Opened 14 months ago
Last modified 5 weeks ago
#29169 needs_review enhancement
Maximal and critical angles for cones
Reported by:  mjo  Owned by:  

Priority:  major  Milestone:  sage9.4 
Component:  geometry  Keywords:  
Cc:  jipilab, novoselt  Merged in:  
Authors:  Michael Orlitzky  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  u/mjo/ticket/29169 (Commits, GitHub, GitLab)  Commit:  470ee05f27f23e2a8f21fb5b6376b3e15320e238 
Dependencies:  #30605, #30654  Stopgaps: 
Description
My paper with two algorithms for finding the maximal/critical angles between polyhedral convex cones was accepted:
http://www.optimizationonline.org/DB_HTML/2019/01/7048.html
I've already written these algorithms in sage, so it would be nice to add them to the library. I just need to clean up some of the documentation.
Change History (44)
comment:1 Changed 14 months ago by
comment:2 Changed 14 months ago by
 Cc jipilab added
comment:3 Changed 14 months ago by
 Dependencies set to 26623
comment:4 Changed 12 months ago by
 Milestone changed from sage9.1 to sage9.2
Batch modifying tickets that will likely not be ready for 9.1, based on a review of the ticket title, branch/review status, and last modification date.
comment:5 Changed 12 months ago by
 Branch set to u/mjo/ticket/29169
 Commit set to 99d77f01268d0d9e381956ba8f0a228a6ab4c19f
New commits:
c9437f1  Trac #26623: add global entries for pending cone catalog citations.

792ac2b  Trac #26623: add cones.<whatever> shortcuts for common cones.

ddf922c  Trac #26623: add sage.geometry.cone_catalog to the documentation index.

f4a4d34  Trac #26623: update sage.geometry.cone doctests to use the cone catalog.

9c3bf30  Trac #29169: add the Or2020 reference.

6b73284  Trac #29169: add the geometry/cone_critical_angles module.

08dd8aa  Trac #29169: add the critical_angles and max_angle methods.

99d77f0  UNDO ME: add the critical angles module to the doc index.

comment:6 Changed 10 months ago by
 Commit changed from 99d77f01268d0d9e381956ba8f0a228a6ab4c19f to fc255ba01aa5ce3d2f176aa3f217600c76b7a199
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
1edea71  Trac #29169: add the Or2020 reference.

a2a025f  Trac #29169: add the geometry/cone_critical_angles module.

4d15305  Trac #29169: add the critical_angles and max_angle methods.

fc255ba  UNDO ME: add the critical angles module to the doc index.

comment:7 Changed 10 months ago by
 Commit changed from fc255ba01aa5ce3d2f176aa3f217600c76b7a199 to 016564a88267480c9d5f0a684845053a6cfc2576
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
468103b  Trac #29169: add the Or2020 reference.

0481039  Trac #29169: add the geometry/cone_critical_angles module.

b5ac943  Trac #29169: add the critical_angles and max_angle methods.

a3c4535  Trac #29169: fix a broken random_cone() test.

016564a  UNDO ME: add the critical angles module to the doc index.

comment:8 Changed 10 months ago by
 Status changed from new to needs_review
I can keep tweaking the documentation forever, but I think this is in good condition to get some thirdparty feedback.
comment:9 Changed 10 months ago by
(You can check the docs with sage docbuild includetestsblocks underscore
)
comment:10 Changed 10 months ago by
 Dependencies changed from 26623 to #26623
 dependency field was missing #
 Author field is empty
comment:11 Changed 10 months ago by
 Dependencies #26623 deleted
comment:12 Changed 10 months ago by
patchbot complains about coverage and unused import
comment:13 Changed 10 months ago by
 Commit changed from 016564a88267480c9d5f0a684845053a6cfc2576 to 9e917d3730c1783f9f4507039420383284e394e6
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
468103b  Trac #29169: add the Or2020 reference.

7d57406  Trac #29169: add the geometry/cone_critical_angles module.

9c4af89  Trac #29169: add the critical_angles and max_angle methods.

e4683f4  Trac #29169: fix a broken random_cone() test.

9e917d3  UNDO ME: add the critical angles module to the doc index.

comment:14 Changed 10 months ago by
The unused import was legit (and is now fixed), but the coverage warning is for the critical_angles
and max_angle
functions that are wrapped by the methods of the same name in the cone class. All of the documentation (and unit tests) is on the cone methods, because that's what people will use.
(I can add some trivial tests if a happy coverage report is worth it, but so far I have avoided it as it's a complete waste of CPU time.)
comment:15 Changed 10 months ago by
I think that coverage is mandatory, sorry. Very simple tests would do, and you can tag them with #indirect doctest
if they do not use the method directly.
More annoying, the latest patchbot reports a Timed Out
, which is not acceptable.
comment:16 Changed 10 months ago by
 Commit changed from 9e917d3730c1783f9f4507039420383284e394e6 to 017cf1ad3a571dfe69c566b3b73057f2931644f6
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
4037b4e  Trac #29169: add the geometry/cone_critical_angles module.

dfd587e  Trac #29169: add the critical_angles and max_angle methods.

90a1914  Trac #29169: fix a broken random_cone() test.

017cf1a  UNDO ME: add the critical angles module to the doc index.

comment:17 Changed 10 months ago by
I think that will make patchbot happy. I added some trivial tests where they were absent, and fixed the timeout issue (fingers crossed) by adding # long time
in a bunch of places and reducing the max test size in others.
comment:18 Changed 7 months ago by
I'm willing to review this, but I'd much rather go through it one by one. Is it possible to implement the functions one by one?
I didn't check, maybe it all depends on each other.
comment:19 Changed 7 months ago by
They're largely intertwined, but I could still commit some of the helper functions individually if that would make reviewing easier.
The reason for all of the separate functions (and the size of the module) is that critical_angles
and max_angle
do a lot of the same stuff. The max angle is a critical angle  so critical_angles
will find it  but if all we're looking for is the biggest one then we can bail out as soon as we find it. That makes max_angle
faster, but naturally the two share a lot of code, all of which I've tried to factor out into sensiblynamed helper functions.
Once I defined the helper functions, they needed docstrings, tests, and examples.... meaning that a lot of relatively trivial things shared between critical_angles
and max_angle
take up a page or two of code. The inverse_spd
function, for example, is two lines of implementation and a page of docs. If only one of critical_angles
or max_angle
were present, all of those functions would be inlined. Some of them make sense out of context, but others like check_gevp_feasibility
are 100% tied to the implementation of critical_angles
and max_angle
, and are separate only to avoid copy/pasting their code.
comment:20 Changed 7 months ago by
Ok. I think I can also just look at the helper functions and work my way up.
comment:21 Changed 7 months ago by
 Totally minor: If your in this situation, your cone is probably the trivial cone or the ambient space for real. It sounds like you claim that it isn't:
 raise ValueError("this cone cannot be trivial or the ambient space") + raise ValueError("the cone may not be trivial or the ambient space")
or just delete the "this"
Other than this, the changes to src/sage/geometry/cone.py
seem fine to me.
comment:22 Changed 7 months ago by
I see what you're saying, but in informal English I think "may not" suffers from the same problem. Likewise for "must not". How about "the cone should not be..."? I have been unable to trick my brain into reading that incorrectly =)
comment:23 Changed 7 months ago by
the cone should not be
is fine. I wouldn't want to worry about it too much.
comment:24 followup: ↓ 26 Changed 7 months ago by
inverse_spd
: Wouldn't that fit better intomatrix/matrix2.pyx
. This is wherecholesky
is defined._normalize_gevp_solution
: Fine. This error message is a full sentence.
I think just the part in the parenthesis would be a fine error message.
+ ValueError: The ambient dimension must be a positive integer (there + are no nontrivial cones in dimension 0).
otherwise
_random_admissible_cone
is fine

I would propose fixing this.
+ # The standard cone containment tests don't work with normalized + # vectors in QQbar. + u_is_in_P = all( g.inner_product(u) >= 0 for g in P.dual() ) + v_is_in_Q = all( h.inner_product(v) >= 0 for h in Q.dual() )
sage: 3/2*vector([1,1,0]) in P True sage: QQbar(2).sqrt()*vector([1,1,0]) in P ... # very long traceback ValueError: Cannot coerce nonintegral Algebraic Real 1.414213562373095? to Integer
This is awful and inconsistent. There is no way you can convert the point[3/2, 3/2, 0]
to be a lattice point. According to the documentation it should have returnedFalse
. I would propose fixing this as a dependency of this ticket: outsource
dual_rays
or similar fromdual
 use
dual_rays
to improve_contains
to behave coercionlike with your code  then you can just compute
u in P
.
 outsource
If I ask whether a rational or real algebraic point is contained in a cone, I want coercion.
The second thing:
all( z.inner_product(h) >= 0 for h in Q )
could then be reduced toz in Q.dual()
(which is a bit wasteful, but not more than the current state). This could be exposed somehow as well as this is the general question whetherQ
satisfies some inequality, but that is probably not a priority.
gevp_licis
not fast, but if the time of running this is not relevant, it should be fine.
comment:25 Changed 7 months ago by
In examples you define this G_index_sets = list(gevp_licis(G))
without ever using it or printing it.
comment:26 in reply to: ↑ 24 ; followup: ↓ 28 Changed 7 months ago by
 Cc novoselt added
Replying to ghkliem:
This is awful and inconsistent... If I ask whether a rational or real algebraic point is contained in a cone, I want coercion.
Me too, but I anticipate that Andrey will object. The cone module is fairly strict; if you want to do anything "dirty," you have to leave the lattice and move to your own vector space. You've probably seen this in other tickets of mine where I have to throw away the lattice structure of (say) a dual cone to be able to treat its rays as objects in the primal space. It's often annoying, but it's consistent within the cone module. And it's technically correct, even from the convex analysis/geometry perspective, so long as you use the traditional definition of "dual cone" where the elements lie in a dual vector space. So I've learned to live with it.
In either case, you are right that it should return False
as documented.
comment:27 Changed 7 months ago by
 Commit changed from 017cf1ad3a571dfe69c566b3b73057f2931644f6 to 21f1cd2b9ce9838adb7f3f8cda6258dd62e407c2
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
c9cb3d5  Trac #29169: add the Or2020 reference.

583967d  Trac #29169: add the geometry/cone_critical_angles module.

61a46dc  Trac #29169: add the critical_angles and max_angle methods.

c323228  Trac #29169: fix a broken random_cone() test.

ec72863  UNDO ME: add the critical angles module to the doc index.

f32eb63  Trac #29169: tweak two max/critical angle error messages.

c8dd547  Trac #29169: improve error message for _random_admissible_cone().

21f1cd2  Trac #29169: remove two unused example lines.

comment:28 in reply to: ↑ 26 ; followup: ↓ 29 Changed 7 months ago by
How about def contains(self, coerce=False)
or similar. So Andrey can have his way, but we are still not creating copies of stuff at places where they do not belong.
It's still strange that it would accept a vector but not a point in the dual lattice as input.
In a way it makes sense:
sage: 2 in range(2,5) True sage: 2.5 in range(2,5) False
This is completely natural and I can see that you want this behavior for a cone. However, the other question should still be accessible. As you cannot change the base ring of a cone (can you?) it would be nice for the cone to provide some answer for you.
Replying to mjo:
Replying to ghkliem:
This is awful and inconsistent... If I ask whether a rational or real algebraic point is contained in a cone, I want coercion.
Me too, but I anticipate that Andrey will object. The cone module is fairly strict; if you want to do anything "dirty," you have to leave the lattice and move to your own vector space. You've probably seen this in other tickets of mine where I have to throw away the lattice structure of (say) a dual cone to be able to treat its rays as objects in the primal space. It's often annoying, but it's consistent within the cone module. And it's technically correct, even from the convex analysis/geometry perspective, so long as you use the traditional definition of "dual cone" where the elements lie in a dual vector space. So I've learned to live with it.
In either case, you are right that it should return
False
as documented.
comment:29 in reply to: ↑ 28 ; followup: ↓ 31 Changed 7 months ago by
Replying to ghkliem:
It's still strange that it would accept a vector but not a point in the dual lattice as input.
For any vector space with a basis it is quite natural to have conversion from the set of numbers, i.e. a vector from ZZ^n
to that vector space. And the backward map is fairly natural as well. However a composition of such maps does not give a natural map between two vector spaces with chosen bases. On that ground dual lattice elements are not accepted as points in the primal lattice. And the reason why this particular case is explicitly prohibited is that it is a fairly common mistake in toric geometry to work with elements/cones of the wrong lattice, so it helps to catch mistakes. Volker's alternative code was actually having completely unrelated classes for a lattice and its dual to make sure that there is no conversion/coercion happening between them.
So I am strongly against changing this behaviour in any situation. Having explicit nondefault way to mix lattices is perfectly fine, of course.
comment:30 followup: ↓ 32 Changed 7 months ago by
Regarding checking rational/algebraic/float vectors for cone containment  it would be nice for it to work. The problem is, I guess, how to write down the check. For my purposes working with rational numbers was always sufficient and it has the advantage of exact computations, so no need to worry about precision issues. If you can add code to handle more cases  please do it and it has nothing to do with distinction between dual lattices!
comment:31 in reply to: ↑ 29 ; followup: ↓ 34 Changed 7 months ago by
Replying to novoselt:
[...] dual lattice elements are not accepted as points in the primal lattice. And the reason why this particular case is explicitly prohibited is that it is a fairly common mistake in toric geometry to work with elements/cones of the wrong lattice, so it helps to catch mistakes. Volker's alternative code was actually having completely unrelated classes for a lattice and its dual to make sure that there is no conversion/coercion happening between them.
As a side remark, a weakness of the vector space / free module code in sage.modules
is that dual spaces / modules are not implemented. The newer code in sage.tensor.modules
fixes this, and it would be a great improvement if sage.geometry.cone
and sage.geometry.toric_lattice
could integrate with that.
comment:32 in reply to: ↑ 30 Changed 7 months ago by
Replying to novoselt:
If you can add code to handle more cases  please do it and it has nothing to do with distinction between dual lattices!
I was mainly worried about being able to take, say, M(1,1)
and (through coercion) come to the conclusion that it lives in the nonnegative quadrant of the lattice N
. But thanks to some implementation details, that appears not to be a problem. I'll post something soon.
comment:33 Changed 7 months ago by
 Dependencies set to #30605
comment:34 in reply to: ↑ 31 Changed 7 months ago by
Replying to mkoeppe:
As a side remark, a weakness of the vector space / free module code in
sage.modules
is that dual spaces / modules are not implemented. The newer code insage.tensor.modules
fixes this, and it would be a great improvement ifsage.geometry.cone
andsage.geometry.toric_lattice
could integrate with that.
Thank you so much for the pointer! I surely wished for this when I was implementing toric stuff.
comment:35 Changed 7 months ago by
 Commit changed from 21f1cd2b9ce9838adb7f3f8cda6258dd62e407c2 to adeb746e1e5628bc9bb8d9d548dd70889a881069
Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:
f8b8b37  Trac #30605: update polyhedral cone containment documentation.

db132e0  Trac #29169: add the Or2020 reference.

3ff8035  Trac #29169: add the geometry/cone_critical_angles module.

68f339b  Trac #29169: add the critical_angles and max_angle methods.

358aec4  Trac #29169: fix a broken random_cone() test.

fd5ac83  UNDO ME: add the critical angles module to the doc index.

f4fc161  Trac #29169: tweak two max/critical angle error messages.

64c0784  Trac #29169: improve error message for _random_admissible_cone().

31b47af  Trac #29169: remove two unused example lines.

adeb746  Trac #29169: take advantage of improvements in trac #30605.

comment:36 Changed 7 months ago by
 Dependencies changed from #30605 to #30605, #30654
comment:37 Changed 7 months ago by
 Status changed from needs_review to needs_work
I'll need to rebase this again once #30654 is reviewed.
comment:38 Changed 7 months ago by
 Commit changed from adeb746e1e5628bc9bb8d9d548dd70889a881069 to be2d48ec8a2a112e80178e00cb8614531365029b
Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:
aa506fc  Trac #30654: mention inverse_positive_definite() in inverse().

5a834d2  Trac #29169: add the Or2020 reference.

4341a39  Trac #29169: add the geometry/cone_critical_angles module.

cfce9c1  Trac #29169: add the critical_angles and max_angle methods.

970db5d  Trac #29169: fix a broken random_cone() test.

714e3b7  UNDO ME: add the critical angles module to the doc index.

f72376e  Trac #29169: tweak two max/critical angle error messages.

511c360  Trac #29169: improve error message for _random_admissible_cone().

4b452d5  Trac #29169: remove two unused example lines.

be2d48e  Trac #29169: take advantage of improvements in trac #30605.

comment:39 Changed 7 months ago by
 Status changed from needs_work to needs_review
Cherrypicked the two commits from #30654, and replaced the inverse_spd
function with the inverse_positive_definite
method.
comment:40 Changed 6 months ago by
 Milestone changed from sage9.2 to sage9.3
comment:41 Changed 6 months ago by
 Status changed from needs_review to needs_work
red branch => needs work
comment:42 Changed 5 months ago by
 Commit changed from be2d48ec8a2a112e80178e00cb8614531365029b to 470ee05f27f23e2a8f21fb5b6376b3e15320e238
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
dd51796  Trac #29169: add the Or2020 reference.

7b24315  Trac #29169: add the geometry/cone_critical_angles module.

3e35062  Trac #29169: add the critical_angles and max_angle methods.

fb46bcb  Trac #29169: fix a broken random_cone() test.

b9c0e4b  UNDO ME: add the critical angles module to the doc index.

efca675  Trac #29169: tweak two max/critical angle error messages.

115e90a  Trac #29169: improve error message for _random_admissible_cone().

5fc86f2  Trac #29169: remove two unused example lines.

470ee05  Trac #29169: take advantage of improvements in trac #30605.

comment:43 Changed 5 months ago by
 Status changed from needs_work to needs_review
Needed a rebase, I think.
comment:44 Changed 5 weeks ago by
 Milestone changed from sage9.3 to sage9.4
Setting new milestone based on a cursory review of ticket status, priority, and last modification date.
Work in progress on
u/mjo/ticket/29169
. Doesn't build or anything yet.