Parallel Prefix Polymorphism Permits Parallelization, Presentation &amp;amp;amp; Proof

Edelman, Alan

doi:10.1109/hptcdl.2014.9

Cited by 4 publications

(3 citation statements)

References 45 publications

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“…Mathematical thought is naturally polymorphic. Multimethods are a natural mechanism for capturing such polymorphism [6,14]. Consider an operation as fundamental as multiplication: an expression like a*b can mean a matrix-matrix product, a matrix-vector product, or a scalar-vector product, to name just a few possibilities.…”

Section: Generic Functions and Multimethodsmentioning

confidence: 99%

Fast Flexible Function Dispatch in Julia

Bezanson,

Bolewski,

Chen

2018

Preprint

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Technical computing is a challenging application area for programming languages to address. This is evinced by the unusually large number of specialized languages in the area (e.g. MATLAB [47], R [42]), and the complexity of common software stacks, often involving multiple languages and custom code generators. We believe this is ultimately due to key characteristics of the domain: highly complex operators, a need for extensive code specialization for performance, and a desire for permissive high-level programming styles allowing productive experimentation.The Julia language attempts to provide a more effective structure for this kind of programming by allowing programmers to express complex polymorphic behaviors using dynamic multiple dispatch over parametric types. The forms of extension and reuse permitted by this paradigm have proven valuable for technical computing. We report on how this approach has allowed domain experts to express useful abstractions while simultaneously providing a natural path to better performance for high-level technical code.

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Section: Generic Functions and Multimethodsmentioning

confidence: 99%

Fast Flexible Function Dispatch in Julia

Bezanson,

Bolewski,

Chen

2018

Preprint

Self Cite

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“…Others have explored using high-level frameworks for GPU computing with Julia [17]. Chen et al investigated using polymorphic code features in Julia applied to parallel and distributed computing [18]. It has also been shown to work well for classic scientific problems, such as convex optimization [19], PDE solving [20], and discrete event-driven simulation [21].…”

Section: A Overview Of Juliamentioning

confidence: 99%

A Look at Communication-Intensive Performance in Julia

Rizvi,

Hale

2021

Preprint

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The Julia programming language continues to gain popularity both for its potential for programmer productivity and for its impressive performance on scientific code. It thus holds potential for large-scale HPC, but we have not yet seen this potential fully realized. While Julia certainly has the machinery to run at scale, and while others have done so for embarrassingly parallel workloads, we have yet to see an analysis of Julia's performance on communication-intensive codes that are so common in the HPC domain. In this paper we investigate Julia's performance in this light, first with a suite of microbenchmarks within and without the node, and then using the first Julia port of a standard, HPC benchmarking code, high-performance conjugate gradient (HPCG). We show that if programmers properly balance the computation to communication ratio, Julia can actually outperform C/MPI in a cluster computing environment.

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“…The exclamation mark suffix follows the convention in Julia denoting that the function mutates at least one of its arguments. In this case, it caches the best fit X and Y as glrm.X and glrm.Y [CE14].…”

Section: Julia Implementationmentioning

confidence: 99%

Generalized Low Rank Models

Udell

Horn

Zadeh

et al. 2016

FNT in Machine Learning

196

129

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Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, k-means, k-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.

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Parallel Prefix Polymorphism Permits Parallelization, Presentation &amp; Proof

Cited by 4 publications

References 45 publications

Fast Flexible Function Dispatch in Julia

Fast Flexible Function Dispatch in Julia

A Look at Communication-Intensive Performance in Julia

Generalized Low Rank Models

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