HLinear: Exact Dense Linear Algebra in Haskell

نویسندگان

  • Alexandru Ghitza
  • Martin Westerholt-Raum
چکیده

We present an implementation in the functional programming language Haskell of the PLE decomposition of matrices over division rings. We discover in our benchmarks that in a relevant number of cases it is significantly faster than the C-based implementation provided in FLINT. Describing the guiding principles of our work, we introduce the reader to basic ideas from high performance functional program-

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Recursion based parallelization of exact dense linear algebra routines for Gaussian elimination

We present block algorithms and their implementation for the parallelization of sub-cubic Gaussian elimination on shared memory architectures. Contrarily to the classical cubic algorithms in parallel numerical linear algebra, we focus here on recursive algorithms and coarse grain parallelization. Indeed, sub-cubic matrix arithmetic can only be achieved through recursive algorithms making coarse...

متن کامل

Linear v{C}ech closure spaces

In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and pro...

متن کامل

Dense Linear Algebra over Finite Fields: the FFLAS and FFPACK packages

In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide efficient implementations of such algorithms one need to be careful with the underlying arithmetic. It is well known that modular techniques such as the Chine...

متن کامل

A Monadic Calculus for Parallel Costing of a Functional Language of Arrays

Vec is a higher-order functional language of nested arrays, which includes a general folding operation. Static computation of the shape of its programs is used to support a compositional cost calculus based on a cost monad. This, in turn, is based on a cost algebra, whose operations may be customized to handle diierent cost regimes, especially for parallel programming. We present examples based...

متن کامل

Avoiding Communication in Dense Linear Algebra

Avoiding Communication in Dense Linear Algebra

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • CoRR

دوره abs/1605.02532  شماره 

صفحات  -

تاریخ انتشار 2016