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Copy pathBaMSOO_1D.py
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BaMSOO_1D.py
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from math import *
import numpy as np
import sys
#sys.setrecursionlimit(1000)
import matplotlib.pyplot as plt
from numpy import linalg as LA
from numpy.linalg import inv
#from interval import interval, inf, imath
# function need to be optimized
#x = np.linspace(0,1,100) # 100 linearly spaced numbers
#y = (np.sin(13*x)*np.sin(27*x)+1)/2 # computing the values of sin(x)/x
def gland_function(x):
y=x*(1-x)*(4-np.sqrt(abs(np.sin(60*x))))
return y
def function(x):
y = (np.sin(13*x)*np.sin(27*x)+1)/2.0
return y
def mini(x,y):
if x<=y:
return x
else:
return y
def split(x1left,x1right,x2left,x2right):
left_mid=x1left+x1right/2.0
right_mid=x2left+x2right/2.0
def midpoint(p1, p2):
mid=(p1+p2)/2.0
return mid
def tree_depth(node):
dep=[]
print "node len:",len(node)
for i in range(len(node)):
dep.append(node[i].depth)
dindex=np.argmax(dep)
return dep[dindex]
def Branin_function(x1,x2):
y=-((x2-(5.1/(4*(np.pi)**2))*x1**2+(5/np.pi)*x1-6)**2+10*(1-1/(8*np.pi))*np.cos(x1)+10)
return y
def kernel_calculation(idtr,xtr,xte):
ktr=np.zeros((idtr,idtr))
ktr_new=np.matrix(ktr)
kte=np.zeros((1,idtr))
kte_new=np.matrix(kte)
#kte_train=np.zeros((idtr,idtr))
#kte_test=np.zeros((idtr_l,idtr_l))
#kte_kte=np.zeros((idtr,idtr_l))
### training kernel matrix calculation
for i in range(0,idtr):
for j in range(i,idtr):
#ktr_new[i,j]=exp(-0.5*0.03*LA.norm(xtr[:,i]-xtr[:,j])**2)
ktr_new[i,j]=(1+np.sqrt((5*LA.norm(xtr[:,i]-xtr[:,j])**2)/0.15)+
5*LA.norm(xtr[:,i]-xtr[:,j])**2/(3*0.15))*np.exp(-(np.sqrt(5*LA.norm(xtr[:,i]-xtr[:,j])**2)/0.15))
#print ktr[i,j]
#ktr_new[j,i]=ktr_new[i,j]
for i in range(1):
for j in range(0,idtr):
#kte_new[i,j]=exp(-0.5*0.03*(xte[:,i]-xtr[:,j])**2)
kte_new[i,j]=(1+np.sqrt((5*LA.norm(xte[:,i]-xtr[:,j])**2)/0.15)+
5*LA.norm(xte[:,i]-xtr[:,j])**2/(3*0.15))*np.exp(-np.sqrt((5*LA.norm(xte[:,i]-xtr[:,j])**2)/0.15))
#print kte_new.shape
return ktr_new,kte_new
class Node:
def __init__(self, center=None, value=None, depth=None,leftmin=None, rightmax=None, parent = None):
self.parentNode = parent
self.childNodes = []
self.center=center
self.value=value
self.depth=depth
self.leftmin=leftmin
self.rightmax=rightmax
def Selectnode(self,node,h):
leaves_of_depth=[]
index=[]
value=[]
for i in range(len(node)):
if node[i].depth==h:
leaves_of_depth.append(node[i])
index.append(i)
for i in range(len(leaves_of_depth)):
value.append(leaves_of_depth[i].value)
#print value
new_index=np.argmax(value)
#print new_index
#hi=node[index[new_index]].center
#fh=function(hi)
#print hi
#print fh
fh=node[index[new_index]].value
#print "function value:",fh
#gl=function(node[index[new_index]].center)
#print gl
#function_evalution.append(fh)
return node[index[new_index]],index[new_index],fh
def Addnode(self,center_value,value, depth,leftmargin,rightmargin):
n = Node(center=center_value,value=value, depth=depth, leftmin=leftmargin,rightmax=rightmargin, parent = self)
self.childNodes.append(n)
return n
def SOO():
"""set g(0,0)=f(x(0,0))"""
ini_f=float("-inf")
g_function=function(0.5)
"""set f^=g(0,0)"""
f_t=g_function
"""initialize the tree"""
rootnode = Node(center=0.5, value=g_function,depth=0,leftmin=0, rightmax=1)
"""set t=1,n=1,N=1 and D_t={(x00,g00)}"""
t=1 ## represent the number of sampled data
n=1 ## represent the iteration of the algorithm
N=1 ## represent the number of GP calculation
D_x_train=np.array([0.5])
D_y_train=np.array([g_function])
current_node=[]
current_node.append(rootnode)
#print current_node[0].center
node=rootnode
leaf=[]
final=[]
function_evalution=[]
t=1
h_tree=0
#ini_f=float("-inf")
f_eva=0
while n<=2000:
v_max=float("-inf")
h_max=np.sqrt(n)
h_tree=tree_depth(current_node)
loop=mini(h_max,h_tree)
h=0
while h<=n:
#print len(current_node)
#print h
check_leaves=[]
for i in range(len(current_node)):
check_leaves.append(current_node[i].depth)
#print len(check_leaves)
if h in check_leaves:
node,index,g_value = node.Selectnode(current_node,h)
#print "g_value:",g_value
#f_eva=f_eva+1
current_node.pop(index)
#print len(current_node)
if g_value>=v_max:
center=[]
mid=midpoint(node.leftmin, node.rightmax)
left_center=midpoint(node.leftmin,mid)
right_center=midpoint(mid,node.rightmax)
#print left_center,right_center
center.append(left_center)
center.append(right_center)
node_function_value=[]
for i in range(2):
N=N+1
D_x_test=np.array([center[i]])
ktrain,ktest=kernel_calculation(t,np.matrix(D_x_train),np.matrix(D_x_test))
u_N=ktest*inv(ktrain)*np.matrix(D_y_train).T
#print "u_N:",u_N
delta_N=1.0-ktest*inv(ktrain)*ktest.T
#print "delta_N:",delta_N
beta_N=np.sqrt((2*np.log((np.pi)**2*(N**2)))/(6*0.05))
#print "beta_N:",beta_N
U_N=u_N+beta_N*delta_N
#print "U_N:",U_N
#print "f_t:",f_t
if U_N>=f_t:
value=function(center[i])
print "function value:",value
f_eva=f_eva+1
g_value=value
#node_function_value.append(g_value)
if i==0:
current_node.append(node.Addnode(center[i],g_value,node.depth+1,node.leftmin,mid))
if i==1:
current_node.append(node.Addnode(center[i],g_value,node.depth+1,mid,node.rightmax))
t=t+1
D_x_train=np.c_[D_x_train,center[i]]
D_y_train=np.c_[D_y_train,value]
else:
L_N=u_N-beta_N*delta_N
#print "L_N:",L_N
g_value=L_N
node_function_value.append(g_value)
if i==0:
current_node.append(node.Addnode(center[i],g_value,node.depth+1,node.leftmin,mid))
if i==1:
current_node.append(node.Addnode(center[i],g_value,node.depth+1,mid,node.rightmax))
#if i==0:
# current_node.append(node.Addnode(center[i],g_value,node.depth+1,node.leftmin,mid))
#if i==1:
# current_node.append(node.Addnode(center[i],g_value,node.depth+1,mid,node.rightmax))
if g_value>f_t:
f_t=g_value
n=n+1
v_max=g_value
h=h+1
if f_eva>=200:
break
if f_eva>=200:
break
#for i in range(len(current_node)):
#final.append(function(current_node[i].center)
#findex=np.argmax(final)
#print function_evalution
#return current_node[findex].center
d=SOO()
#print d