def get_wavepacket(self, packetindex):
r"""Get the wavepacket :math:`\Psi_j` from the linear combination.
:param index: The index :math:`0 \leq j < J` of the packet to retrieve.
:return: The wavepacket :math:`\Psi_j`.
:type: A :py:class:`HagedornWavepacket` instance.
"""
if packetindex > self._number_packets - 1 or packetindex < 0:
raise ValueError("There is no packet with index {}.".format(packetindex))
HAWP = HagedornWavepacket(self._dimension, self._number_components, self._eps)
K = self._basis_shapes[self._basis_shapes_hashes[packetindex]]
HAWP.set_basis_shapes([K])
q = self._Pis[0][packetindex, :]
p = self._Pis[1][packetindex, :]
Q = self._Pis[2][packetindex, :, :]
P = self._Pis[3][packetindex, :, :]
S = self._Pis[4][packetindex, :]
HAWP.set_parameters([q, p, Q, P, S])
cj = self._wp_coefficients[packetindex, :]
HAWP.set_coefficients(cj, component=0)
return HAWP
def overlap(self, D, Pi, eps):
r"""Compute the overlap matrix:
.. math::
\mathbf{K}_{r,c} := \langle \psi_{\underline{e_r}}[\Pi] | \phi_{\underline{e_c}}[\Pi] \rangle
:param D: The dimension :math:`D`.
:param Pi: The parameter set :math:`\Pi`.
:param eps: The semiclassical scaling parameter :math:`\varepsilon`.
"""
ED = list(lattice_points_norm(D, 1))
BS = SimplexShape(D, 1)
WPo = HagedornWavepacket(D, 1, eps)
WPo.set_parameters(Pi)
WPo.set_basis_shapes([BS])
WPn = HagedornWavepacketPsi(D, 1, eps)
WPn.set_parameters(Pi)
WPn.set_basis_shapes([BS])
TPG = TensorProductQR(D * [GaussHermiteQR(2)])
DHQ = DirectHomogeneousQuadrature(TPG)
G = DHQ.transform_nodes(Pi, eps)
W = TPG.get_weights()
phi = WPo.evaluate_basis_at(G, component=0)
psi = WPn.evaluate_basis_at(G, component=0)
K = zeros((D, D), dtype=complexfloating)
for r, er in enumerate(ED):
for c, ec in enumerate(ED):
K[r, c] = eps**D * sum(
conjugate(psi[BS[er], :]) * phi[BS[ec], :] * W)
return K
def overlap(self, D, Pi, eps):
r"""Compute the overlap matrix:
.. math::
\mathbf{K}_{r,c} := \langle \psi_{\underline{e_r}}[\Pi] | \phi_{\underline{e_c}}[\Pi] \rangle
:param D: The dimension :math:`D`.
:param Pi: The parameter set :math:`\Pi`.
:param eps: The semiclassical scaling parameter :math:`\varepsilon`.
"""
ED = list(lattice_points_norm(D, 1))
BS = SimplexShape(D, 1)
WPo = HagedornWavepacket(D, 1, eps)
WPo.set_parameters(Pi)
WPo.set_basis_shapes([BS])
WPn = HagedornWavepacketPsi(D, 1, eps)
WPn.set_parameters(Pi)
WPn.set_basis_shapes([BS])
TPG = TensorProductQR(D * [GaussHermiteQR(2)])
DHQ = DirectHomogeneousQuadrature(TPG)
G = DHQ.transform_nodes(Pi, eps)
W = TPG.get_weights()
phi = WPo.evaluate_basis_at(G, component=0)
psi = WPn.evaluate_basis_at(G, component=0)
K = zeros((D, D), dtype=complexfloating)
for r, er in enumerate(ED):
for c, ec in enumerate(ED):
K[r, c] = eps**D * sum(conjugate(psi[BS[er], :]) * phi[BS[ec], :] * W)
return K
def create_wavepacket(self, description):
wp_type = description["type"]
if wp_type == "HagedornWavepacket":
from WaveBlocksND.HagedornWavepacket import HagedornWavepacket
# Initialize a packet
WP = HagedornWavepacket(description["dimension"],
description["ncomponents"],
description["eps"])
# Set parameters
if "Pi" in description:
Pi = description["Pi"]
WP.set_parameters(Pi)
# Configure basis shapes
if "basis_shapes" in description:
for component, shapedescr in enumerate(
description["basis_shapes"]):
BS = self.create_basis_shape(shapedescr)
WP.set_basis_shapes(BS, component=component)
# Set coefficients
if "coefficients" in description:
for component, data in enumerate(description["coefficients"]):
BS = WP.get_basis_shapes(component=component)
for index, value in data:
if BS.contains(index):
WP.set_coefficient(component, index, value)
else:
print("Warning: dropped coefficient with index {}".
format(index))
# And the inner product
if "innerproduct" in description:
IP = self.create_inner_product(description["innerproduct"])
WP.set_innerproduct(IP)
else:
print("Warning: no inner product specified!")
elif wp_type == "HagedornWavepacketInhomogeneous":
from WaveBlocksND.HagedornWavepacketInhomogeneous import HagedornWavepacketInhomogeneous
# Initialize a packet
WP = HagedornWavepacketInhomogeneous(description["dimension"],
description["ncomponents"],
description["eps"])
# Set parameters
if "Pi" in description:
Pi = description["Pi"]
WP.set_parameters(Pi)
# Configure basis shapes
if "basis_shapes" in description:
for component, shapedescr in enumerate(
description["basis_shapes"]):
BS = self.create_basis_shape(shapedescr)
WP.set_basis_shapes(BS, component=component)
# Set coefficients
if "coefficients" in description:
for component, data in enumerate(description["coefficients"]):
for index, value in data:
WP.set_coefficient(component, index, value)
# And the quadrature
if "innerproduct" in description:
IP = self.create_inner_product(description["innerproduct"])
WP.set_innerproduct(IP)
else:
print("Warning: no inner product specified!")
else:
raise ValueError("Unknown wavepacket type {}".format(wp_type))
return WP
def create_wavepacket(self, description):
wp_type = description["type"]
if wp_type == "HagedornWavepacket":
from WaveBlocksND.HagedornWavepacket import HagedornWavepacket
# Initialize a packet
WP = HagedornWavepacket(description["dimension"],
description["ncomponents"],
description["eps"])
# Set parameters
if "Pi" in description:
Pi = description["Pi"]
WP.set_parameters(Pi)
# Configure basis shapes
if "basis_shapes" in description:
for component, shapedescr in enumerate(description["basis_shapes"]):
BS = self.create_basis_shape(shapedescr)
WP.set_basis_shapes(BS, component=component)
# Set coefficients
if "coefficients" in description:
for component, data in enumerate(description["coefficients"]):
BS = WP.get_basis_shapes(component=component)
for index, value in data:
if BS.contains(index):
WP.set_coefficient(component, index, value)
else:
print("Warning: dropped coefficient with index {}".format(index))
# And the inner product
if "innerproduct" in description:
IP = self.create_inner_product(description["innerproduct"])
WP.set_innerproduct(IP)
else:
print("Warning: no inner product specified!")
elif wp_type == "HagedornWavepacketInhomogeneous":
from WaveBlocksND.HagedornWavepacketInhomogeneous import HagedornWavepacketInhomogeneous
# Initialize a packet
WP = HagedornWavepacketInhomogeneous(description["dimension"],
description["ncomponents"],
description["eps"])
# Set parameters
if "Pi" in description:
Pi = description["Pi"]
WP.set_parameters(Pi)
# Configure basis shapes
if "basis_shapes" in description:
for component, shapedescr in enumerate(description["basis_shapes"]):
BS = self.create_basis_shape(shapedescr)
WP.set_basis_shapes(BS, component=component)
# Set coefficients
if "coefficients" in description:
for component, data in enumerate(description["coefficients"]):
for index, value in data:
WP.set_coefficient(component, index, value)
# And the quadrature
if "innerproduct" in description:
IP = self.create_inner_product(description["innerproduct"])
WP.set_innerproduct(IP)
else:
print("Warning: no inner product specified!")
else:
raise ValueError("Unknown wavepacket type {}".format(wp_type))
return WP
