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Register a new userA SageTeX Hypermatrix Algebra Package
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Added by
Edinah Gnang K
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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We describe here a rudimentary sage implementation of the Bhattacharya-Mesner hypermatrix algebra package.
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Matrix and tensor operations form the basis of a wide range of fields and applications, and in many cases constitute a substantial part of the overall computational complexity. The ability of general-purpose GPUs to speed up many of these operations and enable others has resulted in a widespread adaptation of these devices. In order for tensor operations to take full advantage of the computational power, specialized software is required, and currently there exist several packages (predominantly in the area of deep learning) that incorporate tensor operations on both CPU and GPU. Nevertheless, a stand-alone framework that supports general tensor operations is still missing. In this paper we fill this gap and propose the Ocean Tensor Library: a modular tensor-support package that is designed to serve as a foundational layer for applications that require dense tensor operations on a variety of device types. The API is carefully designed to be powerful, extensible, and at the same time easy to use. The package is available as open source.
In (Franceschi et al., 2018) we proposed a unified mathematical framework, grounded on bilevel programming, that encompasses gradient-based hyperparameter optimization and meta-learning. We formulated an approximate version of the problem where the inner objective is solved iteratively, and gave sufficient conditions ensuring convergence to the exact problem. In this work we show how to optimize learning rates, automatically weight the loss of single examples and learn hyper-representations with Far-HO, a software package based on the popular deep learning framework TensorFlow that allows to seamlessly tackle both HO and ML problems.
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 Hierarchically Semi-Separable representations (HSS). Such matrices appear in many applications, e.g., finite element methods, boundary element methods, etc. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, relies on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. This work is part of a more global effort, the STRUMPACK (STRUctured Matrices PACKage) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.
We present a Python module named PyCheb, to solve the ordinary differential equations by using spectral collocation method. PyCheb incorporates discretization using Chebyshev points, barycentric interpolation and iterate methods. With this Python module, users can initialize the ODEsolver class by passing attributes, including the both sides of a given differential equation, boundary conditions, and the number of Chebyshev points, which can also be generated automatically by the ideal precision, to the constructor of ODEsolver class. Then, the instance of the ODEsolver class can be used to automatically determine the resolution of the differential equation as well as generate the graph of the high-precision approximate solution. (If you have any questions, please send me an email and I will reply ASAP. e-mail:[email protected]/[email protected])
This document describes the R package UBL that allows the use of several methods for handling utility-based learning problems. Classification and regression problems that assume non-uniform costs and/or benefits pose serious challenges to predictive analytic tasks. In the context of meteorology, finance, medicine, ecology, among many other, specific domain information concerning the preference bias of the users must be taken into account to enhance the models predictive performance. To deal with this problem, a large number of techniques was proposed by the research community for both classification and regression tasks. The main goal of UBL package is to facilitate the utility-based predictive analytic task by providing a set of methods to deal with this type of problems in the R environment. It is a versatile tool that provides mechanisms to handle both regression and classification (binary and multiclass) tasks. Moreover, UBL package allows the user to specify his domain preferences, but it also provides some automatic methods that try to infer those preference bias from the domain, considering some common known settings.
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