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[49148bb]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
6P(r) Inversion Perspective
7==========================
8
9Description
10-----------
11
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
17  |bigphi|\_n(r) = 2.r.sin(|pi|\ .n.r/D_max)
18
19The coefficient of each base function in the expansion is found by performing
20a least square fit with the following fit function
21
22  |chi|\ :sup:`2` = |bigsigma|\ :sub:`i` [ I\ :sub:`meas`\ (Q\ :sub:`i`\ ) - I\ :sub:`th`\ (Q\ :sub:`i`\ ) ] :sup:`2` / (Error) :sup:`2` + Reg_term
23
24where I\ :sub:`meas`\ (Q) is the measured scattering intensity and
25I\ :sub:`th`\ (Q) is the prediction from the Fourier transform of the *P(r)* 
26expansion.
27
28The *Reg_term* term is a regularization term set to the second derivative
29d\ :sup:`2`\ *P(r)* / dr\ :sup:`2` integrated over *r*. It is used to produce a
30smooth *P(r)* output.
31
32.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
33
34Using the perspective
35---------------------
36
37The user must enter
38
39*  *Number of terms*: the number of base functions in the P(r) expansion.
40   
41*  *Regularization constant*: a multiplicative constant to set the size of
42   the regularization term.
43
44*  *Maximum distance*: the maximum distance between any two points in the
45   system.
46
47.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
48
49Reference
50---------
51
52P.B. Moore
53*J. Appl. Cryst.*, 13 (1980) 168-175
54
55.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
56
57.. note::  This help document was last changed by Steve King, 01May2015
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