Error when using symsum in function declaration

I apologize for any obvious errors, this is my first time ever using Matlab, and I'm struggling a bit to get used to the syntax. I have defined 3 functions:

   function fact = fact2(n)
if n == 0
    fact = 1;
elseif n == -1
    fact = 1;
elseif mod(n,2) == 0
    fact = prod(2:2:n);
elseif mod(int8(n),2) == 1
    fact = prod(1:2:n);
end

Note: this function is apparently a built-in function, but when I try to use it, it says it's not defined. I assume that I am missing some package, but have no idea how to go about fixing that, so I wrote it myself. The function is a double factorial.

function sumArgument = asymArgErf(n)
sumArgument = (-1)^n * fact2(2*n-3) / (8^n-1);
end

function Asymptotic = erf2Asym(n)
syms k;
Asymptotic = 1 + (exp(-4)/(2*sqrt(pi))) * symsum(asymArgErf(k), k, 1, n);
end

The first two functions run just fine in my command window, however the third gives me an error

   Error using  :  (line 38)
Unable to compute number of steps from 1 to 2*k - 3 by 2.

   Error in fact2 (line 9)
    fact = prod(1:2:n);

   Error in asymArgErf (line 2)
argument2 = (-1)^n * fact2(2*n-3) / (8^n-1);

   Error in erf2Asym (line 3)
Asymptotic = 1 + (exp(-4)/(2*sqrt(pi))) * symsum(asymArgErf(k), k, 1, n);

This seemed like the function was having problems with me inputting what I'm guessing is a symbol type variable into asymArgErf(k). However when I tried converting the type, I got even longer error messages. Could somebody help me resolve this?

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I also tried a simpler case directly into my command window and got an error:

   >> syms k
   >> symsym(fact2(k), k, 1, 3)
   Output argument "fact" (and maybe others) not assigned during call to "fact2".

Answer 1

[Walter Roberson]

In the line

Asymptotic = 1 + (exp(-4)/(2*sqrt(pi))) * symsum(asymArgErf(k), k, 1, n);

then MATLAB has to evaluate asymArgErf(k) first and the result of that is passed to symsum(), so at the time of the asymArgErf(k) call, asymArgErf(k) is evaluated with a purely symbolic k, causing your fact2 to be evaluated with the symbolic expression 2*n-3 . When you apply mod() to a symbolic expression, it means something pretty different than you would expect: mod(2*n-3,2) is evaluated as mod(2,2)*n + mod(-3,2) which is 0*n + 1 which is 1. That leads you to your branch

fact = prod(1:2:n)

which then tries to prod(1:2:2*n-3) but 1:2:2*n-3 cannot be evaluated as a colon expression because n is symbolic.

You effectively cannot use mod with a symbolic variable in a way such as you might hope.

You are unlikely to be able to compute the expression symbolically for general numeric endpoints. You just might be able to compute symbolically within any one numeric value.

A lot of the time, symsum() is the wrong thing to use in MATLAB. symsum() is for calculating formulae, such as symsum(1/x,x,1,n) = eulergamma + psi(n + 1) . When you have a definite list of terms to add, such as for your

 symsym(fact2(k), k, 1, 3)

where you need fact2(1), fact2(2), fact2(3) evaluated, then you should be calculating each using arrayfun or similar and then sum() them together.

[Jacob Goodman]

Thank you for the response! I had thought to use sum instead of symsum but was having trouble with applying my function to an array. I have since figured it out by reading on the arrayfun function you supplied.

I was able to fix my problems now by changing my erf2Asym(n) function to:

function Asymptotic = erf2Asym(n)
t = 1:n;
A = arrayfun(@asymArgErf, t);
Asymptotic = 1 + (exp(-4)/(2*sqrt(pi))) * sum(A);
end