quelques modifs

[book_gpu.git] / BookGPU / Chapters / chapter11 / ch11.tex

diff --git a/BookGPU/Chapters/chapter11/ch11.tex b/BookGPU/Chapters/chapter11/ch11.tex
index 7e319fdd1b465e098bf79b1e8d4ccc2aadc9c09c..270fcc4174d123ff4c5b2ef203085fac0187d68d 100644 (file)
--- a/BookGPU/Chapters/chapter11/ch11.tex
+++ b/BookGPU/Chapters/chapter11/ch11.tex
@@ -28,14 +28,14 @@ The rest of the chapter is organised as follows. Section \ref{ch11:splines} disc
 \begin{figure}[h]
 \centering
 \includegraphics[angle=0,width=8cm]{Chapters/chapter11/gregory1_plot1.pdf}
 \begin{figure}[h]
 \centering
 \includegraphics[angle=0,width=8cm]{Chapters/chapter11/gregory1_plot1.pdf}

-\caption{Cubic spline (solid) and monotone quadratic spline (dashed) interpolating monotone data from \cite{Gregory1982}. Cubic spline fails to preserve monotonicity of the data.}
+\caption[Cubic spline (solid) and monotone quadratic spline (dashed) interpolating monotone data]{Cubic spline (solid) and monotone quadratic spline (dashed) interpolating monotone data from \cite{Gregory1982}. Cubic spline fails to preserve monotonicity of the data.}

 \label{ch11:fig1}
 \end{figure}
 
 \begin{figure}[h]
 \centering
 \includegraphics[angle=00,width=8cm]{Chapters/chapter11/gregory1_plot2_b.pdf}
 \label{ch11:fig1}
 \end{figure}
 
 \begin{figure}[h]
 \centering
 \includegraphics[angle=00,width=8cm]{Chapters/chapter11/gregory1_plot2_b.pdf}

-\caption{Hermite cubic spline (solid) and Hermite rational spline interpolating monotone data from \cite{Gregory1982} with non-negative prescribed slopes. Despite non-negative slopes, Hermite cubic spline is not monotone.}
+\caption[Hermite cubic spline (solid) and Hermite rational spline interpolating monotone data]{Hermite cubic spline (solid) and Hermite rational spline interpolating monotone data from \cite{Gregory1982} with non-negative prescribed slopes. Despite non-negative slopes, Hermite cubic spline is not monotone.}

 \label{ch11:fig2}
 \end{figure}
 
 \label{ch11:fig2}
 \end{figure}
 


@@ -398,33 +398,33 @@ with $\hat y(k,l)$ being the unrestricted maximum likelihood estimator of $y_k\l
 
 
 %% %\renewcommand{\baselinestretch}{1}
 
 
 %% %\renewcommand{\baselinestretch}{1}

-%% \begin{table}[!h]
-%% \begin{center}
-%% \caption{The average CPU time (sec) of the serial PAVA, MLS and parallel MLS algorithms.  } \label{ch11:table1}
-%% \begin{tabular}{|r|r|r|r|}
-
-%% Data  & PAVA & MLS & GPU MLS \\ \hline
-
-%% monotone increasing $f$ & & & \\
-%% $n=5\times 10^4$ &0.01&5& 0.092\\
-%% $n=10^5$ &0.03&40& 0.35\\
-%% $n=5\times 10^5$ &0.4&1001&8.6 \\
-%% $n=10^6$ &0.8& 5000& 38 \\
-%% $n=2 \times 10^6$ & 1.6 &-- &152 \\
-%% $n=10 \times 10^6$ & 2 &-- & 3500 \\
-%% $n=20 \times 10^6$ & 4.5&-- & --\\
-%% $n=50 \times 10^6$ & 12 &-- & --\\
-%% \hline
-
-%% constant or decreasing $f$ & & & \\
-%% $n=10^6$ &0.2&0.1& 38\\
-%% $n=10 \times 10^6$ &1.9& 1.9& 3500 \\
-%% $n=20 \times 10^6$ &3.5& 4.0&-- \\
-%% $n=50 \times 10^6$ &11& 11& -- \\
-
-%% \end{tabular}
-%% \end{center}
-%% \end{table}
+\begin{table}[!h]
+\begin{center}
+\caption{The average CPU time (sec) of the serial PAVA, MLS and parallel MLS algorithms.  } \label{ch11:table1}
+\begin{tabular}{|r|r|r|r|}
+
+Data  & PAVA & MLS & GPU MLS \\ \hline
+
+monotone increasing $f$ & & & \\
+$n=5\times 10^4$ &0.01&5& 0.092\\
+$n=10^5$ &0.03&40& 0.35\\
+$n=5\times 10^5$ &0.4&1001&8.6 \\
+$n=10^6$ &0.8& 5000& 38 \\
+$n=2 \times 10^6$ & 1.6 &-- &152 \\
+$n=10 \times 10^6$ & 2 &-- & 3500 \\
+$n=20 \times 10^6$ & 4.5&-- & --\\
+$n=50 \times 10^6$ & 12 &-- & --\\
+\hline
+
+constant or decreasing $f$ & & & \\
+$n=10^6$ &0.2&0.1& 38\\
+$n=10 \times 10^6$ &1.9& 1.9& 3500 \\
+$n=20 \times 10^6$ &3.5& 4.0&-- \\
+$n=50 \times 10^6$ &11& 11& -- \\
+
+\end{tabular}
+\end{center}
+\end{table}

 %% %\renewcommand{\baselinestretch}{2}
 
 
 %% %\renewcommand{\baselinestretch}{2}
 
 


@@ -491,6 +491,6 @@ with $\hat y(k,l)$ being the unrestricted maximum likelihood estimator of $y_k\l
 \section{Conclusion} \label{ch11:conc}
 
 We presented three GPU-based parallel algorithms for approximating monotone data: monotone quadratic spline, monotone Hermite rational spline and minimum lower sets algorithm for monotonizing noisy data. These tools are valuable in a number of applications that involve large data sets modeled by monotone nonlinear functions.
 \section{Conclusion} \label{ch11:conc}
 
 We presented three GPU-based parallel algorithms for approximating monotone data: monotone quadratic spline, monotone Hermite rational spline and minimum lower sets algorithm for monotonizing noisy data. These tools are valuable in a number of applications that involve large data sets modeled by monotone nonlinear functions.

-The source code of the package monospline is available from \texttt{www.deakin.edu.au/$\sim$ gleb/monospline.html }
+The source code of the package monospline is available from \texttt{www.deakin.edu.au/$\sim$gleb/monospline.html }

 
 \putbib[Chapters/chapter11/biblio11]
 
 \putbib[Chapters/chapter11/biblio11]