hw2: added plots to report
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\documentclass{scrartcl}
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\usepackage[utf8]{inputenc}
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\usepackage{float}
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\usepackage{graphicx}
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\usepackage{subcaption}
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\usepackage{amsmath}
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@ -72,6 +73,18 @@ use semilogy) as functions of the iterations.}
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The solution of this task can be found in Section 1.5 of the script \texttt{main.m}.
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\begin{figure}[H]
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{\textwidth}{\input{obvalues}}
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\caption{Objective function values w.r.t. iteration number}
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\end{subfigure}
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{\textwidth}{\input{gnorms}}
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\caption{Norm of the gradient w.r.t. iteration number \\ (y-axis is log scaled)}
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\end{subfigure}
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\caption{Plots for Exercise 1.4.}
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\end{figure}
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\subsection{Finally, explain why the Conjugate Gradient method is a Krylov subspace method.}
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Because theorem 5.3 holds, which itself holds mainly because of this (5.10, page 106 [127]):
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@ -104,6 +117,26 @@ and plot it with respect to the number of iteration.}
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The solution of this task can be found in section 2.3 of the \texttt{main.m} MATLAB script.
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\begin{figure}[H]
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{!}{\input{a1}}
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\caption{First matrix}
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\end{subfigure}
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{!}{\input{a2}}
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\caption{Second matrix}
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\end{subfigure}
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{!}{\input{a3}}
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\caption{Third matrix}
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\end{subfigure}
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{!}{\input{a4}}
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\caption{Fourth matrix}
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\end{subfigure}
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\caption{Plots of logarithm energy norm of the error per iteration. Minus infinity logarithms not shown in the plot.}
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\end{figure}
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\subsection{Comment on the convergence of the method for the different matrices. What can you say observing
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the number of iterations obtained and the number of clusters of the eigenvalues of the related
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matrix?}
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Claudio_Maggioni_2/a1.tex
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Claudio_Maggioni_2/a1.tex
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% This file was created by matlab2tikz.
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Claudio_Maggioni_2/a2.tex
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Claudio_Maggioni_2/a2.tex
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% This file was created by matlab2tikz.
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Claudio_Maggioni_2/a3.tex
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Claudio_Maggioni_2/a3.tex
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% This file was created by matlab2tikz.
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31
Claudio_Maggioni_2/a4.tex
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Claudio_Maggioni_2/a4.tex
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% This file was created by matlab2tikz.
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522
Claudio_Maggioni_2/gnorms.tex
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Claudio_Maggioni_2/gnorms.tex
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
278 0.00467663130722396\\
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||||
279 0.00464502050490086\\
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280 0.00461348124703293\\
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||||
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||||
282 0.00455061801642291\\
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||||
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||||
284 0.00448804293013615\\
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||||
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||||
286 0.00442575732116265\\
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||||
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||||
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||||
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||||
290 0.00430205996091684\\
|
||||
291 0.00427131867940353\\
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||||
292 0.00424065097076077\\
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
312 0.00364302938162671\\
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||||
313 0.00361394967000176\\
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||||
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||||
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||||
316 0.00352717809944686\\
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||||
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||||
318 0.00346972213601006\\
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||||
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329 0.0031593998446833\\
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330 0.00313167218554325\\
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331 0.00310402611800003\\
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||||
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||||
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||||
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||||
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||||
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360 0.00233894202518255\\
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364 0.00223918416376428\\
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366 0.00218985137455768\\
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368 0.00214088628711106\\
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369 0.00211654249850854\\
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||||
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||||
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||||
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||||
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||||
385 0.00173994006029262\\
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||||
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387 0.00169461667756041\\
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||||
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||||
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||||
393 0.0015610640834086\\
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||||
394 0.0015391627213757\\
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||||
395 0.00151736474782592\\
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||||
396 0.00149567065545892\\
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||||
397 0.0014740809440871\\
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||||
398 0.00145259612080798\\
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||||
399 0.00143121670018043\\
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||||
400 0.00140994320441235\\
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401 0.00138877616355118\\
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||||
402 0.00136771611567928\\
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||||
403 0.00134676360712423\\
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||||
404 0.0013259191926667\\
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||||
405 0.00130518343576434\\
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||||
406 0.00128455690877751\\
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||||
407 0.00126404019320747\\
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||||
408 0.00124363387994308\\
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||||
409 0.00122333856951558\\
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||||
410 0.00120315487236122\\
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||||
411 0.00118308340910146\\
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||||
412 0.00116312481082477\\
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||||
413 0.00114327971938729\\
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||||
414 0.0011235487877217\\
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||||
415 0.00110393268015729\\
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
485 7.9531522846157e-05\\
|
||||
486 7.15292601814999e-05\\
|
||||
487 6.38142980942563e-05\\
|
||||
488 5.63977281764285e-05\\
|
||||
489 4.9292030273616e-05\\
|
||||
490 4.25113871340903e-05\\
|
||||
491 3.6072108144126e-05\\
|
||||
492 2.99932155320352e-05\\
|
||||
493 2.4297281571859e-05\\
|
||||
494 1.90116702899788e-05\\
|
||||
495 1.4170462377942e-05\\
|
||||
496 9.81758432223143e-06\\
|
||||
497 6.01201802407357e-06\\
|
||||
498 2.83409247558248e-06\\
|
||||
499 4.26545343219991e-16\\
|
||||
};
|
||||
\end{axis}
|
||||
\end{tikzpicture}%
|
||||
|
|
@ -26,11 +26,13 @@ if plots
|
|||
plot(0:(size(ys,1)-1), ys);
|
||||
sgtitle("Objective function values per iteration");
|
||||
axis([-1 500 -inf +inf]);
|
||||
%matlab2tikz('showInfo', false, './obvalues.tex');
|
||||
|
||||
figure;
|
||||
semilogy(0:(size(gnorms,1)-1), gnorms);
|
||||
sgtitle("Log of gradient norm per iteration");
|
||||
axis([-1 500 -inf +inf]);
|
||||
%matlab2tikz('showInfo', false, './gnorms.tex');
|
||||
end
|
||||
%% 2.1 - Matrix definitions
|
||||
|
||||
|
|
@ -56,12 +58,16 @@ n = 10;
|
|||
if plots
|
||||
enl_plot(x1, xs1, A1);
|
||||
sgtitle("Log energy norm of the error per iter. (matrix A1)");
|
||||
%matlab2tikz('showInfo', false, './a1.tex');
|
||||
enl_plot(x2, xs2, A2);
|
||||
sgtitle("Log energy norm of the error per iter. (matrix A2)");
|
||||
%matlab2tikz('showInfo', false, './a2.tex');
|
||||
enl_plot(x3, xs3, A3)
|
||||
sgtitle("Log energy norm of the error per iter. (matrix A3)");
|
||||
%matlab2tikz('showInfo', false, './a3.tex');
|
||||
enl_plot(x4, xs4, A4);
|
||||
sgtitle("Log energy norm of the error per iter. (matrix A4)");
|
||||
%matlab2tikz('showInfo', false, './a4.tex');
|
||||
end
|
||||
|
||||
function enl_plot(xsol, xs, A)
|
||||
|
|
|
|||
520
Claudio_Maggioni_2/obvalues.tex
Normal file
520
Claudio_Maggioni_2/obvalues.tex
Normal file
|
|
@ -0,0 +1,520 @@
|
|||
% This file was created by matlab2tikz.
|
||||
%
|
||||
\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
|
||||
%
|
||||
\begin{tikzpicture}
|
||||
|
||||
\begin{axis}[%
|
||||
width=6.028in,
|
||||
height=4.754in,
|
||||
at={(1.011in,0.642in)},
|
||||
scale only axis,
|
||||
xmin=-1,
|
||||
xmax=500,
|
||||
axis background/.style={fill=white}
|
||||
]
|
||||
\addplot [color=mycolor1, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
0 0\\
|
||||
1 -2.49999498998749e-07\\
|
||||
2 -4.98998000007523e-07\\
|
||||
3 -7.46997511046363e-07\\
|
||||
4 -9.94000040135306e-07\\
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
26 -6.1798834793298e-06\\
|
||||
27 -6.40450963710222e-06\\
|
||||
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|
||||
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||||
30 -7.07270340568605e-06\\
|
||||
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|
||||
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|
||||
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|
||||
34 -7.95043908550132e-06\\
|
||||
35 -8.16753115208339e-06\\
|
||||
36 -8.38369049335685e-06\\
|
||||
37 -8.59891911734177e-06\\
|
||||
38 -8.81321903205812e-06\\
|
||||
39 -9.02659224552598e-06\\
|
||||
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|
||||
41 -9.45056660079637e-06\\
|
||||
42 -9.66117175863905e-06\\
|
||||
43 -9.87085824731335e-06\\
|
||||
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|
||||
45 -1.02874832492371e-05\\
|
||||
46 -1.04944257785266e-05\\
|
||||
47 -1.0700457670728e-05\\
|
||||
48 -1.09055809338613e-05\\
|
||||
49 -1.11097975759464e-05\\
|
||||
50 -1.13131096050035e-05\\
|
||||
51 -1.15155190290526e-05\\
|
||||
52 -1.17170278561137e-05\\
|
||||
53 -1.19176380942069e-05\\
|
||||
54 -1.21173517513522e-05\\
|
||||
55 -1.23161708355696e-05\\
|
||||
56 -1.25140973548793e-05\\
|
||||
57 -1.27111333173011e-05\\
|
||||
58 -1.29072807308553e-05\\
|
||||
59 -1.31025416035617e-05\\
|
||||
60 -1.32969179434405e-05\\
|
||||
61 -1.34904117585117e-05\\
|
||||
62 -1.36830250567953e-05\\
|
||||
63 -1.38747598463113e-05\\
|
||||
64 -1.40656181350799e-05\\
|
||||
65 -1.42556019311211e-05\\
|
||||
66 -1.44447132424548e-05\\
|
||||
67 -1.46329540771011e-05\\
|
||||
68 -1.48203264430801e-05\\
|
||||
69 -1.50068323484119e-05\\
|
||||
70 -1.51924738011164e-05\\
|
||||
71 -1.53772528092136e-05\\
|
||||
72 -1.55611713807237e-05\\
|
||||
73 -1.57442315236667e-05\\
|
||||
74 -1.59264352460625e-05\\
|
||||
75 -1.61077845559314e-05\\
|
||||
76 -1.62882814612932e-05\\
|
||||
77 -1.6467927970168e-05\\
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||||
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||||
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||||
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||||
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||||
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||||
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||||
498 -4.17083322457828e-05\\
|
||||
499 -4.17083332497933e-05\\
|
||||
};
|
||||
\end{axis}
|
||||
\end{tikzpicture}%
|
||||
Reference in a new issue