.. algorithm::

.. summary::

.. relatedalgorithms::

.. properties::

Description
-----------

Given a set of peaks, and given lattice parameters
(:math:`a,b,c,alpha,beta,gamma`), this algorithm will find the
:ref:`UB matrix <Lattice>`, that best fits the data. The algorithm
searches over a large range of possible orientations for the orientation
for which the rotated B matrix best fits the data. The search for the
best orientation involves several steps.

During the first step, a reduced set of peaks typically at lower \|Q\|
are used, since it is easier to index peaks at low \|Q\|. Specifically,
if there are at least 5 peaks, the peaks are shifted to be centered at
the strongest peaks and then sorted in order of increasing distance from
the strongest peak. If there are fewer than 5 peaks the list is just
sorted in order of increasing \|Q\|. Only peaks from the initial portion
of this sorted list are used in the first step. The number of peaks from
this list to be used initially is specified by the user with the
parameter NumInitial. The search first finds a list of possible
orientations for which the :ref:`UB matrix <Lattice>` will index the maximum
number of peaks from the initial set of peaks to within the specified tolerance
on h,k,l values. Subsequently, only the :ref:`UB matrix <Lattice>` that indexes
that maximum number of peaks with the minimum distance between the calculated h,k,l
values and integers is kept and passed on to the second step.

During the second step, additional peaks are gradually added to the
initial list of peaks. Each time peaks are added to the list, the subset
of peaks from the new list that are indexed within the specified
tolerance on k,k,l are used in a least squares calculation to optimize
the :ref:`UB matrix <Lattice>` to best index those peaks. The process of
gradually adding more peaks from the sorted list and optimizing the UB based
on the peaks that are indexed, continues until all peaks have been added to
the list. Finally, one last optimization of the :ref:`UB matrix <Lattice>` is
carried out using the full list of peaks.

Usage
-----

**Example:**

.. testcode:: ExFindUBUsingLatticeParameters

    ws=LoadIsawPeaks("TOPAZ_3007.peaks")
    print("After LoadIsawPeaks does the workspace have an orientedLattice: {}".format(ws.sample().hasOrientedLattice()))

    FindUBUsingLatticeParameters(ws,a=14.131,b=19.247,c=8.606,alpha=90.0,beta=105.071,gamma=90.0,NumInitial=15)
    print("After FindUBUsingLatticeParameters does the workspace have an orientedLattice: {}".format(ws.sample().hasOrientedLattice()))

    print(ws.sample().getOrientedLattice().getUB())


Output:

.. testoutput:: ExFindUBUsingLatticeParameters

    After LoadIsawPeaks does the workspace have an orientedLattice: False
    After FindUBUsingLatticeParameters does the workspace have an orientedLattice: True
    [[ 0.04542062  0.04061954  0.01223576]
     [-0.00140377 -0.00318446 -0.11654506]
     [-0.05749773  0.03223779 -0.02737294]]

.. categories::

.. sourcelink::