2nd order gradient

Assuming I have a function where is a vector. Is there a method that I can use system equation to obtain

Answer 1

[KSSV]

Let b be your N*1 vector and f be your function values evealuated and of size N*1.

df = gradient(f,b) ;  % first derivative 
d2f = gradient(df,b) ;  % second order gradient 

The above is one method. Also you can evaluate the second derivative of f w.r.t. b and then you can substitute the values of b at the end.

Example:

syms b 
f = 3*b^2+2*b+5 ;
d2f = diff(f,b,2)

[Kevin Zhu]

However, df here is a vector due to b is a vector, gradient(df,b) is not applicable I think.

[KSSV]

It is very much applicable.

[Kevin Zhu]

[KSSV]

Show us the whole code...

[Kevin Zhu]

clear all
close all
clc
rng(10,'twister')

N = 4;
S = 2;
F = dftmtx(N)./sqrt(N);
D = 3;
F_SUB = F(:,1:S);
syms b [N 1];
A_var = diag(b)*F_SUB;
W_var = ((A_var'*A_var) + (A_var'*A_var)')./2;
fobj = trace(inv(W_var));
g = gradient(fobj, b);
gg = gradient(g, b);

[KSSV]

The variable g is 4*1. Run gradient i.e. gg for each element.

gg = gradient(g(1), b);

[Kevin Zhu]

Actually I'm wondering if there is way to directly get the second order gradient of it. If that cannot be done, then it would be fine.