Abhinav Singh, Landfried Kraatz, Pietro Incardona, Ivo F. Sbalzarini
We present a distributed algebra system for efficient and compact implementation of numerical time integration schemes on parallel computers and graphics processing units (GPU). The software implementation combines the time integration library Odeint from Boost with the OpenFPM framework for scalable scientific computing. Implementing multi-stage, multi-step, or adaptive time integration methods in distributed-memory parallel codes or on GPUs is challenging. The present algebra system addresses this by making the time integration methods from Odeint available in a concise template-expression language for numerical simulations distributed and parallelized using OpenFPM. This allows using state-of-the-art time integration schemes, or switching between schemes, by changing one line of code, while maintaining parallel scalability. This enables scalable time integration with compact code and facilitates rapid rewriting and deployment of simulation algorithms. We benchmark the present software for exponential and sigmoidal dynamics and present an application example to the 3D Gray-Scott reaction-diffusion problem on both CPUs and GPUs in only 60 lines of code.
{"title":"A Distributed Algebra System for Time Integration on Parallel Computers","authors":"Abhinav Singh, Landfried Kraatz, Pietro Incardona, Ivo F. Sbalzarini","doi":"arxiv-2309.05331","DOIUrl":"https://doi.org/arxiv-2309.05331","url":null,"abstract":"We present a distributed algebra system for efficient and compact\u0000implementation of numerical time integration schemes on parallel computers and\u0000graphics processing units (GPU). The software implementation combines the time\u0000integration library Odeint from Boost with the OpenFPM framework for scalable\u0000scientific computing. Implementing multi-stage, multi-step, or adaptive time\u0000integration methods in distributed-memory parallel codes or on GPUs is\u0000challenging. The present algebra system addresses this by making the time\u0000integration methods from Odeint available in a concise template-expression\u0000language for numerical simulations distributed and parallelized using OpenFPM.\u0000This allows using state-of-the-art time integration schemes, or switching\u0000between schemes, by changing one line of code, while maintaining parallel\u0000scalability. This enables scalable time integration with compact code and\u0000facilitates rapid rewriting and deployment of simulation algorithms. We\u0000benchmark the present software for exponential and sigmoidal dynamics and\u0000present an application example to the 3D Gray-Scott reaction-diffusion problem\u0000on both CPUs and GPUs in only 60 lines of code.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"17 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521153","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}
Dealing with time series with missing values, including those afflicted by low quality or over-saturation, presents a significant signal processing challenge. The task of recovering these missing values, known as imputation, has led to the development of several algorithms. However, we have observed that the efficacy of these algorithms tends to diminish when the time series exhibit non-stationary oscillatory behavior. In this paper, we introduce a novel algorithm, coined Harmonic Level Interpolation (HaLI), which enhances the performance of existing imputation algorithms for oscillatory time series. After running any chosen imputation algorithm, HaLI leverages the harmonic decomposition based on the adaptive nonharmonic model of the initial imputation to improve the imputation accuracy for oscillatory time series. Experimental assessments conducted on synthetic and real signals consistently highlight that HaLI enhances the performance of existing imputation algorithms. The algorithm is made publicly available as a readily employable Matlab code for other researchers to use.
{"title":"Enhancing Missing Data Imputation of Non-stationary Signals with Harmonic Decomposition","authors":"Joaquin Ruiz, Hau-tieng Wu, Marcelo A. Colominas","doi":"arxiv-2309.04630","DOIUrl":"https://doi.org/arxiv-2309.04630","url":null,"abstract":"Dealing with time series with missing values, including those afflicted by\u0000low quality or over-saturation, presents a significant signal processing\u0000challenge. The task of recovering these missing values, known as imputation,\u0000has led to the development of several algorithms. However, we have observed\u0000that the efficacy of these algorithms tends to diminish when the time series\u0000exhibit non-stationary oscillatory behavior. In this paper, we introduce a\u0000novel algorithm, coined Harmonic Level Interpolation (HaLI), which enhances the\u0000performance of existing imputation algorithms for oscillatory time series.\u0000After running any chosen imputation algorithm, HaLI leverages the harmonic\u0000decomposition based on the adaptive nonharmonic model of the initial imputation\u0000to improve the imputation accuracy for oscillatory time series. Experimental\u0000assessments conducted on synthetic and real signals consistently highlight that\u0000HaLI enhances the performance of existing imputation algorithms. The algorithm\u0000is made publicly available as a readily employable Matlab code for other\u0000researchers to use.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"12 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521247","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}
Edward Caunt, Rhodri Nelson, Fabio Luporini, Gerard Gorman
Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Methods currently detailed in the literature are generally limited in scope application-wise or non-trivial to apply to real-world geometries. With this in mind, a general immersed boundary treatment capable of imposing a range of boundary conditions in a relatively equation-agnostic manner has been developed, alongside a framework implementing this approach, intending to complement emerging code-generation paradigms. The approach is distinguished by the use of N-dimensional Taylor-series extrapolants constrained by boundary conditions imposed at some suitably-distributed set of surface points. The extrapolation process is encapsulated in modified derivative stencils applied in the vicinity of the boundary, utilizing hyperspherical support regions. This method ensures boundary representation is consistent with the FD discretization: both must be considered in tandem. Furthermore, high-dimensional and vector boundary conditions can be applied without approximation prior to discretization. A consistent methodology can thus be applied across free and rigid surfaces with the first and second-order acoustic wave equation formulations. Application to both equations is demonstrated, and numerical examples based on analytic and real-world topography implementing free and rigid surfaces in 2D and 3D are presented.
{"title":"A Novel Immersed Boundary Approach for Irregular Topography with Acoustic Wave Equations","authors":"Edward Caunt, Rhodri Nelson, Fabio Luporini, Gerard Gorman","doi":"arxiv-2309.03600","DOIUrl":"https://doi.org/arxiv-2309.03600","url":null,"abstract":"Irregular terrain has a pronounced effect on the propagation of seismic and\u0000acoustic wavefields but is not straightforwardly reconciled with structured\u0000finite-difference (FD) methods used to model such phenomena. Methods currently\u0000detailed in the literature are generally limited in scope application-wise or\u0000non-trivial to apply to real-world geometries. With this in mind, a general\u0000immersed boundary treatment capable of imposing a range of boundary conditions\u0000in a relatively equation-agnostic manner has been developed, alongside a\u0000framework implementing this approach, intending to complement emerging\u0000code-generation paradigms. The approach is distinguished by the use of\u0000N-dimensional Taylor-series extrapolants constrained by boundary conditions\u0000imposed at some suitably-distributed set of surface points. The extrapolation\u0000process is encapsulated in modified derivative stencils applied in the vicinity\u0000of the boundary, utilizing hyperspherical support regions. This method ensures\u0000boundary representation is consistent with the FD discretization: both must be\u0000considered in tandem. Furthermore, high-dimensional and vector boundary\u0000conditions can be applied without approximation prior to discretization. A\u0000consistent methodology can thus be applied across free and rigid surfaces with\u0000the first and second-order acoustic wave equation formulations. Application to\u0000both equations is demonstrated, and numerical examples based on analytic and\u0000real-world topography implementing free and rigid surfaces in 2D and 3D are\u0000presented.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521158","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}
Antony Della Vecchia, Michael Joswig, Benjamin Lorenz
We describe a generic JSON based file format which is suitable for computations in computer algebra. This is implemented in the computer algebra system OSCAR, but we also indicate how it can be used in a different context.
{"title":"A FAIR File Format for Mathematical Software","authors":"Antony Della Vecchia, Michael Joswig, Benjamin Lorenz","doi":"arxiv-2309.00465","DOIUrl":"https://doi.org/arxiv-2309.00465","url":null,"abstract":"We describe a generic JSON based file format which is suitable for\u0000computations in computer algebra. This is implemented in the computer algebra\u0000system OSCAR, but we also indicate how it can be used in a different context.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521251","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}
João V. C. Mazzochin, Gustavo Tiecker, Erick O. Rodrigues
Counting objects in images is a pattern recognition problem that focuses on identifying an element to determine its incidence and is approached in the literature as Visual Object Counting (VOC). In this work, we propose a methodology to count wood logs. First, wood logs are segmented from the image background. This first segmentation step is obtained using the Pix2Pix framework that implements Conditional Generative Adversarial Networks (CGANs). Second, the clusters are counted using Connected Components. The average accuracy of the segmentation exceeds 89% while the average amount of wood logs identified based on total accounted is over 97%.
{"title":"Segmentação e contagem de troncos de madeira utilizando deep learning e processamento de imagens","authors":"João V. C. Mazzochin, Gustavo Tiecker, Erick O. Rodrigues","doi":"arxiv-2309.00123","DOIUrl":"https://doi.org/arxiv-2309.00123","url":null,"abstract":"Counting objects in images is a pattern recognition problem that focuses on\u0000identifying an element to determine its incidence and is approached in the\u0000literature as Visual Object Counting (VOC). In this work, we propose a\u0000methodology to count wood logs. First, wood logs are segmented from the image\u0000background. This first segmentation step is obtained using the Pix2Pix\u0000framework that implements Conditional Generative Adversarial Networks (CGANs).\u0000Second, the clusters are counted using Connected Components. The average\u0000accuracy of the segmentation exceeds 89% while the average amount of wood logs\u0000identified based on total accounted is over 97%.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"19 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521073","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}
Partial differential equations (PDEs) are used to describe a variety of physical phenomena. Often these equations do not have analytical solutions and numerical approximations are used instead. One of the common methods to solve PDEs is the finite element method. Computing derivative information of the solution with respect to the input parameters is important in many tasks in scientific computing. We extend JAX automatic differentiation library with an interface to Firedrake finite element library. High-level symbolic representation of PDEs allows bypassing differentiating through low-level possibly many iterations of the underlying nonlinear solvers. Differentiating through Firedrake solvers is done using tangent-linear and adjoint equations. This enables the efficient composition of finite element solvers with arbitrary differentiable programs. The code is available at github.com/IvanYashchuk/jax-firedrake.
{"title":"Bringing PDEs to JAX with forward and reverse modes automatic differentiation","authors":"Ivan Yashchuk","doi":"arxiv-2309.07137","DOIUrl":"https://doi.org/arxiv-2309.07137","url":null,"abstract":"Partial differential equations (PDEs) are used to describe a variety of\u0000physical phenomena. Often these equations do not have analytical solutions and\u0000numerical approximations are used instead. One of the common methods to solve\u0000PDEs is the finite element method. Computing derivative information of the\u0000solution with respect to the input parameters is important in many tasks in\u0000scientific computing. We extend JAX automatic differentiation library with an\u0000interface to Firedrake finite element library. High-level symbolic\u0000representation of PDEs allows bypassing differentiating through low-level\u0000possibly many iterations of the underlying nonlinear solvers. Differentiating\u0000through Firedrake solvers is done using tangent-linear and adjoint equations.\u0000This enables the efficient composition of finite element solvers with arbitrary\u0000differentiable programs. The code is available at\u0000github.com/IvanYashchuk/jax-firedrake.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138526392","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}
Pierre-David Letourneau, Dalton Jones, Matthew Morse, M. Harper Langston
We present a novel efficient theoretical and numerical framework for solving global non-convex polynomial optimization problems. We analytically demonstrate that such problems can be efficiently reformulated using a non-linear objective over a convex set; further, these reformulated problems possess no spurious local minima (i.e., every local minimum is a global minimum). We introduce an algorithm for solving these resulting problems using the augmented Lagrangian and the method of Burer and Monteiro. We show through numerical experiments that polynomial scaling in dimension and degree is achievable for computing the optimal value and location of previously intractable global polynomial optimization problems in high dimension.
{"title":"An Efficient Framework for Global Non-Convex Polynomial Optimization over the Hypercube","authors":"Pierre-David Letourneau, Dalton Jones, Matthew Morse, M. Harper Langston","doi":"arxiv-2308.16731","DOIUrl":"https://doi.org/arxiv-2308.16731","url":null,"abstract":"We present a novel efficient theoretical and numerical framework for solving\u0000global non-convex polynomial optimization problems. We analytically demonstrate\u0000that such problems can be efficiently reformulated using a non-linear objective\u0000over a convex set; further, these reformulated problems possess no spurious\u0000local minima (i.e., every local minimum is a global minimum). We introduce an\u0000algorithm for solving these resulting problems using the augmented Lagrangian\u0000and the method of Burer and Monteiro. We show through numerical experiments\u0000that polynomial scaling in dimension and degree is achievable for computing the\u0000optimal value and location of previously intractable global polynomial\u0000optimization problems in high dimension.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"16 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521156","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}
Mai Peng, Zeneng She, Delaram Yazdani, Danial Yazdani, Wenjian Luo, Changhe Li, Juergen Branke, Trung Thanh Nguyen, Amir H. Gandomi, Yaochu Jin, Xin Yao
Many real-world optimization problems possess dynamic characteristics. Evolutionary dynamic optimization algorithms (EDOAs) aim to tackle the challenges associated with dynamic optimization problems. Looking at the existing works, the results reported for a given EDOA can sometimes be considerably different. This issue occurs because the source codes of many EDOAs, which are usually very complex algorithms, have not been made publicly available. Indeed, the complexity of components and mechanisms used in many EDOAs makes their re-implementation error-prone. In this paper, to assist researchers in performing experiments and comparing their algorithms against several EDOAs, we develop an open-source MATLAB platform for EDOAs, called Evolutionary Dynamic Optimization LABoratory (EDOLAB). This platform also contains an education module that can be used for educational purposes. In the education module, the user can observe a) a 2-dimensional problem space and how its morphology changes after each environmental change, b) the behaviors of individuals over time, and c) how the EDOA reacts to environmental changes and tries to track the moving optimum. In addition to being useful for research and education purposes, EDOLAB can also be used by practitioners to solve their real-world problems. The current version of EDOLAB includes 25 EDOAs and three fully-parametric benchmark generators. The MATLAB source code for EDOLAB is publicly available and can be accessed from [https://github.com/EDOLAB-platform/EDOLAB-MATLAB].
{"title":"Evolutionary Dynamic Optimization Laboratory: A MATLAB Optimization Platform for Education and Experimentation in Dynamic Environments","authors":"Mai Peng, Zeneng She, Delaram Yazdani, Danial Yazdani, Wenjian Luo, Changhe Li, Juergen Branke, Trung Thanh Nguyen, Amir H. Gandomi, Yaochu Jin, Xin Yao","doi":"arxiv-2308.12644","DOIUrl":"https://doi.org/arxiv-2308.12644","url":null,"abstract":"Many real-world optimization problems possess dynamic characteristics.\u0000Evolutionary dynamic optimization algorithms (EDOAs) aim to tackle the\u0000challenges associated with dynamic optimization problems. Looking at the\u0000existing works, the results reported for a given EDOA can sometimes be\u0000considerably different. This issue occurs because the source codes of many\u0000EDOAs, which are usually very complex algorithms, have not been made publicly\u0000available. Indeed, the complexity of components and mechanisms used in many\u0000EDOAs makes their re-implementation error-prone. In this paper, to assist\u0000researchers in performing experiments and comparing their algorithms against\u0000several EDOAs, we develop an open-source MATLAB platform for EDOAs, called\u0000Evolutionary Dynamic Optimization LABoratory (EDOLAB). This platform also\u0000contains an education module that can be used for educational purposes. In the\u0000education module, the user can observe a) a 2-dimensional problem space and how\u0000its morphology changes after each environmental change, b) the behaviors of\u0000individuals over time, and c) how the EDOA reacts to environmental changes and\u0000tries to track the moving optimum. In addition to being useful for research and\u0000education purposes, EDOLAB can also be used by practitioners to solve their\u0000real-world problems. The current version of EDOLAB includes 25 EDOAs and three\u0000fully-parametric benchmark generators. The MATLAB source code for EDOLAB is\u0000publicly available and can be accessed from\u0000[https://github.com/EDOLAB-platform/EDOLAB-MATLAB].","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"27 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138526417","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}
We present a technical enhancement within the p4est software for parallel adaptive mesh refinement. In p4est primitives are stored as octants in three and quadrants in two dimensions. While, classically, they are encoded by the native approach using its spatial and refinement level, any other mathematically equivalent encoding might be used instead. Recognizing this, we add two alternative representations to the classical, explicit version, based on a long monotonic index and 128-bit AVX quad integers, respectively. The first one requires changes in logic for low-level quadrant manipulating algorithms, while the other exploits data level parallelism and requires algorithms to be adapted to SIMD instructions. The resultant algorithms and data structures lead to higher performance and lesser memory usage in comparison with the standard baseline. We benchmark selected algorithms on a cluster with two Intel(R) Xeon(R) Gold 6130 Skylake family CPUs per node, which provides support for AVX2 extensions, 192 GB RAM per node, and up to 512 computational cores in total.
{"title":"Alternative quadrant representations with Morton index and AVX2 vectorization for AMR algorithms within the p4est software library","authors":"Mikhail KirilinINS, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany, Carsten BursteddeINS, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany","doi":"arxiv-2308.13615","DOIUrl":"https://doi.org/arxiv-2308.13615","url":null,"abstract":"We present a technical enhancement within the p4est software for parallel\u0000adaptive mesh refinement. In p4est primitives are stored as octants in three\u0000and quadrants in two dimensions. While, classically, they are encoded by the\u0000native approach using its spatial and refinement level, any other\u0000mathematically equivalent encoding might be used instead. Recognizing this, we add two alternative representations to the classical,\u0000explicit version, based on a long monotonic index and 128-bit AVX quad\u0000integers, respectively. The first one requires changes in logic for low-level\u0000quadrant manipulating algorithms, while the other exploits data level\u0000parallelism and requires algorithms to be adapted to SIMD instructions. The\u0000resultant algorithms and data structures lead to higher performance and lesser\u0000memory usage in comparison with the standard baseline. We benchmark selected algorithms on a cluster with two Intel(R) Xeon(R) Gold\u00006130 Skylake family CPUs per node, which provides support for AVX2 extensions,\u0000192 GB RAM per node, and up to 512 computational cores in total.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138526429","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}
With lowrank approximation the storage requirements for dense data are reduced down to linear complexity and with the addition of hierarchy this also works for data without global lowrank properties. However, the lowrank factors itself are often still stored using double precision numbers. Newer approaches exploit the different IEEE754 floating point formats available nowadays in a mixed precision approach. However, these formats show a significant gap in storage (and accuracy), e.g. between half, single and double precision. We therefore look beyond these standard formats and use adaptive compression for storing the lowrank and dense data and investigate how that affects the arithmetic of such matrices.
{"title":"Hierarchical Lowrank Arithmetic with Binary Compression","authors":"Ronald Kriemann","doi":"arxiv-2308.10960","DOIUrl":"https://doi.org/arxiv-2308.10960","url":null,"abstract":"With lowrank approximation the storage requirements for dense data are\u0000reduced down to linear complexity and with the addition of hierarchy this also\u0000works for data without global lowrank properties. However, the lowrank factors\u0000itself are often still stored using double precision numbers. Newer approaches\u0000exploit the different IEEE754 floating point formats available nowadays in a\u0000mixed precision approach. However, these formats show a significant gap in\u0000storage (and accuracy), e.g. between half, single and double precision. We\u0000therefore look beyond these standard formats and use adaptive compression for\u0000storing the lowrank and dense data and investigate how that affects the\u0000arithmetic of such matrices.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138526390","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}
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