X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Frearrangement.py;h=0bbf95bb7603bed819d4b9e91a4b148856dc464c;hb=refs%2Fheads%2Fmaster;hp=76b0dadf4f5ddc791c0cb6d95e5db9d811ac78b0;hpb=d6b360ff88d5c1b0e7d29a06bd85d0dcc1e6eac9;p=sage.d.git

diff --git a/mjo/cone/rearrangement.py b/mjo/cone/rearrangement.py
deleted file mode 100644
index 76b0dad..0000000
--- a/mjo/cone/rearrangement.py
+++ /dev/null
@@ -1,148 +0,0 @@
-from sage.all import *
-
-def rearrangement_cone(p,n):
-    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.
-
-    OUTPUT:
-
-    A polyhedral closed convex cone object representing a rearrangement
-    cone of order ``p`` in ``n`` dimensions.
-
-    REFERENCES:
-
-    .. [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
-
-    .. [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
-
-    .. [Jeong] Juyoung Jeong.
-       Spectral sets and functions on Euclidean Jordan algebras.
-
-    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::
-
-        sage: all( rearrangement_cone(p,n).is_proper()
-        ....:              for n in xrange(10)
-        ....:              for p in xrange(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::
-
-        sage: all( rearrangement_cone(p,n).lyapunov_rank() == n
-        ....:              for n in xrange(2, 10)
-        ....:              for p in [1, n-1] )
-        True
-        sage: all( rearrangement_cone(p,n).lyapunov_rank() == 1
-        ....:              for n in xrange(3, 10)
-        ....:              for p in xrange(2, n-1) )
-        True
-
-    TESTS:
-
-    The rearrangement cone is permutation-invariant::
-
-        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: set_random_seed()
-        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 xrange(2, 10)
-        ....:    for p in xrange(1, n-1)
-        ....: )
-        True
-
-    The rearrangenent cone of order ``p`` is contained in the
-    rearrangement cone of order ``p + 1``::
-
-        sage: set_random_seed()
-        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 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 p < 1 or p > n:
-        raise ValueError('order p=%d should be between 1 and n=%d, inclusive'
-                         %
-                         (p,n))
-
-    def d(j):
-        v = [1]*n    # Create the list of all ones...
-        v[j] = 1 - p # Now "fix" the ``j``th entry.
-        return v
-
-    G = identity_matrix(ZZ,n).rows() + [ d(j) for j in xrange(n) ]
-    return Cone(G)