Changeset 0391dae in sasview

Timestamp:

Sep 6, 2016 1:59:56 AM (8 years ago)

Author:

butler

Branches:

master, 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, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload

Children:

fd196cb

Parents:

f9b0c81

Message:

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

File:

• src/sas/sasgui/perspectives/pr/media/pr_help.rst (modified) (3 diffs)

src/sas/sasgui/perspectives/pr/media/pr_help.rst

@@ -15 +15 @@
 *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
@@ -45 +47 @@
    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
 
@@ -55 +74 @@
 .. 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