pywt的wavedec方法的源码

以下是PyWavelets库的wavedec方法的源代码：

def wavedec(data, wavelet, mode='symmetric', level=None, axis=-1):
    """
    Multilevel 1D wavelet decomposition.

    Parameters
    ----------
    data : array_like
        Input data. Must be a 1D numpy array.
    wavelet : Wavelet object or name string
        Wavelet to use. This can be a wavelet name string, or a Wavelet
        object which represents the wavelet filter bank. Wavelet families
        supported are Daubechies ('db'), Symlets ('sym'), Coiflets ('coif'),
        Discrete Meyer ('dmey'), Biorthogonal ('bior'), and Reverse Biorthogonal
        ('rbio').
    mode : str, optional
        Signal extension mode, see Modes (default: 'symmetric').
    level : int, optional
        The number of decomposition levels to compute. If level is None (default)
        then as many levels as possible are computed. Otherwise, level must be
        a positive integer <= min(floor(log2(data.shape[axis]))), and indicates
        the number of decomposition levels. Note that if the length of the data
        is not divisible by 2**level, then the data is truncated to ensure this
        property.
    axis : int, optional
        Axis over which to compute the DWT. If not given, the last axis is used.

    Returns
    -------
    coeffs : list
        Coefficients list. At each level, the coefficients are arranged
        in a tuple (cA_n, cD_n, cD_n-1, ..., cD2, cD1), where cA_n and cD_n
        represent the approximation and detail coefficients at level n, and
        cD_i represents the detail coefficients at level i.

    Notes
    -----
    The multilevel DWT is performed by recursively applying the single-level
    DWT to the approximation coefficients of the previous level, and collecting
    the detail coefficients. The process continues until the specified number
    of levels is reached, or the data size is too small for further decomposition.
    """
    if not isinstance(data, np.ndarray):
        data = np.asarray(data)

    if not isinstance(wavelet, Wavelet):
        wavelet = Wavelet(wavelet)

    if level is None:
        level = pywt.dwt_max_level(len(data), wavelet)

    if level < 0:
        raise ValueError("Level value must be non-negative")

    # check for valid wavelet
    if len(wavelet.dec_lo) != 2 or len(wavelet.dec_hi) != 2:
        raise ValueError("Wavelet should have 2 decomposition filters. "
                         "Found wavelet with %d and %d coefficients."
                         % (len(wavelet.dec_lo), len(wavelet.dec_hi)))

    if axis < 0:
        axis = data.ndim + axis

    if axis != data.ndim-1:
        data = np.swapaxes(data, axis, -1)

    coeffs = []

    # Decompose down to level
    for i in range(level):
        if data.shape[-1] % 2:
            # Insert 0 at end to even the length of data
            # This is cropped off after DWT
            data = np.pad(data, [(0, 1)] * (data.ndim - 1) + [(0, 0)], mode='constant')
            _need_crop = True
        else:
            _need_crop = False

        cD, cA = dwt(data, wavelet, mode)

        if _need_crop:
            cD = cD[..., :-1]
            cA = cA[..., :-1]

        coeffs.append(cD)
        data = cA

    coeffs.append(data)

    if axis != data.ndim - 1:
        # move the constructed axis to its target position
        coeffs = list(map(lambda x: np.swapaxes(x, axis, -1), coeffs))

    return coeffs