Replacing sym with function handle

I gave my script below. In order to get my result i used 'sym' function.

But i want to implement without symbolic math toolbox, how to implement the same script with function handles?

syms phi
w = 2;
Nr = 20;
nr = sym(zeros(1, Nr));
wr = sym(zeros(1, Nr));
for n = 1:Nr
    for i = 1:w
        Awr = 50*(cos(i*2)-cos(i*9));
        nr(1, n) = nr(1, n)+Awr*cos(i*(phi+2*n));
    end
    wr(1, n) = nr(1, n);
end
NR = vpa(nr+(56*3/2), 4)

NR = 

WR = vpa(wr, 4)

WR = 

Answer 1

[Alan Stevens]

Do you mean something like this?

phi = pi/3;
[nr, wr] = fn(phi);

disp(phi)

    1.0472

disp(nr(4)+56*3/2)

   13.1554

disp(wr(4))

  -70.8446

function [nr, wr] = fn(phi)
         w = 2;
         Nr = 20;
         nr = zeros(1, Nr);
        wr = zeros(1, Nr);

        for n = 1:Nr
            for i = 1:w
                Awr = 50*(cos(i*2)-cos(i*9));
                nr(1, n) = nr(1, n)+Awr*cos(i*(phi+2*n));
            end
            wr(1, n) = nr(1, n);
        end
end

[Bathala Teja]

I want nr and wr are interms of phi as shown in my script.

But here you are assigning value to the phi.

[Alan Stevens]

Your question specified not using the symbolic toolbox!

I chose a single value of phi as an example. You can pass as many values of phi as you like to the function, by using a loop.

[Bathala Teja]

After forming these set functions in nr, i want to integrate all the functions w.r.t phi individually.

If i dont get in function handles then how to integrate?

[Alan Stevens]

You can use trapz. For example:

philo = 0;
phihi = pi;

phi = linspace(philo, phihi, 100);
dphi = (phihi-philo)/99;

nr = zeros(numel(phi),20);
wr = zeros(numel(phi),20);
Integral_nr = zeros(1,20);
Integral_wr = zeros(1,20);

for m = 1:numel(phi)
    [nr(m,:), wr(m,:)] = fn(phi(m));  
end

for k = 1:20
    
   Integral_nr(k) = trapz(nr(:,k))*dphi; 
 
end

plot(1:20,Integral_nr,'--o'),grid
xlabel('1:Nr'), ylabel('Integrals of nr')

function [nr, wr] = fn(phi)
         w = 2;
         Nr = 20;
         nr = zeros(1, Nr);
         wr = zeros(1, Nr);

        for n = 1:Nr
            for i = 1:w
                Awr = 50*(cos(i*2)-cos(i*9));
                nr(1, n) = nr(1, n)+Awr*cos(i*(phi+2*n));
            end
            wr(1, n) = nr(1, n);
        end
end