def restore_RCF(self, use_QR=True, update_l=True, diag_l=True):
"""Use a gauge-transformation to restore right canonical form.
Implements the conditions for right canonical form from sub-section
3.1, theorem 1 of arXiv:quant-ph/0608197v2.
It is possible to skip the diagonalization of the l's, such that
only the right orthonormalization condition (r_n = eye) is met.
By default, the l's are updated even if diag_l=False.
Parameters
----------
update_l : bool
Whether to call calc_l() after completion (defaults to True)
diag_l : bool
Whether to put l in diagonal form (defaults to True)
"""
if use_QR:
tm.restore_RCF_r_seq(self.A, self.r, sanity_checks=self.sanity_checks,
sc_data="restore_RCF_r")
else:
G_n_i = sp.eye(self.D[self.N], dtype=self.typ) #This is actually just the number 1
for n in xrange(self.N, 0, -1):
self.r[n - 1], G_n, G_n_i = tm.restore_RCF_r(self.A[n], self.r[n],
G_n_i, sc_data=('site', n),
zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
if self.sanity_checks:
if not sp.allclose(self.r[0].A, 1, atol=1E-12, rtol=1E-12):
log.warning("Sanity Fail in restore_RCF!: r_0 is bad / norm failure")
if diag_l:
tm.restore_RCF_l_seq(self.A, self.l, sanity_checks=self.sanity_checks,
sc_data="restore_RCF_l")
if self.sanity_checks:
if not sp.allclose(self.l[self.N].A, 1, atol=1E-12, rtol=1E-12):
log.warning("Sanity Fail in restore_RCF!: l_N is bad / norm failure")
log.warning("l_N = %s", self.l[self.N].squeeze().real)
for n in xrange(1, self.N + 1):
r_nm1 = tm.eps_r_noop(self.r[n], self.A[n], self.A[n])
#r_nm1 = tm.eps_r_noop(m.eyemat(self.D[n], self.typ), self.A[n], self.A[n])
if not sp.allclose(r_nm1, self.r[n - 1], atol=1E-11, rtol=1E-11):
log.warning("Sanity Fail in restore_RCF!: r_%u is bad (off by %g)", n, la.norm(r_nm1 - self.r[n - 1]))
elif update_l:
self.calc_l()
def restore_RCF(self, use_QR=True, update_l=True, diag_l=True):
"""Use a gauge-transformation to restore right canonical form.
Implements the conditions for right canonical form from sub-section
3.1, theorem 1 of arXiv:quant-ph/0608197v2.
It is possible to skip the diagonalization of the l's, such that
only the right orthonormalization condition (r_n = eye) is met.
By default, the l's are updated even if diag_l=False.
Parameters
----------
update_l : bool
Whether to call calc_l() after completion (defaults to True)
diag_l : bool
Whether to put l in diagonal form (defaults to True)
"""
if use_QR:
tm.restore_RCF_r_seq(self.A, self.r, sanity_checks=self.sanity_checks,
sc_data="restore_RCF_r")
else:
G_n_i = sp.eye(self.D[self.N], dtype=self.typ) #This is actually just the number 1
for n in xrange(self.N, 0, -1):
self.r[n - 1], G_n, G_n_i = tm.restore_RCF_r(self.A[n], self.r[n],
G_n_i, sc_data=('site', n),
zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
if self.sanity_checks:
if not sp.allclose(self.r[0].A, 1, atol=1E-12, rtol=1E-12):
log.warning("Sanity Fail in restore_RCF!: r_0 is bad / norm failure")
if diag_l:
tm.restore_RCF_l_seq(self.A, self.l, sanity_checks=self.sanity_checks,
sc_data="restore_RCF_l")
if self.sanity_checks:
if not sp.allclose(self.l[self.N].A, 1, atol=1E-12, rtol=1E-12):
log.warning("Sanity Fail in restore_RCF!: l_N is bad / norm failure")
log.warning("l_N = %s", self.l[self.N].squeeze().real)
for n in xrange(1, self.N + 1):
r_nm1 = tm.eps_r_noop(self.r[n], self.A[n], self.A[n])
#r_nm1 = tm.eps_r_noop(m.eyemat(self.D[n], self.typ), self.A[n], self.A[n])
if not sp.allclose(r_nm1, self.r[n - 1], atol=1E-11, rtol=1E-11):
log.warning("Sanity Fail in restore_RCF!: r_%u is bad (off by %g)", n, la.norm(r_nm1 - self.r[n - 1]))
elif update_l:
self.calc_l()
def take_step_split(self, dtau, ham_is_Herm=True):
"""Take a time-step dtau using the split-step integrator.
This is the one-site version of a DMRG-like time integrator described
at:
http://arxiv.org/abs/1408.5056
It has a fourth-order local error and is symmetric. It requires
iteratively computing two matrix exponentials per site, and thus
has less predictable CPU time requirements than the Euler or RK4
methods.
NOTE:
This requires the expokit extension, which is included in evoMPS but
must be compiled during, e.g. using setup.py to build all extensions.
Parameters
----------
dtau : complex
The (imaginary or real) amount of imaginary time (tau) to step.
ham_is_Herm : bool
Whether the Hamiltonian is really Hermitian. If so, the lanczos
method will be used for imaginary time evolution.
"""
#TODO: Compute eta.
self.eta_sq.fill(0)
self.eta = 0
assert self.canonical_form == 'right', 'take_step_split only implemented for right canonical form'
assert self.ham_sites == 2, 'take_step_split only implemented for nearest neighbour Hamiltonians'
dtau *= -1
from expokit_expmv import zexpmv, zexpmvh
if sp.iscomplex(dtau) or not ham_is_Herm:
expmv = zexpmv
fac = 1.j
dtau = sp.imag(dtau)
else:
expmv = zexpmvh
fac = 1
norm_est = abs(self.H_expect.real)
KL = [None] * (self.N + 1)
KL[1] = sp.zeros((self.D[1], self.D[1]), dtype=self.typ)
for n in xrange(1, self.N + 1):
lop = Vari_Opt_Single_Site_Op(self, n, KL[n - 1], tau=fac)
#print "Befor A", n, sp.inner(self.A[n].ravel().conj(), lop.matvec(self.A[n].ravel())).real
An = expmv(lop, self.A[n].ravel(), dtau/2., norm_est=norm_est)
self.A[n] = An.reshape((self.q[n], self.D[n - 1], self.D[n]))
self.l[n] = tm.eps_l_noop(self.l[n - 1], self.A[n], self.A[n])
norm = m.adot(self.l[n], self.r[n])
self.A[n] /= sp.sqrt(norm)
#print "After A", n, sp.inner(self.A[n].ravel().conj(), lop.matvec(self.A[n].ravel())).real, norm.real
#shift centre matrix right (RCF is like having a centre "matrix" at "1")
G = tm.restore_LCF_l_seq(self.A[n - 1:n + 1], self.l[n - 1:n + 1],
sanity_checks=self.sanity_checks)
if n > 1:
self.AA[n - 1] = tm.calc_AA(self.A[n - 1], self.A[n])
self.C[n - 1] = tm.calc_C_mat_op_AA(self.ham[n - 1], self.AA[n - 1])
KL[n], ex = tm.calc_K_l(KL[n - 1], self.C[n - 1], self.l[n - 2],
self.r[n], self.A[n], self.AA[n - 1])
if n < self.N:
lop2 = Vari_Opt_SC_op(self, n, KL[n], tau=fac)
#print "Befor G", n, sp.inner(G.ravel().conj(), lop2.matvec(G.ravel())).real
G = expmv(lop2, G.ravel(), -dtau/2., norm_est=norm_est)
G = G.reshape((self.D[n], self.D[n]))
norm = sp.trace(self.l[n].dot(G).dot(self.r[n].dot(G.conj().T)))
G /= sp.sqrt(norm)
#print "After G", n, sp.inner(G.ravel().conj(), lop2.matvec(G.ravel())).real, norm.real
for s in xrange(self.q[n + 1]):
self.A[n + 1][s] = G.dot(self.A[n + 1][s])
self.AA[n] = tm.calc_AA(self.A[n], self.A[n + 1])
self.C[n] = tm.calc_C_mat_op_AA(self.ham[n], self.AA[n])
for n in xrange(self.N, 0, -1):
lop = Vari_Opt_Single_Site_Op(self, n, KL[n - 1], tau=fac, sanity_checks=self.sanity_checks)
#print "Before A", n, sp.inner(self.A[n].ravel().conj(), lop.matvec(self.A[n].ravel())).real
An = expmv(lop, self.A[n].ravel(), dtau/2., norm_est=norm_est)
self.A[n] = An.reshape((self.q[n], self.D[n - 1], self.D[n]))
self.l[n] = tm.eps_l_noop(self.l[n - 1], self.A[n], self.A[n])
norm = m.adot(self.l[n], self.r[n])
self.A[n] /= sp.sqrt(norm)
#print "After A", n, sp.inner(self.A[n].ravel().conj(), lop.matvec(self.A[n].ravel())).real, norm.real
#shift centre matrix left (LCF is like having a centre "matrix" at "N")
Gi = tm.restore_RCF_r_seq(self.A[n - 1:n + 1], self.r[n - 1:n + 1],
sanity_checks=self.sanity_checks)
if n < self.N:
self.AA[n] = tm.calc_AA(self.A[n], self.A[n + 1])
self.C[n] = tm.calc_C_mat_op_AA(self.ham[n], self.AA[n])
self.calc_K(n_low=n, n_high=n)
if n > 1:
lop2 = Vari_Opt_SC_op(self, n - 1, KL[n - 1], tau=fac, sanity_checks=self.sanity_checks)
Gi = expmv(lop2, Gi.ravel(), -dtau/2., norm_est=norm_est)
Gi = Gi.reshape((self.D[n - 1], self.D[n - 1]))
norm = sp.trace(self.l[n - 1].dot(Gi).dot(self.r[n - 1].dot(Gi.conj().T)))
G /= sp.sqrt(norm)
#print "After G", n, sp.inner(Gi.ravel().conj(), lop2.matvec(Gi.ravel())).real, norm.real
for s in xrange(self.q[n - 1]):
self.A[n - 1][s] = self.A[n - 1][s].dot(Gi)
self.AA[n - 1] = tm.calc_AA(self.A[n - 1], self.A[n])
self.C[n - 1] = tm.calc_C_mat_op_AA(self.ham[n - 1], self.AA[n - 1])
def vari_opt_ss_sweep(self, ncv=None):
"""Perform a DMRG-style optimizing sweep to reduce the energy.
This carries out the MPS version of the one-site DMRG algorithm.
Combined with imaginary time evolution, this can dramatically improve
convergence speed.
"""
assert self.canonical_form == 'right', 'vari_opt_ss_sweep only implemented for right canonical form'
KL = [None] * (self.N + 1)
KL[1] = sp.zeros((self.D[1], self.D[1]), dtype=self.typ)
for n in xrange(1, self.N + 1):
if n > 2:
k = n - 1
KL[k], ex = tm.calc_K_l(KL[k - 1], self.C[k - 1], self.l[k - 2],
self.r[k], self.A[k], self.AA[k - 1])
lop = Vari_Opt_Single_Site_Op(self, n, KL[n - 1], sanity_checks=self.sanity_checks)
evs, eVs = las.eigsh(lop, k=1, which='SA', v0=self.A[n].ravel(), ncv=ncv)
self.A[n] = eVs[:, 0].reshape((self.q[n], self.D[n - 1], self.D[n]))
#shift centre matrix right (RCF is like having a centre "matrix" at "1")
G = tm.restore_LCF_l_seq(self.A[n - 1:n + 1], self.l[n - 1:n + 1],
sanity_checks=self.sanity_checks)
#This is not strictly necessary, since r[n] is not used again,
self.r[n] = G.dot(self.r[n].dot(G.conj().T))
if n < self.N:
for s in xrange(self.q[n + 1]):
self.A[n + 1][s] = G.dot(self.A[n + 1][s])
#All needed l and r should now be up to date
#All needed KR should be valid still
#AA and C must be updated
if n > 1:
self.AA[n - 1] = tm.calc_AA(self.A[n - 1], self.A[n])
self.C[n - 1] = tm.calc_C_mat_op_AA(self.ham[n - 1], self.AA[n - 1])
if n < self.N:
self.AA[n] = tm.calc_AA(self.A[n], self.A[n + 1])
self.C[n] = tm.calc_C_mat_op_AA(self.ham[n], self.AA[n])
for n in xrange(self.N, 0, -1):
if n < self.N:
self.calc_K(n_low=n + 1, n_high=n + 1)
lop = Vari_Opt_Single_Site_Op(self, n, KL[n - 1], sanity_checks=self.sanity_checks)
evs, eVs = las.eigsh(lop, k=1, which='SA', v0=self.A[n].ravel(), ncv=ncv)
self.A[n] = eVs[:, 0].reshape((self.q[n], self.D[n - 1], self.D[n]))
#shift centre matrix left (LCF is like having a centre "matrix" at "N")
Gi = tm.restore_RCF_r_seq(self.A[n - 1:n + 1], self.r[n - 1:n + 1],
sanity_checks=self.sanity_checks)
#This is not strictly necessary, since l[n - 1] is not used again
self.l[n - 1] = Gi.conj().T.dot(self.l[n - 1].dot(Gi))
if n > 1:
for s in xrange(self.q[n - 1]):
self.A[n - 1][s] = self.A[n - 1][s].dot(Gi)
#All needed l and r should now be up to date
#All needed KL should be valid still
#AA and C must be updated
if n > 1:
self.AA[n - 1] = tm.calc_AA(self.A[n - 1], self.A[n])
self.C[n - 1] = tm.calc_C_mat_op_AA(self.ham[n - 1], self.AA[n - 1])
if n < self.N:
self.AA[n] = tm.calc_AA(self.A[n], self.A[n + 1])
self.C[n] = tm.calc_C_mat_op_AA(self.ham[n], self.AA[n])
