def test_diagonalization(self):
"""Test automatic diagonalization.
"""
var = Variable((2, 5))
K = np.array([[-1, 1]])
expr = 2 * vstack([conv(K, var), conv(K, var)])
assert expr.is_gram_diag(freq=True)
def test_diagonalization(self):
"""Test automatic diagonalization.
"""
var = Variable((2, 5))
K = np.array([[-1, 1]])
expr = 2*vstack([conv(K, var), conv(K, var)])
assert expr.is_gram_diag(freq=True)
def test_conv(self):
"""Test convolution lin op.
"""
# Forward.
var = Variable((2, 3))
kernel = np.array([[1, 2, 3], [4, 5, 6]]) # 2x3
fn = conv(kernel, var)
x = np.arange(6) * 1.0
x = np.reshape(x, (2, 3))
out = np.zeros(fn.shape)
fn.forward([x], [out])
ks = np.array(kernel.shape)
cc = np.floor((ks - 1) / 2.0).astype(np.int) # Center coordinate
y = np.zeros((2, 3))
for i in range(2):
for j in range(3):
for s in range(2):
for t in range(3):
y[i, j] += kernel[ks[0] - 1 - s, ks[1] - 1 - t] * \
x[(s + i - cc[0]) % 2, (t + j - cc[1]) % 3]
# For loop same as convolve
# y = ndimage.convolve(x, kernel, mode='wrap')
self.assertItemsAlmostEqual(out, y)
# Adjoint.#
x = np.arange(6) * 1.0
x = np.reshape(x, (2, 3))
out = np.zeros(var.shape)
fn.adjoint([x], [out])
y = np.zeros((2, 3))
for i in range(2):
for j in range(3):
for s in range(2):
for t in range(3):
y[i, j] += kernel[s, t] * x[(s + i -
(ks[0] - 1 - cc[0])) % 2,
(t + j -
(ks[1] - 1 - cc[1])) % 3]
# For loop same as correlate
# y = ndimage.correlate(x, kernel, mode='wrap')
self.assertItemsAlmostEqual(out, y)
# Diagonal form.
x = Variable(5)
kernel = np.arange(5)
fn = conv(kernel, x)
assert fn.is_diag(freq=True)
assert not fn.is_diag(freq=False)
forward_kernel = psf2otf(kernel, (5, ), 1)
self.assertItemsAlmostEqual(fn.get_diag(freq=True)[x], forward_kernel)
def test_conv(self):
"""Test convolution lin op.
"""
# Forward.
var = Variable((2, 3))
kernel = np.array([[1, 2, 3], [4, 5, 6]]) # 2x3
fn = conv(kernel, var)
x = np.arange(6) * 1.0
x = np.reshape(x, (2, 3))
out = np.zeros(fn.shape)
fn.forward([x], [out])
ks = np.array(kernel.shape)
cc = np.floor((ks - 1) / 2.0).astype(np.int) # Center coordinate
y = np.zeros((2, 3))
for i in range(2):
for j in range(3):
for s in range(2):
for t in range(3):
y[i, j] += kernel[ks[0] - 1 - s, ks[1] - 1 - t] * \
x[(s + i - cc[0]) % 2, (t + j - cc[1]) % 3]
# For loop same as convolve
#y = ndimage.convolve(x, kernel, mode='wrap')
self.assertItemsAlmostEqual(out, y)
# Adjoint.#
x = np.arange(6) * 1.0
x = np.reshape(x, (2, 3))
out = np.zeros(var.shape)
fn.adjoint([x], [out])
y = np.zeros((2, 3))
for i in range(2):
for j in range(3):
for s in range(2):
for t in range(3):
y[i, j] += kernel[s, t] * x[(s + i - (ks[0] - 1 - cc[0])) % 2,
(t + j - (ks[1] - 1 - cc[1])) % 3]
# For loop same as correlate
#y = ndimage.correlate(x, kernel, mode='wrap')
self.assertItemsAlmostEqual(out, y)
# Diagonal form.
x = Variable(5)
kernel = np.arange(5)
fn = conv(kernel, x)
assert fn.is_diag(freq=True)
assert not fn.is_diag(freq=False)
forward_kernel = psf2otf(kernel, (5,), 1)
self.assertItemsAlmostEqual(fn.get_diag(freq=True)[x],
forward_kernel)
def test_combo(self):
"""Test subsampling followed by convolution.
"""
# Forward.
var = Variable((2, 3))
kernel = np.array([[1, 2, 3]]) # 2x3
fn = vstack([conv(kernel, subsample(var, (2, 1)))])
fn = CompGraph(fn)
x = np.arange(6) * 1.0
x = np.reshape(x, (2, 3))
out = np.zeros(fn.output_size)
fn.forward(x.flatten(), out)
y = np.zeros((1, 3))
xsub = x[::2, ::1]
y = ndimage.convolve(xsub, kernel, mode='wrap')
self.assertItemsAlmostEqual(np.reshape(out, y.shape), y)
# Adjoint.
x = np.arange(3) * 1.0
x = np.reshape(x, (1, 3))
out = np.zeros(var.size)
fn.adjoint(x.flatten(), out)
y = ndimage.correlate(x, kernel, mode='wrap')
y2 = np.zeros((2, 3))
y2[::2, :] = y
self.assertItemsAlmostEqual(np.reshape(out, y2.shape), y2)
out = np.zeros(var.size)
fn.adjoint(x.flatten(), out)
self.assertItemsAlmostEqual(np.reshape(out, y2.shape), y2)
def test_combo(self):
"""Test subsampling followed by convolution.
"""
# Forward.
var = Variable((2, 3))
kernel = np.array([[1, 2, 3]]) # 2x3
fn = vstack([conv(kernel, subsample(var, (2, 1)))])
fn = CompGraph(fn)
x = np.arange(6) * 1.0
x = np.reshape(x, (2, 3))
out = np.zeros(fn.output_size)
fn.forward(x.flatten(), out)
y = np.zeros((1, 3))
xsub = x[::2, ::1]
y = ndimage.convolve(xsub, kernel, mode='wrap')
self.assertItemsAlmostEqual(np.reshape(out, y.shape), y)
# Adjoint.
x = np.arange(3) * 1.0
x = np.reshape(x, (1, 3))
out = np.zeros(var.size)
fn.adjoint(x.flatten(), out)
y = ndimage.correlate(x, kernel, mode='wrap')
y2 = np.zeros((2, 3))
y2[::2, :] = y
self.assertItemsAlmostEqual(np.reshape(out, y2.shape), y2)
out = np.zeros(var.size)
fn.adjoint(x.flatten(), out)
self.assertItemsAlmostEqual(np.reshape(out, y2.shape), y2)
