Source Code for Module minfx.hestenes_stiefel_cg

  1  ############################################################################### 
  2  #                                                                             # 
  3  # Copyright (C) 2003-2013 Edward d'Auvergne                                   # 
  4  #                                                                             # 
  5  # This file is part of the minfx optimisation library,                        # 
  6  # https://gna.org/projects/minfx                                              # 
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 21  ############################################################################### 
 22   
 23  # Module docstring. 
 24  """Hestenes-Stiefel conjugate gradient optimization. 
 25   
 26  This file is part of the U{minfx optimisation library<https://gna.org/projects/minfx>}. 
 27  """ 
 28   
 29  # Python module imports. 
 30  from numpy import dot 
 31   
 32  # Minfx module imports. 
 33  from minfx.base_classes import Conjugate_gradient, Line_search, Min 
 34   
 35   
 36 -def hestenes_stiefel(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=""): 
 37      """Hestenes-Stiefel conjugate gradient algorithm. 
 38   
 39      Page 122 from 'Numerical Optimization' by Jorge Nocedal and Stephen J. Wright, 1999, 2nd ed.  The algorithm is: 
 40   
 41          - Given x0 
 42          - Evaluate f0 = f(x0), g0 = g(x0) 
 43          - Set p0 = -g0, k = 0 
 44          - while g0 != 0: 
 45              - Compute ak and set xk+1 = xk + ak.pk 
 46              - Evaluate gk+1 
 47              - bk+1 = dot(gk+1, (gk+1 - gk)) / dot((gk+1 - gk), pk) 
 48              - pk+1 = -gk+1 + bk+1.pk 
 49              - k = k + 1 
 50      """ 
 51   
 52      if print_flag: 
 53          if print_flag >= 2: 
 54              print(print_prefix) 
 55          print(print_prefix) 
 56          print(print_prefix + "Hestenes-Stiefel conjugate gradient minimisation") 
 57          print(print_prefix + "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~") 
 58      min = Hestenes_stiefel(func, dfunc, args, x0, min_options, func_tol, grad_tol, maxiter, a0, mu, eta, full_output, print_flag, print_prefix) 
 59      if min.init_failure: 
 60          print(print_prefix + "Initialisation of minimisation has failed.") 
 61          return None 
 62      results = min.minimise() 
 63      return results 
 64   
 65   
 66 -class Hestenes_stiefel(Conjugate_gradient, Line_search, Min): 
 67 -    def __init__(self, func, dfunc, args, x0, min_options, func_tol, grad_tol, maxiter, a0, mu, eta, full_output, print_flag, print_prefix): 
 68          """Class for Hestenes-Stiefel conjugate gradient minimisation specific functions. 
 69   
 70          Unless you know what you are doing, you should call the function 'hestenes_stiefel' rather than using this class. 
 71          """ 
 72   
 73          # Function arguments. 
 74          self.func = func 
 75          self.dfunc = dfunc 
 76          self.args = args 
 77          self.xk = x0 
 78          self.func_tol = func_tol 
 79          self.grad_tol = grad_tol 
 80          self.maxiter = maxiter 
 81          self.full_output = full_output 
 82          self.print_flag = print_flag 
 83          self.print_prefix = print_prefix 
 84   
 85          # Set a0. 
 86          self.a0 = a0 
 87   
 88          # Line search constants for the Wolfe conditions. 
 89          self.mu = mu 
 90          self.eta = eta 
 91   
 92          # Initialise. 
 93          self.init_failure = 0 
 94   
 95          # Setup the line search options and algorithm. 
 96          self.line_search_options(min_options) 
 97          self.setup_line_search() 
 98   
 99          # Initialise the function, gradient, and Hessian evaluation counters. 
100          self.f_count = 0 
101          self.g_count = 0 
102          self.h_count = 0 
103   
104          # Initialise the warning string. 
105          self.warning = None 
106   
107          # Set the convergence test function. 
108          self.setup_conv_tests() 
109   
110          # Calculate the initial function value and gradient vector. 
111          self.fk, self.f_count = self.func(*(self.xk,)+self.args), self.f_count + 1 
112          self.dfk, self.g_count = self.dfunc(*(self.xk,)+self.args), self.g_count + 1 
113          self.pk = -self.dfk 
114          self.dot_dfk = dot(self.dfk, self.dfk) 
115   
116   
117 -    def calc_bk(self): 
118          """Function to calculate the Hestenes-Stiefel beta value.""" 
119   
120          # Calculate beta at k+1. 
121          diff = self.dfk_new - self.dfk 
122          return dot(self.dfk_new, diff) / dot(diff, self.pk) 
123