def test_init(exponent):
# Validate that the different init patterns work and do not crash.
space = odl.FunctionSpace(odl.Interval(0, 1))
part = odl.uniform_partition_fromintv(space.domain, 10)
rn = odl.Rn(10, exponent=exponent)
odl.DiscreteLp(space, part, rn, exponent=exponent)
odl.DiscreteLp(space, part, rn, exponent=exponent, interp='linear')
# Normal discretization of unit interval with complex
complex_space = odl.FunctionSpace(odl.Interval(0, 1),
field=odl.ComplexNumbers())
cn = odl.Cn(10, exponent=exponent)
odl.DiscreteLp(complex_space, part, cn, exponent=exponent)
space = odl.FunctionSpace(odl.Rectangle([0, 0], [1, 1]))
part = odl.uniform_partition_fromintv(space.domain, (10, 10))
rn = odl.Rn(100, exponent=exponent)
odl.DiscreteLp(space, part, rn, exponent=exponent,
interp=['nearest', 'linear'])
# Real space should not work with complex
with pytest.raises(ValueError):
odl.DiscreteLp(space, part, cn)
# Complex space should not work with reals
with pytest.raises(ValueError):
odl.DiscreteLp(complex_space, part, rn)
# Wrong size of underlying space
rn_wrong_size = odl.Rn(20)
with pytest.raises(ValueError):
odl.DiscreteLp(space, part, rn_wrong_size)
def test_dspace_type_cuda():
# Plain function set -> Ntuples-like
fset = odl.FunctionSet(odl.Interval(0, 1), odl.Strings(2))
assert dspace_type(fset, 'cuda') == odl.CudaNtuples
assert dspace_type(fset, 'cuda', np.int) == odl.CudaNtuples
# Real space
rspc = odl.FunctionSpace(odl.Interval(0, 1), field=odl.RealNumbers())
assert dspace_type(rspc, 'cuda') == odl.CudaFn
assert dspace_type(rspc, 'cuda', np.float64) == odl.CudaFn
assert dspace_type(rspc, 'cuda', np.int) == odl.CudaFn
with pytest.raises(TypeError):
dspace_type(rspc, 'cuda', np.complex)
with pytest.raises(TypeError):
dspace_type(rspc, 'cuda', np.dtype('<U2'))
# Complex space (not implemented)
cspc = odl.FunctionSpace(odl.Interval(0, 1), field=odl.ComplexNumbers())
with pytest.raises(NotImplementedError):
dspace_type(cspc, 'cuda')
with pytest.raises(NotImplementedError):
dspace_type(cspc, 'cuda', np.complex64)
with pytest.raises(TypeError):
dspace_type(cspc, 'cuda', np.float)
with pytest.raises(TypeError):
assert dspace_type(cspc, 'cuda', np.int)
def test_dspace_type_numpy():
# Plain function set -> Ntuples-like
fset = odl.FunctionSet(odl.Interval(0, 1), odl.Strings(2))
assert dspace_type(fset, 'numpy') == odl.Ntuples, None
assert dspace_type(fset, 'numpy', np.int) == odl.Ntuples
# Real space
rspc = odl.FunctionSpace(odl.Interval(0, 1), field=odl.RealNumbers())
assert dspace_type(rspc, 'numpy') == odl.Fn
assert dspace_type(rspc, 'numpy', np.float32) == odl.Fn
assert dspace_type(rspc, 'numpy', np.int) == odl.Fn
with pytest.raises(TypeError):
dspace_type(rspc, 'numpy', np.complex)
with pytest.raises(TypeError):
dspace_type(rspc, 'numpy', np.dtype('<U2'))
# Complex space
cspc = odl.FunctionSpace(odl.Interval(0, 1), field=odl.ComplexNumbers())
assert dspace_type(cspc, 'numpy') == odl.Fn
assert dspace_type(cspc, 'numpy', np.complex64) == odl.Fn
with pytest.raises(TypeError):
dspace_type(cspc, 'numpy', np.float)
with pytest.raises(TypeError):
assert dspace_type(cspc, 'numpy', np.int)
with pytest.raises(TypeError):
dspace_type(cspc, 'numpy', np.dtype('<U2'))
def test_fspace_equality():
intv = odl.Interval(0, 1)
intv2 = odl.Interval(-1, 1)
fspace = FunctionSpace(intv)
fspace_r = FunctionSpace(intv, field=odl.RealNumbers())
fspace_c = FunctionSpace(intv, field=odl.ComplexNumbers())
fspace_intv2 = FunctionSpace(intv2)
assert fspace == fspace_r
assert fspace != fspace_c
assert fspace != fspace_intv2
def test_fspace_vector_init():
# 1d, real
intv = odl.Interval(0, 1)
fspace = FunctionSpace(intv)
fspace.element(func_1d_oop)
fspace.element(func_1d_oop, vectorized=False)
fspace.element(func_1d_oop, vectorized=True)
fspace.element(func_1d_ip, vectorized=True)
fspace.element(func_1d_dual, vectorized=True)
# 2d, real
rect = odl.Rectangle([0, 0], [1, 2])
fspace = FunctionSpace(rect)
fspace.element(func_2d_novec, vectorized=False)
fspace.element(func_2d_vec_oop)
fspace.element(func_2d_vec_oop, vectorized=True)
fspace.element(func_2d_vec_ip, vectorized=True)
fspace.element(func_2d_vec_dual, vectorized=True)
# 2d, complex
fspace = FunctionSpace(rect, field=odl.ComplexNumbers())
fspace.element(cfunc_2d_novec, vectorized=False)
fspace.element(cfunc_2d_vec_oop)
fspace.element(cfunc_2d_vec_oop, vectorized=True)
fspace.element(cfunc_2d_vec_ip, vectorized=True)
fspace.element(cfunc_2d_vec_dual, vectorized=True)
def make_projector(n):
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20, -20], [20, 20, 20],
[n] * 3,
dtype='float32')
# Geometry
src_rad = 1000
det_rad = 100
angle_intvl = odl.Interval(0, 2 * np.pi)
dparams = odl.Rectangle([-50, -50], [50, 50])
agrid = odl.uniform_sampling(angle_intvl, n)
dgrid = odl.uniform_sampling(dparams, [n] * 2)
geom = odl.tomo.CircularConeFlatGeometry(angle_intvl, dparams, src_rad,
det_rad, agrid, dgrid)
# X-ray transform
projector = odl.tomo.XrayTransform(discr_reco_space,
geom,
backend='astra_cuda')
phantom = projector.domain.one()
projector._adjoint *= projector(phantom).inner(
projector(phantom)) / phantom.inner(
projector.adjoint(projector(phantom)))
return 0.08 * projector
def test_nearest_interpolation_1d_complex():
intv = odl.Interval(0, 1)
part = odl.uniform_partition_fromintv(intv, 5, nodes_on_bdry=False)
# Coordinate vectors are:
# [0.1, 0.3, 0.5, 0.7, 0.9]
space = odl.FunctionSpace(intv, field=odl.ComplexNumbers())
dspace = odl.Cn(part.size)
interp_op = NearestInterpolation(space, part, dspace)
function = interp_op([0 + 1j, 1 + 2j, 2 + 3j, 3 + 4j, 4 + 5j])
# Evaluate at single point
val = function(0.35) # closest to index 1 -> 1 + 2j
assert val == 1.0 + 2.0j
# Input array, with and without output array
pts = np.array([0.4, 0.0, 0.65, 0.95])
true_arr = [1 + 2j, 0 + 1j, 3 + 4j, 4 + 5j]
assert all_equal(function(pts), true_arr)
# Should also work with a (1, N) array
pts = pts[None, :]
assert all_equal(function(pts), true_arr)
out = np.empty(4, dtype='complex128')
function(pts, out=out)
assert all_equal(out, true_arr)
# Input meshgrid, with and without output array
# Same as array for 1d
mg = sparse_meshgrid([0.4, 0.0, 0.65, 0.95])
true_mg = [1 + 2j, 0 + 1j, 3 + 4j, 4 + 5j]
assert all_equal(function(mg), true_mg)
function(mg, out=out)
assert all_equal(out, true_mg)
def test_nearest_interpolation_1d_variants():
intv = odl.Interval(0, 1)
part = odl.uniform_partition_fromintv(intv, 5, nodes_on_bdry=False)
# Coordinate vectors are:
# [0.1, 0.3, 0.5, 0.7, 0.9]
space = odl.FunctionSpace(intv)
dspace = odl.Rn(part.size)
# 'left' variant
interp_op = NearestInterpolation(space, part, dspace, variant='left')
function = interp_op([0, 1, 2, 3, 4])
# Testing two midpoints and the extreme values
pts = np.array([0.4, 0.8, 0.0, 1.0])
true_arr = [1, 3, 0, 4]
assert all_equal(function(pts), true_arr)
# 'right' variant
interp_op = NearestInterpolation(space, part, dspace, variant='right')
function = interp_op([0, 1, 2, 3, 4])
# Testing two midpoints and the extreme values
pts = np.array([0.4, 0.8, 0.0, 1.0])
true_arr = [2, 4, 0, 4]
assert all_equal(function(pts), true_arr)
def test_bwt1d(wbasis):
# Verify that the operator works as axpected
# 1D test
n = 16
x = np.zeros(n)
x[5:10] = 1
nscales = 2
# Define a discretized domain
domain = odl.FunctionSpace(odl.Interval([-1], [1]))
nPoints = np.array([n])
disc_domain = odl.uniform_discr_fromspace(domain, nPoints)
disc_phantom = disc_domain.element(x)
# Create the discrete wavelet transform operator.
# Only the domain of the operator needs to be defined
Wop = BiorthWaveletTransform(disc_domain, nscales, wbasis)
# Compute the discrete wavelet transform of discrete imput image
coeffs = Wop(disc_phantom)
# Compute the inverse wavelet transform
reconstruction = Wop.inverse(coeffs)
# Verify that reconstructions lie in correct discretized domain
assert reconstruction in disc_domain
assert all_almost_equal(reconstruction.asarray(), x)
def test_fspace_astype():
rspace = FunctionSpace(odl.Interval(0, 1))
cspace = FunctionSpace(odl.Interval(0, 1), field=odl.ComplexNumbers())
rspace_s = FunctionSpace(odl.Interval(0, 1), out_dtype='float32')
cspace_s = FunctionSpace(odl.Interval(0, 1), out_dtype='complex64')
assert rspace.astype('complex64') == cspace_s
assert rspace.astype('complex128') == cspace
assert rspace.astype('complex128') is rspace._complex_space
assert rspace.astype('float32') == rspace_s
assert rspace.astype('float64') is rspace._real_space
assert cspace.astype('float32') == rspace_s
assert cspace.astype('float64') == rspace
assert cspace.astype('float64') is cspace._real_space
assert cspace.astype('complex64') == cspace_s
assert cspace.astype('complex128') is cspace._complex_space
def test_fspace_simple_attributes():
intv = odl.Interval(0, 1)
fspace = FunctionSpace(intv)
fspace_r = FunctionSpace(intv, field=odl.RealNumbers())
fspace_c = FunctionSpace(intv, field=odl.ComplexNumbers())
assert fspace.domain == intv
assert fspace.range == odl.RealNumbers()
assert fspace_r.range == odl.RealNumbers()
assert fspace_c.range == odl.ComplexNumbers()
def test_fspace_vector_ufunc():
intv = odl.Interval(0, 1)
points = _points(intv, num=5)
mg = _meshgrid(intv, shape=(5, ))
fspace = FunctionSpace(intv)
f_vec = fspace.element(np.sin)
assert f_vec(0.5) == np.sin(0.5)
assert all_equal(f_vec(points), np.sin(points.squeeze()))
assert all_equal(f_vec(mg), np.sin(mg[0]))
def test_partition_init():
vec1 = np.array([2, 4, 5, 7])
vec2 = np.array([-4, -3, 0, 1, 4])
begin = [2, -5]
end = [10, 4]
# Simply test if code runs
odl.RectPartition(odl.Rectangle(begin, end), odl.TensorGrid(vec1, vec2))
odl.RectPartition(odl.Interval(begin[0], end[0]), odl.TensorGrid(vec1))
# Degenerate dimensions should work, too
vec2 = np.array([1.0])
odl.RectPartition(odl.Rectangle(begin, end), odl.TensorGrid(vec1, vec2))
def test_astra_projection_geometry():
"""Create ASTRA projection geometry from geometry objects."""
with pytest.raises(TypeError):
odl.tomo.astra_projection_geometry(None)
apart = odl.uniform_partition(0, 2 * np.pi, 5)
dpart = odl.uniform_partition(-40, 40, 10)
# motion sampling grid, detector sampling grid but not RegularGrid
dpart_0 = odl.RectPartition(odl.Interval(0, 0), odl.TensorGrid([0]))
geom_p2d = odl.tomo.Parallel2dGeometry(apart, dpart=dpart_0)
with pytest.raises(ValueError):
odl.tomo.astra_projection_geometry(geom_p2d)
# detector sampling grid, motion sampling grid
geom_p2d = odl.tomo.Parallel2dGeometry(apart, dpart)
odl.tomo.astra_projection_geometry(geom_p2d)
# Parallel 2D geometry
geom_p2d = odl.tomo.Parallel2dGeometry(apart, dpart)
astra_geom = odl.tomo.astra_projection_geometry(geom_p2d)
assert astra_geom['type'] == 'parallel'
# Fan flat
src_rad = 10
det_rad = 5
geom_ff = odl.tomo.FanFlatGeometry(apart, dpart, src_rad, det_rad)
astra_geom = odl.tomo.astra_projection_geometry(geom_ff)
assert astra_geom['type'] == 'fanflat_vec'
dpart = odl.uniform_partition([-40, -3], [40, 3], (10, 5))
# Parallel 3D geometry
geom_p3d = odl.tomo.Parallel3dAxisGeometry(apart, dpart)
odl.tomo.astra_projection_geometry(geom_p3d)
astra_geom = odl.tomo.astra_projection_geometry(geom_p3d)
assert astra_geom['type'] == 'parallel3d_vec'
# Circular conebeam flat
geom_ccf = odl.tomo.CircularConeFlatGeometry(apart, dpart, src_rad,
det_rad)
astra_geom = odl.tomo.astra_projection_geometry(geom_ccf)
assert astra_geom['type'] == 'cone_vec'
# Helical conebeam flat
pitch = 1
geom_hcf = odl.tomo.HelicalConeFlatGeometry(apart, dpart, src_rad, det_rad,
pitch)
astra_geom = odl.tomo.astra_projection_geometry(geom_hcf)
assert astra_geom['type'] == 'cone_vec'
def test_proj():
# `DiscreteLp` volume space
vol_shape = (100,) * 3
discr_vol_space = odl.uniform_discr([-50] * 3, [50] * 3, vol_shape,
dtype='float32')
# Angles: 0 and pi/2
angle_intvl = odl.Interval(0, np.pi / 2)
angle_grid = odl.uniform_sampling(angle_intvl, 2, as_midp=False)
# agrid = angle_grid.points() / np.pi
# Detector
dparams = odl.Rectangle([-50] * 2, [50] * 2)
det_grid = odl.uniform_sampling(dparams, (100, 100))
def projector(index):
axis = np.roll(np.array([1, 0, 0]), index)
axis2 = np.roll(axis, 1)
geom = odl.tomo.Parallel3dGeometry(angle_intvl, dparams, angle_grid,
det_grid, axis=axis,
origin_to_det=axis2)
# Projection space
proj_space = odl.FunctionSpace(geom.params)
discr_data = odl.util.phantom.indicate_proj_axis(discr_vol_space, 0.5)
# `DiscreteLp` projection space
proj_shape = geom.grid.shape
discr_proj_space = odl.uniform_discr_fromspace(proj_space, proj_shape,
dtype='float32')
# Forward
proj_data = odl.tomo.astra_cuda_forward_projector(
discr_data, geom, discr_proj_space)
return proj_data
proj_data = projector(0)
proj_data.show(indices=(0, np.s_[:], np.s_[:]))
proj_data.show(indices=(1, np.s_[:], np.s_[:]))
proj_data = projector(1)
proj_data.show(indices=(0, np.s_[:], np.s_[:]))
proj_data.show(indices=(1, np.s_[:], np.s_[:]))
proj_data = projector(2)
proj_data.show(indices=(0, np.s_[:], np.s_[:]))
proj_data.show(indices=(1, np.s_[:], np.s_[:]))
plt.show(block=True)
def test_fspace_vector_copy():
fspace = FunctionSpace(odl.Interval(0, 1))
f_novec = fspace.element(func_1d_oop, vectorized=False)
f_vec_ip = fspace.element(func_1d_ip, vectorized=True)
f_vec_dual = fspace.element(func_1d_dual, vectorized=True)
f_out = f_novec.copy()
assert f_out == f_novec
f_out = f_vec_ip.copy()
assert f_out == f_vec_ip
f_out = f_vec_dual.copy()
assert f_out == f_vec_dual
def test_fwd_diff():
# Continuous definition of problem
space = odl.FunctionSpace(odl.Interval(0, 1))
# Discretization
n = 6
d = odl.uniform_discr(space, n, impl='cuda')
fun = d.element([1, 2, 5, 3, 2, 1])
# Create operator
diff = ForwardDiff(d)
assert all_almost_equal(diff(fun), [0, 3, -2, -1, -1, 0])
assert all_almost_equal(diff.adjoint(fun), [0, -1, -3, 2, 1, 0])
assert all_almost_equal(diff.adjoint(diff(fun)), [0, -3, 5, -1, 0, 0])
def test_norm_interval(exponent):
# Test the function f(x) = x^2 on the interval (0, 1). Its
# L^p-norm is (1 + 2*p)^(-1/p) for finite p and 1 for p=inf
p = exponent
fspace = odl.FunctionSpace(odl.Interval(0, 1))
lpdiscr = odl.uniform_discr_fromspace(fspace, 10, exponent=p)
testfunc = fspace.element(lambda x: x ** 2)
discr_testfunc = lpdiscr.element(testfunc)
if p == float('inf'):
assert discr_testfunc.norm() <= 1 # Max at boundary not hit
else:
true_norm = (1 + 2 * p) ** (-1 / p)
assert almost_equal(discr_testfunc.norm(), true_norm, places=2)
def test_linear_interpolation_1d():
intv = odl.Interval(0, 1)
part = odl.uniform_partition_fromintv(intv, 5, nodes_on_bdry=False)
# Coordinate vectors are:
# [0.1, 0.3, 0.5, 0.7, 0.9]
space = odl.FunctionSpace(intv)
dspace = odl.Rn(part.size)
interp_op = LinearInterpolation(space, part, dspace)
function = interp_op([1, 2, 3, 4, 5])
# Evaluate at single point
val = function(0.35)
true_val = 0.75 * 2 + 0.25 * 3
assert almost_equal(val, true_val)
# Input array, with and without output array
pts = np.array([0.4, 0.0, 0.65, 0.95])
true_arr = [2.5, 0.5, 3.75, 3.75]
assert all_almost_equal(function(pts), true_arr)
def test_fspace_init():
intv = odl.Interval(0, 1)
FunctionSpace(intv)
FunctionSpace(intv, field=odl.RealNumbers())
FunctionSpace(intv, field=odl.ComplexNumbers())
rect = odl.Rectangle([0, 0], [1, 2])
FunctionSpace(rect)
FunctionSpace(rect, field=odl.RealNumbers())
FunctionSpace(rect, field=odl.ComplexNumbers())
cube = odl.Cuboid([0, 0, 0], [1, 2, 3])
FunctionSpace(cube)
FunctionSpace(cube, field=odl.RealNumbers())
FunctionSpace(cube, field=odl.ComplexNumbers())
ndbox = odl.IntervalProd([0] * 10, np.arange(1, 11))
FunctionSpace(ndbox)
FunctionSpace(ndbox, field=odl.RealNumbers())
FunctionSpace(ndbox, field=odl.ComplexNumbers())
def test_yzproj():
# `DiscreteLp` volume space
vol_shape = (100,) * 3
discr_vol_space = odl.uniform_discr([-50] * 3, [50] * 3, vol_shape,
dtype='float32')
# Angles: 0 and pi/2
angle_intvl = odl.Interval(0, np.pi / 2)
angle_grid = odl.uniform_sampling(angle_intvl, 2, as_midp=False)
# agrid = angle_grid.points() / np.pi
# Detector
dparams = odl.Rectangle([-50] * 2, [50] * 2)
det_grid = odl.uniform_sampling(dparams, (100, 100))
axis = (0, 1, 0)
origin_to_det = (0, 0, 1)
geom = odl.tomo.Parallel3dGeometry(angle_intvl, dparams,
angle_grid,
det_grid, axis=axis,
origin_to_det=origin_to_det)
# Projection space
proj_space = odl.FunctionSpace(geom.params)
discr_data = odl.util.phantom.indicate_proj_axis(discr_vol_space, 0.5)
# `DiscreteLp` projection space
proj_shape = geom.grid.shape
discr_proj_space = odl.uniform_discr_fromspace(proj_space,
proj_shape,
dtype='float32')
# Forward
proj_data = odl.tomo.astra_cuda_forward_projector(discr_data,
geom,
discr_proj_space)
plt.switch_backend('qt4agg')
proj_data.show(indices=np.s_[0, :, :])
plt.show()
scale1.lincomb(1, scale1, I * mu1(E), tmp)
return odl.ReductionOperator(odl.MultiplyOperator(scale0),
odl.MultiplyOperator(scale1))
n = 200
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20, -20], [20, 20, 20],
[n]*3, dtype='float32')
# Geometry
src_rad = 1000
det_rad = 100
angle_intvl = odl.Interval(0, 2 * np.pi)
dparams = odl.Rectangle([-50, -50], [50, 50])
agrid = odl.uniform_sampling(angle_intvl, n)
dgrid = odl.uniform_sampling(dparams, [n]*2)
geom = odl.tomo.CircularConeFlatGeometry(angle_intvl, dparams,
src_rad, det_rad,
agrid, dgrid)
# X-ray transform
proj = odl.tomo.DiscreteXrayTransform(discr_reco_space, geom,
backend='astra_cuda')
# Create phantom
phantom0 = odl.util.shepp_logan(discr_reco_space, True)
phantom1 = odl.util.derenzo_sources(discr_reco_space)
super().__init__(self.space, self.space, linear=True)
def _call(self, rhs, out):
ndimage.convolve(rhs.ntuple.data, self.kernel.ntuple.data,
output=out.ntuple.data, mode='wrap')
@property
def adjoint(self):
return Convolution(self.adjkernel, self.kernel)
def opnorm(self):
return self.norm
# Continuous definition of the problem
cont_space = odl.FunctionSpace(odl.Interval(0, 10))
# Complicated functions to check performance
cont_kernel = cont_space.element(lambda x: np.exp(x / 2) * np.cos(x * 1.172))
cont_phantom = cont_space.element(lambda x: x ** 2 * np.sin(x) ** 2 * (x > 5))
# Discretization
discr_space = odl.uniform_discr_fromspace(cont_space, 500, impl='numpy')
kernel = discr_space.element(cont_kernel)
phantom = discr_space.element(cont_phantom)
# Create operator
conv = Convolution(kernel)
# Dampening parameter for landweber
iterations = 100
def test_dwt():
# Verify that the operator works as axpected
# 1D test
n = 16
x = np.zeros(n)
x[5:10] = 1
wbasis = pywt.Wavelet('db1')
nscales = 2
mode = 'sym'
size_list = coeff_size_list((n,), nscales, wbasis, mode)
# Define a discretized domain
domain = odl.FunctionSpace(odl.Interval([-1], [1]))
nPoints = np.array([n])
disc_domain = odl.uniform_discr_fromspace(domain, nPoints)
disc_phantom = disc_domain.element(x)
# Create the discrete wavelet transform operator.
# Only the domain of the operator needs to be defined
Wop = WaveletTransform(disc_domain, nscales, wbasis, mode)
# Compute the discrete wavelet transform of discrete imput image
coeffs = Wop(disc_phantom)
# Determine the correct range for Wop and verify that coeffs
# is an element of it
ran_size = np.prod(size_list[0])
ran_size += sum(np.prod(shape) for shape in size_list[1:-1])
disc_range = disc_domain.dspace_type(ran_size, dtype=disc_domain.dtype)
assert coeffs in disc_range
# Compute the inverse wavelet transform
reconstruction1 = Wop.inverse(coeffs)
# With othogonal wavelets the inverse is the adjoint
reconstruction2 = Wop.adjoint(coeffs)
# Verify that the output of Wop.inverse and Wop.adjoint are the same
assert all_almost_equal(reconstruction1.asarray(),
reconstruction2.asarray())
# Verify that reconstructions lie in correct discretized domain
assert reconstruction1 in disc_domain
assert reconstruction2 in disc_domain
assert all_almost_equal(reconstruction1.asarray(), x)
assert all_almost_equal(reconstruction2.asarray(), x)
# ---------------------------------------------------------------
# 2D test
n = 16
x = np.zeros((n, n))
x[5:10, 5:10] = 1
wbasis = pywt.Wavelet('db1')
nscales = 2
mode = 'sym'
size_list = coeff_size_list((n, n), nscales, wbasis, mode)
# Define a discretized domain
domain = odl.FunctionSpace(odl.Rectangle([-1, -1], [1, 1]))
nPoints = np.array([n, n])
disc_domain = odl.uniform_discr_fromspace(domain, nPoints)
disc_phantom = disc_domain.element(x)
# Create the discrete wavelet transform operator.
# Only the domain of the operator needs to be defined
Wop = WaveletTransform(disc_domain, nscales, wbasis, mode)
# Compute the discrete wavelet transform of discrete imput image
coeffs = Wop(disc_phantom)
# Determine the correct range for Wop and verify that coeffs
# is an element of it
ran_size = np.prod(size_list[0])
ran_size += sum(3 * np.prod(shape) for shape in size_list[1:-1])
disc_range = disc_domain.dspace_type(ran_size, dtype=disc_domain.dtype)
assert coeffs in disc_range
# Compute the inverse wavelet transform
reconstruction1 = Wop.inverse(coeffs)
# With othogonal wavelets the inverse is the adjoint
reconstruction2 = Wop.adjoint(coeffs)
# Verify that the output of Wop.inverse and Wop.adjoint are the same
assert all_almost_equal(reconstruction1.asarray(),
reconstruction2.asarray())
# Verify that reconstructions lie in correct discretized domain
assert reconstruction1 in disc_domain
assert reconstruction2 in disc_domain
assert all_almost_equal(reconstruction1.asarray(), x)
assert all_almost_equal(reconstruction2.asarray(), x)
# -------------------------------------------------------------
# 3D test
n = 16
x = np.zeros((n, n, n))
x[5:10, 5:10, 5:10] = 1
wbasis = pywt.Wavelet('db2')
nscales = 1
mode = 'per'
size_list = coeff_size_list((n, n, n), nscales, wbasis, mode)
# Define a discretized domain
domain = odl.FunctionSpace(odl.Cuboid([-1, -1, -1], [1, 1, 1]))
nPoints = np.array([n, n, n])
disc_domain = odl.uniform_discr_fromspace(domain, nPoints)
disc_phantom = disc_domain.element(x)
# Create the discrete wavelet transform operator related to 3D transform.
Wop = WaveletTransform(disc_domain, nscales, wbasis, mode)
# Compute the discrete wavelet transform of discrete imput image
coeffs = Wop(disc_phantom)
# Determine the correct range for Wop and verify that coeffs
# is an element of it
ran_size = np.prod(size_list[0])
ran_size += sum(7 * np.prod(shape) for shape in size_list[1:-1])
disc_range = disc_domain.dspace_type(ran_size, dtype=disc_domain.dtype)
assert coeffs in disc_range
# Compute the inverse wavelet transform
reconstruction1 = Wop.inverse(coeffs)
# With othogonal wavelets the inverse is the adjoint
reconstruction2 = Wop.adjoint(coeffs)
# Verify that the output of Wop.inverse and Wop.adjoint are the same
assert all_almost_equal(reconstruction1, reconstruction2)
# Verify that reconstructions lie in correct discretized domain
assert reconstruction1 in disc_domain
assert reconstruction2 in disc_domain
assert all_almost_equal(reconstruction1.asarray(), x)
assert all_almost_equal(reconstruction2, disc_phantom)
def test_init_cuda(exponent):
# Normal discretization of unit interval
space = odl.FunctionSpace(odl.Interval(0, 1), out_dtype='float32')
part = odl.uniform_partition_fromintv(space.domain, 10)
rn = odl.CudaRn(10, exponent=exponent)
odl.DiscreteLp(space, part, rn, exponent=exponent)
def test_xray_trafo_parallel2d():
"""3D parallel-beam discrete X-ray transform with ASTRA CUDA."""
# Discrete reconstruction space
xx = 5
nn = 5
# xx = 5.5
# nn = 11
discr_vol_space = odl.uniform_discr([-xx] * 2, [xx] * 2, [nn] * 2,
dtype='float32')
# Angle
angle_intvl = odl.Interval(0, 2 * np.pi) - np.pi / 4
agrid = odl.uniform_sampling(angle_intvl, 4)
# Detector
yy = 11
mm = 11
# yy = 10.5
# mm = 21
dparams = odl.Interval(-yy, yy)
dgrid = odl.uniform_sampling(dparams, mm)
# Geometry
geom = odl.tomo.Parallel2dGeometry(angle_intvl, dparams, agrid, dgrid)
# Projection space
proj_space = odl.FunctionSpace(geom.params)
# `DiscreteLp` projection space
proj_shape = geom.grid.shape
discr_proj_space = odl.uniform_discr_fromspace(proj_space, proj_shape,
dtype='float32')
# X-ray transform
A = odl.tomo.XrayTransform(discr_vol_space, geom,
backend='astra_cuda')
# Domain element
f = A.domain.one()
# Forward projection
Af = A(f)
A0f = odl.tomo.astra_cuda_forward_projector(f, geom,
discr_proj_space)
# Range element
g = A.range.one()
# Back projection
Adg = A.adjoint(g)
Adg0 = odl.tomo.astra_cuda_back_projector(g, geom,
discr_vol_space)
print('\nvol stride', discr_vol_space.grid.stride)
print('proj stride', geom.grid.stride)
print('angle intv:', angle_intvl.size)
# f = discr_vol_space3.one()
# print(f.asarray()[:, :, np.round(f.shape[2]/2)])
print('forward')
print(Af.asarray()[0])
print(A0f.asarray()[0])
print('backward')
print(Adg.asarray() / float(agrid.stride) / agrid.ntotal)
print(Adg0.asarray() / agrid.ntotal)
def projector(request):
n_angles = 200
geom, impl, angle = request.param.split()
if angle == 'uniform':
apart = odl.uniform_partition(0, 2 * np.pi, n_angles)
elif angle == 'random':
# Linearly spaced with random noise
min_pt = 2 * (2.0 * np.pi) / n_angles
max_pt = (2.0 * np.pi) - 2 * (2.0 * np.pi) / n_angles
points = np.linspace(min_pt, max_pt, n_angles)
points += np.random.rand(n_angles) * (max_pt - min_pt) / (5 * n_angles)
agrid = odl.TensorGrid(points)
apart = odl.RectPartition(odl.Interval(0, 2 * np.pi), agrid)
elif angle == 'nonuniform':
# Angles spaced quadratically
min_pt = 2 * (2.0 * np.pi) / n_angles
max_pt = (2.0 * np.pi) - 2 * (2.0 * np.pi) / n_angles
points = np.linspace(min_pt**0.5, max_pt**0.5, n_angles)**2
agrid = odl.TensorGrid(points)
apart = odl.RectPartition(odl.Interval(0, 2 * np.pi), agrid)
else:
raise ValueError('angle not valid')
if geom == 'par2d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20], [20, 20], [100, 100],
dtype='float32')
# Geometry
dpart = odl.uniform_partition(-30, 30, 200)
geom = tomo.Parallel2dGeometry(apart, dpart)
# Ray transform
return tomo.RayTransform(discr_reco_space, geom, impl=impl)
elif geom == 'par3d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20, -20], [20, 20, 20],
[100, 100, 100],
dtype='float32')
# Geometry
dpart = odl.uniform_partition([-30, -30], [30, 30], [200, 200])
geom = tomo.Parallel3dAxisGeometry(apart, dpart, axis=[1, 0, 0])
# Ray transform
return tomo.RayTransform(discr_reco_space, geom, impl=impl)
elif geom == 'cone2d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20], [20, 20], [100, 100],
dtype='float32')
# Geometry
dpart = odl.uniform_partition(-30, 30, 200)
geom = tomo.FanFlatGeometry(apart,
dpart,
src_radius=200,
det_radius=100)
# Ray transform
return tomo.RayTransform(discr_reco_space, geom, impl=impl)
elif geom == 'cone3d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20, -20], [20, 20, 20],
[100, 100, 100],
dtype='float32')
# Geometry
dpart = odl.uniform_partition([-30, -30], [30, 30], [200, 200])
geom = tomo.CircularConeFlatGeometry(apart,
dpart,
src_radius=200,
det_radius=100,
axis=[1, 0, 0])
# Ray transform
return tomo.RayTransform(discr_reco_space, geom, impl=impl)
elif geom == 'helical':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20, 0], [20, 20, 40],
[100, 100, 100],
dtype='float32')
# Geometry
# TODO: angles
n_angle = 700
apart = odl.uniform_partition(0, 8 * 2 * np.pi, n_angle)
dpart = odl.uniform_partition([-30, -3], [30, 3], [200, 20])
geom = tomo.HelicalConeFlatGeometry(apart,
dpart,
pitch=5.0,
src_radius=200,
det_radius=100)
# Ray transform
return tomo.RayTransform(discr_reco_space, geom, impl=impl)
else:
raise ValueError('param not valid')
plt.close()
# Create `DiscreteLp` space for volume data
vol_shape = (100, 110)
discr_vol_space = odl.uniform_discr([-1, -1.1], [1, 1.1],
vol_shape,
dtype='float32')
# Create an element in the volume space
discr_vol_data = odl.util.phantom.cuboid(discr_vol_space, 0.2, 0.3)
save_slice(discr_vol_data, 'phantom 2d cpu')
# Angles
angle_intvl = odl.Interval(0, 2 * np.pi)
angle_grid = odl.uniform_sampling(angle_intvl, 180)
# Detector
dparams = odl.Interval(-2, 2)
det_grid = odl.uniform_sampling(dparams, 100)
# Create geometry instances for the projection space parameter
geom = odl.tomo.Parallel2dGeometry(angle_intvl, dparams, angle_grid, det_grid)
# Projection space
proj_space = odl.FunctionSpace(geom.params)
# `DiscreteLp` projection space
discr_proj_space = odl.uniform_discr_fromspace(proj_space,
geom.grid.shape,
