List of C-APIs

`spg_get_major_version`

,`spg_get_minor_version`

,`spg_get_micro_version`

`spg_get_error_code`

and`spg_get_error_message`

`spg_get_symmetry`

`spg_get_international`

`spg_get_schoenflies`

`spg_standardize_cell`

`spg_find_primitive`

`spg_refine_cell`

`spg_get_dataset`

and`spg_get_dataset_with_hall_number`

`spg_free_dataset`

`spg_get_spacegroup_type`

`spg_get_symmetry_from_database`

`spg_get_multiplicity`

`spg_get_symmetry_with_collinear_spin`

`spg_niggli_reduce`

`spg_delaunay_reduce`

`spg_get_ir_reciprocal_mesh`

`spg_get_stabilized_reciprocal_mesh`

`spg_get_hall_number_from_symmetry`

`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].

`spg_get_error_code`

and `spg_get_error_message`

¶**New in version 1.9.5**

These methods may be used to see why spglib failed though error handling in spglib is not very sophisticated.

```
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));
```

`spg_get_symmetry`

¶This function finds a set of representative symmetry operations for primitive cells or its extension with lattice translations for supercells. 0 is returned if it failed.

```
int spg_get_symmetry(int rotation[][3][3],
double translation[][3],
const int max_size,
const double lattice[3][3],
const double position[][3],
const int types[],
const int num_atom,
const double symprec);
```

The operations are stored in `rotation`

and `translation`

. The
number of operations is return as the return value. Rotations and
translations are given in fractional coordinates, and `rotation[i]`

and `translation[i]`

with same index give a symmetry operations,
i.e., these have to be used together.

As an exceptional case, if a supercell has the basis vectors of the lattice that break crsytallographic point group, the crystallographic symmetry operations are searched with this broken symmetry, i.e., at most the crystallographic point group found in this case is the point group of the lattice. For example, this happens for the \(2\times 1\times 1\) supercell of a conventional cubic unit cell. This may not be understandable in crystallographic sense, but is practically useful treatment for research in computational materials science.

`spg_get_international`

¶Space group type is found and returned in international table symbol
to `symbol`

and also as a number (return value). 0 is returned if
it failed.

```
int spg_get_international(char symbol[11],
const double lattice[3][3],
const double position[][3],
const int types[],
const int num_atom,
const double symprec);
```

`spg_get_schoenflies`

¶Space group type is found and returned in schoenflies to `symbol`

and also as a number (return value). 0 is returned if it failed.

```
int spg_get_schoenflies(char symbol[7],
const double lattice[3][3],
const double position[][3],
const int types[],
const int num_atom,
const double symprec);
```

`spg_standardize_cell`

¶The standardized unit cell (see Conventions of standardized unit cell) is
generated from an input unit cell structure and its space group type
determined about a symmetry search tolerance. 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 matricies 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=1`

disables to idealize lengths and angles of basis
vectors and positions of atoms according to crystal symmetry. The
detail of the idealization (`no_idealize=0`

) is written at
Idealization of unit cell structure. `no_idealize=1`

may be used when we want to
leave basis vectors and atomic positions in Cartesianl 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.

`spg_refine_cell`

¶**This function exists for backward compatibility since it is same as** `spg_standardize_cell`

**with** `to_primitive=0`

**and** `leave_distorted=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.

`spg_get_dataset`

and `spg_get_dataset_with_hall_number`

¶**Changed in version 1.8.1**

For an input unit cell structure, symmetry operations of the crystal
are searched. Then they are compared with the crsytallographic
database and the space group type is determined. The result is
returned as the `SpglibDataset`

structure as a dataset. The default
choice of setting of basis vectors in spglib is explained in the
manuscript found at http://arxiv.org/abs/1506.01455.

Dataset corresponding to the space group type in the standard setting
is obtained by `spg_get_dataset`

. If this symmetry search fails,
`NULL`

is returned in version 1.8.1 or later (spacegroup_number = 0
is returned in the previous versions). In this function, the other
crystallographic setting is not obtained.

```
SpglibDataset * spg_get_dataset(const double lattice[3][3],
const double position[][3],
const int types[],
const int num_atom,
const double symprec);
```

To specify the other crystallographic choice (setting, origin, axis,
or cell choice), `spg_get_dataset_with_hall_number`

is used.

```
SpglibDataset * spg_get_dataset_with_hall_number(SPGCONST double lattice[3][3],
SPGCONST double position[][3],
const int types[],
const int num_atom,
const int hall_number,
const double symprec)
```

where `hall_number`

is used to specify the choice. The possible
choices and those serial numbers are found at list of space groups
(Seto’s web site).
The crystal structure has to possess the space-group type of the Hall
symbol. If the symmetry search fails or the specified `hall_number`

is not in the list of Hall symbols for the space group type of the
crystal structure, `spacegroup_number`

in the `SpglibDataset`

structure is set 0.

Finally, its allocated memory space must be freed by calling
`spg_free_dataset`

.

**At version 1.9.4, SpglibDataset was modified.** The member
name `setting`

is changed to `choice`

and `pointgroup_number`

is
removed.

The dataset is accessible through the C-structure given by

```
typedef struct {
int spacegroup_number;
int hall_number;
char international_symbol[11];
char hall_symbol[17];
char choice[6];
double transformation_matrix[3][3];
double origin_shift[3];
int n_operations;
int (*rotations)[3][3];
double (*translations)[3];
int n_atoms;
int *wyckoffs;
int *equivalent_atoms;
int *mapping_to_primitive;
int n_std_atoms; /* n_brv_atoms before version 1.8.1 */
double std_lattice[3][3]; /* brv_lattice before version 1.8.1 */
int *std_types; /* brv_types before version 1.8.1 */
double (*std_positions)[3]; /* brv_positions before version 1.8.1 */
int *std_mapping_to_primitive;
char pointgroup_symbol[6];
} SpglibDataset;
```

**At versions before 1.8.1**, the member names of `n_std_atoms`

,
`std_lattice`

, `std_types`

, and `std_positions`

were
`n_brv_atoms`

, `brv_lattice`

, `brv_types`

, and
`brv_positions`

, respectively.

`spacegroup_number`

is the space group type number defined in
International Tables for Crystallography (ITA). `hall_number`

is the
serial number between 1 and 530 which are found at list of space
groups (Seto’s web site).
The (full) Hermann–Mauguin notation of space group type is given by
`international_symbol`

. The Hall symbol is stored in
`hall_symbol`

. The information on unique axis,
setting or cell choices is found in `choice`

.

The symmetry operations of the input unit cell are stored in
`rotations`

and `translations`

. A crystallographic symmetry
operation \((\boldsymbol{W}, \boldsymbol{w})\) is made from a pair
of rotation \(\boldsymbol{W}\) and translation
\(\boldsymbol{w}\) parts with the same index. Number of symmetry
operations is given as `n_operations`

. The detailed explanation of
the values is found at spg_get_symmetry.

`n_atoms`

is the number of atoms of the input unit
cell. `wyckoffs`

gives Wyckoff letters that are assigned to atomic
positions of the input unit cell. The numbers of 0, 1, 2,
\(\ldots\), correspond to the a, b, c, \(\ldots\),
respectively. Number of elements in `wyckoffs`

is same as
`n_atoms`

. `equivalent_atoms`

is a list of atomic indices that map
to indices of symmetrically independent atoms, where the list index
corresponds to atomic index of the input crystal structure.

In version 1.10 or later, `mapping_to_primitive`

is available. This
gives a list of atomic indices in the primitive cell of the input
crystal structure, where the same number presents the same atom in the
primitive cell. By collective the atoms having the same number, a set
of relative lattice points in the the input crystal structure is
obtained.

**Changed in version 1.8.1**

`transformation_matrix`

and `origin_shift`

are obtained as a
result of space-group-type matching under a set of unique axis,
setting and cell choices. In this matching, basis vectors and atomic
point coordinates have to be standardized to compare with the database
of symmetry operations. The basis vectors are transformed to those of
a standardized unit cell. Atomic point coordinates are shifted so that
symmetry operations have the standard
origin. `transformation_matrix`

(\(\boldsymbol{P}\)) is the
matrix to transform the input basis vectors to the standardized basis
vectors, wihch is represented as

\[( \mathbf{a} \; \mathbf{b} \; \mathbf{c} )
= ( \mathbf{a}_\mathrm{s} \; \mathbf{b}_\mathrm{s} \; \mathbf{c}_\mathrm{s} ) \boldsymbol{P}\]

where \(\mathbf{a}\), \(\mathbf{b}\), and \(\mathbf{c}\)
are the input (original) basis vectors, and
\(\mathbf{a}_\mathrm{s}\), \(\mathbf{b}_\mathrm{s}\), and
\(\mathbf{c}_\mathrm{s}\) are the standardized basis vectors. The
`origin_shift`

(\(\boldsymbol{p}\)) is the vector from the
origin of the standardized coordinate system to the origin of the
input (original) coordinate system measured in the standardized
coordinate system. The atomic point shift is measured from the
standardized unit cell (conventional unit cell) to the original unit
cell measured in the coordinates of the standardized unit cell. An
atomic point in the original unit cell \(\boldsymbol{x}\) (input
data) is mapped to that in the standardized unit cell
\(\boldsymbol{x}_\mathrm{s}\) by

\[\boldsymbol{x}_\mathrm{s} = \boldsymbol{P}\boldsymbol{x} +
\boldsymbol{p} \;\;(\mathrm{mod}\; \mathbf{1}).\]

In **versions 1.7.x and 1.8 or before**, `transformation_matrix`

and
`origin_shift`

are defined as follows:

\[( \mathbf{a}_\mathrm{s} \; \mathbf{b}_\mathrm{s} \;
\mathbf{c}_\mathrm{s} ) = ( \mathbf{a} \; \mathbf{b} \; \mathbf{c}
) \boldsymbol{P} \;\; \text{and} \;\; \boldsymbol{x}_\mathrm{s} =
\boldsymbol{P}^{-1}\boldsymbol{x} - \boldsymbol{p}
\;\;(\mathrm{mod}\; \mathbf{1}),\]

respectively.

**Changed in version 1.8.1**

The standardized crystal structure corresponding to a Hall symbol is
stored in `n_std_atoms`

, `std_lattice`

, `std_types`

, and
`std_positions`

.

**At versions 1.7.x and 1.8 or before**, the variable names of the
members corresponding to those above are `n_brv_atoms`

,
`brv_lattice`

, `brv_types`

, and `brv_positions`

, respectively.

**At versions 1.10 or later**, `std_mapping_to_primitive`

is
available. This gives a list of atomic indices in the primitive cell
of the standardized crystal structure, where the same number presents
the same atom in the primitive cell. By collective the atoms having
the same number, a set of relative lattice points in the the
standardized crystal structure is obtained.

**New in version 1.8.1**

`pointgroup_number`

is the serial number of the crystallographic
point group, which refers list of space
groups (Seto’s web site).
`pointgroup_symbol`

is the symbol of the crystallographic point
group in the Hermann–Mauguin notation.

`spg_free_dataset`

¶Allocated memoery space of the C-structure of `SpglibDataset`

is
freed by calling `spg_free_dataset`

.

```
void spg_free_dataset(SpglibDataset *dataset);
```

`spg_get_spacegroup_type`

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

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];
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_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_multiplicity`

¶This function returns exact number of symmetry operations. 0 is returned when it failed.

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

This function may be used in advance to allocate memoery space for symmetry operations.

`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 Site symmetry
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_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.

`spg_get_ir_reciprocal_mesh`

¶Irreducible reciprocal grid points are searched from uniform mesh grid
points specified by `mesh`

and `is_shift`

.

```
int spg_get_ir_reciprocal_mesh(int grid_address[][3],
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 spg_get_stabilized_reciprocal_mesh(int grid_address[][3],
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}`

.

`spg_get_hall_number_from_symmetry`

¶**experimental**

`hall_number`

is obtained from the set of symmetry operations. 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. `symprec`

is in the length of the fractional
coordinates and 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)
```