mpi4py_fft package

Subpackages

Submodules

mpi4py_fft.libfft module

class mpi4py_fft.libfft.FFT(shape, axes=None, dtype=<class 'float'>, padding=False, backend='fftw', transforms=None, **kw)[source]

Bases: FFTBase

Class for serial FFT transforms

Parameters

  • shape (list or tuple of ints) – shape of input array planned for

  • axes (None, int or tuple of ints, optional) – axes to transform over. If None transform over all axes

  • dtype (np.dtype, optional) – Type of input array

  • padding (bool, number or list of numbers) – If False, then no padding. If number, then apply this number as padding factor for all axes. If list of numbers, then each number gives the padding for each axis. Must be same length as axes.

  • backend (str, optional) – Choose backend for serial transforms (fftw, pyfftw, numpy, scipy, mkl_fft). Default is fftw

  • transforms (None or dict, optional) – Dictionary of axes to serial transforms (forward and backward) along those axes. For example:

    {(0, 1): (dctn, idctn), (2, 3): (dstn, idstn)}

    If missing the default is to use rfftn/irfftn for real input arrays and fftn/ifftn for complex input arrays. Real-to-real transforms can be configured using this dictionary and real-to-real transforms from the fftw.xfftn module.

  • kw (dict) – Parameters passed to serial transform object

forward(input_array=None, output_array=None, \*\*options)

Generic serial forward transform

Parameters

  • input_array (array, optional)

  • output_array (array, optional)

  • options (dict) – parameters to serial transforms

Returns

output_array

Return type

array

backward(input_array=None, output_array=None, \*\*options)

Generic serial backward transform

Parameters

  • input_array (array, optional)

  • output_array (array, optional)

  • options (dict) – parameters to serial transforms

Returns

output_array

Return type

array

class mpi4py_fft.libfft.FFTBase(shape, axes=None, dtype=<class 'float'>, padding=False)[source]

Bases: object

Base class for serial FFT transforms

Parameters

  • shape (list or tuple of ints) – shape of input array planned for

  • axes (None, int or tuple of ints, optional) – axes to transform over. If None transform over all axes

  • dtype (np.dtype, optional) – Type of input array

  • padding (bool, number or list of numbers) – If False, then no padding. If number, then apply this number as padding factor for all axes. If list of numbers, then each number gives the padding for each axis. Must be same length as axes.

mpi4py_fft.mpifft module

class mpi4py_fft.mpifft.PFFT(comm, shape=None, axes=None, dtype=<class 'float'>, grid=None, padding=False, collapse=False, backend='fftw', transforms=None, darray=None, **kw)[source]

Bases: object

Base class for parallel FFT transforms

Parameters

  • comm (MPI communicator)

  • shape (sequence of ints, optional) – shape of input array planned for

  • axes (None, int, sequence of ints or sequence of sequence of ints, optional) – axes to transform over.

    • None -> All axes are transformed

    • int -> Just one axis to transform over

    • sequence of ints -> e.g., (0, 1, 2) or (0, 2, 1)

    • sequence of sequence of ints -> e.g., ((0,), (1,)) or ((0,), (1, 2)) For seq. of seq. of ints all but the last transformed sequence may be longer than 1. This corresponds to collapsing axes, where serial FFTs are performed for all collapsed axes in one single call

  • dtype (np.dtype, optional) – Type of input array

  • grid (sequence of ints, optional) – Define processor grid sizes. Non positive values act as wildcards to allow MPI compute optimal decompositions. The sequence is padded with ones to match the global transform dimension. Use (-1,) to get a slab decomposition on the first axis. Use (1, -1) to get a slab decomposition on the second axis. Use (P, Q) or (P, Q, 1) to get a 3D transform with 2D-pencil decomposition on a PxQ processor grid with the last axis non distributed. Use (P, 1, Q) to get a 3D transform with 2D-pencil decomposition on a PxQ processor grid with the second to last axis non distributed.

  • padding (bool, number or sequence of numbers, optional) – If False, then no padding. If number, then apply this number as padding factor for all axes. If sequence of numbers, then each number gives the padding for each axis. Must be same length as axes.

  • collapse (bool, optional) – If True try to collapse several serial transforms into one

  • backend (str, optional) – Choose backend for serial transforms (fftw, pyfftw, numpy, scipy, mkl_fft). Default is fftw

  • transforms (None or dict, optional) – Dictionary of axes to serial transforms (forward and backward) along those axes. For example:

    {(0, 1): (dctn, idctn), (2, 3): (dstn, idstn)}

    If missing the default is to use rfftn/irfftn for real input arrays and fftn/ifftn for complex input arrays. Real-to-real transforms can be configured using this dictionary and real-to-real transforms from the fftw.xfftn module. See Examples.

Other Parameters

  • darray (DistArray object, optional) – Create PFFT using information contained in darray, neglecting most optional Parameters above

  • slab (bool or int, optional) – DEPRECATED. If True then distribute only one axis of the global array.

forward(input_array=None, output_array=None, \*\*kw)

Parallel forward transform. The method is an instance of the Transform class. See Transform.__call__()

Parameters

  • input_array (array, optional)

  • output_array (array, optional)

  • kw (dict) – parameters to serial transforms

Returns

output_array

Return type

array

backward(input_array=None, output_array=None, \*\*kw)

Parallel backward transform. The method is an instance of the Transform class. See Transform.__call__()

Parameters

  • input_array (array, optional)

  • output_array (array, optional)

  • kw (dict) – parameters to serial transforms

Returns

output_array

Return type

array

Examples

>>> import numpy as np
>>> from mpi4py import MPI
>>> from mpi4py_fft import PFFT, newDistArray
>>> N = np.array([12, 14, 15], dtype=int)
>>> fft = PFFT(MPI.COMM_WORLD, N, axes=(0, 1, 2))
>>> u = newDistArray(fft, False)
>>> u[:] = np.random.random(u.shape).astype(u.dtype)
>>> u_hat = fft.forward(u)
>>> uj = np.zeros_like(u)
>>> uj = fft.backward(u_hat, uj)
>>> assert np.allclose(uj, u)

Now configure with real-to-real discrete cosine transform type 3

>>> from mpi4py_fft.fftw import rfftn, irfftn, dctn, idctn
>>> import functools
>>> dct = functools.partial(dctn, type=3)
>>> idct = functools.partial(idctn, type=3)
>>> transforms = {(1, 2): (dct, idct)}
>>> r2c = PFFT(MPI.COMM_WORLD, N, axes=((0,), (1, 2)), transforms=transforms)
>>> u = newDistArray(r2c, False)
>>> u[:] = np.random.random(u.shape).astype(u.dtype)
>>> u_hat = r2c.forward(u)
>>> uj = np.zeros_like(u)
>>> uj = r2c.backward(u_hat, uj)
>>> assert np.allclose(uj, u)
destroy()[source]
property dimensions

The number of dimensions for transformed arrays

dtype(forward_output=False)[source]

The type of transformed arrays

Parameters

forward_output (bool, optional) – If True then return dtype of an array that is the result of a forward transform. Otherwise, return the dtype of an array that is input to a forward transform.

global_shape(forward_output=False)[source]

Return global shape of associated tensors

Parameters

forward_output (bool, optional) – If True then return global shape of spectral space, i.e., the input to a backward transfer. If False then return shape of physical space, i.e., the input to a forward transfer.

local_slice(forward_output=True)[source]

The local view into the global data

Parameters

forward_output (bool, optional) – Return local slices of output array (spectral space) if True, else return local slices of input array (physical space)

shape(forward_output=True)[source]

The local (to each processor) shape of data

Parameters

forward_output (bool, optional) – Return shape of output array (spectral space) if True, else return shape of input array (physical space)

class mpi4py_fft.mpifft.Transform(xfftn, transfer, pencil)[source]

Bases: object

Class for performing any parallel transform, forward or backward

Parameters

  • xfftn (list of serial transform objects)

  • transfer (list of global redistribution objects)

  • pencil (list of two pencil objects) – The two pencils represent the input and final output configuration of the distributed global arrays

__call__(input_array=None, output_array=None, **kw)[source]

Compute transform

Parameters

  • input_array (array, optional)

  • output_array (array, optional)

  • kw (dict) – parameters to serial transforms Note in particular that the keyword ‘normalize’=True/False can be used to turn normalization on or off. Default is to enable normalization for forward transforms and disable it for backward.

Note

If input_array/output_array are not given, then use predefined arrays as planned with serial transform object _xfftn.

property input_array

Return input array of Transform

property input_pencil

Return input pencil of Transform

property output_array

Return output array of Transform

property output_pencil

Return output pencil of Transform

mpi4py_fft.pencil module

class mpi4py_fft.pencil.Pencil(subcomm, shape, axis=-1)[source]

Bases: object

Class to represent a distributed array (pencil)

Parameters

  • subcomm (MPI communicator)

  • shape (sequence of ints) – Shape of global array

  • axis (int, optional) – Pencil is aligned in this direction

Examples

Create two pencils for a 4-dimensional array of shape (8, 8, 8, 8) using 4 processors in total. The input pencil will be distributed in the first two axes, whereas the output pencil will be distributed in axes 1 and 2. Note that the Subcomm instance below may distribute any axis where an entry 0 is found, whereas an entry of 1 means that this axis should not be distributed.

>>> import subprocess
>>> fx = open('pencil_script.py', 'w')
>>> h = fx.write('''
... import numpy as np
... from mpi4py import MPI
... from mpi4py_fft.pencil import Subcomm, Pencil
... comm = MPI.COMM_WORLD
... N = (8, 8, 8, 8)
... subcomms = Subcomm(comm, [0, 0, 1, 0])
... axis = 2
... p0 = Pencil(subcomms, N, axis)
... p1 = p0.pencil(0)
... shape0 = comm.gather(p0.subshape)
... shape1 = comm.gather(p1.subshape)
... if comm.Get_rank() == 0:
...     print('Subshapes all 4 processors pencil p0:')
...     print(np.array(shape0))
...     print('Subshapes all 4 processors pencil p1:')
...     print(np.array(shape1))''')
>>> fx.close()
>>> print(subprocess.getoutput('mpirun -np 4 python pencil_script.py'))
Subshapes all 4 processors pencil p0:
[[4 4 8 8]
 [4 4 8 8]
 [4 4 8 8]
 [4 4 8 8]]
Subshapes all 4 processors pencil p1:
[[8 4 4 8]
 [8 4 4 8]
 [8 4 4 8]
 [8 4 4 8]]

Two index sets of the global data of shape (8, 8, 8, 8) are distributed. This means that the current distribution is using two groups of processors, with 2 processors in each group (4 in total). One group shares axis 0 and the other axis 1 on the input arrays. On the output, one group shares axis 1, whereas the other shares axis 2. Note that the call p1 = p0.pencil(0) creates a new pencil (p1) that is non-distributed in axes 0. It is, in other words, aligned in axis 0. Hence the first 8 in the lists with [8 4 4 8] above. The alignment is configurable, and p1 = p0.pencil(1) would lead to an output pencil aligned in axis 1.

pencil(axis)[source]

Return a Pencil aligned with axis

Parameters

axis (int) – The axis along which the pencil is aligned

transfer(pencil, dtype)[source]

Return an appropriate instance of the Transfer class

The returned Transfer class is used for global redistribution from this pencil’s instance to the pencil instance provided.

Parameters

  • pencil (Pencil) – The receiving pencil of a forward transform

  • dtype (dtype) – The type of the sending pencil

class mpi4py_fft.pencil.Subcomm(comm, dims=None, reorder=True)[source]

Bases: tuple

Class returning a tuple of subcommunicators of any dimensionality

Parameters

  • comm (A communicator or group of communicators)

  • dims (None, int or sequence of ints) – dims = [0, 0, 1] will give communicators distributed in the two first indices, whereas the third will not be distributed

Examples

>>> import subprocess
>>> fx = open('subcomm_script.py', 'w')
>>> h = fx.write('''
... from mpi4py import MPI
... comm = MPI.COMM_WORLD
... from mpi4py_fft.pencil import Subcomm
... subcomms = Subcomm(comm, [0, 0, 1])
... if comm.Get_rank() == 0:
...     for subcomm in subcomms:
...         print(subcomm.Get_size())''')
>>> fx.close()
>>> print(subprocess.getoutput('mpirun -np 4 python subcomm_script.py'))
2
2
1
>>> print(subprocess.getoutput('mpirun -np 6 python subcomm_script.py'))
3
2
1
destroy()[source]
class mpi4py_fft.pencil.Transfer(comm, shape, dtype, subshapeA, axisA, subshapeB, axisB)[source]

Bases: object

Class for performing global redistributions

Parameters

  • comm (MPI communicator)

  • shape (sequence of ints) – shape of input array planned for

  • dtype (np.dtype, optional) – Type of input array

  • subshapeA (sequence of ints) – Shape of input pencil

  • axisA (int) – Input array aligned in this direction

  • subshapeB (sequence of ints) – Shape of output pencil

  • axisB (int) – Output array aligned in this direction

Examples

Create two pencils for a 4-dimensional array of shape (8, 8, 8, 8) using 4 processors in total. The input pencil will be distributed in the first two axes, whereas the output pencil will be distributed in axes 1 and 2. Create a random array of shape according to the input pencil and transfer its values to an array of the output shape.

>>> import subprocess
>>> fx = open('transfer_script.py', 'w')
>>> h = fx.write('''
... import numpy as np
... from mpi4py import MPI
... from mpi4py_fft.pencil import Subcomm, Pencil
... comm = MPI.COMM_WORLD
... N = (8, 8, 8, 8)
... subcomms = Subcomm(comm, [0, 0, 1, 0])
... axis = 2
... p0 = Pencil(subcomms, N, axis)
... p1 = p0.pencil(0)
... transfer = p0.transfer(p1, float)
... a0 = np.zeros(p0.subshape, dtype=float)
... a1 = np.zeros(p1.subshape)
... a0[:] = np.random.random(a0.shape)
... transfer.forward(a0, a1)
... s0 = comm.reduce(np.sum(a0**2))
... s1 = comm.reduce(np.sum(a1**2))
... if comm.Get_rank() == 0:
...     assert np.allclose(s0, s1)''')
>>> fx.close()
>>> h=subprocess.getoutput('mpirun -np 4 python transfer_script.py')
backward(arrayB, arrayA)[source]

Global redistribution from arrayB to arrayA

Parameters

  • arrayB (array) – Array of shape subshapeB, containing data to be redistributed

  • arrayA (array) – Array of shape subshapeA, for receiving data

destroy()[source]
forward(arrayA, arrayB)[source]

Global redistribution from arrayA to arrayB

Parameters

  • arrayA (array) – Array of shape subshapeA, containing data to be redistributed

  • arrayB (array) – Array of shape subshapeB, for receiving data

mpi4py_fft.distarray module

class mpi4py_fft.distarray.DistArray(global_shape, subcomm=None, val=None, dtype=<class 'float'>, buffer=None, strides=None, alignment=None, rank=0)[source]

Bases: ndarray

Distributed Numpy array

This Numpy array is part of a larger global array. Information about the distribution is contained in the attributes.

Parameters

  • global_shape (sequence of ints) – Shape of non-distributed global array

  • subcomm (None, Subcomm object or sequence of ints, optional) – Describes how to distribute the array

  • val (Number or None, optional) – Initialize array with this number if buffer is not given

  • dtype (np.dtype, optional) – Type of array

  • buffer (Numpy array, optional) – Array of correct shape. The buffer owns the memory that is used for this array.

  • alignment (None or int, optional) – Make sure array is aligned in this direction. Note that alignment does not take rank into consideration.

  • rank (int, optional) – Rank of tensor (number of free indices, a scalar is zero, vector one, matrix two)

For more information, see numpy.ndarray

Note

Tensors of rank higher than 0 are not distributed in the first rank indices. For example,

>>> from mpi4py_fft import DistArray
>>> a = DistArray((3, 8, 8, 8), rank=1)
>>> print(a.pencil.shape)
(8, 8, 8)

The array a cannot be distributed in the first axis of length 3 since rank is 1 and this first index represent the vector component. The pencil attribute of a thus only considers the last three axes.

Also note that the alignment keyword does not take rank into consideration. Setting alignment=2 for the array above means that the last axis will be aligned, also when rank>0.

property alignment

Return alignment of local self array

Note

For tensors of rank > 0 the array is actually aligned along alignment+rank

property commsizes

Return number of processors along each axis of self

property dimensions

Return dimensions of array not including rank

get(gslice)[source]

Return global slice of self

Parameters

gslice (sequence of slice(None) and ints) – The slice of the global array.

Returns

The slice of the global array is returned on rank 0, whereas the remaining ranks return None

Return type

Numpy array

Example

>>> import subprocess
>>> fx = open('gs_script.py', 'w')
>>> h = fx.write('''
... from mpi4py import MPI
... from mpi4py_fft.distarray import DistArray
... comm = MPI.COMM_WORLD
... N = (6, 6, 6)
... z = DistArray(N, dtype=float, alignment=0)
... z[:] = comm.Get_rank()
... g = z.get((0, slice(None), 0))
... if comm.Get_rank() == 0:
...     print(g)''')
>>> fx.close()
>>> print(subprocess.getoutput('mpirun -np 4 python gs_script.py'))
[0. 0. 0. 2. 2. 2.]
get_pencil_and_transfer(axis)[source]

Return pencil and transfer objects for alignment along axis

Parameters

axis (int) – The new axis to align data with

Returns

2-tuple where first item is a Pencil aligned in axis. Second item is a Transfer object for executing the redistribution of data

Return type

2-tuple

property global_shape

Return global shape of self

local_slice()[source]

Return local view into global self array

Returns

Each item of the returned list is the slice along that axis, describing the view of the self array into the global array.

Return type

List of slices

Example

Print local_slice of a global array of shape (16, 14, 12) using 4 processors.

>>> import subprocess
>>> fx = open('ls_script.py', 'w')
>>> h = fx.write('''
... from mpi4py import MPI
... from mpi4py_fft.distarray import DistArray
... comm = MPI.COMM_WORLD
... N = (16, 14, 12)
... z = DistArray(N, dtype=float, alignment=0)
... ls = comm.gather(z.local_slice())
... if comm.Get_rank() == 0:
...     for l in ls:
...         print(l)''')
>>> fx.close()
>>> print(subprocess.getoutput('mpirun -np 4 python ls_script.py'))
(slice(0, 16, None), slice(0, 7, None), slice(0, 6, None))
(slice(0, 16, None), slice(0, 7, None), slice(6, 12, None))
(slice(0, 16, None), slice(7, 14, None), slice(0, 6, None))
(slice(0, 16, None), slice(7, 14, None), slice(6, 12, None))
property pencil

Return pencil describing distribution of self

property rank

Return tensor rank of self

read(filename, name='darray', step=0)[source]

Read data name at index step``from file ``filename into self

Note

Only whole arrays can be read from file, not slices.

Parameters

  • filename (str or instance of FileBase) – The name of the file (or the file itself) holding the data that is loaded into self.

  • name (str, optional) – Internal name in file of snapshot to be read.

  • step (int, optional) – Index of field to be read. Default is 0.

Example

>>> from mpi4py_fft import DistArray
>>> u = DistArray((8, 8), val=1)
>>> u.write('h5file.h5', 'u', 0)
>>> v = DistArray((8, 8))
>>> v.read('h5file.h5', 'u', 0)
>>> assert np.allclose(u, v)
redistribute(axis=None, out=None)[source]

Global redistribution of local self array

Parameters

  • axis (int, optional) – Align local self array along this axis

  • out (DistArray, optional) – Copy data to this array of possibly different alignment

Returns

DistArray – The self array globally redistributed. If keyword out is None then a new DistArray (aligned along axis) is created and returned. Otherwise the provided out array is returned.

Return type

out

property subcomm

Return tuple of subcommunicators for all axes of self

property substart

Return starting indices of local self array

property v

Return local self array as an ndarray object

write(filename, name='darray', step=0, global_slice=None, domain=None, as_scalar=False)[source]

Write snapshot step of self to file filename

Parameters

  • filename (str or instance of FileBase) – The name of the file (or the file itself) that is used to store the requested data in self

  • name (str, optional) – Name used for storing snapshot in file.

  • step (int, optional) – Index used for snapshot in file.

  • global_slice (sequence of slices or integers, optional) – Store only this global slice of self

  • domain (sequence, optional) – An optional spatial mesh or domain to go with the data. Sequence of either

    • 2-tuples, where each 2-tuple contains the (origin, length) of each dimension, e.g., (0, 2*pi).

    • Arrays of coordinates, e.g., np.linspace(0, 2*pi, N). One array per dimension

  • as_scalar (boolean, optional) – Whether to store rank > 0 arrays as scalars. Default is False.

Example

>>> from mpi4py_fft import DistArray
>>> u = DistArray((8, 8), val=1)
>>> u.write('h5file.h5', 'u', 0)
>>> u.write('h5file.h5', 'u', (slice(None), 4))
mpi4py_fft.distarray.Function(*args, **kwargs)[source]
mpi4py_fft.distarray.newDistArray(pfft, forward_output=True, val=0, rank=0, view=False)[source]

Return a new DistArray object for provided PFFT object

Parameters

  • pfft (PFFT object)

  • forward_output (boolean, optional) – If False then create DistArray of shape/type for input to forward transform, otherwise create DistArray of shape/type for output from forward transform.

  • val (int or float, optional) – Value used to initialize array.

  • rank (int, optional) – Scalar has rank 0, vector 1 and matrix 2.

  • view (bool, optional) – If True return view of the underlying Numpy array, i.e., return cls.view(np.ndarray). Note that the DistArray still will be accessible through the base attribute of the view.

Returns

A new DistArray object. Return the ndarray view if keyword view is True.

Return type

DistArray

Examples

>>> from mpi4py import MPI
>>> from mpi4py_fft import PFFT, newDistArray
>>> FFT = PFFT(MPI.COMM_WORLD, [64, 64, 64])
>>> u = newDistArray(FFT, False, rank=1)
>>> u_hat = newDistArray(FFT, True, rank=1)

Module contents

This is the mpi4py-fft package

What is mpi4py-fft?

The Python package mpi4py-fft is a tool primarily for working with Fast Fourier Transforms (FFTs) of (large) multidimensional arrays. There is really no limit as to how large the arrays can be, just as long as there is sufficient computing powers available. Also, there are no limits as to how transforms can be configured. Just about any combination of transforms from the FFTW library is supported. Furthermore, mpi4py-fft can also be used simply to perform global redistributions (distribute and communicate) of large arrays with MPI, without any transforms at all.

For more information, see documentation.