#10709: speed up matrix actions on Manin symbols
-----------------------------+----------------------------------------------
Reporter: AlexGhitza | Owner: craigcitro
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.7
Component: modular forms | Keywords: manin symbol binomial
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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The patch (basically written by William at #8614) speeds up these actions
by changing the way the binomial coefficients are obtained.
Some timings (the weight seems to be the important parameter here):
BEFORE THE PATCH:
{{{
sage: from sage.modular.modsym.manin_symbols import ManinSymbolList_gamma0
sage: m = ManinSymbolList_gamma0(5, 8)
sage: timeit("n = m.apply_T(4)")
625 loops, best of 3: 132 µs per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 26 µs per loop
sage: m = ManinSymbolList_gamma0(5, 30)
sage: timeit("n = m.apply_T(4)")
625 loops, best of 3: 541 µs per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 25.8 µs per loop
sage: m = ManinSymbolList_gamma0(5, 100)
sage: timeit("n = m.apply_T(4)")
125 loops, best of 3: 1.92 ms per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 25.8 µs per loop
sage: eps = DirichletGroup(4).gen(0)
sage: from sage.modular.modsym.manin_symbols import
ManinSymbolList_character
sage: m = ManinSymbolList_character(eps, 2)
sage: timeit("n = m.apply_T(4)")
625 loops, best of 3: 141 µs per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 103 µs per loop
sage: m = ManinSymbolList_character(eps, 30)
sage: timeit("n = m.apply_T(4)")
125 loops, best of 3: 2.75 ms per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 105 µs per loop
sage: m = ManinSymbolList_character(eps, 100)
sage: timeit("n = m.apply_T(4)")
25 loops, best of 3: 9.35 ms per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 103 µs per loop
}}}
AFTER THE PATCH:
{{{
sage: from sage.modular.modsym.manin_symbols import ManinSymbolList_gamma0
sage: m = ManinSymbolList_gamma0(5, 8)
sage: timeit("n = m.apply_T(4)")
625 loops, best of 3: 21.6 µs per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 13.8 µs per loop
sage: m = ManinSymbolList_gamma0(5, 30)
sage: timeit("n = m.apply_T(4)")
625 loops, best of 3: 74.4 µs per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 13.7 µs per loop
sage: m = ManinSymbolList_gamma0(5, 100)
sage: timeit("n = m.apply_T(4)")
625 loops, best of 3: 297 µs per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 13.8 µs per loop
sage: eps = DirichletGroup(4).gen(0)
sage: from sage.modular.modsym.manin_symbols import
ManinSymbolList_character
sage: m = ManinSymbolList_character(eps, 2)
sage: timeit("n = m.apply_T(4)")
625 loops, best of 3: 126 µs per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 90.5 µs per loop
sage: m = ManinSymbolList_character(eps, 30)
sage: timeit("n = m.apply_T(4)")
125 loops, best of 3: 2.26 ms per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 91.3 µs per loop
sage: m = ManinSymbolList_character(eps, 100)
sage: timeit("n = m.apply_T(4)")
125 loops, best of 3: 7.7 ms per loop
sage: timeit("n = m.apply_TT(4)")
625 loops, best of 3: 90.6 µs per loop
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10709>
Sage <http://www.sagemath.org>
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