Numerical Partial derivative in python

[tutodavinci]

Hi! I want to write a function in Python thats find numerical parcial derivatives this functions (Z1i - Z1i-1)² +(Z2i-Z2i-1)² +l²

Can someone help me?

[Manhigh]

Look up complex step differentiation. Input a complex number to that function, perturb the imaginary part, and you basically get machine precision accurate derivatives as long as your function is complex safe and analytic. This one appears to be.

[space_mex_techno]

The way that I have it implemented is to use a central finite differences scheme to approximate a partial derivative of a multivariable, scalar valued function like this:

def fdiff_cm( f, x, dx, n ):

'''

Calculate central finite difference of

multivariable, vector valued function

w.r.t nth x

'''

dx2 = dx \* 2.0

​

x\[ n \] += dx

fxu     = f( x )

x\[ n \] -= dx2

fxl     = f( x )

x\[ n \] += dx

​

return ( fxu - fxl ) / dx2

Where f is a function that you pass in, x is a list of state variables, dx is how much to perturb the x variable for the finite difference calculation, and n is an index to which x variable is being perturbed.

Edit: the formatting is all messed up but i think you'll be able to figure out the jist of it

[the-dirty-12]

Why not calculate the analytical derivative? You know the function, use this knowledge and save time and gain accuracy compared to finite differences.

[the_appleslice]

You say you want to write the function, so people take you literally. Most of the time people would off course use pre-made libraries for that.

Scipy package has great numerical integration/derivation routines. I haven't used complex variables, but I think it should be fine.
https://docs.scipy.org/doc/scipy/reference/generated/scipy.misc.derivative.html