hyperplane arrangements raises error on regions

asked 2020-02-02 19:59:28 -0500

muradtuk gravatar image

updated 2020-02-03 06:26:51 -0500

Dear all,

When computing the regions of a hyperplane arrangements, it fails and raises the following:

ValueError: *Input Error: Input format is not correct.
*Format:
 begin
   m   n  NumberType(real, rational or integer)
   b  -A
 end

Yet when running the command vertices, it computes it which is confusing!

The full code is:

P = [[-0.48,  0.83], [-5.33,  9.23]]
Q = [[0.43, 0.        ], [9.04, 0.        ]]
Z =  [[-0.35, -0.60], [-1.44, -2.49]]

V = VoronoiDiagram(P)
R = [r for r in V.regions().items()]
s = R[0][1].hyperplane_arrangement()

V = VoronoiDiagram(Q)
R = [r for r in V.regions().items()]
s = s.add_hyperplane(R[0][1].hyperplane_arrangement())

V = VoronoiDiagram(Z)
R = [r for r in V.regions().items()]
s = s.add_hyperplane(R[0][1].hyperplane_arrangement())

s.regions()

How can I overcome this eerie bug?

This means that there is an intersection but the sage cant attain the regions which is weird as stated before!

P.s. The full traceback:

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-6-4ba993d8025f> in <module>()
----> 1 s.regions()

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/misc/cachefunc.pyx in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__ (build/cythonized/sage/misc/cachefunc.c:12712)()
   2308         if self.cache is None:
   2309             f = self.f
-> 2310             self.cache = f(self._instance)
   2311         return self.cache
   2312

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/hyperplane_arrangement/arrangement.py in regions(self)
   1608         R = self.base_ring()
   1609         dim = self.dimension()
-> 1610         universe = Polyhedron(eqns=[[0] + [0] * dim], base_ring=R)
   1611         regions = [universe]
   1612         for hyperplane in self:

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/constructor.py in Polyhedron(vertices, rays, lines, ieqs, eqns, ambient_dim, base_ring, minimize, verbose, backend)
    660     if got_Vrep:
    661         Vrep = [vertices, rays, lines]
--> 662     return parent(Vrep, Hrep, convert=convert, verbose=verbose)

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/structure/parent.pyx in sage.structure.parent.Parent.__call__ (build/cythonized/sage/structure/parent.c:9245)()
    900                 return mor._call_(x)
    901             else:
--> 902                 return mor._call_with_args(x, args, kwds)
    903
    904         raise TypeError(_LazyString(_lazy_format, ("No conversion defined from %s to %s", R, self), {}))

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/structure/coerce_maps.pyx in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args (build/cythonized/sage/structure/coerce_maps.c:5081)()
    178                 print(type(C), C)
    179                 print(type(C._element_constructor), C._element_constructor)
--> 180             raise
    181
    182

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/structure/coerce_maps.pyx in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args (build/cythonized/sage/structure/coerce_maps.c:4969)()
    173                     return C._element_constructor(x, *args)
    174                 else:
--> 175                     return C._element_constructor(x, *args, **kwds)
    176         except Exception:
    177             if print_warnings:

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/parent.py in _element_constructor_(self, *args, **kwds)
    523             if convert and Vrep:
    524                 Vrep = [convert_base_ring(_) for _ in Vrep]
--> 525             return self.element_class(self, Vrep, Hrep, **kwds)
    526         if nargs == 1 and is_Polyhedron(args[0]):
    527             polyhedron = args[0]

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/backend_cdd.py in __init__(self, parent, Vrep, Hrep, **kwds)
    459             sage: TestSuite(p).run()
    460         """
--> 461         Polyhedron_cdd.__init__(self, parent, Vrep, Hrep, **kwds)

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/base.py in __init__(self, parent, Vrep, Hrep, **kwds)
    125         elif Hrep is not None:
    126             ieqs, eqns = Hrep
--> 127             self._init_from_Hrepresentation(ieqs, eqns, **kwds)
    128         else:
    129             self._init_empty_polyhedron()

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/backend_cdd.py in _init_from_Hrepresentation(self, ieqs, eqns, verbose)
    114         s = cdd_Hrepresentation(self._cdd_type, ieqs, eqns)
    115         s = self._run_cdd(s, '--redcheck', verbose=verbose)
--> 116         s = self._run_cdd(s, '--repall', verbose=verbose)
    117         self._init_from_cdd_output(s)
    118         if not self.base_ring().is_exact():

/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/backend_cdd.py in _run_cdd(self, cdd_input_string, cmdline_arg, verbose)
    163         if 'Error:' in ans + err:
    164             # cdd reports errors on stdout and misc information on stderr
--> 165             raise ValueError(ans.strip())
    166         return ans
    167

ValueError: *Input Error: Input format is not correct.
*Format:
 begin
   m   n  NumberType(real, rational or integer)
   b  -A
 end
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Comments

1

Trying the code on my system or SageMathCell does not reproduce the error. What operating system are you using, what version of SageMath, how did you install SageMath, and how are you interacting with SageMath (notebook, command line, script, etc.)?

rburing gravatar imagerburing ( 2020-02-03 05:53:56 -0500 )edit

I am using Windows and also my college used linux and on both systems it failed. We tried running it inside the sage shell, notebook and even from python itself (writing a script and running the command "sage -python script_name.py".

Note that it has been run on sagemath 9.0 (the newest version)

I added also the full traceback of running the piece of code from inside the sage shell

muradtuk gravatar imagemuradtuk ( 2020-02-03 06:19:18 -0500 )edit

The bug can be seen more clearly as follows (it occurs sometimes, not always):

from sage.geometry.polyhedron.parent import Polyhedra
parent = Polyhedra(RDF, 2, backend='cdd')
from sage.geometry.polyhedron.backend_cdd import Polyhedron_RDF_cdd
p = Polyhedron_RDF_cdd(parent, None, [[], [[0,0,0]]], verbose=True)

Apparently, the output of cddexec --redcheck is sometimes either incomplete, or not read correctly. The process communication is done in Polyhedron_RDF_cdd._run_cdd.

rburing gravatar imagerburing ( 2020-02-03 08:18:51 -0500 )edit

This SageMathCell does suggest that cddexec --redcheck sometimes segfaults.

rburing gravatar imagerburing ( 2020-02-03 09:18:03 -0500 )edit

I would also try to use rational numbers instead of floats, this might facilitate the computations. You probably do not need floats, as the size of the input is reasonable.

say 83/100 instead of 0.83 ...

jipilab gravatar imagejipilab ( 2020-02-07 11:59:29 -0500 )edit