ACM Transactions on Mathematical Software (TOMS)最新文献_第10页

Analysis and Performance Evaluation of Adjoint-guided Adaptive Mesh Refinement for Linear Hyperbolic PDEs Using Clawpack 基于Clawpack的线性双曲型偏微分方程伴导自适应网格细化分析及性能评价

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2018-10-01 DOI: 10.1145/3392775

B. Davis, R. LeVeque

{"title":"Analysis and Performance Evaluation of Adjoint-guided Adaptive Mesh Refinement for Linear Hyperbolic PDEs Using Clawpack","authors":"B. Davis, R. LeVeque","doi":"10.1145/3392775","DOIUrl":"https://doi.org/10.1145/3392775","url":null,"abstract":"Adaptive mesh refinement (AMR) is often used when solving time-dependent partial differential equations using numerical methods. It enables time-varying regions of much higher resolution, which can selectively refine areas to track discontinuities in the solution. The open source Clawpack software implements block-structured AMR to refine around propagating waves in the AMRClaw package. For problems where the solution must be computed over a large domain but is only of interest in a small area, this approach often refines waves that will not impact the target area. We seek a method that enables the identification and refinement of only the waves that will influence the target area. Here we show that solving the time-dependent adjoint equation and using a suitable inner product allows for a more precise refinement of the relevant waves. We present the adjoint methodology in general and give details on the implementation of this method in AMRClaw. Examples and a computational performance analysis for linear acoustics equations are presented. The adjoint method is compared to AMR methods already available in AMRClaw, and the advantages and disadvantages are discussed. The approach presented here is implemented in Clawpack, in Version 5.6.1, and code for all examples presented is archived on Github.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"88 1","pages":"1 - 28"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83840199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

A Safe Computational Framework for Integer Programming Applied to Chvátal’s Conjecture 应用于Chvátal猜想的整数规划安全计算框架

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2018-09-05 DOI: 10.1145/3485630

L. Eifler, A. Gleixner, Jonad Pulaj

{"title":"A Safe Computational Framework for Integer Programming Applied to Chvátal’s Conjecture","authors":"L. Eifler, A. Gleixner, Jonad Pulaj","doi":"10.1145/3485630","DOIUrl":"https://doi.org/10.1145/3485630","url":null,"abstract":"We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a rational branch-and-bound certificate produced by an exact integer programming solver, SCIP, in order to circumvent floating-point round-off errors present in most state-of-the-art solvers for mixed-integer programs. The resulting certificates are self-contained and checker software exists that can verify their correctness independently of the integer programming solver used to produce the certificate. This acts as a safeguard against programming errors that may be present in complex solver software. The viability of this approach is tested by applying it to finite cases of Chvátal’s conjecture, a long-standing open question in extremal combinatorics. We take particular care to verify also the correctness of the input for this specific problem, using the Coq formal proof assistant. As a result, we are able to provide the first machine-assisted proof that Chvátal’s conjecture holds for all downsets whose union of sets contains seven elements or less.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"56 1","pages":"1 - 12"},"PeriodicalIF":0.0,"publicationDate":"2018-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86847182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Algorithm 999 算法999

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2018-09-05 DOI: 10.1145/3321514

H. Speleers

引用次数: 22

BLASFEO BLASFEO

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2018-07-31 DOI: 10.1145/3210754

G. Frison, D. Kouzoupis, Tommaso Sartor, Andrea Zanelli, M. Diehl

{"title":"BLASFEO","authors":"G. Frison, D. Kouzoupis, Tommaso Sartor, Andrea Zanelli, M. Diehl","doi":"10.1145/3210754","DOIUrl":"https://doi.org/10.1145/3210754","url":null,"abstract":"Basic Linear Algebra Subroutines for Embedded Optimization (BLASFEO) is a dense linear algebra library providing high-performance implementations of BLAS- and LAPACK-like routines for use in embedded optimization and small-scale high-performance computing, in general. A key difference with respect to existing high-performance implementations of BLAS is that the computational performance is optimized for small- to medium-scale matrices, i.e., for sizes up to a few hundred. BLASFEO comes with three different implementations: a high-performance implementation aimed at providing the highest performance for matrices fitting in cache, a reference implementation providing portability and embeddability and optimized for very small matrices, and a wrapper to standard BLAS and LAPACK providing high performance on large matrices. The three implementations of BLASFEO together provide high-performance dense linear algebra routines for matrices ranging from very small to large. Compared to both open-source and proprietary highly tuned BLAS libraries, for matrices of size up to about 100, the high-performance implementation of BLASFEO is about 20--30% faster than the corresponding level 3 BLAS routines and two to three times faster than the corresponding LAPACK routines.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"51 1","pages":"1 - 30"},"PeriodicalIF":0.0,"publicationDate":"2018-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81224600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 74

ROPTLIB

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2018-07-31 DOI: 10.1145/3218822

Wen Huang, P. Absil, K. Gallivan, Paul Hand

引用次数: 50

Algorithm 989 算法989

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2018-07-26 DOI: 10.1145/3206429

Ekhine Irurozki, Josu Ceberio, Josean Santamaria, Roberto Santana, A. Mendiburu

{"title":"Algorithm 989","authors":"Ekhine Irurozki, Josu Ceberio, Josean Santamaria, Roberto Santana, A. Mendiburu","doi":"10.1145/3206429","DOIUrl":"https://doi.org/10.1145/3206429","url":null,"abstract":"Permutation problems are combinatorial optimization problems whose solutions are naturally codified as permutations. Due to their complexity, motivated principally by the factorial cardinality of the search space of solutions, they have been a recurrent topic for the artificial intelligence and operations research community. Recently, among the vast number of metaheuristic algorithms, new advances on estimation of distribution algorithms (EDAs) have shown outstanding performance when solving some permutation problems. These novel EDAs implement distance-based exponential probability models such as the Mallows and Generalized Mallows models. In this article, we present a Matlab package, perm_mateda, of estimation of distribution algorithms on permutation problems, which has been implemented as an extension to the Mateda-2.0 toolbox of EDAs. Particularly, we provide implementations of the Mallows and Generalized Mallows EDAs under the Kendall’s-τ, Cayley, and Ulam distances. In addition, four classical permutation problems have also been implemented: Traveling Salesman Problem, Permutation Flowshop Scheduling Problem, Linear Ordering Problem, and Quadratic Assignment Problem.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"1 1","pages":"1 - 13"},"PeriodicalIF":0.0,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75563241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

Secure and Fast Encryption (SAFE) with Classical Random Number Generators 安全与快速加密(SAFE)与经典随机数生成器

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2018-07-14 DOI: 10.1145/3212673

L. Deng, J. H. Shiau, Henry Horng-Shing Lu, D. Bowman

{"title":"Secure and Fast Encryption (SAFE) with Classical Random Number Generators","authors":"L. Deng, J. H. Shiau, Henry Horng-Shing Lu, D. Bowman","doi":"10.1145/3212673","DOIUrl":"https://doi.org/10.1145/3212673","url":null,"abstract":"Pseudo-random number generators (PRNGs) play an important role in both areas of computer simulation and computer security. Currently, there appears to be a huge divide between the types of PRNGs used in these two areas. For PRNGs in computer security applications, the security concern is extremely important. For PRNGs in computer simulation applications, the properties of high-dimensional equi-distribution, efficiency, long period-length, and portability are important. In recent years, there have been many PRNGs proposed in the area of computer simulation satisfying these nice properties. However, most of them are linear generators, thus sharing the same weakness in predictability. The major aim of this article is to propose a general class of secure generators, called SAFE (secure and fast encryption) generators, by properly “mixing” two baseline generators with the aforementioned properties to obtain a secure generator that would inherit these nice properties. Specifically, we propose applying a general mutual-shuffling method to certain linear generators, such as the currently most popular MT19937 generator and large-order multiple recursive generators, as well as outputting certain nonlinear transformations of the generated variates to construct secure PRNGS.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"54 1","pages":"1 - 17"},"PeriodicalIF":0.0,"publicationDate":"2018-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74044702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Architecture and Performance of Devito, a System for Automated Stencil Computation 自动模板计算系统Devito的结构与性能

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2018-07-09 DOI: 10.1145/3374916

F. Luporini, Michael Lange, M. Louboutin, Navjot Kukreja, J. Hückelheim, Charles R. Yount, Philipp A. Witte, P. Kelly, G. Gorman, F. Herrmann

{"title":"Architecture and Performance of Devito, a System for Automated Stencil Computation","authors":"F. Luporini, Michael Lange, M. Louboutin, Navjot Kukreja, J. Hückelheim, Charles R. Yount, Philipp A. Witte, P. Kelly, G. Gorman, F. Herrmann","doi":"10.1145/3374916","DOIUrl":"https://doi.org/10.1145/3374916","url":null,"abstract":"Stencil computations are a key part of many high-performance computing applications, such as image processing, convolutional neural networks, and finite-difference solvers for partial differential equations. Devito is a framework capable of generating highly optimized code given symbolic equations expressed in Python, specialized in, but not limited to, affine (stencil) codes. The lowering process—from mathematical equations down to C++ code—is performed by the Devito compiler through a series of intermediate representations. Several performance optimizations are introduced, including advanced common sub-expressions elimination, tiling, and parallelization. Some of these are obtained through well-established stencil optimizers, integrated in the backend of the Devito compiler. The architecture of the Devito compiler, as well as the performance optimizations that are applied when generating code, are presented. The effectiveness of such performance optimizations is demonstrated using operators drawn from seismic imaging applications.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"98 1","pages":"1 - 28"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76107823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 90

The Implementation of the Colored Abstract Simplicial Complex and Its Application to Mesh Generation 彩色抽象简单复合体的实现及其在网格生成中的应用

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2018-07-04 DOI: 10.1145/3321515

Christopher T. Lee, John B. Moody, Rommie E. Amaro, J. McCammon, M. Holst

引用次数: 7

Solution of Dense Linear Systems via Roundoff-Error-Free Factorization Algorithms 用无舍入误差分解算法求解密集线性系统

ACM Transactions on Mathematical Software (TOMS) Pub Date : 2018-06-16 DOI: 10.1145/3199571

Adolfo R. Escobedo, Erick Moreno-Centeno, Christopher Lourenco

{"title":"Solution of Dense Linear Systems via Roundoff-Error-Free Factorization Algorithms","authors":"Adolfo R. Escobedo, Erick Moreno-Centeno, Christopher Lourenco","doi":"10.1145/3199571","DOIUrl":"https://doi.org/10.1145/3199571","url":null,"abstract":"Exact solving of systems of linear equations (SLEs) is a fundamental subroutine within number theory, formal verification of mathematical proofs, and exact-precision mathematical programming. Moreover, efficient exact SLE solution methods could be valuable for a growing body of science and engineering applications where current fixed-precision standards have been deemed inadequate. This article contains key derivations relating, and computational tests comparing, two exact direct solution frameworks: roundoff-error-free (REF) LU factorization and rational arithmetic LU factorization. Specifically, both approaches solve the linear system Ax=b by factoring the matrix A into the product of a lower triangular (L) and upper triangular (U) matrix, A=LU. Most significantly, the featured findings reveal that the integer-preserving REF factorization framework solves dense SLEs one order of magnitude faster than the exact rational arithmetic approach while requiring half the memory. Since rational LU is utilized for basic solution validation in exact linear and mixed-integer programming, these results offer preliminary evidence of the potential of the REF factorization framework to be utilized within this specific context. Additionally, this article develops and analyzes an efficient streamlined version of Edmonds’s Q-matrix approach that can be implemented as another basic solution validation approach. Further experiments demonstrate that the REF factorization framework also outperforms this alternative integer-preserving approach in terms of memory requirements and computational effort. General purpose codes to solve dense SLEs exactly via any of the aforementioned methods have been made available to the research and academic communities.","PeriodicalId":7036,"journal":{"name":"ACM Transactions on Mathematical Software (TOMS)","volume":"42 1","pages":"1 - 24"},"PeriodicalIF":0.0,"publicationDate":"2018-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90832876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5