Backend

The Introduction to EDRIXS describes the four stages of a calculation. Stages two to four – building operators, diagonalizing, and assembling spectra – delegate their numerical work to a backend selected with backend when calling build_op or get_ops:

• 'dense' builds full NumPy matrices and uses exact dense diagonalization and explicit eigenstate sums. It is intended for small problems, reference calculations, and pedagogy.

• 'scipy' builds SciPy CSR matrices and uses LOBPCG, Lanczos, and GMRES. It is the default backend.

• 'fortran' uses the native MPI solvers and communicates through files in the current working directory. We provide the function edrixs.get_ops_disk to load the setup from disk if desired.

• 'petsc' uses distributed PETSc matrices, SLEPc eigensolvers, and PETSc Krylov solvers. It is intended for larger Hilbert spaces and MPI runs.

Backend-specific numerical controls belong in a backend_kws mapping. The mapping is specific to both the backend and the operation.

Operator factories and solver dispatch

build_op returns a callable that constructs the matrix when called. This lets callers defer matrix allocation and recreate matrices when needed. Its .backend attribute identifies the numerical backend and the matrix representation it will produce.

Numerical get_ops returns these callables for both Hamiltonians and every transition component. Public ed and rixs dispatch using hmat_i.backend; xas uses hmat_n.backend. They pass the factories unchanged to the selected backend and assume all operators are suitable for it. Dense, SciPy, and PETSc ED call every supplied factory at calculation start. Repeated arguments may be instantiated independently. PETSc XAS and RIXS accept matrix_lifetime in backend_kws; see PETSc keywords. All staged solver entry points, including backend-specific functions, require factories or callable Fortran disk handles.

For matrix arithmetic or direct access to matrix methods, call the factory explicitly:

number_op = edrixs.build_op(number_coefficients, None, basis, backend='dense')
number_matrix = number_op()

Numerical precision

XAS and RIXS thermally average over the retained initial eigenstates. Request enough eigenpairs from ed to keep every thermally populated state in the ground-state manifold, including complete degenerate or nearly degenerate multiplets; otherwise the Boltzmann average is incomplete.

EDRIXS uses established numerical linear-algebra packages, but floating-point and iterative solvers are not exact. If numerical accuracy is a concern, repeat the calculation with varied solver settings and check that the result is unchanged. Relevant settings include tol or eigval_tol, maxiter, blocksize or ncv, nkryl, and the RIXS linsys_* options documented below.

Backend keyword reference

Choose the backend whose keywords you need:

• SciPy keywords

• Dense keywords

• Fortran keywords

• PETSc keywords

These references apply to the staged get_ops / ed / xas / rixs interface. The legacy ed_*_fort, xas_*_fort, and rixs_*_fort functions retain their existing explicit parameters.