Using anonymous functions with vectors of unknown number of elements and getting the coefficients associated with the variables

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Hello everyone,
I hope that everyone is doing good.
I am aware that the description or summary of my question is quite not clear, so I will explain here what I mean exactly by the title, and feel free to ask any question if you feel things are still not clear.
So I have the following example, from the book (Kernel Adaptive Filtering: A Comprehensive Introduction):
and basically, what I am trying to implement (1.29), such that u will be a (1 x n) vector given by the user, and then c will be (1 x n) arbitrary vector with the values [c1 c2 c3 c4 ... cn]. So obviously, I do not know the number of elements in c unless I know the number of elements of the given vector, u.
So that is my first concern, how I can identify a function with a vector of unknown variables, such that the number of variables is equal to the number of elements in the given vector.
Second, after implementing this function, I want to find the coefficients of c1, c2, c1c2, such that Ii put the coefficients in an array.
Can anyone help me with this? I have been looking for some helpful functions in matlab, but I did not find any.
Thank you
Ahmed AR
Ahmed Radhi
Ahmed Radhi on 22 Sep 2022
So basically, through some inputs, the user will declare the dimension of the vector
% n_u = input("input dimension n_u: ");
% n_s = input("state dimension n_s: ");
% n_y = input("output dimension n_y: ");
Based on the inputs, I will have a randomly initialized vector of size (1 x n_s) as shown in the following code:
% Assume n_s = 0
n_s = 2;
u = randi([-9999, 9999], 1, n_s)
u = 1×2
6113 1041
So yah, that is how we initially supply the vector.

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Accepted Answer

Torsten on 22 Sep 2022
n_s = 2;
u = randi([-9999, 9999], 1, n_s)
u = 1×2
-5089 -4994
c = sym('c',size(u));
kappa = expand((1+u*c.')^2)
kappa = 
coefficients = coeffs(kappa)
coefficients = 

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