// alpha is the K2=2*K dimensional vector containing the real and imaginary part of \alpha_t
//fktilde contains the quantities 2a/(L*\pi)*(2\gamma_t-1)
void PHI_gVg(double t, double gamma[K2], double tktilde[K]){
  int i,i2,i3;
  double tmp,tmp2,tmp3,costmp,sintmp;
  double re_s=0.0;//re_s contains real part of sum over \alpha_t(k)
  double im_s=0.0;//im_s contains imaginary part of sum over \alpha_t(k)
  for(i=0;i<K;i++){
	  i2=2*i;
	  re_s+=alpha[i2];
	  im_s+=alpha[i2+1];
  }
  re_s*=fourapi;//fourapi=4*a/(L*\pi) is fixed at the beginning of the simulation
  im_s*=fourapi;
  tmp2=(costmpV*re_s+sintmpV*im_s)/4.0;//costmpV contains cos(c) which has been fixed at the beginning of the simulation, sintmpV contains sin(c)
  tmp3=(costmpV*im_s-sintmpV*re_s)/4.0;//tmp2 and tmp3 are the real and the imaginary part appearing in \ii\cdot s\cdot e of the algorithm
  double re_s_tilde=0.0;//re_s_tilde contains new real part of sum over all alpha
  double im_s_tilde=0.0;//im_s_tilde contains new real part of sum over all alpha
  for(i=0;i<K;i++){
    i2=2*i;
    i3=i2+1;
    fktilde[i]+=t*(re_s*alpha[i3]-im_s*alpha[i2]);
    tmp=fktilde[i];
    alpha[i2]+=tmp*tmp2;
    alpha[i3]+=tmp*tmp3;
    re_s_tilde+=alpha[i2];
    im_s_tilde+=alpha[i3];
  }
  //
  re_s_tilde*=fourapi;
  im_s_tilde*=fourapi;
  for(i=0;i<K;i++){
    i2=2*i;
    fktilde[i]+=t*(re_s*alpha[i2+1]-im_s*alpha[i2]);
  }
}