7 files changed, 193 insertions, 65 deletions
diff --git a/inst/doc/Makefile b/inst/doc/Makefile
index 637b193..26fe678 100644
--- a/inst/doc/Makefile
+++ b/inst/doc/Makefile
@@ -1,6 +1,6 @@
 # Makefile for Sweave documents containing both Latex and R code
 # Author:	Johannes Ranke <jranke@uni-bremen.de>
-# Last Change: 2006 Mai 10
+# Last Change: 2006 Mai 11
 # based on the Makefile of Nicholas Lewin-Koh
 # in turn based on work of Rouben Rostmaian
 # SVN: $Id: Makefile.rnoweb 50 2006-04-18 11:13:52Z ranke $
@@ -14,14 +14,8 @@ TARGETS = $(patsubst %.Rnw,%.tex,$(RNWFILE)) $(patsubst %.Rnw,%.pdf,$(RNWFILES))
 %.pdf: %.tex
 	pdflatex $<
 
-all: all-recursive $(TARGETS)
+all: $(TARGETS)
 
-clean: clean-recursive
+clean: 
 	rm -f *.aux *.log *.bbl *.blg *.brf *.cb *.ind *.idx *.ilg  \
           *.inx *.ps *.dvi *.toc *.out *.lot *~ *.lof *.ttt *.fff
-
-all-recursive:
-	for dir in $(wildcard *); do if [ -d $$dir ] && [ -f $$dir/Makefile ]; then cd $$dir; $(MAKE) all; cd ..; fi; done
-
-clean-recursive:
-	for dir in $(wildcard *); do if [ -d $$dir ] && [ -f $$dir/Makefile ]; then cd $$dir; $(MAKE) clean; cd ..; fi; done
diff --git a/inst/doc/chemCal-001.pdf b/inst/doc/chemCal-001.pdf
index e5c8f5f..6e2f9b8 100644
--- a/inst/doc/chemCal-001.pdf
+++ b/inst/doc/chemCal-001.pdf
@@ -2,8 +2,8 @@
 %佲併佅佊\r
 1 0 obj
 <<
-/CreationDate (D:20060510174125)
-/ModDate (D:20060510174125)
+/CreationDate (D:20060511175039)
+/ModDate (D:20060511175039)
 /Title (R Graphics Output)
 /Producer (R 2.3.0)
 /Creator (R)
diff --git a/inst/doc/chemCal.Rnw b/inst/doc/chemCal.Rnw
index 2c902ab..26b224f 100644
--- a/inst/doc/chemCal.Rnw
+++ b/inst/doc/chemCal.Rnw
@@ -20,7 +20,7 @@ inverse prediction method given in \cite{massart97} would be implemented,
 since it also covers the case of weighted regression.
 
 At the moment, the package only consists of two functions, working
-on univariate linear models of class \texttt{lm}.
+on univariate linear models of class \texttt{lm} or \texttt{rlm}.
 
 When calibrating an analytical method, the first task is to generate
 a suitable model. If we want to use the \chemCal{} functions, we
@@ -59,9 +59,9 @@ given by the user in the case of weighted regression. By default,
 the mean of the weights used in the linear regression is used.
 
 \section*{Theory}
-Equation 8.28 in \cite{massart97} gives a general equation for predicting x
-from measurements of y according to the linear calibration function
-$ y = b_0 + b_1 \cdot x$:
+Equation 8.28 in \cite{massart97} gives a general equation for predicting the
+standard error $s_{\hat{x_s}}$ for an x value predicted from measurements of y
+according to the linear calibration function $ y = b_0 + b_1 \cdot x$:
 
 \begin{equation}
 s_{\hat{x_s}} = \frac{s_e}{b_1} \sqrt{\frac{1}{w_s m} + \frac{1}{\sum{w_i}} +
@@ -72,9 +72,30 @@ s_{\hat{x_s}} = \frac{s_e}{b_1} \sqrt{\frac{1}{w_s m} + \frac{1}{\sum{w_i}} +
 with
 
 \begin{equation}
-s_e = \sqrt{ \frac{\sum w_i (y_i - \hat{y})^2}{n - 2}}
+s_e = \sqrt{ \frac{\sum w_i (y_i - \hat{y_i})^2}{n - 2}}
 \end{equation}
 
+where $w_i$ is the weight for calibration standard $i$, $y_i$ is the mean $y$
+value (!) observed for standard $i$, $\hat{y_i}$ is the estimated value for
+standard $i$, $n$ is the number calibration standards, $w_s$ is the weight
+attributed to the sample $s$, $m$ is the number of replicate measurements of
+sample $s$, $\bar{y_s}$ is the mean response for the sample, 
+$\bar{y_w} = \frac{\sum{w_i y_i}}{\sum{w_i}}$ is the weighted mean of responses
+$y_i$, and $x_i$ is the given $x$ value for standard $i$.
+
+The weight $w_s$ for the sample should be estimated or calculated in accordance
+to the weights used in the linear regression. 
+
+I adjusted the above equation in order to be able to take a different precisions
+in standards and samples into account. In analogy to Equation 8.26 from \cite{massart97}
+we get
+
+\begin{equation}
+s_{\hat{x_s}} = \frac{1}{b_1} \sqrt{\frac{{s_s}^2}{w_s m} + 
+    {s_e}^2 \left( \frac{1}{\sum{w_i}} +
+        \frac{(\bar{y_s} - \bar{y_w})^2 \sum{w_i}}
+            {{b_1}^2 \left( \sum{w_i} \sum{w_i {x_i}^2} - {\left( \sum{ w_i x_i } \right)}^2 \right) } \right) }
+\end{equation}
 
 \begin{thebibliography}{1}
 \bibitem{massart97}
diff --git a/inst/doc/chemCal.aux b/inst/doc/chemCal.aux
index 0eb51cc..20bfc98 100644
--- a/inst/doc/chemCal.aux
+++ b/inst/doc/chemCal.aux
@@ -14,4 +14,5 @@
 \citation{massart97}
 \citation{massart97}
 \citation{massart97}
+\citation{massart97}
 \bibcite{massart97}{1}
diff --git a/inst/doc/chemCal.log b/inst/doc/chemCal.log
index fadbc89..805f382 100644
--- a/inst/doc/chemCal.log
+++ b/inst/doc/chemCal.log
@@ -1,4 +1,4 @@
-This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=pdflatex 2006.4.5)  10 MAY 2006 17:41
+This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=pdflatex 2006.4.5)  11 MAY 2006 17:50
 entering extended mode
 **chemCal.tex
 (./chemCal.tex
@@ -129,7 +129,7 @@ Style option: `fancyvrb' v2.6, with DG/SPQR fixes <1998/07/17> (tvz)
 \FV@OutFile=\write4
 
 No file fancyvrb.cfg.
-) (/usr/share/texmf-tetex/tex/latex/upquote/upquote.sty
+) (/usr/share/R/share/texmf/upquote.sty
 Package: upquote 2003/08/11 v1.1 Covington's upright-quote modification to verb
 atim and verb
 
@@ -301,64 +301,49 @@ LaTeX Font Info:    Try loading font information for T1+aett on input line 16.
  (/usr/share/texmf-tetex/tex/latex/ae/t1aett.fd
 File: t1aett.fd 1997/11/16 Font definitions for T1/aett.
 )
-
-LaTeX Warning: Citation `massart97' on page 1 undefined on input line 20.
-
 <chemCal-001.pdf, id=7, 433.62pt x 433.62pt>
 File: chemCal-001.pdf Graphic file (type pdf)
  <use chemCal-001.pdf> [1
 
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-
-LaTeX Warning: Citation `massart97' on page 2 undefined on input line 50.
-
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-(Font)              using `TS1/cmr/m/n' instead
-(Font)              for symbol `textasciigrave' on input line 65.
-
-
-LaTeX Warning: Citation `massart97' on page 2 undefined on input line 81.
+ (/usr/share/R/share/texmf/ts1aett.fd
+File: ts1aett.fd 
+)
+LaTeX Font Info:    Try loading font information for TS1+cmtt on input line 65.
 
+ (/usr/share/texmf-tetex/tex/latex/base/ts1cmtt.fd
+File: ts1cmtt.fd 1999/05/25 v2.5h Standard LaTeX font definitions
+)
+LaTeX Font Info:    Font shape `TS1/aett/m/n' in size <10> not available
+(Font)              Font shape `TS1/cmtt/m/n' tried instead on input line 65.
 LaTeX Font Info:    External font `cmex10' loaded for size
-(Font)              <7> on input line 83.
+(Font)              <7> on input line 82.
 LaTeX Font Info:    External font `cmex10' loaded for size
-(Font)              <5> on input line 83.
-[2 <./chemCal-001.pdf>] [3] (./chemCal.aux)
-
-LaTeX Font Warning: Some font shapes were not available, defaults substituted.
-
-
-LaTeX Warning: There were undefined references.
-
-
-LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.
-
- ) 
+(Font)              <5> on input line 82.
+ [2 <./chemCal-001.pdf>]
+[3] (./chemCal.aux) ) 
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+</usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmr17.pfb>
+Output written on chemCal.pdf (3 pages, 107614 bytes).
diff --git a/inst/doc/chemCal.pdf b/inst/doc/chemCal.pdf
index b0da323..e3c6a8c 100644
--- a/inst/doc/chemCal.pdf
+++ b/inst/doc/chemCal.pdf
diff --git a/inst/doc/chemCal.tex b/inst/doc/chemCal.tex
new file mode 100644
index 0000000..a4b4459
--- /dev/null
+++ b/inst/doc/chemCal.tex
@@ -0,0 +1,127 @@
+\documentclass[a4paper]{article}
+%\VignetteIndexEntry{Short manual for the chemCal package}
+\newcommand{\chemCal}{{\tt chemCal}}
+\newcommand{\calplot}{{\tt calplot}}
+\newcommand{\calpredict}{{\tt calpredict}}
+\newcommand{\R}{{\tt R}}
+\usepackage{hyperref}
+
+\title{Basic calibration functions for analytical chemistry}
+\author{Johannes Ranke}
+
+\usepackage{/usr/share/R/share/texmf/Sweave}
+\begin{document}
+\maketitle
+
+The \chemCal{} package was first designed in the course of a lecture and lab
+course on "analytics of organic trace contaminants" at the University of Bremen
+from October to December 2004. In the fall 2005, an email exchange with 
+Ron Wehrens led to the belief that it could be heavily improved if the
+inverse prediction method given in \cite{massart97} would be implemented,
+since it also covers the case of weighted regression.
+
+At the moment, the package only consists of two functions, working
+on univariate linear models of class \texttt{lm} or \texttt{rlm}.
+
+When calibrating an analytical method, the first task is to generate
+a suitable model. If we want to use the \chemCal{} functions, we
+will have to restrict ourselves to univariate, possibly weighted, linear
+regression so far.
+
+Once such a model has been created, the calibration can be graphically
+shown by using the \texttt{calplot} function:
+
+\begin{Schunk}
+\begin{Sinput}
+> library(chemCal)
+> data(massart97ex3)
+> attach(massart97ex3)
+> yx <- split(y, factor(x))
+> ybar <- sapply(yx, mean)
+> s <- round(sapply(yx, sd), digits = 2)
+> w <- round(1/(s^2), digits = 3)
+> weights <- w[factor(x)]
+> m <- lm(y ~ x, w = weights)
+> calplot(m)
+\end{Sinput}
+\end{Schunk}
+\includegraphics{chemCal-001}
+
+This is a reproduction of Example 8 in \cite{massart97}. We can
+see the influence of the weighted regression on the confidence
+and prediction bands of the calibration.
+
+If we now want to predict a new x value from measured y values,
+we use the \texttt{inverse.predict} function:
+
+\begin{Schunk}
+\begin{Sinput}
+> inverse.predict(m, 15, ws = 1.67)
+\end{Sinput}
+\begin{Soutput}
+$Prediction
+[1] 5.865367
+
+$`Standard Error`
+[1] 10.66054
+
+$Confidence
+[1] 29.59840
+
+$`Confidence Limits`
+[1] -23.73303  35.46376
+\end{Soutput}
+\end{Schunk}
+
+The weight \texttt{ws} assigned to the measured y value has to be 
+given by the user in the case of weighted regression. By default, 
+the mean of the weights used in the linear regression is used.
+
+\section*{Theory}
+Equation 8.28 in \cite{massart97} gives a general equation for predicting the
+standard error $s_{\hat{x_s}}$ for an x value predicted from measurements of y
+according to the linear calibration function $ y = b_0 + b_1 \cdot x$:
+
+\begin{equation}
+s_{\hat{x_s}} = \frac{s_e}{b_1} \sqrt{\frac{1}{w_s m} + \frac{1}{\sum{w_i}} +
+    \frac{(\bar{y_s} - \bar{y_w})^2 \sum{w_i}}
+        {{b_1}^2 \left( \sum{w_i} \sum{w_i {x_i}^2} - {\left( \sum{ w_i x_i } \right)}^2 \right) }}
+\end{equation}
+
+with
+
+\begin{equation}
+s_e = \sqrt{ \frac{\sum w_i (y_i - \hat{y_i})^2}{n - 2}}
+\end{equation}
+
+where $w_i$ is the weight for calibration standard $i$, $y_i$ is the mean $y$
+value (!) observed for standard $i$, $\hat{y_i}$ is the estimated value for
+standard $i$, $n$ is the number calibration standards, $w_s$ is the weight
+attributed to the sample $s$, $m$ is the number of replicate measurements of
+sample $s$, $\bar{y_s}$ is the mean response for the sample, 
+$\bar{y_w} = \frac{\sum{w_i y_i}}{\sum{w_i}}$ is the weighted mean of responses
+$y_i$, and $x_i$ is the given $x$ value for standard $i$.
+
+The weight $w_s$ for the sample should be estimated or calculated in accordance
+to the weights used in the linear regression. 
+
+I adjusted the above equation in order to be able to take a different precisions
+in standards and samples into account. In analogy to Equation 8.26 from \cite{massart97}
+we get
+
+\begin{equation}
+s_{\hat{x_s}} = \frac{1}{b_1} \sqrt{\frac{{s_s}^2}{w_s m} + 
+    {s_e}^2 \left( \frac{1}{\sum{w_i}} +
+        \frac{(\bar{y_s} - \bar{y_w})^2 \sum{w_i}}
+            {{b_1}^2 \left( \sum{w_i} \sum{w_i {x_i}^2} - {\left( \sum{ w_i x_i } \right)}^2 \right) } \right) }
+\end{equation}
+
+\begin{thebibliography}{1}
+\bibitem{massart97}
+Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
+Smeyers-Verbeke, J. 
+\newblock Handbook of Chemometrics and Qualimetrics: Part A,
+\newblock Elsevier, Amsterdam, 1997
+\end{thebibliography}
+
+\end{document}