#5557: [with patch, needs review] implement ridiculously fast 4x4 determinant
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Reporter: boothby | Owner: was
Type: enhancement | Status: new
Priority: minor | Milestone: sage-3.4.1
Component: linear algebra | Keywords:
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Comment(by was):
How fast is it on smaller input? Using PARI more efficiently I was able
to get the following timings (in my branch of Sage):
{{{
sage: M = S.random_element(1,10^8)
sage: timeit('M.det();M._clear_cache()')
625 loops, best of 3: 14.9 µs per loop
sage: M = S.random_element(1,10^10)
sage: timeit('M.det();M._clear_cache()')
625 loops, best of 3: 16.3 µs per loop
}}}
Things slow down for bigger input though:
{{{
sage: M = S.random_element(1,10^200)
sage: timeit('M.det();M._clear_cache()')
625 loops, best of 3: 104 µs per loop
sage: M = S.random_element(1,10^300)
sage: timeit('M.det();M._clear_cache()')
625 loops, best of 3: 186 µs per loop
sage: M = S.random_element(1,10^1000)
sage: timeit('M.det();M._clear_cache()')
625 loops, best of 3: 1.2 ms per loop
}}}
The above is on OS X 32-bit core2duo 2.6Ghz.
William
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5557#comment:5>
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