Python pywt.waverecn() Examples

def test_waverecn_invalid_coeffs():
    # approximation coeffs as None and no valid detail oeffs
    coeffs = [None, {}]
    assert_raises(ValueError, pywt.waverecn, coeffs, 'db1')

    # use of None for a coefficient value
    coeffs = [np.ones((2, 2, 2)), {}, {'daa': None}, ]
    assert_raises(ValueError, pywt.waverecn, coeffs, 'db1')

    # invalid key names in coefficient list
    coeffs = [np.ones((4, 4, 4)), {'daa': np.ones((4, 4, 4)),
                                   'foo': np.ones((4, 4, 4))}]
    assert_raises(ValueError, pywt.waverecn, coeffs, 'db1')

    # mismatched key name lengths
    coeffs = [np.ones((4, 4, 4)), {'daa': np.ones((4, 4, 4)),
                                   'da': np.ones((4, 4, 4))}]
    assert_raises(ValueError, pywt.waverecn, coeffs, 'db1')

    # key name lengths don't match the array dimensions
    coeffs = [[[[1.0]]], {'ad': [[[0.0]]], 'da': [[[0.0]]], 'dd': [[[0.0]]]}]
    assert_raises(ValueError, pywt.waverecn, coeffs, 'db1')

    # input list cannot be empty
    assert_raises(ValueError, pywt.waverecn, [], 'haar') 

def test_waverecn_coeff_reshape_odd():
    # verify round trip is correct:
    #   wavedecn - >coeffs_to_array-> array_to_coeffs -> waverecn
    rng = np.random.RandomState(1234)
    x1 = rng.randn(35, 33)
    for mode in pywt.Modes.modes:
        for wave in ['haar', ]:
            w = pywt.Wavelet(wave)
            maxlevel = pywt.dwt_max_level(np.min(x1.shape), w.dec_len)
            if maxlevel == 0:
                continue
            coeffs = pywt.wavedecn(x1, w, mode=mode)
            coeff_arr, coeff_slices = pywt.coeffs_to_array(coeffs)
            coeffs2 = pywt.array_to_coeffs(coeff_arr, coeff_slices)
            x1r = pywt.waverecn(coeffs2, w, mode=mode)
            # truncate reconstructed values to original shape
            x1r = x1r[[slice(s) for s in x1.shape]]
            assert_allclose(x1, x1r, rtol=1e-4, atol=1e-4) 

def test_wavedecn_coeff_reshape_even():
    # verify round trip is correct:
    #   wavedecn - >coeffs_to_array-> array_to_coeffs -> waverecn
    # This is done for wavedec{1, 2, n}
    rng = np.random.RandomState(1234)
    params = {'wavedec': {'d': 1, 'dec': pywt.wavedec, 'rec': pywt.waverec},
              'wavedec2': {'d': 2, 'dec': pywt.wavedec2, 'rec': pywt.waverec2},
              'wavedecn': {'d': 3, 'dec': pywt.wavedecn, 'rec': pywt.waverecn}}
    N = 28
    for f in params:
        x1 = rng.randn(*([N] * params[f]['d']))
        for mode in pywt.Modes.modes:
            for wave in wavelist:
                w = pywt.Wavelet(wave)
                maxlevel = pywt.dwt_max_level(np.min(x1.shape), w.dec_len)
                if maxlevel == 0:
                    continue

                coeffs = params[f]['dec'](x1, w, mode=mode)
                coeff_arr, coeff_slices = pywt.coeffs_to_array(coeffs)
                coeffs2 = pywt.array_to_coeffs(coeff_arr, coeff_slices,
                                               output_format=f)
                x1r = params[f]['rec'](coeffs2, w, mode=mode)

                assert_allclose(x1, x1r, rtol=1e-4, atol=1e-4) 

def test_waverecn_dtypes():
    x = np.ones((4, 4, 4))
    for dt, tol in dtypes_and_tolerances:
        coeffs = pywt.wavedecn(x.astype(dt), 'db1')
        assert_allclose(pywt.waverecn(coeffs, 'db1'), x, atol=tol, rtol=tol) 

def _call(self, coeffs):
        """Return the inverse wavelet transform of ``coeffs``."""
        if self.impl == 'pywt':
            coeffs = pywt.unravel_coeffs(coeffs,
                                         coeff_slices=self._coeff_slices,
                                         coeff_shapes=self._coeff_shapes,
                                         output_format='wavedecn')
            recon = pywt.waverecn(
                coeffs, wavelet=self.pywt_wavelet, mode=self.pywt_pad_mode,
                axes=self.axes)
            recon_shape = self.range.shape
            if recon.shape != recon_shape:
                # If the original shape was odd along any transformed axes it
                # will have been rounded up to the next even size after the
                # reconstruction. The extra sample should be discarded.
                # The underlying reason is decimation by two in reconstruction
                # must keep ceil(N/2) samples in each band for perfect
                # reconstruction. Reconstruction then upsamples by two.
                # When N is odd, (2 * np.ceil(N/2)) != N.
                recon_slc = []
                for i, (n_recon, n_intended) in enumerate(zip(recon.shape,
                                                              recon_shape)):
                    if n_recon == n_intended + 1:
                        # Upsampling added one entry too much in this axis,
                        # drop last one
                        recon_slc.append(slice(-1))
                    elif n_recon == n_intended:
                        recon_slc.append(slice(None))
                    else:
                        raise ValueError(
                            'in axis {}: expected size {} or {} in '
                            '`recon_shape`, got {}'
                            ''.format(i, n_recon - 1, n_recon,
                                      n_intended))
                recon = recon[tuple(recon_slc)]
            return recon
        else:
            raise RuntimeError("bad `impl` '{}'".format(self.impl)) 

def inverse_wavelet_transform(w_coeffs_rgb, coeff_slices, x_shape):
    x_hat = np.zeros(x_shape)
    for i in range(w_coeffs_rgb.shape[0]):
        w_coeffs_list = pywt.array_to_coeffs(w_coeffs_rgb[i,:,:], coeff_slices)
        x_hat[0,:,:,i] = pywt.waverecn(w_coeffs_list, wavelet='db4', mode='periodization')
    return x_hat 

def test_waverecn_axes_errors():
    data = np.ones((8, 8, 8))
    c = pywt.wavedecn(data, 'haar')
    # repeated axes not allowed
    assert_raises(ValueError, pywt.waverecn, c, 'haar', axes=(1, 1))
    # out of range axis not allowed
    assert_raises(ValueError, pywt.waverecn, c, 'haar', axes=(0, 1, 3)) 

def test_waverecn_int_axis():
    # waverecn should also work for axes as an integer
    rstate = np.random.RandomState(0)
    data = rstate.standard_normal((8, 8))
    for axis in [0, 1]:
        coefs = pywt.wavedecn(data, 'haar', axes=axis)
        rec = pywt.waverecn(coefs, 'haar', axes=axis)
        assert_allclose(rec, data, atol=1e-14) 

def test_waverecn_axes_subsets():
    rstate = np.random.RandomState(0)
    data = rstate.standard_normal((8, 8, 8, 8))
    # test all combinations of 3 out of 4 axes transformed
    for axes in combinations((0, 1, 2, 3), 3):
        coefs = pywt.wavedecn(data, 'haar', axes=axes)
        rec = pywt.waverecn(coefs, 'haar', axes=axes)
        assert_allclose(rec, data, atol=1e-14) 

def test_waverecn_all_wavelets_modes():
    # test 2D case using all wavelets and modes
    rstate = np.random.RandomState(1234)
    r = rstate.randn(80, 96)
    for wavelet in wavelist:
        for mode in pywt.Modes.modes:
            coeffs = pywt.wavedecn(r, wavelet, mode=mode)
            assert_allclose(pywt.waverecn(coeffs, wavelet, mode=mode),
                            r, rtol=tol_single, atol=tol_single) 

def _rmatvec(self, x):
        if self.reshape:
            x = np.reshape(x, self.dimsd)
        x = pywt.array_to_coeffs(x, self.sl, output_format='wavedecn')
        y = pywt.waverecn(x, wavelet=self.waveletadj, mode='periodization',
                          axes=(self.dir, ))
        y = self.pad.rmatvec(y.ravel())
        return y 

def test_wavedecn_complex():
    data = np.ones((4, 4, 4)) + 1j
    coeffs = pywt.wavedecn(data, 'db1')
    assert_allclose(pywt.waverecn(coeffs, 'db1'), data, rtol=1e-12) 

def test_multilevel_dtypes_nd():
    wavelet = pywt.Wavelet('haar')
    for dt_in, dt_out in zip(dtypes_in, dtypes_out):
        # wavedecn, waverecn
        x = np.ones((8, 8), dtype=dt_in)
        errmsg = "wrong dtype returned for {0} input".format(dt_in)
        cA, coeffsD2, coeffsD1 = pywt.wavedecn(x, wavelet, level=2)
        assert_(cA.dtype == dt_out, "wavedecn: " + errmsg)
        for key, c in coeffsD1.items():
            assert_(c.dtype == dt_out, "wavedecn: " + errmsg)
        for key, c in coeffsD2.items():
            assert_(c.dtype == dt_out, "wavedecn: " + errmsg)
        x_roundtrip = pywt.waverecn([cA, coeffsD2, coeffsD1], wavelet)
        assert_(x_roundtrip.dtype == dt_out, "waverecn: " + errmsg) 

def test_waverecn_invalid_coeffs2():
    # shape mismatch should raise an error
    coeffs = [np.ones((4, 4, 4)), {'ada': np.ones((4, 4))}]
    assert_raises(ValueError, pywt.waverecn, coeffs, 'db1') 

def test_waverecn_lists():
    # support coefficient arrays specified as lists instead of arrays
    coeffs = [[[1.0]], {'ad': [[0.0]], 'da': [[0.0]], 'dd': [[0.0]]}]
    assert_equal(pywt.waverecn(coeffs, 'db1').shape, (2, 2)) 

def test_waverecn_empty_coeff():
    coeffs = [np.ones((2, 2, 2)), {}, {}]
    assert_equal(pywt.waverecn(coeffs, 'db1').shape, (8, 8, 8))

    assert_equal(pywt.waverecn(coeffs, 'db1').shape, (8, 8, 8))
    coeffs = [np.ones((2, 2, 2)), {}, {'daa': np.ones((4, 4, 4))}]

    coeffs = [np.ones((2, 2, 2)), {}, {}, {'daa': np.ones((8, 8, 8))}]
    assert_equal(pywt.waverecn(coeffs, 'db1').shape, (16, 16, 16)) 

def test_waverecn():
    rstate = np.random.RandomState(1234)
    # test 1D through 4D cases
    for nd in range(1, 5):
        x = rstate.randn(*(4, )*nd)
        coeffs = pywt.wavedecn(x, 'db1')
        assert_(len(coeffs) == 3)
        assert_allclose(pywt.waverecn(coeffs, 'db1'), x, rtol=tol_double) 

def inverse_wavelet_transform(w_coeffs_rgb, coeff_slices, x_shape):
    x_hat = np.zeros(x_shape)
    for i in range(w_coeffs_rgb.shape[0]):
        w_coeffs_list = pywt.array_to_coeffs(w_coeffs_rgb[i,:,:], coeff_slices)
        x_hat[0,:,:,i] = pywt.waverecn(w_coeffs_list, wavelet='db4', mode='periodization')
    return x_hat