X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fcone.py;h=132c6d9e8e63ebbc5e0065becd813f341e993dd0;hb=babaafed39f4919490631df5c5e9ba7339765cc0;hp=6ade5e628f1035c99294048c7fb55b4b9c1204d9;hpb=7d2f3fba7f494158dbce5f7a3eca1d15ee7f577e;p=sage.d.git diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py index 6ade5e6..132c6d9 100644 --- a/mjo/cone/cone.py +++ b/mjo/cone/cone.py @@ -7,6 +7,13 @@ addsitedir(abspath('../../')) from sage.all import * +# TODO: This test fails, maybe due to a bug in the existing cone code. +# If we request enough generators to span the space, then the returned +# cone should equal the ambient space:: +# +# sage: K = random_cone(min_dim=5, max_dim=5, min_rays=10, max_rays=10) +# sage: K.lines().dimension() == K.lattice_dim() +# True def random_cone(min_dim=0, max_dim=None, min_rays=0, max_rays=None): r""" @@ -17,6 +24,18 @@ def random_cone(min_dim=0, max_dim=None, min_rays=0, max_rays=None): lower bound is left unspecified, it defaults to zero. Unspecified upper bounds will be chosen randomly. + The number of generating rays is naturally limited to twice the + dimension of the ambient space. Take for example $\mathbb{R}^{2}$. + You could have the generators $\left\{ \pm e_{1}, \pm e_{2} + \right\}$, with cardinality $4 = 2 \cdot 2$; however any other ray + in the space is a nonnegative linear combination of those four. + + .. NOTE: + + If you do not explicitly request more than ``2 * max_dim`` rays, + a larger number may still be randomly generated. In that case, + the returned cone will simply be equal to the entire space. + INPUT: - ``min_dim`` (default: zero) -- A nonnegative integer representing the @@ -31,13 +50,24 @@ def random_cone(min_dim=0, max_dim=None, min_rays=0, max_rays=None): cone. - ``max_rays`` (default: random) -- A nonnegative integer representing the - maximum number of generating rays of the - cone. + maximum number of generating rays of + the cone. OUTPUT: A new, randomly generated cone. + A ``ValueError` will be thrown under the following conditions: + + * Any of ``min_dim``, ``max_dim``, ``min_rays``, or ``max_rays`` + are negative. + + * ``max_dim`` is less than ``min_dim``. + + * ``max_rays`` is less than ``min_rays``. + + * ``min_rays`` is greater than twice ``max_dim``. + EXAMPLES: If we set the lower/upper bounds to zero, then our result is @@ -46,12 +76,16 @@ def random_cone(min_dim=0, max_dim=None, min_rays=0, max_rays=None): sage: random_cone(0,0,0,0) 0-d cone in 0-d lattice N - In fact, as long as we ask for zero rays, we should be able to predict - the output when ``min_dim == max_dim``:: + We can predict the dimension when ``min_dim == max_dim``:: sage: random_cone(min_dim=4, max_dim=4, min_rays=0, max_rays=0) 0-d cone in 4-d lattice N + Likewise for the number of rays when ``min_rays == max_rays``:: + + sage: random_cone(min_dim=10, max_dim=10, min_rays=10, max_rays=10) + 10-d cone in 10-d lattice N + TESTS: It's hard to test the output of a random process, but we can at @@ -62,18 +96,33 @@ def random_cone(min_dim=0, max_dim=None, min_rays=0, max_rays=None): sage: is_Cone(K) # long time True + The upper/lower bounds are respected:: + + sage: K = random_cone(min_dim=5, max_dim=10, min_rays=3, max_rays=4) + sage: 5 <= K.lattice_dim() and K.lattice_dim() <= 10 + True + sage: 3 <= K.nrays() and K.nrays() <= 4 + True + Ensure that an exception is raised when either lower bound is greater than its respective upper bound:: sage: random_cone(min_dim=5, max_dim=2) Traceback (most recent call last): ... - ValueError: max_dim must be greater than or equal to min_dim. + ValueError: max_dim cannot be less than min_dim. sage: random_cone(min_rays=5, max_rays=2) Traceback (most recent call last): ... - ValueError: max_rays must be greater than or equal to min_rays. + ValueError: max_rays cannot be less than min_rays. + + And if we request too many rays:: + + sage: random_cone(min_rays=5, max_dim=1) + Traceback (most recent call last): + ... + ValueError: min_rays cannot be larger than twice max_dim. """ @@ -89,14 +138,16 @@ def random_cone(min_dim=0, max_dim=None, min_rays=0, max_rays=None): if max_dim is not None: if max_dim < 0: raise ValueError('max_dim must be nonnegative.') - if (min_dim > max_dim): - raise ValueError('max_dim must be greater than or equal to min_dim.') + if (max_dim < min_dim): + raise ValueError('max_dim cannot be less than min_dim.') + if min_rays > 2*max_dim: + raise ValueError('min_rays cannot be larger than twice max_dim.') if max_rays is not None: if max_rays < 0: raise ValueError('max_rays must be nonnegative.') - if (min_rays > max_rays): - raise ValueError('max_rays must be greater than or equal to min_rays.') + if (max_rays < min_rays): + raise ValueError('max_rays cannot be less than min_rays.') def random_min_max(l,u): @@ -121,11 +172,33 @@ def random_cone(min_dim=0, max_dim=None, min_rays=0, max_rays=None): r = random_min_max(min_rays, max_rays) L = ToricLattice(d) - rays = [L.random_element() for i in range(0,r)] - # The lattice parameter is required when no rays are given, so we - # pass it just in case. - return Cone(rays, lattice=L) + # The rays are trickier to generate, since we could generate v and + # 2*v as our "two rays." In that case, the resuting cone would + # have one generating ray. To avoid such a situation, we start by + # generating ``r`` rays where ``r`` is the number we want to end + # up with. + # + # However, since we're going to *check* whether or not we actually + # have ``r``, we need ``r`` rays to be attainable. So we need to + # limit ``r`` to twice the dimension of the ambient space. + # + r = min(r, 2*d) + rays = [L.random_element() for i in range(0, r)] + + # (The lattice parameter is required when no rays are given, so we + # pass it just in case ``r == 0``). + K = Cone(rays, lattice=L) + + # Now if we generated two of the "same" rays, we'll have fewer + # generating rays than ``r``. In that case, we keep making up new + # rays and recreating the cone until we get the right number of + # independent generators. + while r > K.nrays(): + rays.append(L.random_element()) + K = Cone(rays) + + return K def discrete_complementarity_set(K):