def inverse_fourier_transform(values, lattice, boundary_conditions):
assert isinstance(lattice, Lattice)
assert isinstance(values, collections.Sequence)
if not len(values) == lattice.total_bravais_sites():
raise RuntimeError("wrong number of values provided for lattice fourier transform")
assert valid_closed_boundary_conditions(boundary_conditions, len(lattice.dimensions))
normalization = 1.0 / len(values)
return [sum([exp(two_pi_i * numpy.dot(r, allowed_momentum(momentum_site, lattice, boundary_conditions))) * v
for momentum_site, v in zip(lattice.iterate_bravais_sites(), values)]) * normalization
for r in lattice.iterate_bravais_sites()]
def fourier_transform(values, lattice, boundary_conditions):
"""Performs a Fourier transform on the lattice.
`values` should be a list representing the value on each site, ordered by
the index of each Bravais site on the lattice
"""
assert isinstance(lattice, Lattice)
assert isinstance(values, collections.Sequence)
if not len(values) == lattice.total_bravais_sites():
raise RuntimeError("wrong number of values provided for lattice fourier transform")
assert valid_closed_boundary_conditions(boundary_conditions, len(lattice.dimensions))
return [sum([exp(-two_pi_i * numpy.dot(r, allowed_momentum(momentum_site, lattice, boundary_conditions))) * v
for r, v in zip(lattice.iterate_bravais_sites(), values)])
for momentum_site in lattice.iterate_bravais_sites()]