mp3: other corrections

mp3/Project_3_Maggioni_Claudio/src/Bench_rec_bisection.m

@@ -79,29 +79,33 @@ for c = 1:nc
     % 2. Recursive routines
     % i. Spectral  
     sp8 = runtest(W, coords, @(a, b) bisection_spectral(a, b, 0), ...
-         3, '', 0);
+         3, 'Spectral_8', g);
     sp16 = runtest(W, coords, @(a, b) bisection_spectral(a, b, 0), ...
          4, 'Spectral', g);
    
     % ii. Metis
     m8 = runtest(W, coords, @(a, b) bisection_metis(a, b, 0), ...
-         3, '', 0);
+         3, 'METIS_8', g);
     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);
+         3, 'Coordinate_8', g);
     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);
+         3, 'Inertial_8', g);
     i16 = runtest(W, coords, @(a, b) bisection_inertial(a, b, 0), ...
          4, 'Inertial', g);
     
     close;
+    for ignored = 1:8
+    %    close;
+    end
+    
     
     % 3. Calculate number of cut edges
     % 4. Visualize the partitioning result
@@ -113,29 +117,29 @@ end
 
 %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 
+%airfoil1.mat ...   327    578     320    563     516    819     578    903
 %3elt.mat .......   372    671     395    651     733   1168     880   1342
-%barth4.mat .....   505    758        405    689        875   1306        891   1350 
+%barth4.mat .....   505    758     405    689     875   1306     888   1348
-%mesh3e1.mat ....    75    124         75    117         75    122         67    102 
+%mesh3e1.mat ....    75    124     75    117      75     122      76    116
 %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'));
+        %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));
+        %matlab2tikz('showInfo', false, sprintf('../../ex4_%s.tex', t));
         figure;
     end
 end
 
-function n = recurse(A, xy, algorithm, color, depth, show_graphs) 
+function n = recurse(A, xy, algorithm, color, depth, show_g) 
     warning('off','MATLAB:eigs:IllConditionedA')
     [partA, partB] = algorithm(A, xy);
     warning('on', 'MATLAB:eigs:IllConditionedA')
@@ -147,14 +151,14 @@ function n = recurse(A, xy, algorithm, color, depth, show_graphs)
   
     depth = depth - 1;
     if depth > 0
-        n = n + recurse(A1, xy1, algorithm, color * 1.5, depth, show_graphs);
+        n = n + recurse(A1, xy1, algorithm, color * 1.5, depth, show_g);
-        n = n + recurse(A2, xy2, algorithm, color * 0.5, depth, show_graphs);
+        n = n + recurse(A2, xy2, algorithm, color * 0.5, depth, show_g);
-    elseif show_graphs == 1
+    elseif show_g == 1
         gplot(A1, xy1);
         gplot(A2, xy2);
     end
     
-    if show_graphs == 1
+    if show_g == 1
         A12 = sparse(size(A));
         A12(partA, partB) = A(partA, partB);
         A12(partB, partA) = A(partB, partA);

mp3/Project_3_Maggioni_Claudio/src/bisection_inertial.m

@@ -20,16 +20,17 @@
 
 % Steps
 % 1. Calculate the center of mass.
-m = sum(xy, 1) ./ size(xy, 1);
+m = mean(xy);
 xm = m(1);
 ym = m(2);
 
 % 2. Construct the matrix M.
 %  (Consult the pdf of the assignment for the creation of M) 
-h = [(xy(:, 1) - xm) (xy(:, 2) - ym)];
+sx = (xy(:, 1) - xm);
-X1 = sum(h(:, 1) .^ 2);
+sy = (xy(:, 2) - ym);
-X2 = sum(h(:, 1) .* h(:, 2));
+X1 = sum(sx .^ 2);
-X3 = sum(h(:, 2) .^ 2);
+X2 = dot(sx, sy);
+X3 = sum(sy .^ 2);
 
 M = [X1 X2; X2 X3];
 
@@ -39,13 +40,12 @@ a = u(1);
 b = u(2);
 
 % 4. Find the line L on which the center of mass lies.
-S = -b * (xy(:, 1) - xm) + a * (xy(:, 2) - ym);
+v = [-b; a];
-Sm = median(S);
+v = v / norm(v, 2);
 
 % 5. Partition the points around the line L.
 %   (you may use the function partition.m)
-part1 = find(S < Sm);
+[part1, part2] = partition(xy, v);
-part2 = find(S >= Sm);
 
 if picture == 1
     gplotpart(A,xy,part1);

mp3/ex4_Coordinate.tex

@@ -1,9 +1,5 @@
 % This file was created by matlab2tikz.
 %
-%The latest updates can be retrieved from
-%  http://www.mathworks.com/matlabcentral/fileexchange/22022-matlab2tikz-matlab2tikz
-%where you can also make suggestions and rate matlab2tikz.
-%
 \definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
 \definecolor{mycolor2}{rgb}{0.85000,0.32500,0.09800}%
 \definecolor{mycolor3}{rgb}{0.92900,0.69400,0.12500}%
@@ -25,8 +21,6 @@ xmax=1,
 ymin=0,
 ymax=1,
 axis background/.style={fill=white},
-title style={font=\bfseries},
-title={Coordinate bisection for crack with n=16},
 axis x line*=bottom,
 axis y line*=left
 ]

mp3/ex4_Inertial.tex

@@ -1,9 +1,5 @@
 % This file was created by matlab2tikz.
 %
-%The latest updates can be retrieved from
-%  http://www.mathworks.com/matlabcentral/fileexchange/22022-matlab2tikz-matlab2tikz
-%where you can also make suggestions and rate matlab2tikz.
-%
 \definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
 \definecolor{mycolor2}{rgb}{0.85000,0.32500,0.09800}%
 \definecolor{mycolor3}{rgb}{0.92900,0.69400,0.12500}%
@@ -25,8 +21,6 @@ xmax=1,
 ymin=0,
 ymax=1,
 axis background/.style={fill=white},
-title style={font=\bfseries},
-title={Inertial bisection for crack with n=16},
 axis x line*=bottom,
 axis y line*=left
 ]

mp3/ex4_METIS.tex

@@ -1,9 +1,5 @@
 % This file was created by matlab2tikz.
 %
-%The latest updates can be retrieved from
-%  http://www.mathworks.com/matlabcentral/fileexchange/22022-matlab2tikz-matlab2tikz
-%where you can also make suggestions and rate matlab2tikz.
-%
 \definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
 \definecolor{mycolor2}{rgb}{0.85000,0.32500,0.09800}%
 \definecolor{mycolor3}{rgb}{0.92900,0.69400,0.12500}%
@@ -25,8 +21,6 @@ xmax=1,
 ymin=0,
 ymax=1,
 axis background/.style={fill=white},
-title style={font=\bfseries},
-title={METIS bisection for crack with n=16},
 axis x line*=bottom,
 axis y line*=left
 ]

mp3/ex4_Spectral.tex

@@ -1,9 +1,5 @@
 % This file was created by matlab2tikz.
 %
-%The latest updates can be retrieved from
-%  http://www.mathworks.com/matlabcentral/fileexchange/22022-matlab2tikz-matlab2tikz
-%where you can also make suggestions and rate matlab2tikz.
-%
 \definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
 \definecolor{mycolor2}{rgb}{0.85000,0.32500,0.09800}%
 \definecolor{mycolor3}{rgb}{0.92900,0.69400,0.12500}%
@@ -25,8 +21,6 @@ xmax=1,
 ymin=0,
 ymax=1,
 axis background/.style={fill=white},
-title style={font=\bfseries},
-title={Spectral bisection for crack with n=16},
 axis x line*=bottom,
 axis y line*=left
 ]

mp3/project_3_Maggioni_Claudio.tex

@@ -58,7 +58,7 @@ In figure \ref{fig:run1} there are graph outputs respectively from \textit{Grid9
 
 Colors to represent the partitions and the eigenvector components are the same as the ones used in the the assignment's Figure 3. It is quite easy to evince from these plots that spectral partitioning indeed partitions the graph verticies based on the sign of their respective Fiedler eigenvector component: the only intersection between the Graph plane and the surface the eigenvector entries lay corresponds to the edgecut produced by spectral partitioning. This is due to the fact that in the figure the graph is positioned at $z = 0$.
 
-\begin{figure}[h]
+\begin{figure}
 \begin{subfigure}{0.5\textwidth}
 \centering
 %	\input{ex3_grid9}
@@ -83,7 +83,7 @@ Colors to represent the partitions and the eigenvector components are the same a
 \section{Recursively bisecting meshes \punkte{20}}
 
 I summarize my results in table \ref{table:Rec_bisection}. Additionally, the graph plots
-for a recursive partition in 16 parts of \textit{Crack} are avaliable in figure \ref{fig:bicrack}.
+for a recursive partition in 8 and 16 parts of \textit{Crack} are avaliable in figure \ref{fig:bicrack}.
 
 The figure shows the partitions and edge cuts with colors randomly assigned by MATLAB.
 
@@ -93,32 +93,56 @@ Please note that while computing spectral partitioning for \textit{barth4} MATLA
 in the computation of the adjacency matrix eigenvalues stating that the matrix is ill conditioned.
 This warning was suppressed so as not to interfere with the table printout.
 
-\begin{figure}[h]
+\begin{figure}
+\begin{subfigure}{0.5\textwidth}
+\centering
+	\resizebox{0.8\linewidth}{!}{
+		\input{ex4_Spectral_8}}
+\caption{Spectral bisection for $n=8$}
+\end{subfigure}
+\begin{subfigure}{0.5\textwidth}
+\centering
+	\resizebox{0.8\linewidth}{!}{
+		\input{ex4_Coordinate_8}}
+\caption{Coordinate bisection for $n=8$}
+\end{subfigure}
+\begin{subfigure}{0.5\textwidth}
+\centering
+	\resizebox{0.8\linewidth}{!}{
+		\input{ex4_METIS_8}}
+\caption{METIS bisection for $n=8$}
+\end{subfigure}
+\begin{subfigure}{0.5\textwidth}
+\centering
+	\resizebox{0.8\linewidth}{!}{
+		\input{ex4_Inertial_8}}
+\caption{Inertial bisection for $n=8$}
+\end{subfigure}
 \begin{subfigure}{0.5\textwidth}
 \centering
 	\resizebox{0.8\linewidth}{!}{
 		\input{ex4_Spectral}}
-\caption{Spectral bisection}
+\caption{Spectral bisection for $n=16$}
 \end{subfigure}
 \begin{subfigure}{0.5\textwidth}
 \centering
 	\resizebox{0.8\linewidth}{!}{
 		\input{ex4_Coordinate}}
-\caption{Coordinate bisection}
+\caption{Coordinate bisection for $n=16$}
 \end{subfigure}
 \begin{subfigure}{0.5\textwidth}
 \centering
 	\resizebox{0.8\linewidth}{!}{
 		\input{ex4_METIS}}
-\caption{METIS bisection}
+\caption{METIS bisection for $n=16$}
 \end{subfigure}
 \begin{subfigure}{0.5\textwidth}
 \centering
 	\resizebox{0.8\linewidth}{!}{
 		\input{ex4_Inertial}}
-\caption{Inertial bisection}
+\caption{Inertial bisection for $n=16$}
 \end{subfigure}
-	\caption{Graph outputs for \textit{Crack} graph with $n=16$}
+	\caption{Graph outputs for \textit{Crack} graph with $n=8$ and $n=16$}
 \label{fig:bicrack}
 \end{figure}
 
@@ -130,7 +154,7 @@ The figure shows the resulting partitions with colors randomly assigned by MATLA
 
 I had the suspicion that k-way partitioning would perform better in all cases, since in this the partitioning algorithm has a chance to see the entire problem and to perform decision that could affect all partitions. Instead, for the \texttt{Crack} mesh, recursive partitioning surprisedly performed better than k-way for both $n = 16$ and $n = 32$, producing slighly smaller edge cuts.
 
-\begin{figure}[h]
+\begin{figure}
 \begin{subfigure}{0.5\textwidth}
 \centering
 	\resizebox{0.8\linewidth}{!}{
@@ -162,7 +186,7 @@ I had the suspicion that k-way partitioning would perform better in all cases, s
 
 
 
-\begin{table}[h]
+\begin{table}
 	\caption{Bisection results}
 	\centering
 	\begin{tabular}{|l|r|r|r|r|} \hline\hline
@@ -180,28 +204,43 @@ I had the suspicion that k-way partitioning would perform better in all cases, s
 \end{table}
 
 
-\begin{table}[h]
+\begin{table}
-	\caption{Edge-cut results for recursive bi-partitioning (data for $n=8$ on the left and $n=16$ on the right).}
+	\caption{Edge-cut results for recursive bi-partitioning (data for $n=8$ on the top and $n=16$ on the bottom).}
 	\centering
 	\begin{tabular}{|l|r|r|r|r|p{4cm}|} \hline\hline
-		Case & Spectral & Metis 5.0.2 & Coordinate & Inertial \\ \hline
+		Case $n=8$ & Spectral & Metis 5.0.2 & Coordinate & Inertial \\ \hline
-airfoil1 & 327 \hfill 578  & 320 \hfill 563  & 516  \hfill  819 &  577 \hfill  897\\
+airfoil1 & 327 & 320 & 516  &  578 \\
-3elt     & 372 \hfill 671  & 395 \hfill 651  & 733  \hfill 1168 &  880 \hfill 1342\\
+3elt     & 372 & 395 & 733  &  880 \\
-barth4   & 505 \hfill 758  & 405 \hfill 689  & 875  \hfill 1306 &  891 \hfill 1350\\
+barth4   & 505 & 405 & 875  &  888 \\
-mesh3e1  & 75  \hfill 124  & 75 \hfill  117  & 75   \hfill  122 &   67 \hfill  102\\
+mesh3e1  & 75  & 75 & 75   &   76 \\
-crack    & 804 \hfill 1303 & 784 \hfill 1290 & 1343 \hfill 1860 & 1061 \hfill 1618\\\hline\hline
+crack    & 804 & 784 & 1343 & 1061 \\\hline\hline
+	\end{tabular}\\
+	\vspace{10pt}
+	\begin{tabular}{|l|r|r|r|r|p{4cm}|} \hline\hline
+		Case $n=16$ & Spectral & Metis 5.0.2 & Coordinate & Inertial \\ \hline
+airfoil1 & 578  & 563  & 819 &  903\\
+3elt     & 671  & 651  & 1168 & 1342\\
+barth4   & 758  & 689  & 1306 &  1348\\
+mesh3e1  & 124  & 117  & 122 &   116\\
+crack    & 1303 & 1290 & 1860 & 1618\\\hline\hline
 	\end{tabular}
 	\label{table:Rec_bisection}
 \end{table}
 
 
-\begin{table}[h]
+\begin{table}
-\caption{Comparing the number of cut edges for recursive bisection and direct multiway partitioning in Metis 5.0.2. Results for recursive partitioning shown on the left, k-way on the right.}
+\caption{Comparing the number of cut edges for recursive bisection and direct multiway partitioning in Metis 5.0.2. Results for recursive partitioning shown on top, k-way on the bottom table.}
 \centering
 \begin{tabular}{|l|r|r|r|r|} \hline\hline
-Partitions       &   crack          & airfoil1  \\ \hline
+Recursive part.       &   crack          & airfoil1  \\ \hline
- 16              &   10055 \hfill 10077 & 580 \hfill 564 \\
+ 16              &   10055 & 580 \\
- 32              &   10824 \hfill 10943 & 967 \hfill 947 \\ \hline \hline
+ 32              &   10824 & 967 \\ \hline \hline
+\end{tabular} \\
+	\vspace{10pt}
+\begin{tabular}{|l|r|r|r|r|} \hline\hline
+K-way part.       &   crack          & airfoil1  \\ \hline
+ 16              &   10077 & 564 \\
+ 32              &   10943 & 947 \\ \hline \hline
 \end{tabular}
 \label{table:Compare_Metis}
 \end{table}