Ipcs.m

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Solves the inverse problem for pseudocontact shift by recovering the source term in the Kuprov equation using Tikhonov + maximum entropy regularization procedure. Syntax:

    [source_cube,ranges,pred_pcs,diag_data]=...
                 ipcs(nxyz,expt_pcs,chi,npoints,lambda,margins)

Parameters:

    nxyz     - nuclear coordinates as [x y z] with multiple rows 
               at which PCS has been measured, in Angstroms.
    expt_pcs - pseudocontact shift in ppm at each nucleus.
    chi      - electron magnetic susceptibility tensor, in units
               of Angstrom^3.
    npoints  - number of points in each dimension of the source
               cube, a positive integer greater than 10.
    lambda   - regularization parameters, the first element is 
               the coefficient in front of the maximum entropy
               term and the second element is the coefficient in
               front of the Tikhonov term.
    margins  - a six-element vector specifying margins to take
               around the bounding box of the nuclear coordina-
               tes supplied, to account for the possibility that
               the electron may be located on the periphery.

Outputs:

    source_cube - source term cube with dimensions ordered as
                  [X Y Z].
    ranges      - Cartesian axis extents for the source cube as
                  [xmin xmax ymin ymax zmin zmax] in Angstroms.
    pred_pcs    - pseudocontact shifts produced by the source
                  cube returned in the first parameter.
    diag_data   - the first element is the least squares error
                  in ppm^2, the second element is the entropy
                  penalty in the error functional, the third
                  element is the tikhonov penalty in the error
                  functional.

Note: for further information on the equations and algorithms used in this function see http://dx.doi.org/10.1039/C4CP03106G