def csl_elem_div_thm_l2(t0, l_g2n_g2):
"""
The csl basis vectors are obtained from the diagonal matrix using the
algorithm specified in doi:10.1107/S056773947601231X. There are two
algorithms specified based on numerators or denominators of the T0 matrix.
The denominators are used in this function.
Parameters
---------------
T0: numpy array
The transformation matrix in G1n reference frame
l_g2n_g2: numpy array
The 'new' basis vectors of g2 lattice (g2n) in g2 reference frame
Returns
------------
l_csl_g2: numpy array
The CSL basis vectors in g2 reference frame
"""
t0 = np.array(t0)
l2 = np.array(l_g2n_g2)
if t0.shape[0] == 3:
q1 = int_man.rat(np.array(t0[0, 0]), 1e-06)[1][0][0]
q2 = int_man.rat(np.array(t0[1, 1]), 1e-06)[1][0][0]
q3 = int_man.rat(np.array(t0[2, 2]), 1e-06)[1][0][0]
l_csl_g2 = np.dot(l2, np.array([[q1, 0, 0], [0, q2, 0], [0, 0, q3]]))
elif t0.shape[0] == 2:
q1 = int_man.rat(np.array(t0[0, 0]), 1e-06)[1][0][0]
q2 = int_man.rat(np.array(t0[1, 1]), 1e-06)[1][0][0]
l_csl_g2 = np.dot(l2, np.array([[q1, 0, 0], [0, q2, 0]]))
return l_csl_g2
def csl_elem_div_thm_l1(T0, l_g1n_g1):
"""
The csl basis vectors are obtained from the diagonal matrix using the
algorithm specified in doi:10.1107/S056773947601231X. There are two
algorithms specified based on numerators or denominators of the T0 matrix.
The numerators are used in this function.
Parameters
---------------
T0: numpy array
The transformation matrix in G1n reference frame
l_g1n_g1: numpy array
The 'new' basis vectors of g1 lattice (g1n) in g1 reference frame
Returns
------------
l_csl_g1: numpy array
The CSL basis vectors in g1 reference frame
"""
T0 = np.array(T0)
L1 = np.array(l_g1n_g1)
if T0.shape[0] == 3:
p1 = int_man.rat(np.array(T0[0, 0]), 1e-06)[0][0][0]
p2 = int_man.rat(np.array(T0[1, 1]), 1e-06)[0][0][0]
p3 = int_man.rat(np.array(T0[2, 2]), 1e-06)[0][0][0]
l_csl_g1 = np.dot(L1, np.array([[p1, 0, 0], [0, p2, 0], [0, 0, p3]]))
elif T0.shape[0] == 2:
p1 = int_man.rat(np.array(T0[0, 0]), 1e-06)[0][0][0]
p2 = int_man.rat(np.array(T0[1, 1]), 1e-06)[0][0][0]
l_csl_g1 = np.dot(L1, np.array([[p1, 0, 0], [0, p2, 0]]))
return l_csl_g1
def sigma_calc(t_g1tog2_g1):
"""
Computes the sigma of the transformation matrix
* if det(T) = det(T^{-1}) then sigma1 = sigma2 is returned
* if det(T) \\neq det(T^{-1}) then max(sigma1, sigma2) is returned
"""
R = np.array(t_g1tog2_g1)
R2 = np.linalg.det(R)*np.linalg.inv(R)
n1, d1 = int_man.rat(R)
n2, d2 = int_man.rat(R2)
# -----------------------------
Sigma21 = int_man.lcm_array(d1[:])
# -----------------------------
Sigma22 = int_man.lcm_array(d2[:])
Sigma = np.array([Sigma21, Sigma22]).max()
return Sigma
sig_type = 'specific'
ca_rat = 3
lat_type = 'tP_ca'
l1 = lat.Lattice(lat_type, ca_rat)
elif test_case == 6:
sig_type = 'common'
lat_type = 'cI_Id'
l1 = lat.Lattice(lat_type)
sig_rots = {}
sig_num = np.arange(1000) + 1
for i in sig_num:
print i
sig_rots[str(i)] = csl_util.csl_rotations(i, sig_type, l1)
if sig_type == 'common':
pkl_file = l1.elem_type + '_csl_' + sig_type + '_rotations' + '.pkl'
jar = open(pkl_file, 'wb')
pickle.dump(sig_rots, jar)
jar.close()
if sig_type == 'specific':
lat_tau = l1.lat_params['a']**2/l1.lat_params['c']**2
[N, D] = int_man.rat(lat_tau)
pkl_file = l1.elem_type + '_csl_' + sig_type + \
'_tau_'+str(N[0][0])+'_'+str(D[0][0])+'_rotations' + '.pkl'
jar = open(pkl_file, 'wb')
pickle.dump(sig_rots, jar)
jar.close()
sig_type = 'specific'
ca_rat = 3
lat_type = 'tP_ca'
l1 = lat.Lattice(lat_type, ca_rat)
elif test_case == 6:
sig_type = 'common'
lat_type = 'cP_Id'
l1 = lat.Lattice(lat_type)
sig_rots = {}
sig_num = np.arange(100) + 1
for i in sig_num:
print i
sig_rots[str(i)] = csl_util.csl_rotations(i, sig_type, l1)
if sig_type == 'common':
pkl_file = l1.elem_type + '_csl_' + sig_type + '_rotations' + '.pkl'
jar = open(pkl_file, 'wb')
pickle.dump(sig_rots, jar)
jar.close()
if sig_type == 'specific':
lat_tau = l1.lat_params['a']**2/l1.lat_params['c']**2
[N, D] = int_man.rat(lat_tau)
pkl_file = l1.elem_type + '_csl_' + sig_type + \
'_tau_'+str(N[0][0])+'_'+str(D[0][0])+'_rotations' + '.pkl'
jar = open(pkl_file, 'wb')
pickle.dump(sig_rots, jar)
jar.close()