C++ Theta function implementation - c++

Question

I am trying to implement this function:
but it's not working. A minimal, verifiable example looks like:
#include <iostream>
#include <cmath>
int main()
{
int N {8}; // change this for testing <1..inf>
double q {0.1 / N};
int countN {static_cast<int>(floor(N / 2))};
static const double PI {3.1415926535897932384626433832795};
// Omega[i] = Theta1(u,m) / Theta4(u,m)
double Omega[countN];
for (int i=0; i<countN; ++i)
{
double micro {!(N % 2) * 0.5}; // 0 for odd N, 1/2 for even N
double num[countN] {sin(PI / N * (i + 1 - micro))};
double den[countN] {0.5};
for (int m=1; m<4; ++m)
{
num[i] += pow(-1, m) * pow(q, m*(m + 1)) * sin((2 * m + 1) * PI / N * (i + 1 - micro));
den[i] += pow(-1, m) * pow(q, m*m) * cos(2 * m * PI / N * (i + 1 - micro));
}
Omega[i] = fabs(pow(q, 0.25) * num[i] / den[i]);
std::cout << " " << Omega[i] << "\n";
}
// testing the values, they should be increasing in value
for (const auto &elem: Omega)
std::cout << elem << " ";
std::cout << "\n";
return 0;
}
There is a minor simplification compared to the original: I factored 2 in both numerator and denominator and I used only the q^0.25 outside of the fraction. Also, countN is the r from the original document, micro is only the 1/2 for even N or 0 for odd N, and i is 0 for array's index but i+1 for calculations, but these shouldn't matter overall.
I tried this with wxMaxima:
Theta[1](x,y):=2*y^0.25*sum( (-1)^k*y^(k*(k+1))*sin((2*k+1)*x),k,0,n );
Theta[4](x,y):=1+2*sum( (-1)^k*y^(k^2)*cos(2*k*x),k,1,n );
n:4$
N:8$
a:0.05$
b(i):=%pi/N*(i-(1-mod(N,2))/2)$
for N:8 thru 9 do for i:1 thru N/2 do print(["N=",N,"i=",i],Theta[1](b(i),a)/Theta[4](b(i),a)),numer;
And the results, in C++:
(q=0.05; N=8)
Omega[0]=0.2018370065366672
Omega[1]=0.06058232646142273
Omega[2]=0.01205653570636574
Omega[3]=0.02127667733703158
(q=0.05; N=9)
Omega[0]=0.348078726440638
Omega[1]=0.1178366281313341
Omega[2]=2.559808325080287e-07
Omega[3]=0.02178788541277828
and in wxMaxima:
["N=",8,"i=",1]" "0.2018370065366672" "
["N=",8,"i=",2]" "0.5439269564954693" "
["N=",8,"i=",3]" "0.7569342043740249" "
["N=",8,"i=",4]" "0.850913653939989" "
["N=",9,"i=",1]" "0.348078726440638" "
["N=",9,"i=",2]" "0.6165773889432575" "
["N=",9,"i=",3]" "0.7800391631077094" "
["N=",9,"i=",4]" "0.8532352152763631
To my surprise, the first term is good, for bith N, so I can't tell what in my code is not right. Could someone help me spot the error?
To be clear about it: I am a beginner in C++ and I am not looking for someone to do it for me, but to let me know of my erros in coding (translating math to C++ code).

Answer 1

You had
double den[countN] {0.5};
this initializes the first element of den to 0.5 and all the other elements to 0.0 (default initialization). In other words, the above is equivalent to
double den[countN] {0.5, 0.0, 0.0, 0.0};
with as many zeros as necessary to fill the array. You probably wanted to initialize all the elements to 0.5. In your case, the easiest way to do that is when you first use that element - or, since you access only the single element den[i] during the lifetime of den, make it a plain double rather than an array:
for (int i=0; i<countN; ++i) {
double micro {N % 2 ? 0.0 : 0.5}; // 0 for odd N, 1/2 for even N
double num{sin(PI / N * (i + 1 - micro))};
double den{0.5};
for (int m=1; m<4; ++m) {
num += pow(-1, m) * pow(q, m*(m + 1)) * sin((2 * m + 1) * PI / N * (i + 1 - micro));
den += pow(-1, m) * pow(q, m*m) * cos(2 * m * PI / N * (i + 1 - micro));
}
Omega[i] = fabs(pow(q, 0.25) * num / den);
}