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@(@\newcommand{\B}[1]{{\bf #1}} \newcommand{\R}[1]{{\rm #1}}@)@

Syntax

Purpose

f

x

w

H

Example

*H* = *f*.hessian(*x*, *w*)

This routine computes the Hessian of the weighted sum @[@ w_0 * F_0 (x) + \cdots + w_{m-1} * F_{m-1} (x) @]@ where @(@ F : \B{R}^n \rightarrow \B{R}^m @)@ is the function corresponding to the

`adfun`

object f
.
The object

*f*

must be an adfun
object.
We use level
for the AD ad
level of
this object.
The argument

*x*

is a `numpy.array`

with one dimension
(i.e., a vector) with length equal to the domain size n
for the function
*f*

.
It specifies the argument value at which the derivative is computed.
If the AD level
for
*f*

is zero,
all the elements of
*x*

must be either `int`

or instances
of `float`

.
If the AD level
for
*f*

is one,
all the elements of
*x*

must be `a_float`

objects.
The argument

*w*

is a `numpy.array`

with one dimension
(i.e., a vector) with length equal to the range size m
for the function
*f*

.
It specifies the argument value at which the derivative is computed.
If the AD level
for
*f*

is zero,
all the elements of
*w*

must be either `int`

or instances
of `float`

.
If the AD level
for
*f*

is one,
all the elements of
*w*

must be `a_float`

objects.
The return value

*H*

is a `numpy.array`

with two dimensions
(i.e., a matrix).
Both its first and second dimension size
(row and column size) are equal to n
(the number of domain components in the function
*f*

).
It is set to the Hessian; i.e.,
@[@
H = w_0 * F_0^{(2)} (x) + \cdots + w_{m-1} * F_{m-1}^{(2)} (x)
@]@
If the AD level
for
*f*

is zero,
all the elements of
*H*

will be instances of `float`

.
If the AD level
for
*f*

is one,
all the elements of
*H*

will be `a_float`

objects.
The file hessian.py contains an example and test of this operation.

Input File: pycppad/adfun.cpp