diff --git a/swash/processing/reflex3s.py b/swash/processing/reflex3s.py new file mode 100644 index 0000000..9b61030 --- /dev/null +++ b/swash/processing/reflex3s.py @@ -0,0 +1,47 @@ +import numpy as np +from scipy import fft +from scipy import signal as sgl +from scipy import optimize as opti + + +def reflex3s(eta, x, h, f): + #_welch = [sgl.welch(z, f) for z in eta] + + #eta_psd = np.stack([_w[1] for _w in _welch]) + #f_psd = _welch[0][0] + eta_psd = np.stack([fft.rfft(z) for z in eta]) + f_psd = fft.rfftfreq(eta.shape[1]) + + eta_amp = np.abs(eta_psd) / eta_psd.shape[1] + eta_phase = np.angle(eta_psd) + + g = 9.81 + k = np.asarray([opti.root_scalar( + f=lambda k: k * np.tanh(k) - (2 * np.pi * f) ** 2 / g * h, + fprime=lambda k: np.tanh(k) + k * (1 - np.tanh(k)) ** 2, + x0=0.2, + ).root for f in f_psd]) + + dx = np.roll(x, 1) - x + dphi = np.roll(eta_phase, 1, axis=0) - eta_phase + + ai = np.sqrt( + eta_amp**2 + + np.roll(eta_amp, 1, axis=0)**2 + - 2 + * eta_amp + * np.roll(eta_amp, 1, axis=0) + * np.cos(dphi - k * dx[:, None]) + / (2 * np.abs(np.sin(k * dx[:, None]))) + ) + ar = np.sqrt( + eta_amp**2 + + np.roll(eta_amp, 1, axis=0)**2 + - 2 + * eta_amp + * np.roll(eta_amp, 1, axis=0) + * np.cos(dphi + k * dx[:, None]) + / (2 * np.abs(np.sin(k * dx[:, None]))) + ) + + return f_psd, ar / ai