Blurb::
Performs an incremental Latin Hypercube Sampling (LHS) study
Description::
Use of ``refinement_samples`` replaces
the deprecated ``sample_type`` ``incremental_lhs`` and
``sample_type`` ``incremental_random``.

An incremental random sampling approach will successively add
samples to an initial or existing random sampling study
according to the sequence of ``refinement_samples``. Dakota reports
statistics (mean, variance, percentiles, etc) separately for the
initial ``samples`` and for each ``refinement_samples`` increment at
the end of the study. For an LHS design, the number of
``refinement_samples`` in each refinement
level must result in twice the number of previous samples. For
``sample_type`` ``random``, there is no constraint on the number of
samples that can be added.

Often, this approach is used when you have an initial study with
sample size N1 and you want to perform an additional N1 samples.
The initial N1 samples may be contained in a Dakota restart file so
only N1 (instead of 2 x N1) potentially expensive function
evaluations will be performed.


This process can be extended by repeatedly increasing (for LHS: doubling)
the ``refinement_samples``:

.. code-block::

    method
      sampling
        seed = 1337
        samples = 50
        refinement_samples = 50 100 200 400 800


*Usage Tips*

The incremental approach is useful if it is uncertain how many
simulations can be completed within available time.

See the examples below and
the :ref:`running_dakota-usage<running_dakota-usage>` and :ref:`dakota_restart<dakota_restart>` pages.
Topics::

Examples::
Suppose an initial study is conducted using ``sample_type`` ``lhs``
with ``samples`` = 50.  A follow-on study uses a new input file where
``samples`` = 50, and ``refinement_samples`` = 50, resulting in 50
reused samples (from restart) and 50 new random samples.  The 50 new
samples will be combined with the 50 previous samples to generate a
combined sample of size 100 for the analysis.

One way to ensure the restart file is saved is to specify a non-default name,
via a command line option:

.. code-block::

    dakota -input LHS_50.in -write_restart LHS_50.rst


which uses the input file:


.. code-block::

    # LHS_50.in
    
    environment
      tabular_data
        tabular_data_file = 'LHS_50.dat'
    
    method
      sampling
        seed = 1337
        sample_type lhs
        samples = 50
    
    model
      single
    
    variables
      uniform_uncertain = 2
        descriptors  =   'input1'     'input2'
        lower_bounds =  -2.0     -2.0
        upper_bounds =   2.0      2.0
    
    interface
      analysis_drivers 'text_book'
        fork
    
    responses
      response_functions = 1
      no_gradients
      no_hessians

and the restart file is written to ``LHS_50``.rst.


Then an incremental LHS study can be run with:

.. code-block::

    dakota -input LHS_100.in -read_restart LHS_50.rst -write_restart LHS_100.rst

where ``LHS_100``.in is shown below, and ``inLHS_50``.rst is the restart
file containing the results of the previous LHS study. In the example input
files for the initial and incremental studies, the values for ``seed`` match.
This ensures that the initial 50 samples generated in both runs are the same.

.. code-block::

    # LHS_100.in
    
    environment
      tabular_data
        tabular_data_file = 'LHS_100.dat'
    
    method
      sampling
        seed = 1337
        sample_type lhs
        samples = 50
          refinement_samples = 50
    
    model
      single
    
    variables
      uniform_uncertain = 2
        descriptors  =   'input1'     'input2'
        lower_bounds =  -2.0     -2.0
        upper_bounds =   2.0      2.0
    
    interface
      analysis_drivers 'text_book'
        fork
    
    responses
      response_functions = 1
      no_gradients
      no_hessians


The user will get 50 new LHS samples which
maintain both the correlation and stratification of the original LHS
sample. The new samples will be combined with the original
samples to generate a combined sample of size 100.
Theory::

Faq::

See_Also::
