Python pywt.dwt() Examples

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 

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_roundtrip.dtype == np.float64) 

def test_dwt_short_input_allmodes():
    # some test cases where the input is shorter than the DWT filter
    x = [1, 2, 3]
    wavelet = 'db2'
    # manually pad each end by the filter size (4 for 'db2' used here)
    padded_x = {'zero': [0, 0, 0, 0, 1, 2, 3, 0, 0, 0, 0],
                'constant': [1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3],
                'symmetric': [3, 3, 2, 1, 1, 2, 3, 3, 2, 1, 1],
                'reflect': [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3],
                'periodic': [3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1],
                'smooth': [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7],
                }
    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_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_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 denoise_ecg(ecg_segment):
	"""
	Remove baseline drafts from ECG signal.
	:param ecg_segment: ecg record, a numpy array.
	:return: denoised ecg record, a numpy array.
	
	Example:
	denoising_ecg = denoise_ecg(raw_ecg)
	"""
	
	denoising_wd_level = 6
	denoising_wd_wavelet = "db6"
	coffes_set = []
	cA_signal = np.reshape(ecg_segment, len(ecg_segment))
	for index_dec in range(denoising_wd_level):
		cA, cD = pywt.dwt(cA_signal, denoising_wd_wavelet)
		coffes_set.append(cD)
		cA_signal = cA
	coffes_set.append(cA_signal)
	coffes_set[denoising_wd_level] = np.zeros(len(coffes_set[denoising_wd_level]))
	
	cA_signal = coffes_set[denoising_wd_level]
	for index_dec in range(denoising_wd_level):
		cD_signal = coffes_set[denoising_wd_level - 1 - index_dec]
		if len(cD_signal) != len(cA_signal):
			cA_signal = np.delete(cA_signal, len(cA_signal) - 1, axis=0)
		cA_signal = pywt.idwt(cA_signal, cD_signal, denoising_wd_wavelet)
	cA_signal = np.reshape(cA_signal, (len(ecg_segment), 1))
	return cA_signal 

def _single_tree_analysis_1d(data, first_stage, wavelet, level, mode, axis):
    """
    Single tree of the forward dual-tree complex wavelet transform.
    
    Parameters
    ----------
    data : ndarray, ndim 1
    first_stage : Wavelet object
    wavelet : 2-tuple of Wavelet object
    level : int
    mode : str
    axis : int

    Returns
    -------
    [cA_n, cD_n, cD_n-1, ..., cD2, cD1] : list
        Ordered list of coefficients arrays
        where `n` denotes the level of decomposition. The first element
        (`cA_n`) of the result is approximation coefficients array and the
        following elements (`cD_n` - `cD_1`) are details coefficients arrays.
    """
    approx, first_detail = dwt(data=data, wavelet=first_stage, mode=mode, axis=axis)
    # Use of a deque vs. a list is because deque.appendleft is O(1)
    coeffs_list = deque([first_detail])
    for i, wav in zip(range(level - 1), cycle(wavelet)):
        approx, detail = dwt(data=approx, wavelet=wav, mode=mode, axis=axis)
        coeffs_list.appendleft(detail)

    # Format list ot be compatible to PyWavelet's format. See pywt.wavedec source.
    coeffs_list.appendleft(approx)
    return coeffs_list 

def wavy(arr):
    cA, cD = pywt.dwt(arr, 'db2', mode='symmetric')
    y = pywt.idwt(cA, cD, 'db2')
    return y 

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) 

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_result_modes = {
        '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])
    }

    for mode in pywt.Modes.modes:
        cA, cD = pywt.dwt(x, 'db2', mode)
        assert_allclose(cA, dwt_result_modes[mode][0], rtol=1e-7, atol=1e-8)
        assert_allclose(cD, dwt_result_modes[mode][1], rtol=1e-7, atol=1e-8)
        assert_allclose(pywt.idwt(cA, cD, 'db2', mode), x, rtol=1e-10) 

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', 7)
    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, 7)
    assert_raises(TypeError, pywt.Modes.from_object, None) 

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_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_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 plot_signal_decomp(data, w, title):
    """Decompose and plot a signal S.
    S = An + Dn + Dn-1 + ... + D1
    """
    w = pywt.Wavelet(w)
    a = data
    ca = []
    cd = []
    for i in range(5):
        (a, d) = pywt.dwt(a, w, mode)
        ca.append(a)
        cd.append(d)

    rec_a = []
    rec_d = []

    for i, coeff in enumerate(ca):
        coeff_list = [coeff, None] + [None] * i
        rec_a.append(pywt.waverec(coeff_list, w))

    for i, coeff in enumerate(cd):
        coeff_list = [None, coeff] + [None] * i
        rec_d.append(pywt.waverec(coeff_list, w))

    fig = plt.figure()
    ax_main = fig.add_subplot(len(rec_a) + 1, 1, 1)
    ax_main.set_title(title)
    ax_main.plot(data)
    ax_main.set_xlim(0, len(data) - 1)

    for i, y in enumerate(rec_a):
        ax = fig.add_subplot(len(rec_a) + 1, 2, 3 + i * 2)
        ax.plot(y, 'r')
        ax.set_xlim(0, len(y) - 1)
        ax.set_ylabel("A%d" % (i + 1))

    for i, y in enumerate(rec_d):
        ax = fig.add_subplot(len(rec_d) + 1, 2, 4 + i * 2)
        ax.plot(y, 'g')
        ax.set_xlim(0, len(y) - 1)
        ax.set_ylabel("D%d" % (i + 1)) 

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_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_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 _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) 

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], ]) 

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) 

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))