Class: Minimization::NewtonRaphson

Inherits:
Unidimensional show all
Defined in:
lib/minimization.rb

Overview

Classic Newton-Raphson minimization method. Requires first and second derivative

Usage

f   = lambda {|x| x**2}
fd  = lambda {|x| 2x}
fdd = lambda {|x| 2}
min = Minimization::NewtonRaphson.new(-1000,1000, f,fd,fdd)
min.iterate
min.x_minimum
min.f_minimum

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

Class Method Summary collapse

Instance Method Summary collapse

Methods inherited from Unidimensional

#f, #log_summary

Constructor Details

#initialize(lower, upper, proc, proc_1d, proc_2d) ⇒ NewtonRaphson

Parameters:

  • lower: Lower possible value

  • upper: Higher possible value

  • proc: Original function

  • proc_1d: First derivative

  • proc_2d: Second derivative



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# File 'lib/minimization.rb', line 108

def initialize(lower, upper, proc, proc_1d, proc_2d)
  super(lower,upper,proc)
  @proc_1d=proc_1d
  @proc_2d=proc_2d
end

Class Method Details

.minimize(*args) ⇒ Object

Raises an error



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# File 'lib/minimization.rb', line 114

def self.minimize(*args)
  raise "You should use #new and #iterate"
end

Instance Method Details

#iterate ⇒ Object

Raises:



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# File 'lib/minimization.rb', line 117

def iterate
  # First
  x_prev=@lower
  x=@expected
  failed=true
  k=0
  while (x-x_prev).abs > @epsilon and k<@max_iteration
    k+=1
    x_prev=x
    x=x-(@proc_1d.call(x).quo(@proc_2d.call(x)))
    f_prev=f(x_prev)
    f=f(x)
    x_min,x_max=[x,x_prev].min, [x,x_prev].max
    f_min,f_max=[f,f_prev].min, [f,f_prev].max
    @log << [k, x_min, x_max, f_min, f_max, (x_prev-x).abs, (f-f_prev).abs]
  end
  raise FailedIteration, "Not converged" if k>=@max_iteration
  @x_minimum = x;
  @f_minimum = f(x);
end