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_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)))
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_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_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_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_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_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.")
# Small negative values are rounded to 0.
x.value = -1e-8
self.assertEqual(x.value, 0)
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_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.")
# 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)))
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)
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)
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_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)