Using Adifor to Compute Dense and Sparse Jacobians

ADIFOR is a source translator that, given a collection of Fortran subroutines for the computation of a \function," produces Fortran code for the computation of the derivatives of this function. More speciically, ADIFOR produces code to compute the matrix-matrix product JS, where J is the Jacobian of the \function" with respect to the user-deened independent variables, and S is the composition of the derivative objects corresponding to the independent variables. This interface is exible; by setting S = x, one can compute the matrix-vector product Jx, or by setting S = I, one can compute the whole Jacobian J. Other initializations of S allow one to exploit a known sparsity structure of J. This paper illustrates the proper initialization of ADIFOR-generated derivative codes and the exploitation of a known sparsity structure of J.