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

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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)]

Answers (1)

Matt J
Matt J on 29 Jul 2022
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 = 
Matt J
Matt J on 29 Jul 2022
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.

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