NAGs Libraries and Toolbox

1
NAGs Libraries and Toolbox

• Susan Ing, David Sayers NAG
• Jan Smit, Cosinus

2
Overview

• Introduction Jan Smit
• Product Overview Susan Ing
• NAGs Numerical Libraries
• NAG Toolbox for MATLAB
• NAG Training Session David Sayers

3
Numerical Algorithms Group - What We Do

• NAG provides mathematical and statistical
  algorithm libraries widely used in industry and
  academia
• Established in 1970 with offices in Oxford,
  Manchester, Chicago, Taipei and Tokyo
• Not-for-profit organisation committed to research
  development
• Library code written and contributed by some of
  the worlds most renowned mathematicians and
  computer scientists
• NAGs numerical code is embedded within many
  vendor libraries such as AMD and Intel
• Many collaborative projects e.g. CSE Support to
  the UKs largest supercomputer, HECToR

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Portfolio

• Numerical Libraries
• Highly flexible for use in many computing
  languages, programming environments, hardware
  platforms and for high performance computing
  methods
• Connector Products for MATLAB and Maple
• Giving users of the mathematical software
  packages MATLAB and Maple access to NAGs library
  of highly optimized and often superior numerical
  routines
• NAG Fortran Compiler and GUI based Windows
  Compiler Fortran Builder
• Visualization and graphics software
• Build data visualization applications with NAGs
  IRIS Explorer
• Consultancy services

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Partnerships with leading academics

• University of Aachen
• Prof. Uwe Naumann
• Automatic Differentiation (AD)
• K.U. Leuven
• Prof. Wim Schoutens
• Option Pricing, Advanced Lévy models
• University of Manchester
• Profs. Nick Higham (FRS), Peter Duck and
  Ser-Huang Poon
• Copulas, EVTs, Nearest Correlation Matrix, PDEs,
  Risk,
• University of Oxford
• Profs. Mike Giles, Stephen Roberts
• Working with NAG to develop a Monte Carlo
  simulation engine with latest mathematics
  implemented on high-end SIMD architectures
  (GPUs).
• Algorithmic/Automated Trading
• Universita di Roma I
• Prof. Peter Laurence
• University of Warwick
• Prof. Nick Webber, Prof. Mark Salmon,
• Bayesian Stats, Copulas, Monte Carlo, Option
  Pricing, Wavelets

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NAG Libraries Availability

• Supporting Wide Range of O/S
• Windows
• Linux
• Mac
• Solaris
• AIX
• HPUX
• ..

• Support leading compilers
• (Fortran, C C)
• NAG
• Intel, Pathscale, PGI
• GCC, GFortran
• Absoft, Lahey, Visual C
• ..

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NAG Libraries Ease of Integration

• C (various)
• C / .NET
• Visual Basic
• Java
• Borland Delphi
• Python
• F
• and more

• Excel
• MATLAB
• Mathematica
• Maple
• LabVIEW
• R and S-Plus
• SAS
• and more

ltstart C\Program Files\NAG\FL21\fldll214ml\doc
user notes gt
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NAG and Excel..

• Our libraries are easily accessible from Excel
• Calling DLLs using VBA
• NAG provide VB Declaration Statements and
  Examples
• Excel Add-ins
• NAGs Statistical Add-in for Excel
• Sophisticated Add-in offering 76 statistical
  functions
• Function/ array driven
• NAG Schools Excel Add-in (N-SEA)
• Basic statistical functions including graphs
• Menu Drive

ltstart Excel here - miscgt
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Case study e04uc vs fmincon

• A problem from a customer from a European bank.
• The problem involves 48 variables and has 9
  linear constraints. (No nonlinear constraints.)
• No derivatives supplied.
• fmincon required 1890 evaluations of the
  objective function and tool 87.6 seconds
• e04uc required only 1129 evaluations and took
  49.4 seconds
• OTHER GOOD REFERENCES www.walkingrandomly.com

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Other NAG software

• NAGs High Performance libraries
• NAG SMP Library (for multi/many core/processor)
• NAG Parallel Library (for clusters architectures
  - MPI)
• NAG Library for .NET
• In beta release
• NAG Fortran Compiler
• Windows version with GUI Debugger
• Automatic Differentiation (AD) enabled
• In collaboration with RWTH Aachen University
• Routines for SIMD architectures (GPUs etc)
• Early successes with RNGs on NVIDIA hardware
• In collaboration with Professor Mike Giles
• Monte Carlo simulation engine

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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

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NAG Key Contacts

• www.nag.co.uk
• http//www.nag.co.uk/downloads/index.asp
• Technical Support and Help 01865 311 744
• support_at_nag.co.uk
• Commercial
• jan.smit_at_cosinus.nl
• susan.ing_at_nag.co.uk (BeNeLux Account Manager)
• NAGNews http//www.nag.co.uk/NAGNews/Index.asp

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Useful urls
NAG Products http//www.nag.co.uk/products_and_ser
vices.asp NAG C Library http//www.nag.co.uk/num
eric/CL/CLdescription.asp NAG Fortran Library
http//www.nag.co.uk/numeric/fl/FLdescription.asp
NAG Toolbox for MATLAB http//www.nag.co.uk/nume
ric/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_0
9/Tr4_09.asp NAG Data Mining Components
http//www.nag.co.uk/numeric/dr/drdescription.asp
NAG Fortran Builder http//www.nag.co.uk/nagware
/np/fortranbuilder.asp NAG and Excel
http//www.nag.co.uk/numeric/callingDLLsfromotherl
ang.asp NAG and Java http//www.nag.co.uk/doc/Te
chRep/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
NAGNews http//www.nag.co.uk/NAGNews/index.asp
technical articles and news
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The NAG Toolbox for MATLAB

• David Sayers

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Agenda

• Installation of the Toolbox
• Loading
• Behind the scenes whats happened
• Licence
• Checking installation
• NAG Toolbox for MATLAB Contents
• Fortran Library Contents names etc
• Documentation/Help system
• Requesting routines

NAG Toolbox for MATLAB
Saturday, 12 December 2009
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Agenda

• Using the Toolbox
• Simple Function
• Linear Algebra
• Integration, Optimisation
• Optional Parameters
• Error Mechanism
• Data Types
• User Workspace
• Whats New?
• Conclusions/ Questions

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Installing the Toolbox

• Insert CD Copies available and rely on
  automatic start.
• What has been copied ltSee Explorergt
• A licence is required by the underlying DLL
• Prompted for this during installation or
  afterwards from the START Menu

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Installing Toolbox
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Installing Toolbox
MBW3221DC TRIAL 2009/09/30 "h5pi6kwWpLeoxFiWYay7o4
OoHt"
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Installing the Toolbox

• Check successful implementation
• gtgt a00ac
• ans
• 1

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Installing Toolbox

• Check version
• gtgt a00aa
• NAG Toolbox for MATLAB implementation
  details
• Implementation title Win32/DLL/Intel Fortran
  9.1
• Precision FORTRAN double precision
• Product Code MBW3221DC
• Mark 21E
• End of implementation details

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Toolbox Contents

• Contains essentially all NAG functionality (1617
  user-callable routines at Mark 22)
• Not BLAS as these are present anyway
• Only thread safe versions of NAG routines e.g.
  e04uc is E04UCA not E04UCF.
• Not routines requiring an external file.

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Toolbox Contents

• Each routine has a self-contained document
• Description of method
• Specification of each parameter
• Explanation of error exit
• Document contains example program
• To illustrate calling the routine
• Source, output

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Toolbox Contents

• There are contents and an informative
  introduction to each chapter.
• Each routine in the chapter as its own
  documentation.
• All documentation is available through the MATLAB
  help system.
• If equations are difficult to read, use the
  alternative PDF versions of the documents by
  clicking on the links at the top of each page, or
  accessing them via the NAG website.

NAG Toolbox for MATLAB
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NAG Toolbox for MATLAB

• Lets take a look ...

lt show help gt lt look for gt lt help
contents gt lt chapter intros gt lt example
prog here gt
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Using the Toolbox

• Simple function
• No array arguments
• Linear Algebra
• No sparse array
• Complex arguments
• Int32 Integer arguments
• Integration, Optimisation
• No anonymous functions
• Two ways of passing information

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Optional Parameters

• Optional parameters are provided after all
  compulsory parameters.
• Optional parameters appear in pairs a string
  representing the name followed by the value.
• The pairs can be provided in any order.

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Optional Parameters

• Example
• aOut, ipiv, bOut, info f07aa(a, b,n,3)
• Uses the top 3 rows and columns of a

NAG Toolbox for MATLAB
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Optional Parameters

• Of course a similar outcome can be achieved by
• aOut, ipiv, bOut, info f07aa(a(13,13),
  b(13))
• This has the advantage of producing an aOut of
  the right size.

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Parameter-Setting Routines

• cwsav,lwsav,iwsav,rwsav,ifail e04wb('e04uc')
• lwsav, iwsav, rwsav, inform e04ue('Print
  Level 5', lwsav, iwsav, rwsav)
• ifail x04ad(int32(6)) Close channel 6
• ifail x04ac(int32(6), 'success.res',
  int32(1))
• iter, istate, c, cjac, clamda, objf, objgrd, r,
  x ...
• e04uc(a, bl, bu, 'e04uc_confun',
  'e04uc_objfun', istate, cjac, clamda, r, x,
  lwsav, iwsav, rwsav)

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Error Mechanism

• The NAG routines can return with a number of
  errors flagged
• NAGlicenceError - A valid licence couldnt be
  found.
• NAGarrayBoundError - Array provided is too
  small.
• NAGcallBackError - An error occurred when
  executing an M-File passed as a parameter to the
  routine.
• NAGmissingInputParameters
• NAGoptionalParameterError - Not in name/value
  pairs, or the name provided is not an optional
  parameter..

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Error Mechanism

• NAGtooManyOutputParameters
• NAGtypeError - A parameter is of the wrong type.
• NAGvalueError - An incorrect value has been
  provided for a parameter
• These cannot be trapped in the MATLAB Try Catch
  manner. (Well I havent managed to do so ?)
• Instead test the relevant ifail/info parameter

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Error Mechanism

• In most cases the error message will give more
  precise details of how the error was triggered.
  For example a NAGarrayBoundError might display
  the message
• ??? The dimension of parameter 2 (A) should be
  at least 4

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Error Mechanism

• The NAG routines can produce two warnings
• NAGtruncationWarning - A string was truncated
  when copying cell array of strings to a Fortran
  data structure.
• NAGwarning - The NAG routine returned an error
  or warning.
• The latter is important, and means that on exit
  the value of the parameter ifail /info) was
  non-zero.

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Error Mechanism

• If users do not wish to see a warning then they
  can disable it in the usual way, for example
• warning('off','NAGwarning')
• In this case it is vital that users check the
  value of ifail or info on exit from the routine.

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Data Types - Complex

• The statement c complex(x,y) returns
  the complex result x yi, where x and y are
  identically sized real arrays or scalars of the
  same data type.
• This is used in the NAG examples

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Data Types - Integers

• In general the Toolbox uses int32 integers.
• Use the int32 function to convert e.g.
• myint int32(n)
• 64 bit integers are available (for indexing
  purposes only) under Linux versions of MATLAB.
  NAG is producing a Toolbox to use these.

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User Workspace

• Many routines have parameters for user workspace,
  which are passed unchanged to user-supplied
  functions or subroutines.
• This allows data to be passed to these
  subprograms in a thread-safe way.
• Typically there are two or three such parameters,
  an integer and real array and, sometimes, a
  character array.
• In the MATLAB toolbox these are replaced by a
  single MATLAB object, to provide more
  flexibility.

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User Workspace

• Cell arrays provide a way to collect arrays of
  different size and types into a single array.
• We use the curly braces as a constructor
• gtgtC 13, pi magic(2), A string
• C
• 1x3 double 3.1416
• 2x2 double A string
• The contents of the cells can be displayed as
  arrays but using the curly braces
• gtgtC2,1(1,1)

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User Workspace

• For example in the following case user is a
  cell array containing three pieces of data
• x 0.5 1 1.5
• y 0.14,0.18,0.22, lt snip gt 2.10,4.39
• t 1.0, 15.0, 1.0,
• lt snip gt
• 15.0, 1.0, 1.0
• user y, t, 3
• xOut, fsumsq e04fy(int32(15),
  'e04fy_lsfun1', ...
• x, 'iuser', user)
• The data is then passed on to e04fy_lsfun1.m

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User Workspace

• Another scheme described in
• http//www.nag.co.uk/techtips/techtip036.asp
• is less elegant but possibly more efficient.
• global y t
• set up y, t
• lt prog calling routine with lsfun1 as argumentgt
• function fvecc, user lsfun1(m, n, xc, user)
• global y t
• ltetcgt

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Whats New?

• Uptodate list of implementations at
• http//www.nag.co.uk/numeric/MB/product_availabili
  ty.asp
• Linux systems call already use Mark22 NAG Toolbox
  for MATLAB. Windows systems will have a version
  available very shortly.

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Whats New?

• Global Optimisation
• Nearest Correlation Matrix
• Wavelet Transforms
• Partial Least Squares / Ridge Regression
• Derivative Pricing
• .
• http//www.nag.co.uk/numeric/mb/newatmark22.asp
• Some NAG demos included in Mark 22 release.

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Conclusions

• If you can use MATLAB then you can use the NAG
  Toolbox for MATLAB
• Makes whole areas of mathematics available
  without recourse to additional toolboxes.
• May obtain the equivalent libraries for use
  outside of MATLAB at no extra cost. (Yes if you
  have the MATLAB compiler this works with the NAG
  Toolbox)

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Questions?