def test_level_4_discarding_level_1():
# Test that level >= 2 highpasses 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 highpasses 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_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_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_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_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
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_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
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 main():
GRID_SIZE = 128
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=False)
# 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)
tris = []
rad = 0.99 # so that points plotted latter are not z-clipped
for t1, t2 in zip(thetas[:-1], thetas[1:]):
for p1, p2 in zip(phis[:-1], phis[1:]):
tris.append([
sphere_to_xyz(rad, t1, p1),
sphere_to_xyz(rad, t1, p2),
sphere_to_xyz(rad, t2, p2),
sphere_to_xyz(rad, t2, p1),
])
sphere = Poly3DCollection(tris, facecolor='w', edgecolor=(0.6,0.6,0.6))
ax.add_collection3d(sphere)
locs = []
scale = 1.1
for idx in range(Yh[-1].shape[3]):
Z = Yh[-1][:,:,:,idx]
C = np.abs(Z)
max_loc = np.asarray(np.unravel_index(np.argmax(C), C.shape)) - np.asarray(C.shape)*0.5
max_loc /= np.sqrt(np.sum(max_loc * max_loc))
# Only record directions in the +ve octant (or those from the -ve quadrant
# which can be flipped).
if np.all(np.sign(max_loc) == 1):
locs.append(max_loc)
ax.text(max_loc[0] * scale, max_loc[1] * scale, max_loc[2] * scale, str(idx+1))
elif np.all(np.sign(max_loc) == -1):
locs.append(-max_loc)
ax.text(-max_loc[0] * scale, -max_loc[1] * scale, -max_loc[2] * scale, str(idx+1))
# Plot all directions as a scatter plot
locs = np.asarray(locs)
ax.scatter(locs[:,0], locs[:,1], locs[:,2], c=np.arange(locs.shape[0]))
w = 1.1
ax.auto_scale_xyz([0, w], [0, w], [0, w])
legend()
title('3D DT-CWT subband directions for +ve hemisphere quadrant')
tight_layout()
show()
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_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_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_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 main():
GRID_SIZE = 128
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=False)
# 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)
tris = []
rad = 0.99 # so that points plotted latter are not z-clipped
for t1, t2 in zip(thetas[:-1], thetas[1:]):
for p1, p2 in zip(phis[:-1], phis[1:]):
tris.append([
sphere_to_xyz(rad, t1, p1),
sphere_to_xyz(rad, t1, p2),
sphere_to_xyz(rad, t2, p2),
sphere_to_xyz(rad, t2, p1),
])
sphere = Poly3DCollection(tris, facecolor='w', edgecolor=(0.6, 0.6, 0.6))
ax.add_collection3d(sphere)
locs = []
scale = 1.1
for idx in range(Yh[-1].shape[3]):
Z = Yh[-1][:, :, :, idx]
C = np.abs(Z)
max_loc = np.asarray(np.unravel_index(
np.argmax(C), C.shape)) - np.asarray(C.shape) * 0.5
max_loc /= np.sqrt(np.sum(max_loc * max_loc))
# Only record directions in the +ve octant (or those from the -ve quadrant
# which can be flipped).
if np.all(np.sign(max_loc) == 1):
locs.append(max_loc)
ax.text(max_loc[0] * scale, max_loc[1] * scale, max_loc[2] * scale,
str(idx + 1))
elif np.all(np.sign(max_loc) == -1):
locs.append(-max_loc)
ax.text(-max_loc[0] * scale, -max_loc[1] * scale,
-max_loc[2] * scale, str(idx + 1))
# Plot all directions as a scatter plot
locs = np.asarray(locs)
ax.scatter(locs[:, 0], locs[:, 1], locs[:, 2], c=np.arange(locs.shape[0]))
w = 1.1
ax.auto_scale_xyz([0, w], [0, w], [0, w])
legend()
title('3D DT-CWT subband directions for +ve hemisphere quadrant')
tight_layout()
show()
