# Variables¶

Variables frequently used in C-API are explained. In interfaces of other languages, the definition may be different, e.g., lattice for Python interface is transposed.

## lattice¶

Attention: In Python interface, lattice is transposed (Crystal structure (cell).)

Basis vectors (in Cartesian)

[ [ a_x, b_x, c_x ],
[ a_y, b_y, c_y ],
[ a_z, b_z, c_z ] ]


Cartesian position $$\mathbf{x}_\mathrm{Cart}$$ is obtained by

$\mathbf{x}_\mathrm{Cart} = \mathrm{L}\cdot\mathbf{x}_\mathrm{frac}$

where $$\mathrm{L}$$ is the basis vectors defined above and is $$\mathrm{L}=(\mathbf{a},\mathbf{b},\mathbf{c})$$, and $$\mathbf{x}_\mathrm{frac}$$ is the atomic position in fractional coordinates given below.

## position¶

Atomic points (in fractional coordinates with respect to basis vectors)

[ [ x1_a, x1_b, x1_c ],
[ x2_a, x2_b, x2_c ],
[ x3_a, x3_b, x3_c ],
...                   ]


## types¶

Atomic species are differenciated by integers. The nubmers are just used to distinguishes atoms, and is not releated to atomic numbers.

[ type_1, type_2, type_3, ... ]


The number of elements is same as the number of atoms.

## rotation¶

Rotation matricies (ingeger) of symmetry operations.

[ [ r_aa, r_ab, r_ac ],
[ r_ba, r_bb, r_bc ],
[ r_ca, r_cb, r_cc ] ]


## translation¶

Translation vectors corresponding to symmetry operations in fractional coordinates.

[ t_a, t_b, t_c ]


## symprec¶

Distance tolerance in Cartesian coordinates to find crystal symmetry.

For atomic positions, roughly speaking, two position vectors x and x’ in Cartesian coordinates are considered to be the same if |x' - x| < symprec. For more details, see the spglib paper, Sec. II-A.

The angle distortion between basis vectors is converted to a length and compared with this distance tolerance. For more details, see the spglib paper, Sec. IV-A. It is possible to specify angle tolerance explicitly, see angle_tolerance.

## angle_tolerance¶

Tolerance of angle between basis vectors in degrees to be tolerated in the symmetry finding. To use angle tolerance, another set of functions are prepared for C-API as follows

spgat_get_dataset
spgat_get_symmetry
spgat_get_symmetry_with_collinear_spin
spgat_get_multiplicity
spgat_find_primitive
spgat_get_international
spgat_get_schoenflies
spgat_refine_cell


These functions are called by the same way with an additional argument of const double angle_tolerance in degrees. By specifying a negative value, the behavior becomes the same as usual functions. The default value of angle_tolerance is a negative value. For python-API, the angle tolernce is given with a keyward argument of angle_tolerance.