518 lines
17 KiB
Python
518 lines
17 KiB
Python
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from numbers import Number
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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._pywt import Wavelet, Modes, _check_dtype, wavelist
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from ._extensions._dwt import (dwt_single, dwt_axis, idwt_single, idwt_axis,
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upcoef as _upcoef, downcoef as _downcoef,
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dwt_max_level as _dwt_max_level,
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dwt_coeff_len as _dwt_coeff_len)
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from ._utils import string_types, _as_wavelet
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__all__ = ["dwt", "idwt", "downcoef", "upcoef", "dwt_max_level",
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"dwt_coeff_len", "pad"]
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def dwt_max_level(data_len, filter_len):
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r"""
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dwt_max_level(data_len, filter_len)
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Compute the maximum useful level of decomposition.
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Parameters
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----------
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data_len : int
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Input data length.
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filter_len : int, str or Wavelet
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The wavelet filter length. Alternatively, the name of a discrete
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wavelet or a Wavelet object can be specified.
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Returns
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-------
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max_level : int
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Maximum level.
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Notes
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-----
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The rational for the choice of levels is the maximum level where at least
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one coefficient in the output is uncorrupted by edge effects caused by
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signal extension. Put another way, decomposition stops when the signal
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becomes shorter than the FIR filter length for a given wavelet. This
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corresponds to:
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.. max_level = floor(log2(data_len/(filter_len - 1)))
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.. math::
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\mathtt{max\_level} = \left\lfloor\log_2\left(\mathtt{
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\frac{data\_len}{filter\_len - 1}}\right)\right\rfloor
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Examples
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--------
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>>> import pywt
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>>> w = pywt.Wavelet('sym5')
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>>> pywt.dwt_max_level(data_len=1000, filter_len=w.dec_len)
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6
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>>> pywt.dwt_max_level(1000, w)
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6
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>>> pywt.dwt_max_level(1000, 'sym5')
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6
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"""
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if isinstance(filter_len, Wavelet):
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filter_len = filter_len.dec_len
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elif isinstance(filter_len, string_types):
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if filter_len in wavelist(kind='discrete'):
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filter_len = Wavelet(filter_len).dec_len
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else:
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raise ValueError(
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("'{}', is not a recognized discrete wavelet. A list of "
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"supported wavelet names can be obtained via "
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"pywt.wavelist(kind='discrete')").format(filter_len))
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elif not (isinstance(filter_len, Number) and filter_len % 1 == 0):
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raise ValueError(
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"filter_len must be an integer, discrete Wavelet object, or the "
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"name of a discrete wavelet.")
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if filter_len < 2:
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raise ValueError("invalid wavelet filter length")
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return _dwt_max_level(data_len, filter_len)
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def dwt_coeff_len(data_len, filter_len, mode):
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"""
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dwt_coeff_len(data_len, filter_len, mode='symmetric')
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Returns length of dwt output for given data length, filter length and mode
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Parameters
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----------
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data_len : int
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Data length.
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filter_len : int
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Filter length.
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mode : str, optional
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Signal extension mode, see :ref:`Modes <ref-modes>`.
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Returns
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-------
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len : int
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Length of dwt output.
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Notes
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-----
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For all modes except periodization::
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len(cA) == len(cD) == floor((len(data) + wavelet.dec_len - 1) / 2)
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for periodization mode ("per")::
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len(cA) == len(cD) == ceil(len(data) / 2)
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"""
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if isinstance(filter_len, Wavelet):
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filter_len = filter_len.dec_len
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return _dwt_coeff_len(data_len, filter_len, Modes.from_object(mode))
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def dwt(data, wavelet, mode='symmetric', axis=-1):
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"""
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dwt(data, wavelet, mode='symmetric', axis=-1)
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Single level Discrete Wavelet Transform.
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Parameters
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----------
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data : array_like
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Input signal
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wavelet : Wavelet object or name
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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 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, cD) : tuple
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Approximation and detail coefficients.
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Notes
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-----
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Length of coefficients arrays depends on the selected mode.
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For all modes except periodization:
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``len(cA) == len(cD) == floor((len(data) + wavelet.dec_len - 1) / 2)``
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For periodization mode ("per"):
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``len(cA) == len(cD) == ceil(len(data) / 2)``
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Examples
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--------
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>>> import pywt
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>>> (cA, cD) = pywt.dwt([1, 2, 3, 4, 5, 6], 'db1')
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>>> cA
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array([ 2.12132034, 4.94974747, 7.77817459])
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>>> cD
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array([-0.70710678, -0.70710678, -0.70710678])
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"""
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if not _have_c99_complex and np.iscomplexobj(data):
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data = np.asarray(data)
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cA_r, cD_r = dwt(data.real, wavelet, mode, axis)
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cA_i, cD_i = dwt(data.imag, wavelet, mode, axis)
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return (cA_r + 1j*cA_i, cD_r + 1j*cD_i)
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# accept array_like input; make a copy to ensure a contiguous array
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dt = _check_dtype(data)
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data = np.asarray(data, dtype=dt, order='C')
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mode = Modes.from_object(mode)
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wavelet = _as_wavelet(wavelet)
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if axis < 0:
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axis = axis + data.ndim
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if not 0 <= axis < data.ndim:
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raise ValueError("Axis greater than data dimensions")
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if data.ndim == 1:
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cA, cD = dwt_single(data, wavelet, mode)
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# TODO: Check whether this makes a copy
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cA, cD = np.asarray(cA, dt), np.asarray(cD, dt)
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else:
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cA, cD = dwt_axis(data, wavelet, mode, axis=axis)
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return (cA, cD)
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def idwt(cA, cD, wavelet, mode='symmetric', axis=-1):
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"""
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idwt(cA, cD, wavelet, mode='symmetric', axis=-1)
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Single level Inverse Discrete Wavelet Transform.
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Parameters
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----------
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cA : array_like or None
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Approximation coefficients. If None, will be set to array of zeros
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with same shape as ``cD``.
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cD : array_like or None
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Detail coefficients. If None, will be set to array of zeros
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with same shape as ``cA``.
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wavelet : Wavelet object or name
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Wavelet to use
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mode : str, optional (default: 'symmetric')
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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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Returns
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-------
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rec: array_like
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Single level reconstruction of signal from given coefficients.
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Examples
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--------
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>>> import pywt
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>>> (cA, cD) = pywt.dwt([1,2,3,4,5,6], 'db2', 'smooth')
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>>> pywt.idwt(cA, cD, 'db2', 'smooth')
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array([ 1., 2., 3., 4., 5., 6.])
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One of the neat features of ``idwt`` is that one of the ``cA`` and ``cD``
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arguments can be set to None. In that situation the reconstruction will be
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performed using only the other one. Mathematically speaking, this is
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equivalent to passing a zero-filled array as one of the arguments.
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>>> (cA, cD) = pywt.dwt([1,2,3,4,5,6], 'db2', 'smooth')
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>>> A = pywt.idwt(cA, None, 'db2', 'smooth')
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>>> D = pywt.idwt(None, cD, 'db2', 'smooth')
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>>> A + D
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array([ 1., 2., 3., 4., 5., 6.])
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"""
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# TODO: Lots of possible allocations to eliminate (zeros_like, asarray(rec))
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# accept array_like input; make a copy to ensure a contiguous array
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if cA is None and cD is None:
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raise ValueError("At least one coefficient parameter must be "
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"specified.")
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# for complex inputs: compute real and imaginary separately then combine
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if not _have_c99_complex and (np.iscomplexobj(cA) or np.iscomplexobj(cD)):
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if cA is None:
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cD = np.asarray(cD)
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cA = np.zeros_like(cD)
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elif cD is None:
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cA = np.asarray(cA)
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cD = np.zeros_like(cA)
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return (idwt(cA.real, cD.real, wavelet, mode, axis) +
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1j*idwt(cA.imag, cD.imag, wavelet, mode, axis))
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if cA is not None:
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dt = _check_dtype(cA)
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cA = np.asarray(cA, dtype=dt, order='C')
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if cD is not None:
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dt = _check_dtype(cD)
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cD = np.asarray(cD, dtype=dt, order='C')
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if cA is not None and cD is not None:
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if cA.dtype != cD.dtype:
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# need to upcast to common type
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if cA.dtype.kind == 'c' or cD.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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cA = cA.astype(dtype)
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cD = cD.astype(dtype)
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elif cA is None:
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cA = np.zeros_like(cD)
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elif cD is None:
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cD = np.zeros_like(cA)
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# cA and cD should be same dimension by here
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ndim = cA.ndim
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mode = Modes.from_object(mode)
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wavelet = _as_wavelet(wavelet)
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if axis < 0:
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axis = axis + ndim
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if not 0 <= axis < ndim:
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raise ValueError("Axis greater than coefficient dimensions")
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if ndim == 1:
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rec = idwt_single(cA, cD, wavelet, mode)
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else:
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rec = idwt_axis(cA, cD, wavelet, mode, axis=axis)
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return rec
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def downcoef(part, data, wavelet, mode='symmetric', level=1):
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"""
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downcoef(part, data, wavelet, mode='symmetric', level=1)
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Partial Discrete Wavelet Transform data decomposition.
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Similar to ``pywt.dwt``, but computes only one set of coefficients.
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Useful when you need only approximation or only details at the given level.
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Parameters
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----------
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part : str
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Coefficients type:
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* 'a' - approximations reconstruction is performed
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* 'd' - details reconstruction is performed
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data : array_like
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Input signal.
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wavelet : Wavelet object or name
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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. Default is 1.
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Returns
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-------
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coeffs : ndarray
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1-D array of coefficients.
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See Also
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--------
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upcoef
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"""
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if not _have_c99_complex and np.iscomplexobj(data):
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return (downcoef(part, data.real, wavelet, mode, level) +
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1j*downcoef(part, data.imag, wavelet, mode, level))
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# accept array_like input; make a copy to ensure a contiguous array
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dt = _check_dtype(data)
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data = np.asarray(data, dtype=dt, order='C')
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if data.ndim > 1:
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raise ValueError("downcoef only supports 1d data.")
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if part not in 'ad':
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raise ValueError("Argument 1 must be 'a' or 'd', not '%s'." % part)
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mode = Modes.from_object(mode)
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wavelet = _as_wavelet(wavelet)
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return np.asarray(_downcoef(part == 'a', data, wavelet, mode, level))
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def upcoef(part, coeffs, wavelet, level=1, take=0):
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"""
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upcoef(part, coeffs, wavelet, level=1, take=0)
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Direct reconstruction from coefficients.
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Parameters
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----------
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part : str
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Coefficients type:
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* 'a' - approximations reconstruction is performed
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* 'd' - details reconstruction is performed
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coeffs : array_like
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Coefficients array to recontruct
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wavelet : Wavelet object or name
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Wavelet to use
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level : int, optional
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Multilevel reconstruction level. Default is 1.
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take : int, optional
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Take central part of length equal to 'take' from the result.
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Default is 0.
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Returns
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-------
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rec : ndarray
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1-D array with reconstructed data from coefficients.
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See Also
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--------
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downcoef
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Examples
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--------
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>>> import pywt
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>>> data = [1,2,3,4,5,6]
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|
|
>>> (cA, cD) = pywt.dwt(data, 'db2', 'smooth')
|
||
|
|
>>> pywt.upcoef('a', cA, 'db2') + pywt.upcoef('d', cD, 'db2')
|
||
|
|
array([-0.25 , -0.4330127 , 1. , 2. , 3. ,
|
||
|
|
4. , 5. , 6. , 1.78589838, -1.03108891])
|
||
|
|
>>> n = len(data)
|
||
|
|
>>> pywt.upcoef('a', cA, 'db2', take=n) + pywt.upcoef('d', cD, 'db2', take=n)
|
||
|
|
array([ 1., 2., 3., 4., 5., 6.])
|
||
|
|
|
||
|
|
"""
|
||
|
|
if not _have_c99_complex and np.iscomplexobj(coeffs):
|
||
|
|
return (upcoef(part, coeffs.real, wavelet, level, take) +
|
||
|
|
1j*upcoef(part, coeffs.imag, wavelet, level, take))
|
||
|
|
# accept array_like input; make a copy to ensure a contiguous array
|
||
|
|
dt = _check_dtype(coeffs)
|
||
|
|
coeffs = np.asarray(coeffs, dtype=dt, order='C')
|
||
|
|
if coeffs.ndim > 1:
|
||
|
|
raise ValueError("upcoef only supports 1d coeffs.")
|
||
|
|
wavelet = _as_wavelet(wavelet)
|
||
|
|
if part not in 'ad':
|
||
|
|
raise ValueError("Argument 1 must be 'a' or 'd', not '%s'." % part)
|
||
|
|
return np.asarray(_upcoef(part == 'a', coeffs, wavelet, level, take))
|
||
|
|
|
||
|
|
|
||
|
|
def pad(x, pad_widths, mode):
|
||
|
|
"""Extend a 1D signal using a given boundary mode.
|
||
|
|
|
||
|
|
This function operates like :func:`numpy.pad` but supports all signal
|
||
|
|
extension modes that can be used by PyWavelets discrete wavelet transforms.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
x : ndarray
|
||
|
|
The array to pad
|
||
|
|
pad_widths : {sequence, array_like, int}
|
||
|
|
Number of values padded to the edges of each axis.
|
||
|
|
``((before_1, after_1), … (before_N, after_N))`` unique pad widths for
|
||
|
|
each axis. ``((before, after),)`` yields same before and after pad for
|
||
|
|
each axis. ``(pad,)`` or int is a shortcut for
|
||
|
|
``before = after = pad width`` for all axes.
|
||
|
|
mode : str, optional
|
||
|
|
Signal extension mode, see :ref:`Modes <ref-modes>`.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
pad : ndarray
|
||
|
|
Padded array of rank equal to array with shape increased according to
|
||
|
|
``pad_widths``.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
The performance of padding in dimensions > 1 may be substantially slower
|
||
|
|
for modes ``'smooth'`` and ``'antisymmetric'`` as these modes are not
|
||
|
|
supported efficiently by the underlying :func:`numpy.pad` function.
|
||
|
|
|
||
|
|
Note that the behavior of the ``'constant'`` mode here follows the
|
||
|
|
PyWavelets convention which is different from NumPy (it is equivalent to
|
||
|
|
``mode='edge'`` in :func:`numpy.pad`).
|
||
|
|
"""
|
||
|
|
x = np.asanyarray(x)
|
||
|
|
|
||
|
|
# process pad_widths exactly as in numpy.pad
|
||
|
|
pad_widths = np.array(pad_widths)
|
||
|
|
pad_widths = np.round(pad_widths).astype(np.intp, copy=False)
|
||
|
|
if pad_widths.min() < 0:
|
||
|
|
raise ValueError("pad_widths must be > 0")
|
||
|
|
pad_widths = np.broadcast_to(pad_widths, (x.ndim, 2)).tolist()
|
||
|
|
|
||
|
|
if mode in ['symmetric', 'reflect']:
|
||
|
|
xp = np.pad(x, pad_widths, mode=mode)
|
||
|
|
elif mode in ['periodic', 'periodization']:
|
||
|
|
if mode == 'periodization':
|
||
|
|
# Promote odd-sized dimensions to even length by duplicating the
|
||
|
|
# last value.
|
||
|
|
edge_pad_widths = [(0, x.shape[ax] % 2)
|
||
|
|
for ax in range(x.ndim)]
|
||
|
|
x = np.pad(x, edge_pad_widths, mode='edge')
|
||
|
|
xp = np.pad(x, pad_widths, mode='wrap')
|
||
|
|
elif mode == 'zero':
|
||
|
|
xp = np.pad(x, pad_widths, mode='constant', constant_values=0)
|
||
|
|
elif mode == 'constant':
|
||
|
|
xp = np.pad(x, pad_widths, mode='edge')
|
||
|
|
elif mode == 'smooth':
|
||
|
|
def pad_smooth(vector, pad_width, iaxis, kwargs):
|
||
|
|
# smooth extension to left
|
||
|
|
left = vector[pad_width[0]]
|
||
|
|
slope_left = (left - vector[pad_width[0] + 1])
|
||
|
|
vector[:pad_width[0]] = \
|
||
|
|
left + np.arange(pad_width[0], 0, -1) * slope_left
|
||
|
|
|
||
|
|
# smooth extension to right
|
||
|
|
right = vector[-pad_width[1] - 1]
|
||
|
|
slope_right = (right - vector[-pad_width[1] - 2])
|
||
|
|
vector[-pad_width[1]:] = \
|
||
|
|
right + np.arange(1, pad_width[1] + 1) * slope_right
|
||
|
|
return vector
|
||
|
|
xp = np.pad(x, pad_widths, pad_smooth)
|
||
|
|
elif mode == 'antisymmetric':
|
||
|
|
def pad_antisymmetric(vector, pad_width, iaxis, kwargs):
|
||
|
|
# smooth extension to left
|
||
|
|
# implement by flipping portions symmetric padding
|
||
|
|
npad_l, npad_r = pad_width
|
||
|
|
vsize_nonpad = vector.size - npad_l - npad_r
|
||
|
|
# Note: must modify vector in-place
|
||
|
|
vector[:] = np.pad(vector[pad_width[0]:-pad_width[-1]],
|
||
|
|
pad_width, mode='symmetric')
|
||
|
|
vp = vector
|
||
|
|
r_edge = npad_l + vsize_nonpad - 1
|
||
|
|
l_edge = npad_l
|
||
|
|
# width of each reflected segment
|
||
|
|
seg_width = vsize_nonpad
|
||
|
|
# flip reflected segments on the right of the original signal
|
||
|
|
n = 1
|
||
|
|
while r_edge <= vp.size:
|
||
|
|
segment_slice = slice(r_edge + 1,
|
||
|
|
min(r_edge + 1 + seg_width, vp.size))
|
||
|
|
if n % 2:
|
||
|
|
vp[segment_slice] *= -1
|
||
|
|
r_edge += seg_width
|
||
|
|
n += 1
|
||
|
|
|
||
|
|
# flip reflected segments on the left of the original signal
|
||
|
|
n = 1
|
||
|
|
while l_edge >= 0:
|
||
|
|
segment_slice = slice(max(0, l_edge - seg_width), l_edge)
|
||
|
|
if n % 2:
|
||
|
|
vp[segment_slice] *= -1
|
||
|
|
l_edge -= seg_width
|
||
|
|
n += 1
|
||
|
|
return vector
|
||
|
|
xp = np.pad(x, pad_widths, pad_antisymmetric)
|
||
|
|
elif mode == 'antireflect':
|
||
|
|
xp = np.pad(x, pad_widths, mode='reflect', reflect_type='odd')
|
||
|
|
else:
|
||
|
|
raise ValueError(
|
||
|
|
("unsupported mode: {}. The supported modes are {}").format(
|
||
|
|
mode, Modes.modes))
|
||
|
|
return xp
|