Changeset 0391dae in sasview


Ignore:
Timestamp:
Sep 6, 2016 1:59:56 AM (2 years ago)
Author:
butler
Branches:
master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_Invariant, ESS_GUI_Pr_fixes, ESS_GUI_batch_fitting, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_ordering, SVCC-1, SasView-664, config-error, costrafo411, py37-all, py37-sascalc, py37-sasgui, pytest, release-4.1.1, release-4.1.2, release_4.0.1, setup_clean_up, simplify-c-build, ticket-1094-headless, ticket-1111, ticket-1205-fit-weights, ticket-1218, ticket-1220, ticket-818, ticket-933, ticket885, unittest-saveload, win64bit_conda_vm
Children:
fd196cb
Parents:
f9b0c81
Message:

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

File:
1 edited

Legend:

Unmodified
Added
Removed
  • src/sas/sasgui/perspectives/pr/media/pr_help.rst

    rb64b87c r0391dae  
    1515*P(r)* is set to be equal to an expansion of base functions of the type 
    1616 
    17   |bigphi|\_n(r) = 2.r.sin(|pi|\ .n.r/D_max) 
     17.. math:: 
     18  \Phi_{n(r)} = 2 r sin(\frac{\pi n r}{D_{max}}) 
    1819 
    19 The coefficient of each base function in the expansion is found by performing  
     20The coefficient of each base function in the expansion is found by performing 
    2021a least square fit with the following fit function 
    2122 
    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.. math:: 
    2324 
    24 where I\ :sub:`meas`\ (Q) is the measured scattering intensity and  
    25 I\ :sub:`th`\ (Q) is the prediction from the Fourier transform of the *P(r)*  
    26 expansion.  
     25  \chi^2=\frac{\sum_i (I_{meas}(Q_i)-I_{th}(Q_i))^2}{error^2}+Reg\_term 
     26   
    2727 
    28 The *Reg_term* term is a regularization term set to the second derivative  
    29 d\ :sup:`2`\ *P(r)* / dr\ :sup:`2` integrated over *r*. It is used to produce a  
    30 smooth *P(r)* output. 
     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. 
    3133 
    3234.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
     
    4547   system. 
    4648 
     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 
    4766.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
    4867 
     
    5574.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
    5675 
    57 .. note::  This help document was last changed by Steve King, 01May2015 
     76.. note::  This help document was last modified by Paul Butler, 05 September, 2016 
Note: See TracChangeset for help on using the changeset viewer.