Iterative Cayley-Hamilton

header-only C++ implementation of the iterative Cayley-Hamilton method for the evaluation of matrix power series (and their differentials) of complex square matrices of arbitrary size. For a more detailed description of the method, please see arXiv:2404.07704.

Content

cayley_hamilton.h

contains the implementation of a callable cayley_hamilton class with three overloads, computing

• only the matrix polynomial,
• the matrix polynomial and its derivative in a given direction,
• the matrix polynomial and all its derivatives. cointains two further subroutines:
• get_r_k computes and returns the Cayley-Hamilton decomposition coefficents for the matrix polynomial and of its derivatives
• get_r_dr computes and returns the Cayley-Hamilton decomposition coefficients of the matrix polynomial and the derivatives of these coefficients

See comments in the header file for more details.

sun_algebra.h

contains the implementation of a sun_algebra class, which provides:

• hermitian su(n) basis as sparse_mat objects
• member functions to transform between su(n) vectors and su(n) matrices in either anti-hermition or hermitian rep.:
  • anti-hermitian: get_alg_mat_ah(invec,outmat) <--> proj_ah(inmat,outvec)
  • hermitiaon: get_alg_mat_h(invec,outmat) <--> proj_h(inmat,outvec)
• member function to take matrix log of SU(N) matrices and return corresponding su(n) vector: log_ah(inmat,outvec)
• member function to compute the SU(N) matrix corresponding to an su(n) vector: get_grp_mat(invec,outmat) (using the cayley_hamilton class)

test.cpp

CPP file to run some basic tests with the cayley_hamilton and sun_algebra classes.