Author: bugman
Date: Wed Dec 4 16:31:47 2013
New Revision: 21781
URL: http://svn.gna.org/viewcvs/relax?rev=21781&view=rev
Log:
Added the 'NS MMQ 3-site' parameters to the optimisation section of the
dispersion chapter of the manual.
Modified:
trunk/docs/latex/dispersion.tex
Modified: trunk/docs/latex/dispersion.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/dispersion.tex?rev=21781&r1=21780&r2=21781&view=diff
==============================================================================
--- trunk/docs/latex/dispersion.tex (original)
+++ trunk/docs/latex/dispersion.tex Wed Dec 4 16:31:47 2013
@@ -1224,9 +1224,16 @@
0 \leqslant \PhiexC \leqslant 10, \\
0 \leqslant \pA\dw^2 \leqslant 10, \\
0 \leqslant \dw \leqslant 10, \\
+ 0 \leqslant \dwAB \leqslant 10, \\
+ 0 \leqslant \dwBC \leqslant 10, \\
0 \leqslant \dwH \leqslant 3, \\
+ 0 \leqslant \dwHAB \leqslant 3, \\
+ 0 \leqslant \dwHBC \leqslant 3, \\
0.5 \leqslant \pA \leqslant 1, \\
+ 0.0 \leqslant \pB \leqslant 0.5, \\
0 \leqslant \kex \leqslant 1e^6, \\
+ 0 \leqslant \kexAB \leqslant 1e^6, \\
+ 0 \leqslant \kexBC \leqslant 1e^6, \\
0 \leqslant \kA \leqslant 1e^6, \\
0 \leqslant \kB \leqslant 1e^6, \\
0 \leqslant \kAB \leqslant 1e^6, \\
@@ -1238,7 +1245,11 @@
\begin{subequations}
\begin{gather}
-10 \leqslant \dw \leqslant 10, \\
- -3 \leqslant \dwH \leqslant 3.
+ -10 \leqslant \dwAB \leqslant 10, \\
+ -10 \leqslant \dwBC \leqslant 10, \\
+ -3 \leqslant \dwH \leqslant 3, \\
+ -3 \leqslant \dwHAB \leqslant 3, \\
+ -3 \leqslant \dwHBC \leqslant 3.
\end{gather}
\end{subequations}
@@ -1270,52 +1281,21 @@
To understand this section, please see Section~\ref{sect: constraint
algorithms} on page~\pageref{sect: constraint algorithms}.
For a dispersion analysis, linear constraints are the most useful type of
constraint.
-For most models, the linear constraints in the notation of \eqref{eq: linear
constraint} are
-\begin{small}
+For most models, the linear constraints in the notation of \eqref{eq: linear
constraint} for the relaxation rates are
\begin{equation}
\begin{pmatrix}
- 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
- -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
- 0 &-1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 &-1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &-1 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &-1 & 0 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &-1 & 0 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &-1 & 0 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &-1 & 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
+ 1 & 0 & 0 \\
+ -1 & 0 & 0 \\
+ 0 & 1 & 0 \\
+ 0 &-1 & 0 \\
+ 0 & 0 & 1 \\
+ 0 & 0 &-1 \\
\end{pmatrix}
\cdot
\begin{pmatrix}
\Rtwozero \\
\RtwozeroA \\
\RtwozeroB \\
- \Phiex \\
- \PhiexB \\
- \PhiexC \\
- \pA\dw^2 \\
- \dw \\
- \dwH \\
- \pA \\
- \kex \\
- \kB \\
- \kC \\
- \kAB \\
- \tex \\
\end{pmatrix}
\geqslant
\begin{pmatrix}
@@ -1325,15 +1305,108 @@
-200 \\
0 \\
-200 \\
+ \end{pmatrix},
+\end{equation}
+
+for the $\Phiex$ and $\dw$ parameters as
+\begin{equation}
+ \begin{pmatrix}
+ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
+ \end{pmatrix}
+ \cdot
+ \begin{pmatrix}
+ \Phiex \\
+ \PhiexB \\
+ \PhiexC \\
+ \pA\dw^2 \\
+ \dw \\
+ \dwAB \\
+ \dwBC \\
+ \dwH \\
+ \dwHAB \\
+ \dwHBC \\
+ \end{pmatrix}
+ \geqslant
+ \begin{pmatrix}
0 \\
0 \\
0 \\
0 \\
0 \\
0 \\
+ 0 \\
+ 0 \\
+ 0 \\
+ 0 \\
+ \end{pmatrix},
+\end{equation}
+
+for the population parameters as
+\begin{equation}
+ \begin{pmatrix}
+ -1 & 0 \\
+ 1 & 0 \\
+ 1 & 0 \\
+ -1 &-1 \\
+ 1 & 2 \\
+ \end{pmatrix}
+ \cdot
+ \begin{pmatrix}
+ \pA \\
+ \pB \\
+ \end{pmatrix}
+ \geqslant
+ \begin{pmatrix}
-1 \\
0.5 \\
0.85 \\
+ -1 \\
+ 1 \\
+ \end{pmatrix},
+\end{equation}
+
+and for the exchange rate and time parameters as
+\begin{equation}
+ \begin{pmatrix}
+ 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
+ -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
+ 0 &-1 & 0 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
+ 0 & 0 &-1 & 0 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
+ 0 & 0 & 0 &-1 & 0 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
+ 0 & 0 & 0 & 0 &-1 & 0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
+ 0 & 0 & 0 & 0 & 0 &-1 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
+ \end{pmatrix}
+ \cdot
+ \begin{pmatrix}
+ \kex \\
+ \kexAB \\
+ \kexBC \\
+ \kB \\
+ \kC \\
+ \kAB \\
+ \tex \\
+ \end{pmatrix}
+ \geqslant
+ \begin{pmatrix}
+ 0 \\
+ -2e^6 \\
+ 0 \\
+ -2e^6 \\
0 \\
-2e^6 \\
0 \\
@@ -1345,7 +1418,6 @@
0 \\
\end{pmatrix}.
\end{equation}
-\end{small}
\noindent Through the isolation of each individual element, the constraints
can be seen to be equivalent to
\begin{subequations}
@@ -1357,11 +1429,20 @@
\PhiexB \geqslant 0, \\
\PhiexC \geqslant 0, \\
\dw \geqslant 0, \\
+ \dwAB \geqslant 0, \\
+ \dwBC \geqslant 0, \\
\dwH \geqslant 0, \\
+ \dwHAB \geqslant 0, \\
+ \dwHBC \geqslant 0, \\
\pA\dw^2 \geqslant 0, \\
- \pB \leqslant \pA \leqslant 1, \\
+ \pA \geqslant 0, \\
+ \pB \geqslant 0, \\
+ \pC \geqslant 0, \\
+ \pC \leqslant \pB \leqslant \pA \leqslant 1, \\
\pA \geqslant 0.85 \quad (\textrm{the skewed condition, } \pA \gg \pB),
\\
0 \leqslant \kex \leqslant 2e^6, \\
+ 0 \leqslant \kexAB \leqslant 2e^6, \\
+ 0 \leqslant \kexBC \leqslant 2e^6, \\
0 \leqslant \kA \leqslant 2e^6, \\
0 \leqslant \kB \leqslant 2e^6, \\
0 \leqslant \kAB \leqslant 2e^6, \\
@@ -1382,24 +1463,25 @@
The concept of diagonal scaling is explained in Section~\ref{sect: diagonal
scaling} on page~\pageref{sect: diagonal scaling}.
For the dispersion analysis the scaling factor of 10 is used for the
relaxation rates, 1e$^5$ for the exchange rates, 1e$^{-4}$ for exchange
times, and 1 for all other parameters.
-The scaling matrix for the parameters \{$\Rtwozero$, $\RtwozeroA$,
$\RtwozeroB$, $\Phiex$, $\PhiexB$, $\PhiexC$, $\pA\dw^2$, $\dw$, $\dwH$,
$\pA$, $\kex$, $\kB$, $\kC$, $\kAB$, $\tex$\} is
+The scaling matrix for the parameters \{$\Rtwozero$, $\RtwozeroA$,
$\RtwozeroB$, $\Phiex$, $\PhiexB$, $\PhiexC$, $\pA\dw^2$, $\dw$, $\dwH$,
$\pA$, $\pB$, $\kex$, $\kB$, $\kC$, $\kAB$, $\tex$\} is
\begin{equation}
\begin{pmatrix}
- 10 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
& 0 \\
- 0 & 10 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
& 0 \\
- 0 & 0 & 10 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
& 0 \\
- 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
& 0 \\
- 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
& 0 \\
- 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
& 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0
& 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0
& 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0
& 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0
& 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1e^5 & 0 & 0 & 0
& 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1e^5 & 0 & 0
& 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1e^5 & 0
& 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1e^5
& 0 \\
- 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
& 1e^{-4} \\
+ 10 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
0 & 0 \\
+ 0 & 10 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
0 & 0 \\
+ 0 & 0 & 10 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
0 & 0 \\
+ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
0 & 0 \\
+ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 &
0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 &
0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 &
0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 &
0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1e^5 & 0 & 0 &
0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1e^5 & 0 &
0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1e^5 &
0 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
1e^5 & 0 \\
+ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
0 & 1e^{-4} \\
\end{pmatrix}.
\end{equation}
r21781 - /trunk/docs/latex/dispersion.tex