def belongs(x, A):
"""
Form set membership constraint (x in A)
:param x: :class:`cvxpy_matrix` or array object.
:param A: Set atom.
:rtype: :class:`cvxpy.constr`
"""
# Element is not array-like
if (type(x).__name__ not in ARRAY_OBJS and type(x) is not cvxpy_matrix):
raise ValueError('First argument must be array-like')
# Set is not valid
if (A.type != SET):
raise ValueError('Second argument must be a set')
# Verify dimensions
(m1, n1) = A.shape
(m2, n2) = x.shape
# Dimensions don't match
if ((m1, n1) != (m2, n2)):
raise ValueError('Invalid dimensions')
# Construct and return constraint
return cvxpy_constr(x, 'in', A)
def belongs(x,A):
"""
Form set membership constraint (x in A)
:param x: :class:`cvxpy_matrix` or array object.
:param A: Set atom.
:rtype: :class:`cvxpy.constr`
"""
# Element is not array-like
if(type(x).__name__ not in ARRAY_OBJS and
type(x) is not cvxpy_matrix):
raise ValueError('First argument must be array-like')
# Set is not valid
if(A.type != SET):
raise ValueError('Second argument must be a set')
# Verify dimensions
(m1,n1) = A.shape
(m2,n2) = x.shape
# Dimensions don't match
if((m1,n1) != (m2,n2)):
raise ValueError('Invalid dimensions')
# Construct and return constraint
return cvxpy_constr(x,'in',A)
def compare(obj1, op, obj2):
# Both scalars
if ((np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS)
and (np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
# Upgrade scalars to cvxpy_obj
if (np.isscalar(obj1)):
obj1 = cvxpy_obj(CONSTANT, obj1, str(obj1))
if (np.isscalar(obj2)):
obj2 = cvxpy_obj(CONSTANT, obj2, str(obj2))
# Construct and return constraint
return cvxpy_constr(obj1, op, obj2)
# Upgrate scalars to arrays
if ((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS)
and (np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
(m, n) = obj1.shape
new_exp = cvxpy_expression(m, n)
for i in range(0, m, 1):
for j in range(0, n, 1):
new_exp[i, j] = obj2
obj2 = new_exp
if ((type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS)
and (np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS)):
(m, n) = obj2.shape
new_exp = cvxpy_expression(m, n)
for i in range(0, m, 1):
for j in range(0, n, 1):
new_exp[i, j] = obj1
obj1 = new_exp
# Both arrays
if ((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS) and
(type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS)):
constr = []
if (obj1.shape != obj2.shape):
raise ValueError('Invalid dimensions')
(m, n) = obj1.shape
for i in range(0, m, 1):
for j in range(0, n, 1):
constr += [compare(obj1[i, j], op, obj2[i, j])]
return cvxpy_list(constr)
# Invalid arguments
raise ValueError('Objects not comparable')
def compare(obj1,op,obj2):
# Both scalars
if((np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS) and
(np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
# Upgrade scalars to cvxpy_obj
if(np.isscalar(obj1)):
obj1 = cvxpy_obj(CONSTANT,obj1,str(obj1))
if(np.isscalar(obj2)):
obj2 = cvxpy_obj(CONSTANT,obj2,str(obj2))
# Construct and return constraint
return cvxpy_constr(obj1,op,obj2)
# Upgrate scalars to arrays
if((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS) and
(np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
(m,n) = obj1.shape
new_exp = cvxpy_expression(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
new_exp[i,j] = obj2
obj2 = new_exp
if((type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS) and
(np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS)):
(m,n) = obj2.shape
new_exp = cvxpy_expression(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
new_exp[i,j] = obj1
obj1 = new_exp
# Both arrays
if((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS) and
(type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS)):
constr = []
if(obj1.shape != obj2.shape):
raise ValueError('Invalid dimensions')
(m,n) = obj1.shape
for i in range(0,m,1):
for j in range(0,n,1):
constr += [compare(obj1[i,j],op,obj2[i,j])]
return cvxpy_list(constr)
# Invalid arguments
raise ValueError('Objects not comparable')
def expand(arg):
# Constant
if(type(arg) is cvxpy_obj):
return arg,cvxpy_list([])
# Scalar variable
elif(type(arg) is cvxpy_scalar_var):
return arg,cvxpy_list([])
# Summation
elif(type(arg) is cvxpy_tree and arg.item.name == '+'):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Expand children
new_children = []
new_constr = cvxpy_list([])
for child in children:
# Multiplication
if(child.type == TREE and
child.item.name == '*'):
child_var,child_constr = expand(child.children[1])
new_children += [child.children[0].data*child_var]
new_constr += child_constr
# Else
else:
child_var,child_constr = expand(child)
new_children += [child_var]
new_constr += child_constr
# Return (Always right side is the new variable)
new_tree = cvxpy_tree(item,new_children)
return v,cvxpy_list([equal(new_tree,v)])+new_constr
# Multiplication
elif(type(arg) is cvxpy_tree and arg.item.name == '*'):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Apply expand to second operand (first is a constant)
child_var,child_constr = expand(children[1])
# Return result (Always right side is the new variable)
new_tree = cvxpy_tree(item,[children[0],child_var])
new_eq = cvxpy_list([equal(new_tree,v)])
new_eq += child_constr
return v,new_eq
# Function
elif(type(arg) is cvxpy_tree and arg.item.type == FUNCTION):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Analyze children
new_children = []
new_constr = cvxpy_list([])
for child in children:
child_var,child_constr = expand(child)
new_children += [child_var]
new_constr += child_constr
# Return (Always right side is the new variable)
new_tree = cvxpy_tree(item,new_children)
new_constr += item._range_constr(v)
new_constr += item._dom_constr(new_children)
return v,cvxpy_list([equal(new_tree,v)])+new_constr
# Constraint
elif(type(arg) is cvxpy_constr):
# Not set membership
if(arg.op != 'in'):
# Apply expand to left and right side
obj1,constr_list1 = expand(arg.left)
obj2,constr_list2 = expand(arg.right)
# Return new constraints
new_constr = cvxpy_constr(obj1,arg.op,obj2)
new_list = cvxpy_list([new_constr])
new_list += constr_list1
new_list += constr_list2
return new_list
# Set membership
else:
obj, constr_list = expand(arg.left)
new_constr = cvxpy_constr(obj,arg.op,arg.right)
return cvxpy_list([new_constr])+constr_list
# Array
elif(type(arg) is cvxpy_expression or
type(arg) is cvxpy_var):
(m,n) = arg.shape
new_list = cvxpy_list([])
new_exp = cvxpy_expression(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
# Number: Upgrade
if(np.isscalar(arg[i,j])):
new_exp[i,j] = cvxpy_obj(CONSTANT,arg[i,j],str(arg[i,j]))
# Not a number
else:
obj,constr_list = expand(arg[i,j])
new_exp[i,j] = obj
new_list += constr_list
return new_exp,new_list
# List of constraints
elif(type(arg) is cvxpy_list):
# Empty list
if(len(arg) == 0):
return cvxpy_list([])
else:
new_list = map(expand,arg)
return reduce(lambda x,y:x+y,new_list)
# Invalid
else:
raise ValueError('Invalid argument')
def expand(arg):
# Constant
if (type(arg) is cvxpy_obj):
return arg, cvxpy_list([])
# Scalar variable
elif (type(arg) is cvxpy_scalar_var):
return arg, cvxpy_list([])
# Summation
elif (type(arg) is cvxpy_tree and arg.item.name == '+'):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Expand children
new_children = []
new_constr = cvxpy_list([])
for child in children:
# Multiplication
if (child.type == TREE and child.item.name == '*'):
child_var, child_constr = expand(child.children[1])
new_children += [child.children[0].data * child_var]
new_constr += child_constr
# Else
else:
child_var, child_constr = expand(child)
new_children += [child_var]
new_constr += child_constr
# Return (Always right side is the new variable)
new_tree = cvxpy_tree(item, new_children)
return v, cvxpy_list([equal(new_tree, v)]) + new_constr
# Multiplication
elif (type(arg) is cvxpy_tree and arg.item.name == '*'):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Apply expand to second operand (first is a constant)
child_var, child_constr = expand(children[1])
# Return result (Always right side is the new variable)
new_tree = cvxpy_tree(item, [children[0], child_var])
new_eq = cvxpy_list([equal(new_tree, v)])
new_eq += child_constr
return v, new_eq
# Function
elif (type(arg) is cvxpy_tree and arg.item.type == FUNCTION):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Analyze children
new_children = []
new_constr = cvxpy_list([])
for child in children:
child_var, child_constr = expand(child)
new_children += [child_var]
new_constr += child_constr
# Return (Always right side is the new variable)
new_tree = cvxpy_tree(item, new_children)
new_constr += item._range_constr(v)
new_constr += item._dom_constr(new_children)
return v, cvxpy_list([equal(new_tree, v)]) + new_constr
# Constraint
elif (type(arg) is cvxpy_constr):
# Not set membership
if (arg.op != 'in'):
# Apply expand to left and right side
obj1, constr_list1 = expand(arg.left)
obj2, constr_list2 = expand(arg.right)
# Return new constraints
new_constr = cvxpy_constr(obj1, arg.op, obj2)
new_list = cvxpy_list([new_constr])
new_list += constr_list1
new_list += constr_list2
return new_list
# Set membership
else:
obj, constr_list = expand(arg.left)
new_constr = cvxpy_constr(obj, arg.op, arg.right)
return cvxpy_list([new_constr]) + constr_list
# Array
elif (type(arg) is cvxpy_expression or type(arg) is cvxpy_var):
(m, n) = arg.shape
new_list = cvxpy_list([])
new_exp = cvxpy_expression(m, n)
for i in range(0, m, 1):
for j in range(0, n, 1):
# Number: Upgrade
if (np.isscalar(arg[i, j])):
new_exp[i, j] = cvxpy_obj(CONSTANT, arg[i, j],
str(arg[i, j]))
# Not a number
else:
obj, constr_list = expand(arg[i, j])
new_exp[i, j] = obj
new_list += constr_list
return new_exp, new_list
# List of constraints
elif (type(arg) is cvxpy_list):
# Empty list
if (len(arg) == 0):
return cvxpy_list([])
else:
new_list = map(expand, arg)
return reduce(lambda x, y: x + y, new_list)
# Invalid
else:
raise ValueError('Invalid argument')