Blurb::
Samples variables along points moving out from a center point

Description::
Dakota's centered parameter study computes response data sets along
multiple coordinate-based vectors, one per parameter, centered about
the initial values from the variables specification. This is useful
for investigation of function contours with respect to each parameter
individually in the vicinity of a specific point (e.g.,
post-optimality analysis for verification of a minimum), thereby
avoiding the cost associated with a multidimensional grid.

<b> Default Behavior </b>

By default, the centered parameter study operates over all types of
variables.

The \c centered_parameter_study takes steps along each orthogonal
dimension. Each dimension is treated independently.  The number of
steps are taken in each direction, so that the total number of points
in the parameter study is \f$1+ 2\sum{n} \f$.

<b> Expected Outputs </b>

A centered parameter study produces a set of responses for each
parameter set that is generated.

<b> Expected HDF5 Output </b>

If Dakota was built with HDF5 support and run with the 
\ref environment-results_output-hdf5 keyword, this method
writes the following results to HDF5:

- \ref hdf5_results-pstudies
- \ref hdf5_results-var_slices

Topics::	parameter_studies
Examples::
The following example is a good comparison to the examples on
\ref method-multidim_parameter_study and \ref method-vector_parameter_study.

\verbatim
# tested on Dakota 6.0 on 140501
environment
  tabular_data
    tabular_data_file = 'rosen_centered.dat'

method
  centered_parameter_study
    steps_per_variable = 5 4
    step_vector = 0.4 0.5

model
  single

variables
  continuous_design = 2
    initial_point =   0        0
    descriptors =     'x1'     "x2"

interface
  analysis_driver = 'rosenbrock'
    fork

responses
  response_functions = 1
  no_gradients
  no_hessians

\endverbatim

Theory::
Faq::
See_Also::	method-multidim_parameter_study, method-list_parameter_study, method-vector_parameter_study
