def H(psit_xG):
if self.keep_htpsit:
result_xG = Htpsit_nG
else:
result_xG = reshape(self.operator.work1_xG, psit_xG.shape)
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG,
result_xG)
return result_xG
def H(psit_xG):
if self.keep_htpsit:
result_xG = Htpsit_nG
else:
result_xG = reshape(self.operator.work1_xG, psit_xG.shape)
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG,
result_xG)
hamiltonian.xc.apply_orbital_dependent_hamiltonian(
kpt, psit_xG, result_xG, hamiltonian.dH_asp)
return result_xG
def H(psit_xG):
if self.keep_htpsit:
result_xG = Htpsit_nG
else:
if use_mic:
result_xG = self.operator.work1_xG_mic
else:
result_xG = reshape(self.operator.work1_xG, psit_xG.shape)
if use_mic:
psit_xG.update_device()
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG.array,
result_xG.array)
result_xG.update_device()
stream.sync()
else:
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG,
result_xG)
hamiltonian.xc.apply_orbital_dependent_hamiltonian(
kpt, psit_xG, result_xG, hamiltonian.dH_asp)
return result_xG
def H(psit_xG):
if self.keep_htpsit:
result_xG = Htpsit_nG
else:
if use_mic:
result_xG = self.operator.work1_xG_mic
else:
result_xG = reshape(self.operator.work1_xG, psit_xG.shape)
if use_mic:
psit_xG.update_device()
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG.array,
result_xG.array)
result_xG.update_device()
stream.sync()
else:
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG,
result_xG)
hamiltonian.xc.apply_orbital_dependent_hamiltonian(
kpt, psit_xG, result_xG, hamiltonian.dH_asp)
return result_xG
def iterate_one_k_point(self, hamiltonian, wfs, kpt):
"""Do Davidson iterations for the kpoint"""
niter = self.niter
nbands = self.nbands
gd = wfs.matrixoperator.gd
psit_nG, Htpsit_nG = self.subspace_diagonalize(hamiltonian, wfs, kpt)
# Note that psit_nG is now in self.operator.work1_nG and
# Htpsit_nG is in kpt.psit_nG!
H_2n2n = self.H_2n2n
S_2n2n = self.S_2n2n
eps_2n = self.eps_2n
psit2_nG = reshape(self.Htpsit_nG, psit_nG.shape)
self.timer.start("Davidson")
R_nG = Htpsit_nG
self.calculate_residuals(kpt, wfs, hamiltonian, psit_nG, kpt.P_ani, kpt.eps_n, R_nG)
def integrate(a_G, b_G):
return np.real(wfs.integrate(a_G, b_G, global_integral=False))
for nit in range(niter):
H_2n2n[:] = 0.0
S_2n2n[:] = 0.0
norm_n = np.zeros(nbands)
error = 0.0
for n in range(nbands):
if kpt.f_n is None:
weight = kpt.weight
else:
weight = kpt.f_n[n]
if self.nbands_converge != "occupied":
if n < self.nbands_converge:
weight = kpt.weight
else:
weight = 0.0
error += weight * integrate(R_nG[n], R_nG[n])
ekin = self.preconditioner.calculate_kinetic_energy(psit_nG[n : n + 1], kpt)
psit2_nG[n] = self.preconditioner(R_nG[n : n + 1], kpt, ekin)
if self.normalize:
norm_n[n] = integrate(psit2_nG[n], psit2_nG[n])
H_2n2n[n, n] = kpt.eps_n[n]
S_2n2n[n, n] = 1.0
if self.normalize:
gd.comm.sum(norm_n)
for norm, psit2_G in zip(norm_n, psit2_nG):
psit2_G *= norm ** -0.5
# Calculate projections
P2_ani = wfs.pt.dict(nbands)
wfs.pt.integrate(psit2_nG, P2_ani, kpt.q)
# Hamiltonian matrix
# <psi2 | H | psi>
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit2_nG, Htpsit_nG)
gd.integrate(psit_nG, Htpsit_nG, global_integral=False, _transposed_result=self.H_nn)
# gemm(1.0, psit_nG, Htpsit_nG, 0.0, self.H_nn, 'c')
for a, P_ni in kpt.P_ani.items():
P2_ni = P2_ani[a]
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
self.H_nn += np.dot(P2_ni, np.dot(dH_ii, P_ni.T.conj()))
gd.comm.sum(self.H_nn, 0)
H_2n2n[nbands:, :nbands] = self.H_nn
# <psi2 | H | psi2>
gd.integrate(psit2_nG, Htpsit_nG, global_integral=False, _transposed_result=self.H_nn)
# r2k(0.5 * gd.dv, psit2_nG, Htpsit_nG, 0.0, self.H_nn)
for a, P2_ni in P2_ani.items():
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
self.H_nn += np.dot(P2_ni, np.dot(dH_ii, P2_ni.T.conj()))
gd.comm.sum(self.H_nn, 0)
H_2n2n[nbands:, nbands:] = self.H_nn
# Overlap matrix
# <psi2 | S | psi>
gd.integrate(psit_nG, psit2_nG, global_integral=False, _transposed_result=self.S_nn)
# gemm(1.0, psit_nG, psit2_nG, 0.0, self.S_nn, 'c')
for a, P_ni in kpt.P_ani.items():
P2_ni = P2_ani[a]
dO_ii = wfs.setups[a].dO_ii
self.S_nn += np.dot(P2_ni, np.inner(dO_ii, P_ni.conj()))
gd.comm.sum(self.S_nn, 0)
S_2n2n[nbands:, :nbands] = self.S_nn
# <psi2 | S | psi2>
gd.integrate(psit2_nG, psit2_nG, global_integral=False, _transposed_result=self.S_nn)
# rk(gd.dv, psit2_nG, 0.0, self.S_nn)
for a, P2_ni in P2_ani.items():
dO_ii = wfs.setups[a].dO_ii
self.S_nn += np.dot(P2_ni, np.dot(dO_ii, P2_ni.T.conj()))
gd.comm.sum(self.S_nn, 0)
S_2n2n[nbands:, nbands:] = self.S_nn
if gd.comm.rank == 0:
m = 0
if self.smin:
s_N, U_NN = np.linalg.eigh(S_2n2n)
m = int((s_N < self.smin).sum())
if m == 0:
general_diagonalize(H_2n2n, eps_2n, S_2n2n)
else:
T_Nn = np.dot(U_NN[:, m:], np.diag(s_N[m:] ** -0.5))
H_2n2n[:nbands, nbands:] = H_2n2n[nbands:, :nbands].conj().T
eps_2n[:-m], P_nn = np.linalg.eigh(np.dot(np.dot(T_Nn.T.conj(), H_2n2n), T_Nn))
H_2n2n[:-m] = np.dot(T_Nn, P_nn).T
gd.comm.broadcast(H_2n2n, 0)
gd.comm.broadcast(eps_2n, 0)
kpt.eps_n[:] = eps_2n[:nbands]
# Rotate psit_nG
gd.gemm(1.0, psit_nG, H_2n2n[:nbands, :nbands], 0.0, Htpsit_nG)
gd.gemm(1.0, psit2_nG, H_2n2n[:nbands, nbands:], 1.0, Htpsit_nG)
psit_nG, Htpsit_nG = Htpsit_nG, psit_nG
# Rotate P_uni:
for a, P_ni in kpt.P_ani.items():
P2_ni = P2_ani[a]
gemm(1.0, P_ni.copy(), H_2n2n[:nbands, :nbands], 0.0, P_ni)
gemm(1.0, P2_ni, H_2n2n[:nbands, nbands:], 1.0, P_ni)
if nit < niter - 1:
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_nG, Htpsit_nG)
R_nG = Htpsit_nG
self.calculate_residuals(kpt, wfs, hamiltonian, psit_nG, kpt.P_ani, kpt.eps_n, R_nG)
self.timer.stop("Davidson")
error = gd.comm.sum(error)
return error, psit_nG
def subspace_diagonalize(self, hamiltonian, wfs, kpt):
"""Diagonalize the Hamiltonian in the subspace of kpt.psit_nG
*Htpsit_nG* is a work array of same size as psit_nG which contains
the local part of the Hamiltonian times psit on exit
First, the Hamiltonian (defined by *kin*, *vt_sG*, and
*dH_asp*) is applied to the wave functions, then the *H_nn*
matrix is calculated and diagonalized, and finally, the wave
functions (and also Htpsit_nG are rotated. Also the
projections *P_ani* are rotated.
It is assumed that the wave functions *psit_nG* are orthonormal
and that the integrals of projector functions and wave functions
*P_ani* are already calculated.
Return ratated wave functions and H applied to the rotated
wave functions if self.keep_htpsit is True.
"""
if self.band_comm.size > 1 and wfs.bd.strided:
raise NotImplementedError
self.timer.start('Subspace diag')
if use_mic:
psit_nG = kpt.psit_nG_mic
# psit_nG.update_device()
# stream.sync()
else:
psit_nG = kpt.psit_nG
P_ani = kpt.P_ani
if self.keep_htpsit:
if use_mic:
Htpsit_nG = self.Htpsit_nG_mic
else:
Htpsit_nG = reshape(self.Htpsit_nG, psit_nG.shape)
else:
Htpsit_nG = None
def H(psit_xG):
if self.keep_htpsit:
result_xG = Htpsit_nG
else:
if use_mic:
result_xG = self.operator.work1_xG_mic
else:
result_xG = reshape(self.operator.work1_xG, psit_xG.shape)
if use_mic:
psit_xG.update_device()
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG.array,
result_xG.array)
result_xG.update_device()
stream.sync()
else:
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG,
result_xG)
hamiltonian.xc.apply_orbital_dependent_hamiltonian(
kpt, psit_xG, result_xG, hamiltonian.dH_asp)
return result_xG
def dH(a, P_ni):
return np.dot(P_ni, unpack(hamiltonian.dH_asp[a][kpt.s]))
self.timer.start('calc_h_matrix')
H_nn = self.operator.calculate_matrix_elements(psit_nG, P_ani, H, dH)
hamiltonian.xc.correct_hamiltonian_matrix(kpt, H_nn)
self.timer.stop('calc_h_matrix')
diagonalization_string = repr(self.ksl)
wfs.timer.start(diagonalization_string)
self.ksl.diagonalize(H_nn, kpt.eps_n)
# H_nn now contains the result of the diagonalization.
wfs.timer.stop(diagonalization_string)
self.timer.start('rotate_psi')
psit_nG = self.operator.matrix_multiply(H_nn, psit_nG, P_ani)
if self.keep_htpsit:
if use_mic:
Htpsit_nG = self.operator.matrix_multiply(
H_nn, Htpsit_nG, out_nG=kpt.psit_nG_mic)
else:
Htpsit_nG = self.operator.matrix_multiply(H_nn,
Htpsit_nG,
out_nG=kpt.psit_nG)
# Rotate orbital dependent XC stuff:
hamiltonian.xc.rotate(kpt, H_nn)
self.timer.stop('rotate_psi')
self.timer.stop('Subspace diag')
if use_mic:
psit_nG.update_host()
stream.sync()
if self.keep_htpsit:
Htpsit_nG.update_host()
stream.sync()
return psit_nG.array, Htpsit_nG.array
else:
return psit_nG.array, Htpsit_nG
else:
return psit_nG, Htpsit_nG
def subspace_diagonalize(self, hamiltonian, wfs, kpt):
"""Diagonalize the Hamiltonian in the subspace of kpt.psit_nG
*Htpsit_nG* is a work array of same size as psit_nG which contains
the local part of the Hamiltonian times psit on exit
First, the Hamiltonian (defined by *kin*, *vt_sG*, and
*dH_asp*) is applied to the wave functions, then the *H_nn*
matrix is calculated and diagonalized, and finally, the wave
functions (and also Htpsit_nG are rotated. Also the
projections *P_ani* are rotated.
It is assumed that the wave functions *psit_nG* are orthonormal
and that the integrals of projector functions and wave functions
*P_ani* are already calculated.
Return ratated wave functions and H applied to the rotated
wave functions if self.keep_htpsit is True.
"""
if self.band_comm.size > 1 and wfs.bd.strided:
raise NotImplementedError
self.timer.start('Subspace diag')
if use_mic:
psit_nG = kpt.psit_nG_mic
# psit_nG.update_device()
# stream.sync()
else:
psit_nG = kpt.psit_nG
P_ani = kpt.P_ani
if self.keep_htpsit:
if use_mic:
Htpsit_nG = self.Htpsit_nG_mic
else:
Htpsit_nG = reshape(self.Htpsit_nG, psit_nG.shape)
else:
Htpsit_nG = None
def H(psit_xG):
if self.keep_htpsit:
result_xG = Htpsit_nG
else:
if use_mic:
result_xG = self.operator.work1_xG_mic
else:
result_xG = reshape(self.operator.work1_xG, psit_xG.shape)
if use_mic:
psit_xG.update_device()
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG.array,
result_xG.array)
result_xG.update_device()
stream.sync()
else:
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG,
result_xG)
hamiltonian.xc.apply_orbital_dependent_hamiltonian(
kpt, psit_xG, result_xG, hamiltonian.dH_asp)
return result_xG
def dH(a, P_ni):
return np.dot(P_ni, unpack(hamiltonian.dH_asp[a][kpt.s]))
self.timer.start('calc_h_matrix')
H_nn = self.operator.calculate_matrix_elements(psit_nG, P_ani,
H, dH)
hamiltonian.xc.correct_hamiltonian_matrix(kpt, H_nn)
self.timer.stop('calc_h_matrix')
diagonalization_string = repr(self.ksl)
wfs.timer.start(diagonalization_string)
self.ksl.diagonalize(H_nn, kpt.eps_n)
# H_nn now contains the result of the diagonalization.
wfs.timer.stop(diagonalization_string)
self.timer.start('rotate_psi')
psit_nG = self.operator.matrix_multiply(H_nn, psit_nG, P_ani)
if self.keep_htpsit:
if use_mic:
Htpsit_nG = self.operator.matrix_multiply(H_nn, Htpsit_nG,
out_nG=kpt.psit_nG_mic)
else:
Htpsit_nG = self.operator.matrix_multiply(H_nn, Htpsit_nG,
out_nG=kpt.psit_nG)
# Rotate orbital dependent XC stuff:
hamiltonian.xc.rotate(kpt, H_nn)
self.timer.stop('rotate_psi')
self.timer.stop('Subspace diag')
if use_mic:
psit_nG.update_host()
stream.sync()
if self.keep_htpsit:
Htpsit_nG.update_host()
stream.sync()
return psit_nG.array, Htpsit_nG.array
else:
return psit_nG.array, Htpsit_nG
else:
return psit_nG, Htpsit_nG
def iterate_one_k_point(self, hamiltonian, wfs, kpt):
"""Do conjugate gradient iterations for the k-point"""
niter = self.niter
phi_G = wfs.empty(q=kpt.q)
phi_old_G = wfs.empty(q=kpt.q)
comm = wfs.gd.comm
psit_nG, Htpsit_nG = self.subspace_diagonalize(hamiltonian, wfs, kpt)
# Note that psit_nG is now in self.operator.work1_nG and
# Htpsit_nG is in kpt.psit_nG!
R_nG = reshape(self.Htpsit_nG, psit_nG.shape)
Htphi_G = R_nG[0]
R_nG[:] = Htpsit_nG
self.timer.start('Residuals')
self.calculate_residuals(kpt, wfs, hamiltonian, psit_nG,
kpt.P_ani, kpt.eps_n, R_nG)
self.timer.stop('Residuals')
self.timer.start('CG')
total_error = 0.0
for n in range(self.nbands):
if extra_parameters.get('PK', False):
N = n+1
else:
N = psit_nG.shape[0]+1
R_G = R_nG[n]
Htpsit_G = Htpsit_nG[n]
gamma_old = 1.0
phi_old_G[:] = 0.0
error = np.real(wfs.integrate(R_G, R_G))
for nit in range(niter):
if (error * Hartree**2 < self.tolerance / self.nbands):
break
ekin = self.preconditioner.calculate_kinetic_energy(
psit_nG[n:n + 1], kpt)
pR_G = self.preconditioner(R_nG[n:n + 1], kpt, ekin)
# New search direction
gamma = comm.sum(np.vdot(pR_G, R_G).real)
phi_G[:] = -pR_G - gamma / gamma_old * phi_old_G
gamma_old = gamma
phi_old_G[:] = phi_G[:]
# Calculate projections
P2_ai = wfs.pt.dict()
wfs.pt.integrate(phi_G, P2_ai, kpt.q)
# Orthonormalize phi_G to all bands
self.timer.start('CG: orthonormalize')
self.timer.start('CG: overlap')
overlap_n = wfs.integrate(psit_nG[:N], phi_G,
global_integral=False)
self.timer.stop('CG: overlap')
self.timer.start('CG: overlap2')
for a, P2_i in P2_ai.items():
P_ni = kpt.P_ani[a]
dO_ii = wfs.setups[a].dO_ii
gemv(1.0, P_ni[:N].conjugate(), np.inner(dO_ii, P2_i),
1.0, overlap_n)
self.timer.stop('CG: overlap2')
comm.sum(overlap_n)
# phi_G -= overlap_n * kpt.psit_nG
wfs.matrixoperator.gd.gemv(-1.0, psit_nG[:N], overlap_n,
1.0, phi_G, 'n')
for a, P2_i in P2_ai.items():
P_ni = kpt.P_ani[a]
gemv(-1.0, P_ni[:N], overlap_n, 1.0, P2_i, 'n')
norm = wfs.integrate(phi_G, phi_G, global_integral=False)
for a, P2_i in P2_ai.items():
dO_ii = wfs.setups[a].dO_ii
norm += np.vdot(P2_i, np.inner(dO_ii, P2_i))
norm = comm.sum(np.real(norm).item())
phi_G /= sqrt(norm)
for P2_i in P2_ai.values():
P2_i /= sqrt(norm)
self.timer.stop('CG: orthonormalize')
# find optimum linear combination of psit_G and phi_G
an = kpt.eps_n[n]
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian,
phi_G.reshape((1,) + phi_G.shape),
Htphi_G.reshape((1,) +
Htphi_G.shape))
b = wfs.integrate(phi_G, Htpsit_G, global_integral=False)
c = wfs.integrate(phi_G, Htphi_G, global_integral=False)
for a, P2_i in P2_ai.items():
P_i = kpt.P_ani[a][n]
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
b += dot(P2_i, dot(dH_ii, P_i.conj()))
c += dot(P2_i, dot(dH_ii, P2_i.conj()))
b = comm.sum(np.real(b).item())
c = comm.sum(np.real(c).item())
theta = 0.5 * atan2(2 * b, an - c)
enew = (an * cos(theta)**2 +
c * sin(theta)**2 +
b * sin(2.0 * theta))
# theta can correspond either minimum or maximum
if (enew - kpt.eps_n[n]) > 0.0: # we were at maximum
theta += pi / 2.0
enew = (an * cos(theta)**2 +
c * sin(theta)**2 +
b * sin(2.0 * theta))
kpt.eps_n[n] = enew
psit_nG[n] *= cos(theta)
# kpt.psit_nG[n] += sin(theta) * phi_G
axpy(sin(theta), phi_G, psit_nG[n])
for a, P2_i in P2_ai.items():
P_i = kpt.P_ani[a][n]
P_i *= cos(theta)
P_i += sin(theta) * P2_i
if nit < niter - 1:
Htpsit_G *= cos(theta)
# Htpsit_G += sin(theta) * Htphi_G
axpy(sin(theta), Htphi_G, Htpsit_G)
#adjust residuals
R_G[:] = Htpsit_G - kpt.eps_n[n] * psit_nG[n]
coef_ai = wfs.pt.dict()
for a, coef_i in coef_ai.items():
P_i = kpt.P_ani[a][n]
dO_ii = wfs.setups[a].dO_ii
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
coef_i[:] = (dot(P_i, dH_ii) -
dot(P_i * kpt.eps_n[n], dO_ii))
wfs.pt.add(R_G, coef_ai, kpt.q)
error_new = np.real(wfs.integrate(R_G, R_G))
if error_new / error < self.rtol:
# print >> self.f, "cg:iters", n, nit+1
break
if (self.nbands_converge == 'occupied' and
kpt.f_n is not None and kpt.f_n[n] == 0.0):
# print >> self.f, "cg:iters", n, nit+1
break
error = error_new
if kpt.f_n is None:
weight = 1.0
else:
weight = kpt.f_n[n]
if self.nbands_converge != 'occupied':
weight = kpt.weight * float(n < self.nbands_converge)
total_error += weight * error
# if nit == 3:
# print >> self.f, "cg:iters", n, nit+1
self.timer.stop('CG')
return total_error, psit_nG
def iterate_one_k_point(self, hamiltonian, wfs, kpt):
"""Do conjugate gradient iterations for the k-point"""
niter = self.niter
phi_G = wfs.empty(q=kpt.q)
phi_old_G = wfs.empty(q=kpt.q)
comm = wfs.gd.comm
psit_nG, Htpsit_nG = self.subspace_diagonalize(hamiltonian, wfs, kpt)
# Note that psit_nG is now in self.operator.work1_nG and
# Htpsit_nG is in kpt.psit_nG!
R_nG = reshape(self.Htpsit_nG, psit_nG.shape)
Htphi_G = R_nG[0]
R_nG[:] = Htpsit_nG
self.timer.start('Residuals')
self.calculate_residuals(kpt, wfs, hamiltonian, psit_nG, kpt.P_ani,
kpt.eps_n, R_nG)
self.timer.stop('Residuals')
self.timer.start('CG')
total_error = 0.0
for n in range(self.nbands):
if extra_parameters.get('PK', False):
N = n + 1
else:
N = psit_nG.shape[0] + 1
R_G = R_nG[n]
Htpsit_G = Htpsit_nG[n]
gamma_old = 1.0
phi_old_G[:] = 0.0
error = np.real(wfs.integrate(R_G, R_G))
for nit in range(niter):
if (error * Hartree**2 < self.tolerance / self.nbands):
break
ekin = self.preconditioner.calculate_kinetic_energy(
psit_nG[n:n + 1], kpt)
pR_G = self.preconditioner(R_nG[n:n + 1], kpt, ekin)
# New search direction
gamma = comm.sum(np.vdot(pR_G, R_G).real)
phi_G[:] = -pR_G - gamma / gamma_old * phi_old_G
gamma_old = gamma
phi_old_G[:] = phi_G[:]
# Calculate projections
P2_ai = wfs.pt.dict()
wfs.pt.integrate(phi_G, P2_ai, kpt.q)
# Orthonormalize phi_G to all bands
self.timer.start('CG: orthonormalize')
self.timer.start('CG: overlap')
overlap_n = wfs.integrate(psit_nG[:N],
phi_G,
global_integral=False)
self.timer.stop('CG: overlap')
self.timer.start('CG: overlap2')
for a, P2_i in P2_ai.items():
P_ni = kpt.P_ani[a]
dO_ii = wfs.setups[a].dO_ii
gemv(1.0, P_ni[:N].conjugate(), np.inner(dO_ii, P2_i), 1.0,
overlap_n)
self.timer.stop('CG: overlap2')
comm.sum(overlap_n)
# phi_G -= overlap_n * kpt.psit_nG
wfs.matrixoperator.gd.gemv(-1.0, psit_nG[:N], overlap_n, 1.0,
phi_G, 'n')
for a, P2_i in P2_ai.items():
P_ni = kpt.P_ani[a]
gemv(-1.0, P_ni[:N], overlap_n, 1.0, P2_i, 'n')
norm = wfs.integrate(phi_G, phi_G, global_integral=False)
for a, P2_i in P2_ai.items():
dO_ii = wfs.setups[a].dO_ii
norm += np.vdot(P2_i, np.inner(dO_ii, P2_i))
norm = comm.sum(np.real(norm).item())
phi_G /= sqrt(norm)
for P2_i in P2_ai.values():
P2_i /= sqrt(norm)
self.timer.stop('CG: orthonormalize')
# find optimum linear combination of psit_G and phi_G
an = kpt.eps_n[n]
wfs.apply_pseudo_hamiltonian(
kpt, hamiltonian, phi_G.reshape((1, ) + phi_G.shape),
Htphi_G.reshape((1, ) + Htphi_G.shape))
b = wfs.integrate(phi_G, Htpsit_G, global_integral=False)
c = wfs.integrate(phi_G, Htphi_G, global_integral=False)
for a, P2_i in P2_ai.items():
P_i = kpt.P_ani[a][n]
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
b += dot(P2_i, dot(dH_ii, P_i.conj()))
c += dot(P2_i, dot(dH_ii, P2_i.conj()))
b = comm.sum(np.real(b).item())
c = comm.sum(np.real(c).item())
theta = 0.5 * atan2(2 * b, an - c)
enew = (an * cos(theta)**2 + c * sin(theta)**2 +
b * sin(2.0 * theta))
# theta can correspond either minimum or maximum
if (enew - kpt.eps_n[n]) > 0.0: # we were at maximum
theta += pi / 2.0
enew = (an * cos(theta)**2 + c * sin(theta)**2 +
b * sin(2.0 * theta))
kpt.eps_n[n] = enew
psit_nG[n] *= cos(theta)
# kpt.psit_nG[n] += sin(theta) * phi_G
axpy(sin(theta), phi_G, psit_nG[n])
for a, P2_i in P2_ai.items():
P_i = kpt.P_ani[a][n]
P_i *= cos(theta)
P_i += sin(theta) * P2_i
if nit < niter - 1:
Htpsit_G *= cos(theta)
# Htpsit_G += sin(theta) * Htphi_G
axpy(sin(theta), Htphi_G, Htpsit_G)
#adjust residuals
R_G[:] = Htpsit_G - kpt.eps_n[n] * psit_nG[n]
coef_ai = wfs.pt.dict()
for a, coef_i in coef_ai.items():
P_i = kpt.P_ani[a][n]
dO_ii = wfs.setups[a].dO_ii
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
coef_i[:] = (dot(P_i, dH_ii) -
dot(P_i * kpt.eps_n[n], dO_ii))
wfs.pt.add(R_G, coef_ai, kpt.q)
error_new = np.real(wfs.integrate(R_G, R_G))
if error_new / error < self.rtol:
# print >> self.f, "cg:iters", n, nit+1
break
if (self.nbands_converge == 'occupied'
and kpt.f_n is not None and kpt.f_n[n] == 0.0):
# print >> self.f, "cg:iters", n, nit+1
break
error = error_new
if kpt.f_n is None:
weight = 1.0
else:
weight = kpt.f_n[n]
if self.nbands_converge != 'occupied':
weight = kpt.weight * float(n < self.nbands_converge)
total_error += weight * error
# if nit == 3:
# print >> self.f, "cg:iters", n, nit+1
self.timer.stop('CG')
return total_error, psit_nG
def iterate_one_k_point(self, hamiltonian, wfs, kpt):
"""Do Davidson iterations for the kpoint"""
niter = self.niter
nbands = self.nbands
mynbands = self.mynbands
gd = wfs.matrixoperator.gd
bd = self.operator.bd
psit_nG, Htpsit_nG = self.subspace_diagonalize(hamiltonian, wfs, kpt)
# Note that psit_nG is now in self.operator.work1_nG and
# Htpsit_nG is in kpt.psit_nG!
H_2n2n = self.H_2n2n
S_2n2n = self.S_2n2n
eps_2n = self.eps_2n
self.timer.start('Davidson')
if self.keep_htpsit:
R_nG = Htpsit_nG
psit2_nG = reshape(self.Htpsit_nG, psit_nG.shape)
else:
R_nG = wfs.empty(mynbands, q=kpt.q)
psit2_nG = wfs.empty(mynbands, q=kpt.q)
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_nG, R_nG)
wfs.pt.integrate(psit_nG, kpt.P_ani, kpt.q)
self.calculate_residuals(kpt, wfs, hamiltonian, psit_nG,
kpt.P_ani, kpt.eps_n, R_nG)
def integrate(a_G, b_G):
return np.real(wfs.integrate(a_G, b_G, global_integral=False))
# Note on band parallelization
# The "large" H_2n2n and S_2n2n matrices are at the moment
# global and replicated over band communicator, and the
# general diagonalization is performed in serial i.e. without
# scalapack
for nit in range(niter):
H_2n2n[:] = 0.0
S_2n2n[:] = 0.0
norm_n = np.zeros(mynbands)
error = 0.0
for n in range(mynbands):
if kpt.f_n is None:
weight = kpt.weight
else:
weight = kpt.f_n[n]
if self.nbands_converge != 'occupied':
if n < self.nbands_converge:
weight = kpt.weight
else:
weight = 0.0
error += weight * integrate(R_nG[n], R_nG[n])
ekin = self.preconditioner.calculate_kinetic_energy(
psit_nG[n:n + 1], kpt)
psit2_nG[n] = self.preconditioner(R_nG[n:n + 1], kpt, ekin)
if self.normalize:
norm_n[n] = integrate(psit2_nG[n], psit2_nG[n])
N = bd.global_index(n)
H_2n2n[N, N] = kpt.eps_n[n]
S_2n2n[N, N] = 1.0
bd.comm.sum(H_2n2n)
bd.comm.sum(S_2n2n)
if self.normalize:
gd.comm.sum(norm_n)
for norm, psit2_G in zip(norm_n, psit2_nG):
psit2_G *= norm**-0.5
# Calculate projections
P2_ani = wfs.pt.dict(mynbands)
wfs.pt.integrate(psit2_nG, P2_ani, kpt.q)
self.timer.start('calc. matrices')
# Hamiltonian matrix
# <psi2 | H | psi>
def H(psit_xG):
result_xG = R_nG
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_xG,
result_xG)
return result_xG
def dH(a, P_ni):
return np.dot(P_ni, unpack(hamiltonian.dH_asp[a][kpt.s]))
H_nn = self.operator.calculate_matrix_elements(psit_nG, kpt.P_ani,
H, dH, psit2_nG,
P2_ani)
H_2n2n[nbands:, :nbands] = H_nn
# <psi2 | H | psi2>
def H(psit_xG):
# H | psi2 > already calculated in previous step
result_xG = R_nG
return result_xG
def dH(a, P_ni):
return np.dot(P_ni, unpack(hamiltonian.dH_asp[a][kpt.s]))
H_nn = self.operator.calculate_matrix_elements(psit2_nG, P2_ani,
H, dH)
H_2n2n[nbands:, nbands:] = H_nn
# Overlap matrix
# <psi2 | S | psi>
def S(psit_G):
return psit_G
def dS(a, P_ni):
return np.dot(P_ni, wfs.setups[a].dO_ii)
S_nn = self.operator.calculate_matrix_elements(psit_nG, kpt.P_ani,
S, dS, psit2_nG,
P2_ani)
S_2n2n[nbands:, :nbands] = S_nn
# <psi2 | S | psi2>
S_nn = self.operator.calculate_matrix_elements(psit2_nG, P2_ani,
S, dS)
S_2n2n[nbands:, nbands:] = S_nn
self.timer.stop('calc. matrices')
self.timer.start('diagonalize')
if gd.comm.rank == 0 and bd.comm.rank == 0:
m = 0
if self.smin:
s_N, U_NN = np.linalg.eigh(S_2n2n)
m = int((s_N < self.smin).sum())
if m == 0:
general_diagonalize(H_2n2n, eps_2n, S_2n2n)
else:
T_Nn = np.dot(U_NN[:, m:], np.diag(s_N[m:]**-0.5))
H_2n2n[:nbands, nbands:] = \
H_2n2n[nbands:, :nbands].conj().T
eps_2n[:-m], P_nn = np.linalg.eigh(
np.dot(np.dot(T_Nn.T.conj(), H_2n2n), T_Nn))
H_2n2n[:-m] = np.dot(T_Nn, P_nn).T
gd.comm.broadcast(H_2n2n, 0)
gd.comm.broadcast(eps_2n, 0)
bd.comm.broadcast(H_2n2n, 0)
bd.comm.broadcast(eps_2n, 0)
self.operator.bd.distribute(eps_2n[:nbands], kpt.eps_n[:])
self.timer.stop('diagonalize')
self.timer.start('rotate_psi')
# Rotate psit_nG
# Memory references during rotate:
# Case 1, no band parallelization:
# Before 1. matrix multiply: psit_nG -> operator.work1_xG
# After 1. matrix multiply: psit_nG -> R_nG
# After 2. matrix multiply: tmp_nG -> work1_xG
#
# Case 2, band parallelization
# Work arrays used only in send/recv buffers,
# psit_nG -> psit_nG
# tmp_nG -> psit2_nG
psit_nG = self.operator.matrix_multiply(H_2n2n[:nbands, :nbands],
psit_nG, kpt.P_ani,
out_nG=R_nG)
tmp_nG = self.operator.matrix_multiply(H_2n2n[:nbands, nbands:],
psit2_nG, P2_ani)
if bd.comm.size > 1:
psit_nG += tmp_nG
else:
tmp_nG += psit_nG
psit_nG, R_nG = tmp_nG, psit_nG
for a, P_ni in kpt.P_ani.items():
P2_ni = P2_ani[a]
P_ni += P2_ni
self.timer.stop('rotate_psi')
if nit < niter - 1:
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_nG,
R_nG)
self.calculate_residuals(kpt, wfs, hamiltonian, psit_nG,
kpt.P_ani, kpt.eps_n, R_nG)
self.timer.stop('Davidson')
error = gd.comm.sum(error)
return error, psit_nG
def iterate_one_k_point(self, hamiltonian, wfs, kpt):
"""Do Davidson iterations for the kpoint"""
niter = self.niter
nbands = self.nbands
gd = wfs.matrixoperator.gd
psit_nG, Htpsit_nG = self.subspace_diagonalize(hamiltonian, wfs, kpt)
# Note that psit_nG is now in self.operator.work1_nG and
# Htpsit_nG is in kpt.psit_nG!
H_2n2n = self.H_2n2n
S_2n2n = self.S_2n2n
eps_2n = self.eps_2n
psit2_nG = reshape(self.Htpsit_nG, psit_nG.shape)
self.timer.start('Davidson')
R_nG = Htpsit_nG
self.calculate_residuals(kpt, wfs, hamiltonian, psit_nG, kpt.P_ani,
kpt.eps_n, R_nG)
def integrate(a_G, b_G):
return np.real(wfs.integrate(a_G, b_G, global_integral=False))
for nit in range(niter):
H_2n2n[:] = 0.0
S_2n2n[:] = 0.0
norm_n = np.zeros(nbands)
error = 0.0
for n in range(nbands):
if kpt.f_n is None:
weight = kpt.weight
else:
weight = kpt.f_n[n]
if self.nbands_converge != 'occupied':
if n < self.nbands_converge:
weight = kpt.weight
else:
weight = 0.0
error += weight * integrate(R_nG[n], R_nG[n])
ekin = self.preconditioner.calculate_kinetic_energy(
psit_nG[n:n + 1], kpt)
psit2_nG[n] = self.preconditioner(R_nG[n:n + 1], kpt, ekin)
if self.normalize:
norm_n[n] = integrate(psit2_nG[n], psit2_nG[n])
H_2n2n[n, n] = kpt.eps_n[n]
S_2n2n[n, n] = 1.0
if self.normalize:
gd.comm.sum(norm_n)
for norm, psit2_G in zip(norm_n, psit2_nG):
psit2_G *= norm**-0.5
# Calculate projections
P2_ani = wfs.pt.dict(nbands)
wfs.pt.integrate(psit2_nG, P2_ani, kpt.q)
# Hamiltonian matrix
# <psi2 | H | psi>
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit2_nG, Htpsit_nG)
gd.integrate(psit_nG,
Htpsit_nG,
global_integral=False,
_transposed_result=self.H_nn)
# gemm(1.0, psit_nG, Htpsit_nG, 0.0, self.H_nn, 'c')
for a, P_ni in kpt.P_ani.items():
P2_ni = P2_ani[a]
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
self.H_nn += np.dot(P2_ni, np.dot(dH_ii, P_ni.T.conj()))
gd.comm.sum(self.H_nn, 0)
H_2n2n[nbands:, :nbands] = self.H_nn
# <psi2 | H | psi2>
gd.integrate(psit2_nG,
Htpsit_nG,
global_integral=False,
_transposed_result=self.H_nn)
# r2k(0.5 * gd.dv, psit2_nG, Htpsit_nG, 0.0, self.H_nn)
for a, P2_ni in P2_ani.items():
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
self.H_nn += np.dot(P2_ni, np.dot(dH_ii, P2_ni.T.conj()))
gd.comm.sum(self.H_nn, 0)
H_2n2n[nbands:, nbands:] = self.H_nn
# Overlap matrix
# <psi2 | S | psi>
gd.integrate(psit_nG,
psit2_nG,
global_integral=False,
_transposed_result=self.S_nn)
# gemm(1.0, psit_nG, psit2_nG, 0.0, self.S_nn, 'c')
for a, P_ni in kpt.P_ani.items():
P2_ni = P2_ani[a]
dO_ii = wfs.setups[a].dO_ii
self.S_nn += np.dot(P2_ni, np.inner(dO_ii, P_ni.conj()))
gd.comm.sum(self.S_nn, 0)
S_2n2n[nbands:, :nbands] = self.S_nn
# <psi2 | S | psi2>
gd.integrate(psit2_nG,
psit2_nG,
global_integral=False,
_transposed_result=self.S_nn)
# rk(gd.dv, psit2_nG, 0.0, self.S_nn)
for a, P2_ni in P2_ani.items():
dO_ii = wfs.setups[a].dO_ii
self.S_nn += np.dot(P2_ni, np.dot(dO_ii, P2_ni.T.conj()))
gd.comm.sum(self.S_nn, 0)
S_2n2n[nbands:, nbands:] = self.S_nn
if gd.comm.rank == 0:
m = 0
if self.smin:
s_N, U_NN = np.linalg.eigh(S_2n2n)
m = int((s_N < self.smin).sum())
if m == 0:
general_diagonalize(H_2n2n, eps_2n, S_2n2n)
else:
T_Nn = np.dot(U_NN[:, m:], np.diag(s_N[m:]**-0.5))
H_2n2n[:nbands, nbands:] = \
H_2n2n[nbands:, :nbands].conj().T
eps_2n[:-m], P_nn = np.linalg.eigh(
np.dot(np.dot(T_Nn.T.conj(), H_2n2n), T_Nn))
H_2n2n[:-m] = np.dot(T_Nn, P_nn).T
gd.comm.broadcast(H_2n2n, 0)
gd.comm.broadcast(eps_2n, 0)
kpt.eps_n[:] = eps_2n[:nbands]
# Rotate psit_nG
gd.gemm(1.0, psit_nG, H_2n2n[:nbands, :nbands], 0.0, Htpsit_nG)
gd.gemm(1.0, psit2_nG, H_2n2n[:nbands, nbands:], 1.0, Htpsit_nG)
psit_nG, Htpsit_nG = Htpsit_nG, psit_nG
# Rotate P_uni:
for a, P_ni in kpt.P_ani.items():
P2_ni = P2_ani[a]
gemm(1.0, P_ni.copy(), H_2n2n[:nbands, :nbands], 0.0, P_ni)
gemm(1.0, P2_ni, H_2n2n[:nbands, nbands:], 1.0, P_ni)
if nit < niter - 1:
wfs.apply_pseudo_hamiltonian(kpt, hamiltonian, psit_nG,
Htpsit_nG)
R_nG = Htpsit_nG
self.calculate_residuals(kpt, wfs, hamiltonian, psit_nG,
kpt.P_ani, kpt.eps_n, R_nG)
self.timer.stop('Davidson')
error = gd.comm.sum(error)
return error, psit_nG