def Mlm_matrix_elememt_gen(self, X_p, a_p, p):
pow_max = self.mu.pow + self.nu.pow
C_t = np.zeros(pow_max[0] + 1)
for t in range(0, pow_max[0] + 1):
for i in range(max(0, t - self.nu.pow[0]),
min(self.mu.pow[0], t) + 1):
C_t[t] += binom(self.mu.pow[0], i) * np.power(X_p[0] - self.mu.x[0], self.mu.pow[0]-i) \
* binom(self.nu.pow[0], t-i) * np.power(X_p[0] - self.nu.x[0], self.nu.pow[0]-t+i)
#print("t=", t, "; C_t=", C_t[t])
C_u = np.zeros(pow_max[1] + 1)
for t in range(0, pow_max[1] + 1):
for i in range(max(0, t - self.nu.pow[1]),
min(self.mu.pow[1], t) + 1):
C_u[t] += binom(self.mu.pow[1], i) * np.power(X_p[1] - self.mu.x[1], self.mu.pow[1]-i) \
* binom(self.nu.pow[1], t-i) * np.power(X_p[1] - self.nu.x[1], self.nu.pow[1]-t+i)
#print("u=", t, "; C_u=", C_u[t])
C_v = np.zeros(pow_max[2] + 1)
for t in range(0, pow_max[2] + 1):
for i in range(max(0, t - self.nu.pow[2]),
min(self.mu.pow[2], t) + 1):
C_v[t] += binom(self.mu.pow[2], i) * np.power(X_p[2] - self.mu.x[2], self.mu.pow[2]-i) \
* binom(self.nu.pow[2], t-i) * np.power(X_p[2] - self.nu.x[2], self.nu.pow[2]+i-t)
#print("v=", t, "; C_v=", C_v[t])
Mlm = Vlm(p)
for t in range(0, len(C_t)):
for u in range(0, len(C_u)):
for v in range(0, len(C_v)):
Mlm_G_tuv = ggq_dist(X_p, a_p, C_t[t] * C_u[u] * C_v[v],
[t, u, v])
Mlm.added_to_self(Mlm_G_tuv.Mlm_init(p))
return Mlm
def Mlm_matrix_elememt_gen(self, X_p, a_p, p):
pow_max = self.mu.pow + self.nu.pow
C_t = np.zeros(pow_max[0]+1)
for t in range(0, pow_max[0]+1):
for i in range(max(0, t-self.nu.pow[0]), min(self.mu.pow[0], t)+1):
C_t[t] += binom(self.mu.pow[0], i) * np.power(X_p[0] - self.mu.x[0], self.mu.pow[0]-i) \
* binom(self.nu.pow[0], t-i) * np.power(X_p[0] - self.nu.x[0], self.nu.pow[0]-t+i)
#print("t=", t, "; C_t=", C_t[t])
C_u = np.zeros(pow_max[1]+1)
for t in range(0, pow_max[1]+1):
for i in range(max(0, t-self.nu.pow[1]), min(self.mu.pow[1], t)+1):
C_u[t] += binom(self.mu.pow[1], i) * np.power(X_p[1] - self.mu.x[1], self.mu.pow[1]-i) \
* binom(self.nu.pow[1], t-i) * np.power(X_p[1] - self.nu.x[1], self.nu.pow[1]-t+i)
#print("u=", t, "; C_u=", C_u[t])
C_v = np.zeros(pow_max[2]+1)
for t in range(0, pow_max[2]+1):
for i in range(max(0, t-self.nu.pow[2]), min(self.mu.pow[2], t)+1):
C_v[t] += binom(self.mu.pow[2], i) * np.power(X_p[2] - self.mu.x[2], self.mu.pow[2]-i) \
* binom(self.nu.pow[2], t-i) * np.power(X_p[2] - self.nu.x[2], self.nu.pow[2]+i-t)
#print("v=", t, "; C_v=", C_v[t])
Mlm = Vlm(p)
for t in range(0, len(C_t)):
for u in range(0, len(C_u)):
for v in range(0, len(C_v)):
Mlm_G_tuv = ggq_dist(X_p, a_p, C_t[t]*C_u[u]*C_v[v], [t, u, v])
Mlm.added_to_self(Mlm_G_tuv.Mlm_init(p))
return Mlm
def Mlm_init(self, p):
self.Mlm = Vlm(p)
v = self.pow[2]
if self.pow[0] < self.pow[1]:
t = self.pow[1]
u = self.pow[0]
else:
t = self.pow[0]
u = self.pow[1]
factor1 = np.power(np.pi / self.a, 3 / 2)
factor2 = 1 / (2 * self.a)
if t == 0 and u == 0 and v == 0:
self.Mlm.setlm(0, 0, self.k * factor1)
elif t == 1 and u == 0 and v == 0:
w11 = -self.k * factor2 * factor1 / 2
self.Mlm.setlm(1, 1, w11)
elif t == 0 and u == 0 and v == 1:
w10 = self.k * factor2 * factor1
self.Mlm.setlm(1, 0, w10)
elif t == 2 and u == 0 and v == 0:
w00 = self.k * factor2 * factor1
w20 = -w00 * factor2 / 2
w22 = -w20 / 2
self.Mlm.setlm(0, 0, w00)
self.Mlm.setlm(2, 0, w20)
self.Mlm.setlm(2, 2, w22)
elif t == 1 and u == 1 and v == 0:
w22 = -self.k * (factor2**2) * factor1 * 1j / 4
self.Mlm.setlm(2, 2, w22)
elif t == 1 and u == 0 and v == 1:
w21 = -self.k * (factor2**2) * factor1 / 2
self.Mlm.setlm(2, 1, w21)
elif t == 0 and u == 0 and v == 2:
w00 = self.k * factor2 * factor1
w20 = w00 * factor2
self.Mlm.setlm(0, 0, w00)
self.Mlm.setlm(2, 0, w20)
if self.pow[0] < self.pow[1]:
for l in range(0, min(3, self.Mlm.degree + 1)):
for m in range(0, l + 1):
self.Mlm.setlm(
l, m,
self.Mlm.getlm(l, m).conjugate() * np.power(-1j, m))
for l in range(0, min(3, self.Mlm.degree + 1)):
for m in range(-l, 0):
self.Mlm.setlm(l, m, self.Mlm.getlm(l, -m).conjugate())
return self.Mlm
def M_expansion_to_box(self, box, p):
self.Mlm_init(p)
self.Mlm_array = np.reshape(self.Mlm_array,
np.prod(self.Mlm_array.shape))
self.X_p = np.reshape(self.X_p, (len(self.Mlm_array), 3))
self.Mlm = Vlm(p)
for i in range(0, len(self.Mlm_array)):
self.Mlm.added_to_self(
operation.M2M(self.Mlm_array[i], self.X_p[i] - box.x))
box.added_to_Mlm(self.Mlm)
class q_particle(abstract_source):
"""implementation of particle source"""
def __init__(self, x, q):
super().__init__(x)
self.q = q #charge
def M_expansion_to_box(self, box, p):
self.Mlm = Vlm(p)
self.Mlm.setlm(0, 0, self.q)
super().M_expansion_to_box(box)
def near_field_interaction(self, other, scale_factor):
return 1 / (operation.distance_cal(self.x, other.x) * scale_factor)
def M_expansion_to_box(self, box, p):
self.Mlm_init(p)
self.Mlm_array = np.reshape(self.Mlm_array, np.prod(self.Mlm_array.shape))
self.X_p = np.reshape(self.X_p, (len(self.Mlm_array), 3))
self.Mlm = Vlm(p)
for i in range(0, len(self.Mlm_array)):
self.Mlm.added_to_self(operation.M2M(self.Mlm_array[i], self.X_p[i]-box.x))
box.added_to_Mlm(self.Mlm)
class gs_q_dist(abstract_source):
"""implementation of spherical gaussian charge disctribution"""
def __init__(self, x, a, k):
super().__init__(x)
self.a = a # exponantial coefficient
self.k = k # pre-factor
def M_expansion_to_box(self, box, p):
self.Mlm = Vlm(p)
self.Mlm.setlm(0, 0, self.k * np.power(np.pi / self.a, 3 / 2))
super().M_expansion_to_box(box)
def near_field_interaction(self, other, scale_factor):
pre_factor = np.power(np.pi, 3) * self.k * other.k / ( np.power(self.a * other.a, 3/2)\
* operation.distance_cal(self.x, other.x) * scale_factor)
t_sqrt = np.sqrt(self.a * other.a/ (self.a + other.a)) \
* operation.distance_cal(self.x, other.x) * scale_factor
return pre_factor * erf(t_sqrt)
class shell_pair:
def __init__(self, mu, nu):
if (not type(mu) == CAO_basis) and (not type(nu) == CAO_basis):
raise Exception("Must input contracted atomic basis")
if not mu.basis_type == nu.basis_type:
raise Exception("Must input two basis with same type")
self.mu = mu
self.nu = nu
self.d = np.outer(mu.d, nu.d)
self.a_k = np.outer(mu.a, nu.a)
self.X_p = np.zeros(shape=(len(mu.a), len(nu.a), 3), dtype=np.float64)
self.a_p = np.zeros(shape=self.a_k.shape, dtype=np.float64)
for i in range(0, len(mu.a)):
for j in range(0, len(nu.a)):
self.a_p[i][j] = (mu.a[i] + nu.a[j])
self.X_p[i][j] = (mu.a[i] * mu.x +
nu.a[j] * nu.x) / self.a_p[i][j]
self.a_k /= self.a_p
self.Mlm_array = None
self.Mlm = None
def M_expansion_to_box(self, box, p):
self.Mlm_init(p)
self.Mlm_array = np.reshape(self.Mlm_array,
np.prod(self.Mlm_array.shape))
self.X_p = np.reshape(self.X_p, (len(self.Mlm_array), 3))
self.Mlm = Vlm(p)
for i in range(0, len(self.Mlm_array)):
self.Mlm.added_to_self(
operation.M2M(self.Mlm_array[i], self.X_p[i] - box.x))
box.added_to_Mlm(self.Mlm)
def Mlm_init(self, p):
self.Mlm_array = np.ndarray(shape=self.a_k.shape, dtype=Vlm)
dis_sq = sum((self.mu.x - self.nu.x)**2)
for i in range(0, len(self.mu.a)):
for j in range(0, len(self.nu.a)):
self.Mlm_array[i][j] = self.Mlm_matrix_elememt_gen(
self.X_p[i][j], self.a_p[i][j], p)
scale_factor = np.exp(-self.a_k[i][j] * dis_sq) * self.d[i][j]
self.Mlm_array[i][j].scale(scale_factor)
def Mlm_matrix_elememt_gen(self, X_p, a_p, p):
pow_max = self.mu.pow + self.nu.pow
C_t = np.zeros(pow_max[0] + 1)
for t in range(0, pow_max[0] + 1):
for i in range(max(0, t - self.nu.pow[0]),
min(self.mu.pow[0], t) + 1):
C_t[t] += binom(self.mu.pow[0], i) * np.power(X_p[0] - self.mu.x[0], self.mu.pow[0]-i) \
* binom(self.nu.pow[0], t-i) * np.power(X_p[0] - self.nu.x[0], self.nu.pow[0]-t+i)
#print("t=", t, "; C_t=", C_t[t])
C_u = np.zeros(pow_max[1] + 1)
for t in range(0, pow_max[1] + 1):
for i in range(max(0, t - self.nu.pow[1]),
min(self.mu.pow[1], t) + 1):
C_u[t] += binom(self.mu.pow[1], i) * np.power(X_p[1] - self.mu.x[1], self.mu.pow[1]-i) \
* binom(self.nu.pow[1], t-i) * np.power(X_p[1] - self.nu.x[1], self.nu.pow[1]-t+i)
#print("u=", t, "; C_u=", C_u[t])
C_v = np.zeros(pow_max[2] + 1)
for t in range(0, pow_max[2] + 1):
for i in range(max(0, t - self.nu.pow[2]),
min(self.mu.pow[2], t) + 1):
C_v[t] += binom(self.mu.pow[2], i) * np.power(X_p[2] - self.mu.x[2], self.mu.pow[2]-i) \
* binom(self.nu.pow[2], t-i) * np.power(X_p[2] - self.nu.x[2], self.nu.pow[2]+i-t)
#print("v=", t, "; C_v=", C_v[t])
Mlm = Vlm(p)
for t in range(0, len(C_t)):
for u in range(0, len(C_u)):
for v in range(0, len(C_v)):
Mlm_G_tuv = ggq_dist(X_p, a_p, C_t[t] * C_u[u] * C_v[v],
[t, u, v])
Mlm.added_to_self(Mlm_G_tuv.Mlm_init(p))
return Mlm
class ggq_dist(abstract_source):
"""implementation of generalized gaussian charge disctribution"""
def __init__(self, x, a, k, pow):
super().__init__(x)
self.a = a # exponantial coefficient
self.k = k # pre-factor
self.pow = pow # three d cartesian power [t,u,v]
def M_expansion_to_box(self, box, p):
self.Mlm_init(p)
super().M_expansion_to_box(box)
def near_field_interaction(self, other, scale_factor):
print("call direct evaluation")
def Mlm_init(self, p):
self.Mlm = Vlm(p)
v = self.pow[2]
if self.pow[0] < self.pow[1]:
t = self.pow[1]
u = self.pow[0]
else:
t = self.pow[0]
u = self.pow[1]
factor1 = np.power(np.pi / self.a, 3 / 2)
factor2 = 1 / (2 * self.a)
if t == 0 and u == 0 and v == 0:
self.Mlm.setlm(0, 0, self.k * factor1)
elif t == 1 and u == 0 and v == 0:
w11 = -self.k * factor2 * factor1 / 2
self.Mlm.setlm(1, 1, w11)
elif t == 0 and u == 0 and v == 1:
w10 = self.k * factor2 * factor1
self.Mlm.setlm(1, 0, w10)
elif t == 2 and u == 0 and v == 0:
w00 = self.k * factor2 * factor1
w20 = -w00 * factor2 / 2
w22 = -w20 / 2
self.Mlm.setlm(0, 0, w00)
self.Mlm.setlm(2, 0, w20)
self.Mlm.setlm(2, 2, w22)
elif t == 1 and u == 1 and v == 0:
w22 = -self.k * (factor2**2) * factor1 * 1j / 4
self.Mlm.setlm(2, 2, w22)
elif t == 1 and u == 0 and v == 1:
w21 = -self.k * (factor2**2) * factor1 / 2
self.Mlm.setlm(2, 1, w21)
elif t == 0 and u == 0 and v == 2:
w00 = self.k * factor2 * factor1
w20 = w00 * factor2
self.Mlm.setlm(0, 0, w00)
self.Mlm.setlm(2, 0, w20)
if self.pow[0] < self.pow[1]:
for l in range(0, min(3, self.Mlm.degree + 1)):
for m in range(0, l + 1):
self.Mlm.setlm(
l, m,
self.Mlm.getlm(l, m).conjugate() * np.power(-1j, m))
for l in range(0, min(3, self.Mlm.degree + 1)):
for m in range(-l, 0):
self.Mlm.setlm(l, m, self.Mlm.getlm(l, -m).conjugate())
return self.Mlm
def M_expansion_to_box(self, box, p):
self.Mlm = Vlm(p)
self.Mlm.setlm(0, 0, self.k * np.power(np.pi / self.a, 3 / 2))
super().M_expansion_to_box(box)
def M_expansion_to_box(self, box, p):
self.Mlm = Vlm(p)
self.Mlm.setlm(0, 0, self.q)
super().M_expansion_to_box(box)
class shell_pair:
def __init__(self, mu, nu):
if (not type(mu)== CAO_basis) and (not type(nu)== CAO_basis):
raise Exception("Must input contracted atomic basis")
if not mu.basis_type == nu.basis_type:
raise Exception("Must input two basis with same type")
self.mu = mu
self.nu = nu
self.d = np.outer(mu.d, nu.d)
self.a_k = np.outer(mu.a, nu.a)
self.X_p = np.zeros(shape=(len(mu.a), len(nu.a), 3), dtype=np.float64)
self.a_p = np.zeros(shape=self.a_k.shape, dtype=np.float64)
for i in range(0, len(mu.a)):
for j in range(0, len(nu.a)):
self.a_p[i][j] = (mu.a[i]+nu.a[j])
self.X_p[i][j] = (mu.a[i] * mu.x + nu.a[j] * nu.x) / self.a_p[i][j]
self.a_k /= self.a_p
self.Mlm_array = None
self.Mlm = None
def M_expansion_to_box(self, box, p):
self.Mlm_init(p)
self.Mlm_array = np.reshape(self.Mlm_array, np.prod(self.Mlm_array.shape))
self.X_p = np.reshape(self.X_p, (len(self.Mlm_array), 3))
self.Mlm = Vlm(p)
for i in range(0, len(self.Mlm_array)):
self.Mlm.added_to_self(operation.M2M(self.Mlm_array[i], self.X_p[i]-box.x))
box.added_to_Mlm(self.Mlm)
def Mlm_init(self, p):
self.Mlm_array = np.ndarray(shape=self.a_k.shape, dtype=Vlm)
dis_sq = sum( (self.mu.x-self.nu.x) ** 2 )
for i in range(0, len(self.mu.a)):
for j in range(0, len(self.nu.a)):
self.Mlm_array[i][j] = self.Mlm_matrix_elememt_gen(self.X_p[i][j], self.a_p[i][j], p)
scale_factor = np.exp(-self.a_k[i][j] * dis_sq) * self.d[i][j]
self.Mlm_array[i][j].scale(scale_factor)
def Mlm_matrix_elememt_gen(self, X_p, a_p, p):
pow_max = self.mu.pow + self.nu.pow
C_t = np.zeros(pow_max[0]+1)
for t in range(0, pow_max[0]+1):
for i in range(max(0, t-self.nu.pow[0]), min(self.mu.pow[0], t)+1):
C_t[t] += binom(self.mu.pow[0], i) * np.power(X_p[0] - self.mu.x[0], self.mu.pow[0]-i) \
* binom(self.nu.pow[0], t-i) * np.power(X_p[0] - self.nu.x[0], self.nu.pow[0]-t+i)
#print("t=", t, "; C_t=", C_t[t])
C_u = np.zeros(pow_max[1]+1)
for t in range(0, pow_max[1]+1):
for i in range(max(0, t-self.nu.pow[1]), min(self.mu.pow[1], t)+1):
C_u[t] += binom(self.mu.pow[1], i) * np.power(X_p[1] - self.mu.x[1], self.mu.pow[1]-i) \
* binom(self.nu.pow[1], t-i) * np.power(X_p[1] - self.nu.x[1], self.nu.pow[1]-t+i)
#print("u=", t, "; C_u=", C_u[t])
C_v = np.zeros(pow_max[2]+1)
for t in range(0, pow_max[2]+1):
for i in range(max(0, t-self.nu.pow[2]), min(self.mu.pow[2], t)+1):
C_v[t] += binom(self.mu.pow[2], i) * np.power(X_p[2] - self.mu.x[2], self.mu.pow[2]-i) \
* binom(self.nu.pow[2], t-i) * np.power(X_p[2] - self.nu.x[2], self.nu.pow[2]+i-t)
#print("v=", t, "; C_v=", C_v[t])
Mlm = Vlm(p)
for t in range(0, len(C_t)):
for u in range(0, len(C_u)):
for v in range(0, len(C_v)):
Mlm_G_tuv = ggq_dist(X_p, a_p, C_t[t]*C_u[u]*C_v[v], [t, u, v])
Mlm.added_to_self(Mlm_G_tuv.Mlm_init(p))
return Mlm