Creating a set of equations programmatically

I am trying to create a set of terms programmatically in order to build up a set of equations later in the code. The equations are supposed to be stored in Q. The vectors a and b are fixed parameters and vector T is the unknown variable.

n = 5;
a = [6 5 4 3 2 1];
b = [1 2 3 4 5 6];
L = 3;
k = 1;
while k<=n
  Q{k,1} = @(T) a(k)*b(k)/L*(T(k+1)-T(k));
  k = k+1;
end
Q

What happens when I run the code is that the information in k is passed in the index of Q (so that the terms are stored in different rows) but not in the index of a,b and T:

Q =

5×1 cell array

    {@(T)a(k)*b(k)/L*(T(k+1)-T(k))}
    {@(T)a(k)*b(k)/L*(T(k+1)-T(k))}
    {@(T)a(k)*b(k)/L*(T(k+1)-T(k))}
    {@(T)a(k)*b(k)/L*(T(k+1)-T(k))}
    {@(T)a(k)*b(k)/L*(T(k+1)-T(k))}

For my purpose I'd like to get an output like this:

Q =

5×1 cell array

    {@(T)a(1)*b(1)/L*(T(2)-T(1))}
    {@(T)a(2)*b(2)/L*(T(3)-T(2))}
    {@(T)a(3)*b(3)/L*(T(4)-T(3))}
    {@(T)a(4)*b(4)/L*(T(5)-T(4))}
    {@(T)a(5)*b(5)/L*(T(6)-T(5))}

Does anyone have an idea how to get this output?

[Lennart Vogt]

I also found out that in order to run the functions later, it is necessary to define them not only as a function of T but also of a and b:

Q{k,1} = @(T,a,b) a(k)*b(k)/L*(T(k+1)-T(k));

[Matt J]

That would be true only if you plan to change a and b later.

[Lennart Vogt]

Yes, you are right. My bad.

Answer 1

[Matt J]

Your code already works fine. Each anonymous function Q{k} will use a different value for k, even if that isn't printed to the screen.

[Lennart Vogt]

Alright thanks!

Answer 2

[Adam Danz]

See Matt J's response. This solution will print the values you described by uses sprintf() and str2func().

n = 5; 
a = [6 5 4 3 2 1];
b = [1 2 3 4 5 6];
L = 3;
k = 1;
while k<=n
  Q{k,1} = str2func(sprintf('@(T) a(%d)*b(%d)/L*(T(%d)-T(%d));', k,k,k+1,k)); 
  k = k+1;
end

[Lennart Vogt]

Thank you, this is very helpful, too.