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.

*Default Behavior*

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

The ``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 :math:`1+ 2\sum{n}` .

*Expected Outputs*

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

*Expected HDF5 Output*

If Dakota was built with HDF5 support and run with the
:dakkw:`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
:dakkw:`method-multidim_parameter_study` and :dakkw:`method-vector_parameter_study`.


.. code-block::

    # 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
    


Theory::

Faq::

See_Also::
