experts in numerical algorithms and hpc services numerical excellence françois cassier jonathan...

Experts in numerical algorithms and HPC services

Numerical Excellence

François CassierJonathan Gibson

23rd January 2012CERN

2Numerical Excellence

Agenda

Introduction to NAG NAG Fortran Compiler NAG’s Numerical Libraries and Toolboxes

NAG Fortran and C Libraries NAG Toolbox for MATLAB ...

NAG HPC Services

3Numerical Excellence19 Apr 2023

Introduction to NAG

Founded in 1970 as a co-operative project in UK Operates as a commercial, not-for-profit

organization Worldwide operations

Oxford & Manchester, UK Chicago, US Tokyo, Japan Taipei, Taiwan

Over 3,000 customer sites worldwide Staff of ~100, over 50% technical, over 25 PhDs


Numerical Algorithms Group - What We Do

NAG provides mathematical and statistical algorithm libraries widely used in industry and academia

Committed to research & development Library code written and contributed by some of

the world’s most renowned mathematicians and computer scientists

Many collaborative projects – e.g. CSE Support to the UK’s largest supercomputer, HECToR


Partners


Partnerships with leading academics

University of 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 Shanghai University Stanford University University of

Strathclyde National University of

Singapore University of

Tennessee Tsinghua University University of Warwick

7

NAG COMPILER & LIBRARIES


Portfolio

Numerical Libraries Highly flexible for use in many computing languages,

programming environments, hardware platforms and for high performance computing methods

NAG Fortran Compiler and GUI based Windows Compiler: Fortran Builder

Visualization and graphics software Build data visualization applications with NAG’s IRIS Explorer

Algorithmic Differentiation (New) Also called “Automatic Differentiation”

Consultancy services


NAG development philosophy

First priority: accuracy Second priority: performance

How fast do you want the wrong answer? Algorithms chosen for

usefulness robustness accuracy stability speed


NAG Fortran Compiler

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

most features of Fortran 2003. Regularly updated, fully supported. EXCELLENT (the world’s best) checking compiler


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


Fortran 2008 Features BLOCK construct, ISO_FORTRAN_ENV, etc.

OpenMP 3.0 Most commonly used features

More Fortran 2003 Features FINAL subroutines, etc.

Other New Features Performance improvements, additional error checking,

integrated tools

New Features – NAG Compiler 5.3


Why Use NAG Maths Libraries and Toolboxes?

Global reputation for quality – accuracy, reliability and robustness…

Extensively tested, supported and maintained code Reduce development time Concentrate on your key areas Components

Fit into your environment Simple interfaces to your favourite packages

Regular performance improvements!


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


New Features – NAG Libraries Mark 23Mark 23 has new routines in many areas including...


Best Advice – Use the Decision Trees


NAG Fortran Library (FL) NAG Library for SMP & Multi Cores (FS) NAG Parallel Library (FD) NAG C Library (CL) NAG Library for .NET (DT) NAG Toolbox for MATLAB (MB)

NAG Librairies Availability


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++ ...


NAG Libraries Ease of Integration

C++ (various) CUDA OpenCL Visual Basic Java Borland Delphi Python F# … and more

Excel MATLAB SciLab Octave Mathematica Maple LabVIEW R and S-Plus SAS … and more


NAG Toolbox for MATLAB Contains essentially all NAG Library functionality

not a subset

Fully integrated into MATLAB many routine arguments become optional

easier to read code can be used with MATLAB compiler complete documentation for each routine

inside MATLAB or PDF including examples

Easy migration to production code in C/C++ or Fortran

21Numerical ExcellenceNAG Toolbox help

chapters

MATLAB formatting NAG formatting (in PDF)

22Numerical Excellence MATLAB plotHow to call the

NAG routineCalling the NAG routine

in MATLAB


NAG Toolbox for MATLAB

Offers complementary functionality to MATLAB

Alternative to several specialist toolboxes From www.walkingrandomly.com:

“I really like the NAG Toolbox for MATLAB for the following reasons: It has saved my employer, The University of Manchester, a lot of

money since we don’t need as many licenses for toolboxes such as Statistics, Optimisation, Curve Fitting and Splines.

It can speed up MATLAB calculations – see my article on MATLAB’s interp1 function for example.

Their support team is superb.”

24

NAG LIBRARY FOR SMP & MULTI CORES


NAG Library for SMP & Multicore

Based on standard NAG Fortran Library Uses OpenMP to exploit SMP architecture Mark 23 available soon

Identical interfaces to standard Fortran Library just re-link the application easy access to parallelism for non-specialists

user is shielded from details of parallelism assists rapid migration from serial code

can be used along with user’s own parallelism i.e. within the user’s own OpenMP or MPI code


Interoperability

We want to bring benefits of SMP to multiple environments

Currently: Fortran 77 and 90 (with interface blocks available) From C programs via NAG C Header files Toolbox for Matlab (Windows now, Linux soon)

Investigating technical issues for other possibilities: Better C support via NAG C Library interfaces (“C SMP

Library”) Excel

27

NAG Library Functionality

• Root Finding • Summation of Series (e.g. FFT)• Quadrature• Ordinary Differential Equations• Partial Differential Equations • Numerical Differentiation • Integral Equations • Mesh Generation • Interpolation • Curve and Surface Fitting • Optimisation• Approximations of Special

Functions• Wavelet Transforms

• Dense Linear Algebra• Sparse Linear Algebra• Correlation and Regression

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


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S.V.D. (DBDSQR)

Problem size (N)

Per

form

ance

(M

flop

s)

SMP DBDSQR+ ACML BLAS

NCPU

netlib DBDSQR + ACML BLAS

Improved serial performance too


0

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1 2 4 8

E01THF: evaluate interpolant at given points

E01TGF: generate 3D interpolant

E01TGF/E01THF: InterpolationT

ime

(sec

s)

Number of cores

Intel Xeon E5310 1.6 GHz, N=100,000


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G13EAF: Kalman filter (1 iteration)T

ime

(sec

s)

Number of cores

AMD Magny-Cours, dual socket, 2.2 GHz

N=2000, M=L=1000


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1 2 4 6 8 12 16 24

C09EAF: 2-D discrete wavelet transformT

ime

(sec

s)

Number of cores

AMD Magny-Cours, dual socket, 2.2 GHz

M=N=15000, DB8, Half, Forward


Coming later this year in Mark 23

New parallel routines in the areas of:

Particle Swarm Optimization Pseudo Random Number Generator 2D wavelet routines 4D and 5D interpolation routines

33

NAG HPC SERVICES


Selected NAG HPC activities


HECToR CSE Service


Some CSE successes so far

http://www.hector.ac.uk/cse/reports/

http://www.hector.ac.uk/cse/reports/

Speed and Scalability of Key Materials Science Code (CASTEP) Quadrupled Speed and I/O Performance of Oceanography Code (NEMO) Enhanced Performance of Quantum Monte-Carlo Application (CASINO) Quadrupled Speed and Scalability of Materials Science Simulations (CP2K) Enhanced Performance of Atmospheric Chemistry Simulations (GLOMAP/TOMCAT) Enhanced Performance of Geodynamic Thermal Convection Simulations (CITCOM) Enhanced Scalability of Fluid Turbulence Simulations (EBL) Enhanced up to 40x Simulations of Catalytic Chemistry with ChemShell 8x Faster Scalability of Ocean Modelling Application (Fluidity-ICOM) Dramatically Improved Performance of Molecular Dynamics Application (DL_POLY_3) 20x Faster Capabilities of Key Materials Science Application (CASTEP) Significantly Enhanced Performance of Heart Modelling Application (CARP) 20x Faster Performance of Turbulent Fluid Flow Simulations (Incompact3D) Improved by factor of 6x Performance and Capabilities of Materials Science Code (Conquest) Enhanced Aircraft Noise Simulations (CABARET) Get Faster and Reach Bigger Models


Specialist HPC Training

We offer a wide selection of courses From introductory programming courses

Fortran 95 (2/3 days) Parallel Programming with MPI (2/3 days) OpenMP (2/3 days) An Introduction to CUDA Programming (2 days) An Introduction to OpenCL Programming (2 days)

To courses for more experienced programmers Debugging, Profiling and Optimising (3 days) Parallel I/O (1 day) Multicore (1 day)

As well as bespoke courses to meet your specific requirements


Summary

NAG for Quality, World-leading Numerical Software Components accurate, reliable, robust extensively tested, supported and maintained code updated for new architectures and new algorithms

NAG for Expertise in HPC Services To build HPC capability CSE Services Trainings


NAG Key Contacts

www.nag.co.uk Technical Support and Help

[email protected]

NAG: [email protected]

NAGNews http://www.nag.co.uk/NAGNews/Index.asp


Further InformationNAG Products http://www.nag.co.uk/products_and_services.asp NAG C Library http://www.nag.co.uk/numeric/CL/CLdescription.asp NAG Toolbox for MATLAB http://www.nag.co.uk/numeric/MB/start.asp NAG Toolbox for MATLAB – some demos can be found via here:http://www.nag.co.uk/numeric/MB/product_demonstrations.asp NAG and Octave http://www.nag.co.uk/doc/TechRep/html/Tr4_09/Tr4_09.asp NAG And Scilab http://www.nag.co.uk/doc/techrep/html/TR5_09/TR5_09.asp NAG Data Mining Components http://www.nag.co.uk/numeric/dr/drdescription.asp NAG and Excel http://www.nag.co.uk/numeric/callingDLLsfromotherlang.asp NAG and Java http://www.nag.co.uk/doc/TechRep/html/Tr1_04/Tr1_04.asp NAG and R http://www.nag.co.uk/numeric/RunderWindows.asp NAG and GPUs http://www.nag.co.uk/numeric/GPUs/ NAG Library for .NET (beta) http://www.nag.co.uk/numeric/DT/DTdescription.asp Calling NAG DLLs from C# http://www.nag.co.uk/numeric/csharp.asp

Download software from http://www.nag.co.uk/downloads/index.asp NAGNews http://www.nag.co.uk/NAGNews/index.asp technical articles and news

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