def test_DiagonalOperator(self):
print("test_DiagonalOperator")
M = 3
ig = ImageGeometry(M, M)
x = ig.allocate('random', seed=100)
diag = ig.allocate('random', seed=101)
# Set up example DiagonalOperator
D = DiagonalOperator(diag)
# Apply direct and check whether result equals diag*x as expected.
z = D.direct(x)
numpy.testing.assert_array_equal(z.as_array(), (diag * x).as_array())
# Apply adjoint and check whether results equals diag*(diag*x) as expected.
y = D.adjoint(z)
numpy.testing.assert_array_equal(y.as_array(),
(diag * (diag * x)).as_array())
class WeightedL2NormSquared(Function):
r""" WeightedL2NormSquared function: :math:`F(x) = \| x\|_{w}^{2}_{2} = \underset{i}{\sum}w_{i}*x_{i}^{2} = <x, w*x> = x^{T}*w*x`
"""
def __init__(self, **kwargs):
# Weight can be either a scalar or a DataContainer
# Lispchitz constant L = 2 *||weight||
self.weight = kwargs.get('weight', 1.0)
self.b = kwargs.get('b', None)
tmp_norm = 1.0
self.tmp_space = self.weight * 0.
if isinstance(self.weight, DataContainer):
self.operator_weight = DiagonalOperator(self.weight)
tmp_norm = self.operator_weight.norm()
self.tmp_space = self.operator_weight.domain_geometry().allocate()
if (self.weight < 0).any():
raise ValueError('Weigth contains negative values')
super(WeightedL2NormSquared, self).__init__(L=2 * tmp_norm)
def __call__(self, x):
self.operator_weight.direct(x, out=self.tmp_space)
y = x.dot(self.tmp_space)
if self.b is not None:
self.operator_weight.direct(x - self.b, out=self.tmp_space)
y = (x - self.b).dot(self.tmp_space)
return y
def gradient(self, x, out=None):
if out is not None:
out.fill(x)
if self.b is not None:
out -= self.b
self.operator_weight.direct(out, out=out)
out *= 2
else:
y = x
if self.b is not None:
y = x - self.b
return 2 * self.weight * y
def convex_conjugate(self, x):
tmp = 0
if self.b is not None:
tmp = x.dot(self.b)
return (1. / 4) * (x / self.weight.sqrt()).squared_norm() + tmp
def proximal(self, x, tau, out=None):
if out is None:
if self.b is None:
return x / (1 + 2 * tau * self.weight)
else:
tmp = x.subtract(self.b)
tmp /= (1 + 2 * tau * self.weight)
tmp += self.b
return tmp
else:
if self.b is not None:
x.subtract(self.b, out=out)
out /= (1 + 2 * tau * self.weight)
out += self.b
else:
x.divide((1 + 2 * tau * self.weight), out=out)
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)