# Fdkup.m

From Spinach Documentation Wiki

Returns a finite difference representation of the Kuprov operator:

K[rho]=-(1/3)*Trace(Hessian[rho]*chi)

with the number of stencil points in the finite difference approximation specified by user. Syntax:

K=fdkup(npoints,extents,chi,nstenc)

The following parameters are needed:

npoints - a three-element vector specifying the dimensions of the 3D cube of data that the operator will be acting on, in Angstroms.

chi - the electron magnetic susceptibility tensor in cubic Angstroms.

extents - a three-element vector specifying axis extents in Angstroms.

nstenc - number of finite-difference stencil points for the finite-difference approximations.

The resulting operator is a sparse matrix designed to act on the vectorization of rho. The dimensions of rho are assumed to be ordered as [X Y Z].

For further details see http://dx.doi.org/10.1039/C4CP03106G.