+
+ return tpl.format(indented_L,
+ str(self._K),
+ indented_e1,
+ indented_e2,
+ self.condition())
+
+
+ def _zero(self):
+ """
+ Return a column of zeros that fits ``K``.
+
+ This is used in our CVXOPT construction.
+
+ .. warning::
+
+ It is not safe to cache any of the matrices passed to
+ CVXOPT, because it can clobber them.
+
+ Returns
+ -------
+
+ matrix
+ A ``K.dimension()``-by-``1`` column vector of zeros.
+
+ Examples
+ --------
+
+ >>> from dunshire import *
+ >>> K = NonnegativeOrthant(3)
+ >>> L = identity(3)
+ >>> e1 = [1,1,1]
+ >>> e2 = e1
+ >>> SLG = SymmetricLinearGame(L, K, e1, e2)
+ >>> print(SLG._zero())
+ [0.0000000]
+ [0.0000000]
+ [0.0000000]
+ <BLANKLINE>
+
+ """
+ return matrix(0, (self._K.dimension(), 1), tc='d')
+
+
+ def _A(self):
+ """
+ Return the matrix ``A`` used in our CVXOPT construction.
+
+ This matrix ``A`` appears on the right-hand side of ``Ax = b``
+ in the statement of the CVXOPT conelp program.
+
+ .. warning::
+
+ It is not safe to cache any of the matrices passed to
+ CVXOPT, because it can clobber them.
+
+ Returns
+ -------
+
+ matrix
+ A ``1``-by-``(1 + K.dimension())`` row vector. Its first
+ entry is zero, and the rest are the entries of ``e2``.
+
+ Examples
+ --------
+
+ >>> from dunshire import *
+ >>> K = NonnegativeOrthant(3)
+ >>> L = [[1,1,1],[1,1,1],[1,1,1]]
+ >>> e1 = [1,1,1]
+ >>> e2 = [1,2,3]
+ >>> SLG = SymmetricLinearGame(L, K, e1, e2)
+ >>> print(SLG._A())
+ [0.0000000 1.0000000 2.0000000 3.0000000]
+ <BLANKLINE>
+
+ """
+ return matrix([0, self._e2], (1, self._K.dimension() + 1), 'd')
+
+
+
+ def _G(self):
+ r"""
+ Return the matrix ``G`` used in our CVXOPT construction.
+
+ Thus matrix ``G``that appears on the left-hand side of ``Gx + s = h``
+ in the statement of the CVXOPT conelp program.
+
+ .. warning::
+
+ It is not safe to cache any of the matrices passed to
+ CVXOPT, because it can clobber them.
+
+ Returns
+ -------
+
+ matrix
+ A ``2*K.dimension()``-by-``1 + K.dimension()`` matrix.
+
+ Examples
+ --------
+
+ >>> from dunshire import *
+ >>> K = NonnegativeOrthant(3)
+ >>> L = [[4,5,6],[7,8,9],[10,11,12]]
+ >>> e1 = [1,2,3]
+ >>> e2 = [1,1,1]
+ >>> SLG = SymmetricLinearGame(L, K, e1, e2)
+ >>> print(SLG._G())
+ [ 0.0000000 -1.0000000 0.0000000 0.0000000]
+ [ 0.0000000 0.0000000 -1.0000000 0.0000000]
+ [ 0.0000000 0.0000000 0.0000000 -1.0000000]
+ [ 1.0000000 -4.0000000 -5.0000000 -6.0000000]
+ [ 2.0000000 -7.0000000 -8.0000000 -9.0000000]
+ [ 3.0000000 -10.0000000 -11.0000000 -12.0000000]
+ <BLANKLINE>
+
+ """
+ I = identity(self._K.dimension())
+ return append_row(append_col(self._zero(), -I),
+ append_col(self._e1, -self._L))
+
+
+ def _try_solution(self, c, h, C, b, tolerance):
+ # Actually solve the thing and obtain a dictionary describing
+ # what happened.
+ try:
+ solvers.options['show_progress'] = options.VERBOSE
+ solvers.options['abs_tol'] = tolerance
+ soln_dict = solvers.conelp(c,self._G(),h,C,self._A(),b)
+ except ValueError as e:
+ if str(e) == '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.
+ raise PoorScalingException(self)
+ else:
+ raise e
+
+ # The optimal strategies are named ``p`` and ``q`` in the
+ # background documentation, and we need to extract them from
+ # the CVXOPT ``x`` and ``z`` variables. The objective values
+ # :math:`nu` and :math:`omega` can also be found in the CVXOPT
+ # ``x`` and ``y`` variables; however, they're stored
+ # conveniently as separate entries in the solution dictionary.
+ p1_value = -soln_dict['primal objective']
+ p2_value = -soln_dict['dual objective']
+ p1_optimal = soln_dict['x'][1:]
+ p2_optimal = soln_dict['z'][self._K.dimension():]
+
+ # The "status" field contains "optimal" if everything went
+ # according to plan. Other possible values are "primal
+ # infeasible", "dual infeasible", "unknown", all of which mean
+ # we didn't get a solution. The "infeasible" ones are the
+ # worst, since they indicate that CVXOPT is convinced the
+ # problem is infeasible (and that cannot happen).
+ if soln_dict['status'] in ['primal infeasible', 'dual infeasible']:
+ raise GameUnsolvableException(self, soln_dict)
+ elif soln_dict['status'] == 'unknown':
+ # When we get a status of "unknown", we may still be able
+ # to salvage a solution out of the returned
+ # dictionary. Often this is the result of numerical
+ # difficulty and we can simply check that the primal/dual
+ # objectives match (within a tolerance) and that the
+ # primal/dual optimal solutions are within the cone (to a
+ # tolerance as well).
+ #
+ # The fudge factor of two is basically unjustified, but
+ # makes intuitive sense when you imagine that the primal
+ # value could be under the true optimal by ``ABS_TOL``
+ # and the dual value could be over by the same amount.
+ #
+ if abs(p1_value - p2_value) > tolerance:
+ raise GameUnsolvableException(self, soln_dict)
+ if (p1_optimal not in self._K) or (p2_optimal not in self._K):
+ raise GameUnsolvableException(self, soln_dict)
+
+ return Solution(p1_value, p1_optimal, p2_optimal)
projects / dunshire.git / blobdiff