Suggestion - derivatives

[Fotios Kasolis]

I suggest to include in Octave a function that calculates first derivatives/Jacobian matrix since optimization problems become of increasingly great importance. I am working on that and I have a weakly "optimized" finite difference routine using arbitrary stencils

 

n = 9;
h = 10^(-16/(n - 1));
r = 0;
A = ones (n);
while (rcond (A) < eps)
 x = x0 + [ -(n - 1)*h/2 : h : (n - 1)*h/2 ];
 f = fun (x);
 A_ = repmat (x(:), 1, n);
 n_ = repmat (n - 1:-1:0, n, 1);
 A = A_.^n_;
 h = 2*h
endwhile

p = mldivide (A, f(:));
dfdx = polyval (polyder (p), x0);

 

I will also include the complex variable step derivative

 

imag (fun(x0 + eps*1i)) / eps

 

and finally for analytic functions I ll also implement the Cauchy's integration + fft method which I posted earlier and provides higher derivatives as well. Any other method that someone thinks is of interest and importance (other than the adjoint)? What do you think about this? Is this sth that should be included in Octave or?

 

/Fotios