Documentation

HCL_LinearOp_d is the base class for all linear operators. This class represents a linear operator mapping one vector space to another. The primary methods are:

• Domain Returns a reference to the domain of the operator. This is used primarily for error-checking.
• Range Returns a reference to the range of the operator. This is used primarily for error-checking.
• Image Computes the action of the operator on a vector. Here is an example illustrating the use of Domain, Range, and Image:

     void fcn( HCL_LinearOp_d & L,HCL_Vector_d & x,HCL_Vector_d & y )
     {
        if( x.Space() != L.Domain() || y.Space() != L.Range() )
           // Error condition
        .
        .
        .
        L.Image( x,y ); // y <-- Lx
        .
        .
        .
     }
  

Note that this class makes no assumption about the representation of the operator. Examples include operators defined by dense or sparse matrices and solution operators of (linear) PDEs defined by simulations.