Building symbolic expression with vars from vector

Is it possible, to build a symbolic expression with symbolic parameters/variables like in the minimal example below?

syms x y
syms j  % index var
m = 10  % max index  

p_j = sym('p', [m 2])   % symbolic parameter vector
phi = sym('phi', [m,1]) % symbolic vars      

syms J_j(j) % helper expression 
J_j(j) = sqrt((x-p_j(j,1))^2+(y-p_j(j,1))^2)*phi(j); % <-fails

J = symsum(J_j(j), j, 1, m) % final expression

The error is probably due to accessing a matrix.

I very much appreciate any response.

Many thanks in advance.

Answer 1

[Paul]

Hi ludolfusexe,

It looks like the original code was attempting to use j as a index into an array, but symbolic variables are never allowed to be used as indices.

Here's the working code (I made m smaller to more easily see the final result)

syms x y p_jx p_jy phi_j
%m = 10;
m = 4;
p_j = sym('p', [m 2]);  
phi = sym('phi', [m,1]);       
J_j = sqrt((x-p_jx)^2+(y-p_jy)^2)*phi_j;
J = 0;
for j=1:m
    tmp = subs(J_j,p_jx,  p_j(j,1));
    tmp = subs(tmp,p_jy,  p_j(j,2));
    tmp = subs(tmp,phi_j, phi(j)  );
    J = J + tmp;
end
J

J = 

Symbolic arrays support elementwise and other basic operations, which also support scalar expansion, just like standard numerical arrays. Hence, we can construct J as

J1 = sum(phi.*sqrt((x - p_j(:,1)).^2 + (y - p_j(:,2)).^2))

J1 = 

Check

isAlways(J1 == J)

ans = logical
   1

[ludolfusexe]

Thank you for your reply, your solution is much more elegant than mine!

Answer 2

[ludolfusexe]

syms x y p_jx p_jy phi_j
m = 10   

p_j = sym('p', [m 2])  
phi = sym('phi', [m,1])       

J_j = sqrt((x-p_jx)^2+(y-p_jy)^2)*phi_j;

J = 0;
for j=1:m
    tmp = subs(J_j,p_jx,  p_j(j,1));
    tmp = subs(tmp,p_jy,  p_j(j,2));
    tmp = subs(tmp,phi_j, phi(j)  );
    J = J + tmp;
end
J

That works.