GX-AnalyticContinuation

GreenX library - Analytic Continuation

The analytic continuation component (GX-AC) provides routines to interpolate functions using the thiele pade interpolant.

Note

Key Features

• basic thiele pade algorithm
• greedy algorithm for thiele pade to enhance numerical stability
• arbitrary precision arithmetic using the GMP library for even more numerical stability

Building

If you want to compile only the Analytic Continuation (AC) component of Greenx, change to the GreenX root, then type:

mkdir build && cd build 
cmake -DMINIMAX_COMPONENT=OFF -DLBASIS_COMPONENT=OFF \
      -DPAW_COMPONENT=OFF -DCOMPILE_SUBMODULES=OFF ../
make -j 
make install 

# optional: for running the regression tests
ctest

Linking against GNU Multiple Precision (GMP) Library

If requested, the arithmetic operations to obtain the pade model are carried out using an user specified precision. These arbitrary precision floats are handeled by the GMP library. By default GreenX tries to find and link GMP automatically since it is installed already on most systems that use GNU compilers. However, if GreenX is unable to find the GMP library it will note the user during the cmake configuration step.

Compile and link GMP manually:

If for some reason no GMP is found in your system you can build it manually and specify its path in the GreenX build. Assumes that $GX_ROOT is set to the root of GreenX:

cd $GX_ROOT

# ------------------- Build GMP library
mkdir external && cd external 
wget https://gmplib.org/download/gmp/gmp-6.3.0.tar.xz
tar -xf gmp-6.3.0.tar.xz 
cd gmp-6.3.0/ && mkdir install
GMP_INSTALL_DIR="$(realpath install)"
./configure --prefix="${GMP_INSTALL_DIR}" --enable-cxx
make -j 
make install 
# optionally run unit tests of GMP
#   make check

cd $GX_ROOT

# ------------------- Build GreenX
mkdir build && cd build 
cmake -DCMAKE_PREFIX_PATH=$GMP_INSTALL_DIR ../
make -j 
make install

Turn off GMP:

You can turn of linking to GMP by specifiying ENABLE_GNU_GMP=OFF in the cmake configuration step.

cmake -DENABLE_GNU_GMP=OFF ../              # Default: ENABLE_GNU_GMP=ON

Calling the Analytic Continuation Component

Information on how to use this component is always up-to-date on the GreenX website.

Additionally, take a look at the example script in GX-AnalyticContinuation/examples. This script shows how this component can be used.

Build the Example Script

In the GX-AnalyticContinuation/examples folder you can find a stand-alone fortran program (pade_example.f90) showcasing the usage of the GX-AC component. After building the GreenX library, change into the GX-AnalyticContinuation/examples folder and type:

make 

The program can be executed by running:

./pade_example > output.dat

To plot the reference function and the Padé interpolation call the python script:

python plot.py output.dat comparison.png

The figure is saved as comparison.png. Feel free to change some parameters in the pade_example.f90 script and compile again to see how it is affecting the pade interpolation.

Running the regression tests

Regression tests of the GX-AC component use the testing framework pytest. Simply type ctest in the build directory after the GreenX library has been build.

For more information please refer to the main README.md of this repository.