def _pm_expand(self, constr):
# Get objects
v = constr.left
v = vstack([v[i, 0] for i in range(0, v.shape[0])])
n = v.shape[0] - 1
x = vstack([v[0:n, 0]])
y = v[n, 0]
z = variable()
# One element
if n == 1:
return cvxpy_list([greater_equals(x, 0), greater_equals(x, y)])
# Get power of 2 size
m = 0
while np.log2(n + m) % 1 != 0:
m += 1
# Copy elements of x on a list and restrict them
constr_list = []
el_list = []
for i in range(0, n, 1):
el_list += [x[i, 0]]
if (not np.isscalar(x[i, 0]) and type(x[i, 0]) is not cvxpy_obj):
constr_list += [greater_equals(x[i, 0], 0)]
# Construct expansion
for i in range(0, m, 1):
el_list += [z]
while len(el_list) > 2:
new_list = []
for i in range(0, int(len(el_list) / 2)):
x1 = el_list[2 * i]
x2 = el_list[2 * i + 1]
w = variable()
constr_list += [
belongs(vstack((hstack((x1, w)), hstack((w, x2)))),
semidefinite_cone)
]
new_list += [w]
el_list = new_list
x1 = el_list[0]
x2 = el_list[1]
constr_list += [
belongs(vstack((hstack((x1, z)), hstack((z, x2)))),
semidefinite_cone)
]
constr_list += [greater_equals(z, 0), greater_equals(z, y)]
return cvxpy_list(constr_list)
def _pm_expand(self,constr):
# Get objects
v = constr.left
v = vstack([v[i,0] for i in range(0,v.shape[0])])
n = v.shape[0]-1
x = vstack([v[0:n,0]])
y = v[n,0]
z = variable()
# One element
if n==1:
return cvxpy_list([greater_equals(x,0),
greater_equals(x,y)])
# Get power of 2 size
m = 0
while np.log2(n+m) % 1 != 0:
m += 1
# Copy elements of x on a list and restrict them
constr_list = []
el_list = []
for i in range(0,n,1):
el_list+=[x[i,0]]
if (not np.isscalar(x[i,0]) and
type(x[i,0]) is not cvxpy_obj):
constr_list += [greater_equals(x[i,0],0)]
# Construct expansion
for i in range(0,m,1):
el_list += [z]
while len(el_list) > 2:
new_list = []
for i in range(0,int(len(el_list)/2)):
x1 = el_list[2*i]
x2 = el_list[2*i+1]
w = variable()
constr_list += [belongs(vstack((hstack((x1,w)),
hstack((w,x2)))),
semidefinite_cone)]
new_list += [w]
el_list = new_list
x1 = el_list[0]
x2 = el_list[1]
constr_list += [belongs(vstack((hstack((x1,z)),
hstack((z,x2)))),
semidefinite_cone)]
constr_list += [greater_equals(z,0),greater_equals(z,y)]
return cvxpy_list(constr_list)
def _pm_expand(self,constr):
# Get shape
v = constr.left
n = v.shape[0]-1
x = v[0:n,0]
y = v[n,0]
z = var()
# Get power of 2 size
m = 0
while (np.log2(n+m) % 1 != 0):
m = m + 1
# Copy elements of x on a list and restrict them
constr_list = []
el_list = []
for i in range(0,n,1):
el_list+=[x[i,0]]
if(not np.isscalar(x[i,0]) and
type(x[i,0]) is not cvxpy_obj):
constr_list += [greater(x[i,0],0)]
# Construct expansion
z = var()
for i in range(0,m,1):
el_list += [z]
while(len(el_list) > 2):
new_list = []
for i in range(0,len(el_list)/2):
x1 = el_list[2*i]
x2 = el_list[2*i+1]
w = var()
constr_list += [belongs(vstack((hstack((x1,w)),
hstack((w,x2)))),
sdc(2))]
new_list += [w]
el_list = new_list
x1 = el_list[0]
x2 = el_list[1]
constr_list += [belongs(vstack((hstack((x1,z)),
hstack((z,x2)))),
sdc(2))]
constr_list += [greater(z,0),greater(z,y)]
return cvxpy_list(constr_list)
def _pm_expand(self, constr):
# Get shape
v = constr.left
n = v.shape[0] - 1
x = v[0:n, 0]
y = v[n, 0]
z = var()
# Get power of 2 size
m = 0
while np.log2(n + m) % 1 != 0:
m = m + 1
# Copy elements of x on a list and restrict them
constr_list = []
el_list = []
for i in range(0, n, 1):
el_list += [x[i, 0]]
if not np.isscalar(x[i, 0]) and type(x[i, 0]) is not cvxpy_obj:
constr_list += [greater(x[i, 0], 0)]
# Construct expansion
z = var()
for i in range(0, m, 1):
el_list += [z]
while len(el_list) > 2:
new_list = []
for i in range(0, len(el_list) / 2):
x1 = el_list[2 * i]
x2 = el_list[2 * i + 1]
w = var()
constr_list += [belongs(vstack((hstack((x1, w)), hstack((w, x2)))), sdc(2))]
new_list += [w]
el_list = new_list
x1 = el_list[0]
x2 = el_list[1]
constr_list += [belongs(vstack((hstack((x1, z)), hstack((z, x2)))), sdc(2))]
constr_list += [greater(z, 0), greater(z, y)]
return cvxpy_list(constr_list)
def _linearize(self, args, t2):
"""
Description
-----------
Form linear underestimator or linear
overestimator of the function depeniding
on whether the program represents a convex
or concave function.
Arguments
---------
args: list of arguments
t2: variable of right hand side
"""
x = vstack(args)
x0 = x.get_value()
f_x0 = self._solve_isolating(x0)
lagrange = self.lagrange_mul_eq[0:len(args), 0]
if (self.curvature == CONVEX):
return t2 - (f_x0 - lagrange.T * (x - x0))
else:
return (f_x0 + lagrange.T * (x - x0)) - t2
def _linearize(self,args,t2):
"""
Description
-----------
Form linear underestimator or linear
overestimator of the function depeniding
on whether the program represents a convex
or concave function.
Arguments
---------
args: list of arguments
t2: variable of right hand side
"""
x = vstack(args)
x0 = x.get_value()
f_x0 = self._solve_isolating(x0)
lagrange = self.lagrange_mul_eq[0:len(args),0]
if(self.curvature == CONVEX):
return t2 - (f_x0 - lagrange.T*(x-x0))
else:
return (f_x0 + lagrange.T*(x-x0)) - t2
def _construct(self, el, mp, p):
n = el.shape[0] - 1
u = vstack([el[0:n, 0]])
v = el[n, 0]
# Prepare u
for i in range(0, n, 1):
if type(u[i, 0]) is cvxpy_obj:
u[i, 0] = u[i, 0].value
# Prepare v
if type(v) is cvxpy_obj:
v = v.value
# f
def f(x):
vals = []
for i in range(0, n, 1):
if type(u[i, 0]) is cvxpy_scalar_var:
vals += [x[mp[u[i, 0]]]]
else:
vals += [u[i, 0]]
if type(v) is cvxpy_scalar_var:
y = x[mp[v]]
else:
y = v
return y - reduce(lambda w, z: w * z, vals, 1.)**(1. / (n * 1.))
# grad f
def grad_f(x):
g = opt.spmatrix(0.0, [], [], (p, 1))
if type(v) is cvxpy_scalar_var:
fval = -f(x) + x[mp[v]]
else:
fval = -f(x) + v
for i in range(0, n, 1):
if type(u[i, 0]) is cvxpy_scalar_var:
xi = x[mp[u[i, 0]]]
g[mp[u[i, 0]]] = -fval / (n * xi * 1.)
if type(v) is cvxpy_scalar_var:
g[mp[v]] = 1.
return g
# hess f
def hess_f(x):
h = opt.spmatrix(0.0, [], [], (p, p))
if type(v) is cvxpy_scalar_var:
fval = -f(x) + x[mp[v]]
else:
fval = -f(x) + v
for i in range(0, n, 1):
for j in range(0, n, 1):
if (type(u[i, 0]) is cvxpy_scalar_var
and type(u[j, 0]) is cvxpy_scalar_var):
xi = x[mp[u[i, 0]]]
xj = x[mp[u[j, 0]]]
if i == j:
w = (n - 1.) * fval / (n * n * 1. * xi * xi)
h[mp[u[i, 0]], mp[u[i, 0]]] = w
else:
w = -fval / (1. * n * n * xi * xj)
h[mp[u[i, 0]], mp[u[j, 0]]] = w
h[mp[u[j, 0]], mp[u[i, 0]]] = w
return h
# ind f
def ind_f(x):
for i in range(0, n, 1):
if type(u[i, 0]) is cvxpy_scalar_var:
if x[mp[u[i, 0]]] <= 0:
return False
else:
if u[i, 0] <= 0:
return False
return True
# Return functions
return f, grad_f, hess_f, ind_f
def _construct(self, el, mp, p):
n = int((el.shape[0] - 1.) / 2.)
u = vstack([el[0:n, 0]])
v = vstack([el[n:2 * n, 0]])
t = el[2 * n, 0]
# Prepare u and v
for i in range(0, n):
if type(u[i, 0]) is cvxpy_obj:
u[i, 0] = u[i, 0].value
if type(v[i, 0]) is cvxpy_obj:
v[i, 0] = v[i, 0].value
# Prepare t
if type(t) is cvxpy_obj:
t = t.value
# f
def f(x):
temp = 0
for i in range(0, n):
if type(u[i, 0]) is cvxpy_scalar_var:
u_i = x[mp[u[i, 0]]]
else:
u_i = u[i, 0]
if type(v[i, 0]) is cvxpy_scalar_var:
v_i = x[mp[v[i, 0]]]
else:
v_i = v[i, 0]
temp += u_i * np.log(u_i * 1. / v_i) - u_i + v_i
if type(t) is cvxpy_scalar_var:
return temp - x[mp[t]]
else:
return temp - t
# grad f
def grad_f(x):
g = opt.spmatrix(0.0, [], [], (p, 1))
for i in range(0, n):
if type(u[i, 0]) is cvxpy_scalar_var:
u_i = x[mp[u[i, 0]]]
else:
u_i = u[i, 0]
if type(v[i, 0]) is cvxpy_scalar_var:
v_i = x[mp[v[i, 0]]]
else:
v_i = v[i, 0]
if type(u[i, 0]) is cvxpy_scalar_var:
g[mp[u[i, 0]]] = np.log(u_i * 1. / v_i)
if type(v[i, 0]) is cvxpy_scalar_var:
g[mp[v[i, 0]]] = (-u_i * 1. / v_i) + 1.
if type(t) is cvxpy_scalar_var:
g[mp[t]] = -1.
return g
# hess f
def hess_f(x):
h = opt.spmatrix(0.0, [], [], (p, p))
for i in range(0, n):
if type(u[i, 0]) is cvxpy_scalar_var:
u_i = x[mp[u[i, 0]]]
else:
u_i = u[i, 0]
if type(v[i, 0]) is cvxpy_scalar_var:
v_i = x[mp[v[i, 0]]]
else:
v_i = v[i, 0]
if type(u[i, 0]) is cvxpy_scalar_var:
h[mp[u[i, 0]], mp[u[i, 0]]] = 1. / u_i
if type(v[i, 0]) is cvxpy_scalar_var:
h[mp[v[i, 0]], mp[v[i, 0]]] = u_i * 1. / (v_i**2.)
if (type(u[i, 0]) is cvxpy_scalar_var
and type(v[i, 0]) is cvxpy_scalar_var):
w = -1. / v_i
h[mp[u[i, 0]], mp[v[i, 0]]] = w
h[mp[v[i, 0]], mp[u[i, 0]]] = w
return h
# ind f
def ind_f(x):
for i in range(0, n):
if type(u[i, 0]) is cvxpy_scalar_var:
if x[mp[u[i, 0]]] <= 0:
return False
else:
if u[i, 0] <= 0:
return False
if type(v[i, 0]) is cvxpy_scalar_var:
if x[mp[v[i, 0]]] <= 0:
return False
else:
if v[i, 0] <= 0:
return False
return True
# Return functions
return f, grad_f, hess_f, ind_f
def _construct(self,el,mp,p):
n = int((el.shape[0]-1.)/2.)
u = vstack([el[0:n,0]])
v = vstack([el[n:2*n,0]])
t = el[2*n,0]
# Prepare u and v
for i in range(0,n):
if type(u[i,0]) is cvxpy_obj:
u[i,0] = u[i,0].value
if type(v[i,0]) is cvxpy_obj:
v[i,0] = v[i,0].value
# Prepare t
if type(t) is cvxpy_obj:
t = t.value
# f
def f(x):
temp = 0
for i in range(0,n):
if type(u[i,0]) is cvxpy_scalar_var:
u_i = x[mp[u[i,0]]]
else:
u_i = u[i,0]
if type(v[i,0]) is cvxpy_scalar_var:
v_i = x[mp[v[i,0]]]
else:
v_i = v[i,0]
temp += u_i*np.log(u_i*1./v_i)-u_i+v_i
if type(t) is cvxpy_scalar_var:
return temp - x[mp[t]]
else:
return temp - t
# grad f
def grad_f(x):
g = opt.spmatrix(0.0,[],[],(p,1))
for i in range(0,n):
if type(u[i,0]) is cvxpy_scalar_var:
u_i = x[mp[u[i,0]]]
else:
u_i = u[i,0]
if type(v[i,0]) is cvxpy_scalar_var:
v_i = x[mp[v[i,0]]]
else:
v_i = v[i,0]
if type(u[i,0]) is cvxpy_scalar_var:
g[mp[u[i,0]]] = np.log(u_i*1./v_i)
if type(v[i,0]) is cvxpy_scalar_var:
g[mp[v[i,0]]] = (-u_i*1./v_i)+1.
if type(t) is cvxpy_scalar_var:
g[mp[t]] = -1.
return g
# hess f
def hess_f(x):
h = opt.spmatrix(0.0,[],[],(p,p))
for i in range(0,n):
if type(u[i,0]) is cvxpy_scalar_var:
u_i = x[mp[u[i,0]]]
else:
u_i = u[i,0]
if type(v[i,0]) is cvxpy_scalar_var:
v_i = x[mp[v[i,0]]]
else:
v_i = v[i,0]
if type(u[i,0]) is cvxpy_scalar_var:
h[mp[u[i,0]],mp[u[i,0]]] = 1./u_i
if type(v[i,0]) is cvxpy_scalar_var:
h[mp[v[i,0]],mp[v[i,0]]] = u_i*1./(v_i**2.)
if (type(u[i,0]) is cvxpy_scalar_var and
type(v[i,0]) is cvxpy_scalar_var):
w = -1./v_i
h[mp[u[i,0]],mp[v[i,0]]] = w
h[mp[v[i,0]],mp[u[i,0]]] = w
return h
# ind f
def ind_f(x):
for i in range(0,n):
if type(u[i,0]) is cvxpy_scalar_var:
if x[mp[u[i,0]]] <= 0:
return False
else:
if u[i,0] <= 0:
return False
if type(v[i,0]) is cvxpy_scalar_var:
if x[mp[v[i,0]]] <= 0:
return False
else:
if v[i,0] <= 0:
return False
return True
# Return functions
return f, grad_f, hess_f, ind_f
def _construct(self,el,mp,p):
n = el.shape[0]-1
u = vstack([el[0:n,0]])
v = el[n,0]
# Prepare u
for i in range(0,n,1):
if type(u[i,0]) is cvxpy_obj:
u[i,0] = u[i,0].value
# Prepare v
if type(v) is cvxpy_obj:
v = v.value
# f
def f(x):
vals = []
for i in range(0,n,1):
if type(u[i,0]) is cvxpy_scalar_var:
vals += [x[mp[u[i,0]]]]
else:
vals += [u[i,0]]
if type(v) is cvxpy_scalar_var:
y = x[mp[v]]
else:
y = v
return y - reduce(lambda w,z:w*z,vals,1.)**(1./(n*1.))
# grad f
def grad_f(x):
g = opt.spmatrix(0.0,[],[],(p,1))
if type(v) is cvxpy_scalar_var:
fval = -f(x)+x[mp[v]]
else:
fval = -f(x)+v
for i in range(0,n,1):
if type(u[i,0]) is cvxpy_scalar_var:
xi = x[mp[u[i,0]]]
g[mp[u[i,0]]] = -fval/(n*xi*1.)
if type(v) is cvxpy_scalar_var:
g[mp[v]] = 1.
return g
# hess f
def hess_f(x):
h = opt.spmatrix(0.0,[],[],(p,p))
if type(v) is cvxpy_scalar_var:
fval = -f(x)+x[mp[v]]
else:
fval = -f(x)+v
for i in range(0,n,1):
for j in range(0,n,1):
if (type(u[i,0]) is cvxpy_scalar_var and
type(u[j,0]) is cvxpy_scalar_var):
xi = x[mp[u[i,0]]]
xj = x[mp[u[j,0]]]
if i == j:
w = (n-1.)*fval/(n*n*1.*xi*xi)
h[mp[u[i,0]],mp[u[i,0]]] = w
else:
w = -fval/(1.*n*n*xi*xj)
h[mp[u[i,0]],mp[u[j,0]]] = w
h[mp[u[j,0]],mp[u[i,0]]] = w
return h
# ind f
def ind_f(x):
for i in range(0,n,1):
if type(u[i,0]) is cvxpy_scalar_var:
if x[mp[u[i,0]]] <= 0:
return False
else:
if u[i,0] <= 0:
return False
return True
# Return functions
return f, grad_f, hess_f, ind_f