#8321: numerical integration with arbitrary precision
-------------------------+--------------------------------------------------
Reporter: burcin | Owner:
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.7.2
Component: symbolics | Keywords: numerics,integration
Work_issues: | Upstream: N/A
Reviewer: | Author: Stefan Reiterer
Merged: | Dependencies:
-------------------------+--------------------------------------------------
Comment(by benjaminfjones):
I tried making !TanhSinhRel the default and including the singleton
`__new__` code you gave. Here is the resulting class definition:
{{{
#!python
class TanhSinhRel(TanhSinh):
instance = None
def __new__(cls, *args, **kwds):
if not cls.instance:
cls.instance = super(TanhSinhRel, cls).__new__(cls, *args,
**kwds)
return cls.instance
def estimate_error(self, results, prec, epsilon):
mag = abs(results[-1])
if len(results) == 2:
return abs(results[0]-results[1]) / mag
try:
if results[-1] == results[-2] == results[-3]:
return self.ctx.zero
D1 = self.ctx.log(abs(results[-1]-results[-2])/mag, 10)
D2 = self.ctx.log(abs(results[-1]-results[-3])/mag, 10)
if D2 == 0:
D2 = self.ctx.inf
else:
D2 = self.ctx.one / D2
except ValueError:
return epsilon
D3 = -prec
D4 = min(0, max(D1**2 * D2, 2*D1, D3))
return self.ctx.mpf(10) ** int(D4)
}}}
I couldn't see a timing difference by adding that code to !TanhSinhRel
(but maybe this isn't the right place to add it?). Also, I get a
deprecation warning about arguments passed to `__new__`
Here are two tests in a row, one shows the deprecation warning, the second
doesn't:
{{{
sage: num_int_test_v2(e**(-x**2)*log(x), 17, 42)
GSL: 2.5657285007e-127 time:
0.0059130191803
mpmath: 2.59225286296247e-127 time:
0.0680160522461
/Users/jonesbe/sage/latest/local/bin/sage-ipython:66: DeprecationWarning:
object.__new__() takes no parameters
mpmath_rel_tanh (prec=64): 2.56572850056105156e-127 time:
0.310777187347
mpmath_rel_tanh (prec=100): 2.5657285005610514829173563973e-127 time:
0.541303157806
}}}
and again in the same session to check if timings have improved:
{{{
sage: num_int_test_v2(e**(-x**2)*log(x), 17, 42)
GSL: 2.5657285007e-127 time:
0.00131511688232
mpmath: 2.59225286296247e-127 time:
0.0299959182739
mpmath_rel_tanh (prec=64): 2.56572850056105156e-127 time:
0.211745023727
mpmath_rel_tanh (prec=100): 2.5657285005610514829173563973e-127 time:
0.513824939728
}}}
The timings do improve after the first call which includes
`method=TanhSinhRel`, but not dramatically. Am I missing something?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8321#comment:41>
Sage <http://www.sagemath.org>
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