def var_cone_canon(expr, args):
"""Expand implicit constraints on variable.
"""
# Convert attributes into constraints.
new_attr = expr.attributes.copy()
for key in ['nonneg', 'nonpos', 'symmetric', 'PSD', 'NSD']:
if new_attr[key]:
new_attr[key] = False
if expr.is_symmetric():
n = expr.shape[0]
shape = (n * (n + 1) // 2, 1)
upper_tri = Variable(shape, var_id=expr.id, **new_attr)
fill_coeff = Constant(upper_tri_to_full(n))
full_mat = fill_coeff * upper_tri
obj = reshape(full_mat, (n, n))
else:
obj = Variable(expr.shape, var_id=expr.id, **new_attr)
constr = []
if expr.is_nonneg():
constr.append(obj >= 0)
elif expr.is_nonpos():
constr.append(obj <= 0)
elif expr.attributes['PSD']:
constr.append(obj >> 0)
elif expr.attributes['NSD']:
constr.append(obj << 0)
return (obj, constr)
def scaled_lower_tri(matrix):
"""Returns an expression representing the lower triangular entries
Scales the strictly lower triangular entries by sqrt(2), as required
by SCS.
Parameters
----------
matrix : Expression
A 2-dimensional CVXPY expression.
Returns
-------
Expression
An expression representing the (scaled) lower triangular part of
the supplied matrix expression.
"""
rows = cols = matrix.shape[0]
entries = rows * (cols + 1)//2
row_arr = np.arange(0, entries)
lower_diag_indices = np.tril_indices(rows)
col_arr = np.sort(np.ravel_multi_index(lower_diag_indices, (rows, cols), order='F'))
val_arr = np.zeros((rows, cols))
val_arr[lower_diag_indices] = np.sqrt(2)
np.fill_diagonal(val_arr, 1)
val_arr = np.ravel(val_arr, order='F')
val_arr = val_arr[np.nonzero(val_arr)]
shape = (entries, rows*cols)
coeff = Constant(sp.csc_matrix((val_arr, (row_arr, col_arr)), shape))
vectorized_matrix = reshape(matrix, (rows*cols, 1))
return coeff * vectorized_matrix
def replace_params_with_consts(expr):
if isinstance(expr, list):
return [replace_params_with_consts(elem) for elem in expr]
elif len(expr.parameters()) == 0:
return expr
elif isinstance(expr, Parameter):
if expr.value is None:
raise ParameterError("Problem contains unspecified parameters.")
return Constant(expr.value)
else:
new_args = []
for arg in expr.args:
new_args.append(replace_params_with_consts(arg))
return expr.copy(new_args)
def process_expression(self, expr):
if isinstance(expr, CallbackParam):
data_arg = self.process_expression(expr.atom)
data = CbParamData(expr, [data_arg])
if expr.id not in self.cbparam_ids: # Check if already there.
self.callback_params += [data]
self.cbparam_ids += [expr.id]
elif isinstance(expr, Parameter):
data = ParamData(expr)
if expr.id not in self.param_ids: # Check if already there.
self.named_params += [data]
self.param_ids += [expr.id]
elif isinstance(expr, Constant):
data = ConstData(expr)
self.constants += [data]
elif isinstance(expr, Atom):
if not expr.parameters(): # expr is just a constant without parameters.
data = ConstData(Constant(expr.value))
self.constants += [data]
else: # Recurse on arguments:
if id(expr) in self.expr_ids: # Check if already there.
idx = self.expr_ids.index(id(expr))
self.expressions[idx].force_copy()
data = self.expressions[idx]
else:
arg_data = []
for arg in expr.args:
arg_data += [self.process_expression(arg)]
data_list = get_atom_data(expr, arg_data)
self.expressions += data_list
data = data_list[-1]
self.expr_ids += [id(expr)]
for d in data_list:
if d.macro_name not in self.unique_exprs: # Check if already there.
self.unique_exprs += [d.macro_name]
else:
raise TypeError('Invalid expression tree type: %s' % type(expr))
return data
def scaled_lower_tri(matrix):
"""Returns an expression representing the lower triangular entries
Scales the strictly lower triangular entries by sqrt(2), as required
by SCS.
Parameters
----------
matrix : Expression
A 2-dimensional CVXPY expression.
Returns
-------
Expression
An expression representing the (scaled) lower triangular part of
the supplied matrix expression.
"""
rows = cols = matrix.shape[0]
entries = rows * (cols + 1) // 2
val_arr = []
row_arr = []
col_arr = []
count = 0
for j in range(cols):
for i in range(rows):
if j <= i:
# Index in the original matrix.
col_arr.append(j * rows + i)
# Index in the extracted vector.
row_arr.append(count)
if j == i:
val_arr.append(1.0)
else:
val_arr.append(np.sqrt(2))
count += 1
shape = (entries, rows * cols)
coeff = Constant(
sp.coo_matrix((val_arr, (row_arr, col_arr)), shape).tocsc())
vectorized_matrix = reshape(matrix, (rows * cols, 1))
return coeff * vectorized_matrix
def Semidef(n, name=None):
"""An expression representing a positive semidefinite matrix.
"""
var = SemidefUpperTri(n, name)
fill_mat = Constant(upper_tri_to_full(n))
return cvxtypes.reshape()(fill_mat * var, n, n)
def constant_canon(expr, args):
del args
return Constant(np.log(expr.value)), []
def Symmetric(n, name=None):
"""An expression representing a symmetric matrix.
"""
var = SymmetricUpperTri(n, name)
fill_mat = Constant(upper_tri_to_full(n))
return cvxtypes.reshape()(fill_mat * var, int(n), int(n))