#1173: implement numerical evaluation of erf at complex arguments
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Reporter: was |
Owner: was
Type: enhancement |
Status: needs_work
Priority: major |
Milestone: sage-4.7.2
Component: calculus |
Keywords:
Work_issues: add erf(sqrt(2)) and erf(45000).n(), formatting, speed |
Upstream: N/A
Reviewer: Burcin Erocal |
Author: D. S. McNeil
Merged: |
Dependencies: #11513
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Comment(by dsm):
Okay, this looks a bit better. With trac_1173-move_call.patch,
trac_11885_v2.patch, trac_11513-is_numerically_zero.patch, and
trac_1173_complex_erf_v3.patch:
{{{
alpha3:
0.100000000000000 float 121 µs per loop
0.100000000000000 RDF 51.6 µs per loop
0.100000000000000 RR 61.2 µs per loop
0.100000000000000 RealField(100) 64.5 µs per loop
0.100000000000000 RealField(1000) 304 µs per loop
new:
0.100000000000000 float 49.3 µs per loop
0.100000000000000 RDF 773 ns per loop
0.100000000000000 RR 7.07 µs per loop
0.100000000000000 RealField(100) 10.6 µs per loop
0.100000000000000 RealField(1000) 248 µs per loop
0.100000000000000 complex 131 µs per loop
0.100000000000000 CDF 185 µs per loop
0.100000000000000 CC 254 µs per loop
0.100000000000000 ComplexField(100) 262 µs per loop
0.100000000000000 ComplexField(1000) 470 µs per loop
0.100000000000000*I complex 247 µs per loop
0.100000000000000*I CDF 389 µs per loop
0.100000000000000*I CC 405 µs per loop
0.100000000000000*I ComplexField(100) 470 µs per loop
0.100000000000000*I ComplexField(1000) 565 µs per loop
}}}
Now not only is there no regression, we've improved. The speedups
relative to alpha3 for reals are due to using the existing mpfr .erf()s
instead of pari; float was special-cased through RDF. As I mentioned, I
don't have the new pari, and that's probably faster than mpmath. But at
least it's not killing me anymore.
There's a doctest failure in gamma_inc due to trac_1173-move_call.patch, I
think-- formerly,
{{{
sage: parent(gamma_inc(RDF(1),3))
Complex Field with 53 bits of precision
}}}
but now
{{{
sage: parent(gamma_inc(RDF(1),3))
Real Double Field
}}}
but gamma_inc doesn't preserve types the way I'd have expected. Anyway, I
think this is a step in the right direction.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1173#comment:28>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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