Complex step Jacobian

Calculate Jacobian using complex step differentiation

Description

Complex step differentiation (CSD) has many advantages in efferency and accuracy over finite difference approaches (central, forward and backward). This code demonstrates how the Jacobian matrix of a given function at the reference point can be calculated using the CSD approach.

• MATLAB release: MATLAB 7.5 (R2007b)

[V. Poor]

 

[Angshul Majumdar]

the step size 'eps' is not specified? Do U suggest a value?

[Yi Cao]

Angshul,

eps is the minimal distinguishable vnumer for a particular precision system. For double precision, eps = 2^(-52) and for single precision, eps = 2^(-23). Use "help eps" to find more details.

The complex step differentiation approach can use the minimum step size to get the maximum accuracy. Hence eps is the best step the algorithm can use.

HTH.

Yi

[Martin Drozdik]

Dear mr. Cao,

Your program is working perfectly. However there are two things I am curious about>
1. Why does the step size depend on the number of independent variables?
2. If we are computing a derivative of a function of one independent variable, and the derivative is for example 0.2, we are faced with the division (0.2eps)/eps. Why does Matlab not evaluate 0.2eps as 0 therefore leading to the incorrect derivative 0?

Thank You in forward