Template Function LanczosEigenvalue

Function Documentation

template<typename T, typename HilbertField>
void LanczosEigenvalue(T &H, vector<HilbertField> &gs, vector<double> &alpha, vector<double> &beta, vector<double> &energy, size_t &niter, bool verb = false)

Implementation of the Lanczos method for the lowest eigenvalue.

Applies the Lanczos algorithm for the lowest eigenvalue. Doesn’t calculate the correponding eigenvector. Assumes the multiply-add matrix routine is usually provided by a struct method

The structure H is assumed to have the following elements:

  • A method hamil.multadd(vector<HilbertField> &x, vector<HilbertField> &y) that does y –> y + H.x

Parameters:

  • H – Hamiltonian matrix

  • gs – initial vector

  • alpha – Diagonal of the tridiagonal matrix (allocated on input, provided on output).

  • beta – Second Diagonal of the tridiagonal matrix (allocated on input, provided on output).

  • energy – eigenvalues

  • niter – Number of iterations (maximum number provided on input, actual number on output).