Merge branch 'master' of tea.maggioni.xyz:maggicl/OM
This commit is contained in:
Claudio Maggioni (maggicl)
commit
fe6d660e32
9 changed files with 1194 additions and 0 deletions
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@ -1,5 +1,6 @@
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\documentclass{scrartcl}
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\documentclass{scrartcl}
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\usepackage[utf8]{inputenc}
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\usepackage[utf8]{inputenc}
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\usepackage{float}
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\usepackage{graphicx}
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\usepackage{graphicx}
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\usepackage{subcaption}
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\usepackage{subcaption}
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\usepackage{amsmath}
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\usepackage{amsmath}
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@ -99,6 +100,18 @@ 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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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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\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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Because theorem 5.3 holds, which itself holds mainly because of this (5.10, page 106 [127]):
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@ -131,6 +144,26 @@ 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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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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\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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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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matrix?}
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32
Claudio_Maggioni_2/a1.tex
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Claudio_Maggioni_2/a1.tex
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scale only axis,
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xmin=-1,
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\addplot [color=black, mark=*, mark options={solid, black}, forget plot]
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table[row sep=crcr]{%
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0 0.47805830470258\\
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1 -0.302580121524669\\
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2 -1.39791624910794\\
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3 -2.56715639075687\\
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4 -3.69859649313088\\
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5 -5.18451648631276\\
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6 -7.47482224276235\\
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7 -11.0156865949418\\
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8 -13.5280651039553\\
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9 -17.307632058672\\
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10 -inf\\
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};
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\end{axis}
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\end{tikzpicture}%
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23
Claudio_Maggioni_2/a2.tex
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Claudio_Maggioni_2/a2.tex
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table[row sep=crcr]{%
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0 1.60311336470871\\
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1 -inf\\
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};
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\end{axis}
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\end{tikzpicture}%
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27
Claudio_Maggioni_2/a3.tex
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Claudio_Maggioni_2/a3.tex
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axis background/.style={fill=white}
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\addplot [color=black, mark=*, mark options={solid, black}, forget plot]
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table[row sep=crcr]{%
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1 0.175131370307115\\
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3 -3.07519833588777\\
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4 -6.90756348665296\\
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5 -inf\\
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};
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\end{axis}
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\end{tikzpicture}%
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31
Claudio_Maggioni_2/a4.tex
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Claudio_Maggioni_2/a4.tex
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axis background/.style={fill=white}
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table[row sep=crcr]{%
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9 -inf\\
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};
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\end{axis}
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\end{tikzpicture}%
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522
Claudio_Maggioni_2/gnorms.tex
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||||||
|
495 1.4170462377942e-05\\
|
||||||
|
496 9.81758432223143e-06\\
|
||||||
|
497 6.01201802407357e-06\\
|
||||||
|
498 2.83409247558248e-06\\
|
||||||
|
499 4.26545343219991e-16\\
|
||||||
|
};
|
||||||
|
\end{axis}
|
||||||
|
\end{tikzpicture}%
|
||||||
|
|
@ -35,11 +35,13 @@ if plots
|
||||||
plot(0:(size(ys,1)-1), ys);
|
plot(0:(size(ys,1)-1), ys);
|
||||||
sgtitle("Objective function values per iteration");
|
sgtitle("Objective function values per iteration");
|
||||||
axis([-1 500 -inf +inf]);
|
axis([-1 500 -inf +inf]);
|
||||||
|
%matlab2tikz('showInfo', false, './obvalues.tex');
|
||||||
|
|
||||||
figure;
|
figure;
|
||||||
semilogy(0:(size(gnorms,1)-1), gnorms);
|
semilogy(0:(size(gnorms,1)-1), gnorms);
|
||||||
sgtitle("Log of gradient norm per iteration");
|
sgtitle("Log of gradient norm per iteration");
|
||||||
axis([-1 500 -inf +inf]);
|
axis([-1 500 -inf +inf]);
|
||||||
|
%matlab2tikz('showInfo', false, './gnorms.tex');
|
||||||
end
|
end
|
||||||
%% 2.1 - Matrix definitions
|
%% 2.1 - Matrix definitions
|
||||||
|
|
||||||
|
|
@ -65,12 +67,16 @@ n = 10;
|
||||||
if plots
|
if plots
|
||||||
enl_plot(x1, xs1, A1);
|
enl_plot(x1, xs1, A1);
|
||||||
sgtitle("Log energy norm of the error per iter. (matrix A1)");
|
sgtitle("Log energy norm of the error per iter. (matrix A1)");
|
||||||
|
%matlab2tikz('showInfo', false, './a1.tex');
|
||||||
enl_plot(x2, xs2, A2);
|
enl_plot(x2, xs2, A2);
|
||||||
sgtitle("Log energy norm of the error per iter. (matrix A2)");
|
sgtitle("Log energy norm of the error per iter. (matrix A2)");
|
||||||
|
%matlab2tikz('showInfo', false, './a2.tex');
|
||||||
enl_plot(x3, xs3, A3)
|
enl_plot(x3, xs3, A3)
|
||||||
sgtitle("Log energy norm of the error per iter. (matrix A3)");
|
sgtitle("Log energy norm of the error per iter. (matrix A3)");
|
||||||
|
%matlab2tikz('showInfo', false, './a3.tex');
|
||||||
enl_plot(x4, xs4, A4);
|
enl_plot(x4, xs4, A4);
|
||||||
sgtitle("Log energy norm of the error per iter. (matrix A4)");
|
sgtitle("Log energy norm of the error per iter. (matrix A4)");
|
||||||
|
%matlab2tikz('showInfo', false, './a4.tex');
|
||||||
end
|
end
|
||||||
|
|
||||||
function enl_plot(xsol, xs, A)
|
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\\
|
||||||
|
5 -1.2400075952944e-06\\
|
||||||
|
6 -1.48502218454367e-06\\
|
||||||
|
7 -1.72904581590317e-06\\
|
||||||
|
8 -1.97208049739294e-06\\
|
||||||
|
9 -2.21412823703301e-06\\
|
||||||
|
10 -2.45519104284342e-06\\
|
||||||
|
11 -2.69527092284423e-06\\
|
||||||
|
12 -2.93436988505546e-06\\
|
||||||
|
13 -3.17248993749715e-06\\
|
||||||
|
14 -3.40963308818935e-06\\
|
||||||
|
15 -3.64580134515209e-06\\
|
||||||
|
16 -3.88099671640543e-06\\
|
||||||
|
17 -4.11522120996938e-06\\
|
||||||
|
18 -4.348476833864e-06\\
|
||||||
|
19 -4.58076559610935e-06\\
|
||||||
|
20 -4.81208950472541e-06\\
|
||||||
|
21 -5.04245056773228e-06\\
|
||||||
|
22 -5.27185079314997e-06\\
|
||||||
|
23 -5.50029218899853e-06\\
|
||||||
|
24 -5.72777676329799e-06\\
|
||||||
|
25 -5.95430652406841e-06\\
|
||||||
|
26 -6.1798834793298e-06\\
|
||||||
|
27 -6.40450963710222e-06\\
|
||||||
|
28 -6.6281870054057e-06\\
|
||||||
|
29 -6.85091759226031e-06\\
|
||||||
|
30 -7.07270340568605e-06\\
|
||||||
|
31 -7.29354645370299e-06\\
|
||||||
|
32 -7.51344874433114e-06\\
|
||||||
|
33 -7.73241228559059e-06\\
|
||||||
|
34 -7.95043908550132e-06\\
|
||||||
|
35 -8.16753115208339e-06\\
|
||||||
|
36 -8.38369049335685e-06\\
|
||||||
|
37 -8.59891911734177e-06\\
|
||||||
|
38 -8.81321903205812e-06\\
|
||||||
|
39 -9.02659224552598e-06\\
|
||||||
|
40 -9.2390407657654e-06\\
|
||||||
|
41 -9.45056660079637e-06\\
|
||||||
|
42 -9.66117175863905e-06\\
|
||||||
|
43 -9.87085824731335e-06\\
|
||||||
|
44 -1.00796280748393e-05\\
|
||||||
|
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\\
|
||||||
|
78 -1.66467260905761e-05\\
|
||||||
|
79 -1.6824677830537e-05\\
|
||||||
|
80 -1.70017851980713e-05\\
|
||||||
|
81 -1.71780502011986e-05\\
|
||||||
|
82 -1.73534748479392e-05\\
|
||||||
|
83 -1.75280611463132e-05\\
|
||||||
|
84 -1.77018111043402e-05\\
|
||||||
|
85 -1.78747267300409e-05\\
|
||||||
|
86 -1.80468100314348e-05\\
|
||||||
|
87 -1.82180630165421e-05\\
|
||||||
|
88 -1.8388487693383e-05\\
|
||||||
|
89 -1.85580860699773e-05\\
|
||||||
|
90 -1.87268601543451e-05\\
|
||||||
|
91 -1.88948119545067e-05\\
|
||||||
|
92 -1.90619434784818e-05\\
|
||||||
|
93 -1.92282567342906e-05\\
|
||||||
|
94 -1.93937537299532e-05\\
|
||||||
|
95 -1.95584364734893e-05\\
|
||||||
|
96 -1.97223069729193e-05\\
|
||||||
|
97 -1.98853672362632e-05\\
|
||||||
|
98 -2.0047619271541e-05\\
|
||||||
|
99 -2.02090650867726e-05\\
|
||||||
|
100 -2.03697066899782e-05\\
|
||||||
|
101 -2.05295460891778e-05\\
|
||||||
|
102 -2.06885852923914e-05\\
|
||||||
|
103 -2.08468263076392e-05\\
|
||||||
|
104 -2.10042711429409e-05\\
|
||||||
|
105 -2.11609218063169e-05\\
|
||||||
|
106 -2.13167803057871e-05\\
|
||||||
|
107 -2.14718486493715e-05\\
|
||||||
|
108 -2.16261288450902e-05\\
|
||||||
|
109 -2.17796229009631e-05\\
|
||||||
|
110 -2.19323328250106e-05\\
|
||||||
|
111 -2.20842606252522e-05\\
|
||||||
|
112 -2.22354083097083e-05\\
|
||||||
|
113 -2.2385777886399e-05\\
|
||||||
|
114 -2.25353713633441e-05\\
|
||||||
|
115 -2.26841907485638e-05\\
|
||||||
|
116 -2.28322380500781e-05\\
|
||||||
|
117 -2.29795152759071e-05\\
|
||||||
|
118 -2.31260244340707e-05\\
|
||||||
|
119 -2.32717675325889e-05\\
|
||||||
|
120 -2.3416746579482e-05\\
|
||||||
|
121 -2.35609635827698e-05\\
|
||||||
|
122 -2.37044205504726e-05\\
|
||||||
|
123 -2.38471194906101e-05\\
|
||||||
|
124 -2.39890624112026e-05\\
|
||||||
|
125 -2.41302513202701e-05\\
|
||||||
|
126 -2.42706882258324e-05\\
|
||||||
|
127 -2.44103751359098e-05\\
|
||||||
|
128 -2.45493140585224e-05\\
|
||||||
|
129 -2.46875070016901e-05\\
|
||||||
|
130 -2.48249559734329e-05\\
|
||||||
|
131 -2.4961662981771e-05\\
|
||||||
|
132 -2.50976300347242e-05\\
|
||||||
|
133 -2.52328591403127e-05\\
|
||||||
|
134 -2.53673523065564e-05\\
|
||||||
|
135 -2.55011115414756e-05\\
|
||||||
|
136 -2.56341388530901e-05\\
|
||||||
|
137 -2.57664362494202e-05\\
|
||||||
|
138 -2.58980057384856e-05\\
|
||||||
|
139 -2.60288493283066e-05\\
|
||||||
|
140 -2.61589690269032e-05\\
|
||||||
|
141 -2.62883668422953e-05\\
|
||||||
|
142 -2.6417044782503e-05\\
|
||||||
|
143 -2.65450048555465e-05\\
|
||||||
|
144 -2.66722490694456e-05\\
|
||||||
|
145 -2.67987794322206e-05\\
|
||||||
|
146 -2.69245979518913e-05\\
|
||||||
|
147 -2.70497066364779e-05\\
|
||||||
|
148 -2.71741074940006e-05\\
|
||||||
|
149 -2.72978025324786e-05\\
|
||||||
|
150 -2.74207937599329e-05\\
|
||||||
|
151 -2.75430831843832e-05\\
|
||||||
|
152 -2.76646728138492e-05\\
|
||||||
|
153 -2.77855646563519e-05\\
|
||||||
|
154 -2.79057607199107e-05\\
|
||||||
|
155 -2.80252630125452e-05\\
|
||||||
|
156 -2.81440735422763e-05\\
|
||||||
|
157 -2.8262194317123e-05\\
|
||||||
|
158 -2.83796273451063e-05\\
|
||||||
|
159 -2.84963746342461e-05\\
|
||||||
|
160 -2.8612438192562e-05\\
|
||||||
|
161 -2.87278200280746e-05\\
|
||||||
|
162 -2.88425221488035e-05\\
|
||||||
|
163 -2.89565465627689e-05\\
|
||||||
|
164 -2.90698952779907e-05\\
|
||||||
|
165 -2.91825703024894e-05\\
|
||||||
|
166 -2.92945736442844e-05\\
|
||||||
|
167 -2.94059073113959e-05\\
|
||||||
|
168 -2.95165733118442e-05\\
|
||||||
|
169 -2.96265736536492e-05\\
|
||||||
|
170 -2.9735910344831e-05\\
|
||||||
|
171 -2.98445853934095e-05\\
|
||||||
|
172 -2.99526008074053e-05\\
|
||||||
|
173 -3.00599585948374e-05\\
|
||||||
|
174 -3.01666607637271e-05\\
|
||||||
|
175 -3.02727093220927e-05\\
|
||||||
|
176 -3.0378106277956e-05\\
|
||||||
|
177 -3.04828536393361e-05\\
|
||||||
|
178 -3.05869534142538e-05\\
|
||||||
|
179 -3.06904076107282e-05\\
|
||||||
|
180 -3.07932182367798e-05\\
|
||||||
|
181 -3.08953873004289e-05\\
|
||||||
|
182 -3.09969168096946e-05\\
|
||||||
|
183 -3.10978087725977e-05\\
|
||||||
|
184 -3.11980651971581e-05\\
|
||||||
|
185 -3.12976880913968e-05\\
|
||||||
|
186 -3.13966794633319e-05\\
|
||||||
|
187 -3.14950413209845e-05\\
|
||||||
|
188 -3.15927756723748e-05\\
|
||||||
|
189 -3.16898845255228e-05\\
|
||||||
|
190 -3.17863698884481e-05\\
|
||||||
|
191 -3.18822337691713e-05\\
|
||||||
|
192 -3.19774781757112e-05\\
|
||||||
|
193 -3.20721051160898e-05\\
|
||||||
|
194 -3.21661165983263e-05\\
|
||||||
|
195 -3.22595146304395e-05\\
|
||||||
|
196 -3.23523012204516e-05\\
|
||||||
|
197 -3.24444783763807e-05\\
|
||||||
|
198 -3.25360481062477e-05\\
|
||||||
|
199 -3.26270124180731e-05\\
|
||||||
|
200 -3.27173733198765e-05\\
|
||||||
|
201 -3.28071328196771e-05\\
|
||||||
|
202 -3.28962929254965e-05\\
|
||||||
|
203 -3.29848556453538e-05\\
|
||||||
|
204 -3.30728229872694e-05\\
|
||||||
|
205 -3.31601969592628e-05\\
|
||||||
|
206 -3.32469795693543e-05\\
|
||||||
|
207 -3.33331728255645e-05\\
|
||||||
|
208 -3.34187787359135e-05\\
|
||||||
|
209 -3.35037993084193e-05\\
|
||||||
|
210 -3.35882365511042e-05\\
|
||||||
|
211 -3.36720924719877e-05\\
|
||||||
|
212 -3.37553690790896e-05\\
|
||||||
|
213 -3.38380683804296e-05\\
|
||||||
|
214 -3.39201923840285e-05\\
|
||||||
|
215 -3.40017430979061e-05\\
|
||||||
|
216 -3.40827225300819e-05\\
|
||||||
|
217 -3.41631326885767e-05\\
|
||||||
|
218 -3.42429755814097e-05\\
|
||||||
|
219 -3.43222532166018e-05\\
|
||||||
|
220 -3.4400967602173e-05\\
|
||||||
|
221 -3.44791207461421e-05\\
|
||||||
|
222 -3.45567146565305e-05\\
|
||||||
|
223 -3.46337513413574e-05\\
|
||||||
|
224 -3.47102328086444e-05\\
|
||||||
|
225 -3.47861610664094e-05\\
|
||||||
|
226 -3.48615381226735e-05\\
|
||||||
|
227 -3.49363659854567e-05\\
|
||||||
|
228 -3.50106466627788e-05\\
|
||||||
|
229 -3.50843821626602e-05\\
|
||||||
|
230 -3.51575744931207e-05\\
|
||||||
|
231 -3.52302256621806e-05\\
|
||||||
|
232 -3.53023376778599e-05\\
|
||||||
|
233 -3.53739125481775e-05\\
|
||||||
|
234 -3.54449522811552e-05\\
|
||||||
|
235 -3.55154588848124e-05\\
|
||||||
|
236 -3.55854343671688e-05\\
|
||||||
|
237 -3.56548807362442e-05\\
|
||||||
|
238 -3.57238000000597e-05\\
|
||||||
|
239 -3.57921941666347e-05\\
|
||||||
|
240 -3.5860065243989e-05\\
|
||||||
|
241 -3.59274152401429e-05\\
|
||||||
|
242 -3.59942461631166e-05\\
|
||||||
|
243 -3.60605600209297e-05\\
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||||||
|
};
|
||||||
|
\end{axis}
|
||||||
|
\end{tikzpicture}%
|
||||||
Reference in a new issue