From 1de9034954a3fd8c815e3d9f578576e58b6765a0 Mon Sep 17 00:00:00 2001
From: Lukas Winkler <git@lw1.at>
Date: Mon, 29 Jul 2019 14:00:42 +0200
Subject: [PATCH] add simple visualisation of RBF for the bachelor thesis

---
 rbf-vis.py | 59 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 rbf-vis.py

diff --git a/rbf-vis.py b/rbf-vis.py
new file mode 100644
index 0000000..b3a6046
--- /dev/null
+++ b/rbf-vis.py
@@ -0,0 +1,59 @@
+import numpy as np
+
+from matplotlib import pyplot as plt
+
+np.random.seed(15)
+
+
+def theta(r):
+    return np.exp(-r ** 2)
+
+
+points = [0, 3, 5]
+values = [0.2, 0.8, 0.1]
+
+# points = np.random.rand(15) * 5
+# values = np.sin(points)
+
+plt.scatter(points, values, label="data points")
+
+subtract = np.zeros((len(points), len(points)))
+
+for i in range(len(points)):
+    for j in range(len(points)):
+        subtract[i][j] = abs(points[i] - points[j])
+
+print(subtract)
+
+left_side = theta(subtract)
+print(left_side)
+
+lambdas = np.linalg.solve(left_side, values)
+
+print(lambdas)
+
+
+def s(x, i=None):
+    running_sum = 0
+    for index, lam in enumerate(lambdas):
+        if i is None or i == index:
+            running_sum += lam * theta(x - points[index])
+    return running_sum
+
+
+x = np.linspace(0, 5, 100)
+y = s(x)
+
+plt.plot(x, y, label="$s(x)$", zorder=-1)
+
+for i in range(len(points)):
+    plt.plot(x, s(x, i), label=f"RBF {i}",zorder=-2)
+plt.legend()
+
+# x_interpol = 2.3
+# y_interpol = s(x_interpol)
+# plt.scatter(x_interpol,y_interpol,color="green")
+
+plt.savefig("../arbeit/images/rbf1.pdf")
+# plt.savefig("../arbeit/images/rbf2.pdf")
+plt.show()