# Trying to code a tricky double summation

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Michael Vaughan on 24 Sep 2020
Commented: Ameer Hamza on 24 Sep 2020
So I'm trying to write code that calculates the following:
I have two functions of the same two variables, call them D(x,y) and T(x,y)
I'm trying to write a function that accepts inputs x,y,z and outputs:
So, there are two summations, the outer one takes the sum from i=0 up to min(x,y), and the inner sum takes the summation of terms from k=0 up to x-i
The inner sum isn't as complicated as it looks, it has a (-1)^k at the start and then just multiples the functions D(a,b) and T(a,b)^(z/2) where a and b depend on both where you are in the indexing of your outer summation and inner summation
This is a much harder proram than I have written before, so tips, insights, general advice, and even completed code are welcome!! Thanks for your time

Ameer Hamza on 24 Sep 2020
Something like this should work
s = 0;
for i=0:min(x,y)
for k=0:x-1
s = s + (-1)^k * D(2*x-2*k-2*i, 2*y+2-2*i) * T(2*x-2*k-2*i, 2*y+2-2*i)^(z/2)
end
end

Ameer Hamza on 24 Sep 2020
Yes, it is correct. k should be from 0 to x-i. How are you calling this function? I think that these outputs are displayed on the command window because you have put s after inner for-loop.
function sum = Sum(x,y,z)
s = 0;
for i=0:min(x,y)
for k=0:x-i
s = s + (-1)^k * QuantumDimension(2*x-2*k-2*i, 2*y+2-2*i) * Twist(2*x-2*k-2*i, 2*y+2-2*i)^(z/2);
end
s % remove this from here
end
Michael Vaughan on 24 Sep 2020
Thank you very much. I'm now trying to give this function a call handle,
I type S1 = @Sum1.m
Where Sum1.m is the code:
function sum = Sum1(x,y,z)
s = 0;
for i=0:min(x,y)
for k=0:x-i
s = s + (-1)^k * QuantumDimension(2*x-2*k-2*i, 2*y+2-2*i) * Twist(2*x-2*k-2*i, 2*y+2-2*i)^(z/2);
end
end
s
When I type in S1(3,2,1) I get:
Undefined function 'Sum1.m' for input arguments of type 'double'.
What is going wrong here?? THanks for your patience
Ameer Hamza on 24 Sep 2020
To make a function handle type this
S1 = @Sum1
S1(3,2,1)