# These are mostly actually needed.
from cvxopt import matrix, printing, solvers
-from cones import CartesianProduct, IceCream, NonnegativeOrthant
-from errors import GameUnsolvableException
-from matrices import (append_col, append_row, eigenvalues_re, identity,
- inner_product, norm)
-import options
+from .cones import CartesianProduct, IceCream, NonnegativeOrthant
+from .errors import GameUnsolvableException
+from .matrices import (append_col, append_row, eigenvalues_re, identity,
+ inner_product, norm)
+from . import options
printing.options['dformat'] = options.FLOAT_FORMAT
solvers.options['show_progress'] = options.VERBOSE
Examples
--------
- >>> from cones import NonnegativeOrthant
>>> K = NonnegativeOrthant(3)
>>> L = [[1,-5,-15],[-1,2,-3],[-12,-15,1]]
>>> e1 = [1,1,1]
Lists can (and probably should) be used for every argument::
- >>> from cones import NonnegativeOrthant
>>> K = NonnegativeOrthant(2)
>>> L = [[1,0],[0,1]]
>>> e1 = [1,1]
>>> import cvxopt
>>> import numpy
- >>> from cones import NonnegativeOrthant
>>> K = NonnegativeOrthant(2)
>>> L = [[1,0],[0,1]]
>>> e1 = cvxopt.matrix([1,1])
otherwise indexed by columns::
>>> import cvxopt
- >>> from cones import NonnegativeOrthant
>>> K = NonnegativeOrthant(2)
>>> L = [[1,2],[3,4]]
>>> e1 = [1,1]
This example is computed in Gowda and Ravindran in the section
"The value of a Z-transformation"::
- >>> from cones import NonnegativeOrthant
>>> K = NonnegativeOrthant(3)
>>> L = [[1,-5,-15],[-1,2,-3],[-12,-15,1]]
>>> e1 = [1,1,1]
The value of the following game can be computed using the fact
that the identity is invertible::
- >>> from cones import NonnegativeOrthant
>>> K = NonnegativeOrthant(3)
>>> L = [[1,0,0],[0,1,0],[0,0,1]]
>>> e1 = [1,2,3]
Examples
--------
- >>> from cones import NonnegativeOrthant
>>> K = NonnegativeOrthant(3)
>>> L = [[1,-5,-15],[-1,2,-3],[-12,-15,1]]
>>> e1 = [1,1,1]
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():
"""
Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a
return (L, K, matrix(e1), matrix(e2))
-class SymmetricLinearGameTest(TestCase):
+# Tell pylint to shut up about the large number of methods.
+class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904
"""
Tests for the SymmetricLinearGame and Solution classes.
"""
This test theoretically applies to the ice-cream cone as well,
but we don't know how to make positive operators on that cone.
"""
- (_, K, e1, e2) = _random_orthant_params()
-
- # Ignore that L, we need a nonnegative one.
+ (K, e1, e2) = _random_orthant_params()[1:]
L = _random_nonnegative_matrix(K.dimension())
game = SymmetricLinearGame(L, K, e1, e2)
self.assertTrue(game.solution().game_value() >= -options.ABS_TOL)
- def test_lyapunov_orthant(self):
+ def assert_lyapunov_works(self, L, K, e1, e2):
"""
- Test that a Lyapunov game on the nonnegative orthant works.
+ Check that Lyapunov games act the way we expect.
"""
- (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()
# 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.
+ eigs = eigenvalues_re(L)
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)
+ positive_stable = all([eig > -options.ABS_TOL for eig in eigs])
+ self.assertTrue(positive_stable)
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)
+ negative_stable = all([eig < options.ABS_TOL for eig in eigs])
+ self.assertTrue(negative_stable)
# 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.
+ """
+ (K, e1, e2) = _random_orthant_params()[1:]
+ 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.
+ """
+ (K, e1, e2) = _random_icecream_params()[1:]
+ L = _random_lyapunov_like_icecream(K.dimension())
+
+ self.assert_lyapunov_works(L, K, e1, e2)
projects / dunshire.git / blobdiff