#3498: [with patch, needs review] make numpy the backend for matrices over CDF
and
RDF
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Reporter: jason | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.1.3
Component: linear algebra | Resolution:
Keywords: |
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Comment (by jason):
Some more timings from respectably-sized matrices show that numpy is
indeed way faster most of the time and neck-and-neck the rest of the time.
The GSL determinant speed below is most likely from from caching the LU
decomposition that had been computed for something before and using that
to compute the determinant.
Before patch
{{{
sage: # Before patches: GSL
sage: m=random_matrix(RDF,500,min=-2^32,max=2^32)
sage: timeit('m+m')
125 loops, best of 3: 7.2 ms per loop
sage: timeit('m*m')
5 loops, best of 3: 90.6 ms per loop
sage: timeit('~m')
5 loops, best of 3: 639 ms per loop
sage: timeit('m.det()')
625 loops, best of 3: 19.1 µs per loop
sage: timeit('m.transpose()')
125 loops, best of 3: 5.76 ms per loop
sage: timeit('m.LU()')
5 loops, best of 3: 97.6 ms per loop
sage: %time m.SVD()
CPU times: user 8.26 s, sys: 0.09 s, total: 8.35 s
Wall time: 9.16 s
(500 x 500 dense matrix over Real Double Field,
500 x 500 dense matrix over Real Double Field,
500 x 500 dense matrix over Real Double Field)
sage: %time m.QR()
CPU times: user 2.37 s, sys: 0.05 s, total: 2.42 s
Wall time: 2.68 s
(500 x 500 dense matrix over Real Double Field,
500 x 500 dense matrix over Real Double Field)
sage: b=vector(RDF,range(500))
sage: timeit('m.solve_left(b)')
5 loops, best of 3: 72 ms per loop
sage: %time a=m.eigenspaces()
CPU times: user 26.61 s, sys: 0.42 s, total: 27.03 s
Wall time: 30.09 s
}}}
After patches
{{{
sage: # After patches: numpy
sage: m=random_matrix(RDF,500,min=-2^32,max=2^32)
sage: timeit('m+m')
125 loops, best of 3: 2.78 ms per loop
sage: timeit('m*m')
5 loops, best of 3: 89.2 ms per loop
sage: timeit('~m')
5 loops, best of 3: 224 ms per loop
sage: timeit('m.det()')
5 loops, best of 3: 62 ms per loop
sage: timeit('m.transpose()')
625 loops, best of 3: 32.9 µs per loop
sage: timeit('m.LU()')
5 loops, best of 3: 15.1 ms per loop
sage: timeit('m.SVD()')
5 loops, best of 3: 1.42 s per loop
sage: %time m.SVD()
CPU times: user 1.19 s, sys: 0.06 s, total: 1.25 s
Wall time: 1.42 s
(500 x 500 dense matrix over Real Double Field,
500 x 500 dense matrix over Real Double Field,
500 x 500 dense matrix over Real Double Field)
sage: %time m.QR()
CPU times: user 0.26 s, sys: 0.03 s, total: 0.28 s
Wall time: 0.32 s
(500 x 500 dense matrix over Real Double Field,
500 x 500 dense matrix over Real Double Field)
sage: b=vector(RDF,range(500))
sage: timeit('m.solve_left(b)')
5 loops, best of 3: 68.6 ms per loop
sage: %time a=m.eigenspaces()
CPU times: user 27.52 s, sys: 0.31 s, total: 27.83 s
Wall time: 30.00 s
sage:
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3498#comment:9>
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