.. _method-multidim_parameter_study:

""""""""""""""""""""""""
multidim_parameter_study
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Samples variables on full factorial grid of study points



**Topics**


parameter_studies


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

   method-multidim_parameter_study-partitions
   method-multidim_parameter_study-model_pointer


**Specification**

- *Alias:* None

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+--------------------+---------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword     | Dakota Keyword Description                  |
|                         | Group              |                    |                                             |
+=========================+====================+====================+=============================================+
| Required                                     | `partitions`__     | Samples variables on full factorial grid of |
|                                              |                    | study points                                |
+----------------------------------------------+--------------------+---------------------------------------------+
| Optional                                     | `model_pointer`__  | Identifier for model block to be used by a  |
|                                              |                    | method                                      |
+----------------------------------------------+--------------------+---------------------------------------------+

.. __: method-multidim_parameter_study-partitions.html
__ method-multidim_parameter_study-model_pointer.html



**Description**


Dakota's multidimensional parameter study computes response data sets
for an n-dimensional grid of points. Each continuous and discrete
range variable is partitioned into equally spaced intervals between
its upper and lower bounds, each discrete set variable is partitioned
into equally spaced index intervals. The partition boundaries in
n-dimensional space define a grid of points, and every point is
evaluated.

*Default Behavior*

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

*Expected Outputs*

A multidimensional 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-correlations`

*Usage Tips*

Since the initial values from the variables specification will not be
used, they need not be specified.



**Examples**


This example is taken from the Users Manual and is a good comparison to the examples on
:dakkw:`method-centered_parameter_study` and :dakkw:`method-vector_parameter_study`.

.. code-block::

    # tested on Dakota 6.0 on 140501
    environment
      tabular_data
        tabular_data_file = 'rosen_multidim.dat'
    
    method
      multidim_parameter_study
        partitions = 10 8
    
    model
      single
    
    variables
      continuous_design = 2
        lower_bounds     -2.0     -2.0
        upper_bounds      2.0      2.0
        descriptors       'x1'     "x2"
    
    interface
      analysis_driver = 'rosenbrock'
        fork
    
    responses
      response_functions = 1
      no_gradients
      no_hessians
    


This example illustrates the full factorial combinations of parameter values created
by the multidim_parameter_study. With 10 and 8 partitions, there are actually
11 and 9 values for each variable. This means that :math:`11 \times 9 = 99` 
function evaluations will be required.