660 research outputs found
Efficient numerical diagonalization of hermitian 3x3 matrices
A very common problem in science is the numerical diagonalization of
symmetric or hermitian 3x3 matrices. Since standard "black box" packages may be
too inefficient if the number of matrices is large, we study several
alternatives. We consider optimized implementations of the Jacobi, QL, and
Cuppen algorithms and compare them with an analytical method relying on
Cardano's formula for the eigenvalues and on vector cross products for the
eigenvectors. Jacobi is the most accurate, but also the slowest method, while
QL and Cuppen are good general purpose algorithms. The analytical algorithm
outperforms the others by more than a factor of 2, but becomes inaccurate or
may even fail completely if the matrix entries differ greatly in magnitude.
This can mostly be circumvented by using a hybrid method, which falls back to
QL if conditions are such that the analytical calculation might become too
inaccurate. For all algorithms, we give an overview of the underlying
mathematical ideas, and present detailed benchmark results. C and Fortran
implementations of our code are available for download from
http://www.mpi-hd.mpg.de/~globes/3x3/ .Comment: 13 pages, no figures, new hybrid algorithm added, matches published
version, typo in Eq. (39) corrected; software library available at
http://www.mpi-hd.mpg.de/~globes/3x3
SHARE with CHARM
SHARE with CHARM program (SHAREv3) implements the statistical hadronization
model description of particle production in relativistic heavy-ion collisions.
Given a set of statistical parameters, SHAREv3 program evaluates yields and
therefore also ratios, and furthermore, statistical particle abundance
fluctuations. The physical bulk properties of the particle source is evaluated
based on all hadrons produced, including the fitted yields. The bulk properties
can be prescribed as a fit input complementing and/or replacing the statistical
parameters. The modifications and improvements in the SHARE suite of programs
are oriented towards recent and forthcoming LHC hadron production results
including charm hadrons. This SHAREv3 release incorporates all features seen
previously in SHAREv1.x and v2.x and, beyond, we include a complete treatment
of charm hadrons and their decays, which further cascade and feed lighter
hadron yields. This article is a complete and self-contained manual explaining
and introducing both the conventional and the extended capabilities of SHARE
with CHARM. We complement the particle list derived from the Particle Data
Group tabulation composed of up, down, strange quarks (including
resonances) with hadrons containing charm quarks. We provide a table
of the charm hadron decays including partial widths. The branching ratios of
each charm hadron decays add to unity, which is achieved by including some
charm hadron decay channels based on theoretical consideration in the absence
of direct experimental information. A very successful interpretation of all
available LHC results has been already obtained using this program.Comment: 41 pages, 5 figures, 3 tables. Associated program available at
http://www.physics.arizona.edu/~gtshare/SHARE/share.html (Computer Physics
Communications in press
A Historical Perspective on Runtime Assertion Checking in Software Development
This report presents initial results in the area of software testing and analysis produced as part of the Software Engineering Impact Project. The report describes the historical development of runtime assertion checking, including a description of the origins of and significant features associated with assertion checking mechanisms, and initial findings about current industrial use. A future report will provide a more comprehensive assessment of development practice, for which we invite readers of this report to contribute information
A practical guide to computer simulations
Here practical aspects of conducting research via computer simulations are
discussed. The following issues are addressed: software engineering,
object-oriented software development, programming style, macros, make files,
scripts, libraries, random numbers, testing, debugging, data plotting, curve
fitting, finite-size scaling, information retrieval, and preparing
presentations.
Because of the limited space, usually only short introductions to the
specific areas are given and references to more extensive literature are cited.
All examples of code are in C/C++.Comment: 69 pages, with permission of Wiley-VCH, see http://www.wiley-vch.de
(some screenshots with poor quality due to arXiv size restrictions) A
comprehensively extended version will appear in spring 2009 as book at
Word-Scientific, see http://www.worldscibooks.com/physics/6988.htm
Recommended from our members
Parallelizing a nondeterministic optimization algorithm
This research explores the idea that for certain optimization problems there is a way to parallelize the algorithm such that the parallel efficiency can exceed one hundred percent. Specifically, a parallel compiler, PC, is used to apply shortcutting techniquest to a metaheuristic Ant Colony Optimization (ACO), to solve the well-known Traveling Salesman Problem (TSP) on a cluster running Message Passing Interface (MPI). The results of both serial and parallel execution are compared using test datasets from the TSPLIB
FloatX: A C++ Library for Customized Floating-Point Arithmetic
"© ACM, 2019. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Mathematical Software, {45, 4, (2019)} https://dl.acm.org/doi/10.1145/3368086"[EN] We present FloatX (Float eXtended), a C++ framework to investigate the effect of leveraging customized floating-point formats in numerical applications. FloatX formats are based on binary IEEE 754 with smaller significand and exponent bit counts specified by the user. Among other properties, FloatX facilitates an incremental transformation of the code, relies on hardware-supported floating-point types as back-end to preserve efficiency, and incurs no storage overhead. The article discusses in detail the design principles, programming interface, and datatype casting rules behind FloatX. Furthermore, it demonstrates FloatX's usage and benefits via several case studies from well-known numerical dense linear algebra libraries, such as BLAS and LAPACK; the Ginkgo library for sparse linear systems; and two neural network applications related with image processing and text recognition.This work was supported by the CICYT projects TIN2014-53495-R and TIN2017-82972-R of the MINECO and FEDER, and the EU H2020 project 732631 "OPRECOMP. Open Transprecision Computing."Flegar, G.; Scheidegger, F.; Novakovic, V.; Mariani, G.; Tomás DomĂnguez, AE.; Malossi, C.; Quintana-OrtĂ, ES. (2019). FloatX: A C++ Library for Customized Floating-Point Arithmetic. ACM Transactions on Mathematical Software. 45(4):1-23. https://doi.org/10.1145/3368086S123454Edward Anderson Zhaojun Bai L. Susan Blackford James Demmesl Jack J. Dongarra Jeremy Du Croz Sven Hammarling Anne Greenbaum Alan McKenney and Danny C. Sorensen. 1999. LAPACK Users’ Guide (3rd ed.). SIAM. Edward Anderson Zhaojun Bai L. 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iQIST : An open source continuous-time quantum Monte Carlo impurity solver toolkit
Quantum impurity solvers have a broad range of applications in theoretical studies of strongly correlated electron systems. Especially, they play a key role in dynamical mean-field theory calculations of correlated lattice models and realistic materials. Therefore, the development and implementation of efficient quantum impurity solvers is an important task. In this paper, we present an open source interacting quantum impurity solver toolkit (dubbed iQIST). This package contains several highly optimized quantum impurity solvers which are based on the hybridization expansion continuous-time quantum Monte Carlo algorithm, as well as some essential pre- and post-processing tools. We first introduce the basic principle of continuous-time quantum Monte Carlo algorithm and then discuss the implementation details and optimization strategies. The software framework, major features, and installation procedure for iQIST are also explained. Finally, several simple tutorials are presented in order to demonstrate the usage and power of iQIST
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