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 _process_constr(self, constr, mat_cache, vert_offset):
"""Extract the coefficients from a constraint.
Parameters
----------
constr : LinConstr
The linear constraint to process.
mat_cache : MatrixCache
The cached version of the matrix-vector pair.
vert_offset : int
The row offset of the constraint.
"""
V, I, J = mat_cache.coo_tup
coeffs = op2mat.get_coefficients(constr.expr)
for id_, 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.vec_intf.const_to_matrix(block)
block_size = intf.size(block)
block = self.vec_intf.reshape(
block,
(block_size[0]*block_size[1], 1)
)
mat_cache.const_vec[vert_start:vert_end, :] += block
else:
horiz_offset = self.sym_data.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 = intf.DEFAULT_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)
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 value(self):
# Catch the case when the expression is known to be
# zero through DCP analysis.
if self.is_zero():
result = intf.DEFAULT_INTERFACE.zeros(*self.size)
else:
arg_values = []
for arg in self.args:
# A argument without a value makes all higher level
# values None.
if arg.value is None:
return None
else:
arg_values.append(arg.value)
result = self.numeric(arg_values)
# Reduce to a scalar if possible.
if intf.size(result) == (1, 1):
return intf.scalar_value(result)
else:
return result
def _process_constr(self, constr, mat_cache, vert_offset):
"""Extract the coefficients from a constraint.
Parameters
----------
constr : LinConstr
The linear constraint to process.
mat_cache : MatrixCache
The cached version of the matrix-vector pair.
vert_offset : int
The row offset of the constraint.
"""
V, I, J = mat_cache.coo_tup
coeffs = op2mat.get_coefficients(constr.expr)
for id_, 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.vec_intf.const_to_matrix(block)
block_size = intf.size(block)
block = self.vec_intf.reshape(
block, (block_size[0] * block_size[1], 1))
mat_cache.const_vec[vert_start:vert_end, :] += block
else:
horiz_offset = self.sym_data.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 = intf.DEFAULT_SPARSE_INTERFACE.const_to_matrix(
block)
block = block.tocoo()
V.extend(block.data)
I.extend(block.row + vert_start)
J.extend(block.col + horiz_offset)
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.assertEqual(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.assertEqual(interface.size(mat), (3, 3))
# identity
mat = interface.identity(4)
cmp_mat = interface.const_to_matrix(np.eye(4))
self.assertEqual(interface.size(mat), interface.size(cmp_mat))
assert (mat - cmp_mat).nnz == 0
# 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))
# 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.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 _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_, 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 extract_dual_value(result_vec, offset, constraint):
value = result_vec[offset:offset + constraint.size]
if constraint.size == 1:
value = intf.scalar_value(value)
offset += constraint.size
return value, offset
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)