def test_CompositionOperator_direct3(self):
ig = self.ig
data = self.data
G = GradientOperator(domain_geometry=ig)
Id1 = 2 * IdentityOperator(ig)
Id2 = IdentityOperator(ig)
d = CompositionOperator(G, Id2)
out1 = G.direct(data)
d_out = d.direct(data)
d1 = Id2.direct(data)
d2 = G.direct(d1)
numpy.testing.assert_array_almost_equal(
d2.get_item(0).as_array(),
d_out.get_item(0).as_array())
numpy.testing.assert_array_almost_equal(
d2.get_item(1).as_array(),
d_out.get_item(1).as_array())
G2Id = G.compose(2 * Id2)
d2g = G2Id.direct(data)
numpy.testing.assert_array_almost_equal(
d2g.get_item(0).as_array(), 2 * d_out.get_item(0).as_array())
numpy.testing.assert_array_almost_equal(
d2g.get_item(1).as_array(), 2 * d_out.get_item(1).as_array())
def test_CompositionOperator_adjoint2(self):
ig = self.ig
data = self.data
G = GradientOperator(domain_geometry=ig)
Id1 = 2 * IdentityOperator(ig)
Id2 = IdentityOperator(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_CompositionOperator_direct1(self):
ig = self.ig
data = self.data
G = GradientOperator(domain_geometry=ig)
Id1 = 2 * IdentityOperator(ig)
Id2 = IdentityOperator(ig)
d = CompositionOperator(G, Id2)
out1 = G.direct(data)
out2 = d.direct(data)
numpy.testing.assert_array_almost_equal(
out2.get_item(0).as_array(),
out1.get_item(0).as_array())
numpy.testing.assert_array_almost_equal(
out2.get_item(1).as_array(),
out1.get_item(1).as_array())
def tests_for_LS_weightedLS(self):
ig = ImageGeometry(40, 30)
numpy.random.seed(1)
A = IdentityOperator(ig)
b = ig.allocate('random')
x = ig.allocate('random')
c = numpy.float64(0.3)
weight = ig.allocate('random')
D = DiagonalOperator(weight)
norm_weight = numpy.float64(D.norm())
print("norm_weight", norm_weight)
f1 = LeastSquares(A, b, c, weight)
f2 = LeastSquares(A, b, c)
print("Check LS vs wLS")
# check Lipshitz
numpy.testing.assert_almost_equal(f2.L, 2 * c * (A.norm()**2))
print("unwrapped", 2. * c * norm_weight * (A.norm()**2))
print("f1.L", f1.L)
numpy.testing.assert_almost_equal(
f1.L,
numpy.float64(2.) * c * norm_weight * (A.norm()**2))
print("Lipschitz is ... OK")
# check call with weight
res1 = c * (A.direct(x) - b).dot(weight * (A.direct(x) - b))
res2 = f1(x)
numpy.testing.assert_almost_equal(res1, res2)
print("Call is ... OK")
# check call without weight
#res1 = c * (A.direct(x)-b).dot((A.direct(x) - b))
res1 = c * (A.direct(x) - b).squared_norm()
res2 = f2(x)
numpy.testing.assert_almost_equal(res1, res2)
print("Call without weight is ... OK")
# check gradient with weight
out = ig.allocate(None)
res1 = f1.gradient(x)
#out = f1.gradient(x)
f1.gradient(x, out=out)
res2 = 2 * c * A.adjoint(weight * (A.direct(x) - b))
numpy.testing.assert_array_almost_equal(res1.as_array(),
res2.as_array())
numpy.testing.assert_array_almost_equal(out.as_array(),
res2.as_array())
print("GradientOperator is ... OK")
# check gradient without weight
out = ig.allocate()
res1 = f2.gradient(x)
f2.gradient(x, out=out)
res2 = 2 * c * A.adjoint(A.direct(x) - b)
numpy.testing.assert_array_almost_equal(res1.as_array(),
res2.as_array())
numpy.testing.assert_array_almost_equal(out.as_array(),
res2.as_array())
print("GradientOperator without weight is ... OK")
print(
"Compare Least Squares with DiagonalOperator + CompositionOperator"
)
ig2 = ImageGeometry(100, 100, 100)
A = IdentityOperator(ig2)
b = ig2.allocate('random')
x = ig2.allocate('random')
c = 0.3
weight = ig2.allocate('random')
weight_operator = DiagonalOperator(weight.sqrt())
tmp_A = CompositionOperator(weight_operator, A)
tmp_b = weight_operator.direct(b)
f1 = LeastSquares(tmp_A, tmp_b, c)
f2 = LeastSquares(A, b, c, weight)
t0 = timer()
res1 = f1(x)
t1 = timer()
print("Time with Composition+Diagonal is {}".format(t1 - t0))
t2 = timer()
res2 = f2(x)
t3 = timer()
print("Time with LS + weight is {}".format(t3 - t2))
numpy.testing.assert_almost_equal(res1, res2, decimal=2)