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Cone of positive-semidefinite matrices #30172

Open mkoeppe opened 4 years ago

mkoeppe commented 4 years ago

We define

Related:

Random 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

mkoeppe commented 4 years ago

Dependencies: #30095

mkoeppe commented 3 years ago
comment:4

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

mkoeppe commented 3 years ago

Changed dependencies from #30095 to #31919

mkoeppe commented 3 years ago

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

+
mkoeppe commented 3 years ago

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

-
mkoeppe commented 3 years ago

Author: Matthias Koeppe

mkoeppe commented 3 years ago

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
mkoeppe commented 3 years ago

Changed dependencies from #31919 to #31919, #31959

mkoeppe commented 3 years ago

Branch: u/mkoeppe/cone_of_positive_semidefinite_matrices

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Commit: 7e821cf

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

7e821cfsrc/sage/geometry/semialgebraic/semidefinite.py: Clarify that all matrices are symmetric
mkoeppe commented 3 years ago

Changed dependencies from #31919, #31959 to #31919, #31959, #31990

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 7e821cf to 59acb68

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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
mkoeppe commented 3 years ago

Changed dependencies from #31919, #31959, #31990 to #31919, #31995, #31959, #31990

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 59acb68 to 47e793d

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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
mkoeppe commented 3 years ago

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`
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 47e793d to 5db9a34

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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_
mkoeppe commented 3 years ago

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
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 5db9a34 to 076d78f

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 076d78f to 2a17c37

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

2a17c37Fixup attrcall
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 2a17c37 to 2d890d6

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 2 years ago

Changed commit from 2d890d6 to 7e16b79

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 2 years ago

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
mkoeppe commented 2 years ago

Changed dependencies from #31919, #31995, #31959, #31990 to none