def test_power(self):
x = Variable(3)
y = Variable(3)
self.assertFalse(x.is_constant())
self.assertTrue(x.is_affine())
self.assertTrue(x.is_quadratic())
with warnings.catch_warnings():
warnings.simplefilter("ignore")
s = power(x.T*y, 0)
self.assertTrue(s.is_constant())
self.assertTrue(s.is_affine())
self.assertTrue(s.is_quadratic())
t = power(x-y, 1)
self.assertFalse(t.is_constant())
self.assertTrue(t.is_affine())
self.assertTrue(t.is_quadratic())
u = power(x+2*y, 2)
self.assertFalse(u.is_constant())
self.assertFalse(u.is_affine())
self.assertTrue(u.is_quadratic())
self.assertTrue(u.is_dcp())
w = (x+2*y)**2
self.assertFalse(w.is_constant())
self.assertFalse(w.is_affine())
self.assertTrue(w.is_quadratic())
self.assertTrue(w.is_dcp())
def test_assign_var_value(self):
"""Test assigning a value to a variable.
"""
# Scalar variable.
a = Variable()
a.value = 1
self.assertEqual(a.value, 1)
with self.assertRaises(Exception) as cm:
a.value = [2, 1]
self.assertEqual(str(cm.exception), "Invalid dimensions (2, 1) for Variable value.")
# Test assigning None.
a.value = 1
a.value = None
assert a.value is None
# Vector variable.
x = Variable(2)
x.value = [2, 1]
self.assertItemsAlmostEqual(x.value, [2, 1])
# Matrix variable.
A = Variable(3, 2)
A.value = np.ones((3, 2))
self.assertItemsAlmostEqual(A.value, np.ones((3, 2)))
# Test assigning negative val to nonnegative variable.
x = NonNegative()
with self.assertRaises(Exception) as cm:
x.value = -2
self.assertEqual(str(cm.exception), "Invalid sign for NonNegative value.")
def test_partial_optimize_numeric_fn(self):
x, y = Variable(1), Variable(1)
xval = 4
# Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
p1 = Problem(Minimize(y), [xval + y >= 3])
p1.solve()
# Solve the two-stage problem via partial_optimize
constr = [y >= -100]
p2 = Problem(Minimize(y), [x + y >= 3] + constr)
g = cvxpy.partial_optimize(p2, [y], [x])
x.value = xval
y.value = 42
constr[0].dual_variable.value = 42
result = g.value
self.assertAlmostEqual(result, p1.value)
self.assertAlmostEqual(y.value, 42)
self.assertAlmostEqual(constr[0].dual_value, 42)
# No variables optimized over.
p2 = Problem(Minimize(y), [x + y >= 3])
g = cvxpy.partial_optimize(p2, [], [x, y])
x.value = xval
y.value = 42
p2.constraints[0].dual_variable.value = 42
result = g.value
self.assertAlmostEqual(result, y.value)
self.assertAlmostEqual(y.value, 42)
self.assertAlmostEqual(p2.constraints[0].dual_value, 42)
def test_consistency(self):
"""Test that variables and constraints keep a consistent order.
"""
import itertools
num_solves = 4
vars_lists = []
ineqs_lists = []
for k in range(num_solves):
sum = 0
constraints = []
for i in range(100):
var = Variable(name=str(i))
sum += var
constraints.append(var >= i)
obj = Minimize(sum)
p = Problem(obj, constraints)
objective, constr_map, dims = p.canonicalize()
all_ineq = itertools.chain(constr_map[s.EQ], constr_map[s.INEQ])
var_info = p._get_var_offsets(objective, all_ineq)
sorted_vars, var_offsets, x_length = var_info
vars_lists.append([int(v.name()) for v in sorted_vars])
ineqs_lists.append(constr_map[s.INEQ])
# Verify order of variables is consistent.
for i in range(num_solves):
self.assertEqual(range(100), vars_lists[i])
for i in range(num_solves):
for idx, constr in enumerate(ineqs_lists[i]):
var = constr.variables()[0]
self.assertEqual(idx, int(var.name()))
def test_scipy_sparse(self):
"""Test scipy sparse matrices."""
# Constants.
A = numpy.matrix( numpy.arange(8).reshape((4,2)) )
A = sp.csc_matrix(A)
A = sp.eye(2).tocsc()
key = (slice(0, 1, None), slice(None, None, None))
Aidx = intf.index(A, (slice(0, 2, None), slice(None, None, None)))
Aidx = intf.index(Aidx, key)
self.assertEqual(Aidx.shape, (1, 2))
self.assertEqual(Aidx[0,0], 1)
self.assertEqual(Aidx[0,1], 0)
# Linear ops.
var = Variable(4, 2)
A = numpy.matrix( numpy.arange(8).reshape((4,2)) )
A = sp.csc_matrix(A)
B = sp.hstack([A, A])
self.assertExpression(var + A, (4, 2))
self.assertExpression(A + var, (4, 2))
self.assertExpression(B * var, (4, 2))
self.assertExpression(var - A, (4, 2))
self.assertExpression(A - A - var, (4, 2))
if PY35:
self.assertExpression(var.__rmatmul__(B), (4,2))
def test_power(self):
x = Variable(3)
y = Variable(3)
self.assertFalse(x.is_constant())
self.assertTrue(x.is_affine())
self.assertTrue(x.is_quadratic())
s = power(x.T*y, 0)
self.assertTrue(s.is_constant())
self.assertTrue(s.is_affine())
self.assertTrue(s.is_quadratic())
t = power(x-y, 1)
self.assertFalse(t.is_constant())
self.assertTrue(t.is_affine())
self.assertTrue(t.is_quadratic())
u = power(x+2*y, 2)
self.assertFalse(u.is_constant())
self.assertFalse(u.is_affine())
self.assertTrue(u.is_quadratic())
self.assertTrue(u.is_dcp())
w = (x+2*y)**2
self.assertFalse(w.is_constant())
self.assertFalse(w.is_affine())
self.assertTrue(w.is_quadratic())
self.assertTrue(w.is_dcp())
def test_affine(self):
"""Test grad for affine atoms.
"""
expr = -self.a
self.a.value = 2
self.assertAlmostEquals(expr.grad[self.a], -1)
expr = -(self.x)
self.x.value = [3,4]
val = np.zeros((2,2)) - np.diag([1,1])
self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)
expr = -(self.A)
self.A.value = [[1,2], [3,4]]
val = np.zeros((4,4)) - np.diag([1,1,1,1])
self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)
expr = self.A[0,1]
self.A.value = [[1,2], [3,4]]
val = np.zeros((4,1))
val[2] = 1
self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)
z = Variable(3)
expr = vstack(self.x, z)
self.x.value = [1,2]
z.value = [1,2,3]
val = np.zeros((2,5))
val[:,0:2] = np.eye(2)
self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)
val = np.zeros((3,5))
val[:,2:] = np.eye(3)
self.assertItemsAlmostEqual(expr.grad[z].todense(), val)
def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2,1))
self.assertEqual(y.size, (1,1))
self.assertEqual(x.curvature, u.Curvature.AFFINE)
self.assertEqual(x.canonicalize()[0].size, (2,1))
self.assertEqual(x.canonicalize()[1], [])
# Scalar variable
coeff = self.a.coefficients(self.intf)
self.assertEqual(coeff[self.a], 1)
# Vector variable.
coeffs = x.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), [x])
vec = coeffs[x]
self.assertEqual(vec.size, (2,2))
self.assertEqual(list(vec), [1,0,0,1])
# Matrix variable.
coeffs = self.A.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), [self.A])
mat = coeffs[self.A]
self.assertEqual(mat.size, (2,2))
self.assertEqual(list(mat), [1,0,0,1])
def setUp(self):
self.x = Variable(2, name='x')
self.y = Variable(2, name='y')
self.A = Variable(3,2, name='A')
self.B = Variable(5,2, name='B')
self.C = Constant([[1, 2], [1, 2]])
self.intf = intf.DEFAULT_INTERFACE
def setUp(self):
self.x = Variable(2, name="x")
self.y = Variable(2, name="y")
self.A = Variable(3, 2, name="A")
self.B = Variable(5, 2, name="B")
self.C = Constant([[1, 2], [1, 2]])
self.intf = intf.DEFAULT_INTERFACE
def setUp(self):
self.a = Variable()
self.x = Variable(2, name='x')
self.y = Variable(2, name='y')
self.A = Variable(2,2)
self.c = Constant(3)
self.C = Constant([[1, 2], [1, 2]])
def setUp(self):
self.x = Variable(2, name="x")
self.y = Variable(2, name="y")
self.A = Constant([[1, 2], [1, 2]])
self.xAff = AffObjective([self.x], [deque([self.x])], u.Shape(2, 1))
self.yAff = AffObjective([self.y], [deque([self.y])], u.Shape(2, 1))
self.constAff = AffObjective([self.A], [deque([self.A])], u.Shape(2, 2))
self.intf = intf.DEFAULT_INTERFACE
def setUp(self):
self.a = Variable(name='a')
self.b = Variable(name='b')
self.x = Variable(2, name='x')
self.y = Variable(3, name='y')
self.z = Variable(2, name='z')
self.A = Variable(2,2,name='A')
self.B = Variable(2,2,name='B')
self.C = Variable(3,2,name='C')
def test_var_copy(self):
"""Test the copy function for variable types.
"""
x = Variable(3, 4, name="x")
y = x.copy()
self.assertEqual(y.size, (3, 4))
self.assertEqual(y.name(), "x")
x = Semidef(5, name="x")
y = x.copy()
self.assertEqual(y.size, (5, 5))
def setUp(self):
self.a = Variable(name='a')
self.x = Variable(2, name='x')
self.y = Variable(3, name='y')
self.z = Variable(2, name='z')
self.A = Variable(2,2,name='A')
self.B = Variable(2,2,name='B')
self.C = Variable(3,2,name='C')
self.intf = intf.DEFAULT_INTERFACE
def setUp(self):
self.a = Variable(name="a")
self.x = Variable(2, name="x")
self.y = Variable(3, name="y")
self.z = Variable(2, name="z")
self.A = Variable(2, 2, name="A")
self.B = Variable(2, 2, name="B")
self.C = Variable(3, 2, name="C")
self.intf = intf.DEFAULT_INTERFACE
def setUp(self):
self.a = Variable(name="a")
self.b = Variable(name="b")
self.x = Variable(2, name="x")
self.y = Variable(3, name="y")
self.z = Variable(2, name="z")
self.A = Variable(2, 2, name="A")
self.B = Variable(2, 2, name="B")
self.C = Variable(3, 2, name="C")
def test_matrix_multiplication(self):
x = Variable(3, 5)
y = Variable(3, 5)
self.assertFalse(x.is_constant())
self.assertTrue(x.is_affine())
self.assertTrue(x.is_quadratic())
s = x.T*y
self.assertFalse(s.is_constant())
self.assertFalse(s.is_affine())
self.assertTrue(s.is_quadratic())
self.assertFalse(s.is_dcp())
def test_partial_optimize_dcp(self):
"""Test DCP properties of partial optimize.
"""
# Evaluate the 1-norm in the usual way (i.e., in epigraph form).
dims = 3
x, t = Variable(dims), Variable(dims)
xval = [-5] * dims
p2 = Problem(cvxpy.Minimize(sum_entries(t)), [-t <= x, x <= t])
g = cvxpy.partial_optimize(p2, [t], [x])
self.assertEquals(g.curvature, s.CONVEX)
p2 = Problem(cvxpy.Maximize(sum_entries(t)), [-t <= x, x <= t])
g = cvxpy.partial_optimize(p2, [t], [x])
self.assertEquals(g.curvature, s.CONCAVE)
def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2,1))
self.assertEqual(y.size, (1,1))
self.assertEqual(x.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(x.canonical_form[0].size, (2,1))
self.assertEqual(x.canonical_form[1], [])
# Scalar variable
coeff = self.a.coefficients()
self.assertEqual(coeff[self.a], [1])
# Vector variable.
coeffs = x.coefficients()
self.assertItemsEqual(coeffs.keys(), [x])
vec = coeffs[x][0]
self.assertEqual(vec.size, (2,2))
self.assertEqual(vec[0,0], 1)
# Matrix variable.
coeffs = self.A.coefficients()
self.assertItemsEqual(coeffs.keys(), [self.A])
self.assertEqual(len(coeffs[self.A]), 2)
mat = coeffs[self.A][1]
self.assertEqual(mat.size, (2,4))
self.assertEqual(mat[0,2], 1)
def test_max_sign(self):
# One arg.
self.assertEquals(max(1).sign, u.Sign.POSITIVE_KEY)
self.assertEquals(max(-2).sign, u.Sign.NEGATIVE_KEY)
self.assertEquals(max(Variable()).sign, u.Sign.UNKNOWN_KEY)
self.assertEquals(max(0).sign, u.Sign.ZERO_KEY)
# Two args.
self.assertEquals(max(1, 2).sign, u.Sign.POSITIVE_KEY)
self.assertEquals(max(1, Variable()).sign, u.Sign.POSITIVE_KEY)
self.assertEquals(max(1, -2).sign, u.Sign.POSITIVE_KEY)
self.assertEquals(max(1, 0).sign, u.Sign.POSITIVE_KEY)
self.assertEquals(max(Variable(), 0).sign, u.Sign.POSITIVE_KEY)
self.assertEquals(max(Variable(), Variable()).sign, u.Sign.UNKNOWN_KEY)
self.assertEquals(max(Variable(), -2).sign, u.Sign.UNKNOWN_KEY)
self.assertEquals(max(0, 0).sign, u.Sign.ZERO_KEY)
self.assertEquals(max(0, -2).sign, u.Sign.ZERO_KEY)
self.assertEquals(max(-3, -2).sign, u.Sign.NEGATIVE_KEY)
# Many args.
self.assertEquals(
max(-2, Variable(), 0, -1, Variable(), 1).sign,
u.Sign.POSITIVE_KEY)
def test_power(self):
from fractions import Fraction
for size in (1, 1), (3, 1), (2, 3):
x = Variable(*size)
y = Variable(*size)
exp = x + y
for p in 0, 1, 2, 3, 2.7, .67, -1, -2.3, Fraction(4, 5):
atom = power(exp, p)
self.assertEqual(atom.size, size)
if p > 1 or p < 0:
self.assertEqual(atom.curvature, s.CONVEX)
elif p == 1:
self.assertEqual(atom.curvature, s.AFFINE)
elif p == 0:
self.assertEqual(atom.curvature, s.CONSTANT)
else:
self.assertEqual(atom.curvature, s.CONCAVE)
if p != 1:
self.assertEqual(atom.sign, s.POSITIVE)
# Test copy with args=None
copy = atom.copy()
self.assertTrue(type(copy) is type(atom))
# A new object is constructed, so copy.args == atom.args but copy.args
# is not atom.args.
self.assertEqual(copy.args, atom.args)
self.assertFalse(copy.args is atom.args)
self.assertEqual(copy.get_data(), atom.get_data())
# Test copy with new args
copy = atom.copy(args=[self.y])
self.assertTrue(type(copy) is type(atom))
self.assertTrue(copy.args[0] is self.y)
self.assertEqual(copy.get_data(), atom.get_data())
assert power(-1, 2).value == 1
with self.assertRaises(Exception) as cm:
power(-1, 3).value
self.assertEqual(str(cm.exception),
"power(x, 3.0) cannot be applied to negative values.")
with self.assertRaises(Exception) as cm:
power(0, -1).value
self.assertEqual(str(cm.exception),
"power(x, -1.0) cannot be applied to negative or zero values.")
def test_sum_entries(self):
"""Test the sum_entries atom.
"""
self.assertEquals(sum_entries(1).sign, u.Sign.POSITIVE_KEY)
self.assertEquals(sum_entries([1, -1]).sign, u.Sign.UNKNOWN_KEY)
self.assertEquals(
sum_entries([1, -1]).curvature, u.Curvature.CONSTANT_KEY)
self.assertEquals(sum_entries(Variable(2)).sign, u.Sign.UNKNOWN_KEY)
self.assertEquals(sum_entries(Variable(2)).size, (1, 1))
self.assertEquals(
sum_entries(Variable(2)).curvature, u.Curvature.AFFINE_KEY)
# Mixed curvature.
mat = np.mat("1 -1")
self.assertEquals(
sum_entries(mat * square(Variable(2))).curvature,
u.Curvature.UNKNOWN_KEY)
# Test with axis argument.
self.assertEquals(sum_entries(Variable(2), axis=0).size, (1, 1))
self.assertEquals(sum_entries(Variable(2), axis=1).size, (2, 1))
self.assertEquals(sum_entries(Variable(2, 3), axis=0).size, (1, 3))
self.assertEquals(sum_entries(Variable(2, 3), axis=1).size, (2, 1))
# Invalid axis.
with self.assertRaises(Exception) as cm:
sum_entries(self.x, axis=4)
self.assertEqual(str(cm.exception), "Invalid argument for axis.")
def test_partial_optimize_stacked(self):
# Minimize the 1-norm in the usual way
dims = 3
x, t = Variable(dims), Variable(dims)
p1 = Problem(Minimize(sum_entries(t)), [-t <= x, x <= t])
# Minimize the 1-norm via partial_optimize
g = cvxpy.partial_optimize(p1, [t], [x])
g2 = cvxpy.partial_optimize(Problem(Minimize(g)), [x])
p2 = Problem(Minimize(g2))
p2.solve()
p1.solve()
self.assertAlmostEqual(p1.value, p2.value)
def test_matrix_multiplication(self):
x = Variable(3, 5)
y = Variable(3, 5)
self.assertFalse(x.is_constant())
self.assertTrue(x.is_affine())
self.assertTrue(x.is_quadratic())
with warnings.catch_warnings():
warnings.simplefilter("ignore")
s = x.T*y
self.assertFalse(s.is_constant())
self.assertFalse(s.is_affine())
self.assertTrue(s.is_quadratic())
self.assertFalse(s.is_dcp())
def test_partial_optimize_numeric_fn(self):
x, y = Variable(1), Variable(1)
xval = 4
# Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
p1 = Problem(Minimize(y), [xval+y>=3])
p1.solve()
# Solve the two-stage problem via partial_optimize
p2 = Problem(Minimize(y), [x+y>=3])
g = cvxpy.partial_optimize(p2, [y], [x])
x.value = xval
result = g.value
self.assertAlmostEqual(result, p1.value)
def test_partial_optimize_numeric_fn(self):
x,y = Variable(1), Variable(1)
xval = 4
# Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
p1 = Problem(Minimize(y), [xval+y>=3])
p1.solve()
# Solve the two-stage problem via partial_optimize
p2 = Problem(Minimize(y), [x+y>=3])
g = partial_optimize(p2, [y], [x])
x.value = xval
result = g.value
self.assertAlmostEqual(result, p1.value)
def test_robust_svm(self):
# Create problem data.
m = 100 # num train points
m_pos = math.floor(m / 2)
m_neg = m - m_pos
n = 2 # num dimensions
mu_pos = 2 * numpy.ones(n)
mu_neg = -2 * numpy.ones(n)
sigma = 1
X = numpy.matrix(
numpy.vstack((mu_pos + sigma * numpy.random.randn(m_pos, n),
mu_neg + sigma * numpy.random.randn(m_neg, n))))
y = numpy.hstack((numpy.ones(m_pos), -1 * numpy.ones(m_neg)))
C = 1 # regularization trade-off parameter
ns = 50
eta = 0.1
# Create and solve optimization problem.
w, b, xi = Variable(n), Variable(), NonNegative(m)
constr = []
Sigma = 0.1 * numpy.eye(n)
for i in range(m):
mu = numpy.array(X[i])[0]
x = NormalRandomVariable(mu, Sigma)
chance = prob(-y[i] * (w.T * x + b) >= (xi[i] - 1), ns)
constr += [chance <= eta]
p = Problem(Minimize(norm(w, 2) + C * sum_entries(xi)), constr)
p.solve(verbose=True)
w_new = w.value
b_new = b.value
# Create and solve the canonical SVM problem.
constr = []
for i in range(m):
constr += [y[i] * (X[i] * w + b) >= (1 - xi[i])]
p2 = Problem(Minimize(norm(w, 2) + C * sum_entries(xi)), constr)
p2.solve()
w_old = w.value
b_old = b.value
self.assert_feas(p)
def setUp(self):
self.a = Variable(name='a')
self.x = Variable(2, name='x')
self.y = Variable(3, name='y')
self.z = Variable(2, name='z')
self.A = Variable(2, 2, name='A')
self.B = Variable(2, 2, name='B')
self.C = Variable(3, 2, name='C')
self.intf = intf.DEFAULT_INTF
def test_quad_over_lin(self):
x = Variable(3, 5)
y = Variable(3, 5)
z = Variable()
s = quad_over_lin(x-y, z)
self.assertFalse(s.is_constant())
self.assertFalse(s.is_affine())
self.assertFalse(s.is_quadratic())
self.assertTrue(s.is_dcp())
t = quad_over_lin(x+2*y, 5)
self.assertFalse(t.is_constant())
self.assertFalse(t.is_affine())
self.assertTrue(t.is_quadratic())
self.assertTrue(t.is_dcp())
def test_non_quadratic(self):
x = Variable()
y = Variable()
z = Variable()
with warnings.catch_warnings():
warnings.simplefilter("ignore")
with self.assertRaises(Exception) as cm:
(x*y*z).is_quadratic()
self.assertEqual(str(cm.exception), "Cannot multiply UNKNOWN and AFFINE.")
s = max_entries(vstack(x, y, z))**2
self.assertFalse(s.is_quadratic())
t = max_entries(vstack(x**2, power(y, 2), z))
self.assertFalse(t.is_quadratic())
def test_partial_optimize_eval_1norm(self):
# Evaluate the 1-norm in the usual way (i.e., in epigraph form).
dims = 3
x, t = Variable(dims), Variable(dims)
xval = [-5]*dims
p1 = Problem(cvxpy.Minimize(sum_entries(t)), [-t <= xval, xval <= t])
p1.solve()
# Minimize the 1-norm via partial_optimize.
p2 = Problem(cvxpy.Minimize(sum_entries(t)), [-t <= x, x <= t])
g = cvxpy.partial_optimize(p2, [t], [x])
p3 = Problem(cvxpy.Minimize(g), [x == xval])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
# Minimize the 1-norm using maximize.
p2 = Problem(cvxpy.Maximize(sum_entries(-t)), [-t <= x, x <= t])
g = cvxpy.partial_optimize(p2, opt_vars=[t])
p3 = Problem(cvxpy.Maximize(g), [x == xval])
p3.solve()
self.assertAlmostEqual(p1.value, -p3.value)
# Try leaving out args.
# Minimize the 1-norm via partial_optimize.
p2 = Problem(cvxpy.Minimize(sum_entries(t)), [-t <= x, x <= t])
g = cvxpy.partial_optimize(p2, opt_vars=[t])
p3 = Problem(cvxpy.Minimize(g), [x == xval])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
# Minimize the 1-norm via partial_optimize.
g = cvxpy.partial_optimize(p2, dont_opt_vars=[x])
p3 = Problem(cvxpy.Minimize(g), [x == xval])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
with self.assertRaises(Exception) as cm:
g = cvxpy.partial_optimize(p2)
self.assertEqual(str(cm.exception),
"partial_optimize called with neither opt_vars nor dont_opt_vars.")
with self.assertRaises(Exception) as cm:
g = cvxpy.partial_optimize(p2, [], [x])
self.assertEqual(str(cm.exception),
("If opt_vars and new_opt_vars are both specified, "
"they must contain all variables in the problem.")
)
def setUp(self):
self.a = Variable(name='a')
self.b = Variable(name='b')
self.c = Variable(name='c')
self.x = Variable(2, name='x')
self.y = Variable(3, name='y')
self.z = Variable(2, name='z')
self.A = Variable(2, 2, name='A')
self.B = Variable(2, 2, name='B')
self.C = Variable(3, 2, name='C')
def test_sum_entries(self):
"""Test the sum_entries atom.
"""
self.assertEquals(sum_entries(1).sign, u.Sign.POSITIVE_KEY)
self.assertEquals(sum_entries([1, -1]).sign, u.Sign.UNKNOWN_KEY)
self.assertEquals(
sum_entries([1, -1]).curvature, u.Curvature.CONSTANT_KEY)
self.assertEquals(sum_entries(Variable(2)).sign, u.Sign.UNKNOWN_KEY)
self.assertEquals(sum_entries(Variable(2)).size, (1, 1))
self.assertEquals(
sum_entries(Variable(2)).curvature, u.Curvature.AFFINE_KEY)
# Mixed curvature.
mat = np.mat("1 -1")
self.assertEquals(
sum_entries(mat * square(Variable(2))).curvature,
u.Curvature.UNKNOWN_KEY)
def test_sum_squares(self):
X = Variable(5, 4)
P = np.asmatrix(np.random.randn(3, 5))
Q = np.asmatrix(np.random.randn(4, 7))
M = np.asmatrix(np.random.randn(3, 7))
y = P*X*Q + M
self.assertFalse(y.is_constant())
self.assertTrue(y.is_affine())
self.assertTrue(y.is_quadratic())
self.assertTrue(y.is_dcp())
s = sum_squares(y)
self.assertFalse(s.is_constant())
self.assertFalse(s.is_affine())
self.assertTrue(s.is_quadratic())
self.assertTrue(s.is_dcp())
# Frobenius norm squared is indeed quadratic
# but can't show quadraticity using recursive rules
t = norm(y, 'fro')**2
self.assertFalse(t.is_constant())
self.assertFalse(t.is_affine())
self.assertFalse(t.is_quadratic())
self.assertTrue(t.is_dcp())
def test_atom():
for atom_list, objective_type in atoms:
for atom, obj_val in atom_list:
for row in xrange(atom.size[0]):
for col in xrange(atom.size[1]):
for solver in [ECOS, SCS, CVXOPT]:
# Atoms with Constant arguments.
yield (run_atom, atom,
Problem(objective_type(atom[row, col])),
obj_val[row, col].value, solver)
# Atoms with Variable arguments.
variables = []
constraints = []
for idx, expr in enumerate(atom.subexpressions):
# Special case for MulExpr because
# can't multiply two variables.
if (idx == 0 and isinstance(atom, MulExpression)):
variables.append(expr)
else:
variables.append(Variable(*expr.size))
constraints.append(variables[-1] == expr)
atom_func = atom.__class__
objective = objective_type(
atom_func(*variables)[row, col])
yield (run_atom, atom, Problem(objective, constraints),
obj_val[row, col].value, solver)
# Atoms with Parameter arguments.
parameters = []
for expr in atom.subexpressions:
parameters.append(Parameter(*expr.size))
parameters[-1].value = expr.value
objective = objective_type(
atom_func(*parameters)[row, col])
yield (run_atom, atom, Problem(objective),
obj_val[row, col].value, solver)
def test_value_at_risk(self):
# Create problem data.
n = numpy.random.randint(1, 10)
pbar = numpy.random.randn(n)
Sigma = numpy.eye(n)
p = NormalRandomVariable(pbar, Sigma)
o = numpy.ones((n, 1))
beta = 0.05
num_samples = 50
# Create and solve optimization problem.
x = Variable(n)
p1 = Problem(Minimize(-x.T * pbar), [
prob(-x.T * p >= 0, num_samples) <= beta, x.T * o == 1, x >= -0.1
])
p1.solve()
# Create and solve analytic form of optimization problem (as a check).
p2 = Problem(Minimize(-x.T * pbar), [
x.T * pbar >= scipy.stats.norm.ppf(1 - beta) *
norm2(sqrtm(Sigma) * x), x.T * o == 1, x >= -0.1
])
p2.solve()
tol = 0.1
if numpy.abs(p1.value - p2.value) < tol:
self.assertAlmostEqual(1, 1)
else:
self.assertAlmostEqual(1, 0)
def test_add_expression(self):
# Vectors
c = Constant([2,2])
exp = self.x + c
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
self.assertEqual(exp.canonical_form[0].size, (2,1))
self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), self.x.name() + " + " + c.name())
self.assertEqual(exp.size, (2,1))
z = Variable(2, name='z')
exp = exp + z + self.x
with self.assertRaises(Exception) as cm:
(self.x + self.y)
self.assertEqual(str(cm.exception), "Incompatible dimensions (2, 1) (3, 1)")
# Matrices
exp = self.A + self.B
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.size, (2,2))
with self.assertRaises(Exception) as cm:
(self.A + self.C)
self.assertEqual(str(cm.exception), "Incompatible dimensions (2, 2) (3, 2)")
with self.assertRaises(Exception) as cm:
AddExpression([self.A, self.C])
self.assertEqual(str(cm.exception), "Incompatible dimensions (2, 2) (3, 2)")
# Test that sum is flattened.
exp = self.x + c + self.x
self.assertEqual(len(exp.args), 3)
def test_pnorm(self):
import numpy as np
x = Variable(3, name='x')
a = np.array([1.0, 2, 3])
for p in (1, 1.6, 1.2, 2, 1.99, 3, 3.7, np.inf):
prob = Problem(Minimize(pnorm(x, p=p)), [x.T * a >= 1])
prob.solve()
# formula is true for any a >= 0 with p > 1
if p == np.inf:
x_true = np.ones_like(a) / sum(a)
elif p == 1:
# only works for the particular a = [1,2,3]
x_true = np.array([0, 0, 1.0 / 3])
else:
x_true = a**(1.0 / (p - 1)) / a.dot(a**(1.0 / (p - 1)))
x_alg = np.array(x.value).flatten()
self.assertTrue(np.allclose(x_alg, x_true, 1e-3))
self.assertTrue(np.allclose(prob.value, np.linalg.norm(x_alg, p)))
self.assertTrue(
np.allclose(np.linalg.norm(x_alg, p),
pnorm(x_alg, p).value))
def test_sub_expression(self):
# Vectors
c = Constant([2, 2])
exp = self.x - c
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
self.assertEqual(exp.canonical_form[0].size, (2, 1))
self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), self.x.name() + " - " + Constant([2,2]).name())
self.assertEqual(exp.size, (2, 1))
z = Variable(2, name='z')
exp = exp - z - self.x
with self.assertRaises(Exception) as cm:
(self.x - self.y)
self.assertEqual(str(cm.exception),
"Incompatible dimensions (2, 1) (3, 1)")
# Matrices
exp = self.A - self.B
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.size, (2, 2))
with self.assertRaises(Exception) as cm:
(self.A - self.C)
self.assertEqual(str(cm.exception),
"Incompatible dimensions (2, 2) (3, 2)")
def test_atom():
for atom_list, objective_type in atoms:
for atom, obj_val in atom_list:
for row in xrange(atom.size[0]):
for col in xrange(atom.size[1]):
# Atoms with Constant arguments.
yield run_atom, Problem(objective_type(
atom[row, col])), obj_val[row, col].value
# Atoms with Variable arguments.
variables = []
constraints = []
for expr in atom.subexpressions:
variables.append(Variable(*expr.size))
constraints.append(variables[-1] == expr)
atom_func = atom.__class__
objective = objective_type(atom_func(*variables)[row, col])
yield run_atom, Problem(objective,
constraints), obj_val[row,
col].value
# Atoms with Parameter arguments.
parameters = []
for expr in atom.subexpressions:
parameters.append(Parameter(*expr.size))
parameters[-1].value = expr.value
objective = objective_type(
atom_func(*parameters)[row, col])
yield run_atom, Problem(objective), obj_val[row, col].value
def test_partial_optimize_params(self):
"""Test partial optimize with parameters.
"""
x, y = Variable(1), Variable(1)
gamma = Parameter()
# Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
p1 = Problem(Minimize(x+y), [x+y>=gamma, y>=4, x>=5])
gamma.value = 3
p1.solve()
# Solve the two-stage problem via partial_optimize
p2 = Problem(Minimize(y), [x+y>=gamma, y>=4])
g = partial_optimize(p2, [y], [x])
p3 = Problem(Minimize(x+g), [x>=5])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
def test_atom():
for atom_list, objective_type in atoms:
for atom, size, args, obj_val in atom_list:
for row in range(size[0]):
for col in range(size[1]):
for solver in SOLVERS_TO_TRY:
# Atoms with Constant arguments.
const_args = [Constant(arg) for arg in args]
yield (run_atom, atom,
Problem(
objective_type(atom(*const_args)[row,
col])),
obj_val[row, col].value, solver)
# Atoms with Variable arguments.
variables = []
constraints = []
for idx, expr in enumerate(args):
variables.append(Variable(*intf.size(expr)))
constraints.append(variables[-1] == expr)
objective = objective_type(atom(*variables)[row, col])
yield (run_atom, atom, Problem(objective, constraints),
obj_val[row, col].value, solver)
# Atoms with Parameter arguments.
parameters = []
for expr in args:
parameters.append(Parameter(*intf.size(expr)))
parameters[
-1].value = intf.DEFAULT_INTF.const_to_matrix(
expr)
objective = objective_type(atom(*parameters)[row, col])
yield (run_atom, atom, Problem(objective),
obj_val[row, col].value, solver)
def test_indexing(self):
# Vector variables
p = Problem(Maximize(self.x[0, 0]),
[self.x[0, 0] <= 2, self.x[1, 0] == 3])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertItemsAlmostEqual(self.x.value, [2, 3])
n = 10
A = matrix(range(n * n), (n, n))
x = Variable(n, n)
p = Problem(Minimize(sum_entries(x)), [x == A])
result = p.solve()
answer = n * n * (n * n + 1) / 2 - n * n
self.assertAlmostEqual(result, answer)
# Matrix variables
p = Problem(
Maximize(sum(self.A[i, i] + self.A[i, 1 - i] for i in range(2))),
[self.A <= [[1, -2], [-3, 4]]])
result = p.solve()
self.assertAlmostEqual(result, 0)
self.assertItemsAlmostEqual(self.A.value, [1, -2, -3, 4])
# Indexing arithmetic expressions.
exp = [[1, 2], [3, 4]] * self.z + self.x
p = Problem(Minimize(exp[1, 0]), [self.x == self.z, self.z == [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.x.value, self.z.value)
def test_hstack(self):
c = matrix(1, (1, 5))
p = Problem(Minimize(c * hstack(self.x.T, self.y.T).T),
[self.x == [1, 2], self.y == [3, 4, 5]])
result = p.solve()
self.assertAlmostEqual(result, 15)
c = matrix(1, (1, 4))
p = Problem(Minimize(c * hstack(self.x.T, self.x.T).T),
[self.x == [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix(1, (2, 2))
p = Problem(Minimize(sum_entries(hstack(self.A.T, self.C.T))),
[self.A >= 2 * c, self.C == -2])
result = p.solve()
self.assertAlmostEqual(result, -4)
D = Variable(3, 3)
expr = hstack(self.C, D)
p = Problem(Minimize(expr[0, 1] + sum_entries(hstack(expr, expr))),
[self.C >= 0, D >= 0, D[0, 0] == 2, self.C[0, 1] == 3])
result = p.solve()
self.assertAlmostEqual(result, 13)
c = matrix([1, -1])
p = Problem(Minimize(c.T * hstack(square(self.a).T,
sqrt(self.b).T).T),
[self.a == 2, self.b == 16])
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception),
"Problem does not follow DCP rules.")
def test_variable_name_conflict(self):
var = Variable(name='a')
p = Problem(Maximize(self.a + var), [var == 2 + self.a, var <= 3])
result = p.solve()
self.assertAlmostEqual(result, 4.0)
self.assertAlmostEqual(self.a.value, 1)
self.assertAlmostEqual(var.value, 3)
def test_neg_indices(self):
"""Test negative indices.
"""
c = Constant([[1, 2], [3, 4]])
exp = c[-1, -1]
self.assertEquals(exp.value, 4)
self.assertEquals(exp.size, (1, 1))
self.assertEquals(exp.curvature, u.Curvature.CONSTANT_KEY)
c = Constant([1, 2, 3, 4])
exp = c[1:-1]
self.assertItemsAlmostEqual(exp.value, [2, 3])
self.assertEquals(exp.size, (2, 1))
self.assertEquals(exp.curvature, u.Curvature.CONSTANT_KEY)
c = Constant([1, 2, 3, 4])
exp = c[::-1]
self.assertItemsAlmostEqual(exp.value, [4, 3, 2, 1])
self.assertEquals(exp.size, (4, 1))
self.assertEquals(exp.curvature, u.Curvature.CONSTANT_KEY)
x = Variable(4)
Problem(Minimize(0), [x[::-1] == c]).solve()
self.assertItemsAlmostEqual(x.value, [4, 3, 2, 1])
self.assertEquals(x.size, (4, 1))
def test_min_entries_sign(self):
"""Test sign for min_entries.
"""
# One arg.
self.assertEquals(min_entries(1).sign, u.Sign.POSITIVE_KEY)
self.assertEquals(min_entries(-2).sign, u.Sign.NEGATIVE_KEY)
self.assertEquals(min_entries(Variable()).sign, u.Sign.UNKNOWN_KEY)
self.assertEquals(min_entries(0).sign, u.Sign.ZERO_KEY)
def test_min_entries_sign(self):
"""Test sign for min_entries.
"""
# One arg, test sign.
self.assertEquals(min_entries(1).sign, s.POSITIVE)
self.assertEquals(min_entries(-2).sign, s.NEGATIVE)
self.assertEquals(min_entries(Variable()).sign, s.UNKNOWN)
self.assertEquals(min_entries(0).sign, s.ZERO)
def test_power(self):
x = Variable()
prob = Problem(
Minimize(power(x, 1.7) + power(x, -2.3) - power(x, .45)))
prob.solve()
x = x.value
self.assertTrue(__builtins__['abs'](1.7 * x**.7 - 2.3 * x**-3.3 -
.45 * x**-.55) <= 1e-3)
def test_kl_div(self):
"""Test domain for kl_div.
"""
b = Variable()
dom = kl_div(self.a, b).domain
Problem(Minimize(self.a + b), dom).solve()
self.assertAlmostEqual(self.a.value, 0)
self.assertAlmostEqual(b.value, 0)
class TestVstack(unittest.TestCase):
""" Unit tests for the expressions.affine module. """
def setUp(self):
self.x = Variable(2, name='x')
self.y = Variable(2, name='y')
self.A = Variable(3,2, name='A')
self.B = Variable(5,2, name='B')
self.C = Constant([[1, 2], [1, 2]])
self.intf = intf.DEFAULT_INTERFACE
# Test the variables method.
def test_variables(self):
exp,constr = vstack(self.x, self.y, self.x+self.y).canonical_form
self.assertEquals(constr, [])
self.assertItemsEqual(exp.variables(), [self.x, self.y])
exp = vstack(self.A, self.B, self.C).canonical_form[0]
self.assertItemsEqual(exp.variables(), [self.A, self.B])
# Test coefficients method.
def test_coefficients(self):
exp = vstack(self.x).canonical_form[0]
coeffs = exp.coefficients()
self.assertEqual(coeffs.keys(), self.x.coefficients().keys())
exp = vstack(self.x, self.y).canonical_form[0]
coeffs = exp.coefficients()
self.assertItemsEqual(coeffs.keys(),
self.x.coefficients().keys() + \
self.y.coefficients().keys())
for k,blocks in coeffs.items():
self.assertEqual(len(blocks), 1)
for block in blocks:
self.assertEqual(intf.size(block), (4,2))
exp = vstack(self.A, self.B, self.C).canonical_form[0]
coeffs = exp.coefficients()
blocks = coeffs[self.A.id]
self.assertEqual(len(blocks), 2)
for block in blocks:
self.assertEqual(intf.size(block), (10,6))
class TestAffVstack(unittest.TestCase):
""" Unit tests for the expressions.affine module. """
def setUp(self):
self.x = Variable(2, name='x')
self.y = Variable(2, name='y')
self.A = Variable(3,2, name='A')
self.B = Variable(5,2, name='B')
self.C = Constant([[1, 2], [1, 2]])
self.intf = intf.DEFAULT_INTERFACE
# Test the variables method.
def test_variables(self):
exp = AffVstack(self.x, self.y, self.x+self.y)
self.assertItemsEqual(exp.variables(), [self.x, self.y, self.x, self.y])
exp = AffVstack(self.A, self.B, self.C)
self.assertItemsEqual(exp.variables(), [self.A, self.B])
# Test coefficients method.
def test_coefficients(self):
exp = AffVstack(self.x)
coeffs = exp.coefficients(self.intf)
self.assertEqual(coeffs.keys(), self.x.coefficients(self.intf).keys())
exp = AffVstack(self.x, self.y)
coeffs = exp.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(),
self.x.coefficients(self.intf).keys() + \
self.y.coefficients(self.intf).keys())
for k,v in coeffs.items():
self.assertEqual(intf.size(v), (4,2))
exp = AffVstack(self.A, self.B, self.C)
coeffs = exp.coefficients(self.intf)
v = coeffs[self.A]
self.assertEqual(intf.size(v), (10,3))
def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2,1))
self.assertEqual(y.size, (1,1))
self.assertEqual(x.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(x.canonical_form[0].size, (2,1))
self.assertEqual(x.canonical_form[1], [])
def test_log_det(self):
"""Test gradient for log_det
"""
expr = log_det(self.A)
self.A.value = 2*np.eye(2)
self.assertItemsAlmostEqual(expr.grad[self.A].todense(), 1.0/2*np.eye(2))
mat = np.matrix([[1, 2], [3, 5]])
self.A.value = mat.T*mat
val = np.linalg.inv(self.A.value).T
self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)
self.A.value = np.zeros((2, 2))
self.assertAlmostEqual(expr.grad[self.A], None)
self.A.value = -np.matrix([[1, 2], [3, 4]])
self.assertAlmostEqual(expr.grad[self.A], None)
K = Variable(8, 8)
expr = log_det(K[[1,2]][:,[1,2]])
K.value = np.eye(8)
val = np.zeros((8,8))
val[[1,2],[1,2]] = 1
self.assertItemsAlmostEqual(expr.grad[K].todense(), val)
def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2, 1))
self.assertEqual(y.size, (1, 1))
self.assertEqual(x.curvature, s.AFFINE)
self.assertEqual(x.canonical_form[0].size, (2, 1))
self.assertEqual(x.canonical_form[1], [])
self.assertEqual(repr(self.x), "Variable(2, 1)")
self.assertEqual(repr(self.A), "Variable(2, 2)")
def test_min_elemwise(self):
"""Test domain for min_elemwise.
"""
b = Variable()
expr = min_elemwise(self.a, b)
self.a.value = 2
b.value = 4
self.assertAlmostEqual(expr.grad[self.a], 1)
self.assertAlmostEqual(expr.grad[b], 0)
self.a.value = 3
b.value = 0
self.assertAlmostEqual(expr.grad[self.a], 0)
self.assertAlmostEqual(expr.grad[b], 1)
self.a.value = -1
b.value = 2
self.assertAlmostEqual(expr.grad[self.a], 1)
self.assertAlmostEqual(expr.grad[b], 0)
y = Variable(2)
expr = min_elemwise(self.x, y)
self.x.value = [3, 4]
y.value = [5, -5]
val = np.zeros((2, 2)) + np.diag([1, 0])
self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)
val = np.zeros((2, 2)) + np.diag([0, 1])
self.assertItemsAlmostEqual(expr.grad[y].todense(), val)
expr = min_elemwise(self.x, y)
self.x.value = [-1e-9, 4]
y.value = [1, 4]
val = np.zeros((2, 2)) + np.diag([1, 1])
self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)
val = np.zeros((2, 2)) + np.diag([0, 0])
self.assertItemsAlmostEqual(expr.grad[y].todense(), val)
expr = min_elemwise(self.A, self.B)
self.A.value = [[1, 2], [3, 4]]
self.B.value = [[5, 1], [3, 2.3]]
div = (self.A.value/self.B.value).A.ravel(order='F')
val = np.zeros((4, 4)) + np.diag([1, 0, 1, 0])
self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)
val = np.zeros((4, 4)) + np.diag([0, 1, 0, 1])
self.assertItemsAlmostEqual(expr.grad[self.B].todense(), val)
def test_kl_div(self):
"""Test domain for kl_div.
"""
b = Variable()
expr = kl_div(self.a, b)
self.a.value = 2
b.value = 4
self.assertAlmostEqual(expr.grad[self.a], np.log(2/4))
self.assertAlmostEqual(expr.grad[b], 1 - (2/4))
self.a.value = 3
b.value = 0
self.assertAlmostEqual(expr.grad[self.a], None)
self.assertAlmostEqual(expr.grad[b], None)
self.a.value = -1
b.value = 2
self.assertAlmostEqual(expr.grad[self.a], None)
self.assertAlmostEqual(expr.grad[b], None)
y = Variable(2)
expr = kl_div(self.x, y)
self.x.value = [3, 4]
y.value = [5, 8]
val = np.zeros((2, 2)) + np.diag(np.log([3, 4]) - np.log([5, 8]))
self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)
val = np.zeros((2, 2)) + np.diag([1 - 3/5, 1 - 4/8])
self.assertItemsAlmostEqual(expr.grad[y].todense(), val)
expr = kl_div(self.x, y)
self.x.value = [-1e-9, 4]
y.value = [1, 2]
self.assertAlmostEqual(expr.grad[self.x], None)
self.assertAlmostEqual(expr.grad[y], None)
expr = kl_div(self.A, self.B)
self.A.value = [[1, 2], [3, 4]]
self.B.value = [[5, 1], [3.5, 2.3]]
div = (self.A.value/self.B.value).A.ravel(order='F')
val = np.zeros((4, 4)) + np.diag(np.log(div))
self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)
val = np.zeros((4, 4)) + np.diag(1 - div)
self.assertItemsAlmostEqual(expr.grad[self.B].todense(), val)
class TestExpressions(BaseTest):
""" Unit tests for the expression/expression module. """
def setUp(self):
self.a = Variable(name='a')
self.x = Variable(2, name='x')
self.y = Variable(3, name='y')
self.z = Variable(2, name='z')
self.A = Variable(2,2,name='A')
self.B = Variable(2,2,name='B')
self.C = Variable(3,2,name='C')
self.intf = intf.DEFAULT_INTERFACE
# Test the Variable class.
def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2,1))
self.assertEqual(y.size, (1,1))
self.assertEqual(x.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(x.canonical_form[0].size, (2,1))
self.assertEqual(x.canonical_form[1], [])
self.assertEquals(repr(self.x), "Variable(2, 1)")
self.assertEquals(repr(self.A), "Variable(2, 2)")
# # Scalar variable
# coeff = self.a.coefficients()
# self.assertEqual(coeff[self.a.id], [1])
# # Vector variable.
# coeffs = x.coefficients()
# self.assertItemsEqual(coeffs.keys(), [x.id])
# vec = coeffs[x.id][0]
# self.assertEqual(vec.shape, (2,2))
# self.assertEqual(vec[0,0], 1)
# # Matrix variable.
# coeffs = self.A.coefficients()
# self.assertItemsEqual(coeffs.keys(), [self.A.id])
# self.assertEqual(len(coeffs[self.A.id]), 2)
# mat = coeffs[self.A.id][1]
# self.assertEqual(mat.shape, (2,4))
# self.assertEqual(mat[0,2], 1)
# Test tranposing variables.
def test_transpose_variable(self):
var = self.a.T
self.assertEquals(var.name(), "a")
self.assertEquals(var.size, (1,1))
self.a.save_value(2)
self.assertEquals(var.value, 2)
var = self.x.T
self.assertEquals(var.name(), "x.T")
self.assertEquals(var.size, (1,2))
self.x.save_value( matrix([1,2]) )
self.assertEquals(var.value[0,0], 1)
self.assertEquals(var.value[0,1], 2)
var = self.C.T
self.assertEquals(var.name(), "C.T")
self.assertEquals(var.size, (2,3))
# coeffs = var.canonical_form[0].coefficients()
# mat = coeffs.values()[0][0]
# self.assertEqual(mat.size, (2,6))
# self.assertEqual(mat[1,3], 1)
index = var[1,0]
self.assertEquals(index.name(), "C.T[1, 0]")
self.assertEquals(index.size, (1,1))
var = self.x.T.T
self.assertEquals(var.name(), "x.T.T")
self.assertEquals(var.size, (2,1))
# Test the Constant class.
def test_constants(self):
c = Constant(2)
self.assertEqual(c.name(), str(2))
c = Constant(2)
self.assertEqual(c.value, 2)
self.assertEqual(c.size, (1,1))
self.assertEqual(c.curvature, u.Curvature.CONSTANT_KEY)
self.assertEqual(c.sign, u.Sign.POSITIVE_KEY)
self.assertEqual(Constant(-2).sign, u.Sign.NEGATIVE_KEY)
self.assertEqual(Constant(0).sign, u.Sign.ZERO_KEY)
self.assertEqual(c.canonical_form[0].size, (1,1))
self.assertEqual(c.canonical_form[1], [])
# coeffs = c.coefficients()
# self.assertEqual(coeffs.keys(), [s.CONSTANT])
# self.assertEqual(coeffs[s.CONSTANT], [2])
# Test the sign.
c = Constant([[2], [2]])
self.assertEqual(c.size, (1, 2))
self.assertEqual(c.sign, u.Sign.POSITIVE_KEY)
self.assertEqual((-c).sign, u.Sign.NEGATIVE_KEY)
self.assertEqual((0*c).sign, u.Sign.ZERO_KEY)
c = Constant([[2], [-2]])
self.assertEqual(c.sign, u.Sign.UNKNOWN_KEY)
# Test sign of a complex expression.
c = Constant([1, 2])
A = Constant([[1,1],[1,1]])
exp = c.T*A*c
self.assertEqual(exp.sign, u.Sign.POSITIVE_KEY)
self.assertEqual((c.T*c).sign, u.Sign.POSITIVE_KEY)
exp = c.T.T
self.assertEqual(exp.sign, u.Sign.POSITIVE_KEY)
exp = c.T*self.A
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
# Test repr.
self.assertEqual(repr(c), "Constant(CONSTANT, POSITIVE, (2, 1))")
# def test_1D_array(self):
# """Test NumPy 1D arrays as constants.
# """
# c = np.array([1,2])
# p = Parameter(2)
# with warnings.catch_warnings(record=True) as w:
# # Cause all warnings to always be triggered.
# warnings.simplefilter("always")
# # Trigger a warning.
# Constant(c)
# self.x + c
# p.value = c
# # Verify some things
# self.assertEqual(len(w), 3)
# for warning in w:
# self.assertEqual(str(warning.message), "NumPy 1D arrays are treated as column vectors.")
# Test the Parameter class.
def test_parameters(self):
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.size, (1,1))
p = Parameter(4, 3, sign="positive")
with self.assertRaises(Exception) as cm:
p.value = 1
self.assertEqual(str(cm.exception), "Invalid dimensions (1, 1) for Parameter value.")
val = -np.ones((4,3))
val[0,0] = 2
p = Parameter(4, 3, sign="positive")
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception), "Invalid sign for Parameter value.")
p = Parameter(4, 3, sign="negative")
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception), "Invalid sign for Parameter value.")
# No error for unknown sign.
p = Parameter(4, 3)
p.value = val
# Initialize a parameter with a value.
p = Parameter(value=10)
self.assertEqual(p.value, 10)
with self.assertRaises(Exception) as cm:
p = Parameter(2, 1, sign="negative", value=[2,1])
self.assertEqual(str(cm.exception), "Invalid sign for Parameter value.")
with self.assertRaises(Exception) as cm:
p = Parameter(4, 3, sign="positive", value=[1,2])
self.assertEqual(str(cm.exception), "Invalid dimensions (2, 1) for Parameter value.")
# Test repr.
p = Parameter(4, 3, sign="negative")
self.assertEqual(repr(p), 'Parameter(4, 3, sign="NEGATIVE")')
# Test the AddExpresion class.
def test_add_expression(self):
# Vectors
c = Constant([2,2])
exp = self.x + c
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
self.assertEqual(exp.canonical_form[0].size, (2,1))
self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), self.x.name() + " + " + c.name())
self.assertEqual(exp.size, (2,1))
z = Variable(2, name='z')
exp = exp + z + self.x
with self.assertRaises(Exception) as cm:
(self.x + self.y)
self.assertEqual(str(cm.exception), "Incompatible dimensions (2, 1) (3, 1)")
# Matrices
exp = self.A + self.B
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.size, (2,2))
with self.assertRaises(Exception) as cm:
(self.A + self.C)
self.assertEqual(str(cm.exception), "Incompatible dimensions (2, 2) (3, 2)")
with self.assertRaises(Exception) as cm:
AddExpression([self.A, self.C])
self.assertEqual(str(cm.exception), "Incompatible dimensions (2, 2) (3, 2)")
# Test that sum is flattened.
exp = self.x + c + self.x
self.assertEqual(len(exp.args), 3)
# Test repr.
self.assertEqual(repr(exp), "Expression(AFFINE, UNKNOWN, (2, 1))")
# Test the SubExpresion class.
def test_sub_expression(self):
# Vectors
c = Constant([2,2])
exp = self.x - c
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
self.assertEqual(exp.canonical_form[0].size, (2,1))
self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), self.x.name() + " - " + Constant([2,2]).name())
self.assertEqual(exp.size, (2,1))
z = Variable(2, name='z')
exp = exp - z - self.x
with self.assertRaises(Exception) as cm:
(self.x - self.y)
self.assertEqual(str(cm.exception), "Incompatible dimensions (2, 1) (3, 1)")
# Matrices
exp = self.A - self.B
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.size, (2,2))
with self.assertRaises(Exception) as cm:
(self.A - self.C)
self.assertEqual(str(cm.exception), "Incompatible dimensions (2, 2) (3, 2)")
# Test repr.
self.assertEqual(repr(self.x - c), "Expression(AFFINE, UNKNOWN, (2, 1))")
# Test the MulExpresion class.
def test_mul_expression(self):
# Vectors
c = Constant([[2],[2]])
exp = c*self.x
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual((c[0]*self.x).sign, u.Sign.UNKNOWN_KEY)
self.assertEqual(exp.canonical_form[0].size, (1,1))
self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.size, (1,1))
with self.assertRaises(Exception) as cm:
([2,2,3]*self.x)
self.assertEqual(str(cm.exception), "Incompatible dimensions (3, 1) (2, 1)")
# Matrices
with self.assertRaises(Exception) as cm:
Constant([[2, 1],[2, 2]]) * self.C
self.assertEqual(str(cm.exception), "Incompatible dimensions (2, 2) (3, 2)")
with self.assertRaises(Exception) as cm:
(self.A * self.B)
self.assertEqual(str(cm.exception), "Cannot multiply two non-constants.")
# Constant expressions
T = Constant([[1,2,3],[3,5,5]])
exp = (T + T) * self.B
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.size, (3,2))
# Expression that would break sign multiplication without promotion.
c = Constant([[2], [2], [-2]])
exp = [[1], [2]] + c*self.C
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
# Scalar constants on the right should be moved left
# instead of taking the transpose.
expr = self.C*2
self.assertEqual(expr.args[0].value, 2)
# Test the DivExpresion class.
def test_div_expression(self):
# Vectors
exp = self.x/2
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
self.assertEqual(exp.canonical_form[0].size, (2,1))
self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.size, (2,1))
with self.assertRaises(Exception) as cm:
(self.x/[2,2,3])
print cm.exception
self.assertEqual(str(cm.exception), "Can only divide by a scalar constant.")
# Constant expressions.
c = Constant(2)
exp = c/(3 - 5)
self.assertEqual(exp.curvature, u.Curvature.CONSTANT_KEY)
self.assertEqual(exp.size, (1,1))
self.assertEqual(exp.sign, u.Sign.NEGATIVE_KEY)
# Parameters.
p = Parameter(sign="positive")
exp = 2/p
p.value = 2
self.assertEquals(exp.value, 1)
rho = Parameter(sign="positive")
rho.value = 1
self.assertEquals(rho.sign, u.Sign.POSITIVE_KEY)
self.assertEquals(Constant(2).sign, u.Sign.POSITIVE_KEY)
self.assertEquals((Constant(2)/Constant(2)).sign, u.Sign.POSITIVE_KEY)
self.assertEquals((Constant(2)*rho).sign, u.Sign.POSITIVE_KEY)
self.assertEquals((rho/2).sign, u.Sign.POSITIVE_KEY)
# Test the NegExpression class.
def test_neg_expression(self):
# Vectors
exp = -self.x
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
assert exp.is_affine()
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
assert not exp.is_positive()
self.assertEqual(exp.canonical_form[0].size, (2,1))
self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), "-%s" % self.x.name())
self.assertEqual(exp.size, self.x.size)
# Matrices
exp = -self.C
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.size, (3,2))
# Test promotion of scalar constants.
def test_scalar_const_promotion(self):
# Vectors
exp = self.x + 2
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
assert exp.is_affine()
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
assert not exp.is_negative()
self.assertEqual(exp.canonical_form[0].size, (2,1))
self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), self.x.name() + " + " + Constant(2).name())
self.assertEqual(exp.size, (2,1))
self.assertEqual((4 - self.x).size, (2,1))
self.assertEqual((4 * self.x).size, (2,1))
self.assertEqual((4 <= self.x).size, (2,1))
self.assertEqual((4 == self.x).size, (2,1))
self.assertEqual((self.x >= 4).size, (2,1))
# Matrices
exp = (self.A + 2) + 4
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual((3 * self.A).size, (2,2))
self.assertEqual(exp.size, (2,2))
# Test indexing expression.
def test_index_expression(self):
# Tuple of integers as key.
exp = self.x[1,0]
# self.assertEqual(exp.name(), "x[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
assert exp.is_affine()
self.assertEquals(exp.size, (1,1))
# coeff = exp.canonical_form[0].coefficients()[self.x][0]
# self.assertEqual(coeff[0,1], 1)
self.assertEqual(exp.value, None)
exp = self.x[1,0].T
# self.assertEqual(exp.name(), "x[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEquals(exp.size, (1,1))
with self.assertRaises(Exception) as cm:
(self.x[2,0])
self.assertEqual(str(cm.exception), "Index/slice out of bounds.")
# Slicing
exp = self.C[0:2,1]
# self.assertEquals(exp.name(), "C[0:2,1]")
self.assertEquals(exp.size, (2,1))
exp = self.C[0:,0:2]
# self.assertEquals(exp.name(), "C[0:,0:2]")
self.assertEquals(exp.size, (3,2))
exp = self.C[0::2,0::2]
# self.assertEquals(exp.name(), "C[0::2,0::2]")
self.assertEquals(exp.size, (2,1))
exp = self.C[:3,:1:2]
# self.assertEquals(exp.name(), "C[0:3,0]")
self.assertEquals(exp.size, (3,1))
exp = self.C[0:,0]
# self.assertEquals(exp.name(), "C[0:,0]")
self.assertEquals(exp.size, (3,1))
c = Constant([[1,-2],[0,4]])
exp = c[1, 1]
self.assertEqual(exp.curvature, u.Curvature.CONSTANT_KEY)
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
self.assertEqual(c[0,1].sign, u.Sign.UNKNOWN_KEY)
self.assertEqual(c[1,0].sign, u.Sign.UNKNOWN_KEY)
self.assertEquals(exp.size, (1,1))
self.assertEqual(exp.value, 4)
c = Constant([[1,-2,3],[0,4,5],[7,8,9]])
exp = c[0:3,0:4:2]
self.assertEqual(exp.curvature, u.Curvature.CONSTANT_KEY)
assert exp.is_constant()
self.assertEquals(exp.size, (3,2))
self.assertEqual(exp[0,1].value, 7)
# Slice of transpose
exp = self.C.T[0:2,1]
self.assertEquals(exp.size, (2,1))
# Arithmetic expression indexing
exp = (self.x + self.z)[1,0]
# self.assertEqual(exp.name(), "x[1,0] + z[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
self.assertEquals(exp.size, (1,1))
exp = (self.x + self.a)[1,0]
# self.assertEqual(exp.name(), "x[1,0] + a")
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEquals(exp.size, (1,1))
exp = (self.x - self.z)[1,0]
# self.assertEqual(exp.name(), "x[1,0] - z[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEquals(exp.size, (1,1))
exp = (self.x - self.a)[1,0]
# self.assertEqual(exp.name(), "x[1,0] - a")
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEquals(exp.size, (1,1))
exp = (-self.x)[1,0]
# self.assertEqual(exp.name(), "-x[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEquals(exp.size, (1,1))
c = Constant([[1,2],[3,4]])
exp = (c*self.x)[1,0]
# self.assertEqual(exp.name(), "[[2], [4]] * x[0:,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEquals(exp.size, (1,1))
c = Constant([[1,2],[3,4]])
exp = (c*self.a)[1,0]
# self.assertEqual(exp.name(), "2 * a")
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEquals(exp.size, (1,1))
def test_neg_indices(self):
"""Test negative indices.
"""
c = Constant([[1,2],[3,4]])
exp = c[-1, -1]
self.assertEquals(exp.value, 4)
self.assertEquals(exp.size, (1, 1))
self.assertEquals(exp.curvature, u.Curvature.CONSTANT_KEY)
c = Constant([1,2,3,4])
exp = c[1:-1]
self.assertItemsAlmostEqual(exp.value, [2, 3])
self.assertEquals(exp.size, (2, 1))
self.assertEquals(exp.curvature, u.Curvature.CONSTANT_KEY)
def test_logical_indices(self):
"""Test indexing with logical arrays.
"""
pass
class TestExpressions(unittest.TestCase):
""" Unit tests for the expression/expression module. """
def setUp(self):
self.a = Variable(name='a')
self.x = Variable(2, name='x')
self.y = Variable(3, name='y')
self.z = Variable(2, name='z')
self.A = Variable(2,2,name='A')
self.B = Variable(2,2,name='B')
self.C = Variable(3,2,name='C')
self.intf = intf.DEFAULT_INTERFACE
# Test the Variable class.
def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2,1))
self.assertEqual(y.size, (1,1))
self.assertEqual(x.curvature, u.Curvature.AFFINE)
self.assertEqual(x.canonicalize()[0].size, (2,1))
self.assertEqual(x.canonicalize()[1], [])
# Scalar variable
coeff = self.a.coefficients(self.intf)
self.assertEqual(coeff[self.a], 1)
# Vector variable.
coeffs = x.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), [x])
vec = coeffs[x]
self.assertEqual(vec.size, (2,2))
self.assertEqual(list(vec), [1,0,0,1])
# Matrix variable.
coeffs = self.A.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), [self.A])
mat = coeffs[self.A]
self.assertEqual(mat.size, (2,2))
self.assertEqual(list(mat), [1,0,0,1])
# Test the TransposeVariable class.
def test_transpose_variable(self):
var = self.a.T
self.assertEquals(var.name(), "a")
self.assertEquals(var.size, (1,1))
self.a.save_value(2)
self.assertEquals(var.value, 2)
var = self.x.T
self.assertEquals(var.name(), "x.T")
self.assertEquals(var.size, (1,2))
self.x.save_value( matrix([1,2]) )
self.assertEquals(var.value[0,0], 1)
self.assertEquals(var.value[0,1], 2)
var = self.C.T
self.assertEquals(var.name(), "C.T")
self.assertEquals(var.size, (2,3))
coeffs = var.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), [var])
mat = coeffs[var]
self.assertEqual(mat.size, (2,2))
self.assertEqual(list(mat), [1,0,0,1])
index = var[1,0]
self.assertEquals(index.name(), "C[0,1]")
self.assertEquals(index.size, (1,1))
var = self.x.T.T
self.assertEquals(var.name(), "x")
self.assertEquals(var.size, (2,1))
# Test the Constant class.
def test_constants(self):
c = Constant(2)
self.assertEqual(c.name(), str(2))
c = Constant(2, name="c")
self.assertEqual(c.name(), "c")
self.assertEqual(c.value, 2)
self.assertEqual(c.size, (1,1))
self.assertEqual(c.curvature, u.Curvature.CONSTANT)
self.assertEqual(c.sign, u.Sign.POSITIVE)
self.assertEqual(Constant(-2).sign, u.Sign.NEGATIVE)
self.assertEqual(Constant(0).sign, u.Sign.ZERO)
self.assertEqual(c.canonicalize()[0].size, (1,1))
self.assertEqual(c.canonicalize()[1], [])
coeffs = c.coefficients(self.intf)
self.assertEqual(coeffs.keys(), [s.CONSTANT])
self.assertEqual(coeffs[s.CONSTANT], 2)
# Test the sign.
c = Constant([[2],[2]])
self.assertEqual(c.size, (1,2))
self.assertEqual(c.sign.neg_mat.value.shape, (1,2))
# Test the Parameter class.
def test_parameters(self):
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.size, (1,1))
# Test the AddExpresion class.
def test_add_expression(self):
# Vectors
c = Constant([2,2])
exp = self.x + c
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.sign, u.Sign.UNKNOWN)
self.assertEqual(exp.canonicalize()[0].size, (2,1))
self.assertEqual(exp.canonicalize()[1], [])
self.assertEqual(exp.name(), self.x.name() + " + " + c.name())
self.assertEqual(exp.size, (2,1))
z = Variable(2, name='z')
exp = exp + z + self.x
with self.assertRaises(Exception) as cm:
(self.x + self.y)
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
# Matrices
exp = self.A + self.B
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.size, (2,2))
with self.assertRaises(Exception) as cm:
(self.A + self.C)
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
# Test the SubExpresion class.
def test_sub_expression(self):
# Vectors
c = Constant([2,2])
exp = self.x - c
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.sign, u.Sign.UNKNOWN)
self.assertEqual(exp.canonicalize()[0].size, (2,1))
self.assertEqual(exp.canonicalize()[1], [])
self.assertEqual(exp.name(), self.x.name() + " - " + Constant([2,2]).name())
self.assertEqual(exp.size, (2,1))
z = Variable(2, name='z')
exp = exp - z - self.x
with self.assertRaises(Exception) as cm:
(self.x - self.y)
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
# Matrices
exp = self.A - self.B
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.size, (2,2))
with self.assertRaises(Exception) as cm:
(self.A - self.C)
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
# Test the MulExpresion class.
def test_mul_expression(self):
# Vectors
c = Constant([[2],[2]])
exp = c*self.x
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual((c[0]*self.x).sign, u.Sign.UNKNOWN)
self.assertEqual(exp.canonicalize()[0].size, (1,1))
self.assertEqual(exp.canonicalize()[1], [])
self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.size, (1,1))
with self.assertRaises(Exception) as cm:
([2,2,3]*self.x)
const_name = Constant([2,2,3]).name()
self.assertEqual(str(cm.exception),
"Incompatible dimensions.")
# Matrices
with self.assertRaises(Exception) as cm:
Constant([[2, 1],[2, 2]]) * self.C
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
with self.assertRaises(Exception) as cm:
(self.A * self.B)
self.assertEqual(str(cm.exception), "Cannot multiply two non-constants.")
# Constant expressions
T = Constant([[1,2,3],[3,5,5]])
exp = (T + T) * self.B
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.size, (3,2))
# Expression that would break sign multiplication without promotion.
c = Constant([[2],[2],[-2]])
exp = [[1],[2]] + c*self.C
self.assertEqual(exp.sign.pos_mat.value.shape, (1,2))
# Test the NegExpression class.
def test_neg_expression(self):
# Vectors
exp = -self.x
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.sign, u.Sign.UNKNOWN)
self.assertEqual(exp.canonicalize()[0].size, (2,1))
self.assertEqual(exp.canonicalize()[1], [])
self.assertEqual(exp.name(), "-%s" % self.x.name())
self.assertEqual(exp.size, self.x.size)
# Matrices
exp = -self.C
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.size, (3,2))
# Test promotion of scalar constants.
def test_scalar_const_promotion(self):
# Vectors
exp = self.x + 2
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.sign, u.Sign.UNKNOWN)
self.assertEqual(exp.canonicalize()[0].size, (2,1))
self.assertEqual(exp.canonicalize()[1], [])
self.assertEqual(exp.name(), self.x.name() + " + " + Constant(2).name())
self.assertEqual(exp.size, (2,1))
self.assertEqual((4 - self.x).size, (2,1))
self.assertEqual((4 * self.x).size, (2,1))
self.assertEqual((4 <= self.x).size, (2,1))
self.assertEqual((4 == self.x).size, (2,1))
self.assertEqual((self.x >= 4).size, (2,1))
# Matrices
exp = (self.A + 2) + 4
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual((3 * self.A).size, (2,2))
self.assertEqual(exp.size, (2,2))
# Test indexing expression.
def test_index_expression(self):
# Tuple of integers as key.
exp = self.x[1,0]
self.assertEqual(exp.name(), "x[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
coeff = exp.coefficients(self.intf)
self.assertEqual(coeff[exp], 1)
self.assertEqual(exp.value, None)
with self.assertRaises(Exception) as cm:
(self.x[2,0])
self.assertEqual(str(cm.exception), "Invalid indices 2,0 for 'x'.")
# Slicing
exp = self.C[0:2,1]
self.assertEquals(exp.name(), "C[0:2,1]")
self.assertEquals(exp.size, (2,1))
exp = self.C[0:,0:2]
self.assertEquals(exp.name(), "C[0:,0:2]")
self.assertEquals(exp.size, (3,2))
exp = self.C[0::2,0::2]
self.assertEquals(exp.name(), "C[0::2,0::2]")
self.assertEquals(exp.size, (2,1))
exp = self.C[:3,:1:2]
self.assertEquals(exp.name(), "C[0:3,0]")
self.assertEquals(exp.size, (3,1))
c = Constant([[1,-2],[0,4]])
exp = c[1,1]
print exp
self.assertEqual(exp.curvature, u.Curvature.CONSTANT)
self.assertEqual(exp.sign, u.Sign.POSITIVE)
self.assertEqual(c[0,1].sign, u.Sign.ZERO)
self.assertEqual(c[1,0].sign, u.Sign.NEGATIVE)
self.assertEquals(exp.size, (1,1))
self.assertEqual(exp.value, 4)
c = Constant([[1,-2,3],[0,4,5],[7,8,9]])
exp = c[0:3,0:4:2]
self.assertEqual(exp.curvature, u.Curvature.CONSTANT)
self.assertEquals(exp.size, (3,2))
self.assertEqual(exp[0,1].value, 7)
# Arithmetic expression indexing
exp = (self.x + self.z)[1,0]
self.assertEqual(exp.name(), "x[1,0] + z[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.sign, u.Sign.UNKNOWN)
self.assertEquals(exp.size, (1,1))
exp = (self.x + self.a)[1,0]
self.assertEqual(exp.name(), "x[1,0] + a")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
exp = (self.x - self.z)[1,0]
self.assertEqual(exp.name(), "x[1,0] - z[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
exp = (self.x - self.a)[1,0]
self.assertEqual(exp.name(), "x[1,0] - a")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
exp = (-self.x)[1,0]
self.assertEqual(exp.name(), "-x[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
c = Constant([[1,2],[3,4]])
exp = (c*self.x)[1,0]
self.assertEqual(exp.name(), "[[2], [4]] * x[0:,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
c = Constant([[1,2],[3,4]])
exp = (c*self.a)[1,0]
self.assertEqual(exp.name(), "2 * a")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
