def get_propagation(self, ham, psi_init, steps, dz, norm=False):
"""
Get the time evolution.
:param ham: sparse.csr_matrix. Tight-Binding Hamilonian.
:param psi_init: np.ndarray. Initial state.
:param steps: Positive Integer. Number of steps.
:param dz: Positive number. Step.
:param norm: Boolean. Default value True. Normalize the norm to 1 at each step.
"""
error_handling.empty_ham(ham)
error_handling.ndarray(psi_init, "psi_init", self.lat.sites)
error_handling.positive_int(steps, "steps")
error_handling.positive_real(dz, "dz")
error_handling.boolean(norm, "norm")
self.steps = steps
self.dz = dz
self.prop = np.empty((self.lat.sites, self.steps), "c16")
self.prop[:, 0] = psi_init
diag = 1j * np.ones(self.lat.sites, "c16")
A = (sparse.diags(diag, 0) - 0.5 * self.dz * ham).toarray()
B = (sparse.diags(diag, 0) + 0.5 * self.dz * ham).toarray()
mat = np.dot(LA.inv(A), B)
for i in range(1, self.steps):
self.prop[:, i] = np.dot(mat, self.prop[:, i - 1])
if norm:
self.prop[:, i] /= np.abs(self.prop[:, i]).sum()
def get_propagation(self, ham, psi_init, steps, dz, norm=False):
'''
Get the time evolution.
:param ham: sparse.csr_matrix. Tight-Binding Hamilonian.
:param psi_init: np.ndarray. Initial state.
:param steps: Positive Integer. Number of steps.
:param dz: Positive number. Step.
:param norm: Boolean. Default value True. Normalize the norm to 1 at each step.
'''
error_handling.empty_ham(ham)
error_handling.ndarray(psi_init, 'psi_init', self.lat.sites)
error_handling.positive_int(steps, 'steps')
error_handling.positive_real(dz, 'dz')
error_handling.boolean(norm, 'norm')
self.steps = steps
self.dz = dz
self.prop = np.empty((self.lat.sites, self.steps), 'c16')
self.prop[:, 0] = psi_init
diag = 1j*np.ones(self.lat.sites, 'c16')
A = (sparse.diags(diag, 0) - 0.5 * self.dz * ham).toarray()
B = (sparse.diags(diag, 0) + 0.5 * self.dz * ham).toarray()
mat = (np.dot(LA.inv(A), B))
for i in range(1, self.steps):
self.prop[:, i] = np.dot(mat, self.prop[:, i-1])
if norm:
self.prop[:, i] /= np.abs(self.prop[:, i]).sum()
def get_eig(self, eigenvec=False, left=False):
'''
Get the eigenergies, eigenvectors and polarisation.
:param eigenvec: Boolean. Default value False.
If True, get the eigenvectors.
:param left: Boolean. Default value False.
If True, get the left eigenvectors too.
Relevant for non-Hermitian matrices.
'''
error_handling.empty_ham(self.ham)
error_handling.boolean(eigenvec, 'eigenvec')
error_handling.boolean(left, 'left')
if eigenvec:
if (self.ham.H != self.ham).nnz:
if not left:
self.en, self.rn = LA.eig(self.ham.toarray())
else:
self.en, self.rn, self.ln = LA.eig(self.ham.toarray(),
left=left)
ind = np.argsort(self.en.real)
self.en = self.en[ind]
self.rn = self.rn[:, ind]
if self.ln.size:
self.ln = self.ln[:, ind]
else:
self.en, self.rn = LA.eigh(self.ham.toarray())
self.intensity = np.abs(self.rn)**2
self.pola = np.zeros((self.lat.sites, len(self.lat.tags)))
for i, tag in enumerate(self.lat.tags):
self.pola[:, i] = np.sum(
self.intensity[self.lat.coor['tag'] == tag, :], axis=0)
else:
if (self.ham.H != self.ham).nnz:
self.en = LA.eigvals(self.ham.toarray())
ind = np.argsort(self.en.real)
self.en = self.en[ind]
else:
self.en = LA.eigvalsh(self.ham.toarray())
def get_eig(self, eigenvec=False, left=False):
'''
Get the eigenergies, eigenvectors and polarisation.
:param eigenvec: Boolean. Default value False.
If True, get the eigenvectors.
:param left: Boolean. Default value False.
If True, get the left eigenvectors too.
Relevant for non-Hermitian matrices.
'''
error_handling.empty_ham(self.ham)
error_handling.boolean(eigenvec, 'eigenvec')
error_handling.boolean(left, 'left')
if eigenvec:
if (self.ham.H != self.ham).nnz:
if not left:
self.en, self.rn = LA.eig(self.ham.toarray())
else:
self.en, self.rn, self.ln = LA.eig(self.ham.toarray(), left=left)
ind = np.argsort(self.en.real)
self.en = self.en[ind]
self.rn = self.rn[:, ind]
if self.ln.size:
self.ln = self.ln[:, ind]
else:
self.en, self.rn = LA.eigh(self.ham.toarray())
self.intensity = np.abs(self.rn) ** 2
self.pola = np.zeros((self.lat.sites, len(self.lat.tags)))
for i, tag in enumerate(self.lat.tags):
self.pola[:, i] = np.sum(self.intensity[self.lat.coor['tag'] == tag, :], axis=0)
else:
if (self.ham.H != self.ham).nnz:
self.en = LA.eigvals(self.ham.toarray())
ind = np.argsort(self.en.real)
self.en = self.en[ind]
else:
self.en = LA.eigvalsh(self.ham.toarray())
