/tools/Ruby/lib/ruby/1.8/bigdecimal/newton.rb

 1#
 2# newton.rb 
 3#
 4# Solves the nonlinear algebraic equation system f = 0 by Newton's method.
 5# This program is not dependent on BigDecimal.
 6#
 7# To call:
 8#    n = nlsolve(f,x)
 9#  where n is the number of iterations required,
10#        x is the initial value vector
11#        f is an Object which is used to compute the values of the equations to be solved.
12# It must provide the following methods:
13#
14# f.values(x):: returns the values of all functions at x
15#
16# f.zero:: returns 0.0
17# f.one:: returns 1.0
18# f.two:: returns 1.0
19# f.ten:: returns 10.0
20#
21# 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.
22#
23# On exit, x is the solution vector.
24#
25require "bigdecimal/ludcmp"
26require "bigdecimal/jacobian"
27
28module Newton
29  include LUSolve
30  include Jacobian
31  
32  def norm(fv,zero=0.0)
33    s = zero
34    n = fv.size
35    for i in 0...n do
36      s += fv[i]*fv[i]
37    end
38    s
39  end
40
41  def nlsolve(f,x)
42    nRetry = 0
43    n = x.size
44
45    f0 = f.values(x)
46    zero = f.zero
47    one  = f.one
48    two  = f.two
49    p5 = one/two
50    d  = norm(f0,zero)
51    minfact = f.ten*f.ten*f.ten
52    minfact = one/minfact
53    e = f.eps
54    while d >= e do
55      nRetry += 1
56      # Not yet converged. => Compute Jacobian matrix
57      dfdx = jacobian(f,f0,x)
58      # Solve dfdx*dx = -f0 to estimate dx
59      dx = lusolve(dfdx,f0,ludecomp(dfdx,n,zero,one),zero)
60      fact = two
61      xs = x.dup
62      begin
63        fact *= p5
64        if fact < minfact then
65          raise "Failed to reduce function values."
66        end
67        for i in 0...n do
68          x[i] = xs[i] - dx[i]*fact
69        end
70        f0 = f.values(x)
71        dn = norm(f0,zero)
72      end while(dn>=d)
73      d = dn
74    end
75    nRetry
76  end
77end