fx.h File Reference

A header file for a user defined mathematical function. More...

#include <math.h>
#include <assert.h>
#include <armadillo>

Go to the source code of this file.

Classes
class	FX

Macros
#define	_USE_MATH_DEFINES

Detailed Description

A header file for a user defined mathematical function.

Author

Auralius Manurung

Date

28 Jan 2017

DESCRIPTION

Example: A function of vector, with 3 input parameters and 2 output parameters.

\[y = \begin{bmatrix} f_1(x_1,x_2,x_3) \\ f_2(x_1,x_2,x_3) \end{bmatrix} \]

\[Jac(y)=\begin{bmatrix} \frac{\partial f_1}{\partial x_1} \frac{\partial f_1}{\partial x_2} \frac{\partial f_1}{\partial x_3} \\ \frac{\partial f_2}{\partial x_1} \frac{\partial f_2}{\partial x_2} \frac{\partial f_2}{\partial x_3} \end{bmatrix} \]

\[Hess(y(1)) =\begin{bmatrix} \frac{\partial^2 f_1}{\partial x_1^2} \frac{\partial^2 f_1}{\partial x_1 \partial x_2} \frac{\partial^2 f_1}{\partial x_1 \partial x_3} \\ \frac{\partial^2 f_1}{\partial x_2 \partial x_1} \frac{\partial^2 f_1}{\partial x_2^2} \frac{\partial^2 f_1}{\partial x_2 \partial x_3} \\ \frac{\partial^2 f_1}{\partial x_3 \partial x_1} \frac{\partial^2 f_1}{\partial x_3 \partial x_2} \frac{\partial^2 f_1}{\partial x_3^2} \end{bmatrix} \]

\[Hess(y(2)) =\begin{bmatrix} \frac{\partial^2 f_2}{\partial x_1^2} \frac{\partial^2 f_2}{\partial x_1 \partial x_2} \frac{\partial^2 f_2}{\partial x_1 \partial x_3} \\ \frac{\partial^2 f_2}{\partial x_2 \partial x_1} \frac{\partial^2 f_2}{\partial x_2^2} \frac{\partial^2 f_2}{\partial x_2 \partial x_3} \\ \frac{\partial^2 f_2}{\partial x_3 \partial x_1} \frac{\partial^2 f_2}{\partial x_3 \partial x_2} \frac{\partial^2 f_2}{\partial x_3^2} \end{bmatrix} \]

Macro Definition Documentation

_USE_MATH_DEFINES

#define _USE_MATH_DEFINES