scipy.fft.

dctn#

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

Return multidimensional Discrete Cosine Transform along the specified axes.

Parameters:

xarray_like: The input array.
type{1, 2, 3, 4}, optional: Type of the DCT (see Notes). Default type is 2.
sint 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.
axesint 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_xbool, optional: If True, the contents of x can be destroyed; the default is False.
workersint, 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.
orthogonalizebool, 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:

yndarray 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