The NAG Toolbox for MATLAB

1. The NAG Toolbox for MATLAB University of Cambridge Mick Pont, John Holden - NAG

2. 2 The NAG Toolbox for MATLAB Agenda… NAG licences at Cambridge   NAG Toolbox for MATLAB Optimization and other topics

3. 3 The NAG Toolbox for MATLAB Licences at the University of Cambridge Site Licence Covering: NAG’s Serial Libraries Fortran 77, 90, C & DMC NAG’s High Performance Libraries SMP & Parallel Fortran Compiler and Fortran Tools: NAG Toolbox for MATLAB

4. 4 The NAG Toolbox for MATLAB What does the University licence cover? Unlimited use for the licensed implementations As long as for academic or research purposes Installation may be on any university, staff or student machine Full access to NAG Support support@nag.co.uk Better to use an @xxxx.ac.uk e-mail address Our software: Includes online documentation - also www.nag.co.uk Supplied with extensive example programs data and results

5. 5 The NAG Toolbox for MATLAB How do I get the software? Help yourself from: http://www.nag.co.uk/downloads/index.asp Get on the official NAG / University of Cambridge list to get permanent licence keys: http://sales-web-server.csx.cam.ac.uk/software/ or e-mail: sales@ucs.cam.ac.uk Temporary Licence keys via support@nag.co.uk

6. 6 The NAG Toolbox for MATLAB Technical Agenda The NAG Engine Wrapper functionality Algorithmic contents Navigating around the NAG toolbox in MATLAB NAG Optimization Chapters Random numbers

7. 7 The NAG Toolbox for MATLAB The NAG Engine

8. 8 The NAG Toolbox for MATLAB NAG Libraries Ease of Integration C++ (various) C# / .NET Visual Basic Java Borland Delphi Python … … and more Excel MATLAB Maple LabVIEW R and S-Plus SAS Simfit … and more http://www.nag.co.uk/numeric/LabView.asp http://www.nag.co.uk/numeric/LabView.asp

9. 9 The NAG Toolbox for MATLAB NAG Toolbox for MATLAB Built as MATLAB mex files Auto-generated from XML documentation Contains essentially all NAG functionality not a subset Currently runs under Windows (32-bit) or Linux (32/64-bit) Installed under the usual MATLAB toolbox directory Makes use of a DLL or shared version of the NAG Library

10. 10 The NAG Toolbox for MATLAB NAG Library 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 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

11. 11 The NAG Toolbox for MATLAB NAG naming scheme Based on ACM modified SHARE classification John Bolstad - A proposed classification scheme for computer program libraries. ACM SIGNUM Newsletter, November 1975 References: Nottingham (England) Algorithms Group, First Annual Report, June, 1974. Routines separated into chapters Each routine has a 5-letter base name for ease of classification, e.g. (MATLAB/Fortran / C) c06eb / C06EBF / c06ebc nag_fft_hermitian (long name for readability) Each routine is independently documented, with complete example program

12. 12 The NAG Toolbox for MATLAB Chapter e04 – Minimization / Maximization

13. 13 The NAG Toolbox for MATLAB Unconstrained optimization

14. 14 The NAG Toolbox for MATLAB Linearly constrained optimization

15. 15 The NAG Toolbox for MATLAB Nonlinear constraints

16. 16 The NAG Toolbox for MATLAB Chapter e04

17. 17 The NAG Toolbox for MATLAB E04WD Sequential quadratic programming (SQP) algorithm obtains search directions from a sequence of QP subproblems. designed for problems with many variables and constraints P. Gill (San Diego), W. Murray (Stanford) and M. Saunders (Stanford)

18. 18 The NAG Toolbox for MATLAB Chapter e04

19. 19 The NAG Toolbox for MATLAB Some routines available in Chapter e04 e04ab: minimize a function of one variable e04dg: minimization using conjugate gradients e04mf: linear programming e04nc: linear least-squares e04nf: quadratic programming e04nq: LP or QP (for sparse problems) e04un: nonlinear least-squares e04vh: general sparse constrained nonlinear e04wd: general nonlinear all-purpose etc.

20. 20 The NAG Toolbox for MATLAB New optimization coming at next Mark

21. 21 The NAG Toolbox for MATLAB Local optimization

22. 22 The NAG Toolbox for MATLAB Global requirements

23. 23 The NAG Toolbox for MATLAB New NAG Chapter – E05 Main routine named E05JB Plus initialization and option setting routines Currently handles only bound constraints:

24. 24 The NAG Toolbox for MATLAB Chapter g05 – Random Numbers

25. 25 The NAG Toolbox for MATLAB Chapter g05 – Random Numbers

26. 26 The NAG Toolbox for MATLAB Some routines available in Chapter g05 g05ca: pseudo-random from uniform distribution g05cb / g05cc: initialize generator to repeatable or non-repeatable sequence respectively g05db: exponential distribution g05dd: normal distribution g05fe: beta distribution g05ff: gamma distribution g05ya: quasi-random numbers Other distributions, plus GARCH, copula, etc.

27. 27 The NAG Toolbox for MATLAB Pseudo- versus Quasi-Random Numbers

28. 28 The NAG Toolbox for MATLAB Other NAG software We’d welcome contact on our other software: Maple-NAG Connector NAG's Excel related products Fortran Builder (NAG’s Windows Fortran compiler) New library functionality NAG’s High Performance libraries ..

29. 29 The NAG Toolbox for MATLAB NAG Toolbox for MATLAB - summary