Re: r22904 - /trunk/lib/dispersion/b14.py -- May 02, 2014

Hi Troels,

I have a few small points about this commit:

- Each paragraph should be on one line.  This is for better formatting
of the API documentation (http://www.nmr-relax.com/api/).  I.e. the
sentences of the same paragraph should not start on a the next line.

- An empty line between the text and "::" and the equation is
recommended - again for formatting in the API docs.

- One equation does not have the double colon :: at the end of the
introducing text.  This causes the API documentation build to fail
(try running "scons api_manual_html" to see the "Improper paragraph
indentation" warning message).

- Are the CR72 model links at the end correct?

Cheers,

Edward


On 1 May 2014 09:21,  <tlinnet@xxxxxxxxxxxxx> wrote:

Author: tlinnet
Date: Thu May  1 09:21:29 2014
New Revision: 22904

URL: http://svn.gna.org/viewcvs/relax?rev=22904&view=rev
Log:
Extended docstring in b14.py file.

sr #3154: (https://gna.org/support/?3154) Implementation of Baldwin (2014) 
B14 model - 2-site exact solution model for all time scales

Modified:
    trunk/lib/dispersion/b14.py

Modified: trunk/lib/dispersion/b14.py
URL: 
http://svn.gna.org/viewcvs/relax/trunk/lib/dispersion/b14.py?rev=22904&r1=22903&r2=22904&view=diff
==============================================================================
--- trunk/lib/dispersion/b14.py (original)
+++ trunk/lib/dispersion/b14.py Thu May  1 09:21:29 2014
@@ -1,6 +1,7 @@
 
###############################################################################
 #                                                                          
   #
 # Copyright (C) 2014 Troels E. Linnet                                      
   #
+# Copyright (C) 2014 Andrew Baldwin                                        
   #
 #                                                                          
   #
 # This file is part of the program relax (http://www.nmr-relax.com).       
   #
 #                                                                          
   #
@@ -20,7 +21,81 @@
 
###############################################################################

 # Module docstring.
-"""
+"""The Baldwin (2014) 2-site exact solution model for all time scales 
U{B14<http://wiki.nmr-relax.com/B14>}.
+
+Description
+===========
+
+This module is for the function, gradient and Hessian of the 
U{B14<http://wiki.nmr-relax.com/B14>} model.
+
+
+References
+==========
+
+The model is named after the reference:
+
+    - Andrew J. Baldwin (2014).  An exact solution for R2,eff in CPMG 
experiments in the case of two site chemical exchange.  I{J. Magn. Reson.}. 
 (U{DOI: 10.1016/j.jmr.2014.02.023 
<http://dx.doi.org/10.1016/j.jmr.2014.02.023>}).
+
+
+Equations
+=========
+
+The equation used is::
+            R2A0 + R2B0 + kex      Ncyc                      1      ( 1+y  
          1-y                          )
+    R2eff = ------------------ -  ------ * cosh^-1 * v1c - ------ ln( --- 
+ ------------------ * (v2 + 2*kAB*pD ) )
+                  2                Trel                     Trel    (  2   
 2*sqrt(v1c^2 -1 )                     )
+
+                            1      ( 1+y            1-y                    
      )
+          = R2eff(CR72) - ------ ln( --- + ------------------ * (v2 + 
2*kAB*pD ) )
+                           Trel    (  2    2*sqrt(v1c^2 -1 )               
      )
+
+Which have these following definitions::
+    v1c = F0 * cosh(tauCP * E0)- F2 * cosh(tauCP * E2)
+    v1s = F0 * sinh(tauCP * E0)- F2 * sinh(tauCP * E2)
+    v2*N = v1s * (OB-OA) + 4OB * F1^a * sinh(tauCP * E1)
+    pD N = v1s + (F1^a + F1^b) * sinh(tauCP * E1)
+    v3 = ( v2^2 + 4 * kBA * kAB * pD^2 )^1/2
+    y = ( (v1c-v3)/(v1c+v3) )^NCYC
+
+Note, E2 is complex. If |x| denotes the complex modulus:<br>
+    cosh(tauCP * E2) = cos(tauCP * |E2|)
+    sinh(tauCP * E2) = i sin(tauCP * |E2|)
+
+The term pD is based on product of the off diagonal elements in the CPMG 
propagator (Supplementary Section 3).
+
+It is interesting to consider the region of validity of the Carver 
Richards result.
+The two results are equal when the correction is zero, which is true when
+
+    sqrt(v1c^2-1) ~ v2 + 2*kAB * pD
+
+This occurs when 2*kAB * pD tends to zero, and so v2=v3.
+Setting "kAB * pD" to zero, amounts to neglecting magnetisation that 
starts on the ground state ensemble and end on the excited state ensemble 
and vice versa.
+This will be a good approximation when pA >> p_B.
+
+In practise, significant deviations from the Carver Richards equation can 
be incurred if pB > 1 %.
+Incorporation of the correction term into equation (50), results in an 
improved description of the CPMG experiment over the Carver Richards 
equation.
+
+kex is the chemical exchange rate constant, pA and pB are the populations 
of states A and B, and delta_omega is the chemical shift difference between 
the two states in ppm.
+
+
+Links
+=====
+
+More information on the B14 model can be found in the:
+
+    - U{relax wiki<http://wiki.nmr-relax.com/B14>},
+
+Comparison to CR72 model can be found in the:
+
+    - U{relax wiki<http://wiki.nmr-relax.com/CR72>},
+    - U{relax 
manual<http://www.nmr-relax.com/manual/reduced_CR72_2_site_CPMG_model.html>},
+    - U{relaxation dispersion page of the relax 
website<http://www.nmr-relax.com/analyses/relaxation_dispersion.html#CR72>}.
+
+Comparison to CR72 full model can be found in the:
+
+    - U{relax wiki<http://wiki.nmr-relax.com/CR72_full>},
+    - U{relax 
manual<http://www.nmr-relax.com/manual/full_CR72_2_site_CPMG_model.html>},
+    - U{relaxation dispersion page of the relax 
website<http://www.nmr-relax.com/analyses/relaxation_dispersion.html#CR72_full>}.
 """

 # Python module imports.


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Re: r22904 - /trunk/lib/dispersion/b14.py

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