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Mathematical and VisualizationSoftware
By Ed HallITC Research Computing Support Group
Topics
• Problem Solving Environments• Scientific Computing Libraries• Data Visualization • Scientific Word Processing• www.itc.virginia.edu/researchers/services.html
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.
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.
Problem Solving Environments• Matlab• Mathematica• Maple• IDL• Gauss• LabView• PSE homepagewww-cgi.cs.purdue.edu/cgi-bin/acc/pses.cgi
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
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.
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.
Matlab Applications
• Data analysis and exploration.• Visualization and image processing.• Algorithm prototyping and development.• Modeling and simulation.• Programming and application development.
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/funct
ions/functions.shtml
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.
Matlab Examples
• >>demos
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
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.
Maple Functionality
• Over 3,000 computional functions.• Symbolic and numeric coverage of many
areas of mathematics.• www.maplesoft.com/products/Maple7/funct
ionality.shtml• New in Maple 7.0www.maplesoft.com/products/Maple7/benefits.shtml
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
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
Mathematica Key Features (cont.)
• Smart Numerics: adaptively choses best algorithm.
• Advanced Programming Methods.• Tour of Features
Mathematica Functionality
• Standard Add-On Packages (> 1000 functions)
Algebra,Calculus, Discrete Mathematics, Geometry, Graphics, Linear Algebra, Number Theory, and Statistics.
• Application Packageswww.wolfram.com/products/applications/
Mathematica Inventor
• Stephen Wolfram, physicistwww.stephenwolfram.com/about-sw/interviews/• His Book “New Kind of Science”www.wolframscience.com/
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
IDL Key Features
• www.rsinc.com/idl/features.cfm• Efficient image processing/visualizationwww.rsinc.com/gallery/index.cfm?product=IDL&ProductFamilyID=-100
IDL Functionality
• Summary.www.rsinc.com/idl/detail.cfm• Wavelet Toolkit www.rsinc.com/idl/Wavelet.cfm• IDL Tech Tipswww.rsinc.com/services/prodspec.cfm?product=IDL
Gauss
• Fast, extendable, matrix programming language.
• Mathematical and statistical numerics. • Used by statisticians, biometricians,
econometricians.• www.itc.virginia.edu/research/gauss.html
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
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
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
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
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
Matlab C/C++ Math Libraries
• Overviewwww.mathworks.com/products/mathlibrary/description/overview.shtml• Function Listingwww.mathworks.com/products/mathlibrary/
functions.shtml
Visualization Software
• IRIS Explorer• XGobi and XGvis• Grace
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
XGobi and XGvis
• XGobi for multivariate data visualization.• XGvis for multidimensional scaling.• www.research.att.com/areas/stat/xgobi/
Grace
• Wysiwyg for two-dimensional plots of numerical data.
www.itc.virginia.edu/research/xmgrace_docs/
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