Intervals
Codac provides data structures for handling basic interval sets. These structures represent the building blocks of most domain structures provided in Codac. The elementary interval structures are:
The Interval class: represents a real bounded interval \([x^{-},x^{+}]\).
IntervalVector(orIntervalRow): represents a vector (or row) where each component is an interval.IntervalMatrix: represents a matrix where each element is an interval.
Integration with the Eigen library
The IntervalVector and IntervalMatrix structures of Codac are built upon the Eigen library, using the Interval type as a template parameter. Eigen is a well-known C++ library for linear algebra, providing optimized operations for vectors and matrices.
Leveraging Eigen offers several advantages:
Performance: Eigen provides highly optimized matrix and vector operations, making interval computations more efficient.
Flexibility: Using templates allows for seamless integration of interval arithmetic into Eigen’s existing functionalities.
Scalability: Eigen’s design allows for handling large-scale numerical computations effectively.
By building on Eigen, Codac ensures that interval arithmetic benefits from modern, high-performance linear algebra techniques.
However, some Eigen algorithms do not work with the Interval type as a template parameter. For instance, the decomposition of an IntervalMatrix will require a specific algorithm designed for intervals, instead of reals.
Some implementations are provided in Codac for interval algebra, see the dedicated pages of this manual.