Mathematical and Visualization Software

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Mathematical and VisualizationSoftware

• By Ed Hall
• ITC Research Computing Support Group
• res-consult_at_virginia.edu

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Topics

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

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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.

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More General Advice

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

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Problem Solving Environments

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

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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

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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.

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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.

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Matlab Applications

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

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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/functi
  ons.shtml

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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.

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Matlab Examples

• gtgtdemos

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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

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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.

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Maple Functionality

• Over 3,000 computional functions.
• Symbolic and numeric coverage of many areas of
  mathematics.
• www.maplesoft.com/products/Maple7/functionality.sh
  tml
• New in Maple 7.0
• www.maplesoft.com/products/Maple7/benefits.shtml

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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

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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

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Mathematica Key Features (cont.)

• Smart Numerics adaptively choses best algorithm.
• Advanced Programming Methods.
• Tour of Features

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Mathematica Functionality

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

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Mathematica Inventor

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

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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

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IDL Key Features

• www.rsinc.com/idl/features.cfm
• Efficient image processing/visualization
• www.rsinc.com/gallery/index.cfm?productIDLProduc
  tFamilyID-100

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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?productIDL

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Gauss

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

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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

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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

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LabVIEW Analysis Tools

• www.ni.com/analysis/

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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

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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

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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

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Matlab C/C Math Libraries

• Overview
• www.mathworks.com/products/mathlibrary/description
  /overview.shtml
• Function Listing
• www.mathworks.com/products/mathlibrary/functions.s
  html

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Visualization Software

• IRIS Explorer
• XGobi and XGvis
• Grace

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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

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XGobi and XGvis

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

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Grace

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

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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