From 1563df4bbfbc94f6933437a1507e7c061b3fc228 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Wed, 9 Dec 2020 11:52:25 +0100 Subject: Updated the spectra figure with insets. --- bezout.tex | 40 +++++++++++++--------------------------- fig/spectra_0.0.pdf | Bin 0 -> 23571 bytes fig/spectra_0.5.pdf | Bin 0 -> 23917 bytes fig/spectra_1.0.pdf | Bin 0 -> 24516 bytes fig/spectra_1.5.pdf | Bin 0 -> 24327 bytes fig/spectra_eigenvalue_0.0.pdf | Bin 6861 -> 0 bytes fig/spectra_eigenvalue_0.5.pdf | Bin 6865 -> 0 bytes fig/spectra_eigenvalue_1.0.pdf | Bin 6859 -> 0 bytes fig/spectra_eigenvalue_1.5.pdf | Bin 6865 -> 0 bytes fig/spectra_singular_0.0.pdf | Bin 9319 -> 0 bytes fig/spectra_singular_0.5.pdf | Bin 9871 -> 0 bytes fig/spectra_singular_1.0.pdf | Bin 10376 -> 0 bytes fig/spectra_singular_1.5.pdf | Bin 10256 -> 0 bytes 13 files changed, 13 insertions(+), 27 deletions(-) create mode 100644 fig/spectra_0.0.pdf create mode 100644 fig/spectra_0.5.pdf create mode 100644 fig/spectra_1.0.pdf create mode 100644 fig/spectra_1.5.pdf delete mode 100644 fig/spectra_eigenvalue_0.0.pdf delete mode 100644 fig/spectra_eigenvalue_0.5.pdf delete mode 100644 fig/spectra_eigenvalue_1.0.pdf delete mode 100644 fig/spectra_eigenvalue_1.5.pdf delete mode 100644 fig/spectra_singular_0.0.pdf delete mode 100644 fig/spectra_singular_0.5.pdf delete mode 100644 fig/spectra_singular_1.0.pdf delete mode 100644 fig/spectra_singular_1.5.pdf diff --git a/bezout.tex b/bezout.tex index a55b4bd..81e4718 100644 --- a/bezout.tex +++ b/bezout.tex @@ -220,36 +220,22 @@ is shifted by $p\epsilon$. \begin{figure}[htpb] \centering - \raisebox{60pt}{$|\epsilon|=0$} - \hfill - \raisebox{5pt}{\includegraphics[scale=1.0]{fig/spectra_eigenvalue_0.0.pdf}} - \hspace{2pt} - \includegraphics{fig/spectra_singular_0.0.pdf}\\ - \raisebox{60pt}{$|\epsilon|=\frac12|\epsilon_{\mathrm{th}}|$} - \hfill - \raisebox{5pt}{\includegraphics[scale=1.0]{fig/spectra_eigenvalue_0.5.pdf}} - \hspace{2pt} - \includegraphics{fig/spectra_singular_0.5.pdf}\\ - \raisebox{60pt}{$|\epsilon|=|\epsilon_{\mathrm{th}}|$} - \hfill - \raisebox{5pt}{\includegraphics[scale=1.0]{fig/spectra_eigenvalue_1.0.pdf}} - \hspace{2pt} - \includegraphics{fig/spectra_singular_1.0.pdf}\\ - \raisebox{60pt}{$|\epsilon|=\frac32|\epsilon_{\mathrm{th}}|$} - \hfill - \raisebox{5pt}{\includegraphics[scale=1.0]{fig/spectra_eigenvalue_1.5.pdf}} - \hspace{2pt} - \includegraphics{fig/spectra_singular_1.5.pdf} + \includegraphics{fig/spectra_0.0.pdf} + \includegraphics{fig/spectra_0.5.pdf}\\ + \includegraphics{fig/spectra_1.0.pdf} + \includegraphics{fig/spectra_1.5.pdf} \caption{ Eigenvalue and singular value spectra of the matrix $\partial\partial H$ - for $p=3$, $a=\frac54$, $\kappa=\frac34e^{i3\pi/4}$, and - $\epsilon=i|\epsilon|$ with various values of $|\epsilon|$. The shaded - region of the lefthand plots shows the support of the eigenvalue - distribution. The solid line on the righthand plots shows the distribution - of singular values, while the overlaid histograms show empirical - distributions from $2^{10}\times2^{10}$ complex normal matrices with the - same covariance and diagonal shift as $\partial\partial H$. + for $p=3$, $a=\frac54$, and $\kappa=\frac34e^{i3\pi/4}$ with (a) + $\epsilon=0$, (b) $\epsilon=\frac12|\epsilon_{\mathrm{th}}|$, (c) + $\epsilon=|\epsilon_{\mathrm{th}}|$, and (d) + $\epsilon=\frac32|\epsilon_{\mathrm{th}}|$. The shaded region of each inset + shows the support of the eigenvalue distribution. The solid line on each + plot shows the distribution of singular values, while the overlaid + histogram shows the empirical distribution from $2^{10}\times2^{10}$ complex + normal matrices with the same covariance and diagonal shift as + $\partial\partial H$. } \label{fig:spectra} \end{figure} diff --git a/fig/spectra_0.0.pdf b/fig/spectra_0.0.pdf new file mode 100644 index 0000000..5d519e4 Binary files /dev/null and b/fig/spectra_0.0.pdf differ diff --git a/fig/spectra_0.5.pdf b/fig/spectra_0.5.pdf new file mode 100644 index 0000000..d58dc05 Binary files /dev/null and b/fig/spectra_0.5.pdf differ diff --git a/fig/spectra_1.0.pdf b/fig/spectra_1.0.pdf new file mode 100644 index 0000000..cfe372c Binary files /dev/null and b/fig/spectra_1.0.pdf differ diff --git a/fig/spectra_1.5.pdf b/fig/spectra_1.5.pdf new file mode 100644 index 0000000..92223f4 Binary files /dev/null and b/fig/spectra_1.5.pdf differ diff --git a/fig/spectra_eigenvalue_0.0.pdf b/fig/spectra_eigenvalue_0.0.pdf deleted file mode 100644 index 6b9b83e..0000000 Binary files a/fig/spectra_eigenvalue_0.0.pdf and /dev/null differ diff --git a/fig/spectra_eigenvalue_0.5.pdf b/fig/spectra_eigenvalue_0.5.pdf deleted file mode 100644 index 63104d6..0000000 Binary files a/fig/spectra_eigenvalue_0.5.pdf and /dev/null differ diff --git a/fig/spectra_eigenvalue_1.0.pdf b/fig/spectra_eigenvalue_1.0.pdf deleted file mode 100644 index 6e3ebe1..0000000 Binary files a/fig/spectra_eigenvalue_1.0.pdf and /dev/null differ diff --git a/fig/spectra_eigenvalue_1.5.pdf b/fig/spectra_eigenvalue_1.5.pdf deleted file mode 100644 index b68706e..0000000 Binary files a/fig/spectra_eigenvalue_1.5.pdf and /dev/null differ diff --git a/fig/spectra_singular_0.0.pdf b/fig/spectra_singular_0.0.pdf deleted file mode 100644 index 86c945d..0000000 Binary files a/fig/spectra_singular_0.0.pdf and /dev/null differ diff --git a/fig/spectra_singular_0.5.pdf b/fig/spectra_singular_0.5.pdf deleted file mode 100644 index b25caa0..0000000 Binary files a/fig/spectra_singular_0.5.pdf and /dev/null differ diff --git a/fig/spectra_singular_1.0.pdf b/fig/spectra_singular_1.0.pdf deleted file mode 100644 index 4cae0c1..0000000 Binary files a/fig/spectra_singular_1.0.pdf and /dev/null differ diff --git a/fig/spectra_singular_1.5.pdf b/fig/spectra_singular_1.5.pdf deleted file mode 100644 index e6f43fd..0000000 Binary files a/fig/spectra_singular_1.5.pdf and /dev/null differ -- cgit v1.2.3-70-g09d2