From fde57297b3efbef28d09a532e1b3895d2b2ad917 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Patrik=20M=C3=BCller?= <patrik.mueller@ost.ch>
Date: Thu, 14 Jul 2022 15:03:28 +0200
Subject: Correct Makefile, add text to gamma.tex, separate python-scripts for
 each image

---
 buch/papers/laguerre/scripts/targets.py | 48 +++++++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)
 create mode 100644 buch/papers/laguerre/scripts/targets.py

(limited to 'buch/papers/laguerre/scripts/targets.py')

diff --git a/buch/papers/laguerre/scripts/targets.py b/buch/papers/laguerre/scripts/targets.py
new file mode 100644
index 0000000..73d6e03
--- /dev/null
+++ b/buch/papers/laguerre/scripts/targets.py
@@ -0,0 +1,48 @@
+import numpy as np
+import scipy.special
+
+import gamma_approx as ga
+
+
+def find_best_loc(N=200, a=1.375, b=0.5, ns=None):
+    if ns is None:
+        ns = np.arange(2, 13)
+    bests = []
+    step = 1 / (N - 1)
+    x = np.linspace(step, 1 - step, N + 1)
+    gamma = scipy.special.gamma(x)[:, None]
+    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))
+        best = np.argmin(rel_error, -1) + targets[0]
+        bests.append(best)
+    return np.stack(bests, 0)
+
+
+if __name__ == "__main__":
+    import matplotlib.pyplot as plt
+    N = 200
+    ns = np.arange(2, 13)
+    
+    bests = find_best_loc(N, ns=ns)
+
+    fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(4, 2.4))
+    v = ax.imshow(bests, cmap="inferno", aspect="auto", interpolation="nearest")
+    plt.colorbar(v, ax=ax, label=r"$m^*$")
+    ticks = np.arange(0, N + 1, N // 5)
+    ax.set_xlim(0, 1)
+    ax.set_xticks(ticks)
+    ax.set_xticklabels([f"{v:.2f}" for v in ticks / N])
+    ax.set_xticks(np.arange(0, N + 1, N // 20), minor=True)
+    ax.set_yticks(np.arange(len(ns)))
+    ax.set_yticklabels(ns)
+    ax.set_xlabel(r"$z$")
+    ax.set_ylabel(r"$n$")
+    fig.savefig(f"{ga.img_path}/targets.pgf")
-- 
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