5. 2 Linearized Expressions as Data Types

The implementation of linearized expressions as data types can be performed via operator overloading. The class comprises an associative data structure, e.g. a map which is used to assign each solution variable a coefficient. If the matrix is sparse, the use of a map seems to be more appropriate, because only few values have to be stored. It is also possible to integrate line-wise compressed data structures of a matrix data type into the linearized equation interface. If full matrices are used, the appropriate data structure for the linear expression is a simple vector or an array. However, for the following considerations the map related implementation is preferred.