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@@ -1,6 +1,6 @@
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import numpy as np
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import plotly.graph_objects as go
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from scipy.stats import f as f_dist
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from scipy.stats import f
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import pandas as pd
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@@ -57,99 +57,143 @@ class Genauigkeitsmaße:
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def standardellipse(Qxx, s0_apost, unbekannten_liste, dim_labels=3):
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@staticmethod
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def standardellipse(Qxx, s0_apost, unbekannten_liste):
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Qxx = np.asarray(Qxx, float)
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data = []
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daten = []
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namen_str = [str(sym) for sym in unbekannten_liste]
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n_punkte = len(unbekannten_liste) // dim_labels
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punkt_ids = []
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for n in namen_str:
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if n.upper().startswith('X'):
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punkt_ids.append(n[1:])
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for i in range(n_punkte):
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sym_x = str(unbekannten_liste[dim_labels * i]) # z.B. "X10009"
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punkt = sym_x[1:] # -> "10009"
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for pid in punkt_ids:
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try:
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idx_x = next(i for i, n in enumerate(namen_str) if n.upper() == f"X{pid}".upper())
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idx_y = next(i for i, n in enumerate(namen_str) if n.upper() == f"Y{pid}".upper())
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ix = dim_labels * i
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iy = dim_labels * i + 1
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qxx = Qxx[idx_x, idx_x]
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qyy = Qxx[idx_y, idx_y]
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qyx = Qxx[idx_y, idx_x]
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# 2x2-Kofaktorblock
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Qxx_ = Qxx[ix, ix]
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Qyy_ = Qxx[iy, iy]
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Qyx_ = Qxx[iy, ix]
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# Standardabweichungen
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sx = s0_apost * np.sqrt(qxx)
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sy = s0_apost * np.sqrt(qyy)
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sxy = (s0_apost ** 2) * qyx
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# Standardabweichungen der Koordinatenkomponenten
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sx = s0_apost * np.sqrt(Qxx_)
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sy = s0_apost * np.sqrt(Qyy_)
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sxy = (s0_apost ** 2) * Qyx_
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k = np.sqrt((qxx - qyy) ** 2 + 4 * (qyx ** 2))
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# k und Eigenwerte (Q_dmax, Q_dmin)
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k = np.sqrt((Qxx_ - Qyy_) ** 2 + 4 * (Qyx_ ** 2))
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Q_dmax = 0.5 * (Qxx_ + Qyy_ + k)
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Q_dmin = 0.5 * (Qxx_ + Qyy_ - k)
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# Q_dmax/min = 0.5 * (Qyy + Qxx +/- k)
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q_dmax = 0.5 * (qyy + qxx + k)
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q_dmin = 0.5 * (qyy + qxx - k)
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# Halbachsen (Standardabweichungen entlang Hauptachsen)
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s_max = s0_apost * np.sqrt(Q_dmax)
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s_min = s0_apost * np.sqrt(Q_dmin)
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# Halbachsen
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s_max = s0_apost * np.sqrt(q_dmax)
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s_min = s0_apost * np.sqrt(q_dmin)
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# Richtungswinkel theta (Hauptachse) in rad:
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theta_rad = 0.5 * np.arctan2(2 * Qyx_, (Qxx_ - Qyy_))
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# Richtungswinkel theta in gon:
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zaehler = 2 * qyx
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nenner = qxx - qyy
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t_grund = 0.5 * np.arctan(abs(zaehler) / abs(nenner)) * (200 / np.pi)
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# in gon
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theta_gon = theta_rad * (200 / np.pi)
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if theta_gon < 0:
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theta_gon += 200.0
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# Quadrantenabfrage
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if nenner > 0 and qyx > 0: # Qxx - Qyy > 0 und Qyx > 0
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t_gon = t_grund # 0 - 50 gon
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elif nenner < 0 and qyx > 0: # Qxx - Qyy < 0 und Qyx > 0
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t_gon = 100 - t_grund # 50 - 100 gon
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elif nenner < 0 and qyx < 0: # Qxx - Qyy < 0 und Qyx < 0
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t_gon = 100 + t_grund # 100 - 150 gon
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elif nenner > 0 and qyx < 0: # Qxx - Qyy > 0 und Qyx < 0
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t_gon = 200 - t_grund # 150 - 200 gon
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else:
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t_gon = 0.0
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data.append([
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punkt,
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float(sx), float(sy), float(sxy),
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float(s_max), float(s_min),
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float(theta_gon)
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])
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daten.append([
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pid,
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float(sx), float(sy), float(sxy),
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float(s_max), float(s_min),
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float(t_gon)
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])
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standardellipse = pd.DataFrame(data, columns=["Punkt", "σx", "σy", "σxy", "s_max", "s_min", "θ [gon]"])
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except:
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continue
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standardellipse = pd.DataFrame(daten, columns=["Punkt", "σx", "σy", "σxy", "s_max", "s_min", "θ [gon]"])
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return standardellipse
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def konfidenzellipse(Qxx, s0_apost, unbekannten_liste, R, alpha=0.05):
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@staticmethod
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def konfidenzellipse(Qxx, s0_apost, unbekannten_liste, R, alpha):
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Qxx = np.asarray(Qxx, float)
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daten = []
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namen_str = [str(sym) for sym in unbekannten_liste]
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data = []
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n_punkte = len(unbekannten_liste) // 3 # X,Y,Z je Punkt angenommen
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punkt_ids = [n[1:] for n in namen_str if n.upper().startswith('X')]
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k = float(np.sqrt(2.0 * f_dist.ppf(1.0 - alpha, 2, R)))
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# Faktor für Konfidenzellipse (F-Verteilung)
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kk = float(np.sqrt(2.0 * f.ppf(1.0 - alpha, 2, R)))
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for i in range(n_punkte):
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punkt = str(unbekannten_liste[3 * i])[1:] # "X10009" -> "10009"
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for pid in punkt_ids:
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try:
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idx_x = next(i for i, n in enumerate(namen_str) if n.upper() == f"X{pid}".upper())
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idx_y = next(i for i, n in enumerate(namen_str) if n.upper() == f"Y{pid}".upper())
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ix = 3 * i
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iy = 3 * i + 1
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qxx = Qxx[idx_x, idx_x]
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qyy = Qxx[idx_y, idx_y]
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qyx = Qxx[idx_y, idx_x]
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Qxx_ = Qxx[ix, ix]
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Qyy_ = Qxx[iy, iy]
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Qxy_ = Qxx[iy, ix] # = Qyx
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# Standardabweichungen
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sx = s0_apost * np.sqrt(qxx)
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sy = s0_apost * np.sqrt(qyy)
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sxy = (s0_apost ** 2) * qyx
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# k für Eigenwerte
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kk = np.sqrt((Qxx_ - Qyy_) ** 2 + 4 * (Qxy_ ** 2))
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Q_dmax = 0.5 * (Qxx_ + Qyy_ + kk)
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Q_dmin = 0.5 * (Qxx_ + Qyy_ - kk)
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k = np.sqrt((qxx - qyy) ** 2 + 4 * (qyx ** 2))
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# Standard-Halbachsen (1-sigma)
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s_max = s0_apost * np.sqrt(Q_dmax)
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s_min = s0_apost * np.sqrt(Q_dmin)
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# Q_dmax/min = 0.5 * (Qyy + Qxx +/- k)
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q_dmax = 0.5 * (qyy + qxx + k)
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q_dmin = 0.5 * (qyy + qxx - k)
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# Orientierung (Hauptachse) in gon
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theta_rad = 0.5 * np.arctan2(2 * Qxy_, (Qxx_ - Qyy_))
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theta_gon = theta_rad * (200 / np.pi)
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if theta_gon < 0:
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theta_gon += 200.0
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# Halbachsen der Standardellipse
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s_max = s0_apost * np.sqrt(q_dmax)
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s_min = s0_apost * np.sqrt(q_dmin)
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# Konfidenz-Halbachsen
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a_K = k * s_max
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b_K = k * s_min
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# Halbachsen der Konfidenzellipse
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A_K = kk * s_max
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B_K = kk * s_min
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data.append([punkt, float(a_K), float(b_K), float(theta_gon)])
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# Richtungswinkel theta in gon:
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zaehler = 2 * qyx
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nenner = qxx - qyy
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t_grund = 0.5 * np.arctan(abs(zaehler) / abs(nenner)) * (200 / np.pi)
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# Quadrantenabfrage
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if nenner > 0 and qyx > 0:
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t_gon = t_grund # 0 - 50 gon
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elif nenner < 0 and qyx > 0:
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t_gon = 100 - t_grund # 50 - 100 gon
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elif nenner < 0 and qyx < 0:
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t_gon = 100 + t_grund # 100 - 150 gon
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elif nenner > 0 and qyx < 0:
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t_gon = 200 - t_grund # 150 - 200 gon
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else:
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t_gon = 0.0
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daten.append([
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pid,
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float(sx), float(sy), float(sxy),
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float(A_K), float(B_K),
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float(t_gon)
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])
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except:
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continue
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konfidenzellipse = pd.DataFrame(daten, columns= ["Punkt", "σx", "σy", "σxy", "a_K", "b_K","θ [gon]"])
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return konfidenzellipse
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konfidenzellipsen = pd.DataFrame(data, columns=["Punkt", "a_K", "b_K", "θ [gon]"])
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return konfidenzellipsen
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def plot_netz_komplett_final(x_vektor, unbekannten_labels, beobachtungs_labels, Qxx, sigma0_apost,
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