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Up-> cppad_py library py_lib py_fun py_fun_hessian

cppad_py-> setup.py library whats_new_2018

library-> py_lib cpp_lib

py_lib-> py_fun py_sparse py_utility more_py

py_fun-> py_independent py_abort_recording py_fun_ctor py_fun_property py_fun_new_dynamic py_fun_jacobian py_fun_hessian py_fun_forward py_fun_reverse py_fun_optimize

py_fun_hessian-> fun_hessian_xam.py

Headings-> Syntax f f(x) g(x) x w H Example

@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@Hessian of an AD Function
Syntax
H = f.hessian(x, w)

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 .

g(x)
We use the notation @(@ g: \B{R}^n \rightarrow \B{R} @)@ for the function defined by @[@ g(x) = \sum_{i=0}^{n-1} w_i f_i (x) @]@

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 Hessian @(@ g^{(2)}(x) @)@.

w
If f is a d_fun or a_fun, w is a numpy vector with float (a_double) elements and size m . It specifies the vector w in the definition of @(@ g(x) @)@ above.

H
The result is a numpy matrix with float (a_double) elements, n rows and n columns. For i between zero and n-1 and j between zero and n-1 , @[@ H [ i, j ] = \frac{ \partial^2 g }{ \partial x_i \partial x_j } (x) @]@

Example
fun_hessian_xam.py

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Input File: lib/python/fun_hessian.py