Reverse Communication Interface

The reverse communication  interface is one of the most important aspects of the design of ARPACK. This interface avoids having to express a matrix-vector product through a subroutine with a fixed calling sequence. This means that the user is free to choose any convenient data structure for the matrix representation. Moreover, if the matrix is not available explicitly, the user is free to express the action of the matrix on a vector through a subroutine call or a code segment. It is not necessary to conform to a fixed format for a subroutine interface and hence there is no need to communicate data through the use of COMMON .

A typical usage of this interface is illustrated with the example in Figure 1.1. This shows a code segment of the routine the user must write to set up the reverse communication call to the top level ARPACK routine snaupd to solve a nonsymmetric eigenvalue problem. As usual, with reverse communication, control is returned to the calling program when interaction with the matrix ${\bf A}$ is required. The action requested of the calling program is simply to perform the task indicated by the reverse communication parameter ido  (in this case multiply the vector held in the array workd beginning at location ipntr(1) and inserting the result into the array workd beginning at location ipntr(2)). Note that the call to the subroutine matvec in this code segment is simply meant to indicate that this matrix-vector operation is taking place. The user is free to use any available mechanism or subroutine to accomplish this task. In particular, no specific data structure is imposed and indeed, no explicit representation of the matrix is even required. One only needs to supply the action of the matrix on the specified vector.

  

Figure 1.1: An example of the reverse communication interface used by ARPACK.

 10  continue
     call snaupd (ido, bmat, n, which,...,workd,..., info)
     if (ido .eq. newprod) then
        call matvec ('A', n, workd(ipntr(1)), workd(ipntr(2)))
     else
        return
     endif
     go to 10