def ode2es(L, rho0):
"""Creates an exponential series that describes the time evolution for the
initial density matrix (or state vector) `rho0`, given the Liouvillian
(or Hamiltonian) `L`.
.. deprecated:: 4.6.0
:obj:`~ode2es` will be removed in QuTiP 5. Please use
:obj:`Qobj.eigenstates` to get the eigenstates and -values, and use
:obj:`~QobjEvo` for general time-dependence.
Parameters
----------
L : qobj
Liouvillian of the system.
rho0 : qobj
Initial state vector or density matrix.
Returns
-------
eseries : :class:`qutip.eseries`
``eseries`` represention of the system dynamics.
"""
if issuper(L):
# check initial state
if isket(rho0):
# Got a wave function as initial state: convert to density matrix.
rho0 = rho0 * rho0.dag()
# check if state is below error threshold
if abs(rho0.full()).sum() < 1e-10 + 1e-24:
# enforce zero operator
return eseries(qzero(rho0.dims[0]))
w, v = L.eigenstates()
v = np.hstack([ket.full() for ket in v])
# w[i] = eigenvalue i
# v[:,i] = eigenvector i
rlen = np.prod(rho0.shape)
r0 = mat2vec(rho0.full())
v0 = la.solve(v, r0)
vv = v * sp.spdiags(v0.T, 0, rlen, rlen)
out = None
for i in range(rlen):
qo = Qobj(vec2mat(vv[:, i]), dims=rho0.dims, shape=rho0.shape)
if out:
out += eseries(qo, w[i])
else:
out = eseries(qo, w[i])
elif isoper(L):
if not isket(rho0):
raise TypeError('Second argument must be a ket if first' +
'is a Hamiltonian.')
# check if state is below error threshold
if abs(rho0.full()).sum() < 1e-5 + 1e-20:
# enforce zero operator
dims = rho0.dims
return eseries(
Qobj(sp.csr_matrix((dims[0][0], dims[1][0]), dtype=complex)))
w, v = L.eigenstates()
v = np.hstack([ket.full() for ket in v])
# w[i] = eigenvalue i
# v[:,i] = eigenvector i
rlen = np.prod(rho0.shape)
r0 = rho0.full()
v0 = la.solve(v, r0)
vv = v * sp.spdiags(v0.T, 0, rlen, rlen)
out = None
for i in range(rlen):
qo = Qobj(np.array(vv[:, i]).T, dims=rho0.dims, shape=rho0.shape)
if out:
out += eseries(qo, -1.0j * w[i])
else:
out = eseries(qo, -1.0j * w[i])
else:
raise TypeError('First argument must be a Hamiltonian or Liouvillian.')
return estidy(out)
def ode2es(L, rho0):
"""Creates an exponential series that describes the time evolution for the
initial density matrix (or state vector) `rho0`, given the Liouvillian
(or Hamiltonian) `L`.
Parameters
----------
L : qobj
Liouvillian of the system.
rho0 : qobj
Initial state vector or density matrix.
Returns
-------
eseries : :class:`qutip.eseries`
``eseries`` represention of the system dynamics.
"""
if issuper(L):
# check initial state
if isket(rho0):
# Got a wave function as initial state: convert to density matrix.
rho0 = rho0 * rho0.dag()
w, v = L.eigenstates()
v = np.hstack([ket.full() for ket in v])
# w[i] = eigenvalue i
# v[:,i] = eigenvector i
rlen = np.prod(rho0.shape)
r0 = mat2vec(rho0.full())
v0 = la.solve(v, r0)
vv = v * sp.spdiags(v0.T, 0, rlen, rlen)
out = None
for i in range(rlen):
qo = Qobj(vec2mat(vv[:, i]), dims=rho0.dims, shape=rho0.shape)
if out:
out += eseries(qo, w[i])
else:
out = eseries(qo, w[i])
elif isoper(L):
if not isket(rho0):
raise TypeError("Second argument must be a ket if first" + "is a Hamiltonian.")
w, v = L.eigenstates()
v = np.hstack([ket.full() for ket in v])
# w[i] = eigenvalue i
# v[:,i] = eigenvector i
rlen = np.prod(rho0.shape)
r0 = rho0.full()
v0 = la.solve(v, r0)
vv = v * sp.spdiags(v0.T, 0, rlen, rlen)
out = None
for i in range(rlen):
qo = Qobj(np.matrix(vv[:, i]).T, dims=rho0.dims, shape=rho0.shape)
if out:
out += eseries(qo, -1.0j * w[i])
else:
out = eseries(qo, -1.0j * w[i])
else:
raise TypeError("First argument must be a Hamiltonian or Liouvillian.")
return estidy(out)
def ode2es(L, rho0):
"""Creates an exponential series that describes the time evolution for the
initial density matrix (or state vector) `rho0`, given the Liouvillian
(or Hamiltonian) `L`.
Parameters
----------
L : qobj
Liouvillian of the system.
rho0 : qobj
Initial state vector or density matrix.
Returns
-------
eseries : :class:`qutip.eseries`
``eseries`` represention of the system dynamics.
"""
if issuper(L):
# check initial state
if isket(rho0):
# Got a wave function as initial state: convert to density matrix.
rho0 = rho0 * rho0.dag()
w, v = L.eigenstates()
v = np.hstack([ket.full() for ket in v])
# w[i] = eigenvalue i
# v[:,i] = eigenvector i
rlen = prod(rho0.shape)
r0 = mat2vec(rho0.full())
v0 = la.solve(v, r0)
vv = v * sp.spdiags(v0.T, 0, rlen, rlen)
out = None
for i in range(rlen):
qo = Qobj(vec2mat(vv[:, i]), dims=rho0.dims, shape=rho0.shape)
if out:
out += eseries(qo, w[i])
else:
out = eseries(qo, w[i])
elif isoper(L):
if not isket(rho0):
raise TypeError('Second argument must be a ket if first' +
'is a Hamiltonian.')
w, v = L.eigenstates()
v = np.hstack([ket.full() for ket in v])
# w[i] = eigenvalue i
# v[:,i] = eigenvector i
rlen = prod(rho0.shape)
r0 = rho0.full()
v0 = la.solve(v, r0)
vv = v * sp.spdiags(v0.T, 0, rlen, rlen)
out = None
for i in range(rlen):
qo = Qobj(np.matrix(vv[:, i]).T, dims=rho0.dims, shape=rho0.shape)
if out:
out += eseries(qo, -1.0j * w[i])
else:
out = eseries(qo, -1.0j * w[i])
else:
raise TypeError('First argument must be a Hamiltonian or Liouvillian.')
return estidy(out)