def vstack(seq):
"""
| Stacks objects vertically.
:param seq: tuple or list of numbers,
:ref:`scalar objects<scalar_ref>` or
:ref:`multidimensional objects<multi_ref>`.
:return: :ref:`array<array_obj>` or
:ref:`matrix<matrix_obj>`.
"""
# Check input
if (type(seq) is not tuple and type(seq) is not list):
raise TypeError('Invalid argument')
# Process input
new_list = []
numeric = True
for x in seq:
if np.isscalar(x):
new_list += [matrix(x)]
elif type(x) is cvxpy_obj:
new_list += [matrix(x.value)]
elif type(x).__name__ in SCALAR_OBJS:
numeric = False
new_x = cvxpy_array(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 TypeError('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 array
m = int(np.sum([x.shape[0] for x in new_list]))
new_ar = cvxpy_array(m, n)
# Fill new array
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_ar[i + k, j] = x[i, j]
k = k + x.shape[0]
# Return new array
return new_ar
def diag(v):
"""
| Extracts diagonal or constructs a diagonal array.
:param v: number,
:ref:`scalar object<scalar_ref>`,
square or one dimensional
:ref:`multidimensional object<multi_ref>`.
:return: number,
:ref:`scalar object<scalar_ref>` or
:ref:`multidimensional object<multi_ref>`.
"""
# Check input
if (np.isscalar(v) or
type(v).__name__ in SCALAR_OBJS):
return v
elif (type(v) is cvxpy_matrix or
type(v).__name__ in ARRAY_OBJS):
if v.shape[1]==1:
v = v.T
else:
raise TypeError('Invalid argument type')
# Get shape
(m,n) = v.shape
# Input is 2D
if m!=1 and n!=1:
# Must be square
if m!=n:
raise ValueError('Invalid dimensions')
# cvxpy matrix
if type(v) is cvxpy_matrix:
return matrix(np.diag(v)).T
# Object array
else:
new_ar = cvxpy_array(m,1)
for i in range(0,m,1):
new_ar[i,0] = v[i,i]
return new_ar
# Input is 1D
else:
# cvxpy matrix
if type(v) is cvxpy_matrix:
return matrix(np.diagflat(v))
# Object array
else:
new_ar = cvxpy_array(n,n)
for i in range(0,n,1):
new_ar[i,i] = v[0,i]
return new_ar
def diag(v):
"""
| Extracts diagonal or constructs a diagonal array.
:param v: number,
:ref:`scalar object<scalar_ref>`,
square or one dimensional
:ref:`multidimensional object<multi_ref>`.
:return: number,
:ref:`scalar object<scalar_ref>` or
:ref:`multidimensional object<multi_ref>`.
"""
# Check input
if (np.isscalar(v) or type(v).__name__ in SCALAR_OBJS):
return v
elif (type(v) is cvxpy_matrix or type(v).__name__ in ARRAY_OBJS):
if v.shape[1] == 1:
v = v.T
else:
raise TypeError('Invalid argument type')
# Get shape
(m, n) = v.shape
# Input is 2D
if m != 1 and n != 1:
# Must be square
if m != n:
raise ValueError('Invalid dimensions')
# cvxpy matrix
if type(v) is cvxpy_matrix:
return matrix(np.diag(v)).T
# Object array
else:
new_ar = cvxpy_array(m, 1)
for i in range(0, m, 1):
new_ar[i, 0] = v[i, i]
return new_ar
# Input is 1D
else:
# cvxpy matrix
if type(v) is cvxpy_matrix:
return matrix(np.diagflat(v))
# Object array
else:
new_ar = cvxpy_array(n, n)
for i in range(0, n, 1):
new_ar[i, i] = v[0, i]
return new_ar
def compare(obj1, constraint_type, obj2):
"""
Compares obj1 with obj2.
:param obj1: Left hand side obejct.
:param constraint_type: Keyword (See cvxpy.defs.).
:param obj2: Right hand side object.
"""
# 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, constraint_type, 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_ar = cvxpy_array(m, n)
for i in range(0, m, 1):
for j in range(0, n, 1):
new_ar[i, j] = obj2
obj2 = new_ar
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_ar = cvxpy_array(m, n)
for i in range(0, m, 1):
for j in range(0, n, 1):
new_ar[i, j] = obj1
obj1 = new_ar
# 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], constraint_type, obj2[i, j])]
return cvxpy_list(constr)
# Invalid arguments
raise TypeError('Objects not comparable')
def compare(obj1,constraint_type,obj2):
"""
Compares obj1 with obj2.
:param obj1: Left hand side obejct.
:param constraint_type: Keyword (See cvxpy.defs.).
:param obj2: Right hand side object.
"""
# 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,constraint_type,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_ar = cvxpy_array(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
new_ar[i,j] = obj2
obj2 = new_ar
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_ar = cvxpy_array(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
new_ar[i,j] = obj1
obj1 = new_ar
# 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],constraint_type,obj2[i,j])]
return cvxpy_list(constr)
# Invalid arguments
raise TypeError('Objects not comparable')
def sqrt(x):
"""
| :math:`\mbox{sqrt} :
\mathbb{R}_+^{m \\times n} \\to \mathbb{R}^{m \\times n},
\ \mbox{sqrt}(X)_{ij} = \sqrt{X_{ij}}`.
| Concave and increasing.
:param x: number,
:ref:`scalar object<scalar_ref>` or
:ref:`multidimensional object<multi_ref>`.
:return: number,
:ref:`tree<tree_obj>`,
:ref:`matrix<matrix_obj>` or
:ref:`array<array_obj>`.
"""
# Prepare input
if (np.isscalar(x) or
type(x).__name__ in SCALAR_OBJS):
arg = vstack([x])
elif (type(x) is cvxpy_matrix or
type(x).__name__ in ARRAY_OBJS):
arg = x
else:
raise TypeError('Invalid argument')
# Prepare output
if type(arg) is cvxpy_matrix:
output = zeros(arg.shape)
else:
output = cvxpy_array(arg.shape[0],arg.shape[1])
# Construct program
for i in range(0,arg.shape[0],1):
for j in range(0,arg.shape[1],1):
t = variable()
z = variable()
v = variable()
p = program(maximize(t),
[belongs(vstack((hstack((1.,t)),
hstack((t,v)))),
semidefinite_cone),
greater_equals(z,v)],
[z],
name='sqrt')
output[i,j] = p(arg[i,j])
# Return output
if output.shape == (1,1):
return output[0,0]
else:
return output
def log_norm_cdf(x):
"""
| :math:`\mbox{log\_norm\_cdf} :
\mathbb{R}^{m \\times n} \\to \mathbb{R}^{m \\times n},
\ \mbox{log\_norm\_cdf}(X)_{ij} =
\mbox{log} \\big(
\int_{-\infty}^{X_{ij}} \\frac{1}{\sqrt{2\pi}}
e^{-\\frac{1}{2}u^2} \mathrm{d}u \\big)`.
| Concave and increasing.
:param x: number,
:ref:`scalar object<scalar_ref>` or
:ref:`multidimensional object<multi_ref>`.
:return: number,
:ref:`tree<tree_obj>`,
:ref:`matrix<matrix_obj>` or
:ref:`array<array_obj>`.
"""
# Prepare input
if (np.isscalar(x) or type(x).__name__ in SCALAR_OBJS):
arg = vstack([x])
elif (type(x) is cvxpy_matrix or type(x).__name__ in ARRAY_OBJS):
arg = x
else:
raise TypeError('Invalid argument')
# Prepare output
if type(arg) is cvxpy_matrix:
output = zeros(arg.shape)
else:
output = cvxpy_array(arg.shape[0], arg.shape[1])
# Construct program
for i in range(0, arg.shape[0], 1):
for j in range(0, arg.shape[1], 1):
t = variable()
v = variable()
z = variable()
p = program(maximize(t), [
belongs(vstack((v, t)), log_norm_cdf_hypo),
less_equals(v, z)
], [z],
name='log_norm_cdf')
output[i, j] = p(arg[i, j])
# Return output
if output.shape == (1, 1):
return output[0, 0]
else:
return output
def sqrt(x):
"""
| :math:`\mbox{sqrt} :
\mathbb{R}_+^{m \\times n} \\to \mathbb{R}^{m \\times n},
\ \mbox{sqrt}(X)_{ij} = \sqrt{X_{ij}}`.
| Concave and increasing.
:param x: number,
:ref:`scalar object<scalar_ref>` or
:ref:`multidimensional object<multi_ref>`.
:return: number,
:ref:`tree<tree_obj>`,
:ref:`matrix<matrix_obj>` or
:ref:`array<array_obj>`.
"""
# Prepare input
if (np.isscalar(x) or type(x).__name__ in SCALAR_OBJS):
arg = vstack([x])
elif (type(x) is cvxpy_matrix or type(x).__name__ in ARRAY_OBJS):
arg = x
else:
raise TypeError('Invalid argument')
# Prepare output
if type(arg) is cvxpy_matrix:
output = zeros(arg.shape)
else:
output = cvxpy_array(arg.shape[0], arg.shape[1])
# Construct program
for i in range(0, arg.shape[0], 1):
for j in range(0, arg.shape[1], 1):
t = variable()
z = variable()
v = variable()
p = program(maximize(t), [
belongs(vstack((hstack((1., t)), hstack(
(t, v)))), semidefinite_cone),
greater_equals(z, v)
], [z],
name='sqrt')
output[i, j] = p(arg[i, j])
# Return output
if output.shape == (1, 1):
return output[0, 0]
else:
return output
def dub_step(x):
#print 'input: ', x
#print 'input.value: ', x.value
#
# Prepare input
if (np.isscalar(x) or
type(x).__name__ in SCALAR_OBJS):
arg = vstack([x])
elif (type(x) is cvxpy_matrix or
type(x).__name__ in ARRAY_OBJS):
arg = x
else:
raise TypeError('Invalid argument')
# Prepare output
if type(arg) is cvxpy_matrix:
output = zeros(arg.shape)
else:
output = cvxpy_array(arg.shape[0],arg.shape[1])
# helper parameter
p = parameter(name = 'p')
# Construct program
for i in range(0,arg.shape[0],1):
for j in range(0,arg.shape[1],1):
t = variable()
v = variable()
p = program(minimize(t),
[less_equals(v,t),less_equals(-t,v)],
[v],
name='abs')
output[i,j] = p(arg[i,j])
"""
print 'arg[0,0]: ', arg[0,0]
print 'arg[0,0].value: ', arg[0,0].value
if arg[0,0].value >= 0:
p.value = 1
output[i,j] = p
else:
p.value = -1
output[i,j] = p
"""
# Return output
if output.shape == (1,1):
return output[0,0]
else:
return output
def abs(x):
"""
| :math:`\mbox{abs} :
\mathbb{R}^{m \\times n} \\to \mathbb{R}^{m \\times n},
\ \mbox{abs}(X)_{ij} = |X_{ij}|`.
| Convex.
:param x: number,
:ref:`scalar object<scalar_ref>` or
:ref:`multidimensional object<multi_ref>`.
:return: number,
:ref:`tree<tree_obj>`,
:ref:`matrix<matrix_obj>` or
:ref:`array<array_obj>`.
"""
# Prepare input
if (np.isscalar(x) or
type(x).__name__ in SCALAR_OBJS):
arg = vstack([x])
elif (type(x) is cvxpy_matrix or
type(x).__name__ in ARRAY_OBJS):
arg = x
else:
raise TypeError('Invalid argument')
# Prepare output
if type(arg) is cvxpy_matrix:
output = zeros(arg.shape)
else:
output = cvxpy_array(arg.shape[0],arg.shape[1])
# Construct program
for i in range(0,arg.shape[0],1):
for j in range(0,arg.shape[1],1):
t = variable()
v = variable()
p = program(minimize(t),
[less_equals(v,t),less_equals(-t,v)],
[v],
name='abs')
output[i,j] = p(arg[i,j])
# Return output
if output.shape == (1,1):
return output[0,0]
else:
return output
def dub_step(x):
#print 'input: ', x
#print 'input.value: ', x.value
#
# Prepare input
if (np.isscalar(x) or type(x).__name__ in SCALAR_OBJS):
arg = vstack([x])
elif (type(x) is cvxpy_matrix or type(x).__name__ in ARRAY_OBJS):
arg = x
else:
raise TypeError('Invalid argument')
# Prepare output
if type(arg) is cvxpy_matrix:
output = zeros(arg.shape)
else:
output = cvxpy_array(arg.shape[0], arg.shape[1])
# helper parameter
p = parameter(name='p')
# Construct program
for i in range(0, arg.shape[0], 1):
for j in range(0, arg.shape[1], 1):
t = variable()
v = variable()
p = program(
minimize(t),
[less_equals(v, t), less_equals(-t, v)], [v],
name='abs')
output[i, j] = p(arg[i, j])
"""
print 'arg[0,0]: ', arg[0,0]
print 'arg[0,0].value: ', arg[0,0].value
if arg[0,0].value >= 0:
p.value = 1
output[i,j] = p
else:
p.value = -1
output[i,j] = p
"""
# Return output
if output.shape == (1, 1):
return output[0, 0]
else:
return output
def reshape(v, newshape):
"""
| Reshapes the array to dimensions newshape (see np.reshape)
| in FORTRAN (column-major) order.
:param v: :ref:`array<array_obj>` or
:ref:`matrix<matrix_obj>`.
:param newshape: tuple with two integers.
:return: the reshaped variable or matrix,
:ref:`array<array_obj>` or
:ref:`matrix<matrix_obj>`.
"""
# Check input
if (type(v) is cvxpy_matrix or
type(v).__name__ in ARRAY_OBJS):
pass
else:
raise TypeError('Invalid argument type')
if not (hasattr(newshape, '__iter__') and
len(newshape) == 2):
raise TypeError('Invalid argument for newshape')
# Get shape
(m,n) = v.shape
# Get new shape
(mn,nn) = newshape
if mn*nn != m*n:
raise ValueError('Output dimension size does not match input dimension')
# cvxpy matrix
if type(v) is cvxpy_matrix:
return matrix(np.reshape(v, newshape, order='F'))
# Object array
else:
new_ar = cvxpy_array(mn,nn)
for j in range(0,n,1):
for i in range(0,m,1):
k = j*m + i
new_ar[k % mn,k / mn] = v[i,j]
return new_ar
def reshape(v, newshape):
"""
| Reshapes the array to dimensions newshape (see np.reshape)
| in FORTRAN (column-major) order.
:param v: :ref:`array<array_obj>` or
:ref:`matrix<matrix_obj>`.
:param newshape: tuple with two integers.
:return: the reshaped variable or matrix,
:ref:`array<array_obj>` or
:ref:`matrix<matrix_obj>`.
"""
# Check input
if (type(v) is cvxpy_matrix or type(v).__name__ in ARRAY_OBJS):
pass
else:
raise TypeError('Invalid argument type')
if not (hasattr(newshape, '__iter__') and len(newshape) == 2):
raise TypeError('Invalid argument for newshape')
# Get shape
(m, n) = v.shape
# Get new shape
(mn, nn) = newshape
if mn * nn != m * n:
raise ValueError(
'Output dimension size does not match input dimension')
# cvxpy matrix
if type(v) is cvxpy_matrix:
return matrix(np.reshape(v, newshape, order='F'))
# Object array
else:
new_ar = cvxpy_array(mn, nn)
for j in range(0, n, 1):
for i in range(0, m, 1):
k = j * m + i
new_ar[k % mn, k / mn] = v[i, j]
return new_ar
def huber(x,M=1):
"""
| :math:`\mbox{huber} :
\mathbb{R}^{m \\times n} \\times \mathbb{R}_{++} \\to
\mathbb{R}^{m \\times n},
\ \mbox{huber}(X,M)_{ij} = \\left\{
\\begin{array}{ll}
X_{ij}^2, & |X_{ij}| \leq M \\\\
M(2|X_{ij}| - M), & |X_{ij}| > M
\\end{array} \\right.`.
| Convex.
:param x: number,
:ref:`scalar object<scalar_ref>` or
:ref:`multidimensional object<multi_ref>`.
:param M: number.
:return: number,
:ref:`tree<tree_obj>`,
:ref:`matrix<matrix_obj>` or
:ref:`array<array_obj>`.
"""
# Prepare input
if (np.isscalar(x) or
type(x).__name__ in SCALAR_OBJS):
arg = vstack([x])
elif (type(x) is cvxpy_matrix or
type(x).__name__ in ARRAY_OBJS):
arg = x
else:
raise TypeError('Invalid first argument')
# M must be a positive constant
if not np.isscalar(M):
raise TypeError('Invalid second argument')
if M <= 0:
raise ValueError('Second argument must be positive')
# Prepare output
if type(arg) is cvxpy_matrix:
output = zeros(arg.shape)
else:
output = cvxpy_array(arg.shape[0],arg.shape[1])
# Construct program
for i in range(0,arg.shape[0],1):
for j in range(0,arg.shape[1],1):
v = variable()
w = variable()
z = variable()
p = program(minimize(2*v+square(w)),
[less_equals(abs(z),w+v),
greater_equals(v,0),
greater_equals(w,0),
less_equals(w,1)],
[z],
name='huber')
output[i,j] = (M**2.)*p((1./(M*1.))*arg[i,j])
# Return output
if output.shape == (1,1):
return output[0,0]
else:
return output
def __mulhandle__(self,other):
"""
Handles left and right multiply.
Important: If other is a constant, the multiplication
tree formed has the constant object as the first child.
:param other: Other operand.
"""
# Create operator
operator = cvxpy_obj(OPERATOR,np.NaN,MULTIPLICATION)
# 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 == SUMMATION):
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 == MULTIPLICATION and
self.children[0].type == CONSTANT):
new_object = other*self.children[0]
if new_object.value == 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.value*other,
str(self.value*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,n) = other.shape
new_ar = cvxpy_array(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
new_ar[i,j] = other[i,j]*self
return new_ar
# Sparse matrix
elif type(other) is cvxpy_spmatrix:
(m,n) = other.shape
new_ar = cvxpy_sparray(m,n)
for i in range(0,m,1):
rowi_indeces = other.rows[i]
rowi_values = other.data[i]
for k in range(0,len(rowi_indeces)):
new_ar[i,rowi_indeces[k]] = rowi_values[k]*self
return new_ar
# Scalar param
elif type(other) is cvxpy_scalar_param:
return cvxpy_tree(operator,[other,self])
# Tree
elif type(other) is cvxpy_tree:
if not len(self.variables):
return cvxpy_tree(operator,[self,other])
elif not len(other.variables):
return cvxpy_tree(operator,[other,self])
else:
return NotImplemented
# Not implemented
else:
return NotImplemented
def vstack(seq):
"""
| Stacks objects vertically.
:param seq: tuple or list of numbers,
:ref:`scalar objects<scalar_ref>` or
:ref:`multidimensional objects<multi_ref>`.
:return: :ref:`array<array_obj>` or
:ref:`matrix<matrix_obj>`.
"""
# Check input
if (type(seq) is not tuple and
type(seq) is not list):
raise TypeError('Invalid argument')
# Process input
new_list = []
numeric = True
for x in seq:
if np.isscalar(x):
new_list += [matrix(x)]
elif type(x) is cvxpy_obj:
new_list += [matrix(x.value)]
elif type(x).__name__ in SCALAR_OBJS:
numeric = False
new_x = cvxpy_array(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 TypeError('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 array
m = int(np.sum([x.shape[0] for x in new_list]))
new_ar = cvxpy_array(m,n)
# Fill new array
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_ar[i+k,j] = x[i,j]
k = k + x.shape[0]
# Return new array
return new_ar
def __raddsub__(self,other,op):
"""
Handles right add and right subtract.
:param other: Left hand side.
:param op: Keyword (See cvxpy.defs)
"""
# Create operator
operator = cvxpy_obj(OPERATOR,np.NaN,SUMMATION)
# Create args to combine
if (type(self) is cvxpy_tree and
self.item.name == SUMMATION):
if op == SUMMATION:
args = self.children
else:
args = [-x for x in self.children]
else:
if op == SUMMATION:
args = [self]
else:
args = [-self]
# Number
if np.isscalar(other):
if other == 0.0:
if op == SUMMATION:
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 == SUMMATION:
return cvxpy_tree(operator,other.children+args)
else:
return cvxpy_tree(operator,[other]+args)
# Matrix
elif type(other) is cvxpy_matrix:
(m,n) = other.shape
new_ar = cvxpy_array(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
if op == SUMMATION:
new_ar[i,j] = other[i,j]+self
else:
new_ar[i,j] = other[i,j]-self
return new_ar
# Not implemented
else:
return NotImplemented
def power_abs(x, p):
"""
| :math:`\mbox{power\_abs} :
\mathbb{R}^{m \\times n} \\times [1,\infty) \\to \mathbb{R}^{m \\times n},
\ \mbox{power\_abs}(X,p)_{ij} = |X_{ij}|^p`.
| Convex.
:param x: number,
:ref:`scalar object<scalar_ref>` or
:ref:`multidimensional object<multi_ref>`.
:param p: number, greater than or equal to one.
:return: number,
:ref:`tree<tree_obj>`,
:ref:`matrix<matrix_obj>` or
:ref:`array<array_obj>`.
"""
# Prepare input
if (np.isscalar(x) or type(x).__name__ in SCALAR_OBJS):
arg = vstack([x])
elif (type(x) is cvxpy_matrix or type(x).__name__ in ARRAY_OBJS):
arg = x
else:
raise TypeError('Invalid argument')
# Check p
if not (np.isscalar(p)):
raise TypeError('Invalid argument')
elif p < 1.:
raise ValueError('Invalid argument value')
# Prepare output
if type(arg) is cvxpy_matrix:
output = zeros(arg.shape)
else:
output = cvxpy_array(arg.shape[0], arg.shape[1])
# Construct program
for i in range(0, arg.shape[0], 1):
for j in range(0, arg.shape[1], 1):
t = variable()
v = variable()
z = variable()
if p > 1.:
prog = program(minimize(t), [
belongs(vstack((v, t)), power_pos_epi(p)),
less_equals(-z, v),
less_equals(z, v)
], [z],
name='power_abs')
else:
prog = program(
minimize(t),
[less_equals(z, t), less_equals(-z, t)], [z],
name='power_abs')
output[i, j] = prog(arg[i, j])
# Return output
if output.shape == (1, 1):
return output[0, 0]
else:
return output
def power_p(x,p):
"""
| :math:`\mbox{power\_p} :
\mathbb{R}^{m \\times n} \\times [1,\infty) \\to \mathbb{R}^{m \\times n},
\ \mbox{power\_p}(X,p)_{ij} = \\left\{
\\begin{array}{ll}
X_{ij}^p, & X_{ij} \geq 0 \\\\
+\infty, & X_{ij} < 0.
\\end{array} \\right.`
| Convex.
:param x: number,
:ref:`scalar object<scalar_ref>` or
:ref:`multidimensional object<multi_ref>`.
:param p: number, greater than or equal to one.
:return: number,
:ref:`tree<tree_obj>`,
:ref:`matrix<matrix_obj>` or
:ref:`array<array_obj>`.
"""
# Prepare input
if (np.isscalar(x) or
type(x).__name__ in SCALAR_OBJS):
arg = vstack([x])
elif (type(x) is cvxpy_matrix or
type(x).__name__ in ARRAY_OBJS):
arg = x
else:
raise TypeError('Invalid argument')
# Check p
if not (np.isscalar(p)):
raise TypeError('Invalid argument')
elif p < 1.:
raise ValueError('Invalid argument value')
# Prepare output
if type(arg) is cvxpy_matrix:
output = zeros(arg.shape)
else:
output = cvxpy_array(arg.shape[0],arg.shape[1])
# Construct program
for i in range(0,arg.shape[0],1):
for j in range(0,arg.shape[1],1):
t = variable()
z = variable()
if p > 1.:
prog = program(minimize(t),
[belongs(vstack((z,t)),
power_pos_epi(p)),
greater_equals(z,0)],
[z],
name='power_p')
else:
prog = program(minimize(t),
[less_equals(z,t),
greater_equals(z,0)],
[z],
name='power_p')
if np.isscalar(arg[i,j]) and arg[i,j] < 0.:
output[i,j] = np.inf
else:
output[i,j] = prog(arg[i,j])
# Return output
if output.shape == (1,1):
return output[0,0]
else:
return output
def expand(arg):
# Constant
if type(arg) is cvxpy_obj:
return arg, []
# Scalar variable
elif type(arg) is cvxpy_scalar_var:
return arg, []
# Summation
elif (type(arg) is cvxpy_tree and arg.item.type == OPERATOR
and arg.item.name == SUMMATION):
# Get item and children
item = arg.item
children = arg.children
# New variale
v = variable()
# Expand children
new_children = []
new_constr = []
for child in children:
# Multiplication
if (child.type == TREE and child.item.type == OPERATOR
and child.item.name == MULTIPLICATION):
child_var, child_constr = expand(child.children[1])
new_children += [child.children[0].value * 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, [equals(new_tree, v)] + new_constr
# Multiplication
elif (type(arg) is cvxpy_tree and arg.item.type == OPERATOR
and arg.item.name == MULTIPLICATION):
# Get item and children
item = arg.item
children = arg.children
# New variable
v = variable()
# 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 = [equals(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 varibale
v = variable()
# Analyze children
new_children = []
new_constr = []
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)
if arg.is_convex():
new_constr += [less_equals(new_tree, v)]
else:
new_constr += [greater_equals(new_tree, v)]
return v, new_constr
# Constraint
elif type(arg) is cvxpy_constr:
# Not set membership
if arg.type != BELONGS:
# 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.type, obj2)
new_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.type, arg.right)
return [new_constr] + constr_list
# Array
elif (type(arg) is cvxpy_array or type(arg) is cvxpy_var):
(m, n) = arg.shape
new_list = []
new_ar = cvxpy_array(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_ar[i, j] = cvxpy_obj(CONSTANT, arg[i, j], str(arg[i,
j]))
# Not a number
else:
obj, constr_list = expand(arg[i, j])
new_ar[i, j] = obj
new_list += constr_list
return new_ar, new_list
# List of constraints
elif (type(arg) is list or type(arg) is cvxpy_list):
return reduce(lambda x, y: x + y, list(map(expand, arg)), [])
# Invalid
else:
raise TypeError('Invalid argument')
