From 31f49a9d987fe26c15e780fbcca74831bff56a9f Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sat, 18 May 2024 16:59:24 -0400 Subject: [PATCH] mjo/cone/rearrangement.py: bye, use sage's cones.rearrangement() instead --- mjo/cone/all.py | 1 - mjo/cone/rearrangement.py | 194 -------------------------------------- 2 files changed, 195 deletions(-) delete mode 100644 mjo/cone/rearrangement.py diff --git a/mjo/cone/all.py b/mjo/cone/all.py index 7dd3c94..2ef437f 100644 --- a/mjo/cone/all.py +++ b/mjo/cone/all.py @@ -7,6 +7,5 @@ from mjo.cone.completely_positive import * from mjo.cone.doubly_nonnegative import * from mjo.cone.faces import * from mjo.cone.permutation_invariant import * -from mjo.cone.rearrangement import * from mjo.cone.symmetric_pd import * from mjo.cone.symmetric_psd import * diff --git a/mjo/cone/rearrangement.py b/mjo/cone/rearrangement.py deleted file mode 100644 index 0bbf95b..0000000 --- a/mjo/cone/rearrangement.py +++ /dev/null @@ -1,194 +0,0 @@ -from sage.all import * - -def rearrangement_cone(p,n,lattice=None): - r""" - Return the rearrangement cone of order ``p`` in ``n`` dimensions. - - The rearrangement cone in ``n`` dimensions has as its elements - vectors of length ``n``. For inclusion in the cone, the smallest - ``p`` components of a vector must sum to a nonnegative number. - - For example, the rearrangement cone of order ``p == 1`` has its - single smallest component nonnegative. This implies that all - components are nonnegative, and that therefore the rearrangement - cone of order one is the nonnegative orthant. - - When ``p == n``, the sum of all components of a vector must be - nonnegative for inclusion in the cone. That is, the cone is a - half-space in ``n`` dimensions. - - INPUT: - - - ``p`` -- The number of components to "rearrange." - - - ``n`` -- The dimension of the ambient space for the resulting cone. - - - ``lattice`` -- (default: ``None``) an ambient lattice of rank ``n`` - to be passed to the :func:`Cone` constructor. - - OUTPUT: - - A polyhedral closed convex cone object representing a rearrangement - cone of order ``p`` in ``n`` dimensions. Each generating ray will - have the integer ring as its base ring. - - If a ``lattice`` was specified, then the resulting cone will live in - that lattice unless its rank is incompatible with the dimension - ``n`` (in which case a ``ValueError`` is raised). - - ALGORITHM: - - The generators for the rearrangement cone are given by [Jeong]_ - Theorem 5.2.3. - - REFERENCES: - - .. [GowdaJeong] Muddappa Seetharama Gowda and Juyoung Jeong. - Spectral cones in Euclidean Jordan algebras. - Linear Algebra and its Applications, 509, 286-305. - doi:10.1016/j.laa.2016.08.004 - - .. [HenrionSeeger] Rene Henrion and Alberto Seeger. - Inradius and Circumradius of Various Convex Cones Arising in - Applications. Set-Valued and Variational Analysis, 18(3-4), - 483-511, 2010. doi:10.1007/s11228-010-0150-z - - .. [Jeong] Juyoung Jeong. - Spectral sets and functions on Euclidean Jordan algebras. - University of Maryland, Baltimore County, Ph.D. thesis, 2017. - - SETUP:: - - sage: from mjo.cone.rearrangement import rearrangement_cone - - EXAMPLES: - - The rearrangement cones of order one are nonnegative orthants:: - - sage: rearrangement_cone(1,1) == Cone([(1,)]) - True - sage: rearrangement_cone(1,2) == Cone([(0,1),(1,0)]) - True - sage: rearrangement_cone(1,3) == Cone([(0,0,1),(0,1,0),(1,0,0)]) - True - - When ``p == n``, the resulting cone will be a half-space, so we - expect its lineality to be one less than ``n`` because it will - contain a hyperplane but is not the entire space:: - - sage: rearrangement_cone(5,5).lineality() - 4 - - All rearrangement cones are proper when ``p`` is less than ``n`` by - [Jeong]_ Proposition 5.2.1:: - - sage: all( rearrangement_cone(p,n).is_proper() - ....: for n in range(10) - ....: for p in range(1, n) ) - True - - The Lyapunov rank of the rearrangement cone of order ``p`` in ``n`` - dimensions is ``n`` for ``p == 1`` or ``p == n`` and one otherwise, - by [Jeong]_ Corollary 5.2.4:: - - sage: all( rearrangement_cone(p,n).lyapunov_rank() == n - ....: for n in range(2, 10) - ....: for p in [1, n-1] ) - True - sage: all( rearrangement_cone(p,n).lyapunov_rank() == 1 - ....: for n in range(3, 10) - ....: for p in range(2, n-1) ) - True - - TESTS: - - All rearrangement cones are permutation-invariant by [Jeong]_ - Proposition 5.2.1:: - - sage: n = ZZ.random_element(2,10).abs() - sage: p = ZZ.random_element(1,n) - sage: K = rearrangement_cone(p,n) - sage: P = SymmetricGroup(n).random_element().matrix() - sage: all( K.contains(P*r) for r in K ) - True - - The smallest ``p`` components of every element of the rearrangement - cone should sum to a nonnegative number (this tests that the - generators really are what we think they are):: - - sage: def _has_rearrangement_property(v,p): - ....: return sum( sorted(v)[0:p] ) >= 0 - sage: all( _has_rearrangement_property( - ....: rearrangement_cone(p,n).random_element(), - ....: p - ....: ) - ....: for n in range(2, 10) - ....: for p in range(1, n-1) - ....: ) - True - - The rearrangenent cone of order ``p`` is contained in the rearrangement - cone of order ``p + 1`` by [Jeong]_ Proposition 5.2.1:: - - sage: n = ZZ.random_element(2,10) - sage: p = ZZ.random_element(1,n) - sage: K1 = rearrangement_cone(p,n) - sage: K2 = rearrangement_cone(p+1,n) - sage: all( x in K2 for x in K1 ) - True - - The rearrangement cone of order ``p`` is linearly isomorphic to the - rearrangement cone of order ``n - p`` when ``p`` is less than ``n``, - by [Jeong]_ Proposition 5.2.1:: - - sage: n = ZZ.random_element(2,10) - sage: p = ZZ.random_element(1,n) - sage: K1 = rearrangement_cone(p,n) - sage: K2 = rearrangement_cone(n-p, n) - sage: Mp = (1/p)*matrix.ones(QQ,n) - identity_matrix(QQ,n) - sage: Cone( (Mp*K2.rays()).columns() ).is_equivalent(K1) - True - - The order ``p`` should be between ``1`` and ``n``, inclusive:: - - sage: rearrangement_cone(0,3) - Traceback (most recent call last): - ... - ValueError: order p=0 should be between 1 and n=3, inclusive - sage: rearrangement_cone(5,3) - Traceback (most recent call last): - ... - ValueError: order p=5 should be between 1 and n=3, inclusive - - If a ``lattice`` was given, it is actually used:: - - sage: L = ToricLattice(3, 'M') - sage: rearrangement_cone(2, 3, lattice=L) - 3-d cone in 3-d lattice M - - Unless the rank of the lattice disagrees with ``n``:: - - sage: L = ToricLattice(1, 'M') - sage: rearrangement_cone(2, 3, lattice=L) - Traceback (most recent call last): - ... - ValueError: lattice rank=1 and dimension n=3 are incompatible - - """ - if p < 1 or p > n: - raise ValueError('order p=%d should be between 1 and n=%d, inclusive' - % - (p,n)) - - if lattice is None: - lattice = ToricLattice(n) - - if lattice.rank() != n: - raise ValueError('lattice rank=%d and dimension n=%d are incompatible' - % - (lattice.rank(), n)) - - I = identity_matrix(ZZ,n) - M = matrix.ones(ZZ,n) - p*I - G = identity_matrix(ZZ,n).rows() + M.rows() - return Cone(G, lattice=lattice) -- 2.44.2