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code_Rcpp.cpp
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code_Rcpp.cpp
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#include <RcppArmadillo.h>
// [[Rcpp::depends(RcppArmadillo)]]
using namespace Rcpp;
using namespace std;
//------------------------------------------------------------------------------
// Authors: Anna Melnykova, Irene Tubikanec
// Date: 2023-08-18
//
// Description: auxiliary functions required for the implementation
// of Algorithm MMLH, proposed in the paper:
//
// Granger Causal Inference in Multivariate Hawkes Processes
// by Minimum Message Length, by K. Hlavackova-Schindler, A. Melnykova and I. Tubikanec
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
// Auxiliary search function
//------------------------------------------------------------------------------
// [[Rcpp::export]]
int which_cpp(double val_time, NumericVector vec_times)
{
int index_k=0;
int vec_size=vec_times.size();
while (vec_times[index_k] < val_time && index_k<(vec_size))
{
index_k=index_k+1;
}
return index_k;
};
//------------------------------------------------------------------------------
// Implementation of expressions Aij(t) in Section 4.3 for node i
//------------------------------------------------------------------------------
// [[Rcpp::export]]
NumericMatrix A_i_cpp(NumericVector beta, List y, int i_in)
{
int p=beta.size();
int i=i_in-1;
NumericVector yi=y[i];
int ni=yi.size();
NumericMatrix ret(ni, p);
int k_index;
double sum1;
NumericVector yj;
for(int j = 0; j < p; j++)
{
yj=y[j];
for(int l=0; l < ni; l++)
{
k_index=which_cpp(yi[l],yj);
sum1=0.0;
for(int k=0; k<k_index; k++)
{
sum1=sum1+exp(-beta[i]*(yi[l]-yj[k]));
}
ret(l,j)=sum1;
}
}
return ret;
};
//------------------------------------------------------------------------------
// Implementation of 2nd derivatives required for the Hessian matrix in Section 4.3
//------------------------------------------------------------------------------
//#H_mu_cpp
// [[Rcpp::export]]
double H_mu_cpp(double mu, NumericVector alpha, NumericVector beta, NumericVector yi, NumericMatrix Ai)
{
int p=beta.size();
double sum1;
double sum2;
sum1=0.0;
for(int l = 0; l < yi.size(); l++)
{
sum2=0.0;
for(int j = 0; j < p; j++)
{
sum2=sum2+alpha[j]*Ai(l,j);
}
sum1=sum1+1/((mu+sum2)*(mu+sum2));
}
return sum1;
};
//#H_mu_alphak_cpp
// [[Rcpp::export]]
double H_mu_alphak_cpp(double mu, NumericVector alpha, NumericVector beta, NumericVector yi, int k_in, NumericMatrix Ai)
{
int p=beta.size();
double sum1;
double sum2;
int k=k_in-1;
sum1=0.0;
for(int l = 0; l < yi.size(); l++)
{
sum2=0.0;
for(int j = 0; j < p; j++)
{
sum2=sum2+alpha[j]*Ai(l,j);
}
sum1=sum1+((Ai(l,k))/((mu+sum2)*(mu+sum2)));
}
return sum1;
};
//#H_alphak_alpham_cpp
// [[Rcpp::export]]
double H_alphak_alpham_cpp(double mu, NumericVector alpha, NumericVector beta, NumericVector yi, int k_in, int m_in, NumericMatrix Ai)
{
int p=beta.size();
double sum1;
double sum2;
int k=k_in-1;
int m=m_in-1;
sum1=0.0;
for(int l = 0; l < yi.size(); l++)
{
sum2=0.0;
for(int j = 0; j < p; j++)
{
sum2=sum2+alpha[j]*Ai(l,j);
}
sum1=sum1+((Ai(l,k)*Ai(l,m))/((mu+sum2)*(mu+sum2)));
}
return sum1;
};
//------------------------------------------------------------------------------
// Implementation of the Hessian matrix for node i in Section 4.3
//------------------------------------------------------------------------------
// [[Rcpp::export]]
NumericMatrix Hessian_exact_i_cpp(double mu, NumericVector alpha, NumericVector beta, NumericVector yi, int i, NumericMatrix Ai)
{
int p=beta.size();
NumericMatrix ret(p+1,p+1);
ret(0,0)=H_mu_cpp(mu,alpha,beta,yi,Ai);
for(int k = 0; k < p; k++)
{
ret(0,k+1)=H_mu_alphak_cpp(mu, alpha, beta, yi, k+1, Ai);
ret(k+1,0)=ret(0,k+1);
for(int m = 0; m <= k; m++)
{
ret(k+1,m+1)=H_alphak_alpham_cpp(mu, alpha, beta, yi, k+1, m+1, Ai);
if(m!=k)
{
ret(m+1,k+1)=ret(k+1,m+1);
}
}
}
return ret;
};
//------------------------------------------------------------------------------
// Implementation of the negative log-likelihood for node i in Section 4.2
//------------------------------------------------------------------------------
// [[Rcpp::export]]
double Likelihood_i_cpp(double mu, NumericVector alpha, NumericVector beta, List y, int i_in, NumericMatrix Ai)
{
double sum1;
double sum2;
double sum3;
double sum4;
int i=i_in-1;
int p=beta.size();
NumericVector yi=y[i];
int ni=yi.size();
NumericVector yj;
int nj;
double ret;
//Part I
sum1=0.0;
for(int j = 0; j < p; j++)
{
yj=y[j];
nj=yj.size();
sum2=0.0;
for(int k = 0; k < nj; k++)
{
sum2=sum2+(1.0-exp(-beta[i]*(yi[ni-1]-yj[k])));
}
sum1=sum1+(alpha[j]/beta[i])*sum2;
}
//Part II
sum3=0.0;
for(int l = 0; l < ni; l++)
{
sum4=0.0;
for(int j = 0; j < p; j++)
{
sum4=sum4+alpha[j]*Ai(l,j);
}
sum3=sum3+log( mu + sum4 );
}
ret=mu*yi[ni-1]+sum1-sum3;
return ret;
};