Compute Jacobian of a function using Automatic Differentiation

I have a vector valued function,, and would like to compute the jacobian of f using automatic differentiation. To accomplish this, my original idea was to use the deep learning toolbox and the built in 'dlgradient' function. However 'dlgradient' seems to only work with scalar valued functions. Is there a way to use automatic differentiation in Matlab to compute the Jacobian of a vector valued function?

Answer 1

[Aditya]

Hi,

Your observation is correct. You cannot use autodiff from Deep Learning Toolbox to compute Jacobian of a Vector valued function. However, You can use the jacobian from the Symbolic Math Toolbox to calculate the jacobian matrix of a vector valued function.

syms x y z
jacobian([x*y*z,y^2,x + z],[x,y,z])

ans = 

The above example computes the Jacobian Matrix of [x*y*z,y^2,x + z] with respect to [x,y,z].

[Nick]

I've found that jacobian from the Symblic Math Toolbox does not scale well to larger more complex functions in terms of copmutation time, espeically if I want to generate a function file for the function. I've started using CasADi instead because of this. Do you think there will be any functionality added that will make this possible in MATLAB any time soon?

Answer 2

[Matt J]

You can do so numerically using, for example, this:

https://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation?s_tid=ta_fx_results