# Spglib for Python¶

## Installation¶

The source code is downloaded at https://github.com/spglib/spglib/tags. But minor updates are not included in this package. If you want the latest version, you can git-clone the spglib repository:

```
% git clone https://github.com/spglib/spglib.git
```

It is also possible to install spglib for python via the following package distribution services or from building using setup.py.

The following pip and conda packages are made and maintained by Paweł T. Jochym, which is of great help to keeping spglib handy and useful.

### Using pip¶

Numpy is required before the python-spglib installation. The command to install spglib is:

```
% pip install --user spglib
```

If you see the error message like below in the installation process:

```
_spglib.c:35:20: fatal error: Python.h: No such file or directory
```

development tools for building python module are additionally necessary and are installed using OS’s package management system, e.g.,:

```
% sudo apt-get install python-dev
```

If your installation by pip failed, you may need to upgrade setuptools, e.g., by:

```
% pip install --upgrade --user setuptools
```

### Building using setup.py¶

To manually install python-spglib using `setup.py`

, python header
files (python-dev), C-compiler (e.g., gcc, clang), and numpy are
required before the build. The installation steps are shown as
follows:

Go to the

`python`

directoryType the command:

% python setup.py install --user

Document about where spglib is installed is found at the links below:

If your installation by setup.py failed, you may need to upgrade setuptools, e.g., by:

```
% pip install --upgrade --user setuptools
```

## Test¶

The test script `test_spglib.py`

is found in `python/test`

directory. Got to this directory and run this script. It will be like below:

```
% python test_spglib.py
test_find_primitive (__main__.TestSpglib) ... ok
test_get_symmetry (__main__.TestSpglib) ... ok
test_get_symmetry_dataset (__main__.TestSpglib) ... ok
test_refine_cell (__main__.TestSpglib) ... ok
----------------------------------------------------------------------
Ran 4 tests in 13.147s
OK
```

## How to import spglib module¶

**Change in version 1.9.0!**

For versions 1.9.x or later:

```
import spglib
```

For versions 1.8.x or before:

```
from pyspglib import spglib
```

If the version is not sure:

```
try:
import spglib as spg
except ImportError:
from pyspglib import spglib as spg
```

## Version number¶

In version 1.8.3 or later, the version number is obtained by
`spglib.__version__`

or get_version.

## Variables¶

### Crystal structure (`cell`

)¶

A crystal structure is given by a **tuple**. This tuple format is
supported at version 1.9.1 or later.

The tuple format is shown as follows. There are three or four elements
in the tuple: `cell = (lattice, positions, numbers)`

or ```
cell =
(lattice, positions, numbers, magmoms)
```

where `magmoms`

represents
collinear polarizations on atoms and is optional.

Lattice parameters `lattice`

are given by a 3x3 matrix with floating
point values, where \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are
given as rows, which results in the transpose of the definition for
C-API (lattice). Fractional atomic positions
`positions`

are given by a Nx3 matrix with floating point values,
where N is the number of atoms. Numbers to distinguish atomic species
`numbers`

are given by a list of N integers. The collinear polarizations
`magmoms`

only work with `get_symmetry`

and are given
as a list of N floating point values.

```
lattice = [[a_x, a_y, a_z],
[b_x, b_y, b_z],
[c_x, c_y, c_z]]
positions = [[a_1, b_1, c_1],
[a_2, b_2, c_2],
[a_3, b_3, c_3],
...]
numbers = [n_1, n_2, n_3, ...]
magmoms = [m_1, m_2, m_3, ...] # Only works with get_symmetry
```

For example, the crystal structure (`cell`

) of L1 _{2} -type AlNi _{3} is:

```
lattice = [[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0]]
positions = [[0.0, 0.0, 0.0], # Al
[0.5, 0.5, 0.0], # Ni
[0.0, 0.5, 0.5], # Ni
[0.5, 0.0, 0.5]] # Ni
numbers = [1, 2, 2, 2] # Al, Ni, Ni, Ni
```

Version 1.9.5 or later: The methods that use the crsytal strcutre
will return `None`

when a crystal structure is not properly given.

#### ASE Atoms-like input is deprecated.¶

In the previous versions, ASE Atoms-like input was supported, but it
is deprecated. It is recommended to use the above tuple-style input
for the future support. `DeprecationWarning`

is issued at version
1.10.0 or later.

The reason to make this feature deprecated is that ASE Atoms class is too huge and users may expect spglib can understand its full feature. However spglib actually collects only the following values from the ASE Atoms-class instance:

```
lattice = cell.get_cell()
positions = cell.get_scaled_positions()
numbers = cell.get_atomic_numbers()
magmoms = None
```

for which the corresponding code is written out of API and it is found
at here. Nevertheless
the ASE Atoms-like input will be accepted for a while. An alternative
Atoms class (atoms.py)
that contains minimum set of methods is prepared in the examples
directory. `get_symmetry`

with collinear polarizations is not
supported when ASE Atoms-class instance.

### Symmetry tolerance (`symprec`

)¶

Distance tolerance in Cartesian coordinates to find crystal symmetry. For more details, see symprec

## Methods¶

`get_version`

¶

**New in version 1.8.3**

```
version = get_version()
```

This returns version number of spglib by tuple with three numbers.

`get_error_message`

¶

**New in version 1.9.5**

**Be careful. This method is not thread safe, i.e., only safely usable
when calling one spglib method per process.**

This method is used to see roughly why spglib failed.

```
error_message = get_error_message()
```

`get_spacegroup`

¶

```
spacegroup = get_spacegroup(cell, symprec=1e-5)
```

International space group short symbol and number are obtained as a
string. With `symbol_type=1`

, Schoenflies symbol is given instead of
international symbol.

`get_symmetry`

¶

```
symmetry = get_symmetry(cell, symprec=1e-5)
```

Symmetry operations are obtained as a dictionary. The key `rotation`

contains a numpy array of integer, which is “number of symmetry
operations” x “3x3 matrices”. The key `translation`

contains a numpy
array of float, which is “number of symmetry operations” x
“vectors”. The orders of the rotation matrices and the translation
vectors correspond with each other, e.g. , the second symmetry
operation is organized by the set of the second rotation matrix and second
translation vector in the respective arrays. Therefore a set of
symmetry operations may obtained by:

```
[(r, t) for r, t in zip(dataset['rotations'], dataset['translations'])]
```

The operations are given with respect to the fractional coordinates (not for Cartesian coordinates). The rotation matrix and translation vector are used as follows:

```
new_vector[3x1] = rotation[3x3] * vector[3x1] + translation[3x1]
```

The three values in the vector are given for the a, b, and c axes,
respectively. The key `equivalent_atoms`

gives a mapping table of
atoms to symmetrically independent atoms. This is used to find
symmetrically equivalent atoms. The numbers contained are the indices
of atoms starting from 0, i.e., the first atom is numbered as 0, and
then 1, 2, 3, … `np.unique(equivalent_atoms)`

gives representative
symmetrically independent atoms. A list of atoms that are
symmetrically euivalent to some independent atom (here for example 1
is in `equivalent_atom`

) is found by
`np.where(equivalent_atom=1)[0]`

. When the search failed, `None`

is returned.

If `cell`

is given as a tuple and collinear polarizations are given
as the fourth element of this tuple, symmetry operations are searched
considering this freedome. In ASE Atoms-class object, this is not supported.

`refine_cell`

¶

**Behaviour changed in version 1.8.x**

```
lattice, scaled_positions, numbers = refine_cell(cell, symprec=1e-5)
```

Standardized crystal structure is obtained as a tuple of lattice (a
3x3 numpy array), atomic scaled positions (a numpy array of
[number_of_atoms,3]), and atomic numbers (a 1D numpy array) that are
symmetrized following space group type. When the search failed,
`None`

is returned. About the default choice of the setting, see the
documentation of `hall_number`

argument of
get_symmetry_dataset.

The detailed control of standardization of unit cell is achieved using
`standardize_cell`

.

`find_primitive`

¶

**Behaviour changed in version 1.8.x**

```
lattice, scaled_positions, numbers = find_primitive(cell, symprec=1e-5)
```

When a primitive cell is found, lattice parameters (a 3x3 numpy array),
scaled positions (a numpy array of [number_of_atoms,3]), and atomic
numbers (a 1D numpy array) is returned. When the search failed,
`None`

is returned.

The detailed control of standardization of unit cell can be done using
`standardize_cell`

.

`standardize_cell`

¶

**New in version 1.8.x**

```
lattice, scaled_positions, numbers = standardize_cell(bulk, to_primitive=False, no_idealize=False, symprec=1e-5)
```

`to_primitive=True`

is used to create the standardized primitive
cell, and `no_idealize=True`

disables to idealize lengths and angles
of basis vectors and positions of atoms according to crystal
symmetry. Now `refine_cell`

and `find_primitive`

are shorthands of
this method with combinations of these options. When the search
failed, `None`

is returned. is returned. About the default choice
of the setting, see the documentation of `hall_number`

argument of
get_symmetry_dataset. More detailed explanation is
shown in the spglib (C-API) document.

`get_symmetry_dataset`

¶

**At version 1.9.4, the member ‘choice’ is added.**

```
dataset = get_symmetry_dataset(cell, symprec=1e-5, angle_tolerance=-1.0, hall_number=0)
```

The arguments are:

`cell`

and`symprec`

: See Variables.`angle_tolerance`

: An experimental argument that controls angle tolerance between basis vectors. Normally it is not recommended to use this argument. See a bit more detail at angle_tolerance.`hall_number`

(see the definition of this number at Space group type): The argument to constrain the space-group-type search only for the Hall symbol corresponding to it. The mapping from Hall symbols to a space-group-type is the many-to-one mapping. Without specifying this option (i.e., in the case of`hall_number=0`

), always the first one (the smallest serial number corresponding to the space-group-type in list of space groups (Seto’s web site)) among possible choices and settings is chosen as default. This argument is useful when the other choice (or settting) is expected to be hooked. This affects to the obtained values of`international`

,`hall`

,`hall_number`

,`choice`

,`transformation_matrix`

,`origin shift`

,`wyckoffs`

,`std_lattice`

,`std_positions`

,`std_types`

and`std_rotation_matrix`

, but not to`rotations`

and`translations`

since the later set is defined with respect to the basis vectors of user’s input (the`cell`

argument).

`dataset`

is a dictionary. Short explanations of the values of the
keys are shown below. More details are found at Spglib dataset.

`number`

: International space group number`international`

: International short symbol`hall`

: Hall symbol`hall_number`

: Hall number. This number is used in get_symmetry_from_database and get_spacegroup_type.`choice`

: Centring, origin, basis vector setting`transformation_matrix`

: See the detail at Transformation matrix and origin shift.`origin shift`

: See the detail at Transformation matrix and origin shift.`wyckoffs`

: Wyckoff letters`site_symmetry_symbols`

: Site-symmetry symbols (**experimental**)`equivalent_atoms`

: Mapping table to equivalent atoms`crystallographic_orbits`

: Mapping table to equivalent atoms (see this for the difference between`equivalent_atoms`

and`crystallographic_orbits`

)`primitive_lattice`

: Basis vectors of a primitive cell`mapping_to_primitive`

: Mapping table to atoms in the primitive cell`rotations`

and`translations`

: Rotation matrices and translation vectors. See get_symmetry for more details.`pointgroup`

: Symbol of the crystallographic point group in the Hermann–Mauguin notation.`std_lattice`

,`std_positions`

,`std_types`

: Standardized crystal structure corresponding to a Hall symbol found. These are equivalently given in the array formats of`lattice`

,`positions`

, and`numbers`

presented at Crystal structure (cell), respectively.`std_rotation_matrix`

: See the detail at Standardized crystal structure after idealization.`std_mapping_to_primitive`

: Mapping table from atoms in the standardized crystal structure to the atoms in the primitive cell.

When the search failed, `None`

is returned.

`get_symmetry_from_database`

¶

```
symmetry = get_symmetry_from_database(hall_number)
```

A set of crystallographic symmetry operations corresponding to
`hall_number`

is returned by a dictionary where rotation parts and
translation parts are accessed by the keys `rotations`

and
`translations`

, respectively. The definition of `hall_number`

is
found at Space group type.

When something wrong happened, `None`

is returned.

`get_spacegroup_type`

¶

**New at version 1.9.4**

```
spacegroup_type = get_spacegroup_type(hall_number)
```

This function allows to directly access to the space-group-type
database in spglib (spg_database.c). A dictionary is returned. 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. The keys of the returned
dictionary is as follows:

```
number
international_short
international_full
international
schoenflies
hall_symbol
choice
pointgroup_schoenflies
pointgroup_international
arithmetic_crystal_class_number
arithmetic_crystal_class_symbol
```

Here `spacegroup_type['international_short']`

is equivalent to
`dataset['international']`

of `get_symmetry_dataset`

,
`spacegroup_type['hall_symbol']`

is equivalent to
`dataset['hall']`

of `get_symmetry_dataset`

, and
`spacegroup_type['pointgroup_international']`

is equivalent to
`dataset['pointgroup_symbol']`

of `get_symmetry_dataset`

.

When something wrong happened, `None`

is returned.

`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
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`

.

```
get_hall_number_from_symmetry(rotations, translations, symprec=1e-5)
```

`niggli_reduce`

¶

**New at version 1.9.4**

```
niggli_lattice = niggli_reduce(lattice, eps=1e-5)
```

Niggli reduction is achieved using this method. The algorithm detail
is found at https://atztogo.github.io/niggli/ and the references are
there in. Original basis vectors are stored in `lattice`

and the
Niggli reduced basis vectors are given in `niggli_lattice`

. The
format of basis vectors are found at
Crystal structure (cell). `esp`

is the tolerance
parameter, but unlike `symprec`

the unit is not a length. This is
used to check if difference of norms of two basis vectors is close to
zero or not and if two basis vectors are orthogonal by the value of
dot product being close to zero or not. The detail is shown at
https://atztogo.github.io/niggli/.

When the search failed, `None`

is returned.

The transformation from original basis vectors \(( \mathbf{a} \; \mathbf{b} \; \mathbf{c} )\) to final baiss 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.

`delaunay_reduce`

¶

**New at version 1.9.4**

```
delaunay_lattice = delaunay_reduce(lattice, eps=1e-5)
```

Delaunay reduction is achieved using this method. The algorithm is
found in the international tables for crystallography
volume A. Original basis vectors are stored in `lattice`

and the
Delaunay reduced basis vectors are given in `delaunay_lattice`

,
where the format of basis vectors are shown in
Crystal structure (cell). `esp`

is the tolerance
parameter, but unlike `symprec`

the unit is not a length. This is
used as the criterion if volume is close to zero or not and if two
basis vectors are orthogonal by the value of dot product being close
to zero or not.

When the search failed, `None`

is returned.

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.

`get_ir_reciprocal_mesh`

¶

```
mapping, grid = get_ir_reciprocal_mesh(mesh, cell, is_shift=[0, 0, 0])
```

Irreducible k-points are obtained from a sampling mesh of k-points.
`mesh`

is given by three integers by array and specifies mesh
numbers along reciprocal primitive axis. `is_shift`

is given by the
three integers by array. When `is_shift`

is set for each reciprocal
primitive axis, the mesh is shifted along the axis in half of adjacent
mesh points irrespective of the mesh numbers. When the value is not 0,
`is_shift`

is set.

`mapping`

and `grid`

are returned. `grid`

gives the mesh points in
fractional coordinates in reciprocal space. `mapping`

gives mapping to
the irreducible k-point indices that are obtained by

```
np.unique(mapping)
```

Here `np`

means the numpy module. The grid point is accessed by
`grid[index]`

.

When the sesarch failed, `None`

is returned.

An example is shown below:

```
import numpy as np
import spglib
lattice = np.array([[0.0, 0.5, 0.5],
[0.5, 0.0, 0.5],
[0.5, 0.5, 0.0]]) * 5.4
positions = [[0.875, 0.875, 0.875],
[0.125, 0.125, 0.125]]
numbers= [1,] * 2
cell = (lattice, positions, numbers)
print(spglib.get_spacegroup(cell, symprec=1e-5))
mesh = [8, 8, 8]
#
# Gamma centre mesh
#
mapping, grid = spglib.get_ir_reciprocal_mesh(mesh, cell, is_shift=[0, 0, 0])
# All k-points and mapping to ir-grid points
for i, (ir_gp_id, gp) in enumerate(zip(mapping, grid)):
print("%3d ->%3d %s" % (i, ir_gp_id, gp.astype(float) / mesh))
# Irreducible k-points
print("Number of ir-kpoints: %d" % len(np.unique(mapping)))
print(grid[np.unique(mapping)] / np.array(mesh, dtype=float))
#
# With shift
#
mapping, grid = spglib.get_ir_reciprocal_mesh(mesh, cell, is_shift=[1, 1, 1])
# All k-points and mapping to ir-grid points
for i, (ir_gp_id, gp) in enumerate(zip(mapping, grid)):
print("%3d ->%3d %s" % (i, ir_gp_id, (gp + [0.5, 0.5, 0.5]) / mesh))
# Irreducible k-points
print("Number of ir-kpoints: %d" % len(np.unique(mapping)))
print((grid[np.unique(mapping)] + [0.5, 0.5, 0.5]) / mesh)
```