Source Code for Module minimise.generic_trust_region

 1  from Numeric import copy, dot, sqrt 
 2   
 3   
 4 -class generic_trust_region: 
 5 -        def __init__(self): 
 6                  "Class containing non-specific trust region algorithm code." 
 7   
 8   
 9 -        def new_param_func(self): 
10                  """An algorithm for trust region radius selection. 
11   
12                  Page 68 from 'Numerical Optimization' by Jorge Nocedal and Stephen J. Wright, 1999 
13                  """ 
14   
15                  # Optain pk. 
16                  self.calc_pk() 
17   
18                  # Evaluate rho. 
19                  self.calc_rho() 
20   
21                  # Calculate the Euclidean norm of pk. 
22                  self.norm_pk = sqrt(dot(self.pk, self.pk)) 
23   
24                  if self.print_flag == 2: 
25                          print "Delta orig: " + `self.delta` 
26                          print "rho:        " + `self.rho` 
27                          print "pk:         " + `self.pk` 
28                          print "||pk||:     " + `self.norm_pk` 
29                          print "dfk:        " + `self.dfk` 
30   
31                  # Choose the trust region radius for the next iteration. 
32                  # Rho is close to zero or negative, therefore the trust region is shrunk. 
33                  if self.rho < 0.25: 
34                          self.delta_new = 0.25 * self.norm_pk 
35                  # Rho is close to one and pk has reached the boundary of the trust region, therefore the trust region is expanded. 
36                  elif self.rho > 0.75 and self.norm_pk == self.delta: 
37                          self.delta_new = min(2.0*self.delta, self.delta_max) 
38                  # Rho is positive but not close to one, therefore the trust region is unaltered. 
39                  else: 
40                          self.delta_new = self.delta 
41   
42                  if self.print_flag == 2: 
43                          print "Delta fin: " + `self.delta` 
44   
45                  # Choose the position for the next iteration. 
46                  if self.rho > self.eta: 
47                          self.xk_new = self.xk + self.pk 
48                  else: 
49                          self.xk_new = copy.deepcopy(self.xk) 
50   
51   
52 -        def calc_rho(self): 
53                  """Function to calculate the ratio rho used to choose the trust region radius. 
54   
55                  The ratio is defined as: 
56   
57                                  f(xk) - f(xk + pk) 
58                          rho  =  ------------------ 
59                                    mk(0) - mk(pk) 
60   
61                  Where the numerator is called the actual reduction and the denominator is the predicted reduction. 
62                  """ 
63   
64                  # Actual reduction. 
65                  fxkpk, self.f_count = apply(self.func, (self.xk + self.pk,)+self.args), self.f_count + 1 
66                  act_red = self.fk - fxkpk 
67   
68                  # Predicted reduction. 
69                  mk_pk = self.fk + dot(self.dfk, self.pk) + 0.5 * dot(self.pk, dot(self.d2fk, self.pk)) 
70                  pred_red = self.fk - mk_pk 
71   
72                  # Rho. 
73                  self.rho = act_red / pred_red 
74