Modifying Smolyak Sweeps
========================

Extending
---------

If a Smolyak Sweep does not produce a good response surface, it is likely
because the polynomial level was set too low.  Fortunately we can easily
extend a previous run, increasing its level by one. This is actually very
efficient because each level uses all the information from the lower level.
So some additional jobs will run and those results will be combined with
all the previous results.  For example::

    ~/puq/examples/rosen> puq extend sweep_140682290.hdf5
    Extending sweep_140682290.hdf5 using Smolyak
    Extending Smolyak to level 4

    Processing <HDF5 dataset "z": shape (65,), type "<f8">
	    Surface   = 100.0*x**4 - 200.0*x**2*y + 1.0*x**2 - 2.0*x + 100.0*y**2 + 1.0
	    RMSE      = 3.96e-09 (1.10e-10 %)

    SENSITIVITY:
    Var      u*            dev
    -----------------------------
    x    5.0835e+03    6.9637e+03
    y    1.9661e+03    1.7441e+03


.. _smolyak_mod:

Modifying Parameters & Reusing Response Surfaces
------------------------------------------------

Sometimes after you run a simulation, you get new information that causes you to adjust
your input parameters by a bit. Perhaps a new set of measurements allowed you to tighten
up the deviation a bit. Or maybe the mean shifted some.  If the input range has not widened significantly, the response
surface should still be valid and you can use it with your updated input PDF(s). All PUQ has
to do is sample the response surface with the updated PDF(s) to generate new output
PDF(s).

For example, take a look at puq/examples/test1.

.. literalinclude:: ../../../examples/test1/test1.py
    :linenos:
    :language: python

Run it to generate the response surface::

	~/puq/examples/test1> puq start test1
	Saving run to sweep_145215760.hdf5

	Processing <HDF5 dataset "kinetic_energy": shape (29,), type "<f8">
		Surface   = 0.5*m*v**2
		RMSE      = 4.15e-08 (3.53e-10 %)

	SENSITIVITY:
	Var      u*            dev
	-----------------------------
	v    8.7761e+03    3.0974e+03
	m    2.7263e+03    1.6263e+03
	~/puq/examples/test1> mv sweep_145215760.hdf5 test1.hdf5

Later you want to recompute the output with new input PDFs. You will need to put the
new Parameters in a file, with the same names (the first arg to *Parameter*). For example,

.. literalinclude:: ../../../examples/test1/new_pdfs.py
    :language: python

Then you do 'puq plot --using filename'::

	/puq/examples/test1> puq plot --using new_pdfs.py  test1.hdf5
	plotting PDF for kinetic_energy
	REPLACING
		NormalParameter m (mass)
		PDF [63.9 - 126] 100 intervals
	    mean=95  dev=7.99  mode=94.7
	WITH
		NormalParameter m (mass)
		PDF [85.5 - 124] 100 intervals
	    mean=105  dev=5  mode=105

	REPLACING
		NormalParameter v (velocity)
		PDF [4.16 - 15.8] 100 intervals
	    mean=10  dev=1.5  mode=9.94
	WITH
		NormalParameter v (velocity)
		PDF [7.11 - 14.9] 100 intervals
	    mean=11  dev=0.999  mode=11

test2.py is test1.py updated with the new parameters.  You can do 'puq start' on it and compute a new response surface and PDF
from scratch.  It should match the one from test1 using the new parameters.

.. note:: PDFs are plotted by sampling the response surface with random numbers generated by the input PDFs.  The resulting plot has some minor variances due to the randomness of the inputs.



.. figure:: images/test1.png
	:align: left
	:width: 500px

	**PDF from test1.py**

.. figure:: images/test1_new.png
	:align: left
	:width: 500px

	**PDF from test1 --using new_pdfs.py**

.. figure:: images/test2.png
	:align: right
	:width: 500px

	**PDF from test2.py.**