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Efficient Interval Matrix Computation with IntBLAS in C++

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This paper introduces IntBLAS, a powerful library for performing interval matrix computations in C++. It highlights the motivations for using interval arithmetic and the benefits of IntBLAS, including ease of installation and cross-platform compatibility. The library offers a comprehensive set of subroutines for basic interval arithmetic and linear algebra, encapsulated in a user-friendly package. Additionally, core and auxiliary classes manage interval objects efficiently. The document concludes with future work directions, including support for banded matrices and arbitrary precision arithmetic.

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Efficient Interval Matrix Computation with IntBLAS in C++

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  1. A Computational Environment for Interval Matrices in C++ Michael Nooner and Chenyi Hu Computer Science Department, University of Central Arkansas

  2. Introduction • Motivations • What is IntBLAS • Why use IntBLAS • The package

  3. Motivations • Profil, IntLAB, IntLib • Easy to use • Cross platform

  4. What Is IntBLAS • Interval BLAS Standard • Basic Interval Arithmetic Subroutines (IntLib) • Interval Basic Linear Algebra Subroutines • Level 1, 2, 3 • C++ Implementation • Three core objects • Three auxiliary objects

  5. Why use IntBLAS • Easy to install • GCC • Visual Studio • More on the way … • Cross Platform • Open Source (LGPL) • Well Documented • Easy to use

  6. The Package • One header • IntBLAS.h • Two Static Libraries • intblas.lib (optimized) • intblas_d.lib (debug) • One Namespace • intblas • One Initialization Function • INIT_INTERVAL()

  7. The Package #include<IntBLAS.h> using namespace intblas; int main() { INIT_INTERVAL(); Interval a( .1 ); IntervalMatrix m( 2, 2 ), result; m[0][0] = 2.3; m[0][1] = 3.3; m[1][0] = 5.5; m[1][1] = a; result = m + a;

  8. Core Classes

  9. Core Classes • Three Main Classes • Interval • IntervalVector • IntervalMatrix

  10. Interval Class • IntLib • Double precision • Rounding • Round Up: add one ε • Round Down: subtract one ε • 16th – 18th significant digit

  11. Interval Class • Arithmetic operators • Standard Functions • ipow, isin, isqrt, ilog, iatan … • Additional interval set routines • isEmpty(), midpoint(), width(), …

  12. IntervalVector and IntervalMatrix • BLAS Standard • Method/Function pairs double norm( NORMTYPE n ); friend double norm( IntervalMatrix& a, NORMTYPE n ); • Arithmetic operators • Assignment operator • Intermediate values

  13. Auxiliary Classes

  14. Error Handling • INTERVAL_EXCEPTION int code char msg[200] • Global Error Object • 32 predefined codes setError( int code, const char* msg = NULL ) getLastError()

  15. IntervalVectorT & IntervalMatrixT • Enables strong dimension checking • Typdef common matrices and vectorstypedef IntervalMatrixT<2,2> IMatrix2x2;. . .IMatrix2x2 m, n, o;

  16. Demo

  17. Problem • Solve the following set of linear equations:

  18. Problem • By paper the solution is

  19. Conclusion • Interval Basic Linear Algebra Subprograms • Easy to install • Cross Platform • Open Source • Well Documented • Easy to use • Download it from http://www.geocities.com/mike_nooner

  20. Future Work • Banded and Sparse Matrices • Arbitrary precision arithmetic • Fuzzy Logic Module • Interval Based LU Decomposition • Other cool stuff!

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