Add gen_vec_fields.py and remove unnecessary code

src/2025-01-07/presentation.tex

@@ -18,9 +18,6 @@
 \usepackage[outputdir=build/]{minted}
 \usemintedstyle{gruvbox-light}
 
-\definecolor{gruvbox-bg}{HTML}{ffffff}
-% \definecolor{gruvbox-bg}{HTML}{282828}
-
 
 %
 %
@@ -69,7 +66,7 @@
 %
 
 
-\title{HiWi Notes: Minimization Code Constraint Polynomial using Homotopy
+\title{HiWi Notes: Minimization of Code Constraint Polynomial using Homotopy
     Continuation Methods}
 \subtitle{\small 07.01.2025}
 \author{\vspace{1.5mm} Andreas Tsouchlos}
@@ -164,7 +161,7 @@
                               ]
                                 table[col sep=comma, discard if not={t}{0.0}] {\res/H.csv};
 
-                            \addplot[mark=*] coordinates {(0,0)} node[above] {$\bm{x}_0$};
+                    \addplot[mark=*] coordinates {(0,0)} node[above] {$\bm{x}_0$};
 
                 \end{axis}
             \end{tikzpicture}

src/2025-01-07/res/gen_vec_fields.py

@@ -0,0 +1,46 @@
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+
+def main():
+    def F(x1, x2):
+        return np.array([x1 + x2, x2 + 0.5])
+
+    def G(x1, x2):
+        return np.array([x1, x2])
+
+    def H(x1, x2, t):
+        return (1 - t) * G(x1, x2) + t * F(x1, x2)
+
+    # x = np.linspace(-1, 1, 10)
+    # y = np.linspace(-1, 1, 10)
+    # X1, X2 = np.meshgrid(x, y)
+    #
+    # fig, axes = plt.subplots(1, 4, figsize=(20, 4))
+    #
+    # for i, t in enumerate(np.linspace(0, 1, 4)):
+    #     H_ = H(X1, X2, t)
+    #     axes[i].quiver(X1, X2, *H_, color='r')
+    #     axes[i].set_title(f't = {t}')
+    #
+    # plt.show()
+
+    df_dict = {"x1": [], "x2": [], "t": [], "H1": [], "H2": [], "Hmag": []}
+
+    for x1 in np.linspace(-1, 1, 10):
+        for x2 in np.linspace(-1, 1, 10):
+            for t in [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1]:
+                df_dict["x1"].append(x1)
+                df_dict["x2"].append(x2)
+                df_dict["t"].append(t)
+                H_ = H(x1, x2, t)
+                df_dict["H1"].append(H_[0])
+                df_dict["H2"].append(H_[1])
+                df_dict["Hmag"].append(np.sqrt(H_[0]**2 + H_[1]**2))
+
+    df = pd.DataFrame(df_dict).sort_values(by=["t", "x2", "x1"])
+
+    df.to_csv("H.csv", index=False)
+
+if __name__=="__main__":
+    main()