mp5: correction to terminating condition of myCG
This commit is contained in:
parent
f001099b7a
commit
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11 changed files with 61 additions and 164 deletions
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@ -127,6 +127,9 @@ My implementation is in the file \texttt{deblurring.m}. Plots for the original i
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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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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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\ref{fig:mycg}, \ref{fig:pcg}, and \ref{fig:rvec}.
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As a terminating condition for the \texttt{myCG} implementation, I chose to check if the residual divided by the 2-norm of
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$b$ is less than the given tolerance. This mimicks the behaviour of MATLAB's \texttt{pcg} to allow for a better comparison.
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\begin{figure}[h]
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\begin{figure}[h]
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\begin{subfigure}{0.33\textwidth}
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\begin{subfigure}{0.33\textwidth}
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\centering
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\centering
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@ -26,7 +26,7 @@ bt = A' * b;
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IL = ichol(AT, struct('type', 'nofill', 'diagcomp', 0.01));
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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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[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, flag, ~, ~, rvec2] = pcg(AT, bt, 1e-6, 200, IL, IL');
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X2 = zeros(250, 250);
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X2 = zeros(250, 250);
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for i = 0:249
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for i = 0:249
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@ -17,7 +17,7 @@ function [x,rvec] = myCG(A, b, x0, max_itr, tol)
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delta_old = delta_new;
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delta_old = delta_new;
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rvec(i + 1) = delta_new;
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rvec(i + 1) = delta_new;
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if delta_new < tol
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if delta_new / norm(b) < tol
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rvec = rvec(1:i+1);
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rvec = rvec(1:i+1);
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break
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break
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end
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end
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BIN
mp5/img_my-1.png
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mp5/img_my-1.png
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@ -3,12 +3,12 @@
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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=2.604in,
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width=1.736in,
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height=2.604in,
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height=1.736in,
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at={(0.962in,0.66in)},
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at={(0.75in,0.653in)},
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scale only axis,
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scale only axis,
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point meta min=-0.0128979816802523,
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point meta min=-0.0235938830592792,
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point meta max=0.983438722992887,
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point meta max=0.99393991750956,
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axis on top,
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axis on top,
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xmin=0.5,
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xmin=0.5,
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xmax=250.5,
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xmax=250.5,
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@ -3,9 +3,9 @@
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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=2.604in,
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width=1.736in,
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height=2.604in,
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height=1.736in,
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at={(0.962in,0.66in)},
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at={(0.75in,0.653in)},
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scale only axis,
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scale only axis,
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point meta min=0.0282583971491394,
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point meta min=0.0282583971491394,
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point meta max=0.921555841989536,
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point meta max=0.921555841989536,
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@ -3,12 +3,12 @@
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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=2.604in,
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width=1.736in,
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height=2.604in,
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height=1.736in,
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at={(0.962in,0.66in)},
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at={(0.75in,0.653in)},
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scale only axis,
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scale only axis,
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point meta min=-0.0235938830592846,
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point meta min=0.0282583971491394,
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point meta max=0.993939917509565,
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point meta max=0.921555841989536,
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axis on top,
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axis on top,
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xmin=0.5,
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xmin=0.5,
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xmax=250.5,
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xmax=250.5,
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192
mp5/res_log.tex
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mp5/res_log.tex
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@ -6,14 +6,14 @@
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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=4.521in,
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width=6.028in,
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height=3.566in,
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height=4.754in,
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at={(0.758in,0.481in)},
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at={(1.011in,0.642in)},
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scale only axis,
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scale only axis,
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xmin=0,
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xmin=0,
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xmax=160,
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xmax=50,
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ymode=log,
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ymode=log,
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ymin=1e-10,
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ymin=1e-07,
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ymax=1,
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ymax=1,
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yminorticks=true,
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yminorticks=true,
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axis background/.style={fill=white},
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axis background/.style={fill=white},
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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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1 1\\
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1 1\\
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2 0.557596535615506\\
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2 0.557596535615506\\
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3 0.0776565625508994\\
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3 0.0776565625508993\\
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4 0.0198777323861488\\
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4 0.0198777323861488\\
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5 0.0079699888022587\\
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5 0.00796998880225869\\
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6 0.00379999756962288\\
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6 0.00379999756962287\\
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7 0.00203749487265271\\
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7 0.0020374948726527\\
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8 0.00117378505868276\\
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8 0.00117378505868276\\
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9 0.000679072640424651\\
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9 0.000679072640424649\\
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10 0.000460205525227465\\
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10 0.000460205525227464\\
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11 0.000299176988582771\\
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11 0.000299176988582771\\
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12 0.000208705837325249\\
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12 0.000208705837325249\\
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13 0.000154155368421639\\
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13 0.000154155368421638\\
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14 0.000112123271112138\\
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14 0.000112123271112138\\
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15 8.51723029158507e-05\\
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15 8.51723029158506e-05\\
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16 6.84145894011082e-05\\
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16 6.84145894011081e-05\\
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17 5.22773173463894e-05\\
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17 5.22773173463893e-05\\
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18 4.19658990284637e-05\\
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18 4.19658990284636e-05\\
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19 3.35813556680048e-05\\
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19 3.35813556680048e-05\\
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20 2.69909819855067e-05\\
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20 2.69909819855066e-05\\
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21 2.16953761012216e-05\\
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21 2.16953761012216e-05\\
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22 1.75366202909715e-05\\
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22 1.75366202909715e-05\\
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23 1.58613744370523e-05\\
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23 1.58613744370523e-05\\
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24 1.07527796769547e-05\\
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24 1.07527796769547e-05\\
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25 1.21386374874815e-05\\
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25 1.21386374874815e-05\\
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26 1.0281869987924e-05\\
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26 1.02818699879239e-05\\
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27 8.94827138078528e-06\\
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27 8.94827138078525e-06\\
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28 7.32098660262364e-06\\
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28 7.32098660262362e-06\\
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29 6.29855369167728e-06\\
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29 6.29855369167726e-06\\
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30 5.75608316894849e-06\\
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30 5.75608316894847e-06\\
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31 5.01303204699424e-06\\
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31 5.01303204699423e-06\\
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32 4.32711144148809e-06\\
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32 4.32711144148808e-06\\
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33 3.75161010629662e-06\\
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33 3.75161010629661e-06\\
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34 3.13429056757288e-06\\
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34 3.13429056757287e-06\\
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35 2.97535388105767e-06\\
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35 2.97535388105766e-06\\
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36 2.59579082920429e-06\\
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36 2.59579082920428e-06\\
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37 2.35613630297938e-06\\
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37 2.35613630297938e-06\\
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38 2.13570046200869e-06\\
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38 2.13570046200869e-06\\
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39 1.91918226507556e-06\\
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39 1.91918226507556e-06\\
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@ -65,115 +65,9 @@ title={Residual norms over iteration (y is log)}
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41 1.60497187780807e-06\\
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41 1.60497187780807e-06\\
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42 1.50673230165654e-06\\
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42 1.50673230165654e-06\\
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43 1.29912483256279e-06\\
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43 1.29912483256279e-06\\
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44 1.18346887626956e-06\\
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44 1.18346887626955e-06\\
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45 1.20647020748118e-06\\
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45 1.20647020748118e-06\\
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46 9.32512402536184e-07\\
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46 9.3251240253618e-07\\
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47 1.04433975171041e-06\\
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48 7.81977076368343e-07\\
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49 7.06367946061841e-07\\
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50 6.44485405918065e-07\\
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51 5.85991971721864e-07\\
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52 5.19890971305921e-07\\
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53 4.77565688325085e-07\\
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54 4.45837257417216e-07\\
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55 4.52354751810169e-07\\
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56 4.29038013881607e-07\\
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57 4.1992973890364e-07\\
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58 3.83172910236925e-07\\
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59 3.69121286102558e-07\\
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60 3.71629459514197e-07\\
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61 3.46046785121528e-07\\
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62 3.27576103337777e-07\\
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63 3.15320978192872e-07\\
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64 2.96758711344721e-07\\
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65 2.96817636331728e-07\\
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66 2.71124713000926e-07\\
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67 2.6290901313501e-07\\
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68 2.43462036182129e-07\\
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69 2.28404291071362e-07\\
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70 2.24415864473542e-07\\
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71 2.28468445317066e-07\\
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72 2.16184931431008e-07\\
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73 2.03658004162589e-07\\
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74 1.83416377348944e-07\\
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75 1.77025922497327e-07\\
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76 1.70006600401104e-07\\
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77 1.63491825605372e-07\\
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78 1.57088823572822e-07\\
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79 1.62321574880195e-07\\
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80 1.55517018193352e-07\\
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81 1.44132341985947e-07\\
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82 1.33984748126281e-07\\
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83 1.2519682821657e-07\\
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84 1.21215390780982e-07\\
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85 1.15338855777103e-07\\
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86 1.08276150400166e-07\\
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87 1.0480512415693e-07\\
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88 1.01804326380995e-07\\
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89 1.00101662634653e-07\\
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90 9.48101967192299e-08\\
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91 8.8924065689681e-08\\
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92 8.8198911570793e-08\\
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93 8.26647202805877e-08\\
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94 7.78552030683553e-08\\
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95 8.16807953528378e-08\\
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96 7.66807903210005e-08\\
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97 7.25436978662762e-08\\
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98 6.71702595720641e-08\\
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99 7.01343166575373e-08\\
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100 6.80449977565033e-08\\
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101 6.68192875014314e-08\\
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102 6.22828481503882e-08\\
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103 6.14945471895139e-08\\
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104 6.70743224722515e-08\\
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105 6.88753801346864e-08\\
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106 6.74234915968034e-08\\
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107 6.3875299735169e-08\\
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108 6.10832293660889e-08\\
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109 5.60972305769167e-08\\
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110 5.08646226784856e-08\\
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111 4.9561687694454e-08\\
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112 4.46580704300798e-08\\
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113 4.26878173046204e-08\\
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114 4.10291136047614e-08\\
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115 3.78768817391897e-08\\
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116 3.73532345146491e-08\\
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117 3.51670172399507e-08\\
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118 3.22365221922065e-08\\
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119 3.09141086362976e-08\\
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120 3.02505083958211e-08\\
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121 2.87114562212435e-08\\
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122 2.66853094500274e-08\\
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123 2.6004937830953e-08\\
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124 2.5128996812777e-08\\
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125 2.3900587385536e-08\\
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126 2.2409516154494e-08\\
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127 2.01607767874174e-08\\
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128 1.92165407176116e-08\\
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129 1.82690090540455e-08\\
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130 1.78770817200396e-08\\
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131 1.90428945268579e-08\\
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132 1.79884322125703e-08\\
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133 1.63052075399289e-08\\
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134 1.64180505448727e-08\\
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135 1.53303006209212e-08\\
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136 1.4871760637339e-08\\
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137 1.49330577072074e-08\\
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138 1.41966980752516e-08\\
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139 1.34094869141848e-08\\
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140 1.38131070735712e-08\\
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141 1.32790829181307e-08\\
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142 1.29281208590769e-08\\
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143 1.15621456920523e-08\\
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144 1.12246784883697e-08\\
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145 1.09924839400482e-08\\
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146 1.05286801140992e-08\\
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147 9.87772386372883e-09\\
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148 9.8725860305187e-09\\
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149 9.86619410929918e-09\\
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150 9.8729284798242e-09\\
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151 8.57478280643735e-09\\
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152 7.71779322745324e-09\\
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};
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};
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\addplot [color=mycolor2, forget plot]
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\addplot [color=mycolor2, forget plot]
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table[row sep=crcr]{%
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table[row sep=crcr]{%
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@ -185,24 +79,24 @@ title={Residual norms over iteration (y is log)}
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6 6.2599388664747e-05\\
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6 6.2599388664747e-05\\
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7 3.67776811885644e-05\\
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7 3.67776811885644e-05\\
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8 2.26985377046381e-05\\
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8 2.26985377046381e-05\\
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9 2.75130507463433e-05\\
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9 2.75130507463434e-05\\
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10 1.74951186586757e-05\\
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10 1.74951186586756e-05\\
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11 2.49605697423791e-05\\
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11 2.49605697423791e-05\\
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12 1.12366572676273e-05\\
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12 1.12366572676273e-05\\
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13 1.54813768580115e-05\\
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13 1.54813768580115e-05\\
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14 1.23158281548519e-05\\
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14 1.23158281548519e-05\\
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15 8.3580459050464e-06\\
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15 8.35804590504644e-06\\
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16 1.06813390449761e-05\\
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16 1.06813390449761e-05\\
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17 4.65224806020401e-06\\
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17 4.65224806020403e-06\\
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18 4.34451840639607e-06\\
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18 4.34451840639611e-06\\
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19 1.9597444994322e-06\\
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19 1.95974449943222e-06\\
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20 1.88311897094725e-06\\
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20 1.88311897094728e-06\\
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21 1.76128803348424e-06\\
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21 1.76128803348428e-06\\
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22 1.27524022549895e-06\\
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22 1.275240225499e-06\\
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23 1.36310372428712e-06\\
|
23 1.36310372428718e-06\\
|
||||||
24 1.03510657531695e-06\\
|
24 1.03510657531701e-06\\
|
||||||
25 1.00121067351792e-06\\
|
25 1.00121067351798e-06\\
|
||||||
26 9.55653227050214e-07\\
|
26 9.55653227048963e-07\\
|
||||||
};
|
};
|
||||||
\end{axis}
|
\end{axis}
|
||||||
\end{tikzpicture}%
|
\end{tikzpicture}%
|
||||||
Reference in a new issue