Add rule of thumb, analyse integrand, correct mistake in integration SLP<->LP

1 files changed, 14 insertions, 13 deletions

diff --git a/buch/papers/laguerre/scripts/integrand.py b/buch/papers/laguerre/scripts/integrand.py
index 43fc1bf..0cf43d1 100644
--- a/buch/papers/laguerre/scripts/integrand.py
+++ b/buch/papers/laguerre/scripts/integrand.py
@@ -20,29 +20,30 @@ t = np.logspace(*xlims, 1001)[:, None]
 z = np.array([-4.5, -2, -1, -0.5, 0.0, 0.5, 1, 2, 4.5])
 r = t ** z
 
-fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(6, 4))
+fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 3))
 ax.semilogx(t, r)
 ax.set_xlim(*(10.0 ** xlims))
 ax.set_ylim(1e-3, 40)
-ax.set_xlabel(r"$t$")
-ax.set_ylabel(r"$t^z$")
+ax.set_xlabel(r"$x$")
+ax.set_ylabel(r"$x^z$")
 ax.grid(1, "both")
-labels = [f"$z={zi:.1f}$" for zi in np.squeeze(z)]
-ax.legend(labels, ncol=2, loc="upper left")
+labels = [f"$z={zi: 3.1f}$" for zi in np.squeeze(z)]
+ax.legend(labels, ncol=2, loc="upper left", fontsize="small")
 fig.savefig(f"{img_path}/integrands.pgf")
 
 z2 = np.array([-1, -0.5, 0.0, 0.5, 1, 2, 3, 4, 4.5])
-r2 = t**z2 * np.exp(-t)
+e = np.exp(-t)
+r2 = t ** z2 * e
 
-fig2, ax2 = plt.subplots(num=2, clear=True, constrained_layout=True, figsize=(6, 4))
+fig2, ax2 = plt.subplots(num=2, clear=True, constrained_layout=True, figsize=(5, 3))
 ax2.semilogx(t, r2)
 # ax2.plot(t,np.exp(-t))
-ax2.set_xlim(10**(-2), 20)
+ax2.set_xlim(10 ** (-2), 20)
 ax2.set_ylim(1e-3, 10)
-ax2.set_xlabel(r"$t$")
-ax2.set_ylabel(r"$t^z e^{-t}$")
+ax2.set_xlabel(r"$x$")
+ax2.set_ylabel(r"$x^z e^{-x}$")
 ax2.grid(1, "both")
-labels = [f"$z={zi:.1f}$" for zi in np.squeeze(z2)]
-ax2.legend(labels, ncol=2, loc="upper left")
+labels =[f"$z={zi: 3.1f}$" for zi in np.squeeze(z2)]
+ax2.legend(labels, ncol=2, loc="upper left", fontsize="small")
 fig2.savefig(f"{img_path}/integrands_exp.pgf")
-plt.show()
+# plt.show()