def rhom_9_24(n):
"""Finds the symmetry preserving HNFs for the trigonal lattices
with a determinant of n. Assuming A = [[1,2,2],[2,1,2],[4,3,3]] for basis 9
A = [[-0.255922,-1.44338,0.92259],[1.51184,0,-0.845178],[1.255922,1.44338,0.07741]]
for basis 24.
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#alpha3 condition
if f%a==0:
#beta1 condition
if c%2==0:
bs = [0,c/2]
else:
bs = [0]
for b in bs:
#beta3 condition
beta13 = f+b*f/float(a)
if beta13%c==0:
#find e values alpha2 condition
e = 0
while (e<f):
beta22 = e+b*e/float(a)
g21= c+2*e
g11 = b+2*b*e/float(c)
if beta22%c==0 and g21%f==0 and g11%f==0:
#find d from alpha1 condition
d = 0
while (d<f):
#beta2 condition
beta12 = -a+b+d+d*b/float(a)
g12 = -b-d+d*d/float(a)-e*beta12/float(c)
g22 = -c-2*e+d*e/float(a)-e*beta22/float(c)
if beta12%c==0 and g12%f==0 and g22%f==0:
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
d += a
e += a
return spHNFs
def hex_12(n):
"""Finds the symmetry preserving HNFs for the hexagonal lattices
with a determinant of n. Assuming A = [[1,0,0],[0.5,-0.8660254037844386,0],[0,0,2]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#alpha2 condition
if c % a == 0:
b = 0
#alpha1 condition
while (b < c):
beta13 = a + 2 * b
beta11 = 2 * b + b * b / float(a)
if beta13 % c == 0 and beta11 % c == 0:
#gamma2 condition
if f % 2 == 0:
es = [0, f / 2]
else:
es = [0]
for e in es:
gamma13 = (a + 2 * b) * e / float(c)
if gamma13 % f == 0:
for d in range(f):
gamma11 = b * d / float(
a) - e * beta11 / float(c)
gamma12 = 2 * d + b * d / float(
a) - e * beta11 / float(c)
gamma21 = c * d / float(
a) - 2 * e - b * e / float(a)
gamma22 = (c * d - b * e) / float(a)
if gamma11 % f == 0 and gamma12 % f == 0 and gamma21 % f == 0 and gamma22 % f == 0:
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
spHNFs.append(HNF)
b += a
return spHNFs
def body_ortho_19(n):
"""Finds the symmetry preserving HNFs for the body centered
orthorhombic lattices with a determinant of n. Assuming A =
[[0.5,1,1.5],[0,2,0],[0,0,3]] (3rd basis choince in
notes/body_centered_ortho).
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#beta1 condition
if c%2==0:
bs = [0,c/2]
else:
bs = [0]
#gamma1 and gamma2 conditions
if f%2==0:
es = [0,f/2]
else:
es = [0]
for b in range(c):
#beta1 condition
beta13 = a+2*b
if beta13%c==0:
for e in es:
#gamma1 condition
gamma13 = e*beta13/float(c)
if gamma13%f==0:
for d in range(f):
#gamma1 condition
gamma12 = a+2*d
if gamma12%f==0:
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
return spHNFs
def stet_11(n):
"""Finds the symmetry preserving HNFs for the simple tetragonal lattices
with a determinant of n. Assuming A = [[1,0,0],[0,1,0],[0,0,2]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#alpha2 condition
if c % a == 0:
#use beta1 condition (c divisible by 2) and gamma2
#condition (f divisible by 2) to find b and e vals.
if c % 2 == 0:
bs = [0, c / 2]
else:
bs = [0]
if f % 2 == 0:
es = [0, f / 2]
else:
es = [0]
#loop over values for e and b.
for b in bs:
#alpha1 condition
if b % a == 0:
beta13 = -a + b * b / float(a)
if beta13 % c == 0:
for e in es:
g12 = 2 * b * e / float(c)
if g12 % f == 0:
for d in range(f):
g13 = -e * beta13 / float(c) + d * (
b / float(a) - 1)
g23 = -e * (b / float(a) +
1) + d * c / float(a)
if g13 % f == 0 and g23 % f == 0:
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
spHNFs.append(HNF)
return spHNFs
def body_tet_6_7_15_18(n):
"""Finds the symmetry preserving HNFs for the body centered tetragonal
lattices with a determinant of n. Assuming :
A = [[1.80278,-1.47253,0.762655],[2.80278,0.13535,-0.791285],
[0.80278,-0.47253,2.762655]] for 6,
A = [[1.95095, 1.19163, 0.879663],[0.0, 2.60788, 0.44606],
[0.95095, -0.41625, 2.433603]] for 7,
A = [[-1.0,-1.0,2.0],[0.0,-2.0,0.0],[-2.0,0.0,0.0]] for 15,
A = [[-2.0,-1.0,1.0],[-3.0,1.0,0.0],[-1.0,-3.0,0.0]] for 18.
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if f % c == 0:
if f % 2 == 0:
es = [0, f // 2.]
else:
es = [0]
for e in es:
if e % c == 0:
g21 = -c + (e * e / float(c))
if g21 % f == 0:
for d in range(f):
g13 = a + 2 * d
if g13 % f == 0:
for b in range(c):
b12 = b - d
if b12 % c == 0:
g12 = -b + d - (b12 * e / float(c))
if g12 % f == 0:
HNF = [[a, 0, 0], [b, c, 0],
[d, e, f]]
spHNFs.append(HNF)
return spHNFs
def rhom_4_2(n):
"""Finds the symmetry preserving HNFs for the rhombohedral lattice
that matches niggli conditions for niggli cells number 2 and 4
with a determinant of n. Assuming A =
[[-1.11652,-0.610985,0.616515],[0.0,-1.32288,-0.5],[1.0,1.32288,1.5]]
for basis 2 and A =
[[-0.548584,0.774292,1.04858],[0.0,-1.32288,0.5],[1.0,1.32288,0.5]]
for basis 4.
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
# conditions alpha 3 and betta3
if f%a == 0:
if c%2==0:
bs = [0,c/2]
else:
bs = [0]
for b in bs:
beta32 = -f+b*f/float(a)
if beta32%c==0:
for e in range(f):
beta22 = -e+b*e/float(a)
gamma11 = b-2*b*e/float(c)
gamma21 = c-2*e
if e%a==0 and beta22%c==0 and gamma11%f==0 and gamma21%f==0:
for d in range(f):
beta12 = -a+b-d+b*d/float(a)
gamma12 = -a+d*d/float(a)-e*beta12/float(c)
gamma22 = -e+d*e/float(a)-e*beta22/float(c)
if d%a==0 and beta12%c==0 and gamma12%f==0 and gamma22%f==0:
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
return spHNFs
def base_ortho_36(n):
"""Finds the symmetry preserving HNFs for the base centered
orthorhombic lattices with a determinant of n. Assuming A = [[1,
1, 1], [1.41421, -1.41421, 0], [-1.43541, -1.43541, 1.37083]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if f%a==0:
if f%2==0:
es = [0,f//2.]
else:
es = [0]
if c%2==0:
bs = [0,c//2.]
else:
bs = [0]
for b in bs:
b32 = -b*f/float(a)
if b32%c==0:
for e in es:
b22 = -b*e/float(a)
g13 = -2*b*e/float(c)
if b22%c==0 and g13%f==0 and e%a==0:
for d in range(0,f,a):
b12 = -b*d/float(a)
g12 = 2*d-d*d/float(a)-b12*e/float(c)
g22 = 2*e-d*e/float(a)-b22*e/float(c)
if b12%c==0 and g12%f==0 and g22%f==0:
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
return spHNFs
def base_ortho_38_13(n):
"""Finds the symmetry preserving HNFs for the base centered
orthorhombic lattices with a determinant of n. Assuming A =
[[0.5,1,0],[0.5,-1,0],[0,0,3]] (1st basis choince in
notes/base_ortho) for case 38 and A = [[ 1. , 1. , 1. ], [ 1.
, -1. , -1. ], [ 0. , -1.73205, 1.73205]] for case 13.
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#alpha2 condition
if c%a==0:
#gamma1 and gamma2 conditions
if f%2==0:
ed_vals = [0,f/2]
else:
ed_vals = [0]
b=0
#alhpa1 condition
while (b<c):
#beta1 condition
beta13=-a+b*b/float(a)
if beta13%c==0:
for e in ed_vals:
for d in ed_vals:
#gamma1 and gamma2 conditions
g13 = -d+b*d/float(a) -e*beta13/float(c)
g23 = c*d/float(a)-e-b*e/float(a)
if g13%f==0 and g23%f==0:
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
b += a
return spHNFs
def base_ortho_23(n):
"""Finds the symmetry preserving HNFs for the base centered
orthorhombic lattices with a determinant of n. Assuming A =
[[-0.3333333, -1.54116 , 1.87449 ], [ 1. , 1. , 1. ], [ 2. ,
-1. , -1. ]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if f%a==0:
if c%2==0:
bs = [0,c//2.]
else:
bs = [0]
if f%2==0:
es = [0,f//2.]
else:
es = [0]
for b in bs:
if b*f%(a*c)==0:
for e in es:
if b*e%(a*c)==0 and 2*b*e%(c*f)==0 and e%a==0:
for d in range(0,f,a):
b13 = -b+b*d/float(a)
g13 = -a+d*d/float(a)-b13*e/float(c)
g23 = e+d*e/float(a)-b*e*e/float(a*c)
if b13%c==0 and g13%f==0 and g23%f==0:
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
return spHNFs
def stet_21(n):
"""Finds the symmetry preserving HNFs for the simple tetragonal
lattices with a determinant of n in Niggli setting 21. Assuming A
= [[0,0,0.5],[1,0,0],[0,1,0]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if f % c == 0:
if c % 2 == 0:
bs = [0, c / 2]
else:
bs = [0]
for b in bs:
if f % 2 == 0: #This condition reached by inspection
es = [0, f / 2]
else:
es = [0]
for d in es:
b13 = b - d
if b13 % c == 0:
for e in es:
g12 = 2 * d - 2 * d * e / float(c)
g13 = -b + d - b13 * e / float(c)
g23 = -c + e * e / float(c)
if g12 % f == 0 and g13 % f == 0 and g23 % f == 0:
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
spHNFs.append(HNF)
return spHNFs
def sm_33(n):
"""Finds the symmetry preserving HNFs for the simple monoclinic
lattices with a determinant of n. Assuming A =
[[2,0,0],[0,2,0],[0.5,0,2]].
Args:
n (int): The determinant of the HNFs.
Returns:
srHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
srHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#beta1 condition
if c % 2 == 0:
bs = [0, c / 2]
else:
bs = [0]
#gamma2 condition
if f % 2 == 0:
es = [0, f / 2]
else:
es = [0]
for b in bs:
for e in es:
#gamma1 condition and gamma1 condition
gamma12 = 2 * b * e / float(c)
if gamma12 % f == 0:
for d in range(f):
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
srHNFs.append(HNF)
return srHNFs
def body_ortho_8(n):
"""Finds the symmetry preserving HNFs for the body centered
orthorhombic lattices with niggli setting 8 a determinant of
n. Assuming A = [[ 1.41144 , 0.0885622, -2. ], [-0.99868 ,
2.21232 , 1.268178 ], [ 3.41012 , -1.1237578, -1.268178 ]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if 2*f%c==0:
if c%2==0:
bs = [0,c//2.]
else:
bs = [0]
for b in bs:
for e in range(f):
b21 = 2*e
g21 = -b21+b21*e/float(c)
if b21%c==0 and g21%f==0:
for d in range(f):
b11 = -a+2*b-2*d
g11 = -b11*e/float(c)
g13 = a+2*d-b21*b/float(c)
if b11%c==0 and g11%f==0 and g13%f==0:
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
return spHNFs
def base_mono_10_14_17_27_37_39_41(n):
"""Finds the symmetry preserving HNFs for the base centered monoclinic
lattices with a determinant of n. Assuming:
for basis 10 A = [[1, -1, 1],[-1.46391, 0, 1.96391],[0, 2, 0]],
for basis 14 A = [[-1,1,0],[0.5,0,2],[0,-2,0]],
for basis 17 A = [[-1.05387,-1.61088,1.51474],[-0.244302,-2.77045,0.51474],[1.809568,-0.15957,0.0]]
for basis 27 A = [[-1.464824,0.464824,1.907413],[-0.153209,0.153209,-2.907413],[1.0,1.0,0.0]],
for basis 37 A = [[-1.79092,-1.47209,0.790922],[1.0,-1.41421,-1.0],[1.0,0.0,1.0]],
for basis 39 A = [[0, -1.73205,-1],[-1.66542, -0.672857, 1.66542], [1,0,1]],
for basis 41 A = [[-1.85397, -0.854143, 1.35397],[1, 0, 1],[1, -1.41421, -1]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#gamma 2
if f % 2 == 0:
es = [0, f // 2]
else:
es = [0]
for e in es:
for d in range(f):
g11 = -a + 2 * d
if g11 % f == 0:
for b in range(c):
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
spHNFs.append(HNF)
return spHNFs
def body_ortho_42(n):
"""Finds the symmetry preserving HNFs for the body centered
orthorhombic lattices with niggli setting 42 a determinant of
n. Assuming A = [[-1.53633, 1.36706, -1.33073], [ 1. , 1. , 1.
], [ 1.61803, -0.61803, -1. ]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if f%2==0:
es = [0,f//2]
else:
es = [0]
for e in es:
for b in range(c):
b11 = -a+2*b
g12 = -b11*e/float(c)
if b11%c==0 and g12%f==0:
for d in range(f):
g11 = -a+2*d-b11*e/float(c)
g13 = -a+2*d
if g11%f==0 and g13%f==0:
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
return spHNFs
def bcc_5(n):
"""Finds the symmetry preserving HNFs for the base centered cubic lattices
with a determinant of n. Assuming A = [[-1,1,1],[1,-1,1],[1,1,-1]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if a==c and a==f:
b = 0
d = 0
e = 0
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
elif a==c and f/float(a)==2:
b = 0
d = a
e = a
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
elif a==c and f/float(a)==4:
b=0
d= 3*a
e = 3*a
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
return spHNFs
def face_ortho_26(n):
"""Finds the symmetry preserving HNFs for the face centered
orthorhombic lattices with a determinant of n. Assuming A =
[[0,1,1.5],[0.5,0,1.5],[0,0,3]] (10th basis choince in
notes/body_centered_ortho).
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#beta1 candition
if c%2==0:
bs = [0,c/2]
else:
bs = [0]
for b in bs:
for e in range(f):
#gamma2 condition and gamma1 condition
gamma23 = c+2*e
gamma12 = b+2*b*e/float(c)
if gamma23%f==0 and gamma12%f==0:
for d in range(f):
#gamma1 condition
gamma13 = a+b+2*d
if gamma13%f==0:
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
return spHNFs
def base_mono_20_25(n):
"""Finds the symmetry preserving HNFs for the base centered monoclinic
lattices with a determinant of n. Assuming for basis 20 A = [[ 1.
, 1. , 1. ], [ 1.70119 , -1.45119 , 1. ], [ 0.69779 ,
-1.4322505, 3.23446 ]], for basis 25 A = [[ 1. , 1. , 1. ], [
1.45119, -1.70119, -1. ], [ 0.28878, -3.26895, 0.48018]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if c % 2 == 0:
bs = [0, c // 2.]
else:
bs = [0]
for e in range(f):
g22 = -c - 2 * e
if g22 % f == 0:
for b in bs:
g12 = -b - 2 * b * e / float(c)
if g12 % f == 0:
for d in range(f):
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
spHNFs.append(HNF)
return spHNFs
def so_32(n):
"""Finds the symmetry preserving HNFs for the simple orthorhombic lattices
with a determinant of n. Assuming A = [[1,0,0],[0,2,0],[0,0,3]].
Args:
n (int): The determinant of the HNFs.
Returns:
srHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
srHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#beta1 condition
if c % 2 == 0:
bs = [0, c / 2]
else:
bs = [0]
#gamma1 and gamma2 condition
if f % 2 == 0:
ed_vals = [0, f / 2]
else:
ed_vals = [0]
for b in bs:
for e in ed_vals:
#gamma1 condition
if (2 * b * e) % (f * c) == 0:
for d in ed_vals:
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
srHNFs.append(HNF)
return srHNFs
def sm_34(n):
"""Finds the symmetry preserving HNFs for the simple monoclinic
lattices with a determinant of n. Assuming A =
[[1,1,1],[1.22474487,-1.22474487,-1],[-0.16598509,-1.64308297,1.80906806]].
Args:
n (int): The determinant of the HNFs.
Returns:
srHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
srHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#gamma1 condition
if f % 2 == 0:
ds = [0, f / 2]
else:
ds = [0]
#gamma2 condition
if f % 2 == 0:
es = [0, f / 2]
else:
es = [0]
for d in ds:
for e in es:
for b in range(c):
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
srHNFs.append(HNF)
return srHNFs
def face_ortho_16(n):
"""Finds the symmetry preserving HNFs for the face centered
orthorhombic lattices with a niggli cell of 26 and a determinant
of n. Assuming A = [[1.04442, 1.43973, 1.68415], [0.779796, -1.1789, 1.0
], [1.779796, -0.1789, 0]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs=[]
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#beta 1 condition
if c%2==0:
bs = [c/2,0]
else:
bs = [0]
#gamma 1 condition
for b in bs:
for e in range(f):
g11=-b-2*b*e/float(c)
g21=c+2*e
if g11%f==0 and g21%f==0:
for d in range(f):
g12=a+2*d-(2*b*e)/float(c)
if g12%f==0:
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
return spHNFs
def base_ortho_40(n):
"""Finds the symmetry preserving HNFs for the base centered
orthorhombic lattices with a determinant of n. Assuming A = [[ 1.
, 1. , 1. ], [ 1.61803 , -0.618034, -1. ], [-1.05557 , 1.99895
, -0.943376]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if f%c==0:
for e in range(0,f,c):
g22 = 2*e-e*e/float(c)
if g22%f==0:
for d in range(0,f,c):
g12 = 2*d-d*e/float(c)
if g12%f==0:
for b in range(c):
b13 = 2*b-d
g13 = b13*e/float(c)
if b13%c==0 and g13%f==0:
HNF = [[a,0,0],[b,c,0],[d,e,f]]
spHNFs.append(HNF)
return spHNFs
def sm_35(n):
"""Finds the symmetry preserving HNFs for the simple monoclinic
lattices with a determinant of n. Assuming A =[[-0.668912,1.96676,-1.29785],
[1.61803,-0.618034,-1.0],[1.0,1.0,1.0]]
Args:
n (int): The determinant of the HNFs.
Returns:
srHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
srHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
#gamme12 and gamma22
if f % 2 == 0:
ds = [0, f / 2]
es = [0, f / 2]
else:
ds = [0]
es = [0]
for e in es:
for d in ds:
for b in range(c):
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
srHNFs.append(HNF)
return srHNFs
def base_mono_29_30(n):
"""Finds the symmetry preserving HNFs for the base centered monoclinic
lattices with a determinant of n. Assuming for basis 29 A =
[[-0.666125, 1.16613 , 2.04852 ], [ 1. , 1. , 0. ], [ 1.61803 ,
-0.618034, 1. ]], for basis 30 A = [[ 1. , 1. , 0. ], [
1.61803 , -0.618034 , 1. ], [-0.0361373, 0.536137 , 2.38982 ]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if f % c == 0:
for e in range(0, f, c):
g21 = 2 * e + e * e / float(c)
if g21 % f == 0:
for d in range(0, f, c):
g11 = 2 * d + d * e / float(c)
if g11 % f == 0:
for b in range(c):
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
spHNFs.append(HNF)
return spHNFs
def base_mono_43(n):
"""Finds the symmetry preserving HNFs for the base centered monoclinic
lattices with a determinant of n. Assuming A = [[-0.39716,
-0.34718, 2.49434], [ 2.64194, -0.14194, 0. ], [-1.39716,
-1.34718, 1.49434]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if f % c == 0:
for e in range(0, f, c):
g22 = 2 * e - e * e / float(c)
if g22 % f == 0:
for d in range(f):
b12 = a + d
g12 = 2 * a + 2 * d - b12 * e / float(c)
if b12 % c == 0 and g12 % f == 0:
for b in range(c):
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
spHNFs.append(HNF)
return spHNFs
def base_mono_28(n):
"""Finds the symmetry preserving HNFs for the base centered monoclinic
lattices with a determinant of n. Assuming A = [[-1.44896 ,
0.948958, -1. ], [-1. , -1. , 0. ], [ 0.342424, -1.342424,
-2.02006 ]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if f % c == 0:
for e in range(0, f, c):
g21 = 2 * e + e * e / float(c)
if g21 % f == 0:
for d in range(0, f, c):
g11 = 2 * d + d * e / float(c)
if g11 % f == 0:
for b in range(c):
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
spHNFs.append(HNF)
return spHNFs
def hex_22(n):
"""Finds the symmetry preserving HNFs for the hexagonal lattices
with a determinant of n. Assuming A = [[0,0,-0.5],[1,0,0],[-0.5,0.8660254037844386,0]].
Args:
n (int): The determinant of the HNFs.
Returns:
spHNFs (list of lists): The symmetry preserving HNFs.
"""
from opf_python.universal import get_HNF_diagonals
diags = get_HNF_diagonals(n)
spHNFs = []
for diag in diags:
a = diag[0]
c = diag[1]
f = diag[2]
if f % c == 0:
for e in range(0, f, c):
g21 = -c + 2 * e
g22 = -c + e - e * e / float(c)
if g21 % f == 0 and g22 % f == 0 and e % c == 0:
for b in range(c):
for d in range(0, f, c):
g11 = -b + 2 * d
g12 = -b + d - d * e / float(c)
if g11 % f == 0 and g12 % f == 0:
HNF = [[a, 0, 0], [b, c, 0], [d, e, f]]
spHNFs.append(HNF)
return spHNFs
