script dump

extrapolation_blow-up_v2.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+# -----------------------------
+# Generate realistic fake SFs
+# -----------------------------
+np.random.seed(2)
+
+n_ref = 2000
+
+# Apo SFs
+Fa_amp = np.random.uniform(50, 200, n_ref)
+Fa_phi = np.random.uniform(-np.pi, np.pi, n_ref)
+Fa = Fa_amp * np.exp(1j * Fa_phi)
+
+# Difference signal (correlated phases!)
+dF_amp = np.random.uniform(5, 25, n_ref)
+dF_phi = Fa_phi + np.random.normal(0, 0.3, n_ref)
+dF = dF_amp * np.exp(1j * dF_phi)
+
+# Mixed SFs
+Fab = Fa + dF
+
+# -----------------------------
+# Occupancies to test
+# -----------------------------
+b_values = [1.0, 0.5, 0.2, 0.1, 0.05]
+
+# -----------------------------
+# Compute resultants
+# -----------------------------
+R_Fa = np.sum(Fa)
+R_Fab = np.sum(Fab)
+R_dF = np.sum(Fab - Fa)
+
+R_Fb = []
+R_dF_scaled = []
+
+for b in b_values:
+    Fb = Fa + (Fab - Fa) / b
+    R_Fb.append(np.sum(Fb))
+    R_dF_scaled.append(R_dF / b)
+
+# -----------------------------
+# Plot resultants
+# -----------------------------
+plt.figure(figsize=(6, 6))
+
+# Reference resultants
+plt.arrow(0, 0, R_Fa.real, R_Fa.imag,
+          head_width=200, length_includes_head=True,
+          label="R(Fa)", color="black")
+
+plt.arrow(0, 0, R_Fab.real, R_Fab.imag,
+          head_width=200, length_includes_head=True,
+          label="R(Fab)", color="blue")
+
+# Extrapolated vs difference resultants
+for b, Rb, Rd in zip(b_values, R_Fb, R_dF_scaled):
+    plt.arrow(0, 0, Rb.real, Rb.imag,
+              head_width=200, length_includes_head=True,
+              alpha=0.7, label=f"R(Fb), b={b}")
+    plt.arrow(0, 0, Rd.real, Rd.imag,
+              head_width=200, length_includes_head=True,
+              linestyle="dashed", alpha=0.7)
+
+plt.axhline(0, color="grey", lw=0.5)
+plt.axvline(0, color="grey", lw=0.5)
+plt.gca().set_aspect("equal")
+
+plt.xlabel("Real")
+plt.ylabel("Imag")
+plt.title("Resultant vectors: extrapolation vs difference")
+plt.legend(fontsize=8)
+plt.tight_layout()
+plt.show()