X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2Fdunshire%2Fgames.py;h=3d4b09ad8c0c12ff1bba0294a1c5c87ae8ff72bf;hb=bd5a4b0c8519de2a938663acdbc080560f829628;hp=692a0ae550305c3ae56833d500c263498f070889;hpb=1c7a9200a0e65869f46eda49682f76a4f134dccd;p=dunshire.git diff --git a/src/dunshire/games.py b/src/dunshire/games.py index 692a0ae..3d4b09a 100644 --- a/src/dunshire/games.py +++ b/src/dunshire/games.py @@ -14,7 +14,8 @@ from unittest import TestCase from cvxopt import matrix, printing, solvers from cones import CartesianProduct, IceCream, NonnegativeOrthant from errors import GameUnsolvableException -from matrices import append_col, append_row, identity, inner_product, norm +from matrices import (append_col, append_row, eigenvalues_re, identity, + inner_product, norm) import options printing.options['dformat'] = options.FLOAT_FORMAT @@ -504,13 +505,63 @@ class SymmetricLinearGame: -def _random_square_matrix(dims): +def _random_matrix(dims): """ - Generate a random square (``dims``-by-``dims``) matrix, - represented as a list of rows. This is used only by the + Generate a random square (``dims``-by-``dims``) matrix. This is used + only by the :class:`SymmetricLinearGameTest` class. + """ + 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. This is used only by the + :class:`SymmetricLinearGameTest` class. + """ + L = _random_matrix(dims) + 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. 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)*int(i == j) for i in range(dims)] + for j in range(dims)]) + + +def _random_skew_symmetric_matrix(dims): + """ + Generate a random skew-symmetrix (``dims``-by-``dims``) matrix. + + Examples + -------- + + >>> 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): + """ + Generate a random Lyapunov-like matrix over the ice-cream cone in + ``dims`` dimensions. + """ + a = matrix([uniform(-10,10)], (1,1)) + b = matrix([uniform(-10,10) for idx 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_params(): @@ -523,8 +574,8 @@ def _random_orthant_params(): K = NonnegativeOrthant(ambient_dim) e1 = [uniform(0.5, 10) for idx in range(K.dimension())] e2 = [uniform(0.5, 10) for idx in range(K.dimension())] - L = _random_square_matrix(K.dimension()) - return (L, K, e1, e2) + L = _random_matrix(K.dimension()) + return (L, K, matrix(e1), matrix(e2)) def _random_icecream_params(): @@ -550,9 +601,9 @@ def _random_icecream_params(): fudge_factor = 1.0 / (2.0*sqrt(K.dimension() - 1.0)) e1 += [fudge_factor*uniform(0, 1) for idx in range(K.dimension() - 1)] e2 += [fudge_factor*uniform(0, 1) for idx in range(K.dimension() - 1)] - L = _random_square_matrix(K.dimension()) + L = _random_matrix(K.dimension()) - return (L, K, e1, e2) + return (L, K, matrix(e1), matrix(e2)) class SymmetricLinearGameTest(TestCase): @@ -581,14 +632,13 @@ 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) @@ -632,9 +682,6 @@ 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() @@ -667,23 +714,19 @@ 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. @@ -719,16 +762,11 @@ 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) - - # 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() + # 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) - # Likewise, this is the "correct" representation of ``M``, but + # This is the "correct" representation of ``M``, but # COLUMN indexed... M = -L.trans() @@ -770,17 +808,14 @@ 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) @@ -814,11 +849,60 @@ class SymmetricLinearGameTest(TestCase): This test theoretically applies to the ice-cream cone as well, but we don't know how to make positive operators on that cone. """ - (L, K, e1, e2) = _random_orthant_params() + (_, K, e1, e2) = _random_orthant_params() - # Make the entries of ``L`` nonnegative... this makes it a - # positive operator on ``K``. - L = [[abs(entry) for entry in row] for row in L] + # Ignore that L, we need a nonnegative one. + L = _random_nonnegative_matrix(K.dimension()) game = SymmetricLinearGame(L, K, e1, e2) self.assertTrue(game.solution().game_value() >= -options.ABS_TOL) + + + def assert_lyapunov_works(self, L, K, e1, e2): + """ + Check that Lyapunov games act the way we expect. + """ + game = SymmetricLinearGame(L, K, e1, e2) + soln = game.solution() + + # 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. + if soln.game_value() > options.ABS_TOL: + # L should be positive stable + ps = all([eig > -options.ABS_TOL for eig in eigenvalues_re(L)]) + self.assertTrue(ps) + elif soln.game_value() < -options.ABS_TOL: + # L should be negative stable + ns = all([eig < options.ABS_TOL for eig in eigenvalues_re(L)]) + self.assertTrue(ns) + + # The dual game's value should always equal the primal's. + dualsoln = game.dual().solution() + self.assert_within_tol(dualsoln.game_value(), soln.game_value()) + + + def test_lyapunov_orthant(self): + """ + Test that a Lyapunov game on the nonnegative orthant works. + """ + (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()) + + self.assert_lyapunov_works(L, K, e1, e2) + + + def test_lyapunov_icecream(self): + """ + Test that a Lyapunov game on the ice-cream cone works. + """ + (L, K, e1, e2) = _random_icecream_params() + + # Ignore that L, we need a diagonal (Lyapunov-like) one. + # (And we don't need to transpose those.) + L = _random_lyapunov_like_icecream(K.dimension()) + + self.assert_lyapunov_works(L, K, e1, e2)