minimise.steepest

30 """Steepest descent minimisation.""" 31 32 if print_flag: 33 if print_flag >= 2: 34 print print_prefix 35 print print_prefix 36 print print_prefix + "Steepest descent minimisation" 37 print print_prefix + "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" 38 min = Steepest_descent(func, dfunc, args, x0, min_options, func_tol, grad_tol, maxiter, a0, mu, eta, full_output, print_flag, print_prefix) 39 if min.init_failure: 40 print print_prefix + "Initialisation of minimisation has failed." 41 return None 42 results = min.minimise() 43 return results

47 - def __init__(self, func, dfunc, args, x0, min_options, func_tol, grad_tol, maxiter, a0, mu, eta, full_output, print_flag, print_prefix):

48 """Class for steepest descent minimisation specific functions. 49 50 Unless you know what you are doing, you should call the function 'steepest_descent' rather 51 than using this class. 52 """ 53 54 # Function arguments. 55 self.func = func 56 self.dfunc = dfunc 57 self.args = args 58 self.xk = x0 59 self.func_tol = func_tol 60 self.grad_tol = grad_tol 61 self.maxiter = maxiter 62 self.full_output = full_output 63 self.print_flag = print_flag 64 self.print_prefix = print_prefix 65 66 # Set a0. 67 self.a0 = a0 68 69 # Line search constants for the Wolfe conditions. 70 self.mu = mu 71 self.eta = eta 72 73 # Initialisation failure flag. 74 self.init_failure = 0 75 76 # Setup the line search options and algorithm. 77 self.line_search_options(min_options) 78 self.setup_line_search() 79 80 # Initialise the function, gradient, and Hessian evaluation counters. 81 self.f_count = 0 82 self.g_count = 0 83 self.h_count = 0 84 85 # Initialise the warning string. 86 self.warning = None 87 88 # Set the convergence test function. 89 self.setup_conv_tests() 90 91 # Calculate the function value and gradient vector. 92 self.fk, self.f_count = apply(self.func, (self.xk,)+self.args), self.f_count + 1 93 self.dfk, self.g_count = apply(self.dfunc, (self.xk,)+self.args), self.g_count + 1

94 95

96 - def new_param_func(self):

97 """The new parameter function. 98 99 Find the search direction, do a line search, and get xk+1 and fk+1. 100 """ 101 102 # Calculate the steepest descent direction. 103 self.pk = -self.dfk 104 105 # Update a0 using information about the last iteration. 106 try: 107 self.a0 = self.alpha * dot(self.dfk_last, -self.dfk_last) / dot(self.dfk, -self.dfk) 108 except AttributeError: 109 "First iteration." 110 pass 111 112 # Line search. 113 self.line_search() 114 115 # Find the new parameter vector and function value at that point. 116 self.xk_new = self.xk + self.alpha * self.pk 117 self.fk_new, self.f_count = apply(self.func, (self.xk_new,)+self.args), self.f_count + 1 118 self.dfk_new, self.g_count = apply(self.dfunc, (self.xk_new,)+self.args), self.g_count + 1

119 120

121 - def update(self):

122 """Function to update the function value, gradient vector, and Hessian matrix.""" 123 124 # Store old data. 125 self.fk_last = self.fk 126 self.dfk_last = self.dfk * 1.0 127 128 # Shift k+1 data to k. 129 self.xk = self.xk_new * 1.0 130 self.fk = self.fk_new 131 self.dfk = self.dfk_new * 1.0

Source Code for Module minimise.steepest_descent