mp5: done
This commit is contained in:
Claudio Maggioni (maggicl)
parent
0b1939a9d2
commit
f001099b7a
11 changed files with 296 additions and 366 deletions
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@ -89,7 +89,8 @@ The plot of the squared residual 2-norms over all iterations can be found in Fig
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\ref{fig:plot1}.
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\ref{fig:plot1}.
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\begin{figure}[h]
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\begin{figure}[h]
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\input{test_semilogy}
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\centering
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\resizebox{0.6\textwidth}{!}{\input{test_semilogy}}
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\caption{Semilog plot of the plot of the squared residual 2-norms over all iterations}\label{fig:plot1}
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\caption{Semilog plot of the plot of the squared residual 2-norms over all iterations}\label{fig:plot1}
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\end{figure}
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\end{figure}
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@ -104,7 +105,8 @@ reflected in the eigenvalue plot, which shows a not so
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drastic increase of the first eigenvalues ordered in increasing order.
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drastic increase of the first eigenvalues ordered in increasing order.
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\begin{figure}[h]
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\begin{figure}[h]
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\input{A_eig}
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\centering
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\resizebox{0.6\textwidth}{!}{\input{A_eig}}
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\caption{Semilog plot of the eigenvalues of A}\label{fig:plot2}
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\caption{Semilog plot of the eigenvalues of A}\label{fig:plot2}
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\end{figure}
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\end{figure}
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@ -120,13 +122,39 @@ $max\_iter=200$ $tol= 10^{-6}$. Plot the convergence (residual
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vs iteration) of each solver and display the original and final
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vs iteration) of each solver and display the original and final
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deblurred image.}
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deblurred image.}
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Plots already rendered.
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My implementation is in the file \texttt{deblurring.m}. Plots for the original image, the deblurred image from
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\texttt{myCG}, the deblurred image from \texttt{pcg}, and a semi-logarithmic plot on the y-axis of the residuals
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from the two conjugate gradient functions over the iteration count can be found respectively in figure \ref{fig:orig},
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\ref{fig:mycg}, \ref{fig:pcg}, and \ref{fig:rvec}.
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\begin{figure}[h]
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\begin{subfigure}{0.33\textwidth}
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\centering
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\resizebox{0.8\textwidth}{!}{\input{img_orig}}
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\caption{Original image grayscale matrix}\label{fig:orig}
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\end{subfigure}
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\begin{subfigure}{0.33\textwidth}
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\centering
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\resizebox{0.8\textwidth}{!}{\input{img_my}}
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\caption{Deblurred image using \texttt{myCG}}\label{fig:mycg}
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\end{subfigure}
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\begin{subfigure}{0.33\textwidth}
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\centering
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\resizebox{0.8\textwidth}{!}{\input{img_rcg}}
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\caption{Deblurred image using \texttt{rcg}}\label{fig:pcg}
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\end{subfigure}
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\caption{Blurred and deblurred images}
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\end{figure}
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\begin{figure}[h]
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\centering
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\resizebox{0.6\textwidth}{!}{\input{res_log}}
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\caption{Residuals of \texttt{myCG} (in blue) and \texttt{rcg} (in orange) over iteration count (y axis is a log scale)}\label{fig:rvec}
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\end{figure}
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\subsection{ When would \texttt{pcg} be worth the added computational cost?
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\subsection{ When would \texttt{pcg} be worth the added computational cost?
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What about if you are debluring lots of images with the same
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What about if you are debluring lots of images with the same
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blur operator?}
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blur operator?}
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\textit{pcg} better for many, myCG better for one thanks to cost of ichol.
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The \textit{pcg} algorithm provided by MATLAB would be worth for many deblurring operations useing the same blur operator, since the cost of computing the incomplete cholesky decomposition (i.e. \texttt{ichol}) can be payed only once and thus amortized. \texttt{myCG} is better for few iterations thanks to not needing any seed that is expensive to compute.
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\end{document}
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\end{document}
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@ -14,6 +14,7 @@ im_l=min(min(B));
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im_u=max(max(B));
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im_u=max(max(B));
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imshow(B,[im_l,im_u])
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imshow(B,[im_l,im_u])
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title('Blured Image')
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title('Blured Image')
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matlab2tikz('showInfo', false, '../img_orig.tex');
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% Vectorize the image (row by row)
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% Vectorize the image (row by row)
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b=B';
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b=B';
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@ -64,15 +65,3 @@ im_u=max(max(X2));
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imshow(X2,[im_l,im_u])
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imshow(X2,[im_l,im_u])
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title('Sharp Image (rcg)')
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title('Sharp Image (rcg)')
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matlab2tikz('showInfo', false, '../img_rcg.tex');
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matlab2tikz('showInfo', false, '../img_rcg.tex');
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%% Validate Test values
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load('test_data/A_test.mat');
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load('test_data/x_test_exact.mat');
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load('test_data/b_test.mat');
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%res=||x^*-A^{-1}b||
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res=x_test_exact-inv(A_test)*b_test;
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norm(res);
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%(Now do it with your CG and Matlab's PCG routine!!!)
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69
mp5/Project_5_Maggioni_Claudio/deblurring.m
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69
mp5/Project_5_Maggioni_Claudio/deblurring.m
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@ -0,0 +1,69 @@
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close all;
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clear; clc;
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addpath /Users/maggicl/Git/matlab2tikz/src/;
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%% Load Default Img Data
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load('blur_data/B.mat');
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B=double(B);
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load('blur_data/A.mat');
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A=double(A);
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% Show Image
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figure;
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im_l=min(min(B));
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im_u=max(max(B));
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imshow(B,[im_l,im_u])
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title('Blurred Image')
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matlab2tikz('showInfo', false, '../img_orig.tex');
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% Vectorize the image (row by row)
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b=B';
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b=b(:);
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AT = A' * A;
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bt = A' * b;
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IL = ichol(AT, struct('type', 'nofill', 'diagcomp', 0.01));
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[x, rvec] = myCG(AT, bt, zeros(size(b)), 200, 1e-6);
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[x2, ~, ~, ~, rvec2] = pcg(AT, bt, 1e-6, 200, IL, IL');
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X2 = zeros(250, 250);
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for i = 0:249
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for j = 1:250
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X2(i + 1, j) = x2(i * 250 + j);
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end
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end
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figure;
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im_l=min(min(X2));
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im_u=max(max(X2));
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imshow(X2,[im_l,im_u])
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title('Sharp Image (rcg)')
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matlab2tikz('showInfo', false, '../img_rcg.tex');
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X = zeros(250, 250);
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for i = 0:249
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for j = 1:250
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X(i + 1, j) = x(i * 250 + j);
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end
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end
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figure;
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im_l=min(min(X));
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im_u=max(max(X));
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imshow(X,[im_l,im_u])
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title('Sharp Image (myCG)')
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matlab2tikz('showInfo', false, '../img_my.tex');
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figure;
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semilogy(rvec / norm(bt));
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hold on;
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semilogy(rvec2 / norm(bt));
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hold off;
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title('Residual norms over iteration (y is log)')
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matlab2tikz('showInfo', false, '../res_log.tex');
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BIN
mp5/img_my-1.png
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mp5/img_my-1.png
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Before Width: | Height: | Size: 56 KiB After Width: | Height: | Size: 58 KiB |
212
mp5/img_my.tex
212
mp5/img_my.tex
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@ -1,208 +1,26 @@
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% This file was created by matlab2tikz.
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% This file was created by matlab2tikz.
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%
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%
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\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
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\definecolor{mycolor2}{rgb}{0.85000,0.32500,0.09800}%
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%
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\begin{tikzpicture}
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\begin{tikzpicture}
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\begin{axis}[%
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\begin{axis}[%
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width=6.028in,
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width=2.604in,
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height=4.754in,
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height=2.604in,
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at={(1.011in,0.642in)},
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at={(0.962in,0.66in)},
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scale only axis,
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scale only axis,
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xmin=0,
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point meta min=-0.0128979816802523,
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xmax=160,
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point meta max=0.983438722992887,
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ymode=log,
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axis on top,
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ymin=1e-09,
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xmin=0.5,
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ymax=1,
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xmax=250.5,
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yminorticks=true,
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tick align=outside,
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axis background/.style={fill=white},
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y dir=reverse,
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ymin=0.5,
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ymax=250.5,
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axis line style={draw=none},
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ticks=none,
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title style={font=\bfseries},
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title style={font=\bfseries},
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title={Sharp Image (myCG)}
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title={Sharp Image (myCG)}
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]
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]
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\addplot [color=mycolor1, forget plot]
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\addplot [forget plot] graphics [xmin=0.5, xmax=250.5, ymin=0.5, ymax=250.5] {img_my-1.png};
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table[row sep=crcr]{%
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1 1\\
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2 0.557596535615506\\
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3 0.0776565625508993\\
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4 0.0198777323861488\\
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5 0.00796998880225869\\
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6 0.00379999756962287\\
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7 0.0020374948726527\\
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8 0.00117378505868276\\
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9 0.000679072640424649\\
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10 0.000460205525227464\\
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11 0.000299176988582771\\
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12 0.000208705837325249\\
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13 0.000154155368421638\\
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14 0.000112123271112138\\
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15 8.51723029158506e-05\\
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16 6.84145894011081e-05\\
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17 5.22773173463893e-05\\
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18 4.19658990284636e-05\\
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19 3.35813556680048e-05\\
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20 2.69909819855066e-05\\
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21 2.16953761012216e-05\\
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22 1.75366202909715e-05\\
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23 1.58613744370523e-05\\
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24 1.07527796769547e-05\\
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25 1.21386374874815e-05\\
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26 1.02818699879239e-05\\
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27 8.94827138078525e-06\\
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28 7.32098660262362e-06\\
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29 6.29855369167726e-06\\
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30 5.75608316894847e-06\\
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31 5.01303204699423e-06\\
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32 4.32711144148808e-06\\
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33 3.75161010629661e-06\\
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34 3.13429056757287e-06\\
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35 2.97535388105766e-06\\
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36 2.59579082920428e-06\\
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37 2.35613630297938e-06\\
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38 2.13570046200869e-06\\
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39 1.91918226507556e-06\\
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40 1.79412386278695e-06\\
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41 1.60497187780807e-06\\
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42 1.50673230165654e-06\\
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43 1.29912483256279e-06\\
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44 1.18346887626955e-06\\
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45 1.20647020748118e-06\\
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46 9.3251240253618e-07\\
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47 1.0443397517104e-06\\
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48 7.81977076368339e-07\\
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49 7.06367946061837e-07\\
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50 6.4448540591806e-07\\
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51 5.8599197172186e-07\\
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52 5.19890971305916e-07\\
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53 4.77565688325081e-07\\
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54 4.45837257417211e-07\\
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55 4.52354751810163e-07\\
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56 4.29038013881601e-07\\
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57 4.19929738903634e-07\\
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58 3.83172910236919e-07\\
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59 3.69121286102551e-07\\
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60 3.7162945951419e-07\\
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61 3.46046785121521e-07\\
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62 3.2757610333777e-07\\
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63 3.15320978192865e-07\\
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64 2.96758711344714e-07\\
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65 2.96817636331721e-07\\
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66 2.71124713000919e-07\\
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67 2.62909013135003e-07\\
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68 2.43462036182122e-07\\
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69 2.28404291071355e-07\\
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70 2.24415864473535e-07\\
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71 2.28468445317059e-07\\
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72 2.16184931431001e-07\\
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73 2.03658004162582e-07\\
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74 1.83416377348938e-07\\
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75 1.77025922497321e-07\\
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76 1.70006600401098e-07\\
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77 1.63491825605367e-07\\
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78 1.57088823572816e-07\\
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79 1.6232157488019e-07\\
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80 1.55517018193347e-07\\
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81 1.44132341985942e-07\\
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82 1.33984748126276e-07\\
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83 1.25196828216566e-07\\
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84 1.21215390780978e-07\\
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85 1.15338855777099e-07\\
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86 1.08276150400162e-07\\
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87 1.04805124156927e-07\\
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88 1.01804326380992e-07\\
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89 1.0010166263465e-07\\
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90 9.48101967192271e-08\\
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91 8.89240656896784e-08\\
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92 8.81989115707906e-08\\
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93 8.26647202805855e-08\\
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94 7.78552030683533e-08\\
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95 8.16807953528358e-08\\
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96 7.66807903209987e-08\\
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97 7.25436978662745e-08\\
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98 6.71702595720625e-08\\
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99 7.01343166575355e-08\\
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100 6.80449977565014e-08\\
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101 6.68192875014292e-08\\
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102 6.22828481503855e-08\\
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103 6.14945471895087e-08\\
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104 6.70743224722449e-08\\
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105 6.88753801346713e-08\\
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106 6.74234915967769e-08\\
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107 6.38752997351369e-08\\
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108 6.10832293660283e-08\\
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109 5.60972305767953e-08\\
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110 5.08646226781961e-08\\
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111 4.95616876939365e-08\\
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112 4.46580704289759e-08\\
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113 4.2687817302539e-08\\
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114 4.10291135987935e-08\\
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115 3.78768817309767e-08\\
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116 3.73532344958446e-08\\
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117 3.51670172127996e-08\\
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118 3.22365221541983e-08\\
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119 3.0914108557954e-08\\
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120 3.02505081670252e-08\\
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121 2.87114558023773e-08\\
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122 2.66853087438055e-08\\
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123 2.60049357892773e-08\\
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124 2.51289922847544e-08\\
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125 2.39005712471205e-08\\
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126 2.24094810183141e-08\\
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127 2.01607019229326e-08\\
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128 1.92164353138885e-08\\
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129 1.82687256142865e-08\\
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130 1.78764123154733e-08\\
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131 1.90420480961642e-08\\
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133 1.62987103158868e-08\\
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134 1.64054691550642e-08\\
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135 1.53093691487969e-08\\
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136 1.48209887890633e-08\\
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|
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137 1.48119659868498e-08\\
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138 1.39479300275188e-08\\
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|
||||||
139 1.30269784768553e-08\\
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|
||||||
140 1.39128297693094e-08\\
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|
||||||
141 1.35601176412506e-08\\
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|
||||||
142 1.31199716923384e-08\\
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|
||||||
143 1.16605449828788e-08\\
|
|
||||||
144 1.1256315915413e-08\\
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|
||||||
145 1.10059046096852e-08\\
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|
||||||
146 1.05336940404569e-08\\
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|
||||||
147 9.87947792918718e-09\\
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|
||||||
148 9.87385221564589e-09\\
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|
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149 9.86634931285779e-09\\
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|
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150 9.87265433744658e-09\\
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|
||||||
151 8.57424740655266e-09\\
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152 7.71781430780305e-09\\
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|
||||||
};
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table[row sep=crcr]{%
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1 1\\
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mp5/img_orig-1.png
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mp5/img_orig.tex
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@ -0,0 +1,26 @@
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||||||
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% This file was created by matlab2tikz.
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%
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y dir=reverse,
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ymax=250.5,
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axis line style={draw=none},
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ticks=none,
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title style={font=\bfseries},
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||||||
|
title={Blurred Image}
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||||||
|
]
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@ -3,12 +3,12 @@
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296
mp5/res_log.tex
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mp5/res_log.tex
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@ -6,14 +6,14 @@
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scale only axis,
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@ -24,40 +24,40 @@ title={Residual norms over iteration (y is log)}
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||||||
table[row sep=crcr]{%
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table[row sep=crcr]{%
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||||||
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|
|
@ -65,115 +65,115 @@ title={Residual norms over iteration (y is log)}
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|
130 1.78770817200396e-08\\
|
||||||
131 1.90420480961642e-08\\
|
131 1.90428945268579e-08\\
|
||||||
132 1.79866998160551e-08\\
|
132 1.79884322125703e-08\\
|
||||||
133 1.62987103158868e-08\\
|
133 1.63052075399289e-08\\
|
||||||
134 1.64054691550642e-08\\
|
134 1.64180505448727e-08\\
|
||||||
135 1.53093691487969e-08\\
|
135 1.53303006209212e-08\\
|
||||||
136 1.48209887890633e-08\\
|
136 1.4871760637339e-08\\
|
||||||
137 1.48119659868498e-08\\
|
137 1.49330577072074e-08\\
|
||||||
138 1.39479300275188e-08\\
|
138 1.41966980752516e-08\\
|
||||||
139 1.30269784768553e-08\\
|
139 1.34094869141848e-08\\
|
||||||
140 1.39128297693094e-08\\
|
140 1.38131070735712e-08\\
|
||||||
141 1.35601176412506e-08\\
|
141 1.32790829181307e-08\\
|
||||||
142 1.31199716923384e-08\\
|
142 1.29281208590769e-08\\
|
||||||
143 1.16605449828788e-08\\
|
143 1.15621456920523e-08\\
|
||||||
144 1.1256315915413e-08\\
|
144 1.12246784883697e-08\\
|
||||||
145 1.10059046096852e-08\\
|
145 1.09924839400482e-08\\
|
||||||
146 1.05336940404569e-08\\
|
146 1.05286801140992e-08\\
|
||||||
147 9.87947792918718e-09\\
|
147 9.87772386372883e-09\\
|
||||||
148 9.87385221564589e-09\\
|
148 9.8725860305187e-09\\
|
||||||
149 9.86634931285779e-09\\
|
149 9.86619410929918e-09\\
|
||||||
150 9.87265433744658e-09\\
|
150 9.8729284798242e-09\\
|
||||||
151 8.57424740655266e-09\\
|
151 8.57478280643735e-09\\
|
||||||
152 7.71781430780305e-09\\
|
152 7.71779322745324e-09\\
|
||||||
};
|
};
|
||||||
\addplot [color=mycolor2, forget plot]
|
\addplot [color=mycolor2, forget plot]
|
||||||
table[row sep=crcr]{%
|
table[row sep=crcr]{%
|
||||||
|
|
@ -185,24 +185,24 @@ title={Residual norms over iteration (y is log)}
|
||||||
6 6.2599388664747e-05\\
|
6 6.2599388664747e-05\\
|
||||||
7 3.67776811885644e-05\\
|
7 3.67776811885644e-05\\
|
||||||
8 2.26985377046381e-05\\
|
8 2.26985377046381e-05\\
|
||||||
9 2.75130507463434e-05\\
|
9 2.75130507463433e-05\\
|
||||||
10 1.74951186586756e-05\\
|
10 1.74951186586757e-05\\
|
||||||
11 2.49605697423791e-05\\
|
11 2.49605697423791e-05\\
|
||||||
12 1.12366572676273e-05\\
|
12 1.12366572676273e-05\\
|
||||||
13 1.54813768580115e-05\\
|
13 1.54813768580115e-05\\
|
||||||
14 1.23158281548519e-05\\
|
14 1.23158281548519e-05\\
|
||||||
15 8.35804590504644e-06\\
|
15 8.3580459050464e-06\\
|
||||||
16 1.06813390449761e-05\\
|
16 1.06813390449761e-05\\
|
||||||
17 4.65224806020403e-06\\
|
17 4.65224806020401e-06\\
|
||||||
18 4.34451840639611e-06\\
|
18 4.34451840639607e-06\\
|
||||||
19 1.95974449943222e-06\\
|
19 1.9597444994322e-06\\
|
||||||
20 1.88311897094728e-06\\
|
20 1.88311897094725e-06\\
|
||||||
21 1.76128803348428e-06\\
|
21 1.76128803348424e-06\\
|
||||||
22 1.275240225499e-06\\
|
22 1.27524022549895e-06\\
|
||||||
23 1.36310372428718e-06\\
|
23 1.36310372428712e-06\\
|
||||||
24 1.03510657531701e-06\\
|
24 1.03510657531695e-06\\
|
||||||
25 1.00121067351798e-06\\
|
25 1.00121067351792e-06\\
|
||||||
26 9.55653227048963e-07\\
|
26 9.55653227050214e-07\\
|
||||||
};
|
};
|
||||||
\end{axis}
|
\end{axis}
|
||||||
\end{tikzpicture}%
|
\end{tikzpicture}%
|
||||||
Reference in a new issue