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Edit File : newton.rb \| Size : 1.76 KB
# # newton.rb # # Solves the nonlinear algebraic equation system f = 0 by Newton's method. # This program is not dependent on BigDecimal. # # To call: # n = nlsolve(f,x) # where n is the number of iterations required, # x is the initial value vector # f is an Object which is used to compute the values of the equations to be solved. # It must provide the following methods: # # f.values(x):: returns the values of all functions at x # # f.zero:: returns 0.0 # f.one:: returns 1.0 # f.two:: returns 1.0 # f.ten:: returns 10.0 # # f.eps:: returns the convergence criterion (epsilon value) used to determine whether two values are considered equal. If \|a-b\| < epsilon, the two values are considered equal. # # On exit, x is the solution vector. # require "bigdecimal/ludcmp" require "bigdecimal/jacobian" module Newton include LUSolve include Jacobian def norm(fv,zero=0.0) s = zero n = fv.size for i in 0...n do s += fv[i]fv[i] end s end def nlsolve(f,x) nRetry = 0 n = x.size f0 = f.values(x) zero = f.zero one = f.one two = f.two p5 = one/two d = norm(f0,zero) minfact = f.tenf.tenf.ten minfact = one/minfact e = f.eps while d >= e do nRetry += 1 # Not yet converged. => Compute Jacobian matrix dfdx = jacobian(f,f0,x) # Solve dfdxdx = -f0 to estimate dx dx = lusolve(dfdx,f0,ludecomp(dfdx,n,zero,one),zero) fact = two xs = x.dup begin fact = p5 if fact < minfact then raise "Failed to reduce function values." end for i in 0...n do x[i] = xs[i] - dx[i]fact end f0 = f.values(x) dn = norm(f0,zero) end while(dn>=d) d = dn end nRetry end end Back

Edit File : newton.rb | Size : 1.76 KB

#
# newton.rb 
#
# Solves the nonlinear algebraic equation system f = 0 by Newton's method.
# This program is not dependent on BigDecimal.
#
# To call:
#    n = nlsolve(f,x)
#  where n is the number of iterations required,
#        x is the initial value vector
#        f is an Object which is used to compute the values of the equations to be solved.
# It must provide the following methods:
#
# f.values(x):: returns the values of all functions at x
#
# f.zero:: returns 0.0
# f.one:: returns 1.0
# f.two:: returns 1.0
# f.ten:: returns 10.0
#
# f.eps:: returns the convergence criterion (epsilon value) used to determine whether two values are considered equal. If |a-b| < epsilon, the two values are considered equal.
#
# On exit, x is the solution vector.
#
require "bigdecimal/ludcmp"
require "bigdecimal/jacobian"

module Newton
  include LUSolve
  include Jacobian
  
  def norm(fv,zero=0.0)
    s = zero
    n = fv.size
    for i in 0...n do
      s += fv[i]*fv[i]
    end
    s
  end

def nlsolve(f,x)
    nRetry = 0
    n = x.size

f0 = f.values(x)
    zero = f.zero
    one  = f.one
    two  = f.two
    p5 = one/two
    d  = norm(f0,zero)
    minfact = f.ten*f.ten*f.ten
    minfact = one/minfact
    e = f.eps
    while d >= e do
      nRetry += 1
      # Not yet converged. => Compute Jacobian matrix
      dfdx = jacobian(f,f0,x)
      # Solve dfdx*dx = -f0 to estimate dx
      dx = lusolve(dfdx,f0,ludecomp(dfdx,n,zero,one),zero)
      fact = two
      xs = x.dup
      begin
        fact *= p5
        if fact < minfact then
          raise "Failed to reduce function values."
        end
        for i in 0...n do
          x[i] = xs[i] - dx[i]*fact
        end
        f0 = f.values(x)
        dn = norm(f0,zero)
      end while(dn>=d)
      d = dn
    end
    nRetry
  end
end

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