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_INTF
# 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.shape, (2, ))
self.assertEqual(y.shape, tuple())
self.assertEqual(x.curvature, s.AFFINE)
# self.assertEqual(x.canonical_form[0].shape, (2, 1))
# self.assertEqual(x.canonical_form[1], [])
self.assertEqual(repr(self.x), "Variable((2,))")
self.assertEqual(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) or 0 in self.shape
# mat = coeffs[self.A.id][1]
# self.assertEqual(mat.shape, (2,4))
# self.assertEqual(mat[0,2], 1)
with self.assertRaises(Exception) as cm:
Variable((2, 2), diag=True, symmetric=True)
self.assertEqual(
str(cm.exception),
"Cannot set more than one special attribute in Variable.")
with self.assertRaises(Exception) as cm:
Variable((2, 0))
self.assertEqual(str(cm.exception), "Invalid dimensions (2, 0).")
with self.assertRaises(Exception) as cm:
Variable((2, .5))
self.assertEqual(str(cm.exception), "Invalid dimensions (2, 0.5).")
with self.assertRaises(Exception) as cm:
Variable(2, 1)
self.assertEqual(str(cm.exception),
"Variable name 1 must be a string.")
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,) 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 = Variable(nonneg=True)
with self.assertRaises(Exception) as cm:
x.value = -2
self.assertEqual(str(cm.exception),
"Variable value must be nonnegative.")
# Test tranposing variables.
def test_transpose_variable(self):
var = self.a.T
self.assertEqual(var.name(), "a")
self.assertEqual(var.shape, tuple())
self.a.save_value(2)
self.assertEqual(var.value, 2)
var = self.x
self.assertEqual(var.name(), "x")
self.assertEqual(var.shape, (2, ))
x = Variable((2, 1), name='x')
var = x.T
self.assertEqual(var.name(), "x.T")
self.assertEqual(var.shape, (1, 2))
x.save_value(np.array([[1, 2]]).T)
self.assertEqual(var.value[0, 0], 1)
self.assertEqual(var.value[0, 1], 2)
var = self.C.T
self.assertEqual(var.name(), "C.T")
self.assertEqual(var.shape, (2, 3))
# coeffs = var.canonical_form[0].coefficients()
# mat = coeffs.values()[0][0]
# self.assertEqual(mat.shape, (2,6))
# self.assertEqual(mat[1,3], 1)
index = var[1, 0]
self.assertEqual(index.name(), "C.T[1, 0]")
self.assertEqual(index.shape, tuple())
var = x.T.T
self.assertEqual(var.name(), "x.T.T")
self.assertEqual(var.shape, (2, 1))
# Test the Constant class.
def test_constants(self):
c = Constant(2.0)
self.assertEqual(c.name(), str(2.0))
c = Constant(2)
self.assertEqual(c.value, 2)
self.assertEqual(c.shape, tuple())
self.assertEqual(c.curvature, s.CONSTANT)
self.assertEqual(c.sign, s.NONNEG)
self.assertEqual(Constant(-2).sign, s.NONPOS)
self.assertEqual(Constant(0).sign, s.ZERO)
# self.assertEqual(c.canonical_form[0].shape, (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.shape, (1, 2))
self.assertEqual(c.sign, s.NONNEG)
self.assertEqual((-c).sign, s.NONPOS)
self.assertEqual((0 * c).sign, s.ZERO)
c = Constant([[2], [-2]])
self.assertEqual(c.sign, s.UNKNOWN)
c = Constant(np.zeros((2, 1)))
self.assertEqual(c.shape, (2, 1))
# Test sign of a complex expression.
c = Constant([1, 2])
self.assertEqual(c.shape, (2, ))
A = Constant([[1, 1], [1, 1]])
exp = c.T * A * c
self.assertEqual(exp.sign, s.NONNEG)
self.assertEqual((c.T * c).sign, s.NONNEG)
exp = c.T.T
self.assertEqual(exp.sign, s.NONNEG)
exp = c.T * self.A
self.assertEqual(exp.sign, s.UNKNOWN)
# Test repr.
self.assertEqual(repr(c), "Constant(CONSTANT, NONNEGATIVE, (2,))")
def test_1D_array(self):
"""Test NumPy 1D arrays as constants.
"""
c = np.array([1, 2])
p = Parameter(2)
p.value = [1, 1]
self.assertEqual((c * p).value, 3)
self.assertEqual((c * self.x).shape, tuple())
# Test Parameter class on good inputs.
def test_parameters_successes(self):
# Parameter names and dimensions
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.shape, tuple())
# Entry-wise constraints on parameter values.
val = -np.ones((4, 3))
val[0, 0] = 2
p = Parameter((4, 3))
p.value = val
# Initialize a parameter with a value; later, set it to None.
p = Parameter(value=10)
self.assertEqual(p.value, 10)
p.value = 10
p.value = None
self.assertEqual(p.value, None)
# Test parameter representation.
p = Parameter((4, 3), nonpos=True)
self.assertEqual(repr(p), 'Parameter((4, 3), nonpos=True)')
# Test valid diagonal parameter.
p = Parameter((2, 2), diag=True)
p.value = sp.csc_matrix(np.eye(2))
self.assertItemsAlmostEqual(p.value.todense(), np.eye(2), places=10)
def test_psd_nsd_parameters(self):
# Test valid rank-deficeint PSD parameter.
np.random.seed(42)
a = np.random.normal(size=(100, 95))
a2 = a.dot(a.T) # This must be a PSD matrix.
p = Parameter((100, 100), PSD=True)
p.value = a2
self.assertItemsAlmostEqual(p.value, a2, places=10)
# Test positive definite matrix with non-distinct eigenvalues
m, n = 10, 5
A = np.random.randn(
m, n) + 1j * np.random.randn(m, n) # a random complex matrix
A = np.dot(A.T.conj(),
A) # a random Hermitian positive definite matrix
A = np.vstack([
np.hstack([np.real(A), -np.imag(A)]),
np.hstack([np.imag(A), np.real(A)])
])
p = Parameter(shape=(2 * n, 2 * n), PSD=True)
p.value = A
self.assertItemsAlmostEqual(p.value, A)
# Test invalid PSD parameter
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), PSD=True, value=[[1, 0], [0, -1]])
self.assertEqual(str(cm.exception),
"Parameter value must be positive semidefinite.")
# Test invalid NSD parameter
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), NSD=True, value=[[1, 0], [0, -1]])
self.assertEqual(str(cm.exception),
"Parameter value must be negative semidefinite.")
# Test arithmetic.
p = Parameter(shape=(2, 2), PSD=True)
self.assertTrue((2 * p).is_psd())
self.assertTrue((p + p).is_psd())
self.assertTrue((-p).is_nsd())
self.assertTrue(((-2) * (-p)).is_psd())
# Test the Parameter class on bad inputs.
def test_parameters_failures(self):
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.shape, tuple())
p = Parameter((4, 3), nonneg=True)
with self.assertRaises(Exception) as cm:
p.value = 1
self.assertEqual(str(cm.exception),
"Invalid dimensions () for Parameter value.")
val = -np.ones((4, 3))
val[0, 0] = 2
p = Parameter((4, 3), nonneg=True)
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception),
"Parameter value must be nonnegative.")
p = Parameter((4, 3), nonpos=True)
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception),
"Parameter value must be nonpositive.")
with self.assertRaises(Exception) as cm:
p = Parameter(2, 1, nonpos=True, value=[2, 1])
self.assertEqual(str(cm.exception),
"Parameter value must be nonpositive.")
with self.assertRaises(Exception) as cm:
p = Parameter((4, 3), nonneg=True, value=[1, 2])
self.assertEqual(str(cm.exception),
"Invalid dimensions (2,) for Parameter value.")
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), diag=True, symmetric=True)
self.assertEqual(
str(cm.exception),
"Cannot set more than one special attribute in Parameter.")
# Boolean
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), boolean=True, value=[[1, 1], [1, -1]])
self.assertEqual(str(cm.exception), "Parameter value must be boolean.")
# Integer
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), integer=True, value=[[1, 1.5], [1, -1]])
self.assertEqual(str(cm.exception), "Parameter value must be integer.")
# Diag.
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), diag=True, value=[[1, 1], [1, -1]])
self.assertEqual(str(cm.exception),
"Parameter value must be diagonal.")
# Symmetric.
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), symmetric=True, value=[[1, 1], [-1, -1]])
self.assertEqual(str(cm.exception),
"Parameter value must be symmetric.")
def test_symmetric(self):
"""Test symmetric variables.
"""
with self.assertRaises(Exception) as cm:
v = Variable((4, 3), symmetric=True)
self.assertEqual(
str(cm.exception),
"Invalid dimensions (4, 3). Must be a square matrix.")
v = Variable((2, 2), symmetric=True)
assert v.is_symmetric()
v = Variable((2, 2), PSD=True)
assert v.is_symmetric()
v = Variable((2, 2), NSD=True)
assert v.is_symmetric()
v = Variable((2, 2), diag=True)
assert v.is_symmetric()
assert self.a.is_symmetric()
assert not self.A.is_symmetric()
v = Variable((2, 2), symmetric=True)
expr = v + v
assert expr.is_symmetric()
expr = -v
assert expr.is_symmetric()
expr = v.T
assert expr.is_symmetric()
expr = cp.real(v)
assert expr.is_symmetric()
expr = cp.imag(v)
assert expr.is_symmetric()
expr = cp.conj(v)
assert expr.is_symmetric()
expr = cp.promote(Variable(), (2, 2))
assert expr.is_symmetric()
def test_hermitian(self):
"""Test Hermitian variables.
"""
with self.assertRaises(Exception) as cm:
v = Variable((4, 3), hermitian=True)
self.assertEqual(
str(cm.exception),
"Invalid dimensions (4, 3). Must be a square matrix.")
v = Variable((2, 2), hermitian=True)
assert v.is_hermitian()
# v = Variable((2,2), PSD=True)
# assert v.is_symmetric()
# v = Variable((2,2), NSD=True)
# assert v.is_symmetric()
v = Variable((2, 2), diag=True)
assert v.is_hermitian()
v = Variable((2, 2), hermitian=True)
expr = v + v
assert expr.is_hermitian()
expr = -v
assert expr.is_hermitian()
expr = v.T
assert expr.is_hermitian()
expr = cp.real(v)
assert expr.is_hermitian()
expr = cp.imag(v)
assert expr.is_hermitian()
expr = cp.conj(v)
assert expr.is_hermitian()
expr = cp.promote(Variable(), (2, 2))
assert expr.is_hermitian()
def test_round_attr(self):
"""Test rounding for attributes.
"""
# Nonpos
v = Variable(1, nonpos=True)
self.assertAlmostEqual(v.project(1), 0)
v = Variable(2, nonpos=True)
self.assertItemsAlmostEqual(v.project(np.array([1, -1])), [0, -1])
# Nonneg
v = Variable(1, nonneg=True)
self.assertAlmostEqual(v.project(-1), 0)
v = Variable(2, nonneg=True)
self.assertItemsAlmostEqual(v.project(np.array([1, -1])), [1, 0])
# Boolean
v = Variable((2, 2), boolean=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, 0]]).T),
[1, 0, 1, 0])
# Integer
v = Variable((2, 2), integer=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1.6], [1, 0]]).T),
[1, -2, 1, 0])
# Symmetric
v = Variable((2, 2), symmetric=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, 0]])),
[1, 0, 0, 0])
# PSD
v = Variable((2, 2), PSD=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, -1]])),
[1, 0, 0, 0])
# NSD
v = Variable((2, 2), NSD=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, -1]])),
[0, 0, 0, -1])
# diag
v = Variable((2, 2), diag=True)
self.assertItemsAlmostEqual(
v.project(np.array([[1, -1], [1, 0]])).todense(), [1, 0, 0, 0])
# Hermitian
v = Variable((2, 2), hermitian=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1j], [1, 0]])),
[1, 0.5 + 0.5j, 0.5 - 0.5j, 0])
A = Constant(np.array([[1.0]]))
self.assertEqual(A.is_psd(), True)
self.assertEqual(A.is_nsd(), False)
A = Constant(np.array([[-1.0]]))
self.assertEqual(A.is_psd(), False)
self.assertEqual(A.is_nsd(), True)
A = Constant(np.array([[0.0]]))
self.assertEqual(A.is_psd(), True)
self.assertEqual(A.is_nsd(), True)
# Test the AddExpresion class.
def test_add_expression(self):
# Vectors
c = Constant([2, 2])
exp = self.x + c
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), self.x.name() + " + " + c.name())
self.assertEqual(exp.shape, (2, ))
z = Variable(2, name='z')
exp = exp + z + self.x
# Incompatible dimensions
with self.assertRaises(ValueError):
(self.x + self.y)
# Matrices
exp = self.A + self.B
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (2, 2))
# Incompatible dimensions
with self.assertRaises(ValueError):
(self.A + self.C)
# Incompatible dimensions
with self.assertRaises(ValueError):
AddExpression([self.A, self.C])
# 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,))")
# Test the SubExpresion class.
def test_sub_expression(self):
# Vectors
c = Constant([2, 2])
exp = self.x - c
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), self.x.name() + " - " + Constant([2,2]).name())
self.assertEqual(exp.shape, (2, ))
z = Variable(2, name='z')
exp = exp - z - self.x
# Incompatible dimensions
with self.assertRaises(ValueError):
(self.x - self.y)
# Matrices
exp = self.A - self.B
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (2, 2))
# Incompatible dimensions
with self.assertRaises(ValueError):
(self.A - self.C)
# Test repr.
self.assertEqual(repr(self.x - c), "Expression(AFFINE, UNKNOWN, (2,))")
# Test the MulExpresion class.
def test_mul_expression(self):
# Vectors
c = Constant([[2], [2]])
exp = c * self.x
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual((c[0] * self.x).sign, s.UNKNOWN)
# self.assertEqual(exp.canonical_form[0].shape, (1, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.shape, (1, ))
# Incompatible dimensions
with self.assertRaises(ValueError):
([2, 2, 3] * self.x)
# Matrices: Incompatible dimensions
with self.assertRaises(ValueError):
Constant([[2, 1], [2, 2]]) * self.C
# Affine times affine is okay
with warnings.catch_warnings():
warnings.simplefilter("ignore")
q = self.A * self.B
self.assertTrue(q.is_quadratic())
# Constant expressions
T = Constant([[1, 2, 3], [3, 5, 5]])
exp = (T + T) * self.B
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (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, s.UNKNOWN)
def test_matmul_expression(self):
"""Test matmul function, corresponding to .__matmul__( operator.
"""
# Vectors
c = Constant([[2], [2]])
exp = c.__matmul__(self.x)
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
# self.assertEqual(exp.name(), c.name() + " .__matmul__( " + self.x.name())
self.assertEqual(exp.shape, (1, ))
with self.assertRaises(Exception) as cm:
self.x.__matmul__(2)
self.assertEqual(str(cm.exception),
"Scalar operands are not allowed, use '*' instead")
# Incompatible dimensions
with self.assertRaises(ValueError) as cm:
(self.x.__matmul__(np.array([2, 2, 3])))
# Incompatible dimensions
with self.assertRaises(Exception) as cm:
Constant([[2, 1], [2, 2]]).__matmul__(self.C)
# Affine times affine is okay
with warnings.catch_warnings():
warnings.simplefilter("ignore")
q = self.A.__matmul__(self.B)
self.assertTrue(q.is_quadratic())
# # Nonaffine times nonconstant raises error
# with warnings.catch_warnings():
# warnings.simplefilter("ignore")
# with self.assertRaises(Exception) as cm:
# (self.A.__matmul__(self.B).__matmul__(self.A))
# self.assertEqual(str(cm.exception), "Cannot multiply UNKNOWN and AFFINE.")
# Constant expressions
T = Constant([[1, 2, 3], [3, 5, 5]])
exp = (T + T).__matmul__(self.B)
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (3, 2))
# Expression that would break sign multiplication without promotion.
c = Constant([[2], [2], [-2]])
exp = [[1], [2]] + c.__matmul__(self.C)
self.assertEqual(exp.sign, s.UNKNOWN)
# Testing shape.
a = Parameter((1, ))
x = Variable(shape=(1, ))
expr = a.__matmul__(x)
self.assertEqual(expr.shape, ())
# Testing shape.
a = Parameter((1, ))
x = Variable(shape=(1, ))
expr = a.__matmul__(x)
self.assertEqual(expr.shape, ())
A = Parameter((4, 4))
z = Variable((4, 1))
expr = A.__matmul__(z)
self.assertEqual(expr.shape, (4, 1))
v = Variable((1, 1))
col_scalar = Parameter((1, 1))
assert v.shape == col_scalar.shape == col_scalar.T.shape
# Test the DivExpresion class.
def test_div_expression(self):
# Vectors
exp = self.x / 2
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.shape, (2, ))
with self.assertRaises(Exception) as cm:
(self.x / [2, 2, 3])
print(cm.exception)
self.assertRegexpMatches(str(cm.exception),
"Incompatible shapes for division.*")
c = Constant([3.0, 4.0, 12.0])
self.assertItemsAlmostEqual((c / Constant([1.0, 2.0, 3.0])).value,
np.array([3.0, 2.0, 4.0]))
# Constant expressions.
c = Constant(2)
exp = c / (3 - 5)
self.assertEqual(exp.curvature, s.CONSTANT)
self.assertEqual(exp.shape, tuple())
self.assertEqual(exp.sign, s.NONPOS)
# Parameters.
p = Parameter(nonneg=True)
exp = 2 / p
p.value = 2
self.assertEqual(exp.value, 1)
rho = Parameter(nonneg=True)
rho.value = 1
self.assertEqual(rho.sign, s.NONNEG)
self.assertEqual(Constant(2).sign, s.NONNEG)
self.assertEqual((Constant(2) / Constant(2)).sign, s.NONNEG)
self.assertEqual((Constant(2) * rho).sign, s.NONNEG)
self.assertEqual((rho / 2).sign, s.NONNEG)
# Test the NegExpression class.
def test_neg_expression(self):
# Vectors
exp = -self.x
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (2, ))
assert exp.is_affine()
self.assertEqual(exp.sign, s.UNKNOWN)
assert not exp.is_nonneg()
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), "-%s" % self.x.name())
self.assertEqual(exp.shape, self.x.shape)
# Matrices
exp = -self.C
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (3, 2))
# Test promotion of scalar constants.
def test_scalar_const_promotion(self):
# Vectors
exp = self.x + 2
self.assertEqual(exp.curvature, s.AFFINE)
assert exp.is_affine()
self.assertEqual(exp.sign, s.UNKNOWN)
assert not exp.is_nonpos()
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), self.x.name() + " + " + Constant(2).name())
self.assertEqual(exp.shape, (2, ))
self.assertEqual((4 - self.x).shape, (2, ))
self.assertEqual((4 * self.x).shape, (2, ))
self.assertEqual((4 <= self.x).shape, (2, ))
self.assertEqual((4 == self.x).shape, (2, ))
self.assertEqual((self.x >= 4).shape, (2, ))
# Matrices
exp = (self.A + 2) + 4
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual((3 * self.A).shape, (2, 2))
self.assertEqual(exp.shape, (2, 2))
# Test indexing expression.
def test_index_expression(self):
# Tuple of integers as key.
exp = self.x[1]
# self.assertEqual(exp.name(), "x[1,0]")
self.assertEqual(exp.curvature, s.AFFINE)
assert exp.is_affine()
self.assertEqual(exp.shape, tuple())
# coeff = exp.canonical_form[0].coefficients()[self.x][0]
# self.assertEqual(coeff[0,1], 1)
self.assertEqual(exp.value, None)
exp = self.x[1].T
# self.assertEqual(exp.name(), "x[1,0]")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, tuple())
with self.assertRaises(Exception) as cm:
(self.x[2, 0])
self.assertEqual(str(cm.exception), "Too many indices for expression.")
with self.assertRaises(Exception) as cm:
(self.x[2])
self.assertEqual(str(cm.exception),
"Index 2 is out of bounds for axis 0 with size 2.")
# Slicing
exp = self.C[0:2, 1]
# self.assertEqual(exp.name(), "C[0:2,1]")
self.assertEqual(exp.shape, (2, ))
exp = self.C[0:, 0:2]
# self.assertEqual(exp.name(), "C[0:,0:2]")
self.assertEqual(exp.shape, (3, 2))
exp = self.C[0::2, 0::2]
# self.assertEqual(exp.name(), "C[0::2,0::2]")
self.assertEqual(exp.shape, (2, 1))
exp = self.C[:3, :1:2]
# self.assertEqual(exp.name(), "C[0:3,0]")
self.assertEqual(exp.shape, (3, 1))
exp = self.C[0:, 0]
# self.assertEqual(exp.name(), "C[0:,0]")
self.assertEqual(exp.shape, (3, ))
c = Constant([[1, -2], [0, 4]])
exp = c[1, 1]
self.assertEqual(exp.curvature, s.CONSTANT)
self.assertEqual(exp.sign, s.UNKNOWN)
self.assertEqual(c[0, 1].sign, s.UNKNOWN)
self.assertEqual(c[1, 0].sign, s.UNKNOWN)
self.assertEqual(exp.shape, tuple())
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, s.CONSTANT)
assert exp.is_constant()
self.assertEqual(exp.shape, (3, 2))
self.assertEqual(exp[0, 1].value, 7)
# Slice of transpose
exp = self.C.T[0:2, 1:2]
self.assertEqual(exp.shape, (2, 1))
# Arithmetic expression indexing
exp = (self.x + self.z)[1]
# self.assertEqual(exp.name(), "x[1,0] + z[1,0]")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
self.assertEqual(exp.shape, tuple())
exp = (self.x + self.a)[1:2]
# self.assertEqual(exp.name(), "x[1,0] + a")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (1, ))
exp = (self.x - self.z)[1:2]
# self.assertEqual(exp.name(), "x[1,0] - z[1,0]")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (1, ))
exp = (self.x - self.a)[1]
# self.assertEqual(exp.name(), "x[1,0] - a")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, tuple())
exp = (-self.x)[1]
# self.assertEqual(exp.name(), "-x[1,0]")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, tuple())
c = Constant([[1, 2], [3, 4]])
exp = (c * self.x)[1]
# self.assertEqual(exp.name(), "[[2], [4]] * x[0:,0]")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, tuple())
c = Constant([[1, 2], [3, 4]])
exp = (c * self.a)[1, 0:1]
# self.assertEqual(exp.name(), "2 * a")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (1, ))
def test_none_idx(self):
"""Test None as index.
"""
expr = self.a[None, None]
self.assertEqual(expr.shape, (1, 1))
expr = self.x[:, None]
self.assertEqual(expr.shape, (2, 1))
expr = self.x[None, :]
self.assertEqual(expr.shape, (1, 2))
expr = Constant([1, 2])[None, :]
self.assertEqual(expr.shape, (1, 2))
self.assertItemsAlmostEqual(expr.value, [1, 2])
def test_out_of_bounds(self):
"""Test out of bounds indices.
"""
with self.assertRaises(Exception) as cm:
self.x[100]
self.assertEqual(str(cm.exception),
"Index 100 is out of bounds for axis 0 with size 2.")
with self.assertRaises(Exception) as cm:
self.x[-100]
self.assertEqual(
str(cm.exception),
"Index -100 is out of bounds for axis 0 with size 2.")
exp = self.x[:-100]
self.assertEqual(exp.size, (0, ))
self.assertItemsAlmostEqual(exp.value, np.array([]))
exp = self.C[100:2]
self.assertEqual(exp.shape, (0, 2))
exp = self.C[:, -199:2]
self.assertEqual(exp.shape, (3, 2))
exp = self.C[:, -199:-3]
self.assertEqual(exp.shape, (3, 0))
def test_neg_indices(self):
"""Test negative indices.
"""
c = Constant([[1, 2], [3, 4]])
exp = c[-1, -1]
self.assertEqual(exp.value, 4)
self.assertEqual(exp.shape, tuple())
self.assertEqual(exp.curvature, s.CONSTANT)
c = Constant([1, 2, 3, 4])
exp = c[1:-1]
self.assertItemsAlmostEqual(exp.value, [2, 3])
self.assertEqual(exp.shape, (2, ))
self.assertEqual(exp.curvature, s.CONSTANT)
c = Constant([1, 2, 3, 4])
exp = c[::-1]
self.assertItemsAlmostEqual(exp.value, [4, 3, 2, 1])
self.assertEqual(exp.shape, (4, ))
self.assertEqual(exp.curvature, s.CONSTANT)
x = Variable(4)
self.assertEqual(x[::-1].shape, (4, ))
Problem(Minimize(0), [x[::-1] == c]).solve()
self.assertItemsAlmostEqual(x.value, [4, 3, 2, 1])
x = Variable(2)
self.assertEqual(x[::-1].shape, (2, ))
x = Variable(100, name="x")
self.assertEqual("x[0:99]", str(x[:-1]))
c = Constant([[1, 2], [3, 4]])
expr = c[0, 2:0:-1]
self.assertEqual(expr.shape, (1, ))
self.assertAlmostEqual(expr.value, 3)
expr = c[0, 2::-1]
self.assertEqual(expr.shape, (2, ))
self.assertItemsAlmostEqual(expr.value, [3, 1])
def test_logical_indices(self):
"""Test indexing with boolean arrays.
"""
A = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
C = Constant(A)
# Boolean array.
expr = C[A <= 2]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[A <= 2], expr.value)
expr = C[A % 2 == 0]
self.assertEqual(expr.shape, (6, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[A % 2 == 0], expr.value)
# Boolean array for rows, index for columns.
expr = C[np.array([True, False, True]), 3]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[np.array([True, False, True]), 3],
expr.value)
# Index for row, boolean array for columns.
expr = C[1, np.array([True, False, False, True])]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[1,
np.array([True, False, False, True])],
expr.value)
# Boolean array for rows, slice for columns.
expr = C[np.array([True, True, True]), 1:3]
self.assertEqual(expr.shape, (3, 2))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[np.array([True, True, True]), 1:3],
expr.value)
# Slice for row, boolean array for columns.
expr = C[1:-1, np.array([True, False, True, True])]
self.assertEqual(expr.shape, (1, 3))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(
A[1:-1, np.array([True, False, True, True])], expr.value)
# Boolean arrays for rows and columns.
# Not sure what this does.
expr = C[np.array([True, True, True]),
np.array([True, False, True, True])]
self.assertEqual(expr.shape, (3, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(
A[np.array([True, True, True]),
np.array([True, False, True, True])], expr.value)
def test_selector_list_indices(self):
"""Test indexing with lists/ndarrays of indices.
"""
A = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
C = Constant(A)
# List for rows.
expr = C[[1, 2]]
self.assertEqual(expr.shape, (2, 4))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[[1, 2]], expr.value)
# List for rows, index for columns.
expr = C[[0, 2], 3]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[[0, 2], 3], expr.value)
# Index for row, list for columns.
expr = C[1, [0, 2]]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[1, [0, 2]], expr.value)
# List for rows, slice for columns.
expr = C[[0, 2], 1:3]
self.assertEqual(expr.shape, (2, 2))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[[0, 2], 1:3], expr.value)
# Slice for row, list for columns.
expr = C[1:-1, [0, 2]]
self.assertEqual(expr.shape, (1, 2))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[1:-1, [0, 2]], expr.value)
# Lists for rows and columns.
expr = C[[0, 1], [1, 3]]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[[0, 1], [1, 3]], expr.value)
# Ndarray for rows, list for columns.
expr = C[np.array([0, 1]), [1, 3]]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[np.array([0, 1]), [1, 3]], expr.value)
# Ndarrays for rows and columns.
expr = C[np.array([0, 1]), np.array([1, 3])]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[np.array([0, 1]),
np.array([1, 3])], expr.value)
def test_powers(self):
exp = self.x**2
self.assertEqual(exp.curvature, s.CONVEX)
exp = self.x**0.5
self.assertEqual(exp.curvature, s.CONCAVE)
exp = self.x**-1
self.assertEqual(exp.curvature, s.CONVEX)
def test_sum(self):
"""Test cvxpy sum function.
"""
self.a.value = 1
expr = cp.sum(self.a)
self.assertEqual(expr.value, 1)
self.x.value = [1, 2]
expr = cp.sum(self.x)
self.assertEqual(expr.value, 3)
def test_var_copy(self):
"""Test the copy function for variable types.
"""
x = Variable((3, 4), name="x")
y = x.copy()
self.assertEqual(y.shape, (3, 4))
self.assertEqual(y.name(), "x")
x = Variable((5, 5), PSD=True, name="x")
y = x.copy()
self.assertEqual(y.shape, (5, 5))
def test_param_copy(self):
"""Test the copy function for Parameters.
"""
x = Parameter((3, 4), name="x", nonneg=True)
y = x.copy()
self.assertEqual(y.shape, (3, 4))
self.assertEqual(y.name(), "x")
self.assertEqual(y.sign, "NONNEGATIVE")
def test_constant_copy(self):
"""Test the copy function for Constants.
"""
x = Constant(2)
y = x.copy()
self.assertEqual(y.shape, tuple())
self.assertEqual(y.value, 2)
def test_is_pwl(self):
"""Test is_pwl()
"""
A = np.ones((2, 3))
b = np.ones(2)
expr = A * self.y - b
self.assertEqual(expr.is_pwl(), True)
expr = cp.maximum(1, 3 * self.y)
self.assertEqual(expr.is_pwl(), True)
expr = cp.abs(self.y)
self.assertEqual(expr.is_pwl(), True)
expr = cp.pnorm(3 * self.y, 1)
self.assertEqual(expr.is_pwl(), True)
expr = cp.pnorm(3 * self.y**2, 1)
self.assertEqual(expr.is_pwl(), False)
class TestExpressions(BaseTest):
""" Unit tests for the expression/expression module. """
def setUp(self) -> None:
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
# Test the Variable class.
def test_variable(self) -> None:
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.shape, (2, ))
self.assertEqual(y.shape, tuple())
self.assertEqual(x.curvature, s.AFFINE)
# self.assertEqual(x.canonical_form[0].shape, (2, 1))
# self.assertEqual(x.canonical_form[1], [])
self.assertEqual(repr(self.x), "Variable((2,))")
self.assertEqual(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) or 0 in self.shape
# mat = coeffs[self.A.id][1]
# self.assertEqual(mat.shape, (2,4))
# self.assertEqual(mat[0,2], 1)
with self.assertRaises(Exception) as cm:
Variable((2, 2), diag=True, symmetric=True)
self.assertEqual(
str(cm.exception),
"Cannot set more than one special attribute in Variable.")
with self.assertRaises(Exception) as cm:
Variable((2, 0))
self.assertEqual(str(cm.exception), "Invalid dimensions (2, 0).")
with self.assertRaises(Exception) as cm:
Variable((2, .5))
self.assertEqual(str(cm.exception), "Invalid dimensions (2, 0.5).")
with self.assertRaises(Exception) as cm:
Variable(2, 1)
self.assertEqual(str(cm.exception),
"Variable name 1 must be a string.")
def test_assign_var_value(self) -> None:
"""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,) 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 = Variable(nonneg=True)
with self.assertRaises(Exception) as cm:
x.value = -2
self.assertEqual(str(cm.exception),
"Variable value must be nonnegative.")
# Test tranposing variables.
def test_transpose_variable(self) -> None:
var = self.a.T
self.assertEqual(var.name(), "a")
self.assertEqual(var.shape, tuple())
self.a.save_value(2)
self.assertEqual(var.value, 2)
var = self.x
self.assertEqual(var.name(), "x")
self.assertEqual(var.shape, (2, ))
x = Variable((2, 1), name='x')
var = x.T
self.assertEqual(var.name(), "x.T")
self.assertEqual(var.shape, (1, 2))
x.save_value(np.array([[1, 2]]).T)
self.assertEqual(var.value[0, 0], 1)
self.assertEqual(var.value[0, 1], 2)
var = self.C.T
self.assertEqual(var.name(), "C.T")
self.assertEqual(var.shape, (2, 3))
# coeffs = var.canonical_form[0].coefficients()
# mat = coeffs.values()[0][0]
# self.assertEqual(mat.shape, (2,6))
# self.assertEqual(mat[1,3], 1)
index = var[1, 0]
self.assertEqual(index.name(), "C.T[1, 0]")
self.assertEqual(index.shape, tuple())
var = x.T.T
self.assertEqual(var.name(), "x.T.T")
self.assertEqual(var.shape, (2, 1))
# Test the Constant class.
def test_constants(self) -> None:
c = Constant(2.0)
self.assertEqual(c.name(), str(2.0))
c = Constant(2)
self.assertEqual(c.value, 2)
self.assertEqual(c.shape, tuple())
self.assertEqual(c.curvature, s.CONSTANT)
self.assertEqual(c.sign, s.NONNEG)
self.assertEqual(Constant(-2).sign, s.NONPOS)
self.assertEqual(Constant(0).sign, s.ZERO)
# self.assertEqual(c.canonical_form[0].shape, (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.shape, (1, 2))
self.assertEqual(c.sign, s.NONNEG)
self.assertEqual((-c).sign, s.NONPOS)
self.assertEqual((0 * c).sign, s.ZERO)
c = Constant([[2], [-2]])
self.assertEqual(c.sign, s.UNKNOWN)
c = Constant(np.zeros((2, 1)))
self.assertEqual(c.shape, (2, 1))
# Test sign of a complex expression.
c = Constant([1, 2])
self.assertEqual(c.shape, (2, ))
A = Constant([[1, 1], [1, 1]])
exp = c.T @ A @ c
self.assertEqual(exp.sign, s.NONNEG)
self.assertEqual((c.T @ c).sign, s.NONNEG)
exp = c.T.T
self.assertEqual(exp.sign, s.NONNEG)
exp = c.T @ self.A
self.assertEqual(exp.sign, s.UNKNOWN)
# Test repr.
self.assertEqual(repr(c), "Constant(CONSTANT, NONNEGATIVE, (2,))")
def test_constant_psd_nsd(self):
n = 5
np.random.randn(0)
U = np.random.randn(n, n)
U = U @ U.T
(evals, U) = np.linalg.eigh(U) # U is now an orthogonal matrix
# Try four indefinite matrices with different eigenvalue
# spread around the origin.
v1 = np.array([3, 2, 1, 1e-8, -1])
P = Constant(U @ np.diag(v1) @ U.T)
self.assertFalse(P.is_psd())
self.assertFalse(P.is_nsd())
v2 = np.array([3, 2, 2, 1e-6, -1])
P = Constant(U @ np.diag(v2) @ U.T)
self.assertFalse(P.is_psd())
self.assertFalse(P.is_nsd())
v3 = np.array([3, 2, 2, 1e-4, -1e-6])
P = Constant(U @ np.diag(v3) @ U.T)
self.assertFalse(P.is_psd())
self.assertFalse(P.is_nsd())
v4 = np.array([-1, 3, 0, 0, 0])
P = Constant(U @ np.diag(v4) @ U.T)
self.assertFalse(P.is_psd())
self.assertFalse(P.is_nsd())
# Try a test case given in GitHub issue 1451.
# (Should be equivalent to v4 above).
P = Constant(np.array([[1, 2], [2, 1]]))
x = Variable(shape=(2, ))
expr = cp.quad_form(x, P)
self.assertFalse(expr.is_dcp())
self.assertFalse((-expr).is_dcp())
self.assertFalse(gershgorin_psd_check(P.value, tol=0.99))
# Useful Gershgorin disc check
P = Constant(np.array([[2, 1], [1, 2]]))
self.assertTrue(gershgorin_psd_check(P.value, tol=0.0))
# Verify good behavior for large eigenvalues
P = Constant(np.diag(9 * [1e-4] + [-1e4]))
self.assertFalse(P.is_psd())
self.assertFalse(P.is_nsd())
# Check a case when the matrix is in fact PSD.
P = Constant(np.ones(shape=(5, 5)))
self.assertTrue(P.is_psd())
self.assertFalse(P.is_nsd())
# Check with sparse inputs
P = Constant(sp.eye(10))
self.assertTrue(gershgorin_psd_check(P.value, s.EIGVAL_TOL))
self.assertTrue(P.is_psd())
self.assertTrue((-P).is_nsd())
Q = -s.EIGVAL_TOL / 2 * P
self.assertTrue(gershgorin_psd_check(Q.value, s.EIGVAL_TOL))
Q = -1.1 * s.EIGVAL_TOL * P
self.assertFalse(gershgorin_psd_check(Q.value, s.EIGVAL_TOL))
self.assertFalse(Q.is_psd())
def test_1D_array(self) -> None:
"""Test NumPy 1D arrays as constants.
"""
c = np.array([1, 2])
p = Parameter(2)
p.value = [1, 1]
self.assertEqual((c @ p).value, 3)
self.assertEqual((c @ self.x).shape, tuple())
# Test Parameter class on good inputs.
def test_parameters_successes(self) -> None:
# Parameter names and dimensions
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.shape, tuple())
# Entry-wise constraints on parameter values.
val = -np.ones((4, 3))
val[0, 0] = 2
p = Parameter((4, 3))
p.value = val
# Initialize a parameter with a value; later, set it to None.
p = Parameter(value=10)
self.assertEqual(p.value, 10)
p.value = 10
p.value = None
self.assertEqual(p.value, None)
# Test parameter representation.
p = Parameter((4, 3), nonpos=True)
self.assertEqual(repr(p), 'Parameter((4, 3), nonpos=True)')
# Test valid diagonal parameter.
p = Parameter((2, 2), diag=True)
p.value = sp.csc_matrix(np.eye(2))
self.assertItemsAlmostEqual(p.value.todense(), np.eye(2), places=10)
def test_psd_nsd_parameters(self) -> None:
# Test valid rank-deficeint PSD parameter.
np.random.seed(42)
a = np.random.normal(size=(100, 95))
a2 = a.dot(a.T) # This must be a PSD matrix.
p = Parameter((100, 100), PSD=True)
p.value = a2
self.assertItemsAlmostEqual(p.value, a2, places=10)
# Test positive definite matrix with non-distinct eigenvalues
m, n = 10, 5
A = np.random.randn(
m, n) + 1j * np.random.randn(m, n) # a random complex matrix
A = np.dot(A.T.conj(),
A) # a random Hermitian positive definite matrix
A = np.vstack([
np.hstack([np.real(A), -np.imag(A)]),
np.hstack([np.imag(A), np.real(A)])
])
p = Parameter(shape=(2 * n, 2 * n), PSD=True)
p.value = A
self.assertItemsAlmostEqual(p.value, A)
# Test arithmetic.
p = Parameter(shape=(2, 2), PSD=True)
self.assertTrue((2 * p).is_psd())
self.assertTrue((p + p).is_psd())
self.assertTrue((-p).is_nsd())
self.assertTrue(((-2) * (-p)).is_psd())
# Test invalid PSD and NSD parameters
n = 5
P = Parameter(shape=(n, n), PSD=True)
N = Parameter(shape=(n, n), NSD=True)
np.random.randn(0)
U = np.random.randn(n, n)
U = U @ U.T
(evals, U) = np.linalg.eigh(U) # U is now an orthogonal matrix
v1 = np.array([3, 2, 1, 1e-8, -1])
v2 = np.array([3, 2, 2, 1e-6, -1])
v3 = np.array([3, 2, 2, 1e-4, -1e-6])
v4 = np.array([-1, 3, 0, 0, 0])
vs = [v1, v2, v3, v4]
for vi in vs:
with self.assertRaises(Exception) as cm:
P.value = U @ np.diag(vi) @ U.T
self.assertEqual(str(cm.exception),
"Parameter value must be positive semidefinite.")
with self.assertRaises(Exception) as cm:
N.value = -U @ np.diag(vi) @ U.T
self.assertEqual(str(cm.exception),
"Parameter value must be negative semidefinite.")
# Test the Parameter class on bad inputs.
def test_parameters_failures(self) -> None:
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.shape, tuple())
p = Parameter((4, 3), nonneg=True)
with self.assertRaises(Exception) as cm:
p.value = 1
self.assertEqual(str(cm.exception),
"Invalid dimensions () for Parameter value.")
val = -np.ones((4, 3))
val[0, 0] = 2
p = Parameter((4, 3), nonneg=True)
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception),
"Parameter value must be nonnegative.")
p = Parameter((4, 3), nonpos=True)
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception),
"Parameter value must be nonpositive.")
with self.assertRaises(Exception) as cm:
p = Parameter(2, 1, nonpos=True, value=[2, 1])
self.assertEqual(str(cm.exception),
"Parameter value must be nonpositive.")
with self.assertRaises(Exception) as cm:
p = Parameter((4, 3), nonneg=True, value=[1, 2])
self.assertEqual(str(cm.exception),
"Invalid dimensions (2,) for Parameter value.")
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), diag=True, symmetric=True)
self.assertEqual(
str(cm.exception),
"Cannot set more than one special attribute in Parameter.")
# Boolean
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), boolean=True, value=[[1, 1], [1, -1]])
self.assertEqual(str(cm.exception), "Parameter value must be boolean.")
# Integer
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), integer=True, value=[[1, 1.5], [1, -1]])
self.assertEqual(str(cm.exception), "Parameter value must be integer.")
# Diag.
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), diag=True, value=[[1, 1], [1, -1]])
self.assertEqual(str(cm.exception),
"Parameter value must be diagonal.")
# Symmetric.
with self.assertRaises(Exception) as cm:
p = Parameter((2, 2), symmetric=True, value=[[1, 1], [-1, -1]])
self.assertEqual(str(cm.exception),
"Parameter value must be symmetric.")
def test_symmetric(self) -> None:
"""Test symmetric variables.
"""
with self.assertRaises(Exception) as cm:
v = Variable((4, 3), symmetric=True)
self.assertEqual(
str(cm.exception),
"Invalid dimensions (4, 3). Must be a square matrix.")
v = Variable((2, 2), symmetric=True)
assert v.is_symmetric()
v = Variable((2, 2), PSD=True)
assert v.is_symmetric()
v = Variable((2, 2), NSD=True)
assert v.is_symmetric()
v = Variable((2, 2), diag=True)
assert v.is_symmetric()
assert self.a.is_symmetric()
assert not self.A.is_symmetric()
v = Variable((2, 2), symmetric=True)
expr = v + v
assert expr.is_symmetric()
expr = -v
assert expr.is_symmetric()
expr = v.T
assert expr.is_symmetric()
expr = cp.real(v)
assert expr.is_symmetric()
expr = cp.imag(v)
assert expr.is_symmetric()
expr = cp.conj(v)
assert expr.is_symmetric()
expr = cp.promote(Variable(), (2, 2))
assert expr.is_symmetric()
def test_hermitian(self) -> None:
"""Test Hermitian variables.
"""
with self.assertRaises(Exception) as cm:
v = Variable((4, 3), hermitian=True)
self.assertEqual(
str(cm.exception),
"Invalid dimensions (4, 3). Must be a square matrix.")
v = Variable((2, 2), hermitian=True)
assert v.is_hermitian()
# v = Variable((2,2), PSD=True)
# assert v.is_symmetric()
# v = Variable((2,2), NSD=True)
# assert v.is_symmetric()
v = Variable((2, 2), diag=True)
assert v.is_hermitian()
v = Variable((2, 2), hermitian=True)
expr = v + v
assert expr.is_hermitian()
expr = -v
assert expr.is_hermitian()
expr = v.T
assert expr.is_hermitian()
expr = cp.real(v)
assert expr.is_hermitian()
expr = cp.imag(v)
assert expr.is_hermitian()
expr = cp.conj(v)
assert expr.is_hermitian()
expr = cp.promote(Variable(), (2, 2))
assert expr.is_hermitian()
def test_round_attr(self) -> None:
"""Test rounding for attributes.
"""
# Nonpos
v = Variable(1, nonpos=True)
self.assertAlmostEqual(v.project(1), 0)
v = Variable(2, nonpos=True)
self.assertItemsAlmostEqual(v.project(np.array([1, -1])), [0, -1])
# Nonneg
v = Variable(1, nonneg=True)
self.assertAlmostEqual(v.project(-1), 0)
v = Variable(2, nonneg=True)
self.assertItemsAlmostEqual(v.project(np.array([1, -1])), [1, 0])
# Boolean
v = Variable((2, 2), boolean=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, 0]]).T),
[1, 0, 1, 0])
# Integer
v = Variable((2, 2), integer=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1.6], [1, 0]]).T),
[1, -2, 1, 0])
# Symmetric
v = Variable((2, 2), symmetric=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, 0]])),
[1, 0, 0, 0])
# PSD
v = Variable((2, 2), PSD=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, -1]])),
[1, 0, 0, 0])
# NSD
v = Variable((2, 2), NSD=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, -1]])),
[0, 0, 0, -1])
# diag
v = Variable((2, 2), diag=True)
self.assertItemsAlmostEqual(
v.project(np.array([[1, -1], [1, 0]])).todense(), [1, 0, 0, 0])
# Hermitian
v = Variable((2, 2), hermitian=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1j], [1, 0]])),
[1, 0.5 + 0.5j, 0.5 - 0.5j, 0])
A = Constant(np.array([[1.0]]))
self.assertEqual(A.is_psd(), True)
self.assertEqual(A.is_nsd(), False)
A = Constant(np.array([[-1.0]]))
self.assertEqual(A.is_psd(), False)
self.assertEqual(A.is_nsd(), True)
A = Constant(np.array([[0.0]]))
self.assertEqual(A.is_psd(), True)
self.assertEqual(A.is_nsd(), True)
# Test the AddExpresion class.
def test_add_expression(self) -> None:
# Vectors
c = Constant([2, 2])
exp = self.x + c
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), self.x.name() + " + " + c.name())
self.assertEqual(exp.shape, (2, ))
z = Variable(2, name='z')
exp = exp + z + self.x
# Incompatible dimensions
with self.assertRaises(ValueError):
(self.x + self.y)
# Matrices
exp = self.A + self.B
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (2, 2))
# Incompatible dimensions
with self.assertRaises(ValueError):
(self.A + self.C)
# Incompatible dimensions
with self.assertRaises(ValueError):
AddExpression([self.A, self.C])
# 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,))")
# Test the SubExpresion class.
def test_sub_expression(self) -> None:
# Vectors
c = Constant([2, 2])
exp = self.x - c
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), self.x.name() + " - " + Constant([2,2]).name())
self.assertEqual(exp.shape, (2, ))
z = Variable(2, name='z')
exp = exp - z - self.x
# Incompatible dimensions
with self.assertRaises(ValueError):
(self.x - self.y)
# Matrices
exp = self.A - self.B
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (2, 2))
# Incompatible dimensions
with self.assertRaises(ValueError):
(self.A - self.C)
# Test repr.
self.assertEqual(repr(self.x - c), "Expression(AFFINE, UNKNOWN, (2,))")
# Test the MulExpresion class.
def test_mul_expression(self) -> None:
# Vectors
c = Constant([[2], [2]])
exp = c @ self.x
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual((c[0] @ self.x).sign, s.UNKNOWN)
# self.assertEqual(exp.canonical_form[0].shape, (1, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.shape, (1, ))
# Incompatible dimensions
with self.assertRaises(ValueError):
([2, 2, 3] @ self.x)
# Matrices: Incompatible dimensions
with self.assertRaises(ValueError):
Constant([[2, 1], [2, 2]]) @ self.C
# Affine times affine is okay
with warnings.catch_warnings():
warnings.simplefilter("ignore")
q = self.A @ self.B
self.assertTrue(q.is_quadratic())
# Constant expressions
T = Constant([[1, 2, 3], [3, 5, 5]])
exp = (T + T) @ self.B
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (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, s.UNKNOWN)
# By default, warnings are raised if we access matmul from *.
c = Constant([[2], [2]])
with warnings.catch_warnings(record=True) as w:
c * self.x
self.assertEqual(2, len(w))
self.assertEqual(w[0].category, UserWarning)
self.assertEqual(w[1].category, DeprecationWarning)
# repeat, to make sure warnings continue to be displayed
c * self.x
self.assertEqual(4, len(w))
self.assertEqual(w[2].category, UserWarning)
self.assertEqual(w[3].category, DeprecationWarning)
# suppress one of the two warnings
warnings.simplefilter('ignore', DeprecationWarning)
c * self.x
self.assertEqual(5, len(w))
# suppress both warnings
warnings.simplefilter('ignore', UserWarning)
c * self.x
self.assertEqual(len(w), 5)
# verify that an error can be raised.
warnings.simplefilter("error", UserWarning)
with self.assertRaises(UserWarning):
c * self.x
def test_matmul_expression(self) -> None:
"""Test matmul function, corresponding to .__matmul__( operator.
"""
# Vectors
c = Constant([[2], [2]])
exp = c.__matmul__(self.x)
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
# self.assertEqual(exp.name(), c.name() + " .__matmul__( " + self.x.name())
self.assertEqual(exp.shape, (1, ))
with self.assertRaises(Exception) as cm:
self.x.__matmul__(2)
self.assertEqual(str(cm.exception),
"Scalar operands are not allowed, use '*' instead")
# Incompatible dimensions
with self.assertRaises(ValueError) as cm:
(self.x.__matmul__(np.array([2, 2, 3])))
# Incompatible dimensions
with self.assertRaises(Exception) as cm:
Constant([[2, 1], [2, 2]]).__matmul__(self.C)
# Affine times affine is okay
with warnings.catch_warnings():
warnings.simplefilter("ignore")
q = self.A.__matmul__(self.B)
self.assertTrue(q.is_quadratic())
# # Nonaffine times nonconstant raises error
# with warnings.catch_warnings():
# warnings.simplefilter("ignore")
# with self.assertRaises(Exception) as cm:
# (self.A.__matmul__(self.B).__matmul__(self.A))
# self.assertEqual(str(cm.exception), "Cannot multiply UNKNOWN and AFFINE.")
# Constant expressions
T = Constant([[1, 2, 3], [3, 5, 5]])
exp = (T + T).__matmul__(self.B)
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (3, 2))
# Expression that would break sign multiplication without promotion.
c = Constant([[2], [2], [-2]])
exp = [[1], [2]] + c.__matmul__(self.C)
self.assertEqual(exp.sign, s.UNKNOWN)
# Testing shape.
a = Parameter((1, ))
x = Variable(shape=(1, ))
expr = a.__matmul__(x)
self.assertEqual(expr.shape, ())
# Testing shape.
a = Parameter((1, ))
x = Variable(shape=(1, ))
expr = a.__matmul__(x)
self.assertEqual(expr.shape, ())
A = Parameter((4, 4))
z = Variable((4, 1))
expr = A.__matmul__(z)
self.assertEqual(expr.shape, (4, 1))
v = Variable((1, 1))
col_scalar = Parameter((1, 1))
assert v.shape == col_scalar.shape == col_scalar.T.shape
# Test the DivExpresion class.
def test_div_expression(self) -> None:
# Vectors
exp = self.x / 2
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.shape, (2, ))
with self.assertRaises(Exception) as cm:
(self.x / [2, 2, 3])
print(cm.exception)
self.assertRegex(str(cm.exception),
"Incompatible shapes for division.*")
c = Constant([3.0, 4.0, 12.0])
self.assertItemsAlmostEqual((c / Constant([1.0, 2.0, 3.0])).value,
np.array([3.0, 2.0, 4.0]))
# Constant expressions.
c = Constant(2)
exp = c / (3 - 5)
self.assertEqual(exp.curvature, s.CONSTANT)
self.assertEqual(exp.shape, tuple())
self.assertEqual(exp.sign, s.NONPOS)
# Parameters.
p = Parameter(nonneg=True)
exp = 2 / p
p.value = 2
self.assertEqual(exp.value, 1)
rho = Parameter(nonneg=True)
rho.value = 1
self.assertEqual(rho.sign, s.NONNEG)
self.assertEqual(Constant(2).sign, s.NONNEG)
self.assertEqual((Constant(2) / Constant(2)).sign, s.NONNEG)
self.assertEqual((Constant(2) * rho).sign, s.NONNEG)
self.assertEqual((rho / 2).sign, s.NONNEG)
# Broadcasting.
x = cp.Variable((3, 3))
c = np.arange(1, 4)[:, None]
expr = x / c
self.assertEqual((3, 3), expr.shape)
x.value = np.ones((3, 3))
A = np.ones((3, 3)) / c
self.assertItemsAlmostEqual(A, expr.value)
with self.assertRaises(Exception) as cm:
(x / c[:, 0])
print(cm.exception)
self.assertRegex(str(cm.exception),
"Incompatible shapes for division.*")
# Test the NegExpression class.
def test_neg_expression(self) -> None:
# Vectors
exp = -self.x
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (2, ))
assert exp.is_affine()
self.assertEqual(exp.sign, s.UNKNOWN)
assert not exp.is_nonneg()
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), "-%s" % self.x.name())
self.assertEqual(exp.shape, self.x.shape)
# Matrices
exp = -self.C
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (3, 2))
# Test promotion of scalar constants.
def test_scalar_const_promotion(self) -> None:
# Vectors
exp = self.x + 2
self.assertEqual(exp.curvature, s.AFFINE)
assert exp.is_affine()
self.assertEqual(exp.sign, s.UNKNOWN)
assert not exp.is_nonpos()
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), self.x.name() + " + " + Constant(2).name())
self.assertEqual(exp.shape, (2, ))
self.assertEqual((4 - self.x).shape, (2, ))
self.assertEqual((4 * self.x).shape, (2, ))
self.assertEqual((4 <= self.x).shape, (2, ))
self.assertEqual((4 == self.x).shape, (2, ))
self.assertEqual((self.x >= 4).shape, (2, ))
# Matrices
exp = (self.A + 2) + 4
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual((3 * self.A).shape, (2, 2))
self.assertEqual(exp.shape, (2, 2))
# Test indexing expression.
def test_index_expression(self) -> None:
# Tuple of integers as key.
exp = self.x[1]
# self.assertEqual(exp.name(), "x[1,0]")
self.assertEqual(exp.curvature, s.AFFINE)
assert exp.is_affine()
self.assertEqual(exp.shape, tuple())
# coeff = exp.canonical_form[0].coefficients()[self.x][0]
# self.assertEqual(coeff[0,1], 1)
self.assertEqual(exp.value, None)
exp = self.x[1].T
# self.assertEqual(exp.name(), "x[1,0]")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, tuple())
with self.assertRaises(Exception) as cm:
(self.x[2, 0])
self.assertEqual(str(cm.exception), "Too many indices for expression.")
with self.assertRaises(Exception) as cm:
(self.x[2])
self.assertEqual(str(cm.exception),
"Index 2 is out of bounds for axis 0 with size 2.")
# Slicing
exp = self.C[0:2, 1]
# self.assertEqual(exp.name(), "C[0:2,1]")
self.assertEqual(exp.shape, (2, ))
exp = self.C[0:, 0:2]
# self.assertEqual(exp.name(), "C[0:,0:2]")
self.assertEqual(exp.shape, (3, 2))
exp = self.C[0::2, 0::2]
# self.assertEqual(exp.name(), "C[0::2,0::2]")
self.assertEqual(exp.shape, (2, 1))
exp = self.C[:3, :1:2]
# self.assertEqual(exp.name(), "C[0:3,0]")
self.assertEqual(exp.shape, (3, 1))
exp = self.C[0:, 0]
# self.assertEqual(exp.name(), "C[0:,0]")
self.assertEqual(exp.shape, (3, ))
c = Constant([[1, -2], [0, 4]])
exp = c[1, 1]
self.assertEqual(exp.curvature, s.CONSTANT)
self.assertEqual(exp.sign, s.UNKNOWN)
self.assertEqual(c[0, 1].sign, s.UNKNOWN)
self.assertEqual(c[1, 0].sign, s.UNKNOWN)
self.assertEqual(exp.shape, tuple())
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, s.CONSTANT)
assert exp.is_constant()
self.assertEqual(exp.shape, (3, 2))
self.assertEqual(exp[0, 1].value, 7)
# Slice of transpose
exp = self.C.T[0:2, 1:2]
self.assertEqual(exp.shape, (2, 1))
# Arithmetic expression indexing
exp = (self.x + self.z)[1]
# self.assertEqual(exp.name(), "x[1,0] + z[1,0]")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
self.assertEqual(exp.shape, tuple())
exp = (self.x + self.a)[1:2]
# self.assertEqual(exp.name(), "x[1,0] + a")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (1, ))
exp = (self.x - self.z)[1:2]
# self.assertEqual(exp.name(), "x[1,0] - z[1,0]")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (1, ))
exp = (self.x - self.a)[1]
# self.assertEqual(exp.name(), "x[1,0] - a")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, tuple())
exp = (-self.x)[1]
# self.assertEqual(exp.name(), "-x[1,0]")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, tuple())
c = Constant([[1, 2], [3, 4]])
exp = (c @ self.x)[1]
# self.assertEqual(exp.name(), "[[2], [4]] * x[0:,0]")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, tuple())
c = Constant([[1, 2], [3, 4]])
exp = (c * self.a)[1, 0:1]
# self.assertEqual(exp.name(), "2 * a")
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.shape, (1, ))
def test_none_idx(self) -> None:
"""Test None as index.
"""
expr = self.a[None, None]
self.assertEqual(expr.shape, (1, 1))
expr = self.x[:, None]
self.assertEqual(expr.shape, (2, 1))
expr = self.x[None, :]
self.assertEqual(expr.shape, (1, 2))
expr = Constant([1, 2])[None, :]
self.assertEqual(expr.shape, (1, 2))
self.assertItemsAlmostEqual(expr.value, [1, 2])
def test_out_of_bounds(self) -> None:
"""Test out of bounds indices.
"""
with self.assertRaises(Exception) as cm:
self.x[100]
self.assertEqual(str(cm.exception),
"Index 100 is out of bounds for axis 0 with size 2.")
with self.assertRaises(Exception) as cm:
self.x[-100]
self.assertEqual(
str(cm.exception),
"Index -100 is out of bounds for axis 0 with size 2.")
exp = self.x[:-100]
self.assertEqual(exp.size, (0, ))
self.assertItemsAlmostEqual(exp.value, np.array([]))
exp = self.C[100:2]
self.assertEqual(exp.shape, (0, 2))
exp = self.C[:, -199:2]
self.assertEqual(exp.shape, (3, 2))
exp = self.C[:, -199:-3]
self.assertEqual(exp.shape, (3, 0))
def test_neg_indices(self) -> None:
"""Test negative indices.
"""
c = Constant([[1, 2], [3, 4]])
exp = c[-1, -1]
self.assertEqual(exp.value, 4)
self.assertEqual(exp.shape, tuple())
self.assertEqual(exp.curvature, s.CONSTANT)
c = Constant([1, 2, 3, 4])
exp = c[1:-1]
self.assertItemsAlmostEqual(exp.value, [2, 3])
self.assertEqual(exp.shape, (2, ))
self.assertEqual(exp.curvature, s.CONSTANT)
c = Constant([1, 2, 3, 4])
exp = c[::-1]
self.assertItemsAlmostEqual(exp.value, [4, 3, 2, 1])
self.assertEqual(exp.shape, (4, ))
self.assertEqual(exp.curvature, s.CONSTANT)
x = Variable(4)
self.assertEqual(x[::-1].shape, (4, ))
Problem(Minimize(0), [x[::-1] == c]).solve(solver=cp.SCS)
self.assertItemsAlmostEqual(x.value, [4, 3, 2, 1])
x = Variable(2)
self.assertEqual(x[::-1].shape, (2, ))
x = Variable(100, name="x")
self.assertEqual("x[0:99]", str(x[:-1]))
c = Constant([[1, 2], [3, 4]])
expr = c[0, 2:0:-1]
self.assertEqual(expr.shape, (1, ))
self.assertAlmostEqual(expr.value, 3)
expr = c[0, 2::-1]
self.assertEqual(expr.shape, (2, ))
self.assertItemsAlmostEqual(expr.value, [3, 1])
def test_logical_indices(self) -> None:
"""Test indexing with boolean arrays.
"""
A = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
C = Constant(A)
# Boolean array.
expr = C[A <= 2]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[A <= 2], expr.value)
expr = C[A % 2 == 0]
self.assertEqual(expr.shape, (6, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[A % 2 == 0], expr.value)
# Boolean array for rows, index for columns.
expr = C[np.array([True, False, True]), 3]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[np.array([True, False, True]), 3],
expr.value)
# Index for row, boolean array for columns.
expr = C[1, np.array([True, False, False, True])]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[1,
np.array([True, False, False, True])],
expr.value)
# Boolean array for rows, slice for columns.
expr = C[np.array([True, True, True]), 1:3]
self.assertEqual(expr.shape, (3, 2))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[np.array([True, True, True]), 1:3],
expr.value)
# Slice for row, boolean array for columns.
expr = C[1:-1, np.array([True, False, True, True])]
self.assertEqual(expr.shape, (1, 3))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(
A[1:-1, np.array([True, False, True, True])], expr.value)
# Boolean arrays for rows and columns.
# Not sure what this does.
expr = C[np.array([True, True, True]),
np.array([True, False, True, True])]
self.assertEqual(expr.shape, (3, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(
A[np.array([True, True, True]),
np.array([True, False, True, True])], expr.value)
def test_selector_list_indices(self) -> None:
"""Test indexing with lists/ndarrays of indices.
"""
A = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
C = Constant(A)
# List for rows.
expr = C[[1, 2]]
self.assertEqual(expr.shape, (2, 4))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[[1, 2]], expr.value)
# List for rows, index for columns.
expr = C[[0, 2], 3]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[[0, 2], 3], expr.value)
# Index for row, list for columns.
expr = C[1, [0, 2]]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[1, [0, 2]], expr.value)
# List for rows, slice for columns.
expr = C[[0, 2], 1:3]
self.assertEqual(expr.shape, (2, 2))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[[0, 2], 1:3], expr.value)
# Slice for row, list for columns.
expr = C[1:-1, [0, 2]]
self.assertEqual(expr.shape, (1, 2))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[1:-1, [0, 2]], expr.value)
# Lists for rows and columns.
expr = C[[0, 1], [1, 3]]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[[0, 1], [1, 3]], expr.value)
# Ndarray for rows, list for columns.
expr = C[np.array([0, 1]), [1, 3]]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[np.array([0, 1]), [1, 3]], expr.value)
# Ndarrays for rows and columns.
expr = C[np.array([0, 1]), np.array([1, 3])]
self.assertEqual(expr.shape, (2, ))
self.assertEqual(expr.sign, s.NONNEG)
self.assertItemsAlmostEqual(A[np.array([0, 1]),
np.array([1, 3])], expr.value)
def test_powers(self) -> None:
exp = self.x**2
self.assertEqual(exp.curvature, s.CONVEX)
exp = self.x**0.5
self.assertEqual(exp.curvature, s.CONCAVE)
exp = self.x**-1
self.assertEqual(exp.curvature, s.CONVEX)
def test_sum(self) -> None:
"""Test cvxpy sum function.
"""
self.a.value = 1
expr = cp.sum(self.a)
self.assertEqual(expr.value, 1)
self.x.value = [1, 2]
expr = cp.sum(self.x)
self.assertEqual(expr.value, 3)
def test_var_copy(self) -> None:
"""Test the copy function for variable types.
"""
x = Variable((3, 4), name="x")
y = x.copy()
self.assertEqual(y.shape, (3, 4))
self.assertEqual(y.name(), "x")
x = Variable((5, 5), PSD=True, name="x")
y = x.copy()
self.assertEqual(y.shape, (5, 5))
def test_param_copy(self) -> None:
"""Test the copy function for Parameters.
"""
x = Parameter((3, 4), name="x", nonneg=True)
y = x.copy()
self.assertEqual(y.shape, (3, 4))
self.assertEqual(y.name(), "x")
self.assertEqual(y.sign, "NONNEGATIVE")
def test_constant_copy(self) -> None:
"""Test the copy function for Constants.
"""
x = Constant(2)
y = x.copy()
self.assertEqual(y.shape, tuple())
self.assertEqual(y.value, 2)
def test_is_pwl(self) -> None:
"""Test is_pwl()
"""
A = np.ones((2, 3))
b = np.ones(2)
expr = A @ self.y - b
self.assertEqual(expr.is_pwl(), True)
expr = cp.maximum(1, 3 * self.y)
self.assertEqual(expr.is_pwl(), True)
expr = cp.abs(self.y)
self.assertEqual(expr.is_pwl(), True)
expr = cp.pnorm(3 * self.y, 1)
self.assertEqual(expr.is_pwl(), True)
expr = cp.pnorm(3 * self.y**2, 1)
self.assertEqual(expr.is_pwl(), False)
def test_broadcast_mul(self) -> None:
"""Test multiply broadcasting.
"""
y = Parameter((3, 1))
z = Variable((1, 3))
y.value = np.arange(3)[:, None]
z.value = (np.arange(3) - 1)[None, :]
expr = cp.multiply(y, z)
self.assertItemsAlmostEqual(expr.value, y.value * z.value)
prob = cp.Problem(cp.Minimize(cp.sum(expr)), [z == z.value])
prob.solve(solver=cp.SCS)
self.assertItemsAlmostEqual(expr.value, y.value * z.value)
np.random.seed(0)
m, n = 3, 4
A = np.random.rand(m, n)
col_scale = Variable(n)
with self.assertRaises(ValueError) as cm:
cp.multiply(A, col_scale)
self.assertEqual(str(cm.exception),
"Cannot broadcast dimensions (3, 4) (4,)")
col_scale = Variable([1, n])
C = cp.multiply(A, col_scale)
self.assertEqual(C.shape, (m, n))
row_scale = Variable([m, 1])
R = cp.multiply(A, row_scale)
self.assertEqual(R.shape, (m, n))
def test_broadcast_add(self) -> None:
"""Test addition broadcasting.
"""
y = Parameter((3, 1))
z = Variable((1, 3))
y.value = np.arange(3)[:, None]
z.value = (np.arange(3) - 1)[None, :]
expr = y + z
self.assertItemsAlmostEqual(expr.value, y.value + z.value)
prob = cp.Problem(cp.Minimize(cp.sum(expr)), [z == z.value])
prob.solve(solver=cp.SCS)
self.assertItemsAlmostEqual(expr.value, y.value + z.value)
np.random.seed(0)
m, n = 3, 4
A = np.random.rand(m, n)
col_scale = Variable(n)
with self.assertRaises(ValueError) as cm:
A + col_scale
self.assertEqual(str(cm.exception),
"Cannot broadcast dimensions (3, 4) (4,)")
col_scale = Variable([1, n])
C = A + col_scale
self.assertEqual(C.shape, (m, n))
row_scale = Variable([m, 1])
R = A + row_scale
self.assertEqual(R.shape, (m, n))
def test_log_log_curvature(self) -> None:
"""Test that the curvature string is populated for log-log expressions.
"""
x = Variable(pos=True)
monomial = x * x * x
assert monomial.curvature == s.LOG_LOG_AFFINE
posynomial = x * x * x + x
assert posynomial.curvature == s.LOG_LOG_CONVEX
llcv = 1 / (x * x * x + x)
assert llcv.curvature == s.LOG_LOG_CONCAVE
