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optlib.py
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optlib.py
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# -*- coding: utf-8 -*-
import copy
import numpy as np
np.set_printoptions(precision=6,threshold=1e3)
from scipy.optimize import minimize
def sca_fmincon(libopt,h_d,G,f,theta,x,K2,RISON):
N=libopt.N
L=libopt.L
I=sum(x)
tau=libopt.tau
if theta is None:
theta=np.ones([L],dtype=complex)
if not RISON:
theta=np.zeros([L],dtype=complex)
result=np.zeros(libopt.nit)
h=np.zeros([N,I],dtype=complex)
for i in range(I):
h[:,i]=h_d[:,i]+G[:,:,i]@theta
if f is None:
f=h[:,0]/np.linalg.norm(h[:,0])
obj=min(np.abs(np.conjugate(f)@h)**2/K2)
threshold=libopt.threshold
for it in range(libopt.nit):
obj_pre=copy.deepcopy(obj)
a=np.zeros([N,I],dtype=complex)
b=np.zeros([L,I],dtype=complex)
c=np.zeros([1,I],dtype=complex)
F_cro=np.outer(f,np.conjugate(f));
for i in range(I):
a[:,i]=tau*K2[i]*f+np.outer(h[:,i],np.conjugate(h[:,i]))@f
if RISON:
b[:,i]=tau*K2[i]*theta+G[:,:,i].conj().T@F_cro@h[:,i]
c[:,i]=np.abs(np.conjugate(f)@h[:,i])**2+2*tau*K2[i]*(L+1)+2*np.real((theta.conj().T)@(G[:,:,i].conj().T)@F_cro@h[:,i])
else:
c[:,i]=np.abs(np.conjugate(f)@h[:,i])**2+2*tau*K2[i]
#print(c.shape)
fun=lambda mu: np.real(2*np.linalg.norm(a@mu)+2*np.linalg.norm(b@mu,ord=1)-c@mu)
cons = ({'type': 'eq', 'fun': lambda mu: K2@mu-1})
bnds=((0,None) for i in range(I))
res = minimize(fun, 1/K2, bounds=tuple(bnds), constraints=cons)
if ~res.success:
pass
#print('Iteration: {}, solution:{} obj:{:.6f}'.format(it,res.x,res.fun[0]))
#print(res.message)
#return
fn=a@res.x
thetan=b@res.x
fn=fn/np.linalg.norm(fn)
# thetan=thetan/np.abs(thetan)
if RISON:
thetan=thetan/np.abs(thetan)
theta=thetan
f=fn
for i in range(I):
h[:,i]=h_d[:,i]+G[:,:,i]@theta
obj=min(np.abs(np.conjugate(f)@h)**2/K2)
result[it]=copy.deepcopy(obj)
if libopt.verbose>2:
print(' Iteration {} Obj {:.6f} Opt Obj {:.6f}'.format(it,result[it],res.fun[0]))
if np.abs(obj-obj_pre)/min(1,abs(obj))<=threshold:
break
#print(res)
if libopt.verbose>1:
print(' SCA Take {} iterations with final obj {:.6f}'.format(it+1,result[it]))
result=result[0:it]
return f,theta,result
def find_obj_inner(libopt,x,K,K2,Ksum2,h_d,G,f0,theta0,RISON):
N=libopt.N
L=libopt.L
M=libopt.M
if sum(x)==0:
obj=np.inf
theta=np.ones([L],dtype=complex)
f=h_d[:,0]/np.linalg.norm(h_d[:,0])
if not RISON:
theta=np.zeros([L])
else:
index=(x==1)
#print(index)
f,theta,_=sca_fmincon(libopt,h_d[:,index],G[:,:,index],f0,theta0,x,K2[index],RISON)
h=np.zeros([N,M],dtype=complex)
for i in range(M):
h[:,i]=h_d[:,i]+G[:,:,i]@theta
gain=K2/(np.abs(np.conjugate(f)@h)**2)*libopt.sigma
#print(gain)
#print(gain)
#print(2/Ksum2*(sum(K[~index]))**2)
#print(np.max(gain[index])/(sum(K[index]))**2)
obj=np.max(gain[index])/(sum(K[index]))**2+4/Ksum2*(sum(K[~index]))**2
return obj,x,f,theta
def Gibbs(libopt,h_d,G,x0,RISON,Joint):
#initial
N=libopt.N
L=libopt.L
M=libopt.M
Jmax=libopt.Jmax
K=libopt.K/np.mean(libopt.K) #normalize K to speed up floating computation
K2=K**2
Ksum2=sum(K)**2
x=x0
# inital the return values
obj_new=np.zeros(Jmax+1)
f_store=np.zeros([N,Jmax+1],dtype = complex)
theta_store=np.zeros([L,Jmax+1],dtype = complex)
x_store=np.zeros([Jmax+1,M],dtype=int)
#the first loop
ind=0
[obj_new[ind],x_store[ind,:],f,theta]=find_obj_inner(libopt,x,K,K2,Ksum2,h_d,G,None,None,RISON)
theta_store[:,ind]=copy.deepcopy(theta)
f_store[:,ind]=copy.deepcopy(f)
# beta=min(max(obj_new[ind],1)
beta=min(1,obj_new[ind])
# print(beta)
alpha=0.9
if libopt.verbose>1:
print('The inital guess: {}, obj={:.6f}'.format(x,obj_new[ind]))
elif libopt.verbose==1:
print('The inital guess obj={:.6f}'.format(obj_new[ind]))
f_loop=np.tile(f,(M+1,1))
theta_loop=np.tile(theta,(M+1,1))
#print(theta_loop.shape)
#print(theta_loop[0].shape)
for j in range(Jmax):
if libopt.verbose>1:
print('This is the {}-th Gibbs sampling iteration, beta= {:.6f}'.format(j+1,beta));
#store the possible transition solution and their objectives
X_sample=np.zeros([M+1,M],dtype=int)
Temp=np.zeros(M+1)
#the first transition => no change
X_sample[0,:]=copy.deepcopy(x)
Temp[0]=copy.deepcopy(obj_new[ind])
f_loop[0]=copy.deepcopy(f)
theta_loop[0]=copy.deepcopy(theta)
#2--M+1-th trnasition, change only 1 position
for m in range(M):
if libopt.verbose>1:
print('the {}-th:'.format(m+1))
#filp the m-th position
x_sam=copy.deepcopy(x)
x_sam[m]=copy.deepcopy((x_sam[m]+1)%2)
X_sample[m+1,:]=copy.deepcopy(x_sam);
Temp[m+1],_,f_loop[m+1],theta_loop[m+1]=find_obj_inner(libopt,
x_sam,K,K2,Ksum2,h_d,G,f_loop[m+1],theta_loop[m+1],RISON)
if libopt.verbose>1:
print(' sol:{} with obj={:.6f}'.format(x_sam,Temp[m+1]))
temp2=Temp;
Lambda=np.exp(-1*temp2/beta);
Lambda=Lambda/sum(Lambda);
while np.isnan(Lambda).any():
if libopt.verbose>1:
print('There is NaN, increase beta')
beta=beta/alpha;
Lambda=np.exp(-1.*temp2/beta);
Lambda=Lambda/sum(Lambda);
if libopt.verbose>1:
print('The obj distribution: {}'.format(temp2))
print('The Lambda distribution: {}'.format(Lambda))
kk_prime=np.random.choice(M+1,p=Lambda)
x=copy.deepcopy(X_sample[kk_prime,:])
f=copy.deepcopy(f_loop[kk_prime])
theta=copy.deepcopy(theta_loop[kk_prime])
ind=ind+1
obj_new[ind]=copy.deepcopy(Temp[kk_prime])
x_store[ind,:]=copy.deepcopy(x)
theta_store[:,ind]=copy.deepcopy(theta)
f_store[:,ind]=copy.deepcopy(f)
if libopt.verbose>1:
print('Choose the solution {}, with objective {:.6f}'.format(x,obj_new[ind]))
if libopt.verbose:
print('This is the {}-th Gibbs sampling iteration, beta= {:.6f},obj={:.6f}'.format(j+1,beta,obj_new[ind]));
beta=max(alpha*beta,1e-4);
return x_store,obj_new,f_store,theta_store