Blurb::
Step size used when computing gradients and Hessians
Description::
``fd_step_size`` specifies the relative finite
difference step size to be used in the computations. Either a single
value may be entered for use with all parameters, or a list of step
sizes may be entered, one for each parameter.

The latter option of a list of step sizes is only valid for use with
the Dakota finite differencing routine. For Dakota with an interval
scaling type of ``absolute``, the differencing interval will be
``fd_step_size``.

For Dakota with and interval scaling type of ``bounds``, the
differencing intervals are computed by multiplying
``fd_step_size`` with the range of the parameter. For Dakota
(with an interval scaling type of ``relative``), DOT, CONMIN, and
OPT++, the differencing intervals are computed by multiplying the
``fd_step_size`` with the current parameter value. In this case,
a minimum absolute differencing interval is needed when the current
parameter value is close to zero. This prevents finite difference
intervals for the parameter which are too small to distinguish
differences in the response quantities being computed. Dakota, DOT,
CONMIN, and OPT++ all use <tt>.01*fd_step_size</tt> as their
minimum absolute differencing interval. With a
<tt>fd_step_size = .001</tt>, for example, Dakota, DOT,
CONMIN, and OPT++ will use intervals of .001*current value with a
minimum interval of 1.e-5. NPSOL and NLSSOL use a different formula
for their finite difference intervals:
<tt>fd_step_size*(1+|current parameter value|)</tt>. This
definition has the advantage of eliminating the need for a minimum
absolute differencing interval since the interval no longer goes to
zero as the current parameter value goes to zero.

ROL's finite difference step size can not be controlled via Dakota.
Therefore, ``fd_step_size`` will be ignored when ROL's finite
differencing routines are used (vendor FD gradients are specified).
ROL's differencing intervals are computed by multiplying the current
parameter value with the square root of machine precision.
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