def smooth1d(x, window_len):
s = np.r_[2*x[0] - x[window_len:1:-1], x, 2*x[-1] - x[-1:-window_len:-1]]
w = np.hanning(window_len)
y = np.convolve(w/w.sum(), s, mode='same')
return y[window_len-1:-window_len+1]
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