Open mkoeppe opened 4 years ago
Dependencies: #30095
Setting new milestone based on a cursory review of ticket status, priority, and last modification date.
Changed dependencies from #30095 to #31919
Description changed:
---
+++
@@ -1,3 +1,13 @@
-This is an nonpolyhedral convex cone.
+We define
+- the subspace 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`.
+
+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
+
Description changed:
---
+++
@@ -9,5 +9,10 @@
- #31981 `ManifoldSubset` corresponding to a CVXPY `Leaf` (`Variable`/`Parameter`)
- #30495 `sage.manifolds`: Connect to Pymanopt
+Random references:
+- Jean-Baptiste Hiriart-Urruty, Jérôme Malick, A Fresh Variational-Analysis Look at the Positive
+Semidefinite Matrices World, https://hal.archives-ouvertes.fr/hal-00651605/document
+- Yuhan Jiang & Bernd Sturmfels, Bad projections of the PSD cone, 2021, https://link.springer.com/article/10.1007/s13348-021-00319-4
+- Lek-Heng Lim , Rodolphe Sepulchre, Ke Ye, Geometric Distance Between Positive Definite
+Matrices of Different Dimensions, https://www.stat.uchicago.edu/~lekheng/work/ellipsoids.pdf
-
Author: Matthias Koeppe
Description changed:
---
+++
@@ -10,9 +10,7 @@
- #30495 `sage.manifolds`: Connect to Pymanopt
Random references:
-- Jean-Baptiste Hiriart-Urruty, Jérôme Malick, A Fresh Variational-Analysis Look at the Positive
-Semidefinite Matrices World, https://hal.archives-ouvertes.fr/hal-00651605/document
+- Jean-Baptiste Hiriart-Urruty, Jérôme Malick, A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World, https://hal.archives-ouvertes.fr/hal-00651605/document
- Yuhan Jiang & Bernd Sturmfels, Bad projections of the PSD cone, 2021, https://link.springer.com/article/10.1007/s13348-021-00319-4
-- Lek-Heng Lim , Rodolphe Sepulchre, Ke Ye, Geometric Distance Between Positive Definite
-Matrices of Different Dimensions, https://www.stat.uchicago.edu/~lekheng/work/ellipsoids.pdf
+- Lek-Heng Lim , Rodolphe Sepulchre, Ke Ye, Geometric Distance Between Positive Definite Matrices of Different Dimensions, https://www.stat.uchicago.edu/~lekheng/work/ellipsoids.pdf
Changed dependencies from #31919 to #31919, #31959
Commit: 7e821cf
Branch pushed to git repo; I updated commit sha1. New commits:
7e821cf | src/sage/geometry/semialgebraic/semidefinite.py: Clarify that all matrices are symmetric |
Changed dependencies from #31919, #31959 to #31919, #31959, #31990
Branch pushed to git repo; I updated commit sha1. New commits:
7323b10 | ConvexSet_base._test_contains: Only test extension to AA for exact base rings |
94e6858 | RelativeInterior.ambient, ambient_vector_space, is_universe: New |
0c9bc94 | ConvexSet_base: Add default implementations of ambient, ambient_dim; add doctests |
7d3ae5c | Merge #31959 |
2b1040c | ConvexSet_base.{an_element,some_elements}, Polyhedron.some_elements, RelativeInterior.some_elements: New |
a884517 | PolyhedronFace.some_elements: New |
a0c6c48 | Merge #31990 |
59acb68 | src/sage/geometry/semialgebraic/semidefinite.py: Expand |
Changed dependencies from #31919, #31959, #31990 to #31919, #31995, #31959, #31990
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
ce91e44 | src/sage/geometry/relative_interior.py: Fix doctest output |
b19b3cc | Merge #31959 |
f0e7c58 | ambient_vector_space docstring: Fix bad blocks |
200d967 | ConvexSet_base.ambient doctest: Actually test the method |
1c2bef5 | Merge #31959 |
ed898e6 | ConvexSet_base.an_element, some_elements: Go through generator method `_some_elements_`, make some_elements return a list |
b3ac0f3 | ConvexSet_base.an_element, some_elements: Raise NotImplementedError if `_some_elements_` is NotImplemented |
7152e1f | ConvexSet_base._test_contains: Test some_elements too |
d2dc07e | Merge #31990 |
47e793d | SemidefiniteMatrices_base.affine_hull: Add doctests |
Description changed:
---
+++
@@ -1,7 +1,8 @@
We define
-- the subspace of symmetric matrices
+- 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`
Description changed:
---
+++
@@ -14,4 +14,4 @@
- Jean-Baptiste Hiriart-Urruty, Jérôme Malick, A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World, https://hal.archives-ouvertes.fr/hal-00651605/document
- Yuhan Jiang & Bernd Sturmfels, Bad projections of the PSD cone, 2021, https://link.springer.com/article/10.1007/s13348-021-00319-4
- Lek-Heng Lim , Rodolphe Sepulchre, Ke Ye, Geometric Distance Between Positive Definite Matrices of Different Dimensions, https://www.stat.uchicago.edu/~lekheng/work/ellipsoids.pdf
-
+- James Saunderson, Limitations on the expressive power of convex cones without long chains of faces, https://arxiv.org/abs/1902.06401v2
Branch pushed to git repo; I updated commit sha1. New commits:
44f52b8 | sage.geometry.semialgebraic.semidefinite: More examples, code refinements |
076d78f | ConvexSet_conic, ConvexSet_closed_conic, ConvexSet_proper_conic: New; move some methods here from ConvexRationalPolyhedralCone, PositiveSemidefiniteMatrices |
Branch pushed to git repo; I updated commit sha1. New commits:
2a17c37 | Fixup attrcall |
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
76f8368 | sage.geometry.semialgebraic.semidefinite: New |
d9be74b | src/sage/geometry/semialgebraic/semidefinite.py: Clarify that all matrices are symmetric |
a8f8306 | src/sage/geometry/semialgebraic/semidefinite.py: Expand |
dd1d87c | SemidefiniteMatrices_base.affine_hull: Add doctests |
3d61099 | SemidefiniteMatrices_base: Raise NotImplementedError for non-frield rings; implement _some_elements_ |
9a123f4 | sage.geometry.semialgebraic.semidefinite: More examples, code refinements |
8dce371 | ConvexSet_conic, ConvexSet_closed_conic, ConvexSet_proper_conic: New; move some methods here from ConvexRationalPolyhedralCone, PositiveSemidefiniteMatrices |
f7d233a | Fixup attrcall |
7e16b79 | ConvexSet_proper_conic.affine_hull, dim: New |
Changed dependencies from #31919, #31995, #31959, #31990 to none
We define
ambient
= the full matrix space;affine_hull
= the above subspace), implementing the ABC for convex sets (#31919)relative_interior
.MatrixSpace
Related:
30095
sage.tensor.modules
: AddSymPowerFreeModule
30218 Category
InnerProductSpaces
31981
ManifoldSubset
corresponding to a CVXPYLeaf
(Variable
/Parameter
)30495
sage.manifolds
: Connect to PymanoptRandom references:
CC: @dimpase @yuan-zhou @orlitzky @kliem
Component: geometry
Author: Matthias Koeppe
Branch/Commit: u/mkoeppe/cone_of_positive_semidefinite_matrices @
7e16b79
Issue created by migration from https://trac.sagemath.org/ticket/30172