very slow matrix product

[sagetrac-pang]

The following code takes a very long time in Sage 4.4 up to and including 4.6:

sage: var('t')
sage: curva = vector((sin(2*t), cos(2*t), 0))
sage: M = identity_matrix(RDF,3)
sage: time M*curva
CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s
Wall time: 0.50 s
(sin(2*t), cos(2*t), 0)

The times depend on the computer, and decrease on the second call, but it is consistently, and significatively longer than the time required for:

sage: time sum(a*b for a,b in zip(curva,M.rows()))
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
(sin(2*t), cos(2*t), 0) 

The first call is forwarded, I think to maxima. The waiting time is probably due to waiting for the maxima process. Profile revealed that most of the time was spent on "select.select".

Component: performance

Issue created by migration from https://trac.sagemath.org/ticket/10947

[mezzarobba]

comment:1

Still true in 6.1:

sage: sage: var('t')
t
sage: sage: curva = vector((sin(2*t), cos(2*t), 0))
sage: sage: M = identity_matrix(RDF,3)
sage: %time M*curva
CPU times: user 0.72 s, sys: 0.02 s, total: 0.74 s
Wall time: 0.74 s
(sin(2*t), cos(2*t), 0)
sage: %timeit M*curva
100 loops, best of 3: 3.69 ms per loop
sage: 
sage: %time sum(a*b for a,b in zip(curva,M.rows()))
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
(sin(2*t), cos(2*t), 0)
sage: %timeit sum(a*b for a,b in zip(curva,M.rows()))
1000 loops, best of 3: 279 us per loop

[a-andre]

comment:2

sage: var('t')
sage: curva = vector((sin(2*t), cos(2*t), 0))
sage: M = identity_matrix(RDF,3)
sage: %timeit M*curva
1000 loops, best of 3: 478 µs per loop
sage: %timeit sum(a*b for a,b in zip(curva,M.rows()))
1000 loops, best of 3: 321 µs per loop

after a restart of sage:

sage: var('t')
sage: curva = vector((sin(2*t), cos(2*t), 0))
sage: M = identity_matrix(RDF,3)
sage: %time M*curva
CPU times: user 6.67 ms, sys: 0 ns, total: 6.67 ms
Wall time: 4.67 ms
(sin(2*t), cos(2*t), 0)
sage: %time sum(a*b for a,b in zip(curva,M.rows()))
CPU times: user 3.33 ms, sys: 0 ns, total: 3.33 ms
Wall time: 3.77 ms
(sin(2*t), cos(2*t), 0)

So no significant difference here. Maybe because of an SSD.

[mezzarobba]

comment:3

Yes, this now appears to work for me as well.