def test_chebyshev_center(self):
# The goal is to find the largest Euclidean ball (i.e. its center and
# radius) that lies in a polyhedron described by linear inequalites in this
# fashion: P = {x : a_i'*x <= b_i, i=1,...,m} where x is in R^2
# Generate the input data
a1 = np.matrix("2; 1")
a2 = np.matrix(" 2; -1")
a3 = np.matrix("-1; 2")
a4 = np.matrix("-1; -2")
b = np.ones([4,1])
# Create and solve the model
r = Variable(name='r')
x_c = Variable(2,name='x_c')
obj = Maximize(r)
constraints = [ #TODO have atoms compute values for constants.
a1.T*x_c + np.linalg.norm(a1)*r <= b[0],
a2.T*x_c + np.linalg.norm(a2)*r <= b[1],
a3.T*x_c + np.linalg.norm(a3)*r <= b[2],
a4.T*x_c + np.linalg.norm(a4)*r <= b[3],
]
p = Problem(obj, constraints)
result = p.solve()
self.assertAlmostEqual(result, 0.4472)
self.assertAlmostEqual(r.value, result)
self.assertAlmostEqual(x_c.value, [0,0])
def test_numpy_matrices(self):
# Vector
v = numpy.matrix( numpy.arange(2).reshape((2,1)) )
self.assertEquals((self.x + v).size, (2,1))
self.assertEquals((v + v + self.x).size, (2,1))
self.assertEquals((self.x - v).size, (2,1))
self.assertEquals((v - v - self.x).size, (2,1))
self.assertEquals((self.x <= v).size, (2,1))
self.assertEquals((v <= self.x).size, (2,1))
self.assertEquals((self.x == v).size, (2,1))
self.assertEquals((v == self.x).size, (2,1))
# Matrix
A = numpy.matrix( numpy.arange(8).reshape((4,2)) )
self.assertEquals((A*self.x).size, (4,1))
self.assertEquals(( (A.T*A) * self.x).size, (2,1))
def test_numpy_matrix(self):
interface = intf.get_matrix_interface(np.matrix)
# const_to_matrix
mat = interface.const_to_matrix([1,2,3])
self.assertEquals(interface.size(mat), (3,1))
mat = interface.const_to_matrix([[1],[2],[3]])
self.assertEquals(mat[0,0], 1)
# identity
mat = interface.identity(4)
cvxopt_dense = intf.get_matrix_interface(cvxopt.matrix)
cmp_mat = interface.const_to_matrix(cvxopt_dense.identity(4))
self.assertEquals(interface.size(mat), interface.size(cmp_mat))
assert not (mat - cmp_mat).any()
# scalar_matrix
mat = interface.scalar_matrix(2,4,3)
self.assertEquals(interface.size(mat), (4,3))
self.assertEquals(interface.index(mat, (1,2)), 2)
# reshape
mat = interface.const_to_matrix([[1,2,3],[3,4,5]])
mat = interface.reshape(mat, (6,1))
self.assertEquals(interface.index(mat, (4,0)), 4)
# index
mat = interface.const_to_matrix([[1,2,3,4],[3,4,5,6]])
self.assertEquals( interface.index(mat, (0,1)), 3)
mat = interface.index(mat, (slice(1,4,2), slice(0,2,None)))
assert not (mat - np.matrix("2 4; 4 6")).any()
def test_chebyshev_center(self):
# The goal is to find the largest Euclidean ball (i.e. its center and
# radius) that lies in a polyhedron described by linear inequalites in this
# fashion: P = {x : a_i'*x <= b_i, i=1,...,m} where x is in R^2
# Generate the input data
a1 = np.matrix("2; 1")
a2 = np.matrix(" 2; -1")
a3 = np.matrix("-1; 2")
a4 = np.matrix("-1; -2")
b = np.ones([4,1])
# Create and solve the model
r = Variable(name='r')
x_c = Variable(2,name='x_c')
obj = Maximize(r)
constraints = [ #TODO have atoms compute values for constants.
a1.T*x_c + np.linalg.norm(a1)*r <= b[0],
a2.T*x_c + np.linalg.norm(a2)*r <= b[1],
a3.T*x_c + np.linalg.norm(a3)*r <= b[2],
a4.T*x_c + np.linalg.norm(a4)*r <= b[3],
]
p = Problem(obj, constraints)
result = p.solve()
self.assertAlmostEqual(result, 0.4472)
self.assertAlmostEqual(r.value, result)
self.assertAlmostEqual(x_c.value, [0,0])
# # Risk return tradeoff curve
# def test_risk_return_tradeoff(self):
# from math import sqrt
# from cvxopt import matrix
# from cvxopt.blas import dot
# from cvxopt.solvers import qp, options
# import scipy
# n = 4
# S = matrix( [[ 4e-2, 6e-3, -4e-3, 0.0 ],
# [ 6e-3, 1e-2, 0.0, 0.0 ],
# [-4e-3, 0.0, 2.5e-3, 0.0 ],
# [ 0.0, 0.0, 0.0, 0.0 ]] )
# pbar = matrix([.12, .10, .07, .03])
# N = 100
# # CVXPY
# Sroot = numpy.asmatrix(scipy.linalg.sqrtm(S))
# x = Variable(n, name='x')
# mu = Parameter(name='mu')
# mu.value = 1 # TODO Parameter("positive")
# objective = Minimize(-pbar*x + mu*quad_over_lin(Sroot*x,1))
# constraints = [sum(x) == 1, x >= 0]
# p = Problem(objective, constraints)
# mus = [ 10**(5.0*t/N-1.0) for t in range(N) ]
# xs = []
# for mu_val in mus:
# mu.value = mu_val
# p.solve()
# xs.append(x.value)
# returns = [ dot(pbar,x) for x in xs ]
# risks = [ sqrt(dot(x, S*x)) for x in xs ]
# # QP solver
