Module: Jacobian

Included in:
Newton
Defined in:
lib/bigdecimal/jacobian.rb

Overview

require 'bigdecimal/jacobian'

Provides methods to compute the Jacobian matrix of a set of equations at a point x. In the methods below:

f is an Object which is used to compute the Jacobian matrix of the equations. 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.

x is the point at which to compute the Jacobian.

fx is f.values(x).

Instance Method Summary collapse

Instance Method Details

#dfdxi(f, fx, x, i) ⇒ Object

Computes the derivative of f at x. fx is the value of f at x.



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# File 'lib/bigdecimal/jacobian.rb', line 42

def dfdxi(f,fx,x,i)
  nRetry = 0
  n = x.size
  xSave = x[i]
  ok = 0
  ratio = f.ten*f.ten*f.ten
  dx = x[i].abs/ratio
  dx = fx[i].abs/ratio if isEqual(dx,f.zero,f.zero,f.eps)
  dx = f.one/f.ten     if isEqual(dx,f.zero,f.zero,f.eps)
  until ok>0 do
    s = f.zero
    deriv = []
    if(nRetry>100) then
       raize "Singular Jacobian matrix. No change at x[" + i.to_s + "]"
    end
    dx = dx*f.two
    x[i] += dx
    fxNew = f.values(x)
    for j in 0...n do
      if !isEqual(fxNew[j],fx[j],f.zero,f.eps) then
         ok += 1
         deriv <<= (fxNew[j]-fx[j])/dx
      else
         deriv <<= f.zero
      end
    end
    x[i] = xSave
  end
  deriv
end

#isEqual(a, b, zero = 0.0, e = 1.0e-8) ⇒ Object

--



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# File 'lib/bigdecimal/jacobian.rb', line 25

def isEqual(a,b,zero=0.0,e=1.0e-8)
  aa = a.abs
  bb = b.abs
  if aa == zero &&  bb == zero then
        true
  else
        if ((a-b)/(aa+bb)).abs < e then
           true
        else
           false
        end
  end
end

#jacobian(f, fx, x) ⇒ Object

Computes the Jacobian of f at x. fx is the value of f at x.



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# File 'lib/bigdecimal/jacobian.rb', line 74

def jacobian(f,fx,x)
  n = x.size
  dfdx = Array::new(n*n)
  for i in 0...n do
    df = dfdxi(f,fx,x,i)
    for j in 0...n do
       dfdx[j*n+i] = df[j]
    end
  end
  dfdx
end