Problems with symsum () function in Symbolic Math Toolbox
I am having some problems when using a function symsum
in MATLAB Symbolic Math Toolbox. My code should return:
ans = sin(x) + x*cos(x) - x^2 / 2 * sin(x)
I think it has something to do with symbolic variables, but I am new to MATLAB, so help would 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 above.
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This is because it diff(f,x,i)
evaluates to zero. When using, symsum
you need to know that, like any Matlab function, the input arguments will be evaluated before being passed. use a loop for
( sym/diff
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 can try this form (in this case, just three indices 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 diff(f,x,i)
is it evaluated to zero even though it i
is a symbol? 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 does not support symbolic variables to indicate the order of integration. The order, n
(or i
in your code) is also limited by a scalar. Unfortunately, MuPAD related features also have similar limitations.
In my opinion, sym/diff
should throw an error if it has this constraint, not a garbage return. I would recommend that you submit a service request to MathWorks to report this issue. You can also request a function update to handle symbolic variables for the integration input order.
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