�
�F�VB � @ s3 d Z d d l Z d d l Z d d l Z d d l Z d d l Z d d l Z d d l Z d d l
m Z e j d k r� d d � Z
n d d � Z
d d � Z d d
d � Z f d d
d � Z d d d d � Z d d d d � Z d! d d d d � Z d d � Z d d � Z e d k r/e � e � n d S)"zLReplace symmetries of Kwant builders with momentum parameters to the
system.� N)� herm_conj� c C s t | t j � S)N)�
isinstance� collections�Hashable)�obj� r �../code/wraparound.py� _hashable s r
c C s# t | t j � o" t | t j � S)N)r r r �np�ndarray)r r r r r
s c s � � f d d � } i � | S)a� Decorator to memoize a function that works even with unhashable args.
This decorator will even work with functions whose args are not hashable.
The cache key is made up by the hashable arguments and the ids of the
non-hashable args. It is up to the user to make sure that non-hashable
args do not change during the lifetime of the decorator.
This decorator will keep reevaluating functions that return None.
c sO t d d � | D� � } � j | � } | d k rK � | � � | <} n | S)Nc s s- | ]# } t | � r | n t | � Vq d S)N)r
�id)�.0�argr r r � <genexpr>( s z+_memoize.<locals>.lookup.<locals>.<genexpr>)�tuple�get)�args�key�result)�cache�fr r �lookup' s
z_memoize.<locals>.lookupr )r r r )r r r �_memoize s
r c sZ t � f d d � � } t � � f d d � � } t � � f d d � � } t d d � � } | d k r� t j � } | j � nB t | j j � } t j t j | j | � � � } t j | � � t � j � � x? | j � D]1 \ } } t
| � r| | � n | g | | <q� Wx� | j � D]� \ }
} |
\ } } � j | � }
� j
|
| � } | | k r�| | j | |
| � � q%| | k s�t
| � r�| |
| � } n | | f | k r�| | | f j | � q%| g | | | f <q%Wi } xX t j | j � | j � � D]8 \ } } t | � d
k rB| d n | | � | | <qW| S) a@ Replace translational symmetries by momentum parameters.
A new Builder instance is returned. By default, each symmetry is replaced
by one scalar momentum parameter that is appended to the already existing
arguments of the system. Optionally, one symmetry may be kept by using the
`keep` argument.
c s% t � � s t � � � f d d � S)Nc s � | | d � � � S)Nr )�ar )�mnp�valr r �<lambda>= s z/wraparound.<locals>.bind_site.<locals>.<lambda>)�callable�AssertionError)r )r )r r � bind_site: s z wraparound.<locals>.bind_sitec s � � � � f d d � } | S)Nc s{ t j d t j � | � d � � � } t � � r] � | � j � | � | d � � � n � } | | } | t | � S)Ny �?)�cmath�exp�ta�dotr �actr )r r �phase�v�pv)�elemr �symr r r r A s ):
z3wraparound.<locals>.bind_hopping_as_site.<locals>.fr )r) r r )r r* )r) r r �bind_hopping_as_site? s z(wraparound.<locals>.bind_hopping_as_sitec s � � � � f d d � } | S)Nc sk t j d t j � | � d � � � } t � � r] � | � j � | � | d � � � n � } | | S)Ny �?)r! r" r# r$ r r% )r �br r& r' )r) r r* r r r r J s ):z+wraparound.<locals>.bind_hopping.<locals>.fr )r) r r )r r* )r) r r � bind_hoppingH s z wraparound.<locals>.bind_hoppingc s � f d d � S)Nc s t � f d d � � D� � S)Nc 3 s- | ]# } t | � r! | � � n | Vq d S)N)r )r r )r r r r R s zAwraparound.<locals>.bind_sum.<locals>.<lambda>.<locals>.<genexpr>)�sum)r )�vals)r r r R s z.wraparound.<locals>.bind_sum.<locals>.<lambda>r )r/ r )r/ r �bind_sumP s z wraparound.<locals>.bind_sumN� r )r �kwant�Builder�symmetry�list�periods�TranslationalSymmetry�pop�len�site_value_pairsr �hopping_value_pairs�whichr% �append� itertools�chain)�builder�keepr r+ r- r0 �retr6 �siter �hopr r, Zb_domZb_waZ summed_valsZ site_or_hopr/ r )r r* r �
wraparound1 s: !) 0rE � c sL d d l m } d d l m } t � t j j � sD t d � � n | j � } | j
d d � } t j t j
t j
| d � } t j t j
t j
| d � � � � � f d d � | D� } t j | � } t j | � � \ } }
xS t | j d
� D]> } | j | |
| d
d
� d
d
� | f d d d d �q� W| j � d
S)z>Plot the bands of a system with two wrapped-around symmetries.r )�Axes3D)�pyplotz!Need a system without symmetries.�
projection�3dr1 c s/ g | ]% � � � � f d d � � D� � q S)c sG g | ]= } t j t j j � j � � | f d d �� j � � q S)�sparseF)r �sort�linalg�eigvalsh�hamiltonian_submatrix�real)r �ky)r �kx�systr r �
<listcomp>� s z,plot_bands_2d.<locals>.<listcomp>.<listcomp>r )r )r �kysrS )rR r rT � s z!plot_bands_2d.<locals>.<listcomp>N�rstride�cstride�����)�mpl_toolkits.mplot3drG �
matplotlibrH r r2 �system� FiniteSystem� TypeError�figure�gcar �linspace�pi�array�meshgrid�range�shape�plot_wireframe�show) rS r �momentarG rH �fig�axZkxs�energiesZmesh_xZmesh_y�ir )r rU rS r �
plot_bands_2d� s
+rm r1 c C sf t j | j d � | j d � � } t j | � } | | | j d d � d � <| | | j d � <| S)z.Create a builder for a simple infinite system.r1 r c S s d S)NTr )�pr r r r � s z _simple_syst.<locals>.<lambda>)r1 r )r r1 )r r )r2 r7 �vecr3 re � neighbors)�lat�E�tr* rS r r r � _simple_syst� s
$ rt gffffff�?c s; t j t j t j | � } xt j j � t j j � g D]� } t | � } t | d d �j � } t | � j � } t j
j | | f � � � f d d � t j d k r� | n t
| � D� } g } xT | D]L } | j | | f d d �}
t j t j j |
� j � } | j | � q� Wt j j | | � q; Wd S)NrA r1 c s g | ] } � | � � q Sr r )r rQ )�bandsr r rT � s z/test_consistence_with_bands.<locals>.<listcomp>z1.0rK F)r r` ra r2 �lattice� honeycomb�squarert rE � finalized�physics�Bands� __version__�reversedrO rL rM rN rP r= �testing�assert_almost_equal) rR ZnkysrU rq rS Z wa_keep_1Z wa_keep_noneZ
energies_aZ
energies_brQ �HZevsr )ru r �test_consistence_with_bands� s % %
r� g�������?� �?c sr xkt j j � t j j � g D]K} t t | | | � � j � } | j | d d �} xt | � t | � f t j
| g g t � t j
d g g t � f t j
| g g t � t j
d g g t � f g D]� \ � � x� � � f d d � g D]o } xf � � f d d � g D]L } t t | | | � � j � } | j | d d �} t j j
| | � qWq� Wq� Wq Wd S)NrK Fr1 c s � S)Nr )r )�E1r r r � s z"test_value_types.<locals>.<lambda>c s � S)Nr )r r, )�t1r r r � s )r2 rv rw rx rE rt ry rO �floatr rb r# r~ � assert_equal) �krr rs rq rS r� ZE2�t2ZH_altr )r� r� r �test_value_types� s % -= r� c C s t � t � d S)N)r� r� r r r r �test� s r� c C s5 t j j � } t t | � � j � } t | � d S)z2Calculate and plot the band structure of graphene.N)r2 rv rw rE rt ry rm )rq rS r r r �demo� s r� �__main__)r r )rF rF 皙�����)r� r� )�__doc__�sysr> r r! �numpyr � tinyarrayr# r2 Z
kwant.builderr � version_infor
r rE rm rt r� r� r� r� �__name__r r r r �<module> s, P 