From 568402283154c166d3a39f5f6d3ef74e836db9d4 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Thu, 13 Oct 2016 12:33:31 -0400 Subject: [PATCH] Return CVXOPT matrices from the random matrix functions. --- src/dunshire/games.py | 79 ++++++++++++++++++------------------------- 1 file changed, 32 insertions(+), 47 deletions(-) diff --git a/src/dunshire/games.py b/src/dunshire/games.py index a039e1f..1364fdd 100644 --- a/src/dunshire/games.py +++ b/src/dunshire/games.py @@ -507,29 +507,29 @@ class SymmetricLinearGame: def _random_matrix(dims): """ - Generate a random square (``dims``-by-``dims``) matrix, - represented as a list of rows. This is used only by the - :class:`SymmetricLinearGameTest` class. + Generate a random square (``dims``-by-``dims``) matrix. This is used + only by the :class:`SymmetricLinearGameTest` class. """ - return [[uniform(-10, 10) for i in range(dims)] for j in range(dims)] + return matrix([[uniform(-10, 10) for i in range(dims)] + for j in range(dims)]) def _random_nonnegative_matrix(dims): """ Generate a random square (``dims``-by-``dims``) matrix with - nonnegative entries, represented as a list of rows. This is used - only by the :class:`SymmetricLinearGameTest` class. + nonnegative entries. This is used only by the + :class:`SymmetricLinearGameTest` class. """ L = _random_matrix(dims) - return [[abs(entry) for entry in row] for row in L] + return matrix([abs(entry) for entry in L], (dims, dims)) def _random_diagonal_matrix(dims): """ Generate a random square (``dims``-by-``dims``) matrix with nonzero - entries only on the diagonal, represented as a list of rows. This is - used only by the :class:`SymmetricLinearGameTest` class. + entries only on the diagonal. This is used only by the + :class:`SymmetricLinearGameTest` class. """ - return [[uniform(-10, 10)*int(i == j) for i in range(dims)] - for j in range(dims)] + return matrix([[uniform(-10, 10)*int(i == j) for i in range(dims)] + for j in range(dims)]) def _random_orthant_params(): """ @@ -542,7 +542,7 @@ def _random_orthant_params(): e1 = [uniform(0.5, 10) for idx in range(K.dimension())] e2 = [uniform(0.5, 10) for idx in range(K.dimension())] L = _random_matrix(K.dimension()) - return (L, K, e1, e2) + return (L, K, matrix(e1), matrix(e2)) def _random_icecream_params(): @@ -570,7 +570,7 @@ def _random_icecream_params(): e2 += [fudge_factor*uniform(0, 1) for idx in range(K.dimension() - 1)] L = _random_matrix(K.dimension()) - return (L, K, e1, e2) + return (L, K, matrix(e1), matrix(e2)) class SymmetricLinearGameTest(TestCase): @@ -599,14 +599,13 @@ class SymmetricLinearGameTest(TestCase): Given the parameters needed to construct a SymmetricLinearGame, ensure that that game has a solution. """ - G = SymmetricLinearGame(L, K, e1, e2) - soln = G.solution() - # The matrix() constructor assumes that ``L`` is a list of # columns, so we transpose it to agree with what # SymmetricLinearGame() thinks. - L_matrix = matrix(L).trans() - expected = inner_product(L_matrix*soln.player1_optimal(), + G = SymmetricLinearGame(L.trans(), K, e1, e2) + soln = G.solution() + + expected = inner_product(L*soln.player1_optimal(), soln.player2_optimal()) self.assert_within_tol(soln.game_value(), expected) @@ -650,9 +649,6 @@ class SymmetricLinearGameTest(TestCase): Test that scaling ``L`` by a nonnegative number scales the value of the game by the same number. """ - # Make ``L`` a matrix so that we can scale it by alpha. Its - # random, so who cares if it gets transposed. - L = matrix(L) game1 = SymmetricLinearGame(L, K, e1, e2) value1 = game1.solution().game_value() @@ -685,23 +681,19 @@ class SymmetricLinearGameTest(TestCase): Check that translating ``L`` by alpha*(e1*e2.trans()) increases the value of the associated game by alpha. """ - e1 = matrix(e1, (K.dimension(), 1)) - e2 = matrix(e2, (K.dimension(), 1)) - game1 = SymmetricLinearGame(L, K, e1, e2) + # We need to use ``L`` later, so make sure we transpose it + # before passing it in as a column-indexed matrix. + game1 = SymmetricLinearGame(L.trans(), K, e1, e2) soln1 = game1.solution() value1 = soln1.game_value() x_bar = soln1.player1_optimal() y_bar = soln1.player2_optimal() - # Make ``L`` a CVXOPT matrix so that we can do math with - # it. Note that this gives us the "correct" representation of - # ``L`` (in agreement with what G has), but COLUMN indexed. alpha = uniform(-10, 10) - L = matrix(L).trans() tensor_prod = e1*e2.trans() - # Likewise, this is the "correct" representation of ``M``, but - # COLUMN indexed... + # This is the "correct" representation of ``M``, but COLUMN + # indexed... M = L + alpha*tensor_prod # so we have to transpose it when we feed it to the constructor. @@ -737,16 +729,11 @@ class SymmetricLinearGameTest(TestCase): value that is the negation of the original game. Comes from some corollary. """ - e1 = matrix(e1, (K.dimension(), 1)) - e2 = matrix(e2, (K.dimension(), 1)) - game1 = SymmetricLinearGame(L, K, e1, e2) + # We need to use ``L`` later, so make sure we transpose it + # before passing it in as a column-indexed matrix. + game1 = SymmetricLinearGame(L.trans(), K, e1, e2) - # Make ``L`` a CVXOPT matrix so that we can do math with - # it. Note that this gives us the "correct" representation of - # ``L`` (in agreement with what G has), but COLUMN indexed. - L = matrix(L).trans() - - # Likewise, this is the "correct" representation of ``M``, but + # This is the "correct" representation of ``M``, but # COLUMN indexed... M = -L.trans() @@ -788,17 +775,14 @@ class SymmetricLinearGameTest(TestCase): Two orthogonality relations hold at an optimal solution, and we check them here. """ - game = SymmetricLinearGame(L, K, e1, e2) + # We need to use ``L`` later, so make sure we transpose it + # before passing it in as a column-indexed matrix. + game = SymmetricLinearGame(L.trans(), K, e1, e2) soln = game.solution() x_bar = soln.player1_optimal() y_bar = soln.player2_optimal() value = soln.game_value() - # Make these matrices so that we can compute with them. - L = matrix(L).trans() - e1 = matrix(e1, (K.dimension(), 1)) - e2 = matrix(e2, (K.dimension(), 1)) - ip1 = inner_product(y_bar, L*x_bar - value*e1) self.assert_within_tol(ip1, 0) @@ -840,13 +824,15 @@ class SymmetricLinearGameTest(TestCase): game = SymmetricLinearGame(L, K, e1, e2) self.assertTrue(game.solution().game_value() >= -options.ABS_TOL) + def test_lyapunov_orthant(self): """ Test that a Lyapunov game on the nonnegative orthant works. """ - (_, K, e1, e2) = _random_orthant_params() + (L, K, e1, e2) = _random_orthant_params() # Ignore that L, we need a diagonal (Lyapunov-like) one. + # (And we don't need to transpose those.) L = _random_diagonal_matrix(K.dimension()) game = SymmetricLinearGame(L, K, e1, e2) soln = game.solution() @@ -854,7 +840,6 @@ class SymmetricLinearGameTest(TestCase): # We only check for positive/negative stability if the game # value is not basically zero. If the value is that close to # zero, we just won't check any assertions. - L = matrix(L).trans() if soln.game_value() > options.ABS_TOL: # L should be positive stable ps = all([eig > -options.ABS_TOL for eig in eigenvalues_re(L)]) -- 2.44.2