From: Michael Orlitzky Date: Sun, 24 May 2015 14:50:25 +0000 (-0400) Subject: Remove is_full_space() and random_cone(); see Sage trac #18454. X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=81a763e35b3e4322be6c60a815064be1f0dfcc3c;p=sage.d.git Remove is_full_space() and random_cone(); see Sage trac #18454. --- diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py index 424a907..777d45e 100644 --- a/mjo/cone/cone.py +++ b/mjo/cone/cone.py @@ -8,229 +8,6 @@ addsitedir(abspath('../../')) from sage.all import * -def is_full_space(K): - r""" - Return whether or not this cone is equal to its ambient vector space. - - OUTPUT: - - ``True`` if this cone is the entire vector space and ``False`` - otherwise. - - EXAMPLES: - - A ray in two dimensions is not equal to the entire space:: - - sage: K = Cone([(1,0)]) - sage: is_full_space(K) - False - - Neither is the nonnegative orthant:: - - sage: K = Cone([(1,0),(0,1)]) - sage: is_full_space(K) - False - - The right half-space contains a vector subspace, but it is still not - equal to the entire plane:: - - sage: K = Cone([(1,0),(-1,0),(0,1)]) - sage: is_full_space(K) - False - - But if we include nonnegative sums from both axes, then the resulting - cone is the entire two-dimensional space:: - - sage: K = Cone([(1,0),(-1,0),(0,1),(0,-1)]) - sage: is_full_space(K) - True - - """ - return K.linear_subspace() == K.lattice().vector_space() - - -def random_cone(min_dim=0, max_dim=None, min_rays=0, max_rays=None): - r""" - Generate a random rational convex polyhedral cone. - - Lower and upper bounds may be provided for both the dimension of the - ambient space and the number of generating rays of the cone. If a - lower bound is left unspecified, it defaults to zero. Unspecified - upper bounds will be chosen randomly. - - The lower bound on the number of rays is limited to twice the - maximum dimension of the ambient vector space. To see why, consider - the space $\mathbb{R}^{2}$, and suppose we have generated four rays, - $\left\{ \pm e_{1}, \pm e_{2} \right\}$. Clearly any other ray in - the space is a nonnegative linear combination of those four, - so it is hopeless to generate more. It is therefore an error - to request more in the form of ``min_rays``. - - .. 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 - minimum dimension of the ambient lattice. - - - ``max_dim`` (default: random) -- A nonnegative integer representing - the maximum dimension of the ambient - lattice. - - - ``min_rays`` (default: zero) -- A nonnegative integer representing the - minimum number of generating rays of the - cone. - - - ``max_rays`` (default: random) -- A nonnegative integer representing the - 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 - predictable:: - - sage: random_cone(0,0,0,0) - 0-d cone in 0-d lattice N - - 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 - least make sure that we get a cone back:: - - sage: from sage.geometry.cone import is_Cone # long time - sage: K = random_cone() # long time - 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 cannot be less than min_dim. - - sage: random_cone(min_rays=5, max_rays=2) - Traceback (most recent call last): - ... - 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. - - """ - - # Catch obvious mistakes so that we can generate clear error - # messages. - - if min_dim < 0: - raise ValueError('min_dim must be nonnegative.') - - if min_rays < 0: - raise ValueError('min_rays must be nonnegative.') - - if max_dim is not None: - if max_dim < 0: - raise ValueError('max_dim must be nonnegative.') - 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 (max_rays < min_rays): - raise ValueError('max_rays cannot be less than min_rays.') - - - def random_min_max(l,u): - r""" - We need to handle two cases for the upper bounds, and we need to do - the same thing for max_dim/max_rays. So we consolidate the logic here. - """ - if u is None: - # The upper bound is unspecified; return a random integer - # in [l,infinity). - return l + ZZ.random_element().abs() - else: - # We have an upper bound, and it's greater than or equal - # to our lower bound. So we generate a random integer in - # [0,u-l], and then add it to l to get something in - # [l,u]. To understand the "+1", check the - # ZZ.random_element() docs. - return l + ZZ.random_element(u - l + 1) - - d = random_min_max(min_dim, max_dim) - r = random_min_max(min_rays, max_rays) - - L = ToricLattice(d) - - # 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... - 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. We can obviously stop if ``K`` is the - # entire ambient vector space. - while r > K.nrays() and not is_full_space(K): - rays.append(L.random_element()) - K = Cone(rays) - - return K - - def discrete_complementarity_set(K): r""" Compute the discrete complementarity set of this cone.