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#ifndef Ldokchitser_H
#define Ldokchitser_H
//finding the explicit taylor series for \phi(t) using Dokchitser algo
#define MYDIGITS 5 // estimate of precision ... will be set using the precision variable
void mult_poly_taylor(Complex *, Complex *, Complex *, int );
template <class ttype>
void L_function <ttype>::
phi_series(int precision)
{
cout << "-----------------------------------------------"<< endl << endl;
cout << "phi series for " << name << " L_function" << endl << endl;
int j,k;
// constructing the equivalence classes Lambda[k] for k = 1 to N
int pordtmp[a+1];
Complex diff;
Complex *lambda_k;
int *l;
for (j=1;j<=a;j++)
pordtmp[j]= 1;
for (j=1;j<=a;j++)
for (k=1;k<=a;k++)
if (j != k)
{
diff = 2*(lambda[j] - lambda[k]);
if((imag(diff)==0) && (fmod(real(diff),2) == 0) && (real(diff)<=0))
{
pordtmp[j]+=pordtmp[k];
pordtmp[k]=0;
}
}
Complex temp_lambda_k[a];
int temp_l[a];
j=1;
for (k=1;k<=a;k++)
if (pordtmp[k]!=0)
{
temp_lambda_k[j]= lambda[k];
temp_l[j]=pordtmp[k];
j++;
}
int N = j-1;
lambda_k = new Complex[N+1];
l = new int[N+1];
for (j=1;j<=N;j++)
{
lambda_k[j] = temp_lambda_k[j];
l[j] = temp_l[j];
}
cout << "-----------------------------------------------"<< endl << endl;
cout << "There are "<< N << " equivalence classes Lambda[j]"<<endl;
cout<< "The equivalence classes Lambda[j] for poles are represented by"<<endl;
for (j=1;j<=N;j++)
{
cout << "lambda_k["<<j<<"] = "<< lambda_k[j] << " with order l["<<j<<"] = "<<l[j]<<endl;
}
cout<<endl;
// compute the values m[j] for the respective lambda_k[j]
std::vector<Complex> m(N+1);
for (j=1;j<=N;j++)
m[j] = -2*lambda_k[j] + 2;
// compute sum_{k=1}^a log Gamma((s+m[j]+2*lambda[k])/2) for each j
int n,fact_n;
Complex log_Gamma[N+1][a+1][MYDIGITS+1];
std:vector<std::vector<Complex> > sum_log_Gamma(N+1);
for (j=1;j<=N;j++) sum_log_Gamma[j].resize(MYDIGITS+1);
for (j=1;j<=N;j++)
for (n=0;n<=MYDIGITS;n++)
sum_log_Gamma[j][n] = 0;
for (j=1;j<=N;j++)
{
for (k=1;k<=a;k++)
{
fact_n = 1;
for (n=0;n<=MYDIGITS;n++)
{
if (n!=0)
fact_n = fact_n*n;
log_Gamma[j][k][n] = pow(0.5,n)*(log_GAMMA((m[j]/2 + lambda[k]),n))/fact_n;
sum_log_Gamma[j][n] = sum_log_Gamma[j][n] + log_Gamma[j][k][n];
}
}
}
cout << endl;
// compute the exponential taylor series for gamma = exp(sum_log_Gamma)
std::vector<std::vector<std::vector<Complex> > > exp_sum_log_Gamma(N+1); // symmetric functions
std::vector<std::vector<Complex> > gamma(N+1); // gamma(s+m[j]) for j = 1 to N
for (j=1;j<=N;j++){
exp_sum_log_Gamma[j].resize(MYDIGITS+1);
gamma[j].resize(MYDIGITS+1);
}
for (j=1;j<=N;j++) for (n=0;n<=MYDIGITS;n++) exp_sum_log_Gamma[j][n].resize(MYDIGITS+1);
Complex temp_gamma[MYDIGITS+1];
Complex temp_mult_gamma[MYDIGITS+1];
Complex temp_exp_sum_log_Gamma[MYDIGITS+1];
int fact_n_k;
for (j=1;j<=N;j++)
{
for (n=0;n<=MYDIGITS;n++)
exp_sum_log_Gamma[j][0][n] = 0;
exp_sum_log_Gamma[j][0][0] = exp(sum_log_Gamma[j][0]);
for (k=1;k<=MYDIGITS;k++)
{
fact_n_k = 1;
for (n=0;n<=MYDIGITS;n++)
{
if(n%k == 0)
{
if (n/k != 0)
fact_n_k = fact_n_k*(n/k);
exp_sum_log_Gamma[j][k][n] = pow(sum_log_Gamma[j][k],n/k)/fact_n_k;
}
else
exp_sum_log_Gamma[j][k][n] = 0;
}
}
}
for (j=1;j<=N;j++)
{
for (n=0;n<=MYDIGITS;n++)
temp_mult_gamma[n] = exp_sum_log_Gamma[j][0][n];
for (k=1;k<=MYDIGITS;k++)
{
for (n=0;n<=MYDIGITS;n++)
{
temp_exp_sum_log_Gamma[n] = exp_sum_log_Gamma[j][k][n];
temp_gamma[n] = temp_mult_gamma[n];
}
mult_poly_taylor(temp_gamma,temp_exp_sum_log_Gamma,temp_mult_gamma,MYDIGITS);
}
for (n=0;n<=MYDIGITS;n++)
gamma[j][n] = temp_mult_gamma[n];
}
cout << "-----------------------------------------------"<< endl;
cout << "The gamma(s+m[j]) coefficients are as follows"<< endl<<endl;
for(j=1;j<=N;j++)
{
cout<<"gamma(s+m["<<j<<"]) = "<<"gamma(s+"<<m[j]<<") = "<<gamma[j][0];
for (n=1;n<=MYDIGITS;n++)
cout << " + " << gamma[j][n] <<" s^"<<n;
cout<<endl;
}
cout << "-----------------------------------------------"<< endl;
}
#endif
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