minfx.bfgs

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

55 """Class for Quasi-Newton BFGS minimisation specific functions. 56 57 Unless you know what you are doing, you should call the function 'bfgs' rather than using this class. 58 """ 59 60 # Function arguments. 61 self.func = func 62 self.dfunc = dfunc 63 self.args = args 64 self.xk = x0 65 self.func_tol = func_tol 66 self.grad_tol = grad_tol 67 self.maxiter = maxiter 68 self.full_output = full_output 69 self.print_flag = print_flag 70 self.print_prefix = print_prefix 71 72 # Set a0. 73 self.a0 = a0 74 75 # Line search constants for the Wolfe conditions. 76 self.mu = mu 77 self.eta = eta 78 79 # Initialisation failure flag. 80 self.init_failure = 0 81 82 # Setup the line search options and algorithm. 83 self.line_search_options(min_options) 84 self.setup_line_search() 85 86 # Initialise the function, gradient, and Hessian evaluation counters. 87 self.f_count = 0 88 self.g_count = 0 89 self.h_count = 0 90 91 # Initialise the warning string. 92 self.warning = None 93 94 # Set the convergence test function. 95 self.setup_conv_tests() 96 97 # BFGS setup function. 98 self.setup_bfgs() 99 100 # Set the update function. 101 self.update = self.update_bfgs

102 103

104 - def new_param_func(self):

105 """The new parameter function. 106 107 Find the search direction, do a line search, and get xk+1 and fk+1. 108 """ 109 110 # Calculate the BFGS direction. 111 self.pk = -dot(self.Hk, self.dfk) 112 113 # Line search. 114 self.line_search() 115 116 # Find the new parameter vector and function value at that point. 117 self.xk_new = self.xk + self.alpha * self.pk 118 self.fk_new, self.f_count = self.func(*(self.xk_new,)+self.args), self.f_count + 1 119 self.dfk_new, self.g_count = self.dfunc(*(self.xk_new,)+self.args), self.g_count + 1 120 121 # Debugging. 122 if self.print_flag >= 2: 123 print(self.print_prefix + "pk: " + repr(self.pk)) 124 print(self.print_prefix + "alpha: " + repr(self.alpha)) 125 print(self.print_prefix + "xk: " + repr(self.xk)) 126 print(self.print_prefix + "xk+1: " + repr(self.xk_new)) 127 print(self.print_prefix + "fk: " + repr(self.fk)) 128 print(self.print_prefix + "fk+1: " + repr(self.fk_new))

129 130

131 - def setup_bfgs(self):

132 """Setup function. 133 134 Create the identity matrix I and calculate the function, gradient and initial BFGS inverse Hessian matrix. 135 """ 136 137 # Set the Identity matrix I. 138 self.I = identity(len(self.xk), float64) 139 140 # The initial BFGS function value, gradient vector, and BFGS approximation to the inverse Hessian matrix. 141 self.fk, self.f_count = self.func(*(self.xk,)+self.args), self.f_count + 1 142 self.dfk, self.g_count = self.dfunc(*(self.xk,)+self.args), self.g_count + 1 143 self.Hk = self.I * 1.0

144 145

146 - def update_bfgs(self):

147 """Function to update the function value, gradient vector, and the BFGS matrix.""" 148 149 # sk and yk. 150 sk = self.xk_new - self.xk 151 yk = self.dfk_new - self.dfk 152 dot_yk_sk = dot(yk, sk) 153 154 # rho k. 155 if dot_yk_sk == 0: 156 self.warning = "The BFGS matrix is indefinite. This should not occur." 157 rk = 1e99 158 else: 159 rk = 1.0 / dot_yk_sk 160 161 # Preconditioning. 162 if self.k == 0: 163 self.Hk = dot_yk_sk / dot(yk, yk) * self.I 164 165 self.Hk = dot(self.I - rk*outer(sk, yk), self.Hk) 166 self.Hk = dot(self.Hk, self.I - rk*outer(yk, sk)) 167 self.Hk = self.Hk + rk*outer(sk, sk) 168 169 # Shift xk+1 data to xk. 170 self.xk = self.xk_new * 1.0 171 self.fk = self.fk_new 172 self.dfk = self.dfk_new * 1.0

Source Code for Module minfx.bfgs