construction of diagonal matrix of functions

I have three functions: f_1, f_2, and f_3.

I want to construct the matrix A for the following linear system:

so the first line of the system will be f_2(x_1) + f_3(x_2) = q_1

second line will be f_1(x_1) + f_2(x_2) + f_3(x_3) = q_2

third line f_1(x_2) + f_2(x_3) + f_3(x_4) = q_3

and so on.

Thank you.

Answer 1

[Matt J]

This might be what you want. It assumes that f_1,2,3(x) work element-wise.

function A=func(x)

 f1=f_1(x(1:end-1));
 f2=f_2(x);
 f3=f_3(x(2:end));

 A=diag(f1,-1)+diag(f2)+diag(f3,+1);
 
end

Answer 2

[Matt J]

function A=func(x,n)

  e=zeros(1,n-2);
  f1=f_1(x);
  f2=f_2(x);
  f3=f_3(x);
  
  A=toeplitz([f2,f1,e], [f2,f3,e]);

end

[danielle sisserman]

x here is the vector [x1, ... , xn]?

[Matt J]

No, it is the x in your drawing on which your f_i depend.

[danielle sisserman]

Okay, thank you for your reply. I'm not sure how to construct the matrix A using the above function.

I have [x1, x2, ..., x3]. not one x. sorry for not being clear.

so the first line of the system will be f_2(x_1) + f_3(x_2) = q_1

second line will be f_1(x_1) + f_2(x_2) + f_3(x_3) = q_2

third line f_1(x_2) + f_2(x_3) + f_3(x_4) = q_3

and so on.

Thank you.

[Matt J]

so the first line of the system will be f_2(x_1) + f_3(x_2) = q_1

I'm still not sure what you want, because your drawings and your equations say different things. You're new drawing is equivalent to,

 x_1*f_2(alpha) + x_2*f_3(alpha) = q_1

 x_1*f_1(alpha) + x_2*f_2(alpha) + x_3*f_3(alpha) = q_2
 
 ...