code: def dct(
      x,
      type=2,
      n=None,
      axis=-1,
      norm=None,
      overwrite_x=False,
      workers=None,
  ):
      r"""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 : {"backward", "ortho", "forward"}, optional
          Normalization mode (see Notes). Default is "backward".
      overwrite_x : bool, optional
          If True, the contents of `x` can be destroyed; the default is False.
      workers : int, optional
          Maximum number of workers to use for parallel computation. If negative,
          the value wraps around from ``os.cpu_count()``.
          See :func:`~scipy.fft.fft` for more details.
  
      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)``.
  
      For ``norm="backward"``, there is no scaling on `dct` and the `idct` is
      scaled by ``1/N`` where ``N`` is the "logical" size of the DCT. For
      ``norm="forward"`` the ``1/N`` normalization is applied to the forward
      `dct` instead and the `idct` is unnormalized. For ``norm='ortho'`` both
      directions are scaled by the same factor of ``1/sqrt(N)``.
  
      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="backward"``)
  
      .. math::
  
         y_k = x_0 + (-1)^k x_{N-1} + 2 \sum_{n=1}^{N-2} x_n \cos\left(
         \frac{\pi k n}{N-1} \right)
  
      If ``norm='ortho'``, ``x[0]`` and ``x[N-1]`` are multiplied by a scaling
      factor of :math:`\sqrt{2}`, and ``y[k]`` is multiplied by a scaling factor
      ``f``
  
      .. math::
  
          f = \begin{cases}
           \frac{1}{2}\sqrt{\frac{1}{N-1}} & \text{if }k=0\text{ or }N-1, \\
           \frac{1}{2}\sqrt{\frac{2}{N-1}} & \text{otherwise} \end{cases}
  
      .. 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="backward"``)
  
      .. math::
  
         y_k = 2 \sum_{n=0}^{N-1} x_n \cos\left(\frac{\pi k(2n+1)}{2N} \right)
  
      If ``norm="ortho"``, ``y[k]`` is multiplied by a scaling factor ``f``
  
      .. math::
         f = \begin{cases}
         \sqrt{\frac{1}{4N}} & \text{if }k=0, \\
         \sqrt{\frac{1}{2N}} & \text{otherwise} \end{cases}
  
      which makes the corresponding matrix of coefficients orthonormal
      (``O @ O.T = np.eye(N)``).
  
      **Type III**
  
      There are several definitions, we use the following (for
      ``norm="backward"``)
  
      .. math::
  
         y_k = x_0 + 2 \sum_{n=1}^{N-1} x_n \cos\left(\frac{\pi(2k+1)n}{2N}\right)
  
      or, for ``norm="ortho"``
  
      .. math::
  
         y_k = \frac{x_0}{\sqrt{N}} + \sqrt{\frac{2}{N}} \sum_{n=1}^{N-1} x_n
         \cos\left(\frac{\pi(2k+1)n}{2N}\right)
  
      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="backward"``)
  
      .. math::
  
         y_k = 2 \sum_{n=0}^{N-1} x_n \cos\left(\frac{\pi(2k+1)(2n+1)}{4N} \right)
  
      If ``norm="ortho"``, ``y[k]`` is multiplied by a scaling factor ``f``
  
      .. math::
  
          f = \frac{1}{\sqrt{2N}}
  
      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.fft 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 (Dispatchable(x, np.ndarray),)
  
file_path: catboost/contrib/python/scipy/py3/scipy/fft/_realtransforms.py
imports: from ._basic import _dispatch
  from scipy._lib.uarray import Dispatchable
  import numpy
label_desc: Use image node_id 5 for calling a global function with example usage: dct(x, type, n, axis, norm, overwrite_x, workers) and returns: Dispatchable