Fixed database typo and removed unnecessary class identifier.

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)