Related papers: HLinear: Exact Dense Linear Algebra in Haskell

One of the greatest efforts of computational scientists is to translate the mathematical model describing a class of physical phenomena into large and complex codes. Many of these codes face the difficulty of implementing the mathematical…

Domain-specific languages raise the level of abstraction in software development. While it is evident that programmers can more easily reason about very high-level programs, the same holds for compilers only if the compiler has an accurate…

We propose an amortized analysis that approximates the resource usage of a Haskell expression. Using the plugin API of GHC, we convert the Haskell code into a simplified representation called GHC Core. We then apply a type-based system…

The $\ell$FEM MATLAB package provides a simple, efficient, and flexible implementation of isoparametric finite elements in bulk domains and on surfaces. The finite element matrix assemblies are based on MATLAB's paged operators and…

Both high-level and high-resolution feature representations are of great importance in various visual understanding tasks. To acquire high-resolution feature maps with high-level semantic information, one common strategy is to adopt dilated…

Standard Transformer architectures rely heavily on dense linear transformations, treating feature projection as a monolithic, full-rank operation. We argue that this formulation is inefficient and lacks the structural inductive bias…

Dense linear algebra kernels are critical for wireless applications, and the oncoming proliferation of 5G only amplifies their importance. Many such matrix algorithms are inductive, and exhibit ample amounts of fine-grain ordered…

Superpixel segmentation can be used as an intermediary step in many applications, often to improve object delineation and reduce computer workload. However, classical methods do not incorporate information about the desired object.…

We present a prototypical linear algebra compiler that automatically exploits domain-specific knowledge to generate high-performance algorithms. The input to the compiler is a target equation together with knowledge of both the structure of…

Obtaining good performance when programming heterogeneous computing platforms poses significant challenges. We present a program transformation environment, implemented in Haskell, where architecture-agnostic scientific C code with semantic…

We present CutLang, an analysis description language and runtime interpreter for high energy collider physics data analyses. An analysis description language is a declerative domain specific language that can express all elements of a data…

We extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension. Both of the reductions are incorporated into one algorithm. As an application, we present an additive…

During the past decade, Deep Learning (DL) algorithms, programming systems and hardware have converged with the High Performance Computing (HPC) counterparts. Nevertheless, the programming methodology of DL and HPC systems is stagnant,…

We introduce HP, an implementation of density-functional perturbation theory, designed to compute Hubbard parameters (on-site $U$ and inter-site $V$) in the framework of DFT+$U$ and DFT+$U$+$V$. The code does not require the use of…

We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…

Infinitesimal deformations are governed by partition Lie algebras. In characteristic $0$, these higher categorical structures are modelled by differential graded Lie algebras, but in characteristic $p$, they are more subtle. We give…

Modern research in code generators for dense linear algebra computations has shown the ability to produce optimized code with a performance which compares and often exceeds the one of state-of-the-art implementations by domain experts.…

This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral decomposition of input data. We present several theoretical…

A simple MATLAB implementation of hierarchical shape functions on 2D rectangles is explained and available for download. Global shape functions are ordered for a given polynomial degree according to the indices of the nodes, edges, or…

We show how to give a coherent semantics to programs that are well-specified in a version of separation logic for a language with higher types: idealized algol extended with heaps (but with immutable stack variables). In particular, we…