GitLocker: The Coding Marketplace

Description:

greenac 0.2.4

█▀▀█ █▀▀█ █▀▀ █▀▀ █▀▀▄
█ ▄▄ █▄▄▀ █▀▀ █▀▀ █ █
█▄▄█ ▀ ▀▀ ▀▀▀ ▀▀▀ ▀ ▀

█▀▀█ █▀▀█ █▀▀▄ ▀▀█▀▀ ▀ █▀▀▄ █ █ █▀▀█ ▀▀█▀▀ ▀ █▀▀█ █▀▀▄
█ █ █ █ █ █ ▀█▀ █ █ █ █ █▄▄█ █ ▀█▀ █ █ █ █
█▄▄█ ▀▀▀▀ ▀ ▀ ▀ ▀▀▀ ▀ ▀ ▀▀▀ ▀ ▀ ▀ ▀▀▀ ▀▀▀▀ ▀ ▀

Green/Continuation is an Analytical continuation toolkit for Green Software Package
Installation
Green/Continuation comes in two forms

C++ application
Python package

Dependencies
Green/Continuation has the following required external dependencies

HDF5 library version >= 1.10.2
Message Passing Interface >= 3.1 (for C++ application)
Eigen3 library >= 3.4.0
GNU Multiprecision library
pybind11 (optional to build python wrapper)

To build Green/Continuation CMake version 3.18 or above is required
Build and Install C++ application
The following example will build, test and install Green/Continuation to /path/to/weakcoupling/install/dir directory.
$ git clone https://github.com/Green-Phys/green-ac
$ cd green-ac
$ mkdir build && cd build
$ cmake -DCMAKE_BUILD_TYPE=Release \
-DCMAKE_INSTALL_PREFIX=/path/to/install/dir ..
$ make
$ make test
$ make install

Installation of Python package
We provide pre-built binaries for major Linux distributions and recent MacOS version via pip.
For installation using pip simply type pip install green-ac.
If pre-built binaries can not be used, package will be built from sources.
Usage
C++ application
After the Green/Continuation is built and installed, spectral function could be obtained by calling
<install dir>/bin/ac.exe --BETA <Inverse temperature> --grid_file <grid file> \
--input_file <input file> --output_file <output file> --group <HDF5 group with data> \
--e_min -5.0 --e_max 5.0 --n_omega 4000 --eta 0.01 \
--kind Nevanlinna

BETA -- the inverse temperature that was used to obtain results
grid_file -- name of the grid file that was used to obtain results
input_file -- name of the file that contains imaginary time data
output_file -- name of the file to store results of the continuation
group -- name of the group that contains data and mesh datasets with imaginary time data and grid
e_min -- lowest frequency on the real axis
e_max -- largest frequency on the real axis
n_omega -- number of frequency points on the real axis
eta -- broadening parameter
kind -- type of continuation to be used (current version only supports Nevanlinna)

After the completetion, results will be stored in group HDF5 group in the output_file file.
Python
In addition to C++ application, Green/Continuation provides a convinient Python package that can work directly with
numpy arrays. It supports two types of parallelism, using ProcessPoolExecutor from concurrent.futures and
MPI parallelization using mpi4py library.
To use Green/Continuation simply import it in your script as
import green_ac

and call solve function with the following parameters:

Type of the continuation (currently we only provide Nevanlinna)
Matsubara frequency grid
Real frequency grid
Data in Matsubara frequency domain
Precision

Here is an example how to obtain real frequency Green's function for a simple two-pole non-interacting Green's function with precision at least 512 bits:
imgrid = (2*np.linspace(-50,49,100) + 1) * 1.j *np.pi/ 2
grid = np.linspace(-2,2,1001) + 0.01j
data = 0.5*(1/(imgrid + 0.5) + 1/(imgrid - 0.5))
data_out = green_ac.solve("Nevanlinna", imgrid, grid, data, 512)

Here we have 100 positive and negative Matsubara frequencies, define real frequency grid to have 1000 points and to be from -2 to 2 with broadening parameter 0.01,
We define Green's function on Matsubara grid with poles at -0.5 and 0.5. Real frequency data will be stored in data_out array.
Acknowledgements
This work is supported by National Science Foundation under the award OCA-2310582