Merge remote-tracking branch 'refs/remotes/origin/main2'
# Conflicts: # GHA_triaxial/ES_gha2.py
This commit is contained in:
@@ -8,179 +8,134 @@ from GHA_triaxial.panou_2013_2GHA_num import gha2_num
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from utils import sigma2alpha
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ell_ES: EllipsoidTriaxial = None
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P_start: NDArray = None
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P_prev: NDArray = None
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P_next: NDArray = None
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P_end: NDArray = None
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stepLen: float = None
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P_left: NDArray = None
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P_right: NDArray = None
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def Bogenlaenge(P1: NDArray, P2: NDArray) -> float:
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def Sehne(P1: NDArray, P2: NDArray) -> float:
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"""
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Berechnung der mittleren Bogenlänge zwischen zwei kartesischen Punkten
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Berechnung der 3D-Distanz zwischen zwei kartesischen Punkten
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:param P1: kartesische Koordinate Punkt 1
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:param P2: kartesische Koordinate Punkt 2
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:return: Bogenlänge s
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"""
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R1 = np.linalg.norm(P1)
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R2 = np.linalg.norm(P2)
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R = 0.5 * (R1 + R2)
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theta = arccos(P1 @ P2 / (R1 * R2))
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s = float(R * theta)
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R12 = P2-P1
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s = np.linalg.norm(R12)
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return s
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def gha2_ES(ell: EllipsoidTriaxial, P0: NDArray, Pk: NDArray, stepLenTarget: float = None, sigmaStep: float = 1e-5, stopeval: int = 1000, maxSteps: int = 10000, all_points: bool = False):
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def midpoint_fitness(x: tuple) -> float:
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"""
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Fitness für einen Mittelpunkt P_middle zwischen P_left und P_right auf dem triaxialen Ellipsoid:
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- Minimiert d(P_left, P_middle) + d(P_middle, P_right)
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- Erzwingt d(P_left,P_middle) ≈ d(P_middle,P_right) (echter Mittelpunkt im Sinne der Polygonkette)
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:param x: enthält die Startwerte von u und v
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:return: Fitnesswert (f)
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"""
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global ell_ES, P_left, P_right
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u, v = x
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P_middle = ell_ES.para2cart(u, v)
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d1 = Sehne(P_left, P_middle)
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d2 = Sehne(P_middle, P_right)
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base = d1 + d2
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# midpoint penalty (dimensionslos)
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# relative Differenz, skaliert stabil über verschiedene Segmentlängen
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denom = max(base, 1e-9)
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pen_equal = ((d1 - d2) / denom) ** 2
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w_equal = 10.0
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f = base + denom * w_equal * pen_equal
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return f
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def gha2_ES(ell: EllipsoidTriaxial, P0: NDArray, Pk: NDArray, maxSegLen: float = None, stopeval: int = 2000, maxIter: int = 10000, all_points: bool = False):
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"""
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Berechnen der 2. GHA mithilfe der CMA-ES.
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Die CMA-ES optimiert sukzessive einzelne Punkte, die einen definierten Abstand (stepLenTarget) zum vorherigen und den kürzesten
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Abstand zum Zielpunkt aufweisen. Der Abbruch der Optimierung erfolgt, wenn die Restdistanz zwischen vorherigen und Zielpunkt die
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'stepLenTarget' unterschreitet. Die Distanzen zwischen den einzelnen Punkten werden als mittlere Bogenlänge berechnet und aufaddiert.
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Die CMA-ES optimiert sukzessive den Mittelpunkt zwischen Start- und Zielpunkt. Der Abbruch der Berechnung erfolgt, wenn alle Segmentlängen <= maxSegLen sind.
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Die Distanzen zwischen den einzelnen Punkten werden als direkte 3D-Distanzen berechnet und aufaddiert.
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:param ell: Parameter des triaxialen Ellipsoids
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:param P0: Startpunkt
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:param Pk: Zielpunkt
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:param stepLenTarget: Abstand zwischen vorherigen und optimierten Punkt
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:param sigmaStep: Sigma Startwert für die CMA-ES (Suchraum um den zu optimierenden Punkt)
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:param stopeval: maximale Iterationen
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:param maxSteps: maximale Anzahl der zu optimierenden Punkte
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:param maxSegLen: maximale Segmentlänge
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:param stopeval: maximale Durchläufe der CMA-ES
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:param maxIter: maximale Durchläufe der Mittelpunktsgenerierung
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:param all_points: Ergebnisliste mit allen Punkte, die wahlweise mit ausgegeben werden kann
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:return: Richtungswinkel des Start- und Zielpunktes, totalLen
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:return: Richtungswinkel des Start- und Zielpunktes und Gesamtlänge
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"""
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global ell_ES, P_start, P_prev, P_next, P_end, stepLen
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global ell_ES
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ell_ES = ell
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P_start = P0
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P_end = Pk
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if stepLenTarget is None:
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R0 = (ell.ax + ell.ay + ell.b) / 3
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stepLenTarget = R0 * 1 / 600
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stepLen = stepLenTarget
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if maxSegLen is None:
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maxSegLen = R0 * 1 / (637.4) # 10km Segment bei mittleren Erdradius
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P_all = [P_start]
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totalLen = 0
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sigma_uv_nom = 1e-3 * (maxSegLen / R0) # ~1e-5
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P_prev = P_start
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points: list[NDArray] = [P0, Pk]
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startIter = 0
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level = 0
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for i in range(1, maxSteps):
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d_remain = Bogenlaenge(P_prev, P_end)
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# Abbruch: letzter "Rest-Schritt" ist < 10 km -> Ziel anhängen
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if d_remain <= stepLen:
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P_all.append(P_end)
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totalLen += d_remain
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print(f'[Punkt {i}] Stop: Restdistanz {round(d_remain, 3)} m <= {round(stepLen, 3)} m, Ziel angehängt.')
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while True:
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seg_lens = [Sehne(points[i], points[i+1]) for i in range(len(points)-1)]
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max_len = max(seg_lens)
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if max_len <= maxSegLen:
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break
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# Globals für Fitness: aktueller Start(P0) und Ziel(Pk)
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# P0 = P_prev;
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# Pk = P_end;
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level += 1
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new_points: list[NDArray] = [points[0]]
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# Näherung für die ES ermitteln
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# % d = P_end - P_prev;
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# % L = Bogenlaenge(P_prev, P_end);
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# % t = min(stepLen / L, 1.0);
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# % Q = P_prev + t * d;
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# % q = [Q(1) / a;
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# Q(2) / b;
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# Q(3) / c];
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# % nq = norm(q);
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# % q = q / nq;
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for i in range(len(points) - 1):
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A = points[i]
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B = points[i+1]
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dAB = Sehne(A, B)
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print(dAB)
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# %q
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# entspricht[cos(u)
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# cos(v);
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# cos(u)
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# sin(v);
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# sin(u)] auf
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# Einheitskugel
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#arg_u = max(-1, min(1, q(3)));
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#
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# %Quadrantenabfrage
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#u0 = mod(asin(arg_u) + pi / 2, pi) - pi / 2;
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#v0 = atan2(q(2), q(1));
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#xmean_init = [u0;v0];
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xmean_init = ell.point_onto_ellipsoid(P_prev + stepLen * (P_end - P_prev) / np.linalg.norm(P_end - P_prev))
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if dAB > maxSegLen:
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global P_left, P_right
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P_left, P_right = A, B
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Au, Av = ell_ES.cart2para(A)
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Bu, Bv = ell_ES.cart2para(B)
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u0 = (Au + Bu) / 2
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v0 = Av + 0.5 * np.arctan2(np.sin(Bv - Av), np.cos(Bv - Av))
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xmean = [u0, v0]
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# [~, ~, aux] = geoLength(xmean_init);
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# print('Startguess: d_step=%.3f (soll %.3f), d_to_target=%.3f\n', aux(1), stepLen, aux(2));
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sigmaStep = sigma_uv_nom * (Sehne(A, B) / maxSegLen)
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print(f'[Punkt {i}] Optimiere nächsten Punkt: Restdistanz = {round(d_remain, 3)} m')
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xmean_init = np.array(ell_ES.cart2para(xmean_init))
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u, v = escma(geoLength, N=2, xmean=xmean_init, sigma=sigmaStep, stopfitness=-np.inf, stopeval=stopeval)
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u, v = escma(midpoint_fitness, N=2, xmean=xmean, sigma=sigmaStep, stopfitness=-np.inf,
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stopeval=stopeval)
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P_next = ell.para2cart(u, v)
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new_points.append(P_next)
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startIter += 1
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if startIter > maxIter:
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raise RuntimeError("Abbruch: maximale Iterationen überschritten.")
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d_step = Bogenlaenge(P_prev, P_next)
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d_new = Bogenlaenge(P_next, P_end)
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d_old = Bogenlaenge(P_prev, P_end)
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new_points.append(B)
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print(f'[Punkt {i}] Ergebnis: Schritt = {round(d_step, 3)} m (soll {round(stepLen, 3)}), Rest neu = {round(d_new, 3)} m')
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points = new_points
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print(f"[Level {level}] Punkte: {len(points)} | max Segment: {max_len:.3f} m")
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# Sicherheitscheck: wenn wir nicht näher kommen, abbrechen
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if d_new >= d_old:
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print(f'Punkt {i}: Neuer Punkt ist nicht naeher am Ziel ({d_old} -> {d_new}). Abbruch.')
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P_all.append(P_end)
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totalLen += Bogenlaenge(P_prev, P_end)
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break
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P_all = np.vstack(points)
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totalLen = float(np.sum(np.linalg.norm(P_all[1:] - P_all[:-1], axis=1)))
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P_all.append(P_next)
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totalLen += d_step
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P_prev = P_next
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print('Maximale Schrittanzahl erreicht.')
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# P_all.append(P_end)
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totalLen += Bogenlaenge(P_prev, P_end)
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p0i = ell.point_onto_ellipsoid(P0 + stepLenTarget/1000 * (P_all[1] - P0) / np.linalg.norm(P_all[1] - P0))
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if len(points) >= 3:
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p0i = ell_ES.point_onto_ellipsoid(P0 + 10.0 * (points[1] - P0) / np.linalg.norm(points[1] - P0))
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sigma0 = (p0i - P0) / np.linalg.norm(p0i - P0)
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alpha0 = sigma2alpha(ell_ES, sigma0, P0)
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p1i = ell.point_onto_ellipsoid(Pk - stepLenTarget/1000 * (Pk - P_all[-2]) / np.linalg.norm(Pk - P_all[-2]))
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p1i = ell_ES.point_onto_ellipsoid(Pk - 10.0 * (Pk - points[-2]) / np.linalg.norm(Pk - points[-2]))
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sigma1 = (Pk - p1i) / np.linalg.norm(Pk - p1i)
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alpha1 = sigma2alpha(ell_ES, sigma1, Pk)
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else:
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alpha0 = None
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alpha1 = None
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if all_points:
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return alpha0, alpha1, totalLen, np.array(P_all)
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else:
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return alpha0, alpha1, totalLen, P_all
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return alpha0, alpha1, totalLen
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def geoLength(P_candidate: Tuple) -> float:
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"""
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Berechung der Fitness eines Kandidaten anhand der Strecken
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:param P_candidate: Kandidat in parametrischen Koordinaten
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:return: Fitness-Wert
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"""
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# P_candidate = [u;v] des naechsten Punktes.
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# Ziel: Distanz zum Ziel minimieren, aber Schrittlaenge ~ stepLenTarget erzwingen.
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u, v = P_candidate
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global ell_ES, P_start, P_prev, P_next, P_end, stepLen
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# Punkt auf Ellipsoid
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P_next = ell_ES.para2cart(u, v)
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# Distanzen
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d_step = Bogenlaenge(P_prev, P_next)
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d_to_target = Bogenlaenge(P_end, P_next)
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d_prev_to_target = Bogenlaenge(P_end, P_prev)
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# Penalties(dimensionslos)
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pen_step = ((d_step - stepLen) / stepLen)**2
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# falls Punkt "weg" vom Ziel geht, extra bestrafen
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pen_away = max(0.0, (d_to_target - d_prev_to_target) / stepLen)**2
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# Gewichtungen
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alpha = 1e2
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# Schrittlaenge sehr hart
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gamma = 1e2 # "nicht weg vom Ziel" hart
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f = d_to_target * (1 + alpha * pen_step + gamma * pen_away)
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# Für Debug / Extraktion
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# aux = [d_step, d_to_target]
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return f # , P_candidate, aux
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def show_points(points: NDArray, pointsES: NDArray, p0: NDArray, p1: NDArray):
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"""
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Anzeigen der Punkte
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@@ -210,7 +165,7 @@ def show_points(points: NDArray, pointsES: NDArray, p0: NDArray, p1: NDArray):
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if __name__ == '__main__':
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ell = EllipsoidTriaxial.init_name("Fiction")
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ell = EllipsoidTriaxial.init_name("Bursa1970")
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beta0, lamb0 = (0.2, 0.1)
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P0 = ell.ell2cart(beta0, lamb0)
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@@ -223,6 +178,8 @@ if __name__ == '__main__':
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points_num.append(ell.ell2cart(beta, lamb))
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points_num = np.array(points_num)
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alpha0, alpha1, s, points = gha2_ES(ell, P0, P1, all_points=True, sigmaStep=1e-5)
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alpha0, alpha1, s, points = gha2_ES(ell, P0, P1, all_points=True)
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print(s_num)
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print(s)
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print(s - s_num)
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show_points(points, points_num, P0, P1)
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