def Fletcher_Reeves_conj():
f = conj_f3
c,b,A = f()
x0 = np.matrix('10.;-5.')
g0 = A * x0 + b
v0 = -g0
#pdb.set_trace()
lamb0, f_x0 = golden_section_search(lambda k:f_value(f, x0 + k*v0), [0,2], 0.001)
x1 = x0 + lamb0 * v0
g1 = A*x1 + b
v1 = -g1 + np.dot(g1.T, g1)[0,0]/np.dot(g0.T, g0)[0,0] * v0
lamb1, f_x1 = golden_section_search(lambda k:f_value(f, x1 + k*v1), [0,2], 0.001)
x2 = x1 + lamb1 * v1
return x2, f_x1
def BFGS(f, f_deriv, x0, epsilon):
x_k = x0
B_k = np.eye(x0.shape[0])
D_k = np.linalg.inv(B_k)
g_k = f_deriv(x0)
while True:
def_field = [-100., 100.]
d = -1. * D_k * g_k
k, min_fk = golden_section_search(lambda k: f(x_k + k * d), def_field,
epsilon)
sk = k * d
x_k1 = x_k + sk
g_k1 = f_deriv(x_k1)
yk = g_k1 - g_k
g_sum = np.sqrt(np.sum((g_k1.T * g_k1)))
if g_sum < epsilon:
break
#下一个点的D
I = np.eye(x0.shape[0])
rho = 1. / (yk.T * sk)[0, 0]
V = I - sk * yk.T * rho
#D_k1 = (I - rho * sk * yk.T) * D_k * (I - rho* yk*sk.T) + rho * sk * sk.T
D_k1 = V * D_k * V.T + rho * sk * sk.T #与上式等价
D_k = D_k1
x_k = x_k1
g_k = g_k1
return x_k1, f(x_k1)
def powell_conj():
'''
u1=[-11.14, -24.46]
u2=[-1.8, -0.28]
'''
x0 = np.matrix('20.;20.')
#v1,v2线性无关
v = np.matrix('1.,1.;-1.,1.')
c, b, A = f_powell()
u = np.matrix('0.,0.;0.,0.')
lamb = np.matrix('0.;0.')
id = 0
total = 0
while total < 3:
k, min_fk = golden_section_search(
lambda k: f_value(f_powell, x0 + k * v[:, 0]), [-100., 100], 0.001)
x1 = x0 + k * v[:, 0]
k, min_fk = golden_section_search(
lambda k: f_value(f_powell, x1 + k * v[:, 1]), [-100., 100], 0.001)
x2 = x1 + k * v[:, 1]
#找到u向量
u[:, id] = x2 - x0
k, min_fk = golden_section_search(
lambda k: f_value(f_powell, x2 + k * u[:, id]), [-100., 100],
0.001)
x0 = x2 + k * u[:, id]
v[:, 0] = v[:, 1]
v[:, 1] = u[:, id]
id = (id + 1) % len(lamb)
total += 1
conj = u[:, 0].T * A * u[:, 1]
#print "conj: ", conj
x_star = x0
return x_star, f_value(f_powell, x_star)
def conj_grandient_method_for_f2():
u1 = np.matrix('1.;0.')
u2 = np.matrix('0.;1.')
x0 = np.matrix('0.;0.')
def_field = [-1,1]
esplison = 0.005
c,b, A = f2()
'''
线性搜索用的一次函数, 参数为k
f = f(xi + kui)
'''
k1 = golden_section_search(lambda k:f_value(f2, x0 + k*u1), def_field, esplison)
x1 = x0 + k1[0] * x0
k2 = golden_section_search(lambda k:f_value(f2, x1 + k*u2), def_field, esplison)
x2 = x0 + k1[0] * u1 + k2[0] * u2
return x2, f_value(f2, x2)
def BFGS_simple(f, f_deriv, x0, epsilon):
x_k = x0
B_k = np.eye(x0.shape[0])
g_k = f_deriv(x0)
while True:
def_field = [-100., 100.]
#D_k = np.linalg.inv(B_k)
#d = -1. * D_k * g_k
d = np.linalg.solve(B_k, g_k)
k, min_fk = golden_section_search(lambda k: f(x_k + k * d), def_field,
epsilon)
x_k1 = x_k + k * d
g_k1 = f_deriv(x_k1)
#pdb.set_trace()
g_sum = np.sum((g_k1.T * g_k1))
g_sum = np.sqrt(g_sum)
if g_sum < epsilon:
break
sk = x_k1 - x_k
yk = g_k1 - g_k
v = yk
u = B_k * sk
alpha = 1. / (v.T * sk)[0, 0]
beta = -1. / (u.T * sk)[0, 0]
delta_B = alpha * v * v.T + beta * u * u.T
#下一个点的D
B_k = B_k + delta_B
x_k = x_k1
g_k = g_k1
return x_k1, f(x_k1)
def DFP(f, f_deriv, x0, epsilon):
x_k = x0
D_k = np.eye(x0.shape[0])
g_k = f_deriv(x0)
while True:
def_field = [-100., 100.]
d = -1. * D_k * g_k
k, min_fk = golden_section_search(lambda k: f(x_k + k * d), def_field,
epsilon)
x_k1 = x_k + k * d
g_k1 = f_deriv(x_k1)
#pdb.set_trace()
g_sum = np.sum((g_k1.T * g_k1))
g_sum = np.sqrt(g_sum)
if g_sum < epsilon:
break
sk = x_k1 - x_k
yk = g_k1 - g_k
v = sk
u = D_k * yk
alpha = 1. / (v.T * yk)[0, 0]
beta = -1. / (u.T * yk)[0, 0]
delta_D = alpha * v * v.T + beta * u * u.T
#下一个点的D
D_k = D_k + delta_D
x_k = x_k1
g_k = g_k1
return x_k1, f(x_k1)