Source Code for Module minimise.polak_ribiere_plus_cg

  1  ############################################################################### 
  2  #                                                                             # 
  3  # Copyright (C) 2003 Edward d'Auvergne                                        # 
  4  #                                                                             # 
  5  # This file is part of the program relax.                                     # 
  6  #                                                                             # 
  7  # relax is free software; you can redistribute it and/or modify               # 
  8  # it under the terms of the GNU General Public License as published by        # 
  9  # the Free Software Foundation; either version 2 of the License, or           # 
 10  # (at your option) any later version.                                         # 
 11  #                                                                             # 
 12  # relax is distributed in the hope that it will be useful,                    # 
 13  # but WITHOUT ANY WARRANTY; without even the implied warranty of              # 
 14  # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the               # 
 15  # GNU General Public License for more details.                                # 
 16  #                                                                             # 
 17  # You should have received a copy of the GNU General Public License           # 
 18  # along with relax; if not, write to the Free Software                        # 
 19  # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA   # 
 20  #                                                                             # 
 21  ############################################################################### 
 22   
 23   
 24  from Numeric import dot 
 25   
 26  from base_classes import Conjugate_gradient, Line_search, Min 
 27   
 28   
 29 -def polak_ribiere_plus(func=None, dfunc=None, args=(), x0=None, min_options=None, func_tol=1e-25, grad_tol=None, maxiter=1e6, a0=1.0, mu=0.0001, eta=0.1, full_output=0, print_flag=0, print_prefix=""): 
 30      """Polak-Ribiere + conjugate gradient algorithm. 
 31   
 32      Page 122 from 'Numerical Optimization' by Jorge Nocedal and Stephen J. Wright, 1999, 2nd ed. 
 33   
 34      The algorithm is: 
 35   
 36      Given x0 
 37      Evaluate f0 = f(x0), g0 = g(x0) 
 38      Set p0 = -g0, k = 0 
 39      while g0 != 0: 
 40          Compute ak and set xk+1 = xk + ak.pk 
 41          Evaluate gk+1 
 42          bk+1 = max(dot(gk+1, (gk+1 - gk)) / dot(gk, gk), 0) 
 43          pk+1 = -gk+1 + bk+1.pk 
 44          k = k + 1 
 45      """ 
 46   
 47      if print_flag: 
 48          if print_flag >= 2: 
 49              print print_prefix 
 50          print print_prefix 
 51          print print_prefix + "Polak-Ribiere + conjugate gradient minimisation" 
 52          print print_prefix + "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" 
 53      min = Polak_ribiere_plus(func, dfunc, args, x0, min_options, func_tol, grad_tol, maxiter, a0, mu, eta, full_output, print_flag, print_prefix) 
 54      if min.init_failure: 
 55          print print_prefix + "Initialisation of minimisation has failed." 
 56          return None 
 57      results = min.minimise() 
 58      return results 
 59   
 60   
 61 -class Polak_ribiere_plus(Conjugate_gradient, Line_search, Min): 
 62 -    def __init__(self, func, dfunc, args, x0, min_options, func_tol, grad_tol, maxiter, a0, mu, eta, full_output, print_flag, print_prefix): 
 63          """Class for Polak-Ribiere + conjugate gradient minimisation specific functions. 
 64   
 65          Unless you know what you are doing, you should call the function 'polak_ribiere_plus' rather 
 66          than using this class. 
 67          """ 
 68   
 69          # Function arguments. 
 70          self.func = func 
 71          self.dfunc = dfunc 
 72          self.args = args 
 73          self.xk = x0 
 74          self.func_tol = func_tol 
 75          self.grad_tol = grad_tol 
 76          self.maxiter = maxiter 
 77          self.full_output = full_output 
 78          self.print_flag = print_flag 
 79          self.print_prefix = print_prefix 
 80   
 81          # Set a0. 
 82          self.a0 = a0 
 83   
 84          # Line search constants for the Wolfe conditions. 
 85          self.mu = mu 
 86          self.eta = eta 
 87   
 88          # Initialisation failure flag. 
 89          self.init_failure = 0 
 90   
 91          # Setup the line search options and algorithm. 
 92          self.line_search_options(min_options) 
 93          self.setup_line_search() 
 94   
 95          # Initialise the function, gradient, and Hessian evaluation counters. 
 96          self.f_count = 0 
 97          self.g_count = 0 
 98          self.h_count = 0 
 99   
100          # Initialise the warning string. 
101          self.warning = None 
102   
103          # Set the convergence test function. 
104          self.setup_conv_tests() 
105   
106          # Calculate the initial function value and gradient vector. 
107          self.fk, self.f_count = apply(self.func, (self.xk,)+self.args), self.f_count + 1 
108          self.dfk, self.g_count = apply(self.dfunc, (self.xk,)+self.args), self.g_count + 1 
109          self.pk = -self.dfk 
110          self.dot_dfk = dot(self.dfk, self.dfk) 
111   
112   
113 -    def calc_bk(self): 
114          """Function to calcaluate the Polak-Ribiere + beta value.""" 
115   
116          # Calculate beta at k+1. 
117          bk_new = dot(self.dfk_new, self.dfk_new - self.dfk) / self.dot_dfk 
118          return max(bk_new, 0.0) 
119