Class: Flt::Solver::RFSecantSolver

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

Overview

Regula-Falsi/Secant method solver Secant is used if no bracketing is available

Example of use:

require 'solver'
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(*args, &blk) ⇒ RFSecantSolver

Returns a new instance of RFSecantSolver.



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# File 'lib/solver/rfsecant.rb', line 24

def initialize(*args, &blk)
  super
  @half = num(Rational(1,2))
  reset
end

Instance Method Details

#reset ⇒ Object 



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# File 'lib/solver/rfsecant.rb', line 30

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

#step ⇒ Object 



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# File 'lib/solver/rfsecant.rb', line 36

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

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

  if !regula_falsi
    next_x = @x - ((@x - @l_x)*@fx)/dy
    regula_falsi = true if @bracketing && (next_x < @a || next_x > @b)
  end
  next_x = @b - (@b - @a)*@fb/(@fb - @fa) if regula_falsi
  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
  # puts "br: #{@bracketing} r-f: #{regula_falsi} x:#{@x}[#{@fx}] l_x:#{@l_x}[#{@l_fx}] #{next_x}"
  next_x
end

#validate ⇒ Object 



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

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