From be8d72338a51aede7f168380e8caaeb2a256a579 Mon Sep 17 00:00:00 2001 From: Enzo De Carvalho Bittencourt <enzo.decarvalhobittencourt@ensiie.eu> Date: Mon, 11 Dec 2023 20:06:51 +0100 Subject: [PATCH] updated report --- MonteCarlo/rapport/rendu.pdf | Bin 0 -> 180054 bytes Normal/rapport/rendu.pdf | Bin 0 -> 1317252 bytes README.md | 9 ++++ Sequences/main.py | 4 +- Sequences/rapport/rendu.aux | 13 +----- Sequences/rapport/rendu.fdb_latexmk | 27 ++++------- Sequences/rapport/rendu.fls | 26 +---------- Sequences/rapport/rendu.log | 32 ++++--------- Sequences/rapport/rendu.out | 3 -- Sequences/rapport/rendu.pdf | Bin 0 -> 19512 bytes Sequences/rapport/rendu.synctex.gz | Bin 6132 -> 2668 bytes Sequences/rapport/rendu.tex | 69 +--------------------------- rendu.pdf | Bin 0 -> 1561568 bytes 13 files changed, 32 insertions(+), 151 deletions(-) create mode 100644 MonteCarlo/rapport/rendu.pdf create mode 100644 Normal/rapport/rendu.pdf create mode 100644 Sequences/rapport/rendu.pdf create mode 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@@ Ce dossier contient les projets de SIGI (Simulations Informatiques et Gestions des Incertitudes) contact : enzo.decarvalhobittencourt@ensiie.eu + +dépendances (disponibles sur pip): + - numpy + - seaborn + - matplotlib + +Pour lancer les différents calculs : +- Pour chaque projet, se placer dans le dossier et éxecuter le main.py +(`python3 main.py`) diff --git a/Sequences/main.py b/Sequences/main.py index c61a012..fb63bdb 100644 --- a/Sequences/main.py +++ b/Sequences/main.py @@ -145,8 +145,8 @@ if __name__ == "__main__": jobs = [ #[j_testVenDerMany,[]], - #[j_testVenDerManyD,[]], - [j_MonteCarlo,[]] + [j_testVenDerManyD,[]], + #[j_MonteCarlo,[]] ] diff --git a/Sequences/rapport/rendu.aux b/Sequences/rapport/rendu.aux index 5c9a6a5..5f97655 100644 --- a/Sequences/rapport/rendu.aux +++ b/Sequences/rapport/rendu.aux @@ -17,16 +17,5 @@ \providecommand*\HyPL@Entry[1]{} \HyPL@Entry{0<</S/D>>} \babel@aux{english}{} -\@writefile{toc}{\contentsline {section}{\numberline {1}Calcul 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Le but est ici de travailler sur la méthode de Monte Carlo, mesurer son erreur et son intervalle de confiance. Pour cela, nous utilisons ici \textit{Python}. Le code sur lequel ce rendu s'appuie est mis à dispositions dans le dossier -\texttt{MonteCarlo} du dêpot git sur +\texttt{Sequence} du dêpot git sur \hyperlink{https://git.iiens.net/de-carva2021/SIGI/}{\texttt{https://git.iiens.net/de-carva2021/SIGI/}} - -\section{Calcul d'intégrales} -Le but est ici de calculer l'intégrale $J$ : -$$ J = \int_{0.1}^{0.9} \frac{1}{2}e^{\arcsin(x)} \frac{x}{\sqrt{1-x^2}}dx $$ -\`A partir de différentes méthode numérique, et de comparer les résultats -obtenus, et la convergence des méthodes. - -On comparera nos résultats avec une solution analytique, cacluler à l'aide de -cette expression : -{\center -\texttt{ I = .25*(np.exp(np.arcsin(.9))*(.9 - np.sqrt(0.19)) -\\+ np.exp(np.arcsin(.1))*(np.sqrt(0.99) - 0.1))}\\ -} -(\texttt{np} faisant ici référence au paquet -\texttt{numpy} de python.) - -\subsection{Méthode de Quadrature} -On opte pour une méthode des rectangles (intégrale de Riemann), puis pour une -méthode des trapèzes. On trace ensuite l'évolution de l'erreur (différence) -entre les intégrales obtenues de cette manière avec la solution I -[\ref{fig:tra}], [\ref{fig:rec}]. - -On note que ces méthodes converge de manière inverse. - -\begin{figure} - \centering - \includegraphics - {figures/Error_evolution_of_jQuadrature_rect_by_number_of_points.png} - \caption{\'Evolution de l'erreur par la méthode des rectangles} - \label{fig:rec} -\end{figure} - -\begin{figure} - \centering - \includegraphics - {figures/Error_evolution_of_jQuadrature_trap_by_number_of_points.png} - \caption{\'Evolution de l'erreur par la méthode des trapèzes} - \label{fig:tra} -\end{figure} - - -\subsection{Méthode de MonteCarlo} -Pour la méthode de MonteCarlo, on tire N valeurs aléatoires entre 0.1 et 0.9, -sur lequels ensuite l'on calcule leurs images par la fonction à intégrer, et -l'on multiplie la somme de ces résultats par $\frac{0.9 - 0.1}{N}$. L'on note -que les résultats obtenus convergent beaucoup moins vite. -\begin{figure} - \centering - \includegraphics - {figures/Error_evolution_of_jMonteCarlo_by_number_of_points.png} - \caption{\'Evolution de l'erreur par la méthode de Monte-Carlo} - \label{fig:MC} -\end{figure} - -Afin de mieux représenter l'évolution de l'erreur comise par la méthode de -MonteCarlo, on réalise plusieurs tests, et on les affiches superposés -(\ref{fig:lot}). - -\begin{figure} - \centering - \includegraphics{figures/Error evolution of jMonteCarlo_lot by number of points.png} - \caption{Superpositions de 120 tests par la Méthode de MonteCarlo} - \label{fig:lot} -\end{figure} - \end{document} diff --git a/rendu.pdf b/rendu.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c8b8f68561e5f391d7139db4014a08a930eede52 GIT binary patch literal 1561568 zcmc$^1#lg~mL+HlEtV{1W@ct)W@ct)i<z03nOU-!(PCy<mc?w*lz+qTneN@_-I(1` zRAjuTmz9-y;hb}C6sdxU7%d|mD>Uih)%g=N6B_{ofxVFxG!GBGn5B)2sS~}JjiHOF 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