Added plot showing sorted eigenvectors (#175)

* Added plot showing sorted eigenvectors

I added a few lines so that users can see how to plot the eigenvectors with the lowest/highest growth rates.

It took me a while to figure out the new `set_state` method API that requires specifying the `subsystem` in addition to the index, so I thought it would be useful to include it in at least one of the EVP examples.

* Update waves_on_a_string.py

Author: hdrake

examples/evp_1d_waves_on_a_string/waves_on_a_string.py

@@ -67,3 +67,14 @@
 plt.tight_layout()
 plt.savefig('eigenvalue_error.pdf')
 
+plt.figure(figsize=(6, 4))
+x = dist.local_grid(xbasis)
+for n, idx in enumerate(np.argsort(solver.eigenvalues)[:5], start=1):
+    solver.set_state(idx, solver.subsystems[0])
+    plt.plot(x, (u['g']/np.max(u['g'])).real, label=f"n={n}")
+plt.xlim(0, 1)
+plt.legend(loc="lower right")
+plt.ylabel(r"mode structure")
+plt.xlabel(r"x")
+plt.tight_layout()
+plt.savefig("eigenvectors.pdf")