PointwiseInner

class odl.PointwiseInner(*args, **kwargs)

Bases: PointwiseInnerBase

Take the point-wise inner product with a given vector field.

This operator takes the (weighted) inner product

<F(x), G(x)> = sum_j ( w_j * F_j(x) * conj(G_j(x)) )

for a given vector field G, where F is the vector field acting as a variable to this operator.

This implies that the Operator.domain is a power space of a discretized function space. For example, if X is a DiscretizedSpace space, then ProductSpace(X, d) is a valid domain for any positive integer d.

__init__(vfspace, vecfield, weighting=None)[source]

Initialize a new instance.

Parameters

vfspaceProductSpace: Space of vector fields on which the operator acts. It has to be a product space of identical spaces, i.e. a power space.
vecfieldvfspace element-like: Vector field with which to calculate the point-wise inner product of an input vector field
weightingarray-like or float, optional: Weighting array or constant for the norm. If an array is given, its length must be equal to len(domain), and all entries must be positive. By default, the weights are is taken from domain.weighting. Note that this excludes unusual weightings with custom inner product, norm or dist.

Examples

We make a tiny vector field space in 2D and create the point-wise inner product operator with a fixed vector field. The operator maps a vector field to a scalar function:

>>> spc = odl.uniform_discr([-1, -1], [1, 1], (1, 2))
>>> vfspace = odl.ProductSpace(spc, 2)
>>> fixed_vf = np.array([[[0, 1]],
...                      [[1, -1]]])
>>> pw_inner = PointwiseInner(vfspace, fixed_vf)
>>> pw_inner.range == spc
True

Now we can calculate the inner product in each point:

>>> x = vfspace.element([[[1, -4]],
...                      [[0, 3]]])
>>> print(pw_inner(x))
[[ 0., -7.]]