# source:sasview/src/sas/sasgui/perspectives/pr/media/pr_help.rst@0391dae

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[ec392464]1.. pr_help.rst
2
3.. This is a port of the original SasView html help file to ReSTructured text
4.. by S King, ISIS, during SasView CodeCamp-III in Feb 2015.
5
[b64b87c]6P(r) Calculation
7================
[ec392464]8
[8a22b5b]9Description
10-----------
[ec392464]11
[8a22b5b]12This tool calculates a real-space distance distribution function, *P(r)*, using
13the inversion approach (Moore, 1908).
14
15*P(r)* is set to be equal to an expansion of base functions of the type
16
[0391dae]17.. math::
18  \Phi_{n(r)} = 2 r sin(\frac{\pi n r}{D_{max}})
[ec392464]19
[0391dae]20The coefficient of each base function in the expansion is found by performing
[8a22b5b]21a least square fit with the following fit function
22
[0391dae]23.. math::
[ec392464]24
[0391dae]25  \chi^2=\frac{\sum_i (I_{meas}(Q_i)-I_{th}(Q_i))^2}{error^2}+Reg\_term
26
[ec392464]27
[0391dae]28where $I_{meas}(Q_i)$ is the measured scattering intensity and $I_{th}(Q_i)$ is
29the prediction from the Fourier transform of the *P(r)* expansion.
30
31The $Reg\_term$ term is a regularization term set to the second derivative
32$d^2P(r)/d^2r$ integrated over $r$. It is used to produce a smooth *P(r)* output.
[ec392464]33
[8a22b5b]34.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
[ec392464]35
[b64b87c]36Using P(r) inversion
37--------------------
[ec392464]38
[8a22b5b]39The user must enter
40
41*  *Number of terms*: the number of base functions in the P(r) expansion.
[ec392464]42
[8a22b5b]43*  *Regularization constant*: a multiplicative constant to set the size of
[ec392464]44   the regularization term.
45
[8a22b5b]46*  *Maximum distance*: the maximum distance between any two points in the
[ec392464]47   system.
[8a22b5b]48
[0391dae]49P(r) inversion requires that the background be perfectly subtracted.  This is
50often difficult to do well and thus many data sets will include a background.
51For those cases, the user should check the "estimate background" box and the
52module will do its best to estimate it.
53
54The P(r) module is constantly computing in the background what the optimum
55*number of terms* should be as well as the optimum *regularization constant*.
56These are constantly updated in the buttons next to the entry boxes on the GUI.
57These are almost always close and unless the user has a good reason to choose
58differently they should just click on the buttons to accept both.  {D_max} must
59still be set by the user.  However, besides looking at the output, the user can
60click the explore button which will bring up a graph of chi^2 vs Dmax over a
61range around the current Dmax.  The user can change the range and the number of
62points to explore in that range.  They can also choose to plot several other
63parameters as a function of Dmax including: I0, Rg, Oscillation parameter,
64background, positive fraction, and 1-sigma positive fraction.
65
[8a22b5b]66.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
67
68Reference
69---------
70
71P.B. Moore
72*J. Appl. Cryst.*, 13 (1980) 168-175
73
74.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
75
[0391dae]76.. note::  This help document was last modified by Paul Butler, 05 September, 2016
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