Mathematical and VisualizationSoftware

By Ed HallITC Research Computing Support Group

res-consult@virginia.edu

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

LabVIEW Analysis Tools

• www.ni.com/analysis/

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