# Changeset 6027eb3 in sasview

Ignore:
Timestamp:
Sep 15, 2016 8:33:57 AM (5 years ago)
Branches:
ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc
Children:
4c930a2
Parents:
35f4d43
git-author:
paul butler <butlerpd@…> (09/06/16 01:59:56)
git-committer:
Piotr Rozyczko <rozyczko@…> (09/15/16 08:33:57)
Message:

update Pr documentation on how to use and converted equations to LaTex?.

File:
1 edited

### Legend:

Unmodified
 r1f1e4f0 *P(r)* is set to be equal to an expansion of base functions of the type |bigphi|\_n(r) = 2.r.sin(|pi|\ .n.r/D_max) .. math:: \Phi_{n(r)} = 2 r sin(\frac{\pi n r}{D_{max}}) The coefficient of each base function in the expansion is found by performing The coefficient of each base function in the expansion is found by performing a least square fit with the following fit function |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 .. math:: where I\ :sub:meas\ (Q) is the measured scattering intensity and I\ :sub:th\ (Q) is the prediction from the Fourier transform of the *P(r)* expansion. \chi^2=\frac{\sum_i (I_{meas}(Q_i)-I_{th}(Q_i))^2}{error^2}+Reg\_term The *Reg_term* term is a regularization term set to the second derivative d\ :sup:2\ *P(r)* / dr\ :sup:2 integrated over *r*. It is used to produce a smooth *P(r)* output. where $I_{meas}(Q_i)$ is the measured scattering intensity and $I_{th}(Q_i)$ is the prediction from the Fourier transform of the *P(r)* expansion. The $Reg\_term$ term is a regularization term set to the second derivative $d^2P(r)/d^2r$ integrated over $r$. It is used to produce a smooth *P(r)* output. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ system. P(r) inversion requires that the background be perfectly subtracted.  This is often difficult to do well and thus many data sets will include a background. For those cases, the user should check the "estimate background" box and the module will do its best to estimate it. The P(r) module is constantly computing in the background what the optimum *number of terms* should be as well as the optimum *regularization constant*. These are constantly updated in the buttons next to the entry boxes on the GUI. These are almost always close and unless the user has a good reason to choose differently they should just click on the buttons to accept both.  {D_max} must still be set by the user.  However, besides looking at the output, the user can click the explore button which will bring up a graph of chi^2 vs Dmax over a range around the current Dmax.  The user can change the range and the number of points to explore in that range.  They can also choose to plot several other parameters as a function of Dmax including: I0, Rg, Oscillation parameter, background, positive fraction, and 1-sigma positive fraction. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ .. note::  This help document was last changed by Steve King, 01May2015 .. note::  This help document was last modified by Paul Butler, 05 September, 2016