Numerical Excellence Franois Cassier fcassier@nag.com Introduction - - PowerPoint PPT Presentation

Experts in numerical algorithms and HPC services

Numerical Excellence

François Cassier fcassier@nag.com

Introduction to « Multicore Demystified » lecture RWTH Aachen 18th November 2014

Numerical Excellence

Agenda

• Few words about NAG
• NAG Software Products:

 NAG Numerical Libraries & Toolbox  NAG Fortran Compiler

• NAG License at RWTH Aachen
• Services

Numerical Excellence

• Founded in 1970

 Not-for-profit organisation  Surpluses fund on-going R&D

• Mathematical and Statistical Expertise

 Libraries of numerical components  Consulting

• HPC Services

 Computational Science and Engineering (CSE) support  Procurement advice, market watch, benchmarking

NAG Background

Numerical Excellence

Partnerships with leading academics

• RWTH Aachen
• University of Birmingham
• Illinois Institute of

Technology

• Fudan University
• K U Leuven
• Kings College London
• University of Manchester
• New York University
• Osaka City University
• University of Oxford
• Universita di Roma I
• T

.U. Eindhoven

• Shanghai University
• Stanford University
• University of Strathclyde
• National University of

Singapore

• University of Tennessee
• Tsinghua University
• University of Warwick

5

NAG SOFTWARE NAG FORTRAN COMPILER

Numerical Excellence

NAG Fortran Compiler

• World’s first Fortran 90 compiler
• Developed and enhanced to include Fortran 95 +

close to 100% features of Fortran 2003 + partial support for the new Fortran 2008 features

• Regularly updated, fully supported.
• EXCELLENT (the world’s best) checking compiler

Numerical Excellence

NAG Fortran Builder (Windows version)

• Integrated Development Environment for NAG

compiler on Windows PC

• Perfectly integrated with NAG Library

 NAG example program templates

• Extra facilities: tools e.g. Fortran Polisher, Fortran

converter, LAPACK examples

• Integrated debugger

Numerical Excellence

• Support for OpenMP 3.1 in addition to OpenMP 3.0
• Maximum rank of an array is increased
• Internal procedures can be passed as actual arguments or assigned to a

procedure pointer

• G0 and G0.d edit descriptors, and * (infinite) repeat factor
• CONTIGUOUS attribute and IS_CONTIGUOUS intrinsic function
• ERF, EFRC, ERFC_SCALED, GAMMA, LOG_GAMMA intrinsic functions
• Implied-shape named array constants
• ERROR_STOP statement
• Kind type parameters for derived types
• New interface generator (nagfor =interfaces)
• Additional options within the polisher tool

New Features – NAG Compiler 6.0

9

NAG SOFTWARE NAG NUMERICAL LIBRARIES & TOOLBOX

Numerical Excellence

NAG development philosophy

• First priority: accuracy & performance
• Algorithms chosen for

 usefulness  robustness  accuracy  stability  speed

Numerical Excellence

Why Use NAG Maths Libraries and Toolboxes?

• +1700 math/stat software components
• High quality software – accuracy, reliability and

robustness

• Extensively tested, supported and maintained code
• Reduce development time
• Components for:

 Most programming languages  Most environments for modelling and data analysis

• Designed to get high performance

Numerical Excellence

NAG Library and Toolbox Contents

• Root Finding
• Summation of Series
• Quadrature
• Ordinary Differential

Equations

• Partial Differential Equations
• Numerical Differentiation
• Integral Equations
• Mesh Generation
• Interpolation
• Curve and Surface Fitting
• Optimization
• Approximations of Special

Functions

• Dense Linear Algebra
• Sparse Linear Algebra
• Correlation & Regression

Analysis

• Multivariate Methods
• Analysis of Variance
• Random Number Generators
• Univariate Estimation
• Nonparametric Statistics
• Smoothing in Statistics
• Contingency Table Analysis
• Survival Analysis
• Time Series Analysis
• Operations Research

Numerical Excellence

• Hypergeometric function



Robust accurate real confluent hypergeometric function

• Nearest correlation matrix



Elementwise weighted nearest correlation matrix

• Wavelet Transforms & FFTs



Three dimensional discrete single level and multi-level wavelet transforms.



Fast Fourier Transforms (FFTs) for two- dimensional and three dimensional real data.

• Matrix Operations



Matrix exponentials (Schur–Parlett)



Combines two sums of squares matrices to allow large datasets to be summarised



Matrix functions including calculation of condition numbers

• Interpolation



5D interpolation and higher dimensions

• Optimization



Local optimization: Non-negative least squares



Global optimization: Multi-start versions of general nonlinear programming and least squares routines

• RNG’s



Brownian bridge and random fields

• Statistics



Gaussian mixture model



Best subsets of given size (branch and bound )



Vectoized probabilities and probability density functions of distributions.



Inhomogeneous time series analysis, moving averages

NAG Library : new Mark 24 (1 of 2)

Mark 24 has new routines in many areas including...

Numerical Excellence

• Data fitting



Fit of 2D scattered data by two-stage approximation (suitable for large datasets)

• Quadrature



1D adaptive for badly-behaved integrals

• Sparse eigenproblem



Driver for real general matrix, driver for banded complex eigenproblem

• Sparse linear systems



block diagonal pre conditioners and solvers

• ODE solvers



Thread safe initial value ODE solvers

NAG Library : new Mark 24 (2 of 2)

Mark 24 has new routines in many areas including... (page 2)

Numerical Excellence

• NAG Fortran Library
• NAG Library for SMP & Multi Cores
• NAG Parallel Library
• NAG C Library
• NAG Toolbox for MATLAB
• NAG Library for Xeon Phi
• NAG Library for .NET
• NAG Components for GPU/CUDA
• + Additional interfaces (e.g. Python, Java, R)

NAG Library & Toolbox Products

Numerical Excellence

O/S & Compilers

Supporting Wide Range of O/S

• Windows
• Linux
• Mac
• Solaris
• AIX
• HP-UX
• 32-bit, 64-bit
• ...

Support leading compilers (Fortran, C & C++, .NET)

• NAG
• Intel, Pathscale, PGI
• GCC, GFortran
• Absoft, Lahey, Visual C++
• ...

Numerical Excellence

NAG Libraries Ease of Integration

• C++ (various)
• OpenCL
• Visual Basic
• Java
• Delphi
• Python
• F#
• …
• and more
• Excel
• SciLab
• Octave
• Mathematica
• Maple
• LabVIEW
• R and S-Plus
• SAS
• …
• and more

18

NAG SOFTWARE AT RWTH AACHEN

Numerical Excellence

• NAG Fortran Compiler & NAG Fortran Builder
• NAG Fortran Library
• NAG Library for SMP & Multi Cores
• NAG Parallel Library
• NAG C Library
• NAG Toolbox for MATLAB
• NAG Library for Xeon Phi
• NAG Library for .NET
• NAG Components for GPU/CUDA
• + Additional interfaces (e.g. Python, Java, R)

NRW State Wide License Includes

Numerical Excellence

How do I get the software?

• Help yourself from:

 http://www.nag.co.uk/downloads/index.asp

• For all supported combinations of o/s and compiler

 On Workstations, clusters & home systems

• License keys can be requested at:

 servicedesk@rz.rwth-aachen.de (Andrea Lindner Lorenz)

Numerical Excellence

How do I get some help?

• Direct access to technical support:

 support@nag.co.uk

22

NUMERICAL & HPC SERVICES

Numerical Excellence

Consulting Services from NAG

• Numerical & Statistical Library support



Customised routines for NAG Libraries



Integration of NAG libraries into customer environments



Customisation of customer code

• HPC support



Supporting the business

 HPC technology planning, collaborative research  Impartial advice, benchmarking, procurement consulting



Supporting the developer/user

 Parallel software engineering expertise & services

 Porting, scalability, optimisation, new algorithms, restructuring, …

• Product and HPC Training
• Collaborative R&D for new technology (manycore, GPU, …)

Experts in Numerical Engineering

Numerical Excellence

NAG Key Contacts

www.nag.co.uk

Technical Support and Help support@nag.co.uk francois.cassier@nag.com (commercial contact) viktor.mosenkis@nag.co.uk (local technical contact) NAGNews http://www.nag.co.uk/NAGNews/Index.asp