#13355: Plot fails if a function implicitly needs complex intermediate values
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Reporter: tkluck | Owner: burcin
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.3
Component: symbolics | Resolution:
Keywords: needs-review | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Description changed by tkluck:
Old description:
> Plotting currently fails when plotting a symbolic function that evaluates
> to complex values:
>
> {{{
> sage: def evalf_func(self,x,parent):
> ....: return parent(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.
New description:
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.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13355#comment:2>
Sage <http://www.sagemath.org>
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