TaoAppDefaultComputeGradient(TAO_APPLICATION, Vec, Vec, void*);,
TaoAppDefaultComputeHessian( TAO_APPLICATION, Vec, Mat*, Mat*, MatStructure*, void*);and
TaoAppDefaultComputeHessianColor( TAO_APPLICATION, Vec, Mat*, Mat*, MatStructure*, void* );These routines can be set using TaoAppSetGradientRoutine() and TaoAppSetHessianRoutine() or through the options database. If finite differencing is used with coloring, the routine
TaoAppSetColoring(TAO_APPLICATION, ISColoring);should be used to specify the coloring.
It is also possible to use finite difference approximations to directly check the correctness of an application's gradient and/or Hessian evaluation routines. This can be done using the special TAO solver tao_fd_test together with the options -tao_test_gradient or -tao_test_hessian.