Hi,

The function generate_spline_matrix in fouriertransform.C in the dmft folder shows the comments as follows:

// A is the matrix whose inverse defines spline_matrix
//
//      6                   6
//      1 4 1
//         1 4 1
// A =        ...
//
//                    1 4 1
//    -2 0              0 2

However, the following codes,

dense_matrix A = 4*dt/6.*boost::numeric::ublas::identity_matrix<double>(Np1);

for (int i=1; i<Np1-1; i++) {
    A(i,i-1) = dt/6.;
    A(i,i+1) = dt/6.;
}
A(0,0) = 1.;
A(0, Np1-1) = 1.;
A(Np1-1, 0) = -2.*dt/6.;
A(Np1-1, 1) = -1.*dt/6.;
A(Np1-1, Np1-2) = 1*dt/6.;
A(Np1-1, Np1-1) = 2*dt/6.;

the red lines will make the matrix looks like

//      6                   6
//      1 4 1
//         1 4 1
// A =        ...
//
//                    1 4 1
//    -2 -1             1 2

Is the comment correct or the code correct? Any reference for this algorithm?

Thank you,
Kuang-Shing Chen