312 lines
11 KiB
Python
312 lines
11 KiB
Python
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# Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
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# Copyright (c) 2012-2016 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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2D and nD Discrete Wavelet Transforms and Inverse Discrete Wavelet Transforms.
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"""
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from __future__ import division, print_function, absolute_import
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from itertools import product
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import numpy as np
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from ._c99_config import _have_c99_complex
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from ._extensions._dwt import dwt_axis, idwt_axis
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from ._utils import _wavelets_per_axis, _modes_per_axis
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__all__ = ['dwt2', 'idwt2', 'dwtn', 'idwtn']
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def dwt2(data, wavelet, mode='symmetric', axes=(-2, -1)):
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"""
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2D Discrete Wavelet Transform.
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Parameters
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----------
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data : array_like
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2D array with 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 strings, optional
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Signal extension mode, see :ref:`Modes <ref-modes>`. This can
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also be a tuple of modes specifying the mode to use on each axis in
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``axes``.
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axes : 2-tuple of ints, optional
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Axes over which to compute the DWT. Repeated elements mean the DWT will
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be performed multiple times along these axes.
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Returns
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-------
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(cA, (cH, cV, cD)) : tuple
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Approximation, horizontal detail, vertical detail and diagonal
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detail coefficients respectively. Horizontal refers to array axis 0
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(or ``axes[0]`` for user-specified ``axes``).
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Examples
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--------
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>>> import numpy as np
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>>> import pywt
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>>> data = np.ones((4,4), dtype=np.float64)
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>>> coeffs = pywt.dwt2(data, 'haar')
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>>> cA, (cH, cV, cD) = coeffs
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>>> cA
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array([[ 2., 2.],
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[ 2., 2.]])
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>>> cV
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array([[ 0., 0.],
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[ 0., 0.]])
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"""
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axes = tuple(axes)
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data = np.asarray(data)
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if len(axes) != 2:
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raise ValueError("Expected 2 axes")
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if data.ndim < len(np.unique(axes)):
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raise ValueError("Input array has fewer dimensions than the specified "
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"axes")
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coefs = dwtn(data, wavelet, mode, axes)
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return coefs['aa'], (coefs['da'], coefs['ad'], coefs['dd'])
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def idwt2(coeffs, wavelet, mode='symmetric', axes=(-2, -1)):
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"""
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2-D Inverse Discrete Wavelet Transform.
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Reconstructs data from coefficient arrays.
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Parameters
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----------
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coeffs : tuple
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(cA, (cH, cV, cD)) A tuple with approximation coefficients and three
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details coefficients 2D arrays like from ``dwt2``. If any of these
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components are set to ``None``, it will be treated as zeros.
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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 strings, optional
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Signal extension mode, see :ref:`Modes <ref-modes>`. This can
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also be a tuple of modes specifying the mode to use on each axis in
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``axes``.
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axes : 2-tuple of ints, optional
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Axes over which to compute the IDWT. Repeated elements mean the IDWT
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will be performed multiple times along these axes.
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Examples
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--------
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>>> import numpy as np
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>>> import pywt
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>>> data = np.array([[1,2], [3,4]], dtype=np.float64)
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>>> coeffs = pywt.dwt2(data, 'haar')
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>>> pywt.idwt2(coeffs, 'haar')
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array([[ 1., 2.],
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[ 3., 4.]])
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"""
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# L -low-pass data, H - high-pass data
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LL, (HL, LH, HH) = coeffs
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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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coeffs = {'aa': LL, 'da': HL, 'ad': LH, 'dd': HH}
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return idwtn(coeffs, wavelet, mode, axes)
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def dwtn(data, wavelet, mode='symmetric', axes=None):
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"""
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Single-level n-dimensional Discrete Wavelet Transform.
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Parameters
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----------
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data : array_like
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n-dimensional array with 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 string, optional
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Signal extension mode used in the decomposition,
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see :ref:`Modes <ref-modes>`. This can also be a tuple of modes
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specifying the mode to use on each axis in ``axes``.
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axes : sequence of ints, optional
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Axes over which to compute the DWT. Repeated elements mean the DWT will
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be performed multiple times along these axes. A value of ``None`` (the
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default) selects all axes.
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Axes may be repeated, but information about the original size may be
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lost if it is not divisible by ``2 ** nrepeats``. The reconstruction
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will be larger, with additional values derived according to the
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``mode`` parameter. ``pywt.wavedecn`` should be used for multilevel
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decomposition.
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Returns
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-------
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coeffs : dict
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Results are arranged in a dictionary, where key specifies
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the transform type on each dimension and value is a n-dimensional
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coefficients array.
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For example, for a 2D case the result will look something like this::
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{'aa': <coeffs> # A(LL) - approx. on 1st dim, approx. on 2nd dim
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'ad': <coeffs> # V(LH) - approx. on 1st dim, det. on 2nd dim
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'da': <coeffs> # H(HL) - det. on 1st dim, approx. on 2nd dim
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'dd': <coeffs> # D(HH) - det. on 1st dim, det. on 2nd dim
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}
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For user-specified ``axes``, the order of the characters in the
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dictionary keys map to the specified ``axes``.
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"""
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data = np.asarray(data)
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if not _have_c99_complex and np.iscomplexobj(data):
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real = dwtn(data.real, wavelet, mode, axes)
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imag = dwtn(data.imag, wavelet, mode, axes)
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return dict((k, real[k] + 1j * imag[k]) for k in real.keys())
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if data.dtype == np.dtype('object'):
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raise TypeError("Input must be a numeric array-like")
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if data.ndim < 1:
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raise ValueError("Input data must be at least 1D")
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if axes is None:
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axes = range(data.ndim)
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axes = [a + data.ndim if a < 0 else a for a in axes]
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modes = _modes_per_axis(mode, axes)
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wavelets = _wavelets_per_axis(wavelet, axes)
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coeffs = [('', data)]
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for axis, wav, mode in zip(axes, wavelets, modes):
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new_coeffs = []
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for subband, x in coeffs:
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cA, cD = dwt_axis(x, wav, mode, axis)
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new_coeffs.extend([(subband + 'a', cA),
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(subband + 'd', cD)])
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coeffs = new_coeffs
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return dict(coeffs)
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def _fix_coeffs(coeffs):
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missing_keys = [k for k, v in coeffs.items() if v is None]
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if missing_keys:
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raise ValueError(
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"The following detail coefficients were set to None:\n"
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"{0}\n"
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"For multilevel transforms, rather than setting\n"
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"\tcoeffs[key] = None\n"
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"use\n"
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"\tcoeffs[key] = np.zeros_like(coeffs[key])\n".format(
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missing_keys))
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invalid_keys = [k for k, v in coeffs.items() if
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not set(k) <= set('ad')]
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if invalid_keys:
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raise ValueError(
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"The following invalid keys were found in the detail "
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"coefficient dictionary: {}.".format(invalid_keys))
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key_lengths = [len(k) for k in coeffs.keys()]
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if len(np.unique(key_lengths)) > 1:
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raise ValueError(
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"All detail coefficient names must have equal length.")
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return dict((k, np.asarray(v)) for k, v in coeffs.items())
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def idwtn(coeffs, wavelet, mode='symmetric', axes=None):
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"""
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Single-level n-dimensional Inverse Discrete Wavelet Transform.
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Parameters
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----------
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coeffs: dict
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Dictionary as in output of ``dwtn``. Missing or ``None`` items
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will be treated as zeros.
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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 list of string, optional
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Signal extension mode used in the decomposition,
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see :ref:`Modes <ref-modes>`. This can also be a tuple of modes
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specifying the mode to use on each axis in ``axes``.
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axes : sequence of ints, optional
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Axes over which to compute the IDWT. Repeated elements mean the IDWT
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will be performed multiple times along these axes. A value of ``None``
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(the default) selects all axes.
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For the most accurate reconstruction, the axes should be provided in
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the same order as they were provided to ``dwtn``.
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Returns
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-------
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data: ndarray
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Original signal reconstructed from input data.
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"""
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# drop the keys corresponding to value = None
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coeffs = dict((k, v) for k, v in coeffs.items() if v is not None)
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# Raise error for invalid key combinations
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coeffs = _fix_coeffs(coeffs)
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if (not _have_c99_complex and
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any(np.iscomplexobj(v) for v in coeffs.values())):
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real_coeffs = dict((k, v.real) for k, v in coeffs.items())
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imag_coeffs = dict((k, v.imag) for k, v in coeffs.items())
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return (idwtn(real_coeffs, wavelet, mode, axes) +
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1j * idwtn(imag_coeffs, wavelet, mode, axes))
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# key length matches the number of axes transformed
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ndim_transform = max(len(key) for key in coeffs.keys())
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try:
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coeff_shapes = (v.shape for k, v in coeffs.items()
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if v is not None and len(k) == ndim_transform)
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coeff_shape = next(coeff_shapes)
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except StopIteration:
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raise ValueError("`coeffs` must contain at least one non-null wavelet "
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"band")
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if any(s != coeff_shape for s in coeff_shapes):
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raise ValueError("`coeffs` must all be of equal size (or None)")
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if axes is None:
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axes = range(ndim_transform)
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ndim = ndim_transform
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else:
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ndim = len(coeff_shape)
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axes = [a + ndim if a < 0 else a for a in axes]
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modes = _modes_per_axis(mode, axes)
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wavelets = _wavelets_per_axis(wavelet, axes)
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for key_length, (axis, wav, mode) in reversed(
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list(enumerate(zip(axes, wavelets, modes)))):
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if axis < 0 or axis >= ndim:
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raise ValueError("Axis greater than data dimensions")
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new_coeffs = {}
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new_keys = [''.join(coef) for coef in product('ad', repeat=key_length)]
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for key in new_keys:
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L = coeffs.get(key + 'a', None)
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H = coeffs.get(key + 'd', None)
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if L is not None and H is not None:
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if L.dtype != H.dtype:
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# upcast to a common dtype (float64 or complex128)
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if L.dtype.kind == 'c' or H.dtype.kind == 'c':
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dtype = np.complex128
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else:
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dtype = np.float64
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L = np.asarray(L, dtype=dtype)
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H = np.asarray(H, dtype=dtype)
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new_coeffs[key] = idwt_axis(L, H, wav, mode, axis)
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coeffs = new_coeffs
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return coeffs['']
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