实用优化算法.helper 文件
我在写这门课的实验代码的时候，发现算法有一些公用的函数，我把这些公用的函数放到了一个helper文件中,减少了代码的重复性,和编写的难度。
import numpy as np
from sympy import *
import math
from scipy.optimize import fmin_bfgs
x1,a,b,x2,x3 = symbols('x1,a,b,x2,x3')
def get_grad(x,f):
if len(x) == 2:
ans = [[],[]]
ans[0].append(diff(f,x1).subs(x1,x[0][0]).subs(x2,x[1][0]))
ans[1].append(diff(f,x2).subs(x1,x[0][0]).subs(x2,x[1][0]))
ans = np.array(ans)
return ans
elif len(x) == 3:
ans = [[],[],[]]
ans[0].append(diff(f,x1).subs(x1,x[0][0]).subs(x2,x[1][0]).subs(x3,x[2][0]))
ans[1].append(diff(f,x2).subs(x1,x[0][0]).subs(x2,x[1][0]).subs(x3,x[2][0]))
ans[2].append(diff(f,x3).subs(x1,x[0][0]).subs(x2,x[1][0]).subs(x3,x[2][0]))
ans = np.array(ans)
return ans
def get_len_grad(x):
s = 0
for i in x:
s += pow(i[0],2)
return math.sqrt(s)
# ----------------------------------------------------------------------------------------------------------------------
def get_value(t,xx,d,f):
test_x = xx + t*d
if len(test_x) == 3:
return f.subs(x1,test_x[0][0]).subs(x2,test_x[1][0]).subs(x3,test_x[2][0])
elif len(test_x) == 2:
return f.subs(x1, test_x[0][0]).subs(x2, test_x[1][0])
def golden_search(st,ed,xx,d,f):
a = st
b = ed
cnt = 1
x1 = a + 0.382*(b - a)
x2 = a + 0.618*(b - a)
while b - a > 1e-10:
x1_value = get_value(x1,xx,d,f)
x2_value = get_value(x2,xx,d,f)
if x1_value < x2_value:
b = x2
x2 = x1
x1 = a + 0.382*(b - a)
elif x1_value > x2_value:
a = x1
x1 = x2
x2 = a + 0.618*(b - a)
elif x1_value == x2_value:
a = x1
b = x2
x1 = a + 0.382 * (b - a)
x2 = a + 0.618 * (b - a)
cnt += 1
ans = ( b + a )/ 2
return ans
#----------------------------------------------------------------------------------------------------------------------------
def non_accuracy_search(x0,d,f):
alpha = 1
berta = 0.5
p = 0.25
xk = x0
tmp1 = f.subs(x1,(xk + alpha*d)[0][0]).subs(x2,(xk + alpha*d)[1][0])
tmp2 = f.subs(x1,xk[0][0]).subs(x2,xk[1][0]) + p*alpha*(np.dot(get_grad(xk,f).T,d))
while tmp1 > tmp2:
alpha = berta*alpha
tmp1 = f.subs(x1, (xk + alpha * d)[0][0]).subs(x2, (xk + alpha * d)[1][0])
tmp2 = f.subs(x1, xk[0][0]).subs(x2, xk[1][0]) + p * alpha * np.dot((get_grad(xk,f).T),d)
print('非精确搜索步长',alpha)
return alpha
#----------------------------------------------------------------------------------------------------------------------------
def get_grad_grad(x,f):
ans = [[],[]]
t = diff(f,x1)
tt = diff(t,x1)
ans[0].append(tt.subs(x1,x[0][0]).subs(x2, x[1][0]))
tt = diff(t,x2)
ans[0].append(tt.subs(x1,x[0][0]).subs(x2, x[1][0]))
t = diff(f,x2)
tt = diff(t,x1)
ans[1].append(tt.subs(x1,x[0][0]).subs(x2, x[1][0]))
tt = diff(t,x2)
ans[1].append(tt.subs(x1,x[0][0]).subs(x2, x[1][0]))
ans = np.array(ans)
return ans
#----------------------------------------------------------------------------------------------------------------------------
def get_biet(g0,g1):
return (np.dot(g1.T,g1) / np.dot(g0.T,g0))[0][0]
def get_biet_PRP(k,g0,g1):
if k == 0:
return 0
return (np.dot(g1.T,(g1 - g0))/(np.dot(g0.T,g0)))[0][0]
def FR_Newton(x,f):
g = get_grad(x,f)
g1 = g
k = 0
n = 5
next_x = x
d = -1*g1
while get_len_grad(g1) >= 0.0001:
if k == 0 or k % n == 0:
d = -1*g1
else:
bt = get_biet(g, g1)
d = -1*g1 + bt * d
step = golden_search(0,2,x,d,f) # 调用实验一的黄金分割法进行精确搜索
# step = non_accuracy_search(x,d,f)
next_x = x + step*d
k += 1
g = g1
x = next_x
g1 = get_grad(next_x,f)
# print(x)
return next_x
# ------------------DFP--------------------------------------------------------------------------------------------------------
def DFP(x0,h,f):
k = 1
while get_len_grad(get_grad(x0,f)) > 0.00001:
d = -1 * np.dot(h, get_grad(x0,f))
step = golden_search(0, 2, x0, d, f)
x1 = x0 + step * d
s = x1 - x0
y = get_grad(x1,f) - get_grad(x0,f)
t1 = np.dot(h,y)
t2 = np.dot(t1,y.T)
t3 = np.dot(t2,h) # 分子
t4 = np.dot(y.T,h)
t5 = np.dot(t4,y) # 分母
t6 = np.dot(s,s.T) # 分子
t7 = np.dot(y.T, s) # 分母
h = h - t3*(1/t5[0][0]) + (1/t7[0][0]) * t6
x0 = x1
# print(k,' ',x0)
k += 1
return x0