cpp_fun_jacobian#

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Jacobian of an AD Function#

Syntax#

J = f.jacobian ( x )

f#

This is either a d_fun or a_fun function object. Upon return, the zero order taylor_coefficients in f correspond to the value of x . The other Taylor coefficients in f are unspecified.

f(x)#

We use the notation \(f: \B{R}^n \rightarrow \B{R}^m\) for the function corresponding to f . Note that n is the size of ax and m is the size of ay in to the constructor for f .

x#

If f is a d_fun or a_fun , this argument has prototype

      const vec_double& x
      const vec_a_double& x

and its size must be n . It specifies the argument value at we are computing the Jacobian \(f'(x)\).

J#

If f is a d_fun or a_fun , the result has prototype

      vec_double J
      vec_a_double J

respectively and its size is m * n . For i between zero and m -1 and j between zero and n -1 ,

\[J [ i * n + j ] = \frac{ \partial f_i }{ \partial x_j } (x)\]

Example#

fun_jacobian_xam.cpp