Is there a way to improve the speed of these lines? - c++

Question

I am trying to optimise some code which runs unreasonably slowly for what is required. The top answer here describes the method I am trying (although I am not 100% sure I am implementing it correctly).
Only a few lines show up repeatedly on the top of the call stack as I pause the program randomly, however I do not know how I could increase the codes performance given these lines.
The essential function of the code is updating a lattice of points repeatedly using the values of the points surrounding a given point. The relevant code for the first line that comes up:
The class definition:
template<typename T> class lattice{
private:
const unsigned int N; //size
std::vector<std::vector<T>> lattice_points =
std::vector<std::vector<T>>(N,std::vector<T>(N)); //array of points
protected:
static double mod(double, double) ;
public:
lattice(unsigned int);
lattice(const lattice&);
lattice& operator=(const lattice&);
~lattice() {};
T point(int, int) const;
void set(int, int, T);
unsigned int size() const;
};
These lines show up quite often:
template <typename T>
T lattice<T>::point(int x, int y) const {
return (*this).lattice_points[x % N][y % N]; //mod for periodic boundaries
};
template <typename T>
void lattice<T>::set(int x, int y, T val) {
this->lattice_points[x % N][y % N] = val; //mod for periodic boundaries
};
They are used here:
angle_lattice update_lattice(const angle_lattice& lat, const parameters& par, double dt) {
std::random_device rd;
std::mt19937 gen(rd());
std::uniform_real_distribution<> dis(-0.5,0.5);
double sqrtdt = sqrt(dt);
angle_lattice new_lat(lat.size());
int N = lat.size();
for(int i=0; i < N; i++) {
for(int j=0; j < N; j++) {
double val = lat.point(i,j)+
dt*(-par.Dx*( sin_points(lat, i, j, i+1, j) + sin_points(lat, i, j, i-1, j) )
-par.Dy*( sin_points(lat, i, j, i, j+1) + sin_points(lat, i, j, i, j-1) )
-par.Lx/2*( cos_points(lat, i, j, i+1, j) + cos_points(lat, i, j, i-1, j) -2)
-par.Ly/2*( cos_points(lat, i, j, i, j+1) + cos_points(lat, i, j, i, j-1) -2))
+sqrtdt*2*M_PI*par.Cl*dis(gen);
new_lat.set(i,j,val);
}
}
return new_lat;
};
double sin_points(const angle_lattice& lat, int i1, int j1, int i2, int j2) {
return sin(lat.point(i1, j1) - lat.point(i2, j2));
};
double cos_points(const angle_lattice& lat, int i1, int j1, int i2, int j2) {
return cos(lat.point(i1, j1) - lat.point(i2, j2));
};
here angle_lattice is just a lattice where the template parameter is a angle. The set function is overloaded so that the angle is mod 2pi. The only other two functions that appear in the call stack are cos_points and sin_points , as well as generating the random number, but I assume the latter cannot be helped.
Is there anything that can be done? Help would be appreciated.
Edit: I changed the code following some of the suggestions and now the cosine and sine calculation are the highest. I am not sure what