def test_FiniteDifference(self):
print ("test FiniteDifference")
##
N, M = 2, 3
ig = ImageGeometry(N, M)
Id = Identity(ig)
FD = FiniteDiff(ig, direction = 0, bnd_cond = 'Neumann')
u = FD.domain_geometry().allocate('random_int')
res = FD.domain_geometry().allocate(ImageGeometry.RANDOM_INT)
FD.adjoint(u, out=res)
w = FD.adjoint(u)
self.assertNumpyArrayEqual(res.as_array(), w.as_array())
res = Id.domain_geometry().allocate(ImageGeometry.RANDOM_INT)
Id.adjoint(u, out=res)
w = Id.adjoint(u)
self.assertNumpyArrayEqual(res.as_array(), w.as_array())
self.assertNumpyArrayEqual(u.as_array(), w.as_array())
G = Gradient(ig)
u = G.range_geometry().allocate(ImageGeometry.RANDOM_INT)
res = G.domain_geometry().allocate()
G.adjoint(u, out=res)
w = G.adjoint(u)
self.assertNumpyArrayEqual(res.as_array(), w.as_array())
u = G.domain_geometry().allocate(ImageGeometry.RANDOM_INT)
res = G.range_geometry().allocate()
G.direct(u, out=res)
w = G.direct(u)
self.assertBlockDataContainerEqual(res, w)
def test_CompositionOperator_adjoint6(self):
ig = self.ig
data = self.data
G = Gradient(domain_geometry=ig)
Id1 = 3 * Identity(ig)
Id = ZeroOperator(ig)
d = G.compose(Id)
da = d.direct(data)
out1 = G.adjoint(da)
out2 = d.adjoint(da)
numpy.testing.assert_array_almost_equal(out2.as_array(), 0 * out1.as_array())
def test_CompositionOperator_adjoint2(self):
ig = self.ig
data = self.data
G = Gradient(domain_geometry=ig)
Id1 = 2 * Identity(ig)
Id2 = Identity(ig)
d = CompositionOperator(G, Id1)
da = d.direct(data)
out1 = G.adjoint(da)
out2 = d.adjoint(da)
numpy.testing.assert_array_almost_equal(out2.as_array(), 2 * out1.as_array())
def test_Gradient(self):
N, M, K = 20, 30, 40
channels = 10
numpy.random.seed(1)
# check range geometry, examples
ig1 = ImageGeometry(voxel_num_x=M, voxel_num_y=N)
ig2 = ImageGeometry(voxel_num_x=M, voxel_num_y=N, voxel_num_z=K)
ig3 = ImageGeometry(voxel_num_x=M, voxel_num_y=N, channels=channels)
ig4 = ImageGeometry(voxel_num_x=M,
voxel_num_y=N,
channels=channels,
voxel_num_z=K)
G1 = Gradient(ig1, correlation='Space', backend='numpy')
print(G1.range_geometry().shape, '2D no channels')
G4 = Gradient(ig3, correlation='SpaceChannels', backend='numpy')
print(G4.range_geometry().shape, '2D with channels corr')
G5 = Gradient(ig3, correlation='Space', backend='numpy')
print(G5.range_geometry().shape, '2D with channels no corr')
G6 = Gradient(ig4, correlation='Space', backend='numpy')
print(G6.range_geometry().shape, '3D with channels no corr')
G7 = Gradient(ig4, correlation='SpaceChannels', backend='numpy')
print(G7.range_geometry().shape, '3D with channels with corr')
u = ig1.allocate(ImageGeometry.RANDOM)
w = G1.range_geometry().allocate(ImageGeometry.RANDOM_INT)
LHS = (G1.direct(u) * w).sum()
RHS = (u * G1.adjoint(w)).sum()
numpy.testing.assert_approx_equal(LHS, RHS, significant=1)
numpy.testing.assert_approx_equal(G1.norm(),
numpy.sqrt(2 * 4),
significant=1)
u1 = ig3.allocate('random')
w1 = G4.range_geometry().allocate('random')
LHS1 = (G4.direct(u1) * w1).sum()
RHS1 = (u1 * G4.adjoint(w1)).sum()
numpy.testing.assert_approx_equal(LHS1, RHS1, significant=1)
numpy.testing.assert_almost_equal(G4.norm(),
numpy.sqrt(3 * 4),
decimal=0)
u2 = ig4.allocate('random')
w2 = G7.range_geometry().allocate('random')
LHS2 = (G7.direct(u2) * w2).sum()
RHS2 = (u2 * G7.adjoint(w2)).sum()
numpy.testing.assert_approx_equal(LHS2, RHS2, significant=3)
numpy.testing.assert_approx_equal(G7.norm(),
numpy.sqrt(3 * 4),
significant=1)
#check direct/adjoint for space/channels correlation
ig_channel = ImageGeometry(voxel_num_x=2, voxel_num_y=3, channels=2)
G_no_channel = Gradient(ig_channel,
correlation='Space',
backend='numpy')
G_channel = Gradient(ig_channel,
correlation='SpaceChannels',
backend='numpy')
u3 = ig_channel.allocate('random_int')
res_no_channel = G_no_channel.direct(u3)
res_channel = G_channel.direct(u3)
print(" Derivative for 3 directions, first is wrt Channel direction\n")
print(res_channel[0].as_array())
print(res_channel[1].as_array())
print(res_channel[2].as_array())
print(" Derivative for 2 directions, no Channel direction\n")
print(res_no_channel[0].as_array())
print(res_no_channel[1].as_array())
ig2D = ImageGeometry(voxel_num_x=2, voxel_num_y=3)
u4 = ig2D.allocate('random_int')
G2D = Gradient(ig2D, backend='numpy')
res = G2D.direct(u4)
print(res[0].as_array())
print(res[1].as_array())
M, N = 20, 30
ig = ImageGeometry(M, N)
arr = ig.allocate('random_int')
# check direct of Gradient and sparse matrix
G = Gradient(ig, backend='numpy')
norm1 = G.norm(iterations=300)
print("should be sqrt(8) {} {}".format(numpy.sqrt(8), norm1))
numpy.testing.assert_almost_equal(norm1, numpy.sqrt(8), decimal=1)
ig4 = ImageGeometry(M, N, channels=3)
G4 = Gradient(ig4, correlation="SpaceChannels", backend='numpy')
norm4 = G4.norm(iterations=300)
print("should be sqrt(12) {} {}".format(numpy.sqrt(12), norm4))
self.assertTrue((norm4 - numpy.sqrt(12)) / norm4 < 0.2)
def test_Gradient_4D_allocate(self):
nc, nz, ny, nx = 3, 4, 5, 6
size = nc * nz * ny * nx
dim = [nc, nz, ny, nx]
ig = ImageGeometry(voxel_num_x=nx,
voxel_num_y=ny,
voxel_num_z=nz,
channels=nc)
arr = numpy.arange(size).reshape(dim).astype(numpy.float32)**2
data = ig.allocate()
data.fill(arr)
#numpy
grad1 = Gradient(ig,
bnd_cond='Neumann',
correlation='SpaceChannels',
backend='numpy')
gold_direct = grad1.direct(data)
gold_adjoint = grad1.adjoint(gold_direct)
grad2 = Gradient(ig,
bnd_cond='Neumann',
correlation='SpaceChannels',
backend='numpy')
out_direct = grad2.range_geometry().allocate()
out_adjoint = grad2.domain_geometry().allocate()
grad2.direct(data, out=out_direct)
grad2.adjoint(out_direct, out=out_adjoint)
#print("GradientOperator, 4D, bnd_cond='Neumann', direct")
numpy.testing.assert_array_equal(
out_direct.get_item(0).as_array(),
gold_direct.get_item(0).as_array())
numpy.testing.assert_array_equal(
out_direct.get_item(1).as_array(),
gold_direct.get_item(1).as_array())
numpy.testing.assert_array_equal(
out_direct.get_item(2).as_array(),
gold_direct.get_item(2).as_array())
numpy.testing.assert_array_equal(
out_direct.get_item(3).as_array(),
gold_direct.get_item(3).as_array())
#print("GradientOperator, 4D, bnd_cond='Neumann', adjoint")
numpy.testing.assert_array_equal(out_adjoint.as_array(),
gold_adjoint.as_array())
#c
grad1 = Gradient(ig,
bnd_cond='Neumann',
correlation='SpaceChannels',
backend='c')
gold_direct = grad1.direct(data)
gold_adjoint = grad1.adjoint(gold_direct)
grad2 = Gradient(ig,
bnd_cond='Neumann',
correlation='SpaceChannels',
backend='c')
out_direct = grad2.range_geometry().allocate()
out_adjoint = grad2.domain_geometry().allocate()
grad2.direct(data, out=out_direct)
grad2.adjoint(out_direct, out=out_adjoint)
#print("GradientOperator, 4D, bnd_cond='Neumann', direct")
numpy.testing.assert_array_equal(
out_direct.get_item(0).as_array(),
gold_direct.get_item(0).as_array())
numpy.testing.assert_array_equal(
out_direct.get_item(1).as_array(),
gold_direct.get_item(1).as_array())
numpy.testing.assert_array_equal(
out_direct.get_item(2).as_array(),
gold_direct.get_item(2).as_array())
numpy.testing.assert_array_equal(
out_direct.get_item(3).as_array(),
gold_direct.get_item(3).as_array())
#print("GradientOperator, 4D, bnd_cond='Neumann', adjoint")
numpy.testing.assert_array_equal(out_adjoint.as_array(),
gold_adjoint.as_array())