow we want 12 or 12*I as a result too, but for this the function needs a simplify() member like hypergeometric (#2516) has.