def vstack(t):
"""
Vertical stack.
"""
# Verify input type
new_list = []
numeric = True
for x in t:
if (np.isscalar(x)):
new_list += [matrix(x)]
elif (type(x) is cvxpy_obj):
new_list += [matrix(x.data)]
elif (type(x).__name__ in SCALAR_OBJS):
numeric = False
new_x = cvxpy_expression(1, 1)
new_x[0, 0] = x
new_list += [new_x]
elif (type(x).__name__ in ARRAY_OBJS):
numeric = False
new_list += [x]
elif (type(x) is cvxpy_matrix):
new_list += [x]
else:
raise ValueError('Invalid Input')
# Input is numeric
if (numeric):
return np.vstack(new_list)
# Verify dimensions
n = new_list[0].shape[1]
for x in new_list:
if (x.shape[1] != n):
raise ValueError('Invalid Dimensions')
# Allocate new expression
m = 0
for x in new_list:
m += x.shape[0]
new_exp = cvxpy_expression(m, n)
# Fill new expression
k = 0
for x in new_list:
for i in range(0, x.shape[0], 1):
for j in range(0, x.shape[1], 1):
new_exp[i + k, j] = x[i, j]
k = k + x.shape[0]
# Return new expression
return new_exp
def vstack(t):
"""
Vertical stack.
"""
# Verify input type
new_list = []
numeric = True
for x in t:
if(np.isscalar(x)):
new_list += [matrix(x)]
elif(type(x) is cvxpy_obj):
new_list += [matrix(x.data)]
elif(type(x).__name__ in SCALAR_OBJS):
numeric = False
new_x = cvxpy_expression(1,1)
new_x[0,0] = x
new_list += [new_x]
elif(type(x).__name__ in ARRAY_OBJS):
numeric = False
new_list += [x]
elif(type(x) is cvxpy_matrix):
new_list += [x]
else:
raise ValueError('Invalid Input')
# Input is numeric
if(numeric):
return np.vstack(new_list)
# Verify dimensions
n = new_list[0].shape[1]
for x in new_list:
if(x.shape[1] != n):
raise ValueError('Invalid Dimensions')
# Allocate new expression
m = 0
for x in new_list:
m += x.shape[0]
new_exp = cvxpy_expression(m,n)
# Fill new expression
k = 0
for x in new_list:
for i in range(0,x.shape[0],1):
for j in range(0,x.shape[1],1):
new_exp[i+k,j] = x[i,j]
k = k + x.shape[0]
# Return new expression
return new_exp
def diagflat(arg):
"""
List, row or column vector to diagonal matrix.
"""
# Argument is a list
if (type(arg) is list):
arg = hstack(arg)
# Argument is a matrix or object array
elif (type(arg) is cvxpy_matrix or type(arg).__name__ in ARRAY_OBJS):
(m, n) = arg.shape
if (m != 1 and n != 1):
raise ValueError('Argument must be one dimensional')
elif (n == 1):
arg = arg.T
# Invalid argument
else:
raise ValueError('Invalid argument')
# Argument is numeric
numeric = True
for i in range(0, arg.shape[1], 1):
if (not np.isscalar(arg[0, i])):
numeric = False
if (numeric):
return matrix(np.diagflat(arg))
# Not numeric
(m, n) = arg.shape
new_exp = cvxpy_expression(n, n)
for i in range(0, n, 1):
new_exp[i, i] = arg[0, i]
return new_exp
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 __call__(self,*arg):
# Check number of arguments
if(len(arg) != 1):
raise ValueError('Invalid number of arguments')
# Extract argument
if(type(arg[0]) is list):
x = arg[0][0]
else:
x = arg[0]
# Process
if(type(x).__name__ in SCALAR_OBJS):
return cvxpy_tree(self,[x])
elif(type(x).__name__ in ARRAY_OBJS):
(m,n) = x.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] = self(x[i,j])
return new_exp
else:
return np.square(x)
def diag(arg):
"""
Extract the diagonal from square array-like object.
"""
# Check size
(m, n) = arg.shape
if (m != n):
raise ValueError('Invalid dimensions')
# cvxpy matrix
if (type(arg) is cvxpy_matrix):
return matrix(np.diag(arg)).T
# Object array
elif (type(arg).__name__ in ARRAY_OBJS):
new_exp = cvxpy_expression(m, 1)
for i in range(0, m, 1):
new_exp[i, 0] = arg[i, i]
return new_exp
# Error
else:
raise ValueError('Invalid argument type')
def __call__(self, *arg):
# Check number of arguments
if (len(arg) != 1):
raise ValueError('Invalid number of arguments')
# Extract argument
if (type(arg[0]) is list):
x = arg[0][0]
else:
x = arg[0]
# Process
if (type(x).__name__ in SCALAR_OBJS):
return cvxpy_tree(self, [x])
elif (type(x).__name__ in ARRAY_OBJS):
(m, n) = x.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] = self(x[i, j])
return new_exp
else:
return np.square(x)
def diagflat(arg):
"""
List, row or column vector to diagonal matrix.
"""
# Argument is a list
if(type(arg) is list):
arg = hstack(arg)
# Argument is a matrix or object array
elif(type(arg) is cvxpy_matrix or
type(arg).__name__ in ARRAY_OBJS):
(m,n) = arg.shape
if(m!=1 and n!=1):
raise ValueError('Argument must be one dimensional')
elif(n == 1):
arg = arg.T
# Invalid argument
else:
raise ValueError('Invalid argument')
# Argument is numeric
numeric = True
for i in range(0,arg.shape[1],1):
if(not np.isscalar(arg[0,i])):
numeric = False
if(numeric):
return matrix(np.diagflat(arg))
# Not numeric
(m,n) = arg.shape
new_exp = cvxpy_expression(n,n)
for i in range(0,n,1):
new_exp[i,i] = arg[0,i]
return new_exp
def diag(arg):
"""
Extract the diagonal from square array-like object.
"""
# Check size
(m,n) = arg.shape
if(m!=n):
raise ValueError('Invalid dimensions')
# cvxpy matrix
if(type(arg) is cvxpy_matrix):
return matrix(np.diag(arg)).T
# Object array
elif(type(arg).__name__ in ARRAY_OBJS):
new_exp = cvxpy_expression(m,1)
for i in range(0,m,1):
new_exp[i,0] = arg[i,i]
return new_exp
# Error
else:
raise ValueError('Invalid argument type')
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 __addsub__(self,other,op):
"""
Description
-----------
Handles left add or left subtract.
Arguments
---------
other: right hand object.
op: Character (+ or -)
"""
# Create operator (I should create another class for this)
operator = cvxpy_obj(OPERATOR,None,'+')
# Create args to combine
if(type(self) is cvxpy_tree and
self.item.name == '+'):
args = self.children
else:
args = [self]
# Number
if(np.isscalar(other)):
if(other == 0.0):
return self
if(op == '+'):
constant = cvxpy_obj(CONSTANT,other,str(other))
else:
constant = cvxpy_obj(CONSTANT,-other,str(-other))
return cvxpy_tree(operator,args+[constant])
# Scalar variable or scalar param
elif(type(other) is cvxpy_scalar_var or
type(other) is cvxpy_scalar_param):
if(op == '+'):
return cvxpy_tree(operator,args+[other])
else:
return cvxpy_tree(operator,args+[-other])
# Tree
elif(type(other) is cvxpy_tree):
if(other.item.name == '+'):
if(op == '+'):
return cvxpy_tree(operator,
args+other.children)
else:
return cvxpy_tree(operator,
args+[-x for x in other.children])
else:
if(op == '+'):
return cvxpy_tree(operator,args+[other])
else:
return cvxpy_tree(operator,args+[-other])
# Matrix
elif(type(other) is cvxpy_matrix):
m = other.shape[0]
n = other.shape[1]
new_exp = cvxpy_expression(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
if(op == '+'):
new_exp[i,j] = self+other[i,j]
else:
new_exp[i,j] = self-other[i,j]
return new_exp
# Not implemented
else:
return NotImplemented
def __mulhandle__(self,other):
"""
Description
-----------
Handles multiply.
Note: If other is numeric, the multiplication
tree formed has the constant object as first child.
Argument
--------
other: Other object.
"""
# Create operator
operator = cvxpy_obj(OPERATOR,None,'*')
# Number
if(np.isscalar(other)):
# Multiplication by 0
if(other == 0.0):
return 0.0
# Multiplication by 1
elif(other == 1.0):
return self
# Distribution over addition
elif(type(self) is cvxpy_tree and
self.item.name == '+'):
new_children = []
for child in self.children:
new_children += [other*child]
return cvxpy_tree(self.item,new_children)
# Associativity
elif(type(self) is cvxpy_tree and
self.item.name == '*' and
self.children[0].type == CONSTANT):
new_object = other*self.children[0]
if(new_object.data == 1.0):
return self.children[1]
else:
return cvxpy_tree(self.item,[new_object,
self.children[1]])
# Constant times constant
elif(type(self) is cvxpy_obj):
new_const = cvxpy_obj(CONSTANT,self.data*other,
str(self.data*other))
return new_const
# Else
else:
constant = cvxpy_obj(CONSTANT,other,str(other))
return cvxpy_tree(operator,[constant,self])
# Matrix
elif(type(other) is cvxpy_matrix):
m = other.shape[0]
n = other.shape[1]
new_exp = cvxpy_expression(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
new_exp[i,j] = other[i,j]*self
return new_exp
# Scalar param
elif(type(other) is cvxpy_scalar_param):
return cvxpy_tree(operator,[other,self])
# Tree
elif(type(other) is cvxpy_tree):
if(len(self.get_vars()) == 0 ):
return cvxpy_tree(operator,[self,other])
elif(len(other.get_vars()) == 0):
return cvxpy_tree(operator,[other,self])
else:
return NotImplemented
# Not implemented
else:
return NotImplemented
def __raddsub__(self,other,op):
"""
Description
-----------
Handles right add or right subtract.
Arguments
---------
other: left hand object.
op: Character (+ or -)
"""
# Create operator
operator = cvxpy_obj(OPERATOR,None,'+')
# Create args to combine
if(type(self) is cvxpy_tree and
self.item.name == '+'):
if(op == '+'):
args = self.children
else:
args = [-x for x in self.children]
else:
if(op == '+'):
args = [self]
else:
args = [-self]
# Number
if(np.isscalar(other)):
if(other == 0.0):
if(op == '+'):
return self
else:
return -self
constant = cvxpy_obj(CONSTANT,other,str(other))
return cvxpy_tree(operator,[constant]+args)
# Scalar variable or scalar param
elif(type(other) is cvxpy_scalar_var or
type(other) is cvxpy_scalar_param):
return cvxpy_tree(operator,[other]+args)
# Tree
elif(type(other) is cvxpy_tree):
if(other.item.name == '+'):
return cvxpy_tree(operator,other.children+args)
else:
return cvxpy_tree(operator,[other]+args)
# Matrix
elif(type(other) is cvxpy_matrix):
m = other.shape[0]
n = other.shape[1]
new_exp = cvxpy_expression(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
if(op == '+'):
new_exp[i,j] = other[i,j]+self
else:
new_exp[i,j] = other[i,j]-self
return new_exp
# Not implemented
else:
return NotImplemented
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 re_eval(arg,param_map):
"""
Description
-----------
Replaces parameters found in arg using the param_map
and re-evaluates the resulting object.
Arguments
---------
arg: Argument to be re-evaluated.
param_map: Dictionery that maps the parameters
to objects.
"""
# Number
if(np.isscalar(arg)):
return arg
# Constant object
elif(type(arg) is cvxpy_obj):
return arg.get_value()
# Scalar variable
elif(type(arg) is cvxpy_scalar_var):
return arg
# Scalar param
elif(type(arg) is cvxpy_scalar_param):
return re_eval(param_map[arg],param_map)
# Summation
elif(type(arg) is cvxpy_tree and arg.item.name == '+'):
new_children = map(lambda x:re_eval(x,param_map),arg.children)
return sum(new_children)
# Multiplication
elif(type(arg) is cvxpy_tree and arg.item.name == '*'):
child1 = re_eval(arg.children[0],param_map)
child2 = re_eval(arg.children[1],param_map)
return child1*child2
# Function
elif(type(arg) is cvxpy_tree and arg.item.type == FUNCTION):
new_children = map(lambda x:re_eval(x,param_map),arg.children)
return arg.item(new_children)
# Constraint
elif(type(arg) is cvxpy_constr):
# Not set membership
if(arg.op != 'in'):
left = re_eval(arg.left ,param_map)
right= re_eval(arg.right,param_map)
if(arg.op == '=='):
return equal(left,right)
elif(arg.op == '<='):
return less(left,right)
else:
return greater(left,right)
# Set membership
else:
left = re_eval(arg.left,param_map)
return belongs(left,arg.right)
# Array
elif(type(arg) is cvxpy_expression or
type(arg) is cvxpy_var or
type(arg) is cvxpy_param):
(m,n) = arg.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] = re_eval(arg[i,j],param_map)
return new_exp
# List
elif(type(arg) is cvxpy_list):
new_list = cvxpy_list([])
for c in arg:
new_list += cvxpy_list([re_eval(c,param_map)])
return new_list
# Invalid
else:
raise ValueError('Invalid argument')
