def test_adjoint_scaling_factor(self):
"""Test if back-projector A^* is adjoint of forward projector A:
<A x, y>_D = <x,A^* y>_I .
Define scaling factor as A^* = s B where is the implemented
back-projector. Thus,
s = <A x, y>_D / <x,B y>_I ,
or using y = A x
s = <A x, A x>_D / <x,B A x>_I .
"""
geom = Geometry(2)
# x = ones() and y = A x
vol_rn = Rn(geom.vol_size)
vol_rn_ones = vol_rn.element(1)
proj_rn = Rn(geom.proj_size)
projector = ODLProjector(geom, vol_rn, proj_rn)
proj = projector.forward(vol_rn_ones)
vol = projector.backward(proj)
s0 = proj.norm() ** 2 / vol_rn._inner(vol, vol_rn_ones)
# x = ones(), y = ones()
vol_rn = Rn(geom.vol_size)
vol_rn_ones = vol_rn.element(1)
proj_rn = Rn(geom.proj_size)
proj_rn_ones = proj_rn.element(1)
projector = ODLProjector(geom, vol_rn, proj_rn)
proj = projector.forward(vol_rn_ones)
vol = projector.backward(proj_rn_ones)
s1 = proj.inner(proj_rn_ones) / vol_rn_ones.inner(vol)
# implemented function
proj_vec = Rn(geom.proj_size).element(1)
cp = ODLChambollePock(geom, proj_vec)
cp.adjoint_scaling_factor()
s2 = cp.adj_scal_fac
self.assertEqual(s1, s2)
print('Scaling factors:', s0, s1, s2)
projector.clear_astra_memory()
def test_adjoint_scaling_factor(self):
# x
vol_rn = Rn(self.geom.vol_size)
vol_rn_ones = vol_rn.element(1)
# y
proj_rn = Rn(self.geom.proj_size)
proj_rn_ones = proj_rn.element(1)
# A
projector = ODLProjector(self.geom, vol_rn, proj_rn)
# A x
proj = projector.forward(vol_rn_ones)
# A^* y
vol = projector.backward(proj_rn_ones)
# scaling factor for x[:] = 1 and y[:] = 1
s0 = proj.inner(proj_rn_ones) / vol_rn_ones.inner(vol)
# A^* A x
volp = projector.backward(proj)
# scaling factor for x[:] = 1 and y = A x
s1 = proj.norm() ** 2 / vol_rn._inner(volp, vol_rn_ones)
cp = self.cp_class(self.geom, self.proj_vec)
self.assertEqual(cp.adj_scal_fac, 1)
cp.adjoint_scaling_factor()
s2 = cp.adj_scal_fac
self.assertFalse(s2 == 1)
self.assertEqual(s0, s2)
print ('Test adjoint')
print (' Scaling factor for backprojector', s0, s1, s2)
projector.clear_astra_memory()
