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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def dft_preprocess_data(arr, shift=True, axes=None, sign='-', out=None):
 """Pre-process the real-space data before DFT. This function multiplies the given data with the separable function:: p(x) = exp(+- 1j * dot(x - x[0], xi[0])) where ``x[0]`` and ``xi[0]`` are the minimum coodinates of the real-space and reciprocal grids, respectively. The sign of the exponent depends on the choice of ``sign``. In discretized form, this function becomes an array:: p[k] = exp(+- 1j * k * s * xi[0]) If the reciprocal grid is not shifted, i.e. symmetric around 0, it is ``xi[0] = pi/s * (-1 + 1/N)``, hence:: p[k] = exp(-+ 1j * pi * k * (1 - 1/N)) For a shifted grid, we have :math:``xi[0] = -pi/s``, thus the array is given by:: p[k] = (-1)**k Parameters arr : `array-like` Array to be pre-processed. If its data type is a real non-floating type, it is converted to 'float64'. shift : bool or or sequence of bools, optional If ``True``, the grid is shifted by half a stride in the negative direction. With a sequence, this option is applied separately on each axis. axes : int or sequence of ints, optional Dimensions in which to calculate the reciprocal. The sequence must have the same length as ``shift`` if the latter is given as a sequence. Default: all axes. sign : {'-', '+'}, optional Sign of the complex exponent. out : `numpy.ndarray`, optional Array in which the result is stored. If ``out is arr``, an in-place modification is performed. For real data type, this is only possible for ``shift=True`` since the factors are complex otherwise. Returns ------- out : `numpy.ndarray` Result of the pre-processing. If ``out`` was given, the returned object is a reference to it. Notes ----- If ``out`` is not specified, the data type of the returned array is the same as that of ``arr`` except when ``arr`` has real data type and ``shift`` is not ``True``. In this case, the return type is the complex counterpart of ``arr.dtype``. """

    arr = np.asarray(arr)
    if not is_numeric_dtype(arr.dtype):
        raise ValueError('array has non-numeric data type {}'
                         ''.format(dtype_repr(arr.dtype)))
    elif is_real_dtype(arr.dtype) and not is_real_floating_dtype(arr.dtype):
        arr = arr.astype('float64')

    if axes is None:
        axes = list(range(arr.ndim))
    else:
        try:
            axes = [int(axes)]
        except TypeError:
            axes = list(axes)

    shape = arr.shape
    shift_list = normalized_scalar_param_list(shift, length=len(axes),
                                              param_conv=bool)

    # Make a copy of arr with correct data type if necessary, or copy values.
    if out is None:
        if is_real_dtype(arr.dtype) and not all(shift_list):
            out = np.array(arr, dtype=complex_dtype(arr.dtype), copy=True)
        else:
            out = arr.copy()
    else:
        out[:] = arr

    if is_real_dtype(out.dtype) and not shift:
        raise ValueError('cannot pre-process real input in-place without '
                         'shift')

    if sign == '-':
        imag = -1j
    elif sign == '+':
        imag = 1j
    else:
        raise ValueError("`sign` '{}' not understood".format(sign))

    def _onedim_arr(length, shift):
        if shift:
            # (-1)^indices
            factor = np.ones(length, dtype=out.dtype)
            factor[1::2] = -1
        else:
            factor = np.arange(length, dtype=out.dtype)
            factor *= -imag * np.pi * (1 - 1.0 / length)
            np.exp(factor, out=factor)
        return factor.astype(out.dtype, copy=False)

    onedim_arrs = []
    for axis, shift in zip(axes, shift_list):
        length = shape[axis]
        onedim_arrs.append(_onedim_arr(length, shift))

    fast_1d_tensor_mult(out, onedim_arrs, axes=axes, out=out)
    return out