X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fcone.py;h=b7456e21abc170d6479f9010a2b7ccdd5ab9438d;hb=1bbade9f41ffbfe366b15d0db657f666bc1f025d;hp=23043381bca83acd6d7f17479ef4769980b9960f;hpb=012175f3a2591586099b4e955bb440958f2d63d7;p=sage.d.git

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index 2304338..b7456e2 100644
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -1,141 +1,23 @@
-# Sage doesn't load ~/.sage/init.sage during testing (sage -t), so we
-# have to explicitly mangle our sitedir here so that "mjo.cone"
-# resolves.
-from os.path import abspath
-from site import addsitedir
-addsitedir(abspath('../../'))
-
 from sage.all import *
 
-
-def lyapunov_rank(K):
-    r"""
-    Compute the Lyapunov (or bilinearity) rank of this cone.
-
-    The Lyapunov rank of a cone can be thought of in (mainly) two ways:
-
-    1. The dimension of the Lie algebra of the automorphism group of the
-       cone.
-
-    2. The dimension of the linear space of all Lyapunov-like
-       transformations on the cone.
-
-    INPUT:
-
-    A closed, convex polyhedral cone.
-
-    OUTPUT:
-
-    An integer representing the Lyapunov rank of the cone. If the
-    dimension of the ambient vector space is `n`, then the Lyapunov rank
-    will be between `1` and `n` inclusive; however a rank of `n-1` is
-    not possible (see the first reference).
-
-    .. note::
-
-        In the references, the cones are always assumed to be proper. We
-        do not impose this restriction.
-
-    .. seealso::
-
-        :meth:`is_proper`
-
-    ALGORITHM:
-
-    The codimension formula from the second reference is used. We find
-    all pairs `(x,s)` in the complementarity set of `K` such that `x`
-    and `s` are rays of our cone. It is known that these vectors are
-    sufficient to apply the codimension formula. Once we have all such
-    pairs, we "brute force" the codimension formula by finding all
-    linearly-independent `xs^{T}`.
-
-    REFERENCES:
-
-    1. M.S. Gowda and J. Tao. On the bilinearity rank of a proper cone
-       and Lyapunov-like transformations, Mathematical Programming, 147
-       (2014) 155-170.
-
-    2. G. Rudolf, N. Noyan, D. Papp, and F. Alizadeh, Bilinear
-       optimality constraints for the cone of positive polynomials,
-       Mathematical Programming, Series B, 129 (2011) 5-31.
-
-    EXAMPLES:
-
-    The nonnegative orthant in `\mathbb{R}^{n}` always has rank `n`::
-
-        sage: positives = Cone([(1,)])
-        sage: lyapunov_rank(positives)
-        1
-        sage: quadrant = Cone([(1,0), (0,1)])
-        sage: lyapunov_rank(quadrant)
-        2
-        sage: octant = Cone([(1,0,0), (0,1,0), (0,0,1)])
-        sage: lyapunov_rank(octant)
-        3
-
-    The `L^{3}_{1}` cone is known to have a Lyapunov rank of one::
-
-        sage: L31 = Cone([(1,0,1), (0,-1,1), (-1,0,1), (0,1,1)])
-        sage: lyapunov_rank(L31)
-        1
-
-    Likewise for the `L^{3}_{\infty}` cone::
-
-        sage: L3infty = Cone([(0,1,1), (1,0,1), (0,-1,1), (-1,0,1)])
-        sage: lyapunov_rank(L3infty)
-        1
-
-    The Lyapunov rank should be additive on a product of cones::
-
-        sage: L31 = Cone([(1,0,1), (0,-1,1), (-1,0,1), (0,1,1)])
-        sage: octant = Cone([(1,0,0), (0,1,0), (0,0,1)])
-        sage: K = L31.cartesian_product(octant)
-        sage: lyapunov_rank(K) == lyapunov_rank(L31) + lyapunov_rank(octant)
-        True
-
-    Two isomorphic cones should have the same Lyapunov rank. The cone
-    ``K`` in the following example is isomorphic to the nonnegative
-    octant in `\mathbb{R}^{3}`::
-
-        sage: K = Cone([(1,2,3), (-1,1,0), (1,0,6)])
-        sage: lyapunov_rank(K)
-        3
-
-    The dual cone `K^{*}` of ``K`` should have the same Lyapunov rank as ``K``
-    itself::
-
-        sage: K = Cone([(2,2,4), (-1,9,0), (2,0,6)])
-        sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
-        True
-
-    """
-    V = K.lattice().vector_space()
-
-    xs = [V(x) for x in K.rays()]
-    ss = [V(s) for s in K.dual().rays()]
-
-    # WARNING: This isn't really C(K), it only contains the pairs
-    # (x,s) in C(K) where x,s are extreme in their respective cones.
-    C_of_K = [(x,s) for x in xs for s in ss if x.inner_product(s) == 0]
-
-    matrices = [x.column() * s.row() for (x,s) in C_of_K]
-
-    # Sage doesn't think matrices are vectors, so we have to convert
-    # our matrices to vectors explicitly before we can figure out how
-    # many are linearly-indepenedent.
-    #
-    # The space W has the same base ring as V, but dimension
-    # dim(V)^2. So it has the same dimension as the space of linear
-    # transformations on V. In other words, it's just the right size
-    # to create an isomorphism between it and our matrices.
-    W = VectorSpace(V.base_ring(), V.dimension()**2)
-
-    def phi(m):
-        r"""
-        Convert a matrix to a vector isomorphically.
-        """
-        return W(m.list())
-
-    vectors = [phi(m) for m in matrices]
-
-    return (W.dimension() - W.span(vectors).rank())
+def LL_cone(K):
+    gens = K.lyapunov_like_basis()
+    L = ToricLattice(K.lattice_dim()**2)
+    return Cone(( g.list() for g in gens ), lattice=L, check=False)
+
+def Sigma_cone(K):
+    gens = K.cross_positive_operators_gens()
+    L = ToricLattice(K.lattice_dim()**2)
+    return Cone(( g.list() for g in gens ), lattice=L, check=False)
+
+def Z_cone(K):
+    gens = K.Z_operators_gens()
+    L = ToricLattice(K.lattice_dim()**2)
+    return Cone(( g.list() for g in gens ), lattice=L, check=False)
+
+def pi_cone(K1, K2=None):
+    if K2 is None:
+        K2 = K1
+    gens = K1.positive_operators_gens(K2)
+    L = ToricLattice(K1.lattice_dim()*K2.lattice_dim())
+    return Cone(( g.list() for g in gens ), lattice=L, check=False)