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_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_nearest_interpolation_2d_string():
rect = odl.Rectangle([0, 0], [1, 1])
grid = odl.uniform_sampling(rect, [4, 2], as_midp=True)
# Coordinate vectors are:
# [0.125, 0.375, 0.625, 0.875], [0.25, 0.75]
space = odl.FunctionSet(rect, odl.Strings(1))
dspace = odl.Ntuples(grid.ntotal, dtype='U1')
interp_op = NearestInterpolation(space, grid, dspace)
values = np.array([c for c in 'mystring'])
function = interp_op(values)
# Evaluate at single point
val = function([0.3, 0.6]) # closest to index (1, 1) -> 3
assert val == 't'
# Input array, with and without output array
pts = np.array([[0.3, 0.6],
[1.0, 1.0]])
true_arr = ['t', 'g']
assert all_equal(function(pts.T), true_arr)
out = np.empty(2, dtype='U1')
function(pts.T, out=out)
assert all_equal(out, true_arr)
# Input meshgrid, with and without output array
mg = sparse_meshgrid([0.3, 1.0], [0.4, 1.0])
# Indices: (1, 3) x (0, 1)
true_mg = [['s', 't'],
['n', 'g']]
assert all_equal(function(mg), true_mg)
out = np.empty((2, 2), dtype='U1')
function(mg, out=out)
assert all_equal(out, true_mg)
def test_init(exponent):
# Validate that the different init patterns work and do not crash.
space = odl.FunctionSpace(odl.Interval(0, 1))
grid = odl.uniform_sampling(space.domain, 10)
rn = odl.Rn(10, exponent=exponent)
odl.DiscreteLp(space, grid, rn, exponent=exponent)
# 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, grid, cn, exponent=exponent)
# Real space should not work with complex
with pytest.raises(ValueError):
odl.DiscreteLp(space, grid, cn)
# Complex space should not work with reals
with pytest.raises(ValueError):
odl.DiscreteLp(complex_space, grid, rn)
# Wrong size of underlying space
rn_wrong_size = odl.Rn(20)
with pytest.raises(ValueError):
odl.DiscreteLp(space, grid, rn_wrong_size)
def test_collocation_interpolation_identity():
# Check if interpolation followed by collocation on the same grid
# is the identity
rect = odl.Rectangle([0, 0], [1, 1])
grid = odl.uniform_sampling(rect, [4, 2], as_midp=True)
space = odl.FunctionSpace(rect)
dspace = odl.Rn(grid.ntotal)
# Testing 'C' and 'F' ordering and all interpolation schemes
coll_op_c = GridCollocation(space, grid, dspace, order='C')
coll_op_f = GridCollocation(space, grid, dspace, order='F')
interp_ops_c = [
NearestInterpolation(space, grid, dspace, order='C', variant='left'),
NearestInterpolation(space, grid, dspace, order='C', variant='right'),
LinearInterpolation(space, grid, dspace, order='C'),
PerAxisInterpolation(space, grid, dspace, order='C',
schemes=['linear', 'nearest'])]
interp_ops_f = [
NearestInterpolation(space, grid, dspace, order='F', variant='left'),
NearestInterpolation(space, grid, dspace, order='F', variant='right'),
LinearInterpolation(space, grid, dspace, order='F'),
PerAxisInterpolation(space, grid, dspace, order='F',
schemes=['linear', 'nearest'])]
values = np.arange(1, 9, dtype='float64')
for interp_op_c in interp_ops_c:
ident_values = coll_op_c(interp_op_c(values))
assert all_almost_equal(ident_values, values)
for interp_op_f in interp_ops_f:
ident_values = coll_op_f(interp_op_f(values))
assert all_almost_equal(ident_values, values)
def test_nearest_interpolation_1d_complex():
intv = odl.Interval(0, 1)
grid = odl.uniform_sampling(intv, 5, as_midp=True)
# Coordinate vectors are:
# [0.1, 0.3, 0.5, 0.7, 0.9]
space = odl.FunctionSpace(intv, field=odl.ComplexNumbers())
dspace = odl.Cn(grid.ntotal)
interp_op = NearestInterpolation(space, grid, 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)
grid = odl.uniform_sampling(intv, 5, as_midp=True)
# Coordinate vectors are:
# [0.1, 0.3, 0.5, 0.7, 0.9]
space = odl.FunctionSpace(intv)
dspace = odl.Rn(grid.ntotal)
# 'left' variant
interp_op = NearestInterpolation(space, grid, 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, grid, 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_nearest_interpolation_2d_float():
rect = odl.Rectangle([0, 0], [1, 1])
grid = odl.uniform_sampling(rect, [4, 2], as_midp=True)
# Coordinate vectors are:
# [0.125, 0.375, 0.625, 0.875], [0.25, 0.75]
space = odl.FunctionSpace(rect)
dspace = odl.Rn(grid.ntotal)
interp_op = NearestInterpolation(space, grid, dspace)
function = interp_op([0, 1, 2, 3, 4, 5, 6, 7])
# Evaluate at single point
val = function([0.3, 0.6]) # closest to index (1, 1) -> 3
assert val == 3.0
# Input array, with and without output array
pts = np.array([[0.3, 0.6],
[1.0, 1.0]])
true_arr = [3, 7]
assert all_equal(function(pts.T), true_arr)
out = np.empty(2, dtype='float64')
function(pts.T, out=out)
assert all_equal(out, true_arr)
# Input meshgrid, with and without output array
mg = sparse_meshgrid([0.3, 1.0], [0.4, 1.0])
# Indices: (1, 3) x (0, 1)
true_mg = [[2, 3],
[6, 7]]
assert all_equal(function(mg), true_mg)
out = np.empty((2, 2), dtype='float64')
function(mg, out=out)
assert all_equal(out, true_mg)
def test_reciprocal_grid_nd_halfcomplex():
grid = odl.uniform_sampling([0] * 3, [1] * 3, shape=(3, 4, 5))
s = grid.stride
n = np.array(grid.shape)
stride_last = 2 * np.pi / (s[-1] * n[-1])
n[-1] = n[-1] // 2 + 1
# Without shift
rgrid = reciprocal_grid(grid, shift=False, halfcomplex=True)
assert all_equal(rgrid.shape, n)
assert rgrid.max_pt[-1] == 0 # last dim is odd
# With shift
rgrid = reciprocal_grid(grid, shift=True, halfcomplex=True)
assert all_equal(rgrid.shape, n)
assert rgrid.max_pt[-1] == -stride_last / 2
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, halfcomplex=True,
halfcx_parity='odd')
assert irgrid.approx_equals(grid, atol=1e-6)
with pytest.raises(ValueError):
realspace_grid(rgrid, grid.min_pt, halfcomplex=True,
halfcx_parity='+')
def test_reciprocal_grid_nd_axes():
grid = odl.uniform_sampling([0] * 3, [1] * 3, shape=(3, 4, 5))
s = grid.stride
n = np.array(grid.shape)
axes_list = [[1, -1], [0], 0, [0, 2, 1], [2, 0]]
for axes in axes_list:
active = np.zeros(grid.ndim, dtype=bool)
active[axes] = True
inactive = np.logical_not(active)
true_recip_stride = np.empty(grid.ndim)
true_recip_stride[active] = 2 * np.pi / (s[active] * n[active])
true_recip_stride[inactive] = s[inactive]
# Without shift altogether
rgrid = reciprocal_grid(grid, shift=False, axes=axes,
halfcomplex=False)
assert all_equal(rgrid.shape, n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
assert all_almost_equal(rgrid.min_pt[active], -rgrid.max_pt[active])
assert all_equal(rgrid.min_pt[inactive], grid.min_pt[inactive])
assert all_equal(rgrid.max_pt[inactive], grid.max_pt[inactive])
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, axes=axes,
halfcomplex=False)
assert irgrid.approx_equals(grid, atol=1e-6)
def test_per_axis_interpolation():
rect = odl.Rectangle([0, 0], [1, 1])
grid = odl.uniform_sampling(rect, [4, 2], as_midp=True)
# Coordinate vectors are:
# [0.125, 0.375, 0.625, 0.875], [0.25, 0.75]
space = odl.FunctionSpace(rect)
dspace = odl.Rn(grid.ntotal)
schemes = ['linear', 'nearest']
variants = [None, 'right']
interp_op = PerAxisInterpolation(space, grid, dspace, schemes=schemes,
nn_variants=variants)
values = np.arange(1, 9, dtype='float64')
function = interp_op(values)
rvals = values.reshape([4, 2])
# Evaluate at single point
val = function([0.3, 0.5])
l1 = (0.3 - 0.125) / (0.375 - 0.125)
# 0.5 equally far from both neighbors -> 'right' chooses 0.75
true_val = (1 - l1) * rvals[0, 1] + l1 * rvals[1, 1]
assert almost_equal(val, true_val)
# Input array, with and without output array
pts = np.array([[0.3, 0.6],
[0.1, 0.25],
[1.0, 1.0]])
l1 = (0.3 - 0.125) / (0.375 - 0.125)
true_val_1 = (1 - l1) * rvals[0, 1] + l1 * rvals[1, 1]
l1 = (0.125 - 0.1) / (0.375 - 0.125)
true_val_2 = (1 - l1) * rvals[0, 0] # only lower left contributes
l1 = (1.0 - 0.875) / (0.875 - 0.625)
true_val_3 = (1 - l1) * rvals[3, 1] # lower left only
true_arr = [true_val_1, true_val_2, true_val_3]
assert all_equal(function(pts.T), true_arr)
out = np.empty(3, dtype='float64')
function(pts.T, out=out)
assert all_equal(out, true_arr)
# Input meshgrid, with and without output array
mg = sparse_meshgrid([0.3, 1.0], [0.4, 0.85])
# Indices: (1, 3) x (0, 1)
lx1 = (0.3 - 0.125) / (0.375 - 0.125)
lx2 = (1.0 - 0.875) / (0.875 - 0.625)
true_val_11 = (1 - lx1) * rvals[0, 0] + lx1 * rvals[1, 0]
true_val_12 = ((1 - lx1) * rvals[0, 1] + lx1 * rvals[1, 1])
true_val_21 = (1 - lx2) * rvals[3, 0]
true_val_22 = (1 - lx2) * rvals[3, 1]
true_mg = [[true_val_11, true_val_12],
[true_val_21, true_val_22]]
assert all_equal(function(mg), true_mg)
out = np.empty((2, 2), dtype='float64')
function(mg, out=out)
assert all_equal(out, true_mg)
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()
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_reciprocal_grid_1d(halfcomplex, shift, parity):
shape = 10 if parity == 'even' else 11
grid = odl.uniform_sampling(0, 1, shape=shape)
s = grid.stride
n = np.array(grid.shape)
rgrid = reciprocal_grid(grid, shift=shift, halfcomplex=halfcomplex)
# Independent of halfcomplex, shift and parity
true_recip_stride = 2 * np.pi / (s * n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
if halfcomplex:
assert all_equal(rgrid.shape, n // 2 + 1)
if parity == 'odd' and shift:
# Max point should be half a negative recip stride
assert all_almost_equal(rgrid.max_pt, -true_recip_stride / 2)
elif parity == 'even' and not shift:
# Max point should be half a positive recip stride
assert all_almost_equal(rgrid.max_pt, true_recip_stride / 2)
elif (parity == 'odd' and not shift) or (parity == 'even' and shift):
# Max should be zero
assert all_almost_equal(rgrid.max_pt, 0)
else:
raise RuntimeError('parameter combination not covered')
else: # halfcomplex = False
assert all_equal(rgrid.shape, n)
if (parity == 'even' and shift) or (parity == 'odd' and not shift):
# Zero should be at index n // 2
assert all_almost_equal(rgrid[n // 2], 0)
elif (parity == 'odd' and shift) or (parity == 'even' and not shift):
# No point should be closer to 0 than half a recip stride
atol = 0.999 * true_recip_stride / 2
assert not rgrid.approx_contains(0, atol=atol)
else:
raise RuntimeError('parameter combination not covered')
if not shift:
# Grid Should be symmetric
assert all_almost_equal(rgrid.min_pt, -rgrid.max_pt)
if parity == 'odd':
# Midpoint should be 0
assert all_almost_equal(rgrid.mid_pt, 0)
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, halfcomplex=halfcomplex,
halfcx_parity=parity)
assert irgrid.approx_equals(grid, atol=1e-6)
def test_reciprocal_grid_nd():
grid = odl.uniform_sampling([0] * 3, [1] * 3, shape=(3, 4, 5))
s = grid.stride
n = np.array(grid.shape)
true_recip_stride = 2 * np.pi / (s * n)
# Without shift altogether
rgrid = reciprocal_grid(grid, shift=False, halfcomplex=False)
assert all_equal(rgrid.shape, n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
assert all_almost_equal(rgrid.min_pt, -rgrid.max_pt)
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, halfcomplex=False)
assert irgrid.approx_equals(grid, atol=1e-6)
def test_linear_interpolation_1d():
intv = odl.Interval(0, 1)
grid = odl.uniform_sampling(intv, 5, as_midp=True)
# Coordinate vectors are:
# [0.1, 0.3, 0.5, 0.7, 0.9]
space = odl.FunctionSpace(intv)
dspace = odl.Rn(grid.ntotal)
interp_op = LinearInterpolation(space, grid, 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_reciprocal_grid_nd_shift_list():
grid = odl.uniform_sampling([0] * 3, [1] * 3, shape=(3, 4, 5))
s = grid.stride
n = np.array(grid.shape)
shift = [False, True, False]
true_recip_stride = 2 * np.pi / (s * n)
# Shift only the even dimension, then zero must be contained
rgrid = reciprocal_grid(grid, shift=shift, halfcomplex=False)
noshift = np.where(np.logical_not(shift))
assert all_equal(rgrid.shape, n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
assert all_almost_equal(rgrid.min_pt[noshift], -rgrid.max_pt[noshift])
assert all_almost_equal(rgrid[n // 2], [0] * 3)
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, halfcomplex=False)
assert irgrid.approx_equals(grid, atol=1e-6)
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)
# Adjoint currently bugged, needs to be fixed
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,
dtype='float32',
# vpts = 5
xx = 5.5
vpts = 11
# xx = 5.25
# vpts = 21
# xx = 8
# vpts = 16
# xx = 6
# vpts = 6
discr_vol_space_2d = odl.uniform_discr([-xx] * 2, [xx] * 2, [vpts] * 2,
dtype='float32')
discr_vol_space_3d = odl.uniform_discr([-xx] * 3, [xx] * 3, [vpts] * 3,
dtype='float32')
# Angle grid
agrid = odl.uniform_sampling(-.25 * np.pi, 0.75 * np.pi, 2)
astride = float(agrid.stride)
num_angle = agrid.size
# Detector grid
# dx = 11
# dpts = 11
dx = 10.5
dpts = 21
# dx = 5.5
# dpts = 11
# dx = 5.25
# dpts = 21
dgrid_2d = odl.uniform_sampling(-dx, dx, dpts)
dy = 1.0 * dx
dgrid_3d = odl.uniform_sampling([-dx, -dy], [dx, dy], [dpts] * 2)
def test_init_cuda(exponent):
# Normal discretization of unit interval
space = odl.FunctionSpace(odl.Interval(0, 1))
grid = odl.uniform_sampling(space.domain, 10)
rn = odl.CudaRn(10, exponent=exponent)
odl.DiscreteLp(space, grid, rn, exponent=exponent)
def numba_example():
# Some functions are not easily vectorized, here we can use Numba to
# improve performance.
# See http://numba.pydata.org/
try:
import numba
except ImportError:
print('Numba not installed, skipping.')
return
def myfunc(x):
"""Return x - y if x > y, otherwise return x + y."""
if x[0] > x[1]:
return x[0] - x[1]
else:
return x[0] + x[1]
# Numba expects functions f(x1, x2, x3, ...), while we have the
# convention f(x) with x = (x1, x2, x3, ...). Therefore we need
# to wrap the Numba-vectorized function.
vectorized = numba.vectorize(lambda x, y: x - y if x > y else x + y)
def myfunc_vec(x):
"""Return x - y if x > y, otherwise return x + y."""
return vectorized(x[0], x[1])
def myfunc_native_vec(x):
"""Return x - y if x > y, otherwise return x + y."""
# This implementation uses Numpy's fast built-in vectorization
# directly. The function np.where checks the condition in the
# first argument and takes the values from the second argument
# for all entries where the condition is `True`, otherwise
# the values from the third argument are taken. The arrays are
# automatically broadcast, i.e. the broadcast shape of the
# condition expression determines the output shape.
return np.where(x[0] > x[1], x[0] - x[1], x[0] + x[1])
# Create (continuous) functions in the space of function defined
# on the rectangle [0, 1] x [0, 1].
fspace = odl.FunctionSpace(odl.Rectangle([0, 0], [1, 1]))
f_default = fspace.element(myfunc, vectorized=False)
f_numba = fspace.element(myfunc_vec)
f_native = fspace.element(myfunc_native_vec, vectorized=True)
# Create a unform grid in [0, 1] x [0, 1] (fspace.domain) with 2000
# samples per dimension.
grid = odl.uniform_sampling(fspace.domain, [2000, 2000])
# The points() method really creates all grid points (2000^2) and
# stores them one-by-one (row-wise) in a large array with shape
# (2000*2000, 2). Since the function expects points[i] to be the
# array of i-th components of all points, we need to transpose.
points = grid.points().T
# The meshgrid property only returns a sparse representation of the
# grid, a tuple whose i-th entry is the vector of all possible i-th
# components in the grid (2000). Extra dimensions are added to the
# vector in order to support automatic broadcasting. This is both
# faster and more memory-friendly than creating the full point array.
# See the numpy.meshgrid function for more information.
mesh = grid.meshgrid # Returns a sparse meshgrid (2000 * 2)
print('Non-Vectorized runtime (points): {:5f}'
''.format(timeit.timeit(lambda: f_default(points), number=1)))
print('Non-Vectorized runtime (meshgrid): {:5f}'
''.format(timeit.timeit(lambda: f_default(mesh), number=1)))
print('Numba vectorized runtime (points): {:5f}'
''.format(timeit.timeit(lambda: f_numba(points), number=1)))
print('Numba vectorized runtime (meshgrid): {:5f}'
''.format(timeit.timeit(lambda: f_numba(mesh), number=1)))
print('Native vectorized runtime (points): {:5f}'
''.format(timeit.timeit(lambda: f_native(points), number=1)))
print('Native vectorized runtime (meshgrid): {:5f}'
''.format(timeit.timeit(lambda: f_native(mesh), number=1)))
indices=[slice(None), y, slice(None)])
data.show('imshow',
saveto=pth.join(path, '{}_x{:03d}.png'.format(
name.replace(' ', '_'), x)),
title='{} [{},:,:]'.format(name, x),
indices=[x, slice(None), slice(None)])
plt.close('all')
# `DiscreteLp` volume space
vol_shape = (80, 70, 60)
discr_vol_space = odl.uniform_discr([-40, -35, -30], [40, 35, 30],
vol_shape, dtype='float32')
# Angles
angle_intvl = odl.Interval(0, 2 * np.pi)
angle_grid = odl.uniform_sampling(angle_intvl, 90, as_midp=False)
# Detector
dparams = odl.Rectangle([-50, -45], [50, 45])
det_grid = odl.uniform_sampling(dparams, (100, 90))
# Cone beam parameter
src_rad = 1000
det_rad = 10
pitch_factor = 0
# Create an element in the volume space
# discr_data = odl.util.phantom.cuboid(discr_vol_space,
# (0.1, 0.15, 0.2,), (0.4, 0.35, 0.3))
discr_data = odl.util.phantom.indicate_proj_axis(discr_vol_space)
sli = 0.5
def test_linear_interpolation_2d():
rect = odl.Rectangle([0, 0], [1, 1])
grid = odl.uniform_sampling(rect, [4, 2], as_midp=True)
# Coordinate vectors are:
# [0.125, 0.375, 0.625, 0.875], [0.25, 0.75]
space = odl.FunctionSpace(rect)
dspace = odl.Rn(grid.ntotal)
interp_op = LinearInterpolation(space, grid, dspace)
values = np.arange(1, 9, dtype='float64')
function = interp_op(values)
rvals = values.reshape([4, 2])
# Evaluate at single point
val = function([0.3, 0.6])
l1 = (0.3 - 0.125) / (0.375 - 0.125)
l2 = (0.6 - 0.25) / (0.75 - 0.25)
true_val = ((1 - l1) * (1 - l2) * rvals[0, 0] +
(1 - l1) * l2 * rvals[0, 1] +
l1 * (1 - l2) * rvals[1, 0] +
l1 * l2 * rvals[1, 1])
assert almost_equal(val, true_val)
# Input array, with and without output array
pts = np.array([[0.3, 0.6],
[0.1, 0.25],
[1.0, 1.0]])
l1 = (0.3 - 0.125) / (0.375 - 0.125)
l2 = (0.6 - 0.25) / (0.75 - 0.25)
true_val_1 = ((1 - l1) * (1 - l2) * rvals[0, 0] +
(1 - l1) * l2 * rvals[0, 1] +
l1 * (1 - l2) * rvals[1, 0] +
l1 * l2 * rvals[1, 1])
l1 = (0.125 - 0.1) / (0.375 - 0.125)
# l2 = 0
true_val_2 = (1 - l1) * rvals[0, 0] # only lower left contributes
l1 = (1.0 - 0.875) / (0.875 - 0.625)
l2 = (1.0 - 0.75) / (0.75 - 0.25)
true_val_3 = (1 - l1) * (1 - l2) * rvals[3, 1] # lower left only
true_arr = [true_val_1, true_val_2, true_val_3]
assert all_equal(function(pts.T), true_arr)
out = np.empty(3, dtype='float64')
function(pts.T, out=out)
assert all_equal(out, true_arr)
# Input meshgrid, with and without output array
mg = sparse_meshgrid([0.3, 1.0], [0.4, 0.75])
# Indices: (1, 3) x (0, 1)
lx1 = (0.3 - 0.125) / (0.375 - 0.125)
lx2 = (1.0 - 0.875) / (0.875 - 0.625)
ly1 = (0.4 - 0.25) / (0.75 - 0.25)
# ly2 = 0
true_val_11 = ((1 - lx1) * (1 - ly1) * rvals[0, 0] +
(1 - lx1) * ly1 * rvals[0, 1] +
lx1 * (1 - ly1) * rvals[1, 0] +
lx1 * ly1 * rvals[1, 1])
true_val_12 = ((1 - lx1) * rvals[0, 1] + lx1 * rvals[1, 1]) # ly2 = 0
true_val_21 = ((1 - lx2) * (1 - ly1) * rvals[3, 0] +
(1 - lx2) * ly1 * rvals[3, 1]) # high node 1.0, no upper
true_val_22 = (1 - lx2) * rvals[3, 1] # ly2 = 0, no upper for 1.0
true_mg = [[true_val_11, true_val_12],
[true_val_21, true_val_22]]
assert all_equal(function(mg), true_mg)
out = np.empty((2, 2), dtype='float64')
function(mg, out=out)
assert all_equal(out, true_mg)
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)
# 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,
dtype='float32',