Dakota Reference Manual: fd_step_size

| Dakota Reference Manual Version 6.15 Explore and Predict with Confidence

- Main Page
- Related Pages

All Pages
fd_step_size

Step size used when computing gradients and Hessians

## Specification

Alias: fd_gradient_step_size

Argument(s): REALLIST

Default: 0.001

## 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 `.01*fd_step_size` as their minimum absolute differencing interval. With a `fd_step_size = .001`, 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: `fd_step_size*(1+|current parameter value|)`. 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.