def init_amplitudes(self, ham):
"""
Initialize amplitudes from interaction
"""
e_ai = cc_denom(ham.f, 2, 'dir', 'full')
e_abij = cc_denom(ham.f, 4, 'dir', 'full')
nocc = self.mos.nocc
nvir = self.mos.nvir
t1 = ham.f.ov.transpose().conj() * (- e_ai)
v_vovo = einsum("pia,pjb->aibj", ham.l.pov, ham.l.pov).conj()
t2_full = v_vovo.transpose([0, 2, 1, 3]) * (- e_abij)
t2names = ['x1', 'x2', 'x3', 'x4']
t3names = ['x1', 'x2', 'x3', 'x4', 'x5', 'x6']
t2x = cpd_initialize(t2_full.shape, self.rankt.t2)
t2x = als_dense(t2x, t2_full, max_cycle=100,
tensor_format='cpd')
t3x = cpd_initialize((nvir,) * 3 + (nocc,) * 3,
self.rankt.t3, init_function=np.zeros)
return Tensors(t1=t1, t2=Tensors(zip(t2names, t2x)),
t3=Tensors(zip(t3names, t3x)))
def solve_amps(self, h, a, g):
"""
Solving for new T amlitudes using RHS and denominator
It is assumed that the order of fields in the RHS
is consistent with the order in amplitudes
"""
# Symmetrize T3 RHS
g3 = ((+g.t3 + g.t3.transpose([1, 2, 0, 4, 5, 3]) + g.t3.transpose(
[2, 0, 1, 5, 3, 4]) + g.t3.transpose([0, 2, 1, 3, 5, 4]) +
g.t3.transpose([2, 1, 0, 5, 4, 3]) +
g.t3.transpose([1, 0, 2, 4, 3, 5])) / 12)
# Symmetrize T2 RHS
g2 = 1 / 2 * (g.t2 + g.t2.transpose([1, 0, 3, 2]))
# Solve
t2 = g2 * (-cc_denom(h.f, g.t2.ndim, 'dir', 'full'))
t3 = g3 * (-cc_denom(h.f, g.t3.ndim, 'dir', 'full'))
# Symmetrize amplitudes
t2 = 1 / 2 * (t2 + t2.transpose([1, 0, 3, 2]))
t3 = ((+t3 + t3.transpose([1, 2, 0, 4, 5, 3]) + t3.transpose(
[2, 0, 1, 5, 3, 4]) + t3.transpose([0, 2, 1, 3, 5, 4]) +
t3.transpose([2, 1, 0, 5, 4, 3]) +
t3.transpose([1, 0, 2, 4, 3, 5])) / 6)
return Tensors(t1=g.t1 * (-cc_denom(h.f, g.t1.ndim, 'dir', 'full')),
t2=t2,
t3=t3)
def solve_amps(self, h, a, g):
"""
Solving for new T amlitudes using RHS and denominator
It is assumed that the order of fields in the RHS
is consistent with the order in amplitudes
"""
# Apply n_body symmetry, which builds all
# other spin parts of the unitary group residual
g3s = (+g.t3 - g.t3.transpose([0, 1, 2, 3, 5, 4]) +
g.t3.transpose([0, 1, 2, 4, 5, 3]))
g3 = ((+g.t3 + g.t3.transpose([1, 2, 0, 4, 5, 3]) + g.t3.transpose(
[2, 0, 1, 5, 3, 4]) + g.t3.transpose([0, 2, 1, 3, 5, 4]) +
g.t3.transpose([2, 1, 0, 5, 4, 3]) +
g.t3.transpose([1, 0, 2, 4, 3, 5]) + 2 * g3s) / 12)
g2 = 1 / 2 * (g.t2 + g.t2.transpose([1, 0, 3, 2]))
t2 = g2 * (-cc_denom(h.f, g.t2.ndim, 'dir', 'full'))
t3 = g3 * (-cc_denom(h.f, g.t3.ndim, 'dir', 'full'))
# Symmetrize
t2 = 1 / 2 * (t2 + t2.transpose([1, 0, 3, 2]))
t3 = ((+t3 + t3.transpose([1, 2, 0, 4, 5, 3]) + t3.transpose(
[2, 0, 1, 5, 3, 4]) + t3.transpose([0, 2, 1, 3, 5, 4]) +
t3.transpose([2, 1, 0, 5, 4, 3]) +
t3.transpose([1, 0, 2, 4, 3, 5])) / 6)
return Tensors(t1=g.t1 * (-cc_denom(h.f, g.t1.ndim, 'dir', 'full')),
t2=t2,
t3=t3)
def calculate_update(self, h, a):
"""
Calculate new amplitudes
"""
names_abij = ['x1', 'x2', 'x3', 'x4']
xs = [a.t2[key] for key in names_abij]
# symmetrize t2 before feeding into res
xs_sym = cpd_symmetrize(xs, {(1, 0, 3, 2): ('ident', )})
r = self.calc_residuals(
h, Tensors(t1=a.t1, t2=Tensors(zip(names_abij, xs_sym))))
# Solve T1
t1 = a.t1 - r.t1 * (cc_denom(h.f, 2, 'dir', 'full'))
# Symmetrize T2 residuals
r2 = 1 / 2 * (r.t2 + r.t2.transpose([1, 0, 3, 2]))
# Solve T2
r2_d = -r2 * cc_denom(h.f, 4, 'dir', 'full')
t2 = [f for f in xs]
for idx in range(len(t2)):
g = (als_contract_dense(t2, r2_d, idx, tensor_format='cpd') +
als_contract_cpd(t2, xs_sym, idx, tensor_format='cpd'))
s = als_pseudo_inverse(t2, t2, idx)
f = np.dot(g, s)
t2[idx] = f
return Tensors(t1=t1, t2=Tensors(zip(names_abij, t2)))
def calculate_update(self, h, a):
"""
Calculate new amplitudes
"""
names_abij = sorted(a.t2.keys())
xs = [elem for elem in a.t2.to_generator()]
# symmetrize t2 before feeding into res
xs_sym = cpd_symmetrize(xs, {(1, 0, 3, 2): ('ident', )})
a_sym = Tensors(t1=a.t1, t2=Tensors(zip(names_abij, xs_sym)))
# Calculate residuals
r1 = _rccsd_cpd_ls_t_true_calc_r1(h, a_sym)
# Solve T1
t1 = a.t1 - r1 * (cc_denom(h.f, 2, 'dir', 'full'))
namesd_abij = ['d1', 'd2', 'd3', 'd4']
d = Tensors(
t2=Tensors(zip(namesd_abij, cc_denom(h.f, 4, 'dir', 'cpd'))))
new_a = Tensors(t1=t1, t2=Tensors(zip(names_abij, xs)))
for idx, name in enumerate(sorted(a_sym.t2.keys())):
g = (-self._calculate_r2d_projection(name, h, a_sym, new_a, d) +
als_contract_cpd(new_a.t2.to_list(),
a_sym.t2.to_list(),
idx,
tensor_format='cpd'))
s = als_pseudo_inverse(new_a.t2.to_list(), new_a.t2.to_list(), idx)
f = np.dot(g, s)
new_a.t2[name] = f
return new_a
def solve_amps(self, h, a, g):
"""
Solving for new T amlitudes using RHS and denominator
It is assumed that the order of fields in the RHS
is consistent with the order in amplitudes
"""
# Solve T2 (see RCCSD_UNIT)
t2 = ((2 * g.t2 + g.t2.transpose([0, 1, 3, 2])) / (-6) *
cc_denom(h.f, 4, 'dir', 'full'))
# Symmetrize
t2 = (+t2 + t2.transpose([1, 0, 3, 2])) / 2
# Solve T3
t3 = (g.t3 / 12 * (-cc_denom(h.f, g.t3.ndim, 'dir', 'full')))
# Symmetrize
t3 = ((+t3 + t3.transpose([1, 2, 0, 4, 5, 3]) + t3.transpose(
[2, 0, 1, 5, 3, 4]) + t3.transpose([0, 2, 1, 3, 5, 4]) +
t3.transpose([2, 1, 0, 5, 4, 3]) +
t3.transpose([1, 0, 2, 4, 3, 5])) / 6)
return Tensors(t1=g.t1 * (-cc_denom(h.f, g.t1.ndim, 'dir', 'full')),
t2=t2,
t3=t3)
def update_rhs(self, h, a, r):
"""
Updates right hand side of the CC equations, commonly referred as G
"""
return Tensors(t1=r.t1 - a.t1 / cc_denom(h.f, 2, 'dir', 'full'),
t2=r.t2 - cpd_rebuild(
(a.t2.x1, a.t2.x2, a.t2.x3, a.t2.x4)) /
cc_denom(h.f, 4, 'dir', 'full'))
def update_rhs(self, h, a, r):
"""
Calculates right hand side of CC equations
"""
return Tensors(t1=r.t1 - a.t1 / cc_denom(h.f, 2, 'dir', 'full'),
t2=r.t2 - a.t2 / cc_denom(h.f, 4, 'dir', 'full'),
t3=r.t3 - (a.t3 - a.t3.transpose([0, 1, 2, 4, 3, 5])) /
cc_denom(h.f, 6, 'dir', 'full'))
def update_rhs(self, h, a, r):
"""
Calculates RHS of the fixed point iteration of CC equations
"""
return Tensors(t1=r.t1 - 2 * a.t1 / cc_denom(h.f, 2, 'dir', 'full'),
t2=r.t2 - 2 *
(2 * a.t2 - a.t2.transpose([0, 1, 3, 2])) /
cc_denom(h.f, 4, 'dir', 'full'))
def init_amplitudes(self, ham):
"""
Initialize amplitudes from interaction
"""
e_ai = cc_denom(ham.f, 2, 'dir', 'full')
e_abij = cc_denom(ham.f, 4, 'dir', 'full')
t1 = ham.f.ov.transpose().conj() * (-e_ai)
t2 = ham.v.oovv.transpose([2, 3, 0, 1]).conj() * (-e_abij)
return Tensors(t1=t1, t2=t2)
def update_rhs(self, h, a, r):
"""
Calculates right hand side of CC equations
"""
return Tensors(
t1=r.t1 - a.t1 / cc_denom(h.f, 2, 'dir', 'full'),
t2=r.t2 - a.t2 / cc_denom(h.f, 4, 'dir', 'full'),
t3=r.t3 - (ncpd_rebuild(
(a.t3.xlam, a.t3.x1, a.t3.x2, a.t3.x3, a.t3.x4, a.t3.x5,
a.t3.x6)) - ncpd_rebuild(
(a.t3.xlam, a.t3.x1, a.t3.x2, a.t3.x3, a.t3.x5, a.t3.x4,
a.t3.x6))) / cc_denom(h.f, 6, 'dir', 'full'))
def solve_amps(self, h, a, g):
"""
Solving for new T amlitudes using RHS and denominator
It is assumed that the order of fields in the RHS
is consistent with the order in amplitudes
"""
# Symmetrize T3 RHS - see RCCSDT code
g3 = (+g.t3 + g.t3.transpose([1, 2, 0, 4, 5, 3]) + g.t3.transpose(
[2, 0, 1, 5, 3, 4]) + g.t3.transpose([0, 2, 1, 3, 5, 4]) +
g.t3.transpose([2, 1, 0, 5, 4, 3]) +
g.t3.transpose([1, 0, 2, 4, 3, 5])) / 6
# Solve T3
t3 = g3 * (-cc_denom(h.f, g.t3.ndim, 'dir', 'full'))
# Symmetrize
t3 = (+t3 + t3.transpose([1, 2, 0, 4, 5, 3]) + t3.transpose(
[2, 0, 1, 5, 3, 4]) + t3.transpose([0, 2, 1, 3, 5, 4]) +
t3.transpose([2, 1, 0, 5, 4, 3]) +
t3.transpose([1, 0, 2, 4, 3, 5])) / 6
# Symmetrize T2 RHS
g2 = 1 / 2 * (g.t2 + g.t2.transpose([1, 0, 3, 2]))
# Solve T2
t2 = g2 * (-cc_denom(h.f, g.t2.ndim, 'dir', 'full'))
# Symmetrize
t2 = 1 / 2 * (t2 + t2.transpose([1, 0, 3, 2]))
# Solve for factors
t2x = als_dense([a.t2.xlam, a.t2.x1, a.t2.x2, a.t2.x3, a.t2.x4],
t2,
max_cycle=1,
tensor_format='ncpd')
t3x = als_dense(
[a.t3.xlam, a.t3.x1, a.t3.x2, a.t3.x3, a.t3.x4, a.t3.x5, a.t3.x6],
t3,
max_cycle=1,
tensor_format='ncpd')
return Tensors(
t1=g.t1 * (-cc_denom(h.f, g.t1.ndim, 'dir', 'full')),
t2=Tensors(xlam=t2x[0], x1=t2x[1], x2=t2x[2], x3=t2x[3],
x4=t2x[4]),
t3=Tensors(xlam=t3x[0],
x1=t3x[1],
x2=t3x[2],
x3=t3x[3],
x4=t3x[4],
x5=t3x[5],
x6=t3x[6]),
)
def init_amplitudes(self, ham):
"""
Initialize amplitudes from interaction
"""
e_ai = cc_denom(ham.f, 2, 'dir', 'full')
e_abij = cc_denom(ham.f, 4, 'dir', 'full')
t1 = ham.f.ov.transpose().conj() * (-e_ai)
v_vvoo = np.einsum("pia,pjb->abij", ham.l.pov, ham.l.pov).conj()
t2 = v_vvoo * (-e_abij)
return Tensors(t1=t1, t2=t2)
def solve_amps(self, h, a, g):
"""
Solving for new T amlitudes using RHS and denominator
It is assumed that the order of fields in the RHS
is consistent with the order in amplitudes
"""
# Solve
t2 = ((2 * g.t2 + g.t2.transpose([0, 1, 3, 2])) / (-6) *
cc_denom(h.f, 4, 'dir', 'full'))
# Symmetrize
t2 = 1 / 2 * (t2 + t2.transpose([1, 0, 3, 2]))
return Tensors(t1=g.t1 / (-2) * cc_denom(h.f, 2, 'dir', 'full'), t2=t2)
def init_amplitudes(self, ham):
"""
Initialize amplitudes from interaction
"""
e_ai = cc_denom(ham.f, 2, 'dir', 'full')
e_abij = cc_denom(ham.f, 4, 'dir', 'full')
nocc = self.mos.nocc
nvir = self.mos.nvir
t1 = ham.f.ov.transpose().conj() * (-e_ai)
t2 = ham.v.oovv.transpose([2, 3, 0, 1]).conj() * (-e_abij)
t3 = np.zeros((nvir, ) * 3 + (nocc, ) * 3)
return Tensors(t1=t1, t2=t2, t3=t3)
def update_rhs(self, h, a, r):
"""
Calculates right hand side of CC equations
"""
return Tensors(
t1=r.t1 - a.t1 / cc_denom(h.f, 2, 'dir', 'full'),
t2=r.t2 - 2 * (2 * a.t2 - a.t2.transpose([0, 1, 3, 2])) /
cc_denom(h.f, 4, 'dir', 'full'),
t3=r.t3 -
(+4 * a.t3.transpose([0, 1, 2, 4, 3, 5]) + 4 * a.t3.transpose(
[0, 1, 2, 5, 4, 3]) + 4 * a.t3.transpose([0, 1, 2, 3, 5, 4]) -
2 * a.t3.transpose([0, 1, 2, 5, 3, 4]) -
2 * a.t3.transpose([0, 1, 2, 4, 5, 3]) - 8 * a.t3) /
cc_denom(h.f, 6, 'dir', 'full'))
def solve_amps(self, h, a, g):
"""
Solving for new T amlitudes using RHS and denominator
It is assumed that the order of fields in the RHS
is consistent with the order in amplitudes
"""
t1 = g.gt1 / (-cc_denom(h.f, 2, 'mul', 'full'))
A1 = gen_A1(a.x1, a.x2, a.x3, a.x4, a.x5)
A2 = gen_A2(a.x1, a.x2, a.x3, a.x4, a.x5)
A3 = gen_A3(a.x1, a.x2, a.x3, a.x4, a.x5)
A4 = gen_A4(a.x1, a.x2, a.x3, a.x4, a.x5)
AZl = gen_AZl(a.x1, a.x2, a.x3, a.x4, a.x5)
AZr = gen_AZr(a.x1, a.x2, a.x3, a.x4, a.x5)
a_new = [
-dot(g.gx1, pinv(A1, rcond=1e-10)) + a.x1,
-dot(g.gx2, pinv(A2, rcond=1e-10)) + a.x2,
-dot(g.gx3, pinv(A3, rcond=1e-10)) + a.x3,
-dot(g.gx4, pinv(A4, rcond=1e-10)) + a.x4,
-dot(dot(pinv(AZl, rcond=1e-10), g.gx5), pinv(AZr, rcond=1e-10)) +
a.x5
]
# Normalize columns to 1 in X factors, Hermitize Z
a_new = [factor / norm(factor, axis=0) for factor in a_new[:4]] + [
1 / 2 * (a_new[4] + a_new[4].T),
]
return self.types.AMPLITUDES_TYPE(t1, *a_new)
def init_amplitudes(self, ham):
"""
Initialize amplitudes from interaction
"""
e_ai = cc_denom(ham.f, 2, 'dir', 'full')
e_abij = cc_denom(ham.f, 4, 'dir', 'full')
nocc = self.mos.nocc
nvir = self.mos.nvir
t1 = ham.f.ov.transpose().conj() * (-e_ai)
v_vovo = einsum("pia,pjb->aibj", ham.l.pov, ham.l.pov).conj()
t2 = v_vovo.transpose([0, 2, 1, 3]) * (-e_abij)
t3 = np.zeros((nvir, ) * 3 + (nocc, ) * 3)
return Tensors(t1=t1, t2=t2, t3=t3)
def solve_amps(self, h, a, g):
"""
Solving for new T amlitudes using RHS and denominator
It is assumed that the order of fields in the RHS
is consistent with the order in amplitudes
"""
# Form symmetric RHS for T2
g2 = 1 / 2 * (g.t2 + g.t2.transpose([1, 0, 3, 2]))
# Solve T2
t2 = g2 * (-cc_denom(h.f, g.t2.ndim, 'dir', 'full'))
# Symmetrize
t2 = (t2 + t2.transpose([1, 0, 3, 2])) / 2
# This version coincides with So
# Hirata. To do full unitary residuals uncomment blocks
# %1 and %2 below
# g3s = (+ g.t3 # %1
# - g.t3.transpose([0, 1, 2, 3, 5, 4])
# + g.t3.transpose([0, 1, 2, 4, 5, 3]))
# Apply n_body symmetry, which builds all
# "opposite spin" parts of the unitary group residual
g3 = ((
+g.t3 + g.t3.transpose([1, 2, 0, 4, 5, 3]) + g.t3.transpose(
[2, 0, 1, 5, 3, 4]) + g.t3.transpose([0, 2, 1, 3, 5, 4]) +
g.t3.transpose([2, 1, 0, 5, 4, 3]) +
g.t3.transpose([1, 0, 2, 4, 3, 5])
# + 2 * g3s) / 12 # %2
) / 6)
# Solve T3
t3 = g3 * (-cc_denom(h.f, g.t3.ndim, 'dir', 'full'))
# Symmetrize
t3 = ((+t3 + t3.transpose([1, 2, 0, 4, 5, 3]) + t3.transpose(
[2, 0, 1, 5, 3, 4]) + t3.transpose([0, 2, 1, 3, 5, 4]) +
t3.transpose([2, 1, 0, 5, 4, 3]) +
t3.transpose([1, 0, 2, 4, 3, 5])) / 6)
return Tensors(t1=g.t1 * (-cc_denom(h.f, g.t1.ndim, 'dir', 'full')),
t2=t2,
t3=t3)
def init_amplitudes(self, ham):
"""
Initialize amplitudes from interaction
"""
e_ai = cc_denom(ham.f, 2, 'dir', 'full')
e_abij = cc_denom(ham.f, 4, 'dir', 'full')
t1 = 2 * ham.f.ov.transpose().conj() * (-e_ai)
v_vovo = einsum("pia,pjb->aibj", ham.l.pov, ham.l.pov).conj()
t2_full = 2 * v_vovo.transpose([0, 2, 1, 3]) * (-e_abij)
xs = cpd_initialize(t2_full.shape, self.rankt.t2)
xs = als_dense(xs, t2_full, max_cycle=100)
names = ['x1', 'x2', 'x3', 'x4']
return Tensors(t1=t1, t2=Tensors(zip(names, xs)))
def init_amplitudes(self, ham):
"""
Initialize amplitudes from interaction
"""
e_ai = cc_denom(ham.f, 2, 'dir', 'full')
e_abij = cc_denom(ham.f, 4, 'dir', 'full')
t1 = ham.f.ov.transpose().conj() * (-e_ai)
v_vovo = einsum("pia,pjb->aibj", ham.l.pov, ham.l.pov).conj()
t2_full = v_vovo.transpose([0, 2, 1, 3]) * (-e_abij)
xs = ncpd_initialize(t2_full.shape, self.rankt.t2)
xs = als_dense(xs, t2_full, max_cycle=100, tensor_format='ncpd')
# xs_sym = cpd_symmetrize(xs, {(1, 0, 3, 2): ('ident',)})
names = ['xlam', 'x1', 'x2', 'x3', 'x4']
return Tensors(t1=t1, t2=Tensors(zip(names, xs)))
def solve_amps(self, h, a, g):
"""
Solve for new amplitudes using RHS and denominator
"""
t1 = g.t1 * (-cc_denom(h.f, 2, 'dir', 'full'))
# Symmetrize T2 HS
g2 = 1 / 2 * (g.t2 + g.t2.transpose([1, 0, 3, 2]))
# Solve T2
t2_full = g2 * (-cc_denom(h.f, 4, 'dir', 'full'))
xs = als_dense([a.t2.x1, a.t2.x2, a.t2.x3, a.t2.x4],
t2_full,
max_cycle=1,
tensor_format='cpd')
return Tensors(t1=t1,
t2=Tensors(x1=xs[0], x2=xs[1], x3=xs[2], x4=xs[3]))
def init_amplitudes(self, ham):
"""
Initialize amplitudes from interaction
"""
e_ai = cc_denom(ham.f, 2, 'dir', 'full')
e_abij = cc_denom(ham.f, 4, 'dir', 'full')
nocc = self.mos.nocc
nvir = self.mos.nvir
t1 = ham.f.ov.transpose().conj() * (-e_ai)
v_vovo = einsum("pia,pjb->aibj", ham.l.pov, ham.l.pov).conj()
t2_full = v_vovo.transpose([0, 2, 1, 3]) * (-e_abij)
t3names = ['xlam', 'x1', 'x2', 'x3', 'x4', 'x5', 'x6']
t3x = ncpd_initialize(
(nvir, ) * 3 + (nocc, ) * 3,
self.rankt.t3,
init_function=(lambda x: 0.001 * np.random.rand(*x)))
return Tensors(t1=t1, t2=t2_full, t3=Tensors(zip(t3names, t3x)))
def solve_amps(self, h, a, g):
"""
Solving for new T amlitudes using RHS and denominator
It is assumed that the order of fields in the RHS
is consistent with the order in amplitudes
"""
t1 = g.t1 / (-2) * cc_denom(h.f, 2, 'dir', 'full')
# Build unit RHS
g2 = (2 * g.t2 + g.t2.transpose([0, 1, 3, 2])) / 6
# Symmetrize RHS
g2 = 1 / 2 * (g2 + g2.transpose([1, 0, 3, 2]))
# Solve
t2_full = g2 * (-cc_denom(h.f, 4, 'dir', 'full'))
xs = als_dense([a.t2.x1, a.t2.x2, a.t2.x3, a.t2.x4],
t2_full,
max_cycle=1)
names = ['x1', 'x2', 'x3', 'x4']
return Tensors(t1=t1, t2=Tensors(zip(names, xs)))
def solve_amps(self, h, a, g):
"""
Solving for new T amlitudes using RHS and denominator
It is assumed that the order of fields in the RHS
is consistent with the order in amplitudes
"""
# Solve
t3 = g.t3 / 24 * (-cc_denom(h.f, g.t3.ndim, 'dir', 'full'))
# Antisymmetrize over all indices (upper and lower separately)
t3 = 1 / 6 * (+t3 - t3.transpose([1, 0, 2, 3, 4, 5]) + t3.transpose(
[1, 2, 0, 3, 4, 5]) - t3.transpose([2, 1, 0, 3, 4, 5]) +
t3.transpose([2, 0, 1, 3, 4, 5]) -
t3.transpose([0, 2, 1, 3, 4, 5]))
t3 = 1 / 6 * (+t3 - t3.transpose([0, 1, 2, 4, 3, 5]) + t3.transpose(
[0, 1, 2, 4, 5, 3]) - t3.transpose([0, 1, 2, 5, 4, 3]) +
t3.transpose([0, 1, 2, 5, 3, 4]) -
t3.transpose([0, 1, 2, 3, 5, 4]))
return Tensors(t1=g.t1 * (-cc_denom(h.f, g.t1.ndim, 'dir', 'full')),
t2=(2 * g.t2 + g.t2.transpose([0, 1, 3, 2])) / 6 *
(-cc_denom(h.f, 4, 'dir', 'full')),
t3=t3)
def update_rhs(self, h, a, r):
"""
Updates right hand side of the CC equations, commonly referred as G
"""
# Here we simply copy the residuals of T2 factors
# to the RHS arrays
return self.types.RHS_TYPE(gt1=r.rt1 -
a.t1 / cc_denom(h.f, 2, 'mul', 'full'),
gx1=r.rx1,
gx2=r.rx2,
gx3=r.rx3,
gx4=r.rx4,
gx5=r.rx5)
def init_amplitudes(self, ham):
"""
Initialize amplitudes from interaction
"""
e_ai = cc_denom(ham.f, 2, 'mul', 'full')
t1 = ham.f.ov.transpose().conj() * (-e_ai)
no = self.mos.nocc
nv = self.mos.nvir
v_vovo_factors = (ham.v.x1.v, ham.v.x2.o, ham.v.x3.v, ham.v.x4.o,
ham.v.x5)
v_vovo_norm = thc_contract_thc(v_vovo_factors, v_vovo_factors)
x1, x2, x3, x4, x5 = thc_initialize((nv, no, nv, no),
self.rankt,
scale_to_norm=1.0)
return self.types.AMPLITUDES_TYPE(t1, x1, x2, x3, x4, x5)
def calc_residuals(self, h, a):
"""
Calculates CC residuals for CC equations
"""
rt1 = gen_R1(h.f, h.v.x1, h.v.x2, h.v.x3, h.v.x4, h.v.x5, a.t1, a.x1,
a.x2, a.x3, a.x4, a.x5)
d = cc_denom(h.f, 4, ordering='mul', kind='cpd')
rx1 = gen_RY1(h.f, h.v.x1, h.v.x2, h.v.x3, h.v.x4, h.v.x5, a.t1, a.x1,
a.x2, a.x3, a.x4, a.x5, d[0], d[1], d[2], d[3])
rx2 = gen_RY2(h.f, h.v.x1, h.v.x2, h.v.x3, h.v.x4, h.v.x5, a.t1, a.x1,
a.x2, a.x3, a.x4, a.x5, d[0], d[1], d[2], d[3])
rx3 = gen_RY3(h.f, h.v.x1, h.v.x2, h.v.x3, h.v.x4, h.v.x5, a.t1, a.x1,
a.x2, a.x3, a.x4, a.x5, d[0], d[1], d[2], d[3])
rx4 = gen_RY4(h.f, h.v.x1, h.v.x2, h.v.x3, h.v.x4, h.v.x5, a.t1, a.x1,
a.x2, a.x3, a.x4, a.x5, d[0], d[1], d[2], d[3])
rx5 = gen_RZ(h.f, h.v.x1, h.v.x2, h.v.x3, h.v.x4, h.v.x5, a.t1, a.x1,
a.x2, a.x3, a.x4, a.x5, d[0], d[1], d[2], d[3])
return self.types.RESIDUALS_TYPE(rt1, rx1, rx2, rx3, rx4, rx5)
def divide_by_inverse(x):
return x / (cc_denom(h.f, x.ndim, 'dir', 'full'))
def calculate_update(self, h, a):
"""
Calculate new amplitudes
"""
t3names = ['xlam', 'x1', 'x2', 'x3', 'x4', 'x5', 'x6']
t3x = [a.t3[key] for key in t3names]
# Running residuals with symmetrized amplitudes.
# symmetrizetion is done inside calc_residuals
r = self.calc_residuals(
h,
Tensors(t1=a.t1, t2=a.t2,
t3=Tensors(zip(t3names, t3x)))
)
t1 = a.t1 - r.t1 * (cc_denom(h.f, 2, 'dir', 'full'))
# Solve T2
r2_d = - r.t2 * cc_denom(h.f, 4, 'dir', 'full')
t2 = a.t2 + r2_d
# Symmetrize
t2 = 1 / 2 * (t2 + t2.transpose([1, 0, 3, 2]))
# Build full unit residual
r3s = (+ r.t3
- r.t3.transpose([0, 1, 2, 3, 5, 4])
+ r.t3.transpose([0, 1, 2, 4, 5, 3]))
r3u = ((+ r.t3
+ r.t3.transpose([1, 2, 0, 4, 5, 3])
+ r.t3.transpose([2, 0, 1, 5, 3, 4])
+ r.t3.transpose([0, 2, 1, 3, 5, 4])
+ r.t3.transpose([2, 1, 0, 5, 4, 3])
+ r.t3.transpose([1, 0, 2, 4, 3, 5])
+ 2 * r3s) / 12)
# Solve
r3_d = - r3u * cc_denom(h.f, 6, 'dir', 'full')
# symmetrize inital T3
t3x_sym = ncpd_symmetrize(t3x, {(1, 2, 0, 4, 5, 3): ('ident',),
(2, 0, 1, 5, 3, 4): ('ident',),
(0, 2, 1, 3, 5, 4): ('ident',),
(2, 1, 0, 5, 4, 3): ('ident',),
(1, 0, 2, 4, 3, 5): ('ident',)})
# 0 1 2 4 3 5 permutation of t3
t3x_sym_a = [t3x_sym[0], t3x_sym[1], t3x_sym[2], t3x_sym[3],
t3x_sym[5], t3x_sym[4], t3x_sym[6]]
# Build combinations of T for unitary residual
t3x_u = ncpd_symmetrize(
t3x_sym,
{(0, 1, 2, 4, 3, 5): ('neg',),
(0, 1, 2, 5, 4, 3): ('neg',),
(0, 1, 2, 3, 5, 4): ('neg',),
(0, 1, 2, 5, 3, 4): ('ident',),
(0, 1, 2, 4, 5, 3): ('ident',), },
weights=[2 / 3, 1 / 3, 1 / 3, 1 / 3, 1 / 6, 1 / 6])
t3x_au = ncpd_symmetrize(
t3x_sym_a,
{(0, 1, 2, 4, 3, 5): ('neg',),
(0, 1, 2, 5, 4, 3): ('neg',),
(0, 1, 2, 3, 5, 4): ('neg',),
(0, 1, 2, 5, 3, 4): ('ident',),
(0, 1, 2, 4, 5, 3): ('ident',), },
weights=[2 / 3, 1 / 3, 1 / 3, 1 / 3, 1 / 6, 1 / 6])
t3 = [f for f in t3x]
for idx in range(len(t3)):
g = (als_contract_dense(t3, r3_d, idx,
tensor_format='ncpd')
+ als_contract_cpd(t3, t3x_u, idx,
tensor_format='ncpd')
- als_contract_cpd(t3, t3x_au, idx,
tensor_format='ncpd')
)
s = als_pseudo_inverse(t3, t3, idx)
f = np.dot(g, s)
t3[idx] = f
return Tensors(t1=t1, t2=t2,
t3=Tensors(zip(t3names, t3)))
