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PyOED: An Extensible Suite for Data Assimilation and Model-Constrained Optimal Design of Experiments ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-20 Abhijit Chowdhary, Shady E. Ahmed, Ahmed Attia
This paper describes PyOED, a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-constrained OED. The package targets scientists and researchers interested in understanding the details of OED formulations and approaches. It is also meant
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A LAPACK Implementation of the Dynamic Mode Decomposition ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-16 Zlatko Drmač
The Dynamic Mode Decomposition (DMD) is a method for computational analysis of nonlinear dynamical systems in data driven scenarios. Based on high fidelity numerical simulations or experimental data, the DMD can be used to reveal the latent structures in the dynamics or as a forecasting or a model order reduction tool. The theoretical underpinning of the DMD is the Koopman operator on a Hilbert space
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Hermitian Dynamic Mode Decomposition - Numerical Analysis and Software Solution ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-16 Zlatko Drmač
The Dynamic Mode Decomposition (DMD) is a versatile and increasingly popular method for data driven analysis of dynamical systems that arise in a variety of applications in, e.g., computational fluid dynamics, robotics or machine learning. In the framework of numerical linear algebra, it is a data driven Rayleigh-Ritz procedure applied to a DMD matrix that is derived from the supplied data. In some
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Data-flow Reversal and Garbage Collection ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-16 Laurent Hascoët
Data-flow reversal is at the heart of source-transformation reverse algorithmic differentiation (reverse ST-AD), arguably the most efficient way to obtain gradients of numerical models. However, when the model implementation language uses garbage collection (GC), for instance, in Java or Python, the notion of address that is needed for data-flow reversal disappears. Moreover, GC is asynchronous and
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Efficient and Validated Numerical Evaluation of Abelian Integrals ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-16 Florent Bréhard, Nicolas Brisebarre, Mioara Joldes, Warwick Tucker
Abelian integrals play a key role in the infinitesimal version of Hilbert’s 16th problem. Being able to evaluate such integrals—with guaranteed error bounds—is a fundamental step in computer-aided proofs aimed at this problem. Using interpolation by trigonometric polynomials and quasi-Newton-Kantorovitch validation, we develop a validated numerics method for computing Abelian integrals in a quasi-linear
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An Interface-Preserving Moving Mesh in Multiple Space Dimensions ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-16 Maria Alkämper, Jim Magiera, Christian Rohde
An interface-preserving moving mesh algorithm in two or higher dimensions is presented. It resolves a moving (d-1)-dimensional manifold directly within the d-dimensional mesh, which means that the interface is represented by a subset of moving mesh cell-surfaces. The underlying mesh is a conforming simplicial partition that fulfills the Delaunay property. The local remeshing algorithms allow for strong
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Algorithm 1039: Automatic Generators for a Family of Matrix Multiplication Routines with Apache TVM ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-16 Guillermo Alaejos, Adrián Castelló, Pedro Alonso-Jordá, Francisco D. Igual, Héctor Martínez, Enrique S. Quintana-Ortí
We explore the utilization of the Apache TVM open source framework to automatically generate a family of algorithms that follow the approach taken by popular linear algebra libraries, such as GotoBLAS2, BLIS, and OpenBLAS, to obtain high-performance blocked formulations of the general matrix multiplication (gemm). In addition, we fully automatize the generation process by also leveraging the Apache
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Algorithm 1040: The Sparse Grids Matlab Kit - a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-16 Chiara Piazzola, Lorenzo Tamellini
The Sparse Grids Matlab Kit provides a Matlab implementation of sparse grids, and can be used for approximating high-dimensional functions and, in particular, for surrogate-model-based uncertainty quantification. It is lightweight, high-level and easy to use, good for quick prototyping and teaching; however, it is equipped with some features that allow its use also in realistic applications. The goal
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Algorithm 1041: HiPPIS—A High-order Positivity-preserving Mapping Software for Structured Meshes ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-16 Timbwoga A. J. Ouermi, Robert M. Kirby, Martin Berzins
Polynomial interpolation is an important component of many computational problems. In several of these computational problems, failure to preserve positivity when using polynomials to approximate or map data values between meshes can lead to negative unphysical quantities. Currently, most polynomial-based methods for enforcing positivity are based on splines and polynomial rescaling. The spline-based
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Avoiding breakdown in incomplete factorizations in low precision arithmetic ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-12 Jennifer Scott, Miroslav Tůma
The emergence of low precision floating-point arithmetic in computer hardware has led to a resurgence of interest in the use of mixed precision numerical linear algebra. For linear systems of equations, there has been renewed enthusiasm for mixed precision variants of iterative refinement. We consider the iterative solution of large sparse systems using incomplete factorization preconditioners. The
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Algorithm xxx: PyGenStability, a multiscale community detection with generalized Markov Stability ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-11 Alexis Arnaudon, Dominik J. Schindler, Robert L. Peach, Adam Gosztolai, Maxwell Hodges, Michael T. Schaub, Mauricio Barahona
We present PyGenStability, a general-use Python software package that provides a suite of analysis and visualisation tools for unsupervised multiscale community detection in graphs. PyGenStability finds optimized partitions of a graph at different levels of resolution by maximizing the generalized Markov Stability quality function with the Louvain or Leiden algorithms. The package includes automatic
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Optimal Re-Materialization Strategies for Heterogeneous Chains: How to Train Deep Neural Networks with Limited Memory ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-05 Olivier Beaumont, Lionel Eyraud-Dubois, Julien Herrmann, Alexis Joly, Alena Shilova
Training in Feed Forward Deep Neural Networks is a memory-intensive operation which is usually performed on GPUs with limited memory capacities. This may force data scientists to limit the depth of the models or the resolution of the input data if data does not fit in the GPU memory. The re-materialization technique, whose idea comes from the checkpointing strategies developed in the Automatic Differentiation
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Algorithm XXX: Sparse Precision Matrix Estimation With SQUIC ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2024-03-05 Aryan Eftekhari, Lisa Gaedke-Merzhäuser, Dimosthenis Pasadakis, Matthias Bollhöfer, Simon Scheidegger, Olaf Schenk
We present SQUIC, a fast and scalable package for sparse precision matrix estimation. The algorithm employs a second-order method to solve the \(\ell_{1}\)-regularized maximum likelihood problem, utilizing highly optimized linear algebra subroutines. In comparative tests using synthetic datasets, we demonstrate that SQUIC not only scales to datasets of up to a million random variables but also consistently
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HAZniCS – Software Components for Multiphysics Problems ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-12-15 Ana Budiša, Xiaozhe Hu, Miroslav Kuchta, Kent-André Mardal, Ludmil T. Zikatanov
We introduce the software toolbox HAZniCS for solving interface-coupled multiphysics problems. HAZniCS is a suite of modules that combines the well-known FEniCS framework for finite element discretization with solver and graph library HAZmath. The focus of this article is on the design and implementation of robust and efficient solver algorithms which tackle issues related to the complex interfacial
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IEEE-754 Precision-p base-β Arithmetic Implemented in Binary ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-12-15 Siegfried M. Rump
We show how an IEEE-754 conformant precision-p base-β arithmetic can be implemented based on some binary floating-point and/or integer arithmetic. This includes the four basic operations and square root subject to the five IEEE-754 rounding modes, namely the nearest roundings with roundTiesToEven and roundTiesToAway, the directed roundings downwards and upwards, as well as rounding towards zero. Exceptional
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Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-12-15 Seth D. Axen, Mateusz Baran, Ronny Bergmann, Krzysztof Rzecki
We present the Julia package Manifolds.jl, providing a fast and easy-to-use library of Riemannian manifolds and Lie groups. This package enables working with data defined on a Riemannian manifold, such as the circle, the sphere, symmetric positive definite matrices, or one of the models for hyperbolic spaces. We introduce a common interface, available in ManifoldsBase.jl, with which new manifolds,
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Parametric Information Geometry with the Package Geomstats ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-12-15 Alice Le Brigant, Jules Deschamps, Antoine Collas, Nina Miolane
We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher–Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta, Dirichlet distributions, and more. The module further gives the Fisher–Rao Riemannian geometry of any parametric family of distributions of interest, given a parameterized
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Computation of Turing Bifurcation Normal Form for n-Component Reaction-Diffusion Systems ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-12-15 Edgardo Villar-Sepúlveda, Alan Champneys
General expressions are derived for the amplitude equation valid at a Turing bifurcation of a system of reaction-diffusion equations in one spatial dimension, with an arbitrary number of components. The normal form is computed up to fifth order, which enables the detection and analysis of codimension-two points where the criticality of the bifurcation changes. The expressions are implemented within
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Efficient Implementation of Modern Entropy Stable and Kinetic Energy Preserving Discontinuous Galerkin Methods for Conservation Laws ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-12-15 Hendrik Ranocha, Michael Schlottke-Lakemper, Jesse Chan, Andrés M. Rueda-Ramírez, Andrew R. Winters, Florian Hindenlang, Gregor J. Gassner
Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entropy stability. While these techniques increase the robustness of DG methods significantly, they are also computationally more demanding than standard weak form nodal DG methods. We present several implementation techniques
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KiT-RT: An Extendable Framework for Radiative Transfer and Therapy ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-12-15 Jonas Kusch, Steffen Schotthöfer, Pia Stammer, Jannick Wolters, Tianbai Xiao
In this article, we present Kinetic Transport Solver for Radiation Therapy (KiT-RT), an open source C++-based framework for solving kinetic equations in therapy applications available at https://github.com/CSMMLab/KiT-RT. This software framework aims to provide a collection of classical deterministic solvers for unstructured meshes that allow for easy extendability. Therefore, KiT-RT is a convenient
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New Subspace Method for Unconstrained Derivative-Free Optimization ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-12-15 Morteza Kimiaei, Arnold Neumaier, Parvaneh Faramarzi
This article defines an efficient subspace method, called SSDFO, for unconstrained derivative-free optimization problems where the gradients of the objective function are Lipschitz continuous but only exact function values are available. SSDFO employs line searches along directions constructed on the basis of quadratic models. These approximate the objective function in a subspace spanned by some previous
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Algorithm 1038: KCC: A MATLAB Package for k-Means-based Consensus Clustering ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-12-15 Hao Lin, Hongfu Liu, Junjie Wu, Hong Li, Stephan Günnemann
Consensus clustering is gaining increasing attention for its high quality and robustness. In particular, k-means-based Consensus Clustering (KCC) converts the usual computationally expensive problem to a classic k-means clustering with generalized utility functions, bringing potentials for large-scale data clustering on different types of data. Despite KCC’s applicability and generalizability, implementing
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Approximating Inverse Cumulative Distribution Functions to Produce Approximate Random Variables ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-09-19 Michael Giles, Oliver Sheridan-Methven
For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced using approximations to a distribution’s inverse cumulative distribution function. These approximations are designed to be computationally inexpensive and much cheaper than library functions, which are exact to within machine precision and, thus, highly suitable for use
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Cache Optimization and Performance Modeling of Batched, Small, and Rectangular Matrix Multiplication on Intel, AMD, and Fujitsu Processors ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-09-19 Sameer Deshmukh, Rio Yokota, George Bosilca
Factorization and multiplication of dense matrices and tensors are critical, yet extremely expensive pieces of the scientific toolbox. Careful use of low rank approximation can drastically reduce the computation and memory requirements of these operations. In addition to a lower arithmetic complexity, such methods can, by their structure, be designed to efficiently exploit modern hardware architectures
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Sparse Approximate Multifrontal Factorization with Composite Compression Methods ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-09-19 Lisa Claus, Pieter Ghysels, Yang Liu, Thái Anh Nhan, Ramakrishnan Thirumalaisamy, Amneet Pal Singh Bhalla, Sherry Li
This article presents a fast and approximate multifrontal solver for large sparse linear systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver leveraging the butterfly algorithm and its hierarchical matrix extension, HODBF (hierarchical off-diagonal butterfly) compression to compress large frontal matrices. The resulting multifrontal solver can attain quasi-linear
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Algorithms for Parallel Generic hp-Adaptive Finite Element Software ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-09-19 Marc Fehling, Wolfgang Bangerth
The hp-adaptive finite element method—where one independently chooses the mesh size (h) and polynomial degree (p) to be used on each cell—has long been known to have better theoretical convergence properties than either h- or p-adaptive methods alone. However, it is not widely used, owing at least in part to the difficulty of the underlying algorithms and the lack of widely usable implementations.
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Array-Aware Matching: Taming the Complexity of Large-Scale Simulation Models ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-09-19 Massimo Fioravanti, Daniele Cattaneo, Federico Terraneo, Silvano Seva, Stefano Cherubin, Giovanni Agosta, Francesco Casella, Alberto Leva
Equation-based modelling is a powerful approach to tame the complexity of large-scale simulation problems. Equation-based tools automatically translate models into imperative languages. When confronted with nowadays’ problems, however, well assessed model translation techniques exhibit scalability issues that are particularly severe when models contain very large arrays. In fact, such models can be
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Algorithm 1037: SuiteSparse:GraphBLAS: Parallel Graph Algorithms in the Language of Sparse Linear Algebra ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-09-19 Timothy A. Davis
SuiteSparse:GraphBLAS is a full parallel implementation of the GraphBLAS standard, which defines a set of sparse matrix operations on an extended algebra of semirings using an almost unlimited variety of operators and types. When applied to sparse adjacency matrices, these algebraic operations are equivalent to computations on graphs. A description of the parallel implementation of SuiteSparse:GraphBLAS
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Improvements to SLEPc in Releases 3.14–3.18 ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-09-19 Jose E. Roman, Fernando Alvarruiz, Carmen Campos, Lisandro Dalcin, Pierre Jolivet, Alejandro Lamas Daviña
This short article describes the main new features added to SLEPc, the Scalable Library for Eigenvalue Problem Computations, in the past two and a half years, corresponding to five release versions. The main novelty is the extension of the SVD module with new problem types, such as the generalized SVD or the hyperbolic SVD. Additionally, many improvements have been incorporated in different parts of
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IFISS3D: A Computational Laboratory for Investigating Finite Element Approximation in Three Dimensions ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-09-19 Georgios Papanikos, Catherine E. Powell, David J. Silvester
IFISS is an established MATLAB finite element software package for studying strategies for solving partial differential equations (PDEs). IFISS3D is a new add-on toolbox that extends IFISS capabilities for elliptic PDEs from two to three space dimensions. The open-source MATLAB framework provides a computational laboratory for experimentation and exploration of finite element approximation and error
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emgr – EMpirical GRamian Framework Version 5.99 ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-09-19 Christian Himpe
Version 5.99 of the empirical Gramian framework – emgr – completes a development cycle which focused on parametric model order reduction of gas network models while preserving compatibility to the previous development for the application of combined state and parameter reduction for neuroscience network models. Second, new features concerning empirical Gramian types, perturbation design, and trajectory
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emgr – EMpirical GRamian Framework Version 5.99 ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-07-20 Christian Himpe
Version 5.99 of the empirical Gramian framework – emgr – completes a development cycle which focused on parametric model order reduction of gas network models while preserving compatibility to the previous development for the application of combined state and parameter reduction for neuroscience network models. Secondarily, new features concerning empirical Gramian types, perturbation design, and trajectory
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IFISS3D: A computational laboratory for investigating finite element approximation in three dimensions ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-20 Georgios Papanikos, Catherine E. Powell, David J. Silvester
IFISS is an established MATLAB finite element software package for studying strategies for solving partial differential equations (PDEs). IFISS3D is a new add-on toolbox that extends IFISS capabilities for elliptic PDEs from two to three space dimensions. The open-source MATLAB framework provides a computational laboratory for experimentation and exploration of finite element approximation and error
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Approximating inverse cumulative distribution functions to produce approximate random variables ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-17 Michael Giles, Oliver Sheridan-Methven
For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced using approximations to a distribution’s inverse cumulative distribution function. These approximations are designed to be computationally inexpensive, and much cheaper than library functions which are exact to within machine precision, and thus highly suitable for use
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ARKODE: A Flexible IVP Solver Infrastructure for One-step Methods ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-15 Daniel R. Reynolds, David J. Gardner, Carol S. Woodward, Rujeko Chinomona
We describe the ARKODE library of one-step time integration methods for ordinary differential equation (ODE) initial-value problems (IVPs). In addition to providing standard explicit and diagonally implicit Runge–Kutta methods, ARKODE supports one-step methods designed to treat additive splittings of the IVP, including implicit-explicit (ImEx) additive Runge–Kutta methods and multirate infinitesimal
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FastSpline: Automatic Generation of Interpolants for Lattice Samplings ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-15 Joshua Horacsek, Usman Alim
Interpolation is a foundational concept in scientific computing and is at the heart of many scientific visualization techniques. There is usually a tradeoff between the approximation capabilities of an interpolation scheme and its evaluation efficiency. For many applications, it is important for a user to navigate their data in real time. In practice, evaluation efficiency outweighs any incremental
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Computing with B-series ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-15 David I. Ketcheson, Hendrik Ranocha
We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the theory of B-series and associated concepts and provide examples of their use, including method composition and backward error analysis. The associated software is
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Distributed ℋ2-Matrices for Boundary Element Methods ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-15 Steffen Börm
Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and efficient compression techniques like the fast multipole method or hierarchical matrices. If the underlying mesh is very large, running the corresponding algorithms on a distributed computer is attractive, e.g., since distributed
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Task-based Parallel Programming for Scalable Matrix Product Algorithms ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-15 Emmanuel Agullo, Alfredo Buttari, Abdou Guermouche, Julien Herrmann, Antoine Jego
Task-based programming models have succeeded in gaining the interest of the high-performance mathematical software community because they relieve part of the burden of developing and implementing distributed-memory parallel algorithms in an efficient and portable way.In increasingly larger, more heterogeneous clusters of computers, these models appear as a way to maintain and enhance more complex algorithms
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Truncated Log-concave Sampling for Convex Bodies with Reflective Hamiltonian Monte Carlo ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-15 Apostolos Chalkis, Vissarion Fisikopoulos, Marios Papachristou, Elias Tsigaridas
We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm to sample from a log-concave distribution restricted to a convex body. The random walk is based on incorporating reflections to the Hamiltonian dynamics such that the support of the target density is the convex body. We develop an efficient open source implementation of ReHMC and perform an experimental study on various
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hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-15 Ki-Tae Kim, Umberto Villa, Matthew Parno, Youssef Marzouk, Omar Ghattas, Noemi Petra
Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ
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CPFloat: A C Library for Simulating Low-precision Arithmetic ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-17 Massimiliano Fasi, Mantas Mikaitis
One can simulate low-precision floating-point arithmetic via software by executing each arithmetic operation in hardware and then rounding the result to the desired number of significant bits. For IEEE-compliant formats, rounding requires only standard mathematical library functions, but handling subnormals, underflow, and overflow demands special attention, and numerical errors can cause mathematically
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Algorithm 1035: A Gradient-based Implementation of the Polyhedral Active Set Algorithm ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-15 William W. Hager, Hongchao Zhang
The Polyhedral Active Set Algorithm (PASA) is designed to optimize a general nonlinear function over a polyhedron. Phase one of the algorithm is a nonmonotone gradient projection algorithm, while phase two is an active set algorithm that explores faces of the constraint polyhedron. A gradient-based implementation is presented, where a projected version of the conjugate gradient algorithm is employed
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Algorithm 1036: ATC, An Advanced Tucker Compression Library for Multidimensional Data ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-15 Wouter Baert, Nick Vannieuwenhoven
We present ATC, a C++ library for advanced Tucker-based lossy compression of dense multidimensional numerical data in a shared-memory parallel setting, based on the sequentially truncated higher-order singular value decomposition (ST-HOSVD) and bit plane truncation. Several techniques are proposed to improve speed, memory usage, error control and compression rate. First, a hybrid truncation scheme
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Enabling Research through the SCIP Optimization Suite 8.0 ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-15 Ksenia Bestuzheva, Mathieu Besançon, Wei-Kun Chen, Antonia Chmiela, Tim Donkiewicz, Jasper van Doornmalen, Leon Eifler, Oliver Gaul, Gerald Gamrath, Ambros Gleixner, Leona Gottwald, Christoph Graczyk, Katrin Halbig, Alexander Hoen, Christopher Hojny, Rolf van der Hulst, Thorsten Koch, Marco Lübbecke, Stephen J. Maher, Frederic Matter, Erik Mühmer, Benjamin Müller, Marc E. Pfetsch, Daniel Rehfeldt,
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP’s main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version
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Improvements to SLEPc in Releases 3.14–3.18 ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-07 Jose E. Roman, Fernando Alvarruiz, Carmen Campos, Lisandro Dalcin, Pierre Jolivet, Alejandro Lamas Daviña
This short paper describes the main new features added to SLEPc, the Scalable Library for Eigenvalue Problem Computations, in the last two and a half years, corresponding to five release versions. The main novelty is the extension of the SVD module with new problem types such as the generalized SVD or the hyperbolic SVD. Additionally, many improvements have been incorporated in different parts of the
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Algorithms for Parallel Generic hp-adaptive Finite Element Software ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-06-05 Marc Fehling, Wolfgang Bangerth
The hp-adaptive finite element method (FEM) – where one independently chooses the mesh size (h) and polynomial degree (p) to be used on each cell – has long been known to have better theoretical convergence properties than either h- or p-adaptive methods alone. However, it is not widely used, owing at least in parts to the difficulty of the underlying algorithms and the lack of widely usable implementations
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Event-Based Automatic Differentiation of OpenMP with OpDiLib ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-03-21 Johannes Blühdorn, Max Sagebaum, Nicolas Gauger
We present the new software OpDiLib, a universal add-on for classical operator overloading AD tools that enables the automatic differentiation (AD) of OpenMP parallelized code. With it, we establish support for OpenMP features in a reverse mode operator overloading AD tool to an extent that was previously only reported on in source transformation tools. We achieve this with an event-based implementation
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Accurate Calculation of Euclidean Norms Using Double-word Arithmetic ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-03-21 Vincent Lefèvre, Nicolas Louvet, Jean-Michel Muller, Joris Picot, Laurence Rideau
We consider the computation of the Euclidean (or L2) norm of an n-dimensional vector in floating-point arithmetic. We review the classical solutions used to avoid spurious overflow or underflow and/or to obtain very accurate results. We modify a recently published algorithm (that uses double-word arithmetic) to allow for a very accurate solution, free of spurious overflows and underflows. To that purpose
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Robust Topological Construction of All-hexahedral Boundary Layer Meshes ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-03-21 Maxence Reberol, Kilian Verhetsel, François Henrotte, David Bommes, Jean-François Remacle
We present a robust technique to build a topologically optimal all-hexahedral layer on the boundary of a model with arbitrarily complex ridges and corners. The generated boundary layer mesh strictly respects the geometry of the input surface mesh, and it is optimal in the sense that the hexahedral valences of the boundary edges are as close as possible to their ideal values (local dihedral angle divided
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Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-03-21 Patrick Amestoy, Alfredo Buttari, Nicholas J. Higham, Jean-Yves L’Excellent, Theo Mary, Bastien Vieublé
The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis
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A Geometric Multigrid Method for Space-Time Finite Element Discretizations of the Navier–Stokes Equations and its Application to 3D Flow Simulation ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-03-21 Mathias Anselmann, Markus Bause
We present a parallelized geometric multigrid (GMG) method, based on the cell-based Vanka smoother, for higher order space-time finite element methods (STFEM) to the incompressible Navier–Stokes equations. The STFEM is implemented as a time marching scheme. The GMG solver is applied as a preconditioner for generalized minimal residual iterations. Its performance properties are demonstrated for 2D and
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Algorithm 1031: MQSI—Monotone Quintic Spline Interpolation ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-03-21 Thomas Lux, Layne T. Watson, Tyler Chang, William Thacker
MQSI is a Fortran 2003 subroutine for constructing monotone quintic spline interpolants to univariate monotone data. Using sharp theoretical monotonicity constraints, first and second derivative estimates at data provided by a quadratic facet model are refined to produce a univariate C2 monotone interpolant. Algorithm and implementation details, complexity and sensitivity analyses, usage information
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Algorithm 1032: Bi-cubic Splines for Polyhedral Control Nets ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-03-21 Jörg Peters, Kyle Lo, Kȩstutis Karčiauskas
For control nets outlining a large class of topological polyhedra, not just tensor-product grids, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each vertex. Akin to tensor-product splines, the resulting smooth surface approximates the polyhedron. Admissible polyhedral control nets consist of quadrilateral faces in a grid-like
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Algorithm 1033: Parallel Implementations for Computing the Minimum Distance of a Random Linear Code on Distributed-memory Architectures ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-03-21 Gregorio Quintana-Ortí, Fernando Hernando, Francisco D. Igual
The minimum distance of a linear code is a key concept in information theory. Therefore, the time required by its computation is very important to many problems in this area. In this article, we introduce a family of implementations of the Brouwer–Zimmermann algorithm for distributed-memory architectures for computing the minimum distance of a random linear code over 𝔽2. Both current commercial and
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Algorithm 1034: An Accelerated Algorithm to Compute the Qn Robust Statistic, with Corrections to Constants ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-03-21 Thierry Fahmy
The robust scale estimator Qn developed by Croux and Rousseeuw [3], for the computation of which they provided a deterministic algorithm, has proven to be very useful in several domains including in quality management and time series analysis. It has interesting mathematical (50% breakdown, 82% Asymptotic Relative Efficiency) and computing (O(nlogn) time, O(n) space) properties. While working on a
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Newly Released Capabilities in the Distributed-Memory SuperLU Sparse Direct Solver ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-03-21 Xiaoye S. Li, Paul Lin, Yang Liu, Piyush Sao
We present the new features available in the recent release of SuperLU_DIST, Version 8.1.1. SuperLU_DIST is a distributed-memory parallel sparse direct solver. The new features include (1) a 3D communication-avoiding algorithm framework that trades off inter-process communication for selective memory duplication, (2) multi-GPU support for both NVIDIA GPUs and AMD GPUs, and (3) mixed-precision routines
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Certifying Zeros of Polynomial Systems Using Interval Arithmetic ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-03-21 Paul Breiding, Kemal Rose, Sascha Timme
We establish interval arithmetic as a practical tool for certification in numerical algebraic geometry. Our software HomotopyContinuation.jl now has a built-in function certify, which proves the correctness of an isolated nonsingular solution to a square system of polynomial equations. The implementation rests on Krawczyk’s method. We demonstrate that it dramatically outperforms earlier approaches
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Algorithm xxx: Encapsulated error, a direct approach to evaluate floating-point accuracy ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-02-17 Nestor Demeure, Cédric Chevalier, Christophe Denis, Pierre Dossantos-Uzarralde
Floating-point numbers represent only a subset of real numbers. As such, floating-point arithmetic introduces approximations that can compound and have a significant impact on numerical simulations. We introduce Encapsulated error, a new way to estimate the numerical error of an application and provide a reference implementation, the Shaman library. Our method uses dedicated arithmetic over a type
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Algorithm 10xx: SuiteSparse:GraphBLAS: parallel graph algorithms in the language of sparse linear algebra ACM Trans. Math. Softw. (IF 2.7) Pub Date : 2023-01-25 Timothy A. Davis
SuiteSparse:GraphBLAS is a full parallel implementation of the GraphBLAS standard, which defines a set of sparse matrix operations on an extended algebra of semirings using an almost unlimited variety of operators and types. When applied to sparse adjacency matrices, these algebraic operations are equivalent to computations on graphs. A description of the parallel implementation of SuiteSparse:GraphBLAS