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Small changes to documentation
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bitbucket-pipelines.yml

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# This is a sample build configuration for Python.
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# Check our guides at https://confluence.atlassian.com/x/x4UWN for more examples.
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# Only use spaces to indent your .yml configuration.
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# -----
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# You can specify a custom docker image from Docker Hub as your build environment.
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image: continuumio/miniconda3:latest
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pipelines:

conf/run_test.sh

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pushd tests
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./runtests.sh
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docs/source/conf.py

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#
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import os
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import sys
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import subprocess
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sys.path.insert(0, os.path.abspath('.'))
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sys.path.insert(0, os.path.abspath('../'))
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# -- Project information -----------------------------------------------------
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project = 'mpi4py-fft'
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copyright = '2018, Mikael Mortensen and Lisandro Dalcin'
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copyright = '2019, Mikael Mortensen and Lisandro Dalcin'
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author = 'Mikael Mortensen and Lisandro Dalcin'
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# The short X.Y version
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version = ''
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# The full version, including alpha/beta/rc tags
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release = '1.0-beta'
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p = subprocess.Popen(["git describe --tags | cut -d'-' -f 1"], stdout=subprocess.PIPE, shell=True)
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# The short X.Y version
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version = p.communicate()[0].rstrip().decode('utf-8')
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# The full version, including alpha/beta/rc tags
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release = version
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# -- General configuration ---------------------------------------------------
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napoleon_use_param = False
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napoleon_use_ivar = True
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# For some reason mathjax 2.7.5 renders bold type ugly. Use 2.7.1
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mathjax_path = 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML'
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# Add any paths that contain templates here, relative to this directory.
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templates_path = ['_templates']
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# dir menu entry, description, category)
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texinfo_documents = [
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(master_doc, 'mpi4py-fft', 'mpi4py-fft Documentation',
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author, 'mpi4py-fft', 'One line description of project.',
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author, 'mpi4py-fft', 'Parallel fast Fourier transforms',
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'Miscellaneous'),
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]
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docs/source/io.rst

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mpi4py-fft works with regular Numpy arrays. However, since arrays in parallel
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can become very large, and the arrays live on multiple processors, we require
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parallel IO capabilities that goes beyond Numpys regular methods.
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In the :mod:`.utilities` module there are two helper classes for dumping
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In the :mod:`mpi4py_fft.utilities` module there are two helper classes for dumping
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dataarrays to either `HDF5 <https://www.hdf5.org>`_ or
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`NetCDF <https://www.unidata.ucar.edu/software/netcdf/>`_ format:
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f0 = HDF5File('filename.h5', T, domain=((0, pi), (0, 2*np.pi), (0, 3*np.pi)))
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2) One array giving the coordinates for each dimension. For example::
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2) A sequence of arrays giving the coordinates for each dimension. For example::
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d = (np.arange(N[0], dtype=np.float)*1*np.pi/N[0],
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np.arange(N[1], dtype=np.float)*2*np.pi/N[1],
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opened with `Visit <https://www.visitusers.org>`_.
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To view the HDF5-files we first need to generate some light-weight *xdmf*-files that can
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be understood by both Paraview or Visit. To generate such files, simply throw the
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be understood by both Paraview and Visit. To generate such files, simply throw the
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module :mod:`.utilities.generate_xdmf` on the HDF5-files::
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from mpi4py_fft.utilities import generate_xdmf

docs/source/parallel.rst

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.. math::
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\tilde{u}_{j_0/P,k_1,k_2} &= \mathcal{F}_1( \mathcal{F}_{2}(u_{j_0/P, j_1, j_2}), \\
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\tilde{u}_{j_0/P,k_1,k_2} &= \mathcal{F}_1( \mathcal{F}_{2}(u_{j_0/P, j_1, j_2})), \\
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\tilde{u}_{j_0, k_1/P, k_2} &\xleftarrow[P]{1\rightarrow 0} \tilde{u}_{j_0/P, k_1, k_2}, \\
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\hat{u}_{k_0,k_1/P,k_2} &= \mathcal{F}_0(\tilde{u}_{j_0, k_1/P, k_2}).
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:math:`u_{j_0/P,j_1,j_2}` can transform along both axes 1 and 2 simultaneously,
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without any intermediate global redistributions. By setting
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``collapse=True`` only one object of ``rfftn(u, axes=(1, 2))`` will be
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used instead of two (like ``rfftn(rfftn(u, axes=2), axes=1)``).
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used instead of two (like ``fftn(rfftn(u, axes=2), axes=1)``).
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Note that a collapse can also be configured through the ``axes`` keyword,
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using::
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\widehat{ab}_k &= \int_{0}^{2\pi} \left( \sum_{p=-N/2}^{N/2-1} \hat{a}_p e^{i p x} \sum_{q=-N/2}^{N/2-1} \hat{b}_q e^{i q x} \right) e^{-i k x} dx, \quad \forall \, k \in [-N/2, \ldots, N/2-1] \\
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\widehat{ab}_k &= \sum_{p=-N/2}^{N/2-1} \sum_{q=-N/2}^{N/2-1} \hat{a}_p \hat{b}_q \int_{0}^{2\pi} e^{-i (p+q-k) x} dx, \quad \forall \, k \in [-N/2, \ldots, N/2-1]
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The final integral is unity for :math:`p+q=k` and zero otherwise. Consequently, we get
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The final integral is :math:`2\pi` for :math:`p+q=k` and zero otherwise. Consequently, we get
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.. math::
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:label: ab_convolve2
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\widehat{ab}_k = \sum_{p=-N/2}^{N/2-1}\sum_{q=-N/2}^{N/2-1} \hat{a}_p \hat{b}_{q} \delta_{p+q, k} , \quad \forall \, k \in [-N/2, \ldots, N/2-1]
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\widehat{ab}_k = 2\pi \sum_{p=-N/2}^{N/2-1}\sum_{q=-N/2}^{N/2-1} \hat{a}_p \hat{b}_{q} \delta_{p+q, k} , \quad \forall \, k \in [-N/2, \ldots, N/2-1]
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Unfortunately, the convolution sum :eq:`ab_convolve2` is very expensive to
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compute, and the direct application of :eq:`dft_convolve` leads to

tests/test_fftw.py

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import numpy as np
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from scipy.fftpack import dctn as scipy_dctn
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from scipy.fftpack import dstn as scipy_dstn
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import scipy.fftpack
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import scipy.fftpack # pylint: disable=unused-import
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from mpi4py_fft import fftw
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has_pyfftw = True

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