The document outlines various mathematical and visualization software tools, including Matlab, Mathematica, Maple, IDL, Gauss, and LabVIEW, emphasizing their key features and functionalities for scientific computing. It provides general advice on effective computational practices and the importance of stability in scientific calculations. Additionally, it mentions relevant scientific computing libraries and visualization software used in data analysis and presentation.

1. Mathematical and Visualization
Software
By Ed Hall
ITC Research Computing Support Group
res-consult@virginia.edu

2. Topics
• Problem Solving Environments
• Scientific Computing Libraries
• Data Visualization
• Scientific Word Processing
• www.itc.virginia.edu/researchers/services.html

3. General Advice
• Branches of Science: Theory, Experiment,
Computation.
• The purpose of computing is insight, not
pictures/numbers.
• Use software to vary parameters, modify
problem, play around.
• Take advantage of software tools.

4. More General Advice
• If the answer is highly sensitive to
perturbations, you’ve probably asked the
wrong question.
• Scientific calculation must be stable before
being accurate.
• Large scale computations will inevitably
be carried out in parallel.

5. Problem Solving Environments
• Matlab
• Mathematica
• Maple
• IDL
• Gauss
• LabView
• PSE homepage
www-cgi.cs.purdue.edu/cgi-bin/acc/pses.cgi

6. MATLAB
• MAtrix LABoratory, Cleve Moler founder.
• Integrates mathematical computing,
visualization, programming language.
• Can integrate external routines written in
C/C++, Fortran, and Java.
• Widely used in science and engineering
• www.itc.virginia.edu/research/matlab.html

7. Matlab Key Features
• Numeric computing for quick and accurate
results.
• Graphics to visualize and analyze data.
• Interactive language and programming
environment.
• Tools for building custom GUIs.
• Interfaces to External Languages: C/C++,
Fortran, LabView.

8. Matlab Key Features (cont.)
• Support for wide range of Input/Output.
• Conversion of Matlab applications to
C/C++ with Compiler Suite.
• Advanced Data Analysis Suite.
• Image Processing Suite.
• Platform independent.

9. Matlab Applications
• Data analysis and exploration.
• Visualization and image processing.
• Algorithm prototyping and development.
• Modeling and simulation.
• Programming and application development.

10. Matlab Functionality
• Linear algebra and matrix computations.
• Fourier and statistical analysis functions.
• Differential equation solvers.
• Sparse matrix support.
• Trigonometric and other fundamental math
operations.
• Multidimensional data support.
• www.mathworks.com/products/matlab/functions/f

11. Simulink
• Interactive Tool for modeling, simulating,
and analyzing dynamic systems.
• Visual programming using graphical block
diagrams.
• Simulation applications include DSP ,
control system, and communication systems
design.

12. Matlab Examples
• >>demos

13. Maple
• Numeric and symbolic computation.
• Arbitrary precision numeric calculations.
• Math functionality, graphics capabilites,
and extendable programming language.
• Math typeset document interface.
• Integration with NAG Libraries.
• www.itc.virginia.edu/research/maple.html

14. Maple Key Features
• Maple Application Center
• Maple PowerTools
• Web connectivity: TC/IP sockets, XML and
MathML 2.0.
• Application connectivity: MS Excel,
Matlab, and C or Fortran.

15. Maple Functionality
• Over 3,000 computional functions.
• Symbolic and numeric coverage of many
areas of mathematics.
• www.maplesoft.com/products/Maple7/functionali
• New in Maple 7.0
www.maplesoft.com/products/Maple7/benefits.shtm

16. Mathematica
• Numeric and symbolic computation.
• Arbitrary precision numeric calculations.
• Math functionality, graphics capabilites,
and extendable programming language.
• Math typeset document interface.
• www.itc.virginia.edu/research/mathematica.html

17. Mathematica Key Features
• Sophisticated Technical Environment.
• Notebook document for electronic and print
distribution: HTML, Latex, RTF, MathML.
• Fast numeric calculation.
• Fully integrated hypertext Help Browser.
• MathLink protocol allows connection C/C+
+, Fortran, Java, and LabView.
• Mathematica in a Nutshell

18. Mathematica Key Features
(cont.)
• Smart Numerics: adaptively choses best
algorithm.
• Advanced Programming Methods.
• Tour of Features

19. Mathematica Functionality
• Standard Add-On Packages (> 1000
functions)
Algebra,Calculus, Discrete Mathematics,
Geometry, Graphics, Linear Algebra,
Number Theory, and Statistics.
• Application Packages
www.wolfram.com/products/applications/

20. Mathematica Inventor
• Stephen Wolfram, physicist
www.stephenwolfram.com/about-sw/interviews/
• His Book “New Kind of Science”
www.wolframscience.com/

21. IDL
• Interactive Data Language.
• Data analysis and visualization software.
• Extendable programming language.
• Widely used in Astronomy and biomedical
imaging.
• www.itc.virginia.edu/research/idl.html

22. IDL Key Features
• www.rsinc.com/idl/features.cfm
• Efficient image processing/visualization
www.rsinc.com/gallery/index.cfm?product=IDL&P

23. IDL Functionality
• Summary.
www.rsinc.com/idl/detail.cfm
• Wavelet Toolkit
www.rsinc.com/idl/Wavelet.cfm
• IDL Tech Tips
www.rsinc.com/services/prodspec.cfm?product=ID

24. Gauss
• Fast, extendable, matrix programming
language.
• Mathematical and statistical numerics.
• Used by statisticians, biometricians,
econometricians.
• www.itc.virginia.edu/research/gauss.html

25. Gauss Functionality
• www.aptech.com/weblist.pdf
• 400 built-in functions: BLAS, LINPACK,
EISPACK.
• Interface to Fortran or C.
• Gauss Applications
www.aptech.com/s2_apps.html

26. LabVIEW
• Provide virtual instrument interface for
data acquisition, control, and analysis.
• Dataflow Graphical programming
environment.
• Create standalone applications.
• www.itc.virginia.edu/research/labview.html
• Hands-on Seminar Oct. 4-5

27. LabVIEW Analysis Tools
• www.ni.com/analysis/

28. Scientific Computing Libraries
• IMSL (International Mathematical
Subroutine Libraries)
• NCAR (National Center for Atmospheric
Research)
• Matlab C/C++
• Related Software.
www.itc.virginia.edu/research/mathvislinks.html

29. IMSL
• Fortran77/Fortran90 subroutines.
• MPI-enhanced functionality for parallel
computing.
www.vni.com/products/imsl/f90_mpi.html
• Numerical Functionality.
www.vni.com/products/imsl/fortfunc.html
• www.itc.virginia.edu/research/imsl.html

30. NCAR Graphic Libraries
• Fortran/C graphic utilities.
http://ngwww.ucar.edu/ng4.2/whatisncarg.html
• Examples.
http://ngwww.ucar.edu/ng4.2/examples.html
• www.itc.virginia.edu/research/ncar.html

31. Matlab C/C++ Math Libraries
• Overview
www.mathworks.com/products/mathlibrary/descrip
• Function Listing
www.mathworks.com/products/mathlibrary/fu
nctions.shtml

32. Visualization Software
• IRIS Explorer
• XGobi and XGvis
• Grace

33. IRIS Explorer
• Visual programming environment for 3-D
visualization.
• Built useing OpenGL.
• Case Studies:
www.nag.co.uk/visual/IE/iecbb/Posters/Index.
html
• www.itc.virginia.edu/research/iris.html

34. XGobi and XGvis
• XGobi for multivariate data visualization.
• XGvis for multidimensional scaling.
• www.research.att.com/areas/stat/xgobi/

35. Grace
• Wysiwyg for two-dimensional plots of
numerical data.
www.itc.virginia.edu/research/xmgrace_docs/

36. Scientific Word Processing
• Latex: Standard for scientific word
processing using typeset math notation.
• www.itc.virginia.edu/research/latex.html
• Scientific Word provides Latex wysiwyg.
www.mackichan.com/products/sw30.html
• Gimp: GNU image manipulation program.
• www.itc.virginia.edu/research/gimp.html