code: def dct(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False):
      """
      Return the Discrete Cosine Transform of arbitrary type sequence x.
  
      Parameters
      ----------
      x : array_like
          The input array.
      type : {1, 2, 3, 4}, optional
          Type of the DCT (see Notes). Default type is 2.
      n : int, optional
          Length of the transform.  If ``n < x.shape[axis]``, `x` is
          truncated.  If ``n > x.shape[axis]``, `x` is zero-padded. The
          default results in ``n = x.shape[axis]``.
      axis : int, optional
          Axis along which the dct is computed; the default is over the
          last axis (i.e., ``axis=-1``).
      norm : {None, 'ortho'}, optional
          Normalization mode (see Notes). Default is None.
      overwrite_x : bool, optional
          If True, the contents of `x` can be destroyed; the default is False.
  
      Returns
      -------
      y : ndarray of real
          The transformed input array.
  
      See Also
      --------
      idct : Inverse DCT
  
      Notes
      -----
      For a single dimension array ``x``, ``dct(x, norm='ortho')`` is equal to
      MATLAB ``dct(x)``.
  
      There are theoretically 8 types of the DCT, only the first 4 types are
      implemented in scipy. 'The' DCT generally refers to DCT type 2, and 'the'
      Inverse DCT generally refers to DCT type 3.
  
      **Type I**
  
      There are several definitions of the DCT-I; we use the following
      (for ``norm=None``)::
  
                                           N-2
        y[k] = x[0] + (-1)**k x[N-1] + 2 * sum x[n]*cos(pi*k*n/(N-1))
                                           n=1
  
      If ``norm='ortho'``, ``x[0]`` and ``x[N-1]`` are multiplied by
      a scaling factor of ``sqrt(2)``, and ``y[k]`` is multiplied by a
      scaling factor `f`::
  
        f = 0.5*sqrt(1/(N-1)) if k = 0 or N-1,
        f = 0.5*sqrt(2/(N-1)) otherwise.
  
      .. versionadded:: 1.2.0
         Orthonormalization in DCT-I.
  
      .. note::
         The DCT-I is only supported for input size > 1.
  
      **Type II**
  
      There are several definitions of the DCT-II; we use the following
      (for ``norm=None``)::
  
  
                  N-1
        y[k] = 2* sum x[n]*cos(pi*k*(2n+1)/(2*N)), 0 <= k < N.
                  n=0
  
      If ``norm='ortho'``, ``y[k]`` is multiplied by a scaling factor `f`::
  
        f = sqrt(1/(4*N)) if k = 0,
        f = sqrt(1/(2*N)) otherwise.
  
      Which makes the corresponding matrix of coefficients orthonormal
      (``OO' = Id``).
  
      **Type III**
  
      There are several definitions, we use the following
      (for ``norm=None``)::
  
                          N-1
        y[k] = x[0] + 2 * sum x[n]*cos(pi*(k+0.5)*n/N), 0 <= k < N.
                          n=1
  
      or, for ``norm='ortho'`` and 0 <= k < N::
  
                                            N-1
        y[k] = x[0] / sqrt(N) + sqrt(2/N) * sum x[n]*cos(pi*(k+0.5)*n/N)
                                            n=1
  
      The (unnormalized) DCT-III is the inverse of the (unnormalized) DCT-II, up
      to a factor `2N`. The orthonormalized DCT-III is exactly the inverse of
      the orthonormalized DCT-II.
  
      **Type IV**
  
      There are several definitions of the DCT-IV; we use the following
      (for ``norm=None``)::
  
  
                  N-1
        y[k] = 2* sum x[n]*cos(pi*(2k+1)*(2n+1)/(4*N)), 0 <= k < N.
                  n=0
  
      If ``norm='ortho'``, ``y[k]`` is multiplied by a scaling factor `f`::
  
        f = 0.5*sqrt(2/N)
  
      .. versionadded:: 1.2.0
         Support for DCT-IV.
  
      References
      ----------
      .. [1] 'A Fast Cosine Transform in One and Two Dimensions', by J.
             Makhoul, `IEEE Transactions on acoustics, speech and signal
             processing` vol. 28(1), pp. 27-34,
             :doi:`10.1109/TASSP.1980.1163351` (1980).
      .. [2] Wikipedia, "Discrete cosine transform",
             https://en.wikipedia.org/wiki/Discrete_cosine_transform
  
      Examples
      --------
      The Type 1 DCT is equivalent to the FFT (though faster) for real,
      even-symmetrical inputs.  The output is also real and even-symmetrical.
      Half of the FFT input is used to generate half of the FFT output:
  
      >>> from scipy.fftpack import fft, dct
      >>> fft(np.array([4., 3., 5., 10., 5., 3.])).real
      array([ 30.,  -8.,   6.,  -2.,   6.,  -8.])
      >>> dct(np.array([4., 3., 5., 10.]), 1)
      array([ 30.,  -8.,   6.,  -2.])
  
      """
      return _dct(
          x, type, n, axis, normalize=norm, overwrite_x=overwrite_x
      )
  
imports: from __future__ import division, print_function, absolute_import
  import numpy
  from scipy.fftpack import _fftpack
  from scipy.fftpack.basic import _datacopied, _fix_shape, _asfarray
  from scipy.fftpack.helper import _init_nd_shape_and_axes
  import atexit
label_desc: Use image node_id 5 for calling a global function with example usage: dct(x, type, n, axis, norm, overwrite_x) and returns: _dct