def _level1_xfm_no_highpass(X, h0o, h1o, ext_mode):
"""Perform level 1 of the 3d transform discarding highpass subbands.
"""
# Check shape of input according to ext_mode. Note that shape of X is
# double original input in each direction.
if ext_mode == 4 and np.any(np.fmod(X.shape, 2) != 0):
raise ValueError(
'Input shape should be a multiple of 2 in each direction when self.ext_mode == 4'
)
elif ext_mode == 8 and np.any(np.fmod(X.shape, 4) != 0):
raise ValueError(
'Input shape should be a multiple of 4 in each direction when self.ext_mode == 8'
)
out = np.zeros_like(X)
# Loop over 2nd dimension extracting 2D slice from first and 3rd dimensions
for f in xrange(X.shape[1]):
# extract slice
y = X[:, f, :].T
out[:, f, :] = colfilter(y, h0o).T
# Loop over 3rd dimension extracting 2D slice from first and 2nd dimensions
for f in xrange(X.shape[2]):
y = colfilter(out[:, :, f].T, h0o).T
out[:, :, f] = colfilter(y, h0o)
return out
def _level1_xfm_no_highpass(X, h0o, h1o, ext_mode):
"""Perform level 1 of the 3d transform discarding highpass subbands.
"""
# Check shape of input according to ext_mode. Note that shape of X is
# double original input in each direction.
if ext_mode == 4 and np.any(np.fmod(X.shape, 2) != 0):
raise ValueError('Input shape should be a multiple of 2 in each direction when self.ext_mode == 4')
elif ext_mode == 8 and np.any(np.fmod(X.shape, 4) != 0):
raise ValueError('Input shape should be a multiple of 4 in each direction when self.ext_mode == 8')
out = np.zeros_like(X)
# Loop over 2nd dimension extracting 2D slice from first and 3rd dimensions
for f in xrange(X.shape[1]):
# extract slice
y = X[:, f, :].T
out[:, f, :] = colfilter(y, h0o).T
# Loop over 3rd dimension extracting 2D slice from first and 2nd dimensions
for f in xrange(X.shape[2]):
y = colfilter(out[:, :, f].T, h0o).T
out[:, :, f] = colfilter(y, h0o)
return out
def test_even_size():
y = colfilter(np.zeros_like(mandrill), (-1,1))
assert y.shape == (mandrill.shape[0]+1, mandrill.shape[1])
assert not np.any(y[:] != 0.0)
z = colfilter_gold(np.zeros_like(mandrill), (-1,1))
assert_almost_equal(y, z)
def test_even_size():
y = colfilter(np.zeros_like(mandrill), (-1, 1))
assert y.shape == (mandrill.shape[0] + 1, mandrill.shape[1])
assert not np.any(y[:] != 0.0)
z = colfilter_gold(np.zeros_like(mandrill), (-1, 1))
assert_almost_equal(y, z)
def _level1_ifm_no_highpass(Yl, g0o, g1o):
"""Perform level 1 of the inverse 3d transform assuming highpass
coefficients are zero.
"""
# Create work area
output = np.zeros_like(Yl)
for f in xrange(Yl.shape[2]):
y = colfilter(Yl[:, :, f].T, g0o)
output[:, :, f] = colfilter(y.T, g0o)
for f in xrange(Yl.shape[1]):
y = output[:, f, :].T.copy()
output[:, f, :] = colfilter(y, g0o)
return output
def _level1_ifm_no_highpass(Yl, g0o, g1o):
"""Perform level 1 of the inverse 3d transform assuming highpass
coefficients are zero.
"""
# Create work area
output = np.zeros_like(Yl)
for f in xrange(Yl.shape[2]):
y = colfilter(Yl[:, :, f].T, g0o)
output[:, :, f] = colfilter(y.T, g0o)
for f in xrange(Yl.shape[1]):
y = output[:, f, :].T.copy()
output[:, f, :] = colfilter(y, g0o)
return output
def _level1_ifm(Yl, Yh, g0o, g1o):
"""Perform level 1 of the inverse 3d transform.
"""
# Create work area
work = np.zeros(np.asanyarray(Yl.shape) * 2, dtype=Yl.dtype)
# Work out shape of output
Xshape = np.asanyarray(work.shape) >> 1
if g0o.shape[0] % 2 == 0:
# if we have an even length filter, we need to shrink the output by 1
# to compensate for the addition of an extra row/column/slice in
# the forward transform
Xshape -= 1
# Form some useful slices
s0a = slice(None, work.shape[0] >> 1)
s1a = slice(None, work.shape[1] >> 1)
s2a = slice(None, work.shape[2] >> 1)
s0b = slice(work.shape[0] >> 1, None)
s1b = slice(work.shape[1] >> 1, None)
s2b = slice(work.shape[2] >> 1, None)
x0a = slice(None, Xshape[0])
x1a = slice(None, Xshape[1])
x2a = slice(None, Xshape[2])
x0b = slice(work.shape[0] >> 1, (work.shape[0] >> 1) + Xshape[0])
x1b = slice(work.shape[1] >> 1, (work.shape[1] >> 1) + Xshape[1])
x2b = slice(work.shape[2] >> 1, (work.shape[2] >> 1) + Xshape[2])
# Assign regions of work area
work[s0a, s1a, s2a] = Yl
work[x0a, x1b, x2a] = c2cube(Yh[:, :, :, 0:4])
work[x0b, x1a, x2a] = c2cube(Yh[:, :, :, 4:8])
work[x0b, x1b, x2a] = c2cube(Yh[:, :, :, 8:12])
work[x0a, x1a, x2b] = c2cube(Yh[:, :, :, 12:16])
work[x0a, x1b, x2b] = c2cube(Yh[:, :, :, 16:20])
work[x0b, x1a, x2b] = c2cube(Yh[:, :, :, 20:24])
work[x0b, x1b, x2b] = c2cube(Yh[:, :, :, 24:28])
for f in xrange(work.shape[2]):
# Do odd top-level filters on rows.
y = colfilter(work[:, x1a, f].T, g0o) + colfilter(
work[:, x1b, f].T, g1o)
# Do odd top-level filters on columns.
work[s0a, s1a,
f] = colfilter(y[:, x0a].T, g0o) + colfilter(y[:, x0b].T, g1o)
for f in xrange(work.shape[1] >> 1):
# Do odd top-level filters on 3rd dim.
y = work[s0a, f, :].T
work[s0a, f,
s2a] = (colfilter(y[x2a, :], g0o) + colfilter(y[x2b, :], g1o)).T
if g0o.shape[0] % 2 == 0:
return work[1:(work.shape[0] >> 1), 1:(work.shape[1] >> 1),
1:(work.shape[2] >> 1)]
else:
return work[s0a, s1a, s2a]
def _level1_ifm(Yl, Yh, g0o, g1o):
"""Perform level 1 of the inverse 3d transform.
"""
# Create work area
work = np.zeros(np.asanyarray(Yl.shape) * 2, dtype=Yl.dtype)
# Work out shape of output
Xshape = np.asanyarray(work.shape) >> 1
if g0o.shape[0] % 2 == 0:
# if we have an even length filter, we need to shrink the output by 1
# to compensate for the addition of an extra row/column/slice in
# the forward transform
Xshape -= 1
# Form some useful slices
s0a = slice(None, work.shape[0] >> 1)
s1a = slice(None, work.shape[1] >> 1)
s2a = slice(None, work.shape[2] >> 1)
s0b = slice(work.shape[0] >> 1, None)
s1b = slice(work.shape[1] >> 1, None)
s2b = slice(work.shape[2] >> 1, None)
x0a = slice(None, Xshape[0])
x1a = slice(None, Xshape[1])
x2a = slice(None, Xshape[2])
x0b = slice(work.shape[0] >> 1, (work.shape[0] >> 1) + Xshape[0])
x1b = slice(work.shape[1] >> 1, (work.shape[1] >> 1) + Xshape[1])
x2b = slice(work.shape[2] >> 1, (work.shape[2] >> 1) + Xshape[2])
# Assign regions of work area
work[s0a, s1a, s2a] = Yl
work[x0a, x1b, x2a] = c2cube(Yh[:,:,:, 0:4 ])
work[x0b, x1a, x2a] = c2cube(Yh[:,:,:, 4:8 ])
work[x0b, x1b, x2a] = c2cube(Yh[:,:,:, 8:12])
work[x0a, x1a, x2b] = c2cube(Yh[:,:,:,12:16])
work[x0a, x1b, x2b] = c2cube(Yh[:,:,:,16:20])
work[x0b, x1a, x2b] = c2cube(Yh[:,:,:,20:24])
work[x0b, x1b, x2b] = c2cube(Yh[:,:,:,24:28])
for f in xrange(work.shape[2]):
# Do odd top-level filters on rows.
y = colfilter(work[:, x1a, f].T, g0o) + colfilter(work[:, x1b, f].T, g1o)
# Do odd top-level filters on columns.
work[s0a, s1a, f] = colfilter(y[:, x0a].T, g0o) + colfilter(y[:, x0b].T, g1o)
for f in xrange(work.shape[1]>>1):
# Do odd top-level filters on 3rd dim.
y = work[s0a, f, :].T
work[s0a, f, s2a] = (colfilter(y[x2a, :], g0o) + colfilter(y[x2b, :], g1o)).T
if g0o.shape[0] % 2 == 0:
return work[1:(work.shape[0]>>1), 1:(work.shape[1]>>1), 1:(work.shape[2]>>1)]
else:
return work[s0a, s1a, s2a]
def test_qshift():
y = colfilter(mandrill, qshift('qshift_a')[0])
assert y.shape == (mandrill.shape[0] + 1, mandrill.shape[1])
z = colfilter_gold(mandrill, qshift('qshift_a')[0])
assert_almost_equal(y, z)
def _level1_xfm(X, h0o, h1o, ext_mode):
"""Perform level 1 of the 3d transform.
"""
# Check shape of input according to ext_mode. Note that shape of X is
# double original input in each direction.
if ext_mode == 4 and np.any(np.fmod(X.shape, 2) != 0):
raise ValueError(
'Input shape should be a multiple of 2 in each direction when self.ext_mode == 4'
)
elif ext_mode == 8 and np.any(np.fmod(X.shape, 4) != 0):
raise ValueError(
'Input shape should be a multiple of 4 in each direction when self.ext_mode == 8'
)
# Create work area
work_shape = np.asanyarray(X.shape) * 2
# We need one extra row per octant if filter length is even
if h0o.shape[0] % 2 == 0:
work_shape += 2
work = np.zeros(work_shape, dtype=X.dtype)
# Form some useful slices
s0a = slice(None, work.shape[0] >> 1)
s1a = slice(None, work.shape[1] >> 1)
s2a = slice(None, work.shape[2] >> 1)
s0b = slice(work.shape[0] >> 1, None)
s1b = slice(work.shape[1] >> 1, None)
s2b = slice(work.shape[2] >> 1, None)
x0a = slice(None, X.shape[0])
x1a = slice(None, X.shape[1])
x2a = slice(None, X.shape[2])
x0b = slice(work.shape[0] >> 1, (work.shape[0] >> 1) + X.shape[0])
x1b = slice(work.shape[1] >> 1, (work.shape[1] >> 1) + X.shape[1])
x2b = slice(work.shape[2] >> 1, (work.shape[2] >> 1) + X.shape[2])
# Assign input
if h0o.shape[0] % 2 == 0:
work[:X.shape[0], :X.shape[1], :X.shape[2]] = X
# Copy last rows/cols/slices
work[X.shape[0], :X.shape[1], :X.shape[2]] = X[-1, :, :]
work[:X.shape[0], X.shape[1], :X.shape[2]] = X[:, -1, :]
work[:X.shape[0], :X.shape[1], X.shape[2]] = X[:, :, -1]
work[X.shape[0], X.shape[1], X.shape[2]] = X[-1, -1, -1]
else:
work[s0a, s1a, s2a] = X
# Loop over 2nd dimension extracting 2D slice from first and 3rd dimensions
for f in xrange(work.shape[1] >> 1):
# extract slice
y = work[s0a, f, x2a].T
# Do odd top-level filters on 3rd dim. The order here is important
# since the second filtering will modify the elements of y as well
# since y is merely a view onto work.
work[s0a, f, s2b] = colfilter(y, h1o).T
work[s0a, f, s2a] = colfilter(y, h0o).T
# Loop over 3rd dimension extracting 2D slice from first and 2nd dimensions
for f in xrange(work.shape[2]):
# Do odd top-level filters on rows.
y1 = work[x0a, x1a, f].T
y2 = np.vstack((colfilter(y1, h0o), colfilter(y1, h1o))).T
# Do odd top-level filters on columns.
work[s0a, :, f] = colfilter(y2, h0o)
work[s0b, :, f] = colfilter(y2, h1o)
# Return appropriate slices of output
return (
work[s0a, s1a, s2a], # LLL
np.concatenate(
(
cube2c(work[x0a, x1b, x2a]), # HLL
cube2c(work[x0b, x1a, x2a]), # LHL
cube2c(work[x0b, x1b, x2a]), # HHL
cube2c(work[x0a, x1a, x2b]), # LLH
cube2c(work[x0a, x1b, x2b]), # HLH
cube2c(work[x0b, x1a, x2b]), # LHH
cube2c(work[x0b, x1b, x2b]), # HLH
),
axis=3))
def test_even_size_non_array():
y = colfilter(mandrill.tolist(), (-1,1))
assert y.shape == (mandrill.shape[0]+1, mandrill.shape[1])
z = colfilter_gold(mandrill.tolist(), (-1,1))
assert_almost_equal(y, z)
def test_odd_size_non_array():
y = colfilter(mandrill.tolist(), (-1,2,-1))
assert y.shape == mandrill.shape
z = colfilter_gold(mandrill.tolist(), (-1,2,-1))
assert_almost_equal(y, z)
def test_biort():
y = colfilter(mandrill, biort('antonini')[0])
assert y.shape == mandrill.shape
z = colfilter_gold(mandrill, biort('antonini')[0])
assert_almost_equal(y, z)
def test_even_size_non_array():
y = colfilter(mandrill.tolist(), (-1, 1))
assert y.shape == (mandrill.shape[0] + 1, mandrill.shape[1])
z = colfilter_gold(mandrill.tolist(), (-1, 1))
assert_almost_equal(y, z)
def _level1_xfm(X, h0o, h1o, ext_mode):
"""Perform level 1 of the 3d transform.
"""
# Check shape of input according to ext_mode. Note that shape of X is
# double original input in each direction.
if ext_mode == 4 and np.any(np.fmod(X.shape, 2) != 0):
raise ValueError('Input shape should be a multiple of 2 in each direction when self.ext_mode == 4')
elif ext_mode == 8 and np.any(np.fmod(X.shape, 4) != 0):
raise ValueError('Input shape should be a multiple of 4 in each direction when self.ext_mode == 8')
# Create work area
work_shape = np.asanyarray(X.shape) * 2
# We need one extra row per octant if filter length is even
if h0o.shape[0] % 2 == 0:
work_shape += 2
work = np.zeros(work_shape, dtype=X.dtype)
# Form some useful slices
s0a = slice(None, work.shape[0] >> 1)
s1a = slice(None, work.shape[1] >> 1)
s2a = slice(None, work.shape[2] >> 1)
s0b = slice(work.shape[0] >> 1, None)
s1b = slice(work.shape[1] >> 1, None)
s2b = slice(work.shape[2] >> 1, None)
x0a = slice(None, X.shape[0])
x1a = slice(None, X.shape[1])
x2a = slice(None, X.shape[2])
x0b = slice(work.shape[0] >> 1, (work.shape[0] >> 1) + X.shape[0])
x1b = slice(work.shape[1] >> 1, (work.shape[1] >> 1) + X.shape[1])
x2b = slice(work.shape[2] >> 1, (work.shape[2] >> 1) + X.shape[2])
# Assign input
if h0o.shape[0] % 2 == 0:
work[:X.shape[0], :X.shape[1], :X.shape[2]] = X
# Copy last rows/cols/slices
work[ X.shape[0], :X.shape[1], :X.shape[2]] = X[-1, :, :]
work[:X.shape[0], X.shape[1], :X.shape[2]] = X[:, -1, :]
work[:X.shape[0], :X.shape[1], X.shape[2]] = X[:, :, -1]
work[X.shape[0], X.shape[1], X.shape[2]] = X[-1,-1,-1]
else:
work[s0a, s1a, s2a] = X
# Loop over 2nd dimension extracting 2D slice from first and 3rd dimensions
for f in xrange(work.shape[1] >> 1):
# extract slice
y = work[s0a, f, x2a].T
# Do odd top-level filters on 3rd dim. The order here is important
# since the second filtering will modify the elements of y as well
# since y is merely a view onto work.
work[s0a, f, s2b] = colfilter(y, h1o).T
work[s0a, f, s2a] = colfilter(y, h0o).T
# Loop over 3rd dimension extracting 2D slice from first and 2nd dimensions
for f in xrange(work.shape[2]):
# Do odd top-level filters on rows.
y1 = work[x0a, x1a, f].T
y2 = np.vstack((colfilter(y1, h0o), colfilter(y1, h1o))).T
# Do odd top-level filters on columns.
work[s0a, :, f] = colfilter(y2, h0o)
work[s0b, :, f] = colfilter(y2, h1o)
# Return appropriate slices of output
return (
work[s0a, s1a, s2a], # LLL
np.concatenate((
cube2c(work[x0a, x1b, x2a]), # HLL
cube2c(work[x0b, x1a, x2a]), # LHL
cube2c(work[x0b, x1b, x2a]), # HHL
cube2c(work[x0a, x1a, x2b]), # LLH
cube2c(work[x0a, x1b, x2b]), # HLH
cube2c(work[x0b, x1a, x2b]), # LHH
cube2c(work[x0b, x1b, x2b]), # HLH
), axis=3)
)
def test_even_size():
y = colfilter(mandrill, (-1,1))
assert y.shape == (mandrill.shape[0]+1, mandrill.shape[1])
z = colfilter_gold(mandrill, (-1,1))
assert_almost_equal(y, z)
def test_biort():
y = colfilter(lena, biort('antonini')[0])
assert y.shape == lena.shape
z = colfilter_gold(lena, biort('antonini')[0])
assert_almost_equal(y, z)
def test_qshift():
y = colfilter(lena, qshift('qshift_a')[0])
assert y.shape == (lena.shape[0]+1, lena.shape[1])
z = colfilter_gold(lena, qshift('qshift_a')[0])
assert_almost_equal(y, z)
def test_odd_size():
y = colfilter(lena, (-1,2,-1))
assert y.shape == lena.shape
z = colfilter_gold(lena, (-1,2,-1))
assert_almost_equal(y, z)
def test_even_size():
y = colfilter(lena, (-1,1))
assert y.shape == (lena.shape[0]+1, lena.shape[1])
z = colfilter_gold(lena, (-1,1))
assert_almost_equal(y, z)
def test_odd_size():
y = colfilter(mandrill, (-1, 2, -1))
assert y.shape == mandrill.shape
z = colfilter_gold(mandrill, (-1, 2, -1))
assert_almost_equal(y, z)
def test_biort():
y = colfilter(mandrill, biort('antonini')[0])
assert y.shape == mandrill.shape
z = colfilter_gold(mandrill, biort('antonini')[0])
assert_almost_equal(y, z)
def test_odd_size():
y = colfilter(mandrill, (-1,2,-1))
assert y.shape == mandrill.shape
z = colfilter_gold(mandrill, (-1,2,-1))
assert_almost_equal(y, z)
def test_odd_size_non_array():
y = colfilter(mandrill.tolist(), (-1, 2, -1))
assert y.shape == mandrill.shape
z = colfilter_gold(mandrill.tolist(), (-1, 2, -1))
assert_almost_equal(y, z)
def test_qshift():
y = colfilter(mandrill, qshift('qshift_a')[0])
assert y.shape == (mandrill.shape[0]+1, mandrill.shape[1])
z = colfilter_gold(mandrill, qshift('qshift_a')[0])
assert_almost_equal(y, z)
def test_even_size():
y = colfilter(mandrill, (-1, 1))
assert y.shape == (mandrill.shape[0] + 1, mandrill.shape[1])
z = colfilter_gold(mandrill, (-1, 1))
assert_almost_equal(y, z)
