Ajout de la figure Spare and full polynomial with or no Log.exp

diff --git a/figures/sparse_full_explog.pdf b/figures/sparse_full_explog.pdf
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index 0000000..7100f34
Binary files /dev/null and b/figures/sparse_full_explog.pdf differ

diff --git a/figures/sparse_full_explog.plot b/figures/sparse_full_explog.plot
new file mode 100644 (file)
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+++ b/figures/sparse_full_explog.plot
@@ -0,0 +1,21 @@
+# Analysis description 
+set encoding iso_8859_1
+set terminal x11
+set size 1,0.5
+set term postscript enhanced portrait "Helvetica" 12
+
+set ylabel "execution times (in s)" 
+set xlabel "Sparse and full polynomial's degrees" 
+set logscale x
+set logscale y
+
+#set key on outside left bmargin
+set style line 1 lc rgb '#0060ad' lt 1 lw 2 pt 1 ps 1.5   # --- blue
+set style line 2 lc rgb '#dd181f' lt 1 lw 2 pt 5 ps 1.5   # --- red
+
+  plot'log_exp_Sparse.txt' index 0 using 1:4 t "Sparse polynomial No log.exp"       with linespoints ls 2,\
+ 'log_exp_Sparse.txt' index 0 using 1:2 t "Sparse polynomial with log.exp"      with linespoints ls 1,\
+ 'log_exp_Sparse.txt' index 1 using 1:2 t "Sparse polynomial with log.exp"      with linespoints ls 1,\
+'log_exp.txt' index 0 using 1:4 t "Full polynomial No log.exp"       with linespoints ls 2,\
+ 'log_exp.txt' index 0 using 1:2 t "Full polynomial with log.exp"         with linespoints ls 1,\
+ 'log_exp.txt'index 1 using 1:2 t "Full polynomail withlog.exp"           with linespoints ls 1
\ No newline at end of file

diff --git a/figures/sparse_full_explog.txt b/figures/sparse_full_explog.txt
new file mode 100644 (file)
index 0000000..065de24
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+++ b/figures/sparse_full_explog.txt
@@ -0,0 +1,59 @@
+#sparse polynomial
+# First data block (index 0)
+#EA            With_log_exp                    No_log_exp                                              
+#Taille_Poly   times           nb iter         times           nb iter                         
+5000           0.289431        17              0.256983        15
+10000          0.319229        14              0.317802        14
+15000          0.317802        14              0.393191        13
+25000          0.759156        11              0.849403        11
+30000          1.26306         16              2.08251         20              
+40000          2.57116         19              2.58756         18
+50000          4.17865         18              4.80419         20
+60000          4.43633         16              4.92617         17
+100000         11.7038         15              12.4761         16
+150000         18.6746         11              16.3098         16
+
+# Second index block (index 1)
+#Taille_Poly   times           nb iter
+150000         18.6746         11                              
+200000         67.6199         22
+300000         132.27          20
+350000         159.65          18                              
+400000         258.91          22                                      
+450000         339.47          23              
+500000         419.78          23
+550000         415.94          19
+600000         549.70          21
+650000         612.12          20
+700000         864.21          24
+750000         940.87          23
+800000         1247.16         26
+850000         1702.12         32
+900000         1803.17         30
+950000         2280.07         34
+1000000                2400.51         30
+
+#Full polynomial
+# First data block (index 2)
+#EA            With_log_exp                            No_log_exp                                              
+#Taille_Poly   times           nb iter         times           nb iter                         
+500            0.224633        16              0.23799         17              
+1000           0.348493        24              0.36104         24                      
+1500            0.337472       21              0.339825        20                      
+2000           0.36503         21              0.389243        21                      
+2500           0.389436        22              0.438976        27                      
+3000           0.404811        20              0.403387        27                      
+3500           0.487981        21              0.490296        22                      
+4000           0.506183        23              0.550917        20
+
+# Second index block (index 3)
+#EA            With_log_exp
+#Taille_Poly   times           nb iter
+4000           0.506183        23                              
+#4500          0.946749        23
+5000           0.769945        33
+6000           1.38447         48
+10000          2.15026         32
+100000         306.117         141
+
+

diff --git a/paper.tex b/paper.tex
index c12aeda99cb2c577b87e07c042a188fccd83e50e..1ba7a17a41ed19786a7f6f92f03f65279dd84512 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -662,7 +662,7 @@ The figure 2 show that, the best execution time for both sparse and full polynom
 In this experiment we report the performance of log.exp solution describe in ~\ref{sec2} to compute very high degrees polynomials.   
 \begin{figure}[H]
 \centering
 In this experiment we report the performance of log.exp solution describe in ~\ref{sec2} to compute very high degrees polynomials.   
 \begin{figure}[H]
 \centering

-  \includegraphics[width=0.8\textwidth]{figures/log_exp}
+  \includegraphics[width=0.8\textwidth]{figures/sparse_full_explog}

 \caption{The impact of exp-log solution to compute very high degrees of  polynomial.}
 \label{fig:01}
 \end{figure}
 \caption{The impact of exp-log solution to compute very high degrees of  polynomial.}
 \label{fig:01}
 \end{figure}


@@ -672,12 +672,12 @@ The figure 3, show a comparison between the execution time of the Ehrlich-Aberth
 in fact, when the modulus of the roots are up than \textit{R} given in ~\ref{R},this exceed the limited number in the mantissa of floating points representations and can not compute the iterative function given in ~\ref{eq:Aberth-H-GS} to obtain the root solution, who justify the divergence of the classical Ehrlich-Aberth algorithm. However, applying log.exp solution given in ~\ref{sec2} took into account the limit of floating using the iterative function in(Eq.~\ref{Log_H1},Eq.~\ref{Log_H2}and allows to solve a very large polynomials degrees . 
 
 
 in fact, when the modulus of the roots are up than \textit{R} given in ~\ref{R},this exceed the limited number in the mantissa of floating points representations and can not compute the iterative function given in ~\ref{eq:Aberth-H-GS} to obtain the root solution, who justify the divergence of the classical Ehrlich-Aberth algorithm. However, applying log.exp solution given in ~\ref{sec2} took into account the limit of floating using the iterative function in(Eq.~\ref{Log_H1},Eq.~\ref{Log_H2}and allows to solve a very large polynomials degrees . 
 
 

-\begin{figure}[H]
-\centering
-  \includegraphics[width=0.8\textwidth]{figures/log_exp_Sparse}
-\caption{The impact of exp-log solution to compute very high degrees of  polynomial.}
-\label{fig:01}
-\end{figure}
+%\begin{figure}[H]
+\%centering
+  %\includegraphics[width=0.8\textwidth]{figures/log_exp_Sparse}
+%\caption{The impact of exp-log solution to compute very high degrees of  polynomial.}
+%\label{fig:01}
+%\end{figure}

 
 %we report the performances of the exp.log for the Ehrlich-Aberth algorithm for solving very high degree of polynomial. 
 
 
 %we report the performances of the exp.log for the Ehrlich-Aberth algorithm for solving very high degree of polynomial.