try to find hessian matrix

f(k) = n*ln(k)-n*ln(1/n*sum(i=1 to n)xi^k+(k-1)sum of (1to n)ln(xi))-n

[KSSV]

What have you tried? You are facing any problem or error?

[Taniya]

i could not write the code for the sum series where x sum for 1 to n

[Dyuman Joshi]

The expression you have written above is not clear. Please format it properly.

Answer 1

[Rahul]

Hi Taniya,

Assuming you have k, n and xi, you can try the following code to find the Hessian Matrix:

f = n*log(k) - n*log(1/n * sum(xi^k, i, 1, n) + (k-1) * sum(log(xi), i, 1, n)) - n;

% Calculate the second partial derivatives
d2f_dk2 = diff(f, k, 2);
d2f_dxi_dk = diff(f, k, xi);
d2f_dk_dxi = diff(f, xi, k);
d2f_dxi2 = diff(f, xi, 2);

% Create the Hessian matrix
H = [d2f_dk2, d2f_dxi_dk; d2f_dk_dxi, d2f_dxi2];

Hope this helps.

Thanks.

Answer 2

[Torsten]

The vector of independent variables is (x1,x2,...,xn):

syms i k
n = 3;
x = sym('x',[1 n])

x = 

f = n*log(k) - n*log(1/n*sum(x.^k) + (k-1)*sum(log(x))) - n

f = 

df = gradient(f,x)

df = 

d2f = hessian(f,x)

d2f =