# C-APIs#

## Version#

### spg_get_major_version, spg_get_minor_version, spg_get_micro_version#

New in version 1.8.3

Version number of spglib is obtained. These three functions return integers that correspond to spglib version [major].[minor].[micro].

## Error#

### spg_get_error_code and spg_get_error_message#

New in version 1.9.5

Be careful. These are not thread safe, i.e., only safely usable when calling one spglib function per process.

These functions is used to see roughly why spglib failed.

SpglibError spg_get_error_code(void);
char * spg_get_error_message(SpglibError spglib_error);

The SpglibError type is a enum type as shown below.

typedef enum {
SPGLIB_SUCCESS = 0,
SPGERR_SPACEGROUP_SEARCH_FAILED,
SPGERR_CELL_STANDARDIZATION_FAILED,
SPGERR_SYMMETRY_OPERATION_SEARCH_FAILED,
SPGERR_ATOMS_TOO_CLOSE,
SPGERR_POINTGROUP_NOT_FOUND,
SPGERR_NIGGLI_FAILED,
SPGERR_DELAUNAY_FAILED,
SPGERR_ARRAY_SIZE_SHORTAGE,
SPGERR_NONE,
} SpglibError;

The usage is as follows

SpglibError error;
error = spg_get_error_code();
printf("%s\n", spg_get_error_message(error));

## Standardization and finding primitive cell#

### spg_standardize_cell#

The standardized unit cell (see Spglib conventions of standardized unit cell) is generated from an input unit cell structure and its symmetry found by the symmetry search. The choice of the setting for each space group type is as explained for spg_get_dataset. Usually to_primitive=0 and no_idealize=0 are recommended to set and this setting results in the same behavior as spg_refine_cell. 0 is returned if it failed.

int spg_standardize_cell(double lattice[3][3],
double position[][3],
int types[],
const int num_atom,
const int to_primitive,
const int no_idealize,
const double symprec);

Number of atoms in the found standardized unit (primitive) cell is returned.

to_primitive=1 is used to create the standardized primitive cell with the transformation matrices shown at Transformation to the primitive cell, otherwise to_primitive=0 must be specified. The found basis vectors and atomic point coordinates and types are overwritten in lattice, position, and types, respectively. Therefore with to_primitive=0, at a maximum four times larger array size for position and types than the those size of the input unit cell is required to store a standardized unit cell with face centring found in the case that the input unit cell is a primitive cell.

no_idealize=0 is used to idealize the lengths and angles of basis vectors with adjusting the positions of atoms to nearest exact positions according to crystal symmetry. However the crystal can be rotated in Cartesian coordinates by the idealization of the basis vectors. no_idealize=1 disables this. The detail of the idealization (no_idealize=0) is written at Idealization of unit cell structure. no_idealize=1 may be useful when we want to leave basis vectors and atomic positions in Cartesian coordinates fixed.

### spg_find_primitive#

Behavior is changed. This function is now a shortcut of spg_standardize_cell with to_primitive=1 and no_idealize=0.

A primitive cell is found from an input unit cell. 0 is returned if it failed.

int spg_find_primitive(double lattice[3][3],
double position[][3],
int types[],
const int num_atom,
const double symprec);

lattice, position, and types are overwritten. Number of atoms in the found primitive cell is returned. The crystal can be rotated by this function. To avoid this, please use spg_standardize_cell with to_primitive=1 and no_idealize=1 although the crystal structure is not idealized.

### spg_refine_cell#

This function exists for backward compatibility since it is same as spg_standardize_cell with to_primitive=0 and no_idealize=0.

The standardized crystal structure is obtained from a non-standard crystal structure which may be slightly distorted within a symmetry recognition tolerance, or whose primitive vectors are differently chosen, etc. 0 is returned if it failed.

int spg_refine_cell(double lattice[3][3],
double position[][3],
int types[],
const int num_atom,
const double symprec);

The calculated standardized lattice and atomic positions overwrites lattice, position, and types. The number of atoms in the standardized unit cell is returned as the return value. When the input unit cell is a primitive cell and is the face centring symmetry, the number of the atoms returned becomes four times large. Since this function does not have any means of checking the array size (memory space) of these variables, the array size (memory space) for position and types should be prepared four times more than those required for the input unit cell in general.

## Space-group dataset access#

### spg_get_symmetry_from_database#

This function allows to directly access to the space group operations in the spglib database (spg_database.c). To specify the space group type with a specific choice, hall_number is used. The definition of hall_number is found at Space group type. 0 is returned when it failed.

int spg_get_symmetry_from_database(int rotations[192][3][3],
double translations[192][3],
const int hall_number);

The returned value is the number of space group operations. The space group operations are stored in rotations and translations.

### spg_get_spacegroup_type#

Changed at version 1.9.4: Some members are added and the member name ‘setting’ is changed to ‘choice’. Changed at version 2.0: Add ‘hall_number’ member.

This function allows to directly access to the space-group-type database in spglib (spg_database.c). To specify the space group type with a specific choice, hall_number is used. The definition of hall_number is found at Space group type. number = 0 is returned when it failed.

SpglibSpacegroupType spg_get_spacegroup_type(const int hall_number)

SpglibSpacegroupType structure is as follows:

typedef struct {
int number;
char international_short[11];
char international_full[20];
char international[32];
char schoenflies[7];
char hall_symbol[17];
int hall_number;
char choice[6];
char pointgroup_schoenflies[4];
char pointgroup_international[6];
int arithmetic_crystal_class_number;
char arithmetic_crystal_class_symbol[7];
} SpglibSpacegroupType;

### spg_get_spacegroup_type_from_symmetry#

New at version 2.0

Return space-group type information from symmetry operations. This is the replacement of spg_get_hall_number_from_symmetry (deprecated at v2.0).

This is expected to work well for the set of symmetry operations whose distortion is small. The aim of making this feature is to find space-group-type for the set of symmetry operations given by the other source than spglib.

SpglibSpacegroupType spg_get_spacegroup_type_from_symmetry(
SPGCONST int rotations[][3][3], SPGCONST double translations[][3],
const int num_operations, SPGCONST double lattice[3][3], const double symprec
);

The SpglibSpacegroupType structure is explained at spg_get_spacegroup_type. The parameter lattice is used as the distance measure for symprec. If it is unknown, the following may be a reasonable choice.

lattice[3][3] = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};

## Magnetic symmetry#

### spg_get_symmetry_with_collinear_spin#

This function finds symmetry operations with collinear polarizations (spins) on atoms. Except for the argument of const double spins[], the usage is basically the same as spg_get_symmetry, but as an output, equivalent_atoms are obtained. The size of this array is the same of num_atom. See Wyckoff positions and symmetrically equivalent atoms for the definition equivalent_atoms. 0 is returned when it failed.

int spg_get_symmetry_with_collinear_spin(int rotation[][3][3],
double translation[][3],
int equivalent_atoms[],
const int max_size,
SPGCONST double lattice[3][3],
SPGCONST double position[][3],
const int types[],
const double spins[],
const int num_atom,
const double symprec);

### spg_get_symmetry_with_site_tensors#

Experimental: new at version 2.0

Returns magnetic symmetry operations represented by rotation, translation, and spin_flips from crystal structure with lattice, position, types, and tensors. When you need magnetic symmetry operations of non-collinear spins, set tensor_rank=1, is_axial=1, and tensors with length num_atom * 3 (ordered by $$[ m_{1x}, m_{1y}, m_{1z}, \dots ]$$) in cartesian coordinates. For other combinations of tensor_rank and is_axial, see Flags to control action of magnetic symmetry operations. Returned spin_flips represents sign of site tensors after applying time-reversal operations: 1 for non time reversal, and -1 for time reversal.

int spg_get_symmetry_with_site_tensors(
int rotation[][3][3], double translation[][3], int equivalent_atoms[],
double primitive_lattice[3][3], int *spin_flips, const int max_size,
SPGCONST double lattice[3][3], SPGCONST double position[][3],
const int types[], const double *tensors, const int tensor_rank,
const int num_atom, const int with_time_reversal, const int is_axial,
const double symprec);

### spg_get_magnetic_dataset#

Experimental: new at version 2.0

Return magnetic symmetry operations and standardized structure of given structure with site tensors.

• To search magnetic symmetry operations of a structure with collinear spins, set tensor_rank=0, is_axial=0, and tensors with length num_atom

• To search magnetic symmetry operations of a structure with non-collinear spins, set tensor_rank=1, is_axial=1, and tensors with length num_atom * 3 in cartesian coordinates.

The description of returned dataset is given at Magnetic Spglib dataset (Experimental).

SpglibMagneticDataset *spg_get_magnetic_dataset(
SPGCONST double lattice[3][3], SPGCONST double position[][3],
const int types[], const double *tensors, const int tensor_rank,
const int num_atom, const int is_axial, const double symprec);

### spg_get_magnetic_symmetry_from_database#

Experimental: new at version 2.0

Magnetic space-group operations in built-in database are accessed by UNI number, which is defined as number from 1 to 1651. Optionally alternative settings can be specified with hall_number. For type-I, type-II, and type-III magnetic space groups, hall_number changes settings in family space group. For type-IV, hall_number changes settings in maximal space group. When hall_number = 0, the smallest hall number corresponding to uni_number is used.

int spg_get_magnetic_symmetry_from_database(int rotations[384][3][3],
double translations[384][3],
int time_reversals[384],
const int uni_number,
const int hall_number);

### spg_free_magnetic_dataset#

Experimental: new at version 2.0

void spg_free_magnetic_dataset(SpglibMagneticDataset *dataset);

### spg_get_magnetic_spacegroup_type#

Experimental: new at version 2.0

Magnetic space-group type information is accessed by serial number of UNI (or BNS) symbols. The serial number is between 1 and 1651.

SpglibMagneticSpacegroupType spg_get_magnetic_spacegroup_type(
const int uni_number);

Returned SpglibMagneticSpacegroupType is the following C-structure:

typedef struct {
int uni_number;
int litvin_number;
char bns_number[8];
char og_number[12];
int number;
int type;
} SpglibMagneticSpacegroupType;
• uni_number serial number of UNI (or BNS) symbols

• litvin_number serial number in Litvin’s Magnetic group tables

• bns_number BNS number e.g. “156.32”

• og_number OG number e.g. “153.4.1270”

• number ITA’s serial number of space group for reference setting

• type Type of MSG from 1 to 4

### spg_get_magnetic_spacegroup_type_from_symmetry#

Experimental: new at version 2.0

Return magnetic space-group type information from magnetic symmetry operations. time_reversals takes 0 for ordinary operations and 1 for time-reversal operations.

SpglibMagneticSpacegroupType spg_get_magnetic_spacegroup_type_from_symmetry(
SPGCONST int rotations[][3][3], SPGCONST double translations[][3],
SPGCONST int *time_reversals, const int num_operations,
SPGCONST double lattice[3][3], const double symprec
);

See spg_get_magnetic_spacegroup_type for returned SpglibMagneticSpacegroupType.

## Lattice reduction#

### spg_niggli_reduce#

Niggli reduction is applied to input basis vectors lattice and the reduced basis vectors are overwritten to lattice. 0 is returned if it failed.

int spg_niggli_reduce(double lattice[3][3], const double symprec);

The transformation from original basis vectors $$( \mathbf{a} \; \mathbf{b} \; \mathbf{c} )$$ to final basis vectors $$( \mathbf{a}' \; \mathbf{b}' \; \mathbf{c}' )$$ is achieved by linear combination of basis vectors with integer coefficients without rotating coordinates. Therefore the transformation matrix is obtained by $$\boldsymbol{P} = ( \mathbf{a} \; \mathbf{b} \; \mathbf{c} ) ( \mathbf{a}' \; \mathbf{b}' \; \mathbf{c}' )^{-1}$$ and the matrix elements have to be almost integers.

### spg_delaunay_reduce#

Delaunay reduction is applied to input basis vectors lattice and the reduced basis vectors are overwritten to lattice. 0 is returned if it failed.

int spg_delaunay_reduce(double lattice[3][3], const double symprec);

The transformation from original basis vectors $$( \mathbf{a} \; \mathbf{b} \; \mathbf{c} )$$ to final basis vectors $$( \mathbf{a}' \; \mathbf{b}' \; \mathbf{c}' )$$ is achieved by linear combination of basis vectors with integer coefficients without rotating coordinates. Therefore the transformation matrix is obtained by $$\boldsymbol{P} = ( \mathbf{a} \; \mathbf{b} \; \mathbf{c} ) ( \mathbf{a}' \; \mathbf{b}' \; \mathbf{c}' )^{-1}$$ and the matrix elements have to be almost integers.

## Kpoints#

### spg_get_ir_reciprocal_mesh#

Irreducible reciprocal grid points are searched from uniform mesh grid points specified by mesh and is_shift.

int map[],
const int mesh[3],
const int is_shift[3],
const int is_time_reversal,
const double lattice[3][3],
const double position[][3],
const int types[],
const int num_atom,
const double symprec)

mesh stores three integers. Reciprocal primitive vectors are divided by the number stored in mesh with (0,0,0) point centering. The center of grid mesh is shifted +1/2 of a grid spacing along corresponding reciprocal axis by setting 1 to a is_shift element. No grid mesh shift is made if 0 is set for is_shift.

The reducible uniform grid points are returned in fractional coordinates as grid_address. A map between reducible and irreducible points are returned as map as in the indices of grid_address. The number of the irreducible k-points are returned as the return value. The time reversal symmetry is imposed by setting is_time_reversal 1.

Grid points are stored in the order that runs left most element first, e.g. (4x4x4 mesh).

[[ 0  0  0]
[ 1  0  0]
[ 2  0  0]
[-1  0  0]
[ 0  1  0]
[ 1  1  0]
[ 2  1  0]
[-1  1  0]
....      ]

where the first index runs first. k-qpoints are calculated by (grid_address + is_shift / 2) / mesh. A grid point index is recovered from grid_address by numpy.dot(grid_address % mesh, [1, mesh[0], mesh[0] * mesh[1]]) in Python-numpy notation, where % always returns non-negative integers. The order of grid_address can be changed so that the last index runs first by setting the macro GRID_ORDER_XYZ in kpoint.c. In this case the grid point index is recovered by numpy.dot(grid_address % mesh, [mesh[2] * mesh[1], mesh[2], 1]).

### spg_get_stabilized_reciprocal_mesh#

The irreducible k-points are searched from unique k-point mesh grids from direct (real space) basis vectors and a set of rotation parts of symmetry operations in direct space with one or multiple stabilizers.

int map[],
const int mesh[3],
const int is_shift[3],
const int is_time_reversal,
const int num_rot,
const int rotations[][3][3],
const int num_q,
const double qpoints[][3])

The stabilizers are written in fractional coordinates. Number of the stabilizers are given by num_q. Symmetrically equivalent k-points (stars) in fractional coordinates are stored in map as indices of grid_address. The number of reduced k-points with the stabilizers are returned as the return value.

This function can be used to obtain all mesh grid points by setting num_rot = 1, rotations = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, num_q = 1, and qpoints = {0, 0, 0}.

## Deprecated#

### spg_get_hall_number_from_symmetry#

Deprecated at version 2.0. This function is replaced by spg_get_spacegroup_type_from_symmetry.

Return one of hall_number corresponding to a space-group type of the given set of symmetry operations. When multiple hall_number exist for the space-group type, the smallest one (the first description of the space-group type in International Tables for Crystallography) is chosen. The definition of hall_number is found at Space group type and the corresponding space-group-type information is obtained through spg_get_spacegroup_type.

This is expected to work well for the set of symmetry operations whose distortion is small. The aim of making this feature is to find space-group-type for the set of symmetry operations given by the other source than spglib.

Note that the definition of symprec is different from usual one, but is given in the fractional coordinates and so it should be small like 1e-5.

int spg_get_hall_number_from_symmetry(SPGCONST int rotation[][3][3],
SPGCONST double translation[][3],
const int num_operations,
const double symprec)