Module: Newton

Includes:
Jacobian, LUSolve
Defined in:
lib/bigdecimal/newton.rb

Instance Method Summary collapse

Methods included from Jacobian

#dfdxi, #isEqual, #jacobian

Methods included from LUSolve

#ludecomp, #lusolve

Instance Method Details

#nlsolve(f, x) ⇒ Object 



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# File 'lib/bigdecimal/newton.rb', line 41

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

#norm(fv, zero = 0.0) ⇒ Object 



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# File 'lib/bigdecimal/newton.rb', line 32

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