Opened 3 years ago

Last modified 3 weeks ago

#30172 new enhancement

Cone of positive-semidefinite matrices

Reported by: mkoeppe Owned by:
Priority: major Milestone: sage-9.9
Component: geometry Keywords:
Cc: dimpase, yzh, mjo, gh-kliem Merged in:
Authors: Matthias Koeppe Reviewers:
Report Upstream: N/A Work issues:
Branch: u/mkoeppe/cone_of_positive_semidefinite_matrices (Commits, GitHub, GitLab) Commit: 7e16b79577b4578b432690e32cc2f7d40b213279
Dependencies: Stopgaps:

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Description (last modified by mkoeppe)

We define

  • the subspace/submodule of symmetric matrices
  • the cone of positive-semidefinite matrices (with ambient = the full matrix space; affine_hull = the above subspace), implementing the ABC for convex sets (#31919)
  • the cone of positive-definite matrices as its relative_interior.
  • additive semigroups/monoids of positive-(semi)definite matrices as intersection of the above with a MatrixSpace

Related:

  • #30095 sage.tensor.modules: Add SymPowerFreeModule
  • #30218 Category InnerProductSpaces
  • #31981 ManifoldSubset corresponding to a CVXPY Leaf (Variable/Parameter)
  • #30495 sage.manifolds: Connect to Pymanopt

Random references:

Change History (27)

comment:1 Changed 3 years ago by mkoeppe

Dependencies: #30095

comment:2 Changed 2 years ago by mkoeppe

Milestone: sage-9.2sage-9.3

comment:3 Changed 2 years ago by mjo

Cc: mjo added

comment:4 Changed 2 years ago by mkoeppe

Milestone: sage-9.3sage-9.4

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

comment:5 Changed 20 months ago by mkoeppe

Dependencies: #30095#31919
Description: modified (diff)
Summary: Cone of positive-semidefinite symmetric bilinear formsCone of positive-semidefinite matrices / symmetric bilinear forms

comment:6 Changed 20 months ago by mkoeppe

Description: modified (diff)

comment:7 Changed 20 months ago by mkoeppe

Authors: Matthias Koeppe
Cc: gh-kliem added
Description: modified (diff)
Summary: Cone of positive-semidefinite matrices / symmetric bilinear formsCone of positive-semidefinite matrices

comment:8 Changed 20 months ago by mkoeppe

Dependencies: #31919#31919, #31959

comment:9 Changed 20 months ago by mkoeppe

Branch: u/mkoeppe/cone_of_positive_semidefinite_matrices

comment:10 Changed 20 months ago by git

Commit: 7e821cf6d11e722c93de2757f48955ee5f0b0950

Branch pushed to git repo; I updated commit sha1. New commits:

7e821cfsrc/sage/geometry/semialgebraic/semidefinite.py: Clarify that all matrices are symmetric

comment:11 Changed 20 months ago by mkoeppe

Dependencies: #31919, #31959#31919, #31959, #31990

comment:12 Changed 20 months ago by git

Commit: 7e821cf6d11e722c93de2757f48955ee5f0b095059acb68a6c7a3fa017a01dde758538783169685d

Branch pushed to git repo; I updated commit sha1. New commits:

7323b10ConvexSet_base._test_contains: Only test extension to AA for exact base rings
94e6858RelativeInterior.ambient, ambient_vector_space, is_universe: New
0c9bc94ConvexSet_base: Add default implementations of ambient, ambient_dim; add doctests
7d3ae5cMerge #31959
2b1040cConvexSet_base.{an_element,some_elements}, Polyhedron.some_elements, RelativeInterior.some_elements: New
a884517PolyhedronFace.some_elements: New
a0c6c48Merge #31990
59acb68src/sage/geometry/semialgebraic/semidefinite.py: Expand

comment:13 Changed 20 months ago by mkoeppe

Dependencies: #31919, #31959, #31990#31919, #31995, #31959, #31990

comment:14 Changed 20 months ago by git

Commit: 59acb68a6c7a3fa017a01dde758538783169685d47e793d7bc7f5b42fa37a80587990bf9ecb5f171

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

ce91e44src/sage/geometry/relative_interior.py: Fix doctest output
b19b3ccMerge #31959
f0e7c58ambient_vector_space docstring: Fix bad blocks
200d967ConvexSet_base.ambient doctest: Actually test the method
1c2bef5Merge #31959
ed898e6ConvexSet_base.an_element, some_elements: Go through generator method _some_elements_, make some_elements return a list
b3ac0f3ConvexSet_base.an_element, some_elements: Raise NotImplementedError if _some_elements_ is NotImplemented
7152e1fConvexSet_base._test_contains: Test some_elements too
d2dc07eMerge #31990
47e793dSemidefiniteMatrices_base.affine_hull: Add doctests

comment:15 Changed 20 months ago by mkoeppe

Description: modified (diff)

comment:16 Changed 20 months ago by git

Commit: 47e793d7bc7f5b42fa37a80587990bf9ecb5f1715db9a34a50fddd64aac3f2e07c276725a9f0b561

Branch pushed to git repo; I updated commit sha1. New commits:

e270655Fixing issue when the support is smaller than the dimension.
ad63607Merge #31995
5db9a34SemidefiniteMatrices_base: Raise NotImplementedError for non-frield rings; implement _some_elements_

comment:17 Changed 20 months ago by mkoeppe

Description: modified (diff)

comment:18 Changed 20 months ago by git

Commit: 5db9a34a50fddd64aac3f2e07c276725a9f0b561076d78fca8bfe76eb8f7dd61a83c371e9653ad51

Branch pushed to git repo; I updated commit sha1. New commits:

44f52b8sage.geometry.semialgebraic.semidefinite: More examples, code refinements
076d78fConvexSet_conic, ConvexSet_closed_conic, ConvexSet_proper_conic: New; move some methods here from ConvexRationalPolyhedralCone, PositiveSemidefiniteMatrices

comment:19 Changed 20 months ago by git

Commit: 076d78fca8bfe76eb8f7dd61a83c371e9653ad512a17c37603280f8b38970375bd908386d1d321b8

Branch pushed to git repo; I updated commit sha1. New commits:

2a17c37Fixup attrcall

comment:20 Changed 20 months ago by git

Commit: 2a17c37603280f8b38970375bd908386d1d321b82d890d639009145ddb5e15a290f70a09494359bc

Branch pushed to git repo; I updated commit sha1. New commits:

991419cConvexSet_base._test_convex_set: Do not test _test_as_set_object here
2d890d6ConvexSet_proper_conic.affine_hull, dim: New

comment:21 Changed 19 months ago by mkoeppe

Milestone: sage-9.4sage-9.5

comment:22 Changed 14 months ago by mkoeppe

Milestone: sage-9.5sage-9.6

comment:23 Changed 10 months ago by mkoeppe

Milestone: sage-9.6sage-9.7

comment:24 Changed 5 months ago by git

Commit: 2d890d639009145ddb5e15a290f70a09494359bc7e16b79577b4578b432690e32cc2f7d40b213279

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

76f8368sage.geometry.semialgebraic.semidefinite: New
d9be74bsrc/sage/geometry/semialgebraic/semidefinite.py: Clarify that all matrices are symmetric
a8f8306src/sage/geometry/semialgebraic/semidefinite.py: Expand
dd1d87cSemidefiniteMatrices_base.affine_hull: Add doctests
3d61099SemidefiniteMatrices_base: Raise NotImplementedError for non-frield rings; implement _some_elements_
9a123f4sage.geometry.semialgebraic.semidefinite: More examples, code refinements
8dce371ConvexSet_conic, ConvexSet_closed_conic, ConvexSet_proper_conic: New; move some methods here from ConvexRationalPolyhedralCone, PositiveSemidefiniteMatrices
f7d233aFixup attrcall
7e16b79ConvexSet_proper_conic.affine_hull, dim: New

comment:25 Changed 5 months ago by mkoeppe

Dependencies: #31919, #31995, #31959, #31990

comment:26 Changed 5 months ago by mkoeppe

Milestone: sage-9.7sage-9.8

comment:27 Changed 3 weeks ago by mkoeppe

Milestone: sage-9.8sage-9.9
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