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Change n=6 to n=10

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Cory Balaton 2023-09-25 14:19:58 +02:00
parent d6e0090fb8
commit 8d7c20f919
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3 changed files with 11 additions and 15 deletions
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10
latex/problems/problem-6.tex
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@ -1,18 +1,18 @@
\section*{Problem 6} \section*{Problem 6}
\subsection*{a)} \subsection*{a)}
The plot in Figure \ref{fig:eigenvector_6} is showing the discretization of $\hat{x}$ with $n=6$. The plot in Figure \ref{fig:eigenvector_10} is showing the discretization of $\hat{x}$ with $n=10$.
The eigenvectors and corresponding analytical eigenvectors have a complete overlap suggesting the implementation of the algorithm is correct. The eigenvectors and corresponding analytical eigenvectors have a complete overlap suggesting the implementation of the algorithm is correct.
We have included the boundary points for each vector to show a complete solution. We have included the boundary points for each vector to show a complete solution.
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=0.8\textwidth]{images/eigenvector_6.pdf} \includegraphics[width=0.8\textwidth]{images/eigenvector_10.pdf}
\caption{The plot is showing the elements of eigenvector $\vec{v}_{1}, \vec{v}_{2}, \vec{v}_{3}$, corresponding to the three lowest eigenvalues of matrix $\boldsymbol{A} (6 \cross 6)$, against the position $\hat{x}$. The analytical eigenvectors $\vec{v}^{(1)}, \vec{v}^{(2)}, \vec{v}^{(3)}$ are also included in the plot.} \caption{The plot is showing the elements of eigenvector $\vec{v}_{1}, \vec{v}_{2}, \vec{v}_{3}$, corresponding to the three lowest eigenvalues of matrix $\boldsymbol{A} (10 \cross 10)$, against the position $\hat{x}$. The analytical eigenvectors $\vec{v}^{(1)}, \vec{v}^{(2)}, \vec{v}^{(3)}$ are also included in the plot.}
\label{fig:eigenvector_6} \label{fig:eigenvector_10}
\end{figure} \end{figure}
\subsection*{b)} \subsection*{b)}
For the discretization with $n=100$ the solution is visually close to a continous curve, with a complete overlap of the analytical eigenvectors, presented in Figure \ref{fig:eigenvector_100}. For the discretization with $n=100$ the solution is visually close to a continuous curve, with a complete overlap of the analytical eigenvectors, presented in Figure \ref{fig:eigenvector_100}.
\begin{figure} \begin{figure}
\centering \centering
\includegraphics[width=0.8\textwidth]{images/eigenvector_100.pdf} \includegraphics[width=0.8\textwidth]{images/eigenvector_100.pdf}

6
src/main.cpp
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@ -156,9 +156,9 @@ void write_eigenvec(int N)
int main() int main()
{ {
// write_transformation_tridiag(100); write_transformation_tridiag(100);
// write_transformation_dense(100); write_transformation_dense(100);
write_eigenvec(6); write_eigenvec(10);
write_eigenvec(100); write_eigenvec(100);
return 0; return 0;
} }

8
src/plot.py
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@ -24,7 +24,6 @@ def plot_transformations(save: bool=False) -> None:
fig.savefig("../latex/images/transform.pdf") fig.savefig("../latex/images/transform.pdf")
def plot_eigenvectors(N: int, save: bool=False) -> None: def plot_eigenvectors(N: int, save: bool=False) -> None:
# Load data based on matrix size # Load data based on matrix size
path = f"../latex/output/eigenvector_{N}.csv" path = f"../latex/output/eigenvector_{N}.csv"
@ -46,10 +45,7 @@ def plot_eigenvectors(N: int, save: bool=False) -> None:
fig.savefig(f"../latex/images/eigenvector_{N}.pdf") fig.savefig(f"../latex/images/eigenvector_{N}.pdf")
if __name__ == '__main__': if __name__ == '__main__':
# plot_transformations(True) plot_transformations(True)
plot_eigenvectors(6, True) plot_eigenvectors(10, True)
plot_eigenvectors(100, True) plot_eigenvectors(100, True)
# plt.show()