Source Code for Module minimise.generic_line_search

 1  from re import match 
 2   
 3  # Line search functions. 
 4  from line_search.backtrack import backtrack 
 5  from line_search.nocedal_wright_interpol import nocedal_wright_interpol 
 6  from line_search.nocedal_wright_wolfe import nocedal_wright_wolfe 
 7  from line_search.more_thuente import more_thuente 
 8   
 9   
10 -class generic_line_search: 
11 -        def __init__(self): 
12                  "Class containing non-specific line search algorithm code." 
13   
14   
15 -        def new_param_func(self): 
16                  """Pure Newton minimisation. 
17   
18                  Function options 
19                  ~~~~~~~~~~~~~~~~ 
20   
21                  func                    - The function to minimise. 
22                  dfunc                   - The function which returns the gradient vector. 
23                  d2func                  - The function which returns the hessian matrix. 
24                  x0                      - The initial parameter vector. 
25                  args                    - The tuple of arguments to supply to the functions func, dfunc, and d2func. 
26                  tol                     - The cutoff value used to terminate minimisation by comparison to the difference in function values between iterations. 
27                  maxiter                 - The maximum number of iterations. 
28                  full_output             - A flag specifying what should be returned (see below). 
29                  print_flag              - A flag specifying how much information should be printed to standard output during minimisation: 
30   
31                  The print flag corresponds to: 
32                          0 - No output. 
33                          1 - Minimal output. 
34                          2 - Full output. 
35   
36   
37                  Returned objects 
38                  ~~~~~~~~~~~~~~~~ 
39   
40                  If full_output=0, then only the minimised parameter vector is returned. 
41                  If full_output=1, then the minimised parameter vector, function value at the minimum, number of iterations, and a warning flag are returned. 
42                  The warning flag corresponds to: 
43                          0 - Minimisation terminated successfully. 
44                          1 - Maximum number of iterations have been reached. 
45   
46   
47                  Internal variables 
48                  ~~~~~~~~~~~~~~~~~~ 
49   
50                  k       - The iteration number. 
51                  xk      - Parameter vector at iteration number k. 
52                  fk      - Function value at xk. 
53                  fk_last - Function value at xk-1. 
54                  dfk     - Gradient vector at xk. 
55                  d2fk    - Hessian matrix at xk. 
56                  pk      - Descent direction of the iteration number k. 
57   
58                  """ 
59   
60                  # Initialise. 
61                  fc, gc, hc = 0, 0, 0 
62   
63                  # Calculate the search direction for iteration k. 
64                  self.dir() 
65   
66                  # Get a0. 
67                  try: 
68                          self.get_a0() 
69                  except AttributeError: 
70                          "a0 should not be changed." 
71   
72                  # Backtracking line search. 
73                  if match('^[Bb]ack', self.line_search_algor): 
74                          self.alpha, fc = backtrack(self.func, self.args, self.xk, self.fk, self.dfk, self.pk, a_init=self.a0) 
75                  # Nocedal and Wright interpolation based line search. 
76                  elif match('^[Nn]ocedal[ _][Ww]right[ _][Ii]nt', self.line_search_algor): 
77                          self.alpha, fc = nocedal_wright_interpol(self.func, self.args, self.xk, self.fk, self.dfk, self.pk, a_init=self.a0, mu=self.mu, print_flag=0) 
78                  # Nocedal and Wright line search for the Wolfe conditions. 
79                  elif match('^[Nn]ocedal[ _][Ww]right[ _][Ww]olfe', self.line_search_algor): 
80                          self.alpha, fc, gc = nocedal_wright_wolfe(self.func, self.dfunc, self.args, self.xk, self.fk, self.dfk, self.pk, a_init=self.a0, mu=self.mu, eta=self.eta, print_flag=0) 
81                  # More and Thuente line search. 
82                  elif match('^[Mm]ore[ _][Tt]huente$', self.line_search_algor): 
83                          self.alpha, fc, gc = more_thuente(self.func, self.dfunc, self.args, self.xk, self.fk, self.dfk, self.pk, a_init=self.a0, mu=self.mu, eta=self.eta, print_flag=0) 
84                  # No line search. 
85                  elif match('^[Nn]one$', self.line_search_algor): 
86                          self.alpha = self.a0 
87                  # No match to line search string. 
88                  else: 
89                          raise NameError, "The line search algorithm " + self.line_search_algor + " is not coded.\n" 
90   
91                  self.f_count = self.f_count + fc 
92                  self.g_count = self.g_count + gc 
93                  self.h_count = self.h_count + hc 
94   
95                  # Find the new parameter vector. 
96                  self.xk_new = self.xk + self.alpha * self.pk 
97