Blurb::
Experimental capability to generate a random field representation. 
from data, from simulation 
runs, or from a covariance matrix.  The representation may then be sampled 
for use as a random field input to another simulation.  THIS IS AN EXPERIMENTAL CAPABILITY. 

Description::
Capability to generate a random field representation from data, from simulation 
runs, or from a covariance matrix.  The random field may then be sampled 
for use as a random field input to another simulation.  THIS IS AN EXPERIMENTAL CAPABILITY UNDER ACTIVE DEVELOPMENT. 

<b> Default Behavior </b>
There are three main sections of the \c random_field model. 
The first section tells Dakota what data to use to build the random field. 
This is specified with \c build_source.  The source of data to build the 
random field may be a file with data (where the N rows of data correspond to 
N samples of the random field and the M columns correspond to field values), 
or it may be a simulation that generates field data, or it may be specified 
given a mesh and a covariance matrix governing how the field varies over the mesh. 
In the case of using a simulation to generate field data, the simulation is 
defined with \c dace_method_pointer.  In the case of using a mesh and a 
covariance, the form of the covariance is defined with \c analytic_covariance. 

The next section of the random fiel model specifies the form of the expansion, 
\c expansion_form.  This can be either a Karhunen-Loeve expansion or a 
Principal components analysis.  These are very similar:  both involve the eigenvalues
of the covariance matrix of the field data.  The only difference is in the treatment 
of the estimation of the coefficients of the eigenvector basis functions.  In the 
PCA case, we have developed an approach which makes the coefficients explicit 
functions of the uncertain variables used to generate the random field. 
The specification of the random field can also include the number of bases 
to retain or a truncation tolerance, which defines the percent variance 
that the expansion should capture. 

The final section of the random field model allows the user to specify 
a pointer to a model over which the random field will be propagated,
meaning the model which will be driven with the random field input. 
This part of the specification is optional:  one can build a random field but 
not use it in a downstream model. 
 

Topics::

Examples::
As stated above, this is an emerging capability.  
The syntax currently looks like the following: 
\verbatim
random_field
   build_source
     rf_data_file | dace_method_pointer | analytic_covariance
   expansion_form
     karhunen_loeve | principal_components
     expansion_bases 
     truncation_tolerance 
   propagation_model_pointer 
\endverbatim


Theory::
Faq::
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