Class: Minimization::GoldenSection

Inherits:

Unidimensional

• Object
• Unidimensional
• Minimization::GoldenSection

Defined in:

lib/minimization.rb

Overview

Golden Section Minimizer.

Basic minimization algorithm. Slow, but robust. See Unidimensional for methods.

Usage.

require 'minimization'
min=Minimization::GoldenSection.new(-1000,20000  , proc {|x| (x+1)**2}
min.expected=1.5  # Expected value
min.iterate
min.x_minimum
min.f_minimum
min.log

Constant Summary

Constants inherited from Unidimensional

Unidimensional::EPSILON, Unidimensional::MAX_ITERATIONS

Instance Attribute Summary

Attributes inherited from Unidimensional

#epsilon, #expected, #f_minimum, #iterations, #log, #log_header, #x_minimum

Instance Method Summary

• #iterate ⇒ Object

  Start the iteration.

Methods inherited from Unidimensional

#f, #initialize, #log_summary, minimize

Constructor Details

This class inherits a constructor from Minimization::Unidimensional

Instance Method Details

#iterate ⇒ Object

Start the iteration

# File 'lib/minimization.rb', line 151

def iterate
  ax=@lower
  bx=@expected
  cx=@upper
  c = (3-Math::sqrt(5)).quo(2);
  r = 1-c;

  x0 = ax;
  x3 = cx;
  if ((cx-bx).abs > (bx-ax).abs)
    x1 = bx;
    x2 = bx + c*(cx-bx);
  else
    x2 = bx;
    x1 = bx - c*(bx-ax);
  end
  f1 = f(x1);
  f2 = f(x2);

  k = 1;



  while (x3-x0).abs > @epsilon and k<@max_iteration
    if f2 < f1
      x0 = x1;
      x1 = x2;
      x2 = r*x1 + c*x3;   # x2 = x1+c*(x3-x1)
      f1 = f2;
      f2 = f(x2);
    else
      x3 = x2;
      x2 = x1;
      x1 = r*x2 + c*x0;   # x1 = x2+c*(x0-x2)
      f2 = f1;
      f1 = f(x1);
    end
    @log << [k, x3,x0, f1,f2,(x3-x0).abs, (f1-f2).abs]

    k +=1;
  end

  if f1 < f2
    @x_minimum = x1;
    @f_minimum = f1;
  else
    @x_minimum = x2;
    @f_minimum = f2;
  end
  true
end