1552 lines
55 KiB
Python
1552 lines
55 KiB
Python
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# Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
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# Copyright (c) 2012-2018 The PyWavelets Developers
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# <https://github.com/PyWavelets/pywt>
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# See COPYING for license details.
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"""
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Multilevel 1D and 2D Discrete Wavelet Transform
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and Inverse Discrete Wavelet Transform.
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"""
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from __future__ import division, print_function, absolute_import
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import numbers
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import warnings
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from itertools import product
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from copy import copy
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import numpy as np
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from ._extensions._pywt import Wavelet, Modes
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from ._extensions._dwt import dwt_max_level
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from ._dwt import dwt, idwt, dwt_coeff_len
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from ._multidim import dwt2, idwt2, dwtn, idwtn, _fix_coeffs
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from ._utils import _as_wavelet, _wavelets_per_axis, _modes_per_axis
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__all__ = ['wavedec', 'waverec', 'wavedec2', 'waverec2', 'wavedecn',
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'waverecn', 'coeffs_to_array', 'array_to_coeffs', 'ravel_coeffs',
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'unravel_coeffs', 'dwtn_max_level', 'wavedecn_size',
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'wavedecn_shapes', 'fswavedecn', 'fswaverecn', 'FswavedecnResult']
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def _check_level(sizes, dec_lens, level):
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if np.isscalar(sizes):
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sizes = (sizes, )
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if np.isscalar(dec_lens):
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dec_lens = (dec_lens, )
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max_level = np.min([dwt_max_level(s, d) for s, d in zip(sizes, dec_lens)])
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if level is None:
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level = max_level
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elif level < 0:
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raise ValueError(
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"Level value of %d is too low . Minimum level is 0." % level)
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elif level > max_level:
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warnings.warn(
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("Level value of {} is too high: all coefficients will experience "
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"boundary effects.").format(level))
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return level
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def wavedec(data, wavelet, mode='symmetric', level=None, axis=-1):
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"""
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Multilevel 1D Discrete Wavelet Transform of data.
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Parameters
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----------
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data: array_like
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Input data
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wavelet : Wavelet object or name string
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Wavelet to use
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mode : str, optional
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Signal extension mode, see :ref:`Modes <ref-modes>`.
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level : int, optional
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Decomposition level (must be >= 0). If level is None (default) then it
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will be calculated using the ``dwt_max_level`` function.
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axis: int, optional
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Axis over which to compute the DWT. If not given, the
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last axis is used.
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Returns
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-------
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[cA_n, cD_n, cD_n-1, ..., cD2, cD1] : list
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Ordered list of coefficients arrays
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where ``n`` denotes the level of decomposition. The first element
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(``cA_n``) of the result is approximation coefficients array and the
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following elements (``cD_n`` - ``cD_1``) are details coefficients
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arrays.
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Examples
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--------
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>>> from pywt import wavedec
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>>> coeffs = wavedec([1,2,3,4,5,6,7,8], 'db1', level=2)
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>>> cA2, cD2, cD1 = coeffs
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>>> cD1
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array([-0.70710678, -0.70710678, -0.70710678, -0.70710678])
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>>> cD2
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array([-2., -2.])
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>>> cA2
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array([ 5., 13.])
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"""
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data = np.asarray(data)
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wavelet = _as_wavelet(wavelet)
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try:
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axes_shape = data.shape[axis]
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except IndexError:
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raise ValueError("Axis greater than data dimensions")
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level = _check_level(axes_shape, wavelet.dec_len, level)
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coeffs_list = []
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a = data
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for i in range(level):
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a, d = dwt(a, wavelet, mode, axis)
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coeffs_list.append(d)
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coeffs_list.append(a)
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coeffs_list.reverse()
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return coeffs_list
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def waverec(coeffs, wavelet, mode='symmetric', axis=-1):
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"""
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Multilevel 1D Inverse Discrete Wavelet Transform.
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Parameters
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----------
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coeffs : array_like
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Coefficients list [cAn, cDn, cDn-1, ..., cD2, cD1]
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wavelet : Wavelet object or name string
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Wavelet to use
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mode : str, optional
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Signal extension mode, see :ref:`Modes <ref-modes>`.
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axis: int, optional
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Axis over which to compute the inverse DWT. If not given, the
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last axis is used.
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Notes
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-----
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It may sometimes be desired to run ``waverec`` with some sets of
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coefficients omitted. This can best be done by setting the corresponding
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arrays to zero arrays of matching shape and dtype. Explicitly removing
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list entries or setting them to None is not supported.
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Specifically, to ignore detail coefficients at level 2, one could do::
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coeffs[-2] == np.zeros_like(coeffs[-2])
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Examples
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--------
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>>> import pywt
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>>> coeffs = pywt.wavedec([1,2,3,4,5,6,7,8], 'db1', level=2)
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>>> pywt.waverec(coeffs, 'db1')
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array([ 1., 2., 3., 4., 5., 6., 7., 8.])
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"""
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if not isinstance(coeffs, (list, tuple)):
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raise ValueError("Expected sequence of coefficient arrays.")
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if len(coeffs) < 1:
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raise ValueError(
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"Coefficient list too short (minimum 1 arrays required).")
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elif len(coeffs) == 1:
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# level 0 transform (just returns the approximation coefficients)
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return coeffs[0]
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a, ds = coeffs[0], coeffs[1:]
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for d in ds:
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if d is not None and not isinstance(d, np.ndarray):
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raise ValueError((
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"Unexpected detail coefficient type: {}. Detail coefficients "
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"must be arrays as returned by wavedec. If you are using "
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"pywt.array_to_coeffs or pywt.unravel_coeffs, please specify "
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"output_format='wavedec'").format(type(d)))
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if (a is not None) and (d is not None):
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try:
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if a.shape[axis] == d.shape[axis] + 1:
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a = a[tuple(slice(s) for s in d.shape)]
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elif a.shape[axis] != d.shape[axis]:
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raise ValueError("coefficient shape mismatch")
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except IndexError:
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raise ValueError("Axis greater than coefficient dimensions")
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a = idwt(a, d, wavelet, mode, axis)
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return a
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def wavedec2(data, wavelet, mode='symmetric', level=None, axes=(-2, -1)):
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"""
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Multilevel 2D Discrete Wavelet Transform.
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Parameters
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----------
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data : ndarray
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2D input data
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wavelet : Wavelet object or name string, or 2-tuple of wavelets
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Wavelet to use. This can also be a tuple containing a wavelet to
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apply along each axis in ``axes``.
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mode : str or 2-tuple of str, optional
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Signal extension mode, see :ref:`Modes <ref-modes>`. This can
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also be a tuple containing a mode to apply along each axis in ``axes``.
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level : int, optional
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Decomposition level (must be >= 0). If level is None (default) then it
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will be calculated using the ``dwt_max_level`` function.
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axes : 2-tuple of ints, optional
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Axes over which to compute the DWT. Repeated elements are not allowed.
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Returns
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-------
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[cAn, (cHn, cVn, cDn), ... (cH1, cV1, cD1)] : list
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Coefficients list. For user-specified ``axes``, ``cH*``
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corresponds to ``axes[0]`` while ``cV*`` corresponds to ``axes[1]``.
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The first element returned is the approximation coefficients for the
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nth level of decomposition. Remaining elements are tuples of detail
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coefficients in descending order of decomposition level.
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(i.e. ``cH1`` are the horizontal detail coefficients at the first
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level)
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Examples
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--------
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>>> import pywt
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>>> import numpy as np
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>>> coeffs = pywt.wavedec2(np.ones((4,4)), 'db1')
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>>> # Levels:
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>>> len(coeffs)-1
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2
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>>> pywt.waverec2(coeffs, 'db1')
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array([[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.]])
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"""
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data = np.asarray(data)
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if data.ndim < 2:
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raise ValueError("Expected input data to have at least 2 dimensions.")
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axes = tuple(axes)
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if len(axes) != 2:
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raise ValueError("Expected 2 axes")
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if len(axes) != len(set(axes)):
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raise ValueError("The axes passed to wavedec2 must be unique.")
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try:
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axes_sizes = [data.shape[ax] for ax in axes]
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except IndexError:
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raise ValueError("Axis greater than data dimensions")
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wavelets = _wavelets_per_axis(wavelet, axes)
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dec_lengths = [w.dec_len for w in wavelets]
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level = _check_level(axes_sizes, dec_lengths, level)
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coeffs_list = []
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a = data
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for i in range(level):
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a, ds = dwt2(a, wavelet, mode, axes)
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coeffs_list.append(ds)
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coeffs_list.append(a)
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coeffs_list.reverse()
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return coeffs_list
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def waverec2(coeffs, wavelet, mode='symmetric', axes=(-2, -1)):
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"""
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Multilevel 2D Inverse Discrete Wavelet Transform.
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coeffs : list or tuple
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Coefficients list [cAn, (cHn, cVn, cDn), ... (cH1, cV1, cD1)]
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wavelet : Wavelet object or name string, or 2-tuple of wavelets
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Wavelet to use. This can also be a tuple containing a wavelet to
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|
|
apply along each axis in ``axes``.
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||
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mode : str or 2-tuple of str, optional
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|
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Signal extension mode, see :ref:`Modes <ref-modes>`. This can
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also be a tuple containing a mode to apply along each axis in ``axes``.
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axes : 2-tuple of ints, optional
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Axes over which to compute the IDWT. Repeated elements are not allowed.
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Returns
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-------
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2D array of reconstructed data.
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Notes
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-----
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It may sometimes be desired to run ``waverec2`` with some sets of
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coefficients omitted. This can best be done by setting the corresponding
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|
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arrays to zero arrays of matching shape and dtype. Explicitly removing
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|
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list or tuple entries or setting them to None is not supported.
|
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|
|
|
||
|
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Specifically, to ignore all detail coefficients at level 2, one could do::
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coeffs[-2] == tuple([np.zeros_like(v) for v in coeffs[-2]])
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Examples
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--------
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>>> import pywt
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>>> import numpy as np
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>>> coeffs = pywt.wavedec2(np.ones((4,4)), 'db1')
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>>> # Levels:
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>>> len(coeffs)-1
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2
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>>> pywt.waverec2(coeffs, 'db1')
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array([[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.]])
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"""
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if not isinstance(coeffs, (list, tuple)):
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raise ValueError("Expected sequence of coefficient arrays.")
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if len(axes) != len(set(axes)):
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raise ValueError("The axes passed to waverec2 must be unique.")
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if len(coeffs) < 1:
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raise ValueError(
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"Coefficient list too short (minimum 1 array required).")
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elif len(coeffs) == 1:
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# level 0 transform (just returns the approximation coefficients)
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return coeffs[0]
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a, ds = coeffs[0], coeffs[1:]
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a = np.asarray(a)
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for d in ds:
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if not isinstance(d, (list, tuple)) or len(d) != 3:
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raise ValueError((
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"Unexpected detail coefficient type: {}. Detail coefficients "
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|
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"must be a 3-tuple of arrays as returned by wavedec2. If you "
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||
|
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"are using pywt.array_to_coeffs or pywt.unravel_coeffs, "
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"please specify output_format='wavedec2'").format(type(d)))
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d = tuple(np.asarray(coeff) if coeff is not None else None
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for coeff in d)
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d_shapes = (coeff.shape for coeff in d if coeff is not None)
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try:
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d_shape = next(d_shapes)
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except StopIteration:
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idxs = slice(None), slice(None)
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else:
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if not all(s == d_shape for s in d_shapes):
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raise ValueError("All detail shapes must be the same length.")
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idxs = tuple(slice(None, -1 if a_len == d_len + 1 else None)
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for a_len, d_len in zip(a.shape, d_shape))
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a = idwt2((a[idxs], d), wavelet, mode, axes)
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return a
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def _prep_axes_wavedecn(shape, axes):
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if len(shape) < 1:
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raise ValueError("Expected at least 1D input data.")
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ndim = len(shape)
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if np.isscalar(axes):
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axes = (axes, )
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if axes is None:
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axes = range(ndim)
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else:
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axes = tuple(axes)
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if len(axes) != len(set(axes)):
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raise ValueError("The axes passed to wavedecn must be unique.")
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try:
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axes_shapes = [shape[ax] for ax in axes]
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except IndexError:
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raise ValueError("Axis greater than data dimensions")
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ndim_transform = len(axes)
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return axes, axes_shapes, ndim_transform
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def wavedecn(data, wavelet, mode='symmetric', level=None, axes=None):
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||
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"""
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Multilevel nD Discrete Wavelet Transform.
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Parameters
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----------
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data : ndarray
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nD input data
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wavelet : Wavelet object or name string, or tuple of wavelets
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Wavelet to use. This can also be a tuple containing a wavelet to
|
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apply along each axis in ``axes``.
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mode : str or tuple of str, optional
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Signal extension mode, see :ref:`Modes <ref-modes>`. This can
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also be a tuple containing a mode to apply along each axis in ``axes``.
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level : int, optional
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Decomposition level (must be >= 0). If level is None (default) then it
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will be calculated using the ``dwt_max_level`` function.
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axes : sequence of ints, optional
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Axes over which to compute the DWT. Axes may not be repeated. The
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default is None, which means transform all axes
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(``axes = range(data.ndim)``).
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Returns
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-------
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[cAn, {details_level_n}, ... {details_level_1}] : list
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Coefficients list. Coefficients are listed in descending order of
|
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decomposition level. ``cAn`` are the approximation coefficients at
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level ``n``. Each ``details_level_i`` element is a dictionary
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containing detail coefficients at level ``i`` of the decomposition. As
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a concrete example, a 3D decomposition would have the following set of
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keys in each ``details_level_i`` dictionary::
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{'aad', 'ada', 'daa', 'add', 'dad', 'dda', 'ddd'}
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where the order of the characters in each key map to the specified
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``axes``.
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Examples
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--------
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>>> import numpy as np
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>>> from pywt import wavedecn, waverecn
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>>> coeffs = wavedecn(np.ones((4, 4, 4)), 'db1')
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>>> # Levels:
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>>> len(coeffs)-1
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2
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>>> waverecn(coeffs, 'db1') # doctest: +NORMALIZE_WHITESPACE
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array([[[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.]],
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[[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.]],
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[[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.]],
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[[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.],
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[ 1., 1., 1., 1.]]])
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"""
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data = np.asarray(data)
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axes, axes_shapes, ndim_transform = _prep_axes_wavedecn(data.shape, axes)
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wavelets = _wavelets_per_axis(wavelet, axes)
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dec_lengths = [w.dec_len for w in wavelets]
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level = _check_level(axes_shapes, dec_lengths, level)
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coeffs_list = []
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a = data
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for i in range(level):
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coeffs = dwtn(a, wavelet, mode, axes)
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a = coeffs.pop('a' * ndim_transform)
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coeffs_list.append(coeffs)
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coeffs_list.append(a)
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coeffs_list.reverse()
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return coeffs_list
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def _match_coeff_dims(a_coeff, d_coeff_dict):
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# For each axis, compare the approximation coeff shape to one of the
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# stored detail coeffs and truncate the last element along the axis
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# if necessary.
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if a_coeff is None:
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return None
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if not d_coeff_dict:
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return a_coeff
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d_coeff = d_coeff_dict[next(iter(d_coeff_dict))]
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size_diffs = np.subtract(a_coeff.shape, d_coeff.shape)
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if np.any((size_diffs < 0) | (size_diffs > 1)):
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print(size_diffs)
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raise ValueError("incompatible coefficient array sizes")
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return a_coeff[tuple(slice(s) for s in d_coeff.shape)]
|
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def waverecn(coeffs, wavelet, mode='symmetric', axes=None):
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"""
|
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|
|
Multilevel nD Inverse Discrete Wavelet Transform.
|
||
|
|
|
||
|
|
coeffs : array_like
|
||
|
|
Coefficients list [cAn, {details_level_n}, ... {details_level_1}]
|
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wavelet : Wavelet object or name string, or tuple of wavelets
|
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|
|
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 :ref:`Modes <ref-modes>`. This can
|
||
|
|
also be a tuple containing a mode to apply along each axis in ``axes``.
|
||
|
|
axes : sequence of ints, optional
|
||
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Axes over which to compute the IDWT. Axes may not be repeated.
|
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Returns
|
||
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-------
|
||
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|
nD array of reconstructed data.
|
||
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|
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Notes
|
||
|
|
-----
|
||
|
|
It may sometimes be desired to run ``waverecn`` with some sets of
|
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|
coefficients omitted. This can best be done by setting the corresponding
|
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arrays to zero arrays of matching shape and dtype. Explicitly removing
|
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list or dictionary entries or setting them to None is not supported.
|
||
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|
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Specifically, to ignore all detail coefficients at level 2, one could do::
|
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coeffs[-2] = {k: np.zeros_like(v) for k, v in coeffs[-2].items()}
|
||
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|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> from pywt import wavedecn, waverecn
|
||
|
|
>>> coeffs = wavedecn(np.ones((4, 4, 4)), 'db1')
|
||
|
|
>>> # Levels:
|
||
|
|
>>> len(coeffs)-1
|
||
|
|
2
|
||
|
|
>>> waverecn(coeffs, 'db1') # doctest: +NORMALIZE_WHITESPACE
|
||
|
|
array([[[ 1., 1., 1., 1.],
|
||
|
|
[ 1., 1., 1., 1.],
|
||
|
|
[ 1., 1., 1., 1.],
|
||
|
|
[ 1., 1., 1., 1.]],
|
||
|
|
[[ 1., 1., 1., 1.],
|
||
|
|
[ 1., 1., 1., 1.],
|
||
|
|
[ 1., 1., 1., 1.],
|
||
|
|
[ 1., 1., 1., 1.]],
|
||
|
|
[[ 1., 1., 1., 1.],
|
||
|
|
[ 1., 1., 1., 1.],
|
||
|
|
[ 1., 1., 1., 1.],
|
||
|
|
[ 1., 1., 1., 1.]],
|
||
|
|
[[ 1., 1., 1., 1.],
|
||
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|
[ 1., 1., 1., 1.],
|
||
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|
[ 1., 1., 1., 1.],
|
||
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[ 1., 1., 1., 1.]]])
|
||
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|
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"""
|
||
|
|
if len(coeffs) < 1:
|
||
|
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raise ValueError(
|
||
|
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"Coefficient list too short (minimum 1 array required).")
|
||
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|
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|
|
a, ds = coeffs[0], coeffs[1:]
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|
||
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# this dictionary check must be prior to the call to _fix_coeffs
|
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|
|
if len(ds) > 0 and not all([isinstance(d, dict) for d in ds]):
|
||
|
|
raise ValueError((
|
||
|
|
"Unexpected detail coefficient type: {}. Detail coefficients "
|
||
|
|
"must be a dicionary of arrays as returned by wavedecn. If "
|
||
|
|
"you are using pywt.array_to_coeffs or pywt.unravel_coeffs, "
|
||
|
|
"please specify output_format='wavedecn'").format(type(ds[0])))
|
||
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|
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|
|
# Raise error for invalid key combinations
|
||
|
|
ds = list(map(_fix_coeffs, ds))
|
||
|
|
|
||
|
|
if not ds:
|
||
|
|
# level 0 transform (just returns the approximation coefficients)
|
||
|
|
return coeffs[0]
|
||
|
|
if a is None and not any(ds):
|
||
|
|
raise ValueError(
|
||
|
|
"At least one coefficient must contain a valid value.")
|
||
|
|
|
||
|
|
coeff_ndims = []
|
||
|
|
if a is not None:
|
||
|
|
a = np.asarray(a)
|
||
|
|
coeff_ndims.append(a.ndim)
|
||
|
|
for d in ds:
|
||
|
|
coeff_ndims += [v.ndim for k, v in d.items()]
|
||
|
|
|
||
|
|
# test that all coefficients have a matching number of dimensions
|
||
|
|
unique_coeff_ndims = np.unique(coeff_ndims)
|
||
|
|
if len(unique_coeff_ndims) == 1:
|
||
|
|
ndim = unique_coeff_ndims[0]
|
||
|
|
else:
|
||
|
|
raise ValueError(
|
||
|
|
"All coefficients must have a matching number of dimensions")
|
||
|
|
|
||
|
|
if np.isscalar(axes):
|
||
|
|
axes = (axes, )
|
||
|
|
if axes is None:
|
||
|
|
axes = range(ndim)
|
||
|
|
else:
|
||
|
|
axes = tuple(axes)
|
||
|
|
if len(axes) != len(set(axes)):
|
||
|
|
raise ValueError("The axes passed to waverecn must be unique.")
|
||
|
|
ndim_transform = len(axes)
|
||
|
|
|
||
|
|
for idx, d in enumerate(ds):
|
||
|
|
if a is None and not d:
|
||
|
|
continue
|
||
|
|
# The following if statement handles the case where the approximation
|
||
|
|
# coefficient returned at the previous level may exceed the size of the
|
||
|
|
# stored detail coefficients by 1 on any given axis.
|
||
|
|
if idx > 0:
|
||
|
|
a = _match_coeff_dims(a, d)
|
||
|
|
d['a' * ndim_transform] = a
|
||
|
|
a = idwtn(d, wavelet, mode, axes)
|
||
|
|
|
||
|
|
return a
|
||
|
|
|
||
|
|
|
||
|
|
def _coeffs_wavedec_to_wavedecn(coeffs):
|
||
|
|
"""Convert wavedec coefficients to the wavedecn format."""
|
||
|
|
if len(coeffs) == 0:
|
||
|
|
return coeffs
|
||
|
|
coeffs = copy(coeffs)
|
||
|
|
for n in range(1, len(coeffs)):
|
||
|
|
if coeffs[n] is None:
|
||
|
|
continue
|
||
|
|
if coeffs[n].ndim != 1:
|
||
|
|
raise ValueError("expected a 1D coefficient array")
|
||
|
|
coeffs[n] = dict(d=coeffs[n])
|
||
|
|
return coeffs
|
||
|
|
|
||
|
|
|
||
|
|
def _coeffs_wavedec2_to_wavedecn(coeffs):
|
||
|
|
"""Convert wavedec2 coefficients to the wavedecn format."""
|
||
|
|
if len(coeffs) == 0:
|
||
|
|
return coeffs
|
||
|
|
coeffs = copy(coeffs)
|
||
|
|
for n in range(1, len(coeffs)):
|
||
|
|
if not isinstance(coeffs[n], (tuple, list)) or len(coeffs[n]) != 3:
|
||
|
|
raise ValueError("expected a 3-tuple of detail coefficients")
|
||
|
|
(da, ad, dd) = coeffs[n]
|
||
|
|
if da is None or ad is None or dd is None:
|
||
|
|
raise ValueError(
|
||
|
|
"Expected numpy arrays of detail coefficients. Setting "
|
||
|
|
"coefficients to None is not supported.")
|
||
|
|
coeffs[n] = dict(ad=ad, da=da, dd=dd)
|
||
|
|
return coeffs
|
||
|
|
|
||
|
|
|
||
|
|
def _determine_coeff_array_shape(coeffs, axes):
|
||
|
|
arr_shape = np.asarray(coeffs[0].shape)
|
||
|
|
axes = np.asarray(axes) # axes that were transformed
|
||
|
|
ndim_transform = len(axes)
|
||
|
|
ncoeffs = coeffs[0].size
|
||
|
|
for d in coeffs[1:]:
|
||
|
|
arr_shape[axes] += np.asarray(d['d'*ndim_transform].shape)[axes]
|
||
|
|
for k, v in d.items():
|
||
|
|
ncoeffs += v.size
|
||
|
|
arr_shape = tuple(arr_shape.tolist())
|
||
|
|
# if the total number of coefficients doesn't equal the size of the array
|
||
|
|
# then tight packing is not possible.
|
||
|
|
is_tight_packing = (np.prod(arr_shape) == ncoeffs)
|
||
|
|
return arr_shape, is_tight_packing
|
||
|
|
|
||
|
|
|
||
|
|
def _prepare_coeffs_axes(coeffs, axes):
|
||
|
|
"""Helper function to check type of coeffs and axes.
|
||
|
|
|
||
|
|
This code is used by both coeffs_to_array and ravel_coeffs.
|
||
|
|
"""
|
||
|
|
if not isinstance(coeffs, list) or len(coeffs) == 0:
|
||
|
|
raise ValueError("input must be a list of coefficients from wavedecn")
|
||
|
|
if coeffs[0] is None:
|
||
|
|
raise ValueError("coeffs_to_array does not support missing "
|
||
|
|
"coefficients.")
|
||
|
|
if not isinstance(coeffs[0], np.ndarray):
|
||
|
|
raise ValueError("first list element must be a numpy array")
|
||
|
|
ndim = coeffs[0].ndim
|
||
|
|
|
||
|
|
if len(coeffs) > 1:
|
||
|
|
# convert wavedec or wavedec2 format coefficients to waverecn format
|
||
|
|
if isinstance(coeffs[1], dict):
|
||
|
|
pass
|
||
|
|
elif isinstance(coeffs[1], np.ndarray):
|
||
|
|
coeffs = _coeffs_wavedec_to_wavedecn(coeffs)
|
||
|
|
elif isinstance(coeffs[1], (tuple, list)):
|
||
|
|
coeffs = _coeffs_wavedec2_to_wavedecn(coeffs)
|
||
|
|
else:
|
||
|
|
raise ValueError("invalid coefficient list")
|
||
|
|
|
||
|
|
if len(coeffs) == 1:
|
||
|
|
# no detail coefficients were found
|
||
|
|
return coeffs, axes, ndim, None
|
||
|
|
|
||
|
|
# Determine the number of dimensions that were transformed via key length
|
||
|
|
ndim_transform = len(list(coeffs[1].keys())[0])
|
||
|
|
if axes is None:
|
||
|
|
if ndim_transform < ndim:
|
||
|
|
raise ValueError(
|
||
|
|
"coeffs corresponds to a DWT performed over only a subset of "
|
||
|
|
"the axes. In this case, axes must be specified.")
|
||
|
|
axes = np.arange(ndim)
|
||
|
|
|
||
|
|
if len(axes) != ndim_transform:
|
||
|
|
raise ValueError(
|
||
|
|
"The length of axes doesn't match the number of dimensions "
|
||
|
|
"transformed.")
|
||
|
|
|
||
|
|
return coeffs, axes, ndim, ndim_transform
|
||
|
|
|
||
|
|
|
||
|
|
def coeffs_to_array(coeffs, padding=0, axes=None):
|
||
|
|
"""
|
||
|
|
Arrange a wavelet coefficient list from ``wavedecn`` into a single array.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
|
||
|
|
coeffs : array-like
|
||
|
|
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 : array-like
|
||
|
|
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 two-level 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)
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
coeffs, axes, ndim, ndim_transform = _prepare_coeffs_axes(coeffs, axes)
|
||
|
|
|
||
|
|
# initialize with the approximation coefficients.
|
||
|
|
a_coeffs = coeffs[0]
|
||
|
|
a_shape = a_coeffs.shape
|
||
|
|
|
||
|
|
if len(coeffs) == 1:
|
||
|
|
# only a single approximation coefficient array was found
|
||
|
|
return a_coeffs, [tuple([slice(None)] * ndim)]
|
||
|
|
|
||
|
|
# determine size of output and if tight packing is possible
|
||
|
|
arr_shape, is_tight_packing = _determine_coeff_array_shape(coeffs, axes)
|
||
|
|
|
||
|
|
# preallocate output array
|
||
|
|
if padding is None:
|
||
|
|
if not is_tight_packing:
|
||
|
|
raise ValueError("array coefficients cannot be tightly packed")
|
||
|
|
coeff_arr = np.empty(arr_shape, dtype=a_coeffs.dtype)
|
||
|
|
else:
|
||
|
|
coeff_arr = np.full(arr_shape, padding, dtype=a_coeffs.dtype)
|
||
|
|
|
||
|
|
a_slices = tuple([slice(s) for s in a_shape])
|
||
|
|
coeff_arr[a_slices] = a_coeffs
|
||
|
|
|
||
|
|
# initialize list of coefficient slices
|
||
|
|
coeff_slices = []
|
||
|
|
coeff_slices.append(a_slices)
|
||
|
|
|
||
|
|
# loop over the detail cofficients, adding them to coeff_arr
|
||
|
|
ds = coeffs[1:]
|
||
|
|
for coeff_dict in ds:
|
||
|
|
coeff_slices.append({}) # new dictionary for detail coefficients
|
||
|
|
if np.any([d is None for d in coeff_dict.values()]):
|
||
|
|
raise ValueError("coeffs_to_array does not support missing "
|
||
|
|
"coefficients.")
|
||
|
|
d_shape = coeff_dict['d' * ndim_transform].shape
|
||
|
|
for key in coeff_dict.keys():
|
||
|
|
d = coeff_dict[key]
|
||
|
|
slice_array = [slice(None), ] * ndim
|
||
|
|
for i, let in enumerate(key):
|
||
|
|
ax_i = axes[i] # axis corresponding to this transform index
|
||
|
|
if let == 'a':
|
||
|
|
slice_array[ax_i] = slice(d.shape[ax_i])
|
||
|
|
elif let == 'd':
|
||
|
|
slice_array[ax_i] = slice(a_shape[ax_i],
|
||
|
|
a_shape[ax_i] + d.shape[ax_i])
|
||
|
|
else:
|
||
|
|
raise ValueError("unexpected letter: {}".format(let))
|
||
|
|
slice_array = tuple(slice_array)
|
||
|
|
coeff_arr[slice_array] = d
|
||
|
|
coeff_slices[-1][key] = slice_array
|
||
|
|
a_shape = [a_shape[n] + d_shape[n] for n in range(ndim)]
|
||
|
|
return coeff_arr, coeff_slices
|
||
|
|
|
||
|
|
|
||
|
|
def array_to_coeffs(arr, coeff_slices, output_format='wavedecn'):
|
||
|
|
"""
|
||
|
|
Convert a combined array of coefficients back to a list compatible with
|
||
|
|
``waverecn``.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
|
||
|
|
arr : array-like
|
||
|
|
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: array-like
|
||
|
|
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,
|
||
|
|
... output_format='wavedecn')
|
||
|
|
>>> cam_recon = pywt.waverecn(coeffs_from_arr, wavelet='db2')
|
||
|
|
>>> assert_array_almost_equal(cam, cam_recon)
|
||
|
|
|
||
|
|
"""
|
||
|
|
arr = np.asarray(arr)
|
||
|
|
coeffs = []
|
||
|
|
if len(coeff_slices) == 0:
|
||
|
|
raise ValueError("empty list of coefficient slices")
|
||
|
|
else:
|
||
|
|
coeffs.append(arr[coeff_slices[0]])
|
||
|
|
|
||
|
|
# difference coefficients at each level
|
||
|
|
for n in range(1, len(coeff_slices)):
|
||
|
|
if output_format == 'wavedec':
|
||
|
|
d = arr[coeff_slices[n]['d']]
|
||
|
|
elif output_format == 'wavedec2':
|
||
|
|
d = (arr[coeff_slices[n]['da']],
|
||
|
|
arr[coeff_slices[n]['ad']],
|
||
|
|
arr[coeff_slices[n]['dd']])
|
||
|
|
elif output_format == 'wavedecn':
|
||
|
|
d = {}
|
||
|
|
for k, v in coeff_slices[n].items():
|
||
|
|
d[k] = arr[v]
|
||
|
|
else:
|
||
|
|
raise ValueError(
|
||
|
|
"Unrecognized output format: {}".format(output_format))
|
||
|
|
coeffs.append(d)
|
||
|
|
return coeffs
|
||
|
|
|
||
|
|
|
||
|
|
def 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 :ref:`Modes <ref-modes>`. 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}] : list
|
||
|
|
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)}]
|
||
|
|
"""
|
||
|
|
axes, axes_shapes, ndim_transform = _prep_axes_wavedecn(shape, axes)
|
||
|
|
wavelets = _wavelets_per_axis(wavelet, axes)
|
||
|
|
modes = _modes_per_axis(mode, axes)
|
||
|
|
dec_lengths = [w.dec_len for w in wavelets]
|
||
|
|
|
||
|
|
level = _check_level(min(axes_shapes), max(dec_lengths), level)
|
||
|
|
|
||
|
|
shapes = []
|
||
|
|
for i in range(level):
|
||
|
|
detail_keys = [''.join(c) for c in product('ad', repeat=len(axes))]
|
||
|
|
new_shapes = {k: list(shape) for k in detail_keys}
|
||
|
|
for axis, wav, mode in zip(axes, wavelets, modes):
|
||
|
|
s = dwt_coeff_len(shape[axis], filter_len=wav.dec_len, mode=mode)
|
||
|
|
for k in detail_keys:
|
||
|
|
new_shapes[k][axis] = s
|
||
|
|
for k, v in new_shapes.items():
|
||
|
|
new_shapes[k] = tuple(v)
|
||
|
|
shapes.append(new_shapes)
|
||
|
|
shape = new_shapes.pop('a' * ndim_transform)
|
||
|
|
shapes.append(shape)
|
||
|
|
shapes.reverse()
|
||
|
|
return shapes
|
||
|
|
|
||
|
|
|
||
|
|
def 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
|
||
|
|
"""
|
||
|
|
def _size(x):
|
||
|
|
"""Size corresponding to ``x`` as either a shape tuple or ndarray."""
|
||
|
|
if isinstance(x, np.ndarray):
|
||
|
|
return x.size
|
||
|
|
else:
|
||
|
|
return np.prod(x)
|
||
|
|
ncoeffs = _size(shapes[0])
|
||
|
|
for d in shapes[1:]:
|
||
|
|
for k, v in d.items():
|
||
|
|
if v is None:
|
||
|
|
raise ValueError(
|
||
|
|
"Setting coefficient arrays to None is not supported.")
|
||
|
|
ncoeffs += _size(v)
|
||
|
|
return ncoeffs
|
||
|
|
|
||
|
|
|
||
|
|
def dwtn_max_level(shape, wavelet, axes=None):
|
||
|
|
"""Compute the maximum level of decomposition for n-dimensional data.
|
||
|
|
|
||
|
|
This returns the maximum number of levels of decomposition suitable for use
|
||
|
|
with ``wavedec``, ``wavedec2`` or ``wavedecn``.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
shape : sequence of ints
|
||
|
|
Input data shape.
|
||
|
|
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``.
|
||
|
|
axes : sequence of ints, optional
|
||
|
|
Axes over which to compute the DWT. Axes may not be repeated.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
level : int
|
||
|
|
Maximum level.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
The level returned is the smallest ``dwt_max_level`` over all axes.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import pywt
|
||
|
|
>>> pywt.dwtn_max_level((64, 32), 'db2')
|
||
|
|
3
|
||
|
|
"""
|
||
|
|
# Determine the axes and shape for the transform
|
||
|
|
axes, axes_shapes, ndim_transform = _prep_axes_wavedecn(shape, axes)
|
||
|
|
|
||
|
|
# initialize a Wavelet object per (transformed) axis
|
||
|
|
wavelets = _wavelets_per_axis(wavelet, axes)
|
||
|
|
|
||
|
|
# maximum level of decomposition per axis
|
||
|
|
max_levels = [dwt_max_level(n, wav.dec_len)
|
||
|
|
for n, wav in zip(axes_shapes, wavelets)]
|
||
|
|
return min(max_levels)
|
||
|
|
|
||
|
|
|
||
|
|
def ravel_coeffs(coeffs, axes=None):
|
||
|
|
"""Ravel a set of multilevel wavelet coefficients into a single 1D array.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
coeffs : array-like
|
||
|
|
A list of multilevel wavelet coefficients as returned by
|
||
|
|
``wavedec``, ``wavedec2`` or ``wavedecn``. This function is also
|
||
|
|
compatible with the output of ``swt``, ``swt2`` and ``swtn`` if those
|
||
|
|
functions were called with ``trim_approx=True``.
|
||
|
|
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 : array-like
|
||
|
|
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)
|
||
|
|
|
||
|
|
"""
|
||
|
|
coeffs, axes, ndim, ndim_transform = _prepare_coeffs_axes(coeffs, axes)
|
||
|
|
|
||
|
|
# initialize with the approximation coefficients.
|
||
|
|
a_coeffs = coeffs[0]
|
||
|
|
a_size = a_coeffs.size
|
||
|
|
|
||
|
|
if len(coeffs) == 1:
|
||
|
|
# only a single approximation coefficient array was found
|
||
|
|
return a_coeffs.ravel(), [slice(a_size), ], [a_coeffs.shape, ]
|
||
|
|
|
||
|
|
# preallocate output array
|
||
|
|
arr_size = wavedecn_size(coeffs)
|
||
|
|
coeff_arr = np.empty((arr_size, ), dtype=a_coeffs.dtype)
|
||
|
|
|
||
|
|
a_slice = slice(a_size)
|
||
|
|
coeff_arr[a_slice] = a_coeffs.ravel()
|
||
|
|
|
||
|
|
# initialize list of coefficient slices
|
||
|
|
coeff_slices = []
|
||
|
|
coeff_shapes = []
|
||
|
|
coeff_slices.append(a_slice)
|
||
|
|
coeff_shapes.append(coeffs[0].shape)
|
||
|
|
|
||
|
|
# loop over the detail cofficients, embedding them in coeff_arr
|
||
|
|
ds = coeffs[1:]
|
||
|
|
offset = a_size
|
||
|
|
for coeff_dict in ds:
|
||
|
|
# new dictionaries for detail coefficient slices and shapes
|
||
|
|
coeff_slices.append({})
|
||
|
|
coeff_shapes.append({})
|
||
|
|
if np.any([d is None for d in coeff_dict.values()]):
|
||
|
|
raise ValueError("coeffs_to_array does not support missing "
|
||
|
|
"coefficients.")
|
||
|
|
# sort to make sure key order is consistent across Python versions
|
||
|
|
keys = sorted(coeff_dict.keys())
|
||
|
|
for key in keys:
|
||
|
|
d = coeff_dict[key]
|
||
|
|
sl = slice(offset, offset + d.size)
|
||
|
|
offset += d.size
|
||
|
|
coeff_arr[sl] = d.ravel()
|
||
|
|
coeff_slices[-1][key] = sl
|
||
|
|
coeff_shapes[-1][key] = d.shape
|
||
|
|
return coeff_arr, coeff_slices, coeff_shapes
|
||
|
|
|
||
|
|
|
||
|
|
def unravel_coeffs(arr, coeff_slices, coeff_shapes, output_format='wavedecn'):
|
||
|
|
"""Unravel a raveled array of multilevel wavelet coefficients.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
arr : array-like
|
||
|
|
An array containing all wavelet coefficients. This should have been
|
||
|
|
generated by applying ``ravel_coeffs`` to the output of ``wavedec``,
|
||
|
|
``wavedec2`` or ``wavedecn`` (or via ``swt``, ``swt2`` or ``swtn``
|
||
|
|
with ``trim_approx=True``).
|
||
|
|
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', 'swt', 'swt2', 'swtn'}, 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,
|
||
|
|
... output_format='wavedecn')
|
||
|
|
>>> cam_recon = pywt.waverecn(coeffs_from_arr, wavelet='db2')
|
||
|
|
>>> assert_array_almost_equal(cam, cam_recon)
|
||
|
|
|
||
|
|
"""
|
||
|
|
arr = np.asarray(arr)
|
||
|
|
coeffs = []
|
||
|
|
if len(coeff_slices) == 0:
|
||
|
|
raise ValueError("empty list of coefficient slices")
|
||
|
|
elif len(coeff_shapes) == 0:
|
||
|
|
raise ValueError("empty list of coefficient shapes")
|
||
|
|
elif len(coeff_shapes) != len(coeff_slices):
|
||
|
|
raise ValueError("coeff_shapes and coeff_slices have unequal length")
|
||
|
|
else:
|
||
|
|
coeffs.append(arr[coeff_slices[0]].reshape(coeff_shapes[0]))
|
||
|
|
|
||
|
|
# difference coefficients at each level
|
||
|
|
for n in range(1, len(coeff_slices)):
|
||
|
|
slice_dict = coeff_slices[n]
|
||
|
|
shape_dict = coeff_shapes[n]
|
||
|
|
if output_format in ['wavedec', 'swt']:
|
||
|
|
d = arr[slice_dict['d']].reshape(shape_dict['d'])
|
||
|
|
elif output_format in ['wavedec2', 'swt2']:
|
||
|
|
d = (arr[slice_dict['da']].reshape(shape_dict['da']),
|
||
|
|
arr[slice_dict['ad']].reshape(shape_dict['ad']),
|
||
|
|
arr[slice_dict['dd']].reshape(shape_dict['dd']))
|
||
|
|
elif output_format in ['wavedecn', 'swtn']:
|
||
|
|
d = {}
|
||
|
|
for k, v in coeff_slices[n].items():
|
||
|
|
d[k] = arr[v].reshape(shape_dict[k])
|
||
|
|
else:
|
||
|
|
raise ValueError(
|
||
|
|
"Unrecognized output format: {}".format(output_format))
|
||
|
|
coeffs.append(d)
|
||
|
|
return coeffs
|
||
|
|
|
||
|
|
|
||
|
|
def _check_fswavedecn_axes(data, axes):
|
||
|
|
"""Axes checks common to fswavedecn, fswaverecn."""
|
||
|
|
if len(axes) != len(set(axes)):
|
||
|
|
raise ValueError("The axes passed to fswavedecn must be unique.")
|
||
|
|
try:
|
||
|
|
[data.shape[ax] for ax in axes]
|
||
|
|
except IndexError:
|
||
|
|
raise ValueError("Axis greater than data dimensions")
|
||
|
|
|
||
|
|
|
||
|
|
class FswavedecnResult(object):
|
||
|
|
"""Object representing fully separable wavelet transform coefficients.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
coeffs : ndarray
|
||
|
|
The coefficient array.
|
||
|
|
coeff_slices : list
|
||
|
|
List of slices corresponding to each detail or approximation
|
||
|
|
coefficient array.
|
||
|
|
wavelets : list of pywt.DiscreteWavelet objects
|
||
|
|
The wavelets used. Will be a list with length equal to
|
||
|
|
``len(axes)``.
|
||
|
|
mode_enums : list of int
|
||
|
|
The border modes used. Will be a list with length equal to
|
||
|
|
``len(axes)``.
|
||
|
|
axes : tuple of int
|
||
|
|
The set of axes over which the transform was performed.
|
||
|
|
|
||
|
|
"""
|
||
|
|
def __init__(self, coeffs, coeff_slices, wavelets, mode_enums,
|
||
|
|
axes):
|
||
|
|
self._coeffs = coeffs
|
||
|
|
self._coeff_slices = coeff_slices
|
||
|
|
self._axes = axes
|
||
|
|
if not np.all(isinstance(w, Wavelet) for w in wavelets):
|
||
|
|
raise ValueError(
|
||
|
|
"wavelets must contain pywt.Wavelet objects")
|
||
|
|
self._wavelets = wavelets
|
||
|
|
if not np.all(isinstance(m, int) for m in mode_enums):
|
||
|
|
raise ValueError(
|
||
|
|
"mode_enums must be integers")
|
||
|
|
self._mode_enums = mode_enums
|
||
|
|
|
||
|
|
@property
|
||
|
|
def coeffs(self):
|
||
|
|
"""ndarray: All coefficients stacked into a single array."""
|
||
|
|
return self._coeffs
|
||
|
|
|
||
|
|
@coeffs.setter
|
||
|
|
def coeffs(self, c):
|
||
|
|
if c.shape != self._coeffs.shape:
|
||
|
|
raise ValueError("new coefficient array must match the existing "
|
||
|
|
"coefficient shape")
|
||
|
|
self._coeffs = c
|
||
|
|
|
||
|
|
@property
|
||
|
|
def coeff_slices(self):
|
||
|
|
"""List: List of coefficient slices."""
|
||
|
|
return self._coeff_slices
|
||
|
|
|
||
|
|
@property
|
||
|
|
def ndim(self):
|
||
|
|
"""int: Number of data dimensions."""
|
||
|
|
return self.coeffs.ndim
|
||
|
|
|
||
|
|
@property
|
||
|
|
def ndim_transform(self):
|
||
|
|
"""int: Number of axes transformed."""
|
||
|
|
return len(self.axes)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def axes(self):
|
||
|
|
"""List of str: The axes the transform was performed along."""
|
||
|
|
return self._axes
|
||
|
|
|
||
|
|
@property
|
||
|
|
def levels(self):
|
||
|
|
"""List of int: Levels of decomposition along each transformed axis."""
|
||
|
|
return [len(s) - 1 for s in self.coeff_slices]
|
||
|
|
|
||
|
|
@property
|
||
|
|
def wavelets(self):
|
||
|
|
"""List of pywt.DiscreteWavelet: wavelet for each transformed axis."""
|
||
|
|
return self._wavelets
|
||
|
|
|
||
|
|
@property
|
||
|
|
def wavelet_names(self):
|
||
|
|
"""List of pywt.DiscreteWavelet: wavelet for each transformed axis."""
|
||
|
|
return [w.name for w in self._wavelets]
|
||
|
|
|
||
|
|
@property
|
||
|
|
def modes(self):
|
||
|
|
"""List of str: The border mode used along each transformed axis."""
|
||
|
|
names_dict = {getattr(Modes, mode): mode
|
||
|
|
for mode in Modes.modes}
|
||
|
|
return [names_dict[m] for m in self._mode_enums]
|
||
|
|
|
||
|
|
def _get_coef_sl(self, levels):
|
||
|
|
sl = [slice(None), ] * self.ndim
|
||
|
|
for n, (ax, lev) in enumerate(zip(self.axes, levels)):
|
||
|
|
sl[ax] = self.coeff_slices[n][lev]
|
||
|
|
return tuple(sl)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def approx(self):
|
||
|
|
"""ndarray: The approximation coefficients."""
|
||
|
|
sl = self._get_coef_sl((0, )*self.ndim)
|
||
|
|
return self._coeffs[sl]
|
||
|
|
|
||
|
|
@approx.setter
|
||
|
|
def approx(self, a):
|
||
|
|
sl = self._get_coef_sl((0, )*self.ndim)
|
||
|
|
if self._coeffs[sl].shape != a.shape:
|
||
|
|
raise ValueError(
|
||
|
|
"x does not match the shape of the requested coefficient")
|
||
|
|
self._coeffs[sl] = a
|
||
|
|
|
||
|
|
def _validate_index(self, levels):
|
||
|
|
levels = tuple(levels)
|
||
|
|
|
||
|
|
if len(levels) != len(self.axes):
|
||
|
|
raise ValueError(
|
||
|
|
"levels must match the number of transformed axes")
|
||
|
|
|
||
|
|
# check that all elements are non-negative integers
|
||
|
|
if (not np.all([isinstance(lev, numbers.Number) for lev in levels]) or
|
||
|
|
np.any(np.asarray(levels) % 1 > 0) or
|
||
|
|
np.any([lev < 0 for lev in levels])):
|
||
|
|
raise ValueError("Index must be a tuple of non-negative integers")
|
||
|
|
# convert integer-valued floats to int
|
||
|
|
levels = tuple([int(lev) for lev in levels])
|
||
|
|
|
||
|
|
# check for out of range levels
|
||
|
|
if np.any([lev > maxlev for lev, maxlev in zip(levels, self.levels)]):
|
||
|
|
raise ValueError(
|
||
|
|
"Specified indices exceed the number of transform levels.")
|
||
|
|
|
||
|
|
def __getitem__(self, levels):
|
||
|
|
"""Retrieve a coefficient subband.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
levels : tuple of int
|
||
|
|
The number of degrees of decomposition along each transformed
|
||
|
|
axis.
|
||
|
|
"""
|
||
|
|
self._validate_index(levels)
|
||
|
|
sl = self._get_coef_sl(levels)
|
||
|
|
return self._coeffs[sl]
|
||
|
|
|
||
|
|
def __setitem__(self, levels, x):
|
||
|
|
"""Assign values to a coefficient subband.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
levels : tuple of int
|
||
|
|
The number of degrees of decomposition along each transformed
|
||
|
|
axis.
|
||
|
|
x : ndarray
|
||
|
|
The data corresponding to assign. It must match the expected
|
||
|
|
shape and dtype of the specified subband.
|
||
|
|
"""
|
||
|
|
self._validate_index(levels)
|
||
|
|
sl = self._get_coef_sl(levels)
|
||
|
|
current_dtype = self._coeffs[sl].dtype
|
||
|
|
if self._coeffs[sl].shape != x.shape:
|
||
|
|
raise ValueError(
|
||
|
|
"x does not match the shape of the requested coefficient")
|
||
|
|
if x.dtype != current_dtype:
|
||
|
|
warnings.warn("dtype mismatch: converting the provided array to"
|
||
|
|
"dtype {}".format(current_dtype))
|
||
|
|
self._coeffs[sl] = x
|
||
|
|
|
||
|
|
def detail_keys(self):
|
||
|
|
"""Return a list of all detail coefficient keys.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
keys : list of str
|
||
|
|
List of all detail coefficient keys.
|
||
|
|
"""
|
||
|
|
keys = list(product(*(range(l+1) for l in self.levels)))
|
||
|
|
keys.remove((0, )*len(self.axes))
|
||
|
|
return sorted(keys)
|
||
|
|
|
||
|
|
|
||
|
|
def fswavedecn(data, wavelet, mode='symmetric', levels=None, axes=None):
|
||
|
|
"""Fully Separable Wavelet Decomposition.
|
||
|
|
|
||
|
|
This is a variant of the multilevel discrete wavelet transform where all
|
||
|
|
levels of decomposition are performed along a single axis prior to moving
|
||
|
|
onto the next axis. Unlike in ``wavedecn``, the number of levels of
|
||
|
|
decomposition are not required to be the same along each axis which can be
|
||
|
|
a benefit for anisotropic data.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
data: array_like
|
||
|
|
Input data
|
||
|
|
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 :ref:`Modes <ref-modes>`. This can
|
||
|
|
also be a tuple containing a mode to apply along each axis in ``axes``.
|
||
|
|
levels : int or sequence of ints, optional
|
||
|
|
Decomposition levels along each axis (must be >= 0). If an integer is
|
||
|
|
provided, the same number of levels are used for all axes. If
|
||
|
|
``levels`` is None (default), ``dwt_max_level`` will be used to compute
|
||
|
|
the maximum number of levels possible for each axis.
|
||
|
|
axes : sequence of ints, optional
|
||
|
|
Axes over which to compute the transform. Axes may not be repeated. The
|
||
|
|
default is to transform along all axes.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
fswavedecn_result : FswavedecnResult object
|
||
|
|
Contains the wavelet coefficients, slice objects to allow obtaining
|
||
|
|
the coefficients per detail or approximation level, and more.
|
||
|
|
See ``FswavedecnResult`` for details.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from pywt import fswavedecn
|
||
|
|
>>> fs_result = fswavedecn(np.ones((32, 32)), 'sym2', levels=(1, 3))
|
||
|
|
>>> print(fs_result.detail_keys())
|
||
|
|
[(0, 1), (0, 2), (0, 3), (1, 0), (1, 1), (1, 2), (1, 3)]
|
||
|
|
>>> approx_coeffs = fs_result.approx
|
||
|
|
>>> detail_1_2 = fs_result[(1, 2)]
|
||
|
|
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
This transformation has been variously referred to as the (fully) separable
|
||
|
|
wavelet transform (e.g. refs [1]_, [3]_), the tensor-product wavelet
|
||
|
|
([2]_) or the hyperbolic wavelet transform ([4]_). It is well suited to
|
||
|
|
data with anisotropic smoothness.
|
||
|
|
|
||
|
|
In [2]_ it was demonstrated that fully separable transform performs at
|
||
|
|
least as well as the DWT for image compression. Computation time is a
|
||
|
|
factor 2 larger than that for the DWT.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
fswaverecn : inverse of fswavedecn
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [1] PH Westerink. Subband Coding of Images. Ph.D. dissertation, Dept.
|
||
|
|
Elect. Eng., Inf. Theory Group, Delft Univ. Technol., Delft, The
|
||
|
|
Netherlands, 1989. (see Section 2.3)
|
||
|
|
http://resolver.tudelft.nl/uuid:a4d195c3-1f89-4d66-913d-db9af0969509
|
||
|
|
|
||
|
|
.. [2] CP Rosiene and TQ Nguyen. Tensor-product wavelet vs. Mallat
|
||
|
|
decomposition: A comparative analysis, in Proc. IEEE Int. Symp.
|
||
|
|
Circuits and Systems, Orlando, FL, Jun. 1999, pp. 431-434.
|
||
|
|
|
||
|
|
.. [3] V Velisavljevic, B Beferull-Lozano, M Vetterli and PL Dragotti.
|
||
|
|
Directionlets: Anisotropic Multidirectional Representation With
|
||
|
|
Separable Filtering. IEEE Transactions on Image Processing, Vol. 15,
|
||
|
|
No. 7, July 2006.
|
||
|
|
|
||
|
|
.. [4] RA DeVore, SV Konyagin and VN Temlyakov. "Hyperbolic wavelet
|
||
|
|
approximation," Constr. Approx. 14 (1998), 1-26.
|
||
|
|
"""
|
||
|
|
data = np.asarray(data)
|
||
|
|
if axes is None:
|
||
|
|
axes = tuple(np.arange(data.ndim))
|
||
|
|
_check_fswavedecn_axes(data, axes)
|
||
|
|
|
||
|
|
if levels is None or np.isscalar(levels):
|
||
|
|
levels = [levels, ] * len(axes)
|
||
|
|
if len(levels) != len(axes):
|
||
|
|
raise ValueError("levels must match the length of the axes list")
|
||
|
|
|
||
|
|
modes = _modes_per_axis(mode, axes)
|
||
|
|
wavelets = _wavelets_per_axis(wavelet, axes)
|
||
|
|
|
||
|
|
coeff_slices = [slice(None), ] * len(axes)
|
||
|
|
coeffs_arr = data
|
||
|
|
for ax_count, (ax, lev, wav, mode) in enumerate(
|
||
|
|
zip(axes, levels, wavelets, modes)):
|
||
|
|
coeffs = wavedec(coeffs_arr, wav, mode=mode, level=lev, axis=ax)
|
||
|
|
|
||
|
|
# Slice objects for accessing coefficient subsets.
|
||
|
|
# These can be used to access specific detail coefficient arrays
|
||
|
|
# (e.g. as needed for inverse transformation via fswaverecn).
|
||
|
|
c_shapes = [c.shape[ax] for c in coeffs]
|
||
|
|
c_offsets = np.cumsum([0, ] + c_shapes)
|
||
|
|
coeff_slices[ax_count] = [
|
||
|
|
slice(c_offsets[d], c_offsets[d+1]) for d in range(len(c_shapes))]
|
||
|
|
|
||
|
|
# stack the coefficients from all levels into a single array
|
||
|
|
coeffs_arr = np.concatenate(coeffs, axis=ax)
|
||
|
|
|
||
|
|
return FswavedecnResult(coeffs_arr, coeff_slices, wavelets, modes, axes)
|
||
|
|
|
||
|
|
|
||
|
|
def fswaverecn(fswavedecn_result):
|
||
|
|
"""Fully Separable Inverse Wavelet Reconstruction.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
fswavedecn_result : FswavedecnResult object
|
||
|
|
FswavedecnResult object from ``fswavedecn``.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
reconstructed : ndarray
|
||
|
|
Array of reconstructed data.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
This transformation has been variously referred to as the (fully) separable
|
||
|
|
wavelet transform (e.g. refs [1]_, [3]_), the tensor-product wavelet
|
||
|
|
([2]_) or the hyperbolic wavelet transform ([4]_). It is well suited to
|
||
|
|
data with anisotropic smoothness.
|
||
|
|
|
||
|
|
In [2]_ it was demonstrated that the fully separable transform performs at
|
||
|
|
least as well as the DWT for image compression. Computation time is a
|
||
|
|
factor 2 larger than that for the DWT.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
fswavedecn : inverse of fswaverecn
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [1] PH Westerink. Subband Coding of Images. Ph.D. dissertation, Dept.
|
||
|
|
Elect. Eng., Inf. Theory Group, Delft Univ. Technol., Delft, The
|
||
|
|
Netherlands, 1989. (see Section 2.3)
|
||
|
|
http://resolver.tudelft.nl/uuid:a4d195c3-1f89-4d66-913d-db9af0969509
|
||
|
|
|
||
|
|
.. [2] CP Rosiene and TQ Nguyen. Tensor-product wavelet vs. Mallat
|
||
|
|
decomposition: A comparative analysis, in Proc. IEEE Int. Symp.
|
||
|
|
Circuits and Systems, Orlando, FL, Jun. 1999, pp. 431-434.
|
||
|
|
|
||
|
|
.. [3] V Velisavljevic, B Beferull-Lozano, M Vetterli and PL Dragotti.
|
||
|
|
Directionlets: Anisotropic Multidirectional Representation With
|
||
|
|
Separable Filtering. IEEE Transactions on Image Processing, Vol. 15,
|
||
|
|
No. 7, July 2006.
|
||
|
|
|
||
|
|
.. [4] RA DeVore, SV Konyagin and VN Temlyakov. "Hyperbolic wavelet
|
||
|
|
approximation," Constr. Approx. 14 (1998), 1-26.
|
||
|
|
"""
|
||
|
|
coeffs_arr = fswavedecn_result.coeffs
|
||
|
|
coeff_slices = fswavedecn_result.coeff_slices
|
||
|
|
axes = fswavedecn_result.axes
|
||
|
|
modes = fswavedecn_result.modes
|
||
|
|
wavelets = fswavedecn_result.wavelets
|
||
|
|
|
||
|
|
_check_fswavedecn_axes(coeffs_arr, axes)
|
||
|
|
if len(axes) != len(coeff_slices):
|
||
|
|
raise ValueError("dimension mismatch")
|
||
|
|
|
||
|
|
arr = coeffs_arr
|
||
|
|
csl = [slice(None), ] * arr.ndim
|
||
|
|
# for ax_count, (ax, wav, mode) in reversed(
|
||
|
|
# list(enumerate(zip(axes, wavelets, modes)))):
|
||
|
|
for ax_count, (ax, wav, mode) in enumerate(zip(axes, wavelets, modes)):
|
||
|
|
coeffs = []
|
||
|
|
for sl in coeff_slices[ax_count]:
|
||
|
|
csl[ax] = sl
|
||
|
|
coeffs.append(arr[tuple(csl)])
|
||
|
|
csl[ax] = slice(None)
|
||
|
|
arr = waverec(coeffs, wav, mode=mode, axis=ax)
|
||
|
|
return arr
|