How to use dlgradient for computing second derivative?

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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.

Accepted Answer

Abolfazl Chaman Motlagh
Abolfazl Chaman Motlagh on 10 Sep 2021
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
  5 Comments
Sanaz Zanjani Foumani
Sanaz Zanjani Foumani on 29 Dec 2021 at 8:02
Do you know how I can use dlgradiet in fmincon? I mean I want to use automatic derevative in fmincon insted of analytical derevative.

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