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

 1#
 2# require 'bigdecimal/jacobian'
 3#
 4# Provides methods to compute the Jacobian matrix of a set of equations at a
 5# point x. In the methods below:
 6#
 7# f is an Object which is used to compute the Jacobian matrix of the equations.
 8# It must provide the following methods:
 9#
10# f.values(x):: returns the values of all functions at x
11#
12# f.zero:: returns 0.0
13# f.one:: returns 1.0
14# f.two:: returns 1.0
15# f.ten:: returns 10.0
16#
17# 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.
18#
19# x is the point at which to compute the Jacobian.
20#
21# fx is f.values(x).
22#
23module Jacobian
24  #--
25  def isEqual(a,b,zero=0.0,e=1.0e-8)
26    aa = a.abs
27    bb = b.abs
28    if aa == zero &&  bb == zero then
29          true
30    else
31          if ((a-b)/(aa+bb)).abs < e then
32             true
33          else
34             false
35          end
36    end
37  end
38  #++
39
40  # Computes the derivative of f[i] at x[i].
41  # fx is the value of f at x.
42  def dfdxi(f,fx,x,i)
43    nRetry = 0
44    n = x.size
45    xSave = x[i]
46    ok = 0
47    ratio = f.ten*f.ten*f.ten
48    dx = x[i].abs/ratio
49    dx = fx[i].abs/ratio if isEqual(dx,f.zero,f.zero,f.eps)
50    dx = f.one/f.ten     if isEqual(dx,f.zero,f.zero,f.eps)
51    until ok>0 do
52      s = f.zero
53      deriv = []
54      if(nRetry>100) then
55         raize "Singular Jacobian matrix. No change at x[" + i.to_s + "]"
56      end
57      dx = dx*f.two
58      x[i] += dx
59      fxNew = f.values(x)
60      for j in 0...n do
61        if !isEqual(fxNew[j],fx[j],f.zero,f.eps) then
62           ok += 1
63           deriv <<= (fxNew[j]-fx[j])/dx
64        else
65           deriv <<= f.zero
66        end
67      end
68      x[i] = xSave
69    end
70    deriv
71  end
72
73  # Computes the Jacobian of f at x. fx is the value of f at x.
74  def jacobian(f,fx,x)
75    n = x.size
76    dfdx = Array::new(n*n)
77    for i in 0...n do
78      df = dfdxi(f,fx,x,i)
79      for j in 0...n do
80         dfdx[j*n+i] = df[j]
81      end
82    end
83    dfdx
84  end
85end