arXiv subjects

Takahiro Katagiri

Publications and source records attributed to Takahiro Katagiri.

23 records · Page 2Linked to original sources

arXiv2024

An Auto-tuning Method for Run-time Data Transformation for Sparse Matrix-Vector Multiplication

In this paper, we research the run-time sparse matrix data transformation from Compressed Row Storage (CRS) to Coordinate (COO) storage and an ELL (ELLPACK/ITPACK) format with OpenMP parallelization for sparse matrix-vector multiplication (SpMV). We propose an auto-tuning (AT) method by using the $D_{mat}^i$ - $R_{ell}^i$ graph, which plots the derivation/average for the number of non-zero elements per row ($D_{mat}^i$) and the ratio, SpMV speedups/transformation time from the CRS to ELL ($R_{ell}^i$ ). The experimental results show the ELL format is very effective in the Earth Simulator 2. The speedup factor of 151 with the ELL-Row inner-parallelized format is obtained. The transformation overhead is also very small, such as 0.01 to 1.0 SpMV time with the CRS format. In addition, the $D_{mat}^i$ - $R_{ell}^i$ graph can be modeled for the effectiveness of transformation according to the $D_{mat}^i$ value.

cs.DC↗

arXiv2024

A Communication Avoiding and Reducing Algorithm for Symmetric Eigenproblem for Very Small Matrices

In this paper, a parallel symmetric eigensolver with very small matrices in massively parallel processing is considered. We define very small matrices that fit the sizes of caches per node in a supercomputer. We assume that the sizes also fit the exa-scale computing requirements of current production runs of an application. To minimize communication time, we added several communication avoiding and communication reducing algorithms based on Message Passing Interface (MPI) non-blocking implementations. A performance evaluation with up to full nodes of the FX10 system indicates that (1) the MPI non-blocking implementation is 3x as efficient as the baseline implementation, (2) the hybrid MPI execution is 1.9x faster than the pure MPI execution, (3) our proposed solver is 2.3x and 22x faster than a ScaLAPACK routine with optimized blocking size and cyclic-cyclic distribution, respectively.

cs.DC↗

arXiv2024

Xabclib:A Fully Auto-tuned Sparse Iterative Solver

In this paper, we propose a general application programming interface named OpenATLib for auto-tuning (AT). OpenATLib is designed to establish the reusability of AT functions. By using OpenATLib, we develop a fully auto-tuned sparse iterative solver named Xabclib. Xabclib has several novel run-time AT functions. First, the following new implementations of sparse matrix-vector multiplication (SpMV) for thread processing are implemented:(1) non-zero elements; (2) omission of zero-elements computation for vector reduction; (3) branchless segmented scan (BSS). According to the performance evaluation and the comparison with conventional implementations, the following results are obtained: (1) 14x speedup for non-zero elements and zero-elements computation omission for symmetric SpMV; (2) 4.62x speedup by using BSS. We also develop a "numerical computation policy" that can optimize memory space and computational accuracy. Using the policy, we obtain the following: (1) an averaged 1/45 memory space reduction; (2) avoidance of the "fault convergence" situation, which is a problem of conventional solvers.

cs.MS↗

arXiv2023

Autotuning by Changing Directives and Number of Threads in OpenMP using ppOpen-AT

Recently, computers have diversified architectures. To achieve high numerical calculation software performance, it is necessary to tune the software according to the target computer architecture. However, code optimization for each environment is difficult unless it is performed by a specialist who knows computer architectures well. By applying autotuning (AT), the tuning effort can be reduced. Optimized implementation by AT that enhances computer performance can be used even by non-experts. In this research, we propose a technique for AT for programs using open multi-processing (OpenMP). We propose an AT method using an AT language that changes the OpenMP optimized loop and dynamically changes the number of threads in OpenMP according to computational kernels. Performance evaluation was performed using the Fujitsu PRIMEHPC FX100, which is a K-computer type supercomputer installed at the Information Technology Center, Nagoya University. As a result, we found there was a performance increase of 1.801 times that of the original code in a plasma turbulence analysis.

cs.PF↗

arXiv2023

Bayesian phase difference estimation algorithm for direct calculation of fine structure splitting: accelerated simulation of relativistic and quantum many-body effects

Despite rapid progress in the development of quantum algorithms in quantum computing as well as numerical simulation methods in classical computing for atomic and molecular applications, no systematic and comprehensive electronic structure study of atomic systems that covers almost all of the elements in the periodic table using a single quantum algorithm has been reported. In this work, we address this gap by implementing the recently-proposed quantum algorithm, the Bayesian Phase Difference Estimation (BPDE) approach, to compute accurately fine-structure splittings, which are relativistic in origin and it also depends on quantum many-body (electron correlation) effects, of appropriately chosen states of atomic systems, including highly-charged superheavy ions. Our numerical simulations reveal that the BPDE algorithm, in the Dirac--Coulomb--Breit framework, can predict the fine-structure splitting of Boron-like ions to within 605.3 cm$^{-1}$ of root mean square deviations from the experimental ones, in the (1s, 2s, 2p, 3s, 3p) active space. We performed our simulations of relativistic and electron correlation effects on Graphics Processing Unit (GPU) by utilizing NVIDIA's cuQuantum, and observe a $\times 42.7$ speedup as compared to the CPU-only simulations in an 18-qubit active space.

quant-ph↗