sirius Module Reference

Namespace of the SIRIUS library. More...

Modules
namespace	acc
	Namespace for accelerator-related functions.
namespace	cg
	Conjugate-gradient solver.
namespace	env
	Get environment variables.
namespace	fft
	FFT-related functions and objects.
namespace	la
	Interface to linear algebra BLAS/LAPACK functions.
namespace	local
	Internal implementation of beta-projectors generator.
namespace	lr
	Linear respone functions and objects.
namespace	magma
	Interface to MAGMA functions.
namespace	mixer
	Mixer functions and objects.
namespace	mpi
	MPI related functions and classes.
namespace	r3
	Work with 3D vectors and matrices.
namespace	rte
	Run-time error and warning handling.
namespace	sf
	Special functions.
namespace	smearing
	Occupancy smearing functions.
namespace	wf
	Namespace for the wave-functions.

Data Types
class	angular_momentum
	Angular momentum quantum number. More...
class	any_ptr
	Handle deallocation of a poiniter to an object of any type. More...
class	Array1d
	TODO: Array1d owns data... More...
class	Atom
	Data and methods specific to the actual atom in the unit cell. More...
struct	atom_index_t
class	Atom_symmetry_class
	Data and methods specific to the symmetry class of the atom. More...
struct	atom_symmetry_class_index_t
class	Atom_type
	Defines the properties of atom type. More...
class	Atom_type_base
	Base class for sirius::Atom_type and sirius::Free_atom classes. More...
struct	atom_type_index_t
class	Augmentation_operator
	Augmentation charge operator Q(r) of the ultrasoft pseudopotential formalism. More...
struct	basic_index_t
	Basic index type. More...
struct	basis_function_index_descriptor
class	basis_functions_index
	A helper class to establish various index mappings for the atomic basis functions. More...
struct	beta_chunk_t
	Describe chunk of beta-projectors for a block of atoms. More...
struct	beta_desc_idx
	Named index of a descriptor of beta-projectors. The same order is used by the GPU kernel. More...
class	Beta_projector_generator
class	Beta_projectors
	Stores <G+k | beta> expansion. More...
class	Beta_projectors_base
	Base class for beta-projectors, gradient of beta-projectors and strain derivatives of beta-projectors. More...
struct	beta_projectors_coeffs_t
	Stores a chunk of the beta-projector and metadata. More...
class	Beta_projectors_gradient
	Compute gradient of beta-projectors over atomic positions \( d \langle {\bf G+k} | \beta \rangle / d \tau_{\alpha} \). More...
class	Beta_projectors_strain_deriv
class	Bound_state
struct	callback_functions_t
	Store all callback functions in one place. More...
class	cmd_args
	Simple command line arguments handler. More...
class	Config
class	config_t
class	Crystal_symmetry
	Representation of the crystal symmetry. More...
class	CUDA_timer
class	CUDA_timers_wrapper
class	D_operator
struct	davidson_result_t
	Result of Davidson solver. More...
class	Density
	Generate charge density and magnetization from occupied spinor wave-functions. More...
class	density_matrix_t
class	DFT_ground_state
	The whole DFT ground state implementation. More...
struct	diagonalize_result_t
class	DiagonalPreconditioner
class	Energy
	Kohn-Sham energy. More...
class	Enu_finder
class	ffmt
	Floating-point formatting (precision and width). More...
class	Field4D
	Four-component function consisting of scalar and vector parts. More...
class	Force
	Compute atomic forces. More...
class	Free_atom
	Full potential free atom solver. More...
class	Gaunt_coefficients
	Compact storage of non-zero Gaunt coefficients \( \langle \ell_1 m_1 | \ell_3 m_3 | \ell_2 m_2 \rangle \). More...
struct	gaunt_L1_L2
	Used in the {lm1, lm2, coefficient} : {lm3} way of grouping non-zero Gaunt coefficients. More...
struct	gaunt_L3
	Used in the {lm1, lm2} : {lm3, coefficient} way of grouping non-zero Gaunt coefficients. More...
struct	GPU_Complex
	helper type traits to template kernel function More...
struct	GPU_Complex< double >
struct	GPU_Complex< float >
class	Hamiltonian0
	Represent the k-point independent part of Hamiltonian. More...
class	Hamiltonian_k
	Representation of Kohn-Sham Hamiltonian. More...
class	hbar
	Horisontal bar. More...
class	HDF5_tree
	Interface to the HDF5 library. More...
struct	hdf5_type_wrapper
struct	hdf5_type_wrapper< double >
struct	hdf5_type_wrapper< float >
struct	hdf5_type_wrapper< int >
struct	hdf5_type_wrapper< uint8_t >
class	Hubbard
	Apply Hubbard correction in the collinear case. More...
class	Hubbard_matrix
	Describes Hubbard orbital occupancy or potential correction matrices. More...
class	hubbard_orbital_descriptor
	Structure containing all information about a specific hubbard orbital (including the radial function). More...
struct	identity
class	InverseS_k
class	K_point
	K-point related variables and methods. More...
class	K_point_set
	Set of k-points. More...
struct	kp_index_t
	K-point index type. More...
class	Lattice_relaxation
struct	lo_basis_descriptor
	Descriptor of the local-orbital part of the LAPW+lo basis. More...
class	Local_operator
	Representation of the local operator. More...
struct	local_orbital_descriptor
	Descriptor of a local orbital radial function. More...
struct	magnetic_group_symmetry_descriptor
	Descriptor of the magnetic group symmetry operation. More...
class	Matching_coefficients
class	Matrix
class	Measurement
struct	nearest_neighbour_descriptor
	Descriptor of an atom in a list of nearest neighbours for each atom. More...
class	Non_local_operator
	Non-local part of the Hamiltonian and S-operator in the pseudopotential method. More...
class	null_stream_t
class	Occupation_matrix
struct	paw_atom_index_t
class	PAW_density
	PAW density storage. More...
class	PAW_field4D
	PAW density and potential storage. More...
class	Periodic_function
	Representation of the periodical function on the muffin-tin geometry. More...
struct	periodic_function_ptr_t
	Describe external pointers to periodic function. More...
class	Potential
	Generate effective potential from charge density and magnetization. More...
struct	ps_atomic_wf_descriptor
	Store basic information about radial pseudo wave-functions. More...
class	Q_operator
struct	radial_function_index_descriptor
	Descriptor for the atomic radial functions. More...
class	radial_functions_index
	Radial basis function index. More...
class	Radial_grid
	Base class for radial grids. More...
class	Radial_grid_exp
class	Radial_grid_ext
	External radial grid provided as a list of points. More...
class	Radial_grid_lin
class	Radial_grid_lin_exp
class	Radial_grid_pow
class	Radial_integrals_atomic_wf
	Radial integrals of the atomic centered orbitals. More...
class	Radial_integrals_aug
	Radial integrals of the augmentation operator. More...
class	Radial_integrals_base
	Base class for all kinds of radial integrals. More...
class	Radial_integrals_beta
	Radial integrals of beta projectors. More...
class	Radial_integrals_rho_core_pseudo
class	Radial_integrals_rho_free_atom
class	Radial_integrals_rho_pseudo
struct	radial_integrals_t
	Store all radial integrals in one place. More...
class	Radial_integrals_vloc
struct	radial_solution_descriptor
	Describes radial solution. More...
class	Radial_solver
	Finds a solution to radial Schrodinger, Koelling-Harmon or Dirac equation. More...
struct	Real
struct	Real< gpu_complex_type< double > >
struct	Real< gpu_complex_type< float > >
struct	Real< std::complex< T > >
class	S_k
class	Scalar
class	serializer
	Serialize and deserialize objects. More...
class	SHT
	Spherical harmonics transformations and related oprtations. More...
class	Simulation_context
	Simulation context is a set of parameters and objects describing a single simulation. More...
class	Simulation_parameters
	Set of basic parameters of a simulation. More...
type	sirius_context_handler
	Opaque wrapper for simulation context handler. More...
interface	sirius_free_handler
	Free any of the SIRIUS handlers (context, ground state or k-points). More...
type	sirius_ground_state_handler
	Opaque wrapper for DFT ground statee handler. More...
type	sirius_kpoint_set_handler
	Opaque wrapper for K-point set handler. More...
class	Smooth_periodic_function
	Representation of a smooth (Fourier-transformable) periodic function. More...
struct	smooth_periodic_function_ptr_t
class	Smooth_periodic_vector_function
	Vector of the smooth periodic functions. More...
struct	space_group_symmetry_descriptor
	Descriptor of the space group symmetry operation. More...
class	Spheric_function
	Function in spherical harmonics or spherical coordinates representation. More...
class	Spheric_function_set
struct	spheric_function_set_ptr_t
class	Spheric_vector_function
	3D vector function. More...
class	splindex
	Base class for split index. More...
class	splindex_block
class	splindex_block_cyclic
class	splindex_chunk
	Externally defined block distribution. More...
class	splindex_iterator_t
class	Spline
	Cubic spline with a not-a-knot boundary conditions. More...
struct	step_function_t
	Representation of the unit step function. More...
class	Stress
	Stress tensor. More...
class	strong_type
class	Teter
class	U_operator
class	Ultrasoft_preconditioner
class	Unit_cell
	Representation of a unit cell. More...
struct	unit_cell_parameters_descriptor
class	XC_functional
	Interface class to Libxc. More...
class	XC_functional_base
	Interface class to Libxc. More...

Typedefs
using	acc_stream_t = cudaStream_t
using	acc_error_t = cudaError_t
using	acc_complex_float_t = cuFloatComplex
using	acc_complex_double_t = cuDoubleComplex
template<typename T >
using	gpu_complex_type = typename GPU_Complex< T >::type
template<typename T >
using	real_type = typename Real< T >::type
using	n_blocks = strong_type< int, struct __n_blocks_tag >
	Number of blocks to which the global index is split. More...
using	block_id = strong_type< int, struct __block_id_tag >
	ID of the block. More...
using	time_point_t = std::chrono::high_resolution_clock::time_point
template<class X >
using	identity_t = typename identity< X >::type
typedef std::vector< radial_solution_descriptor >	radial_solution_descriptor_set
	Set of radial solution descriptors, used to construct augmented waves or local orbitals. More...
using	Flm = Spheric_function< function_domain_t::spectral, double >
using	Ftp = Spheric_function< function_domain_t::spatial, double >
using	lmax_t = strong_type< int, struct __lmax_t_tag >
using	rf_index = strong_type< int, struct __rf_index_tag >
	Radial function index. More...
using	rf_aw_index = strong_type< int, struct __rf_aw_index_tag >
	Augmented wave radial function index. More...
using	rf_lo_index = strong_type< int, struct __rf_lo_index_tag >
	Local orbital radial function index. More...
using	bf_index = strong_type< int, struct __bf_index_tag >
	Basis function index. More...
using	bf_aw_index = strong_type< int, struct __bf_aw_index_tag >
	Augmented wave basis function index. More...
using	bf_lo_index = strong_type< int, struct __bf_lo_index_tag >
	Local orbital basis function index. More...
using	json = nlohmann::json

Enumerations
enum class	hdf5_access_t { truncate , read_write , read_only }
enum class	index_domain_t { global , local }
enum class	spin_block_t {   nm , uu , dd , ud ,   du }
	Spin-blocks of the Hamiltonian. More...
enum class	electronic_structure_method_t { full_potential_lapwlo , pseudopotential }
	Type of electronic structure methods. More...
enum class	function_domain_t { spatial , spectral }
	Type of a function domain. More...
enum class	relativity_t {   none , koelling_harmon , zora , iora ,   dirac }
	Type of relativity treatment in the case of LAPW. More...
enum class	davidson_evp_t { hamiltonian , overlap }
enum class	sync_band_t { energy , occupancy }
enum class	radial_grid_t : int { linear = 0 , exponential = 1 , power = 2 , lin_exp = 3 }
	Types of radial grid. More...

Functions/Subroutines
character(kind=c_char, len=1) function, dimension(len_trim(f_string)+1)	string_f2c (f_string)
	Internal function that adds trailing null character to the string to make it C-style. More...
character(kind=c_char, len=size(c_string) - 1) function	string_c2f (c_string)
	Internal function that converts C-string (with trailing null character) to the Fortran string. More...
subroutine	sirius_initialize (call_mpi_init, error_code)
	Initialize the SIRIUS library. More...
subroutine	sirius_finalize (call_mpi_fin, call_device_reset, call_fftw_fin, error_code)
	Shut down the SIRIUS library. More...
subroutine	sirius_start_timer (name, error_code)
	Start the timer. More...
subroutine	sirius_stop_timer (name, error_code)
	Stop the running timer. More...
subroutine	sirius_print_timers (flatten, error_code)
	Print all timers. More...
subroutine	sirius_serialize_timers (fname, error_code)
	Save all timers to JSON file. More...
subroutine	sirius_context_initialized (handler, status, error_code)
	Check if the simulation context is initialized. More...
subroutine	sirius_create_context (fcomm, handler, fcomm_k, fcomm_band, error_code)
	Create context of the simulation. More...
subroutine	sirius_import_parameters (handler, str, error_code)
	Import parameters of simulation from a JSON string. More...
subroutine	sirius_set_parameters (handler, lmax_apw, lmax_rho, lmax_pot, num_fv_states, num_bands, num_mag_dims, pw_cutoff, gk_cutoff, fft_grid_size, auto_rmt, gamma_point, use_symmetry, so_correction, valence_rel, core_rel, iter_solver_tol_empty, iter_solver_type, verbosity, hubbard_correction, hubbard_correction_kind, hubbard_full_orthogonalization, hubbard_orbitals, sht_coverage, min_occupancy, smearing, smearing_width, spglib_tol, electronic_structure_method, error_code)
	Set parameters of the simulation. More...
subroutine	sirius_get_parameters (handler, lmax_apw, lmax_rho, lmax_pot, num_fv_states, num_bands, num_spins, num_mag_dims, pw_cutoff, gk_cutoff, fft_grid_size, auto_rmt, gamma_point, use_symmetry, so_correction, iter_solver_tol, iter_solver_tol_empty, verbosity, hubbard_correction, evp_work_count, num_loc_op_applied, num_sym_op, electronic_structure_method, error_code)
	Get parameters of the simulation. More...
subroutine	sirius_add_xc_functional (handler, name, error_code)
	Add one of the XC functionals. More...
subroutine	sirius_set_mpi_grid_dims (handler, ndims, dims, error_code)
	Set dimensions of the MPI grid. More...
subroutine	sirius_set_lattice_vectors (handler, a1, a2, a3, error_code)
	Set vectors of the unit cell. More...
subroutine	sirius_initialize_context (handler, error_code)
	Initialize simulation context. More...
subroutine	sirius_update_context (handler, error_code)
	Update simulation context after changing lattice or atomic positions. More...
subroutine	sirius_print_info (handler, error_code)
	Print basic info. More...
subroutine	sirius_free_object_handler (handler, error_code)
	Free any object handler created by SIRIUS. More...
subroutine	sirius_set_periodic_function_ptr (handler, label, f_mt, lmmax, nrmtmax, num_atoms, f_rg, size_x, size_y, size_z, offset_z, error_code)
	Set pointer to density or magnetization. More...
subroutine	sirius_set_periodic_function (handler, label, f_mt, lmmax, nrmtmax, num_atoms, f_rg, size_x, size_y, size_z, offset_z, error_code)
	Set values of the periodic function. More...
subroutine	sirius_get_periodic_function (handler, label, f_mt, lmmax, nrmtmax, num_atoms, f_rg, size_x, size_y, size_z, offset_z, error_code)
	Get values of the periodic function. More...
subroutine	sirius_create_kset (handler, num_kpoints, kpoints, kpoint_weights, init_kset, kset_handler, error_code)
	Create k-point set from the list of k-points. More...
subroutine	sirius_create_kset_from_grid (handler, k_grid, k_shift, use_symmetry, kset_handler, error_code)
	Create k-point set from a grid. More...
subroutine	sirius_create_ground_state (ks_handler, gs_handler, error_code)
	Create a ground state object. More...
subroutine	sirius_initialize_kset (ks_handler, count, error_code)
	Initialize k-point set. More...
subroutine	sirius_find_ground_state (gs_handler, density_tol, energy_tol, iter_solver_tol, initial_guess, max_niter, save_state, converged, niter, rho_min, error_code)
	Find the ground state. More...
subroutine	sirius_check_scf_density (gs_handler, error_code)
	Check the self-consistent density. More...
subroutine	sirius_update_ground_state (gs_handler, error_code)
	Update a ground state object after change of atomic coordinates or lattice vectors. More...
subroutine	sirius_add_atom_type (handler, label, fname, zn, symbol, mass, spin_orbit, error_code)
	Add new atom type to the unit cell. More...
subroutine	sirius_set_atom_type_radial_grid (handler, label, num_radial_points, radial_points, error_code)
	Set radial grid of the atom type. More...
subroutine	sirius_set_atom_type_radial_grid_inf (handler, label, num_radial_points, radial_points, error_code)
	Set radial grid of the free atom (up to effectice infinity). More...
subroutine	sirius_add_atom_type_radial_function (handler, atom_type, label, rf, num_points, n, l, idxrf1, idxrf2, occ, error_code)
	Add one of the radial functions. More...
subroutine	sirius_set_atom_type_hubbard (handler, label, l, n, occ, U, J, alpha, beta, J0, error_code)
	Set the hubbard correction for the atomic type. More...
subroutine	sirius_set_atom_type_dion (handler, label, num_beta, dion, error_code)
	Set ionic part of D-operator matrix. More...
subroutine	sirius_set_atom_type_paw (handler, label, core_energy, occupations, num_occ, error_code)
	Set PAW related data. More...
subroutine	sirius_add_atom (handler, label, position, vector_field, error_code)
	Add atom to the unit cell. More...
subroutine	sirius_set_atom_position (handler, ia, position, error_code)
	Set new atomic position. More...
subroutine	sirius_set_pw_coeffs (handler, label, pw_coeffs, transform_to_rg, ngv, gvl, comm, error_code)
	Set plane-wave coefficients of a periodic function. More...
subroutine	sirius_get_pw_coeffs (handler, label, pw_coeffs, ngv, gvl, comm, error_code)
	Get plane-wave coefficients of a periodic function. More...
subroutine	sirius_initialize_subspace (gs_handler, ks_handler, error_code)
	Initialize the subspace of wave-functions. More...
subroutine	sirius_find_eigen_states (gs_handler, ks_handler, precompute_pw, precompute_rf, precompute_ri, iter_solver_tol, error_code)
	Find eigen-states of the Hamiltonian. More...
subroutine	sirius_generate_initial_density (handler, error_code)
	Generate initial density. More...
subroutine	sirius_generate_effective_potential (handler, error_code)
	Generate effective potential and magnetic field. More...
subroutine	sirius_generate_density (gs_handler, add_core, transform_to_rg, paw_only, error_code)
	Generate charge density and magnetization. More...
subroutine	sirius_set_band_occupancies (ks_handler, ik, ispn, band_occupancies, error_code)
	Set band occupancies. More...
subroutine	sirius_get_band_occupancies (ks_handler, ik, ispn, band_occupancies, error_code)
	Set band occupancies. More...
subroutine	sirius_get_band_energies (ks_handler, ik, ispn, band_energies, error_code)
	Get band energies. More...
subroutine	sirius_get_energy (handler, label, energy, error_code)
	Get one of the total energy components. More...
subroutine	sirius_get_forces (handler, label, forces, error_code)
	Get one of the total force components. More...
subroutine	sirius_get_stress_tensor (handler, label, stress_tensor, error_code)
	Get one of the stress tensor components. More...
subroutine	sirius_get_num_beta_projectors (handler, label, num_bp, error_code)
	Get the number of beta-projectors for an atom type. More...
subroutine	sirius_get_wave_functions (ks_handler, vkl, spin, num_gvec_loc, gvec_loc, evec, ld, num_spin_comp, error_code)
	Get wave-functions. More...
subroutine	sirius_add_atom_type_aw_descriptor (handler, label, n, l, enu, dme, auto_enu, error_code)
	Add descriptor of the augmented wave radial function. More...
subroutine	sirius_add_atom_type_lo_descriptor (handler, label, ilo, n, l, enu, dme, auto_enu, error_code)
	Add descriptor of the local orbital radial function. More...
subroutine	sirius_set_atom_type_configuration (handler, label, n, l, k, occupancy, core, error_code)
	Set configuration of atomic levels. More...
subroutine	sirius_generate_coulomb_potential (handler, vh_el, error_code)
	Generate Coulomb potential by solving Poisson equation. More...
subroutine	sirius_generate_xc_potential (handler, error_code)
	Generate XC potential using LibXC. More...
subroutine	sirius_get_kpoint_inter_comm (handler, fcomm, error_code)
	Get communicator which is used to split k-points. More...
subroutine	sirius_get_kpoint_inner_comm (handler, fcomm, error_code)
	Get communicator which is used to parallise band problem. More...
subroutine	sirius_get_fft_comm (handler, fcomm, error_code)
	Get communicator which is used to parallise FFT. More...
subroutine	sirius_get_num_gvec (handler, num_gvec, error_code)
	Get total number of G-vectors on the fine grid. More...
subroutine	sirius_get_gvec_arrays (handler, gvec, gvec_cart, gvec_len, index_by_gvec, error_code)
	Get G-vector arrays. More...
subroutine	sirius_get_num_fft_grid_points (handler, num_fft_grid_points, error_code)
	Get local number of FFT grid points. More...
subroutine	sirius_get_fft_index (handler, fft_index, error_code)
	Get mapping between G-vector index and FFT index. More...
subroutine	sirius_get_max_num_gkvec (ks_handler, max_num_gkvec, error_code)
	Get maximum number of G+k vectors across all k-points in the set. More...
subroutine	sirius_get_gkvec_arrays (ks_handler, ik, num_gkvec, gvec_index, gkvec, gkvec_cart, gkvec_len, gkvec_tp, error_code)
	Get all G+k vector related arrays. More...
subroutine	sirius_get_step_function (handler, cfunig, cfunrg, num_rg_points, error_code)
	Get the unit-step function. More...
subroutine	sirius_set_h_radial_integrals (handler, ia, lmmax, val, l1, o1, ilo1, l2, o2, ilo2, error_code)
	Set LAPW Hamiltonian radial integrals. More...
subroutine	sirius_set_o_radial_integral (handler, ia, val, l, o1, ilo1, o2, ilo2, error_code)
	Set LAPW overlap radial integral. More...
subroutine	sirius_set_o1_radial_integral (handler, ia, val, l1, o1, ilo1, l2, o2, ilo2, error_code)
	Set a correction to LAPW overlap radial integral. More...
subroutine	sirius_set_radial_function (handler, ia, deriv_order, f, l, o, ilo, error_code)
	Set LAPW radial functions. More...
subroutine	sirius_set_equivalent_atoms (handler, equivalent_atoms, error_code)
	Set equivalent atoms. More...
subroutine	sirius_update_atomic_potential (handler, error_code)
	Set the new spherical potential. More...
subroutine	sirius_option_get_number_of_sections (length, error_code)
	Return the total number of sections defined in the input JSON schema. More...
subroutine	sirius_option_get_section_name (elem, section_name, section_name_length, error_code)
	Return the name of a given section. More...
subroutine	sirius_option_get_section_length (section, length, error_code)
	Return the number of options in a given section. More...
subroutine	sirius_option_get_info (section, elem, key_name, key_name_len, type, length, enum_size, title, title_len, description, description_len, error_code)
	Return information about the option. More...
subroutine	sirius_option_get (section, name, type, data_ptr, max_length, enum_idx, error_code)
	Return the default value of the option as defined in the JSON schema. More...
subroutine	sirius_option_set (handler, section, name, type, data_ptr, max_length, append, error_code)
	Set the value of the option name in a (internal) json dictionary. More...
subroutine	sirius_dump_runtime_setup (handler, filename, error_code)
	Dump the runtime setup in a file. More...
subroutine	sirius_get_fv_eigen_vectors (handler, ik, fv_evec, ld, num_fv_states, error_code)
	Get the first-variational eigen vectors. More...
subroutine	sirius_get_fv_eigen_values (handler, ik, fv_eval, num_fv_states, error_code)
	Get the first-variational eigen values. More...
subroutine	sirius_get_sv_eigen_vectors (handler, ik, sv_evec, num_bands, error_code)
	Get the second-variational eigen vectors. More...
subroutine	sirius_set_rg_values (handler, label, grid_dims, local_box_origin, local_box_size, fcomm, values, transform_to_pw, error_code)
	Set the values of the function on the regular grid. More...
subroutine	sirius_get_rg_values (handler, label, grid_dims, local_box_origin, local_box_size, fcomm, values, transform_to_rg, error_code)
	Get the values of the function on the regular grid. More...
subroutine	sirius_get_total_magnetization (handler, mag, error_code)
	Get the total magnetization of the system. More...
subroutine	sirius_get_num_kpoints (handler, num_kpoints, error_code)
	Get the total number of kpoints. More...
subroutine	sirius_get_kpoint_properties (handler, ik, weight, coordinates, error_code)
	Get the kpoint properties. More...
subroutine	sirius_set_callback_function (handler, label, fptr, error_code)
	Set callback function to compute various radial integrals. More...
subroutine	sirius_nlcg (handler, ks_handler, error_code)
	Robust wave function optimizer. More...
subroutine	sirius_nlcg_params (handler, ks_handler, temp, smearing, kappa, tau, tol, maxiter, restart, processing_unit, converged, error_code)
	Robust wave function optimizer. More...
subroutine	sirius_add_hubbard_atom_pair (handler, atom_pair, translation, n, l, coupling, error_code)
	Add a non-local Hubbard interaction V for a pair of atoms. More...
subroutine	sirius_create_h0 (handler, error_code)
	Generate H0. More...
subroutine	sirius_linear_solver (handler, vkq, num_gvec_kq_loc, gvec_kq_loc, dpsi, psi, eigvals, dvpsi, ld, num_spin_comp, alpha_pv, spin, nbnd_occ, tol, niter, error_code)
	Interface to linear solver. More...
subroutine	sirius_generate_d_operator_matrix (handler, error_code)
	Generate D-operator matrix. More...
subroutine	sirius_save_state (gs_handler, file_name, error_code)
	Save DFT ground state (density and potential) More...
subroutine	sirius_load_state (handler, file_name, error_code)
	Save DFT ground state (density and potential) More...
subroutine	sirius_set_density_matrix (handler, ia, dm, ld, error_code)
	Set density matrix. More...
subroutine	sirius_free_handler_ctx (handler, error_code)
subroutine	sirius_free_handler_ks (handler, error_code)
subroutine	sirius_free_handler_dft (handler, error_code)
void	create_beta_gk_gpu (int num_atoms, int num_gkvec, int const *beta_desc, std::complex< float > const *beta_gk_t, double const *gkvec, double const *atom_pos, std::complex< float > *beta_gk)
void	create_beta_gk_gpu (int num_atoms, int num_gkvec, int const *beta_desc, std::complex< double > const *beta_gk_t, double const *gkvec, double const *atom_pos, std::complex< double > *beta_gk)
void	create_beta_gk_gpu_float (int num_atoms, int num_gkvec, int const *beta_desc, std::complex< float > const *beta_gk_t, double const *gkvec, double const *atom_pos, std::complex< float > *beta_gk)
void	create_beta_gk_gpu_double (int num_atoms, int num_gkvec, int const *beta_desc, std::complex< double > const *beta_gk_t, double const *gkvec, double const *atom_pos, std::complex< double > *beta_gk)
template<typename F , typename T >
std::enable_if_t< std::is_same< T, real_type< F > >::value, la::dmatrix< F > >	inner_prod_beta (spla::Context &spla_ctx, sddk::memory_t mem__, sddk::memory_t host_mem__, bool result_on_device, beta_projectors_coeffs_t< T > &beta_coeffs__, wf::Wave_functions< T > const &phi__, wf::spin_index ispn__, wf::band_range br__)
template<class T >
sddk::matrix< std::complex< T > >	inner_beta (const Beta_projectors_base< T > &beta, const Simulation_context &ctx)
	computes <beta|beta> and returns result on ctx.processing_unit_memory_t More...
template<class T , class Op >
sddk::matrix< std::complex< T > >	inner_beta (const Beta_projectors_base< T > &beta, const Simulation_context &ctx, Op &&op)
	inner product <beta|Op|beta>, return resulting dmatrix<complex> in ctx.processing_unit_memory_t More...
std::string const	locked_msg ("parameters are locked")
template<typename OUT >
void	print_memory_usage (OUT &&out__, std::string file_and_line__="")
template<typename T >
static std::ostringstream	option_print_vector__ (const std::vector< T > &vec)
void	compose_default_json (nlohmann::json const &schema__, nlohmann::json &output__)
	Compose JSON dictionary with default parameters based on input schema. More...
void	compose_json (nlohmann::json const &schema__, nlohmann::json const &in__, nlohmann::json &inout__)
	Append the input dictionary to the existing dictionary. More...
nlohmann::json const &	get_options_dictionary ()
	Get all possible options for initializing sirius. It is a json dictionary. More...
nlohmann::json const &	get_section_options (std::string const &section__)
	Get all possible options of a given input section. It is a json dictionary. More...
void	scale_matrix_rows_gpu (int nrow, int ncol, acc_complex_double_t *mtrx, double const *v)
void	scale_matrix_elements_gpu (acc_complex_double_t *ptr__, int ld__, int nrow__, int ncol__, double beta__)
void	ddiagmm (const double *diag, int n, const double *X, int lda_x, int ncols, double *Y, int lda_y, double alpha)
void	sdiagmm (const float *diag, int n, const float *X, int lda_x, int ncols, float *Y, int lda_y, float alpha)
void	zdiagmm (const std::complex< double > *diag, int n, const std::complex< double > *X, int lda_x, int ncols, std::complex< double > *Y, int lda_y, std::complex< double > alpha)
template<>
std::string	cmd_args::value< std::string > (const std::string key__) const
template<>
std::string	cmd_args::value< std::string > (const std::string key__, const std::string default_val__) const
template<>
std::vector< double >	cmd_args::value< std::vector< double > > (const std::string key__) const
template<>
std::vector< int >	cmd_args::value< std::vector< int > > (const std::string key__) const
auto	confined_polynomial (double r, double R, int p1, int p2, int dm)
template<typename T >
int	sign (T val)
	Sign of the variable. More...
template<typename T >
bool	is_int (T val__, T eps__)
	Checks if number is integer with a given tolerance. More...
template<typename T >
T	factorial (int n)
	Compute a factorial. More...
auto	round (double a__, int n__)
auto	round (std::complex< double > a__, int n__)
auto	hash (void const *buff, size_t size, uint64_t h=5381)
	Simple hash function. More...
uint32_t	random_uint32 (bool reset=false)
	Simple random number generator. More...
template<typename T >
T	random ()
template<>
int	random< int > ()
template<>
double	random< double > ()
template<>
std::complex< double >	random< std::complex< double > > ()
template<>
float	random< float > ()
template<>
std::complex< float >	random< std::complex< float > > ()
template<typename T >
auto	abs_diff (T a, T b)
template<typename T >
auto	rel_diff (T a, T b)
auto	conj (double x__)
	Return complex conjugate of a number. For a real value this is the number itself. More...
auto	conj (std::complex< double > x__)
	Return complex conjugate of a number. More...
template<typename T >
T	zero_if_not_complex (T x__)
template<typename T >
T	zero_if_not_complex (std::complex< T > x__)
null_stream_t &	null_stream ()
std::string	boolstr (bool b__)
std::ostream &	operator<< (std::ostream &out, hbar &&b)
	Inject horisontal bar to ostream. More...
std::ostream &	operator<< (std::ostream &out, ffmt &&f)
	Inject floating point format to ostream. More...
template<typename T >
std::ostream &	operator<< (std::ostream &out, std::vector< T > &v)
	Print std::vector to ostream. More...
std::string	double_to_string (double val, int precision=-1)
	Convert double to a string with a given precision. More...
template<typename T , typename OUT >
void	print_checksum (std::string label__, T value__, OUT &&out__)
template<typename OUT >
void	print_hash (std::string label__, unsigned long long int hash__, OUT &&out__)
int	packed_index (int i__, int j__)
	Pack two indices into one for symmetric matrices. More...
template<typename T , int N>
nlohmann::json	serialize (sddk::mdarray< T, N > const &a__)
template<typename T , int N>
nlohmann::json	serialize (sddk::mdarray< std::complex< T >, N > const &a__)
template<typename T , int N>
void	write_to_json_file (sddk::mdarray< T, N > const &a__, std::string const &fname__)
template<typename T >
void	serialize (serializer &s__, T var__)
	Serialize a single element. More...
template<typename T >
void	deserialize (serializer &s__, T &var__)
	Deserialize a single element. More...
template<typename T >
void	serialize (serializer &s__, std::vector< T > const &vec__)
	Serialize a vector. More...
template<typename T >
void	deserialize (serializer &s__, std::vector< T > &vec__)
	Deserialize a vector. More...
template<typename T , int N>
void	serialize (serializer &s__, sddk::mdarray< T, N > const &array__)
	Serialize multidimentional array. More...
template<typename T , int N>
void	deserialize (serializer &s__, sddk::mdarray< T, N > &array__)
	Deserialize multidimentional array. More...
void	serialize (serializer &s__, mpi::block_data_descriptor const &dd__)
	Serialize block data descriptor. More...
void	deserialize (serializer &s__, mpi::block_data_descriptor &dd__)
	Deserialize block data descriptor. More...
template<>
void	SHT::backward_transform< std::complex< double > > (int ld, std::complex< double > const *flm, int nr, int lmmax, std::complex< double > *ftp) const
template<>
void	SHT::forward_transform< std::complex< double > > (std::complex< double > const *ftp, int nr, int lmmax, int ld, std::complex< double > *flm) const
int	major_version ()
int	minor_version ()
int	revision ()
std::string	git_hash ()
std::string	git_branchname ()
std::string	build_date ()
int	num_blocks (int length__, int block_size__)
	Return the maximum number of blocks (with size 'block_size') needed to split the 'length' elements. More...
auto	split_in_blocks (int length__, int block_size__)
	Split the 'length' elements into blocks with the initial block size. More...
template<typename Index_t >
auto	begin_global (splindex< Index_t > const &a__)
template<typename Index_t >
auto	end_global (splindex< Index_t > const &a__)
template<typename Index_t >
auto	begin (splindex< Index_t > const &a__)
template<typename Index_t >
auto	end (splindex< Index_t > const &a__)
auto	split (std::string const str__, char delim__)
	Split multi-line string into a list of strings. More...
std::string &	ltrim (std::string &str, const std::string &chars="\t\n\v\f\r ")
std::string &	rtrim (std::string &str, const std::string &chars="\t\n\v\f\r ")
std::string &	trim (std::string &str, const std::string &chars="\t\n\v\f\r ")
bool	file_exists (std::string file_name)
	Check if file exists. More...
auto	hostname ()
	Get host name. More...
long	get_page_size ()
long	get_num_pages ()
long	get_total_memory ()
auto	get_proc_status ()
int	get_proc_threads ()
auto	timestamp (std::string fmt)
	Return the timestamp string in a specified format. More...
double	wtime ()
	Wall-clock time in seconds. More...
auto	time_now ()
double	time_interval (std::chrono::high_resolution_clock::time_point t0)
relativity_t	get_relativity_t (std::string name__)
std::ostream &	operator<< (std::ostream &out, radial_solution_descriptor const &rsd)
void	add_square_sum_gpu_double (std::complex< double > const *wf__, int num_rows_loc__, int nwf__, int reduced__, int mpi_rank__, double *result__)
void	add_square_sum_gpu_float (std::complex< float > const *wf__, int num_rows_loc__, int nwf__, int reduced__, int mpi_rank__, float *result__)
void	scale_matrix_columns_gpu_double (int nrow__, int ncol__, std::complex< double > *mtrx__, double *a__)
void	scale_matrix_columns_gpu_float (int nrow__, int ncol__, std::complex< float > *mtrx__, float *a__)
void	add_checksum_gpu_double (void const *wf__, int ld__, int num_rows_loc__, int nwf__, void *result__)
void	add_checksum_gpu_float (void const *wf__, int ld__, int num_rows_loc__, int nwf__, void *result__)
void	inner_diag_local_gpu_double_complex_double (void const *wf1__, int ld1__, void const *wf2__, int ld2__, int ngv_loc__, int nwf__, void *result__)
void	inner_diag_local_gpu_double_double (void const *wf1__, int ld1__, void const *wf2__, int ld2__, int ngv_loc__, int nwf__, int reduced__, void *result__)
void	axpby_gpu_double_complex_double (int nwf__, void const *alpha__, void const *x__, int ld1__, void const *beta__, void *y__, int ld2__, int ngv_loc__)
void	axpby_gpu_double_double (int nwf__, void const *alpha__, void const *x__, int ld1__, void const *beta__, void *y__, int ld2__, int ngv_loc__)
void	axpy_scatter_gpu_double_complex_double (int nwf__, void const *alpha__, void const *x__, int ld1__, void const *idx__, void *y__, int ld2__, int ngv_loc__)
void	axpy_scatter_gpu_double_double (int nwf__, void const *alpha__, void const *x__, int ld1__, void const *idx__, void *y__, int ld2__, int ngv_loc__)
template<typename T >
auto	checksum_gpu (std::complex< T > const *wf__, int ld__, int num_rows_loc__, int nwf__)
	Add checksum for the arrays on GPUs. More...
template<typename F >
void	iterate_aug_atom_types (Unit_cell const &uc__, F &&f__)
auto	max_l_aug (Unit_cell const &uc__)
auto	max_na_aug (Unit_cell const &uc__)
auto	max_nb_aug (Unit_cell const &uc__)
void	update_density_rg_1_real_gpu (int size__, float const *psi_rg__, float wt__, float *density_rg__)
void	update_density_rg_1_real_gpu (int size__, double const *psi_rg__, double wt__, double *density_rg__)
void	update_density_rg_1_complex_gpu (int size__, std::complex< float > const *psi_rg__, float wt__, float *density_rg__)
void	update_density_rg_1_complex_gpu (int size__, std::complex< double > const *psi_rg__, double wt__, double *density_rg__)
void	update_density_rg_2_gpu (int size__, std::complex< float > const *psi_rg_up__, std::complex< float > const *psi_rg_dn__, float wt__, float *density_x_rg__, float *density_y_rg__)
void	update_density_rg_2_gpu (int size__, std::complex< double > const *psi_rg_up__, std::complex< double > const *psi_rg_dn__, double wt__, double *density_x_rg__, double *density_y_rg__)
template<typename T >
static void	add_k_point_contribution_rg_collinear (fft::spfft_transform_type< T > &fft__, int ispn__, T w__, T const *inp_wf__, int nr__, bool gamma__, sddk::mdarray< T, 2 > &density_rg__)
	Compute non-magnetic or up- or dn- contribution of the wave-functions to the charge density. More...
template<typename T >
static void	add_k_point_contribution_rg_noncollinear (fft::spfft_transform_type< T > &fft__, T w__, T const *inp_wf_up__, T const *inp_wf_dn__, int nr__, sddk::mdarray< std::complex< T >, 1 > &psi_r_up__, sddk::mdarray< T, 2 > &density_rg__)
	Compute contribution to density and megnetisation from the 2-component spinor wave-functions. More...
template<typename T >
static void	add_k_point_contribution_dm_fplapw (Simulation_context const &ctx__, K_point< T > const &kp__, density_matrix_t &density_matrix__)
template<typename T , typename F >
static void	add_k_point_contribution_dm_pwpp_collinear (Simulation_context &ctx__, K_point< T > &kp__, beta_projectors_coeffs_t< T > &bp_coeffs__, density_matrix_t &density_matrix__)
template<typename T , typename F >
static void	add_k_point_contribution_dm_pwpp_noncollinear (Simulation_context &ctx__, K_point< T > &kp__, beta_projectors_coeffs_t< T > &bp_coeffs__, density_matrix_t &density_matrix__)
template<typename T , typename F >
static void	add_k_point_contribution_dm_pwpp (Simulation_context &ctx__, K_point< T > &kp__, density_matrix_t &density_matrix__)
auto	get_rho_up_dn (int num_mag_dims__, double rho__, r3::vector< double > mag__)
	Use Kuebler's trick to get rho_up and rho_dn from density and magnetisation. More...
void	copy (Density const &src__, Density &dest__)
template<bool add_pseudo_core__>
std::array< std::unique_ptr< Smooth_periodic_function< double > >, 2 >	get_rho_up_dn (Density const &density__, double add_delta_rho_xc__=0.0, double add_delta_mag_xc__=0.0)
void	copy (density_matrix_t const &src__, density_matrix_t &dest__)
void	copy (Occupation_matrix const &src__, Occupation_matrix &dest__)
double	ewald_energy (const Simulation_context &ctx, const fft::Gvec &gvec, const Unit_cell &unit_cell)
	Compute the ion-ion electrostatic energy using Ewald method. More...
double	energy_vxc (Density const &density, Potential const &potential)
	Returns exchange correlation potential. More...
double	energy_exc (Density const &density, Potential const &potential)
	Returns exchange correlation energy. More...
double	energy_vha (Potential const &potential)
	Returns Hatree potential. More...
double	energy_bxc (const Density &density, const Potential &potential)
	TODO doc. More...
double	energy_enuc (Simulation_context const &ctx, Potential const &potential)
	Return nucleus energy in the electrostatic field. More...
double	energy_vloc (Density const &density, Potential const &potential)
	TODO doc. More...
double	core_eval_sum (Unit_cell const &unit_cell)
	Return eigen-value sum of core states. More...
double	eval_sum (Unit_cell const &unit_cell, K_point_set const &kset)
	TODO doc. More...
double	energy_veff (Density const &density, Potential const &potential)
	TODO doc. More...
double	energy_kin (Simulation_context const &ctx, K_point_set const &kset, Density const &density, Potential const &potential)
	Return kinetic energy. More...
double	ks_energy (Simulation_context const &ctx, const std::map< std::string, double > &energies)
double	ks_energy (Simulation_context const &ctx, K_point_set const &kset, Density const &density, Potential const &potential, double ewald_energy)
double	total_energy (Simulation_context const &ctx, K_point_set const &kset, Density const &density, Potential const &potential, double ewald_energy)
	Total energy of the electronic subsystem. More...
std::map< std::string, double >	total_energy_components (Simulation_context const &ctx, const K_point_set &kset, Density const &density, Potential const &potential, double ewald_energy)
double	hubbard_energy (Density const &density)
double	one_electron_energy (Density const &density, Potential const &potential)
double	one_electron_energy_hubbard (Density const &density, Potential const &potential)
double	energy_potential (Density const &density, Potential const &potential)
double	valence_eval_sum (K_point_set const &kset)
	TODO doc.
auto	energy_dict (Simulation_context const &ctx__, K_point_set const &kset__, Density const &density__, Potential const &potential__, double ewald_energy__, double scf_correction__=0)
template<index_domain_t index_domain, typename F >
auto	make_periodic_function (Unit_cell const &uc__, fft::Gvec const &gv__, sddk::mdarray< std::complex< double >, 2 > const &phase_factors_t__, F &&form_factors__)
	Make periodic function out of form factors. More...
template<index_domain_t index_domain>
auto	make_periodic_function (Unit_cell const &uc__, fft::Gvec const &gv__, sddk::mdarray< std::complex< double >, 2 > const &phase_factors_t__, sddk::mdarray< double, 2 > const &form_factors__)
	Make periodic out of form factors computed for G-shells. More...
template<typename T >
T	inner (PAW_field4D< T > const &x__, PAW_field4D< T > const &y__)
template<typename T >
T	inner (Periodic_function< T > const &f__, Periodic_function< T > const &g__)
template<typename T >
void	copy (Periodic_function< T > const &src__, periodic_function_ptr_t< T > dest__)
	Copy values of the function to the external location. More...
template<typename T >
void	copy (periodic_function_ptr_t< T > const src__, Periodic_function< T > &dest__)
	Copy the values of the function from the external location. More...
template<typename T >
void	check_smooth_periodic_function_ptr (smooth_periodic_function_ptr_t< T > const &ptr__, fft::spfft_transform_type< T > const &spfft__)
template<typename T >
Smooth_periodic_vector_function< T >	gradient (Smooth_periodic_function< T > &f__)
	Gradient of the function in the plane-wave domain. More...
template<typename T >
Smooth_periodic_function< T >	divergence (Smooth_periodic_vector_function< T > &g__)
	Divergence of the vecor function. More...
template<typename T >
Smooth_periodic_function< T >	laplacian (Smooth_periodic_function< T > &f__)
	Laplacian of the function in the plane-wave domain. More...
template<typename T >
Smooth_periodic_function< T >	dot (Smooth_periodic_vector_function< T > &vf__, Smooth_periodic_vector_function< T > &vg__)
template<typename T , typename F >
T	inner_local (Smooth_periodic_function< T > const &f__, Smooth_periodic_function< T > const &g__, F &&theta__)
	Compute local contribution to inner product <f|g> More...
template<typename T >
T	inner_local (Smooth_periodic_function< T > const &f__, Smooth_periodic_function< T > const &g__)
template<typename T , typename F >
T	inner (Smooth_periodic_function< T > const &f__, Smooth_periodic_function< T > const &g__, F &&theta__)
template<typename T >
T	inner (Smooth_periodic_function< T > const &f__, Smooth_periodic_function< T > const &g__)
	Compute inner product <f|g> More...
template<typename T >
void	copy (Smooth_periodic_function< T > const &src__, smooth_periodic_function_ptr_t< T > dest__)
	Copy real-space values from the function to external pointer. More...
template<typename T >
void	copy (smooth_periodic_function_ptr_t< T > const src__, Smooth_periodic_function< T > &dest__)
	Copy real-space values from the external pointer to function. More...
template<typename T >
void	copy (Smooth_periodic_function< T > const &src__, Smooth_periodic_function< T > &dest__)
template<typename T >
void	scale (T alpha__, Smooth_periodic_function< T > &x__)
template<typename T >
void	axpy (T alpha__, Smooth_periodic_function< T > const &x__, Smooth_periodic_function< T > &y__)
template<typename T >
auto	operator* (Spheric_function< function_domain_t::spatial, T > const &a__, Spheric_function< function_domain_t::spatial, T > const &b__)
	Multiplication of two functions in spatial domain. More...
auto	operator* (Spheric_vector_function< function_domain_t::spatial, double > const &f, Spheric_vector_function< function_domain_t::spatial, double > const &g)
	Dot product of two gradiensts of real functions in spatial domain. More...
template<function_domain_t domain_t, typename T >
auto	operator+ (Spheric_function< domain_t, T > const &a__, Spheric_function< domain_t, T > const &b__)
	Summation of two functions. More...
template<function_domain_t domain_t, typename T >
auto	operator- (Spheric_function< domain_t, T > const &a__, Spheric_function< domain_t, T > const &b__)
	Subtraction of functions. More...
template<function_domain_t domain_t, typename T >
auto	operator* (T a__, Spheric_function< domain_t, T > const &b__)
	Multiply function by a scalar. More...
template<function_domain_t domain_t, typename T >
auto	operator* (Spheric_function< domain_t, T > const &b__, T a__)
	Multiply function by a scalar (inverse order). More...
template<function_domain_t domain_t, typename T >
auto	inner (Spheric_function< domain_t, T > const &f1, Spheric_function< domain_t, T > const &f2)
	Inner product of two spherical functions. More...
template<typename T >
auto	laplacian (Spheric_function< function_domain_t::spectral, T > const &f__)
	Compute Laplacian of the spheric function. More...
void	convert (Spheric_function< function_domain_t::spectral, std::complex< double > > const &f__, Spheric_function< function_domain_t::spectral, double > &g__)
	Convert from Ylm to Rlm representation. More...
auto	convert (Spheric_function< function_domain_t::spectral, std::complex< double > > const &f__)
	Convert from Ylm to Rlm representation. More...
void	convert (Spheric_function< function_domain_t::spectral, double > const &f__, Spheric_function< function_domain_t::spectral, std::complex< double > > &g__)
	Convert from Rlm to Ylm representation. More...
auto	convert (Spheric_function< function_domain_t::spectral, double > const &f__)
	Convert from Rlm to Ylm representation. More...
template<typename T >
void	transform (SHT const &sht__, Spheric_function< function_domain_t::spectral, T > const &f__, Spheric_function< function_domain_t::spatial, T > &g__)
template<typename T >
auto	transform (SHT const &sht__, Spheric_function< function_domain_t::spectral, T > const &f__)
	Transform to spatial domain (to r, \theta, \phi coordinates). More...
template<typename T >
void	transform (SHT const &sht__, Spheric_function< function_domain_t::spatial, T > const &f__, Spheric_function< function_domain_t::spectral, T > &g__)
template<typename T >
auto	transform (SHT const &sht__, Spheric_function< function_domain_t::spatial, T > const &f__)
	Transform to spectral domain. More...
auto	gradient (Spheric_function< function_domain_t::spectral, std::complex< double > > const &f)
	Gradient of the function in complex spherical harmonics. More...
auto	gradient (Spheric_function< function_domain_t::spectral, double > const &f__)
	Gradient of the function in real spherical harmonics. More...
auto	divergence (Spheric_vector_function< function_domain_t::spectral, std::complex< double > > const &vf__)
	Divergence of the vector function in complex spherical harmonics. More...
auto	divergence (Spheric_vector_function< function_domain_t::spectral, double > const &vf)
template<typename T , typename I >
T	inner (Spheric_function_set< T, I > const &f1__, Spheric_function_set< T, I > const &f2__)
template<typename T , typename I >
void	copy (Spheric_function_set< T, I > const &src__, spheric_function_set_ptr_t< T > dest__)
	Copy from Spheric_function_set to external pointer. More...
template<typename T , typename I >
void	copy (spheric_function_set_ptr_t< T > const src__, Spheric_function_set< T, I > &dest__)
	Copy from external pointer to Spheric_function_set. More...
template<typename T , typename I >
void	copy (Spheric_function_set< T, I > const &src__, Spheric_function_set< T, I > &dest__)
template<typename T , typename I >
void	scale (T alpha__, Spheric_function_set< T, I > &x__)
template<typename T , typename I >
void	axpy (T alpha__, Spheric_function_set< T, I > const &x__, Spheric_function_set< T, I > &y__)
template<typename T , typename F >
void	add_k_point_contribution_nonlocal (Simulation_context &ctx__, Beta_projectors_base< T > &bp_base__, K_point< T > &kp__, sddk::mdarray< real_type< F >, 2 > &collect_res__)
void	wavefunctions_strain_deriv (Simulation_context const &ctx__, K_point< double > &kp__, wf::Wave_functions< double > &dphi__, sddk::mdarray< double, 2 > const &rlm_g__, sddk::mdarray< double, 3 > const &rlm_dg__, int nu__, int mu__)
template<typename T , typename F >
void	check_wave_functions (Hamiltonian_k< real_type< T > > const &Hk__, wf::Wave_functions< T > &psi__, wf::spin_range sr__, wf::band_range br__, double *eval__)
template<typename T , typename F >
void	project_out_subspace (::spla::Context &spla_ctx__, sddk::memory_t mem__, wf::spin_range spins__, wf::Wave_functions< T > &phi__, wf::Wave_functions< T > &sphi__, int N__, int n__, la::dmatrix< F > &o__)
template<typename T , typename F , davidson_evp_t what>
auto	davidson (Hamiltonian_k< T > const &Hk__, K_point< T > &kp__, wf::num_bands num_bands__, wf::num_mag_dims num_mag_dims__, wf::Wave_functions< T > &psi__, std::function< double(int, int)> tolerance__, double res_tol__, int num_steps__, bool locking__, int subspace_size__, bool estimate_eval__, bool extra_ortho__, std::ostream &out__, int verbosity__, wf::Wave_functions< T > *phi_extra__=nullptr)
	Solve the eigen-problem using Davidson iterative method. More...
template<typename T , typename F >
auto	diagonalize (Hamiltonian0< T > const &H0__, K_point_set &kset__, double itsol_tol__)
	Diagonalize KS Hamiltonian for all k-points in the set. More...
void	diagonalize_fp_fv_exact (Hamiltonian_k< float > const &, K_point< float > &)
void	diagonalize_fp_fv_exact (Hamiltonian_k< double > const &Hk__, K_point< double > &kp__)
void	get_singular_components (Hamiltonian_k< double > const &Hk__, K_point< double > &kp__, double itsol_tol__)
void	diagonalize_fp_fv_davidson (Hamiltonian_k< float > const &, K_point< float > &, double)
void	diagonalize_fp_fv_davidson (Hamiltonian_k< double > const &Hk__, K_point< double > &kp__, double itsol_tol__)
void	diagonalize_fp_sv (Hamiltonian_k< float > const &, K_point< float > &)
void	diagonalize_fp_sv (Hamiltonian_k< double > const &Hk__, K_point< double > &kp)
	Diagonalize second-variational Hamiltonian. More...
template<typename T >
void	diagonalize_fp (Hamiltonian_k< T > const &Hk__, K_point< T > &kp__, double itsol_tol__)
	Diagonalize a full-potential LAPW Hamiltonian. More...
template<typename T , typename F >
std::enable_if_t<!std::is_same< T, real_type< F > >::value, void >	diagonalize_pp_exact (int ispn__, Hamiltonian_k< T > const &Hk__, K_point< T > &kp)
template<typename T , typename F >
std::enable_if_t< std::is_same< T, real_type< F > >::value, void >	diagonalize_pp_exact (int ispn__, Hamiltonian_k< T > const &Hk__, K_point< T > &kp__)
template<typename T , typename F >
sddk::mdarray< real_type< F >, 1 >	diag_S_davidson (Hamiltonian_k< T > const &Hk__, K_point< T > &kp__)
	Diagonalize S-operator of the ultrasoft or PAW methods. More...
template<typename T , typename F >
auto	diagonalize_pp (Hamiltonian_k< T > const &Hk__, K_point< T > &kp__, double itsol_tol__, double empy_tol__)
template<typename T , typename F >
void	generate_subspace_matrix (Simulation_context &ctx__, int N__, int n__, int num_locked__, wf::Wave_functions< T > &phi__, wf::Wave_functions< T > &op_phi__, la::dmatrix< F > &mtrx__, la::dmatrix< F > *mtrx_old__=nullptr)
	Generate subspace matrix for the iterative diagonalization. More...
template<typename T , typename F >
void	initialize_subspace (Hamiltonian_k< T > const &Hk__, K_point< T > &kp__, int num_ao__)
	Initialize the wave-functions subspace at a given k-point. More...
template<typename T >
void	initialize_subspace (K_point_set &kset__, Hamiltonian0< T > &H0__)
template<typename T >
static void	mul_by_veff (fft::spfft_transform_type< T > &spfftk__, T const *in__, std::array< std::unique_ptr< Smooth_periodic_function< T > >, 6 > const &veff_vec__, int idx_veff__, T *out__)
	Multiply FFT buffer by the effective potential. More...
template<typename T , typename F >
void	apply_non_local_D_Q (sddk::memory_t mem__, wf::spin_range spins__, wf::band_range br__, Beta_projector_generator< T > &beta__, beta_projectors_coeffs_t< T > &beta_coeffs__, wf::Wave_functions< T > const &phi__, D_operator< T > const *d_op__, wf::Wave_functions< T > *hphi__, Q_operator< T > const *q_op__, wf::Wave_functions< T > *sphi__)
template<typename T , typename F >
void	apply_S_operator (sddk::memory_t mem__, wf::spin_range spins__, wf::band_range br__, Beta_projector_generator< T > &beta__, beta_projectors_coeffs_t< T > &beta_coeffs__, wf::Wave_functions< T > const &phi__, Q_operator< T > const *q_op__, wf::Wave_functions< T > &sphi__)
	Compute |sphi> = (1 + Q)|phi> More...
template<typename T >
void	apply_U_operator (Simulation_context &ctx__, wf::spin_range spins__, wf::band_range br__, wf::Wave_functions< T > const &hub_wf__, wf::Wave_functions< T > const &phi__, U_operator< T > const &um__, wf::Wave_functions< T > &hphi__)
void	apply_S_operator_strain_deriv (sddk::memory_t mem__, int comp__, Beta_projector_generator< double > &bp__, beta_projectors_coeffs_t< double > &bp_coeffs__, Beta_projector_generator< double > &bp_strain_deriv__, beta_projectors_coeffs_t< double > &bp_strain_deriv_coeffs__, wf::Wave_functions< double > &phi__, Q_operator< double > &q_op__, wf::Wave_functions< double > &ds_phi__)
	Apply strain derivative of S-operator to all scalar functions. More...
template<typename T >
dmatrix< T >	pseudopotential_hmatrix (K_point &kp__, int ispn__, Hamiltonian &H__)
template<typename T >
static void	compute_residuals (sddk::memory_t mem__, wf::spin_range spins__, wf::num_bands num_bands__, sddk::mdarray< T, 1 > const &eval__, wf::Wave_functions< T > const &hpsi__, wf::Wave_functions< T > const &opsi__, wf::Wave_functions< T > &res__)
	Compute band residuals. More...
template<typename T >
void	apply_preconditioner (sddk::memory_t mem__, wf::spin_range spins__, wf::num_bands num_bands__, wf::Wave_functions< T > &res__, sddk::mdarray< T, 2 > const &h_diag__, sddk::mdarray< T, 2 > const &o_diag__, sddk::mdarray< T, 1 > const &eval__)
	Apply preconditioner to the residuals. More...
template<typename T , typename F >
static auto	normalized_preconditioned_residuals (sddk::memory_t mem__, wf::spin_range spins__, wf::num_bands num_bands__, sddk::mdarray< T, 1 > const &eval__, wf::Wave_functions< T > const &hpsi__, wf::Wave_functions< T > const &opsi__, wf::Wave_functions< T > &res__, sddk::mdarray< T, 2 > const &h_diag__, sddk::mdarray< T, 2 > const &o_diag__, T norm_tolerance__, bool gamma__)
template<typename T , typename F >
auto	residuals (Simulation_context &ctx__, sddk::memory_t mem__, wf::spin_range sr__, int N__, int num_bands__, int num_locked__, sddk::mdarray< real_type< F >, 1 > &eval__, la::dmatrix< F > &evec__, wf::Wave_functions< T > &hphi__, wf::Wave_functions< T > &ophi__, wf::Wave_functions< T > &hpsi__, wf::Wave_functions< T > &opsi__, wf::Wave_functions< T > &res__, sddk::mdarray< T, 2 > const &h_diag__, sddk::mdarray< T, 2 > const &o_diag__, bool estimate_eval__, T norm_tolerance__, std::function< bool(int, int)> is_converged__)
	Compute residuals from eigen-vectors. More...
template void	apply_U_operator< double > (Simulation_context &, wf::spin_range, wf::band_range, const wf::Wave_functions< double > &, const wf::Wave_functions< double > &, U_operator< double > const &, wf::Wave_functions< double > &)
void	generate_potential (Hubbard_matrix const &om__, Hubbard_matrix &um__)
double	energy (Hubbard_matrix const &om__)
double	one_electron_energy_hubbard (Hubbard_matrix const &om__, Hubbard_matrix const &pm__)
void	copy (Hubbard_matrix const &src__, Hubbard_matrix &dest__)
static void	update_density_matrix_deriv (la::lib_t la__, sddk::memory_t mt__, int nwfh__, int nbnd__, std::complex< double > *alpha__, la::dmatrix< std::complex< double > > const &phi_hub_s_psi_deriv__, la::dmatrix< std::complex< double > > const &psi_s_phi_hub__, std::complex< double > *dn__, int ld__)
static void	build_phi_hub_s_psi_deriv (Simulation_context const &ctx__, int nbnd__, int nawf__, la::dmatrix< std::complex< double > > const &ovlp__, la::dmatrix< std::complex< double > > const &inv_sqrt_O__, la::dmatrix< std::complex< double > > const &phi_atomic_s_psi__, la::dmatrix< std::complex< double > > const &phi_atomic_ds_psi__, std::vector< int > const &atomic_wf_offset__, std::vector< int > const &hubbard_wf_offset__, la::dmatrix< std::complex< double > > &phi_hub_s_psi_deriv__)
static void	compute_inv_sqrt_O_deriv (la::dmatrix< std::complex< double > > &O_deriv__, la::dmatrix< std::complex< double > > &evec_O__, std::vector< double > &eval_O__, int nawf__)
static void	generate_potential_collinear_nonlocal (Simulation_context const &ctx__, const int index__, sddk::mdarray< std::complex< double >, 3 > const &om__, sddk::mdarray< std::complex< double >, 3 > &um__)
static void	generate_potential_collinear_local (Simulation_context const &ctx__, Atom_type const &atom_type__, const int idx_hub_wf, sddk::mdarray< std::complex< double >, 3 > const &om__, sddk::mdarray< std::complex< double >, 3 > &um__)
static double	calculate_energy_collinear_nonlocal (Simulation_context const &ctx__, const int index__, sddk::mdarray< std::complex< double >, 3 > const &om__)
static double	calculate_energy_collinear_local (Simulation_context const &ctx__, Atom_type const &atom_type__, const int idx_hub_wf, sddk::mdarray< std::complex< double >, 3 > const &om__)
static void	generate_potential_non_collinear_local (Simulation_context const &ctx__, Atom_type const &atom_type__, const int idx_hub_wf, sddk::mdarray< std::complex< double >, 3 > const &om__, sddk::mdarray< std::complex< double >, 3 > &um__)
static double	calculate_energy_non_collinear_local (Simulation_context const &ctx__, Atom_type const &atom_type__, const int idx_hub_wf, sddk::mdarray< std::complex< double >, 3 > const &om__)
template<typename T >
auto	wave_function_factory (Simulation_context const &ctx__, K_point< T > const &kp__, wf::num_bands num_wf__, wf::num_mag_dims num_md__, bool mt_part__)
template void	K_point_set::sync_band< double, sync_band_t::energy > ()
template void	K_point_set::sync_band< double, sync_band_t::occupancy > ()
template<class F >
double	bisection_search (F &&f, double a, double b, double tol, int maxstep=1000)
template<class Nt , class DNt , class D2Nt >
auto	newton_minimization_chemical_potential (Nt &&N, DNt &&dN, D2Nt &&ddN, double mu0, double ne, double tol, int maxstep=1000)
template<bool conjugate, typename T >
auto	generate_alm_block (Simulation_context const &ctx__, int atom_begin__, int num_atoms__, Matching_coefficients const &alm__)
	Generate matching coefficients for a block of atoms. More...
auto	generate_gvec_ylm (Simulation_context const &ctx__, int lmax__)
	Generate complex spherical harmonics for the local set of G-vectors. More...
auto	generate_sbessel_mt (Simulation_context const &ctx__, int lmax__)
	Compute values of spherical Bessel functions at MT boundary. More...
double	unit_step_function_form_factors (double R__, double g__)
	Utility function to generate LAPW unit step function. More...
auto	init_step_function (Unit_cell const &uc__, fft::Gvec const &gv__, fft::Gvec_fft const &gvec_fft__, sddk::mdarray< std::complex< double >, 2 > const &phase_factors_t__, fft::spfft_transform_type< double > spfft__)
	Unit step function is defined to be 1 in the interstitial and 0 inside muffin-tins. More...
auto	sum_fg_fl_yg (Simulation_context const &ctx__, int lmax__, std::complex< double > const *fpw__, sddk::mdarray< double, 3 > &fl__, sddk::matrix< std::complex< double > > &gvec_ylm__)
template<class numeric_t >
auto	make_matrix_view (nlcglib::buffer_protocol< numeric_t, 2 > &buf)
void	apply_hamiltonian (Hamiltonian0< double > &H0, K_point< double > &kp, wf::Wave_functions< double > &wf_out, wf::Wave_functions< double > &wf, std::shared_ptr< wf::Wave_functions< double > > swf)
void	call_nlcg (Simulation_context &ctx, config_t::nlcg_t const &nlcg_params, Energy &energy, K_point_set &kset, Potential &potential)
void	check_xc_potential (Density const &rho__)
void	mul_veff_with_phase_factors_gpu (int num_atoms__, int num_gvec_loc__, std::complex< double > const *veff__, int const *gvx__, int const *gvy__, int const *gvz__, double const *atom_pos__, double *veff_a__, int ld__, int stream_id__)
double	xc_mt_paw (std::vector< XC_functional > const &xc_func__, int lmax__, int num_mag_dims__, SHT const &sht__, Radial_grid< double > const &rgrid__, std::vector< Flm const * > rho__, std::vector< double > const &rho_core__, std::vector< Flm > &vxc__, Flm &exclm__)
double	density_residual_hartree_energy (Density const &rho1__, Density const &rho2__)
double	xc_mt (Radial_grid< double > const &rgrid__, SHT const &sht__, std::vector< XC_functional > const &xc_func__, int num_mag_dims__, std::vector< Flm const * > rho__, std::vector< Flm * > vxc__, Flm *exc__)
void	xc_mt_nonmagnetic (Radial_grid< double > const &rgrid__, SHT const &sht__, std::vector< XC_functional > const &xc_func__, Flm const &rho_lm__, Ftp &rho_tp__, Flm &vxc_lm__, Flm &exc_lm__)
void	xc_mt_magnetic (Radial_grid< double > const &rgrid__, SHT const &sht__, int num_mag_dims__, std::vector< XC_functional > const &xc_func__, std::vector< Ftp > const &rho_tp__, std::vector< Flm * > vxc__, Flm &exc__)
template<typename T >
Radial_grid< T >	Radial_grid_factory (radial_grid_t grid_type__, int num_points__, T rmin__, T rmax__, double p__)
std::pair< radial_grid_t, double >	get_radial_grid_t (std::string str__)
template<typename T , typename U = double>
Spline< T, U >	operator* (Spline< T, U > const &a__, Spline< T, U > const &b__)
void	spline_inner_product_gpu_v3 (int const *idx_ri__, int num_ri__, int num_points__, double const *x__, double const *dx__, double const *f__, double const *g__, double *result__)
template<typename T >
T	inner (Spline< T > const &f__, Spline< T > const &g__, int m__, int num_points__)
template<typename T >
T	inner (Spline< T > const &f__, Spline< T > const &g__, int m__)
static bool &	is_initialized ()
	Return the status of the library (initialized or not). More...
void	initialize (bool call_mpi_init__=true)
	Initialize the library. More...
void	finalize (bool call_mpi_fin__=true, bool reset_device__=true, bool fftw_cleanup__=true)
	Shut down the library. More...
void	check_gvec (fft::Gvec const &gvec__, Crystal_symmetry const &sym__)
void	check_gvec (fft::Gvec_shells const &gvec_shells__, Crystal_symmetry const &sym__)
static std::pair< std::vector< int >, std::vector< r3::vector< int > > >	find_sym_atom (int num_atoms__, sddk::mdarray< double, 2 > const &positions__, r3::matrix< int > const &R__, r3::vector< double > const &t__, double tolerance__, bool inverse__=false)
static space_group_symmetry_descriptor	get_spg_sym_op (int isym_spg__, SpglibDataset *spg_dataset__, r3::matrix< double > const &lattice_vectors__, int num_atoms__, sddk::mdarray< double, 2 > const &positions__, double tolerance__)
static space_group_symmetry_descriptor	get_identity_spg_sym_op (int num_atoms__)
std::tuple< int, std::vector< double >, std::vector< std::array< double, 3 > > >	get_irreducible_reciprocal_mesh (Crystal_symmetry const &sym__, r3::vector< int > k_mesh__, r3::vector< int > is_shift__)
auto	metric_tensor (r3::matrix< double > const &lat_vec__)
	Compute a metric tensor. More...
double	metric_tensor_error (r3::matrix< double > const &lat_vec__, r3::matrix< int > const &R__)
	Compute error of the symmetry-transformed metric tensor. More...
auto	find_lat_sym (r3::matrix< double > const &lat_vec__, double tol__, double *mt_error__=nullptr)
double	phi_by_sin_cos (double sinp, double cosp)
	Return angle phi in the range [0, 2Pi) by its values of sin(phi) and cos(phi). More...
auto	rotation_matrix_su2 (std::array< double, 3 > u__, double theta__)
	Generate SU(2) rotation matrix from the axes and angle. More...
auto	rotation_matrix_su2 (r3::matrix< double > R__)
	Generate SU2(2) rotation matrix from a 3x3 rotation matrix in Cartesian coordinates. More...
auto	axis_angle (r3::matrix< double > R__)
	Get axis and angle from rotation matrix. More...
auto	rot_mtrx_cart (r3::vector< double > euler_angles__)
	Generate rotation matrix from three Euler angles. More...
auto	euler_angles (r3::matrix< double > const &rot__, double tolerance__)
	Compute Euler angles corresponding to the proper rotation matrix. More...
void	apply_symmetry_to_density_matrix (sddk::mdarray< std::complex< double >, 3 > const &dm_ia__, basis_functions_index const &indexb__, const int num_mag_comp__, std::vector< sddk::mdarray< double, 2 > > const &rotm__, sddk::mdarray< std::complex< double >, 2 > const &spin_rot_su2__, sddk::mdarray< std::complex< double >, 3 > &dm_ja__)
void	symmetrize_density_matrix (Unit_cell const &uc__, density_matrix_t &dm__, int num_mag_comp__)
	Symmetrize density matrix. More...
void	symmetrize_field4d (Field4D &f__)
void	symmetrize_forces (Unit_cell const &uc__, sddk::mdarray< double, 2 > &f__)
template<typename Index_t >
void	symmetrize_mt_function (Crystal_symmetry const &sym__, mpi::Communicator const &comm__, int num_mag_dims__, std::vector< Spheric_function_set< double, Index_t > * > frlm__)
void	symmetrize_occupation_matrix (Occupation_matrix &om__)
void	symmetrize_pw_function (Crystal_symmetry const &sym__, fft::Gvec_shells const &gvec_shells__, sddk::mdarray< std::complex< double >, 3 > const &sym_phase_factors__, int num_mag_dims__, std::vector< Smooth_periodic_function< double > * > frg__)
	Symmetrize scalar or vector function. More...
void	symmetrize_stress_tensor (Crystal_symmetry const &sym__, r3::matrix< double > &s__)
template<typename F >
int	call_test (std::string label__, F &&f__)
template<typename F >
int	call_test (std::string label__, F &&f__, cmd_args const &args__)
template<typename T >
auto	random_symmetric (int N__, int bs__, la::BLACS_grid const &blacs_grid__)
template<typename T >
auto	random_positive_definite (int N__, int bs__=16, la::BLACS_grid const *blacs_grid__=nullptr)
auto	create_simulation_context (nlohmann::json const &conf__, r3::matrix< double > L__, int num_atoms__, std::vector< r3::vector< double > > coord__, bool add_vloc__, bool add_dion__)
template<typename T >
void	randomize (wf::Wave_functions< T > &wf__)
std::ostream &	operator<< (std::ostream &out, ps_atomic_wf_descriptor const &wfd)
auto	begin (basis_functions_index const &idx__)
auto	end (basis_functions_index const &idx__)
std::ostream &	operator<< (std::ostream &out, hubbard_orbital_descriptor const &ho)
bool	operator== (angular_momentum lhs__, angular_momentum rhs__)
bool	operator!= (angular_momentum lhs__, angular_momentum rhs__)
std::ostream &	operator<< (std::ostream &out, angular_momentum am)
	Output angular momentum to a stream. More...
auto	begin (radial_functions_index const &idx__)
auto	end (radial_functions_index const &idx__)

Variables
integer, parameter, public	sirius_integer_type = 1
integer, parameter, public	sirius_logical_type = 2
integer, parameter, public	sirius_string_type = 3
integer, parameter, public	sirius_number_type = 4
integer, parameter, public	sirius_object_type = 5
integer, parameter, public	sirius_array_type = 6
integer, parameter, public	sirius_integer_array_type = 7
integer, parameter, public	sirius_logical_array_type = 8
integer, parameter, public	sirius_number_array_type = 9
integer, parameter, public	sirius_string_array_type = 10
integer, parameter, public	sirius_object_array_type = 11
integer, parameter, public	sirius_array_array_type = 12
const double	speed_of_light = 137.035999139
	NIST value for the inverse fine structure (http://physics.nist.gov/cuu/Constants/index.html) More...
const double	bohr_radius = 0.52917721067
	Bohr radius in angstroms. More...
const double	pi = 3.1415926535897932385
	\( \pi \) More...
const double	twopi = 6.2831853071795864769
	\( 2\pi \) More...
const double	fourpi = 12.566370614359172954
	\( 4\pi \) More...
const double	y00 = 0.28209479177387814347
	First spherical harmonic \( Y_{00} = \frac{1}{\sqrt{4\pi}} \). More...
const double	ha2ev = 27.21138505
	Hartree in electron-volt units. More...
const char *const	storage_file_name = "sirius.h5"
const std::complex< double >	pauli_matrix [4][2][2]
	Pauli matrices in {I, Z, X, Y} order. More...
::rt_graph::Timer	global_rtgraph_timer
template<class T >
constexpr bool	is_real_v = std::is_same<T, real_type<T>>::value
const std::map< std::string, int >	libxc_functionals
json	sirius_options_parser_

Detailed Description

Namespace of the SIRIUS library.

Typedef Documentation

acc_stream_t

using sirius::acc_stream_t = typedef cudaStream_t

Definition at line 62 of file acc.hpp.

acc_error_t

using sirius::acc_error_t = typedef cudaError_t

Definition at line 70 of file acc.hpp.

acc_complex_float_t

using sirius::acc_complex_float_t = typedef cuFloatComplex

Definition at line 78 of file acc.hpp.

acc_complex_double_t

using sirius::acc_complex_double_t = typedef cuDoubleComplex

Definition at line 79 of file acc.hpp.

gpu_complex_type

template<typename T >

using sirius::gpu_complex_type = typedef typename GPU_Complex<T>::type

Definition at line 124 of file acc.hpp.

real_type

template<typename T >

using sirius::real_type = typedef typename Real<T>::type

Definition at line 48 of file acc_common.hpp.

n_blocks

using sirius::n_blocks = typedef strong_type<int, struct __n_blocks_tag>

Number of blocks to which the global index is split.

Definition at line 105 of file splindex.hpp.

block_id

using sirius::block_id = typedef strong_type<int, struct __block_id_tag>

ID of the block.

The id of the block has the range [0, n_blocks)

Definition at line 108 of file splindex.hpp.

time_point_t

using sirius::time_point_t = typedef std::chrono::high_resolution_clock::time_point

Definition at line 54 of file time_tools.hpp.

identity_t

template<class X >

using sirius::identity_t = typedef typename identity<X>::type

Definition at line 37 of file traits.hpp.

radial_solution_descriptor_set

typedef std::vector<radial_solution_descriptor> sirius::radial_solution_descriptor_set

Set of radial solution descriptors, used to construct augmented waves or local orbitals.

Definition at line 155 of file typedefs.hpp.

Flm

using sirius::Flm = typedef Spheric_function<function_domain_t::spectral, double>

Definition at line 205 of file spheric_function.hpp.

Ftp

using sirius::Ftp = typedef Spheric_function<function_domain_t::spatial, double>

Definition at line 206 of file spheric_function.hpp.

lmax_t

using sirius::lmax_t = typedef strong_type<int, struct __lmax_t_tag>

Definition at line 9 of file spheric_function_set.hpp.

rf_index

using sirius::rf_index = typedef strong_type<int, struct __rf_index_tag>

Radial function index.

Definition at line 34 of file radial_functions_index.hpp.

rf_aw_index

using sirius::rf_aw_index = typedef strong_type<int, struct __rf_aw_index_tag>

Augmented wave radial function index.

Definition at line 36 of file radial_functions_index.hpp.

rf_lo_index

using sirius::rf_lo_index = typedef strong_type<int, struct __rf_lo_index_tag>

Local orbital radial function index.

Definition at line 38 of file radial_functions_index.hpp.

bf_index

using sirius::bf_index = typedef strong_type<int, struct __bf_index_tag>

Basis function index.

Definition at line 40 of file radial_functions_index.hpp.

bf_aw_index

using sirius::bf_aw_index = typedef strong_type<int, struct __bf_aw_index_tag>

Augmented wave basis function index.

Definition at line 42 of file radial_functions_index.hpp.

bf_lo_index

using sirius::bf_lo_index = typedef strong_type<int, struct __bf_lo_index_tag>

Local orbital basis function index.

Definition at line 44 of file radial_functions_index.hpp.

json

using sirius::json = typedef nlohmann::json

Definition at line 36 of file unit_cell.hpp.

Enumeration Type Documentation

hdf5_access_t

enum class sirius::hdf5_access_t

strong

Definition at line 38 of file hdf5_tree.hpp.

index_domain_t

enum class sirius::index_domain_t

strong

Enumerator
global	Global index.
local	Local index.

Definition at line 110 of file splindex.hpp.

spin_block_t

enum class sirius::spin_block_t

strong

Spin-blocks of the Hamiltonian.

Enumerator
nm	Non-magnetic case.
uu	Up-up block.
dd	Down-donw block.
ud	Up-down block.
du	Down-up block.

Definition at line 56 of file typedefs.hpp.

electronic_structure_method_t

enum class sirius::electronic_structure_method_t

strong

Type of electronic structure methods.

Enumerator
full_potential_lapwlo	Full potential linearized augmented plane waves with local orbitals.
pseudopotential	Pseudopotential (ultrasoft, norm-conserving, PAW).

Definition at line 75 of file typedefs.hpp.

function_domain_t

enum class sirius::function_domain_t

strong

Type of a function domain.

Enumerator
spatial	Spatial domain.
spectral	Spectral domain.

Definition at line 85 of file typedefs.hpp.

relativity_t

enum class sirius::relativity_t

strong

Type of relativity treatment in the case of LAPW.

Definition at line 94 of file typedefs.hpp.

davidson_evp_t

enum class sirius::davidson_evp_t

strong

Definition at line 48 of file davidson.hpp.

sync_band_t

enum class sirius::sync_band_t

strong

Definition at line 33 of file k_point_set.hpp.

radial_grid_t

enum class sirius::radial_grid_t : int

strong

Types of radial grid.

Definition at line 34 of file radial_grid.hpp.

Function/Subroutine Documentation

string_f2c()

character(kind=c_char,len=1) function, dimension(len_trim(f_string) + 1) sirius::string_f2c

(

character(kind=c_char,len=*), intent(in)

f_string

)

Internal function that adds trailing null character to the string to make it C-style.

Definition at line 46 of file sirius.f90.

string_c2f()

character(kind=c_char,len=size(c_string) - 1) function sirius::string_c2f

(

character(kind=c_char,len=1), dimension(:), intent(in)

c_string

)

Internal function that converts C-string (with trailing null character) to the Fortran string.

Definition at line 58 of file sirius.f90.

sirius_initialize()

subroutine sirius::sirius_initialize	(	logical, intent(in), target	call_mpi_init,
		integer, intent(out), optional, target	error_code
	)

Initialize the SIRIUS library.

Parameters

[in]	call_mpi_init	If .true. then MPI_Init must be called prior to initialization.
[out]	error_code	Error code.

Definition at line 77 of file sirius.f90.

sirius_finalize()

subroutine sirius::sirius_finalize	(	logical, intent(in), optional, target	call_mpi_fin,
		logical, intent(in), optional, target	call_device_reset,
		logical, intent(in), optional, target	call_fftw_fin,
		integer, intent(out), optional, target	error_code
	)

Shut down the SIRIUS library.

Parameters

[in]	call_mpi_fin	If .true. then MPI_Finalize must be called after the shutdown.
[in]	call_device_reset	If .true. then cuda device is reset after shutdown.
[in]	call_fftw_fin	If .true. then fft_cleanup must be called after the shutdown.
[out]	error_code	Error code.

Definition at line 112 of file sirius.f90.

sirius_start_timer()

subroutine sirius::sirius_start_timer	(	character(*), intent(in), target	name,
		integer, intent(out), optional, target	error_code
	)

Start the timer.

Parameters

[in]	name	Timer label.
[out]	error_code	Error code.

Definition at line 172 of file sirius.f90.

sirius_stop_timer()

subroutine sirius::sirius_stop_timer	(	character(*), intent(in), target	name,
		integer, intent(out), optional, target	error_code
	)

Stop the running timer.

Parameters

[in]	name	Timer label.
[out]	error_code	Error code.

Definition at line 207 of file sirius.f90.

sirius_print_timers()

subroutine sirius::sirius_print_timers	(	logical, intent(in), target	flatten,
		integer, intent(out), optional, target	error_code
	)

Print all timers.

Parameters

[in]	flatten	If true, flat list of timers is printed.
[out]	error_code	Error code.

Definition at line 242 of file sirius.f90.

sirius_serialize_timers()

subroutine sirius::sirius_serialize_timers	(	character(*), intent(in), target	fname,
		integer, intent(out), optional, target	error_code
	)

Save all timers to JSON file.

Parameters

[in]	fname	Name of the output JSON file.
[out]	error_code	Error code.

Definition at line 275 of file sirius.f90.

sirius_context_initialized()

subroutine sirius::sirius_context_initialized	(	type(sirius_context_handler), intent(in), target	handler,
		logical, intent(out), target	status,
		integer, intent(out), optional, target	error_code
	)

Check if the simulation context is initialized.

Parameters

[in]	handler	Simulation context handler.
[out]	status	Status of the library (true if initialized)
[out]	error_code	Error code.

Definition at line 311 of file sirius.f90.

sirius_create_context()

subroutine sirius::sirius_create_context	(	integer, intent(in), value	fcomm,
		type(sirius_context_handler), intent(out), target	handler,
		integer, intent(in), optional, target	fcomm_k,
		integer, intent(in), optional, target	fcomm_band,
		integer, intent(out), optional, target	error_code
	)

Create context of the simulation.

Simulation context is the complex data structure that holds all the parameters of the individual simulation. The context must be created, populated with the correct parameters and initialized before using all subsequent SIRIUS functions.

Parameters

[in]	fcomm	Entire communicator of the simulation.
[out]	handler	New empty simulation context.
[in]	fcomm_k	Communicator for k-point parallelization.
[in]	fcomm_band	Communicator for band parallelization.
[out]	error_code	Error code.

Definition at line 355 of file sirius.f90.

sirius_import_parameters()

subroutine sirius::sirius_import_parameters	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	str,
		integer, intent(out), optional, target	error_code
	)

Import parameters of simulation from a JSON string.

Parameters

[in]	handler	Simulation context handler.
[in]	str	JSON string with parameters or a JSON file.
[out]	error_code	Error code

Definition at line 403 of file sirius.f90.

sirius_set_parameters()

subroutine sirius::sirius_set_parameters	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(in), optional, target	lmax_apw,
		integer, intent(in), optional, target	lmax_rho,
		integer, intent(in), optional, target	lmax_pot,
		integer, intent(in), optional, target	num_fv_states,
		integer, intent(in), optional, target	num_bands,
		integer, intent(in), optional, target	num_mag_dims,
		real(8), intent(in), optional, target	pw_cutoff,
		real(8), intent(in), optional, target	gk_cutoff,
		integer, dimension(3), intent(in), optional, target	fft_grid_size,
		integer, intent(in), optional, target	auto_rmt,
		logical, intent(in), optional, target	gamma_point,
		logical, intent(in), optional, target	use_symmetry,
		logical, intent(in), optional, target	so_correction,
		character(*), intent(in), optional, target	valence_rel,
		character(*), intent(in), optional, target	core_rel,
		real(8), intent(in), optional, target	iter_solver_tol_empty,
		character(*), intent(in), optional, target	iter_solver_type,
		integer, intent(in), optional, target	verbosity,
		logical, intent(in), optional, target	hubbard_correction,
		integer, intent(in), optional, target	hubbard_correction_kind,
		logical, intent(in), optional, target	hubbard_full_orthogonalization,
		character(*), intent(in), optional, target	hubbard_orbitals,
		integer, intent(in), optional, target	sht_coverage,
		real(8), intent(in), optional, target	min_occupancy,
		character(*), intent(in), optional, target	smearing,
		real(8), intent(in), optional, target	smearing_width,
		real(8), intent(in), optional, target	spglib_tol,
		character(*), intent(in), optional, target	electronic_structure_method,
		integer, intent(out), optional, target	error_code
	)

Set parameters of the simulation.

Parameters

[in]	handler	Simulation context handler
[in]	lmax_apw	Maximum orbital quantum number for APW functions.
[in]	lmax_rho	Maximum orbital quantum number for density.
[in]	lmax_pot	Maximum orbital quantum number for potential.
[in]	num_fv_states	Number of first-variational states.
[in]	num_bands	Number of bands.
[in]	num_mag_dims	Number of magnetic dimensions.
[in]	pw_cutoff	Cutoff for G-vectors.
[in]	gk_cutoff	Cutoff for G+k-vectors.
[in]	fft_grid_size	Size of the fine-grain FFT grid.
[in]	auto_rmt	Set the automatic search of muffin-tin radii.
[in]	gamma_point	True if this is a Gamma-point calculation.
[in]	use_symmetry	True if crystal symmetry is taken into account.
[in]	so_correction	True if spin-orbit correnctio is enabled.
[in]	valence_rel	Valence relativity treatment.
[in]	core_rel	Core relativity treatment.
[in]	iter_solver_tol_empty	Tolerance for the empty states.
[in]	iter_solver_type	Type of iterative solver.
[in]	verbosity	Verbosity level.
[in]	hubbard_correction	True if LDA+U correction is enabled.
[in]	hubbard_correction_kind	Type of LDA+U implementation (simplified or full).
[in]	hubbard_full_orthogonalization	Use all atomic orbitals found in all ps potentials to compute the orthogonalization operator.
[in]	hubbard_orbitals	Type of localized orbitals.
[in]	sht_coverage	Type of spherical coverage (0 for Lebedev-Laikov, 1 for uniform).
[in]	min_occupancy	Minimum band occupancy to trat is as "occupied".
[in]	smearing	Type of occupancy smearing.
[in]	smearing_width	Smearing width
[in]	spglib_tol	Tolerance for the spglib symmetry search.
[in]	electronic_structure_method	Type of electronic structure method.
[out]	error_code	Error code.

Definition at line 471 of file sirius.f90.

sirius_get_parameters()

subroutine sirius::sirius_get_parameters	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(out), optional, target	lmax_apw,
		integer, intent(out), optional, target	lmax_rho,
		integer, intent(out), optional, target	lmax_pot,
		integer, intent(out), optional, target	num_fv_states,
		integer, intent(out), optional, target	num_bands,
		integer, intent(out), optional, target	num_spins,
		integer, intent(out), optional, target	num_mag_dims,
		real(8), intent(out), optional, target	pw_cutoff,
		real(8), intent(out), optional, target	gk_cutoff,
		integer, dimension(3), intent(out), optional, target	fft_grid_size,
		integer, intent(out), optional, target	auto_rmt,
		logical, intent(out), optional, target	gamma_point,
		logical, intent(out), optional, target	use_symmetry,
		logical, intent(out), optional, target	so_correction,
		real(8), intent(out), optional, target	iter_solver_tol,
		real(8), intent(out), optional, target	iter_solver_tol_empty,
		integer, intent(out), optional, target	verbosity,
		logical, intent(out), optional, target	hubbard_correction,
		real(8), intent(out), optional, target	evp_work_count,
		integer, intent(out), optional, target	num_loc_op_applied,
		integer, intent(out), optional, target	num_sym_op,
		character(*), intent(out), optional, target	electronic_structure_method,
		integer, intent(out), optional, target	error_code
	)

Get parameters of the simulation.

Parameters

[in]	handler	Simulation context handler
[out]	lmax_apw	Maximum orbital quantum number for APW functions.
[out]	lmax_rho	Maximum orbital quantum number for density.
[out]	lmax_pot	Maximum orbital quantum number for potential.
[out]	num_fv_states	Number of first-variational states.
[out]	num_bands	Number of bands.
[out]	num_spins	Number of spins.
[out]	num_mag_dims	Number of magnetic dimensions.
[out]	pw_cutoff	Cutoff for G-vectors.
[out]	gk_cutoff	Cutoff for G+k-vectors.
[out]	fft_grid_size	Size of the fine-grain FFT grid.
[out]	auto_rmt	Set the automatic search of muffin-tin radii.
[out]	gamma_point	True if this is a Gamma-point calculation.
[out]	use_symmetry	True if crystal symmetry is taken into account.
[out]	so_correction	True if spin-orbit correnctio is enabled.
[out]	iter_solver_tol	Tolerance of the iterative solver (deprecated).
[out]	iter_solver_tol_empty	Tolerance for the empty states.
[out]	verbosity	Verbosity level.
[out]	hubbard_correction	True if LDA+U correction is enabled.
[out]	evp_work_count	Internal counter of total eigen-value problem work.
[out]	num_loc_op_applied	Internal counter of the number of wave-functions to which Hamiltonian was applied.
[out]	num_sym_op	Number of symmetry operations discovered by spglib
[out]	electronic_structure_method	Type of electronic structure method.
[out]	error_code	Error code.

Definition at line 792 of file sirius.f90.

sirius_add_xc_functional()

subroutine sirius::sirius_add_xc_functional	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	name,
		integer, intent(out), optional, target	error_code
	)

Add one of the XC functionals.

Parameters

[in]	handler	Simulation context handler
[in]	name	LibXC label of the functional.
[out]	error_code	Error code.

Definition at line 1011 of file sirius.f90.

sirius_set_mpi_grid_dims()

subroutine sirius::sirius_set_mpi_grid_dims	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(in), target	ndims,
		integer, dimension(ndims), intent(in), target	dims,
		integer, intent(out), optional, target	error_code
	)

Set dimensions of the MPI grid.

Parameters

[in]	handler	Simulation context handler
[in]	ndims	Number of dimensions.
[in]	dims	Size of each dimension.
[out]	error_code	Error code.

Definition at line 1053 of file sirius.f90.

sirius_set_lattice_vectors()

subroutine sirius::sirius_set_lattice_vectors	(	type(sirius_context_handler), intent(in), target	handler,
		real(8), dimension(3), intent(in), target	a1,
		real(8), dimension(3), intent(in), target	a2,
		real(8), dimension(3), intent(in), target	a3,
		integer, intent(out), optional, target	error_code
	)

Set vectors of the unit cell.

Parameters

[in]	handler	Simulation context handler
[in]	a1	1st vector
[in]	a2	2nd vector
[in]	a3	3rd vector
[out]	error_code	Error code.

Definition at line 1097 of file sirius.f90.

sirius_initialize_context()

subroutine sirius::sirius_initialize_context	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(out), optional, target	error_code
	)

Initialize simulation context.

Parameters

[in]	handler	Simulation context handler.
[out]	error_code	Error code.

Definition at line 1143 of file sirius.f90.

sirius_update_context()

subroutine sirius::sirius_update_context	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(out), optional, target	error_code
	)

Update simulation context after changing lattice or atomic positions.

Parameters

[in]	handler	Simulation context handler.
[out]	error_code	Error code.

Definition at line 1174 of file sirius.f90.

sirius_print_info()

subroutine sirius::sirius_print_info	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(out), optional, target	error_code
	)

Print basic info.

Parameters

[in]	handler	Simulation context handler.
[out]	error_code	Error code.

Definition at line 1205 of file sirius.f90.

sirius_free_object_handler()

subroutine sirius::sirius_free_object_handler	(	type(c_ptr), intent(inout), target	handler,
		integer, intent(out), optional, target	error_code
	)

Free any object handler created by SIRIUS.

This is an internal function. Use sirius_free_handler() in your code.

Parameters

[in,out]	handler	Handler of the object.
[out]	error_code	Error code

Definition at line 1238 of file sirius.f90.

sirius_set_periodic_function_ptr()

subroutine sirius::sirius_set_periodic_function_ptr	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		real(8), dimension(:,:,:), intent(in), optional, target	f_mt,
		integer, intent(in), optional, target	lmmax,
		integer, intent(in), optional, target	nrmtmax,
		integer, intent(in), optional, target	num_atoms,
		real(8), dimension(:), intent(in), optional, target	f_rg,
		integer, intent(in), optional, target	size_x,
		integer, intent(in), optional, target	size_y,
		integer, intent(in), optional, target	size_z,
		integer, intent(in), optional, target	offset_z,
		integer, intent(out), optional, target	error_code
	)

Set pointer to density or magnetization.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Label of the function.
[in]	f_mt	Pointer to the muffin-tin part of the function.
[in]	lmmax	Number of lm components.
[in]	nrmtmax	Maximum number of muffin-tin points.
[in]	num_atoms	Total number of atoms.
[in]	f_rg	Pointer to the regular-grid part of the function.
[in]	size_x	Size of X-dimension of FFT grid.
[in]	size_y	Size of Y-dimension of FFT grid.
[in]	size_z	Local or global size of Z-dimension of FFT grid depending on offset_z
[in]	offset_z	Offset in the Z-dimension of FFT grid for this MPI rank.
[out]	error_code	Error code

Definition at line 1279 of file sirius.f90.

sirius_set_periodic_function()

subroutine sirius::sirius_set_periodic_function	(	type(sirius_ground_state_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		real(8), dimension(:,:,:), intent(in), optional, target	f_mt,
		integer, intent(in), optional, target	lmmax,
		integer, intent(in), optional, target	nrmtmax,
		integer, intent(in), optional, target	num_atoms,
		real(8), dimension(:), intent(in), optional, target	f_rg,
		integer, intent(in), optional, target	size_x,
		integer, intent(in), optional, target	size_y,
		integer, intent(in), optional, target	size_z,
		integer, intent(in), optional, target	offset_z,
		integer, intent(out), optional, target	error_code
	)

Set values of the periodic function.

Parameters

[in]	handler	Handler of the DFT ground state object.
[in]	label	Label of the function.
[in]	f_mt	Pointer to the muffin-tin part of the function.
[in]	lmmax	Number of lm components.
[in]	nrmtmax	Maximum number of muffin-tin points.
[in]	num_atoms	Total number of atoms.
[in]	f_rg	Pointer to the regular-grid part of the function.
[in]	size_x	Size of X-dimension of FFT grid.
[in]	size_y	Size of Y-dimension of FFT grid.
[in]	size_z	Local or global size of Z-dimension of FFT grid depending on offset_z
[in]	offset_z	Offset in the Z-dimension of FFT grid for this MPI rank.
[out]	error_code	Error code.

Definition at line 1396 of file sirius.f90.

sirius_get_periodic_function()

subroutine sirius::sirius_get_periodic_function	(	type(sirius_ground_state_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		real(8), dimension(:,:,:), intent(in), optional, target	f_mt,
		integer, intent(in), optional, target	lmmax,
		integer, intent(in), optional, target	nrmtmax,
		integer, intent(in), optional, target	num_atoms,
		real(8), dimension(:), intent(in), optional, target	f_rg,
		integer, intent(in), optional, target	size_x,
		integer, intent(in), optional, target	size_y,
		integer, intent(in), optional, target	size_z,
		integer, intent(in), optional, target	offset_z,
		integer, intent(out), optional, target	error_code
	)

Get values of the periodic function.

Parameters

[in]	handler	Handler of the DFT ground state object.
[in]	label	Label of the function.
[in]	f_mt	Pointer to the muffin-tin part of the function.
[in]	lmmax	Number of lm components.
[in]	nrmtmax	Maximum number of muffin-tin points.
[in]	num_atoms	Total number of atoms.
[in]	f_rg	Pointer to the regular-grid part of the function.
[in]	size_x	Size of X-dimension of FFT grid.
[in]	size_y	Size of Y-dimension of FFT grid.
[in]	size_z	Local or global size of Z-dimension of FFT grid depending on offset_z
[in]	offset_z	Offset in the Z-dimension of FFT grid for this MPI rank.
[out]	error_code	Error code

Definition at line 1512 of file sirius.f90.

sirius_create_kset()

subroutine sirius::sirius_create_kset	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(in), target	num_kpoints,
		real(8), dimension(3,num_kpoints), intent(in), target	kpoints,
		real(8), dimension(num_kpoints), intent(in), target	kpoint_weights,
		logical, intent(in), target	init_kset,
		type(sirius_kpoint_set_handler), intent(out), target	kset_handler,
		integer, intent(out), optional, target	error_code
	)

Create k-point set from the list of k-points.

Parameters

[in]	handler	Simulation context handler.
[in]	num_kpoints	Total number of k-points in the set.
[in]	kpoints	List of k-points in lattice coordinates.
[in]	kpoint_weights	Weights of k-points.
[in]	init_kset	If .true. k-set will be initialized.
[out]	kset_handler	Handler of the newly created k-point set.
[out]	error_code	Error code.

Definition at line 1623 of file sirius.f90.

sirius_create_kset_from_grid()

subroutine sirius::sirius_create_kset_from_grid	(	type(sirius_context_handler), intent(in), target	handler,
		integer, dimension(3), intent(in), target	k_grid,
		integer, dimension(3), intent(in), target	k_shift,
		logical, intent(in), target	use_symmetry,
		type(sirius_kpoint_set_handler), intent(out), target	kset_handler,
		integer, intent(out), optional, target	error_code
	)

Create k-point set from a grid.

Parameters

[in]	handler	Simulation context handler.
[in]	k_grid	dimensions of the k points grid.
[in]	k_shift	k point shifts.
[in]	use_symmetry	If .true. k-set will be generated using symmetries.
[out]	kset_handler	Handler of the newly created k-point set.
[out]	error_code	Error code.

Definition at line 1688 of file sirius.f90.

sirius_create_ground_state()

subroutine sirius::sirius_create_ground_state	(	type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		type(sirius_ground_state_handler), intent(out), target	gs_handler,
		integer, intent(out), optional, target	error_code
	)

Create a ground state object.

Parameters

[in]	ks_handler	Handler of the k-point set.
[out]	gs_handler	Handler of the newly created ground state object.
[out]	error_code	Error code.

Definition at line 1745 of file sirius.f90.

sirius_initialize_kset()

subroutine sirius::sirius_initialize_kset	(	type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		integer, dimension(:), intent(in), optional, target	count,
		integer, intent(out), optional, target	error_code
	)

Initialize k-point set.

Parameters

[in]	ks_handler	K-point set handler.
[in]	count	Local number of k-points for each MPI rank.
[out]	error_code	Error code.

Definition at line 1782 of file sirius.f90.

sirius_find_ground_state()

subroutine sirius::sirius_find_ground_state	(	type(sirius_ground_state_handler), intent(in), target	gs_handler,
		real(8), intent(in), optional, target	density_tol,
		real(8), intent(in), optional, target	energy_tol,
		real(8), intent(in), optional, target	iter_solver_tol,
		logical, intent(in), optional, target	initial_guess,
		integer, intent(in), optional, target	max_niter,
		logical, intent(in), optional, target	save_state,
		logical, intent(out), optional, target	converged,
		integer, intent(out), optional, target	niter,
		real(8), intent(out), optional, target	rho_min,
		integer, intent(out), optional, target	error_code
	)

Find the ground state.

Parameters

[in]	gs_handler	Handler of the ground state.
[in]	density_tol	Tolerance on RMS in density.
[in]	energy_tol	Tolerance in total energy difference.
[in]	iter_solver_tol	Initial tolerance of the iterative solver.
[in]	initial_guess	Boolean variable indicating if we want to start from the initial guess or from previous state.
[in]	max_niter	Maximum number of SCF iterations.
[in]	save_state	Boolean variable indicating if we want to save the ground state.
[out]	converged	Boolean variable indicating if the calculation has converged
[out]	niter	Actual number of SCF iterations.
[out]	rho_min	Minimum value of density on the real-space grid. If negative, total energy can't be trusted. Valid only if SCF calculation is converged.
[out]	error_code	Error code.

Definition at line 1829 of file sirius.f90.

sirius_check_scf_density()

subroutine sirius::sirius_check_scf_density	(	type(sirius_ground_state_handler), intent(in), target	gs_handler,
		integer, intent(out), optional, target	error_code
	)

Check the self-consistent density.

Parameters

[in]	gs_handler	Handler of the ground state.
[out]	error_code	Error code

Definition at line 1939 of file sirius.f90.

sirius_update_ground_state()

subroutine sirius::sirius_update_ground_state	(	type(sirius_ground_state_handler), intent(in), target	gs_handler,
		integer, intent(out), optional, target	error_code
	)

Update a ground state object after change of atomic coordinates or lattice vectors.

Parameters

[in]	gs_handler	Ground-state handler.
[out]	error_code	Error code

Definition at line 1970 of file sirius.f90.

sirius_add_atom_type()

subroutine sirius::sirius_add_atom_type	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		character(*), intent(in), optional, target	fname,
		integer, intent(in), optional, target	zn,
		character(*), intent(in), optional, target	symbol,
		real(8), intent(in), optional, target	mass,
		logical, intent(in), optional, target	spin_orbit,
		integer, intent(out), optional, target	error_code
	)

Add new atom type to the unit cell.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Atom type unique label.
[in]	fname	Species file name (in JSON format).
[in]	zn	Nucleus charge.
[in]	symbol	Atomic symbol.
[in]	mass	Atomic mass.
[in]	spin_orbit	True if spin-orbit correction is enabled for this atom type.
[out]	error_code	Error code.

Definition at line 2007 of file sirius.f90.

sirius_set_atom_type_radial_grid()

subroutine sirius::sirius_set_atom_type_radial_grid	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		integer, intent(in), target	num_radial_points,
		real(8), dimension(num_radial_points), intent(in), target	radial_points,
		integer, intent(out), optional, target	error_code
	)

Set radial grid of the atom type.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Atom type label.
[in]	num_radial_points	Number of radial grid points.
[in]	radial_points	List of radial grid points.
[out]	error_code	Error code.

Definition at line 2103 of file sirius.f90.

sirius_set_atom_type_radial_grid_inf()

subroutine sirius::sirius_set_atom_type_radial_grid_inf	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		integer, intent(in), target	num_radial_points,
		real(8), dimension(num_radial_points), intent(in), target	radial_points,
		integer, intent(out), optional, target	error_code
	)

Set radial grid of the free atom (up to effectice infinity).

Parameters

[in]	handler	Simulation context handler.
[in]	label	Atom type label.
[in]	num_radial_points	Number of radial grid points.
[in]	radial_points	List of radial grid points.
[out]	error_code	Error code.

Definition at line 2159 of file sirius.f90.

sirius_add_atom_type_radial_function()

subroutine sirius::sirius_add_atom_type_radial_function	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	atom_type,
		character(*), intent(in), target	label,
		real(8), dimension(num_points), intent(in), target	rf,
		integer, intent(in), target	num_points,
		integer, intent(in), optional, target	n,
		integer, intent(in), optional, target	l,
		integer, intent(in), optional, target	idxrf1,
		integer, intent(in), optional, target	idxrf2,
		real(8), intent(in), optional, target	occ,
		integer, intent(out), optional, target	error_code
	)

Add one of the radial functions.

Parameters

[in]	handler	Simulation context handler.
[in]	atom_type	Label of the atom type.
[in]	label	Label of the radial function.
[in]	rf	Array with radial function values.
[in]	num_points	Length of radial function array.
[in]	n	Orbital quantum number.
[in]	l	angular momentum.
[in]	idxrf1	First index of radial function (for Q-operator). Indices start from 1.
[in]	idxrf2	Second index of radial function (for Q-operator). Indices start form 1.
[in]	occ	Occupancy of the wave-function.
[out]	error_code	Error code.

Definition at line 2221 of file sirius.f90.

sirius_set_atom_type_hubbard()

subroutine sirius::sirius_set_atom_type_hubbard	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		integer, intent(in), target	l,
		integer, intent(in), target	n,
		real(8), intent(in), target	occ,
		real(8), intent(in), target	U,
		real(8), intent(in), target	J,
		real(8), intent(in), target	alpha,
		real(8), intent(in), target	beta,
		real(8), intent(in), target	J0,
		integer, intent(out), optional, target	error_code
	)

Set the hubbard correction for the atomic type.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Atom type label.
[in]	l	Orbital quantum number.
[in]	n	principal quantum number (s, p, d, f)
[in]	occ	Atomic shell occupancy.
[in]	U	Hubbard U parameter.
[in]	J	Exchange J parameter for the full interaction treatment.
[in]	alpha	J_alpha for the simple interaction treatment.
[in]	beta	J_beta for the simple interaction treatment.
[in]	J0	J0 for the simple interaction treatment.
[out]	error_code	Error code.

Definition at line 2327 of file sirius.f90.

sirius_set_atom_type_dion()

subroutine sirius::sirius_set_atom_type_dion	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		integer, intent(in), target	num_beta,
		real(8), dimension(num_beta, num_beta), intent(in), target	dion,
		integer, intent(out), optional, target	error_code
	)

Set ionic part of D-operator matrix.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Atom type label.
[in]	num_beta	Number of beta-projectors.
[in]	dion	Ionic part of D-operator matrix.
[out]	error_code	Error code.

Definition at line 2413 of file sirius.f90.

sirius_set_atom_type_paw()

subroutine sirius::sirius_set_atom_type_paw	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		real(8), intent(in), target	core_energy,
		real(8), dimension(num_occ), intent(in), target	occupations,
		integer, intent(in), target	num_occ,
		integer, intent(out), optional, target	error_code
	)

Set PAW related data.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Atom type label.
[in]	core_energy	Core-electrons energy contribution.
[in]	occupations	array of orbital occupancies
[in]	num_occ	size of the occupations array
[out]	error_code	Error code.

Definition at line 2467 of file sirius.f90.

sirius_add_atom()

subroutine sirius::sirius_add_atom	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		real(8), dimension(3), intent(in), target	position,
		real(8), dimension(3), intent(in), optional, target	vector_field,
		integer, intent(out), optional, target	error_code
	)

Add atom to the unit cell.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Atom type label.
[in]	position	Atom position in lattice coordinates.
[in]	vector_field	Starting magnetization.
[out]	error_code	Error code.

Definition at line 2528 of file sirius.f90.

sirius_set_atom_position()

subroutine sirius::sirius_set_atom_position	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(in), target	ia,
		real(8), dimension(3), intent(in), target	position,
		integer, intent(out), optional, target	error_code
	)

Set new atomic position.

Parameters

[in]	handler	Simulation context handler.
[in]	ia	Index of atom; index starts form 1
[in]	position	Atom position in lattice coordinates.
[out]	error_code	Error code.

Definition at line 2582 of file sirius.f90.

sirius_set_pw_coeffs()

subroutine sirius::sirius_set_pw_coeffs	(	type(sirius_ground_state_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		complex(8), dimension(:), intent(in), target	pw_coeffs,
		logical, intent(in), optional, target	transform_to_rg,
		integer, intent(in), optional, target	ngv,
		integer, dimension(:,:), intent(in), optional, target	gvl,
		integer, intent(in), optional, target	comm,
		integer, intent(out), optional, target	error_code
	)

Set plane-wave coefficients of a periodic function.

Parameters

[in]	handler	Ground state handler.
[in]	label	Label of the function.
[in]	pw_coeffs	Local array of plane-wave coefficients.
[in]	transform_to_rg	True if function has to be transformed to real-space grid.
[in]	ngv	Local number of G-vectors.
[in]	gvl	List of G-vectors in lattice coordinates (Miller indices).
[in]	comm	MPI communicator used in distribution of G-vectors
[out]	error_code	Error code.

Definition at line 2629 of file sirius.f90.

sirius_get_pw_coeffs()

subroutine sirius::sirius_get_pw_coeffs	(	type(sirius_ground_state_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		complex(8), dimension(:), intent(in), target	pw_coeffs,
		integer, intent(in), optional, target	ngv,
		integer, dimension(:,:), intent(in), optional, target	gvl,
		integer, intent(in), optional, target	comm,
		integer, intent(out), optional, target	error_code
	)

Get plane-wave coefficients of a periodic function.

Parameters

[in]	handler	Ground state handler.
[in]	label	Label of the function.
[in]	pw_coeffs	Local array of plane-wave coefficients.
[in]	ngv	Local number of G-vectors.
[in]	gvl	List of G-vectors in lattice coordinates (Miller indices).
[in]	comm	MPI communicator used in distribution of G-vectors
[out]	error_code	Error code.

Definition at line 2714 of file sirius.f90.

sirius_initialize_subspace()

subroutine sirius::sirius_initialize_subspace	(	type(sirius_ground_state_handler), intent(in), target	gs_handler,
		type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		integer, intent(out), optional, target	error_code
	)

Initialize the subspace of wave-functions.

Parameters

[in]	gs_handler	Ground state handler.
[in]	ks_handler	K-point set handler.
[out]	error_code	Error code.

Definition at line 2782 of file sirius.f90.

sirius_find_eigen_states()

subroutine sirius::sirius_find_eigen_states	(	type(sirius_ground_state_handler), intent(in), target	gs_handler,
		type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		logical, intent(in), optional, target	precompute_pw,
		logical, intent(in), optional, target	precompute_rf,
		logical, intent(in), optional, target	precompute_ri,
		real(8), intent(in), optional, target	iter_solver_tol,
		integer, intent(out), optional, target	error_code
	)

Find eigen-states of the Hamiltonian.

Parameters

[in]	gs_handler	Ground state handler.
[in]	ks_handler	K-point set handler.
[in]	precompute_pw	Generate plane-wave coefficients of the potential
[in]	precompute_rf	Generate radial functions
[in]	precompute_ri	Generate radial integrals
[in]	iter_solver_tol	Iterative solver tolerance.
[out]	error_code	Error code.

Definition at line 2823 of file sirius.f90.

sirius_generate_initial_density()

subroutine sirius::sirius_generate_initial_density	(	type(sirius_ground_state_handler), intent(in), target	handler,
		integer, intent(out), optional, target	error_code
	)

Generate initial density.

Parameters

[in]	handler	Ground state handler.
[out]	error_code	Error code.

Definition at line 2902 of file sirius.f90.

sirius_generate_effective_potential()

subroutine sirius::sirius_generate_effective_potential	(	type(sirius_ground_state_handler), intent(in), target	handler,
		integer, intent(out), optional, target	error_code
	)

Generate effective potential and magnetic field.

Parameters

[in]	handler	Ground state handler.
[out]	error_code	Error code.

Definition at line 2933 of file sirius.f90.

sirius_generate_density()

subroutine sirius::sirius_generate_density	(	type(sirius_ground_state_handler), intent(in), target	gs_handler,
		logical, intent(in), optional, target	add_core,
		logical, intent(in), optional, target	transform_to_rg,
		logical, intent(in), optional, target	paw_only,
		integer, intent(out), optional, target	error_code
	)

Generate charge density and magnetization.

Parameters

[in]	gs_handler	Ground state handler.
[in]	add_core	Add core charge density in the muffin-tins.
[in]	transform_to_rg	If true, density and magnetization are transformed to real-space grid.
[in]	paw_only	it true, only local PAW density is generated
[out]	error_code	Error code.

Definition at line 2967 of file sirius.f90.

sirius_set_band_occupancies()

subroutine sirius::sirius_set_band_occupancies	(	type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		integer, intent(in), target	ik,
		integer, intent(in), target	ispn,
		real(8), dimension(:), intent(in), target	band_occupancies,
		integer, intent(out), optional, target	error_code
	)

Set band occupancies.

Parameters

[in]	ks_handler	K-point set handler.
[in]	ik	Global index of k-point.
[in]	ispn	Spin component index.
[in]	band_occupancies	Array of band occupancies.
[out]	error_code	Error code.

Definition at line 3037 of file sirius.f90.

sirius_get_band_occupancies()

subroutine sirius::sirius_get_band_occupancies	(	type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		integer, intent(in), target	ik,
		integer, intent(in), target	ispn,
		real(8), dimension(:), intent(out), target	band_occupancies,
		integer, intent(out), optional, target	error_code
	)

Set band occupancies.

Parameters

[in]	ks_handler	K-point set handler.
[in]	ik	Global index of k-point.
[in]	ispn	Spin component.
[out]	band_occupancies	Array of band occupancies.
[out]	error_code	Error code.

Definition at line 3087 of file sirius.f90.

sirius_get_band_energies()

subroutine sirius::sirius_get_band_energies	(	type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		integer, intent(in), target	ik,
		integer, intent(in), target	ispn,
		real(8), dimension(:), intent(out), target	band_energies,
		integer, intent(out), optional, target	error_code
	)

Get band energies.

Parameters

[in]	ks_handler	K-point set handler.
[in]	ik	Global index of k-point.
[in]	ispn	Spin component.
[out]	band_energies	Array of band energies.
[out]	error_code	Error code.

Definition at line 3137 of file sirius.f90.

sirius_get_energy()

subroutine sirius::sirius_get_energy	(	type(sirius_ground_state_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		real(8), intent(out), target	energy,
		integer, intent(out), optional, target	error_code
	)

Get one of the total energy components.

Parameters

[in]	handler	DFT ground state handler.
[in]	label	Label of the energy component to get.
[out]	energy	Total energy component.
[out]	error_code	Error code.

Definition at line 3186 of file sirius.f90.

sirius_get_forces()

subroutine sirius::sirius_get_forces	(	type(sirius_ground_state_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		real(8), dimension(:,:), intent(out), target	forces,
		integer, intent(out), optional, target	error_code
	)

Get one of the total force components.

Parameters

[in]	handler	DFT ground state handler.
[in]	label	Label of the force component to get.
[out]	forces	Total force component for each atom.
[out]	error_code	Error code.

Definition at line 3233 of file sirius.f90.

sirius_get_stress_tensor()

subroutine sirius::sirius_get_stress_tensor	(	type(sirius_ground_state_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		real(8), dimension(3, 3), intent(out), target	stress_tensor,
		integer, intent(out), optional, target	error_code
	)

Get one of the stress tensor components.

Parameters

[in]	handler	DFT ground state handler.
[in]	label	Label of the stress tensor component to get.
[out]	stress_tensor	Component of the total stress tensor.
[out]	error_code	Error code.

Definition at line 3280 of file sirius.f90.

sirius_get_num_beta_projectors()

subroutine sirius::sirius_get_num_beta_projectors	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		integer, intent(out), target	num_bp,
		integer, intent(out), optional, target	error_code
	)

Get the number of beta-projectors for an atom type.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Atom type label.
[out]	num_bp	Number of beta projectors for each atom type.
[out]	error_code	Error code.

Definition at line 3327 of file sirius.f90.

sirius_get_wave_functions()

subroutine sirius::sirius_get_wave_functions	(	type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		real(8), dimension(3), intent(in), optional, target	vkl,
		integer, intent(in), optional, target	spin,
		integer, intent(in), optional, target	num_gvec_loc,
		integer, dimension(:,:), intent(in), optional, target	gvec_loc,
		complex(8), dimension(:,:), intent(out), optional, target	evec,
		integer, intent(in), optional, target	ld,
		integer, intent(in), optional, target	num_spin_comp,
		integer, intent(out), optional, target	error_code
	)

Get wave-functions.

Parameters

[in]	ks_handler	K-point set handler.
[in]	vkl	Latttice coordinates of the k-point.
[in]	spin	Spin index in case of collinear magnetism.
[in]	num_gvec_loc	Local number of G-vectors for a k-point.
[in]	gvec_loc	List of G-vectors.
[out]	evec	Wave-functions.
[in]	ld	Leading dimension of evec array.
[in]	num_spin_comp	Number of spin components.
[out]	error_code	Error code

Definition at line 3379 of file sirius.f90.

sirius_add_atom_type_aw_descriptor()

subroutine sirius::sirius_add_atom_type_aw_descriptor	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		integer, intent(in), target	n,
		integer, intent(in), target	l,
		real(8), intent(in), target	enu,
		integer, intent(in), target	dme,
		logical, intent(in), target	auto_enu,
		integer, intent(out), optional, target	error_code
	)

Add descriptor of the augmented wave radial function.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Atom type label.
[in]	n	Principal quantum number.
[in]	l	Orbital quantum number.
[in]	enu	Linearization energy.
[in]	dme	Order of energy derivative.
[in]	auto_enu	True if automatic search of linearization energy is allowed for this radial solution.
[out]	error_code	Error code

Definition at line 3468 of file sirius.f90.

sirius_add_atom_type_lo_descriptor()

subroutine sirius::sirius_add_atom_type_lo_descriptor	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		integer, intent(in), target	ilo,
		integer, intent(in), target	n,
		integer, intent(in), target	l,
		real(8), intent(in), target	enu,
		integer, intent(in), target	dme,
		logical, intent(in), target	auto_enu,
		integer, intent(out), optional, target	error_code
	)

Add descriptor of the local orbital radial function.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Atom type label.
[in]	ilo	Index of the local orbital to which the descriptor is added.
[in]	n	Principal quantum number.
[in]	l	Orbital quantum number.
[in]	enu	Linearization energy.
[in]	dme	Order of energy derivative.
[in]	auto_enu	True if automatic search of linearization energy is allowed for this radial solution.
[out]	error_code	Error code

Definition at line 3545 of file sirius.f90.

sirius_set_atom_type_configuration()

subroutine sirius::sirius_set_atom_type_configuration	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		integer, intent(in), target	n,
		integer, intent(in), target	l,
		integer, intent(in), target	k,
		real(8), intent(in), target	occupancy,
		logical, intent(in), target	core,
		integer, intent(out), optional, target	error_code
	)

Set configuration of atomic levels.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Atom type label.
[in]	n	Principal quantum number.
[in]	l	Orbital quantum number.
[in]	k	kappa (used in relativistic solver).
[in]	occupancy	Level occupancy.
[in]	core	Tru if this is a core state.
[out]	error_code	Error code

Definition at line 3626 of file sirius.f90.

sirius_generate_coulomb_potential()

subroutine sirius::sirius_generate_coulomb_potential	(	type(sirius_ground_state_handler), intent(in), target	handler,
		real(8), dimension(:), intent(out), optional, target	vh_el,
		integer, intent(out), optional, target	error_code
	)

Generate Coulomb potential by solving Poisson equation.

Parameters

[in]	handler	DFT ground state handler
[out]	vh_el	Electronic part of Hartree potential at each atom's origin.
[out]	error_code	Error code

Definition at line 3697 of file sirius.f90.

sirius_generate_xc_potential()

subroutine sirius::sirius_generate_xc_potential	(	type(sirius_ground_state_handler), intent(in), target	handler,
		integer, intent(out), optional, target	error_code
	)

Generate XC potential using LibXC.

Parameters

[in]	handler	Ground state handler
[out]	error_code	Error code

Definition at line 3735 of file sirius.f90.

sirius_get_kpoint_inter_comm()

subroutine sirius::sirius_get_kpoint_inter_comm	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(out), target	fcomm,
		integer, intent(out), optional, target	error_code
	)

Get communicator which is used to split k-points.

Parameters

[in]	handler	Simulation context handler
[out]	fcomm	Fortran communicator
[out]	error_code	Error code

Definition at line 3767 of file sirius.f90.

sirius_get_kpoint_inner_comm()

subroutine sirius::sirius_get_kpoint_inner_comm	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(out), target	fcomm,
		integer, intent(out), optional, target	error_code
	)

Get communicator which is used to parallise band problem.

Parameters

[in]	handler	Simulation context handler
[out]	fcomm	Fortran communicator
[out]	error_code	Error code

Definition at line 3804 of file sirius.f90.

sirius_get_fft_comm()

subroutine sirius::sirius_get_fft_comm	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(out), target	fcomm,
		integer, intent(out), optional, target	error_code
	)

Get communicator which is used to parallise FFT.

Parameters

[in]	handler	Simulation context handler
[out]	fcomm	Fortran communicator
[out]	error_code	Error code

Definition at line 3841 of file sirius.f90.

sirius_get_num_gvec()

subroutine sirius::sirius_get_num_gvec	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(out), target	num_gvec,
		integer, intent(out), optional, target	error_code
	)

Get total number of G-vectors on the fine grid.

Parameters

[in]	handler	Simulation context handler
[out]	num_gvec	Total number of G-vectors
[out]	error_code	Error code

Definition at line 3878 of file sirius.f90.

sirius_get_gvec_arrays()

subroutine sirius::sirius_get_gvec_arrays	(	type(sirius_context_handler), intent(in), target	handler,
		integer, dimension(:,:), intent(in), optional, target	gvec,
		real(8), dimension(:,:), intent(in), optional, target	gvec_cart,
		real(8), dimension(:), intent(in), optional, target	gvec_len,
		integer, dimension(:,:,:), intent(in), optional, target	index_by_gvec,
		integer, intent(out), optional, target	error_code
	)

Get G-vector arrays.

Parameters

[in]	handler	Simulation context handler
[in]	gvec	G-vectors in lattice coordinates.
[in]	gvec_cart	G-vectors in Cartesian coordinates.
[in]	gvec_len	Length of G-vectors.
[in]	index_by_gvec	G-vector index by lattice coordinates.
[out]	error_code	Error code

Definition at line 3918 of file sirius.f90.

sirius_get_num_fft_grid_points()

subroutine sirius::sirius_get_num_fft_grid_points	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(out), target	num_fft_grid_points,
		integer, intent(out), optional, target	error_code
	)

Get local number of FFT grid points.

Parameters

[in]	handler	Simulation context handler
[out]	num_fft_grid_points	Local number of FFT grid points in the real-space mesh.
[out]	error_code	Error code.

Definition at line 3981 of file sirius.f90.

sirius_get_fft_index()

subroutine sirius::sirius_get_fft_index	(	type(sirius_context_handler), intent(in), target	handler,
		integer, dimension(:), intent(out), target	fft_index,
		integer, intent(out), optional, target	error_code
	)

Get mapping between G-vector index and FFT index.

Parameters

[in]	handler	Simulation context handler
[out]	fft_index	Index inside FFT buffer
[out]	error_code	Error code.

Definition at line 4018 of file sirius.f90.

sirius_get_max_num_gkvec()

subroutine sirius::sirius_get_max_num_gkvec	(	type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		integer, intent(out), target	max_num_gkvec,
		integer, intent(out), optional, target	error_code
	)

Get maximum number of G+k vectors across all k-points in the set.

Parameters

[in]	ks_handler	K-point set handler.
[out]	max_num_gkvec	Maximum number of G+k vectors
[out]	error_code	Error code.

Definition at line 4055 of file sirius.f90.

sirius_get_gkvec_arrays()

subroutine sirius::sirius_get_gkvec_arrays	(	type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		integer, intent(in), target	ik,
		integer, intent(out), target	num_gkvec,
		integer, dimension(:), intent(out), target	gvec_index,
		real(8), dimension(:,:), intent(out), target	gkvec,
		real(8), dimension(:,:), intent(out), target	gkvec_cart,
		real(8), dimension(:), intent(out), target	gkvec_len,
		real(8), dimension(:,:), intent(out), target	gkvec_tp,
		integer, intent(out), optional, target	error_code
	)

Get all G+k vector related arrays.

Parameters

[in]	ks_handler	K-point set handler.
[in]	ik	Global index of k-point
[out]	num_gkvec	Number of G+k vectors.
[out]	gvec_index	Index of the G-vector part of G+k vector.
[out]	gkvec	G+k vectors in fractional coordinates.
[out]	gkvec_cart	G+k vectors in Cartesian coordinates.
[out]	gkvec_len	Length of G+k vectors.
[out]	gkvec_tp	Theta and Phi angles of G+k vectors.
[out]	error_code	Error code.

Definition at line 4098 of file sirius.f90.

sirius_get_step_function()

subroutine sirius::sirius_get_step_function	(	type(sirius_context_handler), intent(in), target	handler,
		complex(8), dimension(:), intent(out), target	cfunig,
		real(8), dimension(:), intent(out), target	cfunrg,
		integer, intent(in), target	num_rg_points,
		integer, intent(out), optional, target	error_code
	)

Get the unit-step function.

Parameters

[in]	handler	Simulation context handler
[out]	cfunig	Plane-wave coefficients of step function.
[out]	cfunrg	Values of the step function on the regular grid.
[in]	num_rg_points	Number of real-space points.
[out]	error_code	Error code.

Definition at line 4170 of file sirius.f90.

sirius_set_h_radial_integrals()

subroutine sirius::sirius_set_h_radial_integrals	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(in), target	ia,
		integer, intent(in), target	lmmax,
		real(8), intent(in), target	val,
		integer, intent(in), optional, target	l1,
		integer, intent(in), optional, target	o1,
		integer, intent(in), optional, target	ilo1,
		integer, intent(in), optional, target	l2,
		integer, intent(in), optional, target	o2,
		integer, intent(in), optional, target	ilo2,
		integer, intent(out), optional, target	error_code
	)

Set LAPW Hamiltonian radial integrals.

Parameters

[in]	handler	Simulation context handler.
[in]	ia	Index of atom.
[in]	lmmax	Number of lm-component of the potential.
[in]	val	Values of the radial integrals.
[in]	l1	1st index of orbital quantum number.
[in]	o1	1st index of radial function order for l1.
[in]	ilo1	1st index or local orbital.
[in]	l2	2nd index of orbital quantum number.
[in]	o2	2nd index of radial function order for l2.
[in]	ilo2	2nd index or local orbital.
[out]	error_code	Error code.

Definition at line 4226 of file sirius.f90.

sirius_set_o_radial_integral()

subroutine sirius::sirius_set_o_radial_integral	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(in), target	ia,
		real(8), intent(in), target	val,
		integer, intent(in), target	l,
		integer, intent(in), optional, target	o1,
		integer, intent(in), optional, target	ilo1,
		integer, intent(in), optional, target	o2,
		integer, intent(in), optional, target	ilo2,
		integer, intent(out), optional, target	error_code
	)

Set LAPW overlap radial integral.

Parameters

[in]	handler	Simulation context handler.
[in]	ia	Index of atom.
[in]	val	Value of the radial integral.
[in]	l	Orbital quantum number.
[in]	o1	1st index of radial function order.
[in]	ilo1	1st index or local orbital.
[in]	o2	2nd index of radial function order.
[in]	ilo2	2nd index or local orbital.
[out]	error_code	Error code.

Definition at line 4324 of file sirius.f90.

sirius_set_o1_radial_integral()

subroutine sirius::sirius_set_o1_radial_integral	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(in), target	ia,
		real(8), intent(in), target	val,
		integer, intent(in), optional, target	l1,
		integer, intent(in), optional, target	o1,
		integer, intent(in), optional, target	ilo1,
		integer, intent(in), optional, target	l2,
		integer, intent(in), optional, target	o2,
		integer, intent(in), optional, target	ilo2,
		integer, intent(out), optional, target	error_code
	)

Set a correction to LAPW overlap radial integral.

Parameters

[in]	handler	Simulation context handler.
[in]	ia	Index of atom.
[in]	val	Value of the radial integral.
[in]	l1	1st index of orbital quantum number.
[in]	o1	1st index of radial function order for l1.
[in]	ilo1	1st index or local orbital.
[in]	l2	2nd index of orbital quantum number.
[in]	o2	2nd index of radial function order for l2.
[in]	ilo2	2nd index or local orbital.
[out]	error_code	Error code.

Definition at line 4407 of file sirius.f90.

sirius_set_radial_function()

subroutine sirius::sirius_set_radial_function	(	type(sirius_context_handler), intent(in), target	handler,
		integer, intent(in), target	ia,
		integer, intent(in), target	deriv_order,
		real(8), dimension(:), intent(in), target	f,
		integer, intent(in), optional, target	l,
		integer, intent(in), optional, target	o,
		integer, intent(in), optional, target	ilo,
		integer, intent(out), optional, target	error_code
	)

Set LAPW radial functions.

Parameters

[in]	handler	Simulation context handler.
[in]	ia	Index of atom.
[in]	deriv_order	Radial derivative order.
[in]	f	Values of the radial function.
[in]	l	Orbital quantum number.
[in]	o	Order of radial function for l.
[in]	ilo	Local orbital index.
[out]	error_code	Error code.

Definition at line 4498 of file sirius.f90.

sirius_set_equivalent_atoms()

subroutine sirius::sirius_set_equivalent_atoms	(	type(sirius_context_handler), intent(in), target	handler,
		integer, dimension(:), intent(in), target	equivalent_atoms,
		integer, intent(out), optional, target	error_code
	)

Set equivalent atoms.

Parameters

[in]	handler	Simulation context handler.
[in]	equivalent_atoms	Array with equivalent atom IDs.
[out]	error_code	Error code.

Definition at line 4567 of file sirius.f90.

sirius_update_atomic_potential()

subroutine sirius::sirius_update_atomic_potential	(	type(sirius_ground_state_handler), intent(in), target	handler,
		integer, intent(out), optional, target	error_code
	)

Set the new spherical potential.

Parameters

[in]	handler	Ground state handler.
[out]	error_code	Error code.

Definition at line 4603 of file sirius.f90.

sirius_option_get_number_of_sections()

subroutine sirius::sirius_option_get_number_of_sections	(	integer, intent(out), target	length,
		integer, intent(out), optional, target	error_code
	)

Return the total number of sections defined in the input JSON schema.

Parameters

[out]	length	Number of sections.
[out]	error_code	Error code.

Definition at line 4634 of file sirius.f90.

sirius_option_get_section_name()

subroutine sirius::sirius_option_get_section_name	(	integer, intent(in), value	elem,
		character(*), intent(out), target	section_name,
		integer, intent(in), value	section_name_length,
		integer, intent(out), optional, target	error_code
	)

Return the name of a given section.

Parameters

[in]	elem	Index of the section (starting from 1).
[out]	section_name	Name of the section
[in]	section_name_length	Maximum length of the output string. Enough capacity should be provided.
[out]	error_code	Error code.

Definition at line 4667 of file sirius.f90.

sirius_option_get_section_length()

subroutine sirius::sirius_option_get_section_length	(	character(*), intent(in), target	section,
		integer, intent(out), target	length,
		integer, intent(out), optional, target	error_code
	)

Return the number of options in a given section.

Parameters

[in]	section	Name of the seciton.
[out]	length	Number of options contained in the section.
[out]	error_code	Error code.

Definition at line 4710 of file sirius.f90.

sirius_option_get_info()

subroutine sirius::sirius_option_get_info	(	character(*), intent(in), target	section,
		integer, intent(in), value	elem,
		character(*), intent(out), target	key_name,
		integer, intent(in), value	key_name_len,
		integer, intent(out), target	type,
		integer, intent(out), target	length,
		integer, intent(out), target	enum_size,
		character(*), intent(out), target	title,
		integer, intent(in), value	title_len,
		character(*), intent(out), target	description,
		integer, intent(in), value	description_len,
		integer, intent(out), optional, target	error_code
	)

Return information about the option.

Parameters

[in]	section	Name of the section.
[in]	elem	Index of the option (starting from 1)
[out]	key_name	Name of the option.
[in]	key_name_len	Maximum length for the string (on the caller side). No allocation is done.
[out]	type	Type of the option (real, integer, boolean, string, or array of the same types).
[out]	length	Length of the default value (1 for the scalar types, otherwise the lenght of the array).
[out]	enum_size	Number of elements in the enum type, zero otherwise.
[out]	title	Short description of the option (can be empty).
[in]	title_len	Maximum length for the short description.
[out]	description	Detailed description of the option (can be empty).
[in]	description_len	Maximum length for the detailed description.
[out]	error_code	Error code.

Definition at line 4760 of file sirius.f90.

sirius_option_get()

subroutine sirius::sirius_option_get	(	character(*), intent(in), target	section,
		character(*), intent(in), target	name,
		integer, intent(in), target	type,
		type(c_ptr), intent(in), value	data_ptr,
		integer, intent(in), optional, target	max_length,
		integer, intent(in), optional, target	enum_idx,
		integer, intent(out), optional, target	error_code
	)

Return the default value of the option as defined in the JSON schema.

Parameters

[in]	section	Name of the section of interest.
[in]	name	Name of the element
[in]	type	Type of the option (real, integer, boolean)
[in]	data_ptr	Output buffer for the default value or list of values.
[in]	max_length	Maximum length of the buffer containing the default values.
[in]	enum_idx	Index of the element in case of the enum type.
[out]	error_code	Error code.

Definition at line 4853 of file sirius.f90.

sirius_option_set()

subroutine sirius::sirius_option_set	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	section,
		character(*), intent(in), target	name,
		integer, intent(in), target	type,
		type(c_ptr), intent(in), value	data_ptr,
		integer, intent(in), optional, target	max_length,
		logical, intent(in), optional, target	append,
		integer, intent(out), optional, target	error_code
	)

Set the value of the option name in a (internal) json dictionary.

Parameters

[in]	handler	Simulation context handler.
[in]	section	string containing the options in json format
[in]	name	name of the element to pick
[in]	type	Type of the option (real, integer, boolean)
[in]	data_ptr	Buffer for the value or list of values.
[in]	max_length	Maximum length of the buffer containing the default values.
[in]	append	If true then value is appended to the list of values.
[out]	error_code	Error code.

Definition at line 4926 of file sirius.f90.

sirius_dump_runtime_setup()

subroutine sirius::sirius_dump_runtime_setup	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	filename,
		integer, intent(out), optional, target	error_code
	)

Dump the runtime setup in a file.

Parameters

[in]	handler	Simulation context handler.
[in]	filename	String containing the name of the file.
[out]	error_code	Error code

Definition at line 5004 of file sirius.f90.

sirius_get_fv_eigen_vectors()

subroutine sirius::sirius_get_fv_eigen_vectors	(	type(sirius_kpoint_set_handler), intent(in), target	handler,
		integer, intent(in), target	ik,
		complex(8), dimension(:,:), intent(out), target	fv_evec,
		integer, intent(in), target	ld,
		integer, intent(in), target	num_fv_states,
		integer, intent(out), optional, target	error_code
	)

Get the first-variational eigen vectors.

Parameters

[in]	handler	K-point set handler
[in]	ik	Global index of the k-point
[out]	fv_evec	Output first-variational eigenvector array
[in]	ld	Leading dimension of fv_evec
[in]	num_fv_states	Number of first-variational states
[out]	error_code	Error code

Definition at line 5048 of file sirius.f90.

sirius_get_fv_eigen_values()

subroutine sirius::sirius_get_fv_eigen_values	(	type(sirius_kpoint_set_handler), intent(in), target	handler,
		integer, intent(in), target	ik,
		real(8), dimension(:), intent(out), target	fv_eval,
		integer, intent(in), target	num_fv_states,
		integer, intent(out), optional, target	error_code
	)

Get the first-variational eigen values.

Parameters

[in]	handler	K-point set handler
[in]	ik	Global index of the k-point
[out]	fv_eval	Output first-variational eigenvector array
[in]	num_fv_states	Number of first-variational states
[out]	error_code	Error code

Definition at line 5103 of file sirius.f90.

sirius_get_sv_eigen_vectors()

subroutine sirius::sirius_get_sv_eigen_vectors	(	type(sirius_kpoint_set_handler), intent(in), target	handler,
		integer, intent(in), target	ik,
		complex(8), dimension(:,:), intent(out), target	sv_evec,
		integer, intent(in), target	num_bands,
		integer, intent(out), optional, target	error_code
	)

Get the second-variational eigen vectors.

Parameters

[in]	handler	K-point set handler
[in]	ik	Global index of the k-point
[out]	sv_evec	Output second-variational eigenvector array
[in]	num_bands	Number of second-variational bands.
[out]	error_code	Error code

Definition at line 5153 of file sirius.f90.

sirius_set_rg_values()

subroutine sirius::sirius_set_rg_values	(	type(sirius_ground_state_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		integer, dimension(3), intent(in), target	grid_dims,
		integer, dimension(:,:), intent(in), target	local_box_origin,
		integer, dimension(:,:), intent(in), target	local_box_size,
		integer, intent(in), target	fcomm,
		real(8), intent(in), target	values,
		logical, intent(in), optional, target	transform_to_pw,
		integer, intent(out), optional, target	error_code
	)

Set the values of the function on the regular grid.

Parameters

[in]	handler	DFT ground state handler.
[in]	label	Label of the function.
[in]	grid_dims	Dimensions of the FFT grid.
[in]	local_box_origin	Coordinates of the local box origin for each MPI rank
[in]	local_box_size	Dimensions of the local box for each MPI rank.
[in]	fcomm	Fortran communicator used to partition FFT grid into local boxes.
[in]	values	Values of the function (local buffer for each MPI rank).
[in]	transform_to_pw	If true, transform function to PW domain.
[out]	error_code	Error code

Definition at line 5207 of file sirius.f90.

sirius_get_rg_values()

subroutine sirius::sirius_get_rg_values	(	type(sirius_ground_state_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		integer, dimension(3), intent(in), target	grid_dims,
		integer, dimension(:,:), intent(in), target	local_box_origin,
		integer, dimension(:,:), intent(in), target	local_box_size,
		integer, intent(in), target	fcomm,
		real(8), intent(out), target	values,
		logical, intent(in), optional, target	transform_to_rg,
		integer, intent(out), optional, target	error_code
	)

Get the values of the function on the regular grid.

Parameters

[in]	handler	DFT ground state handler.
[in]	label	Label of the function.
[in]	grid_dims	Dimensions of the FFT grid.
[in]	local_box_origin	Coordinates of the local box origin for each MPI rank
[in]	local_box_size	Dimensions of the local box for each MPI rank.
[in]	fcomm	Fortran communicator used to partition FFT grid into local boxes.
[out]	values	Values of the function (local buffer for each MPI rank).
[in]	transform_to_rg	If true, transform function to regular grid before fetching the values.
[out]	error_code	Error code

Definition at line 5293 of file sirius.f90.

sirius_get_total_magnetization()

subroutine sirius::sirius_get_total_magnetization	(	type(sirius_ground_state_handler), intent(in), target	handler,
		real(8), intent(out), target	mag,
		integer, intent(out), optional, target	error_code
	)

Get the total magnetization of the system.

Parameters

[in]	handler	DFT ground state handler.
[out]	mag	3D magnetization vector (x,y,z components).
[out]	error_code	Error code

Definition at line 5373 of file sirius.f90.

sirius_get_num_kpoints()

subroutine sirius::sirius_get_num_kpoints	(	type(sirius_kpoint_set_handler), intent(in), target	handler,
		integer, intent(out), target	num_kpoints,
		integer, intent(out), optional, target	error_code
	)

Get the total number of kpoints.

Parameters

[in]	handler	Kpoint set handler
[out]	num_kpoints	number of kpoints in the set
[out]	error_code	Error code.

Definition at line 5410 of file sirius.f90.

sirius_get_kpoint_properties()

subroutine sirius::sirius_get_kpoint_properties	(	type(sirius_kpoint_set_handler), intent(in), target	handler,
		integer, intent(in), target	ik,
		real(8), intent(out), target	weight,
		real(8), intent(out), optional, target	coordinates,
		integer, intent(out), optional, target	error_code
	)

Get the kpoint properties.

Parameters

[in]	handler	Kpoint set handler
[in]	ik	Index of the kpoint
[out]	weight	Weight of the kpoint
[out]	coordinates	Coordinates of the kpoint
[out]	error_code	Error code.

Definition at line 5449 of file sirius.f90.

sirius_set_callback_function()

subroutine sirius::sirius_set_callback_function	(	type(sirius_context_handler), intent(in), target	handler,
		character(*), intent(in), target	label,
		type(c_funptr), intent(in), value	fptr,
		integer, intent(out), optional, target	error_code
	)

Set callback function to compute various radial integrals.

Parameters

[in]	handler	Simulation context handler.
[in]	label	Lable of the callback function.
[in]	fptr	Pointer to callback function.
[out]	error_code	Error code.

Definition at line 5500 of file sirius.f90.

sirius_nlcg()

subroutine sirius::sirius_nlcg	(	type(sirius_ground_state_handler), intent(in), target	handler,
		type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		integer, intent(out), optional, target	error_code
	)

Robust wave function optimizer.

Parameters

[in]	handler	Ground state handler.
[in]	ks_handler	K-point set handler.
[out]	error_code	Error code.

Definition at line 5543 of file sirius.f90.

sirius_nlcg_params()

subroutine sirius::sirius_nlcg_params	(	type(sirius_ground_state_handler), intent(in), target	handler,
		type(sirius_kpoint_set_handler), intent(in), target	ks_handler,
		real(8), intent(in), target	temp,
		character(*), intent(in), target	smearing,
		real(8), intent(in), target	kappa,
		real(8), intent(in), target	tau,
		real(8), intent(in), target	tol,
		integer, intent(in), target	maxiter,
		integer, intent(in), target	restart,
		character(*), intent(in), target	processing_unit,
		logical, intent(out), target	converged,
		integer, intent(out), optional, target	error_code
	)

Robust wave function optimizer.

Parameters

[in]	handler	Ground state handler.
[in]	ks_handler	K-point set handler.
[in]	temp	Temperature in Kelvin
[in]	smearing	smearing label
[in]	kappa	pseudo-Hamiltonian scalar preconditioner
[in]	tau	backtracking search reduction parameter
[in]	tol	CG tolerance
[in]	maxiter	CG maxiter
[in]	restart	CG restart
[in]	processing_unit	processing_unit = ["cpu"|"gpu"|"none"]
[out]	converged	None
[out]	error_code	Error code.

Definition at line 5589 of file sirius.f90.

sirius_add_hubbard_atom_pair()

subroutine sirius::sirius_add_hubbard_atom_pair	(	type(sirius_context_handler), intent(in), target	handler,
		integer, dimension(2), intent(in), target	atom_pair,
		integer, dimension(3), intent(in), target	translation,
		integer, dimension(2), intent(in), target	n,
		integer, dimension(2), intent(in), target	l,
		real(8), intent(in), target	coupling,
		integer, intent(out), optional, target	error_code
	)

Add a non-local Hubbard interaction V for a pair of atoms.

Parameters

[in]	handler	Simulation context handler.
[in]	atom_pair	atom pair for the V term
[in]	translation	translation vector between the two unit cells containing the atoms
[in]	n	principal quantum number of the atomic levels involved in the V correction
[in]	l	angular momentum of the atomic levels
[in]	coupling	value of the V constant
[out]	error_code	Error code.

Definition at line 5688 of file sirius.f90.

sirius_create_h0()

subroutine sirius::sirius_create_h0	(	type(sirius_ground_state_handler), intent(in), target	handler,
		integer, intent(out), optional, target	error_code
	)

Generate H0.

Parameters

[in]	handler	Ground state handler.
[out]	error_code	Error code

Definition at line 5747 of file sirius.f90.

sirius_linear_solver()

subroutine sirius::sirius_linear_solver	(	type(sirius_ground_state_handler), intent(in), target	handler,
		real(8), dimension(3), intent(in), target	vkq,
		integer, intent(in), target	num_gvec_kq_loc,
		integer, dimension(3, num_gvec_kq_loc), intent(in), target	gvec_kq_loc,
		complex(8), dimension(ld, num_spin_comp), intent(inout), target	dpsi,
		complex(8), dimension(ld, num_spin_comp), intent(in), target	psi,
		real(8), dimension(*), intent(in), target	eigvals,
		complex(8), dimension(ld, num_spin_comp), intent(inout), target	dvpsi,
		integer, intent(in), target	ld,
		integer, intent(in), target	num_spin_comp,
		real(8), intent(in), target	alpha_pv,
		integer, intent(in), target	spin,
		integer, intent(in), target	nbnd_occ,
		real(8), intent(in), target	tol,
		integer, intent(out), target	niter,
		integer, intent(out), optional, target	error_code
	)

Interface to linear solver.

Parameters

[in]	handler	DFT ground state handler.
[in]	vkq	K+q-point in lattice coordinates
[in]	num_gvec_kq_loc	Local number of G-vectors for k+q-point
[in]	gvec_kq_loc	Local list of G-vectors for k+q-point.
[in,out]	dpsi	Left-hand side of the linear equation.
[in]	psi	Unperturbed eigenvectors.
[in]	eigvals	Unperturbed eigenvalues.
[in,out]	dvpsi	Right-hand side of the linear equation (dV * psi)
[in]	ld	Leading dimension of dpsi, psi, dvpsi.
[in]	num_spin_comp	Number of spin components.
[in]	alpha_pv	Constant for the projector.
[in]	spin	Current spin channel.
[in]	nbnd_occ	Number of occupied bands.
[in]	tol	Tolerance for the unconverged residuals (residual L2-norm should be below this value).
[out]	niter	Average number of iterations.
[out]	error_code	Error code

Definition at line 5792 of file sirius.f90.

sirius_generate_d_operator_matrix()

subroutine sirius::sirius_generate_d_operator_matrix	(	type(sirius_ground_state_handler), intent(in), target	handler,
		integer, intent(out), optional, target	error_code
	)

Generate D-operator matrix.

Parameters

[in]	handler	Ground state handler.
[out]	error_code	Error code

Definition at line 5897 of file sirius.f90.

sirius_save_state()

subroutine sirius::sirius_save_state	(	type(sirius_ground_state_handler), intent(in), target	gs_handler,
		character(*), intent(in), target	file_name,
		integer, intent(out), optional, target	error_code
	)

Save DFT ground state (density and potential)

Parameters

[in]	gs_handler	Ground-state handler.
[in]	file_name	Name of the file that stores the saved data.
[out]	error_code	Error code

Definition at line 5929 of file sirius.f90.

sirius_load_state()

subroutine sirius::sirius_load_state	(	type(sirius_ground_state_handler), intent(in), target	handler,
		character(*), intent(in), target	file_name,
		integer, intent(out), optional, target	error_code
	)

Save DFT ground state (density and potential)

Parameters

[in]	handler	Ground-state handler.
[in]	file_name	Name of the file that stores the saved data.
[out]	error_code	Error code

Definition at line 5970 of file sirius.f90.

sirius_set_density_matrix()

subroutine sirius::sirius_set_density_matrix	(	type(sirius_ground_state_handler), intent(in), target	handler,
		integer, intent(in), target	ia,
		complex(8), dimension(ld, ld, 3), intent(in), target	dm,
		integer, intent(in), target	ld,
		integer, intent(out), optional, target	error_code
	)

Set density matrix.

Parameters

[in]	handler	Ground-state handler.
[in]	ia	Index of atom.
[in]	dm	Input density matrix.
[in]	ld	Leading dimension of the density matrix.
[out]	error_code	Error code.

Definition at line 6013 of file sirius.f90.

sirius_free_handler_ctx()

subroutine sirius::sirius_free_handler_ctx	(	type(sirius_context_handler), intent(inout)	handler,
		integer, intent(out), optional, target	error_code
	)

Definition at line 6056 of file sirius.f90.

sirius_free_handler_ks()

subroutine sirius::sirius_free_handler_ks	(	type(sirius_kpoint_set_handler), intent(inout)	handler,
		integer, intent(out), optional, target	error_code
	)

Definition at line 6063 of file sirius.f90.

sirius_free_handler_dft()

subroutine sirius::sirius_free_handler_dft	(	type(sirius_ground_state_handler), intent(inout)	handler,
		integer, intent(out), optional, target	error_code
	)

Definition at line 6070 of file sirius.f90.

create_beta_gk_gpu() [1/2]

void sirius::create_beta_gk_gpu	(	int	num_atoms,
		int	num_gkvec,
		int const *	beta_desc,
		std::complex< float > const *	beta_gk_t,
		double const *	gkvec,
		double const *	atom_pos,
		std::complex< float > *	beta_gk
	)

Definition at line 36 of file beta_projectors_base.cpp.

create_beta_gk_gpu() [2/2]

void sirius::create_beta_gk_gpu	(	int	num_atoms,
		int	num_gkvec,
		int const *	beta_desc,
		std::complex< double > const *	beta_gk_t,
		double const *	gkvec,
		double const *	atom_pos,
		std::complex< double > *	beta_gk
	)

Definition at line 43 of file beta_projectors_base.cpp.

inner_prod_beta()

template<typename F , typename T >

std::enable_if_t< std::is_same< T, real_type< F > >::value, la::dmatrix< F > > sirius::inner_prod_beta	(	spla::Context &	spla_ctx,
		sddk::memory_t	mem__,
		sddk::memory_t	host_mem__,
		bool	result_on_device,
		beta_projectors_coeffs_t< T > &	beta_coeffs__,
		wf::Wave_functions< T > const &	phi__,
		wf::spin_index	ispn__,
		wf::band_range	br__
	)

The following is matrix computed: <beta|phi>

Template Parameters

F	Type of the resulting inner product matrix (float, double, complex<float> or complex<double>).
T	precision type

Parameters

[in]	spla_ctx	Context of the SPLA library
[in]	mem	Location of the input arrays (wfc and beta-projectors)
[in]	host_mem	Host memory type for result allocation (pinned, non-pinned memory)
[in]	result_on_device	Copy result to device if true
[in]	beta_coeffs	Beta-projector coefficient array
[in]	phi	Wave-function
[in]	ispn	Spin index (wfc)
[in]	br	Band range

Returns

inner product

Definition at line 426 of file beta_projectors_base.hpp.

inner_beta() [1/2]

template<class T >

sddk::matrix< std::complex< T > > sirius::inner_beta	(	const Beta_projectors_base< T > &	beta,
		const Simulation_context &	ctx
	)

computes <beta|beta> and returns result on ctx.processing_unit_memory_t

Definition at line 446 of file beta_projectors_base.hpp.

inner_beta() [2/2]

template<class T , class Op >

sddk::matrix< std::complex< T > > sirius::inner_beta	(	const Beta_projectors_base< T > &	beta,
		const Simulation_context &	ctx,
		Op &&	op
	)

inner product <beta|Op|beta>, return resulting dmatrix<complex> in ctx.processing_unit_memory_t

Definition at line 496 of file beta_projectors_base.hpp.

print_memory_usage()

template<typename OUT >

void sirius::print_memory_usage	(	OUT &&	out__,
		std::string	file_and_line__ = ""
	)

Definition at line 53 of file simulation_context.hpp.

option_print_vector__()

template<typename T >

static std::ostringstream sirius::option_print_vector__ ( const std::vector< T > &  vec )

static

Definition at line 36 of file simulation_parameters.cpp.

compose_default_json()

void sirius::compose_default_json	(	nlohmann::json const &	schema__,
		nlohmann::json &	output__
	)

Compose JSON dictionary with default parameters based on input schema.

Traverse the JSON schema and add nodes with default parameters to the output dictionary. The nodes without default parameters are ignored. Still, user has a possibility to add the missing nodes later by providing a corresponding input JSON dictionary. See compose_json() function.

Definition at line 53 of file simulation_parameters.cpp.

compose_json()

void sirius::compose_json	(	nlohmann::json const &	schema__,
		nlohmann::json const &	in__,
		nlohmann::json &	inout__
	)

Append the input dictionary to the existing dictionary.

Use JSON schema to traverse the existing dictionary and add on top the values from the input dictionary. In this way we can add missing nodes which were not defined in the existing dictionary.

Definition at line 78 of file simulation_parameters.cpp.

get_options_dictionary()

nlohmann::json const & sirius::get_options_dictionary

(

)

Get all possible options for initializing sirius. It is a json dictionary.

Definition at line 136 of file simulation_parameters.cpp.

get_section_options()

nlohmann::json const & sirius::get_section_options

(

std::string const &

section__

)

Get all possible options of a given input section. It is a json dictionary.

Definition at line 146 of file simulation_parameters.cpp.

cmd_args::value< std::string >() [1/2]

template<>

std::string sirius::cmd_args::value< std::string > ( const std::string  key__ ) const

inline

Definition at line 179 of file cmd_args.hpp.

cmd_args::value< std::string >() [2/2]

template<>

std::string sirius::cmd_args::value< std::string > ( const std::string  key__, const std::string  default_val__  ) const

inline

Definition at line 185 of file cmd_args.hpp.

cmd_args::value< std::vector< double > >()

template<>

std::vector< double > sirius::cmd_args::value< std::vector< double > > ( const std::string  key__ ) const

inline

Definition at line 185 of file cmd_args.hpp.

cmd_args::value< std::vector< int > >()

template<>

std::vector< int > sirius::cmd_args::value< std::vector< int > > ( const std::string  key__ ) const

inline

Definition at line 185 of file cmd_args.hpp.

confined_polynomial()

auto sirius::confined_polynomial ( double  r, double  R, int  p1, int  p2, int  dm  )

inline

Definition at line 30 of file math_tools.hpp.

sign()

template<typename T >

int sirius::sign ( T  val )

inline

Sign of the variable.

Definition at line 52 of file math_tools.hpp.

is_int()

template<typename T >

bool sirius::is_int ( T  val__, T  eps__  )

inline

Checks if number is integer with a given tolerance.

Definition at line 59 of file math_tools.hpp.

factorial()

template<typename T >

T sirius::factorial ( int  n )

inline

Compute a factorial.

Definition at line 70 of file math_tools.hpp.

round() [1/2]

auto sirius::round ( double  a__, int  n__  )

inline

Definition at line 81 of file math_tools.hpp.

round() [2/2]

auto sirius::round ( std::complex< double >  a__, int  n__  )

inline

Definition at line 88 of file math_tools.hpp.

hash()

auto sirius::hash ( void const *  buff, size_t  size, uint64_t  h = 5381  )

inline

Simple hash function.

Example: std::printf("hash: %16llX\n", hash());

Definition at line 95 of file math_tools.hpp.

random_uint32()

uint32_t sirius::random_uint32 ( bool  reset = false )

inline

Simple random number generator.

Definition at line 105 of file math_tools.hpp.

random< int >()

template<>

int sirius::random< int > ( )

inline

Definition at line 123 of file math_tools.hpp.

random< double >()

template<>

double sirius::random< double > ( )

inline

Definition at line 129 of file math_tools.hpp.

random< std::complex< double > >()

template<>

std::complex< double > sirius::random< std::complex< double > > ( )

inline

Definition at line 129 of file math_tools.hpp.

random< float >()

template<>

float sirius::random< float > ( )

inline

Definition at line 141 of file math_tools.hpp.

random< std::complex< float > >()

template<>

std::complex< float > sirius::random< std::complex< float > > ( )

inline

Definition at line 141 of file math_tools.hpp.

abs_diff()

template<typename T >

auto sirius::abs_diff	(	T	a,
		T	b
	)

Definition at line 153 of file math_tools.hpp.

rel_diff()

template<typename T >

auto sirius::rel_diff	(	T	a,
		T	b
	)

Definition at line 159 of file math_tools.hpp.

conj() [1/2]

auto sirius::conj ( double  x__ )

inline

Return complex conjugate of a number. For a real value this is the number itself.

Definition at line 165 of file math_tools.hpp.

conj() [2/2]

auto sirius::conj ( std::complex< double >  x__ )

inline

Return complex conjugate of a number.

Definition at line 172 of file math_tools.hpp.

zero_if_not_complex() [1/2]

template<typename T >

T sirius::zero_if_not_complex ( T  x__ )

inline

Definition at line 178 of file math_tools.hpp.

zero_if_not_complex() [2/2]

template<typename T >

T sirius::zero_if_not_complex ( std::complex< T >  x__ )

inline

Definition at line 184 of file math_tools.hpp.

null_stream()

null_stream_t & sirius::null_stream

(

)

Definition at line 29 of file ostream_tools.cpp.

boolstr()

std::string sirius::boolstr ( bool  b__ )

inline

Definition at line 48 of file ostream_tools.hpp.

operator<<() [1/7]

std::ostream & sirius::operator<< ( std::ostream &  out, hbar &&  b  )

inline

Inject horisontal bar to ostream.

Definition at line 79 of file ostream_tools.hpp.

operator<<() [2/7]

std::ostream & sirius::operator<< ( std::ostream &  out, ffmt &&  f  )

inline

Inject floating point format to ostream.

Definition at line 109 of file ostream_tools.hpp.

operator<<() [3/7]

template<typename T >

std::ostream & sirius::operator<< ( std::ostream &  out, std::vector< T > &  v  )

inline

Print std::vector to ostream.

Definition at line 120 of file ostream_tools.hpp.

double_to_string()

std::string sirius::double_to_string ( double  val, int  precision = -1  )

inline

Convert double to a string with a given precision.

Definition at line 136 of file ostream_tools.hpp.

print_checksum()

template<typename T , typename OUT >

void sirius::print_checksum ( std::string  label__, T  value__, OUT &&  out__  )

inline

Definition at line 167 of file ostream_tools.hpp.

print_hash()

template<typename OUT >

void sirius::print_hash ( std::string  label__, unsigned long long int  hash__, OUT &&  out__  )

inline

Definition at line 173 of file ostream_tools.hpp.

packed_index()

int sirius::packed_index ( int  i__, int  j__  )

inline

Pack two indices into one for symmetric matrices.

Definition at line 31 of file packed_index.hpp.

serialize() [1/6]

template<typename T , int N>

nlohmann::json sirius::serialize ( sddk::mdarray< T, N > const &  a__ )

inline

Definition at line 35 of file serialize_mdarray.hpp.

serialize() [2/6]

template<typename T , int N>

nlohmann::json sirius::serialize ( sddk::mdarray< std::complex< T >, N > const &  a__ )

inline

Definition at line 55 of file serialize_mdarray.hpp.

write_to_json_file()

template<typename T , int N>

void sirius::write_to_json_file	(	sddk::mdarray< T, N > const &	a__,
		std::string const &	fname__
	)

Definition at line 76 of file serialize_mdarray.hpp.

serialize() [3/6]

template<typename T >

void sirius::serialize ( serializer &  s__, T  var__  )

inline

Serialize a single element.

Definition at line 100 of file serializer.hpp.

deserialize() [1/4]

template<typename T >

void sirius::deserialize ( serializer &  s__, T &  var__  )

inline

Deserialize a single element.

Definition at line 107 of file serializer.hpp.

serialize() [4/6]

template<typename T >

void sirius::serialize ( serializer &  s__, std::vector< T > const &  vec__  )

inline

Serialize a vector.

Definition at line 114 of file serializer.hpp.

deserialize() [2/4]

template<typename T >

void sirius::deserialize ( serializer &  s__, std::vector< T > &  vec__  )

inline

Deserialize a vector.

Definition at line 122 of file serializer.hpp.

serialize() [5/6]

template<typename T , int N>

void sirius::serialize	(	serializer &	s__,
		sddk::mdarray< T, N > const &	array__
	)

Serialize multidimentional array.

Definition at line 132 of file serializer.hpp.

deserialize() [3/4]

template<typename T , int N>

void sirius::deserialize	(	serializer &	s__,
		sddk::mdarray< T, N > &	array__
	)

Deserialize multidimentional array.

Definition at line 147 of file serializer.hpp.

serialize() [6/6]

void sirius::serialize ( serializer &  s__, mpi::block_data_descriptor const &  dd__  )

inline

Serialize block data descriptor.

Definition at line 167 of file serializer.hpp.

deserialize() [4/4]

void sirius::deserialize ( serializer &  s__, mpi::block_data_descriptor &  dd__  )

inline

Deserialize block data descriptor.

Definition at line 175 of file serializer.hpp.

SHT::backward_transform< std::complex< double > >()

template<>

void sirius::SHT::backward_transform< std::complex< double > >	(	int	ld,
		std::complex< double > const *	flm,
		int	nr,
		int	lmmax,
		std::complex< double > *	ftp
	)		const

Definition at line 254 of file sht.cpp.

SHT::forward_transform< std::complex< double > >()

template<>

void sirius::SHT::forward_transform< std::complex< double > >	(	std::complex< double > const *	ftp,
		int	nr,
		int	lmmax,
		int	ld,
		std::complex< double > *	flm
	)		const

Definition at line 274 of file sht.cpp.

major_version()

int sirius::major_version

(

)

Definition at line 30 of file sirius_version.cpp.

minor_version()

int sirius::minor_version

(

)

Definition at line 35 of file sirius_version.cpp.

revision()

int sirius::revision

(

)

Definition at line 40 of file sirius_version.cpp.

git_hash()

std::string sirius::git_hash

(

)

Definition at line 45 of file sirius_version.cpp.

git_branchname()

std::string sirius::git_branchname

(

)

Definition at line 50 of file sirius_version.cpp.

build_date()

std::string sirius::build_date

(

)

Definition at line 55 of file sirius_version.cpp.

num_blocks()

int sirius::num_blocks ( int  length__, int  block_size__  )

inline

Return the maximum number of blocks (with size 'block_size') needed to split the 'length' elements.

Definition at line 36 of file splindex.hpp.

split_in_blocks()

auto sirius::split_in_blocks ( int  length__, int  block_size__  )

inline

Split the 'length' elements into blocks with the initial block size.

Return vector of block sizes that sum up to the initial 'length'.

Definition at line 43 of file splindex.hpp.

begin_global()

template<typename Index_t >

auto sirius::begin_global

(

splindex< Index_t > const &

a__

)

Definition at line 506 of file splindex.hpp.

end_global()

template<typename Index_t >

auto sirius::end_global

(

splindex< Index_t > const &

a__

)

Definition at line 512 of file splindex.hpp.

begin() [1/3]

template<typename Index_t >

auto sirius::begin

(

splindex< Index_t > const &

a__

)

Definition at line 518 of file splindex.hpp.

end() [1/3]

template<typename Index_t >

auto sirius::end

(

splindex< Index_t > const &

a__

)

Definition at line 526 of file splindex.hpp.

split()

auto sirius::split ( std::string const  str__, char  delim__  )

inline

Split multi-line string into a list of strings.

Definition at line 31 of file string_tools.hpp.

ltrim()

std::string & sirius::ltrim ( std::string &  str, const std::string &  chars = "\t\n\v\f\r "  )

inline

Definition at line 44 of file string_tools.hpp.

rtrim()

std::string & sirius::rtrim ( std::string &  str, const std::string &  chars = "\t\n\v\f\r "  )

inline

Definition at line 50 of file string_tools.hpp.

trim()

std::string & sirius::trim ( std::string &  str, const std::string &  chars = "\t\n\v\f\r "  )

inline

Definition at line 56 of file string_tools.hpp.

file_exists()

bool sirius::file_exists ( std::string  file_name )

inline

Check if file exists.

Parameters

[in]

file_name

Full path to the file being checked.

Returns

True if file exists, false otherwise.

Definition at line 34 of file system_tools.hpp.

hostname()

auto sirius::hostname ( )

inline

Get host name.

Definition at line 41 of file system_tools.hpp.

get_page_size()

long sirius::get_page_size ( )

inline

Definition at line 50 of file system_tools.hpp.

get_num_pages()

long sirius::get_num_pages ( )

inline

Definition at line 55 of file system_tools.hpp.

get_total_memory()

long sirius::get_total_memory ( )

inline

Definition at line 60 of file system_tools.hpp.

get_proc_status()

auto sirius::get_proc_status ( )

inline

Definition at line 65 of file system_tools.hpp.

get_proc_threads()

int sirius::get_proc_threads ( )

inline

Definition at line 113 of file system_tools.hpp.

timestamp()

auto sirius::timestamp ( std::string  fmt )

inline

Return the timestamp string in a specified format.

Typical format strings: "%Y%m%d_%H%M%S", "%Y-%m-%d %H:%M:%S", "%H:%M:%S"

Definition at line 34 of file time_tools.hpp.

wtime()

double sirius::wtime ( )

inline

Wall-clock time in seconds.

Definition at line 47 of file time_tools.hpp.

time_now()

auto sirius::time_now ( )

inline

Definition at line 56 of file time_tools.hpp.

time_interval()

double sirius::time_interval ( std::chrono::high_resolution_clock::time_point  t0 )

inline

Definition at line 61 of file time_tools.hpp.

get_relativity_t()

relativity_t sirius::get_relativity_t ( std::string  name__ )

inline

Definition at line 107 of file typedefs.hpp.

operator<<() [4/7]

std::ostream & sirius::operator<< ( std::ostream &  out, radial_solution_descriptor const &  rsd  )

inline

Definition at line 147 of file typedefs.hpp.

checksum_gpu()

template<typename T >

auto sirius::checksum_gpu	(	std::complex< T > const *	wf__,
		int	ld__,
		int	num_rows_loc__,
		int	nwf__
	)

Add checksum for the arrays on GPUs.

Definition at line 95 of file wave_functions.hpp.

iterate_aug_atom_types()

template<typename F >

void sirius::iterate_aug_atom_types ( Unit_cell const &  uc__, F &&  f__  )

inline

Definition at line 55 of file augmentation_operator.hpp.

max_l_aug()

auto sirius::max_l_aug ( Unit_cell const &  uc__ )

inline

Definition at line 67 of file augmentation_operator.hpp.

max_na_aug()

auto sirius::max_na_aug ( Unit_cell const &  uc__ )

inline

Definition at line 80 of file augmentation_operator.hpp.

max_nb_aug()

auto sirius::max_nb_aug ( Unit_cell const &  uc__ )

inline

Definition at line 94 of file augmentation_operator.hpp.

update_density_rg_1_real_gpu() [1/2]

void sirius::update_density_rg_1_real_gpu	(	int	size__,
		float const *	psi_rg__,
		float	wt__,
		float *	density_rg__
	)

Definition at line 43 of file density.cpp.

update_density_rg_1_real_gpu() [2/2]

void sirius::update_density_rg_1_real_gpu	(	int	size__,
		double const *	psi_rg__,
		double	wt__,
		double *	density_rg__
	)

Definition at line 49 of file density.cpp.

update_density_rg_1_complex_gpu() [1/2]

void sirius::update_density_rg_1_complex_gpu	(	int	size__,
		std::complex< float > const *	psi_rg__,
		float	wt__,
		float *	density_rg__
	)

Definition at line 55 of file density.cpp.

update_density_rg_1_complex_gpu() [2/2]

void sirius::update_density_rg_1_complex_gpu	(	int	size__,
		std::complex< double > const *	psi_rg__,
		double	wt__,
		double *	density_rg__
	)

Definition at line 61 of file density.cpp.

update_density_rg_2_gpu() [1/2]

void sirius::update_density_rg_2_gpu	(	int	size__,
		std::complex< float > const *	psi_rg_up__,
		std::complex< float > const *	psi_rg_dn__,
		float	wt__,
		float *	density_x_rg__,
		float *	density_y_rg__
	)

Definition at line 67 of file density.cpp.

update_density_rg_2_gpu() [2/2]

void sirius::update_density_rg_2_gpu	(	int	size__,
		std::complex< double > const *	psi_rg_up__,
		std::complex< double > const *	psi_rg_dn__,
		double	wt__,
		double *	density_x_rg__,
		double *	density_y_rg__
	)

Definition at line 74 of file density.cpp.

add_k_point_contribution_rg_collinear()

template<typename T >

static void sirius::add_k_point_contribution_rg_collinear ( fft::spfft_transform_type< T > &  fft__, int  ispn__, T  w__, T const *  inp_wf__, int  nr__, bool  gamma__, sddk::mdarray< T, 2 > &  density_rg__  )

static

Compute non-magnetic or up- or dn- contribution of the wave-functions to the charge density.

Definition at line 569 of file density.cpp.

add_k_point_contribution_rg_noncollinear()

template<typename T >

static void sirius::add_k_point_contribution_rg_noncollinear ( fft::spfft_transform_type< T > &  fft__, T  w__, T const *  inp_wf_up__, T const *  inp_wf_dn__, int  nr__, sddk::mdarray< std::complex< T >, 1 > &  psi_r_up__, sddk::mdarray< T, 2 > &  density_rg__  )

static

Compute contribution to density and megnetisation from the 2-component spinor wave-functions.

Definition at line 612 of file density.cpp.

add_k_point_contribution_dm_fplapw()

template<typename T >

static void sirius::add_k_point_contribution_dm_fplapw ( Simulation_context const &  ctx__, K_point< T > const &  kp__, density_matrix_t &  density_matrix__  )

static

Definition at line 770 of file density.cpp.

add_k_point_contribution_dm_pwpp_collinear()

template<typename T , typename F >

static void sirius::add_k_point_contribution_dm_pwpp_collinear ( Simulation_context &  ctx__, K_point< T > &  kp__, beta_projectors_coeffs_t< T > &  bp_coeffs__, density_matrix_t &  density_matrix__  )

static

Definition at line 819 of file density.cpp.

add_k_point_contribution_dm_pwpp_noncollinear()

template<typename T , typename F >

static void sirius::add_k_point_contribution_dm_pwpp_noncollinear ( Simulation_context &  ctx__, K_point< T > &  kp__, beta_projectors_coeffs_t< T > &  bp_coeffs__, density_matrix_t &  density_matrix__  )

static

Definition at line 876 of file density.cpp.

add_k_point_contribution_dm_pwpp()

template<typename T , typename F >

static void sirius::add_k_point_contribution_dm_pwpp ( Simulation_context &  ctx__, K_point< T > &  kp__, density_matrix_t &  density_matrix__  )

static

Definition at line 1011 of file density.cpp.

get_rho_up_dn() [1/2]

auto sirius::get_rho_up_dn ( int  num_mag_dims__, double  rho__, r3::vector< double >  mag__  )

inline

Use Kuebler's trick to get rho_up and rho_dn from density and magnetisation.

Definition at line 80 of file density.hpp.

copy() [1/12]

void sirius::copy ( Density const &  src__, Density &  dest__  )

inline

Definition at line 746 of file density.hpp.

get_rho_up_dn() [2/2]

template<bool add_pseudo_core__>

std::array< std::unique_ptr< Smooth_periodic_function< double > >, 2 > sirius::get_rho_up_dn ( Density const &  density__, double  add_delta_rho_xc__ = 0.0, double  add_delta_mag_xc__ = 0.0  )

inline

Definition at line 764 of file density.hpp.

copy() [2/12]

void sirius::copy ( density_matrix_t const &  src__, density_matrix_t &  dest__  )

inline

Definition at line 49 of file density_matrix.hpp.

copy() [3/12]

void sirius::copy ( Occupation_matrix const &  src__, Occupation_matrix &  dest__  )

inline

Definition at line 131 of file occupation_matrix.hpp.

ewald_energy()

double sirius::ewald_energy	(	const Simulation_context &	ctx,
		const fft::Gvec &	gvec,
		const Unit_cell &	unit_cell
	)

Compute the ion-ion electrostatic energy using Ewald method.

The following contribution (per unit cell) to the total energy has to be computed:

\[ E^{ion-ion} = \frac{1}{N} \frac{1}{2} \sum_{i \neq j} \frac{Z_i Z_j}{|{\bf r}_i - {\bf r}_j|} = \frac{1}{2} \sideset{}{'} \sum_{\alpha \beta {\bf T}} \frac{Z_{\alpha} Z_{\beta}}{|{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|} \]

where \( N \) is the number of unit cells in the crystal. Following the idea of Ewald the Coulomb interaction is split into two terms:

\[ \frac{1}{|{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|} = \frac{{\rm erf}(\sqrt{\lambda} |{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|)}{|{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|} + \frac{{\rm erfc}(\sqrt{\lambda} |{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|)}{|{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|} \]

Second term is computed directly. First term is computed in the reciprocal space. Remembering that

\[ \frac{1}{\Omega} \sum_{\bf G} e^{i{\bf Gr}} = \sum_{\bf T} \delta({\bf r - T}) \]

we rewrite the first term as

\[ \frac{1}{2} \sideset{}{'} \sum_{\alpha \beta {\bf T}} Z_{\alpha} Z_{\beta} \frac{{\rm erf}(\sqrt{\lambda} |{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|)}{|{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|} = \frac{1}{2} \sum_{\alpha \beta {\bf T}} Z_{\alpha} Z_{\beta} \frac{{\rm erf}(\sqrt{\lambda} |{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|)} {|{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|} - \frac{1}{2} \sum_{\alpha} Z_{\alpha}^2 2 \sqrt{\frac{\lambda}{\pi}} = \\ \frac{1}{2} \sum_{\alpha \beta} Z_{\alpha} Z_{\beta} \frac{1}{\Omega} \sum_{\bf G} \int e^{i{\bf Gr}} \frac{{\rm erf}(\sqrt{\lambda} |{\bf r}_{\alpha\beta} + {\bf r}|)}{|{\bf r}_{\alpha\beta} + {\bf r}|} d{\bf r} - \sum_{\alpha} Z_{\alpha}^2 \sqrt{\frac{\lambda}{\pi}} \]

The integral is computed using the \( \ell=0 \) term of the spherical expansion of the plane-wave:

\[ \int e^{i{\bf Gr}} \frac{{\rm erf}(\sqrt{\lambda} |{\bf r}_{\alpha\beta} + {\bf r}|)}{|{\bf r}_{\alpha\beta} + {\bf r}|} d{\bf r} = \int e^{-i{\bf r}_{\alpha \beta}{\bf G}} e^{i{\bf Gr}} \frac{{\rm erf}(\sqrt{\lambda} |{\bf r}|)}{|{\bf r}|} d{\bf r} = e^{-i{\bf r}_{\alpha \beta}{\bf G}} 4 \pi \int_0^{\infty} \frac{\sin({G r})}{G} {\rm erf}(\sqrt{\lambda} r ) dr \]

We will split integral in two parts:

\[ \int_0^{\infty} \sin({G r}) {\rm erf}(\sqrt{\lambda} r ) dr = \int_0^{b} \sin({G r}) {\rm erf}(\sqrt{\lambda} r ) dr + \int_b^{\infty} \sin({G r}) dr = \frac{1}{G} e^{-\frac{G^2}{4 \lambda}} \]

where \( b \) is sufficiently large. To reproduce in Mathrmatica:

Limit[Limit[
Integrate[Sin[g*x]*Erf[Sqrt[nu] * x], {x, 0, b},
Assumptions -> {nu > 0, g >= 0, b > 0}] +
Integrate[Sin[g*(x + I*a)], {x, b, \[Infinity]},
Assumptions -> {a > 0, nu > 0, g >= 0, b > 0}], a -> 0],
b -> \[Infinity], Assumptions -> {nu > 0, g >= 0}]

The first term of the Ewald sum thus becomes:

\[ \frac{2 \pi}{\Omega} \sum_{{\bf G}} \frac{e^{-\frac{G^2}{4 \lambda}}}{G^2} \Big| \sum_{\alpha} Z_{\alpha} e^{-i{\bf r}_{\alpha}{\bf G}} \Big|^2 - \sum_{\alpha} Z_{\alpha}^2 \sqrt{\frac{\lambda}{\pi}} \]

For \( G=0 \) the following is done:

\[ \frac{e^{-\frac{G^2}{4 \lambda}}}{G^2} \approx \frac{1}{G^2}-\frac{1}{4 \lambda } \]

The term \( \frac{1}{G^2} \) is compensated together with the corresponding Hartree terms in electron-electron and electron-ion interactions (cell should be neutral) and we are left with the following conribution:

\[ -\frac{2\pi}{\Omega}\frac{N_{el}^2}{4 \lambda} \]

Final expression for the Ewald energy:

\[ E^{ion-ion} = \frac{1}{2} \sideset{}{'} \sum_{\alpha \beta {\bf T}} Z_{\alpha} Z_{\beta} \frac{{\rm erfc}(\sqrt{\lambda} |{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|)}{|{\bf r}_{\alpha} - {\bf r}_{\beta} + {\bf T}|} + \frac{2 \pi}{\Omega} \sum_{{\bf G}\neq 0} \frac{e^{-\frac{G^2}{4 \lambda}}}{G^2} \Big| \sum_{\alpha} Z_{\alpha} e^{-i{\bf r}_{\alpha}{\bf G}} \Big|^2 - \sum_{\alpha} Z_{\alpha}^2 \sqrt{\frac{\lambda}{\pi}} - \frac{2\pi}{\Omega} \frac{N_{el}^2}{4 \lambda} \]

Definition at line 30 of file energy.cpp.

energy_vxc()

double sirius::energy_vxc	(	Density const &	density,
		Potential const &	potential
	)

Returns exchange correlation potential.

Definition at line 76 of file energy.cpp.

energy_exc()

double sirius::energy_exc	(	Density const &	density,
		Potential const &	potential
	)

Returns exchange correlation energy.

Definition at line 82 of file energy.cpp.

energy_vha()

double sirius::energy_vha

(

Potential const &

potential

)

Returns Hatree potential.

Definition at line 88 of file energy.cpp.

energy_bxc()

double sirius::energy_bxc	(	const Density &	density,
		const Potential &	potential
	)

TODO doc.

Definition at line 94 of file energy.cpp.

energy_enuc()

double sirius::energy_enuc	(	Simulation_context const &	ctx,
		Potential const &	potential
	)

Return nucleus energy in the electrostatic field.

Compute energy of nucleus in the electrostatic potential generated by the total (electrons + nuclei) j* charge density. Diverging self-interaction term z*z/|r=0| is excluded.

Definition at line 104 of file energy.cpp.

energy_vloc()

double sirius::energy_vloc	(	Density const &	density,
		Potential const &	potential
	)

TODO doc.

Definition at line 119 of file energy.cpp.

core_eval_sum()

double sirius::core_eval_sum

(

Unit_cell const &

unit_cell

)

Return eigen-value sum of core states.

Definition at line 125 of file energy.cpp.

eval_sum()

double sirius::eval_sum	(	Unit_cell const &	unit_cell,
		K_point_set const &	kset
	)

TODO doc.

Definition at line 135 of file energy.cpp.

energy_veff()

double sirius::energy_veff	(	Density const &	density,
		Potential const &	potential
	)

TODO doc.

Definition at line 141 of file energy.cpp.

energy_kin()

double sirius::energy_kin	(	Simulation_context const &	ctx,
		K_point_set const &	kset,
		Density const &	density,
		Potential const &	potential
	)

Return kinetic energy.

Definition at line 147 of file energy.cpp.

ks_energy() [1/2]

double sirius::ks_energy	(	Simulation_context const &	ctx,
		const std::map< std::string, double > &	energies
	)

Definition at line 153 of file energy.cpp.

ks_energy() [2/2]

double sirius::ks_energy	(	Simulation_context const &	ctx,
		K_point_set const &	kset,
		Density const &	density,
		Potential const &	potential,
		double	ewald_energy
	)

Definition at line 179 of file energy.cpp.

total_energy()

double sirius::total_energy	(	Simulation_context const &	ctx,
		K_point_set const &	kset,
		Density const &	density,
		Potential const &	potential,
		double	ewald_energy
	)

Total energy of the electronic subsystem.

Full potential total energy

From the definition of the density functional we have:

\[ E[\rho] = T[\rho] + E^{H}[\rho] + E^{XC}[\rho] + E^{ext}[\rho] \]

where \( T[\rho] \) is the kinetic energy, \( E^{H}[\rho] \) - electrostatic energy of electron-electron density interaction, \( E^{XC}[\rho] \) - exchange-correlation energy and \( E^{ext}[\rho] \) - energy in the external field of nuclei.

Electrostatic and external field energies are grouped in the following way:

\[ \frac{1}{2} \int \int \frac{\rho({\bf r})\rho({\bf r'}) d{\bf r} d{\bf r'}}{|{\bf r} - {\bf r'}|} + \int \rho({\bf r}) V^{nuc}({\bf r}) d{\bf r} = \frac{1}{2} \int V^{H}({\bf r})\rho({\bf r})d{\bf r} + \frac{1}{2} \int \rho({\bf r}) V^{nuc}({\bf r}) d{\bf r} \]

Here \( V^{H}({\bf r}) \) is the total (electron + nuclei) electrostatic potential returned by the poisson solver. Next we transform the remaining term:

\[ \frac{1}{2} \int \rho({\bf r}) V^{nuc}({\bf r}) d{\bf r} = \frac{1}{2} \int \int \frac{\rho({\bf r})\rho^{nuc}({\bf r'}) d{\bf r} d{\bf r'}}{|{\bf r} - {\bf r'}|} = \frac{1}{2} \int V^{H,el}({\bf r}) \rho^{nuc}({\bf r}) d{\bf r} \]

Pseudopotential total energy

Total energy in PW-PP method has the following expression:

\[ E_{tot} = \sum_{i} f_i \sum_{\sigma \sigma'} \langle \psi_i^{\sigma'} | \Big( \hat T + \sum_{\xi \xi'} |\beta_{\xi} \rangle D_{\xi \xi'}^{ion} \delta_{\sigma \sigma'} \langle \beta_{\xi'} |\Big) | \psi_i^{\sigma} \rangle + \int V^{ion}({\bf r})\rho({\bf r})d{\bf r} + \frac{1}{2} \int V^{H}({\bf r})\rho({\bf r})d{\bf r} + E^{XC}[\rho + \rho_{core}, |{\bf m}|] \]

Ionic contribution to the non-local part of pseudopotential is diagonal in spin. The following rearrangement is performed next:

\[ \int \rho({\bf r}) \Big( V^{ion}({\bf r}) + \frac{1}{2} V^{H}({\bf r}) \Big) d{\bf r} = \\ \int \rho({\bf r}) \Big( V^{ion}({\bf r}) + V^{H}({\bf r}) + V^{XC}({\bf r}) \Big) d{\bf r} + \int {\bf m}({\bf r}) {\bf B}^{XC}({\bf r}) d{\bf r} - \frac{1}{2} \int V^{H}({\bf r})\rho({\bf r})d{\bf r} - \int V^{XC}({\bf r})\rho({\bf r})d{\bf r} - \int {\bf m}({\bf r}) {\bf B}^{XC}({\bf r}) d{\bf r} = \\ \sum_{\sigma \sigma'}\int \rho_{\sigma \sigma'}({\bf r}) V_{\sigma' \sigma}^{eff}({\bf r}) d{\bf r} - \frac{1}{2} \int V^{H}({\bf r})\rho({\bf r})d{\bf r} - \int V^{XC}({\bf r})\rho({\bf r})d{\bf r} - \int {\bf m}({\bf r}) {\bf B}^{XC}({\bf r}) d{\bf r} \]

Where

\[ \rho_{\sigma \sigma'}({\bf r}) = \sum_{i}^{occ} f_{i} \psi_{i}^{\sigma' *}({\bf r})\psi_{i}^{\sigma}({\bf r}) \]

is a \( 2 \times 2 \) density matrix and

\[ V_{\sigma\sigma'}^{eff}({\bf r})=\Big({\bf I}V^{eff}({\bf r})+{\boldsymbol \sigma}{\bf B}^{XC}({\bf r}) \Big) = \left( \begin{array}{cc} V^{eff}({\bf r})+B_z^{XC}({\bf r}) & B_x^{XC}({\bf r})-iB_y^{XC}({\bf r}) \\ B_x^{XC}({\bf r})+iB_y^{XC}({\bf r}) & V^{eff}({\bf r})-B_z^{XC}({\bf r}) \end{array} \right) \]

is a \( 2 \times 2 \) matrix potential (see Spin-polarized DFT for the full derivation).

We are interested in this term:

\[ \sum_{\sigma \sigma'}\int \rho_{\sigma \sigma'}({\bf r}) V_{\sigma' \sigma}^{eff}({\bf r}) d{\bf r} = \int V^{eff}({\bf r})\rho({\bf r})d{\bf r} + \int {\bf m}({\bf r}) {\bf B}^{XC}({\bf r}) d{\bf r} \]

We are going to split density into two contributions (sum of occupied bands \( \rho^{ps} \) and augmented charge \( \rho^{aug} \)) and use the definition of \( \rho^{aug} \):

\[ \sum_{\sigma \sigma'}\int \rho_{\sigma \sigma'}^{aug}({\bf r}) V_{\sigma' \sigma}^{eff}({\bf r}) d{\bf r} = \sum_{\sigma \sigma'}\int \sum_{i} \sum_{\xi \xi'} f_i \langle \psi_i^{\sigma'} | \beta_{\xi} \rangle Q_{\xi \xi'}({\bf r}) \langle \beta_{\xi'} | \psi_i^{\sigma} \rangle V_{\sigma' \sigma}^{eff}({\bf r}) d{\bf r} = \sum_{\sigma \sigma'} \sum_{i}\sum_{\xi \xi'} f_i \langle \psi_i^{\sigma'} | \beta_{\xi} \rangle D_{\xi \xi', \sigma' \sigma}^{aug} \langle \beta_{\xi'} | \psi_i^{\sigma} \rangle \]

Now we can rewrite the total energy expression:

\[ E_{tot} = \sum_{i} f_i \sum_{\sigma \sigma'} \langle \psi_i^{\sigma'} | \Big( \hat T + \sum_{\xi \xi'} |\beta_{\xi} \rangle D_{\xi \xi'}^{ion} \delta_{\sigma \sigma'} + D_{\xi \xi', \sigma' \sigma}^{aug} \langle \beta_{\xi'} |\Big) | \psi_i^{\sigma} \rangle + \sum_{\sigma \sigma} \int V^{eff}_{\sigma' \sigma}({\bf r})\rho^{ps}_{\sigma \sigma'}({\bf r})d{\bf r} - \frac{1}{2} \int V^{H}({\bf r})\rho({\bf r})d{\bf r} - \int V^{XC}({\bf r})\rho({\bf r}) d{\bf r} - \int {\bf m}({\bf r}) {\bf B}^{XC}({\bf r}) d{\bf r} + E^{XC}[\rho + \rho_{core}, |{\bf m}|] \]

From the Kohn-Sham equations

\[ \hat T |\psi_i^{\sigma} \rangle + \sum_{\sigma'} \sum_{\xi \xi'} \Big( |\beta_{\xi} \rangle D_{\xi \xi', \sigma' \sigma} \langle \beta_{\xi'}| + \hat V^{eff}_{\sigma' \sigma} \Big) | \psi_i^{\sigma'} \rangle = \varepsilon_i \Big( 1+\hat S \Big) |\psi_i^{\sigma} \rangle \]

we immediately obtain that

\[ \sum_{i} f_i \varepsilon_i = \sum_{i} f_i \sum_{\sigma \sigma'} \langle \psi_i^{\sigma'} | \Big( \hat T + \sum_{\xi \xi'} |\beta_{\xi} \rangle D_{\xi \xi', \sigma' \sigma} \langle \beta_{\xi'} |\Big) | \psi_i^{\sigma} \rangle + \sum_{\sigma \sigma} \int V^{eff}_{\sigma' \sigma}({\bf r})\rho^{ps}_{\sigma \sigma'}({\bf r})d{\bf r} \]

and the total energy expression simplifies to:

\[ E_{tot} = \sum_{i} f_i \varepsilon_i - \frac{1}{2} \int V^{H}({\bf r})\rho({\bf r})d{\bf r} - \int V^{XC}({\bf r})\rho({\bf r}) d{\bf r} - \int {\bf m}({\bf r}) {\bf B}^{XC}({\bf r}) d{\bf r} + E^{XC}[\rho + \rho_{core}, |{\bf m}|] \]

Definition at line 186 of file energy.cpp.

total_energy_components()

std::map< std::string, double > sirius::total_energy_components	(	Simulation_context const &	ctx,
		const K_point_set &	kset,
		Density const &	density,
		Potential const &	potential,
		double	ewald_energy
	)

Definition at line 212 of file energy.cpp.

hubbard_energy()

double sirius::hubbard_energy

(

Density const &

density

)

Definition at line 249 of file energy.cpp.

one_electron_energy()

double sirius::one_electron_energy	(	Density const &	density,
		Potential const &	potential
	)

Definition at line 259 of file energy.cpp.

one_electron_energy_hubbard() [1/2]

double sirius::one_electron_energy_hubbard	(	Density const &	density,
		Potential const &	potential
	)

Definition at line 266 of file energy.cpp.

energy_potential()

double sirius::energy_potential	(	Density const &	density,
		Potential const &	potential
	)

Definition at line 276 of file energy.cpp.

energy_dict()

auto sirius::energy_dict ( Simulation_context const &  ctx__, K_point_set const &  kset__, Density const &  density__, Potential const &  potential__, double  ewald_energy__, double  scf_correction__ = 0  )

inline

Definition at line 270 of file energy.hpp.

make_periodic_function() [1/2]

template<index_domain_t index_domain, typename F >

auto sirius::make_periodic_function ( Unit_cell const &  uc__, fft::Gvec const &  gv__, sddk::mdarray< std::complex< double >, 2 > const &  phase_factors_t__, F &&  form_factors__  )

inline

Make periodic function out of form factors.

Return vector of plane-wave coefficients

Definition at line 34 of file make_periodic_function.hpp.

make_periodic_function() [2/2]

template<index_domain_t index_domain>

auto sirius::make_periodic_function ( Unit_cell const &  uc__, fft::Gvec const &  gv__, sddk::mdarray< std::complex< double >, 2 > const &  phase_factors_t__, sddk::mdarray< double, 2 > const &  form_factors__  )

inline

Make periodic out of form factors computed for G-shells.

Definition at line 67 of file make_periodic_function.hpp.

inner() [1/8]

template<typename T >

T sirius::inner	(	PAW_field4D< T > const &	x__,
		PAW_field4D< T > const &	y__
	)

Definition at line 126 of file paw_field4d.hpp.

inner() [2/8]

template<typename T >

T sirius::inner ( Periodic_function< T > const &  f__, Periodic_function< T > const &  g__  )

inline

Definition at line 288 of file periodic_function.hpp.

copy() [4/12]

template<typename T >

void sirius::copy ( Periodic_function< T > const &  src__, periodic_function_ptr_t< T >  dest__  )

inline

Copy values of the function to the external location.

Definition at line 304 of file periodic_function.hpp.

copy() [5/12]

template<typename T >

void sirius::copy ( periodic_function_ptr_t< T > const  src__, Periodic_function< T > &  dest__  )

inline

Copy the values of the function from the external location.

Definition at line 314 of file periodic_function.hpp.

check_smooth_periodic_function_ptr()

template<typename T >

void sirius::check_smooth_periodic_function_ptr ( smooth_periodic_function_ptr_t< T > const &  ptr__, fft::spfft_transform_type< T > const &  spfft__  )

inline

Definition at line 39 of file smooth_periodic_function.hpp.

gradient() [1/3]

template<typename T >

Smooth_periodic_vector_function< T > sirius::gradient ( Smooth_periodic_function< T > &  f__ )

inline

Gradient of the function in the plane-wave domain.

Input functions is expected in the plane wave domain, output function is also in the plane-wave domain

Definition at line 426 of file smooth_periodic_function.hpp.

divergence() [1/3]

template<typename T >

Smooth_periodic_function< T > sirius::divergence ( Smooth_periodic_vector_function< T > &  g__ )

inline

Divergence of the vecor function.

Input and output functions are in plane-wave domain

Definition at line 445 of file smooth_periodic_function.hpp.

laplacian() [1/2]

template<typename T >

Smooth_periodic_function< T > sirius::laplacian ( Smooth_periodic_function< T > &  f__ )

inline

Laplacian of the function in the plane-wave domain.

Definition at line 464 of file smooth_periodic_function.hpp.

dot()

template<typename T >

Smooth_periodic_function< T > sirius::dot ( Smooth_periodic_vector_function< T > &  vf__, Smooth_periodic_vector_function< T > &  vg__  )

inline

Definition at line 481 of file smooth_periodic_function.hpp.

inner_local() [1/2]

template<typename T , typename F >

T sirius::inner_local ( Smooth_periodic_function< T > const &  f__, Smooth_periodic_function< T > const &  g__, F &&  theta__  )

inline

Compute local contribution to inner product <f|g>

Definition at line 503 of file smooth_periodic_function.hpp.

inner_local() [2/2]

template<typename T >

T sirius::inner_local ( Smooth_periodic_function< T > const &  f__, Smooth_periodic_function< T > const &  g__  )

inline

Definition at line 521 of file smooth_periodic_function.hpp.

inner() [3/8]

template<typename T , typename F >

T sirius::inner ( Smooth_periodic_function< T > const &  f__, Smooth_periodic_function< T > const &  g__, F &&  theta__  )

inline

Definition at line 528 of file smooth_periodic_function.hpp.

inner() [4/8]

template<typename T >

T sirius::inner ( Smooth_periodic_function< T > const &  f__, Smooth_periodic_function< T > const &  g__  )

inline

Compute inner product <f|g>

Definition at line 541 of file smooth_periodic_function.hpp.

copy() [6/12]

template<typename T >

void sirius::copy ( Smooth_periodic_function< T > const &  src__, smooth_periodic_function_ptr_t< T >  dest__  )

inline

Copy real-space values from the function to external pointer.

Definition at line 549 of file smooth_periodic_function.hpp.

copy() [7/12]

template<typename T >

void sirius::copy ( smooth_periodic_function_ptr_t< T > const  src__, Smooth_periodic_function< T > &  dest__  )

inline

Copy real-space values from the external pointer to function.

Definition at line 576 of file smooth_periodic_function.hpp.

copy() [8/12]

template<typename T >

void sirius::copy ( Smooth_periodic_function< T > const &  src__, Smooth_periodic_function< T > &  dest__  )

inline

Definition at line 596 of file smooth_periodic_function.hpp.

scale() [1/2]

template<typename T >

void sirius::scale ( T  alpha__, Smooth_periodic_function< T > &  x__  )

inline

Definition at line 604 of file smooth_periodic_function.hpp.

axpy() [1/2]

template<typename T >

void sirius::axpy ( T  alpha__, Smooth_periodic_function< T > const &  x__, Smooth_periodic_function< T > &  y__  )

inline

Definition at line 616 of file smooth_periodic_function.hpp.

operator*() [1/5]

template<typename T >

auto sirius::operator* ( Spheric_function< function_domain_t::spatial, T > const &  a__, Spheric_function< function_domain_t::spatial, T > const &  b__  )

inline

Multiplication of two functions in spatial domain.

The result of the operation is a scalar function in spatial domain

Definition at line 249 of file spheric_function.hpp.

operator*() [2/5]

auto sirius::operator* ( Spheric_vector_function< function_domain_t::spatial, double > const &  f, Spheric_vector_function< function_domain_t::spatial, double > const &  g  )

inline

Dot product of two gradiensts of real functions in spatial domain.

The result of the operation is the real scalar function in spatial domain

Definition at line 273 of file spheric_function.hpp.

operator+()

template<function_domain_t domain_t, typename T >

auto sirius::operator+	(	Spheric_function< domain_t, T > const &	a__,
		Spheric_function< domain_t, T > const &	b__
	)

Summation of two functions.

Definition at line 303 of file spheric_function.hpp.

operator-()

template<function_domain_t domain_t, typename T >

auto sirius::operator-	(	Spheric_function< domain_t, T > const &	a__,
		Spheric_function< domain_t, T > const &	b__
	)

Subtraction of functions.

Definition at line 326 of file spheric_function.hpp.

operator*() [3/5]

template<function_domain_t domain_t, typename T >

auto sirius::operator*	(	T	a__,
		Spheric_function< domain_t, T > const &	b__
	)

Multiply function by a scalar.

Definition at line 349 of file spheric_function.hpp.

operator*() [4/5]

template<function_domain_t domain_t, typename T >

auto sirius::operator*	(	Spheric_function< domain_t, T > const &	b__,
		T	a__
	)

Multiply function by a scalar (inverse order).

Definition at line 365 of file spheric_function.hpp.

inner() [5/8]

template<function_domain_t domain_t, typename T >

auto sirius::inner ( Spheric_function< domain_t, T > const &  f1, Spheric_function< domain_t, T > const &  f2  )

inline

Inner product of two spherical functions.

The result of the operation is a scalar value.

Definition at line 374 of file spheric_function.hpp.

laplacian() [2/2]

template<typename T >

auto sirius::laplacian ( Spheric_function< function_domain_t::spectral, T > const &  f__ )

inline

Compute Laplacian of the spheric function.

Laplacian in spherical coordinates has the following expression:

\[ \Delta = \frac{1}{r^2}\frac{\partial}{\partial r}\Big( r^2 \frac{\partial}{\partial r} \Big) + \frac{1}{r^2}\Delta_{\theta, \phi} \]

Definition at line 401 of file spheric_function.hpp.

convert() [1/4]

void sirius::convert ( Spheric_function< function_domain_t::spectral, std::complex< double > > const &  f__, Spheric_function< function_domain_t::spectral, double > &  g__  )

inline

Convert from Ylm to Rlm representation.

Definition at line 434 of file spheric_function.hpp.

convert() [2/4]

auto sirius::convert ( Spheric_function< function_domain_t::spectral, std::complex< double > > const &  f__ )

inline

Convert from Ylm to Rlm representation.

Definition at line 468 of file spheric_function.hpp.

convert() [3/4]

void sirius::convert ( Spheric_function< function_domain_t::spectral, double > const &  f__, Spheric_function< function_domain_t::spectral, std::complex< double > > &  g__  )

inline

Convert from Rlm to Ylm representation.

Definition at line 477 of file spheric_function.hpp.

convert() [4/4]

auto sirius::convert ( Spheric_function< function_domain_t::spectral, double > const &  f__ )

inline

Convert from Rlm to Ylm representation.

Definition at line 511 of file spheric_function.hpp.

transform() [1/4]

template<typename T >

void sirius::transform ( SHT const &  sht__, Spheric_function< function_domain_t::spectral, T > const &  f__, Spheric_function< function_domain_t::spatial, T > &  g__  )

inline

Definition at line 520 of file spheric_function.hpp.

transform() [2/4]

template<typename T >

auto sirius::transform ( SHT const &  sht__, Spheric_function< function_domain_t::spectral, T > const &  f__  )

inline

Transform to spatial domain (to r, \theta, \phi coordinates).

Definition at line 530 of file spheric_function.hpp.

transform() [3/4]

template<typename T >

void sirius::transform ( SHT const &  sht__, Spheric_function< function_domain_t::spatial, T > const &  f__, Spheric_function< function_domain_t::spectral, T > &  g__  )

inline

Definition at line 539 of file spheric_function.hpp.

transform() [4/4]

template<typename T >

auto sirius::transform ( SHT const &  sht__, Spheric_function< function_domain_t::spatial, T > const &  f__  )

inline

Transform to spectral domain.

Definition at line 548 of file spheric_function.hpp.

gradient() [2/3]

auto sirius::gradient ( Spheric_function< function_domain_t::spectral, std::complex< double > > const &  f )

inline

Gradient of the function in complex spherical harmonics.

Definition at line 557 of file spheric_function.hpp.

gradient() [3/3]

auto sirius::gradient ( Spheric_function< function_domain_t::spectral, double > const &  f__ )

inline

Gradient of the function in real spherical harmonics.

Definition at line 612 of file spheric_function.hpp.

divergence() [2/3]

auto sirius::divergence ( Spheric_vector_function< function_domain_t::spectral, std::complex< double > > const &  vf__ )

inline

Divergence of the vector function in complex spherical harmonics.

Definition at line 627 of file spheric_function.hpp.

divergence() [3/3]

auto sirius::divergence ( Spheric_vector_function< function_domain_t::spectral, double > const &  vf )

inline

Definition at line 640 of file spheric_function.hpp.

inner() [6/8]

template<typename T , typename I >

T sirius::inner ( Spheric_function_set< T, I > const &  f1__, Spheric_function_set< T, I > const &  f2__  )

inline

Definition at line 176 of file spheric_function_set.hpp.

copy() [9/12]

template<typename T , typename I >

void sirius::copy ( Spheric_function_set< T, I > const &  src__, spheric_function_set_ptr_t< T >  dest__  )

inline

Copy from Spheric_function_set to external pointer.

External pointer is assumed to be global.

Definition at line 209 of file spheric_function_set.hpp.

copy() [10/12]

template<typename T , typename I >

void sirius::copy ( spheric_function_set_ptr_t< T > const  src__, Spheric_function_set< T, I > &  dest__  )

inline

Copy from external pointer to Spheric_function_set.

External pointer is assumed to be global.

Definition at line 237 of file spheric_function_set.hpp.

copy() [11/12]

template<typename T , typename I >

void sirius::copy ( Spheric_function_set< T, I > const &  src__, Spheric_function_set< T, I > &  dest__  )

inline

Definition at line 258 of file spheric_function_set.hpp.

scale() [2/2]

template<typename T , typename I >

void sirius::scale ( T  alpha__, Spheric_function_set< T, I > &  x__  )

inline

Definition at line 269 of file spheric_function_set.hpp.

axpy() [2/2]

template<typename T , typename I >

void sirius::axpy ( T  alpha__, Spheric_function_set< T, I > const &  x__, Spheric_function_set< T, I > &  y__  )

inline

Definition at line 280 of file spheric_function_set.hpp.

add_k_point_contribution_nonlocal()

template<typename T , typename F >

void sirius::add_k_point_contribution_nonlocal	(	Simulation_context &	ctx__,
		Beta_projectors_base< T > &	bp_base__,
		K_point< T > &	kp__,
		sddk::mdarray< real_type< F >, 2 > &	collect_res__
	)

Template Parameters

T	Precision type of the wave-functions

Definition at line 38 of file non_local_functor.hpp.

wavefunctions_strain_deriv()

void sirius::wavefunctions_strain_deriv	(	Simulation_context const &	ctx__,
		K_point< double > &	kp__,
		wf::Wave_functions< double > &	dphi__,
		sddk::mdarray< double, 2 > const &	rlm_g__,
		sddk::mdarray< double, 3 > const &	rlm_dg__,
		int	nu__,
		int	mu__
	)

Definition at line 9 of file wavefunction_strain_deriv.hpp.

check_wave_functions()

template<typename T , typename F >

void sirius::check_wave_functions	(	Hamiltonian_k< real_type< T > > const &	Hk__,
		wf::Wave_functions< T > &	psi__,
		wf::spin_range	sr__,
		wf::band_range	br__,
		double *	eval__
	)

Definition at line 34 of file check_wave_functions.hpp.

project_out_subspace()

template<typename T , typename F >

void sirius::project_out_subspace ( ::spla::Context &  spla_ctx__, sddk::memory_t  mem__, wf::spin_range  spins__, wf::Wave_functions< T > &  phi__, wf::Wave_functions< T > &  sphi__, int  N__, int  n__, la::dmatrix< F > &  o__  )

inline

Definition at line 55 of file davidson.hpp.

davidson()

template<typename T , typename F , davidson_evp_t what>

auto sirius::davidson ( Hamiltonian_k< T > const &  Hk__, K_point< T > &  kp__, wf::num_bands  num_bands__, wf::num_mag_dims  num_mag_dims__, wf::Wave_functions< T > &  psi__, std::function< double(int, int)>  tolerance__, double  res_tol__, int  num_steps__, bool  locking__, int  subspace_size__, bool  estimate_eval__, bool  extra_ortho__, std::ostream &  out__, int  verbosity__, wf::Wave_functions< T > *  phi_extra__ = nullptr  )

inline

Solve the eigen-problem using Davidson iterative method.

Template Parameters

T	Precision type of wave-functions (float or double).
F	Type of the subspace matrices (fload or duble for Gamma case, complex<float> or complex<doouble> for general k-point case.
what	What to solve: H|psi> = e*S|psi> or S|psi> = o|psi>

Parameters

[in]	Hk	Hamiltonian for a given k-point.
[in]	num_bands	Number of eigen-states (bands) to compute.
[in]	num_mag_dims	Number of magnetic dimensions (0, 1 or 3).
[in,out]	psi	Wave-functions. On input they are used for the starting guess of the subspace basis. On output they are the solutions of Hk|psi> = e S|psi> eigen-problem.
[in]	tolerance	Lambda-function for the band energy tolerance.
[in]	res_tol	Residual tolerance.
[in]	num_stpes	Number of iterative steps.
[in]	locking	Lock and do not update of the converged wave-functions.
[in]	subspace_size	Size of the diagonalziation subspace.
[in]	estimate_eval	Estimate eigen-values to get the converrged rersiduals.
[in]	extra_ortho	Orthogonalize new subspace basis one extra time.
[out]	out	Output stream.
[in]	verbosity	Verbosity level.
[in]	phi_extra	Pointer to the additional (fixed) auxiliary basis functions (used in LAPW).

Returns

List of eigen-values.

• set the relative tolerance convergence criterion *‍/

Definition at line 141 of file davidson.hpp.

diagonalize()

template<typename T , typename F >

auto sirius::diagonalize ( Hamiltonian0< T > const &  H0__, K_point_set &  kset__, double  itsol_tol__  )

inline

Diagonalize KS Hamiltonian for all k-points in the set.

Template Parameters

T	Precision type of the wave-functions
F	Precition type of the Hamiltonian matrix

Definition at line 46 of file diagonalize.hpp.

diagonalize_fp_fv_exact() [1/2]

void sirius::diagonalize_fp_fv_exact ( Hamiltonian_k< float > const &  , K_point< float > &    )

inline

Definition at line 34 of file diagonalize_fp.hpp.

diagonalize_fp_fv_exact() [2/2]

void sirius::diagonalize_fp_fv_exact ( Hamiltonian_k< double > const &  Hk__, K_point< double > &  kp__  )

inline

Definition at line 40 of file diagonalize_fp.hpp.

get_singular_components()

void sirius::get_singular_components ( Hamiltonian_k< double > const &  Hk__, K_point< double > &  kp__, double  itsol_tol__  )

inline

Definition at line 244 of file diagonalize_fp.hpp.

diagonalize_fp_fv_davidson() [1/2]

void sirius::diagonalize_fp_fv_davidson ( Hamiltonian_k< float > const &  , K_point< float > &  , double    )

inline

Definition at line 271 of file diagonalize_fp.hpp.

diagonalize_fp_fv_davidson() [2/2]

void sirius::diagonalize_fp_fv_davidson ( Hamiltonian_k< double > const &  Hk__, K_point< double > &  kp__, double  itsol_tol__  )

inline

Definition at line 277 of file diagonalize_fp.hpp.

diagonalize_fp_sv() [1/2]

void sirius::diagonalize_fp_sv ( Hamiltonian_k< float > const &  , K_point< float > &    )

inline

Definition at line 347 of file diagonalize_fp.hpp.

diagonalize_fp_sv() [2/2]

void sirius::diagonalize_fp_sv ( Hamiltonian_k< double > const &  Hk__, K_point< double > &  kp  )

inline

Diagonalize second-variational Hamiltonian.

Definition at line 354 of file diagonalize_fp.hpp.

diagonalize_fp()

template<typename T >

void sirius::diagonalize_fp ( Hamiltonian_k< T > const &  Hk__, K_point< T > &  kp__, double  itsol_tol__  )

inline

Diagonalize a full-potential LAPW Hamiltonian.

Definition at line 502 of file diagonalize_fp.hpp.

diagonalize_pp_exact() [1/2]

template<typename T , typename F >

std::enable_if_t<!std::is_same< T, real_type< F > >::value, void > sirius::diagonalize_pp_exact ( int  ispn__, Hamiltonian_k< T > const &  Hk__, K_point< T > &  kp  )

inline

Definition at line 35 of file diagonalize_pp.hpp.

diagonalize_pp_exact() [2/2]

template<typename T , typename F >

std::enable_if_t< std::is_same< T, real_type< F > >::value, void > sirius::diagonalize_pp_exact ( int  ispn__, Hamiltonian_k< T > const &  Hk__, K_point< T > &  kp__  )

inline

Definition at line 42 of file diagonalize_pp.hpp.

diag_S_davidson()

template<typename T , typename F >

sddk::mdarray< real_type< F >, 1 > sirius::diag_S_davidson ( Hamiltonian_k< T > const &  Hk__, K_point< T > &  kp__  )

inline

Diagonalize S-operator of the ultrasoft or PAW methods.

Sometimes this is needed to check the quality of pseudopotential.

Definition at line 218 of file diagonalize_pp.hpp.

diagonalize_pp()

template<typename T , typename F >

auto sirius::diagonalize_pp ( Hamiltonian_k< T > const &  Hk__, K_point< T > &  kp__, double  itsol_tol__, double  empy_tol__  )

inline

Definition at line 294 of file diagonalize_pp.hpp.

generate_subspace_matrix()

template<typename T , typename F >

void sirius::generate_subspace_matrix	(	Simulation_context &	ctx__,
		int	N__,
		int	n__,
		int	num_locked__,
		wf::Wave_functions< T > &	phi__,
		wf::Wave_functions< T > &	op_phi__,
		la::dmatrix< F > &	mtrx__,
		la::dmatrix< F > *	mtrx_old__ = nullptr
	)

Generate subspace matrix for the iterative diagonalization.

Compute \( O_{ii'} = \langle \phi_i | \hat O | \phi_{i'} \rangle \) operator matrix for the subspace spanned by the wave-functions \( \phi_i \). The matrix is always returned in the CPU pointer because most of the standard math libraries start from the CPU.

Template Parameters

T	Precision type of the wave-functions
F	Type of the output subspace matrix.

Parameters

[in]	ctx	Simulation context
[in]	N	Number of existing (old) states phi.
[in]	n	Number of new states phi.
[in]	num_locked	Number of locked states phi. Locked states are excluded from the subspace basis.
[in]	phi	Subspace basis functions phi.
[in]	op_phi	Operator (H, S or overlap) applied to phi.
[out]	mtrx	New subspace matrix.
[in,out]	mtrx_old	Pointer to old subpsace matrix. It is used to store and reuse the subspace matrix of the previous step.

Definition at line 51 of file generate_subspace_matrix.hpp.

initialize_subspace() [1/2]

template<typename T , typename F >

void sirius::initialize_subspace ( Hamiltonian_k< T > const &  Hk__, K_point< T > &  kp__, int  num_ao__  )

inline

Initialize the wave-functions subspace at a given k-point.

If the number of atomic orbitals is smaller than the number of bands, the rest of the initial wave-functions are created from the random numbers.

Definition at line 38 of file initialize_subspace.hpp.

initialize_subspace() [2/2]

template<typename T >

void sirius::initialize_subspace	(	K_point_set &	kset__,
		Hamiltonian0< T > &	H0__
	)

Definition at line 290 of file initialize_subspace.hpp.

mul_by_veff()

template<typename T >

static void sirius::mul_by_veff ( fft::spfft_transform_type< T > &  spfftk__, T const *  in__, std::array< std::unique_ptr< Smooth_periodic_function< T > >, 6 > const &  veff_vec__, int  idx_veff__, T *  out__  )

inlinestatic

Multiply FFT buffer by the effective potential.

Definition at line 210 of file local_operator.cpp.

apply_non_local_D_Q()

template<typename T , typename F >

void sirius::apply_non_local_D_Q	(	sddk::memory_t	mem__,
		wf::spin_range	spins__,
		wf::band_range	br__,
		Beta_projector_generator< T > &	beta__,
		beta_projectors_coeffs_t< T > &	beta_coeffs__,
		wf::Wave_functions< T > const &	phi__,
		D_operator< T > const *	d_op__,
		wf::Wave_functions< T > *	hphi__,
		Q_operator< T > const *	q_op__,
		wf::Wave_functions< T > *	sphi__
	)

Template Parameters

T	Precision of the wave-functions.
F	Type of the subspace.

Parameters

[in]	spins	Range of the spin index.
[in]	N	Starting index of the wave-functions.
[in]	n	Number of wave-functions to which D and Q are applied.
[in]	beta	Beta-projector generator
[in]	beta_coeffs	Beta-projector coefficients
[in]	phi	Wave-functions.
[in]	d_op	Pointer to D-operator.
[out]	hphi	Resulting |beta>D<beta|phi>
[in]	q_op	Pointer to Q-operator.
[out]	sphi	Resulting |beta>Q<beta|phi>

Definition at line 126 of file non_local_operator.hpp.

apply_S_operator()

template<typename T , typename F >

void sirius::apply_S_operator	(	sddk::memory_t	mem__,
		wf::spin_range	spins__,
		wf::band_range	br__,
		Beta_projector_generator< T > &	beta__,
		beta_projectors_coeffs_t< T > &	beta_coeffs__,
		wf::Wave_functions< T > const &	phi__,
		Q_operator< T > const *	q_op__,
		wf::Wave_functions< T > &	sphi__
	)

Compute |sphi> = (1 + Q)|phi>

Definition at line 172 of file non_local_operator.hpp.

apply_U_operator()

template<typename T >

void sirius::apply_U_operator	(	Simulation_context &	ctx__,
		wf::spin_range	spins__,
		wf::band_range	br__,
		wf::Wave_functions< T > const &	hub_wf__,
		wf::Wave_functions< T > const &	phi__,
		U_operator< T > const &	um__,
		wf::Wave_functions< T > &	hphi__
	)

Apply Hubbard U correction

Template Parameters

T	Precision type of wave-functions (flat or double).

Parameters

[in]	hub_wf	Hubbard atomic wave-functions.
[in]	phi	Set of wave-functions to which Hubbard correction is applied.
[out]	hphi	Output wave-functions to which the result is added.

Definition at line 110 of file s_u_operator.cpp.

apply_S_operator_strain_deriv()

void sirius::apply_S_operator_strain_deriv	(	sddk::memory_t	mem__,
		int	comp__,
		Beta_projector_generator< double > &	bp__,
		beta_projectors_coeffs_t< double > &	bp_coeffs__,
		Beta_projector_generator< double > &	bp_strain_deriv__,
		beta_projectors_coeffs_t< double > &	bp_strain_deriv_coeffs__,
		wf::Wave_functions< double > &	phi__,
		Q_operator< double > &	q_op__,
		wf::Wave_functions< double > &	ds_phi__
	)

Apply strain derivative of S-operator to all scalar functions.

Definition at line 193 of file s_u_operator.cpp.

pseudopotential_hmatrix()

template<typename T >

dmatrix< T > sirius::pseudopotential_hmatrix ( K_point &  kp__, int  ispn__, Hamiltonian &  H__  )

inline

Definition at line 6 of file pseudopotential_hmatrix.hpp.

compute_residuals()

template<typename T >

static void sirius::compute_residuals ( sddk::memory_t  mem__, wf::spin_range  spins__, wf::num_bands  num_bands__, sddk::mdarray< T, 1 > const &  eval__, wf::Wave_functions< T > const &  hpsi__, wf::Wave_functions< T > const &  opsi__, wf::Wave_functions< T > &  res__  )

static

Compute band residuals.

Template Parameters

T	Precision type of the wave-functions (float or double).

Definition at line 128 of file residuals.hpp.

apply_preconditioner()

template<typename T >

void sirius::apply_preconditioner	(	sddk::memory_t	mem__,
		wf::spin_range	spins__,
		wf::num_bands	num_bands__,
		wf::Wave_functions< T > &	res__,
		sddk::mdarray< T, 2 > const &	h_diag__,
		sddk::mdarray< T, 2 > const &	o_diag__,
		sddk::mdarray< T, 1 > const &	eval__
	)

Apply preconditioner to the residuals.

Definition at line 166 of file residuals.hpp.

normalized_preconditioned_residuals()

template<typename T , typename F >

static auto sirius::normalized_preconditioned_residuals ( sddk::memory_t  mem__, wf::spin_range  spins__, wf::num_bands  num_bands__, sddk::mdarray< T, 1 > const &  eval__, wf::Wave_functions< T > const &  hpsi__, wf::Wave_functions< T > const &  opsi__, wf::Wave_functions< T > &  res__, sddk::mdarray< T, 2 > const &  h_diag__, sddk::mdarray< T, 2 > const &  o_diag__, T  norm_tolerance__, bool  gamma__  )

static

Definition at line 194 of file residuals.hpp.

residuals()

template<typename T , typename F >

auto sirius::residuals	(	Simulation_context &	ctx__,
		sddk::memory_t	mem__,
		wf::spin_range	sr__,
		int	N__,
		int	num_bands__,
		int	num_locked__,
		sddk::mdarray< real_type< F >, 1 > &	eval__,
		la::dmatrix< F > &	evec__,
		wf::Wave_functions< T > &	hphi__,
		wf::Wave_functions< T > &	ophi__,
		wf::Wave_functions< T > &	hpsi__,
		wf::Wave_functions< T > &	opsi__,
		wf::Wave_functions< T > &	res__,
		sddk::mdarray< T, 2 > const &	h_diag__,
		sddk::mdarray< T, 2 > const &	o_diag__,
		bool	estimate_eval__,
		T	norm_tolerance__,
		std::function< bool(int, int)>	is_converged__
	)

Compute residuals from eigen-vectors.

Template Parameters

T	Precision type of the wave-functions (float or double).
F	Type of the subspace (float or double for Gamma-point calculation, complex<float> or complex<double> otherwise.

The residuals of wave-functions are defined as:

\[ R_{i} = \hat H \psi_{i} - \epsilon_{i} \hat S \psi_{i} \]

Definition at line 277 of file residuals.hpp.

generate_potential()

void sirius::generate_potential	(	Hubbard_matrix const &	om__,
		Hubbard_matrix &	um__
	)

Definition at line 523 of file hubbard_potential_energy.cpp.

energy()

double sirius::energy

(

Hubbard_matrix const &

om__

)

Definition at line 551 of file hubbard_potential_energy.cpp.

one_electron_energy_hubbard() [2/2]

double sirius::one_electron_energy_hubbard	(	Hubbard_matrix const &	om__,
		Hubbard_matrix const &	pm__
	)

Definition at line 593 of file hubbard_potential_energy.cpp.

copy() [12/12]

void sirius::copy ( Hubbard_matrix const &  src__, Hubbard_matrix &  dest__  )

inline

Definition at line 149 of file hubbard_matrix.hpp.

update_density_matrix_deriv()

static void sirius::update_density_matrix_deriv ( la::lib_t  la__, sddk::memory_t  mt__, int  nwfh__, int  nbnd__, std::complex< double > *  alpha__, la::dmatrix< std::complex< double > > const &  phi_hub_s_psi_deriv__, la::dmatrix< std::complex< double > > const &  psi_s_phi_hub__, std::complex< double > *  dn__, int  ld__  )

static

Definition at line 43 of file hubbard_occupancies_derivatives.cpp.

build_phi_hub_s_psi_deriv()

static void sirius::build_phi_hub_s_psi_deriv ( Simulation_context const &  ctx__, int  nbnd__, int  nawf__, la::dmatrix< std::complex< double > > const &  ovlp__, la::dmatrix< std::complex< double > > const &  inv_sqrt_O__, la::dmatrix< std::complex< double > > const &  phi_atomic_s_psi__, la::dmatrix< std::complex< double > > const &  phi_atomic_ds_psi__, std::vector< int > const &  atomic_wf_offset__, std::vector< int > const &  hubbard_wf_offset__, la::dmatrix< std::complex< double > > &  phi_hub_s_psi_deriv__  )

static

Definition at line 59 of file hubbard_occupancies_derivatives.cpp.

compute_inv_sqrt_O_deriv()

static void sirius::compute_inv_sqrt_O_deriv ( la::dmatrix< std::complex< double > > &  O_deriv__, la::dmatrix< std::complex< double > > &  evec_O__, std::vector< double > &  eval_O__, int  nawf__  )

static

Definition at line 112 of file hubbard_occupancies_derivatives.cpp.

generate_potential_collinear_nonlocal()

static void sirius::generate_potential_collinear_nonlocal ( Simulation_context const &  ctx__, const int  index__, sddk::mdarray< std::complex< double >, 3 > const &  om__, sddk::mdarray< std::complex< double >, 3 > &  um__  )

static

Definition at line 32 of file hubbard_potential_energy.cpp.

generate_potential_collinear_local()

static void sirius::generate_potential_collinear_local ( Simulation_context const &  ctx__, Atom_type const &  atom_type__, const int  idx_hub_wf, sddk::mdarray< std::complex< double >, 3 > const &  om__, sddk::mdarray< std::complex< double >, 3 > &  um__  )

static

Definition at line 54 of file hubbard_potential_energy.cpp.

calculate_energy_collinear_nonlocal()

static double sirius::calculate_energy_collinear_nonlocal ( Simulation_context const &  ctx__, const int  index__, sddk::mdarray< std::complex< double >, 3 > const &  om__  )

static

Definition at line 165 of file hubbard_potential_energy.cpp.

calculate_energy_collinear_local()

static double sirius::calculate_energy_collinear_local ( Simulation_context const &  ctx__, Atom_type const &  atom_type__, const int  idx_hub_wf, sddk::mdarray< std::complex< double >, 3 > const &  om__  )

static

Definition at line 192 of file hubbard_potential_energy.cpp.

generate_potential_non_collinear_local()

static void sirius::generate_potential_non_collinear_local ( Simulation_context const &  ctx__, Atom_type const &  atom_type__, const int  idx_hub_wf, sddk::mdarray< std::complex< double >, 3 > const &  om__, sddk::mdarray< std::complex< double >, 3 > &  um__  )

static

Definition at line 327 of file hubbard_potential_energy.cpp.

calculate_energy_non_collinear_local()

static double sirius::calculate_energy_non_collinear_local ( Simulation_context const &  ctx__, Atom_type const &  atom_type__, const int  idx_hub_wf, sddk::mdarray< std::complex< double >, 3 > const &  om__  )

static

Definition at line 417 of file hubbard_potential_energy.cpp.

wave_function_factory()

template<typename T >

auto sirius::wave_function_factory ( Simulation_context const &  ctx__, K_point< T > const &  kp__, wf::num_bands  num_wf__, wf::num_mag_dims  num_md__, bool  mt_part__  )

inline

Definition at line 766 of file k_point.hpp.

bisection_search()

template<class F >

double sirius::bisection_search	(	F &&	f,
		double	a,
		double	b,
		double	tol,
		int	maxstep = 1000
	)

Definition at line 165 of file k_point_set.cpp.

newton_minimization_chemical_potential()

template<class Nt , class DNt , class D2Nt >

auto sirius::newton_minimization_chemical_potential	(	Nt &&	N,
		DNt &&	dN,
		D2Nt &&	ddN,
		double	mu0,
		double	ne,
		double	tol,
		int	maxstep = 1000
	)

Newton minimization to determine the chemical potential.

Parameters

N	number of electrons as a function of \(\mu\)
dN	\(\partial_\mu N(\mu)\)
ddN	\(\partial^2_\mu N(\mu)\)
mu0	initial guess
ne	target number of electrons
tol	tolerance
maxstep	max number of Newton iterations

Definition at line 207 of file k_point_set.cpp.

generate_alm_block()

template<bool conjugate, typename T >

auto sirius::generate_alm_block	(	Simulation_context const &	ctx__,
		int	atom_begin__,
		int	num_atoms__,
		Matching_coefficients const &	alm__
	)

Generate matching coefficients for a block of atoms.

Definition at line 11 of file generate_alm_block.hpp.

generate_gvec_ylm()

auto sirius::generate_gvec_ylm ( Simulation_context const &  ctx__, int  lmax__  )

inline

Generate complex spherical harmonics for the local set of G-vectors.

Definition at line 32 of file generate_gvec_ylm.hpp.

generate_sbessel_mt()

auto sirius::generate_sbessel_mt ( Simulation_context const &  ctx__, int  lmax__  )

inline

Compute values of spherical Bessel functions at MT boundary.

Definition at line 32 of file generate_sbessel_mt.hpp.

unit_step_function_form_factors()

double sirius::unit_step_function_form_factors ( double  R__, double  g__  )

inline

Utility function to generate LAPW unit step function.

Definition at line 34 of file step_function.hpp.

init_step_function()

auto sirius::init_step_function ( Unit_cell const &  uc__, fft::Gvec const &  gv__, fft::Gvec_fft const &  gvec_fft__, sddk::mdarray< std::complex< double >, 2 > const &  phase_factors_t__, fft::spfft_transform_type< double >  spfft__  )

inline

Unit step function is defined to be 1 in the interstitial and 0 inside muffin-tins.

Unit step function is constructed from it's plane-wave expansion coefficients which are computed analytically:

\[ \Theta({\bf r}) = \sum_{\bf G} \Theta({\bf G}) e^{i{\bf Gr}}, \]

where

\[ \Theta({\bf G}) = \frac{1}{\Omega} \int \Theta({\bf r}) e^{-i{\bf Gr}} d{\bf r} = \frac{1}{\Omega} \int_{\Omega} e^{-i{\bf Gr}} d{\bf r} - \frac{1}{\Omega} \int_{MT} e^{-i{\bf Gr}} d{\bf r} = \delta_{\bf G, 0} - \sum_{\alpha} \frac{1}{\Omega} \int_{MT_{\alpha}} e^{-i{\bf Gr}} d{\bf r} \]

Integralof a plane-wave over the muffin-tin volume is taken using the spherical expansion of the plane-wave around central point \( \tau_{\alpha} \):

\[ \int_{MT_{\alpha}} e^{-i{\bf Gr}} d{\bf r} = e^{-i{\bf G\tau_{\alpha}}} \int_{MT_{\alpha}} 4\pi \sum_{\ell m} (-i)^{\ell} j_{\ell}(Gr) Y_{\ell m}(\hat {\bf G}) Y_{\ell m}^{*}(\hat {\bf r}) r^2 \sin \theta dr d\phi d\theta \]

In the above integral only \( \ell=m=0 \) term survives. So we have:

\[ \int_{MT_{\alpha}} e^{-i{\bf Gr}} d{\bf r} = 4\pi e^{-i{\bf G\tau_{\alpha}}} \Theta(\alpha, G) \]

where

\[ \Theta(\alpha, G) = \int_{0}^{R_{\alpha}} \frac{\sin(Gr)}{Gr} r^2 dr = \left\{ \begin{array}{ll} \displaystyle R_{\alpha}^3 / 3 & G=0 \\ \Big( \sin(GR_{\alpha}) - GR_{\alpha}\cos(GR_{\alpha}) \Big) / G^3 & G \ne 0 \end{array} \right. \]

are the so-called step function form factors. With this we have a final expression for the plane-wave coefficients of the unit step function:

\[ \Theta({\bf G}) = \delta_{\bf G, 0} - \sum_{\alpha} \frac{4\pi}{\Omega} e^{-i{\bf G\tau_{\alpha}}} \Theta(\alpha, G) \]

Definition at line 87 of file step_function.hpp.

sum_fg_fl_yg()

auto sirius::sum_fg_fl_yg ( Simulation_context const &  ctx__, int  lmax__, std::complex< double > const *  fpw__, sddk::mdarray< double, 3 > &  fl__, sddk::matrix< std::complex< double > > &  gvec_ylm__  )

inline

Compute sum over plane-wave coefficients and spherical harmonics that apperas in Poisson solver and finding of the MT boundary values. The following operation is performed:

\[ q_{\ell m}^{\alpha} = \sum_{\bf G} 4\pi \rho({\bf G}) e^{i{\bf G}{\bf r}_{\alpha}}i^{\ell}f_{\ell}^{\alpha}(G) Y_{\ell m}^{*}(\hat{\bf G}) \]

Definition at line 39 of file sum_fg_fl_yg.hpp.

make_matrix_view()

template<class numeric_t >

auto sirius::make_matrix_view

(

nlcglib::buffer_protocol< numeric_t, 2 > &

buf

)

Definition at line 228 of file adaptor.hpp.

apply_hamiltonian()

void sirius::apply_hamiltonian ( Hamiltonian0< double > &  H0, K_point< double > &  kp, wf::Wave_functions< double > &  wf_out, wf::Wave_functions< double > &  wf, std::shared_ptr< wf::Wave_functions< double > >  swf  )

inline

Definition at line 38 of file apply_hamiltonian.hpp.

call_nlcg()

void sirius::call_nlcg ( Simulation_context &  ctx, config_t::nlcg_t const &  nlcg_params, Energy &  energy, K_point_set &  kset, Potential &  potential  )

inline

Definition at line 39 of file call_nlcg.hpp.

check_xc_potential()

void sirius::check_xc_potential

(

Density const &

rho__

)

Definition at line 30 of file check_xc_potential.cpp.

xc_mt_paw()

double sirius::xc_mt_paw	(	std::vector< XC_functional > const &	xc_func__,
		int	lmax__,
		int	num_mag_dims__,
		SHT const &	sht__,
		Radial_grid< double > const &	rgrid__,
		std::vector< Flm const * >	rho__,
		std::vector< double > const &	rho_core__,
		std::vector< Flm > &	vxc__,
		Flm &	exclm__
	)

Definition at line 123 of file paw_potential.cpp.

density_residual_hartree_energy()

double sirius::density_residual_hartree_energy	(	Density const &	rho1__,
		Density const &	rho2__
	)

Definition at line 31 of file poisson.cpp.

xc_mt()

double sirius::xc_mt	(	Radial_grid< double > const &	rgrid__,
		SHT const &	sht__,
		std::vector< XC_functional > const &	xc_func__,
		int	num_mag_dims__,
		std::vector< Flm const * >	rho__,
		std::vector< Flm * >	vxc__,
		Flm *	exc__
	)

Definition at line 276 of file xc_mt.cpp.

xc_mt_nonmagnetic()

void sirius::xc_mt_nonmagnetic	(	Radial_grid< double > const &	rgrid__,
		SHT const &	sht__,
		std::vector< XC_functional > const &	xc_func__,
		Flm const &	rho_lm__,
		Ftp &	rho_tp__,
		Flm &	vxc_lm__,
		Flm &	exc_lm__
	)

Definition at line 35 of file xc_mt.cpp.

xc_mt_magnetic()

void sirius::xc_mt_magnetic	(	Radial_grid< double > const &	rgrid__,
		SHT const &	sht__,
		int	num_mag_dims__,
		std::vector< XC_functional > const &	xc_func__,
		std::vector< Ftp > const &	rho_tp__,
		std::vector< Flm * >	vxc__,
		Flm &	exc__
	)

Definition at line 126 of file xc_mt.cpp.

Radial_grid_factory()

template<typename T >

Radial_grid< T > sirius::Radial_grid_factory	(	radial_grid_t	grid_type__,
		int	num_points__,
		T	rmin__,
		T	rmax__,
		double	p__
	)

Definition at line 321 of file radial_grid.hpp.

get_radial_grid_t()

std::pair< radial_grid_t, double > sirius::get_radial_grid_t ( std::string  str__ )

inline

Definition at line 349 of file radial_grid.hpp.

operator*() [5/5]

template<typename T , typename U = double>

Spline< T, U > sirius::operator* ( Spline< T, U > const &  a__, Spline< T, U > const &  b__  )

inline

Definition at line 623 of file spline.hpp.

inner() [7/8]

template<typename T >

T sirius::inner	(	Spline< T > const &	f__,
		Spline< T > const &	g__,
		int	m__,
		int	num_points__
	)

Definition at line 657 of file spline.hpp.

inner() [8/8]

template<typename T >

T sirius::inner	(	Spline< T > const &	f__,
		Spline< T > const &	g__,
		int	m__
	)

Definition at line 786 of file spline.hpp.

is_initialized()

static bool & sirius::is_initialized ( )

inlinestatic

Return the status of the library (initialized or not).

Definition at line 61 of file sirius.hpp.

initialize()

void sirius::initialize ( bool  call_mpi_init__ = true )

inline

Initialize the library.

Definition at line 82 of file sirius.hpp.

finalize()

void sirius::finalize ( bool  call_mpi_fin__ = true, bool  reset_device__ = true, bool  fftw_cleanup__ = true  )

inline

Shut down the library.

Definition at line 143 of file sirius.hpp.

check_gvec() [1/2]

void sirius::check_gvec ( fft::Gvec const &  gvec__, Crystal_symmetry const &  sym__  )

inline

Definition at line 32 of file check_gvec.hpp.

check_gvec() [2/2]

void sirius::check_gvec ( fft::Gvec_shells const &  gvec_shells__, Crystal_symmetry const &  sym__  )

inline

Definition at line 87 of file check_gvec.hpp.

find_sym_atom()

static std::pair< std::vector< int >, std::vector< r3::vector< int > > > sirius::find_sym_atom ( int  num_atoms__, sddk::mdarray< double, 2 > const &  positions__, r3::matrix< int > const &  R__, r3::vector< double > const &  t__, double  tolerance__, bool  inverse__ = false  )

static

Definition at line 34 of file crystal_symmetry.cpp.

get_spg_sym_op()

static space_group_symmetry_descriptor sirius::get_spg_sym_op ( int  isym_spg__, SpglibDataset *  spg_dataset__, r3::matrix< double > const &  lattice_vectors__, int  num_atoms__, sddk::mdarray< double, 2 > const &  positions__, double  tolerance__  )

static

Definition at line 83 of file crystal_symmetry.cpp.

get_identity_spg_sym_op()

static space_group_symmetry_descriptor sirius::get_identity_spg_sym_op ( int  num_atoms__ )

static

Definition at line 157 of file crystal_symmetry.cpp.

get_irreducible_reciprocal_mesh()

std::tuple< int, std::vector< double >, std::vector< std::array< double, 3 > > > sirius::get_irreducible_reciprocal_mesh ( Crystal_symmetry const &  sym__, r3::vector< int >  k_mesh__, r3::vector< int >  is_shift__  )

inline

Definition at line 33 of file get_irreducible_reciprocal_mesh.hpp.

metric_tensor()

auto sirius::metric_tensor ( r3::matrix< double > const &  lat_vec__ )

inline

Compute a metric tensor.

Definition at line 36 of file lattice.hpp.

metric_tensor_error()

double sirius::metric_tensor_error ( r3::matrix< double > const &  lat_vec__, r3::matrix< int > const &  R__  )

inline

Compute error of the symmetry-transformed metric tensor.

Definition at line 43 of file lattice.hpp.

find_lat_sym()

auto sirius::find_lat_sym ( r3::matrix< double > const &  lat_vec__, double  tol__, double *  mt_error__ = nullptr  )

inline

Definition at line 58 of file lattice.hpp.

phi_by_sin_cos()

double sirius::phi_by_sin_cos ( double  sinp, double  cosp  )

inline

Return angle phi in the range [0, 2Pi) by its values of sin(phi) and cos(phi).

Definition at line 36 of file rotation.hpp.

rotation_matrix_su2() [1/2]

auto sirius::rotation_matrix_su2 ( std::array< double, 3 >  u__, double  theta__  )

inline

Generate SU(2) rotation matrix from the axes and angle.

Definition at line 48 of file rotation.hpp.

rotation_matrix_su2() [2/2]

auto sirius::rotation_matrix_su2 ( r3::matrix< double >  R__ )

inline

Generate SU2(2) rotation matrix from a 3x3 rotation matrix in Cartesian coordinates.

Create quaternion components from the 3x3 matrix. The components are just a w = Cos(\Omega/2) and {x,y,z} = unit rotation vector multiplied by Sin(\Omega/2)

See https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation and https://en.wikipedia.org/wiki/Rotation_group_SO(3)#Quaternions_of_unit_norm

Definition at line 70 of file rotation.hpp.

axis_angle()

auto sirius::axis_angle ( r3::matrix< double >  R__ )

inline

Get axis and angle from rotation matrix.

Definition at line 100 of file rotation.hpp.

rot_mtrx_cart()

auto sirius::rot_mtrx_cart ( r3::vector< double >  euler_angles__ )

inline

Generate rotation matrix from three Euler angles.

Euler angles \( \alpha, \beta, \gamma \) define the general rotation as three consecutive rotations:

• about \( \hat e_z \) through the angle \( \gamma \) ( \( 0 \le \gamma < 2\pi \))
• about \( \hat e_y \) through the angle \( \beta \) ( \( 0 \le \beta \le \pi \))
• about \( \hat e_z \) through the angle \( \alpha \) ( \( 0 \le \gamma < 2\pi \))

The total rotation matrix is defined as a product of three rotation matrices:

\[ R(\alpha, \beta, \gamma) = \left( \begin{array}{ccc} \cos(\alpha) & -\sin(\alpha) & 0 \\ \sin(\alpha) & \cos(\alpha) & 0 \\ 0 & 0 & 1 \end{array} \right) \left( \begin{array}{ccc} \cos(\beta) & 0 & \sin(\beta) \\ 0 & 1 & 0 \\ -\sin(\beta) & 0 & \cos(\beta) \end{array} \right) \left( \begin{array}{ccc} \cos(\gamma) & -\sin(\gamma) & 0 \\ \sin(\gamma) & \cos(\gamma) & 0 \\ 0 & 0 & 1 \end{array} \right) = \left( \begin{array}{ccc} \cos(\alpha) \cos(\beta) \cos(\gamma) - \sin(\alpha) \sin(\gamma) & -\sin(\alpha) \cos(\gamma) - \cos(\alpha) \cos(\beta) \sin(\gamma) & \cos(\alpha) \sin(\beta) \\ \sin(\alpha) \cos(\beta) \cos(\gamma) + \cos(\alpha) \sin(\gamma) & \cos(\alpha) \cos(\gamma) - \sin(\alpha) \cos(\beta) \sin(\gamma) & \sin(\alpha) \sin(\beta) \\ -\sin(\beta) \cos(\gamma) & \sin(\beta) \sin(\gamma) & \cos(\beta) \end{array} \right) \]

Definition at line 174 of file rotation.hpp.

euler_angles()

auto sirius::euler_angles ( r3::matrix< double > const &  rot__, double  tolerance__  )

inline

Compute Euler angles corresponding to the proper rotation matrix.

Definition at line 196 of file rotation.hpp.

apply_symmetry_to_density_matrix()

void sirius::apply_symmetry_to_density_matrix ( sddk::mdarray< std::complex< double >, 3 > const &  dm_ia__, basis_functions_index const &  indexb__, const int  num_mag_comp__, std::vector< sddk::mdarray< double, 2 > > const &  rotm__, sddk::mdarray< std::complex< double >, 2 > const &  spin_rot_su2__, sddk::mdarray< std::complex< double >, 3 > &  dm_ja__  )

inline

Definition at line 33 of file symmetrize_density_matrix.hpp.

symmetrize_density_matrix()

void sirius::symmetrize_density_matrix ( Unit_cell const &  uc__, density_matrix_t &  dm__, int  num_mag_comp__  )

inline

Symmetrize density matrix.

Density matrix arises in LAPW or PW methods. In PW it is computed in the basis of beta-projectors. Occupancy matrix is computed for the Hubbard-U correction. In both cases the matrix has the same structure and is symmetrized in the same way The symmetrization does depend explicitly on the beta or wfc. The last parameter is on when the atom has spin-orbit coupling and hubbard correction in that case, we must skip half of the indices because of the averaging of the radial integrals over the total angular momentum

We start from the spectral represntation of the occupancy operator defined for the irreducible Brillouin zone:

\[ \hat N_{IBZ} = \sum_{j} \sum_{{\bf k}}^{IBZ} | \Psi_{j{\bf k}}^{\sigma} \rangle w_{\bf k} n_{j{\bf k}} \langle \Psi_{j{\bf k}}^{\sigma'} | \]

and a set of localized orbitals with the pure angular character (this can be LAPW functions, beta-projectors or localized Hubbard orbitals) :

\[ |\phi_{\ell m}^{\alpha {\bf T}}\rangle \]

The orbitals are labeled by the angular and azimuthal quantum numbers ( \( \ell m \)), atom index ( \( \alpha \)) and a lattice translation vector ( \( {\bf T} \)) such that:

\[ \langle {\bf r} | \phi_{\ell m}^{\alpha {\bf T}} \rangle = \phi_{\ell m}({\bf r - r_{\alpha} - T}) \]

There might be several localized orbitals per atom. We wish to compute the symmetrized occupation matrix:

\[ n_{\ell m \alpha {\bf T} \sigma, \ell' m' \alpha' {\bf T}' \sigma'} = \langle \phi_{\ell m}^{\alpha {\bf T}} | \hat N | \phi_{\ell' m'}^{\alpha' {\bf T'}} \rangle = \sum_{\bf P} \sum_{j} \sum_{{\bf k}}^{IBZ} \langle \phi_{\ell m}^{\alpha {\bf T}} | \hat{\bf P} \Psi_{j{\bf k}}^{\sigma} \rangle w_{\bf k} n_{j{\bf k}} \langle \hat{\bf P} \Psi_{j{\bf k}}^{\sigma'} | \phi_{\ell' m'}^{\alpha' {\bf T'}} \rangle \]

Let's now label the overlap integrals between localized orbitals and KS wave-functions:

\[ A_{\ell m j{\bf k}}^{\alpha {\bf T} \sigma} = \langle \Psi_{j{\bf k}}^{\sigma} | \phi_{\ell m}^{\alpha {\bf T}} \rangle = \int \Psi_{j{\bf k}}^{\sigma *}({\bf r}) \phi_{\ell m}({\bf r} - {\bf r}_{\alpha} - {\bf T}) d{\bf r} \]

and check how it transforms under the symmetry operation \( \hat {\bf P} = \{ {\bf R} | {\bf t} \} \) applied to the KS states.

\[ \int \big( \hat {\bf P}\Psi_{j {\bf k}}^{\sigma *}({\bf r}) \big) \phi_{\ell m}({\bf r} - {\bf r}_{\alpha} - {\bf T}) d{\bf r} = \int \Psi_{j {\bf k}}^{\sigma *}({\bf r}) \big( \hat {\bf P}^{-1} \phi_{\ell m}({\bf r} - {\bf r}_{\alpha} - {\bf T}) \big) d{\bf r} \]

Let's first derive how the inverse symmetry operation acts on the localized orbital centered on the atom inside a unit cell (no T):

\[ \hat {\bf P}^{-1} \phi\big( {\bf r} - {\bf r}_{\alpha} \big) = \phi\big( {\bf R} {\bf r} + {\bf t} - {\bf r}_{\alpha} \big) = \\ \phi\big( {\bf R}({\bf r} - {\bf R}^{-1}({\bf r}_{\alpha} - {\bf t})) \big) = \tilde \phi \big( {\bf r} - {\bf R}^{-1}({\bf r}_{\alpha} - {\bf t}) \big) \]

This operation rotates the orbital and centers it at the position

\[ {\bf r}_{\beta} = {\bf R}^{-1}{\bf r}_{\alpha} - {\bf R}^{-1}{\bf t} = \hat {\bf P}^{-1}{\bf r}_{\alpha} \]

For example, suppose thar we have y-orbital centered at \( {\bf r}_{\alpha} = [1, 0] \) (black dot) and a symmetry operation \( \hat {\bf P} = \{ {\bf R} | {\bf t} \} \) that rotates by \( \pi/2 \) counterclockwise and translates by [1/2, 1/2]:

Under this symmetry operation the atom coordinate will transform into [1/2, 3/2] (red dot), but this is not(!) how the orbital is transformed. The origin of the atom will transform according to the inverse of \( \hat {\bf P} \) into \( {\bf r}_{\beta} = [-1/2, -1/2] \) (blue dot) such that \( \hat {\bf P} {\bf r}_{\beta} = {\bf r}_{\alpha} \):

To be more precise, we should highlight that the transformed atom coordinate can go out of the original unit cell and can be brought back with a translation vector:

\[ \hat {\bf P}^{-1}{\bf r}_{\alpha} = {\bf r}_{\beta} + {\bf T}_{P\alpha\beta} \]

Now let's derive how the inverse symmetry operation acts on the localized orbital \( \phi({\bf r}) \) centered on atom in the arbitrary unit cell:

\[ \hat {\bf P}^{-1} \phi\big( {\bf r} - {\bf r}_{\alpha} - {\bf T} \big) = \phi\big( {\bf R} {\bf r} + {\bf t} - {\bf r}_{\alpha} - {\bf T} \big) = \\ \phi\big( {\bf R}({\bf r} - {\bf R}^{-1}({\bf r}_{\alpha} + {\bf T} - {\bf t})) \big) = \tilde \phi\big( {\bf r} - {\bf R}^{-1}({\bf r}_{\alpha} + {\bf T} - {\bf t}) \big) = \tilde \phi\big( {\bf r} - {\bf r}_{\beta} - {\bf T}_{P\alpha\beta} - {\bf R}^{-1}{\bf T} \big) \]

Now let's check how the atomic orbitals transfrom under the rotational part of the symmetry operation. The atomic functions of ( \( \ell m \)) character is expressed as a product of radial function and a spherical harmonic:

\[ \phi_{\ell m}({\bf r}) = \phi_{\ell}(r) Y_{\ell m}(\theta, \phi) \]

Under rotation the spherical harmonic is transformed as:

\[ Y_{\ell m}({\bf P} \hat{\bf r}) = {\bf P}^{-1}Y_{\ell m}(\hat {\bf r}) = \sum_{m'} D_{m'm}^{\ell}({\bf P}^{-1}) Y_{\ell m'}(\hat {\bf r}) = \sum_{m'} D_{mm'}^{\ell}({\bf P}) Y_{\ell m'}(\hat {\bf r}) \]

so

\[ \tilde \phi_{\ell m}({\bf r}) =\hat {\bf P}^{-1} \phi_{\ell}(r) Y_{\ell m}(\theta, \phi) = \sum_{m'} D_{mm'}^{\ell}({\bf P}) \phi_{\ell}(r) Y_{\ell m'}(\theta, \phi) \]

We will use Bloch theorem to get rid of the translations in the argument of \( \tilde \phi \):

\[ \int \Psi_{j {\bf k}}^{\sigma *}({\bf r}) \tilde \phi_{\ell m} \big( {\bf r} - {\bf r}_{\beta} - {\bf T}_{P\alpha\beta} - {\bf R}^{-1}{\bf T} \big) d{\bf r} = e^{-i{\bf k}({\bf T}_{P\alpha\beta} + {\bf R}^{-1}{\bf T})} \int \Psi_{j {\bf k}}^{\sigma *}({\bf r}) \tilde \phi_{\ell m} \big( {\bf r} - {\bf r}_{\beta} \big) d{\bf r} \]

(the "-" in the phase factor appears because KS wave-functions are complex conjugate) and now we can write

\[ A_{\ell m j\hat {\bf P}{\bf k}}^{\alpha {\bf T} \sigma} = e^{-i{\bf k}({\bf T}_{P\alpha\beta} + {\bf R}^{-1}{\bf T})} \sum_{m'} D_{mm'}^{\ell}({\bf P}) A_{\ell m' j{\bf k}}^{\beta \sigma} \]

The final expression for the symmetrized matrix is then

\[ n_{\ell m \alpha {\bf T} \sigma, \ell' m' \alpha' {\bf T}' \sigma'} = \sum_{\bf P} \sum_{j} \sum_{{\bf k}}^{IBZ} A_{\ell m j\hat {\bf P}{\bf k}}^{\alpha {\bf T} \sigma *} w_{\bf k} n_{j{\bf k}} A_{\ell' m' j\hat {\bf P}{\bf k}}^{\alpha' {\bf T'} \sigma'} = \\ = \sum_{\bf P} \sum_{j} \sum_{{\bf k}}^{IBZ} e^{i{\bf k}({\bf T}_{P\alpha\beta} + {\bf R}^{-1}{\bf T})} e^{-i{\bf k}({\bf T}_{P\alpha'\beta'} + {\bf R}^{-1}{\bf T'})} \sum_{m_1 m_2} D_{mm_1}^{\ell *}({\bf P}) D_{m'm_2}^{\ell'}({\bf P}) A_{\ell m_1 j{\bf k}}^{\beta \sigma *} A_{\ell' m_2 j{\bf k}}^{\beta' \sigma'} w_{\bf k} n_{j{\bf k}} \]

In the case of \( \alpha = \alpha' \) and \( {\bf T}={\bf T}' \) all the phase-factor exponents disappear and we get an expression for the "on-site" occupation matrix:

\[ n_{\ell m \sigma, \ell' m' \sigma'}^{\alpha} = \sum_{\bf P} \sum_{j} \sum_{{\bf k}}^{IBZ} \sum_{m_1 m_2} D_{mm_1}^{\ell *}({\bf P}) D_{m'm_2}^{\ell'}({\bf P}) A_{\ell m_1 j{\bf k}}^{\beta \sigma *} A_{\ell' m_2 j{\bf k}}^{\beta \sigma'} w_{\bf k} n_{j{\bf k}} = \\ = \sum_{\bf P} \sum_{m_1 m_2} D_{mm_1}^{\ell *}({\bf P}) D_{m'm_2}^{\ell'}({\bf P}) \tilde n_{\ell m_1 \sigma, \ell' m_2 \sigma'}^{\beta} \]

To compute the overlap integrals between KS wave-functions and localized Hubbard orbitals we insert resolution of identity (in \( {\bf G+k} \) planve-waves) between bra and ket:

\[ \langle \phi_{\ell m}^{\alpha} | \Psi_{j{\bf k}}^{\sigma} \rangle = \sum_{\bf G} \phi_{\ell m}^{\alpha *}({\bf G+k}) \Psi_{j}^{\sigma}({\bf G+k}) \]

Definition at line 258 of file symmetrize_density_matrix.hpp.

symmetrize_field4d()

void sirius::symmetrize_field4d ( Field4D &  f__ )

inline

Definition at line 35 of file symmetrize_field4d.hpp.

symmetrize_forces()

void sirius::symmetrize_forces ( Unit_cell const &  uc__, sddk::mdarray< double, 2 > &  f__  )

inline

Definition at line 33 of file symmetrize_forces.hpp.

symmetrize_mt_function()

template<typename Index_t >

void sirius::symmetrize_mt_function ( Crystal_symmetry const &  sym__, mpi::Communicator const &  comm__, int  num_mag_dims__, std::vector< Spheric_function_set< double, Index_t > * >  frlm__  )

inline

Definition at line 35 of file symmetrize_mt_function.hpp.

symmetrize_occupation_matrix()

void sirius::symmetrize_occupation_matrix ( Occupation_matrix &  om__ )

inline

Definition at line 33 of file symmetrize_occupation_matrix.hpp.

symmetrize_pw_function()

void sirius::symmetrize_pw_function ( Crystal_symmetry const &  sym__, fft::Gvec_shells const &  gvec_shells__, sddk::mdarray< std::complex< double >, 3 > const &  sym_phase_factors__, int  num_mag_dims__, std::vector< Smooth_periodic_function< double > * >  frg__  )

inline

Symmetrize scalar or vector function.

The following operation is performed:

\[ f_{\mathrm{sym}}({\bf r}) = \frac{1}{N_{\mathrm{sym}}} \sum_{\hat{\bf S}\hat{\bf P}} \hat {\bf S} \hat {\bf P}f({\bf r}) \]

where \( f({\bf r}) \) has to be understood as an unsymmetrized scalar or vector function. In the case of a scalar function \( \hat {\bf S} = 1 \). In the case of vector function \( \hat {\bf S} \) is rotation matrix acting on the Cartesian components of the function. \( \hat {\bf P} = \{{\bf R}|{\bf t}\} \) is a spacial part of the full magentic symmetry operatoin acting on the real-space coordinates.

For the function expanded in plane-waves we have:

\[ f_{\mathrm{sym}}({\bf r}) = \frac{1}{N_{\mathrm{sym}}} \sum_{\hat{\bf S}\hat{\bf P}} \hat {\bf S} \hat {\bf P}f({\bf r}) = \frac{1}{N_{\mathrm{sym}}} \sum_{\hat{\bf S}\hat{\bf P}} \hat {\bf S} \sum_{\bf G} f({\bf G}) e^{i{\bf G}\hat{\bf P}^{-1}{\bf r}} = \\ \frac{1}{N_{\mathrm{sym}}} \sum_{\hat{\bf S}\hat{\bf P}} \sum_{\bf G} \hat {\bf S} f({\bf G}) e^{i{\bf G}({\bf R}^{-1}{\bf r} - {\bf R}^{-1}{\bf t})} = \frac{1}{N_{\mathrm{sym}}} \sum_{\hat{\bf S}\hat{\bf P}} \sum_{\bf G} \hat {\bf S} f({\bf G}) e^{i{\bf G}'{\bf r}} e^{-i{\bf G}'{\bf t}} \]

where \( {\bf G}' = {\bf G}{\bf R}^{-1} = {\bf R}^{-T}{\bf G} \). The last expression establishes the link between unsymmetrized plane-wave coefficient at G-vector and symmetrized coefficient at G'. We will rewrite the expression using inverse relation \( {\bf G} = {\bf R}^{T}{\bf G'} \) and summing over G' (which is just a permutaion of G):

\[ f_{\mathrm{sym}}({\bf r}) = \sum_{\bf G'} e^{i{\bf G}'{\bf r}} \frac{1}{N_{\mathrm{sym}}} \sum_{\hat{\bf S}\hat{\bf P}} \hat {\bf S} f({\bf R}^{T}{\bf G'}) e^{-i{\bf G}'{\bf t}} \]

That gives an expression for the symmetrized plane-wave coefficient at G':

\[ f_{\mathrm{sym}}({\bf G}') = \frac{1}{N_{\mathrm{sym}}} \sum_{\hat{\bf S}\hat{\bf P}} \hat {\bf S} f({\bf R}^{T}{\bf G'}) e^{-i{\bf G}'{\bf t}} \]

Once \( f_{\mathrm{sym}}({\bf G}) \) has been calculated for a single G, its values at a star of G can be calculated using the following relation:

\[ f_{\mathrm{sym}}({\bf r}) = \hat{\bf S}\hat{\bf P} f_{\mathrm{sym}}({\bf r}) = \hat{\bf S} f_{\mathrm{sym}}(\hat {\bf P}^{-1}{\bf r}) \]

which leads to the following relation for the plane-wave coefficient:

\[ \sum_{\bf G} f_{\mathrm{sym}}({\bf G})e^{i{\bf G}{\bf r}} = \sum_{\bf G} \hat{\bf S}f_{\mathrm{sym}}({\bf G})e^{i{\bf G}\hat{\bf P}^{-1}{\bf r}} = \sum_{\bf G} \hat{\bf S}f_{\mathrm{sym}}({\bf G})e^{i{\bf G}{\bf R}^{-1}{\bf r}} e^{-i{\bf G}{\bf R}^{-1}{\bf t}} = \sum_{\bf G'} \hat{\bf S}f_{\mathrm{sym}}({\bf G})e^{i{\bf G}'{\bf r}} e^{-i{\bf G}'{\bf t}} = \sum_{\bf G'} \hat{\bf S}f_{\mathrm{sym}}({\bf G'})e^{i{\bf G}'{\bf r}} \]

and so

\[ f_{\mathrm{sym}}({\bf G}') = \hat{\bf S}f_{\mathrm{sym}}({\bf G})e^{-i{\bf G'}{\bf t}} \]

Parameters

[in]	sym	Description of the crystal symmetry.
[in]	gvec_shells	Description of the G-vector shells.
[in]	sym_phase_factors	Phase factors associated with fractional translations.
[in]	num_mag_dims	Number of magnetic dimensions.
[in,out]	frg	Array of pointers to scalar and vector parts of the filed being symmetrized.

Definition at line 99 of file symmetrize_pw_function.hpp.

symmetrize_stress_tensor()

void sirius::symmetrize_stress_tensor ( Crystal_symmetry const &  sym__, r3::matrix< double > &  s__  )

inline

Definition at line 33 of file symmetrize_stress_tensor.hpp.

call_test() [1/2]

template<typename F >

int sirius::call_test ( std::string  label__, F &&  f__  )

inline

Definition at line 43 of file testing.hpp.

call_test() [2/2]

template<typename F >

int sirius::call_test ( std::string  label__, F &&  f__, cmd_args const &  args__  )

inline

Definition at line 71 of file testing.hpp.

random_symmetric()

template<typename T >

auto sirius::random_symmetric ( int  N__, int  bs__, la::BLACS_grid const &  blacs_grid__  )

inline

Definition at line 111 of file testing.hpp.

random_positive_definite()

template<typename T >

auto sirius::random_positive_definite ( int  N__, int  bs__ = 16, la::BLACS_grid const *  blacs_grid__ = nullptr  )

inline

Definition at line 148 of file testing.hpp.

create_simulation_context()

auto sirius::create_simulation_context ( nlohmann::json const &  conf__, r3::matrix< double >  L__, int  num_atoms__, std::vector< r3::vector< double > >  coord__, bool  add_vloc__, bool  add_dion__  )

inline

Definition at line 181 of file testing.hpp.

randomize()

template<typename T >

void sirius::randomize ( wf::Wave_functions< T > &  wf__ )

inline

Definition at line 262 of file testing.hpp.

operator<<() [5/7]

std::ostream & sirius::operator<< ( std::ostream &  out, ps_atomic_wf_descriptor const &  wfd  )

inline

Definition at line 80 of file atom_type.hpp.

begin() [2/3]

auto sirius::begin ( basis_functions_index const &  idx__ )

inline

Definition at line 195 of file basis_functions_index.hpp.

end() [2/3]

auto sirius::end ( basis_functions_index const &  idx__ )

inline

Definition at line 200 of file basis_functions_index.hpp.

operator<<() [6/7]

std::ostream & sirius::operator<< ( std::ostream &  out, hubbard_orbital_descriptor const &  ho  )

inline

Definition at line 353 of file hubbard_orbitals_descriptor.hpp.

operator==()

bool sirius::operator== ( angular_momentum  lhs__, angular_momentum  rhs__  )

inline

Definition at line 120 of file radial_functions_index.hpp.

operator!=()

bool sirius::operator!= ( angular_momentum  lhs__, angular_momentum  rhs__  )

inline

Definition at line 125 of file radial_functions_index.hpp.

operator<<() [7/7]

std::ostream & sirius::operator<< ( std::ostream &  out, angular_momentum  am  )

inline

Output angular momentum to a stream.

Definition at line 131 of file radial_functions_index.hpp.

begin() [3/3]

auto sirius::begin ( radial_functions_index const &  idx__ )

inline

Definition at line 437 of file radial_functions_index.hpp.

end() [3/3]

auto sirius::end ( radial_functions_index const &  idx__ )

inline

Definition at line 442 of file radial_functions_index.hpp.

Variable Documentation

sirius_integer_type

integer, parameter, public sirius::sirius_integer_type = 1

Definition at line 9 of file sirius.f90.

sirius_logical_type

integer, parameter, public sirius::sirius_logical_type = 2

Definition at line 10 of file sirius.f90.

sirius_string_type

integer, parameter, public sirius::sirius_string_type = 3

Definition at line 11 of file sirius.f90.

sirius_number_type

integer, parameter, public sirius::sirius_number_type = 4

Definition at line 12 of file sirius.f90.

sirius_object_type

integer, parameter, public sirius::sirius_object_type = 5

Definition at line 13 of file sirius.f90.

sirius_array_type

integer, parameter, public sirius::sirius_array_type = 6

Definition at line 14 of file sirius.f90.

sirius_integer_array_type

integer, parameter, public sirius::sirius_integer_array_type = 7

Definition at line 16 of file sirius.f90.

sirius_logical_array_type

integer, parameter, public sirius::sirius_logical_array_type = 8

Definition at line 17 of file sirius.f90.

sirius_number_array_type

integer, parameter, public sirius::sirius_number_array_type = 9

Definition at line 18 of file sirius.f90.

sirius_string_array_type

integer, parameter, public sirius::sirius_string_array_type = 10

Definition at line 19 of file sirius.f90.

sirius_object_array_type

integer, parameter, public sirius::sirius_object_array_type = 11

Definition at line 20 of file sirius.f90.

sirius_array_array_type

integer, parameter, public sirius::sirius_array_array_type = 12

Definition at line 21 of file sirius.f90.

speed_of_light

const double sirius::speed_of_light = 137.035999139

NIST value for the inverse fine structure (http://physics.nist.gov/cuu/Constants/index.html)

Definition at line 33 of file constants.hpp.

bohr_radius

const double sirius::bohr_radius = 0.52917721067

Bohr radius in angstroms.

Definition at line 39 of file constants.hpp.

pi

const double sirius::pi = 3.1415926535897932385

\( \pi \)

Definition at line 42 of file constants.hpp.

twopi

const double sirius::twopi = 6.2831853071795864769

\( 2\pi \)

Definition at line 45 of file constants.hpp.

fourpi

const double sirius::fourpi = 12.566370614359172954

\( 4\pi \)

Definition at line 48 of file constants.hpp.

y00

const double sirius::y00 = 0.28209479177387814347

First spherical harmonic \( Y_{00} = \frac{1}{\sqrt{4\pi}} \).

Definition at line 51 of file constants.hpp.

ha2ev

const double sirius::ha2ev = 27.21138505

Hartree in electron-volt units.

Definition at line 54 of file constants.hpp.

storage_file_name

const char* const sirius::storage_file_name = "sirius.h5"

Definition at line 56 of file constants.hpp.

pauli_matrix

const std::complex<double> sirius::pauli_matrix[4][2][2]

Initial value:

= {
    {{1.0, 0.0}, {0.0, 1.0}},
    {{1.0, 0.0}, {0.0, -1.0}},
    {{0.0, 1.0}, {1.0, 0.0}},
    {{0.0, std::complex<double>(0, -1)}, {std::complex<double>(0, 1), 0.0}}}

Pauli matrices in {I, Z, X, Y} order.

Definition at line 59 of file constants.hpp.

global_rtgraph_timer

extern::rt_graph::Timer sirius::global_rtgraph_timer

Definition at line 28 of file profiler.cpp.

is_real_v

template<class T >

constexpr bool sirius::is_real_v = std::is_same<T, real_type<T>>::value

constexpr

Definition at line 53 of file typedefs.hpp.

libxc_functionals

const std::map<std::string, int> sirius::libxc_functionals

Definition at line 39 of file xc_functional_base.hpp.