Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/pywt/__init__.py

@@ -0,0 +1,40 @@
+# flake8: noqa
+
+# Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
+# Copyright (c) 2012-2016 The PyWavelets Developers
+#                         <https://github.com/PyWavelets/pywt>
+# See COPYING for license details.
+
+"""
+Discrete forward and inverse wavelet transform, stationary wavelet transform,
+wavelet packets signal decomposition and reconstruction module.
+"""
+
+from __future__ import division, print_function, absolute_import
+from distutils.version import LooseVersion
+
+from ._extensions._pywt import *
+from ._functions import *
+from ._multilevel import *
+from ._multidim import *
+from ._thresholding import *
+from ._wavelet_packets import *
+from ._dwt import *
+from ._swt import *
+from ._cwt import *
+
+from . import data
+
+__all__ = [s for s in dir() if not s.startswith('_')]
+try:
+    # In Python 2.x the name of the tempvar leaks out of the list
+    # comprehension.  Delete it to not make it show up in the main namespace.
+    del s
+except NameError:
+    pass
+
+from pywt.version import version as __version__
+
+from ._pytesttester import PytestTester
+test = PytestTester(__name__)
+del PytestTester

venv/Lib/site-packages/pywt/_c99_config.py

@@ -0,0 +1,3 @@
+# Autogenerated file containing compile-time definitions
+
+_have_c99_complex = 0

venv/Lib/site-packages/pywt/_cwt.py

@@ -0,0 +1,203 @@
+from math import floor, ceil
+
+from ._extensions._pywt import (DiscreteContinuousWavelet, ContinuousWavelet,
+                                Wavelet, _check_dtype)
+from ._functions import integrate_wavelet, scale2frequency
+
+
+__all__ = ["cwt"]
+
+
+import numpy as np
+
+try:
+    # Prefer scipy.fft (new in SciPy 1.4)
+    import scipy.fft
+    fftmodule = scipy.fft
+    next_fast_len = fftmodule.next_fast_len
+except ImportError:
+    try:
+        import scipy.fftpack
+        fftmodule = scipy.fftpack
+        next_fast_len = fftmodule.next_fast_len
+    except ImportError:
+        fftmodule = np.fft
+
+        # provide a fallback so scipy is an optional requirement
+        def next_fast_len(n):
+            """Round up size to the nearest power of two.
+
+            Given a number of samples `n`, returns the next power of two
+            following this number to take advantage of FFT speedup.
+            This fallback is less efficient than `scipy.fftpack.next_fast_len`
+            """
+            return 2**ceil(np.log2(n))
+
+
+def cwt(data, scales, wavelet, sampling_period=1., method='conv', axis=-1):
+    """
+    cwt(data, scales, wavelet)
+
+    One dimensional Continuous Wavelet Transform.
+
+    Parameters
+    ----------
+    data : array_like
+        Input signal
+    scales : array_like
+        The wavelet scales to use. One can use
+        ``f = scale2frequency(wavelet, scale)/sampling_period`` to determine
+        what physical frequency, ``f``. Here, ``f`` is in hertz when the
+        ``sampling_period`` is given in seconds.
+    wavelet : Wavelet object or name
+        Wavelet to use
+    sampling_period : float
+        Sampling period for the frequencies output (optional).
+        The values computed for ``coefs`` are independent of the choice of
+        ``sampling_period`` (i.e. ``scales`` is not scaled by the sampling
+        period).
+    method : {'conv', 'fft'}, optional
+        The method used to compute the CWT. Can be any of:
+            - ``conv`` uses ``numpy.convolve``.
+            - ``fft`` uses frequency domain convolution.
+            - ``auto`` uses automatic selection based on an estimate of the
+              computational complexity at each scale.
+
+        The ``conv`` method complexity is ``O(len(scale) * len(data))``.
+        The ``fft`` method is ``O(N * log2(N))`` with
+        ``N = len(scale) + len(data) - 1``. It is well suited for large size
+        signals but slightly slower than ``conv`` on small ones.
+    axis: int, optional
+        Axis over which to compute the CWT. If not given, the last axis is
+        used.
+
+    Returns
+    -------
+    coefs : array_like
+        Continuous wavelet transform of the input signal for the given scales
+        and wavelet. The first axis of ``coefs`` corresponds to the scales.
+        The remaining axes match the shape of ``data``.
+    frequencies : array_like
+        If the unit of sampling period are seconds and given, than frequencies
+        are in hertz. Otherwise, a sampling period of 1 is assumed.
+
+    Notes
+    -----
+    Size of coefficients arrays depends on the length of the input array and
+    the length of given scales.
+
+    Examples
+    --------
+    >>> import pywt
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.arange(512)
+    >>> y = np.sin(2*np.pi*x/32)
+    >>> coef, freqs=pywt.cwt(y,np.arange(1,129),'gaus1')
+    >>> plt.matshow(coef) # doctest: +SKIP
+    >>> plt.show() # doctest: +SKIP
+    ----------
+    >>> import pywt
+    >>> import numpy as np
+    >>> import matplotlib.pyplot as plt
+    >>> t = np.linspace(-1, 1, 200, endpoint=False)
+    >>> sig  = np.cos(2 * np.pi * 7 * t) + np.real(np.exp(-7*(t-0.4)**2)*np.exp(1j*2*np.pi*2*(t-0.4)))
+    >>> widths = np.arange(1, 31)
+    >>> cwtmatr, freqs = pywt.cwt(sig, widths, 'mexh')
+    >>> plt.imshow(cwtmatr, extent=[-1, 1, 1, 31], cmap='PRGn', aspect='auto',
+    ...            vmax=abs(cwtmatr).max(), vmin=-abs(cwtmatr).max())  # doctest: +SKIP
+    >>> plt.show() # doctest: +SKIP
+    """
+
+    # accept array_like input; make a copy to ensure a contiguous array
+    dt = _check_dtype(data)
+    data = np.asarray(data, dtype=dt)
+    dt_cplx = np.result_type(dt, np.complex64)
+    if not isinstance(wavelet, (ContinuousWavelet, Wavelet)):
+        wavelet = DiscreteContinuousWavelet(wavelet)
+    if np.isscalar(scales):
+        scales = np.array([scales])
+    if not np.isscalar(axis):
+        raise ValueError("axis must be a scalar.")
+
+    dt_out = dt_cplx if wavelet.complex_cwt else dt
+    out = np.empty((np.size(scales),) + data.shape, dtype=dt_out)
+    precision = 10
+    int_psi, x = integrate_wavelet(wavelet, precision=precision)
+    int_psi = np.conj(int_psi) if wavelet.complex_cwt else int_psi
+
+    # convert int_psi, x to the same precision as the data
+    dt_psi = dt_cplx if int_psi.dtype.kind == 'c' else dt
+    int_psi = np.asarray(int_psi, dtype=dt_psi)
+    x = np.asarray(x, dtype=data.real.dtype)
+
+    if method == 'fft':
+        size_scale0 = -1
+        fft_data = None
+    elif not method == 'conv':
+        raise ValueError("method must be 'conv' or 'fft'")
+
+    if data.ndim > 1:
+        # move axis to be transformed last (so it is contiguous)
+        data = data.swapaxes(-1, axis)
+
+        # reshape to (n_batch, data.shape[-1])
+        data_shape_pre = data.shape
+        data = data.reshape((-1, data.shape[-1]))
+
+    for i, scale in enumerate(scales):
+        step = x[1] - x[0]
+        j = np.arange(scale * (x[-1] - x[0]) + 1) / (scale * step)
+        j = j.astype(int)  # floor
+        if j[-1] >= int_psi.size:
+            j = np.extract(j < int_psi.size, j)
+        int_psi_scale = int_psi[j][::-1]
+
+        if method == 'conv':
+            if data.ndim == 1:
+                conv = np.convolve(data, int_psi_scale)
+            else:
+                # batch convolution via loop
+                conv_shape = list(data.shape)
+                conv_shape[-1] += int_psi_scale.size - 1
+                conv_shape = tuple(conv_shape)
+                conv = np.empty(conv_shape, dtype=dt_out)
+                for n in range(data.shape[0]):
+                    conv[n, :] = np.convolve(data[n], int_psi_scale)
+        else:
+            # The padding is selected for:
+            # - optimal FFT complexity
+            # - to be larger than the two signals length to avoid circular
+            #   convolution
+            size_scale = next_fast_len(
+                data.shape[-1] + int_psi_scale.size - 1
+            )
+            if size_scale != size_scale0:
+                # Must recompute fft_data when the padding size changes.
+                fft_data = fftmodule.fft(data, size_scale, axis=-1)
+            size_scale0 = size_scale
+            fft_wav = fftmodule.fft(int_psi_scale, size_scale, axis=-1)
+            conv = fftmodule.ifft(fft_wav * fft_data, axis=-1)
+            conv = conv[..., :data.shape[-1] + int_psi_scale.size - 1]
+
+        coef = - np.sqrt(scale) * np.diff(conv, axis=-1)
+        if out.dtype.kind != 'c':
+            coef = coef.real
+        # transform axis is always -1 due to the data reshape above
+        d = (coef.shape[-1] - data.shape[-1]) / 2.
+        if d > 0:
+            coef = coef[..., floor(d):-ceil(d)]
+        elif d < 0:
+            raise ValueError(
+                "Selected scale of {} too small.".format(scale))
+        if data.ndim > 1:
+            # restore original data shape and axis position
+            coef = coef.reshape(data_shape_pre)
+            coef = coef.swapaxes(axis, -1)
+        out[i, ...] = coef
+
+    frequencies = scale2frequency(wavelet, scales, precision)
+    if np.isscalar(frequencies):
+        frequencies = np.array([frequencies])
+    frequencies /= sampling_period
+    return out, frequencies

venv/Lib/site-packages/pywt/_doc_utils.py

@@ -0,0 +1,187 @@
+"""Utilities used to generate various figures in the documentation."""
+from itertools import product
+
+import numpy as np
+from matplotlib import pyplot as plt
+
+from ._dwt import pad
+
+__all__ = ['wavedec_keys', 'wavedec2_keys', 'draw_2d_wp_basis',
+           'draw_2d_fswavedecn_basis', 'boundary_mode_subplot']
+
+
+def wavedec_keys(level):
+    """Subband keys corresponding to a wavedec decomposition."""
+    approx = ''
+    coeffs = {}
+    for lev in range(level):
+        for k in ['a', 'd']:
+            coeffs[approx + k] = None
+        approx = 'a' * (lev + 1)
+        if lev < level - 1:
+            coeffs.pop(approx)
+    return list(coeffs.keys())
+
+
+def wavedec2_keys(level):
+    """Subband keys corresponding to a wavedec2 decomposition."""
+    approx = ''
+    coeffs = {}
+    for lev in range(level):
+        for k in ['a', 'h', 'v', 'd']:
+            coeffs[approx + k] = None
+        approx = 'a' * (lev + 1)
+        if lev < level - 1:
+            coeffs.pop(approx)
+    return list(coeffs.keys())
+
+
+def _box(bl, ur):
+    """(x, y) coordinates for the 4 lines making up a rectangular box.
+
+    Parameters
+    ==========
+    bl : float
+        The bottom left corner of the box
+    ur : float
+        The upper right corner of the box
+
+    Returns
+    =======
+    coords : 2-tuple
+        The first and second elements of the tuple are the x and y coordinates
+        of the box.
+    """
+    xl, xr = bl[0], ur[0]
+    yb, yt = bl[1], ur[1]
+    box_x = [xl, xr,
+             xr, xr,
+             xr, xl,
+             xl, xl]
+    box_y = [yb, yb,
+             yb, yt,
+             yt, yt,
+             yt, yb]
+    return (box_x, box_y)
+
+
+def _2d_wp_basis_coords(shape, keys):
+    # Coordinates of the lines to be drawn by draw_2d_wp_basis
+    coords = []
+    centers = {}  # retain center of boxes for use in labeling
+    for key in keys:
+        offset_x = offset_y = 0
+        for n, char in enumerate(key):
+            if char in ['h', 'd']:
+                offset_x += shape[0] // 2**(n + 1)
+            if char in ['v', 'd']:
+                offset_y += shape[1] // 2**(n + 1)
+        sx = shape[0] // 2**(n + 1)
+        sy = shape[1] // 2**(n + 1)
+        xc, yc = _box((offset_x, -offset_y),
+                      (offset_x + sx, -offset_y - sy))
+        coords.append((xc, yc))
+        centers[key] = (offset_x + sx // 2, -offset_y - sy // 2)
+    return coords, centers
+
+
+def draw_2d_wp_basis(shape, keys, fmt='k', plot_kwargs={}, ax=None,
+                     label_levels=0):
+    """Plot a 2D representation of a WaveletPacket2D basis."""
+    coords, centers = _2d_wp_basis_coords(shape, keys)
+    if ax is None:
+        fig, ax = plt.subplots(1, 1)
+    else:
+        fig = ax.get_figure()
+    for coord in coords:
+        ax.plot(coord[0], coord[1], fmt)
+    ax.set_axis_off()
+    ax.axis('square')
+    if label_levels > 0:
+        for key, c in centers.items():
+            if len(key) <= label_levels:
+                ax.text(c[0], c[1], key,
+                        horizontalalignment='center',
+                        verticalalignment='center')
+    return fig, ax
+
+
+def _2d_fswavedecn_coords(shape, levels):
+    coords = []
+    centers = {}  # retain center of boxes for use in labeling
+    for key in product(wavedec_keys(levels), repeat=2):
+        (key0, key1) = key
+        offsets = [0, 0]
+        widths = list(shape)
+        for n0, char in enumerate(key0):
+            if char in ['d']:
+                offsets[0] += shape[0] // 2**(n0 + 1)
+        for n1, char in enumerate(key1):
+            if char in ['d']:
+                offsets[1] += shape[1] // 2**(n1 + 1)
+        widths[0] = shape[0] // 2**(n0 + 1)
+        widths[1] = shape[1] // 2**(n1 + 1)
+        xc, yc = _box((offsets[0], -offsets[1]),
+                      (offsets[0] + widths[0], -offsets[1] - widths[1]))
+        coords.append((xc, yc))
+        centers[(key0, key1)] = (offsets[0] + widths[0] / 2,
+                                 -offsets[1] - widths[1] / 2)
+    return coords, centers
+
+
+def draw_2d_fswavedecn_basis(shape, levels, fmt='k', plot_kwargs={}, ax=None,
+                             label_levels=0):
+    """Plot a 2D representation of a WaveletPacket2D basis."""
+    coords, centers = _2d_fswavedecn_coords(shape, levels)
+    if ax is None:
+        fig, ax = plt.subplots(1, 1)
+    else:
+        fig = ax.get_figure()
+    for coord in coords:
+        ax.plot(coord[0], coord[1], fmt)
+    ax.set_axis_off()
+    ax.axis('square')
+    if label_levels > 0:
+        for key, c in centers.items():
+            lev = np.max([len(k) for k in key])
+            if lev <= label_levels:
+                ax.text(c[0], c[1], key,
+                        horizontalalignment='center',
+                        verticalalignment='center')
+    return fig, ax
+
+
+def boundary_mode_subplot(x, mode, ax, symw=True):
+    """Plot an illustration of the boundary mode in a subplot axis."""
+
+    # if odd-length, periodization replicates the last sample to make it even
+    if mode == 'periodization' and len(x) % 2 == 1:
+        x = np.concatenate((x, (x[-1], )))
+
+    npad = 2 * len(x)
+    t = np.arange(len(x) + 2 * npad)
+    xp = pad(x, (npad, npad), mode=mode)
+
+    ax.plot(t, xp, 'k.')
+    ax.set_title(mode)
+
+    # plot the original signal in red
+    if mode == 'periodization':
+        ax.plot(t[npad:npad + len(x) - 1], x[:-1], 'r.')
+    else:
+        ax.plot(t[npad:npad + len(x)], x, 'r.')
+
+    # add vertical bars indicating points of symmetry or boundary extension
+    o2 = np.ones(2)
+    left = npad
+    if symw:
+        step = len(x) - 1
+        rng = range(-2, 4)
+    else:
+        left -= 0.5
+        step = len(x)
+        rng = range(-2, 4)
+    if mode in ['smooth', 'constant', 'zero']:
+        rng = range(0, 2)
+    for rep in rng:
+        ax.plot((left + rep * step) * o2, [xp.min() - .5, xp.max() + .5], 'k-')

venv/Lib/site-packages/pywt/_dwt.py

@@ -0,0 +1,517 @@
+from numbers import Number
+
+import numpy as np
+
+from ._c99_config import _have_c99_complex
+from ._extensions._pywt import Wavelet, Modes, _check_dtype, wavelist
+from ._extensions._dwt import (dwt_single, dwt_axis, idwt_single, idwt_axis,
+                               upcoef as _upcoef, downcoef as _downcoef,
+                               dwt_max_level as _dwt_max_level,
+                               dwt_coeff_len as _dwt_coeff_len)
+from ._utils import string_types, _as_wavelet
+
+
+__all__ = ["dwt", "idwt", "downcoef", "upcoef", "dwt_max_level",
+           "dwt_coeff_len", "pad"]
+
+
+def dwt_max_level(data_len, filter_len):
+    r"""
+    dwt_max_level(data_len, filter_len)
+
+    Compute the maximum useful level of decomposition.
+
+    Parameters
+    ----------
+    data_len : int
+        Input data length.
+    filter_len : int, str or Wavelet
+        The wavelet filter length.  Alternatively, the name of a discrete
+        wavelet or a Wavelet object can be specified.
+
+    Returns
+    -------
+    max_level : int
+        Maximum level.
+
+    Notes
+    -----
+    The rational for the choice of levels is the maximum level where at least
+    one coefficient in the output is uncorrupted by edge effects caused by
+    signal extension.  Put another way, decomposition stops when the signal
+    becomes shorter than the FIR filter length for a given wavelet.  This
+    corresponds to:
+
+    .. max_level = floor(log2(data_len/(filter_len - 1)))
+
+    .. math::
+        \mathtt{max\_level} = \left\lfloor\log_2\left(\mathtt{
+            \frac{data\_len}{filter\_len - 1}}\right)\right\rfloor
+
+    Examples
+    --------
+    >>> import pywt
+    >>> w = pywt.Wavelet('sym5')
+    >>> pywt.dwt_max_level(data_len=1000, filter_len=w.dec_len)
+    6
+    >>> pywt.dwt_max_level(1000, w)
+    6
+    >>> pywt.dwt_max_level(1000, 'sym5')
+    6
+    """
+    if isinstance(filter_len, Wavelet):
+        filter_len = filter_len.dec_len
+    elif isinstance(filter_len, string_types):
+        if filter_len in wavelist(kind='discrete'):
+            filter_len = Wavelet(filter_len).dec_len
+        else:
+            raise ValueError(
+                ("'{}', is not a recognized discrete wavelet.  A list of "
+                 "supported wavelet names can be obtained via "
+                 "pywt.wavelist(kind='discrete')").format(filter_len))
+    elif not (isinstance(filter_len, Number) and filter_len % 1 == 0):
+        raise ValueError(
+            "filter_len must be an integer, discrete Wavelet object, or the "
+            "name of a discrete wavelet.")
+
+    if filter_len < 2:
+        raise ValueError("invalid wavelet filter length")
+
+    return _dwt_max_level(data_len, filter_len)
+
+
+def dwt_coeff_len(data_len, filter_len, mode):
+    """
+    dwt_coeff_len(data_len, filter_len, mode='symmetric')
+
+    Returns length of dwt output for given data length, filter length and mode
+
+    Parameters
+    ----------
+    data_len : int
+        Data length.
+    filter_len : int
+        Filter length.
+    mode : str, optional
+        Signal extension mode, see :ref:`Modes <ref-modes>`.
+
+    Returns
+    -------
+    len : int
+        Length of dwt output.
+
+    Notes
+    -----
+    For all modes except periodization::
+
+        len(cA) == len(cD) == floor((len(data) + wavelet.dec_len - 1) / 2)
+
+    for periodization mode ("per")::
+
+        len(cA) == len(cD) == ceil(len(data) / 2)
+
+    """
+    if isinstance(filter_len, Wavelet):
+        filter_len = filter_len.dec_len
+
+    return _dwt_coeff_len(data_len, filter_len, Modes.from_object(mode))
+
+
+def dwt(data, wavelet, mode='symmetric', axis=-1):
+    """
+    dwt(data, wavelet, mode='symmetric', axis=-1)
+
+    Single level Discrete Wavelet Transform.
+
+    Parameters
+    ----------
+    data : array_like
+        Input signal
+    wavelet : Wavelet object or name
+        Wavelet to use
+    mode : str, optional
+        Signal extension mode, see :ref:`Modes <ref-modes>`.
+    axis: int, optional
+        Axis over which to compute the DWT. If not given, the
+        last axis is used.
+
+    Returns
+    -------
+    (cA, cD) : tuple
+        Approximation and detail coefficients.
+
+    Notes
+    -----
+    Length of coefficients arrays depends on the selected mode.
+    For all modes except periodization:
+
+        ``len(cA) == len(cD) == floor((len(data) + wavelet.dec_len - 1) / 2)``
+
+    For periodization mode ("per"):
+
+        ``len(cA) == len(cD) == ceil(len(data) / 2)``
+
+    Examples
+    --------
+    >>> import pywt
+    >>> (cA, cD) = pywt.dwt([1, 2, 3, 4, 5, 6], 'db1')
+    >>> cA
+    array([ 2.12132034,  4.94974747,  7.77817459])
+    >>> cD
+    array([-0.70710678, -0.70710678, -0.70710678])
+
+    """
+    if not _have_c99_complex and np.iscomplexobj(data):
+        data = np.asarray(data)
+        cA_r, cD_r = dwt(data.real, wavelet, mode, axis)
+        cA_i, cD_i = dwt(data.imag, wavelet, mode, axis)
+        return (cA_r + 1j*cA_i, cD_r + 1j*cD_i)
+
+    # accept array_like input; make a copy to ensure a contiguous array
+    dt = _check_dtype(data)
+    data = np.asarray(data, dtype=dt, order='C')
+    mode = Modes.from_object(mode)
+    wavelet = _as_wavelet(wavelet)
+
+    if axis < 0:
+        axis = axis + data.ndim
+    if not 0 <= axis < data.ndim:
+        raise ValueError("Axis greater than data dimensions")
+
+    if data.ndim == 1:
+        cA, cD = dwt_single(data, wavelet, mode)
+        # TODO: Check whether this makes a copy
+        cA, cD = np.asarray(cA, dt), np.asarray(cD, dt)
+    else:
+        cA, cD = dwt_axis(data, wavelet, mode, axis=axis)
+
+    return (cA, cD)
+
+
+def idwt(cA, cD, wavelet, mode='symmetric', axis=-1):
+    """
+    idwt(cA, cD, wavelet, mode='symmetric', axis=-1)
+
+    Single level Inverse Discrete Wavelet Transform.
+
+    Parameters
+    ----------
+    cA : array_like or None
+        Approximation coefficients.  If None, will be set to array of zeros
+        with same shape as ``cD``.
+    cD : array_like or None
+        Detail coefficients.  If None, will be set to array of zeros
+        with same shape as ``cA``.
+    wavelet : Wavelet object or name
+        Wavelet to use
+    mode : str, optional (default: 'symmetric')
+        Signal extension mode, see :ref:`Modes <ref-modes>`.
+    axis: int, optional
+        Axis over which to compute the inverse DWT. If not given, the
+        last axis is used.
+
+    Returns
+    -------
+    rec: array_like
+        Single level reconstruction of signal from given coefficients.
+
+    Examples
+    --------
+    >>> import pywt
+    >>> (cA, cD) = pywt.dwt([1,2,3,4,5,6], 'db2', 'smooth')
+    >>> pywt.idwt(cA, cD, 'db2', 'smooth')
+    array([ 1.,  2.,  3.,  4.,  5.,  6.])
+
+    One of the neat features of ``idwt`` is that one of the ``cA`` and ``cD``
+    arguments can be set to None.  In that situation the reconstruction will be
+    performed using only the other one.  Mathematically speaking, this is
+    equivalent to passing a zero-filled array as one of the arguments.
+
+    >>> (cA, cD) = pywt.dwt([1,2,3,4,5,6], 'db2', 'smooth')
+    >>> A = pywt.idwt(cA, None, 'db2', 'smooth')
+    >>> D = pywt.idwt(None, cD, 'db2', 'smooth')
+    >>> A + D
+    array([ 1.,  2.,  3.,  4.,  5.,  6.])
+
+    """
+    # TODO: Lots of possible allocations to eliminate (zeros_like, asarray(rec))
+    # accept array_like input; make a copy to ensure a contiguous array
+
+    if cA is None and cD is None:
+        raise ValueError("At least one coefficient parameter must be "
+                         "specified.")
+
+    # for complex inputs: compute real and imaginary separately then combine
+    if not _have_c99_complex and (np.iscomplexobj(cA) or np.iscomplexobj(cD)):
+        if cA is None:
+            cD = np.asarray(cD)
+            cA = np.zeros_like(cD)
+        elif cD is None:
+            cA = np.asarray(cA)
+            cD = np.zeros_like(cA)
+        return (idwt(cA.real, cD.real, wavelet, mode, axis) +
+                1j*idwt(cA.imag, cD.imag, wavelet, mode, axis))
+
+    if cA is not None:
+        dt = _check_dtype(cA)
+        cA = np.asarray(cA, dtype=dt, order='C')
+    if cD is not None:
+        dt = _check_dtype(cD)
+        cD = np.asarray(cD, dtype=dt, order='C')
+
+    if cA is not None and cD is not None:
+        if cA.dtype != cD.dtype:
+            # need to upcast to common type
+            if cA.dtype.kind == 'c' or cD.dtype.kind == 'c':
+                dtype = np.complex128
+            else:
+                dtype = np.float64
+            cA = cA.astype(dtype)
+            cD = cD.astype(dtype)
+    elif cA is None:
+        cA = np.zeros_like(cD)
+    elif cD is None:
+        cD = np.zeros_like(cA)
+
+    # cA and cD should be same dimension by here
+    ndim = cA.ndim
+
+    mode = Modes.from_object(mode)
+    wavelet = _as_wavelet(wavelet)
+
+    if axis < 0:
+        axis = axis + ndim
+    if not 0 <= axis < ndim:
+        raise ValueError("Axis greater than coefficient dimensions")
+
+    if ndim == 1:
+        rec = idwt_single(cA, cD, wavelet, mode)
+    else:
+        rec = idwt_axis(cA, cD, wavelet, mode, axis=axis)
+
+    return rec
+
+
+def downcoef(part, data, wavelet, mode='symmetric', level=1):
+    """
+    downcoef(part, data, wavelet, mode='symmetric', level=1)
+
+    Partial Discrete Wavelet Transform data decomposition.
+
+    Similar to ``pywt.dwt``, but computes only one set of coefficients.
+    Useful when you need only approximation or only details at the given level.
+
+    Parameters
+    ----------
+    part : str
+        Coefficients type:
+
+        * 'a' - approximations reconstruction is performed
+        * 'd' - details reconstruction is performed
+
+    data : array_like
+        Input signal.
+    wavelet : Wavelet object or name
+        Wavelet to use
+    mode : str, optional
+        Signal extension mode, see :ref:`Modes <ref-modes>`.
+    level : int, optional
+        Decomposition level.  Default is 1.
+
+    Returns
+    -------
+    coeffs : ndarray
+        1-D array of coefficients.
+
+    See Also
+    --------
+    upcoef
+
+    """
+    if not _have_c99_complex and np.iscomplexobj(data):
+        return (downcoef(part, data.real, wavelet, mode, level) +
+                1j*downcoef(part, data.imag, wavelet, mode, level))
+    # accept array_like input; make a copy to ensure a contiguous array
+    dt = _check_dtype(data)
+    data = np.asarray(data, dtype=dt, order='C')
+    if data.ndim > 1:
+        raise ValueError("downcoef only supports 1d data.")
+    if part not in 'ad':
+        raise ValueError("Argument 1 must be 'a' or 'd', not '%s'." % part)
+    mode = Modes.from_object(mode)
+    wavelet = _as_wavelet(wavelet)
+    return np.asarray(_downcoef(part == 'a', data, wavelet, mode, level))
+
+
+def upcoef(part, coeffs, wavelet, level=1, take=0):
+    """
+    upcoef(part, coeffs, wavelet, level=1, take=0)
+
+    Direct reconstruction from coefficients.
+
+    Parameters
+    ----------
+    part : str
+        Coefficients type:
+        * 'a' - approximations reconstruction is performed
+        * 'd' - details reconstruction is performed
+    coeffs : array_like
+        Coefficients array to recontruct
+    wavelet : Wavelet object or name
+        Wavelet to use
+    level : int, optional
+        Multilevel reconstruction level.  Default is 1.
+    take : int, optional
+        Take central part of length equal to 'take' from the result.
+        Default is 0.
+
+    Returns
+    -------
+    rec : ndarray
+        1-D array with reconstructed data from coefficients.
+
+    See Also
+    --------
+    downcoef
+
+    Examples
+    --------
+    >>> import pywt
+    >>> data = [1,2,3,4,5,6]
+    >>> (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

venv/Lib/site-packages/pywt/_functions.py

@@ -0,0 +1,240 @@
+# Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
+# Copyright (c) 2012-2016 The PyWavelets Developers
+#                         <https://github.com/PyWavelets/pywt>
+# See COPYING for license details.
+
+"""
+Other wavelet related functions.
+"""
+
+from __future__ import division, print_function, absolute_import
+
+import warnings
+
+import numpy as np
+from numpy.fft import fft
+
+from ._extensions._pywt import DiscreteContinuousWavelet, Wavelet, ContinuousWavelet
+
+
+__all__ = ["integrate_wavelet", "central_frequency", "scale2frequency", "qmf",
+           "orthogonal_filter_bank",
+           "intwave", "centrfrq", "scal2frq", "orthfilt"]
+
+
+_DEPRECATION_MSG = ("`{old}` has been renamed to `{new}` and will "
+                    "be removed in a future version of pywt.")
+
+
+def _integrate(arr, step):
+    integral = np.cumsum(arr)
+    integral *= step
+    return integral
+
+
+def intwave(*args, **kwargs):
+    msg = _DEPRECATION_MSG.format(old='intwave', new='integrate_wavelet')
+    warnings.warn(msg, DeprecationWarning)
+    return integrate_wavelet(*args, **kwargs)
+
+
+def centrfrq(*args, **kwargs):
+    msg = _DEPRECATION_MSG.format(old='centrfrq', new='central_frequency')
+    warnings.warn(msg, DeprecationWarning)
+    return central_frequency(*args, **kwargs)
+
+
+def scal2frq(*args, **kwargs):
+    msg = _DEPRECATION_MSG.format(old='scal2frq', new='scale2frequency')
+    warnings.warn(msg, DeprecationWarning)
+    return scale2frequency(*args, **kwargs)
+
+
+def orthfilt(*args, **kwargs):
+    msg = _DEPRECATION_MSG.format(old='orthfilt', new='orthogonal_filter_bank')
+    warnings.warn(msg, DeprecationWarning)
+    return orthogonal_filter_bank(*args, **kwargs)
+
+
+def integrate_wavelet(wavelet, precision=8):
+    """
+    Integrate `psi` wavelet function from -Inf to x using the rectangle
+    integration method.
+
+    Parameters
+    ----------
+    wavelet : Wavelet instance or str
+        Wavelet to integrate.  If a string, should be the name of a wavelet.
+    precision : int, optional
+        Precision that will be used for wavelet function
+        approximation computed with the wavefun(level=precision)
+        Wavelet's method (default: 8).
+
+    Returns
+    -------
+    [int_psi, x] :
+        for orthogonal wavelets
+    [int_psi_d, int_psi_r, x] :
+        for other wavelets
+
+
+    Examples
+    --------
+    >>> from pywt import Wavelet, integrate_wavelet
+    >>> wavelet1 = Wavelet('db2')
+    >>> [int_psi, x] = integrate_wavelet(wavelet1, precision=5)
+    >>> wavelet2 = Wavelet('bior1.3')
+    >>> [int_psi_d, int_psi_r, x] = integrate_wavelet(wavelet2, precision=5)
+
+    """
+    # FIXME: this function should really use scipy.integrate.quad
+
+    if type(wavelet) in (tuple, list):
+        msg = ("Integration of a general signal is deprecated "
+               "and will be removed in a future version of pywt.")
+        warnings.warn(msg, DeprecationWarning)
+    elif not isinstance(wavelet, (Wavelet, ContinuousWavelet)):
+        wavelet = DiscreteContinuousWavelet(wavelet)
+
+    if type(wavelet) in (tuple, list):
+        psi, x = np.asarray(wavelet[0]), np.asarray(wavelet[1])
+        step = x[1] - x[0]
+        return _integrate(psi, step), x
+
+    functions_approximations = wavelet.wavefun(precision)
+
+    if len(functions_approximations) == 2:      # continuous wavelet
+        psi, x = functions_approximations
+        step = x[1] - x[0]
+        return _integrate(psi, step), x
+
+    elif len(functions_approximations) == 3:    # orthogonal wavelet
+        phi, psi, x = functions_approximations
+        step = x[1] - x[0]
+        return _integrate(psi, step), x
+
+    else:                                       # biorthogonal wavelet
+        phi_d, psi_d, phi_r, psi_r, x = functions_approximations
+        step = x[1] - x[0]
+        return _integrate(psi_d, step), _integrate(psi_r, step), x
+
+
+def central_frequency(wavelet, precision=8):
+    """
+    Computes the central frequency of the `psi` wavelet function.
+
+    Parameters
+    ----------
+    wavelet : Wavelet instance, str or tuple
+        Wavelet to integrate.  If a string, should be the name of a wavelet.
+    precision : int, optional
+        Precision that will be used for wavelet function
+        approximation computed with the wavefun(level=precision)
+        Wavelet's method (default: 8).
+
+    Returns
+    -------
+    scalar
+
+    """
+
+    if not isinstance(wavelet, (Wavelet, ContinuousWavelet)):
+        wavelet = DiscreteContinuousWavelet(wavelet)
+
+    functions_approximations = wavelet.wavefun(precision)
+
+    if len(functions_approximations) == 2:
+        psi, x = functions_approximations
+    else:
+        # (psi, x)   for (phi, psi, x)
+        # (psi_d, x) for (phi_d, psi_d, phi_r, psi_r, x)
+        psi, x = functions_approximations[1], functions_approximations[-1]
+
+    domain = float(x[-1] - x[0])
+    assert domain > 0
+
+    index = np.argmax(abs(fft(psi)[1:])) + 2
+    if index > len(psi) / 2:
+        index = len(psi) - index + 2
+
+    return 1.0 / (domain / (index - 1))
+
+
+def scale2frequency(wavelet, scale, precision=8):
+    """
+
+    Parameters
+    ----------
+    wavelet : Wavelet instance or str
+        Wavelet to integrate.  If a string, should be the name of a wavelet.
+    scale : scalar
+    precision : int, optional
+        Precision that will be used for wavelet function approximation computed
+        with ``wavelet.wavefun(level=precision)``.  Default is 8.
+
+    Returns
+    -------
+    freq : scalar
+
+    """
+    return central_frequency(wavelet, precision=precision) / scale
+
+
+def qmf(filt):
+    """
+    Returns the Quadrature Mirror Filter(QMF).
+
+    The magnitude response of QMF is mirror image about `pi/2` of that of the
+    input filter.
+
+    Parameters
+    ----------
+    filt : array_like
+        Input filter for which QMF needs to be computed.
+
+    Returns
+    -------
+    qm_filter : ndarray
+        Quadrature mirror of the input filter.
+
+    """
+    qm_filter = np.array(filt)[::-1]
+    qm_filter[1::2] = -qm_filter[1::2]
+    return qm_filter
+
+
+def orthogonal_filter_bank(scaling_filter):
+    """
+    Returns the orthogonal filter bank.
+
+    The orthogonal filter bank consists of the HPFs and LPFs at
+    decomposition and reconstruction stage for the input scaling filter.
+
+    Parameters
+    ----------
+    scaling_filter : array_like
+        Input scaling filter (father wavelet).
+
+    Returns
+    -------
+    orth_filt_bank : tuple of 4 ndarrays
+        The orthogonal filter bank of the input scaling filter in the order :
+        1] Decomposition LPF
+        2] Decomposition HPF
+        3] Reconstruction LPF
+        4] Reconstruction HPF
+
+    """
+    if not (len(scaling_filter) % 2 == 0):
+        raise ValueError("`scaling_filter` length has to be even.")
+
+    scaling_filter = np.asarray(scaling_filter, dtype=np.float64)
+
+    rec_lo = np.sqrt(2) * scaling_filter / np.sum(scaling_filter)
+    dec_lo = rec_lo[::-1]
+
+    rec_hi = qmf(rec_lo)
+    dec_hi = rec_hi[::-1]
+
+    orth_filt_bank = (dec_lo, dec_hi, rec_lo, rec_hi)
+    return orth_filt_bank

venv/Lib/site-packages/pywt/_multidim.py

@@ -0,0 +1,311 @@
+# Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
+# Copyright (c) 2012-2016 The PyWavelets Developers
+#                         <https://github.com/PyWavelets/pywt>
+# See COPYING for license details.
+
+"""
+2D and nD Discrete Wavelet Transforms and Inverse Discrete Wavelet Transforms.
+"""
+
+from __future__ import division, print_function, absolute_import
+
+from itertools import product
+
+import numpy as np
+
+from ._c99_config import _have_c99_complex
+from ._extensions._dwt import dwt_axis, idwt_axis
+from ._utils import _wavelets_per_axis, _modes_per_axis
+
+
+__all__ = ['dwt2', 'idwt2', 'dwtn', 'idwtn']
+
+
+def dwt2(data, wavelet, mode='symmetric', axes=(-2, -1)):
+    """
+    2D Discrete Wavelet Transform.
+
+    Parameters
+    ----------
+    data : array_like
+        2D array with input data
+    wavelet : Wavelet object or name string, or 2-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 2-tuple of strings, optional
+        Signal extension mode, see :ref:`Modes <ref-modes>`. This can
+        also be a tuple of modes specifying the mode to use on each axis in
+        ``axes``.
+    axes : 2-tuple of ints, optional
+        Axes over which to compute the DWT. Repeated elements mean the DWT will
+        be performed multiple times along these axes.
+
+    Returns
+    -------
+    (cA, (cH, cV, cD)) : tuple
+        Approximation, horizontal detail, vertical detail and diagonal
+        detail coefficients respectively.  Horizontal refers to array axis 0
+        (or ``axes[0]`` for user-specified ``axes``).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import pywt
+    >>> data = np.ones((4,4), dtype=np.float64)
+    >>> coeffs = pywt.dwt2(data, 'haar')
+    >>> cA, (cH, cV, cD) = coeffs
+    >>> cA
+    array([[ 2.,  2.],
+           [ 2.,  2.]])
+    >>> cV
+    array([[ 0.,  0.],
+           [ 0.,  0.]])
+
+    """
+    axes = tuple(axes)
+    data = np.asarray(data)
+    if len(axes) != 2:
+        raise ValueError("Expected 2 axes")
+    if data.ndim < len(np.unique(axes)):
+        raise ValueError("Input array has fewer dimensions than the specified "
+                         "axes")
+
+    coefs = dwtn(data, wavelet, mode, axes)
+    return coefs['aa'], (coefs['da'], coefs['ad'], coefs['dd'])
+
+
+def idwt2(coeffs, wavelet, mode='symmetric', axes=(-2, -1)):
+    """
+    2-D Inverse Discrete Wavelet Transform.
+
+    Reconstructs data from coefficient arrays.
+
+    Parameters
+    ----------
+    coeffs : tuple
+        (cA, (cH, cV, cD)) A tuple with approximation coefficients and three
+        details coefficients 2D arrays like from ``dwt2``.  If any of these
+        components are set to ``None``, it will be treated as zeros.
+    wavelet : Wavelet object or name string, or 2-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 2-tuple of strings, optional
+        Signal extension mode, see :ref:`Modes <ref-modes>`. This can
+        also be a tuple of modes specifying the mode to use on each axis in
+        ``axes``.
+    axes : 2-tuple of ints, optional
+        Axes over which to compute the IDWT. Repeated elements mean the IDWT
+        will be performed multiple times along these axes.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import pywt
+    >>> data = np.array([[1,2], [3,4]], dtype=np.float64)
+    >>> coeffs = pywt.dwt2(data, 'haar')
+    >>> pywt.idwt2(coeffs, 'haar')
+    array([[ 1.,  2.],
+           [ 3.,  4.]])
+
+    """
+    # L -low-pass data, H - high-pass data
+    LL, (HL, LH, HH) = coeffs
+    axes = tuple(axes)
+    if len(axes) != 2:
+        raise ValueError("Expected 2 axes")
+
+    coeffs = {'aa': LL, 'da': HL, 'ad': LH, 'dd': HH}
+    return idwtn(coeffs, wavelet, mode, axes)
+
+
+def dwtn(data, wavelet, mode='symmetric', axes=None):
+    """
+    Single-level n-dimensional Discrete Wavelet Transform.
+
+    Parameters
+    ----------
+    data : array_like
+        n-dimensional array with 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 string, optional
+        Signal extension mode used in the decomposition,
+        see :ref:`Modes <ref-modes>`. This can also be a tuple of modes
+        specifying the mode to use on each axis in ``axes``.
+    axes : sequence of ints, optional
+        Axes over which to compute the DWT. Repeated elements mean the DWT will
+        be performed multiple times along these axes. A value of ``None`` (the
+        default) selects all axes.
+
+        Axes may be repeated, but information about the original size may be
+        lost if it is not divisible by ``2 ** nrepeats``. The reconstruction
+        will be larger, with additional values derived according to the
+        ``mode`` parameter. ``pywt.wavedecn`` should be used for multilevel
+        decomposition.
+
+    Returns
+    -------
+    coeffs : dict
+        Results are arranged in a dictionary, where key specifies
+        the transform type on each dimension and value is a n-dimensional
+        coefficients array.
+
+        For example, for a 2D case the result will look something like this::
+
+            {'aa': <coeffs>  # A(LL) - approx. on 1st dim, approx. on 2nd dim
+             'ad': <coeffs>  # V(LH) - approx. on 1st dim, det. on 2nd dim
+             'da': <coeffs>  # H(HL) - det. on 1st dim, approx. on 2nd dim
+             'dd': <coeffs>  # D(HH) - det. on 1st dim, det. on 2nd dim
+            }
+
+        For user-specified ``axes``, the order of the characters in the
+        dictionary keys map to the specified ``axes``.
+
+    """
+    data = np.asarray(data)
+    if not _have_c99_complex and np.iscomplexobj(data):
+        real = dwtn(data.real, wavelet, mode, axes)
+        imag = dwtn(data.imag, wavelet, mode, axes)
+        return dict((k, real[k] + 1j * imag[k]) for k in real.keys())
+
+    if data.dtype == np.dtype('object'):
+        raise TypeError("Input must be a numeric array-like")
+    if data.ndim < 1:
+        raise ValueError("Input data must be at least 1D")
+
+    if axes is None:
+        axes = range(data.ndim)
+    axes = [a + data.ndim if a < 0 else a for a in axes]
+
+    modes = _modes_per_axis(mode, axes)
+    wavelets = _wavelets_per_axis(wavelet, axes)
+
+    coeffs = [('', data)]
+    for axis, wav, mode in zip(axes, wavelets, modes):
+        new_coeffs = []
+        for subband, x in coeffs:
+            cA, cD = dwt_axis(x, wav, mode, axis)
+            new_coeffs.extend([(subband + 'a', cA),
+                               (subband + 'd', cD)])
+        coeffs = new_coeffs
+    return dict(coeffs)
+
+
+def _fix_coeffs(coeffs):
+    missing_keys = [k for k, v in coeffs.items() if v is None]
+    if missing_keys:
+        raise ValueError(
+            "The following detail coefficients were set to None:\n"
+            "{0}\n"
+            "For multilevel transforms, rather than setting\n"
+            "\tcoeffs[key] = None\n"
+            "use\n"
+            "\tcoeffs[key] = np.zeros_like(coeffs[key])\n".format(
+                missing_keys))
+
+    invalid_keys = [k for k, v in coeffs.items() if
+                    not set(k) <= set('ad')]
+    if invalid_keys:
+        raise ValueError(
+            "The following invalid keys were found in the detail "
+            "coefficient dictionary: {}.".format(invalid_keys))
+
+    key_lengths = [len(k) for k in coeffs.keys()]
+    if len(np.unique(key_lengths)) > 1:
+        raise ValueError(
+            "All detail coefficient names must have equal length.")
+
+    return dict((k, np.asarray(v)) for k, v in coeffs.items())
+
+
+def idwtn(coeffs, wavelet, mode='symmetric', axes=None):
+    """
+    Single-level n-dimensional Inverse Discrete Wavelet Transform.
+
+    Parameters
+    ----------
+    coeffs: dict
+        Dictionary as in output of ``dwtn``. Missing or ``None`` items
+        will be treated as zeros.
+    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 list of string, optional
+        Signal extension mode used in the decomposition,
+        see :ref:`Modes <ref-modes>`. This can also be a tuple of modes
+        specifying the mode to use on each axis in ``axes``.
+    axes : sequence of ints, optional
+        Axes over which to compute the IDWT. Repeated elements mean the IDWT
+        will be performed multiple times along these axes. A value of ``None``
+        (the default) selects all axes.
+
+        For the most accurate reconstruction, the axes should be provided in
+        the same order as they were provided to ``dwtn``.
+
+    Returns
+    -------
+    data: ndarray
+        Original signal reconstructed from input data.
+
+    """
+
+    # drop the keys corresponding to value = None
+    coeffs = dict((k, v) for k, v in coeffs.items() if v is not None)
+
+    # Raise error for invalid key combinations
+    coeffs = _fix_coeffs(coeffs)
+
+    if (not _have_c99_complex and
+            any(np.iscomplexobj(v) for v in coeffs.values())):
+        real_coeffs = dict((k, v.real) for k, v in coeffs.items())
+        imag_coeffs = dict((k, v.imag) for k, v in coeffs.items())
+        return (idwtn(real_coeffs, wavelet, mode, axes) +
+                1j * idwtn(imag_coeffs, wavelet, mode, axes))
+
+    # key length matches the number of axes transformed
+    ndim_transform = max(len(key) for key in coeffs.keys())
+
+    try:
+        coeff_shapes = (v.shape for k, v in coeffs.items()
+                        if v is not None and len(k) == ndim_transform)
+        coeff_shape = next(coeff_shapes)
+    except StopIteration:
+        raise ValueError("`coeffs` must contain at least one non-null wavelet "
+                         "band")
+    if any(s != coeff_shape for s in coeff_shapes):
+        raise ValueError("`coeffs` must all be of equal size (or None)")
+
+    if axes is None:
+        axes = range(ndim_transform)
+        ndim = ndim_transform
+    else:
+        ndim = len(coeff_shape)
+    axes = [a + ndim if a < 0 else a for a in axes]
+
+    modes = _modes_per_axis(mode, axes)
+    wavelets = _wavelets_per_axis(wavelet, axes)
+    for key_length, (axis, wav, mode) in reversed(
+            list(enumerate(zip(axes, wavelets, modes)))):
+        if axis < 0 or axis >= ndim:
+            raise ValueError("Axis greater than data dimensions")
+
+        new_coeffs = {}
+        new_keys = [''.join(coef) for coef in product('ad', repeat=key_length)]
+
+        for key in new_keys:
+            L = coeffs.get(key + 'a', None)
+            H = coeffs.get(key + 'd', None)
+            if L is not None and H is not None:
+                if L.dtype != H.dtype:
+                    # upcast to a common dtype (float64 or complex128)
+                    if L.dtype.kind == 'c' or H.dtype.kind == 'c':
+                        dtype = np.complex128
+                    else:
+                        dtype = np.float64
+                    L = np.asarray(L, dtype=dtype)
+                    H = np.asarray(H, dtype=dtype)
+            new_coeffs[key] = idwt_axis(L, H, wav, mode, axis)
+        coeffs = new_coeffs
+
+    return coeffs['']

venv/Lib/site-packages/pywt/_pytest.py

@@ -0,0 +1,68 @@
+"""common test-related code."""
+import os
+import sys
+import multiprocessing
+import numpy as np
+import pytest
+
+
+__all__ = ['uses_matlab',   # skip if pymatbridge and Matlab unavailable
+           'uses_futures',  # skip if futures unavailable
+           'uses_pymatbridge',  # skip if no PYWT_XSLOW environment variable
+           'uses_precomputed',  # skip if PYWT_XSLOW environment variable found
+           'matlab_result_dict_cwt',   # dict with precomputed Matlab dwt data
+           'matlab_result_dict_dwt',   # dict with precomputed Matlab cwt data
+           'futures',      # the futures module or None
+           'max_workers',  # the number of workers available to futures
+           'size_set',     # the set of Matlab tests to run
+           ]
+
+try:
+    if sys.version_info[0] == 2:
+        import futures
+    else:
+        from concurrent import futures
+    max_workers = multiprocessing.cpu_count()
+    futures_available = True
+except ImportError:
+    futures_available = False
+    futures = None
+
+# check if pymatbridge + MATLAB tests should be run
+matlab_result_dict_dwt = None
+matlab_result_dict_cwt = None
+matlab_missing = True
+use_precomputed = True
+size_set = 'reduced'
+if 'PYWT_XSLOW' in os.environ:
+    try:
+        from pymatbridge import Matlab
+        mlab = Matlab()
+        matlab_missing = False
+        use_precomputed = False
+        size_set = 'full'
+    except ImportError:
+        print("To run Matlab compatibility tests you need to have MathWorks "
+              "MATLAB, MathWorks Wavelet Toolbox and the pymatbridge Python "
+              "package installed.")
+if use_precomputed:
+    # load dictionaries of precomputed results
+    data_dir = os.path.join(os.path.dirname(__file__), 'tests', 'data')
+    matlab_data_file_cwt = os.path.join(
+        data_dir, 'cwt_matlabR2015b_result.npz')
+    matlab_result_dict_cwt = np.load(matlab_data_file_cwt)
+
+    matlab_data_file_dwt = os.path.join(
+        data_dir, 'dwt_matlabR2012a_result.npz')
+    matlab_result_dict_dwt = np.load(matlab_data_file_dwt)
+
+uses_futures = pytest.mark.skipif(
+    not futures_available, reason='futures not available')
+uses_matlab = pytest.mark.skipif(
+    matlab_missing, reason='pymatbridge and/or Matlab not available')
+uses_pymatbridge = pytest.mark.skipif(
+    use_precomputed,
+    reason='PYWT_XSLOW set: skipping tests against precomputed Matlab results')
+uses_precomputed = pytest.mark.skipif(
+    not use_precomputed,
+    reason='PYWT_XSLOW not set: test against precomputed matlab tests')

venv/Lib/site-packages/pywt/_pytesttester.py

@@ -0,0 +1,164 @@
+"""
+Pytest test running.
+
+This module implements the ``test()`` function for NumPy modules. The usual
+boiler plate for doing that is to put the following in the module
+``__init__.py`` file::
+
+    from pywt._pytesttester import PytestTester
+    test = PytestTester(__name__).test
+    del PytestTester
+
+
+Warnings filtering and other runtime settings should be dealt with in the
+``pytest.ini`` file in the pywt repo root. The behavior of the test depends on
+whether or not that file is found as follows:
+
+* ``pytest.ini`` is present (develop mode)
+    All warnings except those explicily filtered out are raised as error.
+* ``pytest.ini`` is absent (release mode)
+    DeprecationWarnings and PendingDeprecationWarnings are ignored, other
+    warnings are passed through.
+
+In practice, tests run from the PyWavelets repo are run in develop mode. That
+includes the standard ``python runtests.py`` invocation.
+
+"""
+from __future__ import division, absolute_import, print_function
+
+import sys
+import os
+
+__all__ = ['PytestTester']
+
+
+def _show_pywt_info():
+    import pywt
+    from pywt._c99_config import _have_c99_complex
+    print("PyWavelets version %s" % pywt.__version__)
+    if _have_c99_complex:
+        print("Compiled with C99 complex support.")
+    else:
+        print("Compiled without C99 complex support.")
+
+
+class PytestTester(object):
+    """
+    Pytest test runner.
+
+    This class is made available in ``pywt.testing``, and a test function
+    is typically added to a package's __init__.py like so::
+
+      from pywt.testing import PytestTester
+      test = PytestTester(__name__).test
+      del PytestTester
+
+    Calling this test function finds and runs all tests associated with the
+    module and all its sub-modules.
+
+    Attributes
+    ----------
+    module_name : str
+        Full path to the package to test.
+
+    Parameters
+    ----------
+    module_name : module name
+        The name of the module to test.
+
+    """
+    def __init__(self, module_name):
+        self.module_name = module_name
+
+    def __call__(self, label='fast', verbose=1, extra_argv=None,
+                 doctests=False, coverage=False, durations=-1, tests=None):
+        """
+        Run tests for module using pytest.
+
+        Parameters
+        ----------
+        label : {'fast', 'full'}, optional
+            Identifies the tests to run. When set to 'fast', tests decorated
+            with `pytest.mark.slow` are skipped, when 'full', the slow marker
+            is ignored.
+        verbose : int, optional
+            Verbosity value for test outputs, in the range 1-3. Default is 1.
+        extra_argv : list, optional
+            List with any extra arguments to pass to pytests.
+        doctests : bool, optional
+            .. note:: Not supported
+        coverage : bool, optional
+            If True, report coverage of NumPy code. Default is False.
+            Requires installation of (pip) pytest-cov.
+        durations : int, optional
+            If < 0, do nothing, If 0, report time of all tests, if > 0,
+            report the time of the slowest `timer` tests. Default is -1.
+        tests : test or list of tests
+            Tests to be executed with pytest '--pyargs'
+
+        Returns
+        -------
+        result : bool
+            Return True on success, false otherwise.
+
+        Examples
+        --------
+        >>> result = np.lib.test() #doctest: +SKIP
+        ...
+        1023 passed, 2 skipped, 6 deselected, 1 xfailed in 10.39 seconds
+        >>> result
+        True
+
+        """
+        import pytest
+
+        module = sys.modules[self.module_name]
+        module_path = os.path.abspath(module.__path__[0])
+
+        # setup the pytest arguments
+        pytest_args = ["-l"]
+
+        # offset verbosity. The "-q" cancels a "-v".
+        pytest_args += ["-q"]
+
+        # Filter out annoying import messages. Want these in both develop and
+        # release mode.
+        pytest_args += [
+            "-W ignore:Not importing directory",
+            "-W ignore:numpy.dtype size changed",
+            "-W ignore:numpy.ufunc size changed", ]
+
+        if doctests:
+            raise ValueError("Doctests not supported")
+
+        if extra_argv:
+            pytest_args += list(extra_argv)
+
+        if verbose > 1:
+            pytest_args += ["-" + "v"*(verbose - 1)]
+
+        if coverage:
+            pytest_args += ["--cov=" + module_path]
+
+        if label == "fast":
+            pytest_args += ["-m", "not slow"]
+        elif label != "full":
+            pytest_args += ["-m", label]
+
+        if durations >= 0:
+            pytest_args += ["--durations=%s" % durations]
+
+        if tests is None:
+            tests = [self.module_name]
+
+        pytest_args += ["--pyargs"] + list(tests)
+
+        # run tests.
+        _show_pywt_info()
+
+        try:
+            code = pytest.main(pytest_args)
+        except SystemExit as exc:
+            code = exc.code
+
+        return code == 0

venv/Lib/site-packages/pywt/_swt.py

@@ -0,0 +1,774 @@
+import warnings
+from itertools import product
+
+import numpy as np
+
+from ._c99_config import _have_c99_complex
+from ._extensions._dwt import idwt_single
+from ._extensions._swt import swt_max_level, swt as _swt, swt_axis as _swt_axis
+from ._extensions._pywt import Wavelet, Modes, _check_dtype
+from ._multidim import idwt2, idwtn
+from ._utils import _as_wavelet, _wavelets_per_axis
+
+
+__all__ = ["swt", "swt_max_level", 'iswt', 'swt2', 'iswt2', 'swtn', 'iswtn']
+
+
+def _rescale_wavelet_filterbank(wavelet, sf):
+    wav = Wavelet(wavelet.name + 'r',
+                  [np.asarray(f) * sf for f in wavelet.filter_bank])
+
+    # copy attributes from the original wavelet
+    wav.orthogonal = wavelet.orthogonal
+    wav.biorthogonal = wavelet.biorthogonal
+    return wav
+
+
+def swt(data, wavelet, level=None, start_level=0, axis=-1,
+        trim_approx=False, norm=False):
+    """
+    Multilevel 1D stationary wavelet transform.
+
+    Parameters
+    ----------
+    data :
+        Input signal
+    wavelet :
+        Wavelet to use (Wavelet object or name)
+    level : int, optional
+        The number of decomposition steps to perform.
+    start_level : int, optional
+        The level at which the decomposition will begin (it allows one to
+        skip a given number of transform steps and compute
+        coefficients starting from start_level) (default: 0)
+    axis: int, optional
+        Axis over which to compute the SWT. If not given, the
+        last axis is used.
+    trim_approx : bool, optional
+        If True, approximation coefficients at the final level are retained.
+    norm : bool, optional
+        If True, transform is normalized so that the energy of the coefficients
+        will be equal to the energy of ``data``. In other words,
+        ``np.linalg.norm(data.ravel())`` will equal the norm of the
+        concatenated transform coefficients when ``trim_approx`` is True.
+
+    Returns
+    -------
+    coeffs : list
+        List of approximation and details coefficients pairs in order
+        similar to wavedec function::
+
+            [(cAn, cDn), ..., (cA2, cD2), (cA1, cD1)]
+
+        where n equals input parameter ``level``.
+
+        If ``start_level = m`` is given, then the beginning m steps are
+        skipped::
+
+            [(cAm+n, cDm+n), ..., (cAm+1, cDm+1), (cAm, cDm)]
+
+        If ``trim_approx`` is ``True``, then the output list is exactly as in
+        ``pywt.wavedec``, where the first coefficient in the list is the
+        approximation coefficient at the final level and the rest are the
+        detail coefficients::
+
+            [cAn, cDn, ..., cD2, cD1]
+
+    Notes
+    -----
+    The implementation here follows the "algorithm a-trous" and requires that
+    the signal length along the transformed axis be a multiple of ``2**level``.
+    If this is not the case, the user should pad up to an appropriate size
+    using a function such as ``numpy.pad``.
+
+    A primary benefit of this transform in comparison to its decimated
+    counterpart (``pywt.wavedecn``), is that it is shift-invariant. This comes
+    at cost of redundancy in the transform (the size of the output coefficients
+    is larger than the input).
+
+    When the following three conditions are true:
+
+        1. The wavelet is orthogonal
+        2. ``swt`` is called with ``norm=True``
+        3. ``swt`` is called with ``trim_approx=True``
+
+    the transform has the following additional properties that may be
+    desirable in applications:
+
+        1. energy is conserved
+        2. variance is partitioned across scales
+
+    When used with ``norm=True``, this transform is closely related to the
+    multiple-overlap DWT (MODWT) as popularized for time-series analysis,
+    although the underlying implementation is slightly different from the one
+    published in [1]_. Specifically, the implementation used here requires a
+    signal that is a multiple of ``2**level`` in length.
+
+    References
+    ----------
+    .. [1] DB Percival and AT Walden. Wavelet Methods for Time Series Analysis.
+        Cambridge University Press, 2000.
+    """
+
+    if not _have_c99_complex and np.iscomplexobj(data):
+        data = np.asarray(data)
+        coeffs_real = swt(data.real, wavelet, level, start_level, trim_approx)
+        coeffs_imag = swt(data.imag, wavelet, level, start_level, trim_approx)
+        if not trim_approx:
+            coeffs_cplx = []
+            for (cA_r, cD_r), (cA_i, cD_i) in zip(coeffs_real, coeffs_imag):
+                coeffs_cplx.append((cA_r + 1j*cA_i, cD_r + 1j*cD_i))
+        else:
+            coeffs_cplx = [cr + 1j*ci
+                           for (cr, ci) in zip(coeffs_real, coeffs_imag)]
+        return coeffs_cplx
+
+    # accept array_like input; make a copy to ensure a contiguous array
+    dt = _check_dtype(data)
+    data = np.array(data, dtype=dt)
+
+    wavelet = _as_wavelet(wavelet)
+    if norm:
+        if not wavelet.orthogonal:
+            warnings.warn(
+                "norm=True, but the wavelet is not orthogonal: \n"
+                "\tThe conditions for energy preservation are not satisfied.")
+        wavelet = _rescale_wavelet_filterbank(wavelet, 1/np.sqrt(2))
+
+    if axis < 0:
+        axis = axis + data.ndim
+    if not 0 <= axis < data.ndim:
+        raise ValueError("Axis greater than data dimensions")
+
+    if level is None:
+        level = swt_max_level(data.shape[axis])
+
+    if data.ndim == 1:
+        ret = _swt(data, wavelet, level, start_level, trim_approx)
+    else:
+        ret = _swt_axis(data, wavelet, level, start_level, axis, trim_approx)
+    return ret
+
+
+def iswt(coeffs, wavelet, norm=False):
+    """
+    Multilevel 1D inverse discrete stationary wavelet transform.
+
+    Parameters
+    ----------
+    coeffs : array_like
+        Coefficients list of tuples::
+
+            [(cAn, cDn), ..., (cA2, cD2), (cA1, cD1)]
+
+        where cA is approximation, cD is details.  Index 1 corresponds to
+        ``start_level`` from ``pywt.swt``.
+    wavelet : Wavelet object or name string
+        Wavelet to use
+    norm : bool, optional
+        Controls the normalization used by the inverse transform. This must
+        be set equal to the value that was used by ``pywt.swt`` to preserve the
+        energy of a round-trip transform.
+
+    Returns
+    -------
+    1D array of reconstructed data.
+
+    Examples
+    --------
+    >>> import pywt
+    >>> coeffs = pywt.swt([1,2,3,4,5,6,7,8], 'db2', level=2)
+    >>> pywt.iswt(coeffs, 'db2')
+    array([ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.])
+    """
+    # copy to avoid modification of input data
+
+    # If swt was called with trim_approx=False, first element is a tuple
+    trim_approx = not isinstance(coeffs[0], (tuple, list))
+
+    if trim_approx:
+        cA = coeffs[0]
+        coeffs = coeffs[1:]
+    else:
+        cA = coeffs[0][0]
+
+    dt = _check_dtype(cA)
+    output = np.array(cA, dtype=dt, copy=True)
+    if not _have_c99_complex and np.iscomplexobj(output):
+        # compute real and imaginary separately then combine
+        if trim_approx:
+            coeffs_real = [c.real for c in coeffs]
+            coeffs_imag = [c.imag for c in coeffs]
+        else:
+            coeffs_real = [(cA.real, cD.real) for (cA, cD) in coeffs]
+            coeffs_imag = [(cA.imag, cD.imag) for (cA, cD) in coeffs]
+        return iswt(coeffs_real, wavelet) + 1j*iswt(coeffs_imag, wavelet)
+
+    # num_levels, equivalent to the decomposition level, n
+    num_levels = len(coeffs)
+    wavelet = _as_wavelet(wavelet)
+    if norm:
+        wavelet = _rescale_wavelet_filterbank(wavelet, np.sqrt(2))
+    mode = Modes.from_object('periodization')
+    for j in range(num_levels, 0, -1):
+        step_size = int(pow(2, j-1))
+        last_index = step_size
+        if trim_approx:
+            cD = coeffs[-j]
+        else:
+            _, cD = coeffs[-j]
+        cD = np.asarray(cD, dtype=_check_dtype(cD))
+        if cD.dtype != output.dtype:
+            # upcast to a common dtype (float64 or complex128)
+            if output.dtype.kind == 'c' or cD.dtype.kind == 'c':
+                dtype = np.complex128
+            else:
+                dtype = np.float64
+            output = np.asarray(output, dtype=dtype)
+            cD = np.asarray(cD, dtype=dtype)
+        for first in range(last_index):  # 0 to last_index - 1
+
+            # Getting the indices that we will transform
+            indices = np.arange(first, len(cD), step_size)
+
+            # select the even indices
+            even_indices = indices[0::2]
+            # select the odd indices
+            odd_indices = indices[1::2]
+
+            # perform the inverse dwt on the selected indices,
+            # making sure to use periodic boundary conditions
+            # Note:  indexing with an array of ints returns a contiguous
+            #        copy as required by idwt_single.
+            x1 = idwt_single(output[even_indices],
+                             cD[even_indices],
+                             wavelet, mode)
+            x2 = idwt_single(output[odd_indices],
+                             cD[odd_indices],
+                             wavelet, mode)
+
+            # perform a circular shift right
+            x2 = np.roll(x2, 1)
+
+            # average and insert into the correct indices
+            output[indices] = (x1 + x2)/2.
+
+    return output
+
+
+def swt2(data, wavelet, level, start_level=0, axes=(-2, -1),
+         trim_approx=False, norm=False):
+    """
+    Multilevel 2D stationary wavelet transform.
+
+    Parameters
+    ----------
+    data : array_like
+        2D array with input data
+    wavelet : Wavelet object or name string, or 2-tuple of wavelets
+        Wavelet to use.  This can also be a tuple of wavelets to apply per
+        axis in ``axes``.
+    level : int
+        The number of decomposition steps to perform.
+    start_level : int, optional
+        The level at which the decomposition will start (default: 0)
+    axes : 2-tuple of ints, optional
+        Axes over which to compute the SWT. Repeated elements are not allowed.
+    trim_approx : bool, optional
+        If True, approximation coefficients at the final level are retained.
+    norm : bool, optional
+        If True, transform is normalized so that the energy of the coefficients
+        will be equal to the energy of ``data``. In other words,
+        ``np.linalg.norm(data.ravel())`` will equal the norm of the
+        concatenated transform coefficients when ``trim_approx`` is True.
+
+    Returns
+    -------
+    coeffs : list
+        Approximation and details coefficients (for ``start_level = m``).
+        If ``trim_approx`` is ``True``, approximation coefficients are
+        retained for all levels::
+
+            [
+                (cA_m+level,
+                    (cH_m+level, cV_m+level, cD_m+level)
+                ),
+                ...,
+                (cA_m+1,
+                    (cH_m+1, cV_m+1, cD_m+1)
+                ),
+                (cA_m,
+                    (cH_m, cV_m, cD_m)
+                )
+            ]
+
+        where cA is approximation, cH is horizontal details, cV is
+        vertical details, cD is diagonal details and m is ``start_level``.
+
+        If ``trim_approx`` is ``False``, approximation coefficients are only
+        retained at the final level of decomposition. This matches the format
+        used by ``pywt.wavedec2``::
+
+            [
+                cA_m+level,
+                (cH_m+level, cV_m+level, cD_m+level),
+                ...,
+                (cH_m+1, cV_m+1, cD_m+1),
+                (cH_m, cV_m, cD_m),
+            ]
+
+    Notes
+    -----
+    The implementation here follows the "algorithm a-trous" and requires that
+    the signal length along the transformed axes be a multiple of ``2**level``.
+    If this is not the case, the user should pad up to an appropriate size
+    using a function such as ``numpy.pad``.
+
+    A primary benefit of this transform in comparison to its decimated
+    counterpart (``pywt.wavedecn``), is that it is shift-invariant. This comes
+    at cost of redundancy in the transform (the size of the output coefficients
+    is larger than the input).
+
+    When the following three conditions are true:
+
+        1. The wavelet is orthogonal
+        2. ``swt2`` is called with ``norm=True``
+        3. ``swt2`` is called with ``trim_approx=True``
+
+    the transform has the following additional properties that may be
+    desirable in applications:
+
+        1. energy is conserved
+        2. variance is partitioned across scales
+
+    """
+    axes = tuple(axes)
+    data = np.asarray(data)
+    if len(axes) != 2:
+        raise ValueError("Expected 2 axes")
+    if len(axes) != len(set(axes)):
+        raise ValueError("The axes passed to swt2 must be unique.")
+    if data.ndim < len(np.unique(axes)):
+        raise ValueError("Input array has fewer dimensions than the specified "
+                         "axes")
+
+    coefs = swtn(data, wavelet, level, start_level, axes, trim_approx, norm)
+    ret = []
+    if trim_approx:
+        ret.append(coefs[0])
+        coefs = coefs[1:]
+    for c in coefs:
+        if trim_approx:
+            ret.append((c['da'], c['ad'], c['dd']))
+        else:
+            ret.append((c['aa'], (c['da'], c['ad'], c['dd'])))
+    return ret
+
+
+def iswt2(coeffs, wavelet, norm=False):
+    """
+    Multilevel 2D inverse discrete stationary wavelet transform.
+
+    Parameters
+    ----------
+    coeffs : list
+        Approximation and details coefficients::
+
+            [
+                (cA_n,
+                    (cH_n, cV_n, cD_n)
+                ),
+                ...,
+                (cA_2,
+                    (cH_2, cV_2, cD_2)
+                ),
+                (cA_1,
+                    (cH_1, cV_1, cD_1)
+                )
+            ]
+
+        where cA is approximation, cH is horizontal details, cV is
+        vertical details, cD is diagonal details and n is the number of
+        levels.  Index 1 corresponds to ``start_level`` from ``pywt.swt2``.
+    wavelet : Wavelet object or name string, or 2-tuple of wavelets
+        Wavelet to use.  This can also be a 2-tuple of wavelets to apply per
+        axis.
+    norm : bool, optional
+        Controls the normalization used by the inverse transform. This must
+        be set equal to the value that was used by ``pywt.swt2`` to preserve
+        the energy of a round-trip transform.
+
+    Returns
+    -------
+    2D array of reconstructed data.
+
+    Examples
+    --------
+    >>> import pywt
+    >>> coeffs = pywt.swt2([[1,2,3,4],[5,6,7,8],
+    ...                     [9,10,11,12],[13,14,15,16]],
+    ...                    'db1', level=2)
+    >>> pywt.iswt2(coeffs, 'db1')
+    array([[  1.,   2.,   3.,   4.],
+           [  5.,   6.,   7.,   8.],
+           [  9.,  10.,  11.,  12.],
+           [ 13.,  14.,  15.,  16.]])
+
+    """
+
+    # If swt was called with trim_approx=False, first element is a tuple
+    trim_approx = not isinstance(coeffs[0], (tuple, list))
+    if trim_approx:
+        cA = coeffs[0]
+        coeffs = coeffs[1:]
+    else:
+        cA = coeffs[0][0]
+
+    # copy to avoid modification of input data
+    dt = _check_dtype(cA)
+    output = np.array(cA, dtype=dt, copy=True)
+
+    if output.ndim != 2:
+        raise ValueError(
+            "iswt2 only supports 2D arrays.  see iswtn for a general "
+            "n-dimensionsal ISWT")
+    # num_levels, equivalent to the decomposition level, n
+    num_levels = len(coeffs)
+    wavelets = _wavelets_per_axis(wavelet, axes=(0, 1))
+    if norm:
+        wavelets = [_rescale_wavelet_filterbank(wav, np.sqrt(2))
+                    for wav in wavelets]
+
+    for j in range(num_levels):
+        step_size = int(pow(2, num_levels-j-1))
+        last_index = step_size
+        if trim_approx:
+            (cH, cV, cD) = coeffs[j]
+        else:
+            _, (cH, cV, cD) = coeffs[j]
+        # We are going to assume cH, cV, and cD are of equal size
+        if (cH.shape != cV.shape) or (cH.shape != cD.shape):
+            raise RuntimeError(
+                "Mismatch in shape of intermediate coefficient arrays")
+
+        # make sure output shares the common dtype
+        # (conversion of dtype for individual coeffs is handled within idwt2 )
+        common_dtype = np.result_type(*(
+            [dt, ] + [_check_dtype(c) for c in [cH, cV, cD]]))
+        if output.dtype != common_dtype:
+            output = output.astype(common_dtype)
+
+        for first_h in range(last_index):  # 0 to last_index - 1
+            for first_w in range(last_index):  # 0 to last_index - 1
+                # Getting the indices that we will transform
+                indices_h = slice(first_h, cH.shape[0], step_size)
+                indices_w = slice(first_w, cH.shape[1], step_size)
+
+                even_idx_h = slice(first_h, cH.shape[0], 2*step_size)
+                even_idx_w = slice(first_w, cH.shape[1], 2*step_size)
+                odd_idx_h = slice(first_h + step_size, cH.shape[0], 2*step_size)
+                odd_idx_w = slice(first_w + step_size, cH.shape[1], 2*step_size)
+
+                # perform the inverse dwt on the selected indices,
+                # making sure to use periodic boundary conditions
+                x1 = idwt2((output[even_idx_h, even_idx_w],
+                           (cH[even_idx_h, even_idx_w],
+                            cV[even_idx_h, even_idx_w],
+                            cD[even_idx_h, even_idx_w])),
+                           wavelets, 'periodization')
+                x2 = idwt2((output[even_idx_h, odd_idx_w],
+                           (cH[even_idx_h, odd_idx_w],
+                            cV[even_idx_h, odd_idx_w],
+                            cD[even_idx_h, odd_idx_w])),
+                           wavelets, 'periodization')
+                x3 = idwt2((output[odd_idx_h, even_idx_w],
+                           (cH[odd_idx_h, even_idx_w],
+                            cV[odd_idx_h, even_idx_w],
+                            cD[odd_idx_h, even_idx_w])),
+                           wavelets, 'periodization')
+                x4 = idwt2((output[odd_idx_h, odd_idx_w],
+                           (cH[odd_idx_h, odd_idx_w],
+                            cV[odd_idx_h, odd_idx_w],
+                            cD[odd_idx_h, odd_idx_w])),
+                           wavelets, 'periodization')
+
+                # perform a circular shifts
+                x2 = np.roll(x2, 1, axis=1)
+                x3 = np.roll(x3, 1, axis=0)
+                x4 = np.roll(x4, 1, axis=0)
+                x4 = np.roll(x4, 1, axis=1)
+                output[indices_h, indices_w] = (x1 + x2 + x3 + x4) / 4
+
+    return output
+
+
+def swtn(data, wavelet, level, start_level=0, axes=None, trim_approx=False,
+         norm=False):
+    """
+    n-dimensional stationary wavelet transform.
+
+    Parameters
+    ----------
+    data : array_like
+        n-dimensional array with input data.
+    wavelet : Wavelet object or name string, or tuple of wavelets
+        Wavelet to use.  This can also be a tuple of wavelets to apply per
+        axis in ``axes``.
+    level : int
+        The number of decomposition steps to perform.
+    start_level : int, optional
+        The level at which the decomposition will start (default: 0)
+    axes : sequence of ints, optional
+        Axes over which to compute the SWT. A value of ``None`` (the
+        default) selects all axes. Axes may not be repeated.
+    trim_approx : bool, optional
+        If True, approximation coefficients at the final level are retained.
+    norm : bool, optional
+        If True, transform is normalized so that the energy of the coefficients
+        will be equal to the energy of ``data``. In other words,
+        ``np.linalg.norm(data.ravel())`` will equal the norm of the
+        concatenated transform coefficients when ``trim_approx`` is True.
+
+    Returns
+    -------
+    [{coeffs_level_n}, ..., {coeffs_level_1}]: list of dict
+        Results for each level are arranged in a dictionary, where the key
+        specifies the transform type on each dimension and value is a
+        n-dimensional coefficients array.
+
+        For example, for a 2D case the result at a given level will look
+        something like this::
+
+            {'aa': <coeffs>  # A(LL) - approx. on 1st dim, approx. on 2nd dim
+             'ad': <coeffs>  # V(LH) - approx. on 1st dim, det. on 2nd dim
+             'da': <coeffs>  # H(HL) - det. on 1st dim, approx. on 2nd dim
+             'dd': <coeffs>  # D(HH) - det. on 1st dim, det. on 2nd dim
+            }
+
+        For user-specified ``axes``, the order of the characters in the
+        dictionary keys map to the specified ``axes``.
+
+        If ``trim_approx`` is ``True``, the first element of the list contains
+        the array of approximation coefficients from the final level of
+        decomposition, while the remaining coefficient dictionaries contain
+        only detail coefficients. This matches the behavior of `pywt.wavedecn`.
+
+    Notes
+    -----
+    The implementation here follows the "algorithm a-trous" and requires that
+    the signal length along the transformed axes be a multiple of ``2**level``.
+    If this is not the case, the user should pad up to an appropriate size
+    using a function such as ``numpy.pad``.
+
+    A primary benefit of this transform in comparison to its decimated
+    counterpart (``pywt.wavedecn``), is that it is shift-invariant. This comes
+    at cost of redundancy in the transform (the size of the output coefficients
+    is larger than the input).
+
+    When the following three conditions are true:
+
+        1. The wavelet is orthogonal
+        2. ``swtn`` is called with ``norm=True``
+        3. ``swtn`` is called with ``trim_approx=True``
+
+    the transform has the following additional properties that may be
+    desirable in applications:
+
+        1. energy is conserved
+        2. variance is partitioned across scales
+
+    """
+    data = np.asarray(data)
+    if not _have_c99_complex and np.iscomplexobj(data):
+        real = swtn(data.real, wavelet, level, start_level, axes, trim_approx)
+        imag = swtn(data.imag, wavelet, level, start_level, axes, trim_approx)
+        if trim_approx:
+            cplx = [real[0] + 1j * imag[0]]
+            offset = 1
+        else:
+            cplx = []
+            offset = 0
+        for rdict, idict in zip(real[offset:], imag[offset:]):
+            cplx.append(
+                dict((k, rdict[k] + 1j * idict[k]) for k in rdict.keys()))
+        return cplx
+
+    if data.dtype == np.dtype('object'):
+        raise TypeError("Input must be a numeric array-like")
+    if data.ndim < 1:
+        raise ValueError("Input data must be at least 1D")
+
+    if axes is None:
+        axes = range(data.ndim)
+    axes = [a + data.ndim if a < 0 else a for a in axes]
+    if len(axes) != len(set(axes)):
+        raise ValueError("The axes passed to swtn must be unique.")
+    num_axes = len(axes)
+
+    wavelets = _wavelets_per_axis(wavelet, axes)
+    if norm:
+        if not np.all([wav.orthogonal for wav in wavelets]):
+            warnings.warn(
+                "norm=True, but the wavelets used are not orthogonal: \n"
+                "\tThe conditions for energy preservation are not satisfied.")
+        wavelets = [_rescale_wavelet_filterbank(wav, 1/np.sqrt(2))
+                    for wav in wavelets]
+    ret = []
+    for i in range(start_level, start_level + level):
+        coeffs = [('', data)]
+        for axis, wavelet in zip(axes, wavelets):
+            new_coeffs = []
+            for subband, x in coeffs:
+                cA, cD = _swt_axis(x, wavelet, level=1, start_level=i,
+                                   axis=axis)[0]
+                new_coeffs.extend([(subband + 'a', cA),
+                                   (subband + 'd', cD)])
+            coeffs = new_coeffs
+
+        coeffs = dict(coeffs)
+        ret.append(coeffs)
+
+        # data for the next level is the approximation coeffs from this level
+        data = coeffs['a' * num_axes]
+        if trim_approx:
+            coeffs.pop('a' * num_axes)
+    if trim_approx:
+        ret.append(data)
+    ret.reverse()
+    return ret
+
+
+def iswtn(coeffs, wavelet, axes=None, norm=False):
+    """
+    Multilevel nD inverse discrete stationary wavelet transform.
+
+    Parameters
+    ----------
+    coeffs : list
+        [{coeffs_level_n}, ..., {coeffs_level_1}]: list of dict
+    wavelet : Wavelet object or name string, or tuple of wavelets
+        Wavelet to use.  This can also be a tuple of wavelets to apply per
+        axis in ``axes``.
+    axes : sequence of ints, optional
+        Axes over which to compute the inverse SWT. Axes may not be repeated.
+        The default is ``None``, which means transform all axes
+        (``axes = range(data.ndim)``).
+    norm : bool, optional
+        Controls the normalization used by the inverse transform. This must
+        be set equal to the value that was used by ``pywt.swtn`` to preserve
+        the energy of a round-trip transform.
+
+    Returns
+    -------
+    nD array of reconstructed data.
+
+    Examples
+    --------
+    >>> import pywt
+    >>> coeffs = pywt.swtn([[1,2,3,4],[5,6,7,8],
+    ...                     [9,10,11,12],[13,14,15,16]],
+    ...                    'db1', level=2)
+    >>> pywt.iswtn(coeffs, 'db1')
+    array([[  1.,   2.,   3.,   4.],
+           [  5.,   6.,   7.,   8.],
+           [  9.,  10.,  11.,  12.],
+           [ 13.,  14.,  15.,  16.]])
+
+    """
+
+    # key length matches the number of axes transformed
+    ndim_transform = max(len(key) for key in coeffs[-1].keys())
+
+    trim_approx = not isinstance(coeffs[0], dict)
+    if trim_approx:
+        cA = coeffs[0]
+        coeffs = coeffs[1:]
+    else:
+        cA = coeffs[0]['a'*ndim_transform]
+
+    # copy to avoid modification of input data
+    dt = _check_dtype(cA)
+    output = np.array(cA, dtype=dt, copy=True)
+    ndim = output.ndim
+
+    if axes is None:
+        axes = range(output.ndim)
+    axes = [a + ndim if a < 0 else a for a in axes]
+    if len(axes) != len(set(axes)):
+        raise ValueError("The axes passed to swtn must be unique.")
+    if ndim_transform != len(axes):
+        raise ValueError("The number of axes used in iswtn must match the "
+                         "number of dimensions transformed in swtn.")
+
+    # num_levels, equivalent to the decomposition level, n
+    num_levels = len(coeffs)
+    wavelets = _wavelets_per_axis(wavelet, axes)
+    if norm:
+        wavelets = [_rescale_wavelet_filterbank(wav, np.sqrt(2))
+                    for wav in wavelets]
+
+    # initialize various slice objects used in the loops below
+    # these will remain slice(None) only on axes that aren't transformed
+    indices = [slice(None), ]*ndim
+    even_indices = [slice(None), ]*ndim
+    odd_indices = [slice(None), ]*ndim
+    odd_even_slices = [slice(None), ]*ndim
+
+    for j in range(num_levels):
+        step_size = int(pow(2, num_levels-j-1))
+        last_index = step_size
+        if not trim_approx:
+            a = coeffs[j].pop('a'*ndim_transform)  # will restore later
+        details = coeffs[j]
+        # make sure dtype matches the coarsest level approximation coefficients
+        common_dtype = np.result_type(*(
+            [dt, ] + [v.dtype for v in details.values()]))
+        if output.dtype != common_dtype:
+            output = output.astype(common_dtype)
+
+        # We assume all coefficient arrays are of equal size
+        shapes = [v.shape for k, v in details.items()]
+        if len(set(shapes)) != 1:
+            raise RuntimeError(
+                "Mismatch in shape of intermediate coefficient arrays")
+
+        # shape of a single coefficient array, excluding non-transformed axes
+        coeff_trans_shape = tuple([shapes[0][ax] for ax in axes])
+
+        # nested loop over all combinations of axis offsets at this level
+        for firsts in product(*([range(last_index), ]*ndim_transform)):
+            for first, sh, ax in zip(firsts, coeff_trans_shape, axes):
+                indices[ax] = slice(first, sh, step_size)
+                even_indices[ax] = slice(first, sh, 2*step_size)
+                odd_indices[ax] = slice(first+step_size, sh, 2*step_size)
+
+            # nested loop over all combinations of odd/even inidices
+            approx = output.copy()
+            output[tuple(indices)] = 0
+            ntransforms = 0
+            for odds in product(*([(0, 1), ]*ndim_transform)):
+                for o, ax in zip(odds, axes):
+                    if o:
+                        odd_even_slices[ax] = odd_indices[ax]
+                    else:
+                        odd_even_slices[ax] = even_indices[ax]
+                # extract the odd/even indices for all detail coefficients
+                details_slice = {}
+                for key, value in details.items():
+                    details_slice[key] = value[tuple(odd_even_slices)]
+                details_slice['a'*ndim_transform] = approx[
+                    tuple(odd_even_slices)]
+
+                # perform the inverse dwt on the selected indices,
+                # making sure to use periodic boundary conditions
+                x = idwtn(details_slice, wavelets, 'periodization', axes=axes)
+                for o, ax in zip(odds, axes):
+                    # circular shift along any odd indexed axis
+                    if o:
+                        x = np.roll(x, 1, axis=ax)
+                output[tuple(indices)] += x
+                ntransforms += 1
+            output[tuple(indices)] /= ntransforms  # normalize
+        if not trim_approx:
+            coeffs[j]['a'*ndim_transform] = a  # restore approx coeffs to dict
+    return output

venv/Lib/site-packages/pywt/_thresholding.py

@@ -0,0 +1,250 @@
+# Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
+# Copyright (c) 2012-2016 The PyWavelets Developers
+#                         <https://github.com/PyWavelets/pywt>
+# See COPYING for license details.
+
+"""
+The thresholding helper module implements the most popular signal thresholding
+functions.
+"""
+
+from __future__ import division, print_function, absolute_import
+import numpy as np
+
+__all__ = ['threshold', 'threshold_firm']
+
+
+def soft(data, value, substitute=0):
+    data = np.asarray(data)
+    magnitude = np.absolute(data)
+
+    with np.errstate(divide='ignore'):
+        # divide by zero okay as np.inf values get clipped, so ignore warning.
+        thresholded = (1 - value/magnitude)
+        thresholded.clip(min=0, max=None, out=thresholded)
+        thresholded = data * thresholded
+
+    if substitute == 0:
+        return thresholded
+    else:
+        cond = np.less(magnitude, value)
+        return np.where(cond, substitute, thresholded)
+
+
+def nn_garrote(data, value, substitute=0):
+    """Non-negative Garrote."""
+    data = np.asarray(data)
+    magnitude = np.absolute(data)
+
+    with np.errstate(divide='ignore'):
+        # divide by zero okay as np.inf values get clipped, so ignore warning.
+        thresholded = (1 - value**2/magnitude**2)
+        thresholded.clip(min=0, max=None, out=thresholded)
+        thresholded = data * thresholded
+
+    if substitute == 0:
+        return thresholded
+    else:
+        cond = np.less(magnitude, value)
+        return np.where(cond, substitute, thresholded)
+
+
+def hard(data, value, substitute=0):
+    data = np.asarray(data)
+    cond = np.less(np.absolute(data), value)
+    return np.where(cond, substitute, data)
+
+
+def greater(data, value, substitute=0):
+    data = np.asarray(data)
+    if np.iscomplexobj(data):
+        raise ValueError("greater thresholding only supports real data")
+    return np.where(np.less(data, value), substitute, data)
+
+
+def less(data, value, substitute=0):
+    data = np.asarray(data)
+    if np.iscomplexobj(data):
+        raise ValueError("less thresholding only supports real data")
+    return np.where(np.greater(data, value), substitute, data)
+
+
+thresholding_options = {'soft': soft,
+                        'hard': hard,
+                        'greater': greater,
+                        'less': less,
+                        'garrote': nn_garrote,
+                        # misspelled garrote for backwards compatibility
+                        'garotte': nn_garrote,
+                        }
+
+
+def threshold(data, value, mode='soft', substitute=0):
+    """
+    Thresholds the input data depending on the mode argument.
+
+    In ``soft`` thresholding [1]_, data values with absolute value less than
+    `param` are replaced with `substitute`. Data values with absolute value
+    greater or equal to the thresholding value are shrunk toward zero
+    by `value`.  In other words, the new value is
+    ``data/np.abs(data) * np.maximum(np.abs(data) - value, 0)``.
+
+    In ``hard`` thresholding, the data values where their absolute value is
+    less than the value param are replaced with `substitute`. Data values with
+    absolute value greater or equal to the thresholding value stay untouched.
+
+    ``garrote`` corresponds to the Non-negative garrote threshold [2]_, [3]_.
+    It is intermediate between ``hard`` and ``soft`` thresholding.  It behaves
+    like soft thresholding for small data values and approaches hard
+    thresholding for large data values.
+
+    In ``greater`` thresholding, the data is replaced with `substitute` where
+    data is below the thresholding value. Greater data values pass untouched.
+
+    In ``less`` thresholding, the data is replaced with `substitute` where data
+    is above the thresholding value. Lesser data values pass untouched.
+
+    Both ``hard`` and ``soft`` thresholding also support complex-valued data.
+
+    Parameters
+    ----------
+    data : array_like
+        Numeric data.
+    value : scalar
+        Thresholding value.
+    mode : {'soft', 'hard', 'garrote', 'greater', 'less'}
+        Decides the type of thresholding to be applied on input data. Default
+        is 'soft'.
+    substitute : float, optional
+        Substitute value (default: 0).
+
+    Returns
+    -------
+    output : array
+        Thresholded array.
+
+    See Also
+    --------
+    threshold_firm
+
+    References
+    ----------
+    .. [1] D.L. Donoho and I.M. Johnstone. Ideal Spatial Adaptation via
+        Wavelet Shrinkage. Biometrika. Vol. 81, No. 3, pp.425-455, 1994.
+        DOI:10.1093/biomet/81.3.425
+    .. [2] L. Breiman. Better Subset Regression Using the Nonnegative Garrote.
+        Technometrics, Vol. 37, pp. 373-384, 1995.
+        DOI:10.2307/1269730
+    .. [3] H-Y. Gao.  Wavelet Shrinkage Denoising Using the Non-Negative
+        Garrote.  Journal of Computational and Graphical Statistics Vol. 7,
+        No. 4, pp.469-488. 1998.
+        DOI:10.1080/10618600.1998.10474789
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import pywt
+    >>> data = np.linspace(1, 4, 7)
+    >>> data
+    array([ 1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ])
+    >>> pywt.threshold(data, 2, 'soft')
+    array([ 0. ,  0. ,  0. ,  0.5,  1. ,  1.5,  2. ])
+    >>> pywt.threshold(data, 2, 'hard')
+    array([ 0. ,  0. ,  2. ,  2.5,  3. ,  3.5,  4. ])
+    >>> pywt.threshold(data, 2, 'garrote')
+    array([ 0.        ,  0.        ,  0.        ,  0.9       ,  1.66666667,
+            2.35714286,  3.        ])
+    >>> pywt.threshold(data, 2, 'greater')
+    array([ 0. ,  0. ,  2. ,  2.5,  3. ,  3.5,  4. ])
+    >>> pywt.threshold(data, 2, 'less')
+    array([ 1. ,  1.5,  2. ,  0. ,  0. ,  0. ,  0. ])
+
+    """
+
+    try:
+        return thresholding_options[mode](data, value, substitute)
+    except KeyError:
+        # Make sure error is always identical by sorting keys
+        keys = ("'{0}'".format(key) for key in
+                sorted(thresholding_options.keys()))
+        raise ValueError("The mode parameter only takes values from: {0}."
+                         .format(', '.join(keys)))
+
+
+def threshold_firm(data, value_low, value_high):
+    """Firm threshold.
+
+    The approach is intermediate between soft and hard thresholding [1]_. It
+    behaves the same as soft-thresholding for values below `value_low` and
+    the same as hard-thresholding for values above `thresh_high`.  For
+    intermediate values, the thresholded value is in between that corresponding
+    to soft or hard thresholding.
+
+    Parameters
+    ----------
+    data : array-like
+        The data to threshold.  This can be either real or complex-valued.
+    value_low : float
+        Any values smaller then `value_low` will be set to zero.
+    value_high : float
+        Any values larger than `value_high` will not be modified.
+
+    Notes
+    -----
+    This thresholding technique is also known as semi-soft thresholding [2]_.
+
+    For each value, `x`, in `data`. This function computes::
+
+        if np.abs(x) <= value_low:
+            return 0
+        elif np.abs(x) > value_high:
+            return x
+        elif value_low < np.abs(x) and np.abs(x) <= value_high:
+            return x * value_high * (1 - value_low/x)/(value_high - value_low)
+
+    ``firm`` is a continuous function (like soft thresholding), but is
+    unbiased for large values (like hard thresholding).
+
+    If ``value_high == value_low`` this function becomes hard-thresholding.
+    If ``value_high`` is infinity, this function becomes soft-thresholding.
+
+    Returns
+    -------
+    val_new : array-like
+        The values after firm thresholding at the specified thresholds.
+
+    See Also
+    --------
+    threshold
+
+    References
+    ----------
+    .. [1] H.-Y. Gao and A.G. Bruce. Waveshrink with firm shrinkage.
+        Statistica Sinica, Vol. 7, pp. 855-874, 1997.
+    .. [2] A. Bruce and H-Y. Gao. WaveShrink: Shrinkage Functions and
+        Thresholds. Proc. SPIE 2569, Wavelet Applications in Signal and
+        Image Processing III, 1995.
+        DOI:10.1117/12.217582
+    """
+
+    if value_low < 0:
+        raise ValueError("value_low must be non-negative.")
+
+    if value_high < value_low:
+        raise ValueError(
+            "value_high must be greater than or equal to value_low.")
+
+    data = np.asarray(data)
+    magnitude = np.absolute(data)
+    with np.errstate(divide='ignore'):
+        # divide by zero okay as np.inf values get clipped, so ignore warning.
+        vdiff = value_high - value_low
+        thresholded = value_high * (1 - value_low/magnitude) / vdiff
+        thresholded.clip(min=0, max=None, out=thresholded)
+        thresholded = data * thresholded
+
+    # restore hard-thresholding behavior for values > value_high
+    large_vals = np.where(magnitude > value_high)
+    if np.any(large_vals[0]):
+        thresholded[large_vals] = data[large_vals]
+    return thresholded

venv/Lib/site-packages/pywt/_utils.py

@@ -0,0 +1,101 @@
+# Copyright (c) 2017 The PyWavelets Developers
+#                    <https://github.com/PyWavelets/pywt>
+# See COPYING for license details.
+import inspect
+import numpy as np
+import sys
+from collections.abc import Iterable
+
+from ._extensions._pywt import (Wavelet, ContinuousWavelet,
+                                DiscreteContinuousWavelet, Modes)
+
+
+# define string_types as in six for Python 2/3 compatibility
+if sys.version_info[0] == 3:
+    string_types = str,
+else:
+    string_types = basestring,
+
+
+def _as_wavelet(wavelet):
+    """Convert wavelet name to a Wavelet object."""
+    if not isinstance(wavelet, (ContinuousWavelet, Wavelet)):
+        wavelet = DiscreteContinuousWavelet(wavelet)
+    if isinstance(wavelet, ContinuousWavelet):
+        raise ValueError(
+            "A ContinuousWavelet object was provided, but only discrete "
+            "Wavelet objects are supported by this function.  A list of all "
+            "supported discrete wavelets can be obtained by running:\n"
+            "print(pywt.wavelist(kind='discrete'))")
+    return wavelet
+
+
+def _wavelets_per_axis(wavelet, axes):
+    """Initialize Wavelets for each axis to be transformed.
+
+    Parameters
+    ----------
+    wavelet : Wavelet or tuple of Wavelets
+        If a single Wavelet is provided, it will used for all axes.  Otherwise
+        one Wavelet per axis must be provided.
+    axes : list
+        The tuple of axes to be transformed.
+
+    Returns
+    -------
+    wavelets : list of Wavelet objects
+        A tuple of Wavelets equal in length to ``axes``.
+
+    """
+    axes = tuple(axes)
+    if isinstance(wavelet, string_types + (Wavelet, )):
+        # same wavelet on all axes
+        wavelets = [_as_wavelet(wavelet), ] * len(axes)
+    elif isinstance(wavelet, Iterable):
+        # (potentially) unique wavelet per axis (e.g. for dual-tree DWT)
+        if len(wavelet) == 1:
+            wavelets = [_as_wavelet(wavelet[0]), ] * len(axes)
+        else:
+            if len(wavelet) != len(axes):
+                raise ValueError((
+                    "The number of wavelets must match the number of axes "
+                    "to be transformed."))
+            wavelets = [_as_wavelet(w) for w in wavelet]
+    else:
+        raise ValueError("wavelet must be a str, Wavelet or iterable")
+    return wavelets
+
+
+def _modes_per_axis(modes, axes):
+    """Initialize mode for each axis to be transformed.
+
+    Parameters
+    ----------
+    modes : str or tuple of strings
+        If a single mode is provided, it will used for all axes.  Otherwise
+        one mode per axis must be provided.
+    axes : tuple
+        The tuple of axes to be transformed.
+
+    Returns
+    -------
+    modes : tuple of int
+        A tuple of Modes equal in length to ``axes``.
+
+    """
+    axes = tuple(axes)
+    if isinstance(modes, string_types + (int, )):
+        # same wavelet on all axes
+        modes = [Modes.from_object(modes), ] * len(axes)
+    elif isinstance(modes, Iterable):
+        if len(modes) == 1:
+            modes = [Modes.from_object(modes[0]), ] * len(axes)
+        else:
+            # (potentially) unique wavelet per axis (e.g. for dual-tree DWT)
+            if len(modes) != len(axes):
+                raise ValueError(("The number of modes must match the number "
+                                  "of axes to be transformed."))
+        modes = [Modes.from_object(mode) for mode in modes]
+    else:
+        raise ValueError("modes must be a str, Mode enum or iterable")
+    return modes

venv/Lib/site-packages/pywt/_wavelet_packets.py

@@ -0,0 +1,733 @@
+# Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
+# Copyright (c) 2012-2016 The PyWavelets Developers
+#                         <https://github.com/PyWavelets/pywt>
+# See COPYING for license details.
+
+"""1D and 2D Wavelet packet transform module."""
+
+from __future__ import division, print_function, absolute_import
+
+__all__ = ["BaseNode", "Node", "WaveletPacket", "Node2D", "WaveletPacket2D"]
+
+import numpy as np
+
+from ._extensions._pywt import Wavelet, _check_dtype
+from ._dwt import dwt, idwt, dwt_max_level
+from ._multidim import dwt2, idwt2
+
+
+def get_graycode_order(level, x='a', y='d'):
+    graycode_order = [x, y]
+    for i in range(level - 1):
+        graycode_order = [x + path for path in graycode_order] + \
+                         [y + path for path in graycode_order[::-1]]
+    return graycode_order
+
+
+class BaseNode(object):
+    """
+    BaseNode for wavelet packet 1D and 2D tree nodes.
+
+    The BaseNode is a base class for `Node` and `Node2D`.
+    It should not be used directly unless creating a new transformation
+    type. It is included here to document the common interface of 1D
+    and 2D node and wavelet packet transform classes.
+
+    Parameters
+    ----------
+    parent :
+        Parent node. If parent is None then the node is considered detached
+        (ie root).
+    data : 1D or 2D array
+        Data associated with the node. 1D or 2D numeric array, depending on the
+        transform type.
+    node_name :
+        A name identifying the coefficients type.
+        See `Node.node_name` and `Node2D.node_name`
+        for information on the accepted subnodes names.
+    """
+
+    # PART_LEN and PARTS attributes that define path tokens for node[] lookup
+    # must be defined in subclasses.
+    PART_LEN = None
+    PARTS = None
+
+    def __init__(self, parent, data, node_name):
+        self.parent = parent
+        if parent is not None:
+            self.wavelet = parent.wavelet
+            self.mode = parent.mode
+            self.level = parent.level + 1
+            self._maxlevel = parent.maxlevel
+            self.path = parent.path + node_name
+        else:
+            self.wavelet = None
+            self.mode = None
+            self.path = ""
+            self.level = 0
+
+        # data - signal on level 0, coeffs on higher levels
+        self.data = data
+        # Need to retain original data size/shape so we can trim any excess
+        # boundary coefficients from the inverse transform.
+        if self.data is None:
+            self._data_shape = None
+        else:
+            self._data_shape = np.asarray(data).shape
+
+        self._init_subnodes()
+
+    def _init_subnodes(self):
+        for part in self.PARTS:
+            self._set_node(part, None)
+
+    def _create_subnode(self, part, data=None, overwrite=True):
+        raise NotImplementedError()
+
+    def _create_subnode_base(self, node_cls, part, data=None, overwrite=True):
+        self._validate_node_name(part)
+        if not overwrite and self._get_node(part) is not None:
+            return self._get_node(part)
+        node = node_cls(self, data, part)
+        self._set_node(part, node)
+        return node
+
+    def _get_node(self, part):
+        return getattr(self, part)
+
+    def _set_node(self, part, node):
+        setattr(self, part, node)
+
+    def _delete_node(self, part):
+        self._set_node(part, None)
+
+    def _validate_node_name(self, part):
+        if part not in self.PARTS:
+            raise ValueError("Subnode name must be in [%s], not '%s'." %
+                             (', '.join("'%s'" % p for p in self.PARTS), part))
+
+    def _evaluate_maxlevel(self, evaluate_from='parent'):
+        """
+        Try to find the value of maximum decomposition level if it is not
+        specified explicitly.
+
+        Parameters
+        ----------
+        evaluate_from : {'parent', 'subnodes'}
+        """
+        assert evaluate_from in ('parent', 'subnodes')
+
+        if self._maxlevel is not None:
+            return self._maxlevel
+        elif self.data is not None:
+            return self.level + dwt_max_level(
+                min(self.data.shape), self.wavelet)
+
+        if evaluate_from == 'parent':
+            if self.parent is not None:
+                return self.parent._evaluate_maxlevel(evaluate_from)
+        elif evaluate_from == 'subnodes':
+            for node_name in self.PARTS:
+                node = getattr(self, node_name, None)
+                if node is not None:
+                    level = node._evaluate_maxlevel(evaluate_from)
+                    if level is not None:
+                        return level
+        return None
+
+    @property
+    def maxlevel(self):
+        if self._maxlevel is not None:
+            return self._maxlevel
+
+        # Try getting the maxlevel from parents first
+        self._maxlevel = self._evaluate_maxlevel(evaluate_from='parent')
+
+        # If not found, check whether it can be evaluated from subnodes
+        if self._maxlevel is None:
+            self._maxlevel = self._evaluate_maxlevel(evaluate_from='subnodes')
+        return self._maxlevel
+
+    @property
+    def node_name(self):
+        return self.path[-self.PART_LEN:]
+
+    def decompose(self):
+        """
+        Decompose node data creating DWT coefficients subnodes.
+
+        Performs Discrete Wavelet Transform on the `~BaseNode.data` and
+        returns transform coefficients.
+
+        Note
+        ----
+        Descends to subnodes and recursively
+        calls `~BaseNode.reconstruct` on them.
+
+        """
+        if self.level < self.maxlevel:
+            return self._decompose()
+        else:
+            raise ValueError("Maximum decomposition level reached.")
+
+    def _decompose(self):
+        raise NotImplementedError()
+
+    def reconstruct(self, update=False):
+        """
+        Reconstruct node from subnodes.
+
+        Parameters
+        ----------
+        update : bool, optional
+            If True, then reconstructed data replaces the current
+            node data (default: False).
+
+        Returns:
+            - original node data if subnodes do not exist
+            - IDWT of subnodes otherwise.
+        """
+        if not self.has_any_subnode:
+            return self.data
+        return self._reconstruct(update)
+
+    def _reconstruct(self):
+        raise NotImplementedError()  # override this in subclasses
+
+    def get_subnode(self, part, decompose=True):
+        """
+        Returns subnode or None (see `decomposition` flag description).
+
+        Parameters
+        ----------
+        part :
+            Subnode name
+        decompose : bool, optional
+            If the param is True and corresponding subnode does not
+            exist, the subnode will be created using coefficients
+            from the DWT decomposition of the current node.
+            (default: True)
+        """
+        self._validate_node_name(part)
+        subnode = self._get_node(part)
+        if subnode is None and decompose and not self.is_empty:
+            self.decompose()
+            subnode = self._get_node(part)
+        return subnode
+
+    def __getitem__(self, path):
+        """
+        Find node represented by the given path.
+
+        Similar to `~BaseNode.get_subnode` method with `decompose=True`, but
+        can access nodes on any level in the decomposition tree.
+
+        Parameters
+        ----------
+        path : str
+            String composed of node names. See `Node.node_name` and
+            `Node2D.node_name` for node naming convention.
+
+        Notes
+        -----
+        If node does not exist yet, it will be created by decomposition of its
+        parent node.
+        """
+        if isinstance(path, str):
+            if (self.maxlevel is not None
+                    and len(path) > self.maxlevel * self.PART_LEN):
+                raise IndexError("Path length is out of range.")
+            if path:
+                return self.get_subnode(path[0:self.PART_LEN], True)[
+                    path[self.PART_LEN:]]
+            else:
+                return self
+        else:
+            raise TypeError("Invalid path parameter type - expected string but"
+                            " got %s." % type(path))
+
+    def __setitem__(self, path, data):
+        """
+        Set node or node's data in the decomposition tree. Nodes are
+        identified by string `path`.
+
+        Parameters
+        ----------
+        path : str
+            String composed of node names.
+        data : array or BaseNode subclass.
+        """
+
+        if isinstance(path, str):
+            if (
+                self.maxlevel is not None
+                and len(self.path) + len(path) > self.maxlevel * self.PART_LEN
+            ):
+                raise IndexError("Path length out of range.")
+            if path:
+                subnode = self.get_subnode(path[0:self.PART_LEN], False)
+                if subnode is None:
+                    self._create_subnode(path[0:self.PART_LEN], None)
+                    subnode = self.get_subnode(path[0:self.PART_LEN], False)
+                subnode[path[self.PART_LEN:]] = data
+            else:
+                if isinstance(data, BaseNode):
+                    self.data = np.asarray(data.data)
+                else:
+                    self.data = np.asarray(data)
+                # convert data to nearest supported dtype
+                dtype = _check_dtype(data)
+                if self.data.dtype != dtype:
+                    self.data = self.data.astype(dtype)
+        else:
+            raise TypeError("Invalid path parameter type - expected string but"
+                            " got %s." % type(path))
+
+    def __delitem__(self, path):
+        """
+        Remove node from the tree.
+
+        Parameters
+        ----------
+        path : str
+            String composed of node names.
+        """
+        node = self[path]
+        # don't clear node value and subnodes (node may still exist outside
+        # the tree)
+        # # node._init_subnodes()
+        # # node.data = None
+        parent = node.parent
+        node.parent = None  # TODO
+        if parent and node.node_name:
+            parent._delete_node(node.node_name)
+
+    @property
+    def is_empty(self):
+        return self.data is None
+
+    @property
+    def has_any_subnode(self):
+        for part in self.PARTS:
+            if self._get_node(part) is not None:  # and not .is_empty
+                return True
+        return False
+
+    def get_leaf_nodes(self, decompose=False):
+        """
+        Returns leaf nodes.
+
+        Parameters
+        ----------
+        decompose : bool, optional
+            (default: True)
+        """
+        result = []
+
+        def collect(node):
+            if node.level == node.maxlevel and not node.is_empty:
+                result.append(node)
+                return False
+            if not decompose and not node.has_any_subnode:
+                result.append(node)
+                return False
+            return True
+        self.walk(collect, decompose=decompose)
+        return result
+
+    def walk(self, func, args=(), kwargs=None, decompose=True):
+        """
+        Traverses the decomposition tree and calls
+        ``func(node, *args, **kwargs)`` on every node. If `func` returns True,
+        descending to subnodes will continue.
+
+        Parameters
+        ----------
+        func : callable
+            Callable accepting `BaseNode` as the first param and
+            optional positional and keyword arguments
+        args :
+            func params
+        kwargs :
+            func keyword params
+        decompose : bool, optional
+            If True (default), the method will also try to decompose the tree
+            up to the `maximum level <BaseNode.maxlevel>`.
+        """
+        if kwargs is None:
+            kwargs = {}
+        if func(self, *args, **kwargs) and self.level < self.maxlevel:
+            for part in self.PARTS:
+                subnode = self.get_subnode(part, decompose)
+                if subnode is not None:
+                    subnode.walk(func, args, kwargs, decompose)
+
+    def walk_depth(self, func, args=(), kwargs=None, decompose=True):
+        """
+        Walk tree and call func on every node starting from the bottom-most
+        nodes.
+
+        Parameters
+        ----------
+        func : callable
+            Callable accepting :class:`BaseNode` as the first param and
+            optional positional and keyword arguments
+        args :
+            func params
+        kwargs :
+            func keyword params
+        decompose : bool, optional
+            (default: False)
+        """
+        if kwargs is None:
+            kwargs = {}
+        if self.level < self.maxlevel:
+            for part in self.PARTS:
+                subnode = self.get_subnode(part, decompose)
+                if subnode is not None:
+                    subnode.walk_depth(func, args, kwargs, decompose)
+        func(self, *args, **kwargs)
+
+    def __str__(self):
+        return self.path + ": " + str(self.data)
+
+
+class Node(BaseNode):
+    """
+    WaveletPacket tree node.
+
+    Subnodes are called `a` and `d`, just like approximation
+    and detail coefficients in the Discrete Wavelet Transform.
+    """
+
+    A = 'a'
+    D = 'd'
+    PARTS = A, D
+    PART_LEN = 1
+
+    def _create_subnode(self, part, data=None, overwrite=True):
+        return self._create_subnode_base(node_cls=Node, part=part, data=data,
+                                         overwrite=overwrite)
+
+    def _decompose(self):
+        """
+
+        See also
+        --------
+        dwt : for 1D Discrete Wavelet Transform output coefficients.
+        """
+        if self.is_empty:
+            data_a, data_d = None, None
+            if self._get_node(self.A) is None:
+                self._create_subnode(self.A, data_a)
+            if self._get_node(self.D) is None:
+                self._create_subnode(self.D, data_d)
+        else:
+            data_a, data_d = dwt(self.data, self.wavelet, self.mode)
+            self._create_subnode(self.A, data_a)
+            self._create_subnode(self.D, data_d)
+        return self._get_node(self.A), self._get_node(self.D)
+
+    def _reconstruct(self, update):
+        data_a, data_d = None, None
+        node_a, node_d = self._get_node(self.A), self._get_node(self.D)
+
+        if node_a is not None:
+            data_a = node_a.reconstruct()  # TODO: (update) ???
+        if node_d is not None:
+            data_d = node_d.reconstruct()  # TODO: (update) ???
+
+        if data_a is None and data_d is None:
+            raise ValueError("Node is a leaf node and cannot be reconstructed"
+                             " from subnodes.")
+        else:
+            rec = idwt(data_a, data_d, self.wavelet, self.mode)
+            if self._data_shape is not None and (
+                    rec.shape != self._data_shape):
+                rec = rec[tuple([slice(sz) for sz in self._data_shape])]
+            if update:
+                self.data = rec
+            return rec
+
+
+class Node2D(BaseNode):
+    """
+    WaveletPacket tree node.
+
+    Subnodes are called 'a' (LL), 'h' (HL), 'v' (LH) and  'd' (HH), like
+    approximation and detail coefficients in the 2D Discrete Wavelet Transform
+    """
+
+    LL = 'a'
+    HL = 'h'
+    LH = 'v'
+    HH = 'd'
+
+    PARTS = LL, HL, LH, HH
+    PART_LEN = 1
+
+    def _create_subnode(self, part, data=None, overwrite=True):
+        return self._create_subnode_base(node_cls=Node2D, part=part, data=data,
+                                         overwrite=overwrite)
+
+    def _decompose(self):
+        """
+        See also
+        --------
+        dwt2 : for 2D Discrete Wavelet Transform output coefficients.
+        """
+        if self.is_empty:
+            data_ll, data_lh, data_hl, data_hh = None, None, None, None
+        else:
+            data_ll, (data_hl, data_lh, data_hh) =\
+                dwt2(self.data, self.wavelet, self.mode)
+        self._create_subnode(self.LL, data_ll)
+        self._create_subnode(self.LH, data_lh)
+        self._create_subnode(self.HL, data_hl)
+        self._create_subnode(self.HH, data_hh)
+        return (self._get_node(self.LL), self._get_node(self.HL),
+                self._get_node(self.LH), self._get_node(self.HH))
+
+    def _reconstruct(self, update):
+        data_ll, data_lh, data_hl, data_hh = None, None, None, None
+
+        node_ll, node_lh, node_hl, node_hh =\
+            self._get_node(self.LL), self._get_node(self.LH),\
+            self._get_node(self.HL), self._get_node(self.HH)
+
+        if node_ll is not None:
+            data_ll = node_ll.reconstruct()
+        if node_lh is not None:
+            data_lh = node_lh.reconstruct()
+        if node_hl is not None:
+            data_hl = node_hl.reconstruct()
+        if node_hh is not None:
+            data_hh = node_hh.reconstruct()
+
+        if (data_ll is None and data_lh is None
+                and data_hl is None and data_hh is None):
+            raise ValueError(
+                "Tree is missing data - all subnodes of `%s` node "
+                "are None. Cannot reconstruct node." % self.path
+            )
+        else:
+            coeffs = data_ll, (data_hl, data_lh, data_hh)
+            rec = idwt2(coeffs, self.wavelet, self.mode)
+            if self._data_shape is not None and (
+                    rec.shape != self._data_shape):
+                rec = rec[tuple([slice(sz) for sz in self._data_shape])]
+            if update:
+                self.data = rec
+            return rec
+
+    def expand_2d_path(self, path):
+        expanded_paths = {
+            self.HH: 'hh',
+            self.HL: 'hl',
+            self.LH: 'lh',
+            self.LL: 'll'
+        }
+        return (''.join([expanded_paths[p][0] for p in path]),
+                ''.join([expanded_paths[p][1] for p in path]))
+
+
+class WaveletPacket(Node):
+    """
+    Data structure representing Wavelet Packet decomposition of signal.
+
+    Parameters
+    ----------
+    data : 1D ndarray
+        Original data (signal)
+    wavelet : Wavelet object or name string
+        Wavelet used in DWT decomposition and reconstruction
+    mode : str, optional
+        Signal extension mode for the `dwt` and `idwt` decomposition and
+        reconstruction functions.
+    maxlevel : int, optional
+        Maximum level of decomposition.
+        If None, it will be calculated based on the `wavelet` and `data`
+        length using `pywt.dwt_max_level`.
+    """
+    def __init__(self, data, wavelet, mode='symmetric', maxlevel=None):
+        super(WaveletPacket, self).__init__(None, data, "")
+
+        if not isinstance(wavelet, Wavelet):
+            wavelet = Wavelet(wavelet)
+        self.wavelet = wavelet
+        self.mode = mode
+
+        if data is not None:
+            data = np.asarray(data)
+            assert data.ndim == 1
+            self.data_size = data.shape[0]
+            if maxlevel is None:
+                maxlevel = dwt_max_level(self.data_size, self.wavelet)
+        else:
+            self.data_size = None
+
+        self._maxlevel = maxlevel
+
+    def reconstruct(self, update=True):
+        """
+        Reconstruct data value using coefficients from subnodes.
+
+        Parameters
+        ----------
+        update : bool, optional
+            If True (default), then data values will be replaced by
+            reconstruction values, also in subnodes.
+        """
+        if self.has_any_subnode:
+            data = super(WaveletPacket, self).reconstruct(update)
+            if update:
+                self.data = data
+            return data
+        return self.data  # return original data
+
+    def get_level(self, level, order="natural", decompose=True):
+        """
+        Returns all nodes on the specified level.
+
+        Parameters
+        ----------
+        level : int
+            Specifies decomposition `level` from which the nodes will be
+            collected.
+        order : {'natural', 'freq'}, optional
+            - "natural" - left to right in tree (default)
+            - "freq" - band ordered
+        decompose : bool, optional
+            If set then the method will try to decompose the data up
+            to the specified `level` (default: True).
+
+        Notes
+        -----
+        If nodes at the given level are missing (i.e. the tree is partially
+        decomposed) and the `decompose` is set to False, only existing nodes
+        will be returned.
+        """
+        assert order in ["natural", "freq"]
+        if level > self.maxlevel:
+            raise ValueError("The level cannot be greater than the maximum"
+                             " decomposition level value (%d)" % self.maxlevel)
+
+        result = []
+
+        def collect(node):
+            if node.level == level:
+                result.append(node)
+                return False
+            return True
+
+        self.walk(collect, decompose=decompose)
+        if order == "natural":
+            return result
+        elif order == "freq":
+            result = dict((node.path, node) for node in result)
+            graycode_order = get_graycode_order(level)
+            return [result[path] for path in graycode_order if path in result]
+        else:
+            raise ValueError("Invalid order name - %s." % order)
+
+
+class WaveletPacket2D(Node2D):
+    """
+    Data structure representing 2D Wavelet Packet decomposition of signal.
+
+    Parameters
+    ----------
+    data : 2D ndarray
+        Data associated with the node.
+    wavelet : Wavelet object or name string
+        Wavelet used in DWT decomposition and reconstruction
+    mode : str, optional
+        Signal extension mode for the `dwt` and `idwt` decomposition and
+        reconstruction functions.
+    maxlevel : int
+        Maximum level of decomposition.
+        If None, it will be calculated based on the `wavelet` and `data`
+        length using `pywt.dwt_max_level`.
+    """
+    def __init__(self, data, wavelet, mode='smooth', maxlevel=None):
+        super(WaveletPacket2D, self).__init__(None, data, "")
+
+        if not isinstance(wavelet, Wavelet):
+            wavelet = Wavelet(wavelet)
+        self.wavelet = wavelet
+        self.mode = mode
+
+        if data is not None:
+            data = np.asarray(data)
+            assert data.ndim == 2
+            self.data_size = data.shape
+            if maxlevel is None:
+                maxlevel = dwt_max_level(min(self.data_size), self.wavelet)
+        else:
+            self.data_size = None
+        self._maxlevel = maxlevel
+
+    def reconstruct(self, update=True):
+        """
+        Reconstruct data using coefficients from subnodes.
+
+        Parameters
+        ----------
+        update : bool, optional
+            If True (default) then the coefficients of the current node
+            and its subnodes will be replaced with values from reconstruction.
+        """
+        if self.has_any_subnode:
+            data = super(WaveletPacket2D, self).reconstruct(update)
+            if update:
+                self.data = data
+            return data
+        return self.data  # return original data
+
+    def get_level(self, level, order="natural", decompose=True):
+        """
+        Returns all nodes from specified level.
+
+        Parameters
+        ----------
+        level : int
+            Decomposition `level` from which the nodes will be
+            collected.
+        order : {'natural', 'freq'}, optional
+            If `natural` (default) a flat list is returned.
+            If `freq`, a 2d structure with rows and cols
+            sorted by corresponding dimension frequency of 2d
+            coefficient array (adapted from 1d case).
+        decompose : bool, optional
+            If set then the method will try to decompose the data up
+            to the specified `level` (default: True).
+        """
+        assert order in ["natural", "freq"]
+        if level > self.maxlevel:
+            raise ValueError("The level cannot be greater than the maximum"
+                             " decomposition level value (%d)" % self.maxlevel)
+
+        result = []
+
+        def collect(node):
+            if node.level == level:
+                result.append(node)
+                return False
+            return True
+
+        self.walk(collect, decompose=decompose)
+
+        if order == "freq":
+            nodes = {}
+            for (row_path, col_path), node in [
+                (self.expand_2d_path(node.path), node) for node in result
+            ]:
+                nodes.setdefault(row_path, {})[col_path] = node
+            graycode_order = get_graycode_order(level, x='l', y='h')
+            nodes = [nodes[path] for path in graycode_order if path in nodes]
+            result = []
+            for row in nodes:
+                result.append(
+                    [row[path] for path in graycode_order if path in row]
+                )
+        return result

venv/Lib/site-packages/pywt/conftest.py

@@ -0,0 +1,6 @@
+import pytest
+
+
+def pytest_configure(config):
+    config.addinivalue_line("markers",
+                            "slow: Tests that are slow.")

venv/Lib/site-packages/pywt/data/__init__.py

@@ -0,0 +1,2 @@
+from ._readers import ascent, aero, ecg, camera, nino
+from ._wavelab_signals import demo_signal

venv/Lib/site-packages/pywt/data/_readers.py

@@ -0,0 +1,185 @@
+import os
+
+import numpy as np
+
+
+def ascent():
+    """
+    Get an 8-bit grayscale bit-depth, 512 x 512 derived image for
+    easy use in demos
+
+    The image is derived from accent-to-the-top.jpg at
+    http://www.public-domain-image.com/people-public-domain-images-pictures/
+
+    Parameters
+    ----------
+    None
+
+    Returns
+    -------
+    ascent : ndarray
+       convenient image to use for testing and demonstration
+
+    Examples
+    --------
+    >>> import pywt.data
+    >>> ascent = pywt.data.ascent()
+    >>> ascent.shape == (512, 512)
+    True
+    >>> ascent.max()
+    255
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.gray()
+    >>> plt.imshow(ascent) # doctest: +ELLIPSIS
+    <matplotlib.image.AxesImage object at ...>
+    >>> plt.show() # doctest: +SKIP
+
+    """
+    fname = os.path.join(os.path.dirname(__file__), 'ascent.npz')
+    ascent = np.load(fname)['data']
+    return ascent
+
+
+def aero():
+    """
+    Get an 8-bit grayscale bit-depth, 512 x 512 derived image for
+    easy use in demos
+
+    Parameters
+    ----------
+    None
+
+    Returns
+    -------
+    aero : ndarray
+       convenient image to use for testing and demonstration
+
+    Examples
+    --------
+    >>> import pywt.data
+    >>> aero = pywt.data.ascent()
+    >>> aero.shape == (512, 512)
+    True
+    >>> aero.max()
+    255
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.gray()
+    >>> plt.imshow(aero) # doctest: +ELLIPSIS
+    <matplotlib.image.AxesImage object at ...>
+    >>> plt.show() # doctest: +SKIP
+
+    """
+    fname = os.path.join(os.path.dirname(__file__), 'aero.npz')
+    aero = np.load(fname)['data']
+    return aero
+
+
+def camera():
+    """
+    Get an 8-bit grayscale bit-depth, 512 x 512 derived image for
+    easy use in demos
+
+    Parameters
+    ----------
+    None
+
+    Returns
+    -------
+    camera : ndarray
+       convenient image to use for testing and demonstration
+
+    Examples
+    --------
+    >>> import pywt.data
+    >>> camera = pywt.data.ascent()
+    >>> camera.shape == (512, 512)
+    True
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.gray()
+    >>> plt.imshow(camera) # doctest: +ELLIPSIS
+    <matplotlib.image.AxesImage object at ...>
+    >>> plt.show() # doctest: +SKIP
+
+    """
+    fname = os.path.join(os.path.dirname(__file__), 'camera.npz')
+    camera = np.load(fname)['data']
+    return camera
+
+
+def ecg():
+    """
+    Get 1024 points of an ECG timeseries.
+
+    Parameters
+    ----------
+    None
+
+    Returns
+    -------
+    ecg : ndarray
+       convenient timeseries to use for testing and demonstration
+
+    Examples
+    --------
+    >>> import pywt.data
+    >>> ecg = pywt.data.ecg()
+    >>> ecg.shape == (1024,)
+    True
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(ecg) # doctest: +ELLIPSIS
+    [<matplotlib.lines.Line2D object at ...>]
+    >>> plt.show() # doctest: +SKIP
+    """
+    fname = os.path.join(os.path.dirname(__file__), 'ecg.npy')
+    ecg = np.load(fname)
+    return ecg
+
+
+def nino():
+    """
+    This data contains the averaged monthly sea surface temperature in degrees
+    Celcius of the Pacific Ocean, between 0-10 degrees South and 90-80 degrees West, from 1950 to 2016.
+    This dataset is in the public domain and was obtained from NOAA.
+    National Oceanic and Atmospheric Administration's National Weather Service
+    ERSSTv4 dataset, nino 3, http://www.cpc.ncep.noaa.gov/data/indices/
+
+    Parameters
+    ----------
+    None
+
+    Returns
+    -------
+    time : ndarray
+       convenient timeseries to use for testing and demonstration
+    sst : ndarray
+       convenient timeseries to use for testing and demonstration
+
+    Examples
+    --------
+    >>> import pywt.data
+    >>> time, sst = pywt.data.nino()
+    >>> sst.shape == (264,)
+    True
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(time,sst) # doctest: +ELLIPSIS
+    [<matplotlib.lines.Line2D object at ...>]
+    >>> plt.show() # doctest: +SKIP
+    """
+    fname = os.path.join(os.path.dirname(__file__), 'sst_nino3.npz')
+    sst_csv = np.load(fname)['sst_csv']
+    # sst_csv = pd.read_csv("http://www.cpc.ncep.noaa.gov/data/indices/ersst4.nino.mth.81-10.ascii", sep=' ', skipinitialspace=True)
+    # take only full years
+    n = int(np.floor(sst_csv.shape[0]/12.)*12.)
+    # Building the mean of three mounth
+    # the 4. column is nino 3
+    sst = np.mean(np.reshape(np.array(sst_csv)[:n, 4], (n//3, -1)), axis=1)
+    sst = (sst - np.mean(sst)) / np.std(sst, ddof=1)
+
+    dt = 0.25
+    time = np.arange(len(sst)) * dt + 1950.0  # construct time array
+    return time, sst

venv/Lib/site-packages/pywt/data/_wavelab_signals.py

@@ -0,0 +1,259 @@
+# -*- coding:utf-8 -*-
+from __future__ import division
+
+import numpy as np
+
+__all__ = ['demo_signal']
+
+_implemented_signals = [
+    'Blocks',
+    'Bumps',
+    'HeaviSine',
+    'Doppler',
+    'Ramp',
+    'HiSine',
+    'LoSine',
+    'LinChirp',
+    'TwoChirp',
+    'QuadChirp',
+    'MishMash',
+    'WernerSorrows',
+    'HypChirps',
+    'LinChirps',
+    'Chirps',
+    'Gabor',
+    'sineoneoverx',
+    'Piece-Regular',
+    'Piece-Polynomial',
+    'Riemann']
+
+
+def demo_signal(name='Bumps', n=None):
+    """Simple 1D wavelet test functions.
+
+    This function can generate a number of common 1D test signals used in
+    papers by David Donoho and colleagues (e.g. [1]_) as well as the wavelet
+    book by Stéphane Mallat [2]_.
+
+    Parameters
+    ----------
+    name : {'Blocks', 'Bumps', 'HeaviSine', 'Doppler', ...}
+        The type of test signal to generate (`name` is case-insensitive). If
+        `name` is set to `'list'`, a list of the avialable test functions is
+        returned.
+    n : int or None
+        The length of the test signal. This should be provided for all test
+        signals except `'Gabor'` and `'sineoneoverx'` which have a fixed
+        length.
+
+    Returns
+    -------
+    f : np.ndarray
+        Array of length ``n`` corresponding to the specified test signal type.
+
+    References
+    ----------
+    .. [1] D.L. Donoho and I.M. Johnstone.  Ideal spatial adaptation by
+           wavelet shrinkage. Biometrika, vol. 81, pp. 425–455, 1994.
+    .. [2] S. Mallat. A Wavelet Tour of Signal Processing: The Sparse Way.
+           Academic Press. 2009.
+
+    Notes
+    -----
+    This function is a partial reimplementation of the `MakeSignal` function
+    from the [Wavelab](https://statweb.stanford.edu/~wavelab/) toolbox. These
+    test signals are provided with permission of Dr. Donoho to encourage
+    reproducible research.
+
+    """
+    if name.lower() == 'list':
+        return _implemented_signals
+
+    if n is not None:
+        if n < 1 or (n % 1) != 0:
+            raise ValueError("n must be an integer >= 1")
+        t = np.arange(1/n, 1 + 1/n, 1/n)
+
+    # The following function types don't allow user-specified `n`.
+    n_hard_coded = ['gabor', 'sineoneoverx']
+
+    name = name.lower()
+    if name in n_hard_coded and n is not None:
+        raise ValueError(
+            "Parameter n must be set to None when name is {}".format(name))
+    elif n is None and name not in n_hard_coded:
+        raise ValueError(
+            "Parameter n must be provided when name is {}".format(name))
+
+    if name == 'blocks':
+        t0s = [.1, .13, .15, .23, .25, .4, .44, .65, .76, .78, .81]
+        hs = [4, -5, 3, -4, 5, -4.2, 2.1, 4.3, -3.1, 2.1, -4.2]
+        f = 0
+        for (t0, h) in zip(t0s, hs):
+            f += h * (1 + np.sign(t - t0)) / 2
+    elif name == 'bumps':
+        t0s = [.1, .13, .15, .23, .25, .4, .44, .65, .76, .78, .81]
+        hs = [4, 5, 3, 4, 5, 4.2, 2.1, 4.3, 3.1, 5.1, 4.2]
+        ws = [.005, .005, .006, .01, .01, .03, .01, .01, .005, .008, .005]
+        f = 0
+        for (t0, h, w) in zip(t0s, hs, ws):
+            f += h / (1 + np.abs((t - t0) / w))**4
+    elif name == 'heavisine':
+        f = 4 * np.sin(4 * np.pi * t) - np.sign(t - 0.3) - np.sign(0.72 - t)
+    elif name == 'doppler':
+        f = np.sqrt(t * (1 - t)) * np.sin(2 * np.pi * 1.05 / (t + 0.05))
+    elif name == 'ramp':
+        f = t - (t >= .37)
+    elif name == 'hisine':
+        f = np.sin(np.pi * (n * .6902) * t)
+    elif name == 'losine':
+        f = np.sin(np.pi * (n * .3333) * t)
+    elif name == 'linchirp':
+        f = np.sin(np.pi * t * ((n * .500) * t))
+    elif name == 'twochirp':
+        f = np.sin(np.pi * t * (n * t)) + np.sin((np.pi / 3) * t * (n * t))
+    elif name == 'quadchirp':
+        f = np.sin((np.pi / 3) * t * (n * t**2))
+    elif name == 'mishmash':  # QuadChirp + LinChirp + HiSine
+        f = np.sin((np.pi / 3) * t * (n * t**2))
+        f += np.sin(np.pi * (n * .6902) * t)
+        f += np.sin(np.pi * t * (n * .125 * t))
+    elif name == 'wernersorrows':
+        f = np.sin(np.pi * t * (n / 2 * t**2))
+        f = f + np.sin(np.pi * (n * .6902) * t)
+        f = f + np.sin(np.pi * t * (n * t))
+        pos = [.1, .13, .15, .23, .25, .40, .44, .65, .76, .78, .81]
+        hgt = [4, 5, 3, 4, 5, 4.2, 2.1, 4.3, 3.1, 5.1, 4.2]
+        wth = [.005, .005, .006, .01, .01, .03, .01, .01, .005, .008, .005]
+        for p, h, w in zip(pos, hgt, wth):
+            f += h / (1 + np.abs((t - p) / w))**4
+    elif name == 'hypchirps':  # Hyperbolic Chirps of Mallat's book
+        alpha = 15 * n * np.pi / 1024
+        beta = 5 * n * np.pi / 1024
+        t = np.arange(1.001, n + .001 + 1) / n
+        f1 = np.zeros(n)
+        f2 = np.zeros(n)
+        f1 = np.sin(alpha / (.8 - t)) * (0.1 < t) * (t < 0.68)
+        f2 = np.sin(beta / (.8 - t)) * (0.1 < t) * (t < 0.75)
+        m = int(np.round(0.65 * n))
+        p = m // 4
+        envelope = np.ones(m)  # the rinp.sing cutoff function
+        tmp = np.arange(1, p + 1)-np.ones(p)
+        envelope[:p] = (1 + np.sin(-np.pi / 2 + tmp / (p - 1) * np.pi)) / 2
+        envelope[m-p:m] = envelope[:p][::-1]
+        env = np.zeros(n)
+        env[int(np.ceil(n / 10)) - 1:m + int(np.ceil(n / 10)) - 1] = \
+            envelope[:m]
+        f = (f1 + f2) * env
+    elif name == 'linchirps':  # Linear Chirps of Mallat's book
+        b = 100 * n * np.pi / 1024
+        a = 250 * n * np.pi / 1024
+        t = np.arange(1, n + 1) / n
+        A1 = np.sqrt((t - 1 / n) * (1 - t))
+        f = A1 * (np.cos(a * t**2) + np.cos(b * t + a * t**2))
+    elif name == 'chirps':  # Mixture of Chirps of Mallat's book
+        t = np.arange(1, n + 1)/n * 10 * np.pi
+        f1 = np.cos(t**2 * n / 1024)
+        a = 30 * n / 1024
+        t = np.arange(1, n + 1)/n * np.pi
+        f2 = np.cos(a * (t**3))
+        f2 = f2[::-1]
+        ix = np.arange(-n, n + 1) / n * 20
+        g = np.exp(-ix**2 * 4 * n / 1024)
+        i1 = slice(n // 2, n // 2 + n)
+        i2 = slice(n // 8, n // 8 + n)
+        j = np.arange(1, n + 1) / n
+        f3 = g[i1] * np.cos(50 * np.pi * j * n / 1024)
+        f4 = g[i2] * np.cos(350 * np.pi * j * n / 1024)
+        f = f1 + f2 + f3 + f4
+        envelope = np.ones(n)  # the rinp.sing cutoff function
+        tmp = np.arange(1, n // 8 + 1) - np.ones(n // 8)
+        envelope[:n // 8] = (
+            1 + np.sin(-np.pi / 2 + tmp / (n / 8 - 1) * np.pi)) / 2
+        envelope[7 * n // 8:n] = envelope[:n // 8][::-1]
+        f = f*envelope
+    elif name == 'gabor':  # two modulated Gabor functions in Mallat's book
+        n = 512
+        t = np.arange(-n, n + 1)*5 / n
+        j = np.arange(1, n + 1) / n
+        g = np.exp(-t**2 * 20)
+        i1 = slice(2*n // 4, 2 * n // 4 + n)
+        i2 = slice(n // 4, n // 4 + n)
+        f1 = 3 * g[i1] * np.exp(1j * (n // 16) * np.pi * j)
+        f2 = 3 * g[i2] * np.exp(1j * (n // 4) * np.pi * j)
+        f = f1 + f2
+    elif name == 'sineoneoverx':  # np.sin(1/x) in Mallat's book
+        n = 1024
+        i1 = np.arange(-n + 1, n + 1, dtype=float)
+        i1[i1 == 0] = 1 / 100
+        i1 = i1 / (n - 1)
+        f = np.sin(1.5 / i1)
+        f = f[512:1536]
+    elif name == 'piece-regular':
+        f = np.zeros(n)
+        n_12 = int(np.fix(n / 12))
+        n_7 = int(np.fix(n / 7))
+        n_5 = int(np.fix(n / 5))
+        n_3 = int(np.fix(n / 3))
+        n_2 = int(np.fix(n / 2))
+        n_20 = int(np.fix(n / 20))
+        f1 = -15 * demo_signal('bumps', n)
+        t = np.arange(1, n_12 + 1) / n_12
+        f2 = -np.exp(4 * t)
+        t = np.arange(1, n_7 + 1) / n_7
+        f5 = np.exp(4 * t)-np.exp(4)
+        t = np.arange(1, n_3 + 1) / n_3
+        fma = 6 / 40
+        f6 = -70 * np.exp(-((t - 0.5) * (t - 0.5)) / (2 * fma**2))
+        f[:n_7] = f6[:n_7]
+        f[n_7:n_5] = 0.5 * f6[n_7:n_5]
+        f[n_5:n_3] = f6[n_5:n_3]
+        f[n_3:n_2] = f1[n_3:n_2]
+        f[n_2:n_2 + n_12] = f2
+        f[n_2 + 2 * n_12 - 1:n_2 + n_12 - 1:-1] = f2
+        f[n_2 + 2 * n_12 + n_20:n_2 + 2 * n_12 + 3 * n_20] = -np.ones(
+            n_2 + 2*n_12 + 3*n_20 - n_2 - 2*n_12 - n_20) * 25
+        k = n_2 + 2 * n_12 + 3 * n_20
+        f[k:k + n_7] = f5
+        diff = n - 5 * n_5
+        f[5 * n_5:n] = f[diff - 1::-1]
+        # zero-mean
+        bias = np.sum(f) / n
+        f = bias - f
+    elif name == 'piece-polynomial':
+        f = np.zeros(n)
+        n_5 = int(np.fix(n / 5))
+        n_10 = int(np.fix(n / 10))
+        n_20 = int(np.fix(n / 20))
+        t = np.arange(1, n_5 + 1) / n_5
+        f1 = 20 * (t**3 + t**2 + 4)
+        f3 = 40 * (2 * t**3 + t) + 100
+        f2 = 10 * t**3 + 45
+        f4 = 16 * t**2 + 8 * t + 16
+        f5 = 20 * (t + 4)
+        f6 = np.ones(n_10) * 20
+        f[:n_5] = f1
+        f[2 * n_5 - 1:n_5 - 1:-1] = f2
+        f[2 * n_5:3 * n_5] = f3
+        f[3 * n_5:4 * n_5] = f4
+        f[4 * n_5:5 * n_5] = f5[n_5::-1]
+        diff = n - 5*n_5
+        f[5 * n_5:n] = f[diff - 1::-1]
+        f[n_20:n_20 + n_10] = np.ones(n_10) * 10
+        f[n - n_10:n + n_20 - n_10] = np.ones(n_20) * 150
+        # zero-mean
+        bias = np.sum(f) / n
+        f = f - bias
+    elif name == 'riemann':
+        # Riemann's Non-differentiable Function
+        sqn = int(np.round(np.sqrt(n)))
+        idx = np.arange(1, sqn + 1)
+        idx *= idx
+        f = np.zeros_like(t)
+        f[idx - 1] = 1. / np.arange(1, sqn + 1)
+        f = np.real(np.fft.ifft(f))
+    else:
+        raise ValueError(
+            "unknown name: {}.  name must be one of: {}".format(
+                name, _implemented_signals))
+    return f

venv/Lib/site-packages/pywt/data/create_dat.py

@@ -0,0 +1,39 @@
+#!/usr/bin/env python
+
+"""Helper script for creating image .dat files by numpy.save
+
+Usage:
+
+    python create_dat.py <name of image file> <name of dat file>
+
+Example (to create aero.dat):
+
+    python create_dat.py aero.png aero.dat
+
+Requires Scipy and PIL.
+"""
+
+from __future__ import print_function
+
+import sys
+
+import numpy as np
+
+
+def main():
+    from scipy.misc import imread
+
+    if len(sys.argv) != 3:
+        print(__doc__)
+        exit()
+
+    image_fname = sys.argv[1]
+    dat_fname = sys.argv[2]
+
+    data = imread(image_fname)
+
+    np.savez_compressed(dat_fname, data=data)
+
+
+if __name__ == "__main__":
+    main()

venv/Lib/site-packages/pywt/tests/data/generate_matlab_data.py

@@ -0,0 +1,96 @@
+""" This script was used to generate dwt_matlabR2012a_result.npz by storing
+the outputs from Matlab R2012a. """
+
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+import pywt
+
+try:
+    from pymatbridge import Matlab
+    mlab = Matlab()
+    _matlab_missing = False
+except ImportError:
+    print("To run Matlab compatibility tests you need to have MathWorks "
+          "MATLAB, MathWorks Wavelet Toolbox and the pymatbridge Python "
+          "package installed.")
+    _matlab_missing = True
+
+if _matlab_missing:
+    raise EnvironmentError("Can't generate matlab data files without MATLAB")
+
+size_set = 'reduced'
+
+# list of mode names in pywt and matlab
+modes = [('zero', 'zpd'),
+         ('constant', 'sp0'),
+         ('symmetric', 'sym'),
+         ('reflect', 'symw'),
+         ('periodic', 'ppd'),
+         ('smooth', 'sp1'),
+         ('periodization', 'per'),
+         ('antisymmetric', 'asym'),
+         ('antireflect', 'asymw')]
+
+families = ('db', 'sym', 'coif', 'bior', 'rbio')
+wavelets = sum([pywt.wavelist(name) for name in families], [])
+
+rstate = np.random.RandomState(1234)
+mlab.start()
+try:
+    all_matlab_results = {}
+    for wavelet in wavelets:
+        w = pywt.Wavelet(wavelet)
+        mlab.set_variable('wavelet', wavelet)
+        if size_set == 'full':
+            data_sizes = list(range(w.dec_len, 40)) + \
+                [100, 200, 500, 1000, 50000]
+        else:
+            data_sizes = (w.dec_len, w.dec_len + 1)
+        for N in data_sizes:
+            data = rstate.randn(N)
+            mlab.set_variable('data', data)
+            for pmode, mmode in modes:
+                # Matlab result
+                if np.any((wavelet == np.array(['coif6', 'coif7', 'coif8', 'coif9', 'coif10', 'coif11', 'coif12', 'coif13', 'coif14', 'coif15', 'coif16', 'coif17'])),axis=0):
+                    mlab.set_variable('Lo_D', w.dec_lo)
+                    mlab.set_variable('Hi_D', w.dec_hi)
+                    mlab_code = ("[ma, md] = dwt(data, Lo_D, Hi_D, "
+                                 "'mode', '%s');" % mmode)
+                else:
+                    mlab_code = ("[ma, md] = dwt(data, wavelet, "
+                                 "'mode', '%s');" % mmode)
+                res = mlab.run_code(mlab_code)
+                if not res['success']:
+                    raise RuntimeError(
+                        "Matlab failed to execute the provided code. "
+                        "Check that the wavelet toolbox is installed.")
+                # need np.asarray because sometimes the output is type float
+                ma = np.asarray(mlab.get_variable('ma'))
+                md = np.asarray(mlab.get_variable('md'))
+                ma_key = '_'.join([mmode, wavelet, str(N), 'ma'])
+                md_key = '_'.join([mmode, wavelet, str(N), 'md'])
+                all_matlab_results[ma_key] = ma
+                all_matlab_results[md_key] = md
+
+                # Matlab result
+                mlab.set_variable('Lo_D', w.dec_lo)
+                mlab.set_variable('Hi_D', w.dec_hi)
+                mlab_code = ("[ma, md] = dwt(data, Lo_D, Hi_D, "
+                             "'mode', '%s');" % mmode)
+                res = mlab.run_code(mlab_code)
+                if not res['success']:
+                    raise RuntimeError(
+                        "Matlab failed to execute the provided code. "
+                        "Check that the wavelet toolbox is installed.")
+                # need np.asarray because sometimes the output is type float
+                ma = np.asarray(mlab.get_variable('ma'))
+                md = np.asarray(mlab.get_variable('md'))
+                ma_key = '_'.join([mmode, wavelet, str(N), 'ma_pywtCoeffs'])
+                md_key = '_'.join([mmode, wavelet, str(N), 'md_pywtCoeffs'])
+                all_matlab_results[ma_key] = ma
+                all_matlab_results[md_key] = md
+finally:
+    mlab.stop()
+
+np.savez('dwt_matlabR2012a_result.npz', **all_matlab_results)

venv/Lib/site-packages/pywt/tests/data/generate_matlab_data_cwt.py

@@ -0,0 +1,86 @@
+""" This script was used to generate dwt_matlabR2012a_result.npz by storing
+the outputs from Matlab R2012a. """
+
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+import pywt
+
+try:
+    from pymatbridge import Matlab
+    mlab = Matlab()
+    _matlab_missing = False
+except ImportError:
+    print("To run Matlab compatibility tests you need to have MathWorks "
+          "MATLAB, MathWorks Wavelet Toolbox and the pymatbridge Python "
+          "package installed.")
+    _matlab_missing = True
+
+if _matlab_missing:
+    raise EnvironmentError("Can't generate matlab data files without MATLAB")
+
+size_set = 'reduced'
+
+# list of mode names in pywt and matlab
+modes = [('zero', 'zpd'),
+         ('constant', 'sp0'),
+         ('symmetric', 'sym'),
+         ('periodic', 'ppd'),
+         ('smooth', 'sp1'),
+         ('periodization', 'per')]
+
+families = ('gaus', 'mexh', 'morl', 'cgau', 'shan', 'fbsp', 'cmor')
+wavelets = sum([pywt.wavelist(name) for name in families], [])
+
+rstate = np.random.RandomState(1234)
+mlab.start()
+try:
+    all_matlab_results = {}
+    for wavelet in wavelets:
+        w = pywt.ContinuousWavelet(wavelet)
+        if np.any((wavelet == np.array(['shan', 'cmor'])),axis=0):
+            mlab.set_variable('wavelet', wavelet+str(w.bandwidth_frequency)+'-'+str(w.center_frequency))
+        elif wavelet == 'fbsp':
+            mlab.set_variable('wavelet', wavelet+str(w.fbsp_order)+'-'+str(w.bandwidth_frequency)+'-'+str(w.center_frequency))
+        else:
+            mlab.set_variable('wavelet', wavelet)
+        if size_set == 'full':
+            data_sizes = list(range(100, 101)) + \
+                [100, 200, 500, 1000, 50000]
+            Scales = (1,np.arange(1,3),np.arange(1,4),np.arange(1,5))
+        else:
+            data_sizes = (1000, 1000 + 1)
+            Scales = (1,np.arange(1,3))
+        mlab_code = ("psi = wavefun(wavelet,10)")
+        res = mlab.run_code(mlab_code)
+        if not res['success']:
+            raise RuntimeError(
+                "Matlab failed to execute the provided code. "
+                "Check that the wavelet toolbox is installed.")
+        psi = np.asarray(mlab.get_variable('psi'))
+        psi_key = '_'.join([wavelet, 'psi'])
+        all_matlab_results[psi_key] = psi
+        for N in data_sizes:
+            data = rstate.randn(N)
+            mlab.set_variable('data', data)
+
+            # Matlab result
+            scale_count = 0
+            for scales in Scales:
+                scale_count += 1
+                mlab.set_variable('scales', scales)
+                mlab_code = ("coefs = cwt(data, scales, wavelet)")
+                res = mlab.run_code(mlab_code)
+                if not res['success']:
+                    raise RuntimeError(
+                        "Matlab failed to execute the provided code. "
+                        "Check that the wavelet toolbox is installed.")
+                # need np.asarray because sometimes the output is type float
+                coefs = np.asarray(mlab.get_variable('coefs'))
+                coefs_key = '_'.join([str(scale_count), wavelet, str(N), 'coefs'])
+                all_matlab_results[coefs_key] = coefs
+
+finally:
+    mlab.stop()
+
+np.savez('cwt_matlabR2015b_result.npz', **all_matlab_results)

venv/Lib/site-packages/pywt/tests/test__pywt.py

@@ -0,0 +1,170 @@
+#!/usr/bin/env python
+
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_, assert_raises
+
+import pywt
+
+
+def test_upcoef_reconstruct():
+    data = np.arange(3)
+    a = pywt.downcoef('a', data, 'haar')
+    d = pywt.downcoef('d', data, 'haar')
+
+    rec = (pywt.upcoef('a', a, 'haar', take=3) +
+           pywt.upcoef('d', d, 'haar', take=3))
+    assert_allclose(rec, data)
+
+
+def test_downcoef_multilevel():
+    rstate = np.random.RandomState(1234)
+    r = rstate.randn(16)
+    nlevels = 3
+    # calling with level=1 nlevels times
+    a1 = r.copy()
+    for i in range(nlevels):
+        a1 = pywt.downcoef('a', a1, 'haar', level=1)
+    # call with level=nlevels once
+    a3 = pywt.downcoef('a', r, 'haar', level=nlevels)
+    assert_allclose(a1, a3)
+
+
+def test_downcoef_complex():
+    rstate = np.random.RandomState(1234)
+    r = rstate.randn(16) + 1j * rstate.randn(16)
+    nlevels = 3
+    a = pywt.downcoef('a', r, 'haar', level=nlevels)
+    a_ref = pywt.downcoef('a', r.real, 'haar', level=nlevels)
+    a_ref = a_ref + 1j * pywt.downcoef('a', r.imag, 'haar', level=nlevels)
+    assert_allclose(a, a_ref)
+
+
+def test_downcoef_errs():
+    # invalid part string (not 'a' or 'd')
+    assert_raises(ValueError, pywt.downcoef, 'f', np.ones(16), 'haar')
+
+
+def test_compare_downcoef_coeffs():
+    rstate = np.random.RandomState(1234)
+    r = rstate.randn(16)
+    # compare downcoef against wavedec outputs
+    for nlevels in [1, 2, 3]:
+        for wavelet in pywt.wavelist():
+            if wavelet in ['cmor', 'shan', 'fbsp']:
+                # skip these CWT families to avoid warnings
+                continue
+            wavelet = pywt.DiscreteContinuousWavelet(wavelet)
+            if isinstance(wavelet, pywt.Wavelet):
+                max_level = pywt.dwt_max_level(r.size, wavelet.dec_len)
+                if nlevels <= max_level:
+                    a = pywt.downcoef('a', r, wavelet, level=nlevels)
+                    d = pywt.downcoef('d', r, wavelet, level=nlevels)
+                    coeffs = pywt.wavedec(r, wavelet, level=nlevels)
+                    assert_allclose(a, coeffs[0])
+                    assert_allclose(d, coeffs[1])
+
+
+def test_upcoef_multilevel():
+    rstate = np.random.RandomState(1234)
+    r = rstate.randn(4)
+    nlevels = 3
+    # calling with level=1 nlevels times
+    a1 = r.copy()
+    for i in range(nlevels):
+        a1 = pywt.upcoef('a', a1, 'haar', level=1)
+    # call with level=nlevels once
+    a3 = pywt.upcoef('a', r, 'haar', level=nlevels)
+    assert_allclose(a1, a3)
+
+
+def test_upcoef_complex():
+    rstate = np.random.RandomState(1234)
+    r = rstate.randn(4) + 1j*rstate.randn(4)
+    nlevels = 3
+    a = pywt.upcoef('a', r, 'haar', level=nlevels)
+    a_ref = pywt.upcoef('a', r.real, 'haar', level=nlevels)
+    a_ref = a_ref + 1j*pywt.upcoef('a', r.imag, 'haar', level=nlevels)
+    assert_allclose(a, a_ref)
+
+
+def test_upcoef_errs():
+    # invalid part string (not 'a' or 'd')
+    assert_raises(ValueError, pywt.upcoef, 'f', np.ones(4), 'haar')
+
+
+def test_upcoef_and_downcoef_1d_only():
+    # upcoef and downcoef raise a ValueError if data.ndim > 1d
+    for ndim in [2, 3]:
+        data = np.ones((8, )*ndim)
+        assert_raises(ValueError, pywt.downcoef, 'a', data, 'haar')
+        assert_raises(ValueError, pywt.upcoef, 'a', data, 'haar')
+
+
+def test_wavelet_repr():
+    from pywt._extensions import _pywt
+    wavelet = _pywt.Wavelet('sym8')
+
+    repr_wavelet = eval(wavelet.__repr__())
+
+    assert_(wavelet.__repr__() == repr_wavelet.__repr__())
+
+
+def test_dwt_max_level():
+    assert_(pywt.dwt_max_level(16, 2) == 4)
+    assert_(pywt.dwt_max_level(16, 8) == 1)
+    assert_(pywt.dwt_max_level(16, 9) == 1)
+    assert_(pywt.dwt_max_level(16, 10) == 0)
+    assert_(pywt.dwt_max_level(16, np.int8(10)) == 0)
+    assert_(pywt.dwt_max_level(16, 10.) == 0)
+    assert_(pywt.dwt_max_level(16, 18) == 0)
+
+    # accepts discrete Wavelet object or string as well
+    assert_(pywt.dwt_max_level(32, pywt.Wavelet('sym5')) == 1)
+    assert_(pywt.dwt_max_level(32, 'sym5') == 1)
+
+    # string input that is not a discrete wavelet
+    assert_raises(ValueError, pywt.dwt_max_level, 16, 'mexh')
+
+    # filter_len must be an integer >= 2
+    assert_raises(ValueError, pywt.dwt_max_level, 16, 1)
+    assert_raises(ValueError, pywt.dwt_max_level, 16, -1)
+    assert_raises(ValueError, pywt.dwt_max_level, 16, 3.3)
+
+
+def test_ContinuousWavelet_errs():
+    assert_raises(ValueError, pywt.ContinuousWavelet, 'qwertz')
+
+
+def test_ContinuousWavelet_repr():
+    from pywt._extensions import _pywt
+    wavelet = _pywt.ContinuousWavelet('gaus2')
+
+    repr_wavelet = eval(wavelet.__repr__())
+
+    assert_(wavelet.__repr__() == repr_wavelet.__repr__())
+
+
+def test_wavelist():
+    for name in pywt.wavelist(family='coif'):
+        assert_(name.startswith('coif'))
+
+    assert_('cgau7' in pywt.wavelist(kind='continuous'))
+    assert_('sym20' in pywt.wavelist(kind='discrete'))
+    assert_(len(pywt.wavelist(kind='continuous')) +
+            len(pywt.wavelist(kind='discrete')) ==
+            len(pywt.wavelist(kind='all')))
+
+    assert_raises(ValueError, pywt.wavelist, kind='foobar')
+
+
+def test_wavelet_errormsgs():
+    try:
+        pywt.Wavelet('gaus1')
+    except ValueError as e:
+        assert_(e.args[0].startswith('The `Wavelet` class'))
+    try:
+        pywt.Wavelet('cmord')
+    except ValueError as e:
+        assert_(e.args[0] == "Invalid wavelet name 'cmord'.")

venv/Lib/site-packages/pywt/tests/test_concurrent.py

@@ -0,0 +1,105 @@
+"""
+Tests used to verify running PyWavelets transforms in parallel via
+concurrent.futures.ThreadPoolExecutor does not raise errors.
+"""
+
+from __future__ import division, print_function, absolute_import
+
+import warnings
+import numpy as np
+from functools import partial
+from numpy.testing import assert_array_equal, assert_allclose
+from pywt._pytest import uses_futures, futures, max_workers
+
+import pywt
+
+
+def _assert_all_coeffs_equal(coefs1, coefs2):
+    # return True only if all coefficients of SWT or DWT match over all levels
+    if len(coefs1) != len(coefs2):
+        return False
+    for (c1, c2) in zip(coefs1, coefs2):
+        if isinstance(c1, tuple):
+            # for swt, swt2, dwt, dwt2, wavedec, wavedec2
+            for a1, a2 in zip(c1, c2):
+                assert_array_equal(a1, a2)
+        elif isinstance(c1, dict):
+            # for swtn, dwtn, wavedecn
+            for k, v in c1.items():
+                assert_array_equal(v, c2[k])
+        else:
+            return False
+    return True
+
+
+@uses_futures
+def test_concurrent_swt():
+    # tests error-free concurrent operation (see gh-288)
+    # swt on 1D data calls the Cython swt
+    # other cases call swt_axes
+    with warnings.catch_warnings():
+        # can remove catch_warnings once the swt2 FutureWarning is removed
+        warnings.simplefilter('ignore', FutureWarning)
+        for swt_func, x in zip([pywt.swt, pywt.swt2, pywt.swtn],
+                               [np.ones(8), np.eye(16), np.eye(16)]):
+            transform = partial(swt_func, wavelet='haar', level=3)
+            for _ in range(10):
+                arrs = [x.copy() for _ in range(100)]
+                with futures.ThreadPoolExecutor(max_workers=max_workers) as ex:
+                    results = list(ex.map(transform, arrs))
+
+        # validate result from  one of the concurrent runs
+        expected_result = transform(x)
+        _assert_all_coeffs_equal(expected_result, results[-1])
+
+
+@uses_futures
+def test_concurrent_wavedec():
+    # wavedec on 1D data calls the Cython dwt_single
+    # other cases call dwt_axis
+    for wavedec_func, x in zip([pywt.wavedec, pywt.wavedec2, pywt.wavedecn],
+                               [np.ones(8), np.eye(16), np.eye(16)]):
+        transform = partial(wavedec_func, wavelet='haar', level=1)
+        for _ in range(10):
+            arrs = [x.copy() for _ in range(100)]
+            with futures.ThreadPoolExecutor(max_workers=max_workers) as ex:
+                results = list(ex.map(transform, arrs))
+
+        # validate result from  one of the concurrent runs
+        expected_result = transform(x)
+        _assert_all_coeffs_equal(expected_result, results[-1])
+
+
+@uses_futures
+def test_concurrent_dwt():
+    # dwt on 1D data calls the Cython dwt_single
+    # other cases call dwt_axis
+    for dwt_func, x in zip([pywt.dwt, pywt.dwt2, pywt.dwtn],
+                           [np.ones(8), np.eye(16), np.eye(16)]):
+        transform = partial(dwt_func, wavelet='haar')
+        for _ in range(10):
+            arrs = [x.copy() for _ in range(100)]
+            with futures.ThreadPoolExecutor(max_workers=max_workers) as ex:
+                results = list(ex.map(transform, arrs))
+
+        # validate result from  one of the concurrent runs
+        expected_result = transform(x)
+        _assert_all_coeffs_equal([expected_result, ], [results[-1], ])
+
+
+@uses_futures
+def test_concurrent_cwt():
+    atol = rtol = 1e-14
+    time, sst = pywt.data.nino()
+    dt = time[1]-time[0]
+    transform = partial(pywt.cwt, scales=np.arange(1, 4), wavelet='cmor1.5-1',
+                        sampling_period=dt)
+    for _ in range(10):
+        arrs = [sst.copy() for _ in range(50)]
+        with futures.ThreadPoolExecutor(max_workers=max_workers) as ex:
+            results = list(ex.map(transform, arrs))
+
+    # validate result from  one of the concurrent runs
+    expected_result = transform(sst)
+    for a1, a2 in zip(expected_result, results[-1]):
+        assert_allclose(a1, a2, atol=atol, rtol=rtol)

venv/Lib/site-packages/pywt/tests/test_cwt_wavelets.py

@@ -0,0 +1,434 @@
+#!/usr/bin/env python
+from __future__ import division, print_function, absolute_import
+from itertools import product
+
+from numpy.testing import (assert_allclose, assert_warns, assert_almost_equal,
+                           assert_raises, assert_equal)
+import pytest
+import numpy as np
+import pywt
+
+
+def ref_gaus(LB, UB, N, num):
+    X = np.linspace(LB, UB, N)
+    F0 = (2./np.pi)**(1./4.)*np.exp(-(X**2))
+    if (num == 1):
+        psi = -2.*X*F0
+    elif (num == 2):
+        psi = -2/(3**(1/2))*(-1 + 2*X**2)*F0
+    elif (num == 3):
+        psi = -4/(15**(1/2))*X*(3 - 2*X**2)*F0
+    elif (num == 4):
+        psi = 4/(105**(1/2))*(3 - 12*X**2 + 4*X**4)*F0
+    elif (num == 5):
+        psi = 8/(3*(105**(1/2)))*X*(-15 + 20*X**2 - 4*X**4)*F0
+    elif (num == 6):
+        psi = -8/(3*(1155**(1/2)))*(-15 + 90*X**2 - 60*X**4 + 8*X**6)*F0
+    elif (num == 7):
+        psi = -16/(3*(15015**(1/2)))*X*(105 - 210*X**2 + 84*X**4 - 8*X**6)*F0
+    elif (num == 8):
+        psi = 16/(45*(1001**(1/2)))*(105 - 840*X**2 + 840*X**4 -
+                                     224*X**6 + 16*X**8)*F0
+    return (psi, X)
+
+
+def ref_cgau(LB, UB, N, num):
+    X = np.linspace(LB, UB, N)
+    F0 = np.exp(-X**2)
+    F1 = np.exp(-1j*X)
+    F2 = (F1*F0)/(np.exp(-1/2)*2**(1/2)*np.pi**(1/2))**(1/2)
+    if (num == 1):
+        psi = F2*(-1j - 2*X)*2**(1/2)
+    elif (num == 2):
+        psi = 1/3*F2*(-3 + 4j*X + 4*X**2)*6**(1/2)
+    elif (num == 3):
+        psi = 1/15*F2*(7j + 18*X - 12j*X**2 - 8*X**3)*30**(1/2)
+    elif (num == 4):
+        psi = 1/105*F2*(25 - 56j*X - 72*X**2 + 32j*X**3 + 16*X**4)*210**(1/2)
+    elif (num == 5):
+        psi = 1/315*F2*(-81j - 250*X + 280j*X**2 + 240*X**3 -
+                        80j*X**4 - 32*X**5)*210**(1/2)
+    elif (num == 6):
+        psi = 1/3465*F2*(-331 + 972j*X + 1500*X**2 - 1120j*X**3 - 720*X**4 +
+                         192j*X**5 + 64*X**6)*2310**(1/2)
+    elif (num == 7):
+        psi = 1/45045*F2*(
+            1303j + 4634*X - 6804j*X**2 - 7000*X**3 + 3920j*X**4 + 2016*X**5 -
+            448j*X**6 - 128*X**7)*30030**(1/2)
+    elif (num == 8):
+        psi = 1/45045*F2*(
+            5937 - 20848j*X - 37072*X**2 + 36288j*X**3 + 28000*X**4 -
+            12544j*X**5 - 5376*X**6 + 1024j*X**7 + 256*X**8)*2002**(1/2)
+
+    psi = psi/np.real(np.sqrt(np.real(np.sum(psi*np.conj(psi)))*(X[1] - X[0])))
+    return (psi, X)
+
+
+def sinc2(x):
+    y = np.ones_like(x)
+    k = np.where(x)[0]
+    y[k] = np.sin(np.pi*x[k])/(np.pi*x[k])
+    return y
+
+
+def ref_shan(LB, UB, N, Fb, Fc):
+    x = np.linspace(LB, UB, N)
+    psi = np.sqrt(Fb)*(sinc2(Fb*x)*np.exp(2j*np.pi*Fc*x))
+    return (psi, x)
+
+
+def ref_fbsp(LB, UB, N, m, Fb, Fc):
+    x = np.linspace(LB, UB, N)
+    psi = np.sqrt(Fb)*((sinc2(Fb*x/m)**m)*np.exp(2j*np.pi*Fc*x))
+    return (psi, x)
+
+
+def ref_cmor(LB, UB, N, Fb, Fc):
+    x = np.linspace(LB, UB, N)
+    psi = ((np.pi*Fb)**(-0.5))*np.exp(2j*np.pi*Fc*x)*np.exp(-(x**2)/Fb)
+    return (psi, x)
+
+
+def ref_morl(LB, UB, N):
+    x = np.linspace(LB, UB, N)
+    psi = np.exp(-(x**2)/2)*np.cos(5*x)
+    return (psi, x)
+
+
+def ref_mexh(LB, UB, N):
+    x = np.linspace(LB, UB, N)
+    psi = (2/(np.sqrt(3)*np.pi**0.25))*np.exp(-(x**2)/2)*(1 - (x**2))
+    return (psi, x)
+
+
+def test_gaus():
+    LB = -5
+    UB = 5
+    N = 1000
+    for num in np.arange(1, 9):
+        [psi, x] = ref_gaus(LB, UB, N, num)
+        w = pywt.ContinuousWavelet("gaus" + str(num))
+        PSI, X = w.wavefun(length=N)
+
+        assert_allclose(np.real(PSI), np.real(psi))
+        assert_allclose(np.imag(PSI), np.imag(psi))
+        assert_allclose(X, x)
+
+
+def test_cgau():
+    LB = -5
+    UB = 5
+    N = 1000
+    for num in np.arange(1, 9):
+        [psi, x] = ref_cgau(LB, UB, N, num)
+        w = pywt.ContinuousWavelet("cgau" + str(num))
+        PSI, X = w.wavefun(length=N)
+
+        assert_allclose(np.real(PSI), np.real(psi))
+        assert_allclose(np.imag(PSI), np.imag(psi))
+        assert_allclose(X, x)
+
+
+def test_shan():
+    LB = -20
+    UB = 20
+    N = 1000
+    Fb = 1
+    Fc = 1.5
+
+    [psi, x] = ref_shan(LB, UB, N, Fb, Fc)
+    w = pywt.ContinuousWavelet("shan{}-{}".format(Fb, Fc))
+    assert_almost_equal(w.center_frequency, Fc)
+    assert_almost_equal(w.bandwidth_frequency, Fb)
+    w.upper_bound = UB
+    w.lower_bound = LB
+    PSI, X = w.wavefun(length=N)
+
+    assert_allclose(np.real(PSI), np.real(psi), atol=1e-15)
+    assert_allclose(np.imag(PSI), np.imag(psi), atol=1e-15)
+    assert_allclose(X, x, atol=1e-15)
+
+    LB = -20
+    UB = 20
+    N = 1000
+    Fb = 1.5
+    Fc = 1
+
+    [psi, x] = ref_shan(LB, UB, N, Fb, Fc)
+    w = pywt.ContinuousWavelet("shan{}-{}".format(Fb, Fc))
+    assert_almost_equal(w.center_frequency, Fc)
+    assert_almost_equal(w.bandwidth_frequency, Fb)
+    w.upper_bound = UB
+    w.lower_bound = LB
+    PSI, X = w.wavefun(length=N)
+
+    assert_allclose(np.real(PSI), np.real(psi), atol=1e-15)
+    assert_allclose(np.imag(PSI), np.imag(psi), atol=1e-15)
+    assert_allclose(X, x, atol=1e-15)
+
+
+def test_cmor():
+    LB = -20
+    UB = 20
+    N = 1000
+    Fb = 1
+    Fc = 1.5
+
+    [psi, x] = ref_cmor(LB, UB, N, Fb, Fc)
+    w = pywt.ContinuousWavelet("cmor{}-{}".format(Fb, Fc))
+    assert_almost_equal(w.center_frequency, Fc)
+    assert_almost_equal(w.bandwidth_frequency, Fb)
+    w.upper_bound = UB
+    w.lower_bound = LB
+    PSI, X = w.wavefun(length=N)
+
+    assert_allclose(np.real(PSI), np.real(psi), atol=1e-15)
+    assert_allclose(np.imag(PSI), np.imag(psi), atol=1e-15)
+    assert_allclose(X, x, atol=1e-15)
+
+    LB = -20
+    UB = 20
+    N = 1000
+    Fb = 1.5
+    Fc = 1
+
+    [psi, x] = ref_cmor(LB, UB, N, Fb, Fc)
+    w = pywt.ContinuousWavelet("cmor{}-{}".format(Fb, Fc))
+    assert_almost_equal(w.center_frequency, Fc)
+    assert_almost_equal(w.bandwidth_frequency, Fb)
+    w.upper_bound = UB
+    w.lower_bound = LB
+    PSI, X = w.wavefun(length=N)
+
+    assert_allclose(np.real(PSI), np.real(psi), atol=1e-15)
+    assert_allclose(np.imag(PSI), np.imag(psi), atol=1e-15)
+    assert_allclose(X, x, atol=1e-15)
+
+
+def test_fbsp():
+    LB = -20
+    UB = 20
+    N = 1000
+    M = 2
+    Fb = 1
+    Fc = 1.5
+
+    [psi, x] = ref_fbsp(LB, UB, N, M, Fb, Fc)
+
+    w = pywt.ContinuousWavelet("fbsp{}-{}-{}".format(M, Fb, Fc))
+    assert_almost_equal(w.center_frequency, Fc)
+    assert_almost_equal(w.bandwidth_frequency, Fb)
+    w.fbsp_order = M
+    w.upper_bound = UB
+    w.lower_bound = LB
+    PSI, X = w.wavefun(length=N)
+
+    assert_allclose(np.real(PSI), np.real(psi), atol=1e-15)
+    assert_allclose(np.imag(PSI), np.imag(psi), atol=1e-15)
+    assert_allclose(X, x, atol=1e-15)
+
+    LB = -20
+    UB = 20
+    N = 1000
+    M = 2
+    Fb = 1.5
+    Fc = 1
+
+    [psi, x] = ref_fbsp(LB, UB, N, M, Fb, Fc)
+    w = pywt.ContinuousWavelet("fbsp{}-{}-{}".format(M, Fb, Fc))
+    assert_almost_equal(w.center_frequency, Fc)
+    assert_almost_equal(w.bandwidth_frequency, Fb)
+    w.fbsp_order = M
+    w.upper_bound = UB
+    w.lower_bound = LB
+    PSI, X = w.wavefun(length=N)
+
+    assert_allclose(np.real(PSI), np.real(psi), atol=1e-15)
+    assert_allclose(np.imag(PSI), np.imag(psi), atol=1e-15)
+    assert_allclose(X, x, atol=1e-15)
+
+    LB = -20
+    UB = 20
+    N = 1000
+    M = 3
+    Fb = 1.5
+    Fc = 1.2
+
+    [psi, x] = ref_fbsp(LB, UB, N, M, Fb, Fc)
+    w = pywt.ContinuousWavelet("fbsp{}-{}-{}".format(M, Fb, Fc))
+    assert_almost_equal(w.center_frequency, Fc)
+    assert_almost_equal(w.bandwidth_frequency, Fb)
+    w.fbsp_order = M
+    w.upper_bound = UB
+    w.lower_bound = LB
+    PSI, X = w.wavefun(length=N)
+    # TODO: investigate why atol = 1e-5 is necessary
+    assert_allclose(np.real(PSI), np.real(psi), atol=1e-5)
+    assert_allclose(np.imag(PSI), np.imag(psi), atol=1e-5)
+    assert_allclose(X, x, atol=1e-15)
+
+
+def test_morl():
+    LB = -5
+    UB = 5
+    N = 1000
+
+    [psi, x] = ref_morl(LB, UB, N)
+    w = pywt.ContinuousWavelet("morl")
+    w.upper_bound = UB
+    w.lower_bound = LB
+    PSI, X = w.wavefun(length=N)
+
+    assert_allclose(np.real(PSI), np.real(psi))
+    assert_allclose(np.imag(PSI), np.imag(psi))
+    assert_allclose(X, x)
+
+
+def test_mexh():
+    LB = -5
+    UB = 5
+    N = 1000
+
+    [psi, x] = ref_mexh(LB, UB, N)
+    w = pywt.ContinuousWavelet("mexh")
+    w.upper_bound = UB
+    w.lower_bound = LB
+    PSI, X = w.wavefun(length=N)
+
+    assert_allclose(np.real(PSI), np.real(psi))
+    assert_allclose(np.imag(PSI), np.imag(psi))
+    assert_allclose(X, x)
+
+    LB = -5
+    UB = 5
+    N = 1001
+
+    [psi, x] = ref_mexh(LB, UB, N)
+    w = pywt.ContinuousWavelet("mexh")
+    w.upper_bound = UB
+    w.lower_bound = LB
+    PSI, X = w.wavefun(length=N)
+
+    assert_allclose(np.real(PSI), np.real(psi))
+    assert_allclose(np.imag(PSI), np.imag(psi))
+    assert_allclose(X, x)
+
+
+def test_cwt_parameters_in_names():
+
+    for func in [pywt.ContinuousWavelet, pywt.DiscreteContinuousWavelet]:
+        for name in ['fbsp', 'cmor', 'shan']:
+            # additional parameters should be specified within the name
+            assert_warns(FutureWarning, func, name)
+
+        for name in ['cmor', 'shan']:
+            # valid names
+            func(name + '1.5-1.0')
+            func(name + '1-4')
+
+            # invalid names
+            assert_raises(ValueError, func, name + '1.0')
+            assert_raises(ValueError, func, name + 'B-C')
+            assert_raises(ValueError, func, name + '1.0-1.0-1.0')
+
+        # valid names
+        func('fbsp1-1.5-1.0')
+        func('fbsp1.0-1.5-1')
+        func('fbsp2-5-1')
+
+        # invalid name (non-integer order)
+        assert_raises(ValueError, func, 'fbsp1.5-1-1')
+        assert_raises(ValueError, func, 'fbspM-B-C')
+
+        # invalid name (too few or too many params)
+        assert_raises(ValueError, func, 'fbsp1.0')
+        assert_raises(ValueError, func, 'fbsp1.0-0.4')
+        assert_raises(ValueError, func, 'fbsp1-1-1-1')
+
+
+@pytest.mark.parametrize('dtype, tol, method',
+                         [(np.float32, 1e-5, 'conv'),
+                          (np.float32, 1e-5, 'fft'),
+                          (np.float64, 1e-13, 'conv'),
+                          (np.float64, 1e-13, 'fft')])
+def test_cwt_complex(dtype, tol, method):
+    time, sst = pywt.data.nino()
+    sst = np.asarray(sst, dtype=dtype)
+    dt = time[1] - time[0]
+    wavelet = 'cmor1.5-1.0'
+    scales = np.arange(1, 32)
+
+    # real-valued tranfsorm as a reference
+    [cfs, f] = pywt.cwt(sst, scales, wavelet, dt, method=method)
+
+    # verify same precision
+    assert_equal(cfs.real.dtype, sst.dtype)
+
+    # complex-valued transform equals sum of the transforms of the real
+    # and imaginary components
+    sst_complex = sst + 1j*sst
+    [cfs_complex, f] = pywt.cwt(sst_complex, scales, wavelet, dt,
+                                method=method)
+    assert_allclose(cfs + 1j*cfs, cfs_complex, atol=tol, rtol=tol)
+    # verify dtype is preserved
+    assert_equal(cfs_complex.dtype, sst_complex.dtype)
+
+
+@pytest.mark.parametrize('axis, method', product([0, 1], ['conv', 'fft']))
+def test_cwt_batch(axis, method):
+    dtype = np.float64
+    time, sst = pywt.data.nino()
+    n_batch = 8
+    batch_axis = 1 - axis
+    sst1 = np.asarray(sst, dtype=dtype)
+    sst = np.stack((sst1, ) * n_batch, axis=batch_axis)
+    dt = time[1] - time[0]
+    wavelet = 'cmor1.5-1.0'
+    scales = np.arange(1, 32)
+
+    # non-batch transform as reference
+    [cfs1, f] = pywt.cwt(sst1, scales, wavelet, dt, method=method, axis=axis)
+
+    shape_in = sst.shape
+    [cfs, f] = pywt.cwt(sst, scales, wavelet, dt, method=method, axis=axis)
+
+    # shape of input is not modified
+    assert_equal(shape_in, sst.shape)
+
+    # verify same precision
+    assert_equal(cfs.real.dtype, sst.dtype)
+
+    # verify expected shape
+    assert_equal(cfs.shape[0], len(scales))
+    assert_equal(cfs.shape[1 + batch_axis], n_batch)
+    assert_equal(cfs.shape[1 + axis], sst.shape[axis])
+
+    # batch result on stacked input is the same as stacked 1d result
+    assert_equal(cfs, np.stack((cfs1,) * n_batch, axis=batch_axis + 1))
+
+
+def test_cwt_small_scales():
+    data = np.zeros(32)
+
+    # A scale of 0.1 was chosen specifically to give a filter of length 2 for
+    # mexh.  This corner case should not raise an error.
+    cfs, f = pywt.cwt(data, scales=0.1, wavelet='mexh')
+    assert_allclose(cfs, np.zeros_like(cfs))
+
+    # extremely short scale factors raise a ValueError
+    assert_raises(ValueError, pywt.cwt, data, scales=0.01, wavelet='mexh')
+
+
+def test_cwt_method_fft():
+    rstate = np.random.RandomState(1)
+    data = rstate.randn(50)
+    data[15] = 1.
+    scales = np.arange(1, 64)
+    wavelet = 'cmor1.5-1.0'
+
+    # build a reference cwt with the legacy np.conv() method
+    cfs_conv, _ = pywt.cwt(data, scales, wavelet, method='conv')
+
+    # compare with the fft based convolution
+    cfs_fft, _ = pywt.cwt(data, scales, wavelet, method='fft')
+    assert_allclose(cfs_conv, cfs_fft, rtol=0, atol=1e-13)

venv/Lib/site-packages/pywt/tests/test_data.py

@@ -0,0 +1,77 @@
+import os
+import numpy as np
+from numpy.testing import assert_allclose, assert_raises, assert_
+
+import pywt.data
+
+data_dir = os.path.join(os.path.dirname(__file__), 'data')
+wavelab_data_file = os.path.join(data_dir, 'wavelab_test_signals.npz')
+wavelab_result_dict = np.load(wavelab_data_file)
+
+
+def test_data_aero():
+    aero = pywt.data.aero()
+
+    ref = np.array([[178, 178, 179],
+                    [170, 173, 171],
+                    [185, 174, 171]])
+
+    assert_allclose(aero[:3, :3], ref)
+
+
+def test_data_ascent():
+    ascent = pywt.data.ascent()
+
+    ref = np.array([[83, 83, 83],
+                    [82, 82, 83],
+                    [80, 81, 83]])
+
+    assert_allclose(ascent[:3, :3], ref)
+
+
+def test_data_camera():
+    ascent = pywt.data.camera()
+
+    ref = np.array([[156, 157, 160],
+                    [156, 157, 159],
+                    [158, 157, 156]])
+
+    assert_allclose(ascent[:3, :3], ref)
+
+
+def test_data_ecg():
+    ecg = pywt.data.ecg()
+
+    ref = np.array([-86, -87, -87])
+
+    assert_allclose(ecg[:3], ref)
+
+
+def test_wavelab_signals():
+    """Comparison with results generated using WaveLab"""
+    rtol = atol = 1e-12
+
+    # get a list of the available signals
+    available_signals = pywt.data.demo_signal('list')
+    assert_('Doppler' in available_signals)
+
+    for signal in available_signals:
+        # reference dictionary has lowercase names for the keys
+        key = signal.replace('-', '_').lower()
+        val = wavelab_result_dict[key]
+        if key in ['gabor', 'sineoneoverx']:
+            # these functions do not allow a size to be provided
+            assert_allclose(val, pywt.data.demo_signal(signal),
+                            rtol=rtol, atol=atol)
+            assert_raises(ValueError, pywt.data.demo_signal, key, val.size)
+        else:
+            assert_allclose(val, pywt.data.demo_signal(signal, val.size),
+                            rtol=rtol, atol=atol)
+            # these functions require a size to be provided
+            assert_raises(ValueError, pywt.data.demo_signal, key)
+
+    # ValueError on unrecognized signal type
+    assert_raises(ValueError, pywt.data.demo_signal, 'unknown_signal', 512)
+
+    # ValueError on invalid length
+    assert_raises(ValueError, pywt.data.demo_signal, 'Doppler', 0)

venv/Lib/site-packages/pywt/tests/test_deprecations.py

@@ -0,0 +1,89 @@
+import warnings
+
+import numpy as np
+from numpy.testing import assert_warns, assert_array_equal
+
+import pywt
+
+
+def test_intwave_deprecation():
+    wavelet = pywt.Wavelet('db3')
+    assert_warns(DeprecationWarning, pywt.intwave, wavelet)
+
+
+def test_centrfrq_deprecation():
+    wavelet = pywt.Wavelet('db3')
+    assert_warns(DeprecationWarning, pywt.centrfrq, wavelet)
+
+
+def test_scal2frq_deprecation():
+    wavelet = pywt.Wavelet('db3')
+    assert_warns(DeprecationWarning, pywt.scal2frq, wavelet, 1)
+
+
+def test_orthfilt_deprecation():
+    assert_warns(DeprecationWarning, pywt.orthfilt, range(6))
+
+
+def test_integrate_wave_tuple():
+    sig = [0, 1, 2, 3]
+    xgrid = [0, 1, 2, 3]
+    assert_warns(DeprecationWarning, pywt.integrate_wavelet, (sig, xgrid))
+
+
+old_modes = ['zpd',
+             'cpd',
+             'sym',
+             'ppd',
+             'sp1',
+             'per',
+             ]
+
+
+def test_MODES_from_object_deprecation():
+    for mode in old_modes:
+        assert_warns(DeprecationWarning, pywt.Modes.from_object, mode)
+
+
+def test_MODES_attributes_deprecation():
+    def get_mode(Modes, name):
+        return getattr(Modes, name)
+
+    for mode in old_modes:
+        assert_warns(DeprecationWarning, get_mode, pywt.Modes, mode)
+
+
+def test_MODES_deprecation_new():
+    def use_MODES_new():
+        return pywt.MODES.symmetric
+
+    assert_warns(DeprecationWarning, use_MODES_new)
+
+
+def test_MODES_deprecation_old():
+    def use_MODES_old():
+        return pywt.MODES.sym
+
+    assert_warns(DeprecationWarning, use_MODES_old)
+
+
+def test_MODES_deprecation_getattr():
+    def use_MODES_new():
+        return getattr(pywt.MODES, 'symmetric')
+
+    assert_warns(DeprecationWarning, use_MODES_new)
+
+
+def test_mode_equivalence():
+    old_new = [('zpd', 'zero'),
+               ('cpd', 'constant'),
+               ('sym', 'symmetric'),
+               ('ppd', 'periodic'),
+               ('sp1', 'smooth'),
+               ('per', 'periodization')]
+    x = np.arange(8.)
+    with warnings.catch_warnings():
+        warnings.simplefilter('ignore', DeprecationWarning)
+        for old, new in old_new:
+            assert_array_equal(pywt.dwt(x, 'db2', mode=old),
+                               pywt.dwt(x, 'db2', mode=new))

venv/Lib/site-packages/pywt/tests/test_doc.py

@@ -0,0 +1,25 @@
+from __future__ import division, print_function, absolute_import
+
+import doctest
+import glob
+import os
+import unittest
+
+try:
+    import numpy as np
+    np.set_printoptions(legacy='1.13')
+except TypeError:
+    pass
+
+pdir = os.path.pardir
+docs_base = os.path.abspath(os.path.join(os.path.dirname(__file__),
+                            pdir, pdir, "doc", "source"))
+
+files = glob.glob(os.path.join(docs_base, "*.rst")) + \
+    glob.glob(os.path.join(docs_base, "*", "*.rst"))
+
+suite = doctest.DocFileSuite(*files, module_relative=False, encoding="utf-8")
+
+
+if __name__ == "__main__":
+    unittest.TextTestRunner().run(suite)

venv/Lib/site-packages/pywt/tests/test_dwt_idwt.py

@@ -0,0 +1,299 @@
+#!/usr/bin/env python
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import (assert_allclose, assert_, assert_raises,
+                           assert_array_equal)
+import pywt
+
+# Check that float32, float64, complex64, complex128 are preserved.
+# Other real types get converted to float64.
+# complex256 gets converted to complex128
+dtypes_in = [np.int8, np.float16, np.float32, np.float64, np.complex64,
+             np.complex128]
+dtypes_out = [np.float64, np.float32, np.float32, np.float64, np.complex64,
+              np.complex128]
+
+# test complex256 as well if it is available
+try:
+    dtypes_in += [np.complex256, ]
+    dtypes_out += [np.complex128, ]
+except AttributeError:
+    pass
+
+
+def test_dwt_idwt_basic():
+    x = [3, 7, 1, 1, -2, 5, 4, 6]
+    cA, cD = pywt.dwt(x, 'db2')
+    cA_expect = [5.65685425, 7.39923721, 0.22414387, 3.33677403, 7.77817459]
+    cD_expect = [-2.44948974, -1.60368225, -4.44140056, -0.41361256,
+                 1.22474487]
+    assert_allclose(cA, cA_expect)
+    assert_allclose(cD, cD_expect)
+
+    x_roundtrip = pywt.idwt(cA, cD, 'db2')
+    assert_allclose(x_roundtrip, x, rtol=1e-10)
+
+    # mismatched dtypes OK
+    x_roundtrip2 = pywt.idwt(cA.astype(np.float64), cD.astype(np.float32),
+                             'db2')
+    assert_allclose(x_roundtrip2, x, rtol=1e-7, atol=1e-7)
+    assert_(x_roundtrip2.dtype == np.float64)
+
+
+def test_idwt_mixed_complex_dtype():
+    x = np.arange(8).astype(float)
+    x = x + 1j*x[::-1]
+    cA, cD = pywt.dwt(x, 'db2')
+
+    x_roundtrip = pywt.idwt(cA, cD, 'db2')
+    assert_allclose(x_roundtrip, x, rtol=1e-10)
+
+    # mismatched dtypes OK
+    x_roundtrip2 = pywt.idwt(cA.astype(np.complex128), cD.astype(np.complex64),
+                             'db2')
+    assert_allclose(x_roundtrip2, x, rtol=1e-7, atol=1e-7)
+    assert_(x_roundtrip2.dtype == np.complex128)
+
+
+def test_dwt_idwt_dtypes():
+    wavelet = pywt.Wavelet('haar')
+    for dt_in, dt_out in zip(dtypes_in, dtypes_out):
+        x = np.ones(4, dtype=dt_in)
+        errmsg = "wrong dtype returned for {0} input".format(dt_in)
+
+        cA, cD = pywt.dwt(x, wavelet)
+        assert_(cA.dtype == cD.dtype == dt_out, "dwt: " + errmsg)
+
+        x_roundtrip = pywt.idwt(cA, cD, wavelet)
+        assert_(x_roundtrip.dtype == dt_out, "idwt: " + errmsg)
+
+
+def test_dwt_idwt_basic_complex():
+    x = np.asarray([3, 7, 1, 1, -2, 5, 4, 6])
+    x = x + 0.5j*x
+    cA, cD = pywt.dwt(x, 'db2')
+    cA_expect = np.asarray([5.65685425, 7.39923721, 0.22414387, 3.33677403,
+                            7.77817459])
+    cA_expect = cA_expect + 0.5j*cA_expect
+    cD_expect = np.asarray([-2.44948974, -1.60368225, -4.44140056, -0.41361256,
+                            1.22474487])
+    cD_expect = cD_expect + 0.5j*cD_expect
+    assert_allclose(cA, cA_expect)
+    assert_allclose(cD, cD_expect)
+
+    x_roundtrip = pywt.idwt(cA, cD, 'db2')
+    assert_allclose(x_roundtrip, x, rtol=1e-10)
+
+
+def test_dwt_idwt_partial_complex():
+    x = np.asarray([3, 7, 1, 1, -2, 5, 4, 6])
+    x = x + 0.5j*x
+
+    cA, cD = pywt.dwt(x, 'haar')
+    cA_rec_expect = np.array([5.0+2.5j, 5.0+2.5j, 1.0+0.5j, 1.0+0.5j,
+                              1.5+0.75j, 1.5+0.75j, 5.0+2.5j, 5.0+2.5j])
+    cA_rec = pywt.idwt(cA, None, 'haar')
+    assert_allclose(cA_rec, cA_rec_expect)
+
+    cD_rec_expect = np.array([-2.0-1.0j, 2.0+1.0j, 0.0+0.0j, 0.0+0.0j,
+                              -3.5-1.75j, 3.5+1.75j, -1.0-0.5j, 1.0+0.5j])
+    cD_rec = pywt.idwt(None, cD, 'haar')
+    assert_allclose(cD_rec, cD_rec_expect)
+
+    assert_allclose(cA_rec + cD_rec, x)
+
+
+def test_dwt_wavelet_kwd():
+    x = np.array([3, 7, 1, 1, -2, 5, 4, 6])
+    w = pywt.Wavelet('sym3')
+    cA, cD = pywt.dwt(x, wavelet=w, mode='constant')
+    cA_expect = [4.38354585, 3.80302657, 7.31813271, -0.58565539, 4.09727044,
+                 7.81994027]
+    cD_expect = [-1.33068221, -2.78795192, -3.16825651, -0.67715519,
+                 -0.09722957, -0.07045258]
+    assert_allclose(cA, cA_expect)
+    assert_allclose(cD, cD_expect)
+
+
+def test_dwt_coeff_len():
+    x = np.array([3, 7, 1, 1, -2, 5, 4, 6])
+    w = pywt.Wavelet('sym3')
+    ln_modes = [pywt.dwt_coeff_len(len(x), w.dec_len, mode) for mode in
+                pywt.Modes.modes]
+
+    expected_result = [6, ] * len(pywt.Modes.modes)
+    expected_result[pywt.Modes.modes.index('periodization')] = 4
+
+    assert_allclose(ln_modes, expected_result)
+    ln_modes = [pywt.dwt_coeff_len(len(x), w, mode) for mode in
+                pywt.Modes.modes]
+    assert_allclose(ln_modes, expected_result)
+
+
+def test_idwt_none_input():
+    # None input equals arrays of zeros of the right length
+    res1 = pywt.idwt([1, 2, 0, 1], None, 'db2', 'symmetric')
+    res2 = pywt.idwt([1, 2, 0, 1], [0, 0, 0, 0], 'db2', 'symmetric')
+    assert_allclose(res1, res2, rtol=1e-15, atol=1e-15)
+
+    res1 = pywt.idwt(None, [1, 2, 0, 1], 'db2', 'symmetric')
+    res2 = pywt.idwt([0, 0, 0, 0], [1, 2, 0, 1], 'db2', 'symmetric')
+    assert_allclose(res1, res2, rtol=1e-15, atol=1e-15)
+
+    # Only one argument at a time can be None
+    assert_raises(ValueError, pywt.idwt, None, None, 'db2', 'symmetric')
+
+
+def test_idwt_invalid_input():
+    # Too short, min length is 4 for 'db4':
+    assert_raises(ValueError, pywt.idwt, [1, 2, 4], [4, 1, 3], 'db4', 'symmetric')
+
+
+def test_dwt_single_axis():
+    x = [[3, 7, 1, 1],
+         [-2, 5, 4, 6]]
+
+    cA, cD = pywt.dwt(x, 'db2', axis=-1)
+
+    cA0, cD0 = pywt.dwt(x[0], 'db2')
+    cA1, cD1 = pywt.dwt(x[1], 'db2')
+
+    assert_allclose(cA[0], cA0)
+    assert_allclose(cA[1], cA1)
+
+    assert_allclose(cD[0], cD0)
+    assert_allclose(cD[1], cD1)
+
+
+def test_idwt_single_axis():
+    x = [[3, 7, 1, 1],
+         [-2, 5, 4, 6]]
+
+    x = np.asarray(x)
+    x = x + 1j*x   # test with complex data
+    cA, cD = pywt.dwt(x, 'db2', axis=-1)
+
+    x0 = pywt.idwt(cA[0], cD[0], 'db2', axis=-1)
+    x1 = pywt.idwt(cA[1], cD[1], 'db2', axis=-1)
+
+    assert_allclose(x[0], x0)
+    assert_allclose(x[1], x1)
+
+
+def test_dwt_axis_arg():
+    x = [[3, 7, 1, 1],
+         [-2, 5, 4, 6]]
+
+    cA_, cD_ = pywt.dwt(x, 'db2', axis=-1)
+    cA, cD = pywt.dwt(x, 'db2', axis=1)
+
+    assert_allclose(cA_, cA)
+    assert_allclose(cD_, cD)
+
+
+def test_idwt_axis_arg():
+    x = [[3, 7, 1, 1],
+         [-2, 5, 4, 6]]
+
+    cA, cD = pywt.dwt(x, 'db2', axis=1)
+
+    x_ = pywt.idwt(cA, cD, 'db2', axis=-1)
+    x = pywt.idwt(cA, cD, 'db2', axis=1)
+
+    assert_allclose(x_, x)
+
+
+def test_dwt_idwt_axis_excess():
+    x = [[3, 7, 1, 1],
+         [-2, 5, 4, 6]]
+    # can't transform over axes that aren't there
+    assert_raises(ValueError,
+                  pywt.dwt, x, 'db2', 'symmetric', axis=2)
+
+    assert_raises(ValueError,
+                  pywt.idwt, [1, 2, 4], [4, 1, 3], 'db2', 'symmetric', axis=1)
+
+
+def test_error_on_continuous_wavelet():
+    # A ValueError is raised if a Continuous wavelet is selected
+    data = np.ones((32, ))
+    for cwave in ['morl', pywt.DiscreteContinuousWavelet('morl')]:
+        assert_raises(ValueError, pywt.dwt, data, cwave)
+
+        cA, cD = pywt.dwt(data, 'db1')
+        assert_raises(ValueError, pywt.idwt, cA, cD, cwave)
+
+
+def test_dwt_zero_size_axes():
+    # raise on empty input array
+    assert_raises(ValueError, pywt.dwt, [], 'db2')
+
+    # >1D case uses a different code path so check there as well
+    x = np.ones((1, 4))[0:0, :]  # 2D with a size zero axis
+    assert_raises(ValueError, pywt.dwt, x, 'db2', axis=0)
+
+
+def test_pad_1d():
+    x = [1, 2, 3]
+    assert_array_equal(pywt.pad(x, (4, 6), 'periodization'),
+                       [1, 2, 3, 3, 1, 2, 3, 3, 1, 2, 3, 3, 1, 2])
+    assert_array_equal(pywt.pad(x, (4, 6), 'periodic'),
+                       [3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3])
+    assert_array_equal(pywt.pad(x, (4, 6), 'constant'),
+                       [1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3])
+    assert_array_equal(pywt.pad(x, (4, 6), 'zero'),
+                       [0, 0, 0, 0, 1, 2, 3, 0, 0, 0, 0, 0, 0])
+    assert_array_equal(pywt.pad(x, (4, 6), 'smooth'),
+                       [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+    assert_array_equal(pywt.pad(x, (4, 6), 'symmetric'),
+                       [3, 3, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3])
+    assert_array_equal(pywt.pad(x, (4, 6), 'antisymmetric'),
+                       [3, -3, -2, -1, 1, 2, 3, -3, -2, -1, 1, 2, 3])
+    assert_array_equal(pywt.pad(x, (4, 6), 'reflect'),
+                       [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1])
+    assert_array_equal(pywt.pad(x, (4, 6), 'antireflect'),
+                       [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+
+    # equivalence of various pad_width formats
+    assert_array_equal(pywt.pad(x, 4, 'periodic'),
+                       pywt.pad(x, (4, 4), 'periodic'))
+
+    assert_array_equal(pywt.pad(x, (4, ), 'periodic'),
+                       pywt.pad(x, (4, 4), 'periodic'))
+
+    assert_array_equal(pywt.pad(x, [(4, 4)], 'periodic'),
+                       pywt.pad(x, (4, 4), 'periodic'))
+
+
+def test_pad_errors():
+    # negative pad width
+    x = [1, 2, 3]
+    assert_raises(ValueError, pywt.pad, x, -2, 'periodic')
+
+    # wrong length pad width
+    assert_raises(ValueError, pywt.pad, x, (1, 1, 1), 'periodic')
+
+    # invalid mode name
+    assert_raises(ValueError, pywt.pad, x, 2, 'bad_mode')
+
+
+def test_pad_nd():
+    for ndim in [2, 3]:
+        x = np.arange(4**ndim).reshape((4, ) * ndim)
+        if ndim == 2:
+            pad_widths = [(2, 1), (2, 3)]
+        else:
+            pad_widths = [(2, 1), ] * ndim
+        for mode in pywt.Modes.modes:
+            xp = pywt.pad(x, pad_widths, mode)
+
+            # expected result is the same as applying along axes separably
+            xp_expected = x.copy()
+            for ax in range(ndim):
+                xp_expected = np.apply_along_axis(pywt.pad,
+                                                  ax,
+                                                  xp_expected,
+                                                  pad_widths=[pad_widths[ax]],
+                                                  mode=mode)
+            assert_array_equal(xp, xp_expected)

venv/Lib/site-packages/pywt/tests/test_functions.py

@@ -0,0 +1,38 @@
+#!/usr/bin/env python
+from __future__ import division, print_function, absolute_import
+
+from numpy.testing import assert_almost_equal, assert_allclose
+
+import pywt
+
+
+def test_centrfreq():
+    # db1 is Haar function, frequency=1
+    w = pywt.Wavelet('db1')
+    expected = 1
+    result = pywt.central_frequency(w, precision=12)
+    assert_almost_equal(result, expected, decimal=3)
+    # db2, frequency=2/3
+    w = pywt.Wavelet('db2')
+    expected = 2/3.
+    result = pywt.central_frequency(w, precision=12)
+    assert_almost_equal(result, expected)
+
+
+def test_scal2frq_scale():
+    scale = 2
+    w = pywt.Wavelet('db1')
+    expected = 1. / scale
+    result = pywt.scale2frequency(w, scale, precision=12)
+    assert_almost_equal(result, expected, decimal=3)
+
+
+def test_intwave_orthogonal():
+    w = pywt.Wavelet('db1')
+    int_psi, x = pywt.integrate_wavelet(w, precision=12)
+    ix = x < 0.5
+    # For x < 0.5, the integral is equal to x
+    assert_allclose(int_psi[ix], x[ix])
+    # For x > 0.5, the integral is equal to (1 - x)
+    # Ignore last point here, there x > 1 and something goes wrong
+    assert_allclose(int_psi[~ix][:-1], 1 - x[~ix][:-1], atol=1e-10)

venv/Lib/site-packages/pywt/tests/test_matlab_compatibility.py

@@ -0,0 +1,160 @@
+"""
+Test used to verify PyWavelets Discrete Wavelet Transform computation
+accuracy against MathWorks Wavelet Toolbox.
+"""
+
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+import pytest
+from numpy.testing import assert_
+
+import pywt
+from pywt._pytest import (uses_pymatbridge, uses_precomputed, size_set)
+from pywt._pytest import matlab_result_dict_dwt as matlab_result_dict
+
+# list of mode names in pywt and matlab
+modes = [('zero', 'zpd'),
+         ('constant', 'sp0'),
+         ('symmetric', 'sym'),
+         ('reflect', 'symw'),
+         ('periodic', 'ppd'),
+         ('smooth', 'sp1'),
+         ('periodization', 'per'),
+         # TODO: Now have implemented asymmetric modes too.
+         #       Would be nice to update the Matlab data to test these as well.
+         ('antisymmetric', 'asym'),
+         ('antireflect', 'asymw'),
+         ]
+
+families = ('db', 'sym', 'coif', 'bior', 'rbio')
+wavelets = sum([pywt.wavelist(name) for name in families], [])
+
+
+def _get_data_sizes(w):
+    """ Return the sizes to test for wavelet w. """
+    if size_set == 'full':
+        data_sizes = list(range(w.dec_len, 40)) + \
+            [100, 200, 500, 1000, 50000]
+    else:
+        data_sizes = (w.dec_len, w.dec_len + 1)
+    return data_sizes
+
+
+@uses_pymatbridge
+@pytest.mark.slow
+def test_accuracy_pymatbridge():
+    Matlab = pytest.importorskip("pymatbridge.Matlab")
+    mlab = Matlab()
+
+    rstate = np.random.RandomState(1234)
+    # max RMSE (was 1.0e-10, is reduced to 5.0e-5 due to different coefficents)
+    epsilon = 5.0e-5
+    epsilon_pywt_coeffs = 1.0e-10
+    mlab.start()
+    try:
+        for wavelet in wavelets:
+            w = pywt.Wavelet(wavelet)
+            mlab.set_variable('wavelet', wavelet)
+            for N in _get_data_sizes(w):
+                data = rstate.randn(N)
+                mlab.set_variable('data', data)
+                for pmode, mmode in modes:
+                    ma, md = _compute_matlab_result(data, wavelet, mmode, mlab)
+                    _check_accuracy(data, w, pmode, ma, md, wavelet, epsilon)
+                    ma, md = _load_matlab_result_pywt_coeffs(data, wavelet, mmode)
+                    _check_accuracy(data, w, pmode, ma, md, wavelet, epsilon_pywt_coeffs)
+
+    finally:
+        mlab.stop()
+
+
+@uses_precomputed
+@pytest.mark.slow
+def test_accuracy_precomputed():
+    # Keep this specific random seed to match the precomputed Matlab result.
+    rstate = np.random.RandomState(1234)
+    # max RMSE (was 1.0e-10, is reduced to 5.0e-5 due to different coefficents)
+    epsilon = 5.0e-5
+    epsilon_pywt_coeffs = 1.0e-10
+    for wavelet in wavelets:
+        w = pywt.Wavelet(wavelet)
+        for N in _get_data_sizes(w):
+            data = rstate.randn(N)
+            for pmode, mmode in modes:
+                ma, md = _load_matlab_result(data, wavelet, mmode)
+                _check_accuracy(data, w, pmode, ma, md, wavelet, epsilon)
+                ma, md = _load_matlab_result_pywt_coeffs(data, wavelet, mmode)
+                _check_accuracy(data, w, pmode, ma, md, wavelet, epsilon_pywt_coeffs)
+
+
+def _compute_matlab_result(data, wavelet, mmode, mlab):
+    """ Compute the result using MATLAB.
+
+    This function assumes that the Matlab variables `wavelet` and `data` have
+    already been set externally.
+    """
+    if np.any((wavelet == np.array(['coif6', 'coif7', 'coif8', 'coif9', 'coif10', 'coif11', 'coif12', 'coif13', 'coif14', 'coif15', 'coif16', 'coif17'])),axis=0):
+        w = pywt.Wavelet(wavelet)
+        mlab.set_variable('Lo_D', w.dec_lo)
+        mlab.set_variable('Hi_D', w.dec_hi)
+        mlab_code = ("[ma, md] = dwt(data, Lo_D, Hi_D, 'mode', '%s');" % mmode)
+    else:
+        mlab_code = "[ma, md] = dwt(data, wavelet, 'mode', '%s');" % mmode
+    res = mlab.run_code(mlab_code)
+    if not res['success']:
+        raise RuntimeError("Matlab failed to execute the provided code. "
+                           "Check that the wavelet toolbox is installed.")
+    # need np.asarray because sometimes the output is a single float64
+    ma = np.asarray(mlab.get_variable('ma'))
+    md = np.asarray(mlab.get_variable('md'))
+    return ma, md
+
+
+def _load_matlab_result(data, wavelet, mmode):
+    """ Load the precomputed result.
+    """
+    N = len(data)
+    ma_key = '_'.join([mmode, wavelet, str(N), 'ma'])
+    md_key = '_'.join([mmode, wavelet, str(N), 'md'])
+    if (ma_key not in matlab_result_dict) or \
+            (md_key not in matlab_result_dict):
+        raise KeyError(
+            "Precompted Matlab result not found for wavelet: "
+            "{0}, mode: {1}, size: {2}".format(wavelet, mmode, N))
+    ma = matlab_result_dict[ma_key]
+    md = matlab_result_dict[md_key]
+    return ma, md
+
+
+def _load_matlab_result_pywt_coeffs(data, wavelet, mmode):
+    """ Load the precomputed result.
+    """
+    N = len(data)
+    ma_key = '_'.join([mmode, wavelet, str(N), 'ma_pywtCoeffs'])
+    md_key = '_'.join([mmode, wavelet, str(N), 'md_pywtCoeffs'])
+    if (ma_key not in matlab_result_dict) or \
+            (md_key not in matlab_result_dict):
+        raise KeyError(
+            "Precompted Matlab result not found for wavelet: "
+            "{0}, mode: {1}, size: {2}".format(wavelet, mmode, N))
+    ma = matlab_result_dict[ma_key]
+    md = matlab_result_dict[md_key]
+    return ma, md
+
+
+def _check_accuracy(data, w, pmode, ma, md, wavelet, epsilon):
+    # PyWavelets result
+    pa, pd = pywt.dwt(data, w, pmode)
+
+    # calculate error measures
+    rms_a = np.sqrt(np.mean((pa - ma) ** 2))
+    rms_d = np.sqrt(np.mean((pd - md) ** 2))
+
+    msg = ('[RMS_A > EPSILON] for Mode: %s, Wavelet: %s, '
+           'Length: %d, rms=%.3g' % (pmode, wavelet, len(data), rms_a))
+    assert_(rms_a < epsilon, msg=msg)
+
+    msg = ('[RMS_D > EPSILON] for Mode: %s, Wavelet: %s, '
+           'Length: %d, rms=%.3g' % (pmode, wavelet, len(data), rms_d))
+    assert_(rms_d < epsilon, msg=msg)

venv/Lib/site-packages/pywt/tests/test_matlab_compatibility_cwt.py

@@ -0,0 +1,174 @@
+"""
+Test used to verify PyWavelets Continuous Wavelet Transform computation
+accuracy against MathWorks Wavelet Toolbox.
+"""
+
+from __future__ import division, print_function, absolute_import
+
+import warnings
+import numpy as np
+import pytest
+from numpy.testing import assert_
+
+import pywt
+from pywt._pytest import (uses_pymatbridge, uses_precomputed, size_set,
+                          matlab_result_dict_cwt)
+
+families = ('gaus', 'mexh', 'morl', 'cgau', 'shan', 'fbsp', 'cmor')
+wavelets = sum([pywt.wavelist(name) for name in families], [])
+
+
+def _get_data_sizes(w):
+    """ Return the sizes to test for wavelet w. """
+    if size_set == 'full':
+        data_sizes = list(range(100, 101)) + \
+            [100, 200, 500, 1000, 50000]
+    else:
+        data_sizes = (1000, 1000 + 1)
+    return data_sizes
+
+
+def _get_scales(w):
+    """ Return the scales to test for wavelet w. """
+    if size_set == 'full':
+        scales = (1, np.arange(1, 3), np.arange(1, 4), np.arange(1, 5))
+    else:
+        scales = (1, np.arange(1, 3))
+    return scales
+
+
+@uses_pymatbridge  # skip this case if precomputed results are used instead
+@pytest.mark.slow
+def test_accuracy_pymatbridge_cwt():
+    Matlab = pytest.importorskip("pymatbridge.Matlab")
+    mlab = Matlab()
+    rstate = np.random.RandomState(1234)
+    # max RMSE (was 1.0e-10, is reduced to 5.0e-5 due to different coefficents)
+    epsilon = 1e-15
+    epsilon_psi = 1e-15
+    mlab.start()
+    try:
+        for wavelet in wavelets:
+            with warnings.catch_warnings():
+                warnings.simplefilter('ignore', FutureWarning)
+                w = pywt.ContinuousWavelet(wavelet)
+            if np.any((wavelet == np.array(['shan', 'cmor'])),axis=0):
+                mlab.set_variable('wavelet', wavelet+str(w.bandwidth_frequency)+'-'+str(w.center_frequency))
+            elif wavelet == 'fbsp':
+                mlab.set_variable('wavelet', wavelet+str(w.fbsp_order)+'-'+str(w.bandwidth_frequency)+'-'+str(w.center_frequency))
+            else:
+                mlab.set_variable('wavelet', wavelet)
+            mlab_code = ("psi = wavefun(wavelet,10)")
+            res = mlab.run_code(mlab_code)
+            psi = np.asarray(mlab.get_variable('psi'))
+            _check_accuracy_psi(w, psi, wavelet, epsilon_psi)
+            for N in _get_data_sizes(w):
+                data = rstate.randn(N)
+                mlab.set_variable('data', data)
+                for scales in _get_scales(w):
+                    coefs = _compute_matlab_result(data, wavelet, scales, mlab)
+                    _check_accuracy(data, w, scales, coefs, wavelet, epsilon)
+
+    finally:
+        mlab.stop()
+
+
+@uses_precomputed  # skip this case if pymatbridge + Matlab are being used
+@pytest.mark.slow
+def test_accuracy_precomputed_cwt():
+    # Keep this specific random seed to match the precomputed Matlab result.
+    rstate = np.random.RandomState(1234)
+    # has to be improved
+    epsilon = 2e-15
+    epsilon32 = 1e-5
+    epsilon_psi = 1e-15
+    for wavelet in wavelets:
+        with warnings.catch_warnings():
+            warnings.simplefilter('ignore', FutureWarning)
+            w = pywt.ContinuousWavelet(wavelet)
+            w32 = pywt.ContinuousWavelet(wavelet,dtype=np.float32)
+        psi = _load_matlab_result_psi(wavelet)
+        _check_accuracy_psi(w, psi, wavelet, epsilon_psi)
+
+        for N in _get_data_sizes(w):
+            data = rstate.randn(N)
+            data32 = data.astype(np.float32)
+            scales_count = 0
+            for scales in _get_scales(w):
+                scales_count += 1
+                coefs = _load_matlab_result(data, wavelet, scales_count)
+                _check_accuracy(data, w, scales, coefs, wavelet, epsilon)
+                _check_accuracy(data32, w32, scales, coefs, wavelet, epsilon32)
+
+
+def _compute_matlab_result(data, wavelet, scales, mlab):
+    """ Compute the result using MATLAB.
+
+    This function assumes that the Matlab variables `wavelet` and `data` have
+    already been set externally.
+    """
+    mlab.set_variable('scales', scales)
+    mlab_code = ("coefs = cwt(data, scales, wavelet)")
+    res = mlab.run_code(mlab_code)
+    if not res['success']:
+        raise RuntimeError("Matlab failed to execute the provided code. "
+                           "Check that the wavelet toolbox is installed.")
+    # need np.asarray because sometimes the output is a single float64
+    coefs = np.asarray(mlab.get_variable('coefs'))
+    return coefs
+
+
+def _load_matlab_result(data, wavelet, scales):
+    """ Load the precomputed result.
+    """
+    N = len(data)
+    coefs_key = '_'.join([str(scales), wavelet, str(N), 'coefs'])
+    if (coefs_key not in matlab_result_dict_cwt):
+        raise KeyError(
+            "Precompted Matlab result not found for wavelet: "
+            "{0}, mode: {1}, size: {2}".format(wavelet, scales, N))
+    coefs = matlab_result_dict_cwt[coefs_key]
+    return coefs
+
+
+def _load_matlab_result_psi(wavelet):
+    """ Load the precomputed result.
+    """
+    psi_key = '_'.join([wavelet, 'psi'])
+    if (psi_key not in matlab_result_dict_cwt):
+        raise KeyError(
+            "Precompted Matlab psi result not found for wavelet: "
+            "{0}}".format(wavelet))
+    psi = matlab_result_dict_cwt[psi_key]
+    return psi
+
+
+def _check_accuracy(data, w, scales, coefs, wavelet, epsilon):
+    # PyWavelets result
+    coefs_pywt, freq = pywt.cwt(data, scales, w)
+
+    # coefs from Matlab are from R2012a which is missing the complex conjugate
+    # as shown in Eq. 2 of Torrence and Compo. We take the complex conjugate of
+    # the precomputed Matlab result to account for this.
+    coefs = np.conj(coefs)
+
+    # calculate error measures
+    err = coefs_pywt - coefs
+    rms = np.real(np.sqrt(np.mean(np.conj(err) * err)))
+
+    msg = ('[RMS > EPSILON] for Scale: %s, Wavelet: %s, '
+           'Length: %d, rms=%.3g' % (scales, wavelet, len(data), rms))
+    assert_(rms < epsilon, msg=msg)
+
+
+def _check_accuracy_psi(w, psi, wavelet, epsilon):
+    # PyWavelets result
+    psi_pywt, x = w.wavefun(length=1024)
+
+    # calculate error measures
+    err = psi_pywt.flatten() - psi.flatten()
+    rms = np.real(np.sqrt(np.mean(np.conj(err) * err)))
+
+    msg = ('[RMS > EPSILON] for  Wavelet: %s, '
+           'rms=%.3g' % (wavelet, rms))
+    assert_(rms < epsilon, msg=msg)

venv/Lib/site-packages/pywt/tests/test_modes.py

@@ -0,0 +1,109 @@
+#!/usr/bin/env python
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import assert_raises, assert_equal, assert_allclose
+
+import pywt
+
+
+def test_available_modes():
+    modes = ['zero', 'constant', 'symmetric', 'periodic', 'smooth',
+             'periodization', 'reflect', 'antisymmetric', 'antireflect']
+    assert_equal(pywt.Modes.modes, modes)
+    assert_equal(pywt.Modes.from_object('constant'), 2)
+
+
+def test_invalid_modes():
+    x = np.arange(4)
+    assert_raises(ValueError, pywt.dwt, x, 'db2', 'unknown')
+    assert_raises(ValueError, pywt.dwt, x, 'db2', -1)
+    assert_raises(ValueError, pywt.dwt, x, 'db2', 9)
+    assert_raises(TypeError, pywt.dwt, x, 'db2', None)
+
+    assert_raises(ValueError, pywt.Modes.from_object, 'unknown')
+    assert_raises(ValueError, pywt.Modes.from_object, -1)
+    assert_raises(ValueError, pywt.Modes.from_object, 9)
+    assert_raises(TypeError, pywt.Modes.from_object, None)
+
+
+def test_dwt_idwt_allmodes():
+    # Test that :func:`dwt` and :func:`idwt` can be performed using every mode
+    x = [1, 2, 1, 5, -1, 8, 4, 6]
+    dwt_results = {
+        'zero': ([-0.03467518, 1.73309178, 3.40612438, 6.32928585, 6.95094948],
+                 [-0.12940952, -2.15599552, -5.95034847, -1.21545369,
+                 -1.8625013]),
+        'constant': ([1.28480404, 1.73309178, 3.40612438, 6.32928585,
+                      7.51935555],
+                     [-0.48296291, -2.15599552, -5.95034847, -1.21545369,
+                      0.25881905]),
+        'symmetric': ([1.76776695, 1.73309178, 3.40612438, 6.32928585,
+                       7.77817459],
+                      [-0.61237244, -2.15599552, -5.95034847, -1.21545369,
+                       1.22474487]),
+        'reflect': ([2.12132034, 1.73309178, 3.40612438, 6.32928585,
+                     6.81224877],
+                    [-0.70710678, -2.15599552, -5.95034847, -1.21545369,
+                     -2.38013939]),
+        'periodic': ([6.9162743, 1.73309178, 3.40612438, 6.32928585,
+                      6.9162743],
+                     [-1.99191082, -2.15599552, -5.95034847, -1.21545369,
+                      -1.99191082]),
+        'smooth': ([-0.51763809, 1.73309178, 3.40612438, 6.32928585,
+                    7.45000519],
+                   [0, -2.15599552, -5.95034847, -1.21545369, 0]),
+        'periodization': ([4.053172, 3.05257099, 2.85381112, 8.42522221],
+                          [0.18946869, 4.18258152, 4.33737503, 2.60428326]),
+        'antisymmetric': ([-1.83711731, 1.73309178, 3.40612438, 6.32928585,
+                           6.12372436],
+                          [0.353553391, -2.15599552, -5.95034847, -1.21545369,
+                           -4.94974747]),
+        'antireflect': ([0.44828774, 1.73309178, 3.40612438, 6.32928585,
+                         8.22646233],
+                        [-0.25881905, -2.15599552, -5.95034847, -1.21545369,
+                         2.89777748])
+    }
+
+    for mode in pywt.Modes.modes:
+        cA, cD = pywt.dwt(x, 'db2', mode)
+        assert_allclose(cA, dwt_results[mode][0], rtol=1e-7, atol=1e-8)
+        assert_allclose(cD, dwt_results[mode][1], rtol=1e-7, atol=1e-8)
+        assert_allclose(pywt.idwt(cA, cD, 'db2', mode), x, rtol=1e-10)
+
+
+def test_dwt_short_input_allmodes():
+    # some test cases where the input is shorter than the DWT filter
+    x = [1, 3, 2]
+    wavelet = 'db2'
+    # manually pad each end by the filter size (4 for 'db2' used here)
+    padded_x = {'zero': [0, 0, 0, 0, 1, 3, 2, 0, 0, 0, 0],
+                'constant': [1, 1, 1, 1, 1, 3, 2, 2, 2, 2, 2],
+                'symmetric': [2, 2, 3, 1, 1, 3, 2, 2, 3, 1, 1],
+                'reflect': [1, 3, 2, 3, 1, 3, 2, 3, 1, 3, 2],
+                'periodic': [2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1],
+                'smooth': [-7, -5, -3, -1, 1, 3, 2, 1, 0, -1, -2],
+                'antisymmetric': [2, -2, -3, -1, 1, 3, 2, -2, -3, -1, 1],
+                'antireflect': [1, -1, 0, -1, 1, 3, 2, 1, 3, 5, 4],
+                }
+    for mode, xpad in padded_x.items():
+        # DWT of the manually padded array.  will discard edges later so
+        # symmetric mode used here doesn't matter.
+        cApad, cDpad = pywt.dwt(xpad, wavelet, mode='symmetric')
+
+        # central region of the padded output (unaffected by mode  )
+        expected_result = (cApad[2:-2], cDpad[2:-2])
+
+        cA, cD = pywt.dwt(x, wavelet, mode)
+        assert_allclose(cA, expected_result[0], rtol=1e-7, atol=1e-8)
+        assert_allclose(cD, expected_result[1], rtol=1e-7, atol=1e-8)
+
+
+def test_default_mode():
+    # The default mode should be 'symmetric'
+    x = [1, 2, 1, 5, -1, 8, 4, 6]
+    cA, cD = pywt.dwt(x, 'db2')
+    cA2, cD2 = pywt.dwt(x, 'db2', mode='symmetric')
+    assert_allclose(cA, cA2)
+    assert_allclose(cD, cD2)
+    assert_allclose(pywt.idwt(cA, cD, 'db2'), x)

venv/Lib/site-packages/pywt/tests/test_multidim.py

@@ -0,0 +1,443 @@
+#!/usr/bin/env python
+
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from itertools import combinations
+from numpy.testing import assert_allclose, assert_, assert_raises, assert_equal
+
+import pywt
+# Check that float32, float64, complex64, complex128 are preserved.
+# Other real types get converted to float64.
+# complex256 gets converted to complex128
+dtypes_in = [np.int8, np.float16, np.float32, np.float64, np.complex64,
+             np.complex128]
+dtypes_out = [np.float64, np.float32, np.float32, np.float64, np.complex64,
+              np.complex128]
+
+# test complex256 as well if it is available
+try:
+    dtypes_in += [np.complex256, ]
+    dtypes_out += [np.complex128, ]
+except AttributeError:
+    pass
+
+
+def test_dwtn_input():
+    # Array-like must be accepted
+    pywt.dwtn([1, 2, 3, 4], 'haar')
+    # Others must not
+    data = dict()
+    assert_raises(TypeError, pywt.dwtn, data, 'haar')
+    # Must be at least 1D
+    assert_raises(ValueError, pywt.dwtn, 2, 'haar')
+
+
+def test_3D_reconstruct():
+    data = np.array([
+        [[0, 4, 1, 5, 1, 4],
+         [0, 5, 26, 3, 2, 1],
+         [5, 8, 2, 33, 4, 9],
+         [2, 5, 19, 4, 19, 1]],
+        [[1, 5, 1, 2, 3, 4],
+         [7, 12, 6, 52, 7, 8],
+         [2, 12, 3, 52, 6, 8],
+         [5, 2, 6, 78, 12, 2]]])
+
+    wavelet = pywt.Wavelet('haar')
+    for mode in pywt.Modes.modes:
+        d = pywt.dwtn(data, wavelet, mode=mode)
+        assert_allclose(data, pywt.idwtn(d, wavelet, mode=mode),
+                        rtol=1e-13, atol=1e-13)
+
+
+def test_dwdtn_idwtn_allwavelets():
+    rstate = np.random.RandomState(1234)
+    r = rstate.randn(16, 16)
+    # test 2D case only for all wavelet types
+    wavelist = pywt.wavelist()
+    if 'dmey' in wavelist:
+        wavelist.remove('dmey')
+    for wavelet in wavelist:
+        if wavelet in ['cmor', 'shan', 'fbsp']:
+            # skip these CWT families to avoid warnings
+            continue
+        if isinstance(pywt.DiscreteContinuousWavelet(wavelet), pywt.Wavelet):
+            for mode in pywt.Modes.modes:
+                coeffs = pywt.dwtn(r, wavelet, mode=mode)
+                assert_allclose(pywt.idwtn(coeffs, wavelet, mode=mode),
+                                r, rtol=1e-7, atol=1e-7)
+
+
+def test_stride():
+    wavelet = pywt.Wavelet('haar')
+
+    for dtype in ('float32', 'float64'):
+        data = np.array([[0, 4, 1, 5, 1, 4],
+                         [0, 5, 6, 3, 2, 1],
+                         [2, 5, 19, 4, 19, 1]],
+                        dtype=dtype)
+
+        for mode in pywt.Modes.modes:
+            expected = pywt.dwtn(data, wavelet)
+            strided = np.ones((3, 12), dtype=data.dtype)
+            strided[::-1, ::2] = data
+            strided_dwtn = pywt.dwtn(strided[::-1, ::2], wavelet)
+            for key in expected.keys():
+                assert_allclose(strided_dwtn[key], expected[key])
+
+
+def test_byte_offset():
+    wavelet = pywt.Wavelet('haar')
+    for dtype in ('float32', 'float64'):
+        data = np.array([[0, 4, 1, 5, 1, 4],
+                         [0, 5, 6, 3, 2, 1],
+                         [2, 5, 19, 4, 19, 1]],
+                        dtype=dtype)
+
+        for mode in pywt.Modes.modes:
+            expected = pywt.dwtn(data, wavelet)
+            padded = np.ones((3, 6), dtype=np.dtype({'data': (data.dtype, 0),
+                                                     'pad': ('byte', data.dtype.itemsize)},
+                                                    align=True))
+            padded[:] = data
+            padded_dwtn = pywt.dwtn(padded['data'], wavelet)
+            for key in expected.keys():
+                assert_allclose(padded_dwtn[key], expected[key])
+
+
+def test_3D_reconstruct_complex():
+    # All dimensions even length so `take` does not need to be specified
+    data = np.array([
+        [[0, 4, 1, 5, 1, 4],
+         [0, 5, 26, 3, 2, 1],
+         [5, 8, 2, 33, 4, 9],
+         [2, 5, 19, 4, 19, 1]],
+        [[1, 5, 1, 2, 3, 4],
+         [7, 12, 6, 52, 7, 8],
+         [2, 12, 3, 52, 6, 8],
+         [5, 2, 6, 78, 12, 2]]])
+    data = data + 1j
+
+    wavelet = pywt.Wavelet('haar')
+    d = pywt.dwtn(data, wavelet)
+    # idwtn creates even-length shapes (2x dwtn size)
+    original_shape = tuple([slice(None, s) for s in data.shape])
+    assert_allclose(data, pywt.idwtn(d, wavelet)[original_shape],
+                    rtol=1e-13, atol=1e-13)
+
+
+def test_idwtn_idwt2():
+    data = np.array([
+        [0, 4, 1, 5, 1, 4],
+        [0, 5, 6, 3, 2, 1],
+        [2, 5, 19, 4, 19, 1]])
+
+    wavelet = pywt.Wavelet('haar')
+
+    LL, (HL, LH, HH) = pywt.dwt2(data, wavelet)
+    d = {'aa': LL, 'da': HL, 'ad': LH, 'dd': HH}
+
+    for mode in pywt.Modes.modes:
+        assert_allclose(pywt.idwt2((LL, (HL, LH, HH)), wavelet, mode=mode),
+                        pywt.idwtn(d, wavelet, mode=mode),
+                        rtol=1e-14, atol=1e-14)
+
+
+def test_idwtn_idwt2_complex():
+    data = np.array([
+        [0, 4, 1, 5, 1, 4],
+        [0, 5, 6, 3, 2, 1],
+        [2, 5, 19, 4, 19, 1]])
+    data = data + 1j
+    wavelet = pywt.Wavelet('haar')
+
+    LL, (HL, LH, HH) = pywt.dwt2(data, wavelet)
+    d = {'aa': LL, 'da': HL, 'ad': LH, 'dd': HH}
+
+    for mode in pywt.Modes.modes:
+        assert_allclose(pywt.idwt2((LL, (HL, LH, HH)), wavelet, mode=mode),
+                        pywt.idwtn(d, wavelet, mode=mode),
+                        rtol=1e-14, atol=1e-14)
+
+
+def test_idwtn_missing():
+    # Test to confirm missing data behave as zeroes
+    data = np.array([
+        [0, 4, 1, 5, 1, 4],
+        [0, 5, 6, 3, 2, 1],
+        [2, 5, 19, 4, 19, 1]])
+
+    wavelet = pywt.Wavelet('haar')
+
+    coefs = pywt.dwtn(data, wavelet)
+
+    # No point removing zero, or all
+    for num_missing in range(1, len(coefs)):
+        for missing in combinations(coefs.keys(), num_missing):
+            missing_coefs = coefs.copy()
+            for key in missing:
+                del missing_coefs[key]
+            LL = missing_coefs.get('aa', None)
+            HL = missing_coefs.get('da', None)
+            LH = missing_coefs.get('ad', None)
+            HH = missing_coefs.get('dd', None)
+
+            assert_allclose(pywt.idwt2((LL, (HL, LH, HH)), wavelet),
+                            pywt.idwtn(missing_coefs, 'haar'), atol=1e-15)
+
+
+def test_idwtn_all_coeffs_None():
+    coefs = dict(aa=None, da=None, ad=None, dd=None)
+    assert_raises(ValueError, pywt.idwtn, coefs, 'haar')
+
+
+def test_error_on_invalid_keys():
+    data = np.array([
+        [0, 4, 1, 5, 1, 4],
+        [0, 5, 6, 3, 2, 1],
+        [2, 5, 19, 4, 19, 1]])
+
+    wavelet = pywt.Wavelet('haar')
+
+    LL, (HL, LH, HH) = pywt.dwt2(data, wavelet)
+
+    # unexpected key
+    d = {'aa': LL, 'da': HL, 'ad': LH, 'dd': HH, 'ff': LH}
+    assert_raises(ValueError, pywt.idwtn, d, wavelet)
+
+    # mismatched key lengths
+    d = {'a': LL, 'da': HL, 'ad': LH, 'dd': HH}
+    assert_raises(ValueError, pywt.idwtn, d, wavelet)
+
+
+def test_error_mismatched_size():
+    data = np.array([
+        [0, 4, 1, 5, 1, 4],
+        [0, 5, 6, 3, 2, 1],
+        [2, 5, 19, 4, 19, 1]])
+
+    wavelet = pywt.Wavelet('haar')
+
+    LL, (HL, LH, HH) = pywt.dwt2(data, wavelet)
+
+    # Pass/fail depends on first element being shorter than remaining ones so
+    # set 3/4 to an incorrect size to maximize chances. Order of dict items
+    # is random so may not trigger on every test run. Dict is constructed
+    # inside idwtn function so no use using an OrderedDict here.
+    LL = LL[:, :-1]
+    LH = LH[:, :-1]
+    HH = HH[:, :-1]
+    d = {'aa': LL, 'da': HL, 'ad': LH, 'dd': HH}
+
+    assert_raises(ValueError, pywt.idwtn, d, wavelet)
+
+
+def test_dwt2_idwt2_dtypes():
+    wavelet = pywt.Wavelet('haar')
+    for dt_in, dt_out in zip(dtypes_in, dtypes_out):
+        x = np.ones((4, 4), dtype=dt_in)
+        errmsg = "wrong dtype returned for {0} input".format(dt_in)
+
+        cA, (cH, cV, cD) = pywt.dwt2(x, wavelet)
+        assert_(cA.dtype == cH.dtype == cV.dtype == cD.dtype,
+                "dwt2: " + errmsg)
+
+        x_roundtrip = pywt.idwt2((cA, (cH, cV, cD)), wavelet)
+        assert_(x_roundtrip.dtype == dt_out, "idwt2: " + errmsg)
+
+
+def test_dwtn_axes():
+    data = np.array([[0, 1, 2, 3],
+                     [1, 1, 1, 1],
+                     [1, 4, 2, 8]])
+    data = data + 1j*data  # test with complex data
+    coefs = pywt.dwtn(data, 'haar', axes=(1,))
+    expected_a = list(map(lambda x: pywt.dwt(x, 'haar')[0], data))
+    assert_equal(coefs['a'], expected_a)
+    expected_d = list(map(lambda x: pywt.dwt(x, 'haar')[1], data))
+    assert_equal(coefs['d'], expected_d)
+
+    coefs = pywt.dwtn(data, 'haar', axes=(1, 1))
+    expected_aa = list(map(lambda x: pywt.dwt(x, 'haar')[0], expected_a))
+    assert_equal(coefs['aa'], expected_aa)
+    expected_ad = list(map(lambda x: pywt.dwt(x, 'haar')[1], expected_a))
+    assert_equal(coefs['ad'], expected_ad)
+
+
+def test_idwtn_axes():
+    data = np.array([[0, 1, 2, 3],
+                     [1, 1, 1, 1],
+                     [1, 4, 2, 8]])
+    data = data + 1j*data  # test with complex data
+    coefs = pywt.dwtn(data, 'haar', axes=(1, 1))
+    assert_allclose(pywt.idwtn(coefs, 'haar', axes=(1, 1)), data, atol=1e-14)
+
+
+def test_idwt2_none_coeffs():
+    data = np.array([[0, 1, 2, 3],
+                     [1, 1, 1, 1],
+                     [1, 4, 2, 8]])
+    data = data + 1j*data  # test with complex data
+    cA, (cH, cV, cD) = pywt.dwt2(data, 'haar', axes=(1, 1))
+
+    # verify setting coefficients to None is the same as zeroing them
+    cD = np.zeros_like(cD)
+    result_zeros = pywt.idwt2((cA, (cH, cV, cD)), 'haar', axes=(1, 1))
+
+    cD = None
+    result_none = pywt.idwt2((cA, (cH, cV, cD)), 'haar', axes=(1, 1))
+
+    assert_equal(result_zeros, result_none)
+
+
+def test_idwtn_none_coeffs():
+    data = np.array([[0, 1, 2, 3],
+                     [1, 1, 1, 1],
+                     [1, 4, 2, 8]])
+    data = data + 1j*data  # test with complex data
+    coefs = pywt.dwtn(data, 'haar', axes=(1, 1))
+
+    # verify setting coefficients to None is the same as zeroing them
+    coefs['dd'] = np.zeros_like(coefs['dd'])
+    result_zeros = pywt.idwtn(coefs, 'haar', axes=(1, 1))
+
+    coefs['dd'] = None
+    result_none = pywt.idwtn(coefs, 'haar', axes=(1, 1))
+
+    assert_equal(result_zeros, result_none)
+
+
+def test_idwt2_axes():
+    data = np.array([[0, 1, 2, 3],
+                     [1, 1, 1, 1],
+                     [1, 4, 2, 8]])
+    coefs = pywt.dwt2(data, 'haar', axes=(1, 1))
+    assert_allclose(pywt.idwt2(coefs, 'haar', axes=(1, 1)), data, atol=1e-14)
+
+    # too many axes
+    assert_raises(ValueError, pywt.idwt2, coefs, 'haar', axes=(0, 1, 1))
+
+
+def test_idwt2_axes_subsets():
+    data = np.array(np.random.standard_normal((4, 4, 4)))
+    # test all combinations of 2 out of 3 axes transformed
+    for axes in combinations((0, 1, 2), 2):
+        coefs = pywt.dwt2(data, 'haar', axes=axes)
+        assert_allclose(pywt.idwt2(coefs, 'haar', axes=axes), data, atol=1e-14)
+
+
+def test_idwtn_axes_subsets():
+    data = np.array(np.random.standard_normal((4, 4, 4, 4)))
+    # test all combinations of 3 out of 4 axes transformed
+    for axes in combinations((0, 1, 2, 3), 3):
+        coefs = pywt.dwtn(data, 'haar', axes=axes)
+        assert_allclose(pywt.idwtn(coefs, 'haar', axes=axes), data, atol=1e-14)
+
+
+def test_negative_axes():
+    data = np.array([[0, 1, 2, 3],
+                     [1, 1, 1, 1],
+                     [1, 4, 2, 8]])
+    coefs1 = pywt.dwtn(data, 'haar', axes=(1, 1))
+    coefs2 = pywt.dwtn(data, 'haar', axes=(-1, -1))
+    assert_equal(coefs1, coefs2)
+
+    rec1 = pywt.idwtn(coefs1, 'haar', axes=(1, 1))
+    rec2 = pywt.idwtn(coefs1, 'haar', axes=(-1, -1))
+    assert_equal(rec1, rec2)
+
+
+def test_dwtn_idwtn_dtypes():
+    wavelet = pywt.Wavelet('haar')
+    for dt_in, dt_out in zip(dtypes_in, dtypes_out):
+        x = np.ones((4, 4), dtype=dt_in)
+        errmsg = "wrong dtype returned for {0} input".format(dt_in)
+
+        coeffs = pywt.dwtn(x, wavelet)
+        for k, v in coeffs.items():
+            assert_(v.dtype == dt_out, "dwtn: " + errmsg)
+
+        x_roundtrip = pywt.idwtn(coeffs, wavelet)
+        assert_(x_roundtrip.dtype == dt_out, "idwtn: " + errmsg)
+
+
+def test_idwtn_mixed_complex_dtype():
+    rstate = np.random.RandomState(0)
+    x = rstate.randn(8, 8, 8)
+    x = x + 1j*x
+    coeffs = pywt.dwtn(x, 'db2')
+
+    x_roundtrip = pywt.idwtn(coeffs, 'db2')
+    assert_allclose(x_roundtrip, x, rtol=1e-10)
+
+    # mismatched dtypes OK
+    coeffs['a' * x.ndim] = coeffs['a' * x.ndim].astype(np.complex64)
+    x_roundtrip2 = pywt.idwtn(coeffs, 'db2')
+    assert_allclose(x_roundtrip2, x, rtol=1e-7, atol=1e-7)
+    assert_(x_roundtrip2.dtype == np.complex128)
+
+
+def test_idwt2_size_mismatch_error():
+    LL = np.zeros((6, 6))
+    LH = HL = HH = np.zeros((5, 5))
+
+    assert_raises(ValueError, pywt.idwt2, (LL, (LH, HL, HH)), wavelet='haar')
+
+
+def test_dwt2_dimension_error():
+    data = np.ones(16)
+    wavelet = pywt.Wavelet('haar')
+
+    # wrong number of input dimensions
+    assert_raises(ValueError, pywt.dwt2, data, wavelet)
+
+    # too many axes
+    data2 = np.ones((8, 8))
+    assert_raises(ValueError, pywt.dwt2, data2, wavelet, axes=(0, 1, 1))
+
+
+def test_per_axis_wavelets_and_modes():
+    # tests seperate wavelet and edge mode for each axis.
+    rstate = np.random.RandomState(1234)
+    data = rstate.randn(16, 16, 16)
+
+    # wavelet can be a string or wavelet object
+    wavelets = (pywt.Wavelet('haar'), 'sym2', 'db4')
+
+    # mode can be a string or a Modes enum
+    modes = ('symmetric', 'periodization',
+             pywt._extensions._pywt.Modes.reflect)
+
+    coefs = pywt.dwtn(data, wavelets, modes)
+    assert_allclose(pywt.idwtn(coefs, wavelets, modes), data, atol=1e-14)
+
+    coefs = pywt.dwtn(data, wavelets[:1], modes)
+    assert_allclose(pywt.idwtn(coefs, wavelets[:1], modes), data, atol=1e-14)
+
+    coefs = pywt.dwtn(data, wavelets, modes[:1])
+    assert_allclose(pywt.idwtn(coefs, wavelets, modes[:1]), data, atol=1e-14)
+
+    # length of wavelets or modes doesn't match the length of axes
+    assert_raises(ValueError, pywt.dwtn, data, wavelets[:2])
+    assert_raises(ValueError, pywt.dwtn, data, wavelets, mode=modes[:2])
+    assert_raises(ValueError, pywt.idwtn, coefs, wavelets[:2])
+    assert_raises(ValueError, pywt.idwtn, coefs, wavelets, mode=modes[:2])
+
+    # dwt2/idwt2 also support per-axis wavelets/modes
+    data2 = data[..., 0]
+    coefs2 = pywt.dwt2(data2, wavelets[:2], modes[:2])
+    assert_allclose(pywt.idwt2(coefs2, wavelets[:2], modes[:2]), data2,
+                    atol=1e-14)
+
+
+def test_error_on_continuous_wavelet():
+    # A ValueError is raised if a Continuous wavelet is selected
+    data = np.ones((16, 16))
+    for dec_fun, rec_fun in zip([pywt.dwt2, pywt.dwtn],
+                                [pywt.idwt2, pywt.idwtn]):
+        for cwave in ['morl', pywt.DiscreteContinuousWavelet('morl')]:
+            assert_raises(ValueError, dec_fun, data, wavelet=cwave)
+
+            c = dec_fun(data, 'db1')
+            assert_raises(ValueError, rec_fun, c, wavelet=cwave)

venv/Lib/site-packages/pywt/tests/test_perfect_reconstruction.py

@@ -0,0 +1,61 @@
+#!/usr/bin/env python
+
+"""
+Verify DWT perfect reconstruction.
+"""
+
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import assert_
+
+import pywt
+
+
+def test_perfect_reconstruction():
+    families = ('db', 'sym', 'coif', 'bior', 'rbio')
+    wavelets = sum([pywt.wavelist(name) for name in families], [])
+    # list of mode names in pywt and matlab
+    modes = [('zero', 'zpd'),
+             ('constant', 'sp0'),
+             ('symmetric', 'sym'),
+             ('periodic', 'ppd'),
+             ('smooth', 'sp1'),
+             ('periodization', 'per')]
+
+    dtypes = (np.float32, np.float64)
+
+    for wavelet in wavelets:
+        for pmode, mmode in modes:
+            for dt in dtypes:
+                check_reconstruction(pmode, mmode, wavelet, dt)
+
+
+def check_reconstruction(pmode, mmode, wavelet, dtype):
+    data_size = list(range(2, 40)) + [100, 200, 500, 1000, 2000, 10000,
+                                      50000, 100000]
+    np.random.seed(12345)
+    # TODO: smoke testing - more failures for different seeds
+
+    if dtype == np.float32:
+        # was 3e-7 has to be lowered as db21, db29, db33, db35, coif14, coif16 were failing
+        epsilon = 6e-7
+    else:
+        epsilon = 5e-11
+
+    for N in data_size:
+        data = np.asarray(np.random.random(N), dtype)
+
+        # compute dwt coefficients
+        pa, pd = pywt.dwt(data, wavelet, pmode)
+
+        # compute reconstruction
+        rec = pywt.idwt(pa, pd, wavelet, pmode)
+
+        if len(data) % 2:
+            rec = rec[:len(data)]
+
+        rms_rec = np.sqrt(np.mean((data-rec)**2))
+        msg = ('[RMS_REC > EPSILON] for Mode: %s, Wavelet: %s, '
+               'Length: %d, rms=%.3g' % (pmode, wavelet, len(data), rms_rec))
+        assert_(rms_rec < epsilon, msg=msg)

venv/Lib/site-packages/pywt/tests/test_swt.py

@@ -0,0 +1,633 @@
+#!/usr/bin/env python
+
+from __future__ import division, print_function, absolute_import
+
+import warnings
+from copy import deepcopy
+from itertools import combinations, permutations
+import numpy as np
+import pytest
+from numpy.testing import (assert_allclose, assert_, assert_equal,
+                           assert_raises, assert_array_equal, assert_warns)
+
+import pywt
+from pywt._extensions._swt import swt_axis
+
+# Check that float32 and complex64 are preserved.  Other real types get
+# converted to float64.
+dtypes_in = [np.int8, np.float16, np.float32, np.float64, np.complex64,
+             np.complex128]
+dtypes_out = [np.float64, np.float32, np.float32, np.float64, np.complex64,
+              np.complex128]
+
+# tolerances used in accuracy comparisons
+tol_single = 1e-6
+tol_double = 1e-13
+
+####
+# 1d multilevel swt tests
+####
+
+
+def test_swt_decomposition():
+    x = [3, 7, 1, 3, -2, 6, 4, 6]
+    db1 = pywt.Wavelet('db1')
+    atol = tol_double
+    (cA3, cD3), (cA2, cD2), (cA1, cD1) = pywt.swt(x, db1, level=3)
+    expected_cA1 = [7.07106781, 5.65685425, 2.82842712, 0.70710678,
+                    2.82842712, 7.07106781, 7.07106781, 6.36396103]
+    assert_allclose(cA1, expected_cA1, rtol=1e-8, atol=atol)
+    expected_cD1 = [-2.82842712, 4.24264069, -1.41421356, 3.53553391,
+                    -5.65685425, 1.41421356, -1.41421356, 2.12132034]
+    assert_allclose(cD1, expected_cD1, rtol=1e-8, atol=atol)
+    expected_cA2 = [7, 4.5, 4, 5.5, 7, 9.5, 10, 8.5]
+    assert_allclose(cA2, expected_cA2, rtol=tol_double, atol=atol)
+    expected_cD2 = [3, 3.5, 0, -4.5, -3, 0.5, 0, 0.5]
+    assert_allclose(cD2, expected_cD2, rtol=tol_double, atol=atol)
+    expected_cA3 = [9.89949494, ] * 8
+    assert_allclose(cA3, expected_cA3, rtol=1e-8, atol=atol)
+    expected_cD3 = [0.00000000, -3.53553391, -4.24264069, -2.12132034,
+                    0.00000000, 3.53553391, 4.24264069, 2.12132034]
+    assert_allclose(cD3, expected_cD3, rtol=1e-8, atol=atol)
+
+    # level=1, start_level=1 decomposition should match level=2
+    res = pywt.swt(cA1, db1, level=1, start_level=1)
+    cA2, cD2 = res[0]
+    assert_allclose(cA2, expected_cA2, rtol=tol_double, atol=atol)
+    assert_allclose(cD2, expected_cD2, rtol=tol_double, atol=atol)
+
+    coeffs = pywt.swt(x, db1)
+    assert_(len(coeffs) == 3)
+    assert_(pywt.swt_max_level(len(x)), 3)
+
+
+def test_swt_max_level():
+    # odd sized signal will warn about no levels of decomposition possible
+    assert_warns(UserWarning, pywt.swt_max_level, 11)
+    with warnings.catch_warnings():
+        warnings.simplefilter('ignore', UserWarning)
+        assert_equal(pywt.swt_max_level(11), 0)
+
+    # no warnings when >= 1 level of decomposition possible
+    assert_equal(pywt.swt_max_level(2), 1)     # divisible by 2**1
+    assert_equal(pywt.swt_max_level(4*3), 2)    # divisible by 2**2
+    assert_equal(pywt.swt_max_level(16), 4)    # divisible by 2**4
+    assert_equal(pywt.swt_max_level(16*3), 4)  # divisible by 2**4
+
+
+def test_swt_axis():
+    x = [3, 7, 1, 3, -2, 6, 4, 6]
+
+    db1 = pywt.Wavelet('db1')
+    (cA2, cD2), (cA1, cD1) = pywt.swt(x, db1, level=2)
+
+    # test cases use 2D arrays based on tiling x along an axis and then
+    # calling swt along the other axis.
+    for order in ['C', 'F']:
+        # test SWT of 2D data along default axis (-1)
+        x_2d = np.asarray(x).reshape((1, -1))
+        x_2d = np.concatenate((x_2d, )*5, axis=0)
+        if order == 'C':
+            x_2d = np.ascontiguousarray(x_2d)
+        elif order == 'F':
+            x_2d = np.asfortranarray(x_2d)
+        (cA2_2d, cD2_2d), (cA1_2d, cD1_2d) = pywt.swt(x_2d, db1, level=2)
+
+        for c in [cA2_2d, cD2_2d, cA1_2d, cD1_2d]:
+            assert_(c.shape == x_2d.shape)
+        # each row should match the 1D result
+        for row in cA1_2d:
+            assert_array_equal(row, cA1)
+        for row in cA2_2d:
+            assert_array_equal(row, cA2)
+        for row in cD1_2d:
+            assert_array_equal(row, cD1)
+        for row in cD2_2d:
+            assert_array_equal(row, cD2)
+
+        # test SWT of 2D data along other axis (0)
+        x_2d = np.asarray(x).reshape((-1, 1))
+        x_2d = np.concatenate((x_2d, )*5, axis=1)
+        if order == 'C':
+            x_2d = np.ascontiguousarray(x_2d)
+        elif order == 'F':
+            x_2d = np.asfortranarray(x_2d)
+        (cA2_2d, cD2_2d), (cA1_2d, cD1_2d) = pywt.swt(x_2d, db1, level=2,
+                                                      axis=0)
+
+        for c in [cA2_2d, cD2_2d, cA1_2d, cD1_2d]:
+            assert_(c.shape == x_2d.shape)
+        # each column should match the 1D result
+        for row in cA1_2d.transpose((1, 0)):
+            assert_array_equal(row, cA1)
+        for row in cA2_2d.transpose((1, 0)):
+            assert_array_equal(row, cA2)
+        for row in cD1_2d.transpose((1, 0)):
+            assert_array_equal(row, cD1)
+        for row in cD2_2d.transpose((1, 0)):
+            assert_array_equal(row, cD2)
+
+    # axis too large
+    assert_raises(ValueError, pywt.swt, x, db1, level=2, axis=5)
+
+
+def test_swt_iswt_integration():
+    # This function performs a round-trip swt/iswt transform test on
+    # all available types of wavelets in PyWavelets - except the
+    # 'dmey' wavelet. The latter has been excluded because it does not
+    # produce very precise results. This is likely due to the fact
+    # that the 'dmey' wavelet is a discrete approximation of a
+    # continuous wavelet. All wavelets are tested up to 3 levels. The
+    # test validates neither swt or iswt as such, but it does ensure
+    # that they are each other's inverse.
+
+    max_level = 3
+    wavelets = pywt.wavelist(kind='discrete')
+    if 'dmey' in wavelets:
+        # The 'dmey' wavelet seems to be a bit special - disregard it for now
+        wavelets.remove('dmey')
+    for current_wavelet_str in wavelets:
+        current_wavelet = pywt.Wavelet(current_wavelet_str)
+        input_length_power = int(np.ceil(np.log2(max(
+            current_wavelet.dec_len,
+            current_wavelet.rec_len))))
+        input_length = 2**(input_length_power + max_level - 1)
+        X = np.arange(input_length)
+        for norm in [True, False]:
+            if norm and not current_wavelet.orthogonal:
+                # non-orthogonal wavelets to avoid warnings when norm=True
+                continue
+            for trim_approx in [True, False]:
+                coeffs = pywt.swt(X, current_wavelet, max_level,
+                                  trim_approx=trim_approx, norm=norm)
+                Y = pywt.iswt(coeffs, current_wavelet, norm=norm)
+                assert_allclose(Y, X, rtol=1e-5, atol=1e-7)
+
+
+def test_swt_dtypes():
+    wavelet = pywt.Wavelet('haar')
+    for dt_in, dt_out in zip(dtypes_in, dtypes_out):
+        errmsg = "wrong dtype returned for {0} input".format(dt_in)
+
+        # swt
+        x = np.ones(8, dtype=dt_in)
+        (cA2, cD2), (cA1, cD1) = pywt.swt(x, wavelet, level=2)
+        assert_(cA2.dtype == cD2.dtype == cA1.dtype == cD1.dtype == dt_out,
+                "swt: " + errmsg)
+
+        # swt2
+        x = np.ones((8, 8), dtype=dt_in)
+        cA, (cH, cV, cD) = pywt.swt2(x, wavelet, level=1)[0]
+        assert_(cA.dtype == cH.dtype == cV.dtype == cD.dtype == dt_out,
+                "swt2: " + errmsg)
+
+
+def test_swt_roundtrip_dtypes():
+    # verify perfect reconstruction for all dtypes
+    rstate = np.random.RandomState(5)
+    wavelet = pywt.Wavelet('haar')
+    for dt_in, dt_out in zip(dtypes_in, dtypes_out):
+        # swt, iswt
+        x = rstate.standard_normal((8, )).astype(dt_in)
+        c = pywt.swt(x, wavelet, level=2)
+        xr = pywt.iswt(c, wavelet)
+        assert_allclose(x, xr, rtol=1e-6, atol=1e-7)
+
+        # swt2, iswt2
+        x = rstate.standard_normal((8, 8)).astype(dt_in)
+        c = pywt.swt2(x, wavelet, level=2)
+        xr = pywt.iswt2(c, wavelet)
+        assert_allclose(x, xr, rtol=1e-6, atol=1e-7)
+
+
+def test_swt_default_level_by_axis():
+    # make sure default number of levels matches the max level along the axis
+    wav = 'db2'
+    x = np.ones((2**3, 2**4, 2**5))
+    for axis in (0, 1, 2):
+        sdec = pywt.swt(x, wav, level=None, start_level=0, axis=axis)
+        assert_equal(len(sdec), pywt.swt_max_level(x.shape[axis]))
+
+
+def test_swt2_ndim_error():
+    x = np.ones(8)
+    with warnings.catch_warnings():
+        warnings.simplefilter('ignore', FutureWarning)
+        assert_raises(ValueError, pywt.swt2, x, 'haar', level=1)
+
+
+@pytest.mark.slow
+def test_swt2_iswt2_integration(wavelets=None):
+    # This function performs a round-trip swt2/iswt2 transform test on
+    # all available types of wavelets in PyWavelets - except the
+    # 'dmey' wavelet. The latter has been excluded because it does not
+    # produce very precise results. This is likely due to the fact
+    # that the 'dmey' wavelet is a discrete approximation of a
+    # continuous wavelet. All wavelets are tested up to 3 levels. The
+    # test validates neither swt2 or iswt2 as such, but it does ensure
+    # that they are each other's inverse.
+
+    max_level = 3
+    if wavelets is None:
+        wavelets = pywt.wavelist(kind='discrete')
+        if 'dmey' in wavelets:
+            # The 'dmey' wavelet is a special case - disregard it for now
+            wavelets.remove('dmey')
+    for current_wavelet_str in wavelets:
+        current_wavelet = pywt.Wavelet(current_wavelet_str)
+        input_length_power = int(np.ceil(np.log2(max(
+            current_wavelet.dec_len,
+            current_wavelet.rec_len))))
+        input_length = 2**(input_length_power + max_level - 1)
+        X = np.arange(input_length**2).reshape(input_length, input_length)
+
+        for norm in [True, False]:
+            if norm and not current_wavelet.orthogonal:
+                # non-orthogonal wavelets to avoid warnings when norm=True
+                continue
+            for trim_approx in [True, False]:
+                coeffs = pywt.swt2(X, current_wavelet, max_level,
+                                   trim_approx=trim_approx, norm=norm)
+                Y = pywt.iswt2(coeffs, current_wavelet, norm=norm)
+                assert_allclose(Y, X, rtol=1e-5, atol=1e-5)
+
+
+def test_swt2_iswt2_quick():
+    test_swt2_iswt2_integration(wavelets=['db1', ])
+
+
+def test_swt2_iswt2_non_square(wavelets=None):
+    for nrows in [8, 16, 48]:
+        X = np.arange(nrows*32).reshape(nrows, 32)
+        current_wavelet = 'db1'
+        with warnings.catch_warnings():
+            warnings.simplefilter('ignore', FutureWarning)
+            coeffs = pywt.swt2(X, current_wavelet, level=2)
+            Y = pywt.iswt2(coeffs, current_wavelet)
+        assert_allclose(Y, X, rtol=tol_single, atol=tol_single)
+
+
+def test_swt2_axes():
+    atol = 1e-14
+    current_wavelet = pywt.Wavelet('db2')
+    input_length_power = int(np.ceil(np.log2(max(
+        current_wavelet.dec_len,
+        current_wavelet.rec_len))))
+    input_length = 2**(input_length_power)
+    X = np.arange(input_length**2).reshape(input_length, input_length)
+
+    (cA1, (cH1, cV1, cD1)) = pywt.swt2(X, current_wavelet, level=1)[0]
+    # opposite order
+    (cA2, (cH2, cV2, cD2)) = pywt.swt2(X, current_wavelet, level=1,
+                                       axes=(1, 0))[0]
+    assert_allclose(cA1, cA2, atol=atol)
+    assert_allclose(cH1, cV2, atol=atol)
+    assert_allclose(cV1, cH2, atol=atol)
+    assert_allclose(cD1, cD2, atol=atol)
+
+    # duplicate axes not allowed
+    assert_raises(ValueError, pywt.swt2, X, current_wavelet, 1,
+                  axes=(0, 0))
+    # too few axes
+    assert_raises(ValueError, pywt.swt2, X, current_wavelet, 1, axes=(0, ))
+
+
+def test_iswt2_2d_only():
+    # iswt2 is not currently compatible with data that is not 2D
+    x_3d = np.ones((4, 4, 4))
+    c = pywt.swt2(x_3d, 'haar', level=1)
+    assert_raises(ValueError, pywt.iswt2, c, 'haar')
+
+
+def test_swtn_axes():
+    atol = 1e-14
+    current_wavelet = pywt.Wavelet('db2')
+    input_length_power = int(np.ceil(np.log2(max(
+        current_wavelet.dec_len,
+        current_wavelet.rec_len))))
+    input_length = 2**(input_length_power)
+    X = np.arange(input_length**2).reshape(input_length, input_length)
+    coeffs = pywt.swtn(X, current_wavelet, level=1, axes=None)[0]
+    # opposite order
+    coeffs2 = pywt.swtn(X, current_wavelet, level=1, axes=(1, 0))[0]
+    assert_allclose(coeffs['aa'], coeffs2['aa'], atol=atol)
+    assert_allclose(coeffs['ad'], coeffs2['da'], atol=atol)
+    assert_allclose(coeffs['da'], coeffs2['ad'], atol=atol)
+    assert_allclose(coeffs['dd'], coeffs2['dd'], atol=atol)
+
+    # 0-level transform
+    empty = pywt.swtn(X, current_wavelet, level=0)
+    assert_equal(empty, [])
+
+    # duplicate axes not allowed
+    assert_raises(ValueError, pywt.swtn, X, current_wavelet, 1, axes=(0, 0))
+
+    # data.ndim = 0
+    assert_raises(ValueError, pywt.swtn, np.asarray([]), current_wavelet, 1)
+
+    # start_level too large
+    assert_raises(ValueError, pywt.swtn, X, current_wavelet,
+                  level=1, start_level=2)
+
+    # level < 1 in swt_axis call
+    assert_raises(ValueError, swt_axis, X, current_wavelet, level=0,
+                  start_level=0)
+    # odd-sized data not allowed
+    assert_raises(ValueError, swt_axis, X[:-1, :], current_wavelet, level=0,
+                  start_level=0, axis=0)
+
+
+@pytest.mark.slow
+def test_swtn_iswtn_integration(wavelets=None):
+    # This function performs a round-trip swtn/iswtn transform for various
+    # possible combinations of:
+    #   1.) 1 out of 2 axes of a 2D array
+    #   2.) 2 out of 3 axes of a 3D array
+    #
+    # To keep test time down, only wavelets of length <= 8 are run.
+    #
+    # This test does not validate swtn or iswtn individually, but only
+    # confirms that iswtn yields an (almost) perfect reconstruction of swtn.
+    max_level = 3
+    if wavelets is None:
+        wavelets = pywt.wavelist(kind='discrete')
+        if 'dmey' in wavelets:
+            # The 'dmey' wavelet is a special case - disregard it for now
+            wavelets.remove('dmey')
+    for ndim_transform in range(1, 3):
+        ndim = ndim_transform + 1
+        for axes in combinations(range(ndim), ndim_transform):
+            for current_wavelet_str in wavelets:
+                wav = pywt.Wavelet(current_wavelet_str)
+                if wav.dec_len > 8:
+                    continue  # avoid excessive test duration
+                input_length_power = int(np.ceil(np.log2(max(
+                    wav.dec_len,
+                    wav.rec_len))))
+                N = 2**(input_length_power + max_level - 1)
+                X = np.arange(N**ndim).reshape((N, )*ndim)
+
+                for norm in [True, False]:
+                    if norm and not wav.orthogonal:
+                        # non-orthogonal wavelets to avoid warnings
+                        continue
+                    for trim_approx in [True, False]:
+                        coeffs = pywt.swtn(X, wav, max_level, axes=axes,
+                                           trim_approx=trim_approx, norm=norm)
+                        coeffs_copy = deepcopy(coeffs)
+                        Y = pywt.iswtn(coeffs, wav, axes=axes, norm=norm)
+                        assert_allclose(Y, X, rtol=1e-5, atol=1e-5)
+
+                # verify the inverse transform didn't modify any coeffs
+                for c, c2 in zip(coeffs, coeffs_copy):
+                    for k, v in c.items():
+                        assert_array_equal(c2[k], v)
+
+
+def test_swtn_iswtn_quick():
+    test_swtn_iswtn_integration(wavelets=['db1', ])
+
+
+def test_iswtn_errors():
+    x = np.arange(8**3).reshape(8, 8, 8)
+    max_level = 2
+    axes = (0, 1)
+    w = pywt.Wavelet('db1')
+    coeffs = pywt.swtn(x, w, max_level, axes=axes)
+
+    # more axes than dimensions transformed
+    assert_raises(ValueError, pywt.iswtn, coeffs, w, axes=(0, 1, 2))
+    # duplicate axes not allowed
+    assert_raises(ValueError, pywt.iswtn, coeffs, w, axes=(0, 0))
+    # mismatched coefficient size
+    coeffs[0]['da'] = coeffs[0]['da'][:-1, :]
+    assert_raises(RuntimeError, pywt.iswtn, coeffs, w, axes=axes)
+
+
+def test_swtn_iswtn_unique_shape_per_axis():
+    # test case for gh-460
+    _shape = (1, 48, 32)  # unique shape per axis
+    wav = 'sym2'
+    max_level = 3
+    rstate = np.random.RandomState(0)
+    for shape in permutations(_shape):
+        # transform only along the non-singleton axes
+        axes = [ax for ax, s in enumerate(shape) if s != 1]
+        x = rstate.standard_normal(shape)
+        c = pywt.swtn(x, wav, max_level, axes=axes)
+        r = pywt.iswtn(c, wav, axes=axes)
+        assert_allclose(x, r, rtol=1e-10, atol=1e-10)
+
+
+def test_per_axis_wavelets():
+    # tests seperate wavelet for each axis.
+    rstate = np.random.RandomState(1234)
+    data = rstate.randn(16, 16, 16)
+    level = 3
+
+    # wavelet can be a string or wavelet object
+    wavelets = (pywt.Wavelet('haar'), 'sym2', 'db4')
+
+    coefs = pywt.swtn(data, wavelets, level=level)
+    assert_allclose(pywt.iswtn(coefs, wavelets), data, atol=1e-14)
+
+    # 1-tuple also okay
+    coefs = pywt.swtn(data, wavelets[:1], level=level)
+    assert_allclose(pywt.iswtn(coefs, wavelets[:1]), data, atol=1e-14)
+
+    # length of wavelets doesn't match the length of axes
+    assert_raises(ValueError, pywt.swtn, data, wavelets[:2], level)
+    assert_raises(ValueError, pywt.iswtn, coefs, wavelets[:2])
+
+    with warnings.catch_warnings():
+        warnings.simplefilter('ignore', FutureWarning)
+        # swt2/iswt2 also support per-axis wavelets/modes
+        data2 = data[..., 0]
+        coefs2 = pywt.swt2(data2, wavelets[:2], level)
+        assert_allclose(pywt.iswt2(coefs2, wavelets[:2]), data2, atol=1e-14)
+
+
+def test_error_on_continuous_wavelet():
+    # A ValueError is raised if a Continuous wavelet is selected
+    data = np.ones((16, 16))
+    for dec_func, rec_func in zip([pywt.swt, pywt.swt2, pywt.swtn],
+                                  [pywt.iswt, pywt.iswt2, pywt.iswtn]):
+        for cwave in ['morl', pywt.DiscreteContinuousWavelet('morl')]:
+            assert_raises(ValueError, dec_func, data, wavelet=cwave,
+                          level=3)
+
+            c = dec_func(data, 'db1', level=3)
+            assert_raises(ValueError, rec_func, c, wavelet=cwave)
+
+
+def test_iswt_mixed_dtypes():
+    # Mixed precision inputs give double precision output
+    x_real = np.arange(16).astype(np.float64)
+    x_complex = x_real + 1j*x_real
+    wav = 'sym2'
+    for dtype1, dtype2 in [(np.float64, np.float32),
+                           (np.float32, np.float64),
+                           (np.float16, np.float64),
+                           (np.complex128, np.complex64),
+                           (np.complex64, np.complex128)]:
+
+        if dtype1 in [np.complex64, np.complex128]:
+            x = x_complex
+            output_dtype = np.complex128
+        else:
+            x = x_real
+            output_dtype = np.float64
+
+        coeffs = pywt.swt(x, wav, 2)
+        # different precision for the approximation coefficients
+        coeffs[0] = [coeffs[0][0].astype(dtype1),
+                     coeffs[0][1].astype(dtype2)]
+        y = pywt.iswt(coeffs, wav)
+        assert_equal(output_dtype, y.dtype)
+        assert_allclose(y, x, rtol=1e-3, atol=1e-3)
+
+
+def test_iswt2_mixed_dtypes():
+    # Mixed precision inputs give double precision output
+    rstate = np.random.RandomState(0)
+    x_real = rstate.randn(8, 8)
+    x_complex = x_real + 1j*x_real
+    wav = 'sym2'
+    for dtype1, dtype2 in [(np.float64, np.float32),
+                           (np.float32, np.float64),
+                           (np.float16, np.float64),
+                           (np.complex128, np.complex64),
+                           (np.complex64, np.complex128)]:
+
+        if dtype1 in [np.complex64, np.complex128]:
+            x = x_complex
+            output_dtype = np.complex128
+        else:
+            x = x_real
+            output_dtype = np.float64
+
+        coeffs = pywt.swt2(x, wav, 2)
+        # different precision for the approximation coefficients
+        coeffs[0] = [coeffs[0][0].astype(dtype1),
+                     tuple([c.astype(dtype2) for c in coeffs[0][1]])]
+        y = pywt.iswt2(coeffs, wav)
+        assert_equal(output_dtype, y.dtype)
+        assert_allclose(y, x, rtol=1e-3, atol=1e-3)
+
+
+def test_iswtn_mixed_dtypes():
+    # Mixed precision inputs give double precision output
+    rstate = np.random.RandomState(0)
+    x_real = rstate.randn(8, 8, 8)
+    x_complex = x_real + 1j*x_real
+    wav = 'sym2'
+    for dtype1, dtype2 in [(np.float64, np.float32),
+                           (np.float32, np.float64),
+                           (np.float16, np.float64),
+                           (np.complex128, np.complex64),
+                           (np.complex64, np.complex128)]:
+
+        if dtype1 in [np.complex64, np.complex128]:
+            x = x_complex
+            output_dtype = np.complex128
+        else:
+            x = x_real
+            output_dtype = np.float64
+
+        coeffs = pywt.swtn(x, wav, 2)
+        # different precision for the approximation coefficients
+        a = coeffs[0].pop('a' * x.ndim)
+        a = a.astype(dtype1)
+        coeffs[0] = {k: c.astype(dtype2) for k, c in coeffs[0].items()}
+        coeffs[0]['a' * x.ndim] = a
+        y = pywt.iswtn(coeffs, wav)
+        assert_equal(output_dtype, y.dtype)
+        assert_allclose(y, x, rtol=1e-3, atol=1e-3)
+
+
+def test_swt_zero_size_axes():
+    # raise on empty input array
+    assert_raises(ValueError, pywt.swt, [], 'db2')
+
+    # >1D case uses a different code path so check there as well
+    x = np.ones((1, 4))[0:0, :]  # 2D with a size zero axis
+    assert_raises(ValueError, pywt.swtn, x, 'db2', level=1, axes=(0,))
+
+
+def test_swt_variance_and_energy_preservation():
+    """Verify that the 1D SWT partitions variance among the coefficients."""
+    # When norm is True and the wavelet is orthogonal, the sum of the
+    # variances of the coefficients should equal the variance of the signal.
+    wav = 'db2'
+    rstate = np.random.RandomState(5)
+    x = rstate.randn(256)
+    coeffs = pywt.swt(x, wav, trim_approx=True, norm=True)
+    variances = [np.var(c) for c in coeffs]
+    assert_allclose(np.sum(variances), np.var(x))
+
+    # also verify L2-norm energy preservation property
+    assert_allclose(np.linalg.norm(x),
+                    np.linalg.norm(np.concatenate(coeffs)))
+
+    # non-orthogonal wavelet with norm=True raises a warning
+    assert_warns(UserWarning, pywt.swt, x, 'bior2.2', norm=True)
+
+
+def test_swt2_variance_and_energy_preservation():
+    """Verify that the 2D SWT partitions variance among the coefficients."""
+    # When norm is True and the wavelet is orthogonal, the sum of the
+    # variances of the coefficients should equal the variance of the signal.
+    wav = 'db2'
+    rstate = np.random.RandomState(5)
+    x = rstate.randn(64, 64)
+    coeffs = pywt.swt2(x, wav, level=4, trim_approx=True, norm=True)
+    coeff_list = [coeffs[0].ravel()]
+    for d in coeffs[1:]:
+        for v in d:
+            coeff_list.append(v.ravel())
+    variances = [np.var(v) for v in coeff_list]
+    assert_allclose(np.sum(variances), np.var(x))
+
+    # also verify L2-norm energy preservation property
+    assert_allclose(np.linalg.norm(x),
+                    np.linalg.norm(np.concatenate(coeff_list)))
+
+    # non-orthogonal wavelet with norm=True raises a warning
+    assert_warns(UserWarning, pywt.swt2, x, 'bior2.2', level=4, norm=True)
+
+
+def test_swtn_variance_and_energy_preservation():
+    """Verify that the nD SWT partitions variance among the coefficients."""
+    # When norm is True and the wavelet is orthogonal, the sum of the
+    # variances of the coefficients should equal the variance of the signal.
+    wav = 'db2'
+    rstate = np.random.RandomState(5)
+    x = rstate.randn(64, 64)
+    coeffs = pywt.swtn(x, wav, level=4, trim_approx=True, norm=True)
+    coeff_list = [coeffs[0].ravel()]
+    for d in coeffs[1:]:
+        for k, v in d.items():
+            coeff_list.append(v.ravel())
+    variances = [np.var(v) for v in coeff_list]
+    assert_allclose(np.sum(variances), np.var(x))
+
+    # also verify L2-norm energy preservation property
+    assert_allclose(np.linalg.norm(x),
+                    np.linalg.norm(np.concatenate(coeff_list)))
+
+    # non-orthogonal wavelet with norm=True raises a warning
+    assert_warns(UserWarning, pywt.swtn, x, 'bior2.2', level=4, norm=True)
+
+
+def test_swt_ravel_and_unravel():
+    # When trim_approx=True, all swt functions can user pywt.ravel_coeffs
+    for ndim, _swt, _iswt, ravel_type in [
+            (1, pywt.swt, pywt.iswt, 'swt'),
+            (2, pywt.swt2, pywt.iswt2, 'swt2'),
+            (3, pywt.swtn, pywt.iswtn, 'swtn')]:
+        x = np.ones((16, ) * ndim)
+        c = _swt(x, 'sym2', level=3, trim_approx=True)
+        arr, slices, shapes = pywt.ravel_coeffs(c)
+        c = pywt.unravel_coeffs(arr, slices, shapes, output_format=ravel_type)
+        r = _iswt(c, 'sym2')
+        assert_allclose(x, r)

venv/Lib/site-packages/pywt/tests/test_thresholding.py

@@ -0,0 +1,169 @@
+from __future__ import division, print_function, absolute_import
+import numpy as np
+from numpy.testing import assert_allclose, assert_raises, assert_, assert_equal
+
+import pywt
+
+
+float_dtypes = [np.float32, np.float64, np.complex64, np.complex128]
+real_dtypes = [np.float32, np.float64]
+
+
+def _sign(x):
+    # Matlab-like sign function (numpy uses a different convention).
+    return x / np.abs(x)
+
+
+def _soft(x, thresh):
+    """soft thresholding supporting complex values.
+
+    Notes
+    -----
+    This version is not robust to zeros in x.
+    """
+    return _sign(x) * np.maximum(np.abs(x) - thresh, 0)
+
+
+def test_threshold():
+    data = np.linspace(1, 4, 7)
+
+    # soft
+    soft_result = [0., 0., 0., 0.5, 1., 1.5, 2.]
+    assert_allclose(pywt.threshold(data, 2, 'soft'),
+                    np.array(soft_result), rtol=1e-12)
+    assert_allclose(pywt.threshold(-data, 2, 'soft'),
+                    -np.array(soft_result), rtol=1e-12)
+    assert_allclose(pywt.threshold([[1, 2]] * 2, 1, 'soft'),
+                    [[0, 1]] * 2, rtol=1e-12)
+    assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'soft'),
+                    [[0, 0]] * 2, rtol=1e-12)
+
+    # soft thresholding complex values
+    assert_allclose(pywt.threshold([[1j, 2j]] * 2, 1, 'soft'),
+                    [[0j, 1j]] * 2, rtol=1e-12)
+    assert_allclose(pywt.threshold([[1+1j, 2+2j]] * 2, 6, 'soft'),
+                    [[0, 0]] * 2, rtol=1e-12)
+    complex_data = [[1+2j, 2+2j]]*2
+    for thresh in [1, 2]:
+        assert_allclose(pywt.threshold(complex_data, thresh, 'soft'),
+                        _soft(complex_data, thresh), rtol=1e-12)
+
+    # test soft thresholding with non-default substitute argument
+    s = 5
+    assert_allclose(pywt.threshold([[1j, 2]] * 2, 1.5, 'soft', substitute=s),
+                    [[s, 0.5]] * 2, rtol=1e-12)
+
+    # soft: no divide by zero warnings when input contains zeros
+    assert_allclose(pywt.threshold(np.zeros(16), 2, 'soft'),
+                    np.zeros(16), rtol=1e-12)
+
+    # hard
+    hard_result = [0., 0., 2., 2.5, 3., 3.5, 4.]
+    assert_allclose(pywt.threshold(data, 2, 'hard'),
+                    np.array(hard_result), rtol=1e-12)
+    assert_allclose(pywt.threshold(-data, 2, 'hard'),
+                    -np.array(hard_result), rtol=1e-12)
+    assert_allclose(pywt.threshold([[1, 2]] * 2, 1, 'hard'),
+                    [[1, 2]] * 2, rtol=1e-12)
+    assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'hard'),
+                    [[0, 2]] * 2, rtol=1e-12)
+    assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'hard', substitute=s),
+                    [[s, 2]] * 2, rtol=1e-12)
+    assert_allclose(pywt.threshold([[1+1j, 2+2j]] * 2, 2, 'hard'),
+                    [[0, 2+2j]] * 2, rtol=1e-12)
+
+    # greater
+    greater_result = [0., 0., 2., 2.5, 3., 3.5, 4.]
+    assert_allclose(pywt.threshold(data, 2, 'greater'),
+                    np.array(greater_result), rtol=1e-12)
+    assert_allclose(pywt.threshold([[1, 2]] * 2, 1, 'greater'),
+                    [[1, 2]] * 2, rtol=1e-12)
+    assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'greater'),
+                    [[0, 2]] * 2, rtol=1e-12)
+    assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'greater', substitute=s),
+                    [[s, 2]] * 2, rtol=1e-12)
+    # greater doesn't allow complex-valued inputs
+    assert_raises(ValueError, pywt.threshold, [1j, 2j], 2, 'greater')
+
+    # less
+    assert_allclose(pywt.threshold(data, 2, 'less'),
+                    np.array([1., 1.5, 2., 0., 0., 0., 0.]), rtol=1e-12)
+    assert_allclose(pywt.threshold([[1, 2]] * 2, 1, 'less'),
+                    [[1, 0]] * 2, rtol=1e-12)
+    assert_allclose(pywt.threshold([[1, 2]] * 2, 1, 'less', substitute=s),
+                    [[1, s]] * 2, rtol=1e-12)
+    assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'less'),
+                    [[1, 2]] * 2, rtol=1e-12)
+
+    # less doesn't allow complex-valued inputs
+    assert_raises(ValueError, pywt.threshold, [1j, 2j], 2, 'less')
+
+    # invalid
+    assert_raises(ValueError, pywt.threshold, data, 2, 'foo')
+
+
+def test_nonnegative_garotte():
+    thresh = 0.3
+    data_real = np.linspace(-1, 1, 100)
+    for dtype in float_dtypes:
+        if dtype in real_dtypes:
+            data = np.asarray(data_real, dtype=dtype)
+        else:
+            data = np.asarray(data_real + 0.1j, dtype=dtype)
+        d_hard = pywt.threshold(data, thresh, 'hard')
+        d_soft = pywt.threshold(data, thresh, 'soft')
+        d_garotte = pywt.threshold(data, thresh, 'garotte')
+
+        # check dtypes
+        assert_equal(d_hard.dtype, data.dtype)
+        assert_equal(d_soft.dtype, data.dtype)
+        assert_equal(d_garotte.dtype, data.dtype)
+
+        # values < threshold are zero
+        lt = np.where(np.abs(data) < thresh)
+        assert_(np.all(d_garotte[lt] == 0))
+
+        # values > than the threshold are intermediate between soft and hard
+        gt = np.where(np.abs(data) > thresh)
+        gt_abs_garotte = np.abs(d_garotte[gt])
+        assert_(np.all(gt_abs_garotte < np.abs(d_hard[gt])))
+        assert_(np.all(gt_abs_garotte > np.abs(d_soft[gt])))
+
+
+def test_threshold_firm():
+    thresh = 0.2
+    thresh2 = 3 * thresh
+    data_real = np.linspace(-1, 1, 100)
+    for dtype in float_dtypes:
+        if dtype in real_dtypes:
+            data = np.asarray(data_real, dtype=dtype)
+        else:
+            data = np.asarray(data_real + 0.1j, dtype=dtype)
+        if data.real.dtype == np.float32:
+            rtol = atol = 1e-6
+        else:
+            rtol = atol = 1e-14
+        d_hard = pywt.threshold(data, thresh, 'hard')
+        d_soft = pywt.threshold(data, thresh, 'soft')
+        d_firm = pywt.threshold_firm(data, thresh, thresh2)
+
+        # check dtypes
+        assert_equal(d_hard.dtype, data.dtype)
+        assert_equal(d_soft.dtype, data.dtype)
+        assert_equal(d_firm.dtype, data.dtype)
+
+        # values < threshold are zero
+        lt = np.where(np.abs(data) < thresh)
+        assert_(np.all(d_firm[lt] == 0))
+
+        # values > than the threshold are equal to hard-thresholding
+        gt = np.where(np.abs(data) >= thresh2)
+        assert_allclose(np.abs(d_hard[gt]), np.abs(d_firm[gt]),
+                        rtol=rtol, atol=atol)
+
+        # other values are intermediate between soft and hard thresholding
+        mt = np.where(np.logical_and(np.abs(data) > thresh,
+                                     np.abs(data) < thresh2))
+        mt_abs_firm = np.abs(d_firm[mt])
+        assert_(np.all(mt_abs_firm < np.abs(d_hard[mt])))
+        assert_(np.all(mt_abs_firm > np.abs(d_soft[mt])))

venv/Lib/site-packages/pywt/tests/test_wavelet.py

@@ -0,0 +1,266 @@
+#!/usr/bin/env python
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_
+
+import pywt
+
+
+def test_wavelet_properties():
+    w = pywt.Wavelet('db3')
+
+    # Name
+    assert_(w.name == 'db3')
+    assert_(w.short_family_name == 'db')
+    assert_(w.family_name, 'Daubechies')
+
+    # String representation
+    fields = ('Family name', 'Short name', 'Filters length', 'Orthogonal',
+              'Biorthogonal', 'Symmetry')
+    for field in fields:
+        assert_(field in str(w))
+
+    # Filter coefficients
+    dec_lo = [0.03522629188210, -0.08544127388224, -0.13501102001039,
+              0.45987750211933, 0.80689150931334, 0.33267055295096]
+    dec_hi = [-0.33267055295096, 0.80689150931334, -0.45987750211933,
+              -0.13501102001039, 0.08544127388224, 0.03522629188210]
+    rec_lo = [0.33267055295096, 0.80689150931334, 0.45987750211933,
+              -0.13501102001039, -0.08544127388224, 0.03522629188210]
+    rec_hi = [0.03522629188210, 0.08544127388224, -0.13501102001039,
+              -0.45987750211933, 0.80689150931334, -0.33267055295096]
+    assert_allclose(w.dec_lo, dec_lo)
+    assert_allclose(w.dec_hi, dec_hi)
+    assert_allclose(w.rec_lo, rec_lo)
+    assert_allclose(w.rec_hi, rec_hi)
+
+    assert_(len(w.filter_bank) == 4)
+
+    # Orthogonality
+    assert_(w.orthogonal)
+    assert_(w.biorthogonal)
+
+    # Symmetry
+    assert_(w.symmetry)
+
+    # Vanishing moments
+    assert_(w.vanishing_moments_phi == 0)
+    assert_(w.vanishing_moments_psi == 3)
+
+
+def test_wavelet_coefficients():
+    families = ('db', 'sym', 'coif', 'bior', 'rbio')
+    wavelets = sum([pywt.wavelist(name) for name in families], [])
+    for wavelet in wavelets:
+        if (pywt.Wavelet(wavelet).orthogonal):
+            check_coefficients_orthogonal(wavelet)
+        elif(pywt.Wavelet(wavelet).biorthogonal):
+            check_coefficients_biorthogonal(wavelet)
+        else:
+            check_coefficients(wavelet)
+
+
+def check_coefficients_orthogonal(wavelet):
+
+    epsilon = 5e-11
+    level = 5
+    w = pywt.Wavelet(wavelet)
+    phi, psi, x = w.wavefun(level=level)
+
+    # Lowpass filter coefficients sum to sqrt2
+    res = np.sum(w.dec_lo)-np.sqrt(2)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    # sum even coef = sum odd coef = 1 / sqrt(2)
+    res = np.sum(w.dec_lo[::2])-1./np.sqrt(2)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+
+    res = np.sum(w.dec_lo[1::2])-1./np.sqrt(2)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    # Highpass filter coefficients sum to zero
+    res = np.sum(w.dec_hi)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    # Scaling function integrates to unity
+
+    res = np.sum(phi) - 2**level
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    # Wavelet function is orthogonal to the scaling function at the same scale
+    res = np.sum(phi*psi)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    # The lowpass and highpass filter coefficients are orthogonal
+    res = np.sum(np.array(w.dec_lo)*np.array(w.dec_hi))
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+
+
+def check_coefficients_biorthogonal(wavelet):
+
+    epsilon = 5e-11
+    level = 5
+    w = pywt.Wavelet(wavelet)
+    phi_d, psi_d, phi_r, psi_r, x = w.wavefun(level=level)
+
+    # Lowpass filter coefficients sum to sqrt2
+    res = np.sum(w.dec_lo)-np.sqrt(2)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    # sum even coef = sum odd coef = 1 / sqrt(2)
+    res = np.sum(w.dec_lo[::2])-1./np.sqrt(2)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    res = np.sum(w.dec_lo[1::2])-1./np.sqrt(2)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    # Highpass filter coefficients sum to zero
+    res = np.sum(w.dec_hi)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    # Scaling function integrates to unity
+    res = np.sum(phi_d) - 2**level
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    res = np.sum(phi_r) - 2**level
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+
+
+def check_coefficients(wavelet):
+    epsilon = 5e-11
+    level = 10
+    w = pywt.Wavelet(wavelet)
+    # Lowpass filter coefficients sum to sqrt2
+    res = np.sum(w.dec_lo)-np.sqrt(2)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    # sum even coef = sum odd coef = 1 / sqrt(2)
+    res = np.sum(w.dec_lo[::2])-1./np.sqrt(2)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+
+    res = np.sum(w.dec_lo[1::2])-1./np.sqrt(2)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+    # Highpass filter coefficients sum to zero
+    res = np.sum(w.dec_hi)
+    msg = ('[RMS_REC > EPSILON] for Wavelet: %s, rms=%.3g' % (wavelet, res))
+    assert_(res < epsilon, msg=msg)
+
+
+class _CustomHaarFilterBank(object):
+    @property
+    def filter_bank(self):
+        val = np.sqrt(2) / 2
+        return ([val]*2, [-val, val], [val]*2, [val, -val])
+
+
+def test_custom_wavelet():
+    haar_custom1 = pywt.Wavelet('Custom Haar Wavelet',
+                                filter_bank=_CustomHaarFilterBank())
+    haar_custom1.orthogonal = True
+    haar_custom1.biorthogonal = True
+
+    val = np.sqrt(2) / 2
+    filter_bank = ([val]*2, [-val, val], [val]*2, [val, -val])
+    haar_custom2 = pywt.Wavelet('Custom Haar Wavelet',
+                                filter_bank=filter_bank)
+
+    # check expected default wavelet properties
+    assert_(~haar_custom2.orthogonal)
+    assert_(~haar_custom2.biorthogonal)
+    assert_(haar_custom2.symmetry == 'unknown')
+    assert_(haar_custom2.family_name == '')
+    assert_(haar_custom2.short_family_name == '')
+    assert_(haar_custom2.vanishing_moments_phi == 0)
+    assert_(haar_custom2.vanishing_moments_psi == 0)
+
+    # Some properties can be set by the user
+    haar_custom2.orthogonal = True
+    haar_custom2.biorthogonal = True
+
+
+def test_wavefun_sym3():
+    w = pywt.Wavelet('sym3')
+    # sym3 is an orthogonal wavelet, so 3 outputs from wavefun
+    phi, psi, x = w.wavefun(level=3)
+    assert_(phi.size == 41)
+    assert_(psi.size == 41)
+    assert_(x.size == 41)
+
+    assert_allclose(x, np.linspace(0, 5, num=x.size))
+    phi_expect = np.array([0.00000000e+00, 1.04132926e-01, 2.52574126e-01,
+                           3.96525521e-01, 5.70356539e-01, 7.18934305e-01,
+                           8.70293448e-01, 1.05363620e+00, 1.24921722e+00,
+                           1.15296888e+00, 9.41669683e-01, 7.55875887e-01,
+                           4.96118565e-01, 3.28293151e-01, 1.67624969e-01,
+                           -7.33690312e-02, -3.35452855e-01, -3.31221131e-01,
+                           -2.32061503e-01, -1.66854239e-01, -4.34091324e-02,
+                           -2.86152390e-02, -3.63563035e-02, 2.06034491e-02,
+                           8.30280254e-02, 7.17779073e-02, 3.85914311e-02,
+                           1.47527100e-02, -2.31896077e-02, -1.86122172e-02,
+                           -1.56211329e-03, -8.70615088e-04, 3.20760857e-03,
+                           2.34142153e-03, -7.73737194e-04, -2.99879354e-04,
+                           1.23636238e-04, 0.00000000e+00, 0.00000000e+00,
+                           0.00000000e+00, 0.00000000e+00])
+
+    psi_expect = np.array([0.00000000e+00, 1.10265752e-02, 2.67449277e-02,
+                           4.19878574e-02, 6.03947231e-02, 7.61275365e-02,
+                           9.21548684e-02, 1.11568926e-01, 1.32278887e-01,
+                           6.45829680e-02, -3.97635130e-02, -1.38929884e-01,
+                           -2.62428322e-01, -3.62246804e-01, -4.62843343e-01,
+                           -5.89607507e-01, -7.25363076e-01, -3.36865858e-01,
+                           2.67715108e-01, 8.40176767e-01, 1.55574430e+00,
+                           1.18688954e+00, 4.20276324e-01, -1.51697311e-01,
+                           -9.42076108e-01, -7.93172332e-01, -3.26343710e-01,
+                           -1.24552779e-01, 2.12909254e-01, 1.75770320e-01,
+                           1.47523075e-02, 8.22192707e-03, -3.02920592e-02,
+                           -2.21119497e-02, 7.30703025e-03, 2.83200488e-03,
+                           -1.16759765e-03, 0.00000000e+00, 0.00000000e+00,
+                           0.00000000e+00, 0.00000000e+00])
+
+    assert_allclose(phi, phi_expect)
+    assert_allclose(psi, psi_expect)
+
+
+def test_wavefun_bior13():
+    w = pywt.Wavelet('bior1.3')
+    # bior1.3 is not an orthogonal wavelet, so 5 outputs from wavefun
+    phi_d, psi_d, phi_r, psi_r, x = w.wavefun(level=3)
+    for arr in [phi_d, psi_d, phi_r, psi_r]:
+        assert_(arr.size == 40)
+
+    phi_d_expect = np.array([0., -0.00195313, 0.00195313, 0.01757813,
+                             0.01367188, 0.00390625, -0.03515625, -0.12890625,
+                             -0.15234375, -0.125, -0.09375, -0.0625, 0.03125,
+                             0.15234375, 0.37890625, 0.78515625, 0.99609375,
+                             1.08203125, 1.13671875, 1.13671875, 1.08203125,
+                             0.99609375, 0.78515625, 0.37890625, 0.15234375,
+                             0.03125, -0.0625, -0.09375, -0.125, -0.15234375,
+                             -0.12890625, -0.03515625, 0.00390625, 0.01367188,
+                             0.01757813, 0.00195313, -0.00195313, 0., 0., 0.])
+    phi_r_expect = np.zeros(x.size, dtype=np.float)
+    phi_r_expect[15:23] = 1
+
+    psi_d_expect = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0,
+                             0.015625, -0.015625, -0.140625, -0.109375,
+                             -0.03125, 0.28125, 1.03125, 1.21875, 1.125, 0.625,
+                             -0.625, -1.125, -1.21875, -1.03125, -0.28125,
+                             0.03125, 0.109375, 0.140625, 0.015625, -0.015625,
+                             0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
+
+    psi_r_expect = np.zeros(x.size, dtype=np.float)
+    psi_r_expect[7:15] = -0.125
+    psi_r_expect[15:19] = 1
+    psi_r_expect[19:23] = -1
+    psi_r_expect[23:31] = 0.125
+
+    assert_allclose(x, np.linspace(0, 5, x.size, endpoint=False))
+    assert_allclose(phi_d, phi_d_expect, rtol=1e-5, atol=1e-9)
+    assert_allclose(phi_r, phi_r_expect, rtol=1e-10, atol=1e-12)
+    assert_allclose(psi_d, psi_d_expect, rtol=1e-10, atol=1e-12)
+    assert_allclose(psi_r, psi_r_expect, rtol=1e-10, atol=1e-12)

venv/Lib/site-packages/pywt/tests/test_wp.py

@@ -0,0 +1,197 @@
+#!/usr/bin/env python
+
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import (assert_allclose, assert_, assert_raises,
+                           assert_equal)
+
+import pywt
+
+
+def test_wavelet_packet_structure():
+    x = [1, 2, 3, 4, 5, 6, 7, 8]
+    wp = pywt.WaveletPacket(data=x, wavelet='db1', mode='symmetric')
+
+    assert_(wp.data == [1, 2, 3, 4, 5, 6, 7, 8])
+    assert_(wp.path == '')
+    assert_(wp.level == 0)
+    assert_(wp['ad'].maxlevel == 3)
+
+
+def test_traversing_wp_tree():
+    x = [1, 2, 3, 4, 5, 6, 7, 8]
+    wp = pywt.WaveletPacket(data=x, wavelet='db1', mode='symmetric')
+
+    assert_(wp.maxlevel == 3)
+
+    # First level
+    assert_allclose(wp['a'].data, np.array([2.12132034356, 4.949747468306,
+                                           7.778174593052, 10.606601717798]),
+                    rtol=1e-12)
+
+    # Second level
+    assert_allclose(wp['aa'].data, np.array([5., 13.]), rtol=1e-12)
+
+    # Third level
+    assert_allclose(wp['aaa'].data, np.array([12.727922061358]), rtol=1e-12)
+
+
+def test_acess_path():
+    x = [1, 2, 3, 4, 5, 6, 7, 8]
+    wp = pywt.WaveletPacket(data=x, wavelet='db1', mode='symmetric')
+
+    assert_(wp['a'].path == 'a')
+    assert_(wp['aa'].path == 'aa')
+    assert_(wp['aaa'].path == 'aaa')
+
+    # Maximum level reached:
+    assert_raises(IndexError, lambda: wp['aaaa'].path)
+
+    # Wrong path
+    assert_raises(ValueError, lambda: wp['ac'].path)
+
+
+def test_access_node_atributes():
+    x = [1, 2, 3, 4, 5, 6, 7, 8]
+    wp = pywt.WaveletPacket(data=x, wavelet='db1', mode='symmetric')
+
+    assert_allclose(wp['ad'].data, np.array([-2., -2.]), rtol=1e-12)
+    assert_(wp['ad'].path == 'ad')
+    assert_(wp['ad'].node_name == 'd')
+    assert_(wp['ad'].parent.path == 'a')
+    assert_(wp['ad'].level == 2)
+    assert_(wp['ad'].maxlevel == 3)
+    assert_(wp['ad'].mode == 'symmetric')
+
+
+def test_collecting_nodes():
+    x = [1, 2, 3, 4, 5, 6, 7, 8]
+    wp = pywt.WaveletPacket(data=x, wavelet='db1', mode='symmetric')
+
+    # All nodes in natural order
+    assert_([node.path for node in wp.get_level(3, 'natural')] ==
+            ['aaa', 'aad', 'ada', 'add', 'daa', 'dad', 'dda', 'ddd'])
+
+    # and in frequency order.
+    assert_([node.path for node in wp.get_level(3, 'freq')] ==
+            ['aaa', 'aad', 'add', 'ada', 'dda', 'ddd', 'dad', 'daa'])
+
+
+def test_reconstructing_data():
+    x = [1, 2, 3, 4, 5, 6, 7, 8]
+    wp = pywt.WaveletPacket(data=x, wavelet='db1', mode='symmetric')
+
+    # Create another Wavelet Packet and feed it with some data.
+    new_wp = pywt.WaveletPacket(data=None, wavelet='db1', mode='symmetric')
+    new_wp['aa'] = wp['aa'].data
+    new_wp['ad'] = [-2., -2.]
+
+    # For convenience, :attr:`Node.data` gets automatically extracted
+    # from the :class:`Node` object:
+    new_wp['d'] = wp['d']
+
+    # Reconstruct data from aa, ad, and d packets.
+    assert_allclose(new_wp.reconstruct(update=False), x, rtol=1e-12)
+
+    # The node's :attr:`~Node.data` will not be updated
+    assert_(new_wp.data is None)
+
+    # When `update` is True:
+    assert_allclose(new_wp.reconstruct(update=True), x, rtol=1e-12)
+    assert_allclose(new_wp.data, np.arange(1, 9), rtol=1e-12)
+
+    assert_([n.path for n in new_wp.get_leaf_nodes(False)] ==
+            ['aa', 'ad', 'd'])
+    assert_([n.path for n in new_wp.get_leaf_nodes(True)] ==
+            ['aaa', 'aad', 'ada', 'add', 'daa', 'dad', 'dda', 'ddd'])
+
+
+def test_removing_nodes():
+    x = [1, 2, 3, 4, 5, 6, 7, 8]
+    wp = pywt.WaveletPacket(data=x, wavelet='db1', mode='symmetric')
+    wp.get_level(2)
+
+    dataleafs = [n.data for n in wp.get_leaf_nodes(False)]
+    expected = np.array([[5., 13.], [-2, -2], [-1, -1], [0, 0]])
+
+    for i in range(4):
+        assert_allclose(dataleafs[i], expected[i, :], atol=1e-12)
+
+    node = wp['ad']
+    del(wp['ad'])
+    dataleafs = [n.data for n in wp.get_leaf_nodes(False)]
+    expected = np.array([[5., 13.], [-1, -1], [0, 0]])
+
+    for i in range(3):
+        assert_allclose(dataleafs[i], expected[i, :], atol=1e-12)
+
+    wp.reconstruct()
+    # The reconstruction is:
+    assert_allclose(wp.reconstruct(),
+                    np.array([2., 3., 2., 3., 6., 7., 6., 7.]), rtol=1e-12)
+
+    # Restore the data
+    wp['ad'].data = node.data
+
+    dataleafs = [n.data for n in wp.get_leaf_nodes(False)]
+    expected = np.array([[5., 13.], [-2, -2], [-1, -1], [0, 0]])
+
+    for i in range(4):
+        assert_allclose(dataleafs[i], expected[i, :], atol=1e-12)
+
+    assert_allclose(wp.reconstruct(), np.arange(1, 9), rtol=1e-12)
+
+
+def test_wavelet_packet_dtypes():
+    N = 32
+    for dtype in [np.float32, np.float64, np.complex64, np.complex128]:
+        x = np.random.randn(N).astype(dtype)
+        if np.iscomplexobj(x):
+            x = x + 1j*np.random.randn(N).astype(x.real.dtype)
+        wp = pywt.WaveletPacket(data=x, wavelet='db1', mode='symmetric')
+        # no unnecessary copy made
+        assert_(wp.data is x)
+
+        # assiging to a node should not change supported dtypes
+        wp['d'] = wp['d'].data
+        assert_equal(wp['d'].data.dtype, x.dtype)
+
+        # full decomposition
+        wp.get_level(wp.maxlevel)
+
+        # reconstruction from coefficients should preserve dtype
+        r = wp.reconstruct(False)
+        assert_equal(r.dtype, x.dtype)
+        assert_allclose(r, x, atol=1e-5, rtol=1e-5)
+
+    # first element of the tuple is the input dtype
+    # second element of the tuple is the transform dtype
+    dtype_pairs = [(np.uint8, np.float64),
+                   (np.intp, np.float64), ]
+    if hasattr(np, "complex256"):
+        dtype_pairs += [(np.complex256, np.complex128), ]
+    if hasattr(np, "half"):
+        dtype_pairs += [(np.half, np.float32), ]
+    for (dtype, transform_dtype) in dtype_pairs:
+        x = np.arange(N, dtype=dtype)
+        wp = pywt.WaveletPacket(x, wavelet='db1', mode='symmetric')
+
+        # no unnecessary copy made of top-level data
+        assert_(wp.data is x)
+
+        # full decomposition
+        wp.get_level(wp.maxlevel)
+
+        # reconstructed data will have modified dtype
+        r = wp.reconstruct(False)
+        assert_equal(r.dtype, transform_dtype)
+        assert_allclose(r, x.astype(transform_dtype), atol=1e-5, rtol=1e-5)
+
+
+def test_db3_roundtrip():
+    original = np.arange(512)
+    wp = pywt.WaveletPacket(data=original, wavelet='db3', mode='smooth',
+                            maxlevel=3)
+    r = wp.reconstruct()
+    assert_allclose(original, r, atol=1e-12, rtol=1e-12)

venv/Lib/site-packages/pywt/tests/test_wp2d.py

@@ -0,0 +1,177 @@
+#!/usr/bin/env python
+
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import (assert_allclose, assert_, assert_raises,
+                           assert_equal)
+
+import pywt
+
+
+def test_traversing_tree_2d():
+    x = np.array([[1, 2, 3, 4, 5, 6, 7, 8]] * 8, dtype=np.float64)
+    wp = pywt.WaveletPacket2D(data=x, wavelet='db1', mode='symmetric')
+
+    assert_(np.all(wp.data == x))
+    assert_(wp.path == '')
+    assert_(wp.level == 0)
+    assert_(wp.maxlevel == 3)
+
+    assert_allclose(wp['a'].data, np.array([[3., 7., 11., 15.]] * 4),
+                    rtol=1e-12)
+    assert_allclose(wp['h'].data, np.zeros((4, 4)), rtol=1e-12, atol=1e-14)
+    assert_allclose(wp['v'].data, -np.ones((4, 4)), rtol=1e-12, atol=1e-14)
+    assert_allclose(wp['d'].data, np.zeros((4, 4)), rtol=1e-12, atol=1e-14)
+
+    assert_allclose(wp['aa'].data, np.array([[10., 26.]] * 2), rtol=1e-12)
+
+    assert_(wp['a']['a'].data is wp['aa'].data)
+    assert_allclose(wp['aaa'].data, np.array([[36.]]), rtol=1e-12)
+
+    assert_raises(IndexError, lambda: wp['aaaa'])
+    assert_raises(ValueError, lambda: wp['f'])
+
+
+def test_accessing_node_atributes_2d():
+    x = np.array([[1, 2, 3, 4, 5, 6, 7, 8]] * 8, dtype=np.float64)
+    wp = pywt.WaveletPacket2D(data=x, wavelet='db1', mode='symmetric')
+
+    assert_allclose(wp['av'].data, np.zeros((2, 2)) - 4, rtol=1e-12)
+    assert_(wp['av'].path == 'av')
+    assert_(wp['av'].node_name == 'v')
+    assert_(wp['av'].parent.path == 'a')
+
+    assert_allclose(wp['av'].parent.data, np.array([[3., 7., 11., 15.]] * 4),
+                    rtol=1e-12)
+    assert_(wp['av'].level == 2)
+    assert_(wp['av'].maxlevel == 3)
+    assert_(wp['av'].mode == 'symmetric')
+
+
+def test_collecting_nodes_2d():
+    x = np.array([[1, 2, 3, 4, 5, 6, 7, 8]] * 8, dtype=np.float64)
+    wp = pywt.WaveletPacket2D(data=x, wavelet='db1', mode='symmetric')
+
+    assert_(len(wp.get_level(0)) == 1)
+    assert_(wp.get_level(0)[0].path == '')
+
+    # First level
+    assert_(len(wp.get_level(1)) == 4)
+    assert_([node.path for node in wp.get_level(1)] == ['a', 'h', 'v', 'd'])
+
+    # Second level
+    assert_(len(wp.get_level(2)) == 16)
+    paths = [node.path for node in wp.get_level(2)]
+    expected_paths = ['aa', 'ah', 'av', 'ad', 'ha', 'hh', 'hv', 'hd', 'va',
+                      'vh', 'vv', 'vd', 'da', 'dh', 'dv', 'dd']
+    assert_(paths == expected_paths)
+
+    # Third level.
+    assert_(len(wp.get_level(3)) == 64)
+    paths = [node.path for node in wp.get_level(3)]
+    expected_paths = ['aaa', 'aah', 'aav', 'aad', 'aha', 'ahh', 'ahv', 'ahd',
+                      'ava', 'avh', 'avv', 'avd', 'ada', 'adh', 'adv', 'add',
+                      'haa', 'hah', 'hav', 'had', 'hha', 'hhh', 'hhv', 'hhd',
+                      'hva', 'hvh', 'hvv', 'hvd', 'hda', 'hdh', 'hdv', 'hdd',
+                      'vaa', 'vah', 'vav', 'vad', 'vha', 'vhh', 'vhv', 'vhd',
+                      'vva', 'vvh', 'vvv', 'vvd', 'vda', 'vdh', 'vdv', 'vdd',
+                      'daa', 'dah', 'dav', 'dad', 'dha', 'dhh', 'dhv', 'dhd',
+                      'dva', 'dvh', 'dvv', 'dvd', 'dda', 'ddh', 'ddv', 'ddd']
+
+    assert_(paths == expected_paths)
+
+
+def test_data_reconstruction_2d():
+    x = np.array([[1, 2, 3, 4, 5, 6, 7, 8]] * 8, dtype=np.float64)
+    wp = pywt.WaveletPacket2D(data=x, wavelet='db1', mode='symmetric')
+
+    new_wp = pywt.WaveletPacket2D(data=None, wavelet='db1', mode='symmetric')
+    new_wp['vh'] = wp['vh'].data
+    new_wp['vv'] = wp['vh'].data
+    new_wp['vd'] = np.zeros((2, 2), dtype=np.float64)
+    new_wp['a'] = [[3.0, 7.0, 11.0, 15.0]] * 4
+    new_wp['d'] = np.zeros((4, 4), dtype=np.float64)
+    new_wp['h'] = wp['h']       # all zeros
+
+    assert_allclose(new_wp.reconstruct(update=False),
+                    np.array([[1.5, 1.5, 3.5, 3.5, 5.5, 5.5, 7.5, 7.5]] * 8),
+                    rtol=1e-12)
+    assert_allclose(wp['va'].data, np.zeros((2, 2)) - 2, rtol=1e-12)
+
+    new_wp['va'] = wp['va'].data
+    assert_allclose(new_wp.reconstruct(update=False), x, rtol=1e-12)
+
+
+def test_data_reconstruction_delete_nodes_2d():
+    x = np.array([[1, 2, 3, 4, 5, 6, 7, 8]] * 8, dtype=np.float64)
+    wp = pywt.WaveletPacket2D(data=x, wavelet='db1', mode='symmetric')
+
+    new_wp = pywt.WaveletPacket2D(data=None, wavelet='db1', mode='symmetric')
+    new_wp['vh'] = wp['vh'].data
+    new_wp['vv'] = wp['vh'].data
+    new_wp['vd'] = np.zeros((2, 2), dtype=np.float64)
+    new_wp['a'] = [[3.0, 7.0, 11.0, 15.0]] * 4
+    new_wp['d'] = np.zeros((4, 4), dtype=np.float64)
+    new_wp['h'] = wp['h']       # all zeros
+
+    assert_allclose(new_wp.reconstruct(update=False),
+                    np.array([[1.5, 1.5, 3.5, 3.5, 5.5, 5.5, 7.5, 7.5]] * 8),
+                    rtol=1e-12)
+
+    new_wp['va'] = wp['va'].data
+    assert_allclose(new_wp.reconstruct(update=False), x, rtol=1e-12)
+
+    del(new_wp['va'])
+    new_wp['va'] = wp['va'].data
+    assert_(new_wp.data is None)
+
+    assert_allclose(new_wp.reconstruct(update=True), x, rtol=1e-12)
+    assert_allclose(new_wp.data, x, rtol=1e-12)
+
+    # TODO: decompose=True
+
+
+def test_lazy_evaluation_2D():
+    # Note: internal implementation detail not to be relied on.  Testing for
+    # now for backwards compatibility, but this test may be broken in needed.
+    x = np.array([[1, 2, 3, 4, 5, 6, 7, 8]] * 8)
+    wp = pywt.WaveletPacket2D(data=x, wavelet='db1', mode='symmetric')
+
+    assert_(wp.a is None)
+    assert_allclose(wp['a'].data, np.array([[3., 7., 11., 15.]] * 4),
+                    rtol=1e-12)
+    assert_allclose(wp.a.data, np.array([[3., 7., 11., 15.]] * 4), rtol=1e-12)
+    assert_allclose(wp.d.data, np.zeros((4, 4)), rtol=1e-12, atol=1e-12)
+
+
+def test_wavelet_packet_dtypes():
+    shape = (16, 16)
+    for dtype in [np.float32, np.float64, np.complex64, np.complex128]:
+        x = np.random.randn(*shape).astype(dtype)
+        if np.iscomplexobj(x):
+            x = x + 1j*np.random.randn(*shape).astype(x.real.dtype)
+        wp = pywt.WaveletPacket2D(data=x, wavelet='db1', mode='symmetric')
+        # no unnecessary copy made
+        assert_(wp.data is x)
+
+        # assiging to a node should not change supported dtypes
+        wp['d'] = wp['d'].data
+        assert_equal(wp['d'].data.dtype, x.dtype)
+
+        # full decomposition
+        wp.get_level(wp.maxlevel)
+
+        # reconstruction from coefficients should preserve dtype
+        r = wp.reconstruct(False)
+        assert_equal(r.dtype, x.dtype)
+        assert_allclose(r, x, atol=1e-5, rtol=1e-5)
+
+
+def test_2d_roundtrip():
+    # test case corresponding to PyWavelets issue 447
+    original = pywt.data.camera()
+    wp = pywt.WaveletPacket2D(data=original, wavelet='db3', mode='smooth',
+                              maxlevel=3)
+    r = wp.reconstruct()
+    assert_allclose(original, r, atol=1e-12, rtol=1e-12)

venv/Lib/site-packages/pywt/version.py

@@ -0,0 +1,10 @@
+
+# THIS FILE IS GENERATED FROM PYWAVELETS SETUP.PY
+short_version = '1.1.1'
+version = '1.1.1'
+full_version = '1.1.1'
+git_revision = '7b2f66b0ef9196fa91bba550a81d1870f5933a36'
+release = True
+
+if not release:
+    version = full_version