def test_level_4_discarding_level_1():
# Test that level >= 2 subbands are identical
Yl1, Yh1 = dtwavexfm3(ellipsoid, 4, discard_level_1=True)
Yl2, Yh2 = dtwavexfm3(ellipsoid, 4, discard_level_1=False)
assert np.abs(Yl1-Yl2).max() < TOLERANCE
for a, b in zip(Yh1[1:], Yh2[1:]):
assert np.abs(a-b).max() < TOLERANCE
def test_level_4_discarding_level_1():
# Test that level >= 2 subbands are identical
Yl1, Yh1 = dtwavexfm3(ellipsoid, 4, discard_level_1=True)
Yl2, Yh2 = dtwavexfm3(ellipsoid, 4, discard_level_1=False)
assert np.abs(Yl1 - Yl2).max() < TOLERANCE
for a, b in zip(Yh1[1:], Yh2[1:]):
assert np.abs(a - b).max() < TOLERANCE
def test_integer_perfect_recon():
# Check that an integer input is correctly coerced into a floating point
# array and reconstructed
A = (np.random.random((4,4,4)) * 5).astype(np.int32)
Yl, Yh = dtwavexfm3(A)
B = dtwaveifm3(Yl, Yh)
assert np.max(np.abs(A-B)) < 1e-12
def test_integer_perfect_recon():
# Check that an integer input is correctly coerced into a floating point
# array and reconstructed
A = (np.random.random((4, 4, 4)) * 5).astype(np.int32)
Yl, Yh = dtwavexfm3(A)
B = dtwaveifm3(Yl, Yh)
assert np.max(np.abs(A - B)) < 1e-12
def test_simple_level_4_recon_ext_mode_4():
# Test for perfect reconstruction with 3 levels
crop_ellipsoid = ellipsoid[:62, :54, :58]
Yl, Yh = dtwavexfm3(crop_ellipsoid, 4, ext_mode=4)
ellipsoid_recon = dtwaveifm3(Yl, Yh)
assert crop_ellipsoid.size == ellipsoid_recon.size
assert np.max(np.abs(crop_ellipsoid - ellipsoid_recon)) < TOLERANCE
def test_simple_level_4_recon_ext_mode_4():
# Test for perfect reconstruction with 3 levels
crop_ellipsoid = ellipsoid[:62,:54,:58]
Yl, Yh = dtwavexfm3(crop_ellipsoid, 4, ext_mode=4)
ellipsoid_recon = dtwaveifm3(Yl, Yh)
assert crop_ellipsoid.size == ellipsoid_recon.size
assert np.max(np.abs(crop_ellipsoid - ellipsoid_recon)) < TOLERANCE
def test_level_4_recon_discarding_level_1():
# Test for non-perfect but reasonable reconstruction
Yl, Yh = dtwavexfm3(ellipsoid, 4, discard_level_1=True)
ellipsoid_recon = dtwaveifm3(Yl, Yh)
assert ellipsoid.size == ellipsoid_recon.size
# Check that we mostly reconstruct correctly
assert np.median(np.abs(ellipsoid - ellipsoid_recon)[:]) < 1e-3
def test_float32_recon():
# Check that an float32 input is correctly output as float32
Yl, Yh = dtwavexfm3(ellipsoid.astype(np.float32))
assert np.issubsctype(Yl.dtype, np.float32)
assert np.all(list(np.issubsctype(x.dtype, np.complex64) for x in Yh))
recon = dtwaveifm3(Yl, Yh)
assert np.issubsctype(recon.dtype, np.float32)
def test_simple_level_4_recon_custom_wavelets():
# Test for perfect reconstruction with 3 levels
b = biort('legall')
q = qshift('qshift_06')
Yl, Yh = dtwavexfm3(ellipsoid, 4, biort=b, qshift=q)
ellipsoid_recon = dtwaveifm3(Yl, Yh, biort=b, qshift=q)
assert ellipsoid.size == ellipsoid_recon.size
assert np.max(np.abs(ellipsoid - ellipsoid_recon)) < TOLERANCE
def test_level_4_recon_discarding_level_1():
# Test for non-perfect but reasonable reconstruction
Yl, Yh = dtwavexfm3(ellipsoid, 4, discard_level_1=True)
ellipsoid_recon = dtwaveifm3(Yl, Yh)
assert ellipsoid.size == ellipsoid_recon.size
# Check that we mostly reconstruct correctly
assert np.median(np.abs(ellipsoid - ellipsoid_recon)[:]) < 1e-3
def test_simple_level_4_recon_custom_wavelets():
# Test for perfect reconstruction with 3 levels
b = biort('legall')
q = qshift('qshift_06')
Yl, Yh = dtwavexfm3(ellipsoid, 4, biort=b, qshift=q)
ellipsoid_recon = dtwaveifm3(Yl, Yh, biort=b, qshift=q)
assert ellipsoid.size == ellipsoid_recon.size
assert np.max(np.abs(ellipsoid - ellipsoid_recon)) < TOLERANCE
def test_float32_recon():
# Check that an float32 input is correctly output as float32
Yl, Yh = dtwavexfm3(ellipsoid.astype(np.float32))
assert np.issubsctype(Yl.dtype, np.float32)
assert np.all(list(np.issubsctype(x.dtype, np.complex64) for x in Yh))
recon = dtwaveifm3(Yl, Yh)
assert np.issubsctype(recon.dtype, np.float32)
def test_simple_level_1_recon_haar():
# Test for perfect reconstruction with 1 level and Haar wavelets
# Form Haar wavelets
h0 = np.array((1.0, 1.0))
g0 = h0
h0 = h0 / np.sum(h0)
g0 = g0 / np.sum(g0)
h1 = g0 * np.cumprod(-np.ones_like(g0))
g1 = -h0 * np.cumprod(-np.ones_like(h0))
haar = (h0, g0, h1, g1)
Yl, Yh = dtwavexfm3(ellipsoid, 1, biort=haar)
ellipsoid_recon = dtwaveifm3(Yl, Yh, biort=haar)
assert ellipsoid.size == ellipsoid_recon.size
assert np.max(np.abs(ellipsoid - ellipsoid_recon)) < TOLERANCE
def test_simple_level_1_recon_haar():
# Test for perfect reconstruction with 1 level and Haar wavelets
# Form Haar wavelets
h0 = np.array((1.0, 1.0))
g0 = h0
h0 = h0 / np.sum(h0)
g0 = g0 / np.sum(g0)
h1 = g0 * np.cumprod(-np.ones_like(g0))
g1 = -h0 * np.cumprod(-np.ones_like(h0))
haar = (h0, g0, h1, g1)
Yl, Yh = dtwavexfm3(ellipsoid, 1, biort=haar)
ellipsoid_recon = dtwaveifm3(Yl, Yh, biort=haar)
assert ellipsoid.size == ellipsoid_recon.size
assert np.max(np.abs(ellipsoid - ellipsoid_recon)) < TOLERANCE
SPHERE_RAD = int(0.45 * GRID_SIZE) + 0.5
# Compute an image of the sphere
grid = np.arange(-(GRID_SIZE>>1), GRID_SIZE>>1)
X, Y, Z = np.meshgrid(grid, grid, grid)
r = np.sqrt(X*X + Y*Y + Z*Z)
sphere = (0.5 + np.clip(SPHERE_RAD-r, -0.5, 0.5)).astype(np.float32)
# Specify number of levels and wavelet family to use
nlevels = 2
b = biort('near_sym_a')
q = qshift('qshift_a')
# Form the DT-CWT of the sphere. We use discard_level_1 since we're
# uninterested in the inverse transform and this saves us some memory.
Yl, Yh = dtwavexfm3(sphere, nlevels, b, q, discard_level_1=True)
# Plot maxima
figure(figsize=(8,8))
ax = gcf().add_subplot(1,1,1, projection='3d')
ax.set_aspect('equal')
ax.view_init(35, 75)
# Plot unit sphere +ve octant
thetas = np.linspace(0, np.pi/2, 10)
phis = np.linspace(0, np.pi/2, 10)
def sphere_to_xyz(r, theta, phi):
st, ct = np.sin(theta), np.cos(theta)
sp, cp = np.sin(phi), np.cos(phi)
def test_simple_level_4_recon():
# Test for perfect reconstruction with 3 levels
Yl, Yh = dtwavexfm3(ellipsoid, 4)
ellipsoid_recon = dtwaveifm3(Yl, Yh)
assert ellipsoid.size == ellipsoid_recon.size
assert np.max(np.abs(ellipsoid - ellipsoid_recon)) < TOLERANCE
def test_simple_level_4_xfm():
# Just tests that the transform broadly works and gives expected size output
Yl, Yh = dtwavexfm3(ellipsoid, 4)
assert Yl.shape == (GRID_SIZE>>3,GRID_SIZE>>3,GRID_SIZE>>3)
assert len(Yh) == 4
def test_integer_input():
# Check that an integer input is correctly coerced into a floating point
# array
Yl, Yh = dtwavexfm3(np.ones((4, 4, 4), dtype=np.int))
assert np.any(Yl != 0)
def test_integer_input():
# Check that an integer input is correctly coerced into a floating point
# array
Yl, Yh = dtwavexfm3(np.ones((4,4,4), dtype=np.int))
assert np.any(Yl != 0)
def test_simple_level_4_xfm():
# Just tests that the transform broadly works and gives expected size output
Yl, Yh = dtwavexfm3(ellipsoid, 4)
assert Yl.shape == (GRID_SIZE >> 3, GRID_SIZE >> 3, GRID_SIZE >> 3)
assert len(Yh) == 4
def test_simple_level_4_xfm_ext_mode_8():
# Just tests that the transform broadly works and gives expected size output
crop_ellipsoid = ellipsoid[:62,:58,:54]
Yl, Yh = dtwavexfm3(crop_ellipsoid, 4, ext_mode=8)
assert len(Yh) == 4
def test_simple_level_4_recon():
# Test for perfect reconstruction with 3 levels
Yl, Yh = dtwavexfm3(ellipsoid, 4)
ellipsoid_recon = dtwaveifm3(Yl, Yh)
assert ellipsoid.size == ellipsoid_recon.size
assert np.max(np.abs(ellipsoid - ellipsoid_recon)) < TOLERANCE
SPHERE_RAD = int(0.45 * GRID_SIZE) + 0.5
# Compute an image of the sphere
grid = np.arange(-(GRID_SIZE >> 1), GRID_SIZE >> 1)
X, Y, Z = np.meshgrid(grid, grid, grid)
r = np.sqrt(X * X + Y * Y + Z * Z)
sphere = (0.5 + np.clip(SPHERE_RAD - r, -0.5, 0.5)).astype(np.float32)
# Specify number of levels and wavelet family to use
nlevels = 2
b = biort('near_sym_a')
q = qshift('qshift_a')
# Form the DT-CWT of the sphere. We use discard_level_1 since we're
# uninterested in the inverse transform and this saves us some memory.
Yl, Yh = dtwavexfm3(sphere, nlevels, b, q, discard_level_1=True)
# Plot maxima
figure(figsize=(8, 8))
ax = gcf().add_subplot(1, 1, 1, projection='3d')
ax.set_aspect('equal')
ax.view_init(35, 75)
# Plot unit sphere +ve octant
thetas = np.linspace(0, np.pi / 2, 10)
phis = np.linspace(0, np.pi / 2, 10)
def sphere_to_xyz(r, theta, phi):
st, ct = np.sin(theta), np.cos(theta)
def test_simple_level_4_xfm_ext_mode_4():
# Just tests that the transform broadly works and gives expected size output
crop_ellipsoid = ellipsoid[:62, :54, :58]
Yl, Yh = dtwavexfm3(crop_ellipsoid, 4, ext_mode=4)
assert len(Yh) == 4
