x = linspace(-4, 4, 4000)
positions = linspace(-0.5, 2.5, 61)
quads1 = []
quads2 = []
quads12 = []
for index, pos in enumerate(positions):
print(pos)
# Moving Gaussian
WP2.set_parameters((1.0j, 1.0, 0.0, 0.0, pos))
# Transform the nodes
nodes1 = squeeze(HQ1.transform_nodes(WP1.get_parameters(), WP1.eps))
nodes2 = squeeze(HQ2.transform_nodes(WP2.get_parameters(), WP2.eps))
nodes12 = squeeze(IHQ.transform_nodes(Pibra, WP2.get_parameters(), WP1.eps))
# Compute inner products
Q1 = IHQ.quadrature(WP1, WP1, summed=True)
Q2 = IHQ.quadrature(WP2, WP2, summed=True)
Q12 = IHQ.quadrature(WP1, WP2, summed=True)
quads1.append(Q1)
quads2.append(Q2)
quads12.append(Q12)
# Evaluate the packets
y = WP1.evaluate_at(x, prefactor=True, component=0)
z = WP2.evaluate_at(x, prefactor=True, component=0)
figure()
def spawn_basis_projection(self, mother, child, component, order=None):
"""Update the superposition coefficients of mother and
spawned wavepacket. We do a full basis projection to the
basis of the spawned wavepacket here.
"""
c_old = mother.get_coefficients(component=component)
# Mother packet
c_new_m = np.zeros(c_old.shape, dtype=np.complexfloating)
# Spawned packet
c_new_s = np.zeros((child.get_basis_size(component=component),1), dtype=np.complexfloating)
# The quadrature
quadrature = InhomogeneousQuadrature()
# Quadrature rule. Assure the "right" quadrature is choosen if
# mother and child have different basis sizes
if mother.get_basis_size(component=component) > child.get_basis_size(component=component):
quadrature.set_qr( mother.get_quadrature().get_qr() )
else:
quadrature.set_qr( child.get_quadrature().get_qr() )
# The quadrature nodes and weights
q0, QS = quadrature.mix_parameters(mother.get_parameters(), child.get_parameters())
nodes = quadrature.transform_nodes(mother.get_parameters(), child.get_parameters(), mother.eps)
weights = quadrature.get_qr().get_weights()
# Basis sets for both packets
basis_m = mother.evaluate_basis_at(nodes, prefactor=True)
basis_s = child.evaluate_basis_at(nodes, prefactor=True)
max_order = min(child.get_basis_size(component=component), self.max_order)
# Project to the basis of the spawned wavepacket
# Original, inefficient code for projection
# R = QR.get_order()
# for i in xrange(max_order):
# # Loop over all quadrature points
# tmp = 0.0j
# for r in xrange(R):
# tmp += np.conj(np.dot( c_old[:,0], basis_m[:,r] )) * basis_s[i,r] * weights[0,r]
# c_new_s[i,0] = self.eps * QS * tmp
# Optimised and vectorised code (in ugly formatting)
c_new_s[:max_order,:] = self.eps * QS * (
np.reshape(
np.sum(
np.transpose(
np.reshape(
np.conj(
np.sum(c_old[:,:] * basis_m[:,:],axis=0)
) ,(-1,1)
)
) * (basis_s[:max_order,:] * weights[:,:]), axis=1
) ,(-1,1)
))
# Reassign the new coefficients
mother.set_coefficients(c_new_m, component=component)
child.set_coefficients(c_new_s, component=component)
return (mother, child)
