Opened 11 months ago
Last modified 11 months ago
#30946 closed enhancement
Add "minimal=True" option to affine_hull_projection — at Version 8
Reported by:  jipilab  Owned by:  

Priority:  major  Milestone:  sage9.3 
Component:  geometry  Keywords:  affine_hull, polytope 
Cc:  ghkliem  Merged in:  
Authors:  JeanPhilippe Labbé  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  u/jipilab/min_affhull (Commits, GitHub, GitLab)  Commit:  529865b7e027d0977ca63c3d98038817138d70bb 
Dependencies:  Stopgaps: 
Description (last modified by )
Currently, the computation of the affine_hull_projection
is done by default in AA
which is not optimal sometimes.
Currently:
sage: A=[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1],[1/4,1/4,1/4,1/4]] sage: n=len(A) sage: A=[vector(v) for v in A] sage: AP = Polyhedron(vertices=A) sage: M,b=AP.affine_hull_projection(orthonormal=True,extend=True,as_affine_map=True) sage: V=[] ....: for i in range(n): ....: for j in range(i+1,n): ....: V.append((A[i]A[j])/2) sage: Z=polytopes.zonotope(V) sage: T = M.matrix().transpose() sage: timeit('T*Z') 5 loops, best of 3: 78.5 ms per loop
With this ticket:
sage: A=[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1],[1/4,1/4,1/4,1/4]] sage: n=len(A) sage: A=[vector(v) for v in A] sage: AP = Polyhedron(vertices=A) sage: M,b=AP.affine_hull_projection(orthonormal=True,extend=True,as_affine_map=True,minimal=True) sage: V=[] ....: for i in range(n): ....: for j in range(i+1,n): ....: V.append((A[i]A[j])/2) sage: Z=polytopes.zonotope(V) sage: T = M.matrix().transpose() sage: timeit('T*Z') 25 loops, best of 3: 18 ms per loop
The idea behind this ticket is that applying T
(the matrix transforming AP
is applied to a different polytope Z
, so it might pay off to make T
minimal so that for a large Z
the computation of the transformation is not slowed by operations in AA
.
Change History (8)
comment:1 Changed 11 months ago by
 Status changed from new to needs_review
comment:2 Changed 11 months ago by
 Description modified (diff)
comment:3 Changed 11 months ago by
comment:4 followup: ↓ 7 Changed 11 months ago by
Apparently it is at least better asymptotically.
sage: P = polytopes.permutahedron(5) sage: %timeit P.affine_hull_projection(orthonormal=True,extend=True) 78.9 ms ± 216 µs per loop (mean ± std. dev. of 7 runs, 10 loops each) sage: %timeit P.affine_hull_projection(orthonormal=True,extend=True,minimal=True) 119 ms ± 362 µs per loop (mean ± std. dev. of 7 runs, 10 loops each) sage: P = polytopes.permutahedron(6) sage: %timeit P.affine_hull_projection(orthonormal=True,extend=True) 334 ms ± 2.84 ms per loop (mean ± std. dev. of 7 runs, 1 loop each) sage: %timeit P.affine_hull_projection(orthonormal=True,extend=True,minimal=True) 276 ms ± 1.68 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
comment:5 Changed 11 months ago by
 Commit changed from ff5aebf80861db9ddb6a88d3c457e6217b5ef8bd to 529865b7e027d0977ca63c3d98038817138d70bb
Branch pushed to git repo; I updated commit sha1. New commits:
529865b  Added Example

comment:6 Changed 11 months ago by
... forgot to add an example. ;)
comment:7 in reply to: ↑ 4 Changed 11 months ago by
Replying to ghkliem:
Apparently it is at least better asymptotically.
sage: P = polytopes.permutahedron(5) sage: %timeit P.affine_hull_projection(orthonormal=True,extend=True) 78.9 ms ± 216 µs per loop (mean ± std. dev. of 7 runs, 10 loops each) sage: %timeit P.affine_hull_projection(orthonormal=True,extend=True,minimal=True) 119 ms ± 362 µs per loop (mean ± std. dev. of 7 runs, 10 loops each) sage: P = polytopes.permutahedron(6) sage: %timeit P.affine_hull_projection(orthonormal=True,extend=True) 334 ms ± 2.84 ms per loop (mean ± std. dev. of 7 runs, 1 loop each) sage: %timeit P.affine_hull_projection(orthonormal=True,extend=True,minimal=True) 276 ms ± 1.68 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
Yes, I am outsourcing of course. The point is of course to apply the matrix to other potential polytopes as it was the idea behind the problem that led to this ticket.
Further, it is an "unfair" comparison, since minimal=True
does more, since it really computes the minimal polynomial (which is not done for polytopes if I am not mistaken, you might disagree here, it has been a while).
But cool that it seems to be a bit faster for larger stuff. :)
comment:8 Changed 11 months ago by
 Description modified (diff)
Looks like you just outsourced the labor. But maybe in larger examples this pays of.