pass algorithm argument to custom numeric evaluation methods

[burcin]

Custom numeric evaluation functions defined in the _evalf_() method of symbolic functions accept only the parent of the result as an argument. We should expand this to allow passing an algorithm parameter as well.

Merge together with dependencies (i.e. there are circular dependencies).

[burcin]

The evalf_dict branch of Pynac ​available here, with the attached patches applied to the Sage library, allows this:

sage: cot(1/2).n(algorithm='foo')
11.0000000000000
sage: cot(1/2).n()
1.83048772171245

The docstrings for _convert() etc. methods of symbolic expressions need to be updated to reflect these changes.

[benjaminfjones]

I'm doing some testing of these patches along with rebasing #1173. Thanks Burcin!

[benjaminfjones]

I'm trying to rebase the patch trac_12289-evalf_dictionary.patch​ to sage-5.0, but I'm running into a problem with the type of py_funcs.py_float. In the patch py_float has type object (*)(object, object) but in sage-5.0, it has type object (*)(object, PyObject *) I guess because of a pynac change in the meantime.

To be more specific, with this type def for py_float:

cdef public object py_float(object n, object kwds) except +:

I rebuild sage and get:

Error compiling Cython file:
------------------------------------------------------------
...
    py_funcs.py_is_prime = &py_is_prime

    py_funcs.py_integer_from_long = &py_integer_from_long
    py_funcs.py_integer_from_python_obj = &py_integer_from_python_obj
    
    py_funcs.py_float = &py_float
                       ^
------------------------------------------------------------

sage/symbolic/pynac.pyx:2040:24: Cannot assign type 'object (*)(object, object)' to 'object (*)(object, PyObject *)'

Any suggestions (burcin?)

[benjaminfjones]

rebase to sage-5.0 + pynac-0.2.4 spkg

[benjaminfjones]

fix py_float delcaration

[benjaminfjones]

I've been working on this ticket today at sd40.5. I've got burcin's changes working in sage-5.0 with a caveat. Here's how to get the example in comment:1 working in sage-5.0:

1. install the patched pynac-0.2.4.p1 spkg at ​http://sage.math.washington.edu/home/bjones/pynac-0.2.4.p1.spkg. this spkg is the pynac-0.2.4 spkg from #12950 which has been patched to include the changes from burcin's pynac-wip branch of pynac mentioned above.

2. apply all patches at #12950, here is a shell script to help that (run from $SAGE_ROOT/devel/sage): ​http://sage.math.washington.edu/home/bjones/trac_12950_apply.sh

3. apply the patches to $SAGE_ROOT/devel/sage
   • trac_12289-evalf_dictionary_rebase.patch​
   • trac_12289-add_algorithm_arg.patch​
   • trac_12289-example.patch​
   • trac_12289_py_float_fix.patch​ (fixes the problem I had in comment:4)

4. sage -b

[kcrisman]

Patchbot, though, should only apply trac_12289-evalf_dictionary_rebase.patch, trac_12289-add_algorithm_arg.patch, and trac_12289_py_float_fix.patch

[dsm]

So that we don't forget to fix it later:

sage: erf(1).n(algorithm='foo')
0.842700792949715
sage: erf(0)
0
sage: parent(erf(0))
Integer Ring
sage: erf(0).n(algorithm='foo')
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/Users/mcneil/sagedev/sage-5.1.beta0b/sage-5.1.beta0/devel/sage-hack2/sage/<ipython console> in <module>()

/Users/mcneil/sagedev/sage-5.1.beta0b/sage-5.1.beta0/local/lib/python2.7/site-packages/sage/structure/element.so in sage.structure.element.Element.numerical_approx (sage/structure/element.c:4988)()

TypeError: numerical_approx() got an unexpected keyword argument 'algorithm'

[kcrisman]

1. install the patched pynac-0.2.4.p1 spkg at ​http://sage.math.washington.edu/home/bjones/pynac-0.2.4.p1.spkg. this spkg is the pynac-0.2.4 spkg from #12950 which has been patched to include the changes from burcin's pynac-wip branch of pynac mentioned above.

Is this stuff in the current Pynac 0.2.6?

2. apply all patches at #12950, here is a shell script to help that (run from $SAGE_ROOT/devel/sage): ​http://sage.math.washington.edu/home/bjones/trac_12950_apply.sh

Can now be skipped, presumably.

3. apply the patches to $SAGE_ROOT/devel/sage
   • trac_12289-evalf_dictionary_rebase.patch​
   • trac_12289-add_algorithm_arg.patch​
   • trac_12289-example.patch​
   • trac_12289_py_float_fix.patch​ (fixes the problem I had in comment:4)

4. sage -b

[kcrisman]

Some of these patches have bitrotted slightly. Updates coming up.

[kcrisman]

Regarding Doug's comment on

erf(0).n(algorithm='foo')

Is this something we want to fix here? I'm not sure whether this is behavior that is supported with this patch, though perhaps it should be. I think that so far this is only putting in infrastructure, right? I don't see any doctests here, for instance.

[kcrisman]

Patchbot, apply trac_12289-evalf_dictionary_rebase.patch , trac_12289-add_algorithm-rebase.patch , and trac_12289-py_float-fix-rebase.patch

[kcrisman]

I think that we definitely need at least one example of how to do this if we aren't going to have any other documentation here.

[kcrisman]

We need to fix this.

----------------------------------------------------------------------
sage -t sage/symbolic/expression.pyx  # 3 doctests failed
sage -t sage/functions/other.py  # Killed due to segmentation fault
sage -t sage/functions/exp_integral.py  # 25 doctests failed
sage -t sage/functions/log.py  # 4 doctests failed
sage -t sage/symbolic/pynac.pyx  # 2 doctests failed
sage -t sage/symbolic/function.pyx  # 1 doctest failed
----------------------------------------------------------------------

But it does work!

[kcrisman]

Okay, Burcin figured out what he forgot here :) and most of the rest should be easily fixable.

[kcrisman]

Okay, everything fixed except a segfault on beta which is exactly the same one which ​this fixed. Burcin says that this needs to be handled properly and so

static ex beta_evalf(const ex & x, const ex & y, PyObject* parent)
{
        if (is_exactly_a<numeric>(x) && is_exactly_a<numeric>(y)) {
                try {
                        return exp(lgamma(ex_to<numeric>(x))+lgamma(ex_to<numeric>(y))-lgamma(ex_to<numeric>(x+y)));
                } catch (const dunno &e) { }
        }

        return beta(x,y).hold();
}

in ginac/inifcns_gamma.cpp needs to be worked on in addition to other stuff.

[kcrisman]

Patchbot, apply trac_12289-evalf_dictionary_rebase.patch , trac_12289-add_algorithm-rebase.patch, trac_12289-py_float-fix-rebase.patch, and trac_12289-more-alg.patch

[burcin]

New patches up. All doctests pass in sage/{symbolics,calculus}/.

[kcrisman]

So that we don't forget to fix it later:

sage: erf(1).n(algorithm='foo')
0.842700792949715
sage: erf(0)
0
sage: parent(erf(0))
Integer Ring
sage: erf(0).n(algorithm='foo')
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/Users/mcneil/sagedev/sage-5.1.beta0b/sage-5.1.beta0/devel/sage-hack2/sage/<ipython console> in <module>()

/Users/mcneil/sagedev/sage-5.1.beta0b/sage-5.1.beta0/local/lib/python2.7/site-packages/sage/structure/element.so in sage.structure.element.Element.numerical_approx (sage/structure/element.c:4988)()

TypeError: numerical_approx() got an unexpected keyword argument 'algorithm'

This is now #14778. Shouldn't impact this being merged.

By which to say, this passes all tests. The most recent fixes are fine. Burcin, what would need to be reviewed still?

[kcrisman]

This (or possibly a closely related patch) fails a doctest, actually. Sorry if this isn't the precise ticket.

sage -t sage/misc/sagedoc.py
**********************************************************************
File "sage/misc/sagedoc.py", line 22, in sage.misc.sagedoc
Failed example:
    for line in open(docfilename):
          if "#sage.symbolic.expression.Expression.N" in line:
              print line
Expected:
    <tt class="descname">N</tt><big>(</big><em>prec=None</em>, <em>digits=None</em><big>)</big>...
Got:
    <tt class="descname">N</tt><big>(</big><em>prec=None</em>, <em>digits=None</em>, <em>algorithm=None</em><big>)</big><a class="headerlink" href="#sage.symbolic.expression.Expression.N" title="Permalink to this definition">¶</a></dt>
    <BLANKLINE>
**********************************************************************
1 item had failures:
   1 of   3 in sage.misc.sagedoc
    [73 tests, 1 failure, 9.81 s]

Patchbot, apply trac_12289-evalf_dictionary_rebase.take2.patch , trac_12289-add_algorithm-rebase.patch , trac_12289-more-alg.patch trac_12289-last_touches.patch

[kcrisman]

Replying to kcrisman:

This (or possibly a closely related patch) fails a doctest, actually. Sorry if this isn't the precise ticket.

sage -t sage/misc/sagedoc.py
**********************************************************************
File "sage/misc/sagedoc.py", line 22, in sage.misc.sagedoc
Failed example:
    for line in open(docfilename):
          if "#sage.symbolic.expression.Expression.N" in line:
              print line
Expected:
    <tt class="descname">N</tt><big>(</big><em>prec=None</em>, <em>digits=None</em><big>)</big>...
Got:
    <tt class="descname">N</tt><big>(</big><em>prec=None</em>, <em>digits=None</em>, <em>algorithm=None</em><big>)</big><a class="headerlink" href="#sage.symbolic.expression.Expression.N" title="Permalink to this definition">¶</a></dt>
    <BLANKLINE>

Yeah, I'm pretty sure this would do it, because of

def _numerical_approx(self, prec=None, digits=None, algorithm=None): 

in the symbolic expression file.

[chapoton]

for the patchbots:

apply trac_12289-evalf_dictionary_rebase.take2.patch trac_12289-add_algorithm-rebase.patch trac_12289-more-alg.patch trac_12289-last_touches.patch

[burcin]

This ticket depends on an SPKG update. The patchbot cannot handle those ATM.

IIRC, the pynac update is complete and waiting for review. See #15198 for details.

[jpflori]

New commits:

​5aa39ce	Use dictionary for custom numerical evaluation.
​d86cef5	Add algorithm keyword to custom numerical evaluation.
​e08b282	Add missing algorithm keywords for custom numerical evaluation.
​008a54f	Fix random issues caused by _evalf_ convention change.
​5d1fd33	Fix rebasing error.

[git]

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

​b658858

Proper fix for the rebasing issue.

[git]

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

​da159a0

Add missing fix for algorithm keyword for custom numerical evaluation.

[jpflori]

I just rebased the old patches and fixed an additional missing new keyword. I'm happy with the changes. There is still the blankline issue of comment:29.

[git]

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

​ef6d2de

Fix documentation for numerical_approximation.

[jpflori]

In fact the doctest was expected to change... so needs review for the two basic changes I made. What was done before was already reviewed and I'm happy in case it was not.

---

New commits:

​ef6d2de

Fix documentation for numerical_approximation.

[kcrisman]

I can't do actual testing now (or any time soon, I've really fallen off the development radar screen) but these minor changes in the last two commits are completely fine as long as the doc change fixes the problem. Hopefully we'll actually start implementing some of these algorithms now...

[jpflori]

Testing will be done automatically by the patchbots, so I'll take your comment as positive review.

[jdemeyer]

Is there any particular reason that this was done for _evalf_ and not also plain _eval_?