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 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.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)
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)
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]
self.assertEqual(len(blocks), 2)
for block in blocks:
self.assertEqual(intf.size(block), (10, 6))
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))
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))
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_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.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._dcp_attr.sign.neg_mat.shape, (1, 2))
# 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._dcp_attr.sign.pos_mat.shape, (2, 1))
exp = c.T * self.A
self.assertEqual(exp._dcp_attr.sign.pos_mat.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))
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
# 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)")
# 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 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)
print cm.exception
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._dcp_attr.sign.pos_mat.shape, (1, 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)
# 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.POSITIVE_KEY)
assert exp.is_positive()
self.assertEqual(c[0, 1].sign, u.Sign.ZERO_KEY)
assert c[0, 1].is_zero()
self.assertEqual(c[1, 0].sign, u.Sign.NEGATIVE_KEY)
assert c[1, 0].is_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_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))
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_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)
# 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._dcp_attr.sign.neg_mat.shape, (1,2))
# 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._dcp_attr.sign.pos_mat.shape, (2,1))
exp = c.T*self.A
self.assertEqual(exp._dcp_attr.sign.pos_mat.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))
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
# 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.")
# 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.")
# 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.")
# 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.")
# 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)
print cm.exception
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_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._dcp_attr.sign.pos_mat.shape, (1,2))
# 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.POSITIVE_KEY)
assert exp.is_positive()
self.assertEqual(c[0,1].sign, u.Sign.ZERO_KEY)
assert c[0, 1].is_zero()
self.assertEqual(c[1,0].sign, u.Sign.NEGATIVE_KEY)
assert c[1,0].is_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_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))
class test_coefficients(unittest.TestCase):
""" Unit tests for the expressions.affine module. """
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 test_leaf_coeffs(self):
"""Test the coefficients for Variables and Constants.
"""
# Scalars
coeffs = self.a.coefficients()
self.assertItemsEqual(coeffs.keys(), [self.a])
blocks = coeffs[self.a]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0], 1)
# Vectors
coeffs = self.x.coefficients()
self.assertItemsEqual(coeffs.keys(), [self.x])
blocks = coeffs[self.x]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].size, (2,2))
# Matrices
coeffs = self.A.coefficients()
self.assertItemsEqual(coeffs.keys(), [self.A])
blocks = coeffs[self.A]
self.assertEqual(len(blocks), 2)
self.assertEqual(blocks[0].size, (2,4))
# Constants
coeffs = self.c.coefficients()
self.assertItemsEqual(coeffs.keys(), [s.CONSTANT])
blocks = coeffs[s.CONSTANT]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0], 3)
coeffs = self.C.coefficients()
self.assertItemsEqual(coeffs.keys(), [s.CONSTANT])
blocks = coeffs[s.CONSTANT]
self.assertEqual(len(blocks), 2)
self.assertEqual(blocks[0].size, (2,1))
self.assertEqual(blocks[0][0,0], 1)
def test_add(self):
"""Test adding coefficients.
"""
coeffs = cu.add(self.x.coefficients(), self.y.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.x]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].size, (2,2))
coeffs = cu.add(coeffs, coeffs)
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.x]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].size, (2,2))
self.assertEqual(blocks[0][0,0], 2)
coeffs = cu.add(coeffs, self.C.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.x, self.y, s.CONSTANT])
blocks = coeffs[s.CONSTANT]
self.assertEqual(len(blocks), 2)
self.assertEqual(blocks[0].size, (2,1))
self.assertEqual(blocks[0][0,0], 1)
def test_neg(self):
"""Test negating coefficients.
"""
coeffs = cu.neg(self.a.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.a])
blocks = coeffs[self.a]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0], -1)
coeffs = cu.neg(self.A.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.A])
blocks = coeffs[self.A]
self.assertEqual(len(blocks), 2)
self.assertEqual(blocks[0].size, (2,4))
self.assertEqual(blocks[0][0,0], -1)
def test_sub(self):
"""Test subtracting coefficients.
"""
coeffs = cu.sub(self.x.coefficients(), self.y.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.y]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].size, (2,2))
self.assertEqual(blocks[0][0,0], -1)
coeffs = cu.sub(coeffs, self.x.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.x]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].size, (2,2))
self.assertEqual(blocks[0][0,0], 0)
def test_mul(self):
"""Test multiplying coefficients.
"""
coeffs = cu.add(self.x.coefficients(), self.y.coefficients())
coeffs = cu.mul(self.C.coefficients(), coeffs)
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.y]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].size, (2,2))
self.assertEqual(blocks[0][1,0], 2)
# Scalar by Matrix multiplication.
coeffs = cu.add(self.x.coefficients(), self.y.coefficients())
coeffs = cu.mul(self.c.coefficients(), coeffs)
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.y]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].size, (2,2))
self.assertEqual(blocks[0][0,0], 3)
# Matrix by Scalar multiplication.
coeffs = self.a.coefficients()
coeffs = cu.mul(self.C.coefficients(), coeffs)
self.assertItemsEqual(coeffs.keys(), [self.a])
blocks = coeffs[self.a]
self.assertEqual(len(blocks), 2)
self.assertEqual(blocks[0].size, (2,1))
self.assertEqual(blocks[0][1,0], 2)
self.assertEqual(blocks[1].size, (2,1))
self.assertEqual(blocks[1][1,0], 2)
def test_index(self):
"""Test indexing/slicing into coefficients.
"""
# Index.
sum_coeffs = cu.add(self.x.coefficients(), self.y.coefficients())
key = ku.validate_key((1, 0), self.x.shape)
coeffs = cu.index(sum_coeffs, key)
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.y]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].size, (1,2))
self.assertEqual(blocks[0][0,0], 0)
# Slice.
sum_coeffs = cu.add(self.A.coefficients(), self.C.coefficients())
key = ku.validate_key((slice(None, None, None), 1), self.A.shape)
coeffs = cu.index(sum_coeffs, key)
self.assertItemsEqual(coeffs.keys(), [self.A, s.CONSTANT])
# Variable.
blocks = coeffs[self.A]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].size, (2,4))
# Constant.
blocks = coeffs[s.CONSTANT]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].size, (2,1))
class test_coefficients(unittest.TestCase):
""" Unit tests for the expressions.affine module. """
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 test_leaf_coeffs(self):
"""Test the coefficients for Variables and Constants.
"""
# Scalars
coeffs = self.a.coefficients()
self.assertItemsEqual(coeffs.keys(), [self.a])
blocks = coeffs[self.a]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0], 1)
# Vectors
coeffs = self.x.coefficients()
self.assertItemsEqual(coeffs.keys(), [self.x])
blocks = coeffs[self.x]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].shape, (2, 2))
# Matrices
coeffs = self.A.coefficients()
self.assertItemsEqual(coeffs.keys(), [self.A])
blocks = coeffs[self.A]
self.assertEqual(len(blocks), 2)
self.assertEqual(blocks[0].shape, (2, 4))
# Constants
coeffs = self.c.coefficients()
self.assertItemsEqual(coeffs.keys(), [s.CONSTANT])
blocks = coeffs[s.CONSTANT]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0], 3)
coeffs = self.C.coefficients()
self.assertItemsEqual(coeffs.keys(), [s.CONSTANT])
blocks = coeffs[s.CONSTANT]
self.assertEqual(len(blocks), 2)
print blocks[0]
self.assertEqual(blocks[0].shape, (2, 1))
self.assertEqual(blocks[0][0, 0], 1)
def test_add(self):
"""Test adding coefficients.
"""
coeffs = cu.add(self.x.coefficients(), self.y.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.x]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].shape, (2, 2))
coeffs = cu.add(coeffs, coeffs)
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.x]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].shape, (2, 2))
self.assertEqual(blocks[0][0, 0], 2)
coeffs = cu.add(coeffs, self.C.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.x, self.y, s.CONSTANT])
blocks = coeffs[s.CONSTANT]
self.assertEqual(len(blocks), 2)
self.assertEqual(blocks[0].shape, (2, 1))
self.assertEqual(blocks[0][0, 0], 1)
def test_neg(self):
"""Test negating coefficients.
"""
coeffs = cu.neg(self.a.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.a])
blocks = coeffs[self.a]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0], -1)
coeffs = cu.neg(self.A.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.A])
blocks = coeffs[self.A]
self.assertEqual(len(blocks), 2)
self.assertEqual(blocks[0].shape, (2, 4))
self.assertEqual(blocks[0][0, 0], -1)
def test_sub(self):
"""Test subtracting coefficients.
"""
coeffs = cu.sub(self.x.coefficients(), self.y.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.y]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].shape, (2, 2))
self.assertEqual(blocks[0][0, 0], -1)
coeffs = cu.sub(coeffs, self.x.coefficients())
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.x]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].shape, (2, 2))
self.assertEqual(blocks[0][0, 0], 0)
def test_mul(self):
"""Test multiplying coefficients.
"""
coeffs = cu.add(self.x.coefficients(), self.y.coefficients())
coeffs = cu.mul(self.C.coefficients(), coeffs)
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.y]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].shape, (2, 2))
self.assertEqual(blocks[0][1, 0], 2)
# Scalar by Matrix multiplication.
coeffs = cu.add(self.x.coefficients(), self.y.coefficients())
coeffs = cu.mul(self.c.coefficients(), coeffs)
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.y]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].shape, (2, 2))
self.assertEqual(blocks[0][0, 0], 3)
# Matrix by Scalar multiplication.
coeffs = self.a.coefficients()
coeffs = cu.mul(self.C.coefficients(), coeffs)
self.assertItemsEqual(coeffs.keys(), [self.a])
blocks = coeffs[self.a]
self.assertEqual(len(blocks), 2)
self.assertEqual(blocks[0].shape, (2, 1))
self.assertEqual(blocks[0][1, 0], 2)
self.assertEqual(blocks[1].shape, (2, 1))
self.assertEqual(blocks[1][1, 0], 2)
def test_index(self):
"""Test indexing/slicing into coefficients.
"""
# Index.
sum_coeffs = cu.add(self.x.coefficients(), self.y.coefficients())
key = ku.validate_key((1, 0), self.x.shape)
coeffs = cu.index(sum_coeffs, key)
self.assertItemsEqual(coeffs.keys(), [self.x, self.y])
blocks = coeffs[self.y]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].shape, (1, 2))
self.assertEqual(blocks[0][0, 0], 0)
# Slice.
sum_coeffs = cu.add(self.A.coefficients(), self.C.coefficients())
key = ku.validate_key((slice(None, None, None), 1), self.A.shape)
coeffs = cu.index(sum_coeffs, key)
self.assertItemsEqual(coeffs.keys(), [self.A, s.CONSTANT])
# Variable.
blocks = coeffs[self.A]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].shape, (2, 4))
# Constant.
blocks = coeffs[s.CONSTANT]
self.assertEqual(len(blocks), 1)
self.assertEqual(blocks[0].shape, (2, 1))
class TestAffObjective(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 = 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
# Test adding AffObjectives.
def test_add(self):
add = self.xAff + self.yAff
self.assertItemsEqual(add._terms, [deque([self.x]), deque([self.y])])
self.assertItemsEqual(add.variables(), [self.x, self.y])
add = self.xAff + self.xAff
self.assertItemsEqual(add._terms, [deque([self.x]), deque([self.x])])
self.assertItemsEqual(add.variables(), [self.x, self.x])
with self.assertRaises(Exception) as cm:
self.xAff + self.constAff
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
# Test multiplying AffObjectives.
def test_mul(self):
mul = self.constAff * self.xAff
self.assertItemsEqual(mul._terms, [deque([self.x, self.A])])
self.assertItemsEqual(mul.variables(), [self.x])
mul = self.constAff * (self.yAff + self.xAff)
self.assertItemsEqual(mul._terms, [deque([self.x, self.A]), deque([self.y, self.A])])
self.assertItemsEqual(mul.variables(), [self.x, self.y])
with self.assertRaises(Exception) as cm:
self.xAff * self.yAff
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
# Test negating AffObjectives.
def test_neg(self):
neg = -self.xAff
self.assertEqual(neg._terms[0][1].name(), "-1")
self.assertItemsEqual(neg.variables(), [self.x])
# Test subtracting AffObjectives.
def test_sub(self):
sub = self.xAff - self.yAff
self.assertItemsEqual(sub._terms, (self.xAff + -self.yAff)._terms)
self.assertItemsEqual(sub.variables(), [self.x, self.y])
with self.assertRaises(Exception) as cm:
self.xAff - self.constAff
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
# Test coefficients method.
def test_coefficients(self):
# Leaf
coeffs = self.xAff.coefficients(self.intf)
self.assertEqual(coeffs.keys(), self.x.coefficients(self.intf).keys())
# Sum with different keys
exp = self.xAff + self.yAff
coeffs = exp.coefficients(self.intf)
keys = self.x.coefficients(self.intf).keys() + self.y.coefficients(self.intf).keys()
self.assertItemsEqual(coeffs.keys(), keys)
# Sum with same keys
exp = self.xAff + self.xAff
coeffs = exp.coefficients(self.intf)
xCoeffs = self.x.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), xCoeffs)
self.assertEqual(list(coeffs[self.x]), [2, 0, 0, 2])
# Product
exp = self.constAff * self.yAff
coeffs = exp.coefficients(self.intf)
yCoeffs = self.y.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), yCoeffs)
self.assertEqual(list(coeffs[self.y]), [1, 2, 1, 2])
# Distributed product
exp = self.constAff * (self.xAff + self.yAff)
coeffs = exp.coefficients(self.intf)
xCoeffs = self.x.coefficients(self.intf)
yCoeffs = self.y.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), xCoeffs.keys() + yCoeffs.keys())
self.assertEqual(list(coeffs[self.x]), [1, 2, 1, 2])
