def _sollya_annotate(self, center, rad, polys):
import sagesollya as sollya
logger = logging.getLogger(__name__ + ".sollya")
logger.info("calling annotatefunction() on %s derivatives", len(polys))
center = QQ(center)
sollya_fun = self._sollya_object
# sollya keeps all annotations, let's not bother with selecting
# the best one
for ord, pol0 in enumerate(polys):
pol = ZZ(ord).factorial() * pol0
sollya_pol = sum(
[c.center() * sollya.x**k for k, c in enumerate(pol)])
dom = RIF(center - rad,
center + rad) # XXX: dangerous when inexact
err_pol = pol.map_coefficients(lambda c: c - c.squash())
err = RIF(err_pol(RBF.zero().add_error(rad)))
with sollya.settings(display=sollya.dyadic):
logger = logging.getLogger(__name__ + ".sollya.annotate")
logger.debug("annotatefunction(%s, %s, %s, %s, %s);",
sollya_fun, sollya_pol, sollya.SollyaObject(dom),
sollya.SollyaObject(err),
sollya.SollyaObject(center))
sollya.annotatefunction(sollya_fun, sollya_pol, dom, err, center)
sollya_fun = sollya.diff(sollya_fun)
logger.info("...done")
def _sollya_(self):
r"""
EXAMPLES::
sage: import logging; logging.basicConfig(level=logging.INFO)
sage: logger = logging.getLogger("ore_algebra.analytic.function.sollya")
sage: logger.setLevel(logging.DEBUG)
sage: import ore_algebra
sage: DiffOps, x, Dx = ore_algebra.DifferentialOperators()
sage: from ore_algebra.analytic.function import DFiniteFunction
sage: f = DFiniteFunction(Dx - 1, [1])
sage: import sagesollya as sollya # optional - sollya
sage: sollya.plot(f, sollya.Interval(0, 1)) # not tested
...
"""
if self._sollya_object is not None:
return self._sollya_object
import sagesollya as sollya
logger = logging.getLogger(__name__ + ".sollya.eval")
Dx = self.dop.parent().gen()
def wrapper(pt, ord, prec):
if RBF(pt.diameter()) >= self.max_rad / 4:
return self._known_bound(RBF(pt), post_transform=Dx**ord)
try:
val = self.approx(pt, prec, post_transform=Dx**ord)
except Exception:
logger.info("pt=%s, ord=%s, prec=%s, error",
pt,
ord,
prec,
exc_info=(pt.absolute_diameter() < .5))
return RIF('nan')
logger.debug("pt=%s, ord=%s, prec=%s, val=%s", pt, ord, prec, val)
if not pt.overlaps(self._sollya_domain):
backtrace = sollya.getbacktrace()
logger.debug("%s not in %s", pt.str(style='brackets'),
self._sollya_domain.str(style='brackets'))
logger.debug("sollya backtrace: %s", [
sollya.objectname(t.struct.called_proc) for t in backtrace
])
return val
wrapper.__name__ = self.name
self._sollya_object = sollya.sagefunction(wrapper)
for pt, ini in self.ini.iteritems():
pt = RIF(pt)
if pt.is_exact():
fun = self._sollya_object
for ord, val in enumerate(ini):
try:
sollya.annotatefunction(fun, val, pt, RIF.zero())
except TypeError:
logger.info("annotation failed: D^%s(%s)(%s) = %s",
ord, self.name, pt, val)
fun = sollya.diff(fun)
self._update_approx_hook = self._sollya_annotate
return self._sollya_object