What are the advantages and differences of using a symbolic function as opposed to a function handle?

I am learning to use MATLAB and have found that a function can be created either as symbolic or as a handle. How do I know which one is better to use?

Answer 1

[Ameer Hamza]

Symbolic expressions are useful if you want to do symbolic computation i.e. get the answer in the form of a general expression, instead of a number. Whereas function handles are useful if you want to solve a numeric problem, in which you want the final answer and don't care about the general form of the solution.

For example, consider a system of two variables

eq1 = a1*x + a2*y == b1;
eq2 = a3*x + a4*y == b2;

solution = solve([eq1, eq2], [x, y]);
solution.x
solution.y

solution.x = -(a2*b2 - a4*b1)/(a1*a4 - a2*a3)
solution.y = (a1*b2 - a3*b1)/(a1*a4 - a2*a3)

This type of general expression is not possible with function handle. Consider another example

syms x
result = int(sin(x))
result =
  -cos(x)

Give you the actual expression of the integration. Not just the numeric result. For such type of calculation, you will definitely need symbolic expressions.

You can also use symbolic toolbox for numeric results for example

syms x
result = int(sin(x), x, 0, pi)

But symbolic calculations are slow as compared to the equivalent calculation with the function handle. For example

f = @(x) sin(x)
result = integral(f, 0, pi)
result = 
  2.0000

The time for function handle version is

Elapsed time is 0.010003 seconds.

whereas for symbolic version

Elapsed time is 0.068826 seconds.

So it depends on what you are trying to do, whether to use a symbolic expression or function handle.

[DanRB]

Thanks for your very explanatory answer!

[Ameer Hamza]

You are welcome.

[Stephen23]

"But numeric calculations are slow as compared to the equivalent calculation with the function handle"

@Ameer Hamza: I think you meant to write "But symbolic calculations are slow ...".

It is also worth noting that many problems cannot be solved symbolically, but numeric solutions or approximations may be possible.

[Ameer Hamza]

Stephan, thanks for the correction and added comment.

[ali yaman]

thanx so much @Ameer Hamza for your clear explanation.