.. _sd4:

*SD4*
=====

**SD4 module performs spatial decorrelation of fourth order
on the second order spatially whitened data**

SD4 module attempts to resolve the intrinsic non-orthogonal dependencies in atomistic fluctuations. The second order 
projections from SD2 are used to build a fourth order spatially correlated cumulant tensor. SD4 approximately diagonalizes
this tensor to return an anharmonic mode matrix. 

**Parameters** ::
 
                 Y       - an mxT spatially whitened matrix (m dimensionality of subspace, T snapshots). May be a numpy array or a matrix where,

                 m       - dimensionality of the subspace we are interested in. Defaults to None, in which case m=n. 

                 T       - number of snapshots of MD trajectory

                 U       - whitening matrix obtained after doing the PCA analysis on m components of real data 

                 verbose - print information on progress. Default is true.

**Returns** ::
 
                 W - a separating matrix for spatial decorrelation of order 4

.. Note:: 

          SD4 implementation using pyANCA is done by making use of TD4 module
          and setting the lag parameter as zero (lag=0)