Class: Flt::Solver::SecantSolver

Inherits:
Base
  • Object
show all
Defined in:
lib/solver/secant.rb

Overview

Secant method solver Bisect method is used is bracketing found (sign(f(a)) != sign(f(b)))

Example of use:

require 'solver'
require 'flt/tolerance'
include Flt
solver = Solver::SecantSolver.new(Float.context, [0.0, 100.0], Tolerance(3, :decimals)) do |x|
  2*x+11.0
end
puts solver.root
# with a guess:
puts solver.root(5.0)

solver = SecantSolver.new(Float.context, [0.0, 10.0], Tolerance(3, :decimals)) do |x|
  y = 2
  y*exp(x)-10
end
puts solver.root

Instance Attribute Summary

Attributes inherited from Base

#iteration, #reason

Instance Method Summary collapse

Methods inherited from Base

#root, #value

Constructor Details

#initialize(context, default_guesses, tol, eqn = nil, &blk) ⇒ SecantSolver 



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# File 'lib/solver/secant.rb', line 25

def initialize(context, default_guesses, tol, eqn=nil, &blk)
  super context, default_guesses, tol, eqn, &blk
  @half = num(Rational(1,2))
  reset
end

Instance Method Details

#reset ⇒ Object 



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# File 'lib/solver/secant.rb', line 31

def reset
  super
  @a = @b = @fa = @fb = nil
  @bracketing = false
end

#step ⇒ Object 



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# File 'lib/solver/secant.rb', line 37

def step
  return @guess[1] if @iteration == 0
  bisect = false
  dy = @fx - @l_fx

  if @tol.zero?(dy)
    if @bracketing
      bisect = true
    else
      @ok = false
      return @x
    end
  end

  if !bisect
    next_x = @x - ((@x - @l_x)*@fx)/dy
    bisect = true if @bracketing && (next_x < @a || next_x > @b)
  end
  next_x = (@a + @b)*@half if bisect
  next_fx = eval_f(next_x)

  if @bracketing
    if @context.sign(@fa) == @context.sign(next_fx)
      @a = next_x
      @fa = next_fx
    else
      @b = next_x
      @fb = next_fx
    end
  else
    if @context.sign(next_fx) != @context.sign(@fx)
      @a, @b = @x, next_x
      @a, @b = @b, @a if @a > @b
      @fa = eval_f(@a)
      @fb = eval_f(@b)
      @bracketing = true
    end
  end
  next_x
end

#validate ⇒ Object 



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# File 'lib/solver/secant.rb', line 78

def validate
  @guess = @guess.uniq
  if @guess.size < 2
    return false if @guess.empty?
    @guess << (@guess.first + 1)
  end
  true
end