' e1 = {:s},\n' \
' e2 = {:s},\n' \
' Condition((L, K, e1, e2)) = {:f}.'
- indented_L = '\n '.join(str(self._L).splitlines())
- indented_e1 = '\n '.join(str(self._e1).splitlines())
- indented_e2 = '\n '.join(str(self._e2).splitlines())
+ indented_L = '\n '.join(str(self.L()).splitlines())
+ indented_e1 = '\n '.join(str(self.e1()).splitlines())
+ indented_e2 = '\n '.join(str(self.e2()).splitlines())
return tpl.format(indented_L,
- str(self._K),
+ str(self.K()),
indented_e1,
indented_e2,
self.condition())
return matrix(0, (self.dimension(), 1), tc='d')
- def _A(self):
+ def A(self):
"""
Return the matrix ``A`` used in our CVXOPT construction.
>>> e1 = [1,1,1]
>>> e2 = [1,2,3]
>>> SLG = SymmetricLinearGame(L, K, e1, e2)
- >>> print(SLG._A())
+ >>> print(SLG.A())
[0.0000000 1.0000000 2.0000000 3.0000000]
<BLANKLINE>
"""
- return matrix([0, self._e2], (1, self.dimension() + 1), 'd')
+ return matrix([0, self.e2()], (1, self.dimension() + 1), 'd')
"""
identity_matrix = identity(self.dimension())
return append_row(append_col(self._zero(), -identity_matrix),
- append_col(self._e1, -self._L))
+ append_col(self.e1(), -self.L()))
def _c(self):
return matrix([-1, self._zero()])
- def _C(self):
+ def C(self):
"""
Return the cone ``C`` used in our CVXOPT construction.
>>> e1 = [1,2,3]
>>> e2 = [1,1,1]
>>> SLG = SymmetricLinearGame(L, K, e1, e2)
- >>> print(SLG._C())
+ >>> print(SLG.C())
Cartesian product of dimension 6 with 2 factors:
* Nonnegative orthant in the real 3-space
* Nonnegative orthant in the real 3-space
@staticmethod
- def _b():
+ def b():
"""
Return the ``b`` vector used in our CVXOPT construction.
>>> e1 = [1,2,3]
>>> e2 = [1,1,1]
>>> SLG = SymmetricLinearGame(L, K, e1, e2)
- >>> print(SLG._b())
+ >>> print(SLG.b())
[1.0000000]
<BLANKLINE>
>>> SLG.solution().game_value() < -ABS_TOL
True
- Tests
- -----
-
The following two games are problematic numerically, but we
should be able to solve them::
- >>> from dunshire import *
- >>> L = [[-0.95237953890954685221, 1.83474556206462535712],
- ... [ 1.30481749924621448500, 1.65278664543326403447]]
- >>> K = NonnegativeOrthant(2)
- >>> e1 = [0.95477167524644313001, 0.63270781756540095397]
- >>> e2 = [0.39633793037154141370, 0.10239281495640320530]
- >>> SLG = SymmetricLinearGame(L, K, e1, e2)
- >>> print(SLG.solution())
- Game value: 18.767...
- Player 1 optimal:
- [-0.000...]
- [ 9.766...]
- Player 2 optimal:
- [1.047...]
- [0.000...]
+ >>> from dunshire import *
+ >>> L = [[-0.95237953890954685221, 1.83474556206462535712],
+ ... [ 1.30481749924621448500, 1.65278664543326403447]]
+ >>> K = NonnegativeOrthant(2)
+ >>> e1 = [0.95477167524644313001, 0.63270781756540095397]
+ >>> e2 = [0.39633793037154141370, 0.10239281495640320530]
+ >>> SLG = SymmetricLinearGame(L, K, e1, e2)
+ >>> print(SLG.solution())
+ Game value: 18.767...
+ Player 1 optimal:
+ [-0.000...]
+ [ 9.766...]
+ Player 2 optimal:
+ [1.047...]
+ [0.000...]
::
- >>> from dunshire import *
- >>> L = [[1.54159395026049472754, 2.21344728574316684799],
- ... [1.33147433507846657541, 1.17913616272988108769]]
- >>> K = NonnegativeOrthant(2)
- >>> e1 = [0.39903040089404784307, 0.12377403622479113410]
- >>> e2 = [0.15695181142215544612, 0.85527381344651265405]
- >>> SLG = SymmetricLinearGame(L, K, e1, e2)
- >>> print(SLG.solution())
- Game value: 24.614...
- Player 1 optimal:
- [ 6.371...]
- [-0.000...]
- Player 2 optimal:
- [2.506...]
- [0.000...]
+ >>> from dunshire import *
+ >>> L = [[1.54159395026049472754, 2.21344728574316684799],
+ ... [1.33147433507846657541, 1.17913616272988108769]]
+ >>> K = NonnegativeOrthant(2)
+ >>> e1 = [0.39903040089404784307, 0.12377403622479113410]
+ >>> e2 = [0.15695181142215544612, 0.85527381344651265405]
+ >>> SLG = SymmetricLinearGame(L, K, e1, e2)
+ >>> print(SLG.solution())
+ Game value: 24.614...
+ Player 1 optimal:
+ [ 6.371...]
+ [-0.000...]
+ Player 2 optimal:
+ [2.506...]
+ [0.000...]
"""
try:
- opts = {'show_progress': options.VERBOSE}
+ opts = {'show_progress': False}
soln_dict = solvers.conelp(self._c(),
self._G(),
self._h(),
- self._C().cvxopt_dims(),
- self._A(),
- self._b(),
+ self.C().cvxopt_dims(),
+ self.A(),
+ self.b(),
options=opts)
except ValueError as error:
if str(error) == 'math domain error':
# Oops, CVXOPT tried to take the square root of a
# negative number. Report some details about the game
# rather than just the underlying CVXOPT crash.
+ printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT
raise PoorScalingException(self)
else:
raise error
# that CVXOPT is convinced the problem is infeasible (and that
# cannot happen).
if soln_dict['status'] in ['primal infeasible', 'dual infeasible']:
+ printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT
raise GameUnsolvableException(self, soln_dict)
# The "optimal" and "unknown" results, we actually treat the
# it) because otherwise CVXOPT might return "unknown" and give
# us two points in the cone that are nowhere near optimal.
if abs(p1_value - p2_value) > 2*options.ABS_TOL:
+ printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT
raise GameUnsolvableException(self, soln_dict)
# And we also check that the points it gave us belong to the
# cone, just in case...
if (p1_optimal not in self._K) or (p2_optimal not in self._K):
+ printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT
raise GameUnsolvableException(self, soln_dict)
# For the game value, we could use any of:
# makes the most sense to just use that, even if it means we
# can't test the fact that p1_value/p2_value are close to the
# payoff.
- payoff = self.payoff(p1_optimal,p2_optimal)
+ payoff = self.payoff(p1_optimal, p2_optimal)
return Solution(payoff, p1_optimal, p2_optimal)
True
"""
- return (condition_number(self._G()) + condition_number(self._A()))/2
+ return (condition_number(self._G()) + condition_number(self.A()))/2
def dual(self):
Condition((L, K, e1, e2)) = 44.476...
"""
- # We pass ``self._L`` right back into the constructor, because
+ # We pass ``self.L()`` right back into the constructor, because
# it will be transposed there. And keep in mind that ``self._K``
# is its own dual.
- return SymmetricLinearGame(self._L,
- self._K,
- self._e2,
- self._e1)
+ return SymmetricLinearGame(self.L(),
+ self.K(),
+ self.e2(),
+ self.e1())
projects / dunshire.git / blobdiff