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))
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(), [Constant])
self.assertEqual(coeffs[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 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)
self.assertEqual((c.T*c).sign, u.Sign.POSITIVE)
exp = c.T.T
self.assertEqual(exp.sign.pos_mat.value.ndim, 2)
exp = c.T*self.A
self.assertEqual(exp.sign.pos_mat.value.ndim, 2)
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))
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))
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))
