Opened 6 years ago
Closed 6 years ago
#18660 closed task (fixed)
Improve efficiency of minors() for BinaryMatroid, TernaryMatroid, QuaternaryMatroid
Reported by:  Rudi  Owned by:  Rudi 

Priority:  major  Milestone:  sage6.8 
Component:  matroid theory  Keywords:  
Cc:  chaoxu, Stefan, yomcat  Merged in:  
Authors:  Rudi Pendavingh  Reviewers:  Travis Scrimshaw 
Report Upstream:  N/A  Work issues:  
Branch:  a5fd2f5 (Commits, GitHub, GitLab)  Commit:  a5fd2f59b7ad6a827e358bc294f560c6ad6309a8 
Dependencies:  Stopgaps: 
Description
The representing matrices of BinaryMatroid?, TernaryMatroid?, QuaternaryMatroid?, are bitpacket. Taking minors, involves constructing a submatrix of such a representing matrix. Since the rows are bitpacked, the relocation of columns in particular is relatively inefficient.
By allowing a submatrix in which the columns are allowed to be permuted, it is possible to reduce the number of column relocations to at most the number of deleted columns, and this will be far more efficient than the current implementation, especially if few columns are deleted.
Change History (12)
comment:1 Changed 6 years ago by
comment:2 Changed 6 years ago by
 Branch set to u/Rudi/improve_efficiency_of_minors___for_binarymatroid__ternarymatroid__quaternarymatroid
comment:3 Changed 6 years ago by
 Commit set to 7deb135d390d4a83ab1fff1742c0015b5b5194ef
First worked on BinaryMatroid? and BinaryMatrix?. The new code seems to be correct:
sage: N = Matroid(MatrixSpace(GF(2), 5,12).random_element()) sage: for X in subsets(N.groundset()): if not BasisMatroid(N\X).equals(BasisMatroid(N)\X): print X
It's more efficient too. Without the patch:
sage: M = Matroid(MatrixSpace(GF(2), 500,1000).random_element()) sage: B = M.basis() sage: timeit("for e in B: M.delete(M._fundamental_cocircuit(B,e))") 5 loops, best of 3: 3.69 s per loop
With the patch:
sage: M = Matroid(MatrixSpace(GF(2), 500,1000).random_element()) sage: B = M.basis() sage: timeit("for e in B: M.delete(M._fundamental_cocircuit(B,e))") 5 loops, best of 3: 692 ms per loop
So, about 5 times faster on this example. This is not all due to the trick announced in the ticket. Replacing a list by a cstyle array here and there did some good too. And just replacing the line
C = [c for c in range(len(self._E)) if self._E[c] not in deletions  contractions]
in _minor
by something that does not compute the union deletions  contractions
for each c made the code 2 times faster right there.
New commits:
7deb135  Added new method for taking submatrix of a BinaryMatrix, used in BinaryMatroid._minor()

comment:4 Changed 6 years ago by
 Commit changed from 7deb135d390d4a83ab1fff1742c0015b5b5194ef to 3ea8ac5263fdc6d4a6fe9c5699fcfdf1942ade61
Branch pushed to git repo; I updated commit sha1. New commits:
3ea8ac5  Improved Ternary and Quaternary along the same lines

comment:5 Changed 6 years ago by
Correctness:
sage: N = Matroid(MatrixSpace(GF(2), 5,10).random_element()) sage: for X in subsets(N.groundset()): for Y in subsets(N.groundset()set(X)): if not BasisMatroid(N.minor(X,Y)).equals(BasisMatroid(N).minor(X,Y)): print X,Y ....: sage: N = Matroid(MatrixSpace(GF(3), 5,10).random_element()) sage: for X in subsets(N.groundset()): for Y in subsets(N.groundset()set(X)): if not BasisMatroid(N.minor(X,Y)).equals(BasisMatroid(N).minor(X,Y)): print X,Y ....: sage: N = Matroid(MatrixSpace(GF(4,x), 5,10).random_element()) sage: for X in subsets(N.groundset()): for Y in subsets(N.groundset()set(X)): if not BasisMatroid(N.minor(X,Y)).equals(BasisMatroid(N).minor(X,Y)): print X,Y
Efficiency before patch:
sage: M = Matroid(MatrixSpace(GF(2), 200,400).random_element()) sage: B = M.basis() sage: timeit("for e in B: M.delete(M._fundamental_cocircuit(B,e))") 5 loops, best of 3: 261 ms per loop sage: M = Matroid(MatrixSpace(GF(3), 200,400).random_element()) sage: B = M.basis() sage: timeit("for e in B: M.delete(M._fundamental_cocircuit(B,e))") 5 loops, best of 3: 7.13 s per loop sage: M = Matroid(MatrixSpace(GF(4,x), 200,400).random_element()) sage: B = M.basis() sage: timeit("for e in B: M.delete(M._fundamental_cocircuit(B,e))") 5 loops, best of 3: 3.95 s per loop
Efficiency after patch:
sage: M = Matroid(MatrixSpace(GF(2), 200,400).random_element()) sage: B = M.basis() sage: timeit("for e in B: M.delete(M._fundamental_cocircuit(B,e))") 5 loops, best of 3: 73.7 ms per loop sage: M = Matroid(MatrixSpace(GF(3), 200,400).random_element()) sage: B = M.basis() sage: timeit("for e in B: M.delete(M._fundamental_cocircuit(B,e))") 5 loops, best of 3: 86.7 ms per loop sage: M = Matroid(MatrixSpace(GF(4,x), 200,400).random_element()) sage: B = M.basis() sage: timeit("for e in B: M.delete(M._fundamental_cocircuit(B,e))") 5 loops, best of 3: 86.4 ms per loop
For TernaryMatrix? and QuaternaryMatrix?, there was no optimized submatrixcode to begin with, hence the 40  80 times speedup. I scaled down the size of the matrix a bit, the ternary benchmark simply wouldn't finish for 500x1000.
I will remove some lingering cython profile directives, and then I'm done.
comment:6 Changed 6 years ago by
 Commit changed from 3ea8ac5263fdc6d4a6fe9c5699fcfdf1942ade61 to 20dc896a4ca85804d161fe6d74577949efc372f4
Branch pushed to git repo; I updated commit sha1. New commits:
20dc896  Cleaned up profiler directives

comment:7 Changed 6 years ago by
 Status changed from new to needs_review
comment:8 Changed 6 years ago by
 Commit changed from 20dc896a4ca85804d161fe6d74577949efc372f4 to a5fd2f59b7ad6a827e358bc294f560c6ad6309a8
Branch pushed to git repo; I updated commit sha1. New commits:
a5fd2f5  removed trailing whitespace

comment:9 Changed 6 years ago by
 Cc yomcat added
Before:
sage: M = Matroid(MatrixSpace(GF(3), 500,1000).random_element()) sage: timeit("M.delete([0])") 5 loops, best of 3: 333 ms per loop
After:
sage: M = Matroid(MatrixSpace(GF(3), 500,1000).random_element()) sage: timeit("M.delete([0])") 625 loops, best of 3: 655 µs per loop
comment:10 followup: ↓ 11 Changed 6 years ago by
 Reviewers set to Travis Scrimshaw
LGTM. I'm slightly unhappy with the fact that it looks like a lot of logic is duplicated across the multiple matrix_from_rows_and_columns_reordered
, but I don't see a way to really combine the common logic. So positive review.
comment:11 in reply to: ↑ 10 Changed 6 years ago by
 Status changed from needs_review to positive_review
Replying to tscrim:
LGTM. I'm slightly unhappy with the fact that it looks like a lot of logic is duplicated across the multiple
matrix_from_rows_and_columns_reordered
, but I don't see a way to really combine the common logic. So positive review.
Thanks for the review.
comment:12 Changed 6 years ago by
 Branch changed from u/Rudi/improve_efficiency_of_minors___for_binarymatroid__ternarymatroid__quaternarymatroid to a5fd2f59b7ad6a827e358bc294f560c6ad6309a8
 Resolution set to fixed
 Status changed from positive_review to closed
Still need to try this out. Hope to do this this week.
Since a cocircuit of a binary matroid M is typically going to have size about
r^*(M) /2
elements, I expect a speedup by a factor of up tor^*(M)/2/E(M)
for the minortaking in Chao's code in ticket #18539.