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157
ES/Hansen_ES_CMA.py
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157
ES/Hansen_ES_CMA.py
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import numpy as np
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from numpy.typing import NDArray
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def felli(x: NDArray) -> float:
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N = x.shape[0]
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if N < 2:
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raise ValueError("dimension must be greater than one")
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exponents = np.arange(N) / (N - 1)
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return float(np.sum((1e6 ** exponents) * (x ** 2)))
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def escma(func, *, N=10, xmean=None, sigma=0.5, stopfitness=1e-14, stopeval=2000,
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func_args=(), func_kwargs=None, seed=0,
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bestEver=np.inf, noImproveGen=0, absTolImprove=1e-12, maxNoImproveGen=100, sigmaImprove=1e-12):
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if func_kwargs is None:
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func_kwargs = {}
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if seed is not None:
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np.random.seed(seed)
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# Initialization (aus Parametern statt hart verdrahtet)
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if xmean is None:
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xmean = np.random.rand(N)
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else:
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xmean = np.asarray(xmean, dtype=float)
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N = xmean.shape[0]
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if stopeval is None:
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stopeval = int(1e3 * N ** 2)
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# Strategy parameter setting: Selection
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lambda_ = 4 + int(np.floor(3 * np.log(N)))
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mu = lambda_ / 2.0
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# muXone recombination weights
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weights = np.log(mu + 0.5) - np.log(np.arange(1, int(mu) + 1))
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mu = int(np.floor(mu))
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weights = weights / np.sum(weights)
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mueff = np.sum(weights) ** 2 / np.sum(weights ** 2)
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# Strategy parameter setting: Adaptation
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cc = (4 + mueff / N) / (N + 4 + 2 * mueff / N)
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cs = (mueff + 2) / (N + mueff + 5)
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c1 = 2 / ((N + 1.3) ** 2 + mueff)
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cmu = min(1 - c1,
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2 * (mueff - 2 + 1 / mueff) / ((N + 2) ** 2 + 2 * mueff))
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damps = 1 + 2 * max(0, np.sqrt((mueff - 1) / (N + 1)) - 1) + cs
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# Initialize dynamic (internal) strategy parameters and constants
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pc = np.zeros(N)
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ps = np.zeros(N)
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B = np.eye(N)
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D = np.eye(N)
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C = B @ D @ (B @ D).T
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eigeneval = 0
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chiN = np.sqrt(N) * (1 - 1 / (4 * N) + 1 / (21 * N ** 2))
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# Generation Loop
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counteval = 0
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arx = np.zeros((N, lambda_))
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arz = np.zeros((N, lambda_))
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arfitness = np.zeros(lambda_)
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gen = 0
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# print(f' [CMA-ES] Start: lambda = {lambda_}, sigma ={round(sigma, 6)}, stopeval = {stopeval}')
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while counteval < stopeval:
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gen += 1
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# Generate and evaluate lambda offspring
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for k in range(lambda_):
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arz[:, k] = np.random.randn(N)
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arx[:, k] = xmean + sigma * (B @ D @ arz[:, k])
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arfitness[k] = float(func(arx[:, k], *func_args, **func_kwargs)) # <-- allgemein
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counteval += 1
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# Sort by fitness and compute weighted mean into xmean
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idx = np.argsort(arfitness)
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arfitness = arfitness[idx]
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arindex = idx
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xold = xmean.copy()
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xmean = arx[:, arindex[:mu]] @ weights
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zmean = arz[:, arindex[:mu]] @ weights
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# Stagnation check
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fbest = arfitness[0]
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if bestEver - fbest > absTolImprove:
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bestEver = fbest
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noImproveGen = 0
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else:
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noImproveGen += 1
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if gen == 1 or gen % 50 == 0:
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# print(f' [CMA-ES] Gen {gen}, best = {round(fbest, 6)}, sigma = {sigma:.3g}')
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pass
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if noImproveGen >= maxNoImproveGen:
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# print(f' [CMA-ES] Abbruch: keine Verbesserung > {round(absTolImprove, 3)} in {maxNoImproveGen} Generationen.')
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break
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if sigma < sigmaImprove:
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# print(f' [CMA-ES] Abbruch: sigma zu klein {sigma:.3g}')
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break
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# Cumulation: Update evolution paths
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ps = (1 - cs) * ps + np.sqrt(cs * (2 - cs) * mueff) * (B @ zmean)
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norm_ps = np.linalg.norm(ps)
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hsig = norm_ps / np.sqrt(1 - (1 - cs) ** (2 * counteval / lambda_)) / chiN < (1.4 + 2 / (N + 1))
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hsig = 1.0 if hsig else 0.0
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pc = (1 - cc) * pc + hsig * np.sqrt(cc * (2 - cc) * mueff) * (B @ D @ zmean)
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# Adapt covariance matrix C
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BDz = B @ D @ arz[:, arindex[:mu]]
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C = (1 - c1 - cmu) * C \
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+ c1 * (np.outer(pc, pc) + (1 - hsig) * cc * (2 - cc) * C) \
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+ cmu * BDz @ np.diag(weights) @ BDz.T
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# Adapt step-size sigma
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sigma = sigma * np.exp((cs / damps) * (norm_ps / chiN - 1))
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# Update B and D from C (Eigenzerlegung, O(N^2))
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if counteval - eigeneval > lambda_ / ((c1 + cmu) * N * 10):
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eigeneval = counteval
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# enforce symmetry
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C = (C + C.T) / 2.0
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eigvals, B = np.linalg.eigh(C)
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D = np.diag(np.sqrt(eigvals))
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# Break, if fitness is good enough
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if arfitness[0] <= stopfitness:
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break
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# Escape flat fitness, or better terminate?
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if arfitness[0] == arfitness[int(np.ceil(0.7 * lambda_)) - 1]:
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sigma = sigma * np.exp(0.2 + cs / damps)
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# print(' [CMA-ES] stopfitness erreicht.')
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# print("warning: flat fitness, consider reformulating the objective")
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break
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# print(f"{counteval}: {arfitness[0]}")
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# Final Message
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# print(f"{counteval}: {arfitness[0]}")
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xmin = arx[:, arindex[0]]
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bestValue = arfitness[0]
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# print(f' [CMA-ES] Ende: Gen = {gen}, best = {round(bestValue, 6)}')
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return xmin
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if __name__ == "__main__":
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xmin = escma(felli, N=10) # <-- Zielfunktion wird übergeben
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print("Bestes gefundenes x:", xmin)
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print("f(xmin) =", felli(xmin))
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0
ES/__init__.py
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0
ES/__init__.py
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247
ES/gha1_ES.py
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247
ES/gha1_ES.py
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from __future__ import annotations
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from typing import List, Tuple
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import numpy as np
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from numpy.typing import NDArray
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import winkelumrechnungen as wu
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from ES.Hansen_ES_CMA import escma
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from GHA_triaxial.gha1_ana import gha1_ana
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from GHA_triaxial.gha1_approx import gha1_approx
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from GHA_triaxial.utils import jacobi_konstante
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from ellipsoid_triaxial import EllipsoidTriaxial
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from utils_angle import wrap_mpi_pi
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def ENU_beta_omega(beta: float, omega: float, ell: EllipsoidTriaxial) \
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-> Tuple[NDArray, NDArray, NDArray, float, float, NDArray]:
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"""
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Analytische ENU-Basis in ellipsoidische Koordinaten (β, ω) nach Karney (2025), S. 2
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:param beta: Beta Koordinate
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:param omega: Omega Koordinate
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:param ell: Ellipsoid
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:return: E_hat = Einheitsrichtung entlang wachsendem ω (East)
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N_hat = Einheitsrichtung entlang wachsendem β (North)
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U_hat = Einheitsnormale (Up)
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En & Nn = Längen der unnormierten Ableitungen
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R (XYZ) = Punkt in XYZ
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"""
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# Berechnungshilfen
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omega = wrap_mpi_pi(omega)
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cb = np.cos(beta)
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sb = np.sin(beta)
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co = np.cos(omega)
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so = np.sin(omega)
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# D = sqrt(a^2 - c^2)
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D = np.sqrt(ell.ax*ell.ax - ell.b*ell.b)
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# Sx = sqrt(a^2 - b^2 sin^2β - c^2 cos^2β)
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Sx = np.sqrt(ell.ax*ell.ax - ell.ay*ell.ay*(sb*sb) - ell.b*ell.b*(cb*cb))
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# Sz = sqrt(a^2 sin^2ω + b^2 cos^2ω - c^2)
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Sz = np.sqrt(ell.ax*ell.ax*(so*so) + ell.ay*ell.ay*(co*co) - ell.b*ell.b)
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# Karney Gl. (4)
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X = ell.ax * co * Sx / D
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Y = ell.ay * cb * so
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Z = ell.b * sb * Sz / D
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R = np.array([X, Y, Z], dtype=float)
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# --- Ableitungen - Karney Gl. (5a,b,c)---
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# E = ∂R/∂ω
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dX_dw = -ell.ax * so * Sx / D
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dY_dw = ell.ay * cb * co
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dZ_dw = ell.b * sb * (so * co * (ell.ax*ell.ax - ell.ay*ell.ay) / Sz) / D
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E = np.array([dX_dw, dY_dw, dZ_dw], dtype=float)
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# N = ∂R/∂β
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dX_db = ell.ax * co * (sb * cb * (ell.b*ell.b - ell.ay*ell.ay) / Sx) / D
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dY_db = -ell.ay * sb * so
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dZ_db = ell.b * cb * Sz / D
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N = np.array([dX_db, dY_db, dZ_db], dtype=float)
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# U = Grad(x^2/a^2 + y^2/b^2 + z^2/c^2 - 1)
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U = np.array([X/(ell.ax*ell.ax), Y/(ell.ay*ell.ay), Z/(ell.b*ell.b)], dtype=float)
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En = float(np.linalg.norm(E))
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Nn = float(np.linalg.norm(N))
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Un = float(np.linalg.norm(U))
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N_hat = N / Nn
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E_hat = E / En
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U_hat = U / Un
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E_hat -= float(np.dot(E_hat, N_hat)) * N_hat
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E_hat = E_hat / max(np.linalg.norm(E_hat), 1e-18)
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return E_hat, N_hat, U_hat, En, Nn, R
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def azimuth_at_ESpoint(P_prev: NDArray, P_curr: NDArray, E_hat_curr: NDArray, N_hat_curr: NDArray, U_hat_curr: NDArray) -> float:
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"""
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Berechnet das Azimut in der lokalen Tangentialebene am aktuellen Punkt P_curr, gemessen
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an der Bewegungsrichtung vom vorherigen Punkt P_prev nach P_curr.
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:param P_prev: vorheriger Punkt
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:param P_curr: aktueller Punkt
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:param E_hat_curr: Einheitsvektor der lokalen Tangentialrichtung am Punkt P_curr
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:param N_hat_curr: Einheitsvektor der lokalen Tangentialrichtung am Punkt P_curr
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:param U_hat_curr: Einheitsnormalenvektor am Punkt P_curr
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:return: Azimut in Radiant
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"""
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v = (P_curr - P_prev).astype(float)
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vT = v - float(np.dot(v, U_hat_curr)) * U_hat_curr
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vTn = max(np.linalg.norm(vT), 1e-18)
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vT_hat = vT / vTn
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sE = float(np.dot(vT_hat, E_hat_curr))
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sN = float(np.dot(vT_hat, N_hat_curr))
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return wrap_mpi_pi(float(np.arctan2(sE, sN)))
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def optimize_next_point(beta_i: float, omega_i: float, alpha_i: float, ds: float, gamma0: float,
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ell: EllipsoidTriaxial, maxSegLen: float = 1000.0, sigma0: float = None) -> Tuple[float, float, NDArray, float]:
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"""
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Berechnung der 1. GHA mithilfe der CMA-ES.
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Die CMA-ES optimiert sukzessive einen Punkt, der maxSegLen vom vorherigen Punkt entfernt und zusätzlich auf der
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geodätischen Linien liegt. Somit entsteht ein Geodäten ähnlicher Polygonzug auf der Oberfläche des dreiachsigen Ellipsoids.
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:param beta_i: Beta Koordinate am Punkt i
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:param omega_i: Omega Koordinate am Punkt i
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:param alpha_i: Azimut am Punkt i
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:param ds: Gesamtlänge
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:param gamma0: Jacobi-Konstante am Startpunkt
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:param ell: Ellipsoid
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:param maxSegLen: maximale Segmentlänge
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:param sigma0:
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:return:
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"""
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# Startbasis
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E_i, N_i, U_i, En_i, Nn_i, P_i = ENU_beta_omega(beta_i, omega_i, ell)
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# Prediktor: dβ ≈ ds cosα / |N|, dω ≈ ds sinα / |E|
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En_eff = max(En_i, 1e-9)
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Nn_eff = max(Nn_i, 1e-9)
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d_beta = ds * np.cos(alpha_i) / Nn_eff
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d_omega = ds * np.sin(alpha_i) / En_eff
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# optional: harte Schritt-Clamps (verhindert wrap-chaos)
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d_beta = float(np.clip(d_beta, -0.2, 0.2)) # rad
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d_omega = float(np.clip(d_omega, -0.2, 0.2)) # rad
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# d_beta = ds * float(np.cos(alpha_i)) / Nn_i
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# d_omega = ds * float(np.sin(alpha_i)) / En_i
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beta_pred = beta_i + d_beta
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omega_pred = wrap_mpi_pi(omega_i + d_omega)
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xmean = np.array([beta_pred, omega_pred], dtype=float)
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if sigma0 is None:
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R0 = (ell.ax + ell.ay + ell.b) / 3
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sigma0 = 1e-5 * (ds / R0)
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def fitness(x: NDArray) -> float:
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"""
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Fitnessfunktion: Fitnesscheck erfolgt anhand der Segmentlänge und der Jacobi-Konstante.
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Die Segmentlänge muss möglichst gut zum Sollwert passen. Die Jacobi-Konstante am Punkt x muss zur
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Jacobi-Konstanten am Startpunkt passen, damit der Polygonzug auf derselben geodätischen Linie bleibt.
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:param x: Koordinate in beta, lambda aus der CMA-ES
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:return: Fitnesswert (f)
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"""
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beta = x[0]
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omega = wrap_mpi_pi(x[1])
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P = ell.ell2cart_karney(beta, omega) # in kartesischer Koordinaten
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d = float(np.linalg.norm(P - P_i)) # Distanz zwischen
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# maxSegLen einhalten
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J_len = ((d - ds) / ds) ** 2
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w_len = 1.0
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# Azimut für Jacobi-Konstante
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E_j, N_j, U_j, _, _, _ = ENU_beta_omega(beta, omega, ell)
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alpha_end = azimuth_at_ESpoint(P_i, P, E_j, N_j, U_j)
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# Jacobi-Konstante
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g_end = jacobi_konstante(beta, omega, alpha_end, ell)
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J_gamma = (g_end - gamma0) ** 2
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w_gamma = 10
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f = float(w_len * J_len + w_gamma * J_gamma)
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return f
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xb = escma(fitness, N=2, xmean=xmean, sigma=sigma0) # Aufruf CMA-ES
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beta_best = xb[0]
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omega_best = wrap_mpi_pi(xb[1])
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P_best = ell.ell2cart_karney(beta_best, omega_best)
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E_j, N_j, U_j, _, _, _ = ENU_beta_omega(beta_best, omega_best, ell)
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alpha_end = azimuth_at_ESpoint(P_i, P_best, E_j, N_j, U_j)
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return beta_best, omega_best, P_best, alpha_end
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def gha1_ES(ell: EllipsoidTriaxial, beta0: float, omega0: float, alpha0: float, s_total: float, maxSegLen: float = 1000, all_points: bool = False)\
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-> Tuple[NDArray, float, NDArray] | Tuple[NDArray, float]:
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"""
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Aufruf der 1. GHA mittels CMA-ES
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:param ell: Ellipsoid
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:param beta0: Beta Startkoordinate
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:param omega0: Omega Startkoordinate
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:param alpha0: Azimut Startkoordinate
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:param s_total: Gesamtstrecke
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:param maxSegLen: maximale Segmentlänge
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:param all_points: Alle Punkte ausgeben?
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:return: Zielpunkt Pk, Azimut am Zielpunkt und Punktliste
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"""
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beta = float(beta0)
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omega = wrap_mpi_pi(float(omega0))
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alpha = wrap_mpi_pi(float(alpha0))
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gamma0 = jacobi_konstante(beta, omega, alpha, ell) # Referenz-γ0
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P_all: List[NDArray] = [ell.ell2cart_karney(beta, omega)]
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alpha_end: List[float] = [alpha]
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s_acc = 0.0
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step = 0
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nsteps_est = int(np.ceil(s_total / maxSegLen))
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while s_acc < s_total - 1e-9:
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step += 1
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ds = min(maxSegLen, s_total - s_acc)
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# print(f"[GHA1-ES] Step {step}/{nsteps_est} ds={ds:.3f} m s_acc={s_acc:.3f} m beta={beta:.6f} omega={omega:.6f} alpha={alpha:.6f}")
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beta, omega, P, alpha = optimize_next_point(beta_i=beta, omega_i=omega, alpha_i=alpha, ds=ds, gamma0=gamma0,
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ell=ell, maxSegLen=maxSegLen)
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s_acc += ds
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P_all.append(P)
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alpha_end.append(wrap_mpi_pi(alpha))
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if step > nsteps_est + 50:
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raise RuntimeError("GHA1_ES: Zu viele Schritte – vermutlich Konvergenzproblem / falsche Azimut-Konvention.")
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Pk = P_all[-1]
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alpha1 = float(alpha_end[-1])
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if all_points:
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return Pk, alpha1, np.array(P_all)
|
||||
else:
|
||||
return Pk, alpha1
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
ell = EllipsoidTriaxial.init_name("BursaSima1980round")
|
||||
s = 180000
|
||||
# alpha0 = 3
|
||||
alpha0 = wu.gms2rad([5, 0, 0])
|
||||
beta = 0
|
||||
omega = 0
|
||||
P0 = ell.ell2cart(beta, omega)
|
||||
point1, alpha1 = gha1_ana(ell, P0, alpha0=alpha0, s=s, maxM=100, maxPartCircum=32)
|
||||
point1app, alpha1app = gha1_approx(ell, P0, alpha0=alpha0, s=s, ds=1000)
|
||||
|
||||
res, alpha, points = gha1_ES(ell, beta0=beta, omega0=-omega, alpha0=alpha0, s_total=s, maxSegLen=1000)
|
||||
|
||||
print(point1)
|
||||
print(res)
|
||||
print(alpha)
|
||||
print(points)
|
||||
# print("alpha1 (am Endpunkt):", res.alpha1)
|
||||
print(res - point1)
|
||||
print(point1app - point1, "approx")
|
||||
182
ES/gha2_ES.py
Normal file
182
ES/gha2_ES.py
Normal file
@@ -0,0 +1,182 @@
|
||||
from typing import Tuple
|
||||
|
||||
import numpy as np
|
||||
import plotly.graph_objects as go
|
||||
from numpy.typing import NDArray
|
||||
|
||||
from GHA_triaxial.gha2_num import gha2_num
|
||||
from GHA_triaxial.utils import sigma2alpha
|
||||
from Hansen_ES_CMA import escma
|
||||
from ellipsoid_triaxial import EllipsoidTriaxial
|
||||
|
||||
|
||||
def Sehne(P1: NDArray, P2: NDArray) -> float:
|
||||
"""
|
||||
Berechnung der 3D-Distanz zwischen zwei kartesischen Punkten
|
||||
:param P1: kartesische Koordinate Punkt 1
|
||||
:param P2: kartesische Koordinate Punkt 2
|
||||
:return: Bogenlänge s
|
||||
"""
|
||||
R12 = P2-P1
|
||||
s = float(np.linalg.norm(R12))
|
||||
|
||||
return s
|
||||
|
||||
|
||||
def gha2_ES(ell: EllipsoidTriaxial, P0: NDArray, Pk: NDArray, maxSegLen: float = None, all_points: bool = False) -> Tuple[float, float, float, NDArray] | Tuple[float, float, float]:
|
||||
"""
|
||||
Berechnen der 2. GHA mithilfe der CMA-ES.
|
||||
Die CMA-ES optimiert sukzessive den Mittelpunkt zwischen Start- und Zielpunkt. Der Abbruch der Berechnung erfolgt, wenn alle Segmentlängen <= maxSegLen sind.
|
||||
Die Distanzen zwischen den einzelnen Punkten werden als direkte 3D-Distanzen berechnet und aufaddiert.
|
||||
:param ell: Ellipsoid
|
||||
:param P0: Startpunkt
|
||||
:param Pk: Zielpunkt
|
||||
:param maxSegLen: maximale Segmentlänge
|
||||
:param all_points: Ergebnisliste mit allen Punkte, die wahlweise mit ausgegeben wird
|
||||
:return: Richtungswinkel in RAD des Start- und Zielpunktes und Gesamtlänge
|
||||
"""
|
||||
P_left: NDArray = None
|
||||
P_right: NDArray = None
|
||||
|
||||
def midpoint_fitness(x: tuple) -> float:
|
||||
"""
|
||||
Fitness für einen Mittelpunkt P_middle zwischen P_left und P_right auf dem triaxialen Ellipsoid:
|
||||
- Minimiert d(P_left, P_middle) + d(P_middle, P_right)
|
||||
- Erzwingt d(P_left,P_middle) ≈ d(P_middle,P_right) (echter Mittelpunkt im Sinne der Polygonkette)
|
||||
:param x: enthält die Startwerte von u und v
|
||||
:return: Fitnesswert (f)
|
||||
"""
|
||||
nonlocal P_left, P_right, ell
|
||||
|
||||
u, v = x
|
||||
P_middle = ell.para2cart(u, v)
|
||||
d1 = Sehne(P_left, P_middle)
|
||||
d2 = Sehne(P_middle, P_right)
|
||||
base = d1 + d2
|
||||
|
||||
# midpoint penalty (dimensionslos)
|
||||
# relative Differenz, skaliert über verschiedene Segmentlängen
|
||||
denom = max(base, 1e-9)
|
||||
pen_equal = ((d1 - d2) / denom) ** 2
|
||||
w_equal = 10.0
|
||||
|
||||
f = base + denom * w_equal * pen_equal
|
||||
|
||||
return f
|
||||
|
||||
R0 = (ell.ax + ell.ay + ell.b) / 3
|
||||
if maxSegLen is None:
|
||||
maxSegLen = R0 * 1 / (637.4*2) # 10km Segment bei mittleren Erdradius
|
||||
|
||||
sigma_uv_nom = 1e-3 * (maxSegLen / R0) # ~1e-5
|
||||
points: list[NDArray] = [P0, Pk]
|
||||
startIter = 0
|
||||
level = 0
|
||||
|
||||
while True:
|
||||
seg_lens = [Sehne(points[i], points[i+1]) for i in range(len(points)-1)]
|
||||
max_len = max(seg_lens)
|
||||
if max_len <= maxSegLen:
|
||||
break
|
||||
|
||||
level += 1
|
||||
new_points: list[NDArray] = [points[0]]
|
||||
for i in range(len(points) - 1):
|
||||
A = points[i]
|
||||
B = points[i+1]
|
||||
dAB = Sehne(A, B)
|
||||
# print(dAB)
|
||||
|
||||
if dAB > maxSegLen:
|
||||
# global P_left, P_right
|
||||
P_left, P_right = A, B
|
||||
Au, Av = ell.cart2para(A)
|
||||
Bu, Bv = ell.cart2para(B)
|
||||
u0 = (Au + Bu) / 2
|
||||
v0 = Av + 0.5 * np.arctan2(np.sin(Bv - Av), np.cos(Bv - Av))
|
||||
xmean = [u0, v0]
|
||||
|
||||
sigmaStep = sigma_uv_nom * (Sehne(A, B) / maxSegLen)
|
||||
|
||||
u, v = escma(midpoint_fitness, N=2, xmean=xmean, sigma=sigmaStep) # Aufruf CMA-ES
|
||||
|
||||
P_next = ell.para2cart(u, v)
|
||||
new_points.append(P_next)
|
||||
startIter += 1
|
||||
maxIter = 10000
|
||||
if startIter > maxIter:
|
||||
raise RuntimeError("GHA2_ES: maximale Iterationen überschritten")
|
||||
new_points.append(B)
|
||||
|
||||
points = new_points
|
||||
# print(f"[Level {level}] Punkte: {len(points)} | max Segment: {max_len:.3f} m")
|
||||
|
||||
P_all = np.vstack(points)
|
||||
totalLen = float(np.sum(np.linalg.norm(P_all[1:] - P_all[:-1], axis=1)))
|
||||
|
||||
if len(points) >= 3:
|
||||
p0i = ell.point_onto_ellipsoid(P0 + 10.0 * (points[1] - P0) / np.linalg.norm(points[1] - P0))
|
||||
sigma0 = (p0i - P0) / np.linalg.norm(p0i - P0)
|
||||
alpha0 = sigma2alpha(ell, sigma0, P0)
|
||||
|
||||
p1i = ell.point_onto_ellipsoid(Pk - 10.0 * (Pk - points[-2]) / np.linalg.norm(Pk - points[-2]))
|
||||
sigma1 = (Pk - p1i) / np.linalg.norm(Pk - p1i)
|
||||
alpha1 = sigma2alpha(ell, sigma1, Pk)
|
||||
else:
|
||||
alpha0 = None
|
||||
alpha1 = None
|
||||
|
||||
if all_points:
|
||||
return alpha0, alpha1, totalLen, P_all
|
||||
return alpha0, alpha1, totalLen
|
||||
|
||||
|
||||
def show_points(points: NDArray, pointsES: NDArray, p0: NDArray, p1: NDArray):
|
||||
"""
|
||||
Anzeigen der Punkte
|
||||
:param points: wahre Punkte der Linie
|
||||
:param pointsES: Punkte der Linie aus ES
|
||||
:param p0: wahrer Startpunkt
|
||||
:param p1: wahrer Endpunkt
|
||||
"""
|
||||
fig = go.Figure()
|
||||
|
||||
fig.add_scatter3d(x=pointsES[:, 0], y=pointsES[:, 1], z=pointsES[:, 2],
|
||||
mode='lines', line=dict(color="green", width=3), name="Numerisch")
|
||||
fig.add_scatter3d(x=points[:, 0], y=points[:, 1], z=points[:, 2],
|
||||
mode='lines', line=dict(color="red", width=3), name="ES")
|
||||
fig.add_scatter3d(x=[p0[0]], y=[p0[1]], z=[p0[2]],
|
||||
mode='markers', marker=dict(color="black"), name="P0")
|
||||
fig.add_scatter3d(x=[p1[0]], y=[p1[1]], z=[p1[2]],
|
||||
mode='markers', marker=dict(color="black"), name="P1")
|
||||
|
||||
fig.update_layout(
|
||||
scene=dict(xaxis_title='X [km]',
|
||||
yaxis_title='Y [km]',
|
||||
zaxis_title='Z [km]',
|
||||
aspectmode='data'))
|
||||
|
||||
fig.show()
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
ell = EllipsoidTriaxial.init_name("Bursa1970")
|
||||
|
||||
beta0, lamb0 = (0.2, 0.1)
|
||||
P0 = ell.ell2cart(beta0, lamb0)
|
||||
beta1, lamb1 = (0.3, 0.2)
|
||||
P1 = ell.ell2cart(beta1, lamb1)
|
||||
|
||||
alpha0, alpha1, s_num, betas, lambs = gha2_num(ell, beta0, lamb0, beta1, lamb1, n=1000, all_points=True)
|
||||
points_num = []
|
||||
for beta, lamb in zip(betas, lambs):
|
||||
points_num.append(ell.ell2cart(beta, lamb))
|
||||
points_num = np.array(points_num)
|
||||
|
||||
alpha0, alpha1, s, points = gha2_ES(ell, P0, P1)
|
||||
print(s_num)
|
||||
print(s)
|
||||
print(alpha0)
|
||||
print(alpha1)
|
||||
print(s - s_num)
|
||||
show_points(points, points_num, P0, P1)
|
||||
Reference in New Issue
Block a user