Handling DWT Coefficients¶
Convenience routines are available for converting the outputs of the multilevel
dwt functions (wavedec
, wavedec2
and wavedecn
) to and from a
single, concatenated coefficient array.
Concatenating all coefficients into a single nd array¶

pywt.
coeffs_to_array
(coeffs, padding=0, axes=None)¶ Arrange a wavelet coefficient list from wavedecn into a single array.
Parameters:  coeffs : arraylike
dictionary of wavelet coefficients as returned by pywt.wavedecn
 padding : float or None, optional
If None, raise an error if the coefficients cannot be tightly packed.
 axes : sequence of ints, optional
Axes over which the DWT that created coeffs was performed. The default value of None corresponds to all axes.
Returns:  coeff_arr : arraylike
Wavelet transform coefficient array.
 coeff_slices : list
List of slices corresponding to each coefficient. As a 2D example, coeff_arr[coeff_slices[1][‘dd’]] would extract the first level detail coefficients from coeff_arr.
See also
array_to_coeffs
 the inverse of coeffs_to_array
Notes
Assume a 2D coefficient dictionary, c, from a twolevel transform.
Then all 2D coefficients will be stacked into a single larger 2D array as follows:
++++      c[0]  c[1]['da']       +++ c[2]['da']       c[1]['ad']  c[1]['dd']       +++ +           c[2]['ad']  c[2]['dd']           +++
Examples
>>> import pywt >>> cam = pywt.data.camera() >>> coeffs = pywt.wavedecn(cam, wavelet='db2', level=3) >>> arr, coeff_slices = pywt.coeffs_to_array(coeffs)
Splitting concatenated coefficient array back into its components¶

pywt.
array_to_coeffs
(arr, coeff_slices, output_format='wavedecn')¶ Convert a combined array of coefficients back to a list compatible with waverecn.
Parameters:  arr : arraylike
An array containing all wavelet coefficients. This should have been generated via coeffs_to_array.
 coeff_slices : list of tuples
List of slices corresponding to each coefficient as obtained from array_to_coeffs.
 output_format : {‘wavedec’, ‘wavedec2’, ‘wavedecn’}
Make the form of the coefficients compatible with this type of multilevel transform.
Returns:  coeffs: arraylike
Wavelet transform coefficient array.
See also
coeffs_to_array
 the inverse of array_to_coeffs
Notes
A single large array containing all coefficients will have subsets stored, into a waverecn list, c, as indicated below:
++++      c[0]  c[1]['da']       +++ c[2]['da']       c[1]['ad']  c[1]['dd']       +++ +           c[2]['ad']  c[2]['dd']           +++
Examples
>>> import pywt >>> from numpy.testing import assert_array_almost_equal >>> cam = pywt.data.camera() >>> coeffs = pywt.wavedecn(cam, wavelet='db2', level=3) >>> arr, coeff_slices = pywt.coeffs_to_array(coeffs) >>> coeffs_from_arr = pywt.array_to_coeffs(arr, coeff_slices) >>> cam_recon = pywt.waverecn(coeffs_from_arr, wavelet='db2') >>> assert_array_almost_equal(cam, cam_recon)
Raveling and unraveling coefficients to/from a 1D array¶

pywt.
ravel_coeffs
(coeffs, axes=None)¶ Ravel a set of multilevel wavelet coefficients into a single 1D array.
Parameters:  coeffs : arraylike
A list of multilevel wavelet coefficients as returned by wavedec, wavedec2 or wavedecn.
 axes : sequence of ints, optional
Axes over which the DWT that created coeffs was performed. The default value of None corresponds to all axes.
Returns:  coeff_arr : arraylike
Wavelet transform coefficient array. All coefficients have been concatenated into a single array.
 coeff_slices : list
List of slices corresponding to each coefficient. As a 2D example,
coeff_arr[coeff_slices[1]['dd']]
would extract the first level detail coefficients from coeff_arr. coeff_shapes : list
List of shapes corresponding to each coefficient. For example, in 2D,
coeff_shapes[1]['dd']
would contain the original shape of the first level detail coefficients array.
See also
unravel_coeffs
 the inverse of ravel_coeffs
Examples
>>> import pywt >>> cam = pywt.data.camera() >>> coeffs = pywt.wavedecn(cam, wavelet='db2', level=3) >>> arr, coeff_slices, coeff_shapes = pywt.ravel_coeffs(coeffs)

pywt.
unravel_coeffs
(arr, coeff_slices, coeff_shapes, output_format='wavedecn')¶ Unravel a raveled array of multilevel wavelet coefficients.
Parameters:  arr : arraylike
An array containing all wavelet coefficients. This should have been generated by applying ravel_coeffs to the output of wavedec, wavedec2 or wavedecn.
 coeff_slices : list of tuples
List of slices corresponding to each coefficient as obtained from ravel_coeffs.
 coeff_shapes : list of tuples
List of shapes corresponding to each coefficient as obtained from ravel_coeffs.
 output_format : {‘wavedec’, ‘wavedec2’, ‘wavedecn’}, optional
Make the form of the unraveled coefficients compatible with this type of multilevel transform. The default is ‘wavedecn’.
Returns:  coeffs: list
List of wavelet transform coefficients. The specific format of the list elements is determined by output_format.
See also
ravel_coeffs
 the inverse of unravel_coeffs
Examples
>>> import pywt >>> from numpy.testing import assert_array_almost_equal >>> cam = pywt.data.camera() >>> coeffs = pywt.wavedecn(cam, wavelet='db2', level=3) >>> arr, coeff_slices, coeff_shapes = pywt.ravel_coeffs(coeffs) >>> coeffs_from_arr = pywt.unravel_coeffs(arr, coeff_slices, coeff_shapes) >>> cam_recon = pywt.waverecn(coeffs_from_arr, wavelet='db2') >>> assert_array_almost_equal(cam, cam_recon)
Multilevel: Total size of all coefficients  wavedecn_size
¶

pywt.
wavedecn_size
(shapes)¶ Compute the total number of wavedecn coefficients.
Parameters:  shapes : list of coefficient shapes
A set of coefficient shapes as returned by wavedecn_shapes. Alternatively, the user can specify a set of coefficients as returned by wavedecn.
Returns:  size : int
The total number of coefficients.
Examples
>>> import numpy as np >>> import pywt >>> data_shape = (64, 32) >>> shapes = pywt.wavedecn_shapes(data_shape, 'db2', mode='periodization') >>> pywt.wavedecn_size(shapes) 2048 >>> coeffs = pywt.wavedecn(np.ones(data_shape), 'sym4', mode='symmetric') >>> pywt.wavedecn_size(coeffs) 3087
Multilevel: nd coefficient shapes  wavedecn_shapes
¶

pywt.
wavedecn_shapes
(shape, wavelet, mode='symmetric', level=None, axes=None)¶ Subband shapes for a multilevel nD discrete wavelet transform.
Parameters:  shape : sequence of ints
The shape of the data to be transformed.
 wavelet : Wavelet object or name string, or tuple of wavelets
Wavelet to use. This can also be a tuple containing a wavelet to apply along each axis in axes.
 mode : str or tuple of str, optional
Signal extension mode, see Modes (default: ‘symmetric’). This can also be a tuple containing a mode to apply along each axis in axes.
 level : int, optional
Decomposition level (must be >= 0). If level is None (default) then it will be calculated using the dwt_max_level function.
 axes : sequence of ints, optional
Axes over which to compute the DWT. Axes may not be repeated. The default is None, which means transform all axes (
axes = range(data.ndim)
).
Returns:  shapes : [cAn, {details_level_n}, … {details_level_1}]
Coefficients shape list. Mirrors the output of wavedecn, except it contains only the shapes of the coefficient arrays rather than the arrays themselves.
Examples
>>> import pywt >>> pywt.wavedecn_shapes((64, 32), wavelet='db2', level=3, axes=(0, )) [(10, 32), {'d': (10, 32)}, {'d': (18, 32)}, {'d': (33, 32)}]