A C++ Implementation of Konno and Ohmachi Smoothing

Joseph P. Vantassel, The University of Texas at Austin

Background

A recent project focused on developing an open-source Python package for for horizontal-to-vertical spectral ratio (HVSR) processing called hvsrpy prompted a study of the computational performance of the HVSR calculation, however this had to be concluded prematurely. This study presents a reexamination of the algorithm’s performance.

HVSR processing involves the following steps: (1) the division of a long time-domain record into smaller time windows (typically 60 – 360 seconds in length), (2) transformation of these windows into the frequency domain using the Discrete Fourier Transform (DFT), (3) the smoothing of these frequency-domain representations (i.e., spectra), and (4) the division of the smoothed horizontal and vertical spectra. Initial performance tests on hvsrpy indicated that approximately 60% of the computational cost incurred in the HVSR calculation was incurred in the smoothing stage. Therefore, this study focuses primarily on the smoothing algorithm.

In particular, this study will compare the performance of a Python implementation, a Python implementation improved using just-in-time (jit) compilation, a serial implementation of the algorithm in C++, and a parallel implementation using C++ and OpenMP. This repository is host to the C++ implementations see the sigpropy repository (a dependency of the hvsrpy package) for the Python implementations.

Results

Figure 1: Comparison of the results of the four methods. All methods are in excellent agreement.

Figure 2: Parallel implementation's strong scaling considering various scheduling schemes.

Figure 3: Runtime comparison between the four methods of interest.

Want to try it for yourself?

Instructions to compile and run the parallel and serial implementations are provided below.

Parallel

1. Download or clone the repository.
2. Run: mkdir build && cd build && cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_CXX_COMPILER=g++ -DCMAKE_CXX_BUILD_OMP=yes ...
3. Run: make clean && make.
4. Run: ./smooth ../examples/data.csv smooth_data.csv.

Serial

Same as parallel, except with the second step swapped with:

2. Run: mkdir build && cd build && cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_CXX_COMPILER=g++ -DCMAKE_BUILD_OMP=no ...