Source Code for Module minimise.hessian_mods.eigenvalue

 1  ############################################################################### 
 2  #                                                                             # 
 3  # Copyright (C) 2003 Edward d'Auvergne                                        # 
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 5  # This file is part of the program relax.                                     # 
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21  ############################################################################### 
22   
23   
24  from LinearAlgebra import eigenvectors, inverse 
25  from Numeric import matrixmultiply, sort 
26   
27   
28 -def eigenvalue(dfk, d2fk, I, print_prefix, print_flag, return_matrix=0): 
29      """The eigenvalue Hessian modification. 
30   
31      This modification is based on equation 6.14 from page 144 of 'Numerical Optimization' by 
32      Jorge Nocedal and Stephen J. Wright, 1999, 2nd ed. 
33   
34      Returns the modified Newton step. 
35      """ 
36   
37      # Calculate the eigenvalues. 
38      eigen = eigenvectors(d2fk) 
39      eigenvals = sort(eigen[0]) 
40   
41      # Modify the Hessian if the smallest eigenvalue is negative. 
42      tau = None 
43      if eigenvals[0] < 0.0: 
44          tau = max(0.0, 1e-2 - eigenvals[0]) 
45          matrix = d2fk + tau * I 
46      else: 
47          matrix = d2fk 
48   
49      # Debugging. 
50      if print_flag >= 3: 
51          eigen_new = eigenvectors(matrix) 
52          eigenvals_new = sort(eigen_new[0]) 
53          print print_prefix + "d2fk:\n" + `d2fk` 
54          print print_prefix + "eigenvals(d2fk): " + `eigenvals` 
55          print print_prefix + "tau: " + `tau` 
56          print print_prefix + "matrix:\n" + `matrix` 
57          print print_prefix + "eigenvals(matrix): " + `eigenvals_new` 
58          print print_prefix + "Newton dir: " + `-matrixmultiply(inverse(matrix), dfk)` 
59   
60      # Calculate the Newton direction. 
61      if return_matrix: 
62          return -matrixmultiply(inverse(matrix), dfk), matrix 
63      else: 
64          return -matrixmultiply(inverse(matrix), dfk) 
65