mp3: done 1-4

mp3/Project_3_Maggioni_Claudio/src/Bench_rec_bisection.m

@@ -10,6 +10,8 @@ addpaths_GP;
 nlevels_a = 3;
 nlevels_b = 4;
 
+%addpath /Users/maggicl/Git/matlab2tikz/src/;
+
 fprintf('       *********************************************\n')
 fprintf('       ***  Recursive graph bisection benchmark  ***\n');
 fprintf('       *********************************************\n')
@@ -58,23 +60,102 @@ for c = 1:nc
     fprintf('%s %s', cases{c}, spacers);
     sparse_matrix = load(cases{c});
     
+    if c == 5
+        g = 1;
+    else
+        g = 0;
+    end
+    
 
     % Recursively bisect the loaded graphs in 8 and 16 subgraphs.
     % Steps
     % 1. Initialize the problem
     [params] = Initialize_case(sparse_matrices(c));
-    W      = params.Adj;
+    A      = params.Adj;
-    coords = params.coords;    
+    coords = params.coords;
+    
+    W = A - diag(diag(A));
+    
     % 2. Recursive routines
-    % i. Spectral    
+    % i. Spectral  
+    sp8 = runtest(W, coords, @(a, b) bisection_spectral(a, b, 0), ...
+         3, '', 0);
+    sp16 = runtest(W, coords, @(a, b) bisection_spectral(a, b, 0), ...
+         4, 'Spectral', g);
+   
     % ii. Metis
-    % iii. Coordinate    
+    m8 = runtest(W, coords, @(a, b) bisection_metis(a, b, 0), ...
+         3, '', 0);
+    m16 = runtest(W, coords, @(a, b) bisection_metis(a, b, 0), ...
+         4, 'METIS', g);
+    
+    % iii. Coordinate 
+    c8 = runtest(W, coords, @(a, b) bisection_coordinate(a, b, 0), ...
+         3, '', 0);
+    c16 = runtest(W, coords, @(a, b) bisection_coordinate(a, b, 0), ...
+         4, 'Coordinate', g);
+    
     % iv. Inertial
+    i8 = runtest(W, coords, @(a, b) bisection_inertial(a, b, 0), ...
+         3, '', 0);
+    i16 = runtest(W, coords, @(a, b) bisection_inertial(a, b, 0), ...
+         4, 'Inertial', g);
+    
+    close;
+    
     % 3. Calculate number of cut edges
     % 4. Visualize the partitioning result
     
+    fprintf('%6d %6d %10d %6d %10d %6d %10d %6d %d\n',sp8,sp16,...
+    m8,m16,c8,c16,i8,i16, nnz(diag(A)));
     
-    fprintf('%6d %6d %10d %6d %10d %6d %10d %6d\n',0,0,...
+end
-    0,0,0,0,0,0);
+
+% Bisection         Spectral          Metis 5.0.2       Coordinate         Inertial
+% Partitions          8     16          8     16          8     16          8     16
+% -----------------------------------------------------------------------------------
+% airfoil1.mat ...   327    578        320    563        516    819        577    897 
+% 3elt.mat .......   372    671        395    651        733   1168        880   1342 
+% barth4.mat .....   505    758        405    689        875   1306        891   1350 
+% mesh3e1.mat ....    72    111         75    117         75    122         67    102
+% crack.mat ......   804   1303        784   1290       1343   1860       1061   1618 
+
+function n = runtest(A, xy, algorithm, depth, t, show_graphs)
+    g = 0;
+    if show_graphs == 1
+        g = 1;
+        title(strcat(t, ' bisection for crack with n=16'));
+        hold on;
+    end
+    n = recurse(A, xy, algorithm, 0.5, depth, g);
+    if show_graphs == 1
+        hold off;
+        %matlab2tikz(sprintf('../../ex4_%s.tex', t));
+        figure;
+    end
+end
+
+function n = recurse(A, xy, algorithm, color, depth, show_graphs) 
+    [partA, partB] = algorithm(A, xy);
+    [n, ~] = cutsize(A, partA);
+    A1 = A(partA, partA);
+    xy1 = xy(partA, :);
+    A2 = A(partB, partB);
+    xy2 = xy(partB, :);
+  
+    depth = depth - 1;
+    if depth > 0
+        n = n + recurse(A1, xy1, algorithm, color * 1.5, depth, show_graphs);
+        n = n + recurse(A2, xy2, algorithm, color * 0.5, depth, show_graphs);
+    elseif show_graphs == 1
+        gplot(A1, xy1);
+        gplot(A2, xy2);
+    end
     
+    if show_graphs == 1
+        A12 = sparse(size(A));
+        A12(partA, partB) = A(partA, partB);
+        A12(partB, partA) = A(partB, partA);
+        gplot(A12, xy);
+    end 
 end

mp3/project_3_Maggioni_Claudio.tex

@@ -11,6 +11,8 @@
 \usepackage{grffile}
 \usepackage{amsmath}
 \usepackage{subcaption}
+\usepgfplotslibrary{external}
+\tikzexternalize
 
 \hyphenation{PageRank}
 \hyphenation{PageRanks}
@@ -59,7 +61,39 @@ In figure \ref{fig:run1} there are graph outputs respectively from \textit{Grid9
 
 \section{Recursively bisecting meshes \punkte{20}}
 
-Summarize your results in table \ref{table:Rec_bisection}.
+I summarize my results in table \ref{table:Rec_bisection}. Additionaly, the graph plots
+for a recursive partition in 16 parts of \textit{Crack} are avaliable in figure \ref{fig:bicrack}.
+
+\begin{figure}[h]
+\begin{subfigure}{0.5\textwidth}
+\centering
+	\resizebox{0.8\linewidth}{!}{
+		\input{ex4_Spectral}}
+\caption{Spectral bisection}
+\end{subfigure}
+\begin{subfigure}{0.5\textwidth}
+\centering
+	\resizebox{0.8\linewidth}{!}{
+		\input{ex4_Coordinate}}
+\caption{Coordinate bisection}
+\end{subfigure}
+\begin{subfigure}{0.5\textwidth}
+\centering
+	\resizebox{0.8\linewidth}{!}{
+		\input{ex4_METIS}}
+\caption{METIS bisection}
+\end{subfigure}
+\begin{subfigure}{0.5\textwidth}
+\centering
+	\resizebox{0.8\linewidth}{!}{
+		\input{ex4_Inertial}}
+\caption{Inertial bisection}
+\end{subfigure}
+	\caption{Graph outputs for \textit{Crack} graph with $n=16$}
+\label{fig:bicrack}
+\end{figure}
+
+
 
 \section{Compare recursive bisection to direct $k$-way partitioning\punkte{10}}
 
@@ -84,15 +118,15 @@ Summarize your results in table \ref{table:Compare_Metis}.
 
 
 \begin{table}[h]
-	\caption{Edge-cut results for recursive bi-partitioning.}
+	\caption{Edge-cut results for recursive bi-partitioning (data for $n=8$ on the left and $n=16$ on the right).}
 	\centering
-	\begin{tabular}{|l|r|r|r|r|r|} \hline\hline
+	\begin{tabular}{|l|r|r|r|r|p{4cm}|} \hline\hline
-		Case            &  Spectral             &  Metis 5.0.2    & Coordinate & Inertial  \\ \hline
+		Case & Spectral & Metis 5.0.2 & Coordinate & Inertial \\ \hline
-		mesh3e1         &                       &                 &            &           \\
+		airfoil1 & 327\hfill578 & 320\hfill563 & 516\hfill819 & 577\hfill897\\
-		airfoil1        &                       &                 &            &           \\
+		3elt & 372\hfill671 & 395\hfill651 & 733\hfill1168 & 880\hfill1342\\
-		3elt            &                       &                 &            &           \\
+		barth4 & 505\hfill758 & 405\hfill689 & 875\hfill1306 & 891\hfill1350\\
-		barth4          &                       &                 &            &           \\
+		mesh3e1 & 72\hfill111 & 75\hfill117 & 75\hfill122 & 67\hfill102\\
-		crack           &                       &                 &            &           \\ \hline \hline
+		crack & 804\hfill1303 & 784\hfill1290 & 1343\hfill1860 & 1061 \hfill 1618\\\hline\hline
 	\end{tabular}
 	\label{table:Rec_bisection}
 \end{table}