def ifft(self, fu, u):
"""Inverse Fourier transforms in y and z"""
Uc_mpi = self.work_arrays[((self.num_processes, self.Np[0], self.Np[1],
self.Nf), self.complex, 0)]
Uc_hatT = self.work_arrays[(self.complex_shape_T(), self.complex, 0)]
self.comm.Alltoall([fu, self.mpitype], [Uc_mpi, self.mpitype])
Uc_hatT[:] = rollaxis(Uc_mpi, 1).reshape(self.complex_shape_T())
u = irfft2(Uc_hatT,
u,
axes=(1, 2),
threads=self.threads,
planner_effort=self.planner_effort['irfft2'])
return u
def backward(self, fu, u, fun, dealias=None):
Uc_hat = self.work_arrays[(self.complex_shape(), self.complex, 0,
False)]
Uc_mpi = Uc_hat.reshape(
(self.num_processes, self.Np[0], self.Np[1], self.Nf))
fun = fun.backward
if dealias == '2/3-rule' and self.dealias.shape == (0, ):
self.dealias = self.get_dealias_filter()
if self.num_processes == 1:
if not dealias == '3/2-rule':
fup = fu
if dealias == '2/3-rule':
fup = self.work_arrays[(fu, 1, False)]
fup[:] = fu
fup *= self.dealias
Uc_hat = fun(fup, Uc_hat)
u = irfft2(Uc_hat,
u,
axes=(1, 2),
overwrite_input=True,
threads=self.threads,
planner_effort=self.planner_effort['irfft2'])
else:
if not self.dealias_cheb:
Upad_hat = self.work_arrays[(self.complex_shape_padded(),
self.complex, 0)]
Upad_hat_z = self.work_arrays[((self.Np[0],
int(self.padsize *
self.N[1]), self.Nf),
self.complex, 0)]
Uc_hat = fun(fu * self.padsize**2, Uc_hat)
Upad_hat_z = SlabShen_R2C.copy_to_padded(
Uc_hat, Upad_hat_z, self.N, 1)
Upad_hat_z[:] = ifft(
Upad_hat_z,
axis=1,
threads=self.threads,
planner_effort=self.planner_effort['ifft'])
Upad_hat = SlabShen_R2C.copy_to_padded(
Upad_hat_z, Upad_hat, self.N, 2)
u = irfft(Upad_hat,
u,
axis=2,
overwrite_input=True,
threads=self.threads,
planner_effort=self.planner_effort['irfft'])
else:
# Intermediate work arrays required for transform
Upad_hat = self.work_arrays[(self.complex_shape_padded_0(),
self.complex, 0, False)]
Upad_hat0 = self.work_arrays[(
self.complex_shape_padded_0(), self.complex, 1)]
Upad_hat1 = self.work_arrays[(
self.complex_shape_padded_1(), self.complex, 0, False)]
Upad_hat2 = self.work_arrays[(
self.complex_shape_padded_2(), self.complex, 0)]
Upad_hat3 = self.work_arrays[(
self.complex_shape_padded_3(), self.complex, 0)]
# Expand in x-direction and perform ifst
Upad_hat0 = SlabShen_R2C.copy_to_padded(
fu * self.padsize**2, Upad_hat0, self.N, 0)
Upad_hat = fun(Upad_hat0, Upad_hat)
Upad_hat2 = SlabShen_R2C.copy_to_padded(
Upad_hat, Upad_hat2, self.N, 1)
Upad_hat2[:] = ifft(
Upad_hat2,
axis=1,
threads=self.threads,
planner_effort=self.planner_effort['ifft'])
# pad in z-direction and perform final irfft
Upad_hat3 = SlabShen_R2C.copy_to_padded(
Upad_hat2, Upad_hat3, self.N, 2)
u = irfft(Upad_hat3,
u,
axis=2,
overwrite_input=True,
threads=self.threads,
planner_effort=self.planner_effort['irfft'])
return u
if not dealias == '3/2-rule':
Uc_hatT = self.work_arrays[(self.complex_shape_T(), self.complex,
0, False)]
if dealias == '2/3-rule':
fu *= self.dealias
Uc_hat = fun(fu, Uc_hat)
if self.communication == 'Alltoall':
self.comm.Alltoall(MPI.IN_PLACE, [Uc_hat, self.mpitype])
Uc_hatT[:] = rollaxis(Uc_mpi,
1).reshape(self.complex_shape_T())
#Uc_mpi = self.work_arrays[((self.num_processes, self.Np[0], self.Np[1], self.Nf), self.complex, 0, False)]
#self.comm.Alltoall([Uc_hat, self.mpitype], [Uc_mpi, self.mpitype])
#Uc_hatT = rollaxis(Uc_mpi, 1).reshape(self.complex_shape_T())
elif self.communication == 'Alltoallw':
if not self._subarraysA:
self._subarraysA, self._subarraysB, self._counts_displs = self.get_subarrays(
)
Uc_hatT = self.work_arrays[(self.complex_shape_T(),
self.complex, 0, False)]
self.comm.Alltoallw(
[Uc_hat, self._counts_displs, self._subarraysA],
[Uc_hatT, self._counts_displs, self._subarraysB])
u = irfft2(Uc_hatT,
u,
axes=(1, 2),
overwrite_input=True,
threads=self.threads,
planner_effort=self.planner_effort['irfft2'])
else:
Uc_hatT = self.work_arrays[(self.complex_shape_T(), self.complex,
0, False)]
if not self.dealias_cheb:
Upad_hatT = self.work_arrays[(self.complex_shape_padded_T(),
self.complex, 0)]
Upad_hat_z = self.work_arrays[((self.Np[0],
int(self.padsize * self.N[1]),
self.Nf), self.complex, 0)]
Uc_hat = fun(fu * self.padsize**2, Uc_hat)
if self.communication == 'Alltoall':
# In-place
#self.comm.Alltoall(MPI.IN_PLACE, [Uc_hat, self.mpitype])
# Not in-place
Uc_mpi = self.work_arrays[((self.num_processes, self.Np[0],
self.Np[1], self.Nf),
self.complex, 0, False)]
self.comm.Alltoall([Uc_hat, self.mpitype],
[Uc_mpi, self.mpitype])
Uc_hatT[:] = rollaxis(Uc_mpi,
1).reshape(self.complex_shape_T())
elif self.communication == 'Alltoallw':
if not self._subarraysA:
self._subarraysA, self._subarraysB, self._counts_displs = self.get_subarrays(
)
self.comm.Alltoallw(
[Uc_hat, self._counts_displs, self._subarraysA],
[Uc_hatT, self._counts_displs, self._subarraysB])
Upad_hat_z = SlabShen_R2C.copy_to_padded(
Uc_hatT, Upad_hat_z, self.N, 1)
Upad_hat_z[:] = ifft(
Upad_hat_z,
axis=1,
threads=self.threads,
planner_effort=self.planner_effort['ifft'])
Upad_hatT = SlabShen_R2C.copy_to_padded(
Upad_hat_z, Upad_hatT, self.N, 2)
u = irfft(Upad_hatT,
u,
axis=2,
overwrite_input=True,
threads=self.threads,
planner_effort=self.planner_effort['irfft'])
else:
assert self.num_processes <= self.N[
0] / 2, "Number of processors cannot be larger than N[0]/2 for 3/2-rule"
# Intermediate work arrays required for transform
Upad_hat = self.work_arrays[(self.complex_shape_padded_0(),
self.complex, 0, False)]
Upad_hat0 = self.work_arrays[(self.complex_shape_padded_0(),
self.complex, 1)]
Upad_hat1 = self.work_arrays[(self.complex_shape_padded_1(),
self.complex, 0, False)]
Upad_hat2 = self.work_arrays[(self.complex_shape_padded_2(),
self.complex, 0)]
Upad_hat3 = self.work_arrays[(self.complex_shape_padded_3(),
self.complex, 0)]
# Expand in x-direction and perform ifst
Upad_hat0 = SlabShen_R2C.copy_to_padded(
fu * self.padsize**2, Upad_hat0, self.N, 0)
Upad_hat = fun(Upad_hat0, Upad_hat)
if self.communication == 'Alltoall':
# Communicate to distribute first dimension (like Fig. 2b but padded in x-dir)
self.comm.Alltoall(MPI.IN_PLACE, [Upad_hat, self.mpitype])
# Transpose data and pad in y-direction before doing ifft. Now data is padded in x and y
U_mpi = Upad_hat.reshape(self.complex_shape_padded_0_I())
Upad_hat1[:] = rollaxis(U_mpi, 1).reshape(Upad_hat1.shape)
elif self.communication == 'Alltoallw':
if not self._subarraysA_pad:
self._subarraysA_pad, self._subarraysB_pad, self._counts_displs = self.get_subarrays(
padsize=self.padsize)
self.comm.Alltoallw(
[Upad_hat, self._counts_displs, self._subarraysA_pad],
[Upad_hat1, self._counts_displs, self._subarraysB_pad])
Upad_hat2 = SlabShen_R2C.copy_to_padded(
Upad_hat1, Upad_hat2, self.N, 1)
Upad_hat2[:] = ifft(Upad_hat2,
axis=1,
threads=self.threads,
planner_effort=self.planner_effort['ifft'])
# pad in z-direction and perform final irfft
Upad_hat3 = SlabShen_R2C.copy_to_padded(
Upad_hat2, Upad_hat3, self.N, 2)
u = irfft(Upad_hat3,
u,
axis=2,
overwrite_input=True,
threads=self.threads,
planner_effort=self.planner_effort['irfft'])
return u