

def cs_diff(x, a, b, period=None, _cache=_cache):
    '\n    Return (a,b)-cosh/sinh pseudo-derivative of a periodic sequence.\n\n    If ``x_j`` and ``y_j`` are Fourier coefficients of periodic functions x\n    and y, respectively, then::\n\n      y_j = -sqrt(-1)*cosh(j*a*2*pi/period)/sinh(j*b*2*pi/period) * x_j\n      y_0 = 0\n\n    Parameters\n    ----------\n    x : array_like\n        The array to take the pseudo-derivative from.\n    a, b : float\n        Defines the parameters of the cosh/sinh pseudo-differential\n        operator.\n    period : float, optional\n        The period of the sequence. Default period is ``2*pi``.\n\n    Returns\n    -------\n    cs_diff : ndarray\n        Pseudo-derivative of periodic sequence `x`.\n\n    Notes\n    -----\n    For even len(`x`), the Nyquist mode of `x` is taken as zero.\n\n    '
    tmp = asarray(x)
    if iscomplexobj(tmp):
        return (cs_diff(tmp.real, a, b, period) + (1j * cs_diff(tmp.imag, a, b, period)))
    if (period is not None):
        a = (((a * 2) * pi) / period)
        b = (((b * 2) * pi) / period)
    n = len(x)
    omega = _cache.get((n, a, b))
    if (omega is None):
        if (len(_cache) > 20):
            while _cache:
                _cache.popitem()

        def kernel(k, a=a, b=b):
            if k:
                return ((- cosh((a * k))) / sinh((b * k)))
            return 0
        omega = convolve.init_convolution_kernel(n, kernel, d=1)
        _cache[(n, a, b)] = omega
    overwrite_x = _datacopied(tmp, x)
    return convolve.convolve(tmp, omega, swap_real_imag=1, overwrite_x=overwrite_x)

dataset/ETHPy150Open scipy/scipy/scipy/fftpack/pseudo_diffs.py cs_diff/original