Author: bugman
Date: Thu Sep 6 10:59:01 2012
New Revision: 17468
URL: http://svn.gna.org/viewcvs/relax?rev=17468&view=rev
Log:
Editing of the "Values, gradients, and Hessians" chapter of the user manual
to make it fit better.
The context of this chapter has been specified by changing the title to
"Optimisation of relaxation
data -- values, gradients, and Hessians" and the intro text has been updated.
As this chapter is no
longer straight after the model-free chapter, this is needed.
Modified:
trunk/docs/latex/maths.tex
Modified: trunk/docs/latex/maths.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/maths.tex?rev=17468&r1=17467&r2=17468&view=diff
==============================================================================
--- trunk/docs/latex/maths.tex (original)
+++ trunk/docs/latex/maths.tex Thu Sep 6 10:59:01 2012
@@ -1,7 +1,7 @@
% Values, gradients, and Hessians.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\chapter{Values, gradients, and Hessians} \label{ch: values, gradients, and
Hessians}
+\chapter{Optimisation of relaxation data -- values, gradients, and Hessians}
\label{ch: values, gradients, and Hessians}
@@ -11,7 +11,7 @@
\section{Introduction}
-A word of warning before reading this chapter, the topics covered here are
quite advanced and are not necessary for understanding how to either use
relax or to implement any of the data analysis techniques present within
relax. The material of this chapter is intended as an in-depth explanation
of the mathematics involved in the optimisation of the parameters of the
model-free models. As such it contains the chi-squared equation, relaxation
equations, spectral density functions, and diffusion tensor equations as well
as their gradients (the vector of first partial derivatives) and Hessians
(the matrix of second partial derivatives). All these equations are used in
the optimisation of models $m0$ to $m9$; models $tm0$ to $tm9$; the
ellipsoidal, spheroidal, and spherical diffusion tensors; and the combination
of the diffusion tensor and the model-free models.
+A word of warning before reading this chapter, the topics covered here are
quite advanced and are not necessary for understanding how to either use
relax or to implement any of the data analysis techniques present within
relax. The material of this chapter is intended as an in-depth explanation
of the mathematics involved in the optimisation of the parameters of the
model-free models, or any theory involving relaxation data. As such it
contains the chi-squared equation, relaxation equations, spectral density
functions, and diffusion tensor equations as well as their gradients (the
vector of first partial derivatives) and Hessians (the matrix of second
partial derivatives). All these equations are used in the optimisation of
model-free models $m0$ to $m9$; models $tm0$ to $tm9$; the ellipsoidal,
spheroidal, and spherical diffusion tensors; and the combination of the
diffusion tensor and the model-free models. They also apply to all other
theories involving the base $\Rone$, $\Rtwo$, and steady-state NOE relaxation
rates.
r17468 - /trunk/docs/latex/maths.tex