Module: Jacobian

Module | Jacobian
In: | bigdecimal/lib/bigdecimal/jacobian.rb

jacobian.rb

Computes Jacobian matrix of f at x

### Methods

dfdxi isEqual jacobian

### Public Instance methods

dfdxi(f,fx,x,i)

[Source]

    # File bigdecimal/lib/bigdecimal/jacobian.rb, line 21
      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)

[Source]

    # File bigdecimal/lib/bigdecimal/jacobian.rb, line 7
      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)

[Source]

    # File bigdecimal/lib/bigdecimal/jacobian.rb, line 52
      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

[Validate]