--- /dev/null
+"""
+Random thing generators used in the rest of the test suite.
+"""
+from random import randint, uniform
+
+from math import sqrt
+from cvxopt import matrix
+from dunshire.cones import NonnegativeOrthant, IceCream
+from dunshire.games import SymmetricLinearGame
+from dunshire.matrices import (append_col, append_row, identity)
+
+MAX_COND = 250
+"""
+The maximum condition number of a randomly-generated game.
+"""
+
+RANDOM_MAX = 10
+"""
+When generating random real numbers or integers, this is used as the
+largest allowed magnitude. It keeps our condition numbers down and other
+properties within reason.
+"""
+
+def random_scalar():
+ """
+ Generate a random scalar in ``[-RANDOM_MAX, RANDOM_MAX]``.
+
+ Returns
+ -------
+
+ float
+
+ Examples
+ --------
+
+ >>> abs(random_scalar()) <= RANDOM_MAX
+ True
+
+ """
+ return uniform(-RANDOM_MAX, RANDOM_MAX)
+
+
+def random_nn_scalar():
+ """
+ Generate a random nonnegative scalar in ``[0, RANDOM_MAX]``.
+
+ Returns
+ -------
+
+ float
+
+ Examples
+ --------
+
+ >>> 0 <= random_nn_scalar() <= RANDOM_MAX
+ True
+
+ """
+ return abs(random_scalar())
+
+
+def random_natural():
+ """
+ Generate a random natural number between ``1 and RANDOM_MAX``
+ inclusive.
+
+ Returns
+ -------
+
+ int
+
+ Examples
+ --------
+
+ >>> 1 <= random_natural() <= RANDOM_MAX
+ True
+
+ """
+ return randint(1, RANDOM_MAX)
+
+
+def random_matrix(dims):
+ """
+ Generate a random square matrix.
+
+ Parameters
+ ----------
+
+ dims : int
+ The number of rows/columns you want in the returned matrix.
+
+ Returns
+ -------
+
+ matrix
+ A new matrix whose entries are random floats chosen uniformly from
+ the interval [-RANDOM_MAX, RANDOM_MAX].
+
+ Examples
+ --------
+
+ >>> A = random_matrix(3)
+ >>> A.size
+ (3, 3)
+
+ """
+ return matrix([[random_scalar()
+ for _ in range(dims)]
+ for _ in range(dims)])
+
+
+def random_nonnegative_matrix(dims):
+ """
+ Generate a random square matrix with nonnegative entries.
+
+ Parameters
+ ----------
+
+ dims : int
+ The number of rows/columns you want in the returned matrix.
+
+ Returns
+ -------
+
+ matrix
+ A new matrix whose entries are chosen by :func:`random_nn_scalar`.
+
+ Examples
+ --------
+
+ >>> A = random_nonnegative_matrix(3)
+ >>> A.size
+ (3, 3)
+ >>> all([entry >= 0 for entry in A])
+ True
+
+ """
+ return matrix([[random_nn_scalar()
+ for _ in range(dims)]
+ for _ in range(dims)])
+
+
+def random_diagonal_matrix(dims):
+ """
+ Generate a random square matrix with zero off-diagonal entries.
+
+ These matrices are Lyapunov-like on the nonnegative orthant, as is
+ fairly easy to see.
+
+ Parameters
+ ----------
+
+ dims : int
+ The number of rows/columns you want in the returned matrix.
+
+ Returns
+ -------
+
+ matrix
+ A new matrix whose diagonal entries are random floats chosen
+ using func:`random_scalar` and whose off-diagonal entries are
+ zero.
+
+ Examples
+ --------
+
+ >>> A = random_diagonal_matrix(3)
+ >>> A.size
+ (3, 3)
+ >>> A[0,1] == A[0,2] == A[1,0] == A[2,0] == A[1,2] == A[2,1] == 0
+ True
+
+ """
+ return matrix([[random_scalar()*int(i == j)
+ for i in range(dims)]
+ for j in range(dims)])
+
+
+def random_skew_symmetric_matrix(dims):
+ """
+ Generate a random skew-symmetrix matrix.
+
+ Parameters
+ ----------
+
+ dims : int
+ The number of rows/columns you want in the returned matrix.
+
+ Returns
+ -------
+
+ matrix
+ A new skew-matrix whose strictly above-diagonal entries are
+ random floats chosen with :func:`random_scalar`.
+
+ Examples
+ --------
+
+ >>> A = random_skew_symmetric_matrix(3)
+ >>> A.size
+ (3, 3)
+
+ >>> from dunshire.matrices import norm
+ >>> A = random_skew_symmetric_matrix(random_natural())
+ >>> norm(A + A.trans()) < options.ABS_TOL
+ True
+
+ """
+ strict_ut = [[random_scalar()*int(i < j)
+ for i in range(dims)]
+ for j in range(dims)]
+
+ strict_ut = matrix(strict_ut, (dims, dims))
+ return strict_ut - strict_ut.trans()
+
+
+def random_lyapunov_like_icecream(dims):
+ r"""
+ Generate a random matrix Lyapunov-like on the ice-cream cone.
+
+ The form of these matrices is cited in Gowda and Tao
+ [GowdaTao]_. The scalar ``a`` and the vector ``b`` (using their
+ notation) are easy to generate. The submatrix ``D`` is a little
+ trickier, but it can be found noticing that :math:`C + C^{T} = 0`
+ for a skew-symmetric matrix :math:`C` implying that :math:`C + C^{T}
+ + \left(2a\right)I = \left(2a\right)I`. Thus we can stick an
+ :math:`aI` with each of :math:`C,C^{T}` and let those be our
+ :math:`D,D^{T}`.
+
+ Parameters
+ ----------
+
+ dims : int
+ The dimension of the ice-cream cone (not of the matrix you want!)
+ on which the returned matrix should be Lyapunov-like.
+
+ Returns
+ -------
+
+ matrix
+ A new matrix, Lyapunov-like on the ice-cream cone in ``dims``
+ dimensions, whose free entries are random floats chosen uniformly
+ from the interval [-RANDOM_MAX, RANDOM_MAX].
+
+ References
+ ----------
+
+ .. [GowdaTao] M. S. Gowda and J. Tao. On the bilinearity rank of a
+ proper cone and Lyapunov-like transformations. Mathematical
+ Programming, 147:155-170, 2014.
+
+ Examples
+ --------
+
+ >>> L = random_lyapunov_like_icecream(3)
+ >>> L.size
+ (3, 3)
+ >>> x = matrix([1,1,0])
+ >>> s = matrix([1,-1,0])
+ >>> abs(inner_product(L*x, s)) < options.ABS_TOL
+ True
+
+ """
+ a = matrix([random_scalar()], (1, 1))
+ b = matrix([random_scalar() for _ in range(dims-1)], (dims-1, 1))
+ D = random_skew_symmetric_matrix(dims-1) + a*identity(dims-1)
+ row1 = append_col(a, b.trans())
+ row2 = append_col(b, D)
+ return append_row(row1, row2)
+
+
+def random_orthant_game():
+ """
+ Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a
+ random game over the nonnegative orthant, and return the
+ corresponding :class:`SymmetricLinearGame`.
+
+ We keep going until we generate a game with a condition number under
+ 5000.
+ """
+ ambient_dim = random_natural() + 1
+ K = NonnegativeOrthant(ambient_dim)
+ e1 = [random_nn_scalar() for _ in range(K.dimension())]
+ e2 = [random_nn_scalar() for _ in range(K.dimension())]
+ L = random_matrix(K.dimension())
+ G = SymmetricLinearGame(L, K, e1, e2)
+
+ if G.condition() <= MAX_COND:
+ return G
+ else:
+ return random_orthant_game()
+
+
+def random_icecream_game():
+ """
+ Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a
+ random game over the ice-cream cone, and return the corresponding
+ :class:`SymmetricLinearGame`.
+ """
+ # Use a minimum dimension of two to avoid divide-by-zero in
+ # the fudge factor we make up later.
+ ambient_dim = random_natural() + 1
+ K = IceCream(ambient_dim)
+ e1 = [1] # Set the "height" of e1 to one
+ e2 = [1] # And the same for e2
+
+ # If we choose the rest of the components of e1,e2 randomly
+ # between 0 and 1, then the largest the squared norm of the
+ # non-height part of e1,e2 could be is the 1*(dim(K) - 1). We
+ # need to make it less than one (the height of the cone) so
+ # that the whole thing is in the cone. The norm of the
+ # non-height part is sqrt(dim(K) - 1), and we can divide by
+ # twice that.
+ fudge_factor = 1.0 / (2.0*sqrt(K.dimension() - 1.0))
+ e1 += [fudge_factor*uniform(0, 1) for _ in range(K.dimension() - 1)]
+ e2 += [fudge_factor*uniform(0, 1) for _ in range(K.dimension() - 1)]
+ L = random_matrix(K.dimension())
+ G = SymmetricLinearGame(L, K, e1, e2)
+
+ if G.condition() <= MAX_COND:
+ return G
+ else:
+ return random_icecream_game()
+
+
+def random_ll_orthant_game():
+ """
+ Return a random Lyapunov game over some nonnegative orthant.
+ """
+ G = random_orthant_game()
+ L = random_diagonal_matrix(G._K.dimension())
+
+ # Replace the totally-random ``L`` with random Lyapunov-like one.
+ G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
+
+ while G.condition() > MAX_COND:
+ # Try again until the condition number is satisfactory.
+ G = random_orthant_game()
+ L = random_diagonal_matrix(G._K.dimension())
+ G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
+
+ return G
+
+
+def random_ll_icecream_game():
+ """
+ Return a random Lyapunov game over some ice-cream cone.
+ """
+ G = random_icecream_game()
+ L = random_lyapunov_like_icecream(G._K.dimension())
+
+ # Replace the totally-random ``L`` with random Lyapunov-like one.
+ G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
+
+ while G.condition() > MAX_COND:
+ # Try again until the condition number is satisfactory.
+ G = random_icecream_game()
+ L = random_lyapunov_like_icecream(G._K.dimension())
+ G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
+
+ return G
+
+
+def random_positive_orthant_game():
+ G = random_orthant_game()
+ L = random_nonnegative_matrix(G._K.dimension())
+
+ # Replace the totally-random ``L`` with the random nonnegative one.
+ G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
+
+ while G.condition() > MAX_COND:
+ # Try again until the condition number is satisfactory.
+ G = random_orthant_game()
+ L = random_nonnegative_matrix(G._K.dimension())
+ G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
+
+ return G
+
+
+def random_nn_scaling(G):
+ alpha = random_nn_scalar()
+ H = SymmetricLinearGame(alpha*G._L.trans(), G._K, G._e1, G._e2)
+
+ while H.condition() > MAX_COND:
+ # Loop until the condition number of H doesn't suck.
+ alpha = random_nn_scalar()
+ H = SymmetricLinearGame(alpha*G._L.trans(), G._K, G._e1, G._e2)
+
+ return (alpha, H)
+
+def random_translation(G):
+ alpha = random_scalar()
+ tensor_prod = G._e1 * G._e2.trans()
+ M = G._L + alpha*tensor_prod
+
+ H = SymmetricLinearGame(M.trans(), G._K, G._e1, G._e2)
+ while H.condition() > MAX_COND:
+ # Loop until the condition number of H doesn't suck.
+ alpha = random_scalar()
+ M = G._L + alpha*tensor_prod
+ H = SymmetricLinearGame(M.trans(), G._K, G._e1, G._e2)
+
+ return (alpha, H)
Unit tests for the :class:`SymmetricLinearGame` class.
"""
-MAX_COND = 250
-"""
-The maximum condition number of a randomly-generated game.
-"""
-
-RANDOM_MAX = 10
-"""
-When generating uniform random real numbers, this will be used as the
-largest allowed magnitude. It keeps our condition numbers down and other
-properties within reason.
-"""
-
-from math import sqrt
-from random import randint, uniform
from unittest import TestCase
-from cvxopt import matrix
-from dunshire.cones import NonnegativeOrthant, IceCream
+from dunshire.cones import NonnegativeOrthant
from dunshire.games import SymmetricLinearGame
-from dunshire.matrices import (append_col, append_row, eigenvalues_re,
- identity, inner_product)
+from dunshire.matrices import eigenvalues_re, inner_product
from dunshire import options
+from .randomgen import (RANDOM_MAX, random_icecream_game,
+ random_ll_icecream_game, random_ll_orthant_game,
+ random_nn_scaling, random_orthant_game,
+ random_positive_orthant_game, random_translation)
-
-def random_matrix(dims):
- """
- Generate a random square matrix.
-
- Parameters
- ----------
-
- dims : int
- The number of rows/columns you want in the returned matrix.
-
- Returns
- -------
-
- matrix
- A new matrix whose entries are random floats chosen uniformly from
- the interval [-RANDOM_MAX, RANDOM_MAX].
-
- Examples
- --------
-
- >>> A = random_matrix(3)
- >>> A.size
- (3, 3)
-
- """
- return matrix([[uniform(-RANDOM_MAX, RANDOM_MAX) for _ in range(dims)]
- for _ in range(dims)])
-
-
-def random_nonnegative_matrix(dims):
- """
- Generate a random square matrix with nonnegative entries.
-
- Parameters
- ----------
-
- dims : int
- The number of rows/columns you want in the returned matrix.
-
- Returns
- -------
-
- matrix
- A new matrix whose entries are random floats chosen uniformly from
- the interval [0, RANDOM_MAX].
-
- Examples
- --------
-
- >>> A = random_nonnegative_matrix(3)
- >>> A.size
- (3, 3)
- >>> all([entry >= 0 for entry in A])
- True
-
- """
- L = random_matrix(dims)
- return matrix([abs(entry) for entry in L], (dims, dims))
-
-
-def random_diagonal_matrix(dims):
- """
- Generate a random square matrix with zero off-diagonal entries.
-
- These matrices are Lyapunov-like on the nonnegative orthant, as is
- fairly easy to see.
-
- Parameters
- ----------
-
- dims : int
- The number of rows/columns you want in the returned matrix.
-
- Returns
- -------
-
- matrix
- A new matrix whose diagonal entries are random floats chosen
- uniformly from the interval [-RANDOM_MAX, RANDOM_MAX] and whose
- off-diagonal entries are zero.
-
- Examples
- --------
-
- >>> A = random_diagonal_matrix(3)
- >>> A.size
- (3, 3)
- >>> A[0,1] == A[0,2] == A[1,0] == A[2,0] == A[1,2] == A[2,1] == 0
- True
-
- """
- return matrix([[uniform(-RANDOM_MAX, RANDOM_MAX)*int(i == j)
- for i in range(dims)]
- for j in range(dims)])
-
-
-def random_skew_symmetric_matrix(dims):
- """
- Generate a random skew-symmetrix matrix.
-
- Parameters
- ----------
-
- dims : int
- The number of rows/columns you want in the returned matrix.
-
- Returns
- -------
-
- matrix
- A new skew-matrix whose strictly above-diagonal entries are
- random floats chosen uniformly from the interval
- [-RANDOM_MAX, RANDOM_MAX].
-
- Examples
- --------
-
- >>> A = random_skew_symmetric_matrix(3)
- >>> A.size
- (3, 3)
-
- >>> from dunshire.matrices import norm
- >>> A = random_skew_symmetric_matrix(randint(1, 10))
- >>> norm(A + A.trans()) < options.ABS_TOL
- True
-
- """
- strict_ut = [[uniform(-10, 10)*int(i < j) for i in range(dims)]
- for j in range(dims)]
-
- strict_ut = matrix(strict_ut, (dims, dims))
- return strict_ut - strict_ut.trans()
-
-
-def random_lyapunov_like_icecream(dims):
- r"""
- Generate a random matrix Lyapunov-like on the ice-cream cone.
-
- The form of these matrices is cited in Gowda and Tao
- [GowdaTao]_. The scalar ``a`` and the vector ``b`` (using their
- notation) are easy to generate. The submatrix ``D`` is a little
- trickier, but it can be found noticing that :math:`C + C^{T} = 0`
- for a skew-symmetric matrix :math:`C` implying that :math:`C + C^{T}
- + \left(2a\right)I = \left(2a\right)I`. Thus we can stick an
- :math:`aI` with each of :math:`C,C^{T}` and let those be our
- :math:`D,D^{T}`.
-
- Parameters
- ----------
-
- dims : int
- The dimension of the ice-cream cone (not of the matrix you want!)
- on which the returned matrix should be Lyapunov-like.
-
- Returns
- -------
-
- matrix
- A new matrix, Lyapunov-like on the ice-cream cone in ``dims``
- dimensions, whose free entries are random floats chosen uniformly
- from the interval [-10, 10].
-
- References
- ----------
-
- .. [GowdaTao] M. S. Gowda and J. Tao. On the bilinearity rank of a
- proper cone and Lyapunov-like transformations. Mathematical
- Programming, 147:155-170, 2014.
-
- Examples
- --------
-
- >>> L = random_lyapunov_like_icecream(3)
- >>> L.size
- (3, 3)
- >>> x = matrix([1,1,0])
- >>> s = matrix([1,-1,0])
- >>> abs(inner_product(L*x, s)) < options.ABS_TOL
- True
-
- """
- a = matrix([uniform(-10, 10)], (1, 1))
- b = matrix([uniform(-10, 10) for _ in range(dims-1)], (dims-1, 1))
- D = random_skew_symmetric_matrix(dims-1) + a*identity(dims-1)
- row1 = append_col(a, b.trans())
- row2 = append_col(b, D)
- return append_row(row1, row2)
-
-
-def random_orthant_game():
- """
- Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a
- random game over the nonnegative orthant, and return the
- corresponding :class:`SymmetricLinearGame`.
-
- We keep going until we generate a game with a condition number under
- 5000.
- """
- ambient_dim = randint(1, 10)
- K = NonnegativeOrthant(ambient_dim)
- e1 = [uniform(0.5, 10) for _ in range(K.dimension())]
- e2 = [uniform(0.5, 10) for _ in range(K.dimension())]
- L = random_matrix(K.dimension())
- G = SymmetricLinearGame(L, K, e1, e2)
-
- if G._condition() <= MAX_COND:
- return G
- else:
- return random_orthant_game()
-
-
-def random_icecream_game():
- """
- Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a
- random game over the ice-cream cone, and return the corresponding
- :class:`SymmetricLinearGame`.
- """
- # Use a minimum dimension of two to avoid divide-by-zero in
- # the fudge factor we make up later.
- ambient_dim = randint(2, 10)
- K = IceCream(ambient_dim)
- e1 = [1] # Set the "height" of e1 to one
- e2 = [1] # And the same for e2
-
- # If we choose the rest of the components of e1,e2 randomly
- # between 0 and 1, then the largest the squared norm of the
- # non-height part of e1,e2 could be is the 1*(dim(K) - 1). We
- # need to make it less than one (the height of the cone) so
- # that the whole thing is in the cone. The norm of the
- # non-height part is sqrt(dim(K) - 1), and we can divide by
- # twice that.
- fudge_factor = 1.0 / (2.0*sqrt(K.dimension() - 1.0))
- e1 += [fudge_factor*uniform(0, 1) for _ in range(K.dimension() - 1)]
- e2 += [fudge_factor*uniform(0, 1) for _ in range(K.dimension() - 1)]
- L = random_matrix(K.dimension())
- G = SymmetricLinearGame(L, K, e1, e2)
-
- if G._condition() <= MAX_COND:
- return G
- else:
- return random_icecream_game()
-
+EPSILON = 2*2*RANDOM_MAX*options.ABS_TOL
+"""
+This is the tolerance constant including fudge factors that we use to
+determine whether or not two numbers are equal in tests.
+
+The factor of two is because if we compare two solutions, both
+of which may be off by ``ABS_TOL``, then the result could be off
+by ``2*ABS_TOL``. The factor of ``RANDOM_MAX`` allows for
+scaling a result (by ``RANDOM_MAX``) that may be off by
+``ABS_TOL``. The final factor of two is to allow for the edge
+cases where we get an "unknown" result and need to lower the
+CVXOPT tolerance by a factor of two.
+"""
# Tell pylint to shut up about the large number of methods.
class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
"""
Test that ``first`` and ``second`` are equal within a multiple of
our default tolerances.
-
- The factor of two is because if we compare two solutions, both
- of which may be off by ``ABS_TOL``, then the result could be off
- by ``2*ABS_TOL``. The factor of ``RANDOM_MAX`` allows for
- scaling a result (by ``RANDOM_MAX``) that may be off by
- ``ABS_TOL``. The final factor of two is to allow for the edge
- cases where we get an "unknown" result and need to lower the
- CVXOPT tolerance by a factor of two.
"""
- self.assertTrue(abs(first - second) < 2*2*RANDOM_MAX*options.ABS_TOL)
+ self.assertTrue(abs(first - second) < EPSILON)
def assert_solution_exists(self, G):
to a smaller nonnegative real number.
"""
G = random_orthant_game()
- self.assertTrue(G._condition() >= 1.0)
+ self.assertTrue(G.condition() >= 1.0)
G = random_icecream_game()
- self.assertTrue(G._condition() >= 1.0)
+ self.assertTrue(G.condition() >= 1.0)
def test_solution_exists_orthant(self):
self.assertTrue(G.solution().game_value() < -options.ABS_TOL)
- def assert_scaling_works(self, game1):
+ def assert_scaling_works(self, G):
"""
Test that scaling ``L`` by a nonnegative number scales the value
of the game by the same number.
"""
- value1 = game1.solution().game_value()
-
- alpha = uniform(0.1, 10)
- game2 = SymmetricLinearGame(alpha*game1._L.trans(),
- game1._K,
- game1._e1,
- game1._e2)
-
- while game2._condition() > MAX_COND:
- # Loop until the condition number of game2 doesn't suck.
- alpha = uniform(0.1, 10)
- game2 = SymmetricLinearGame(alpha*game1._L.trans(),
- game1._K,
- game1._e1,
- game1._e2)
-
- value2 = game2.solution().game_value()
+ (alpha, H) = random_nn_scaling(G)
+ value1 = G.solution().game_value()
+ value2 = H.solution().game_value()
self.assert_within_tol(alpha*value1, value2)
self.assert_scaling_works(G)
- def assert_translation_works(self, game1):
+ def assert_translation_works(self, G):
"""
Check that translating ``L`` by alpha*(e1*e2.trans()) increases
the value of the associated game by alpha.
"""
# We need to use ``L`` later, so make sure we transpose it
# before passing it in as a column-indexed matrix.
- soln1 = game1.solution()
+ soln1 = G.solution()
value1 = soln1.game_value()
x_bar = soln1.player1_optimal()
y_bar = soln1.player2_optimal()
- tensor_prod = game1._e1*game1._e2.trans()
# This is the "correct" representation of ``M``, but COLUMN
# indexed...
- alpha = uniform(-10, 10)
- M = game1._L + alpha*tensor_prod
-
- # so we have to transpose it when we feed it to the constructor.
- game2 = SymmetricLinearGame(M.trans(), game1._K, game1._e1, game1._e2)
- while game2._condition() > MAX_COND:
- # Loop until the condition number of game2 doesn't suck.
- alpha = uniform(-10, 10)
- M = game1._L + alpha*tensor_prod
- game2 = SymmetricLinearGame(M.trans(),
- game1._K,
- game1._e1,
- game1._e2)
-
- value2 = game2.solution().game_value()
+ (alpha, H) = random_translation(G)
+ value2 = H.solution().game_value()
self.assert_within_tol(value1 + alpha, value2)
# Make sure the same optimal pair works.
- self.assert_within_tol(value2, inner_product(M*x_bar, y_bar))
+ self.assert_within_tol(value2, inner_product(H._L*x_bar, y_bar))
def test_translation_orthant(self):
self.assert_translation_works(G)
- def assert_opposite_game_works(self, game1):
+ def assert_opposite_game_works(self, G):
"""
Check the value of the "opposite" game that gives rise to a
value that is the negation of the original game. Comes from
"""
# This is the "correct" representation of ``M``, but
# COLUMN indexed...
- M = -game1._L.trans()
+ M = -G._L.trans()
# so we have to transpose it when we feed it to the constructor.
- # Note: the condition number of game2 should be comparable to game1.
- game2 = SymmetricLinearGame(M.trans(), game1._K, game1._e2, game1._e1)
+ # Note: the condition number of ``H`` should be comparable to ``G``.
+ H = SymmetricLinearGame(M.trans(), G._K, G._e2, G._e1)
- soln1 = game1.solution()
+ soln1 = G.solution()
x_bar = soln1.player1_optimal()
y_bar = soln1.player2_optimal()
- soln2 = game2.solution()
+ soln2 = H.solution()
self.assert_within_tol(-soln1.game_value(), soln2.game_value())
This test theoretically applies to the ice-cream cone as well,
but we don't know how to make positive operators on that cone.
"""
- G = random_orthant_game()
- L = random_nonnegative_matrix(G._K.dimension())
-
- # Replace the totally-random ``L`` with the random nonnegative one.
- G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
-
- while G._condition() > MAX_COND:
- # Try again until the condition number is satisfactory.
- G = random_orthant_game()
- L = random_nonnegative_matrix(G._K.dimension())
- G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
-
+ G = random_positive_orthant_game()
self.assertTrue(G.solution().game_value() >= -options.ABS_TOL)
# See :meth:`assert_within_tol` for an explanation of the
# fudge factors.
eigs = eigenvalues_re(G._L)
- epsilon = 2*2*RANDOM_MAX*options.ABS_TOL
- if soln.game_value() > epsilon:
+
+ if soln.game_value() > EPSILON:
# L should be positive stable
positive_stable = all([eig > -options.ABS_TOL for eig in eigs])
self.assertTrue(positive_stable)
- elif soln.game_value() < -epsilon:
+ elif soln.game_value() < -EPSILON:
# L should be negative stable
negative_stable = all([eig < options.ABS_TOL for eig in eigs])
self.assertTrue(negative_stable)
"""
Test that a Lyapunov game on the nonnegative orthant works.
"""
- G = random_orthant_game()
- L = random_diagonal_matrix(G._K.dimension())
-
- # Replace the totally-random ``L`` with random Lyapunov-like one.
- G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
-
- while G._condition() > MAX_COND:
- # Try again until the condition number is satisfactory.
- G = random_orthant_game()
- L = random_diagonal_matrix(G._K.dimension())
- G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
-
+ G = random_ll_orthant_game()
self.assert_lyapunov_works(G)
"""
Test that a Lyapunov game on the ice-cream cone works.
"""
- G = random_icecream_game()
- L = random_lyapunov_like_icecream(G._K.dimension())
-
- # Replace the totally-random ``L`` with random Lyapunov-like one.
- G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
-
- while G._condition() > MAX_COND:
- # Try again until the condition number is satisfactory.
- G = random_icecream_game()
- L = random_lyapunov_like_icecream(G._K.dimension())
- G = SymmetricLinearGame(L, G._K, G._e1, G._e2)
-
+ G = random_ll_icecream_game()
self.assert_lyapunov_works(G)
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