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  1. function [X, fX, i] = GXfmincg(f, X, options, P1, P2, P3, P4, P5)
  2. % Minimize a continuous differentialble multivariate function. Starting point
  3. % is given by "X" (D by 1), and the function named in the string "f", must
  4. % return a function value and a vector of partial derivatives. The Polack-
  5. % Ribiere flavour of conjugate gradients is used to compute search directions,
  6. % and a line search using quadratic and cubic polynomial approximations and the
  7. % Wolfe-Powell stopping criteria is used together with the slope ratio method
  8. % for guessing initial step sizes. Additionally a bunch of checks are made to
  9. % make sure that exploration is taking place and that extrapolation will not
  10. % be unboundedly large. The "length" gives the length of the run: if it is
  11. % positive, it gives the maximum number of line searches, if negative its
  12. % absolute gives the maximum allowed number of function evaluations. You can
  13. % (optionally) give "length" a second component, which will indicate the
  14. % reduction in function value to be expected in the first line-search (defaults
  15. % to 1.0). The function returns when either its length is up, or if no further
  16. % progress can be made (ie, we are at a minimum, or so close that due to
  17. % numerical problems, we cannot get any closer). If the function terminates
  18. % within a few iterations, it could be an indication that the function value
  19. % and derivatives are not consistent (ie, there may be a bug in the
  20. % implementation of your "f" function). The function returns the found
  21. % solution "X", a vector of function values "fX" indicating the progress made
  22. % and "i" the number of iterations (line searches or function evaluations,
  23. % depending on the sign of "length") used.
  24. %
  25. % Usage: [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
  26. %
  27. % See also: checkgrad
  28. %
  29. % Copyright (C) 2001 and 2002 by Carl Edward Rasmussen. Date 2002-02-13
  30. %
  31. %
  32. % (C) Copyright 1999, 2000 & 2001, Carl Edward Rasmussen
  33. %
  34. % Permission is granted for anyone to copy, use, or modify these
  35. % programs and accompanying documents for purposes of research or
  36. % education, provided this copyright notice is retained, and note is
  37. % made of any changes that have been made.
  38. %
  39. % These programs and documents are distributed without any warranty,
  40. % express or implied. As the programs were written for research
  41. % purposes only, they have not been tested to the degree that would be
  42. % advisable in any important application. All use of these programs is
  43. % entirely at the user's own risk.
  44. %
  45. % [ml-class] Changes Made:
  46. % 1) Function name and argument specifications
  47. % 2) Output display
  48. %
  49.  
  50. % Read options
  51. if exist('options', 'var') && ~isempty(options) && isfield(options, 'MaxIter')
  52. length = options.MaxIter;
  53. else
  54. length = 100;
  55. end
  56.  
  57.  
  58. RHO = 0.01; % a bunch of constants for line searches
  59. SIG = 0.5; % RHO and SIG are the constants in the Wolfe-Powell conditions
  60. INT = 0.1; % don't reevaluate within 0.1 of the limit of the current bracket
  61. EXT = 3.0; % extrapolate maximum 3 times the current bracket
  62. MAX = 20; % max 20 function evaluations per line search
  63. RATIO = 100; % maximum allowed slope ratio
  64.  
  65. argstr = ['feval(f, X']; % compose string used to call function
  66. for i = 1:(nargin - 3)
  67. argstr = [argstr, ',P', int2str(i)];
  68. end
  69. argstr = [argstr, ')'];
  70.  
  71. if max(size(length)) == 2, red=length(2); length=length(1); else red=1; end
  72. S=['Iteration '];
  73.  
  74. i = 0; % zero the run length counter
  75. ls_failed = 0; % no previous line search has failed
  76. fX = [];
  77. [f1 df1] = eval(argstr); % get function value and gradient
  78. i = i + (length<0); % count epochs?!
  79. s = -df1; % search direction is steepest
  80. d1 = -s'*s; % this is the slope
  81. z1 = red/(1-d1); % initial step is red/(|s|+1)
  82.  
  83. while i < abs(length) % while not finished
  84. i = i + (length>0); % count iterations?!
  85.  
  86. X0 = X; f0 = f1; df0 = df1; % make a copy of current values
  87. X = X + z1*s; % begin line search
  88. [f2 df2] = eval(argstr);
  89. i = i + (length<0); % count epochs?!
  90. d2 = df2'*s;
  91. f3 = f1; d3 = d1; z3 = -z1; % initialize point 3 equal to point 1
  92. if length>0, M = MAX; else M = min(MAX, -length-i); end
  93. success = 0; limit = -1; % initialize quanteties
  94. while 1
  95. while ((f2 > f1+z1*RHO*d1) || (d2 > -SIG*d1)) && (M > 0)
  96. limit = z1; % tighten the bracket
  97. if f2 > f1
  98. z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3); % quadratic fit
  99. else
  100. A = 6*(f2-f3)/z3+3*(d2+d3); % cubic fit
  101. B = 3*(f3-f2)-z3*(d3+2*d2);
  102. z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A; % numerical error possible - ok!
  103. end
  104. if isnan(z2) || isinf(z2)
  105. z2 = z3/2; % if we had a numerical problem then bisect
  106. end
  107. z2 = max(min(z2, INT*z3),(1-INT)*z3); % don't accept too close to limits
  108. z1 = z1 + z2; % update the step
  109. X = X + z2*s;
  110. [f2 df2] = eval(argstr);
  111. M = M - 1; i = i + (length<0); % count epochs?!
  112. d2 = df2'*s;
  113. z3 = z3-z2; % z3 is now relative to the location of z2
  114. end
  115. if f2 > f1+z1*RHO*d1 || d2 > -SIG*d1
  116. break; % this is a failure
  117. elseif d2 > SIG*d1
  118. success = 1; break; % success
  119. elseif M == 0
  120. break; % failure
  121. end
  122. A = 6*(f2-f3)/z3+3*(d2+d3); % make cubic extrapolation
  123. B = 3*(f3-f2)-z3*(d3+2*d2);
  124. z2 = -d2*z3*z3/(B+sqrt(B*B-A*d2*z3*z3)); % num. error possible - ok!
  125. if ~isreal(z2) || isnan(z2) || isinf(z2) || z2 < 0 % num prob or wrong sign?
  126. if limit < -0.5 % if we have no upper limit
  127. z2 = z1 * (EXT-1); % the extrapolate the maximum amount
  128. else
  129. z2 = (limit-z1)/2; % otherwise bisect
  130. end
  131. elseif (limit > -0.5) && (z2+z1 > limit) % extraplation beyond max?
  132. z2 = (limit-z1)/2; % bisect
  133. elseif (limit < -0.5) && (z2+z1 > z1*EXT) % extrapolation beyond limit
  134. z2 = z1*(EXT-1.0); % set to extrapolation limit
  135. elseif z2 < -z3*INT
  136. z2 = -z3*INT;
  137. elseif (limit > -0.5) && (z2 < (limit-z1)*(1.0-INT)) % too close to limit?
  138. z2 = (limit-z1)*(1.0-INT);
  139. end
  140. f3 = f2; d3 = d2; z3 = -z2; % set point 3 equal to point 2
  141. z1 = z1 + z2; X = X + z2*s; % update current estimates
  142. [f2 df2] = eval(argstr);
  143. M = M - 1; i = i + (length<0); % count epochs?!
  144. d2 = df2'*s;
  145. end % end of line search
  146.  
  147. if success % if line search succeeded
  148. f1 = f2; fX = [fX' f1]';
  149. fprintf('%s %4i | Cost: %4.6e\r', S, i, f1);
  150. s = (df2'*df2-df1'*df2)/(df1'*df1)*s - df2; % Polack-Ribiere direction
  151. tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
  152. d2 = df1'*s;
  153. if d2 > 0 % new slope must be negative
  154. s = -df1; % otherwise use steepest direction
  155. d2 = -s'*s;
  156. end
  157. z1 = z1 * min(RATIO, d1/(d2-realmin)); % slope ratio but max RATIO
  158. d1 = d2;
  159. ls_failed = 0; % this line search did not fail
  160. else
  161. X = X0; f1 = f0; df1 = df0; % restore point from before failed line search
  162. if ls_failed || i > abs(length) % line search failed twice in a row
  163. break; % or we ran out of time, so we give up
  164. end
  165. tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
  166. s = -df1; % try steepest
  167. d1 = -s'*s;
  168. z1 = 1/(1-d1);
  169. ls_failed = 1; % this line search failed
  170. end
  171. if exist('OCTAVE_VERSION')
  172. fflush(stdout);
  173. end
  174. end
  175. fprintf('\n');
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