I'm having some problems when using the symsum function in MATLAB's Symbolic Math Toolbox. My code should be returning:
ans = sin(x) + x*cos(x) - x^2 / 2 * sin(x)
I think it has something to do with symbolic variables, but I'm new into MATLAB so help will be appreciated.
Here's my code:
syms x i;
f(x) = sin(x);
symsum(x^i/factorial(i)*diff(f,x,i), i, 0, 2)
which returns 0 instead of the correct result indicated above.
This occurs because diff(f,x,i) evaluates to zero. When using symsum, you need to be aware that, like with any Matlab function, the input arguments will be evaluated before being passed in. Just use a for loop (sym/diff is not vectorized in the third argument – see below):
syms x y;
f(x) = sin(x);
n = 0:2;
y = 0;
for i = n
y = y+x^i/factorial(i)*diff(f,x,i);
end
Alternatively, you could try this form (in this case, for just three indexes, the above will probably be more efficient):
syms x y;
f(x) = sin(x);
n = 0:2; % Increasing orders of differentiation
y = diff(f,x,n(1));
yi = [y(x) zeros(1,length(n)-1)]; % To index into array, yi cannot be symfun
for i = 2:length(n)
% Calculate next derivative from previous
yi(i) = diff(yi(i-1),x,n(i)-n(i-1));
end
% Convert yi back to symfun so output is symfun
y = sum(x.^n./factorial(n).*symfun(yi,x));
Why does diff(f,x,i) evaluate to zero even though i is symbolic? From the documentation for sym/diff:
diff(S,n), for a positive integer n, differentiates S n times.
diff(S,'v',n) and diff(S,n,'v') are also acceptable.
In other words, the function doesn't support symbolic variables to specify the order of integration. The order, n (or i in your code) is also limited to a scalar. MuPAD's related functions have similar limitations as well unfortunately.
In my opinion, sym/diff should throw an error if it has this limitation rather than returning garbage. I'd recommend that you file a service request with The MathWorks to report this issue. You could also request that the function be updated to handle symbolic variables for the order of integration input.