A Computational Environment for Interval Matrices in C

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

Introduction 1. 2. 3. 4. Motivations What is Int. BLAS Why use Int. BLAS The package

Motivations • Profil, Int. LAB, Int. Lib • Easy to use • Cross platform

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

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

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

The Package #include <Int. BLAS. h> using namespace intblas; int main() { INIT_INTERVAL(); Interval a(. 1 ); Interval. Matrix 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;

Core Classes

Core Classes • Three Main Classes • Interval. Vector • Interval. Matrix

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

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

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

Auxiliary Classes

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

Interval. Vector. T & Interval. Matrix. T • Enables strong dimension checking • Typdef common matrices and vectors typedef Interval. Matrix. T<2, 2> IMatrix 2 x 2; . . . IMatrix 2 x 2 m, n, o;

Demo

Problem • Solve the following set of linear equations:

Problem • By paper the solution is

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

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