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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
6.. |pi| unicode:: U+03C0
7.. |bigphi| unicode:: U+03A6
8.. |bigsigma| unicode:: U+03A3
9.. |chi| unicode:: U+03C7
10
11P(r) Inversion Perspective
12==========================
13
14Description
15-----------
16
17This tool calculates a real-space distance distribution function, *P(r)*, using
18the inversion approach (Moore, 1908).
19
20*P(r)* is set to be equal to an expansion of base functions of the type
21
22  |bigphi|\_n(r) = 2.r.sin(|pi|\ .n.r/D_max)
23
24The coefficient of each base function in the expansion is found by performing
25a least square fit with the following fit function
26
27  |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
28
29where I\ :sub:`meas`\ (Q) is the measured scattering intensity and
30I\ :sub:`th`\ (Q) is the prediction from the Fourier transform of the *P(r)*
31expansion.
32
33The *Reg_term* term is a regularization term set to the second derivative
34d\ :sup:`2`\ *P(r)* / dr\ :sup:`2` integrated over *r*. It is used to produce a
35smooth *P(r)* output.
36
37.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
38
39Using the perspective
40---------------------
41
42The user must enter
43
44*  *Number of terms*: the number of base functions in the P(r) expansion.
45   
46*  *Regularization constant*: a multiplicative constant to set the size of
47   the regularization term.
48
49*  *Maximum distance*: the maximum distance between any two points in the
50   system.
51
52.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
53
54Reference
55---------
56
57P.B. Moore
58*J. Appl. Cryst.*, 13 (1980) 168-175
59
60.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
61
62.. note::  This help document was last changed by Steve King, 01May2015
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