Matrix gamma_exp(const SMatrix& S,const vector<double>& D,double alpha,double beta) {
const int n = S.size1();
std::vector<double> DP(n);
std::vector<double> DN(n);
for(int i=0; i<D.size(); i++) {
DP[i] = sqrt(D[i]);
DN[i] = 1.0/DP[i];
}
SMatrix S2 = S;
for(int i=0; i<S2.size1(); i++)
for(int j=0; j<=i; j++)
S2(i,j) *= DP[i]*DP[j];
Matrix E = gamma_exp(S2,alpha,beta);
// E = prod(DN,prod<Matrix>(E,DP));
for(int i=0; i<E.size1(); i++)
for(int j=0; j<E.size2(); j++)
E(i,j) *= DN[i]*DP[j];
for(int i=0; i<E.size1(); i++)
for(int j=0; j<E.size2(); j++) {
assert(E(i,j) >= -1.0e-13);
if (E(i,j)<0)
E(i,j)=0;
}
return E;
}
Matrix exp(const SMatrix& S,const vector<double>& D,double t)
{
const int n = S.size1();
// compute S2 = D^1/2 * S * D^1/2
std::vector<double> DP(n);
std::vector<double> DN(n);
for(int i=0; i<D.size(); i++) {
DP[i] = sqrt(D[i]);
DN[i] = 1.0/DP[i];
}
//SMatrix S2 = prod(DP,prod<Matrix>(S,DP));
SMatrix S2 = S;
for(int i=0; i<S2.size1(); i++)
for(int j=0; j<=i; j++)
S2(i,j) *= DP[i]*DP[j];
// compute E = exp(S2)
Matrix E = exp(S2,t);
for(int i=0; i<E.size1(); i++)
for(int j=0; j<E.size2(); j++)
E(i,j) *= DN[i]*DP[j];
// Double-check that E(i,j) is always positive
for(int i=0; i<E.size1(); i++)
for(int j=0; j<E.size2(); j++) {
assert(E(i,j) >= -1.0e-13);
if (E(i,j)<0)
E(i,j)=0;
}
return E;
}