Opened 12 years ago
Last modified 5 years ago
#9888 new defect
matrix multiplication over integer mod ring is slow
Reported by: | dmharvey | Owned by: | tbd |
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Priority: | major | Milestone: | |
Component: | performance | Keywords: | sd90 |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Sage 4.5.3, 2.6GHz Opteron, Linux
This is ok:
sage: M1 = Matrix([[randrange(3^20) for i in range(100)] for j in range(100)]) sage: M2 = Matrix([[randrange(3^20) for i in range(100)] for j in range(100)]) sage: timeit("M3 = M1 * M2") 5 loops, best of 3: 45.6 ms per loop
(That's about 4 times slower than Magma, but I can put up with that, that's a ticket for another day.)
Here is the problem:
sage: R = Integers(3^20) sage: M1 = Matrix([[R.random_element() for i in range(100)] for j in range(100)]) sage: M2 = Matrix([[R.random_element() for i in range(100)] for j in range(100)]) sage: timeit("M3 = M1 * M2") 5 loops, best of 3: 877 ms per loop
In other words, I can multiply the matrices over R roughly 20x faster by multiplying over Z and then reducing! That's ridiculous!
Change History (5)
comment:1 Changed 12 years ago by
comment:2 Changed 7 years ago by
I just tried the timings again:
sage: sage: M1 = Matrix([[randrange(3^20) for i in range(100)] for j in range(100)]) sage: sage: M2 = Matrix([[randrange(3^20) for i in range(100)] for j in range(100)]) sage: sage: timeit("M3 = M1 * M2") 125 loops, best of 3: 5.62 ms per loop sage: sage: R = Integers(3^20) sage: sage: M1 = Matrix([[R.random_element() for i in range(100)] for j in range(100)]) sage: sage: M2 = Matrix([[R.random_element() for i in range(100)] for j in range(100)]) sage: sage: timeit("M3 = M1 * M2") 5 loops, best of 3: 530 ms per loop
so now the discrepancy is up to a factor of 100!
My recollection is that lifting the multiplication up to Z is in fact the correct algorithmic approach. In practice, this hands the problem off to FLINT, where (in this size range) the multiplication is done multimodular.
comment:4 Changed 5 years ago by
Keywords: | sd90 added |
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comment:5 Changed 5 years ago by
There appears to be special-purpose code using Linbox for modulus up to 2^{23} in sage/matrix/matrix_modn_dense_double.pyx
and sage/matrix/matrix_modn_dense_float.pyx
. To handle this issue, it would be best to create a file sage/matrix/matrix_modn_dense.pyx
in which we create the class Matrix_modn_dense
with a special _mul_
method. But we should make sure not to create a regression by disconnecting the existing code for smaller moduli.
I don't think anything has gone into non-word-sized modulus, so this is probably using totally generic per-element wrapping code :(. Should be an easy fix to get better than this, doing something real would be a bit more work.