deac-cpp

A C++ implementation of the Differential Evolution for Analytic Continuation (DEAC) algorithm which uses self adaptive differential evolution to reconstruct the dynamic structure factor from imaginary time density-density correlations.

Quick installation

DEAC uses CMake for build, test and installation automation. For details on using CMake consult https://cmake.org/documentation/. In short, the following steps should work on UNIX-like systems:

git clone [email protected]:nscottnichols/deac-cpp.git
cd deac-cpp
mkdir build
cd build
cmake ../src
make
sudo make install

On Windows try:

git clone [email protected]:nscottnichols/deac-cpp.git
cd deac-cpp
md build
cd build
cmake ../src
cmake --build . --config Release
cmake --build . --target install

Typical installation

As above, and with further details below, but you should consider using the following CMake options with the appropriate value instead of xxx :

• -D USE_HYPERBOLIC_MODEL=1 use hyperbolic model for spectral function S'(ω)=2S(ω)e^(-βω/2)
• -D USE_STANDARD_MODEL=1 use standard model for spectral function S'(ω)=S(ω)
• -D USE_NORMALIZATION_MODEL=1 use normalization model for spectral function S'(ω)=S(ω)(1 + e^(-βω))
• -D GPU_BLOCK_SIZE=xxx equal to the maximum threadblock size and enables GPU acceleration (using AMD's HIP language)
• -D MAX_GPU_STREAMS=xxx equal to maximum number of concurrent streams on GPU device
• -D USE_CUDA=1 use CUDA instead of HIP for GPU acceleration
• -D CMAKE_CUDA_ARCHITECTURES=xxx equal to CUDA device architecture if not properly detected by CMake
• -D USE_TCB_SPAN=1 use Tristan Brindle's span implementation if std::span of gsl::span unsupported
• -D CMAKE_C_COMPILER=xxx equal to the name of the C99 Compiler you wish to use (or the environment variable CC)
• -D CMAKE_CXX_COMPILER=xxx equal to the name of the C++17 compiler you wish to use (or the environment variable CXX)
• -D CMAKE_PREFIX_PATH=xxx to add a non-standard location for CMake to search for libraries, headers or programs
• -D CMAKE_INSTALL_PREFIX=xxx to install pimc to a non-standard location
• -D STATIC=1 to enable a static build
• -D CMAKE_BUILD_TYPE=Debug to build deac in debug mode (deacd.e)
• -D CMAKE_BUILD_TYPE=ZeroT to build deac for zero temperature (deac-zT.e)
• -D CMAKE_BUILD_TYPE=ZeroTDebug to build deac for zero temperature in debug mode (deac-zTd.e)
• -E env CXXFLAGS="xxx" add additional compiler flags
• -E env LDFLAGS="xxx" add additional linker flags

Executables will be installed to CMAKE_INSTALL_PREFIX location or, if the install is skipped, they will be located in build/deac. Executables produced are deac.e, deacd.e, deac-zT.e, and deac-zTd.e for CMAKE_BUILD_TYPE=Release|Debug|ZeroT|ZeroTDebug respectively.

A typical cmake line for building deac in zero temperature mode with gpu acceleration using CUDA on a Tesla V100 device with an undetected CUDA architecture and a compiler not supporting <span> is:

cmake -DUSE_CUDA=1 -DGPU_BLOCK_SIZE=1024 -DCMAKE_CUDA_ARCHITECTURES=70 -DUSE_TCB_SPAN=1 -DCMAKE_BUILD_TYPE=ZeroT ../src

If you run into problems, failures with linking etc., common errors may include not properly setting your LD_LIBRARY_PATH or LIBRARY_PATH and not starting from a clean build directory (issue make clean or rm -rf ./* inside the build directory).

Usage and analysis

Step 1: set up input data

1. get data into numpy arrays (imaginary_time_array, intermediate_scattering_function_array, intermediate_scattering_function_error_array)
2. save data as npz file np.savez(filename, tau = imaginary_time_array, isf = intermediate_scattering_function_array, error = intermediate_scattering_function_error_array)
3. run converter script in tools directory to convert .npz file to binary format used by deac /path/to/DEAC_TOOLS_DIR/convert_isf_data.py /path/to/isf_npz_file /path/to/isf_bin_file

Step 2: run DEAC

A single reconstruction of the dynamic structure factor can be generated using the input data from step 1. For example:

deac.e --number_of_generations 1600000 --temperature 1.35 --population_size 8 --genome_size 4096 --normalize --omega_max 512.0 --save_directory deac_results --seed 1 --stop_minimum_fitness 1.0 isf.bin

This command will save the generated spectrum in the deac_results directory after 1600000 steps or if the desired fitness cutoff of 1.0 is reached. Please see deac.e --help for more command line arguments and further description.

The general recommendation is to generate several spectra using different seeds (--seed) and average the final results. A sample bash script to generate a command file with multiple seeds can be found in the tools directory tools/generate_commands.sh.

Step 3: analyze DEAC results

The data generated by DEAC is in binary format and can be loaded into Python using numpy.

frequency_filename = "/path/to/deac_frequency_file.bin"
dynamic_structure_factor_filename = "/path/to/deac_dsf_file.bin"
frequency = np.fromfile(frequency_filename, dtype=np.double)
dsf = np.fromfile(dynamic_structure_factor_filename, dtype=np.double)

An example script to plot the average for multiple spectra using many seeds (with results saved in the same directory) can be found in the tools directory (tools/plot_simple_average_deac_results.py).

See deac --help for more details.