Change image scripts to PDF format, update Makefile, add complex plane plot

10 files changed, 158 insertions, 26 deletions

diff --git a/buch/papers/laguerre/scripts/estimates.py b/buch/papers/laguerre/scripts/estimates.py
index 207bbd2..21551f3 100644
--- a/buch/papers/laguerre/scripts/estimates.py
+++ b/buch/papers/laguerre/scripts/estimates.py
@@ -1,10 +1,19 @@
 if __name__ == "__main__":
+    import matplotlib as mpl
     import matplotlib.pyplot as plt
     import numpy as np
 
     import gamma_approx as ga
     import targets
 
+    mpl.rcParams.update(
+        {
+            "mathtext.fontset": "stix",
+            "font.family": "serif",
+            "font.serif": "TeX Gyre Termes",
+        }
+    )
+    
     N = 200
     ns = np.arange(2, 13)
     step = 1 / (N - 1)
@@ -32,7 +41,8 @@ if __name__ == "__main__":
     for ax in axs:
         ax.grid(1)
         ax.legend()
-    fig.savefig(f"{ga.img_path}/estimates.pgf")
+    # fig.savefig(f"{ga.img_path}/estimates.pgf")
+    fig.savefig(f"{ga.img_path}/estimates.pdf")
 
     print(f"Intercept={intercept:.6g}, Bias={bias:.6g}")
     predicts = np.ceil(intercept * ns[:, None] + bias - np.real(x))
diff --git a/buch/papers/laguerre/scripts/integrand.py b/buch/papers/laguerre/scripts/integrand.py
index f31f194..e970721 100644
--- a/buch/papers/laguerre/scripts/integrand.py
+++ b/buch/papers/laguerre/scripts/integrand.py
@@ -6,9 +6,18 @@ if __name__ == "__main__":
     import os
     from pathlib import Path
 
+    import matplotlib as mpl
     import matplotlib.pyplot as plt
     import numpy as np
 
+    mpl.rcParams.update(
+        {
+            "mathtext.fontset": "stix",
+            "font.family": "serif",
+            "font.serif": "TeX Gyre Termes",
+        }
+    )
+    
     EPSILON = 1e-12
     xlims = np.array([-3, 3])
 
@@ -30,4 +39,4 @@ if __name__ == "__main__":
     ax.grid(1, "both")
     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}/integrand.pgf")
+    fig.savefig(f"{img_path}/integrand.pdf")
diff --git a/buch/papers/laguerre/scripts/integrand_exp.py b/buch/papers/laguerre/scripts/integrand_exp.py
index 0e50f43..e649b26 100644
--- a/buch/papers/laguerre/scripts/integrand_exp.py
+++ b/buch/papers/laguerre/scripts/integrand_exp.py
@@ -6,8 +6,17 @@ if __name__ == "__main__":
     import os
     from pathlib import Path
 
+    import matplotlib as mpl
     import matplotlib.pyplot as plt
     import numpy as np
+    
+    mpl.rcParams.update(
+        {
+            "mathtext.fontset": "stix",
+            "font.family": "serif",
+            "font.serif": "TeX Gyre Termes",
+        }
+    )
 
     EPSILON = 1e-12
     xlims = np.array([-3, 3])
@@ -32,5 +41,6 @@ if __name__ == "__main__":
     ax.grid(1, "both")
     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}/integrand_exp.pgf")
+    # fig.savefig(f"{img_path}/integrand_exp.pgf")
+    fig.savefig(f"{img_path}/integrand_exp.pdf")
     # plt.show()
diff --git a/buch/papers/laguerre/scripts/laguerre_poly.py b/buch/papers/laguerre/scripts/laguerre_poly.py
index 954a0b1..9700ab4 100644
--- a/buch/papers/laguerre/scripts/laguerre_poly.py
+++ b/buch/papers/laguerre/scripts/laguerre_poly.py
@@ -10,8 +10,17 @@ if __name__ == "__main__":
     import os
     from pathlib import Path
 
+    import matplotlib as mpl
     import matplotlib.pyplot as plt
     import scipy.special as ss
+    
+    mpl.rcParams.update(
+        {
+            "mathtext.fontset": "stix",
+            "font.family": "serif",
+            "font.serif": "TeX Gyre Termes",
+        }
+    )
 
     N = 1000
     step = 5
@@ -34,8 +43,8 @@ if __name__ == "__main__":
     ax.set_xlabel(r"$x$", x=1.0, labelpad=-10, rotation=0, fontsize="large")
 
     ylim = 13
-    ax.set_yticks(np.arange(-ylim, ylim), minor=True)
-    ax.set_yticks(np.arange(-step * (ylim // step), ylim, step))
+    ax.set_yticks(get_ticks(-ylim, ylim), minor=True)
+    ax.set_yticks(get_ticks(-step * (ylim // step), ylim, step))
     ax.set_ylim(-ylim, ylim)
     ax.set_ylabel(r"$y$", y=0.95, labelpad=-18, rotation=0, fontsize="large")
 
@@ -94,5 +103,6 @@ if __name__ == "__main__":
         clip_on=False,
     )
 
-    fig.savefig(f"{img_path}/laguerre_poly.pgf")
+    # fig.savefig(f"{img_path}/laguerre_poly.pgf")
+    fig.savefig(f"{img_path}/laguerre_poly.pdf")
     # plt.show()
diff --git a/buch/papers/laguerre/scripts/rel_error_complex.py b/buch/papers/laguerre/scripts/rel_error_complex.py
new file mode 100644
index 0000000..5be79be
--- /dev/null
+++ b/buch/papers/laguerre/scripts/rel_error_complex.py
@@ -0,0 +1,43 @@
+if __name__ == "__main__":
+    import matplotlib as mpl
+    import matplotlib.pyplot as plt
+    import numpy as np
+    import scipy.special
+
+    import gamma_approx as ga
+
+    mpl.rcParams.update(
+        {
+            "mathtext.fontset": "stix",
+            "font.family": "serif",
+            "font.serif": "TeX Gyre Termes",
+        }
+    )
+    
+    xmax = 4
+    vals = np.linspace(-xmax + ga.EPSILON, xmax, 100)
+    x, y = np.meshgrid(vals, vals)
+    mesh = x + 1j * y
+    input = mesh.flatten()
+
+    lanczos = scipy.special.gamma(mesh)
+    lag = ga.eval_laguerre_gamma(input, n=8, func="optimal_shifted").reshape(mesh.shape)
+    rel_error = np.abs(ga.calc_rel_error(lanczos, lag))
+
+    fig, ax = plt.subplots(clear=True, constrained_layout=True, figsize=(4, 2.4))
+    _c = ax.pcolormesh(
+        x, y, rel_error, shading="gouraud", cmap="inferno", norm=mpl.colors.LogNorm()
+    )
+    cbr = fig.colorbar(_c, ax=ax)
+    cbr.minorticks_off()
+    # ax.set_title("Relative Error")
+    ax.set_xlabel("Re($z$)")
+    ax.set_ylabel("Im($z$)")
+    minor_ticks = np.arange(-xmax, xmax + ga.EPSILON)
+    ticks = np.arange(-xmax, xmax + ga.EPSILON, 2)
+    ax.set_xticks(ticks)
+    ax.set_xticks(minor_ticks, minor=True)
+    ax.set_yticks(ticks)
+    ax.set_yticks(minor_ticks, minor=True)
+    fig.savefig(f"{ga.img_path}/rel_error_complex.pdf")
+    # plt.show()
diff --git a/buch/papers/laguerre/scripts/rel_error_mirror.py b/buch/papers/laguerre/scripts/rel_error_mirror.py
index 05e68e4..7348d5e 100644
--- a/buch/papers/laguerre/scripts/rel_error_mirror.py
+++ b/buch/papers/laguerre/scripts/rel_error_mirror.py
@@ -1,9 +1,18 @@
 if __name__ == "__main__":
+    import matplotlib as mpl
     import matplotlib.pyplot as plt
     import numpy as np
     import scipy.special
 
     import gamma_approx as ga
+    
+    mpl.rcParams.update(
+        {
+            "mathtext.fontset": "stix",
+            "font.family": "serif",
+            "font.serif": "TeX Gyre Termes",
+        }
+    )
 
     xmin = -15
     xmax = 15
@@ -25,4 +34,5 @@ if __name__ == "__main__":
     # ax.set_ylabel("Relativer Fehler")
     ax.legend(ncol=1, loc="upper left", fontsize=ga.fontsize)
     ax.grid(1, "both")
-    fig.savefig(f"{ga.img_path}/rel_error_mirror.pgf")
+    # fig.savefig(f"{ga.img_path}/rel_error_mirror.pgf")
+    fig.savefig(f"{ga.img_path}/rel_error_mirror.pdf")
diff --git a/buch/papers/laguerre/scripts/rel_error_range.py b/buch/papers/laguerre/scripts/rel_error_range.py
index 7c74d76..43b5450 100644
--- a/buch/papers/laguerre/scripts/rel_error_range.py
+++ b/buch/papers/laguerre/scripts/rel_error_range.py
@@ -1,13 +1,21 @@
 if __name__ == "__main__":
+    import matplotlib as mpl
     import matplotlib.pyplot as plt
     import numpy as np
     import scipy.special
 
     import gamma_approx as ga
-
-    N = 1001
-    xmin = -5
-    xmax = 5
+    
+    mpl.rcParams.update(
+        {
+            "mathtext.fontset": "stix",
+            "font.family": "serif",
+            "font.serif": "TeX Gyre Termes",
+        }
+    )
+    N = 1201
+    xmax = 6
+    xmin = -xmax
     ns = np.arange(2, 12, 2)
     ylim = np.array([-11, -1.2])
 
@@ -20,13 +28,14 @@ if __name__ == "__main__":
         ax.semilogy(x, np.abs(rel_err), label=f"$n={n}$")
     ax.set_xlim(x[0], x[-1])
     ax.set_ylim(*(10.0 ** ylim))
-    ax.set_xticks(np.arange(xmin + 1, xmax, 2))
-    ax.set_xticks(np.arange(xmin, xmax), minor=True)
+    ax.set_xticks(np.arange(xmin, xmax + ga.EPSILON, 2))
+    ax.set_xticks(np.arange(xmin, xmax + ga.EPSILON), minor=True)
     ax.set_yticks(10.0 ** np.arange(*ylim, 2))
-    ax.set_yticks(10.0 ** np.arange(*ylim, 1), minor=True)
+    ax.set_yticks(10.0 ** np.arange(*ylim, 1), "", minor=True)
     ax.set_xlabel(r"$z$")
     # ax.set_ylabel("Relativer Fehler")
     ax.legend(ncol=1, loc="upper left", fontsize=ga.fontsize)
     ax.grid(1, "both")
-    fig.savefig(f"{ga.img_path}/rel_error_range.pgf")
+    # fig.savefig(f"{ga.img_path}/rel_error_range.pgf")
+    fig.savefig(f"{ga.img_path}/rel_error_range.pdf")
     # plt.show()
diff --git a/buch/papers/laguerre/scripts/rel_error_shifted.py b/buch/papers/laguerre/scripts/rel_error_shifted.py
index 1515c6e..dc9d177 100644
--- a/buch/papers/laguerre/scripts/rel_error_shifted.py
+++ b/buch/papers/laguerre/scripts/rel_error_shifted.py
@@ -1,10 +1,18 @@
 if __name__ == "__main__":
+    import matplotlib as mpl
     import matplotlib.pyplot as plt
     import numpy as np
     import scipy.special
 
     import gamma_approx as ga
 
+    mpl.rcParams.update(
+        {
+            "mathtext.fontset": "stix",
+            "font.family": "serif",
+            "font.serif": "TeX Gyre Termes",
+        }
+    )
     n = 8  # order of Laguerre polynomial
     N = 200  # number of points in interval
 
@@ -19,7 +27,7 @@ if __name__ == "__main__":
         ax.semilogy(x, rel_error, label=f"$m={target}$", linewidth=3)
     gamma_lgo = ga.eval_laguerre_gamma(x, n=n, func="optimal_shifted")
     rel_error = np.abs(ga.calc_rel_error(gamma, gamma_lgo))
-    ax.semilogy(x, rel_error, "m", linestyle="dotted", label="$m^*$", linewidth=3)
+    ax.semilogy(x, rel_error, "m", linestyle=":", label="$m^*$", linewidth=3)
     ax.set_xlim(x[0], x[-1])
     ax.set_ylim(5e-9, 5e-8)
     ax.set_xlabel(r"$z$")
@@ -27,5 +35,6 @@ if __name__ == "__main__":
     ax.set_xticks(np.linspace(0, 1, 11), minor=True)
     ax.grid(1, "both")
     ax.legend(ncol=1, fontsize=ga.fontsize)
-    fig.savefig(f"{ga.img_path}/rel_error_shifted.pgf")
+    # fig.savefig(f"{ga.img_path}/rel_error_shifted.pgf")
+    fig.savefig(f"{ga.img_path}/rel_error_shifted.pdf")
     # plt.show()
diff --git a/buch/papers/laguerre/scripts/rel_error_simple.py b/buch/papers/laguerre/scripts/rel_error_simple.py
index 0929976..686500b 100644
--- a/buch/papers/laguerre/scripts/rel_error_simple.py
+++ b/buch/papers/laguerre/scripts/rel_error_simple.py
@@ -1,10 +1,21 @@
 if __name__ == "__main__":
+    import matplotlib as mpl
     import matplotlib.pyplot as plt
     import numpy as np
     import scipy.special
 
     import gamma_approx as ga
 
+    # mpl.rc("text", usetex=True)
+    mpl.rcParams.update(
+        {
+            "mathtext.fontset": "stix",
+            "font.family": "serif",
+            "font.serif": "TeX Gyre Termes",
+        }
+    )
+    # mpl.rcParams.update({"font.family": "serif", "font.serif": "TeX Gyre Termes"})
+
     # Simple / naive
     xmin = -5
     xmax = 30
@@ -26,4 +37,5 @@ if __name__ == "__main__":
     # ax.set_ylabel("Relativer Fehler")
     ax.legend(ncol=3, fontsize=ga.fontsize)
     ax.grid(1, "both")
-    fig.savefig(f"{ga.img_path}/rel_error_simple.pgf")
+    # fig.savefig(f"{ga.img_path}/rel_error_simple.pgf")
+    fig.savefig(f"{ga.img_path}/rel_error_simple.pdf")
diff --git a/buch/papers/laguerre/scripts/targets.py b/buch/papers/laguerre/scripts/targets.py
index 73d6e03..206b3a1 100644
--- a/buch/papers/laguerre/scripts/targets.py
+++ b/buch/papers/laguerre/scripts/targets.py
@@ -10,24 +10,33 @@ def find_best_loc(N=200, a=1.375, b=0.5, ns=None):
     bests = []
     step = 1 / (N - 1)
     x = np.linspace(step, 1 - step, N + 1)
-    gamma = scipy.special.gamma(x)[:, None]
+    gamma = scipy.special.gamma(x)
     for n in ns:
         zeros, weights = np.polynomial.laguerre.laggauss(n)
         est = np.ceil(b + a * n)
         targets = np.arange(max(est - 2, 0), est + 3)
-        glag = [
-            ga.eval_laguerre_gamma(x, target=target, x=zeros, w=weights, func="shifted")
-            for target in targets
-        ]
-        gamma_lag = np.stack(glag, -1)
-        rel_error = np.abs(ga.calc_rel_error(gamma, gamma_lag))
+        rel_error = []
+        for target in targets:
+            gamma_lag = ga.eval_laguerre_gamma(x, target=target, x=zeros, w=weights, func="shifted")
+            rel_error.append(np.abs(ga.calc_rel_error(gamma, gamma_lag)))
+        rel_error = np.stack(rel_error, -1)
         best = np.argmin(rel_error, -1) + targets[0]
         bests.append(best)
     return np.stack(bests, 0)
 
 
 if __name__ == "__main__":
+    import matplotlib as mpl
     import matplotlib.pyplot as plt
+
+    mpl.rcParams.update(
+        {
+            "mathtext.fontset": "stix",
+            "font.family": "serif",
+            "font.serif": "TeX Gyre Termes",
+        }
+    )
+    
     N = 200
     ns = np.arange(2, 13)
     
@@ -45,4 +54,5 @@ if __name__ == "__main__":
     ax.set_yticklabels(ns)
     ax.set_xlabel(r"$z$")
     ax.set_ylabel(r"$n$")
-    fig.savefig(f"{ga.img_path}/targets.pgf")
+    # fig.savefig(f"{ga.img_path}/targets.pgf")
+    fig.savefig(f"{ga.img_path}/targets.pdf")