py_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 , x is a numpy vector with float ( a_double ) elements and size n . It specifies the argument value at we are computing the Jacobian \(f'(x)\).

J#

The result is a numpy matrix with float ( a_double ) elements, m rows, and n columns. For i between zero and m -1 and j between zero and n -1 ,

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

Example#

fun_jacobian_xam.py