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authorziejd22017-09-28 15:04:40 -0500
committerziejd22017-09-28 15:04:40 -0500
commit8070dc963753142bb86c4ed698d91fd623ed28e7 (patch)
treed0f6dd8fc46a49b819aa55c1a90faa14d8448883 /sourcecodes/bnt-master/netlab3.3/minbrack.m
parent7cc31810d53176e805532b2789955f4eedbce6bb (diff)
downloadBNW-8070dc963753142bb86c4ed698d91fd623ed28e7.tar.gz
BNW using Octave instead of Matlab.
This version of BNW should perform the same as the original version. The only difference is that it uses Octave instead of Matlab when running BayesNet Toolbox during parameter learning.

I am calling this BNW_1.02. It can be accessed at:
compbio.uthsc.edu/BNW_1.02
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+function  [br_min, br_mid, br_max, num_evals] = minbrack(f, a, b, fa,  ...
+			 varargin)
+%MINBRACK Bracket a minimum of a function of one variable.
+%
+%	Description
+%	BRMIN, BRMID, BRMAX, NUMEVALS] = MINBRACK(F, A, B, FA) finds a
+%	bracket of three points around a local minimum of F.  The function F
+%	must have a one dimensional domain. A < B is an initial guess at the
+%	minimum and maximum points of a bracket, but MINBRACK will search
+%	outside this interval if necessary. The bracket consists of three
+%	points (in increasing order) such that F(BRMID) < F(BRMIN) and
+%	F(BRMID) < F(BRMAX). FA is the value of the function at A: it is
+%	included to avoid unnecessary function evaluations in the
+%	optimization routines. The return value NUMEVALS is the number of
+%	function evaluations in MINBRACK.
+%
+%	MINBRACK(F, A, B, FA, P1, P2, ...) allows additional arguments to be
+%	passed to F
+%
+%	See also
+%	LINEMIN, LINEF
+%
+
+%	Copyright (c) Ian T Nabney (1996-2001)
+
+% Check function string
+f = fcnchk(f, length(varargin));
+
+% Value of golden section (1 + sqrt(5))/2.0
+phi = 1.6180339887499;
+
+% Initialise count of number of function evaluations
+num_evals = 0;
+
+% A small non-zero number to avoid dividing by zero in quadratic interpolation
+TINY = 1.e-10;
+
+% Maximal proportional step to take: don't want to make this too big
+% as then spend a lot of time finding the minimum inside the bracket
+max_step = 10.0;
+
+fb = feval(f, b, varargin{:});
+num_evals = num_evals + 1;
+
+% Assume that we know going from a to b is downhill initially 
+% (usually because gradf(a) < 0).
+if (fb > fa)
+  % Minimum must lie between a and b: do golden section until we find point
+  % low enough to be middle of bracket
+  c = b;
+  b = a + (c-a)/phi;
+  fb = feval(f, b, varargin{:});
+  num_evals = num_evals + 1;
+  while (fb > fa)
+    c = b;
+    b = a + (c-a)/phi;
+    fb = feval(f, b, varargin{:});
+    num_evals = num_evals + 1;
+  end
+else  
+  % There is a valid bracket upper bound greater than b
+  c = b + phi*(b-a);
+  fc = feval(f, c, varargin{:});
+  num_evals = num_evals + 1;
+  bracket_found = 0;
+  
+  while (fb > fc)
+    % Do a quadratic interpolation (i.e. to minimum of quadratic)
+    r = (b-a).*(fb-fc);
+    q = (b-c).*(fb-fa);
+    u = b - ((b-c)*q - (b-a)*r)/(2.0*(sign(q-r)*max([abs(q-r), TINY])));
+    ulimit = b + max_step*(c-b);
+    
+    if ((b-u)'*(u-c) > 0.0)
+      % Interpolant lies between b and c
+      fu = feval(f, u, varargin{:});
+      num_evals = num_evals + 1;
+      if (fu < fc)
+	% Have a minimum between b and c
+	br_min = b;
+	br_mid = u;
+	br_max = c;
+	return;
+      elseif (fu > fb)
+	% Have a minimum between a and u
+	br_min = a;
+	br_mid = c;
+	br_max = u;
+	return;
+      end
+      % Quadratic interpolation didn't give a bracket, so take a golden step
+      u = c + phi*(c-b);
+    elseif ((c-u)'*(u-ulimit) > 0.0)
+      % Interpolant lies between c and limit
+      fu = feval(f, u, varargin{:});
+      num_evals = num_evals + 1;
+      if (fu < fc)
+	% Move bracket along, and then take a golden section step
+	b = c;
+	c = u;
+	u = c + phi*(c-b);
+      else
+	bracket_found = 1;
+      end
+    elseif ((u-ulimit)'*(ulimit-c) >= 0.0)
+      % Limit parabolic u to maximum value
+      u = ulimit;
+    else
+      % Reject parabolic u and use golden section step
+      u = c + phi*(c-b);
+    end
+    if ~bracket_found
+      fu = feval(f, u, varargin{:});
+      num_evals = num_evals + 1;
+    end
+    a = b; b = c; c = u;
+    fa = fb; fb = fc; fc = fu;
+  end % while loop
+end   % bracket found
+br_mid = b;
+if (a < c)
+  br_min = a;
+  br_max = c;
+else
+  br_min = c; 
+  br_max = a;
+end