PointwiseSum

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

Bases: PointwiseInner

Take the point-wise sum of a vector field.

This operator takes the (weighted) sum

sum(F(x)) = [ sum_j( w_j * F_j(x) ) ]

where F is a vector field. 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, 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.
weightingarray-like or float, optional: Weighting array or constant for the sum. If an array is given, its length must be equal to len(domain). 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 standard point-wise sum operator on that space. 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)
>>> pw_sum = PointwiseSum(vfspace)
>>> pw_sum.range == spc
True

Now we can calculate the sum in each point:

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