ENH: add auto_weighting example

Author: Holger Kohr

examples/space/auto_weighting.py

@@ -0,0 +1,57 @@
+"""Example demonstrating the usage of the ``auto_weighting`` decorator."""
+
+import odl
+from odl.space.space_utils import auto_weighting
+
+
+class ScalingOp(odl.Operator):
+
+    """Operator that scales input by a constant."""
+
+    def __init__(self, dom, ran, c):
+        super(ScalingOp, self).__init__(dom, ran, linear=True)
+        self.c = c
+
+    def _call(self, x):
+        return self.c * x
+
+    @property
+    @auto_weighting
+    def adjoint(self):
+        return ScalingOp(self.range, self.domain, self.c)
+
+
+rn = odl.rn(2)  # Constant weight 1
+discr = odl.uniform_discr(0, 4, 2)  # Constant weight 2
+print('*** Spaces ***')
+print('Rn =', rn, '- weight =', rn.weighting.const)
+print('discr =', discr, '- weight =', discr.weighting.const)
+print('')
+
+op1 = ScalingOp(rn, rn, 2)  # Same weightings, no scaling in adjoint
+op2 = ScalingOp(discr, discr, 2)  # Same weightings, no scaling in adjoint
+op3 = ScalingOp(rn, discr, 2)  # Different weightings, adjoint scales
+
+# Look at output of ajoint
+print('*** Ajoint evaluation ***')
+print('Rn -> Rn adjoint at one      :', op1.adjoint(op1.range.one()))
+print('discr -> discr adjoint at one:', op2.adjoint(op2.range.one()))
+print('Rn -> discr adjoint at one   :', op3.adjoint(op3.range.one()))
+print('')
+
+# Check adjointness
+print('*** Check adjointness ***')
+inner1_dom = op1.domain.one().inner(op1.adjoint(op1.range.one()))
+inner1_ran = op1(op1.domain.one()).inner(op1.range.one())
+print('Rn -> Rn:          <Sx, y> = {},  <x, S^*y> = {}'
+      ''.format(inner1_ran, inner1_dom))
+
+inner2_dom = op2.domain.one().inner(op2.adjoint(op2.range.one()))
+inner2_ran = op2(op2.domain.one()).inner(op2.range.one())
+print('discr -> discr:    <Sx, y> = {},  <x, S^*y> = {}'
+      ''.format(inner2_ran, inner2_dom))
+
+inner3_dom = op3.domain.one().inner(op3.adjoint(op3.range.one()))
+inner3_ran = op3(op3.domain.one()).inner(op3.range.one())
+print('Rn -> discr:       <Sx, y> = {},  <x, S^*y> = {}'
+      ''.format(inner3_ran, inner3_dom))