How to use dlgradient for computing second derivative?

The following code gives me an error.

x0 = dlarray([-1,2]);
[fval,gradval] = dlfeval(@rosenbrock,x0)

function [y,dy2dx] = rosenbrock(x)
y = 100*(x(2) - x(1).^2).^2 + (1 - x(1)).^2;
dydx = dlgradient(y,x);
dy2dx= dlgradient(dydx,x);
end

I am using dlgradient to compute the second derivative but getting the following error:

"Error using dlfeval (line 43)

Value to differentiate must be a traced dlarray scalar."

Any help on what am i doing wrong? Thanks.

Answer 1

[Abolfazl Chaman Motlagh]

Hi, You are using dlgradient wrong, first agument of dlgradient should be scalar. after 1 gradient from y respect to x. gradient return 1by2 vector. they are and . so you cannot use dydx again in dlgradient. also for second derivative you have 4 elements : , , ,

also you should specify option EnableHigherDerivatives in dlgradient.

so substiture your function with this :

function [y,dy2dx] = rosenbrock(x)
    y = 100*(x(2) - x(1).^2).^2 + (1 - x(1)).^2;
    dydx = dlgradient(y,x,'EnableHigherDerivatives',true);
    dy2dx(1,1:2)= dlgradient(dydx(1),x);
    dy2dx(2,1:2)= dlgradient(dydx(2),x);
end

[Rahul Gulati]

Thanks a lot Abolfazl!

Also, would you know which version of Matlab should i be using for this?

R2020b gives me an error that 'EnableHigherDerivatives' is unrecognised but this works totally fine in the Matlab online version.

[Abolfazl Chaman Motlagh]

Yes, your are right. the option 'EnableHigherDerivatives' added in 2021a. i test on 2020b. it won't work.

it's seems all example with higher derivative dlgradient just added in 2021a, e.g. WGAN and PDE.

• https://www.mathworks.com/help/deeplearning/ug/trainwasserstein-gan-with-gradient-penalty-wgan-gp.html
• https://www.mathworks.com/help/deeplearning/ug/solve-partial-differential-equations-using-deep-learning.html

[Rahul Gulati]

This is very helpful. Thanks a lot again, Abolfazl!

[Abolfazl Chaman Motlagh]

Glad to help .

[Sanaz Zanjani Foumani]

Do you know how I can use dlgradiet in fmincon? I mean I want to use automatic derevative in fmincon insted of analytical derevative.