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scipy.fft.

# dctn

scipy.fft.dctn(x, type=2, s=None, axes=None, norm=None, overwrite_x=False, workers=None, *, orthogonalize=None)

  Return multidimensional Discrete Cosine Transform along the specified axes.

  Parameters:
    x array_like

      The input array.

    type{1, 2, 3, 4}, optional

      Type of the DCT (see Notes). Default type is 2.

    s int or array_like of ints or None, optional

      The shape of the result. If both s and axes (see below) are None, s is `x.shape`; if s is None but axes is not None, then s is `numpy.take(x.shape, axes, axis=0)`. If `s[i] > x.shape[i]`, the ith dimension of the input is padded with zeros. If `s[i] < x.shape[i]`, the ith dimension of the input is truncated to length `s[i]`. If any element of s is -1, the size of the corresponding dimension of x is used.

    axes int or array_like of ints or None, optional

      Axes over which the DCT is computed. If not given, the last `len(s)` axes are used, or all axes if s is also not specified.

    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 `fft` for more details.

    orthogonalize bool, optional

      Whether to use the orthogonalized DCT variant (see Notes). Defaults to `True` when `norm="ortho"` and `False` otherwise.

      Added in version 1.8.0.

  Returns:
    y ndarray of real

      The transformed input array.

  See also

  `idctn`

    Inverse multidimensional DCT

  Notes

  For full details of the DCT types and normalization modes, as well as references, see `dct`.

  Array API Standard Support

  `dctn` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ⛔
  PyTorch | ✅ | ⛔
  JAX | ✅ | ⛔
  Dask | ⚠️ computes graph | n/a

  > See Support for the array API standard for more information.

  Examples

      >>> import numpy as np
      >>> from scipy.fft import dctn, idctn
      >>> rng = np.random.default_rng()
      >>> y = rng.standard_normal((16, 16))
      >>> np.allclose(y, idctn(dctn(y)))
      True