How to automate the matrix-vector multiplication using the index of a vector?

I have the following

m = 50;
a = 5
b = 2
c = 2
J = @(t,y) [diag(a*ones(1,m)) + diag(b*ones(1,m-1),1) + diag(c*ones(1,m-1),-1)];

I want to obtain the function/function handle (which takes (t,y) as argument) that gives essentially

A = @(t,y)  [J*y]

but I want the output to be in terms of the elements of the vector y, these are y(1), y(2), ..., y(m). That is

[5*y(1) + 2*y(2);
 2*y(1) + 5*y(5) + 2*y(3);
    .
    .
    .
 2*y(m-1) + 5*y(m)]

[Matt J]

t isn't used anywhere in your expressions. What is it's role?

Answer 1

[Matt J]

m = 50;
a = 5;
b = 2;
c = 2;
J = [diag(a*ones(1,m)) + diag(b*ones(1,m-1),1) + diag(c*ones(1,m-1),-1)];

syms y [m,1]

expression = J*y

expression = 

[Romio]

Thanks a lot Matt. The problem is that I can't use the sympolic toolbox in my application (ode solver)

[Matt J]

If you can't use the symbolic toolbox, your question doesn't make sense because you've asked for a symbolic result. If you don't need a symbolic result, then J*y already gives you that.