48 lines
1.2 KiB
Python
48 lines
1.2 KiB
Python
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import numpy as np
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from scipy import fft
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from scipy import signal as sgl
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from scipy import optimize as opti
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def reflex3s(eta, x, h, f):
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#_welch = [sgl.welch(z, f) for z in eta]
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#eta_psd = np.stack([_w[1] for _w in _welch])
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#f_psd = _welch[0][0]
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eta_psd = np.stack([fft.rfft(z) for z in eta])
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f_psd = fft.rfftfreq(eta.shape[1])
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eta_amp = np.abs(eta_psd) / eta_psd.shape[1]
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eta_phase = np.angle(eta_psd)
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g = 9.81
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k = np.asarray([opti.root_scalar(
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f=lambda k: k * np.tanh(k) - (2 * np.pi * f) ** 2 / g * h,
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fprime=lambda k: np.tanh(k) + k * (1 - np.tanh(k)) ** 2,
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x0=0.2,
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).root for f in f_psd])
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dx = np.roll(x, 1) - x
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dphi = np.roll(eta_phase, 1, axis=0) - eta_phase
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ai = np.sqrt(
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eta_amp**2
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+ np.roll(eta_amp, 1, axis=0)**2
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- 2
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* eta_amp
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* np.roll(eta_amp, 1, axis=0)
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* np.cos(dphi - k * dx[:, None])
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/ (2 * np.abs(np.sin(k * dx[:, None])))
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)
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ar = np.sqrt(
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eta_amp**2
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+ np.roll(eta_amp, 1, axis=0)**2
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- 2
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* eta_amp
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* np.roll(eta_amp, 1, axis=0)
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* np.cos(dphi + k * dx[:, None])
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/ (2 * np.abs(np.sin(k * dx[:, None])))
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)
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return f_psd, ar / ai
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