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1559 mathematical and visualization software

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Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics

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1559 mathematical and visualization software

  1. 1. Mathematical and Visualization Software By Ed Hall ITC Research Computing Support Group res-consult@virginia.edu
  2. 2. Topics • Problem Solving Environments • Scientific Computing Libraries • Data Visualization • Scientific Word Processing • www.itc.virginia.edu/researchers/services.html
  3. 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. 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. 5. Problem Solving Environments • Matlab • Mathematica • Maple • IDL • Gauss • LabView • PSE homepage www-cgi.cs.purdue.edu/cgi-bin/acc/pses.cgi
  6. 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. 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. 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. 9. Matlab Applications • Data analysis and exploration. • Visualization and image processing. • Algorithm prototyping and development. • Modeling and simulation. • Programming and application development.
  10. 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. 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. 12. Matlab Examples • >>demos
  13. 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. 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. 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. 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. 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. 18. Mathematica Key Features (cont.) • Smart Numerics: adaptively choses best algorithm. • Advanced Programming Methods. • Tour of Features
  19. 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. 20. Mathematica Inventor • Stephen Wolfram, physicist www.stephenwolfram.com/about-sw/interviews/ • His Book “New Kind of Science” www.wolframscience.com/
  21. 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. 22. IDL Key Features • www.rsinc.com/idl/features.cfm • Efficient image processing/visualization www.rsinc.com/gallery/index.cfm?product=IDL&P
  23. 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. 24. Gauss • Fast, extendable, matrix programming language. • Mathematical and statistical numerics. • Used by statisticians, biometricians, econometricians. • www.itc.virginia.edu/research/gauss.html
  25. 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. 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. 27. LabVIEW Analysis Tools • www.ni.com/analysis/
  28. 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. 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. 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. 31. Matlab C/C++ Math Libraries • Overview www.mathworks.com/products/mathlibrary/descrip • Function Listing www.mathworks.com/products/mathlibrary/fu nctions.shtml
  32. 32. Visualization Software • IRIS Explorer • XGobi and XGvis • Grace
  33. 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. 34. XGobi and XGvis • XGobi for multivariate data visualization. • XGvis for multidimensional scaling. • www.research.att.com/areas/stat/xgobi/
  35. 35. Grace • Wysiwyg for two-dimensional plots of numerical data. www.itc.virginia.edu/research/xmgrace_docs/
  36. 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

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