def test_numpy_matrix(self):
interface = intf.get_matrix_interface(np.matrix)
# const_to_matrix
mat = interface.const_to_matrix([1, 2, 3])
self.assertEquals(interface.size(mat), (3, 1))
mat = interface.const_to_matrix([[1], [2], [3]])
self.assertEquals(mat[0, 0], 1)
# identity
mat = interface.identity(4)
cvxopt_dense = intf.get_matrix_interface(cvxopt.matrix)
cmp_mat = interface.const_to_matrix(cvxopt_dense.identity(4))
self.assertEquals(interface.size(mat), interface.size(cmp_mat))
assert not (mat - cmp_mat).any()
# scalar_matrix
mat = interface.scalar_matrix(2, 4, 3)
self.assertEquals(interface.size(mat), (4, 3))
self.assertEquals(interface.index(mat, (1, 2)), 2)
# reshape
mat = interface.const_to_matrix([[1, 2, 3], [3, 4, 5]])
mat = interface.reshape(mat, (6, 1))
self.assertEquals(interface.index(mat, (4, 0)), 4)
# index
mat = interface.const_to_matrix([[1, 2, 3, 4], [3, 4, 5, 6]])
self.assertEquals(interface.index(mat, (0, 1)), 3)
mat = interface.index(mat, (slice(1, 4, 2), slice(0, 2, None)))
assert not (mat - np.matrix("2 4; 4 6")).any()
# Sign
self.sign_for_intf(interface)
def test_ndarray(self):
interface = intf.get_matrix_interface(np.ndarray)
# const_to_matrix
mat = interface.const_to_matrix([1,2,3])
self.assertEquals(interface.size(mat), (3,1))
mat = interface.const_to_matrix([1,2])
self.assertEquals(interface.size(mat), (2,1))
# CVXOPT sparse conversion
tmp = intf.get_matrix_interface(cvxopt.spmatrix).const_to_matrix([1,2,3])
mat = interface.const_to_matrix(tmp)
assert (mat == interface.const_to_matrix([1,2,3])).all()
# identity
mat = interface.identity(4)
cvxopt_dense = intf.get_matrix_interface(cvxopt.matrix)
cmp_mat = interface.const_to_matrix(cvxopt_dense.identity(4))
self.assertEquals(interface.size(mat), interface.size(cmp_mat))
assert (mat == cmp_mat).all()
# scalar_matrix
mat = interface.scalar_matrix(2,4,3)
self.assertEquals(interface.size(mat), (4,3))
self.assertEquals(interface.index(mat, (1,2)), 2)
# reshape
mat = interface.const_to_matrix([[1,2,3],[3,4,5]])
mat = interface.reshape(mat, (6,1))
self.assertEquals(interface.index(mat, (4,0)), 4)
# index
mat = interface.const_to_matrix([[1,2,3,4],[3,4,5,6]])
self.assertEquals( interface.index(mat, (0,1)), 3)
mat = interface.index(mat, (slice(1,4,2), slice(0,2,None)))
self.assertEquals(list(mat.flatten('C')), [2,4,4,6])
# Scalars and matrices.
scalar = interface.const_to_matrix(2)
mat = interface.const_to_matrix([1,2,3])
assert (scalar*mat == interface.const_to_matrix([2,4,6])).all()
assert (scalar - mat == interface.const_to_matrix([1,0,-1])).all()
def test_conversion_between_intf(self):
"""Test conversion between every pair of interfaces.
"""
interfaces = [intf.get_matrix_interface(cvxopt.matrix),
intf.get_matrix_interface(cvxopt.spmatrix),
intf.get_matrix_interface(np.ndarray),
intf.get_matrix_interface(np.matrix),
intf.get_matrix_interface(sp.csc_matrix)]
cmp_mat = [[1,2,3,4],[3,4,5,6],[-1,0,2,4]]
for i in range(len(interfaces)):
for j in range(i+1, len(interfaces)):
intf1 = interfaces[i]
mat1 = intf1.const_to_matrix(cmp_mat)
intf2 = interfaces[j]
mat2 = intf2.const_to_matrix(cmp_mat)
for col in range(len(cmp_mat)):
for row in range(len(cmp_mat[0])):
key = (slice(row, row+1, None),
slice(col, col+1, None))
self.assertEqual(intf1.index(mat1, key),
intf2.index(mat2, key))
# Convert between the interfaces.
self.assertEqual(cmp_mat[col][row],
intf1.index(intf1.const_to_matrix(mat2), key))
self.assertEqual(intf2.index(intf2.const_to_matrix(mat1), key),
cmp_mat[col][row])
def test_numpy_matrix(self):
interface = intf.get_matrix_interface(np.matrix)
# const_to_matrix
mat = interface.const_to_matrix([1, 2, 3])
self.assertEqual(interface.size(mat), (3, 1))
mat = interface.const_to_matrix([[1], [2], [3]])
self.assertEqual(mat[0, 0], 1)
# identity
# mat = interface.identity(4)
# cvxopt_dense = intf.get_matrix_interface(cvxopt.matrix)
# cmp_mat = interface.const_to_matrix(cvxopt_dense.identity(4))
# self.assertEqual(interface.size(mat), interface.size(cmp_mat))
# assert not (mat - cmp_mat).any()
# scalar_matrix
mat = interface.scalar_matrix(2, 4, 3)
self.assertEqual(interface.size(mat), (4, 3))
self.assertEqual(interface.index(mat, (1, 2)), 2)
# reshape
mat = interface.const_to_matrix([[1, 2, 3], [3, 4, 5]])
mat = interface.reshape(mat, (6, 1))
self.assertEqual(interface.index(mat, (4, 0)), 4)
mat = interface.const_to_matrix(1, convert_scalars=True)
self.assertEqual(type(interface.reshape(mat, (1, 1))), type(mat))
# index
mat = interface.const_to_matrix([[1, 2, 3, 4], [3, 4, 5, 6]])
self.assertEqual(interface.index(mat, (0, 1)), 3)
mat = interface.index(mat, (slice(1, 4, 2), slice(0, 2, None)))
assert not (mat - np.matrix("2 4; 4 6")).any()
# Sign
self.sign_for_intf(interface)
def test_cvxopt_sparse(self):
interface = intf.get_matrix_interface(cvxopt.spmatrix)
# const_to_matrix
mat = interface.const_to_matrix([1, 2, 3])
self.assertEquals(interface.size(mat), (3, 1))
# identity
mat = interface.identity(4)
cmp_mat = interface.const_to_matrix(np.eye(4))
self.assertEquals(interface.size(mat), interface.size(cmp_mat))
assert not mat - cmp_mat
assert intf.is_sparse(mat)
# scalar_matrix
mat = interface.scalar_matrix(2, 4, 3)
self.assertEquals(interface.size(mat), (4, 3))
self.assertEquals(interface.index(mat, (1, 2)), 2)
# reshape
mat = interface.const_to_matrix([[1, 2, 3], [3, 4, 5]])
mat = interface.reshape(mat, (6, 1))
self.assertEquals(interface.index(mat, (4, 0)), 4)
# Test scalars.
scalar = interface.scalar_matrix(1, 1, 1)
self.assertEquals(type(scalar), cvxopt.spmatrix)
scalar = interface.scalar_matrix(1, 1, 3)
self.assertEquals(scalar.size, (1, 3))
# index
mat = interface.const_to_matrix([[1, 2, 3, 4], [3, 4, 5, 6]])
self.assertEquals(interface.index(mat, (0, 1)), 3)
mat = interface.index(mat, (slice(1, 4, 2), slice(0, 2, None)))
self.assertEquals(list(mat), [2, 4, 4, 6])
# Sign
self.sign_for_intf(interface)
def test_mul_elemwise(self):
"""Tests problems with mul_elemwise.
"""
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.A)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.A == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
# Test with a sparse matrix.
import cvxopt
interface = intf.get_matrix_interface(cvxopt.spmatrix)
c = interface.const_to_matrix([1,2])
expr = mul_elemwise(c, self.x)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.x == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, 10])
# Test promotion.
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.a)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.a == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
def test_cvxopt_dense(self):
interface = intf.get_matrix_interface(cvxopt.matrix)
# const_to_matrix
mat = interface.const_to_matrix([1, 2, 3])
self.assertEquals(interface.size(mat), (3, 1))
sp_mat = sp.coo_matrix(([1, 2], ([3, 4], [2, 1])), (5, 5))
mat = interface.const_to_matrix(sp_mat)
self.assertEquals(interface.size(mat), (5, 5))
# identity
mat = interface.identity(4)
cmp_mat = interface.const_to_matrix(np.eye(4))
self.assertEquals(type(mat), type(cmp_mat))
self.assertEquals(interface.size(mat), interface.size(cmp_mat))
assert not mat - cmp_mat
# scalar_matrix
mat = interface.scalar_matrix(2, 4, 3)
self.assertEquals(interface.size(mat), (4, 3))
self.assertEquals(interface.index(mat, (1, 2)), 2)
# reshape
mat = interface.const_to_matrix([[1, 2, 3], [3, 4, 5]])
mat = interface.reshape(mat, (6, 1))
self.assertEquals(interface.index(mat, (4, 0)), 4)
# index
mat = interface.const_to_matrix([[1, 2, 3, 4], [3, 4, 5, 6]])
self.assertEquals(interface.index(mat, (0, 1)), 3)
mat = interface.index(mat, (slice(1, 4, 2), slice(0, 2, None)))
self.assertEquals(list(mat), [2, 4, 4, 6])
# Sign
self.sign_for_intf(interface)
def test_scipy_sparse(self):
interface = intf.get_matrix_interface(sp.csc_matrix)
# const_to_matrix
mat = interface.const_to_matrix([1,2,3])
self.assertEquals(interface.size(mat), (3,1))
C = cvxopt.spmatrix([1,1,1,1,1],[0,1,2,0,0,],[0,0,0,1,2])
mat = interface.const_to_matrix(C)
self.assertEquals(interface.size(mat), (3, 3))
# identity
mat = interface.identity(4)
cmp_mat = interface.const_to_matrix(np.eye(4))
self.assertEquals(interface.size(mat), interface.size(cmp_mat))
assert (mat - cmp_mat).nnz == 0
# scalar_matrix
mat = interface.scalar_matrix(2,4,3)
self.assertEquals(interface.size(mat), (4,3))
self.assertEquals(interface.index(mat, (1,2)), 2)
# reshape
mat = interface.const_to_matrix([[1,2,3],[3,4,5]])
mat = interface.reshape(mat, (6,1))
self.assertEquals(interface.index(mat, (4,0)), 4)
# Test scalars.
scalar = interface.scalar_matrix(1, 1, 1)
self.assertEquals(type(scalar), np.ndarray)
scalar = interface.scalar_matrix(1, 1, 3)
self.assertEquals(scalar.shape, (1,3))
# index
mat = interface.const_to_matrix([[1,2,3,4],[3,4,5,6]])
self.assertEquals( interface.index(mat, (0,1)), 3)
mat = interface.index(mat, (slice(1,4,2), slice(0,2,None)))
assert not (mat - np.matrix("2 4; 4 6")).any()
def test_mul_elemwise(self):
"""Tests problems with mul_elemwise.
"""
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.A)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.A == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
# Test with a sparse matrix.
import cvxopt
interface = intf.get_matrix_interface(cvxopt.spmatrix)
c = interface.const_to_matrix([1,2])
expr = mul_elemwise(c, self.x)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.x == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, 10])
# Test promotion.
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.a)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.a == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
def quad_form(x, P):
""" Alias for :math:`x^T P x`.
"""
x, P = map(Expression.cast_to_const, (x, P))
# Check dimensions.
n = P.size[0]
if P.size[1] != n or x.size != (n,1):
raise Exception("Invalid dimensions for arguments.")
if x.is_constant():
return x.T * P * x
elif P.is_constant():
np_intf = intf.get_matrix_interface(np.ndarray)
P = np_intf.const_to_matrix(P.value)
# Force symmetry
P = (P + P.T) / 2.0
scale, M1, M2 = _decomp_quad(P)
ret = 0
if M1.size > 0:
ret += scale * sum_squares(Constant(M1.T) * x)
if M2.size > 0:
ret -= scale * sum_squares(Constant(M2.T) * x)
return ret
else:
raise Exception("At least one argument to quad_form must be constant.")
def test_cvxopt_sparse(self):
interface = intf.get_matrix_interface(cvxopt.spmatrix)
# const_to_matrix
mat = interface.const_to_matrix([1, 2, 3])
self.assertEquals(interface.size(mat), (3, 1))
# identity
mat = interface.identity(4)
cmp_mat = interface.const_to_matrix(np.eye(4))
self.assertEquals(interface.size(mat), interface.size(cmp_mat))
assert not mat - cmp_mat
assert intf.is_sparse(mat)
# scalar_matrix
mat = interface.scalar_matrix(2, 4, 3)
self.assertEquals(interface.size(mat), (4, 3))
self.assertEquals(interface.index(mat, (1, 2)), 2)
# reshape
mat = interface.const_to_matrix([[1, 2, 3], [3, 4, 5]])
mat = interface.reshape(mat, (6, 1))
self.assertEquals(interface.index(mat, (4, 0)), 4)
mat = interface.const_to_matrix(1, convert_scalars=True)
self.assertEquals(type(interface.reshape(mat, (1, 1))), type(mat))
# Test scalars.
scalar = interface.scalar_matrix(1, 1, 1)
self.assertEquals(type(scalar), cvxopt.spmatrix)
scalar = interface.scalar_matrix(1, 1, 3)
self.assertEquals(scalar.size, (1, 3))
# index
mat = interface.const_to_matrix([[1, 2, 3, 4], [3, 4, 5, 6]])
self.assertEquals(interface.index(mat, (0, 1)), 3)
mat = interface.index(mat, (slice(1, 4, 2), slice(0, 2, None)))
self.assertEquals(list(mat), [2, 4, 4, 6])
# Sign
self.sign_for_intf(interface)
def test_ndarray(self):
interface = intf.get_matrix_interface(np.ndarray)
# const_to_matrix
mat = interface.const_to_matrix([1, 2, 3])
self.assertEquals(interface.size(mat), (3, 1))
mat = interface.const_to_matrix([1, 2])
self.assertEquals(interface.size(mat), (2, 1))
# CVXOPT sparse conversion
tmp = intf.get_matrix_interface(cvxopt.spmatrix).const_to_matrix(
[1, 2, 3])
mat = interface.const_to_matrix(tmp)
assert (mat == interface.const_to_matrix([1, 2, 3])).all()
# identity
mat = interface.identity(4)
cvxopt_dense = intf.get_matrix_interface(cvxopt.matrix)
cmp_mat = interface.const_to_matrix(cvxopt_dense.identity(4))
self.assertEquals(interface.size(mat), interface.size(cmp_mat))
assert (mat == cmp_mat).all()
# scalar_matrix
mat = interface.scalar_matrix(2, 4, 3)
self.assertEquals(interface.size(mat), (4, 3))
self.assertEquals(interface.index(mat, (1, 2)), 2)
# reshape
mat = interface.const_to_matrix([[1, 2, 3], [3, 4, 5]])
mat = interface.reshape(mat, (6, 1))
self.assertEquals(interface.index(mat, (4, 0)), 4)
mat = interface.const_to_matrix(1, convert_scalars=True)
self.assertEquals(type(interface.reshape(mat, (1, 1))), type(mat))
# index
mat = interface.const_to_matrix([[1, 2, 3, 4], [3, 4, 5, 6]])
self.assertEquals(interface.index(mat, (0, 1)), 3)
mat = interface.index(mat, (slice(1, 4, 2), slice(0, 2, None)))
self.assertEquals(list(mat.flatten('C')), [2, 4, 4, 6])
# Scalars and matrices.
scalar = interface.const_to_matrix(2)
mat = interface.const_to_matrix([1, 2, 3])
assert (scalar * mat == interface.const_to_matrix([2, 4, 6])).all()
assert (scalar - mat == interface.const_to_matrix([1, 0, -1])).all()
# Sign
self.sign_for_intf(interface)
# Size.
assert interface.size(np.array([1, 2, 3])) == (3, 1)
def test_conversion_between_intf(self):
"""Test conversion between every pair of interfaces.
"""
interfaces = [intf.get_matrix_interface(np.ndarray),
intf.get_matrix_interface(np.matrix),
intf.get_matrix_interface(sp.csc_matrix)]
cmp_mat = [[1, 2, 3, 4], [3, 4, 5, 6], [-1, 0, 2, 4]]
for i in range(len(interfaces)):
for j in range(i+1, len(interfaces)):
intf1 = interfaces[i]
mat1 = intf1.const_to_matrix(cmp_mat)
intf2 = interfaces[j]
mat2 = intf2.const_to_matrix(cmp_mat)
for col in range(len(cmp_mat)):
for row in range(len(cmp_mat[0])):
key = (slice(row, row+1, None),
slice(col, col+1, None))
self.assertEqual(intf1.index(mat1, key),
intf2.index(mat2, key))
# Convert between the interfaces.
self.assertEqual(cmp_mat[col][row],
intf1.index(intf1.const_to_matrix(mat2), key))
self.assertEqual(intf2.index(intf2.const_to_matrix(mat1), key),
cmp_mat[col][row])
def test_scipy_sparse(self):
"""Test cvxopt sparse interface.
"""
interface = intf.get_matrix_interface(sp.csc_matrix)
# const_to_matrix
mat = interface.const_to_matrix([1, 2, 3])
self.assertEqual(interface.shape(mat), (3, 1))
# C = cvxopt.spmatrix([1, 1, 1, 1, 1], [0, 1, 2, 0, 0, ], [0, 0, 0, 1, 2])
# mat = interface.const_to_matrix(C)
# self.assertEqual(interface.shape(mat), (3, 3))
# identity
mat = interface.identity(4)
cmp_mat = interface.const_to_matrix(np.eye(4))
self.assertEqual(interface.shape(mat), interface.shape(cmp_mat))
assert (mat - cmp_mat).nnz == 0
# scalar_matrix
mat = interface.scalar_matrix(2, (4, 3))
self.assertEqual(interface.shape(mat), (4, 3))
self.assertEqual(interface.index(mat, (1, 2)), 2)
# reshape
mat = interface.const_to_matrix([[1, 2, 3], [3, 4, 5]])
mat = interface.reshape(mat, (6, 1))
self.assertEqual(interface.index(mat, (4, 0)), 4)
# Test scalars.
scalar = interface.scalar_matrix(1, (1, 1))
self.assertEqual(type(scalar), np.ndarray)
scalar = interface.scalar_matrix(1, (1, 3))
self.assertEqual(scalar.shape, (1, 3))
# index
mat = interface.const_to_matrix([[1, 2, 3, 4], [3, 4, 5, 6]])
self.assertEqual(interface.index(mat, (0, 1)), 3)
mat = interface.index(mat, (slice(1, 4, 2), slice(0, 2, None)))
assert not (mat - np.array([[2, 4], [4, 6]])).any()
# scalar value
mat = sp.eye(1)
self.assertEqual(intf.scalar_value(mat), 1.0)
# Sign
self.sign_for_intf(interface)
# Complex
# define sparse matrix [[0, 1j],[-1j,0]]
row = np.array([0, 1])
col = np.array([1, 0])
data = np.array([1j, -1j])
A = sp.csr_matrix((data, (row, col)), shape=(2, 2))
mat = interface.const_to_matrix(A)
self.assertEquals(mat[0, 1], 1j)
self.assertEquals(mat[1, 0], -1j)
def quad_form(x, P):
""" Alias for :math:`x^T P x`.
"""
x, P = map(Expression.cast_to_const, (x, P))
# Check dimensions.
n = P.size[0]
if P.size[1] != n or x.size != (n, 1):
raise Exception("Invalid dimensions for arguments.")
if x.is_constant():
return x.T * P * x
elif P.is_constant():
np_intf = intf.get_matrix_interface(np.ndarray)
P = np_intf.const_to_matrix(P.value)
sgn, scale, M = _decomp_quad(P)
return sgn * scale * square(norm(Constant(M.T) * x))
else:
raise Exception("At least one argument to quad_form must be constant.")
def quad_form(x, P):
""" Alias for :math:`x^T P x`.
"""
x, P = list(map(Expression.cast_to_const, (x, P)))
# Check dimensions.
n = P.size[0]
if P.size[1] != n or x.size != (n,1):
raise Exception("Invalid dimensions for arguments.")
if x.is_constant():
return x.T * P * x
elif P.is_constant():
np_intf = intf.get_matrix_interface(np.ndarray)
P = np_intf.const_to_matrix(P.value)
sgn, scale, M = _decomp_quad(P)
return sgn * scale * square(norm(Constant(M.T) * x))
else:
raise Exception("At least one argument to quad_form must be constant.")
def test_scipy_sparse(self):
interface = intf.get_matrix_interface(sp.csc_matrix)
# const_to_matrix
mat = interface.const_to_matrix([1, 2, 3])
self.assertEquals(interface.size(mat), (3, 1))
C = cvxopt.spmatrix([1, 1, 1, 1, 1], [
0,
1,
2,
0,
0,
], [0, 0, 0, 1, 2])
mat = interface.const_to_matrix(C)
self.assertEquals(interface.size(mat), (3, 3))
# identity
mat = interface.identity(4)
cmp_mat = interface.const_to_matrix(np.eye(4))
self.assertEquals(interface.size(mat), interface.size(cmp_mat))
assert (mat - cmp_mat).nnz == 0
# scalar_matrix
mat = interface.scalar_matrix(2, 4, 3)
self.assertEquals(interface.size(mat), (4, 3))
self.assertEquals(interface.index(mat, (1, 2)), 2)
# reshape
mat = interface.const_to_matrix([[1, 2, 3], [3, 4, 5]])
mat = interface.reshape(mat, (6, 1))
self.assertEquals(interface.index(mat, (4, 0)), 4)
mat = interface.const_to_matrix(1, convert_scalars=True)
self.assertEquals(type(interface.reshape(mat, (1, 1))), type(mat))
# Test scalars.
scalar = interface.scalar_matrix(1, 1, 1)
self.assertEquals(type(scalar), np.ndarray)
scalar = interface.scalar_matrix(1, 1, 3)
self.assertEquals(scalar.shape, (1, 3))
# index
mat = interface.const_to_matrix([[1, 2, 3, 4], [3, 4, 5, 6]])
self.assertEquals(interface.index(mat, (0, 1)), 3)
mat = interface.index(mat, (slice(1, 4, 2), slice(0, 2, None)))
assert not (mat - np.matrix("2 4; 4 6")).any()
# scalar value
mat = sp.eye(1)
self.assertEqual(intf.scalar_value(mat), 1.0)
# Sign
self.sign_for_intf(interface)
def quad_form(x, P):
""" Alias for :math:`x^T P x`.
"""
x, P = map(Expression.cast_to_const, (x, P))
# Check dimensions.
n = P.size[0]
if P.size[1] != n or x.size != (n,1):
raise Exception("Invalid dimensions for arguments.")
if x.is_constant():
return x.T * P * x
elif P.is_constant():
np_intf = intf.get_matrix_interface(np.ndarray)
P = np_intf.const_to_matrix(P.value)
# P must be symmetric.
if not np.allclose(P, P.T):
msg = "P is not symmetric."
raise CvxPyDomainError(msg)
sgn, scale, M = _decomp_quad(P)
return sgn * scale * square(norm(Constant(M.T) * x))
else:
raise Exception("At least one argument to quad_form must be constant.")
def test_numpy_matrix(self) -> None:
interface = intf.get_matrix_interface(np.matrix)
# const_to_matrix
mat = interface.const_to_matrix([1, 2, 3])
self.assertEqual(interface.shape(mat), (3, 1))
mat = interface.const_to_matrix([[1], [2], [3]])
self.assertEqual(mat[0, 0], 1)
mat = interface.scalar_matrix(2, (4, 3))
self.assertEqual(interface.shape(mat), (4, 3))
self.assertEqual(interface.index(mat, (1, 2)), 2)
# reshape
mat = interface.const_to_matrix([[1, 2, 3], [3, 4, 5]])
mat = interface.reshape(mat, (6, 1))
self.assertEqual(interface.index(mat, (4, 0)), 4)
mat = interface.const_to_matrix(1, convert_scalars=True)
self.assertEqual(type(interface.reshape(mat, (1, 1))), type(mat))
# index
mat = interface.const_to_matrix([[1, 2, 3, 4], [3, 4, 5, 6]])
self.assertEqual(interface.index(mat, (0, 1)), 3)
mat = interface.index(mat, (slice(1, 4, 2), slice(0, 2, None)))
self.assertFalse((mat - np.array([[2, 4], [4, 6]])).any())
# Sign
self.sign_for_intf(interface)
def test_cvxopt_dense(self):
interface = intf.get_matrix_interface(cvxopt.matrix)
# const_to_matrix
mat = interface.const_to_matrix([1, 2, 3])
self.assertEquals(interface.size(mat), (3, 1))
# identity
mat = interface.identity(4)
cmp_mat = interface.const_to_matrix(np.eye(4))
self.assertEquals(type(mat), type(cmp_mat))
self.assertEquals(interface.size(mat), interface.size(cmp_mat))
assert not mat - cmp_mat
# scalar_matrix
mat = interface.scalar_matrix(2, 4, 3)
self.assertEquals(interface.size(mat), (4, 3))
self.assertEquals(interface.index(mat, (1, 2)), 2)
# reshape
mat = interface.const_to_matrix([[1, 2, 3], [3, 4, 5]])
mat = interface.reshape(mat, (6, 1))
self.assertEquals(interface.index(mat, (4, 0)), 4)
# index
mat = interface.const_to_matrix([[1, 2, 3, 4], [3, 4, 5, 6]])
self.assertEquals(interface.index(mat, (0, 1)), 3)
mat = interface.index(mat, (slice(1, 4, 2), slice(0, 2, None)))
self.assertEquals(list(mat), [2, 4, 4, 6])
class Problem(u.Canonical):
"""A convex optimization problem.
Attributes
----------
objective : Minimize or Maximize
The expression to minimize or maximize.
constraints : list
The constraints on the problem variables.
"""
# The solve methods available.
REGISTERED_SOLVE_METHODS = {}
# Interfaces for interacting with matrices.
_SPARSE_INTF = intf.DEFAULT_SPARSE_INTERFACE
_DENSE_INTF = intf.DEFAULT_INTERFACE
_CVXOPT_DENSE_INTF = intf.get_matrix_interface(cvxopt.matrix)
_CVXOPT_SPARSE_INTF = intf.get_matrix_interface(cvxopt.spmatrix)
def __init__(self, objective, constraints=None):
if constraints is None:
constraints = []
self.objective = objective
self.constraints = constraints
self._value = None
self._status = None
@property
def value(self):
"""The value from the last time the problem was solved.
Returns
-------
float or None
"""
return self._value
@property
def status(self):
"""The status from the last time the problem was solved.
Returns
-------
str
"""
return self._status
def is_dcp(self):
"""Does the problem satisfy DCP rules?
"""
return all(exp.is_dcp() for exp in self.constraints + [self.objective])
def _filter_constraints(self, constraints):
"""Separate the constraints by type.
Parameters
----------
constraints : list
A list of constraints.
Returns
-------
dict
A map of type key to an ordered set of constraints.
"""
constr_map = {
s.EQ: [],
s.LEQ: [],
s.SOC: [],
s.SOC_EW: [],
s.SDP: [],
s.EXP: []
}
for c in constraints:
if isinstance(c, lo.LinEqConstr):
constr_map[s.EQ].append(c)
elif isinstance(c, lo.LinLeqConstr):
constr_map[s.LEQ].append(c)
elif isinstance(c, SOC):
constr_map[s.SOC].append(c)
elif isinstance(c, SDP):
constr_map[s.SDP].append(c)
elif isinstance(c, ExpCone):
constr_map[s.EXP].append(c)
return constr_map
def canonicalize(self):
"""Computes the graph implementation of the problem.
Returns
-------
tuple
(affine objective,
constraints dict)
"""
constraints = []
obj, constr = self.objective.canonical_form
constraints += constr
unique_constraints = list(unique(self.constraints, key=lambda c: c.id))
for constr in unique_constraints:
constraints += constr.canonical_form[1]
constr_map = self._filter_constraints(constraints)
return (obj, constr_map)
def _format_for_solver(self, constr_map, solver):
"""Formats the problem for the solver.
Parameters
----------
constr_map : dict
A map of constraint type to a list of constraints.
solver: str
The solver being targetted.
Returns
-------
dict
The dimensions of the cones.
"""
dims = {}
dims["f"] = sum(c.size[0] * c.size[1] for c in constr_map[s.EQ])
dims["l"] = sum(c.size[0] * c.size[1] for c in constr_map[s.LEQ])
# Formats SOC, SOC_EW, and SDP constraints for the solver.
nonlin = constr_map[s.SOC] + constr_map[s.SDP]
for constr in nonlin:
for ineq_constr in constr.format():
constr_map[s.LEQ].append(ineq_constr)
# Elemwise SOC constraints have an SOC constraint
# for each element in their arguments.
dims["q"] = []
for constr in constr_map[s.SOC]:
for cone_size in constr.size:
dims["q"].append(cone_size[0])
dims["s"] = [c.size[0] for c in constr_map[s.SDP]]
# Format exponential cone constraints.
if solver == s.CVXOPT:
for constr in constr_map[s.EXP]:
constr_map[s.EQ] += constr.format(s.CVXOPT)
elif solver == s.SCS:
for constr in constr_map[s.EXP]:
constr_map[s.LEQ] += constr.format(s.SCS)
dims["ep"] = sum(c.size[0] * c.size[1] for c in constr_map[s.EXP])
# Remove redundant constraints.
for key in [s.EQ, s.LEQ]:
constraints = unique(constr_map[key], key=lambda c: c.constr_id)
constr_map[key] = list(constraints)
return dims
@staticmethod
def _constraints_count(constr_map):
"""Returns the number of internal constraints.
"""
return sum([len(cset) for cset in constr_map.values()])
def _choose_solver(self, constr_map):
"""Determines the appropriate solver.
Parameters
----------
constr_map: dict
A dict of the canonicalized constraints.
Returns
-------
str
The solver that will be used.
"""
# If no constraints, use ECOS.
if self._constraints_count(constr_map) == 0:
return s.ECOS
# If SDP, defaults to CVXOPT.
elif constr_map[s.SDP]:
return s.CVXOPT
# If EXP cone without SDP, defaults to SCS.
elif constr_map[s.EXP]:
return s.SCS
# Otherwise use ECOS.
else:
return s.ECOS
def _validate_solver(self, constr_map, solver):
"""Raises an exception if the solver cannot solve the problem.
Parameters
----------
constr_map: dict
A dict of the canonicalized constraints.
solver : str
The solver to be used.
"""
if (constr_map[s.SDP] and not solver in s.SDP_CAPABLE) or \
(constr_map[s.EXP] and not solver in s.EXP_CAPABLE) or \
(self._constraints_count(constr_map) == 0 and solver == s.SCS):
raise Exception("The solver %s cannot solve the problem." % solver)
def variables(self):
"""Returns a list of the variables in the problem.
"""
vars_ = self.objective.variables()
for constr in self.constraints:
vars_ += constr.variables()
# Remove duplicates.
return list(set(vars_))
def parameters(self):
"""Returns a list of the parameters in the problem.
"""
params = self.objective.parameters()
for constr in self.constraints:
params += constr.parameters()
# Remove duplicates.
return list(set(params))
def solve(self, *args, **kwargs):
"""Solves the problem using the specified method.
Parameters
----------
method : function
The solve method to use.
solver : str, optional
The solver to use.
verbose : bool, optional
Overrides the default of hiding solver output.
solver_specific_opts : dict, optional
A dict of options that will be passed to the specific solver.
In general, these options will override any default settings
imposed by cvxpy.
Returns
-------
float
The optimal value for the problem, or a string indicating
why the problem could not be solved.
"""
func_name = kwargs.pop("method", None)
if func_name is not None:
func = Problem.REGISTERED_SOLVE_METHODS[func_name]
return func(self, *args, **kwargs)
else:
return self._solve(*args, **kwargs)
@classmethod
def register_solve(cls, name, func):
"""Adds a solve method to the Problem class.
Parameters
----------
name : str
The keyword for the method.
func : function
The function that executes the solve method.
"""
cls.REGISTERED_SOLVE_METHODS[name] = func
def get_problem_data(self, solver):
"""Returns the problem data used in the call to the solver.
Parameters
----------
solver : str
The solver the problem data is for.
Returns
-------
tuple
arguments to solver
"""
objective, constr_map = self.canonicalize()
# Raise an error if the solver cannot handle the problem.
self._validate_solver(constr_map, solver)
dims = self._format_for_solver(constr_map, solver)
all_ineq = constr_map[s.EQ] + constr_map[s.LEQ]
var_offsets, var_sizes, x_length = self._get_var_offsets(
objective, all_ineq)
if solver == s.ECOS and not (constr_map[s.SDP] or constr_map[s.EXP]):
args, offset = self._ecos_problem_data(objective, constr_map, dims,
var_offsets, x_length)
elif solver == s.CVXOPT and not constr_map[s.EXP]:
args, offset = self._cvxopt_problem_data(objective, constr_map,
dims, var_offsets,
x_length)
elif solver == s.SCS:
args, offset = self._scs_problem_data(objective, constr_map, dims,
var_offsets, x_length)
else:
raise Exception("Cannot return problem data for the solver %s." %
solver)
return args
def _solve(self,
solver=None,
ignore_dcp=False,
verbose=False,
solver_specific_opts=None):
"""Solves a DCP compliant optimization problem.
Saves the values of primal and dual variables in the variable
and constraint objects, respectively.
Parameters
----------
solver : str, optional
The solver to use. Defaults to ECOS.
ignore_dcp : bool, optional
Overrides the default of raising an exception if the problem is not
DCP.
verbose : bool, optional
Overrides the default of hiding solver output.
solver_specific_opts : dict, optional
A dict of options that will be passed to the specific solver.
In general, these options will override any default settings
imposed by cvxpy.
Returns
-------
float
The optimal value for the problem, or a string indicating
why the problem could not be solved.
"""
# Safely set default as empty dict.
if solver_specific_opts is None:
solver_specific_opts = {}
if not self.is_dcp():
if ignore_dcp:
print("Problem does not follow DCP rules. "
"Solving a convex relaxation.")
else:
raise Exception("Problem does not follow DCP rules.")
objective, constr_map = self.canonicalize()
# Choose a default solver if none specified.
if solver is None:
solver = self._choose_solver(constr_map)
else:
# Raise an error if the solver cannot handle the problem.
self._validate_solver(constr_map, solver)
dims = self._format_for_solver(constr_map, solver)
all_ineq = constr_map[s.EQ] + constr_map[s.LEQ]
var_offsets, var_sizes, x_length = self._get_var_offsets(
objective, all_ineq)
if solver == s.CVXOPT:
result = self._cvxopt_solve(objective, constr_map, dims,
var_offsets, x_length, verbose,
solver_specific_opts)
elif solver == s.SCS:
result = self._scs_solve(objective, constr_map, dims, var_offsets,
x_length, verbose, solver_specific_opts)
elif solver == s.ECOS:
result = self._ecos_solve(objective, constr_map, dims, var_offsets,
x_length, verbose, solver_specific_opts)
else:
raise Exception("Unknown solver.")
status, value, x, y, z = result
if status == s.OPTIMAL:
self._save_values(x, self.variables(), var_offsets)
self._save_dual_values(y, constr_map[s.EQ], EqConstraint)
self._save_dual_values(z, constr_map[s.LEQ], LeqConstraint)
self._value = value
else:
self._handle_failure(status)
self._status = status
return self.value
def _ecos_problem_data(self, objective, constr_map, dims, var_offsets,
x_length):
"""Returns the problem data for the call to ECOS.
Parameters
----------
objective: Expression
The canonicalized objective.
constr_map: dict
A dict of the canonicalized constraints.
dims: dict
A dict with information about the types of constraints.
var_offsets: dict
A dict mapping variable id to offset in the stacked variable x.
x_length: int
The height of x.
Returns
-------
tuple
((c, G, h, dims, A, b), offset)
"""
c, obj_offset = self._get_obj(objective, var_offsets, x_length,
self._DENSE_INTF, self._DENSE_INTF)
# Convert obj_offset to a scalar.
obj_offset = self._DENSE_INTF.scalar_value(obj_offset)
A, b = self._constr_matrix(constr_map[s.EQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
G, h = self._constr_matrix(constr_map[s.LEQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
# Convert c,h,b to 1D arrays.
c, h, b = map(intf.from_2D_to_1D, [c.T, h, b])
# Return the arguments that would be passed to ECOS.
return ((c, G, h, dims, A, b), obj_offset)
def _ecos_solve(self, objective, constr_map, dims, var_offsets, x_length,
verbose, opts):
"""Calls the ECOS solver and returns the result.
Parameters
----------
objective: Expression
The canonicalized objective.
constr_map: dict
A dict of the canonicalized constraints.
dims: dict
A dict with information about the types of constraints.
var_offsets: dict
A dict mapping variable id to offset in the stacked variable x.
x_length: int
The height of x.
verbose: bool
Should the solver show output?
opts: dict
List of user-specific options for ECOS
Returns
-------
tuple
(status, optimal objective, optimal x,
optimal equality constraint dual,
optimal inequality constraint dual)
"""
prob_data = self._ecos_problem_data(objective, constr_map, dims,
var_offsets, x_length)
obj_offset = prob_data[1]
results = ecos.solve(*prob_data[0], verbose=verbose)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
if status == s.OPTIMAL:
primal_val = results['info']['pcost']
value = self.objective._primal_to_result(primal_val - obj_offset)
return (status, value, results['x'], results['y'], results['z'])
else:
return (status, None, None, None, None)
def _cvxopt_problem_data(self, objective, constr_map, dims, var_offsets,
x_length):
"""Returns the problem data for the call to CVXOPT.
Assumes no exponential cone constraints.
Parameters
----------
objective: Expression
The canonicalized objective.
constr_map: dict
A dict of the canonicalized constraints.
dims: dict
A dict with information about the types of constraints.
var_offsets: dict
A dict mapping variable id to offset in the stacked variable x.
x_length: int
The height of x.
Returns
-------
tuple
((c, G, h, dims, A, b), offset)
"""
c, obj_offset = self._get_obj(objective, var_offsets, x_length,
self._CVXOPT_DENSE_INTF,
self._CVXOPT_DENSE_INTF)
# Convert obj_offset to a scalar.
obj_offset = self._CVXOPT_DENSE_INTF.scalar_value(obj_offset)
A, b = self._constr_matrix(constr_map[s.EQ], var_offsets, x_length,
self._CVXOPT_SPARSE_INTF,
self._CVXOPT_DENSE_INTF)
G, h = self._constr_matrix(constr_map[s.LEQ], var_offsets, x_length,
self._CVXOPT_SPARSE_INTF,
self._CVXOPT_DENSE_INTF)
# Return the arguments that would be passed to CVXOPT.
return ((c.T, G, h, dims, A, b), obj_offset)
def _cvxopt_solve(self, objective, constr_map, dims, var_offsets, x_length,
verbose, opts):
"""Calls the CVXOPT conelp or cpl solver and returns the result.
Parameters
----------
objective: Expression
The canonicalized objective.
constr_map: dict
A dict of the canonicalized constraints.
dims: dict
A dict with information about the types of constraints.
sorted_vars: list
An ordered list of the problem variables.
var_offsets: dict
A dict mapping variable id to offset in the stacked variable x.
x_length: int
The height of x.
verbose: bool
Should the solver show output?
opts: dict
List of user-specific options for CVXOPT;
will be inserted into cvxopt.solvers.options.
Returns
-------
tuple
(status, optimal objective, optimal x,
optimal equality constraint dual,
optimal inequality constraint dual)
"""
prob_data = self._cvxopt_problem_data(objective, constr_map, dims,
var_offsets, x_length)
c, G, h, dims, A, b = prob_data[0]
obj_offset = prob_data[1]
# Save original cvxopt solver options.
old_options = cvxopt.solvers.options
# Silence cvxopt if verbose is False.
cvxopt.solvers.options['show_progress'] = verbose
# Always do one step of iterative refinement after solving KKT system.
cvxopt.solvers.options['refinement'] = 1
# Apply any user-specific options
for key, value in opts.items():
cvxopt.solvers.options[key] = value
# Target cvxopt clp if nonlinear constraints exist
if constr_map[s.EXP]:
# Get the nonlinear constraints.
F = self._merge_nonlin(constr_map[s.EXP], var_offsets, x_length)
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A, F)
results = cvxopt.solvers.cpl(c,
F,
G,
h,
dims,
A,
b,
kktsolver=kktsolver)
else:
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A)
results = cvxopt.solvers.conelp(c,
G,
h,
dims,
A,
b,
kktsolver=kktsolver)
# Restore original cvxopt solver options.
cvxopt.solvers.options = old_options
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
if status == s.OPTIMAL:
primal_val = results['primal objective']
value = self.objective._primal_to_result(primal_val - obj_offset)
if constr_map[s.EXP]:
ineq_dual = results['zl']
else:
ineq_dual = results['z']
return (status, value, results['x'], results['y'], ineq_dual)
else:
return (status, None, None, None, None)
def _scs_problem_data(self, objective, constr_map, dims, var_offsets,
x_length):
"""Returns the problem data for the call to SCS.
Parameters
----------
objective: Expression
The canonicalized objective.
constr_map: dict
A dict of the canonicalized constraints.
dims: dict
A dict with information about the types of constraints.
var_offsets: dict
A dict mapping variable id to offset in the stacked variable x.
x_length: int
The height of x.
Returns
-------
tuple
((data, dims), offset)
"""
c, obj_offset = self._get_obj(objective, var_offsets, x_length,
self._DENSE_INTF, self._DENSE_INTF)
# Convert obj_offset to a scalar.
obj_offset = self._DENSE_INTF.scalar_value(obj_offset)
A, b = self._constr_matrix(constr_map[s.EQ] + constr_map[s.LEQ],
var_offsets, x_length, self._SPARSE_INTF,
self._DENSE_INTF)
# Convert c, b to 1D arrays.
c, b = map(intf.from_2D_to_1D, [c.T, b])
data = {"c": c}
data["A"] = A
data["b"] = b
return ((data, dims), obj_offset)
def _scs_solve(self, objective, constr_map, dims, var_offsets, x_length,
verbose, opts):
"""Calls the SCS solver and returns the result.
Parameters
----------
objective: LinExpr
The canonicalized objective.
constr_map: dict
A dict of the canonicalized constraints.
dims: dict
A dict with information about the types of constraints.
var_offsets: dict
A dict mapping variable id to offset in the stacked variable x.
x_length: int
The height of x.
verbose: bool
Should the solver show output?
opts: dict
A dict of the solver parameters passed to scs
Returns
-------
tuple
(status, optimal objective, optimal x,
optimal equality constraint dual,
optimal inequality constraint dual)
"""
prob_data = self._scs_problem_data(objective, constr_map, dims,
var_offsets, x_length)
obj_offset = prob_data[1]
# Set the options to be VERBOSE plus any user-specific options.
opts = dict({"VERBOSE": verbose}.items() + opts.items())
use_indirect = opts["USE_INDIRECT"] if "USE_INDIRECT" in opts else False
results = scs.solve(*prob_data[0],
opts=opts,
USE_INDIRECT=use_indirect)
status = s.SOLVER_STATUS[s.SCS][results["info"]["status"]]
if status == s.OPTIMAL:
primal_val = results["info"]["pobj"]
value = self.objective._primal_to_result(primal_val - obj_offset)
eq_dual = results["y"][0:dims["f"]]
ineq_dual = results["y"][dims["f"]:]
return (status, value, results["x"], eq_dual, ineq_dual)
else:
return (status, None, None, None, None)
def _handle_failure(self, status):
"""Updates value fields based on the cause of solver failure.
Parameters
----------
status: str
The status of the solver.
"""
# Set all primal and dual variable values to None.
for var_ in self.variables():
var_.save_value(None)
for constr in self.constraints:
constr.save_value(None)
# Set the problem value.
if status == s.INFEASIBLE:
self._value = self.objective._primal_to_result(np.inf)
elif status == s.UNBOUNDED:
self._value = self.objective._primal_to_result(-np.inf)
else: # Solver error
self._value = None
def _get_var_offsets(self, objective, constraints):
"""Maps each variable to a horizontal offset.
Parameters
----------
objective : Expression
The canonicalized objective.
constraints : list
The canonicalized constraints.
Returns
-------
tuple
(map of variable to offset, length of variable vector)
"""
vars_ = lu.get_expr_vars(objective)
for constr in constraints:
vars_ += lu.get_expr_vars(constr.expr)
var_offsets = OrderedDict()
var_sizes = {}
# Ensure the variables are always in the same
# order for the same problem.
var_names = list(set(vars_))
var_names.sort(key=lambda (var_id, var_size): var_id)
# Map var ids to offsets.
vert_offset = 0
for var_id, var_size in var_names:
var_sizes[var_id] = var_size
var_offsets[var_id] = vert_offset
vert_offset += var_size[0] * var_size[1]
return (var_offsets, var_sizes, vert_offset)
def _save_dual_values(self, result_vec, constraints, constr_type):
"""Saves the values of the dual variables.
Parameters
----------
results_vec : array_like
A vector containing the dual variable values.
constraints : list
A list of the LinEqConstr/LinLeqConstr in the problem.
constr_type : type
EqConstr or LeqConstr
"""
constr_offsets = {}
offset = 0
for constr in constraints:
constr_offsets[constr.constr_id] = offset
offset += constr.size[0] * constr.size[1]
active_constraints = []
for constr in self.constraints:
# Ignore constraints of the wrong type.
if type(constr) == constr_type:
active_constraints.append(constr)
self._save_values(result_vec, active_constraints, constr_offsets)
def _save_values(self, result_vec, objects, offset_map):
"""Saves the values of the optimal primal/dual variables.
Parameters
----------
results_vec : array_like
A vector containing the variable values.
objects : list
The variables or constraints where the values will be stored.
offset_map : dict
A map of object id to offset in the results vector.
"""
if len(result_vec) > 0:
# Cast to desired matrix type.
result_vec = self._DENSE_INTF.const_to_matrix(result_vec)
for obj in objects:
rows, cols = obj.size
if obj.id in offset_map:
offset = offset_map[obj.id]
# Handle scalars
if (rows, cols) == (1, 1):
value = intf.index(result_vec, (offset, 0))
else:
value = self._DENSE_INTF.zeros(rows, cols)
self._DENSE_INTF.block_add(
value, result_vec[offset:offset + rows * cols], 0, 0,
rows, cols)
offset += rows * cols
else: # The variable was multiplied by zero.
value = self._DENSE_INTF.zeros(rows, cols)
obj.save_value(value)
def _get_obj(self, objective, var_offsets, x_length, matrix_intf,
vec_intf):
"""Wraps _constr_matrix so it can be called for the objective.
"""
dummy_constr = lu.create_eq(objective)
return self._constr_matrix([dummy_constr], var_offsets, x_length,
matrix_intf, vec_intf)
def _constr_matrix(self, constraints, var_offsets, x_length, matrix_intf,
vec_intf):
"""Returns a matrix and vector representing a list of constraints.
In the matrix, each constraint is given a block of rows.
Each variable coefficient is inserted as a block with upper
left corner at matrix[variable offset, constraint offset].
The constant term in the constraint is added to the vector.
Parameters
----------
constraints : list
A list of constraints.
var_offsets : dict
A dict of variable id to horizontal offset.
x_length : int
The length of the x vector.
matrix_intf : interface
The matrix interface to use for creating the constraints matrix.
vec_intf : interface
The matrix interface to use for creating the constant vector.
Returns
-------
tuple
A (matrix, vector) tuple.
"""
rows = sum([c.size[0] * c.size[1] for c in constraints])
cols = x_length
V, I, J = [], [], []
const_vec = vec_intf.zeros(rows, 1)
vert_offset = 0
for constr in constraints:
coeffs = op2mat.get_coefficients(constr.expr)
for id_, size, block in coeffs:
vert_start = vert_offset
vert_end = vert_start + constr.size[0] * constr.size[1]
if id_ is lo.CONSTANT_ID:
# Flatten the block.
block = self._DENSE_INTF.const_to_matrix(block)
block_size = intf.size(block)
block = self._DENSE_INTF.reshape(
block, (block_size[0] * block_size[1], 1))
const_vec[vert_start:vert_end, :] += block
else:
horiz_offset = var_offsets[id_]
if intf.is_scalar(block):
block = intf.scalar_value(block)
V.append(block)
I.append(vert_start)
J.append(horiz_offset)
else:
# Block is a numpy matrix or
# scipy CSC sparse matrix.
if not intf.is_sparse(block):
block = self._SPARSE_INTF.const_to_matrix(block)
block = block.tocoo()
V.extend(block.data)
I.extend(block.row + vert_start)
J.extend(block.col + horiz_offset)
vert_offset += constr.size[0] * constr.size[1]
# Create the constraints matrix.
if len(V) > 0:
matrix = sp.coo_matrix((V, (I, J)), (rows, cols))
# Convert the constraints matrix to the correct type.
matrix = matrix_intf.const_to_matrix(matrix, convert_scalars=True)
else: # Empty matrix.
matrix = matrix_intf.zeros(rows, cols)
return (matrix, -const_vec)
def _merge_nonlin(self, nl_constr, var_offsets, x_length):
""" TODO: ensure that this works with numpy data structs...
"""
rows = sum([constr.size[0] * constr.size[1] for constr in nl_constr])
cols = x_length
big_x = self._CVXOPT_DENSE_INTF.zeros(cols, 1)
for constr in nl_constr:
constr.place_x0(big_x, var_offsets, self._CVXOPT_DENSE_INTF)
def F(x=None, z=None):
if x is None:
return rows, big_x
big_f = self._CVXOPT_DENSE_INTF.zeros(rows, 1)
big_Df = self._CVXOPT_SPARSE_INTF.zeros(rows, cols)
if z:
big_H = self._CVXOPT_SPARSE_INTF.zeros(cols, cols)
offset = 0
for constr in nl_constr:
constr_entries = constr.size[0] * constr.size[1]
local_x = constr.extract_variables(x, var_offsets,
self._CVXOPT_DENSE_INTF)
if z:
f, Df, H = constr.f(local_x,
z[offset:offset + constr_entries])
else:
result = constr.f(local_x)
if result:
f, Df = result
else:
return None
big_f[offset:offset + constr_entries] = f
constr.place_Df(big_Df, Df, var_offsets, offset,
self._CVXOPT_SPARSE_INTF)
if z:
constr.place_H(big_H, H, var_offsets,
self._CVXOPT_SPARSE_INTF)
offset += constr_entries
if z is None:
return big_f, big_Df
return big_f, big_Df, big_H
return F
def __str__(self):
return repr(self)
def __repr__(self):
return "Problem(%s, %s)" % (repr(self.objective), repr(
self.constraints))
class ExpCone(NonlinearConstraint):
"""A reformulated exponential cone constraint.
Operates elementwise on x, y, z.
Original cone:
K = {(x,y,z) | y > 0, ye^(x/y) <= z}
U {(x,y,z) | x <= 0, y = 0, z >= 0}
Reformulated cone:
K = {(x,y,z) | y, z > 0, y * log(y) + x <= y * log(z)}
U {(x,y,z) | x <= 0, y = 0, z >= 0}
Attributes
----------
x: Variable x in the exponential cone.
y: Variable y in the exponential cone.
z: Variable z in the exponential cone.
"""
CVXOPT_DENSE_INTF = intf.get_matrix_interface(cvxopt.matrix)
CVXOPT_SPARSE_INTF = intf.get_matrix_interface(cvxopt.spmatrix)
def __init__(self, x, y, z):
self.x = x
self.y = y
self.z = z
self.size = (int(self.x.size[0]), int(self.x.size[1]))
super(ExpCone, self).__init__(self._solver_hook,
[self.x, self.y, self.z])
def __str__(self):
return "ExpCone(%s, %s, %s)" % (self.x, self.y, self.z)
def format(self, eq_constr, leq_constr, dims, solver):
"""Formats EXP constraints for the solver.
Parameters
----------
eq_constr : list
A list of the equality constraints in the canonical problem.
leq_constr : list
A list of the inequality constraints in the canonical problem.
dims : dict
A dict with the dimensions of the conic constraints.
solver : str
The solver being called.
"""
if solver.name() == s.CVXOPT:
eq_constr += self.__CVXOPT_format[0]
elif solver.name() == s.SCS:
leq_constr += self.__SCS_format[1]
elif solver.name() == s.ECOS:
leq_constr += self.__ECOS_format[1]
else:
raise SolverError("Solver does not support exponential cone.")
# Update dims.
dims[s.EXP_DIM] += self.size[0] * self.size[1]
@pu.lazyprop
def __ECOS_format(self):
return ([], format_elemwise([self.x, self.z, self.y]))
@pu.lazyprop
def __SCS_format(self):
return ([], format_elemwise([self.x, self.y, self.z]))
@pu.lazyprop
def __CVXOPT_format(self):
constraints = []
for i, var in enumerate(self.vars_):
if not var.type is VARIABLE:
lone_var = lu.create_var(var.size)
constraints.append(lu.create_eq(lone_var, var))
self.vars_[i] = lone_var
return (constraints, [])
def _solver_hook(self, vars_=None, scaling=None):
"""A function used by CVXOPT's nonlinear solver.
Based on f(x,y,z) = y * log(y) + x - y * log(z).
Parameters
----------
vars_: A cvxopt dense matrix with values for (x,y,z).
scaling: A scaling for the Hessian.
Returns
-------
_solver_hook() returns the constraint size and a feasible point.
_solver_hook(x) returns the function value and gradient at x.
_solver_hook(x, z) returns the function value, gradient,
and (z scaled) Hessian at x.
"""
entries = self.size[0] * self.size[1]
if vars_ is None:
x_init = entries * [0.0]
y_init = entries * [0.5]
z_init = entries * [1.0]
return self.size[0], cvxopt.matrix(x_init + y_init + z_init)
# Unpack vars_
x = vars_[0:entries]
y = vars_[entries:2 * entries]
z = vars_[2 * entries:]
# Out of domain.
# TODO what if y == 0.0?
if min(y) <= 0.0 or min(z) <= 0.0:
return None
# Evaluate the function.
f = self.CVXOPT_DENSE_INTF.zeros(entries, 1)
for i in range(entries):
f[i] = x[i] - y[i] * math.log(z[i]) + y[i] * math.log(y[i])
# Compute the gradient.
Df = self.CVXOPT_DENSE_INTF.zeros(entries, 3 * entries)
for i in range(entries):
Df[i, i] = 1.0
Df[i, entries + i] = math.log(y[i]) - math.log(z[i]) + 1.0
Df[i, 2 * entries + i] = -y[i] / z[i]
if scaling is None:
return f, Df
# Compute the Hessian.
big_H = self.CVXOPT_SPARSE_INTF.zeros(3 * entries, 3 * entries)
for i in range(entries):
H = cvxopt.matrix([
[0.0, 0.0, 0.0],
[0.0, 1.0 / y[i], -1.0 / z[i]],
[0.0, -1.0 / z[i], y[i] / (z[i]**2)],
])
big_H[i:3 * entries:entries,
i:3 * entries:entries] = scaling[i] * H
return f, Df, big_H