how to define a gradient vector of a given function?

Hello everybody! I have a function from R^n to R and I have computed its gradient (manually!) now I need to implement an array wich contains in each row the i-th partial derivative that I have manually computed and I don't know how to write it. Every partial derivative is the same and it's equal to x_i^2+2. I could write myself the vector with @(x) [df/dx1(x); df/dx2(x);....] but n is very large so i cannot do like this. What's the best way to do the task i need to do?

Answer 1

[Ameer Hamza]

You can calculate the analytical expression of gradient using the Symbolic Toolbox. For example,

syms x [10 1]

y = sum(x.^3)/3 + 2*sum(x);
dy = gradient(y)

Result

>> dy
dy =
 x1^2 + 2
x10^2 + 2
 x2^2 + 2
 x3^2 + 2
 x4^2 + 2
 x5^2 + 2
 x6^2 + 2
 x7^2 + 2
 x8^2 + 2
 x9^2 + 2

To convert a numeric function handle, using matlabFunction()

dy_fun = matlabFunction(dy, 'Vars', {x});