#15082: speedup of k-Schur functions at t=1
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Reporter: zabrocki | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Mike Zabrocki | Reviewers: Anne Schilling
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by zabrocki:
Old description:
> This patch will implement two improvements to the k-Schur functions at
> t=1. The first is a change to `_to_schur_on_basis` and the second is a
> change to how the product is calculated. Both will improve the algorithm
> for doing these calculations by factoring out k-rectangles which are
> known to multiply by the rule `s_R*s^{(k)}_\lambda = s^{(k)}_{\lambda\cup
> R}`. Currently `_to_schur_on_basis` is computed by determining the
> tableau in the k-atom of a given shape. Factoring out maximal rectangles
> seems to reduce the computation by orders of magnitude for large
> examples.
>
> Before:
> {{{
> sage: Sym = SymmetricFunctions(QQ); ks3 = Sym.kschur(3,1); s = Sym.s()
> sage: timeit("s(ks3([3,3,3,2,2,1,1,1]))", number = 1, repeat = 1)
> 1 loops, best of 1: 7.43 s per loop
> }}}
>
> After:
> {{{
> sage: Sym = SymmetricFunctions(QQ); ks3 = Sym.kschur(3,1); s = Sym.s()
> sage: timeit("s(ks3([3,3,3,2,2,1,1,1]))", number = 1, repeat = 1)
> 1 loops, best of 1: 55.5 ms per loop
> }}}
New description:
This patch will implement two improvements to the k-Schur functions at
t=1. The first is a change to `_to_schur_on_basis` and the second is a
change to how the product is calculated. Both will improve the algorithm
for doing these calculations by factoring out k-rectangles which are known
to multiply by the rule `s_R*s^{(k)}_\lambda = s^{(k)}_{\lambda\cup R}`.
Currently `_to_schur_on_basis` is computed by determining the tableau in
the k-atom of a given shape. Factoring out maximal rectangles seems to
reduce the computation by orders of magnitude for large examples.
Before:
{{{
sage: Sym = SymmetricFunctions(QQ); ks3 = Sym.kschur(3,1); s = Sym.s()
sage: timeit("s(ks3([3,3,3,2,2,1,1,1]))", number = 1, repeat = 1)
1 loops, best of 1: 7.43 s per loop
}}}
After:
{{{
sage: Sym = SymmetricFunctions(QQ); ks3 = Sym.kschur(3,1); s = Sym.s()
sage: timeit("s(ks3([3,3,3,2,2,1,1,1]))", number = 1, repeat = 1)
1 loops, best of 1: 55.5 ms per loop
}}}
This will also add a `scalar` method to the element class of bases of the
k-bounded space.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/15082#comment:1>
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