Note: This package has been superseded by pfd-parallel.
We provide a massively parallel framework for partial fraction decomposition of rational functions based on the Singular/GPI-Space framework.
Our implementation is based on the approach described in the paper
Janko, Boehm, Marcel Wittmann, Zihao Wu, Yingxuan Xu, and Yang Zhang: IBP reduction coefficients made simple, JHEP 12 (2020) 054,
which has been implemened in Singular in the library pfd.lib.
Although applicable in general, it is aimed at the partial fraction decomposition of integration-by-parts coefficients in high energy physics.
Most of the parallelization code is an adapted version of the wait-all-first repository, implemented primarily by Lukas Ristau.
This project provides a function for applying the partial fraction decoposition function to a matrix of rational functions.
To get this project up and running, you need to compile Singular, GPI-Space, some of their dependencies and the project code itself.
For the various dependencies, it is recommended to create a file that exports the various install locations as environment variables. For this purpose, the following command may be run at a convenient location, after which the resulting file should be edited to specify two directory roots, one for purposes of compilation and one for installation of the code. While the first should typically be a fast local file system, the second must be accessible from all computation nodes to be used for running the system.
cat > env_vars_pfd.txt << "EOF"
export software_ROOT=<software-root>
# Some fast location in local system for hosting build directories,
# for example, something like /tmpbig/$USER/pfd or just $HOME/pfd if the user has a
# fast home directory.
export install_ROOT=<install-root>
# The install root is recommended to be some network (nfs) mountpoint, where
# each node of the cluster should be able to read from, for example
# something like /scratch/$USER/pfd
export compile_ROOT=$software_ROOT
# Optionally, this might be set to something like /dev/shm/$USER/pfd that
# stores files purely in memory, thus the contents of this
# location will be lost after reboot. It can speed up the computation times, as
# all disk io becomes memory io.
# GPI-Space dependencies:
export BOOST_ROOT=$install_ROOT/boost
export Libssh2_ROOT=$install_ROOT/libssh
export Libssh2_BUILD_DIR=$compile_ROOT/libssh/build
export LD_LIBRARY_PATH="${Libssh2_ROOT}/lib"${LD_LIBRARY_PATH:+:${LD_LIBRARY_PATH}}
export GASPI_ROOT=$install_ROOT/gpi2
export cpu_arch=$(getconf LONG_BIT)
export PKG_CONFIG_PATH="${GASPI_ROOT}/lib${cpu_arch}/pkgconfig"${PKG_CONFIG_PATH:+:${PKG_CONFIG_PATH}}
export PKG_CONFIG_PATH="${Libssh2_ROOT}/lib/pkgconfig:${Libssh2_ROOT}/lib64/pkgconfig"${PKG_CONFIG_PATH:+:${PKG_CONFIG_PATH}}
# GPI-Space:
export GPI_ROOT_DIR=$software_ROOT
export GPISPACE_REPO=$GPI_ROOT_DIR/gpispace/gpispace
export GPISPACE_BUILD_DIR=$compile_ROOT/gpispace/build
export GPISPACE_INSTALL_DIR=$install_ROOT/gpispace
export GPISpace_ROOT=$GPISPACE_INSTALL_DIR # expected by cmake
export GSPC_HOME=$GPISPACE_INSTALL_DIR # Set mostly for legacy reasons
export SHARED_DIRECTORY_FOR_TESTS=$GPISPACE_BUILD_DIR/tests
# Singular:
export SING_ROOT=$software_ROOT/Singular
export DEP_LIBS=$install_ROOT/sing_dep_libs
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$DEP_LIBS/lib
export SINGULAR_INSTALL_DIR=$install_ROOT/Singular
export SINGULAR_BUILD_DIR=$compile_ROOT/Singular/build
# PFD:
export PFD_ROOT=$software_ROOT/pfd
export PFD_REPO=$PFD_ROOT/pfd
export PFD_INSTALL_DIR=$install_ROOT/pfd
export PFD_BUILD_DIR=$compile_ROOT/pfd/build
export PFD_INPUT_DIR=$PFD_ROOT/input
export PFD_OUTPUT_DIR=$PFD_ROOT/output
EOF
As it is currently structured, the user needs only fill in the <software-root>
and the <install-root>, then all other veriables are set relative to these.
The above structure can of course be altered to suite the compiler's setup,
as long as the scripts in this REAME are altered accordingly, since they assume
the directory structure.
Once all the locations have been set correctly, the variables can easily be
exported with the following call:
source env_vars_pfd.txt
Ensure that the compile and install roots exist:
mkdir -p $software_ROOT
mkdir -p $install_ROOT
mkdir -p $compile_ROOT
GPI-Space targets and has been successfully used on x86-64 Linux systems. Other architectures are not guaranteed to work properly at this point.
The virtual memory layer can be backed with either Ethernet, Infiniband or BeeOND.
GPI-Space supports multiple Linux distributions:
- Centos 6
- Centos 7
- Centos 8
- Ubuntu 18.04 LTS
- Ubuntu 20.04 LTS
Ensure that the GPI_ROOT_DIR exists:
mkdir -p $GPI_ROOT_DIR
| Website | Supported Versions |
|---|---|
| Boost | >= 1.61, <= 1.63 |
Note, that Boost 1.61 is not compatible with OpenSSL >= 1.1, so it is recommended to use Boost 1.63, as follows:
boost_version=1.63.0
cd $GPI_ROOT_DIR
mkdir boost && cd boost
git clone \
--jobs $(nproc) \
--depth 1 \
--shallow-submodules \
--recursive \
--branch boost-${boost_version} \
https://github.com/boostorg/boost.git \
boost
cd boost
./bootstrap.sh --prefix="${BOOST_ROOT}"
./b2 \
-j $(nproc) \
headers
./b2 \
cflags="-fPIC -fno-gnu-unique" \
cxxflags="-fPIC -fno-gnu-unique" \
link=static \
variant=release \
install
| Website | Supported Versions |
|---|---|
| libssh2 | >= 1.7 |
libssh2 is not built with the OpenSSL backend on all systems. Additionally,
some versions available via package manager might not be compatible with
OpenSSH's default settings. For those reasons, it is highly recommended to build
libssh2 1.9 from scratch. Doing so is however straightforward thanks to CMake.
As additional dependencies OpenSSL and Zlib are required (for this any
package manager version should be sufficient). Also, unless Libssh2_ROOT is
set to /usr, the LD_LIBRARY_PATH needs to be set (as in lines 2 and 3 below)
in order for applications to find the correct one.
WARNING:
- libssh2 1.7 is not compatible with OpenSSL >= 1.1.
- libssh2 <= 1.8 is incompatible with the new default SSH-key format in OpenSSH >= 7.8.
cd $GPI_ROOT_DIR
mkdir libssh && cd libssh
libssh2_version=1.9.0
git clone --jobs $(nproc) \
--depth 1 \
--shallow-submodules \
--recursive \
--branch libssh2-${libssh2_version} \
https://github.com/libssh2/libssh2.git \
libssh2
cmake -D CRYPTO_BACKEND=OpenSSL \
-D CMAKE_BUILD_TYPE=Release \
-D CMAKE_INSTALL_PREFIX="${Libssh2_ROOT}" \
-D ENABLE_ZLIB_COMPRESSION=ON \
-D BUILD_SHARED_LIBS=ON \
-B $Libssh2_BUILD_DIR \
-S libssh2
cmake --build $Libssh2_BUILD_DIR \
--target install \
-j $(nproc)
| Website | Supported Versions |
|---|---|
| GPI-2 | 1.3.2 |
If Infiniband support is required, the --with-ethernet option can be omitted.
NOTE:
Compiling GPI2 requires gawk. Please install this with a package manager, if not already present on the system.
cd $GPI_ROOT_DIR
mkdir gpi2 && cd gpi2
gpi2_version=1.3.2 \
&& git clone \
--depth 1 \
--branch v${gpi2_version} \
https://github.com/cc-hpc-itwm/GPI-2.git \
GPI-2 \
&& cd GPI-2 \
&& grep "^CC\s*=\s*gcc$" . -lR \
| xargs sed -i'' -e '/^CC\s*=\s*gcc$/d' \
&& ./install.sh -p "${GASPI_ROOT}" \
--with-fortran=false \
--with-ethernet
NOTE:
Note that
<install-prefix>should be set to the correct path in the script above.
The code listings in this document assume
${GPISPACE_REPO}to be the directory storing the GPI-Space sources.${GPISPACE_BUILD_DIR}to be an empty directory to be used for building GPI-Space.${GPISPACE_INSTALL_DIR}to be a directory to install GPI-Space to. It is suggested to use a previously empty directory on a shared filesystem.${GPISPACE_TEST_DIR}to be an empty directory on a shared filesystem, which used when running the system tests.
Start by cloning gpi-space:
cd $GPI_ROOT_DIR
mkdir gpispace && cd gpispace
git clone \
--depth 1 \
--branch v22.03 \
https://github.com/cc-hpc-itwm/gpispace.git \
gpispace
Should you want to build the tests, run the following command. Note, the tests significantly increase build time, so an experienced user who has built gpi-space on a given machine before might opt not to run to define the build_tests variable.
export build_tests="-DBUILD_TESTING=on
-DSHARED_DIRECTORY_FOR_TESTS=$SHARED_DIRECTORY_FOR_TESTS"
mkdir -p $SHARED_DIRECTORY_FOR_TESTSTo build GPI-Space, run
mkdir -p "${GPISPACE_BUILD_DIR}"
cmake -D CMAKE_INSTALL_PREFIX=${GPISPACE_INSTALL_DIR} \
-D CMAKE_BUILD_TYPE=Release \
-B ${GPISPACE_BUILD_DIR} \
-S ${GPISPACE_REPO} \
${build_tests:-}
cmake --build ${GPISPACE_BUILD_DIR} \
--target install \
-j $(nproc)
NOTE:
GPI-Space requires a working SSH environment with a password-less SSH-key when using the SSH RIF strategy. To ensure this, make sure when generating your ssh keypair to leave the password field empty.
NOTE:
GPI-Space requires a working SSH environment with a password-less SSH-key when using the SSH RIF strategy, the default for most applications.
By default,
${HOME}/.ssh/id_rsais used for authentication. If no such key exists,ssh-keygen -t rsa -b 4096 -N '' -f "${HOME}/.ssh/id_rsa" ssh-copy-id -f -i "${HOME}/.ssh/id_rsa" "${HOSTNAME}"can be used to create and register one.
The following is a simple self test, that should be sufficient for most users.
# to test with multiple nodes, set GSPC_NODEFILE_FOR_TESTS
# Slurm: export GSPC_NODEFILE_FOR_TESTS="$(generate_pbs_nodefile)"
# PBS/Torque: export GSPC_NODEFILE_FOR_TESTS="${PBS_NODEFILE}"
# and SWH_INSTALL_DIR:
# export SWH_INSTALL_DIR=<a-shared-directory-visible-on-all-nodes>
"${GPISpace_ROOT}/share/gspc/example/stochastic_with_heureka/selftest"If GPI-Space has been built with testing enabled, then ctest can be
used to execute the unit- and system tests. It can be ommitted, but is
recommended for first time installations.
cd "${GPISPACE_BUILD_DIR}"
export GPISPACE_TEST_DIR=$SHARED_DIRECTORY_FOR_TESTS # any empty test directoy should be good
hostname > nodefile
export GSPC_NODEFILE_FOR_TESTS="${PWD}/nodefile"
# or to test in a cluster allocation:
# Slurm: export GSPC_NODEFILE_FOR_TESTS="$(generate_pbs_nodefile)"
# PBS/Torque: export GSPC_NODEFILE_FOR_TESTS="${PBS_NODEFILE}"
ctest --output-on-failure \
-j $(nproc)
Some of these tests take a long time (811 seconds on Intel i7), and there are 294 tests in the suite at the time of writing this document.
It is recommended to install the current version of Singular, which will be required by our framework. The version of Singular found in package manager does not generally work with the PFD project.
Besides flint, Singular has various more standard dependencies, which are usually available through the package manager of your distribution. Feel free to refer to the step-by-step instructions to build Singular for more details, taking note of the tools necessary to compile Singular under point 1.b.
This document gives a thorough guide for building the various dependencies and
then finally Singular itself, all the while assuming the user does not have
sudo/root privileges. This guide assumes that mpfr and gmp are installed
by the package manager to /usr
Start by choosing a location where Singular can be cloned. This will be
indicated by $SING_ROOT and compile the various dependencies
mkdir -p $SING_ROOT
The official guides for singular clones the latest development branch of flint. As flint is being actively developed and the APIs changed quite often, this has led to issues in the past. Therefore, it is rather recommended that a release version be downloaded and compiled instead. The newest release with which Singular can be built (at the time of writing) is version 2.6.3.
cd $SING_ROOT
mkdir flint && cd flint
wget http://www.flintlib.org/flint-2.6.3.tar.gz
tar -xvf flint-2.6.3.tar.gz
cd flint-2.6.3
./configure --with-gmp=/usr --prefix=$DEP_LIBS --with-mpfr=/usr
make -j $(nproc)
make install
mkdir -p $compile_ROOT/4ti2/build
cd $SING_ROOT
mkdir 4ti2 && cd 4ti2
wget http://www.4ti2.de/version_1.6/4ti2-1.6.tar.gz
tar xvfz 4ti2-1.6.tar.gz
pushd $compile_ROOT/4ti2/build
$SING_ROOT/4ti2/4ti2-1.6/configure --prefix=$DEP_LIBS
make -j $(nproc)
make install
popd
mkdir -p $compile_ROOT/cddlib/build
cd $SING_ROOT
mkdir cddlib && cd cddlib
wget https://github.com/cddlib/cddlib/releases/download/0.94j/cddlib-0.94j.tar.gz
tar -xvf cddlib-0.94j.tar.gz
pushd $compile_ROOT/cddlib/build
$SING_ROOT/cddlib/cddlib-0.94j/configure --prefix=$DEP_LIBS
make -j $(nproc)
make install
popd
cd $SING_ROOT
mkdir ntl && cd ntl
wget https://libntl.org/ntl-11.4.3.tar.gz
tar -xvf ntl-11.4.3.tar.gz
cd ntl-11.4.3/src # note the extra src
./configure PREFIX=$DEP_LIBS CXXFLAGS=-fPIC #notice PREFIX and CXXFLAGS is capitalized without dashes
make -j $(nproc)
make install
Singular may now be compiled against the libraries compiled and installed above.
cd $SING_ROOT
git clone \
--depth 1 \
https://github.com/Singular/Singular.git \
Sources
cd Sources
./autogen.sh
mkdir -p $SINGULAR_BUILD_DIR && pushd $SINGULAR_BUILD_DIR
CPPFLAGS="-I$DEP_LIBS/include" \
LDFLAGS="-L$DEP_LIBS/lib" \
${SING_ROOT}/Sources/configure \
--prefix=${SINGULAR_INSTALL_DIR} \
--with-flint=$DEP_LIBS \
--with-ntl=$DEP_LIBS \
--enable-gfanlib
make -j $(nproc)
make install
popd
The PFD project can now be compiled and installed.
The following environment variables must be set:
${GPISPACE_REPO}The path to the repository cloned from Github. This is needed for some cmake scripts, amongst other reasons.${GPISPACE_INSTALL_DIR}The install prefix used when compiling and installing gpi-space above.${SINGULAR_INSTALL_DIR}The install prefix used when compiling and installing Singular above.${PFD_REPO}The root of the cloned PFD project.${PFD_BUILD_DIR}The path of the build directory. It is recommended to build in a separate directory to the source code, preferably starting with an empty build directory.${PFD_INSTALL_DIR}The path to where the PFD project should be installed.
mkdir -p $PFD_ROOT && cd $PFD_ROOT
git clone \
--depth 1 \
https://github.com/singular-gpispace/PFD.git \
pfd
mkdir -p $PFD_BUILD_DIR
cmake -D CMAKE_INSTALL_PREFIX=$PFD_INSTALL_DIR \
-D CMAKE_BUILD_TYPE=Release \
-D GSPC_HOME=$GPISPACE_INSTALL_DIR \
-D GPISPACE_REPO=$GPISPACE_REPO \
-D SINGULAR_HOME=$SINGULAR_INSTALL_DIR \
-D FLINT_HOME=$DEP_LIBS \
-B ${PFD_BUILD_DIR} \
-S ${PFD_REPO}
cmake --build ${PFD_BUILD_DIR} \
--target install \
-j $(nproc)
To run an example, we need a Singular script that loads the pfd_gspc.lib
library. A gpi-space configure token needs to be prepared, with some important
configuration: The path of a temporary directory, where files will be stored
during the computation and handling of the various files at runtime, the
location of a nodefile, containing a location on then network where gpi-space is
installed, the number of processes each node should run in parallel, the address
of a running instance of the gpi-space monitoring tool, as well as the port on
which the monitoring tool is listening (Note, the program can be run without the
monitoring tool, in which case the last two options should remain unset). Next,
the ring in which the rational function's numerator and denominator is found is
declared. The input of the system is in the form of files, identified by the
row and column in a matrix where it must be found, in the form
<basename>_<row>_<col>.(txt|ssi), where the suffix is txt if the file is in
plain text format, and ssi if the input files are in this binary format
implemented by singular. To specify the input files to be calculated, put the
coordinates of the matrix entries to be calculated in a list of lists.
Finally, all this is provided to the parallel_pfd function as arguments,
preferably with the optional argument for the path to where the input files are
found. The user may also provide in a separate argument the path of where the
output files should be written.
An example script test_parallel_pfd.sing in Singular for a 4 by 4 matrix might
be
mkdir -p $PFD_ROOT/tempdir
hostname > $PFD_ROOT/nodefile
hostname > $PFD_ROOT/loghostfile
cat > test_parallel_pfd.sing.temp << "EOF"
LIB "pfd_gspc.lib";
// configuration for gpispace
configToken gspcconfig = configure_gspc();
gspcconfig.options.tempdir = "$PFD_ROOT/tempdir";
gspcconfig.options.nodefile = "$PFD_ROOT/nodefile";
gspcconfig.options.procspernode = 8;
// Should the user want to run withouth the gspc-monitor
// the following two lines may be commented out.
gspcconfig.options.loghostfile = "$PFD_ROOT/loghostfile";
gspcconfig.options.logport = 6439;
// configuration for the problem to be computed.
configToken pfdconfig = configure_pfd();
pfdconfig.options.filename = "fraction";
pfdconfig.options.inputdir = "$PFD_INPUT_DIR";
pfdconfig.options.outputdir = "$PFD_OUTPUT_DIR";
pfdconfig.fdconfigptions.algorithm = "fullyParallel";
ring r = 0, x, lp;
list entries = list( list(1, 1), list(1, 2), list(1, 3), list(1, 4)
, list(2, 1), list(2, 2), list(2, 3), list(2, 4)
, list(3, 1), list(3, 2), list(3, 3), list(3, 4)
, list(4, 1), list(4, 2), list(4, 3), list(4, 4)
);
parallel_pfd( entries
, gspcconfig
, pfdconfig
);
exit;
EOF
We want to expand the environment variables in the script above, so create a hacky script for this purpose:
cat > shell_expand_script.sh << "EOF"
echo 'cat <<END_OF_TEXT' > temp.sh
cat "$1" >> temp.sh
echo 'END_OF_TEXT' >> temp.sh
bash temp.sh >> "$2"
rm temp.sh
EOF
chmod a+x shell_expand_script.sh
./shell_expand_script.sh test_parallel_pfd.sing.temp test_parallel_pfd.sing
Next, if you wish to start a monitor, this may be done with the following script:
cat > start_monitor.sh << "EOF"
#!/usr/bin/bash
set -euo pipefail
# raster or native (native for X forwarding)
QT_DEBUG_PLUGINS=0 \
QT_GRAPHICSSYSTEM=native \
$PFD_INSTALL_DIR/libexec/bundle/gpispace/bin/gspc-monitor \
--port 6439 &
EOF
chmod a+x start_monitor.sh
It may simply be run as
./start_monitor.sh
Ensure that the --port number matches the one set in the singular script.
Also, if this is run over ssh on a remote machine, make sure that x forwarding
is enabled.
Create the input files:
mkdir -p $PFD_INPUT_DIR
mkdir -p $PFD_OUTPUT_DIR
pushd $PFD_INPUT_DIR
for r in {1..4}
do
for c in {1..4}
do
echo "x/(x*(x+1))" > fraction_"$r"_"$c".txt
done
done
popd
Finally, the test may be run with the script
cat > run_pfd_example.sh << "EOF"
SINGULARPATH="$PFD_INSTALL_DIR/LIB" \
$SINGULAR_INSTALL_DIR/bin/Singular \
test_parallel_pfd.sing
EOF
chmod a+x run_pfd_example.shwhich can be started with
./run_pfd_example.sh
To run more an example with real PFD data, some data is provided as ssi
("simple Singular interface") files under example_data/ssi, which can be
decomposed with the Singular script real_pfd.sing:
mkdir -p $PFD_ROOT/tempdir
echo $(hostname) > $PFD_ROOT/nodefile
cat > real_pfd.sing.temp << "EOF"
LIB "pfd_gspc.lib";
// configuration for gpispace
configToken gspcconfig = configure_gspc();
gspcconfig.options.tempdir = "$PFD_ROOT/tempdir";
gspcconfig.options.nodefile = "$PFD_ROOT/nodefile";
gspcconfig.options.procspernode = 8;
// Should the user want to run withouth the gspc-monitor
// the following two lines may be commented out.
gspcconfig.options.loghostfile = "$PFD_ROOT/loghostfile";
gspcconfig.options.logport = 6439;
// configuration for the problem to be computed.
configToken pfdconfig = configure_pfd();
pfdconfig.options.filename = "xb_deg5";
pfdconfig.options.inputdir = "$PFD_REPO/example_data/ssi";
pfdconfig.options.outputdir = "$PFD_OUTPUT_DIR";
pfdconfig.fdconfigptions.algorithm = "fullyParallel";
ring r = 0, x, lp;
list l = list( list(1, 1), list(1, 2), list(1, 3), list(1, 4)
, list(1, 5), list(1, 6), list(1, 7), list(1, 8)
, list(1, 9), list(1, 10)
);
parallel_pfd( l
, gspcconfig
, pfdconfig
);
exit;
EOF
./shell_expand_script.sh real_pfd.sing.temp real_pfd.sing
To run the Singular Script, the following bash script may be used:
cat > run_real_pfd.sh << "EOF"
SINGULARPATH="$PFD_INSTALL_DIR/LIB" \
$SINGULAR_INSTALL_DIR/bin/Singular \
real_pfd.sing
EOF
chmod a+x run_pfd_example.sh
It can now be started with
./run_real_pfd.sh
Note, to run the same computation, but without the internal parallelism on each
entry, the algorithm field in the pfdconfig tokens options field may be changed to
waitAll.
Assuming that we are installing on a Ubuntu system (analogous packages exist in other distributions), we give installation instructions for standard packages which are required by the framework and may not be included in your of-the-shelf installation.
Note that the following requires root privileges. If you do not have root access, ask your administator to install these packages. You may want to check with dpkg -l <package name> whether the package is installed already.
-
Version control system Git used for downloading sources:
sudo apt-get install git
-
Tools necessary for compiling the packages:
sudo apt-get install build-essential sudo apt-get install autoconf sudo apt-get install autogen sudo apt-get install libtool sudo apt-get install libreadline6-dev sudo apt-get install libglpk-dev sudo apt-get install cmake sudo apt-get install gawk
Or everything in one command:
sudo apt-get install build-essential autoconf autogen libtool libreadline6-dev libglpk-dev cmake gawk
-
Scientific libraries used by Singular:
sudo apt-get install libgmp-dev sudo apt-get install libmpfr-dev sudo apt-get install libcdd-dev sudo apt-get install libntl-dev
Or everything in one command:
sudo apt-get install libgmp-dev libmpfr-dev libcdd-dev libntl-dev
Note, in the above guide, we only assume libmpfr and libgmp is installed, and libcdd and libntl is built locally from sources.
-
Library required by to build libssh:
sudo apt-get install libssl-dev
-
Libraries required by GPI-Space
sudo apt-get install openssh-server sudo apt-get install hwloc sudo apt-get install libhwloc-dev sudo apt-get install libudev-dev sudo apt-get install qt5-default sudo apt-get install chrpath
Or everything in one command:
sudo apt-get install openssh-server hwloc libhwloc-dev libudev-dev qt5-default chrpath