#6229: [with patch, positive review] efficiency in Lagrange polynomial
interpolation (easy fix...)
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Reporter: ylchapuy | Owner: tbd
Type: defect | Status: new
Priority: minor | Milestone: sage-4.0.1
Component: algebra | Keywords:
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Comment(by mvngu):
The patch contains the suggested fix by ylchapuy. It's ylchapuy's code,
not mine, so authorship credit goes to ylchapuy. I'm just reviewing the
code. Here are some timing statistics on sage.math:
{{{
# BEFORE
sage: R = PolynomialRing(QQ, 'x')
sage: %timeit R.lagrange_polynomial([(0,1),(2,2),(3,-2),(-4,9)])
1000 loops, best of 3: 830 µs per loop
sage: R.lagrange_polynomial([(0,1),(2,2),(3,-2),(-4,9)])
-23/84*x^3 - 11/84*x^2 + 13/7*x + 1
sage: R = PolynomialRing(GF(2**3,'a'), 'x')
sage: a = R.base_ring().gen()
sage: timeit("R.lagrange_polynomial([(a^2+a,a),(a,1),(a^2,a^2+a+1)])")
625 loops, best of 3: 112 µs per loop
sage: R.lagrange_polynomial([(a^2+a,a),(a,1),(a^2,a^2+a+1)])
a^2*x^2 + a^2*x + a^2
# AFTER
sage: R = PolynomialRing(QQ, 'x')
sage: %timeit R.lagrange_polynomial([(0,1),(2,2),(3,-2),(-4,9)])
1000 loops, best of 3: 416 µs per loop
sage: R.lagrange_polynomial([(0,1),(2,2),(3,-2),(-4,9)])
-23/84*x^3 - 11/84*x^2 + 13/7*x + 1
sage: R = PolynomialRing(GF(2**3,'a'), 'x')
sage: a = R.base_ring().gen()
sage: timeit("R.lagrange_polynomial([(a^2+a,a),(a,1),(a^2,a^2+a+1)])")
625 loops, best of 3: 86.2 µs per loop
sage: R.lagrange_polynomial([(a^2+a,a),(a,1),(a^2,a^2+a+1)])
a^2*x^2 + a^2*x + a^2
}}}
So efficiency gain of up to 50%. Positive review.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6229#comment:4>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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