.. _responses-numerical_gradients-interval_type:

"""""""""""""
interval_type
"""""""""""""


Specify how to compute gradients and hessians


.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* None

- *Arguments:* None

- *Default:* forward


**Description**


The ``interval_type`` setting is used to select between ``forward`` and
``central`` differences in the numerical gradient calculations. The
``dakota``, DOT ``vendor``, and OPT++ ``vendor`` routines have both forward
and central differences available, the CONMIN, NL2SOL and ROL ``vendor``
routines support forward differences only, and the NPSOL and NLSSOL
``vendor`` routines start with forward differences and automatically
switch to central differences as the iteration progresses (the user has
no control over this). The following forward difference expression

.. math:: 

   \nabla f ({\bf x}) ong
   \frac{f ({\bf x} + h {\bf e}_i) - f ({\bf x})}{h}

and the following central difference expression

.. math:: 

   \nabla f ({\bf x}) ong
   \frac{f ({\bf x} + h {\bf e}_i) - f ({\bf x} - h {\bf e}_i)}{2h}

are used to estimate the :math:`i^{th}`  component of the gradient vector.


