def steadystate_nonlinear(L_func, rho0, args={}, maxiter=10, random_initial_state=False, tol=1e-6, itertol=1e-5, use_umfpack=True, verbose=False): """ Steady state for the evolution subject to the nonlinear Liouvillian (which depends on the density matrix). .. note:: Experimental. Not at all certain that the inverse power method works for state-dependent Liouvillian operators. """ use_solver(assumeSortedIndices=True, useUmfpack=use_umfpack) if random_initial_state: rhoss = rand_dm(rho0.shape[0], 1.0, dims=rho0.dims) elif isket(rho0): rhoss = ket2dm(rho0) else: rhoss = Qobj(rho0) v = mat2vec(rhoss.full()) n = prod(rhoss.shape) tr_vec = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo') tr_vec = tr_vec.reshape((1, n)) it = 0 while it < maxiter: L = L_func(rhoss, args) L = L.data.tocsc() - (tol**2) * sp.eye(n, n, format='csc') L.sort_indices() v = spsolve(L, v, use_umfpack=use_umfpack) v = v / la.norm(v, np.inf) data = v / sum(tr_vec.dot(v)) data = reshape(data, (rhoss.shape[0], rhoss.shape[1])).T rhoss.data = sp.csr_matrix(data) it += 1 if la.norm(L * v, np.inf) <= tol: break if it >= maxiter: raise ValueError('Failed to find steady state after ' + str(maxiter) + ' iterations') rhoss = 0.5 * (rhoss + rhoss.dag()) return rhoss.tidyup() if qset.auto_tidyup else rhoss
def _steadystate_power(L, maxiter=10, tol=1e-6, itertol=1e-5, use_umfpack=True, verbose=False): """ Inverse power method for steady state solving. """ if verbose: print('Starting iterative power method Solver...') use_solver(assumeSortedIndices=True, useUmfpack=use_umfpack) rhoss = Qobj() sflag = issuper(L) if sflag: rhoss.dims = L.dims[0] rhoss.shape = [prod(rhoss.dims[0]), prod(rhoss.dims[1])] else: rhoss.dims = [L.dims[0], 1] rhoss.shape = [prod(rhoss.dims[0]), 1] n = prod(rhoss.shape) L = L.data.tocsc() - (tol**2) * sp.eye(n, n, format='csc') L.sort_indices() v = mat2vec(rand_dm(rhoss.shape[0], 0.5 / rhoss.shape[0] + 0.5).full()) if verbose: start_time = time.time() it = 0 while (la.norm(L * v, np.inf) > tol) and (it < maxiter): v = spsolve(L, v, use_umfpack=use_umfpack) v = v / la.norm(v, np.inf) it += 1 if it >= maxiter: raise Exception('Failed to find steady state after ' + str(maxiter) + ' iterations') # normalise according to type of problem if sflag: trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo') trow = sp_reshape(trow, (1, n)) data = v / sum(trow.dot(v)) else: data = data / la.norm(v) data = sp.csr_matrix(vec2mat(data)) rhoss.data = 0.5 * (data + data.conj().T) rhoss.isherm = True if verbose: print('Power solver time: ', time.time() - start_time) if qset.auto_tidyup: return rhoss.tidyup() else: return rhoss
def steadystate_nonlinear(L_func, rho0, args={}, maxiter=10, random_initial_state=False, tol=1e-6, itertol=1e-5, use_umfpack=True, verbose=False): """ Steady state for the evolution subject to the nonlinear Liouvillian (which depends on the density matrix). .. note:: Experimental. Not at all certain that the inverse power method works for state-dependent Liouvillian operators. """ use_solver(assumeSortedIndices=True, useUmfpack=use_umfpack) if random_initial_state: rhoss = rand_dm(rho0.shape[0], 1.0, dims=rho0.dims) elif isket(rho0): rhoss = ket2dm(rho0) else: rhoss = Qobj(rho0) v = mat2vec(rhoss.full()) n = prod(rhoss.shape) tr_vec = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo') tr_vec = tr_vec.reshape((1, n)) it = 0 while it < maxiter: L = L_func(rhoss, args) L = L.data.tocsc() - (tol ** 2) * sp.eye(n, n, format='csc') L.sort_indices() v = spsolve(L, v, use_umfpack=use_umfpack) v = v / la.norm(v, np.inf) data = v / sum(tr_vec.dot(v)) data = reshape(data, (rhoss.shape[0], rhoss.shape[1])).T rhoss.data = sp.csr_matrix(data) it += 1 if la.norm(L * v, np.inf) <= tol: break if it >= maxiter: raise ValueError('Failed to find steady state after ' + str(maxiter) + ' iterations') rhoss = 0.5 * (rhoss + rhoss.dag()) return rhoss.tidyup() if qset.auto_tidyup else rhoss
def _steadystate_power(L, maxiter=10, tol=1e-6, itertol=1e-5, verbose=False): """ Inverse power method for steady state solving. """ if verbose: print('Starting iterative power method Solver...') use_solver(assumeSortedIndices=True) rhoss = Qobj() sflag = issuper(L) if sflag: rhoss.dims = L.dims[0] rhoss.shape = [prod(rhoss.dims[0]), prod(rhoss.dims[1])] else: rhoss.dims = [L.dims[0], 1] rhoss.shape = [prod(rhoss.dims[0]), 1] n = prod(rhoss.shape) L = L.data.tocsc() - (tol ** 2) * sp.eye(n, n, format='csc') L.sort_indices() v = mat2vec(rand_dm(rhoss.shape[0], 0.5 / rhoss.shape[0] + 0.5).full()) if verbose: start_time = time.time() it = 0 while (la.norm(L * v, np.inf) > tol) and (it < maxiter): v = spsolve(L, v) v = v / la.norm(v, np.inf) it += 1 if it >= maxiter: raise Exception('Failed to find steady state after ' + str(maxiter) + ' iterations') # normalise according to type of problem if sflag: trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo') trow = sp_reshape(trow, (1, n)) data = v / sum(trow.dot(v)) else: data = data / la.norm(v) data = sp.csr_matrix(vec2mat(data)) rhoss.data = 0.5 * (data + data.conj().T) rhoss.isherm = True if verbose: print('Power solver time: ', time.time() - start_time) if qset.auto_tidyup: return rhoss.tidyup() else: return rhoss
def tensor(*args): """Calculates the tensor product of input operators. Parameters ---------- args : array_like ``list`` or ``array`` of quantum objects for tensor product. Returns ------- obj : qobj A composite quantum object. Examples -------- >>> tensor([sigmax(), sigmax()]) # doctest: +SKIP Quantum object: dims = [[2, 2], [2, 2]], \ shape = [4, 4], type = oper, isHerm = True Qobj data = [[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j] [ 0.+0.j 0.+0.j 1.+0.j 0.+0.j] [ 0.+0.j 1.+0.j 0.+0.j 0.+0.j] [ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]] """ if not args: raise TypeError("Requires at least one input argument") if len(args) == 1 and isinstance(args[0], (list, np.ndarray)): # this is the case when tensor is called on the form: # tensor([q1, q2, q3, ...]) qlist = args[0] elif len(args) == 1 and isinstance(args[0], Qobj): # tensor is called with a single Qobj as an argument, do nothing return args[0] else: # this is the case when tensor is called on the form: # tensor(q1, q2, q3, ...) qlist = args if not all([isinstance(q, Qobj) for q in qlist]): # raise error if one of the inputs is not a quantum object raise TypeError("One of inputs is not a quantum object") out = Qobj() if qlist[0].issuper: out.superrep = qlist[0].superrep if not all([q.superrep == out.superrep for q in qlist]): raise TypeError("In tensor products of superroperators, all must" + "have the same representation") out.isherm = True for n, q in enumerate(qlist): if n == 0: out.data = q.data out.dims = q.dims else: out.data = zcsr_kron(out.data, q.data) out.dims = [out.dims[0] + q.dims[0], out.dims[1] + q.dims[1]] out.isherm = out.isherm and q.isherm if not out.isherm: out._isherm = None return out.tidyup() if qutip.settings.auto_tidyup else out
def tensor(*args): """Calculates the tensor product of input operators. Parameters ---------- args : array_like ``list`` or ``array`` of quantum objects for tensor product. Returns -------- obj : qobj A composite quantum object. Examples -------- >>> tensor([sigmax(), sigmax()]) Quantum object: dims = [[2, 2], [2, 2]], \ shape = [4, 4], type = oper, isHerm = True Qobj data = [[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j] [ 0.+0.j 0.+0.j 1.+0.j 0.+0.j] [ 0.+0.j 1.+0.j 0.+0.j 0.+0.j] [ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]] """ if not args: raise TypeError("Requires at least one input argument") num_args = len(args) step = 0 isherm = True for n in range(num_args): if isinstance(args[n], Qobj): qos = args[n] if step == 0: dat = qos.data dim = qos.dims shp = qos.shape isherm = isherm and qos.isherm step = 1 else: dat = sp.kron(dat, qos.data, format='csr') isherm = isherm and qos.isherm dim = [dim[0] + qos.dims[0], dim[1] + qos.dims[1]] # append dimensions of Qobjs shp = [dat.shape[0], dat.shape[1]] # new shape of matrix elif isinstance(args[n], (list, ndarray)): qos = args[n] items = len(qos) # number of inputs if not all([isinstance(k, Qobj) for k in qos]): # raise error if one of the inputs is not a quantum object raise TypeError("One of inputs is not a quantum object") if items == 1: # if only one Qobj, do nothing if step == 0: dat = qos[0].data dim = qos[0].dims shp = qos[0].shape isherm = isherm and qos[0].isherm step = 1 else: dat = sp.kron(dat, qos[0].data, format='csr') isherm = isherm and qos[0].isherm dim = [dim[0] + qos[0].dims[0], dim[1] + qos[0].dims[1]] # append dimensions of qos shp = [dat.shape[0], dat.shape[1]] # new shape of matrix elif items != 1: if step == 0: dat = qos[0].data dim = qos[0].dims shp = qos[0].shape step = 1 isherm = isherm and qos[0].isherm for k in range(items - 1): # cycle over all items dat = sp.kron(dat, qos[k + 1].data, format='csr') isherm = isherm and qos[k + 1].isherm dim = [ dim[0] + qos[k + 1].dims[0], dim[1] + qos[k + 1].dims[1] ] shp = [dat.shape[0], dat.shape[1]] # new shape of matrix out = Qobj() out.data = dat out.dims = dim out.shape = shp out.type = ischeck(out) out.isherm = isherm if qutip.settings.auto_tidyup: return out.tidyup() # returns tidy Qobj else: return out
def tensor(*args): """Calculates the tensor product of input operators. Parameters ---------- args : array_like ``list`` or ``array`` of quantum objects for tensor product. Returns ------- obj : qobj A composite quantum object. Examples -------- >>> tensor([sigmax(), sigmax()]) Quantum object: dims = [[2, 2], [2, 2]], \ shape = [4, 4], type = oper, isHerm = True Qobj data = [[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j] [ 0.+0.j 0.+0.j 1.+0.j 0.+0.j] [ 0.+0.j 1.+0.j 0.+0.j 0.+0.j] [ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]] """ if not args: raise TypeError("Requires at least one input argument") if len(args) == 1 and isinstance(args[0], (list, np.ndarray)): # this is the case when tensor is called on the form: # tensor([q1, q2, q3, ...]) qlist = args[0] elif len(args) == 1 and isinstance(args[0], Qobj): # tensor is called with a single Qobj as an argument, do nothing return args[0] else: # this is the case when tensor is called on the form: # tensor(q1, q2, q3, ...) qlist = args if not all([isinstance(q, Qobj) for q in qlist]): # raise error if one of the inputs is not a quantum object raise TypeError("One of inputs is not a quantum object") out = Qobj() if qlist[0].issuper: out.superrep = qlist[0].superrep if not all([q.superrep == out.superrep for q in qlist]): raise TypeError("In tensor products of superroperators, all must" + "have the same representation") out.isherm = True for n, q in enumerate(qlist): if n == 0: out.data = q.data out.dims = q.dims else: out.data = sp.kron(out.data, q.data, format='csr') out.dims = [out.dims[0] + q.dims[0], out.dims[1] + q.dims[1]] out.isherm = out.isherm and q.isherm if not out.isherm: out._isherm = None return out.tidyup() if qutip.settings.auto_tidyup else out
def test_tidyup(): small = Qobj([[1e-2, 0], [0, 1]]) small.tidyup(1e-1) assert small.tr() == 1
def tensor(*args): """Calculates the tensor product of input operators. Parameters ---------- args : array_like ``list`` or ``array`` of quantum objects for tensor product. Returns -------- obj : qobj A composite quantum object. Examples -------- >>> tensor([sigmax(), sigmax()]) Quantum object: dims = [[2, 2], [2, 2]], \ shape = [4, 4], type = oper, isHerm = True Qobj data = [[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j] [ 0.+0.j 0.+0.j 1.+0.j 0.+0.j] [ 0.+0.j 1.+0.j 0.+0.j 0.+0.j] [ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]] """ if not args: raise TypeError("Requires at least one input argument") num_args = len(args) step = 0 isherm = True for n in range(num_args): if isinstance(args[n], Qobj): qos = args[n] if step == 0: dat = qos.data dim = qos.dims shp = qos.shape isherm = isherm and qos.isherm step = 1 else: dat = sp.kron(dat, qos.data, format='csr') isherm = isherm and qos.isherm dim = [dim[0] + qos.dims[0], dim[1] + qos.dims[1]] # append dimensions of Qobjs shp = [dat.shape[0], dat.shape[1]] # new shape of matrix elif isinstance(args[n], (list, ndarray)): qos = args[n] items = len(qos) # number of inputs if not all([isinstance(k, Qobj) for k in qos]): # raise error if one of the inputs is not a quantum object raise TypeError("One of inputs is not a quantum object") if items == 1: # if only one Qobj, do nothing if step == 0: dat = qos[0].data dim = qos[0].dims shp = qos[0].shape isherm = isherm and qos[0].isherm step = 1 else: dat = sp.kron(dat, qos[0].data, format='csr') isherm = isherm and qos[0].isherm dim = [dim[0] + qos[0].dims[0], dim[1] + qos[0].dims[1]] # append dimensions of qos shp = [dat.shape[0], dat.shape[1]] # new shape of matrix elif items != 1: if step == 0: dat = qos[0].data dim = qos[0].dims shp = qos[0].shape step = 1 isherm = isherm and qos[0].isherm for k in range(items - 1): # cycle over all items dat = sp.kron(dat, qos[k + 1].data, format='csr') isherm = isherm and qos[k + 1].isherm dim = [dim[0] + qos[k + 1].dims[0], dim[1] + qos[k + 1].dims[1]] shp = [dat.shape[0], dat.shape[1]] # new shape of matrix out = Qobj() out.data = dat out.dims = dim out.shape = shp out.type = ischeck(out) out.isherm = isherm if qutip.settings.auto_tidyup: return out.tidyup() # returns tidy Qobj else: return out