pyqcstrc.ico: for icosahedral quasicrystals

Description

This modules provides algorithm for building 6D structural models of the icosahedral quasicrystals:

  • Translation operation of occupation domain

  • Symmetry operations of occupation domain

  • Intersection of two occupation domains

API Reference

This is the reference for building initial structural models of icosahedral quasicrystals.

Occupation domain

pyqcstrc.ico.occupation_domain.as_it_is(obj)

Returns an object as it is,

Parameters:

obj (numpy.ndarray) – the shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

Returns:

the shape is (num,4,6,3), where num=numbre_of_tetrahedron.

Return type:

Occupation domains (numpy.ndarray)

pyqcstrc.ico.occupation_domain.asymmetric(symmetric_obj, position, vecs)

Asymmetric part of occupation domain.

Parameters:

  • symmetric_obj (numpy.ndarray) – Occupation domain of which the asymmetric part is calculated. The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • position (numpy.ndarray) – 6d coordinate of the site of which the occupation domain centres. The shape is (6,3)

  • vecs (numpy.ndarray) – Three vectors that defines the asymmetric part. The shape is (3,6,3)

Returns:

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

Return type:

Asymmetric part of the occupation domains (numpy.ndarray)

pyqcstrc.ico.occupation_domain.gen_surface(obj, verbose=0)

Generate triangles on the surface of the occupation domain.

Parameters:

  • obj (numpy.ndarray) – the occupation domain The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal)

Returns:

The shape is (num,3,6,3), where num=numbre_of_triangles.

Return type:

Triangles of the occupation domains (numpy.ndarray)

pyqcstrc.ico.occupation_domain.generate_edges(obj, verbose=0)

Generate edges of the occupation domain.

Parameters:

  • obj (numpy.ndarray) – The occupation domain The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • shift (numpy.ndarray) – 6d coordinate to which the occupation domain is shifted. The shape is (6,3)

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal)

Returns:

The shape is (num,2,6,3), where num=numbre_of_edge.

Return type:

Edges of the occupation domains (numpy.ndarray)

pyqcstrc.ico.occupation_domain.read_xyz(path, basename, select='tetrahedron')

Load new occupation domain on input XYZ file.

Parameters:

  • path (str) – Path of the input XYZ file

  • basename (str) – Basename of the input XYZ file

  • select (str) – ‘tetrahedron’: set of tetrahedra (default) ‘vertex’ : set of vertices (default, select = ‘tetrahedron’)

Returns:

Loaded occupation domains. The shape is (num,4,6,3), where num=numbre_of_tetrahedra (select = ‘tetrahedron’). The shape is (num,6,3), where num=numbre_of_vertices (select = ‘vertex’).

Return type:

Occupation domains (numpy.ndarray)

pyqcstrc.ico.occupation_domain.shift(obj, shift, verbose=0)

Shift the occupation domain.

Parameters:

  • obj (numpy.ndarray) – The occupation domain The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • shift (numpy.ndarray) – 6d coordinate to which the occupation domain is shifted. The shape is (6,3)

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal)

Returns:

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

Return type:

Shifted occupation domains (numpy.ndarray)

pyqcstrc.ico.occupation_domain.simpl_add_point(obj, point, verbose=0)

Legacy: simple

pyqcstrc.ico.occupation_domain.simpl_manual(obj, num, verbose_level=0)

Legacy: simple

pyqcstrc.ico.occupation_domain.simpl_manual_2(obj, num, obj_partial, verbose_level=0)

Legacy: simple

pyqcstrc.ico.occupation_domain.simple(obj, select, num_cycle=3, verbose=0, num_cycle_234=[3, 0, 0], num_shuffle_234=[1, 0, 0])

Legacy: simple

pyqcstrc.ico.occupation_domain.simple_hand_step1(obj, path, basename_tmp)

Simplification of occupation domains by hand (step1).

Parameters:

  • obj (numpy.ndarray) – the occupation domain The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • path (str) – path of the tmporal file

  • basename_tmp (str) – name for tmporal file.

Returns:

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

Return type:

Tmporal occupation domains (numpy.ndarray)

pyqcstrc.ico.occupation_domain.simple_hand_step2(obj, merge_list)

Simplification of occupation domains by hand (step2).

Parameters:

  • obj (numpy.ndarray) – the occupation domain The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • merge_list (list[[int,int,int,int,],[],...,[]]) – A list containing lists of indices of vertices of tetrahedron. The indices of vertices of tetrahedron in temporal file obtaind by ‘simple_hand_step1()’.

Returns:

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

Return type:

Simplified occupation domains (numpy.ndarray)

pyqcstrc.ico.occupation_domain.simple_rondom(obj, num_cycle, combination_num, verbose_level=0)

Legacy: simple

pyqcstrc.ico.occupation_domain.simple_special(obj, num, num_cycle, verbose_level=0)

Legacy: simple_special

pyqcstrc.ico.occupation_domain.simple_special_1(obj, num, num_cycle, verbose_level=0)

Legacy: simple

pyqcstrc.ico.occupation_domain.simplification(obj, num_cycle=10, verbose=0)

Simplification of occupation domains.

Parameters:

  • obj (numpy.ndarray) – the occupation domain The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • num_cycle (int) – numbre of cycles

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal) verbose > 2 (detail)

Returns:

Simplified occupation domains (numpy.ndarray)

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

pyqcstrc.ico.occupation_domain.site_symmetry(wyckoff_position, centering, verbose=0)

Symmetry operators in the site symmetry group G and its left coset decomposition.

Parameters:

  • position (Wyckoff) – 6D coordinate. The shape is (6,3).

  • centering – primitive lattice (‘p’) face-centered lattice (‘f’) and body-centered lattice (‘i’)

  • verbose (int)

Returns:

The symmetry operators leaves xyz identical.

List of index of symmetry operators in the left coset representatives of the poibt group G (list):

The symmetry operators generates equivalent positions of the site xyz.

Return type:

List of index of symmetry operators of the site symmetry group G (list)

pyqcstrc.ico.occupation_domain.symmetric(asymmetric_part_obj, position)

Generate symmterical occupation domain by symmetric elements of m-3-5 on the asymmetric unit.

Parameters:

  • asymmetric_part_obj (numpy.ndarray) – Asymmetric unit of the occupation domain The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • position (numpy.ndarray) – 6d coordinate of the site of which the occupation domain centres. The shape is (6,3)

Returns:

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

Return type:

Symmetric occupation domains (numpy.ndarray)

pyqcstrc.ico.occupation_domain.write(obj, path='.', basename='tmp', format='xyz', color='k', verbose=0, select='tetrahedron')

Export occupation domains.

Parameters:

  • obj (numpy.ndarray) – the occupation domain The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • path (str) – Path of the output XYZ file

  • basename (str) – Basename of the output XYZ file

  • format (str) – format of output file format = ‘xyz’ (default) format = ‘vesta’

  • color (str) – one of the characters {‘k’,’r’,’b’,’p’}, which are short-hand notations for shades of black, red, blue, and pink, in case where ‘vesta’ format is selected (default, color = ‘k’).

Returns:

0 (succeed), 1 (fail)

Return type:

int

pyqcstrc.ico.occupation_domain.write_podatm(obj, position, vlist=[0], path='.', basename='tmp', shift=[0.0, 0.0, 0.0, 0.0, 0.0, 0.0], verbose=0)

Generate pod and atom files.

Parameters:

  • obj (numpy.ndarray) – the occupation domain The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • position (numpy.ndarray) – 6D coordinates of the position of the occupation domain.

  • vertices (list)

  • vlist (list)

  • path (str) – Path of the output files

  • basename (str) – Basename of the output files

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal)

Returns:

0 (succeed), 1 (fail)

Return type:

int

pyqcstrc.ico.occupation_domain.write_vesta(obj, path='.', basename='tmp', color='k', select='normal', verbose=0)

Export occupation domains in VESTA format.

Parameters:

  • obj (numpy.ndarray) – the occupation domain The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • path (str) – Path of the output XYZ file

  • basename (str) – Basename of the output XYZ file

  • color (str) – one of the characters {‘k’,’r’,’b’,’p’}, which are short-hand notations for shades of black, red, blue, and pink, in case where ‘vesta’ format is selected (default, color = ‘k’).

  • select (str) – ‘simple’ or ‘normal’ ‘simple’: Merging tetrahedra into one single objecte ‘normal’: Each tetrahedron is set as single objecte (large file) ‘podatm’: same as ‘simple’ but return “vertices” necessary to input (default, select = ‘normal’)

Returns:

0 (succeed), 1 (fail) when select = ‘simple’ or ‘normal’. ndarray: vertices, when select = ‘podatm’.

Return type:

int

pyqcstrc.ico.occupation_domain.write_xyz(obj, path='.', basename='tmp', select='tetrahedron', verbose=0)

Export occupation domains in XYZ format.

Parameters:

  • obj (numpy.ndarray) – the occupation domain The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • path (str) – Path of the output XYZ file

  • basename (str) – Basename of the output XYZ file

  • select (str) – ‘tetrahedron’: set of tetrahedra (default) ‘triangle’ : set of triangles ‘edge’ : set of edges ‘vertex’ : set of vertices (default, select = ‘tetrahedron’)

Returns:

0 (succeed), 1 (fail)

Return type:

int

Two occupation domains

pyqcstrc.ico.two_occupation_domains.genobjv(obj, vlist=[0], path='.', basename='tmp', verbose=0)

Generate objs from vlist.

Parameters:

  • obj (numpy.ndarray) – ndarray contains vertices The shape is (num,4,6,3), where num=numbre_of_vertices.

  • vlist (list)

  • path (str) – Path of the output files

  • basename (str) – Basename of the output files

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal)

Returns:

0 (succeed), 1 (fail)

Return type:

int

pyqcstrc.ico.two_occupation_domains.intersection(obj1, obj2, flag=0, verbose=0)

Intersection of two occupation domains projected onto perp space.

Parameters:

  • obj1 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • obj2 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • flag (int) – flag = 0, Intersection with rough checking. flag = 1, Intersection without checking.

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal)

Returns:

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

Return type:

Common part of two occupation domains projected onto perp space (numpy.ndarray)

pyqcstrc.ico.two_occupation_domains.intersection_2(obj1, obj2, verbose=0)

Intersection of two occupation domains projected onto perp space.

Parameters:

  • obj1 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • obj2 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal)

Returns:

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

Return type:

Common part of two occupation domains projected onto perp space (numpy.ndarray)

pyqcstrc.ico.two_occupation_domains.intersection_3(obj1, obj2, verbose=0)

Intersection of two occupation domains projected onto perp space.

Parameters:

  • obj1 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • obj2 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal)

Returns:

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

Return type:

Common part of two occupation domains projected onto perp space (numpy.ndarray)

pyqcstrc.ico.two_occupation_domains.intersection_convex(obj1, obj2, verbose=0)

Intersection of two occupation domains projected onto perp space. The common part forms convex hull.

Parameters:

  • obj1 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • obj2 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal)

Returns:

Common part of two occupation domains projected onto perp space (numpy.ndarray)

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

pyqcstrc.ico.two_occupation_domains.intersection_old(obj1, obj2, flag=[0, 0, 0], fname='tmp0', verbose=0)

legacy Intersection of two occupation domains projected onto perp space.

Parameters:

  • obj1 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • obj2 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • flag (list) – list = [a1,a2,a3] a1 = 0, rough check intersection of obj1 and obj2; a1 = 1, no a2 = 0, rough check intersection of tetrahedron in obj1 and obj2; a2 = 1, no a3 = 0, rough check intersection of tetrahedron in obj1 and tetrahedron in obj2; a3 = 1, no

  • fname (str) – filename of output

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal)

Returns:

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

Return type:

Common part of two occupation domains projected onto perp space (numpy.ndarray)

pyqcstrc.ico.two_occupation_domains.mergev(obj1, obj2, path='.', basename='tmp', verbose=0)

merge vertices of two obj

pyqcstrc.ico.two_occupation_domains.mergev3(obj1, obj2, obj3, path='.', basename='tmp', verbose=0)

merge vertices of three obj

pyqcstrc.ico.two_occupation_domains.mergev_objs(objs_in_list, path='.', basename='tmp', verbose=0)

merge vertices of objs

pyqcstrc.ico.two_occupation_domains.subtraction(obj1, obj2, obj_common, verbose=0)

obj1 NOT obj2

legacy Substruction of two occupation domains (obj1, obj2) projected onto perp space, obj1 NOT obj2

Parameters:

  • obj1 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • obj2 (numpy.ndarray) – The shape is (num,4,6,3) or (num*4,6,3), where num=numbre_of_tetrahedron.

  • obj_common (numpy.ndarray) – Common part of two occupation domains projected onto perp space. The shape is (num,4,6,3), where num=numbre_of_tetrahedron.

  • verbose (int) – verbose = 0 (silent, default) verbose = 1 (normal)

Returns:

Substructed part of two occupation domains projected onto perp space (numpy.ndarray)

The shape is (num,4,6,3), where num=numbre_of_tetrahedron.