# Ipcs.m

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3D reconstruction of paramagnetic centre probability density from PCS data using Kuprov-Charnock equation (http://dx.doi.org/10.1039/C4CP03106G).

## Syntax

    [source_cube,ranges,pred_pcs,err_ls,reg_a,reg_b]=ipcs(parameters,npoints,lambda)


## Description

This function implements the three-dimensional paramagnetic centre probability density algorithm described in our forthcoming paper on the subject. The user needs to supply atomic coordinates and pseudocontact shifts. The algorithm uses Tikhonov regularisation. In the argument description below, "source" refers to the probability density of the paramagnetic centre that generates the pseudocontact shift, and "solution" refers to the pseudocontact shift itself.

## Arguments

    parameters.xyz      - nuclear coordinates as [x y z] with multiple rows
at which PCS has been measured, in Angstrom.

parameters.xyz_all  - atomic coordinates as [x y z] with multiple rows
for all atoms in the structure, in Angstrom.

parameters.expt_pcs - pseudocontact shift in ppm at each nucleus.

parameters.chi      - effective magnetic susceptibility tensor, in units
of Angstrom^3.

parameters.margins  - a six-element vector specifying margins to take
around the bounding box of the nuclear coordina-
tes supplied, to eliminate the effects of the
periodic boundary conditions.

parameters.box_cent - Cartesian coordinates of the centre of the source
box, in Angstrom

parameters.box_size - size of the source box in X, Y, and Z directions,
in Angstrom

parameters.plot     - a cell array of strings specifying the plotting
options at each iteration:

'diagnostics' - diagnostic output

'density'     - probability density

'molecule'    - molecular structure

'tightzoom'   - zooms the plot to the
molecular bounding box

'box'         - source box

parameters.confine  - source confinement radii (a two-element vector
in Angstrom). The density would only be varied
in points that are no closer than the first ra-
dius to any atom and no further away than the
second radius from the nearest atom.

parameters.sharpen  - source contrast control; leave at zero unless
you know what you are doing.

parameters.guess    - optional initial guess for the source density.
If this is supplied on a different grid from
the current one, it will be resampled by cubic
interpolation

parameters.gpu      - set to 1 of you have an NVidia GPU, otherwise
set to 0.

npoints             - number of grid points in each dimension of the
solution cube, a positive integer; at least 64
is recommended.

lambda              - Tikhonov regularization parameter; start with 1,
then use lcurve.m function to determine it
more precisely


## Returns

    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.

err_ls      - least squares penalty of the final source cube

reg_a       - contrast penalty of the final source cube

reg_b       - Tikhonov penalty of the final source cube


## Examples

See the pseudocontact shift analysis tutorial and the examples in nmr_paramag directory of the standard example set supplied with Spinach.

## Notes

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

## See also

Version 1.9, authors: Elizaveta Suturina, Gareth Charnock, Ilya Kuprov