Source Code for Module minimise.cauchy_point

 1  from Numeric import copy, dot, sqrt 
 2  from trust_region import trust_region 
 3   
 4  from generic_trust_region import generic_trust_region 
 5  from generic_minimise import generic_minimise 
 6   
 7   
 8 -class cauchy_point(generic_trust_region, generic_minimise): 
 9 -        def __init__(self, func, dfunc=None, d2func=None, args=(), x0=None, func_tol=1e-5, maxiter=1000, full_output=0, print_flag=0, delta_max=1e5, delta0=1.0, eta=0.2): 
10                  """Cauchy Point trust-region algorithm. 
11   
12                  Page 70 from 'Numerical Optimization' by Jorge Nocedal and Stephen J. Wright, 1999 
13                  The Cauchy point is defined by: 
14   
15                                           delta 
16                          pCk  =  - tau_k ------- dfk 
17                                          ||dfk|| 
18   
19                  where: 
20                          delta_k is the trust region radius, 
21                          dfk is the gradient vector, 
22   
23                                   / 1                                            if dfk . Bk . dfk <= 0 
24                          tau_k = < 
25                                   \ min(||dfk||**2/(delta . dfk . Bk . dfk), 1)  otherwise. 
26                  """ 
27   
28                  self.func = func 
29                  self.dfunc = dfunc 
30                  self.d2func = d2func 
31                  self.args = args 
32                  self.xk = x0 
33                  self.func_tol = func_tol 
34                  self.maxiter = maxiter 
35                  self.full_output = full_output 
36                  self.print_flag = print_flag 
37   
38                  self.delta_max = delta_max 
39                  self.delta = delta0 
40                  self.eta = eta 
41   
42                  # Initialise the function, gradient, and hessian evaluation counters. 
43                  self.f_count = 0 
44                  self.g_count = 0 
45                  self.h_count = 0 
46   
47                  # Initialise the warning string. 
48                  self.warning = None 
49   
50                  # Initial values before the first iteration. 
51                  self.fk, self.f_count = apply(self.func, (self.xk,)+self.args), self.f_count + 1 
52                  self.dfk, self.g_count = apply(self.dfunc, (self.xk,)+self.args), self.g_count + 1 
53                  self.d2fk, self.h_count = apply(self.d2func, (self.xk,)+self.args), self.h_count + 1 
54   
55                  # Minimisation. 
56                  self.minimise = self.generic_minimise 
57   
58   
59 -        def backup_current_data(self): 
60                  "Function to backup the current data into fk_last." 
61   
62                  self.fk_last = self.fk 
63   
64   
65 -        def calc_pk(self): 
66                  "Find the Cauchy point." 
67   
68                  # tau_k. 
69                  temp = dot(self.dfk, dot(self.d2fk, self.dfk)) 
70   
71                  if temp <= 0.0: 
72                          self.tau_k = 1.0 
73                  else: 
74                          self.tau_k = min(dot(self.dfk, self.dfk) / (self.delta * temp), 1.0) 
75   
76                  if self.print_flag == 2: 
77                          print "dfk . Bk . dfk: " + `temp` 
78                          print "tau_k:          " + `self.tau_k` 
79   
80                  # Cauchy point. 
81                  self.pk = - self.tau_k * self.delta * self.dfk / sqrt(dot(self.dfk, self.dfk)) 
82   
83   
84 -        def update_data(self): 
85                  "Function to update the function value, gradient vector, and hessian matrix" 
86   
87                  self.delta = self.delta_new 
88                  self.xk = copy.deepcopy(self.xk_new) 
89                  self.fk, self.f_count = apply(self.func, (self.xk,)+self.args), self.f_count + 1 
90                  self.dfk, self.g_count = apply(self.dfunc, (self.xk,)+self.args), self.g_count + 1 
91                  self.d2fk, self.h_count = apply(self.d2func, (self.xk,)+self.args), self.h_count + 1 
92